Sub Theme 1 Advances in The Robotics and Mechatronics
Sub Theme 1 Advances in The Robotics and Mechatronics
Sub Theme 1 Advances in The Robotics and Mechatronics
SUB THEME 1
ABSTRACT
Inverse kinematics of manipulator comprises the computation required to find the joint angles for a
given Cartesian position and orientation of the end effector. This computation is fundamental to control of
robot arms but is very difficult to arrive at solution. When a robotic system possesses more degree of
freedom (dof) than those required to execute a given task is called redundant Manipulator. There is no
unique solution for the inverse kinematics thus necessitating application of appropriate predictive models
from the soft computing domain. Artificial neural network is one such technique which can be gainfully
used to yield the desired results. This paper proposes structured artificial neural network (ANN) model to
find the inverse kinematics solution of robot manipulator. The ANN model used is a multi-layered
perceptron Neural Network (MLPNN). Wherein, gradient descent type of learning rules is applied. An
attempt has been made to find the best ANN configuration for the problem. It is found that multi-layered
perceptron Neural Network gives better result and minimum error, as the performance index. Proposed
work using different ANN models for the prediction of the inverse kinematics of redundant manipulator
will be useful source of information for other various configurations of manipulator.
Keywords: 7-DOF manipulator; multilayer perceptron; DH-conventions, kinematically Redundancy
1. INTRODUCTION
Redundancy is relative concept i.e. with respect to given task. Robot is kinematically redundant for the
task if N > M (more degrees of freedom than strictly needed for executing the task) that’s why redundant
manipulator having infinite number of solution for the inverse kinematic problem. It is interesting research
topic in recent years to have solution of inverse kinematic of redundant manipulator. Robot arms with
seven or more degrees-of-freedom (DOF) having more dexterity and versatility over conventional six-
DOF arms (Angeles et al., 1992). These robot arms can be considered as human arm which is having
similar capabilities, which also has seven independent joint degrees-of-freedom (Hasan T et al., 2010).
Extra joint motions are quite complicating for the control problem. Kinematically redundant manipulator
generates infinite sets of possible joint angle trajectories which gives some additional advantages like
collision avoidance, servomotor torque minimization, singularity avoidance or joint limit avoidance.
Kinematically redundant manipulator requires more complicated algorithm for inverse kinematics and
control problems.
Many research methodology and algorithms have been presented on comparative study and analysis of
inverse kinematics of redundant manipulators. Some techniques are imperative for manipulator geometries
with unknown inverse kinematic functions (Shital. S C. and N. Ramesh B, 2010). The conventional
numerical method is much slower and cannot meet the requirement of real-time control of a redundant
manipulator (Wang et al., 2010). So it is requires to fine joint angles for the positioning and orienting the
end effector using techniques from the soft computing domain.
Although the use of ANN is not new in the field of multi-objective and NP-hard problem to arrive at a
very reasonable optimized solution, the multi layered neural network (MLPNN) has been tried to solve
inverse kinematics problem with 7-DOF manipulator. MLP neural network is used to find inverse
kinematics solution which yields multiple and precise solutions with an acceptable error and are suitable
for real-time adaptive control of robotic manipulators (Yang et al., 2007). Therefore, the main aim of this
work is focused on minimizing the mean square error of the neural network-based solution of inverse
kinematics problem. In other words, the angles obtained for each joint are used to compute the Cartesian
coordinate for end effector. The training data of neural network have been selected very precisely.
Especially, unlearned data in each neural network have been chosen, and used to obtain the training set of
the last neural network.
2. KINEMATICS OF THE 7-DOF REDUNDANT MANIPULATOR
The 7-DOF manipulator has an anthropomorphic design with seven revolute joints, as shown in Figure. l.
The arm is composed of a number of modules with roll and pitch motions. The shoulder joint with roll and
pitch motions moves the upper arm; the elbow joint with roll and pitch actions drives the forearm; and the
wrist roll and pitch rotations together with the tool-plate roll move the hand.
For kinematic analysis of the arm, coordinate frames are assigned to the links in such a way that the joint
rotation θi is about the coordinate axis ziand the base frame {xo, yo, zo}is attached to the pedestal. The two
consecutive frames {xi-1, yi-1, zi-1}with origin oi-1 and {xi, yi, zi,} with origin 0i, are related by the 4 x 4
homogeneous transformation matrix "Eq. (2)."Individual transformation matrices A1 to A7 can be obtained
and the general transformation matrix from the first joint to the last joint of the manipulator can be derived
by multiplying all the individual transformation matrices to obtain equation "Eq. (3)."
Elbow
Shoulder Wrist
Figure1. Joint rotations of 7-dof robotic arm
A i Rot ( z , i ) Trans ( 0 , 0 , d i ) Trans ( a i , 0 , 0 ) Rot ( x , i ) (1)
cos i sin i cos i sin i sin i a i cos i
sin cos cos cos i sin i a i sin i
(2)
Ai i i i
0 sin i cos i di
0 0 0 1
nx ox ax px
n oy ay p y (3)
0
T7 A1 A2 A3 A4 A5 A6 A7 y
nz oz az pz
0 0 0 1
Where (px , py , pz ) represents the position and (n x , n y , n z ), (ox , oy , oz ), (a x , a y , a z ) the orientation of the end-
effector. The orientation and position of the end-effector can be calculated in terms of joint angles and the
D-H parameters are shown in table 1.
Forward kinematics of the manipulator:
nx (c7 c6 c5 s 7 s5 )(c3 c4 c12 s 4 s12 ) (c7 s5 c6 s7 c5 ){s3 (s1 s 2 c1c2 )} s6 c7 {c3 s 4 ( s1 s 2 c1c2 ) c4 s12 }
n y (c 7 c 6 c 5 s 7 s 5 )(c 3 c 4 s12 s 4 c12 ) (c 7 s 5 c 6 s 7 c 5 ){ s 3 ( s1 c 2 c1 s 2 )} s 6 c 7 { c 3 s 4 ( s1 c 2 c1 s 2 ) c 4 c12 }
n z c7 c6 c 4 s3 s5 c7 s5 c 6 c3 c7 s 6 s3 c3 c7 s 6 s3 s 4 s 7 c3 c5 s7 s3 s5 c 4
o x c6 {c3 s 4 ( s1 s 2 c1c 2 ) c 4 s12 } s 6 c5 {c 3 c 4 c12 s 4 s12 } s 6 s5 {s3 (s1 s 2 c1c 2 )}
o y c6 {c3 s 4 s12 c4 c12 } s6 c5 {c3 c4 s12 s 4 c12 } s6 s5 { s3 s12 }
o z s 6 s3 c 4 c 5 s 5 c 3 s 6 s 3 c 4 c 6
a x ( s 7 c6 c 5 c7 s 5 ){c3 c 4 c12 s 4 s12 } ( s 7 s 5 c6 c 7 c5 ){s3 ( s1 s 2 c1 c 2 )} s 6 s7 {c 3 s 4 ( s1 s 2 c1 c 2 ) c 4 s12 }
a y ( s 7 c 6 c 5 c 7 s 5 ){c 3 c 4 s12 s 4 c12 } ( s 7 s 5 c 6 c 7 c 5 ){ s 3 s12 } s 6 s 7 {c 3 s 4 s12 c 4 c12 }
a z s 7 c 6 s 3 c 4 c 5 s 7 c 6 s5 c 3 c 7 c 4 s3 s 5 c 3 c 5 c 7
p x {d 7 (s 7 c 6 c5 c 7 s5 )}{c3 c 4 c12 s 4 s12 } {d 7 ( s 7 s 5 c6 c 7 c5 )}{s3 ( s1 s 2 c1c 2 )}
(d 7 s 7 s 6 d 5 ){c3 s 4 (s1 s 2 c1c 2 ) c 4 s12 } { d 3 s12 }
p y {d 7 ( s 7 c 6 c5 c 7 s 5 )}{c 3 c 4 s12 s 4 c12 } {d 7 (s 7 s 5 c 6 c 7 c 5 )}{ s 3 s12 }
(d 7 s 7 s 6 d 5 ){c3 s 4 s12 c 4 c12 }
p z d 7 s 7 s 3 c 6 c 5 c 4 d 7 s 7 s 5 c 6 c 3 d 7 s 7 s 6 s 4 s 3 d 7 s5 s 3 c 7 c 4 d 7 c 7 c 5 c 3 d 5 s 4 s 3 d 1
Table 1 D-H parameters of 7 DOF manipulator model.
i i i
ai di
1 1
-90 0 d1
2 2
+90 0 0
3 3
-90 0 d3
4 4
+90 0 0
5 5
-90 0 d5
6 6
+90 0 0
7 7
0 0 d7
Figure 3 Comparison of desired and predicted value of joint angles theta1
0.5
0 Desired value
Predicted value
Figure 4 Comparison of desired and predicted value of joint angles theta2
2 Desired value
0
-2
Predicted value
Figure 5 Comparison of desired and predicted value of joint angles theta3
2
0 Predicted Value
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
1
6
101
Desired Value
Figure 6 Comparison of desired and predicted value of joint angles theta4
1
Desired Value
0
Predicted Value
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
-1
Figure 7 Comparison of desired and predicted value of joint angles theta5
1
0 Desired Value
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
1
6
101
Predicted Value
Figure 8 Comparison of desired and predicted value of joint angles theta6
1
Predicted Value
0
Desired Value
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
1
6
101
-1
Figure 9 Comparison of desired and predicted value of joint angles theta7
Back-propagation algorithm was used for training the network and for updating the desired weights. In this
work epoch based training method was applied.
As shown in result, the used solution method gives the chance of selecting the output, which has the least
error in the system. So, the solution can be obtained with less error as shown in Figures (3) through (9) for
the best validation performance of the obtained data with the desired data. Generalization tests were
carried out with new random target positions showing that the learned MLP generalize well over the whole
space showing a deviation of 0.937 of the error goal during the learning process. These errors are small
and the MLP algorithm is, therefore, acceptable for obtaining the inverse kinematics solution of the robotic
manipulator.
5. CONCLUSION
Mathematical models rely on assuming the structure of the model in advanced, which may be sub-optimal.
Consequently many mathematical models fail to simulate the complex behaviour of inverse kinematics
problem. In contrast, ANN is based on the input/output data pairs to determine the structure and
parameters of the model. Moreover, they can always be updated to obtain better results by presenting new
training examples as new data become available. In the present problem the error value (mean square
error) is 0.937 which is very much acceptable when compare to the precision figures and repeatability
error values of any typical manipulator. From the present study, it is observed that the MLP gives better
results for inverse kinematics problem considering average percentage error as performance index. This
artificial neural network based joint angles prediction model can be a useful tool for the production
engineers to estimate the motion of the manipulator accurately.
REFERENCES
1. ANGELES, J., RANJBARAN, F. AND PATEL, R.V., “On the design of the kinematic structure of seven‐axes
redundant manipulators for maximum conditioning”, Proceedings of IEEE Int. Conf. Robotics and
Automation, pp. 494–499, ISBN 0‐8186‐2720‐4, Nice, France, May 1992.
2. HASAN T ET AL., “Artificial neural network-based kinematics Jacobian solution for serial manipulator
is passing through singular configurations”, Advances in Engineering Software 41, 359–367, 2010.
3. PHILIP D. W, “Neural Computing: Theory and Practice”, Coriolis Group c/o Publishing Resources
Inc, 1989.
4. SHITAL. S C. AND N. RAMESH B, “Comparison of RBF and MLP neural networks to solve inverse
kinematic problem for 6R serial robot by a fusion approach”, Engineering Applications of
Artificial Intelligence 23 (2010) 1083–1092, 2010.
5. WANG J., LI Y. AND ZHAO X., “Inverse Kinematics and Control of a 7-DOF Redundant Manipulator
Based on the Closed-Loop Algorithm”, International Journal of Advanced Robotic Systems, Vol.
7, No. 4 (2010).
6. YANG Y ET AL., “A New Solution for Inverse Kinematics of 7-DOF Manipulator Based on Neural
Network”, Proceedings of the IEEE International Conference on Automation and Logistics, Jinan,
China, August 18 - 21, 2007.
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID - ICAME2013S1/O2
ABSTRACT
Active Magnetic Bearings (AMBs) support the rotor without any physical contact. Therefore,
compared to the frictional contact and hydrodynamic bearings, AMBs provide advantages of reduced
frictional losses and can support high speed rotors. Stable operation of AMBs is primarily depends on the
working condition of its position sensors and actuators. Fault or failure in sensors or actuators of AMB
system can result in undesired rotor dynamics. Hence, to ensure the safe operation and reliable
performance of AMB system, fault detection and diagnosis (FDD) of AMB system is very essential.
Principal component analysis (PCA) is a model-free and robust statistical method which can detect and
diagnose the faults in engineering systems with high accuracy. Therefore, in the present work, PCA based
methodology is used for the fault detection and diagnosis in sensors and actuators of AMB system.
Simulations have been carried out to diagnose these faults of AMB system. Q-statistic or square prediction
error is used for diagnosing bias and multiplicative faults.
Keywords: Active Magnetic Bearing (AMB), Fault detection and diagnosis (FDD), Principal component
analysis (PCA), Bias faults, Multiplicative faults.
1. INTRODUCTION
Active magnetic bearing (AMB) is a mechatronic device which levitates the rotor by manipulating the
attractive electromagnetic forces. Due to its ability in operating without mechanical friction between the
rotor and stator and high-precision operation, they are most suitable for high speed application such as
turbo machinery and machine tools (Schweitzer et.al., 1994). The desired operation of AMB mainly
depends on performance of displacement sensors and actuators of the system. Fault or failure of any one of
the sensor and actuator can result in destructive rotor dynamics behaviour. Therefore, in order to avoid
such failure of entire system, fault detection and diagnosis (FDD) of AMBs under its operating condition
becomes very essential.
In the present work, an attempt is made to detect and diagnose the sensor and actuator faults in AMBs.
Many FDD methods for AMBs have been discussed in the literature. Kim and Lee (1999) proposed state
estimation FDD method to detect sensor faults in AMBs. An abrupt change in transient state and dual
faults can’t be detected by this methodology. Losch (2002) used position estimation technique to detect the
sensor faults in AMBs. Hu et al. (2004) used multi value logic algebra method to identifying the sensor
faults in AMBs, but it was incapable to diagnosed dual faults at a time. Cade et al. (2005) implemented
wavelet analysis technique (digital signal processing approach) to identify the rotor displacement in
AMBs. Garcia et al. (2007) used redundancy based FDD method to formulate and predict sensor
malfunction and abnormal operating conditions in AMBs, however multiple sensor faults can’t be predict
by this methodology. Tsai et al. (2009) applied Luenberger state estimation technique to diagnose the
multiple sensor faults in AMBs by using the mathematical model of AMB. Beckerle et al. (2012) proposed
balancing filter approach based on parity equation to identify unknown faulty states in AMBs.
However, all the above FDD methods are model and redundancy based and require the precise
mathematical modelling as well as result in increased complexity and cost of AMB system. Therefore, in
this paper, model-free principal component analysis (PCA) based FDD method has been proposed for
AMB sensors and actuators faults diagnosis. PCA is a simple multivariable statistical method with very
high dimensional accuracy (Edward, 1991). Both stationary and dynamic faults in the system can be
detected and isolated by correlating data into lower dimensional subspace (Wang and Xiao, 2003).
2. FAULTS IN AMBs
Faults are defined as the unpermitted deviations of a signal from its normal state (Isermann, 2005). It is a
state that may lead to undesired operation or failure of the entire system. Faults in AMB system can be
broadly classified as external and internal faults. A fault is considered to be external when either it
manifests itself as or its effect can be replicated by external disturbance acting on the system. Internal
faults cannot be represented by external disturbances as they affect the actuation, measurement or control
processes and thereby the system dynamics. Sensors and actuators are the important components of AMB
system. Their performance directly affects the entire operation of the system. Sensor faults occur due to
various factors, such as manufacturing defects, wear and tear with long term usage and incorrect
calibration or mishandling. Basically, there are three types of faults in sensors and actuators of AMB such
as; bias fault, multiplicative fault and noise addition (Kim and Lee, 1999).
3. EIGHT-POLE MAGNETIC BEARING MODELLING
Eight-pole heteropolar configuration of AMB is considered in the present work. Geometry of eight-pole
magnetic bearing is shown in Fig.1. All the poles of the AMB are considered identical. Forces generated
along the positive X and Y axes (Agarwal and Chand, 2009) are given by Eqs.(1)and (2):
8 j2
Fx cos j (1)
j 1 2 0 A j
2
8 j
Fy sin j (2)
j 1 2 0 A j
Fig.1 Eight-pole magnetic bearing geometry Fig.2. Fuzzy Logic controller
Step I: Normalize the data. First data is centered into zero mean and then into unit variance. Centering is
done by subtracting the mean of each column of the matrix D from corresponding element of that column
given by Eq.(3).
Dcentered {d1 j mean( x1 j )} {d 2 j mean(d 2 j )}.. { d 2 j mean( x2 j )} (3)
n m
Then each column of the mean centered matrix is divided by the corresponding column‘s standard
deviation given by Eq.(4).
Dstd {d1 j / std (d1 j )} {d 2 j / std (d 2 j )}.. { d 2 j / std (d 2 j )} (4)
n m
Step II: Calculate the covariance matrix C. The covariance matrix is given by Eq.(5).
D ' Dstd
C std (5)
n 1
Where, covariance matrix C is real symmetrical matrix.
Step III: Finding the loading vectors (P) using Singular Value Decomposition (SVD) of covariance
matrix C (Qinghua, 2008) given by Eq.(6).
P, S , P SVD C P S P ', with PP PP I Identity matrix (6)
Step IV: Optimal numbers of principal components are selected based on the scree plot method as shown
in Fig.4. It is a graphical method in which the principal components are arranged in decreasing order of
their eigenvalues.
Step V: To calculate the threshold of Q statistic or square prediction error (SPE) in residual subspace
(harrow et al., 2012). Upper limit of Q statistic is calculated using Jackson & Mudholkar formula
according Eq.(7):
1
h C 2 se2 se h 1 h h0 m
Q se1 0 1 2 0 2 0 with sei ij (7)
se1 se1 j a 1
2 se1se3
where i=1, 2 &3 and h0 1 , Cα =100(1- α) the value of the normal distribution (α ≤ 0.05).
3se22
4.2 Data generation
Simulation model of AMB with fuzzy logic controller developed in MATLAB® programming environment
is used for generating the training data. Various displaced positions of the rotor are considered and the
corresponding currents in all the coils of AMB are recorded. The trajectories of rotor from the displaced
position to the stable position in all four quadrants of XY- plane are shown in Fig.3. The simulation is
carried out for the 32 displaced rotor positions. For each displaced rotor position, data of 10 variables (8
actuators and 2 position sensors) are noted in 100 equal time intervals of size 0.005 s, starting from
displaced position to stable position of the rotor. The training data is arranged in the form of a matrix given
by Eq.(8).
D I1 I 2 I3 I 4 I 5 I 6 I 7 I8 X Y 320010 (8)
where, I1, I2, I3, I4, I5, I6, I7 , I8are currents to all the eight-pole from actuators and X ,Y are displace position
of the rotor along X and Y axis read from the position sensors respectively.
4
II I 5
2
4
Eigenvalues
0 3
-2 2
III IV 1
-4
0
-4 -2 0 2 4 X10-4 0 1 2 3 4 5 6 7 8 9 10
Rotor displacement along X-axis (m) Principal Components
Fig.3 Rotor trajectory in XY-plane Fig.4 SCREE plot of PCA model
Various simulation tests were conducted to verify the PCA strategy for detecting and diagnosing actuators
and displacement sensors faults of AMB system. In Test-1, bias (10%) fault was added at time 0.005 sec in
one of the sensor or actuator of AMB system. Due to this fault the Q-statistic value is increased
significantly and exceeded the threshold limit. It found that fault is detected in first actuator soon after the
fault occurred as shown in the Fig.5(a). To diagnose the type of the fault (i.e. bias or multiplicative) in the
faulty actuator, Q-statistic value is plotted with respect to time as shown in Fig. 5(b). It can be observed
that once the fault has occurred, Q-statistic value is increased and exceeded the threshold limit and then it
becomes constant with respect to time. It indicates that there is a bias fault in the first actuator.
In Test-2, multiplicative fault was introduced at time 0.005 sec in one of the sensor or actuator of AMB
system. Fig.6(a) shows that fault is in the position sensor along Y-axis. From Fig.6(b) it can be observed
that the Q-statistic value of the faulty sensor varies linearly with respect to time. It indicates that there is
multiplicative type of fault in position sensor along Y-axis.
36
16
32
14
Treshold value
Threshold limit value 28 (I1) Actuator with bias fault
12 24
Q- Statistic value
10 20
8 16
6 12
4 8
2 4
0 0
0 1 2 3 4 5 6 7 8 9 10 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Actuators and Sensors Time (sec)
(a) (b)
Fig.5. Q-statistic plot of simulation Test-1 (a) for fault detection (b) for fault diagnosis
36
16 Treshold value
32
Postion Sensor with multiplicative fault
14 28
Threshold limit Position Sensor normal operation
12 24
Q- Statistic value
Q-Statistic
10 20
8 16
6 12
4 8
2 4
0 0
0 1 2 3 4 5 6 7 8 9 10 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Actuators and Sensors Time (sec)
(a) (b)
Fig.6. Q-statistic plot of simulation Test-2 (a) for fault detection (b) for fault diagnosis
6. CONCLUSION
In the present work, principal component analysis based fault detection and diagnosis methodology has
been proposed to detect and diagnose actuator and sensor faults of AMB system. Modelling of magnetic
bearing has been represented to determine forces generated by eight-pole magnetic bearing along X and Y
axis respectively. Q-statistic or square prediction error evaluated from the principal components is utilized
to detect the actuator and sensor fault of AMB. Once the fault is detected, Q-statistic plot with respect to
time have been employed to diagnose the type of fault (i.e. bias and multiplicative). The simulation results
show that the proposed PCA based fault detection and diagnosis technique can effectively detect and
diagnose different types of faults in AMB system components.
REFERENCES
1. Agarwal P.K. and Chand S.,“Fault-tolerant control of three-pole active magnetic bearing”, Expert
Systems with Applications, 36, 12592–12604 (2009)
2. Alkaya A. and Eker I., “Variance sensitive adaptive threshold-based PCA method for fault
detection with experimental application”, ISA Transactions, 50, 287-302 (2011).
3. Beckerle P., Schaede H. , Butzek N. , Rinderknecht S.,“Balancing filters: An approach to improve
model-based fault diagnosis based on parity equations”, Mechanical Systems and Signal
Processing, 29, 137–147 (2012)
4. Cade I. S., Keogh P. S., Sahinkaya M. N., “Fault Identification in Rotor/Magnetic Bearing Systems
Using Discrete Time Wavelet Coefficients, IEEE/ASME transactions on mechatronics”, vol. 10,
no. 6 (2005).
5. Edward J., “User’s guide to principal components”, Wiley, 1991.
6. García F., Castelo P., Pazos P.,Rolle C.,“On AMBs Diagnosis by Analytical Redundancy”, IEEE
Conference on International Symposium on Industrial Electronics,1-4244-0755-9 (2007).
7. Harrou F., Nounou M. N., and Nounou H.N., “Statistical Detection of Abnormal Ozone Levels
Using Principal Component Analysis”,International Journal of Engineering & Technology IJET-
IJENS, No:06, Vol:12 (2012).
8. HU Y.F., Ku S.P. , ZHOU Z.D., Su Y.X., “Multi-valued Logic And Its Application In The Fault
Diagnosis Of The Sensors Of Magnetic Bearings”, Proceedings of the Third International
Conference on Machine Learning and Cybernetics, Shanghai (2004).
9. ISERMANN R.,“Model-based fault-detection and diagnosis – status and applications”, Annual
Control Review, 29,71–85 (2005).
10. Kim S.J. and Lee C.W.,“Diagnosis of Sensor Faults in Active Magnetic Bearing System Equipped
With Built-In Force Transducers”, IEEE/ASME transactions on mechatronics, vol. 4, no. 2 (1999).
11. Losch F.,“Detection and correction of sensor and actuator faults in active magnetic bearing
system”, 8th international symposium on magnetic bearing, Japan (2002).
12. Qinghua H.E., Xiangyu H.E. and JianxinZ., “Fault detection of excavator’s hydraulic system based
on dynamic principal component analysis”, J. Cent. South Univ. Technol., 15: 700−705 (2008).
13. Schweitzer G., Bleuler H., and Traxler A., “Active Magnetic Bearing”, Zurich, Switzerland vdf
Hochschulverlag A G (1994).
14. Tsai N. C., King Y.H., Lee R.M., “Fault diagnosis for magnetic bearing systems”, Mechanical
Systems and Signal Processing, 23 , 1339–1351 (2009)
15. Wang S. and Xiao F., “AHU sensor fault diagnosis using principal component analysis method”,
Energy and Buildings, 36, 147–160 (2004).
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID - ICAME2013 S1/O3
A REVIEW PAPER ON ADVANCEMENT IN ROBOTIC FISH.
ABSTRACT
A biologically inspired robotic fish needs a controlled kinematic centered environment. A series of
fish like robots with certain mechanical design are required to be used while building a robotic fish.
Models are useful to validate well-formed ideas and to reach a new level of performance close to actual
fish for real applications. The review presented offers a good insight into optimal design of a fin-based
robotic fish which has potentials to offer several advantages including low underwater acoustic noise,
great manoeuvrability and better propulsion efficiency at low speeds. Design features of a robotic fish that
was developed for experimental investigation and for validating computational hydrodynamic models of
an undulating fin are explained. A relatively complete computational model describing the hydrodynamics
of an undulating fin is given. The computational model is to be experimentally validated by comparing the
computed thrust coefficient against measured data based on a prototype flexible-fin mechanism.
Keywords: Biomimetics, roboticfish, carangiform, bodymotion, fin propulsion.
1. INTRODUCTION
Underwater robots provide an engineering tool to practical applications in marine and military fields, such
as monitoring the environment, harvesting natural resources, undersea operation, pipe inspection and many
other applications. MIT’s Robo Tuna I and II are the best known bio-inspired underwater robots. MIT also
developed Robot pike to learn more about the fluid mechanics that fish use to propel themselves with a
purpose to develop small fish-like autonomous vehicles for reduced energy consumption and increased
operation time (Daou and Toming,2012). The University of Essex has developed a series of autonomous
robots G1 to G9 and MT1. The G series have a multi-motor-multi-joint tail structure, which employs 4
servo motors to drive 4 tail joints separately according to a predetermined swimming wave sequence . Fish
show excellent swimming performance in nature, so more and more researchers have focused on
mimicking fish locomotion for developing underwater vehicle with high speed, high manoeuvrability and
high efficiency.
Fish locomotion can be classified into two categories on the basis of the propulsive mechanism used: Body
and/or Caudal Fin (BCF) mode in which fish swim with their body and/or caudal fin and Median and/or
Paired Fin (MPF) mode in which fish propel with their media and/or paired fin. BCF mode displays the
outstanding performance of high speed and high efficiency, while MPF mode is capable of maintaining
good stability. Both types of the propulsion modes have been studied in detail. Mason and Burdick [Liu,
Hu,2010] developed a carangiformprototype and underwent the experiment to testify the supposition of
thrust generated from swinging fin. A carangiformrobotic fish prototype was presented to investigate the
influences of the characteristic parameters on the forward velocity(Yan ie an,2008). Japanese National
Maritime Research Institute developed many kinds of robotic fish prototypes to increase swimming
efficiency. Till now majority of research work has been focused on fish-like propulsion mechanisms, fin
materials, remote operation, multi-agent cooperation and mechanical structures. Typically, there are two
main types of motions under discussion for the research of robotic fish: cruising and
manoeuvring.Basically, cruising indicates swimming at a constant linear or angular speed, whereas
manoeuvring involves actions such as acceleration, deceleration, quick turning, up/down motions, and
hovering. Initially robotic fish research concentrated on cruising efficiency and fluid flow effects (Liu and
Hu,2010). Generally, a biomimetic robotic fish is defined as a fish-like aquatic vehicle based on the
swimming skills and anatomic structure of a fish, including its undulatory/oscillatory body motions, its
highly controllable fins and its large aspect-ratio lunate tail. The RoboTuna and the subsequent RoboPike
projects attempted to create AUVs (Autonomous Underwater Vehicles) with increasing energy savings
and longer mission durations. The motionand controlof robotic fish are analysed recently. For example,
Burdick’s group has studied carangiform locomotion, including complicated control strategies and fluid
dynamic analysis . The propulsion direction of the robotic fish can be controlled by changing the
symmetric centre of undulation, which means that the yaw control needs to calculate the offset of each link
in every control cycle. However, the orientation variation is difficult to control due to the complexity of
the force. ( Zhou, ou, ao, ng, an.2011).
Robotic engineers are able to combine aspects of biology and engineering, while a group of researchers is
actively exploring the lightweight or micro-robotic fish with smart materials for actuation and locomotion.
The marine ecological environment has been deteriorating because of human interaction with them. One
extremely destructive tool used by such human interaction is the propeller, the main propulsion systems
used by most current water vehicles. The broadband noise from cavitating propellers of any motorized
vessel may have severe acoustic effects on marine wildlife, like changes of behaviour, masking of other
signals or causes temporary (or permanent) hearing trauma (low,2009). From the engineering perspective,
the high level of coordination achieved by these simple individuals can bring new ideas to enhance the
performance of many real systems, especially the intelligent robot systems. However, multi-robot systems
also have to deal with many challenging issues that do not exist in single robot systems such as how to
organize the group architecture, how to decompose and allocate tasks, how to avoid conflicts and achieve
coherence, and so forth. Actress is an autonomous and distributed multi-robot system which addresses
various issues of communication, task assignment, and path planning among heterogeneous robots. This is
because the hydro-environment is more complicated than ground or aerial environments and has many
different sources of uncertainty. For example, because of the disturbance of water waves, it is very
difficult, if not impossible, to design precise control methods that will guarantee performance for both
single-robot and multi-robot systems.
There are still many challenging research issues remaining to be addressed in the field of underwater robot
cooperation. The objective of this work is to investigate the cooperation control of a group of micro robots
which uses a fish-like propulsive mechanism. It is known that fish have high efficiency, manoeuvrability,
and lower noise than most of the current marine robots. The robotic fish is a combination of bio-mechanic
and engineering technology. This study ranges from hydrodynamics analysis, to mechatronic construction,
to control schemes. Similarly in practice, the capability of a single fish may be limited due to the
uncertainty of the environment and parallelism of missions. The content of this paper is split into two
areas. First one is presenting a design model of an artificial fish-like robot and building a prototype.
Second area is investigation of the cooperative control problem of multiple robot fish and proposal for a
cooperation mechanism for object transportation. Further an object-transportation task, which is one of the
canonical task domains in the field of ground robots, is implemented on the multi-robot fish system. This
underwater transportation mechanism, after some adaptations, can be applied to submarine systems at
tasks like waste cleaning and environmental protection (Shaoa, ga, ub,2008).
1. Hadi El Daou, Taavi Salum¨ae, Gert Toming and Maarja Kruusmaa “A Bio-inspired Compliant
Robotic Fish: Design and Experiments.”(2012).
2. Jindong Liu and Huosheng Hu. “ Biological Inspiration: From Carangiform Fish to Multi-Joint
Robotic Fish.”Journal of Bionic Engineering 7, 35–48 (2010).
3. Qin Yan, Zhen Han, Shi-wu Zhang and Jie Yang. “Parametric Research of Experiments on a
Carangiform Robotic Fish.” Journal of Bionic Engineering 5, 95-101(2008)
4. Chao Zhou, Zeng-Guang Hou, Zhiqiang Cao , Shuo Wang and Min Tan. “Motion modeling and
neural networks based yaw control of a biomimetic robotic fish.”(2011)
5. J. Shaoa, L. Wanga, and J. Yub .“Development of an artificial fish-like robot and its application in
cooperative transportation.” Control Engineering Practice 16 569–584(2008).
6. K.H. Low. “Modelling and parametric study of modular undulating fin rays for fish
robots”Mechanism and Machine Theory 44 615–632 (2009).
7. Nguyen Truong-Thinh1,a, Nguyen Ngoc-Phuong1,b and Dang Minh-Nhat1. “Swimming of
Robotic Fish based Biologically-Inspired approach.”Automation and Systems (2011).
8. Jian-Xin Xu, Xue-Lei Niu and Zhao-Qin Guo. “Sliding Mode Control Design for a Carangiform
Robotic Fish.”Variable Structure Systems(2012).
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID - ICAME2013 S1/O4
REACTIVE NAVIGATION OF UNDERWATER MOBILE ROBOT BASED ON SHUFFLED
FROG LEAPING ALGORITHM
(3)
2.2 Angular velocity transformation relative to earth reference frame:
For angular velocity, the orientation of the body fixed reference frame with respect to the earth fixed
reference frame is given by:
0 0
p q r 0 Rx ( ) Rx ()Ry ( ) 0
T
0 0
1 0 0 0 1 0 0 cos 0 sin 0
0 0 cos sin 0 cos sin 0
1 0 0
0 0 sin cos 0 0 sin cos sin 0 cos
sin 1 0 sin
cos sin cos 0 cos sin cos
sin cos cos 0 sin cos cos
E W ( , ).b
B 2 (4)
E
As WB ( , ) is undefined or singular for pitch angle of 90 , rotational transformation matrix does not
0
E
satisfy orthogonal property of matrices. Therefore, transpose of B W ( , ) cannot be taken as inverse of
the matrix.
1 sin tan cos tan p
b2 E WB ( , )1 p q r 0
T
cos sin q
0 sin sec cos sec r
(5)
2.3 6DOF Motion Equation:
So, the kinematic equations can be described by two Euler angle representations with different
singularities. Summarizing the linear and angular velocity transformation matrices, kinematic equation can
generalized for 6 DOF motion of body fixed reference frame {B} with respect to earth fixed reference
frame {E} in a reduced form:
x u
y v
b1 z E RB ( , , ) 033 w
; PB T (b2 ) V
E
E 1 (6)
b2 033 WB ( , ) p
q
r
3. FORMULATION OF SHUFFLED FROG LEAPING ALGORITHM:
The shuffled frog-leaping algorithm is a memetic metaheuristic that is designed to seek a global
optimal solution by performing a heuristic search. The SFL algorithm, in essence, combines the benefits of
the genetic-based memetic algorithms and the social behavior based PSO algorithms (Eusuff and Lansey,
2003). A group of frogs has been considered leaping in a swamp which has a number of stones at discrete
locations where the frogs can leap onto. The goal of all the frogs is to find the stone with the maximum
amount of available food as quickly as possible through improving their memes. The frogs can
communicate with each other, and can improve their memes by passing information on each other. A
shuffling strategy allows for the exchange of information between local searches to move toward a global
optimum (Elbeltagi et al., 2005). The SFL algorithm is described by flowchart in Figure 2.
Figure 2. Flowchart of the shuffled frog-leaping algorithm
In the SFL, the population is partitioned into subsets referred to as memeplexes. Within each
memeplex, the individual a frogs hold ideas, that can be influenced by the ideas of other frogs, and evolve
through a process of memetic evolution. After a defined number of memetic evolution steps, ideas are
passed among memeplexes in a shuffling process (Eusuff and Lansey, 2003). The local search and the
shuffling processes continue until defined convergence criteria are satisfied (Aghababa, 2012). The SFL
algorithm can be described as below:
An initial population of P frogs is created randomly. For D dimensional problem (D variables), frog is
represented as Xi = (xi1, xi2 ,..., xiD) , i = 1,2, ..., P Afterwards, the frogs are sorted in a descending order
according to their fitness. Then, the entire population is divided into m memeplexes, each containing s
frogs (i.e. P = m Xs ).
In this process, the first frog goes to the first memeplex, the second frog goes to the second
memeplex, frog m goes to the mthmemeplex, and frog m+1goes back to the first memeplex, etc. Within
each memeplex, the frogs with the best and the worst fitness are identified as Xband Xw, respectively. Also,
the frog with the global best fitness is identified as Xg. Then, a process similar to the PSO algorithm is
applied to improve only the frog with the worst fitness, Xwof every memeplex in each cycle. Accordingly,
the position of the frog with the worst fitness is adjusted as follows:
Change in frog position (∆X ) = rand().(Xb− Xw) (7)
XWn1 XWn X; Xmax X Xmax
(8)
Where rand ( ) is a random number between 0 and 1; n represents the iteration number and ∆Xmax is
the maximum allowed change in a frog’s position. If this process produces a better solution, it replaces the
worst frog. Otherwise, the calculations in Eq. (7) and Eq. (8) are repeated but with respect to the global
best frog (i.e. Xgreplaces Xb). If no improvement becomes possible in this case, then a new solution is
randomly generated to replace that frog. After a defined number of improvement processes, population is
shuffled then the termination criteria are checked and the algorithm is repeated until fulfilling this criteria.
4. SFLA AS PATH PLANNING METHOD:
The problem considered in this section is underwater robot path planning in a partially unknown
environment with static obstacles. The procedure of real-time path planning is divided into the following
three steps:(a) Path planning problem has been transformed into an optimization one, and also defined the
optimization objective based on the target and the obstacles in the environment; (b)Position of the globally
best frog in each iterative is selected, and the underwater robot reaches these positions in sequence;
(c)Update the information detected by its sensors, and the optimization objective function changes
accordingly (Elbeltagi et al., 2007).
As is described in the above optimization process, each position to be reached by the underwater
robot can be evaluated based on the distance between itself and the target and obstacles in the
environment. Therefore the nearer a position to the target, the greater the fitness of the position should be;
on the contrary, the nearer a position to the obstacles, the worse the fitness of the position should be.
Based on the above statement T is denoted as the target, whose coordinate is (xT,yT , zT) . Suppose there are
N obstacles in the environment, and denote them O = {O1,O2 ,……,ON}, assume them as points and their
center coordinates are (xo1, yo1, zo1), (xo2, yo2, zo2) ,……, (xoN, yoN, zoN) .It is possible for algorithm to find
the position that is not free (i.e. that is the region of obstacle) and it is impossible for underwater robot to
go there, so in each step the information is updated by the sensors and if there is a possibility of colliding,
the direction of the movement will be changed by adjusting the speed of wheels. Thereafter the fitness of a
particle Piwhose coordinate is (xi,yi, zi) can be expressed as follows:
1
f Pi w1 w 2 Pi T
m i n Pi Q j .
O j O
(9); Where, is a kind of norm.
Here, the traditional distance has been expressed between two points in 3 dimensional. It can be
seen from Eq. (9) that when Piis close to the target, the value of || Pi−T || will be small. And when Piis far
min Pi Qj
from the obstacles the value of O O j
will be great. Therefore the problem solved by the SFL is a
minimization one. Selecting the position achieved by the globally best frog as the ones to be reached by
the underwater robot in sequence, the path is to be formed with shorter length. So the path will have the
length optimization by utilizing the information of the target. Therefore the frog has little opportunity to
leap the positions near the obstacles.Influence of parameters on the underwater robot’s path can be
analyzed as: When w1 is high, the underwater robot will be far away from the obstacles; otherwise it may
collide with them. When w2 is great, the underwater robot has a strong trend to go to the target, resulting in
the path being short. When the globally best position that was produced by the SFL algorithm, then we
have to find out azimuth and elevation steering angle towards the selected position from the current
position of the underwater robot.
5. SIMULATION RESULTS:
To expound the effectiveness and the robustness of the proposed method in 3D underwater
environment, MATLAB simulation results of mobile robot navigation in various environments are
exhibited. The obstacle avoidance behavior is activated when the readings from any sensors are less than
the minimum threshold values (50mm). In the SFL algorithm, some assumptions are included such as: the
number of frogs and the number of memeplexes are 60 and 6 respectively, maximum step size ∆Xmax is set
to 0.0125 and number of processing generations for each memeplex before shuffling and number of
shuffling iterations is 10 and 150 respectively. Also when the robot reaches near the target and the distance
between the center of the robot and the target is less than 4cm the path planning process is stopped. The
simulation results (Figure 3) show the path of the robot and the positions of the obstacles. The robot truly
recognized obstacles and turned it and reached to the target, it can be seen that the robot reaches the target
without colliding with the obstacles. The result shows that the robot sets out from the start point, when it
detects the obstacles in its path; the information of the obstacles is then transferred to the robot processor
until the robot reaches the target.
(a) (b) (c)
Figure 3. (a) Navigation through cluttered obstacles (b) Escaping from dead end obstacle by Wall Following behavior(c)
Obstacle Avoidance and Target Seeking behavior
6. CONCLUSION:
The major intents of this research work are to find out efficient motion control techniques for
underwater robot navigation in hazardous real world situations by avoiding collision with obstacles
arranged in a chaotic way. In the path planning based on SFL algorithm, the position of globally best frog
in each iterative is selected, reached by the robot in sequence and update the information of the
environment by sensors. The simulation result validates the feasibility of the proposed method. Although
the programmed path has some optimal effect by using the information of the target and obstacles
simultaneously, but the obtained path may not be globally optimal. Also the simulation results show the
effectiveness and robustness of this modified algorithm and the robot moves smoothly toward its target.
The work to be further studied is to focus on dynamic environment and also path planning for multiple
robots.
REFERENCES
1. C. Xin and Y.M. Li, “Smooth path Planning of a mobile robot using stochastic particle swarm
optimization”, in Proc. IEEE. Int. Conf. Mechatronics and Automation Luoyang, China, 2006, pp.
1722– 1727.
2. E. Elbeltagi, T. Hegazy, D. Grierson, “Comparison among five evolutionary-based optimization
algorithms,” Advanced Engineering Information, Vol. 19, 2005, pp 43-53.
3. Emad Elbeltagi, Tarek Hegazyz, Donald Griersonz, “A modified shuffled frog-leaping optimization
algorithm: applications to project management”, Structure and Infrastructure Engineering, Vol. 3, No.
1, March 2007, 53 – 60.
4. Fossen, T. I. and J. P. Strand,“Nonlinear Passive Weather Optimal Positioning Control (WOPC)
System for Ships and Rigs: Experimental Results”, Automatica 37(5), 2001, 701—715.
5. Fossen, T. I. “Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs and
Underwater Vehicles”, Marine Cybernetics. Trondheim, Norway, 2002.
6. Hassanzadeh, K. Madani, M. A. Badamchizadeh, “Mobile Robot Path Planning Based on Shuffled
Frog Leaping Optimization Algorithm”, 6th annual IEEE Conference on Automation Science and
Engineering Marriott Eaton Centre Hotel Toronto, Ontario, Canada, August 21-24, 2010, pp:680-685.
7. M. M. Eusuff and K.E. Lansey, “Optimization of water distribution network design using the shuffled
frog leaping algorithm,” Journal of Water Resources Planning and Management, vol. 129(3), 2003,
pp. 210–225.
8. Mohammad Pourmahmood Aghababa, “3D path planning for underwater vehicles using five
evolutionary optimization algorithms avoiding static and energetic obstacles”, Applied Ocean
Research 38 (2012) 48–62.
9. Y. Hu and S. X. Yang, “A knowledge based genetic a1gorithm for path Planning of a mobile robot”,
in Proc. IEEE Int. Conf. Robotics & Automation, New Orleans, LA, April 2004.
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID - ICAME2013 S1/O6
ABSTRACT
The multi disciplinary and multi directional nature of threats in today’s battlefield has made it
necessary for artillery weapon systems to be fast and accurate. This can be achieved by automating the
different subsystems of an artillery weapon of which one is the ammunition handling system. Autoloaders,
which are a part of the ammunition handling sub system, can be defined as a mechanical aid to or
replacement for an operator responsible for loading ammunition into crew served weapons. The current
work deals with synthesizing and analyzing linkages for the autoloader, in the form of rigid body guidance
of the projectile and the charge pellet from an initial position to a final position defined with respect to the
gun co-ordinate system. Linkages were synthesized from the available position data for achieving the
motion of the projectile and the charge pellet. The time intervals in which these motions were required
were estimated and Kinematic and Kinetic analyses of the linkages were performed. Stress analyses of the
linkages were carried out to investigate the stresses induced and the thickness of the links required to keep
the induced stress values within safe limits.
Keywords: Autoloaders, Linkage Synthesis, Kinematic Analysis, Kinetic Analysis, Stress Analysis
1. INTRODUCTION
To meet the varied demands of today’s battlefield, automation of the different subsystems in an artillery
gun, including the ammunition handling sub system, has become essential. Roy, 2004, in ‘Automation of
Ammunition Handling Systems for Artillery Guns’, gave a detailed description of the necessity of
automation in artillery guns as well as the different areas of the gun in which automation could be
achieved, with a focus on the automation of the ammunition handling system. Ainley, 1980, in ‘Integrated
Artillery Recoil Mechanism and Automated Handling Design for Self Propelled Howitzer’ presented the
details of the design process of the autoloader system for the particular gun. The author’s main objective
was to design an autoloader system for the gun with minimum changes in the existing gun structure and
without affecting the traversing and elevating capability of the weapon. Gupta, 2011, in ‘Ammunition
Handling Systems’, gave a detailed analysis of the currently used ammunition handling systems and the
importance of automating ammunition handling systems. Descriptions of different types of automated
ammunition handling systems were given and the importance of automated loading of the gun was
mentioned. A detailed design and analysis of two different autoloader systems (including the synthesis of
the autoloader linkages, kinematic analysis, kinetic analysis and system reliability calculation) was
presented. The literature reviewed provides an understanding of the need for the autoloader and the
different aspects of autoloader linkage design.
2. PROBLEM DEFINITION
In the current gun system, the autoloader is used to move the projectile and the charge pellet from their
respective initial positions to their respective final positions defined with respect to the gun co-ordinate
system. The movements of the projectile and the charge to be achieved by the autoloader of the current
gun system can be illustrated in figure 1.
Fig 1: Schematic representation of charge pellet and projectile motion
The motions required are divided into two parts as movement of projectile and movement of the charge
pellet. These motions can be achieved by synthesizing linkages that would help to move the projectile and
the charge pellet in the desired manner and analyzing the linkages to determine their suitability for
performing the desired job under the given working conditions.
3. LINKAGE SYNTHESIS
The problem is thus of the form of synthesizing linkages for rigid body guidance of the projectile and the
charge pellet from a defined initial position to a defined final position. The linkages which need to be
synthesized to achieve these motions are the shell loading device and the charge loader link. The shell
loading device is used to transfer the projectile from the loading table to the ramming position in
alignment with the gun barrel axis. In figure 1, the ramming position (final position) is offset from the
loading table position (initial position) in all three directions. Thus the projectile has to be moved along X,
Y and Z axes to bring it from the initial to the final position. This has been done by using two different
planar linkages. One of the linkages is used to move the projectile such that the projectile axis becomes
parallel to the barrel axis. The motion of the projectile into the ramming position can then be achieved
using the other planar linkage. The linkages included in the Shell loading device are Loader arm link and
the Loading tray linkage. The charge loader link is used to place the charge behind the projectile in
alignment with the gun barrel axis. The charge loader link is in the form of a single rotating link pivoted at
a point.
After the types of linkages to be used were decided, the dimensions of the linkages had to be decided so
that the motion requirements of the linkages were satisfied. In the current work, the dimensions of the
linkages were determined analytically using the Dyad form of synthesis. The synthesis process is
explained with the example of the loading tray linkage. The data required for this process is in the form of
successive positions of the tray defined using the gun co-ordinate system as shown in figure 2.
Fig 2: Position Data for synthesis Fig 3: Input data for synthesis
Dyad Form - The dyad form of dimensional synthesis represents linkages in the form of vector pairs called
dyads. These dyads can then be analyzed by developing a system of equations in order to determine the
appropriate dimensions. For the loading tray linkage, three successive positions of the link (Positions 1, 2
and 3) from figure 2 are used as input for dimensional synthesis as shown in figure 3. A particular point on
the first position of the link is assumed to be the reference and the distances of corresponding points in the
other two positions are calculated using this point as a reference. The equations written in the process of
dimensional synthesis can be represented in the form of a matrix as shown in equation (1)
A -B C -D W1 E
F -G H -K X W1 = L -------------- (1)
B A D C Z1 M
G F K H Z1 N
A ….E, F, G, H, K, L, M, N – Variables whose values are determined from given position data
W1 X ,W1Y , Z1X , Z1Y are the dimensions of the linkage which need to be calculated
The results of the synthesis process for the linkages are summarized in Table 1
Table 1: Results of linkage synthesis
LINKAGE NAME LINKAGE TYPE LINK LENGTH
Loader Arm Rotating Link 0.5304 m
Loading 4 Bar Parallelogram Rotating Links : 0.45 m
Tray Base and Coupler Link : 0.35 m
Charge loader Rotating link 0.3298 m
4. TIMING ESTIMATION:
Timing estimation is carried out to estimate the time periods in which the motions of the different linkages
are to take place. The time periods estimated for the different linkages to carry out their to and fro motions
are summarized in the Table 2.
Table 2: Timing Estimation Details
ACTIVITY TIME
Movement of Loader Arm from initial position to final position 0.5 seconds
Movement of loading tray linkage from initial position to final position 0.5 seconds
Movement of charge loader linkage from initial position to final position 0.5 seconds
Ramming 2 seconds
Movement of charge loader linkage from final position to initial position 0.5 seconds
Movement of loading tray linkage from final position to initial position 0.5 seconds
Movement of loader arm linkage from final position to initial position 0.5 seconds
Total Time estimated 5 SECONDS
5. KINEMATIC ANALYSIS
The kinematic analyses of the linkages were carried out to find the necessary displacements, velocities and
accelerations. For this, the loop closure method was used to represent the linkage as vectors forming a
loop. A system of equations was developed and calculations were performed for the necessary variables.
The time interval required for a particular motion of was divided into appropriate subintervals. The
equations of kinematic analysis were then applied to each subinterval to obtain the required instantaneous
values. By doing this for all the subintervals, the variations of displacement, velocity and acceleration over
the assumed time interval were calculated. The loading tray linkage along with the terminology used in the
kinematic analysis shown in figure 4
Fig 4: Acceleration analysis of the loading tray linkage
The output of the kinematic analysis of the loading tray linkage in terms of different parameters
plotted against time is shown in figures 5 to 9.
Fig 5: θ vs. Time Fig 6: ω vs. Time Fig 7: α vs. Time
Fig 8: Velocity vs. Time Fig 9: Acceleration vs. Time
Figure 5 represents the positions of links 3 and link 4 at different instants of time depending on the
position of link 2. Figure 6 shows the variation of the angular velocities of links 3 and 4 with time. It is
observed that since the loader arm linkage is a parallelogram linkage, the coupler link does not rotate.
Therefore, its angular velocity remains zero throughout. The variation of angular velocity of link 4 with
time follows a profile similar to link 2. Figure 7 represents the variation of linear velocities of the points S,
A, P, B and U with time. The linear velocities of the points at any instant of time are calculated based on
the angular velocity of the particular link and their distance from the pivot point of the link. The variations
of the angular accelerations of links 3 and 4 with time are shown in figure 8. Figure 9 represents the
variations of linear accelerations of points S, A, P, B, and U with time. The linear accelerations are
calculated based on the angular acceleration of links and the distances of the points from the link pivots.
Similar calculations were also performed for the loader arm link and the charge loader link.
6. KINETIC ANALYSIS
The reactions at the pivots due to the external forces acting on the links and the forces induced due to
linkage motions, and the torque required to move the input link was estimated in kinetic analysis. The loop
closure method was used for this analysis. The external forces acting on the linkages included the self
weight of the links and the weights of the charge and the projectile. In the calculations, it was assumed that
the loading of charge pellet and the projectile was of the form of impact loading. The variations of the
reactions at the pivot points of the linkage and the torque required at the input link with time are shown in
figures 10 and 11 respectively.
Fig 10: Reaction at pivots vs. Time Fig 11: Torque vs. Time
7. STRESS ANALYSIS
The stress analysis of the linkages was performed to determine the stresses induced in the linkages and to
verify whether the induced stresses were within safe limits. The material of the linkages was assumed to be
plain carbon steel. A free-free run of the meshed model was carried out in order to determine the
connectivity between the different parts before calculating stresses. For the four bar loading tray linkage, it
was found that the stresses induced in the rotating links exceeded the yield strength of the material, thereby
causing failure. To avoid this, the thickness of the links was increased and the stress analysis was repeated.
However, it was observed that although the induced stresses were within the safe limits, due to the
increase in the thickness, the weight of the linkage was increased. Multiple iterations were carried out to
achieve a balance between the induced stresses and the weight. The results of stress analysis are
summarized in Table 3.
Table 3: Stress Analysis Results
LINKAGE MAXIMUM STRESS FACTOR OF SAFETY
8. CONCLUSION
Three linkages were synthesized to meet the given motion requirements of the autoloader. Kinematic
analyses of the linkages were carried out to determine the required displacements, velocities and
accelerations. Kinetic analyses were carried out to analyze the external forces acting on the linkage and
also the forces induced due to the motions of the linkages. Stress analysis was carried out to determine
optimum thickness values for linkages to have induced stresses within safe limits.
REFERENCES
1. Ainley L, “Integrated Artillery Recoil Mechanism and Automated Handling Design for Self
Propelled Howitzer”, ARDE, Pune (1980)
2. Erdman A.G and Sandor G.N, “Mechanism Design (Analysis and Synthesis)”, Prentice-Hall
(1984)
3. “Feasibility Study Report”, ARDE, Pune (2009)
4. Ghosh A and Mallik A.K, “Theory of Mechanisms And Machines”, Third Edition, Affiliated East
West Press Private Limited, New Delhi (1998)
5. Gokhale N, Deshpande S, Bedekar S and Thite A, “Practical Finite Element Analysis” First
Edition, K Joshi and Co, Pune (2008)
6. Gupta A, “Ammunition Handling Systems”, M. Tech Thesis, ARDE, Pune (2011)
7. Hartenberg R and Denavit J, “Kinematic Synthesis of Linkages”, Mcgraw Hill (1980)
8. Norton R.L, Design of Machinery (An Introduction to Synthesis and Analysis of Mechanisms and
Machines), Third edition, Tata Mcgraw Hill, New Delhi (2005)
9. Roy A. K, “Automation of Ammunition Handling Systems for Artillery Guns” in “Introduction to
Weapons and their Configuration”, a CEP course on “Principles Of Weapon Design And
Engineering”, ARDE, Pune (2004)
10. Uicker J.J (Jr), Pennock G and Shigley J, “Theory of Machines and Mechanisms”, Third Edition
(International Version), Oxford University Press, New Delhi (2009)
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID - ICAME2013 S1/P1
NAVIGATION OF MOBILE ROBOT WITH OBSTACLES AVOIDANCE USING FUZZY LOGIC
1. INTRODUCTION
In the area of robotics, one of the main areas of research is to construct an autonomous intelligent mobile
robots, which can plan own motion during navigation through two-dimensional or three dimensional
terrains [1].The area of mobile robot is commonly divided into systems designed for either indoor or
outdoor environments. The other problem is the path planning in which the mobile robot needs to find a
collision free path from its starting to its goal. In order to be able to find that path, the robot needs to run a
suitable path planning algorithm, to calculate the path between any two points [2].Fuzzy logic control is
characterized by the use of linguistic rules to manipulate and implement human knowledge in control
systems so as to handle the uncertainty present in the environment [3]. Navigation and obstacle avoidance
are very important task for the successful employment of an autonomous mobile robot. A mobile robot
navigation path planning system based on fuzzy logic. Fuzzy rules are adopted in the controller of a
mobile robot enable it to avoid obstacles in a cluttered environment. When computing the configuration
sequence, we allow the mobile robot to move from one position to another. When the environment of the
mobile robot is obstacle free, the problem occur less complex to handle. But as far as the environment
becomes complex, motion planning needs much more computations to allow the mobile robot to move
between its current and final configuration without any collision with the surrounding environment [4].
Sensor based mobile robot navigation systems typically relied on ultrasonic sensors or laser scanners
providing one dimensional distance outlines. The major advantage of this type of sensors results from their
ability to directly provide the distance information required for collision avoidance.Ultrasonic sensors or
one dimensional laser rangefinders, which have been widely, used for transportation and navigation tasks
of an autonomous mobile robot [5]. Fuzzy based controls concepts are useful in both global and local path
planning tasks for autonomous mobile robot. The search for an optimal decision table to be used as the
inference engine in fuzzy based planning and navigation algorithms is highly important. Fuzzy controllers
for both navigation and obstacle avoidance have been developed must require [6].
This paper based on the navigation of a mobile robot in dynamic positions with desired goal and number
of obstacles. The control navigation of the mobile robot can be achieved by fuzzy logic system to change
the head angle of robot to reach the destination point while avoiding the collision and obstacles.Generally,
the fuzzy logic controller is constructed by designing the fuzzy rules and membership functions (input and
output) based on expert knowledge, modelling of process or learning. To date, definition of fuzzy logic
controller rules in robot obstacle avoidance are usually based on Mamdani or Takagi–Sugeno–Kang (TSK)
rule base system. However, it is difficult to maintain the correctness, consistency, and completeness of the
generated fuzzy rule base. Fuzzy Interface Sytems (FIS) have been proven to produce better performance
than simple rules in unknown environments [7].
2. DESIGN OF FUZZY CONTROLLER FOR CURRENT ANALYSIS
Fuzzy logic is an attractive method to solve problems of control and simulation of complex systems. A
FLC system consists of three operations- fuzzification, interface engine and difuzzification. In the field of
robotics, to make an autonomous mobile robot, which can plan their self-motion during navigation via
known or unknown terrains? For the fuzzy knowledge base, the mobile robot uses its fuzzy rule base to
find an obstacle free path for a given input of parameters depicting the state of obstacles and the state of
mobile robot. The mobile robot turns around obstacle our projected navigation method supplies the robot
with the turning point for avoiding the obstacle and moving on the collision free path. The inputs of the
fuzzy approach consist of obstacles which stand on the front, right and left of a robot as shown in Fig. 1,
and each input variables has three triangular membership function (MF) close, medium and away as shown
in Fig. 4. The output of this system controls the heading angle of a robot to avoid obstacle and move to
reach the goal, output variable has three triangular membership function (MF) negative, zero and positive
as shown in Fig. 5. To avoid the obstacles, controller operates with user defined rules it functioning under
Mamdani-type FLC. These rules establish the relation between front, left, right obstacles and heading
angle in terms of linguistic term(s) or values. When the obstacle is located at the right and left sides of the
mobile robot, heading angles either positive or negative.
The fuzzy controller as shown in Fig. 2 uses various sensors based informations such as front obstacle
distance (F_O_D), right obstacle distance (R_O_D), and left obstacle distance (L_O_D), and heading
angle (H_A) for select the path while moving near to goal. The fuzzy position function commands the
robot moves to particular position for defending obstacles. The fuzzy logic rules for obstacle avoidance as
follows.
If (L_O_D is close and R_O_D is close and F_O_D is close), Then (heading angle is negative).
If (L_O_D is close and R_O_D is close and F_O_D is medium), Then (heading angle is negative).
If (L_O_D is away and R_O_D is medium and F_O_D is away), Then (heading angle is positive).
If (L_O_D is medium and R_O_D is away and F_O_D is medium), Then (heading angle is positive).
If (L_O_D is away and R_O_D is away and F_O_D is away), Then (heading angle is zero).
Collision
Path
Heading
Angle
Fig. 1. Mobile robot avoiding obstacle using fuzzy logic controller
Front Obstacle Fuzzy
Right Obstacle Heading
Left Obstacle Distance
Fig. 2. Fuzzy logic controller for mobile robot navigation
The fuzzy logic controller that combines fuzzy rules to direct the heading angle of the robot to avoid
obstacle in its path. Fuzzy logic control is safely suited for controlling a mobile robot because it is capable
of making interferences even under uncertainty. It helps rule generation and decision making. It uses set of
linguistic fuzzy rules to implement expert intelligence under different conditions. Fuzzy logic system is
specially designed with two main reasons- obstacle avoidance and goal seeking in any environment. In this
proposed fuzzy model, a mobile robot avoids obstacles and generated the path towards the goal. The fuzzy
evaluation implies to access the possible path of a robot on the basis of information whether the future
location of robot is in the possible driving path or not.
Fig. 3. Fuzzy membership function for front Fig. 4. Fuzzy membership function for
obstacle, left obstacle and right obstacle in metre heading angle in radian
4. SIMULATION RESULTS AND DISCUSSION
The simulation experiment shows that the proposed fuzzy controller, using MATLAB, can perform robot
navigation in known or partially known environments. The trajectory of mobile robot navigation in
unknown environment with one, two and three obstacle(s) as shown in Fig. 5, 6 and 7 respectively, the
beside table on this figures are show that the starting point, obstacle(s), heading angle, and goal point of a
robot. The simulation program offers an excellent alternative based on navigation methods with a fraction
of the processing requirements result a fast responding reliable application. In this paper, we conclude that
present a new mobile robot navigation strategy based on the fuzzy logic approach avoiding the obstacle
drives robot ultimately target at the required distance with the given initial position. We have developed
simulation to test robot trajectory under the unknown environment according to fuzzy logic rules. The
simulated robot collision free path developed and set the number of obstacle(s) at different location of the
environment. When the robot is near to obstacle, it must change its heading angle to avoid obstacle(s). In
the Fig. 5, a robot is controlled by fuzzy controller to changing it heading angle and moves from its start
(0, 0) to the goal (200, 200) avoid single obstacle placed in (80, 80). In Fig. 6, robot moves from its start
(6, 4) to goal (180, 240) avoid two obstacles placed in (50, 70) and (90, 140) respectively. In Fig. 7, robot
moves from its start (0, 0) to goal (240, 260) avoid three obstacles placed in (140, 125), (69, 56) and
(90, 80) respectively. In this simulations show, the robot finds goal in environments with number of
obstacles without hitting the obstacle(s).
Fig. 5. Trajectory of the single mobile robot with one obstacle
Fig. 6. Trajectory of the single mobile robot with two obstacles
5. CONCLUSION
In this paper, the simulation results show that, only using information got by sensors can perform robot
navigation in given environment, such as avoiding obstacles and reach the goal.The goal which the robot
should reach is known, but the geometry and the location of the obstacles are unknown. The heading angle
of the robot’s movement is determined by the direction of the goal and obstacle distance. Fuzzy logic
algorithm will be used for mobile robot navigation with obstacle and collision avoidance. Finally the
simulation results for mobile robot navigation are given.This simulation results behind that implementing
obstacle avoidance uses a fuzzy logic approach and is conducted an autonomous mobile robot platform
which can modify to include sensors. The current research work is to be extended for multiple mobile
robots instead of single mobile robot.
Fig. 7. Trajectory of the single mobile robot with multiple
obstacles
REFERENCES
1. Pratihar Dilip Kumar, Deb Kalyanmoy, Ghosh Amitabha, “A Genetic-Fuzzy Approach for Mobile
Robot Navigation Among Moving Obstacles”, ELSEVIER, 20, 145 (1999)
2. Jaradat Mohammad Abdel Kareem, Al-Rousan Mohammad, Quadan Lara, “Reinforcement Based
Mobile Robot Navigation in Dynamic Environment”, ELSEVIER, 27, 135 (2011)
3. Silva Ivan N. da, Gomide Fernando A. C., Amaral Wagner C. do, “Navigation of Mobile Robots Using
Fuzzy Logic Controllers”, IEEE, 346 (1998)
4. Abdessemed Foudil, Benmahammed Khier, Monacelli Eric, “On Using Evolutionary Programming for
a Mobile Robot Fuzzy Motion Controller”, IEEE, 37 (2000)
5. Wichert Georg von, “Self organizing Visual Perception for Mobile Robot Navigation”, IEEE,
194 (1996)
6. Bentalba S., Hajjaji A. El, Rachid A., “Fuzzy Control of a Mobile Robot: A New Approach”, IEEE,
69 (1997)
7. Samsudin Khairulmizam, Ahmad Faisul Arif, Mashorhor Syamsiah, “A Highly Interpretable Fuzzy
Rule Base Using Ordinal Structure for Obstacle Avoidance of Mobile Robot”, Applied Soft
Computing, 11,1631 (2011)
8. MATLAB, Fuzzy Logic Toolbox.
9. Parhi Dayal R., “Navigation of Mobile Robots Using a Fuzzy Logic Controller”, Springer, 42,
253 (2005)
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S1/P3
KINEMATIC ANALYSIS OF THE PARALLEL JAW GRIPPER OF A
MECHANICAL MASTER-SLAVE MANIPULATOR
Shilpa Bhambure K.Jayarajan V.S.Narwane M.A.Palsodkar
Affiliation: P.G.Student Affiliation:Head Affiliation: Associate Affiliation: W/S Supt.
shilpabhambure@gmail.c Telemanipulator Prof. manojpalsodkar70@rediffmail.c
om Section vsnarwane@yahoo.c om
kjayaraj@barc.gov. om
in
ABSTRACT
Nuclear industry employs many remote handling tools for handling objects in radioactive
environments. Master- slave manipulators (MSMs) are the most versatile among the general purpose
remote handling tools. Highly radioactive materials are typically handled inside heavily shielded
enclosures called hot cells. When the operator grasps the hand grip and manipulates the master arm, the
motion of the master arm is reproduced by the slave arm, performing the desired manipulation task
remotely.
The manipulator as well as its gripper is powered by the operator. As the power of the operator is limited,
design of the gripper and transmission mechanism has to be optimised to obtain required range and
gripping force. This report gives kinematic analysis of gripper used in nuclear industry for mechanical
MSM.
Keywords: Master-slave manipulator, Hot cells, Gripper
1. INTRODUCTION
Remotely operated technology can minimize manual intervention time in hazardous areas, thus enhancing
safety and productivity. Articulated manipulator is one of the several MSMs developed by division of
remote handling and robotics (DRHR) for the use in nuclear industry. It is a compact and versatile
equipment designed for use in small hot cells to carry out various operations in radioactive environment
with minimum friction and maximum rigidity.
A gripper is an interaction device between the environment and the object to be picked and placed to
perform grasping and manipulation task. The motivation of growing research in gripper design came from
human hand. The basic purpose of gripper is to hold, grip, handle and release an object the way a human
hand can do. Manipulator grippers are meant to replace human hands because they are very good for
repetitive cycles, handling heavy loads, and operate under extreme temperatures and environments where
human hands cannot operate.
Figure 1: Mechanical master-slave manipulator
Figure 1 shows mechanical MSM consists of three parts – the slave arm located inside the hot cell, the
master arm located in the control station, and a through-tube connecting the master arm to the slave arm.
When the operator grasps and manipulates the master arm, the motion of his hand is reproduced at the
slave arm performing the necessary task. In most cases, the master arm and slave arm are made
kinematically similar to each other.
Parallel jaw gripper moves in a motion parallel in relation to the gripper’s body. An advantage of parallel
type gripper is that the centre of the jaws does not move perpendicular to the axis of motion. Thus, once
the gripper is centered on the object, it remains centered while the jaws close.
The gripper of the slave arms are powered and controlled by the operator’s hand through the master arm.
From the task area the operator gets visual feedback through a shielding window and force feedback
through the manipulator. Mechanical MSMs are suitable where the work area is constant and not too large
and the force requirement is within the capacity of the operator.
1.1 Power transmission
Power transmission between the master arm and slave arm is the most challenging task. When a master
hand grip is moved the corresponding slave gripper should also move by the same amount in the same
direction. So any application of force onmaster arm should reflect on the slave arm. All transmission
mechanisms should operate in parallel so that slave gripper reproduces the trajectory of the master handle.
Mechanical power transmission across the cell wall is done using wire ropes, metal tapes. Wire ropes and
metal tapes are light weight, compact and flexible compared to other transmission mechanisms. Within the
master and slave arms spur gears, bevel gears and rack and pinion etc are also used for power transmission
and motion conversion.
1.2 Parallelogram mechanism
Parallelogram mechanism ensures that the maximum gripping force is applied at all the times. Another
advantage is that the gripping force is independent of where the contact points are located along the finger.
If weight of the grasped object is small compared to the gripping forces the object can be treated as a two
force member which indicates that the gripping forces will always be normal to both the object and the
finger at the point of contact. The main objective is to perform the analysis of a gripper of mechanical
master slave manipulator used in nuclear industry hot cell for 9 kg payload capacity.
2. HUMAN ERGONOMICS
The human hand was designed to grasp but it was not made to use the same grip or posture for long hours.
Although excellent for performing a variety of tasks, repetitive movements can cause problems. The wrist
is very flexible and allows a great variety of hand positions. The most important and fundamental way to
reduce hand pressure and stress is to increase the mechanical advantage of the tool. There is an optimum
grip diameter for every individual at which point their hand can apply the most force to the tool with the
least stress on the hand tissues. Grip diameter is the width of the handles of the tool measured at the center
of the hand as shown in figure 2.
Figure.2 Grip Span for Handle Figure. 3 Hand Force Requirements
The optimal grip diameter is 2.95" (75mm) for females and 3.15" (80mm) for males. The maximum force
that males can apply at theiroptimum grip diameter is 112 lbs. or 500 N.
Females are able to apply 58.5 lbs. or 260 N at their optimal grip diameter. It is very important to design
tools so that the maximum required force is near the optimal grip diameter.
Much greater forces can be applied with two hands rather than one. Figure 3 shows the handle force
capabilities of males and females for single handed and double handed use for a range of handle spreads.
Tools should be designed for two handed use wherever possible for greatest ease and comfort.
It is necessary in the design of machine mechanisms to know the manner in which forces are transmitted
from input to the output, so that the components of the mechanism can be properly size to withstand the
stresses that are developed. From the literature survey it is found that the two finger grasp is extensively
used for industrial grip, since it is considered the simplest efficient grasping configuration. A gripper is a
critical component as it interacts with the environment and gives great contribution to the practical
success.
The design of a gripper must take into account the constraint for gripping system as lightness, small
dimensions, rigidity, multitask capability, simplicity. This means a good design of two finger gripper
requires to take into account several problems.
The methodology includes finding the mathematical relation between forces, prepare the excel sheet for
calculation of it to plot the graph and verify the same using Matlab tool. Create CAD model of the gripper
and analysis using Ansys software tool.
Figure 4 shows two jaw parallel manipulator gripper with parallelogram linkage mechanism. Figure 5 and
6 shows free body diagram of gripper jaw and the linkage mechanism to find the mathematical relation
between the forces acting on the gripper.
Figure 4:. Basic tong of manipulator gripper
Figure 5 : FBD of Gripper jaw Figure 6: FBD of gripper linkage mechanism
F’ = K1(θ)*Fg (1)
“Eq.(1)” gives mathematical relation between the gripping force and the force on the link.
Table 1 gives the variation of link angle with respect to the jaw horizontal distance as it is changed from
zero to the maximum.
1. Variation of link angle with jaw distance
Figure 8 Deformation Plot Figure 9 Stress Plot
The maximum deformation developed is 3.642 mm at the jaw bottom part as highlighted with Max. in
figure 8 The maximum stress developed is 2085.6MPa at the gripper spring link joint as highlighted with
Max. in figure 9.
4. CONCLUSION
The kinematic analysis carried out gives the mathematical relation between the forces acting in gripper
mechanism in terms of angle ө. Also it gives the tension in wire rope at the master and slave side when the
operator grasps and manipulates the master arm for performing the necessary task.
As it is a mechanical master slave manipulator there is limitation on the force that can be applied by a
human being which required to take into the consideration the human ergonomics part.
The linear static analysis carried out in Ansys v14.0 gives the stress and displacement plots for the gripper
carrying 9 kg payload. The evaluation of stress value is determined by Von Mises’stress. Although these
stresses are in the zone permissible for a given material, there is the possibility of optimizing the geometry.
5. FUTURE SCOPE
REFERENCES
1. Cuadrado J., Naya M.A., Ceccarelli M., Carbone G. “An Optimum Design Procedure For Two-
Finger Grippers: A Case of study”
2. Jayrajan K., and Singh M., “Master Slave Manipulators: Technology and Recent Developments”
BARC Newsletter
3. Jayrajan K.,“Advances in the Remote Handling Technology in Nuclear industry”Annals of the
Indian national Academy of Engineering, Vol. IX.(2012)
4. Raghav V, Kumar J., Senger S.S., “Design and optimization of roboticgripper: A Review”
Conference on Trends and Advances in Mechanical Engineering (2012)
5. Yunming Li, and Zarrugh M.Y., “Kinematics and force control of robot gripper”
6. Dogan B, “ Development of a Two Fingered and four Fingered robotic gripper” (2010)
7. Kong Y., Song Y., Jung M Lee, “Effects of hand position on maximum grip strength and
discomfort” Ergonomics Australia HFESA Conference (2011)
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID - ICAME2013 S1/P4
FUZZY LOGIC BASED INTELLIGENT CONTROL OF A MOBILE ROBOT
ABSTRACT
In this paper, fuzzy logic has been used to control a mobile robot in a cluttered environment. A
mobile robot extracts information from the environment in order to perceive, map and act with the help of
sensors and controller. An intelligent controller enables mobile robot to perform its task effectively and
efficiently by execution of appropriate decision to a particular situation. The effectiveness of the proposed
controller for navigation of robot is validated through MATLAB simulations in different environments.
The simulation results reveal that the robot is able to avoid the obstacles and reaching towards the goal
successfully by following the near optimal path.
Keywords: Fuzzy Logic, Obstacle avoidance, Target Seeking behavior, Mobile Robot, Robot Navigation
1. INTRODUCTION
Navigating a mobile robot in unknown indoor environment or in partially known one, is a fundamental
problem in the field of mobile robotics. Navigation related to mobile robots is the ability of travel from
one position to another by following obstacle free path. Mobile robots, while performing their task travel
from one location to another and follows the obstacle free path. Therefore obstacle avoidance is a prime
necessity for any autonomous mobile robot. Various methods have been presented by different researchers
in order to solve this problem. The methods can be classified as local control and global planning
techniques. In global navigation robot has prior information of the environment, shape and position of the
obstacles whereas in local control, robot uses reactive approaches to navigate successfully without any
prior data of the environment.
The roadmap approach such as visibility graphs and voronoi diagrams is one of the earliest methods used
in robot path planning but its application is limited to static and completely known environment [Piaggio
and Zaccaria, 1998]. (Khatib, 1985) has developed the concept of artificial potential field for avoiding the
obstacles. The method has got popularity among the researchers to overcome the limitations associated
with the approach such as trap situation local minima, oscillations near the closely spaced obstacles, and in
the narrow passages. In these approaches obstacles exerts repulsive forces onto the robot, while the target
applies an attractive force to the robot. The resultant of all forces determines the subsequent direction and
speed of travel. (Barret et. al.1997) have proposed a sensor-based navigation algorithm, combines two
types of obstacle avoidance behaviors, each for the convex obstacles and concave ones. To avoid the
convex obstacles the navigator uses either fuzzy tuned artificial potential field (FTAPF) method or a
behavioral agent, however an automatically online wall-following system using a neuro-fuzzy structure
has been designed for the concave one. (Abdessemed et. al. 2004) have used the fuzzy logic controller in
the development of complete navigation procedure of a mobile robot in a messy environment. An
evolutionary algorithm has been implemented in order to solve the problem of extracting the IF-THEN
rule base. The validity of the proposed method has been demonstrated through simulation results. (Huq et.
al. 2008) have presented a new technique to select different motor schemas using fuzzy perspective
depending blending of robot behaviors for navigation. (Kao et. al. 2010) have used fuzzy set concept
cooperated with a wireless sensor network for building a global map. They have divided the navigation
space into grids and if an obstacle is detected by one or a number of sensors then a grid is to be selected.
Fuzzy set concept has been used to introduce a tool useful for sensor perception. All the sensors work
together as a team to explore all the space and then the global fuzzy map is constructed. The experiments
show that the fuzzy map is more practical and helps the path planning problem to be solved more
efficiently.
2. FUZZY LOGIC CONTROLLER
Fuzzy logic is inspired from the outstanding human ability to judgement with perception based
information. Fuzzy Logic is a tool for modelling uncertain systems by enabling common sense reasoning
in decision-making in the lack of thorough and accurate information. It enables the arrival of a definite
conclusion based on input information, which is unclear, uncertain, noisy and imprecise. The architecture
of the proposed fuzzy controller is shown below in Figure 1.
ODF
CONTROLLER
ODL
OUTPUT
INPUTS
AS
FUZZY
ODR
AT
Figure 1. Proposed Fuzzy Logic Controller
Four inputs to the controller are obstacle distance in front (ODF), left (ODL), right (ODR), and angle of
the target with the robot (AT). Controller provides a value for steering angle (AS) for the robot. Linguistic
terms like Very Very Near (VVN), Very Near (VN), Near (N), Far (F), Very Far (VF) and Very Very Far
(VVF) has been used for the distance of the obstacles from the robot and terms like Very Very Negative
(VVN), Very Negative (VN), Negative (N), Positive (P), Very Positive (VP), and Very Very Positive (VPP)
are used to define the target and steering angle. Rules of fuzzy controller become characterized as follows:
If front obstacle distance (ODF) is A and left obstacle distance (ODL) is B and right obstacle distance
(ODR) is C and target angle (AT) is D Then steering angle (AS) is E.
2.1 Fuzzy membership functions
Hybrid membership function has been used for both inputs and output variables. The hybrid membership
is a combination of different shape of membership functions. In the present work, Triangular, Trapezoidal
and Gaussian membership functions have been used. Figure 2 shows the hybrid membership function for
the front, left and right obstacle distances whereas membership function for target angle and steering angle
are shown in figure 3 and 4 respectively.
Figure 2.Hybrid Membership Function for Front, Left and Right Obstacles Distance.
Figure 3.Hybrid Membership Function for Target Angle.
Figure 4. Hybrid membership Function for Steering Angle.
The range for obstacle distances is 0 to 20 units whereas target angle and steering angle are ranging
between -180 to 180 degrees.
3. BEHAVIOR LEARNING OF CONTROLLER
To offer the robot with the ability to navigate successfully by avoiding static obstacles in crowded
and unknown environment the following behaviors were designed: 1) Obstacle avoidance, 2) Target
seeking and 3) Wall following The behaviours are modelled using If - Then rules.
Distances of the obstacles presents in the front, left and right direction of the robot are the inputs to
obstacle avoidance behavior. From this the distance of any nearby obstacles can be known to the
navigation system and it can send appropriate command according to a particular situation. The controller
considers obstacles present in the front of the robot more dangerous than those presents in the sideways.
The output for the obstacle avoidance behavior is an angle which represents the direction in which robot
should not proceed. Some of the rules for obstacle avoidance behavior are as follows:
IF ODF is VN and ODL is N and ODR is VF and AT is VVP then AS is VP.
A maze type working environment of 150×150 units has been considered for the simulation. Rectangular
and circular shape Obstacles have been used for the simulation. Simulation results have been presented for
different environment using MATLAB. Robot start position, goal position and obstacles are shown below
in figure 5. Initially robot proceeds towards the goal position by following target angle until it detects any
obstacle. When the robot finds any of the obstacles along its path then fuzzy controller comes into action.
It uses fuzzy if - then rules and provide steering angle as output matching to the input values. Finally robot
reaches to its goal position by following an obstacle free path. It uses different behavior to navigate
successfully in the environment. Moreover the robot follows near optimal path while traveling towards the
goal position.
Goal
Goal
Robot Path
Robot Path
Obstacles
Obstacles
Start Start
Figure 5. Mobile Robot Navigation within its Maze Environment
5. CONCLUSION
ABSTRACT
In this paper analysis of ESP cone structure will be carried out for optimization and failure prevention
with the use of different arrangements of stiffeners. Electrostatic precipitators (ESP’s) are widely used for
controlling particulate emissions from boilers and industrial process sources. Majorly ESP failure occurs at
any of cone junction. So the main objective is to understand why these failures are occurring by studying
effect of different stiffeners arrangement and implementing necessary design changes so as to assure safety
of ESP. Plate buckling theories are followed to understand the behavior of a cone structure. Nonlinear
buckling of the structure causes to follow nonlinear analysis. Imperative use of FEA tool will be done to
understand interactions of multiple forces. FEA software package ANSYS 12.0 (Workbench) is used due
its advantages. Also non linear buckling will be needed to simulate in precise manner. Various design
combinations will be simulated using FEA out of which the optimum one will be finalize and will undergo
further study.
Keywords: ESP cone, plate buckling, non linear FEA, stiffeners optimization.
1.INTRODUCTION
ESP’s are similar to the way an ionic breeze works. They take the incoming polluted air and pass it
through a filtration device that purifies the air. Any solid particles left over will fall into a large storage
container called a hopper and the clean air is brought out. Electrostatic Precipitator is a particle control
device that uses electrical forces to move the particles out of the flowing gas stream and onto collector
plates. The particles are given an electrical charge by forcing them to pass through a corona, a region in
which gaseous ions flow. The electrical field that forces the charged particles to the walls comes from
electrodes maintained at high voltage in the center of the flow lane. Once the particles are collected on the
plates, they must be removed from the plates without re-entraining them into the gas stream. This is
usually accomplished by knocking them loose from the plates, allowing the collected layer of particles to
slide down into a hopper from which they are evacuated. Some precipitators remove the particles by
intermittent or continuous washing with water (Turner et al, 1995). Generally ESP’s are heavy structures
having 23m height and over 30-50m of length. It have to be undergone high temperatures about 300-500
degrees.
At many of ESP fields, it is observed that failure of cone structure is major concern. So to get rid of this
problem it is important to study the behavior of cone structure under normal operating conditions of ESP
with the influence of different arrangement of stiffeners. Stiffeners provide improvement to load carrying
capacity of structures. The benefit of stiffening of a structure lies in achieving lightweight and robust
design of the structure. The objective of this study is to carry out a deep interest and investigation about
the effect of stiffener location on the overall deformation of the cone structure. Parametric studies are
carried out in order to investigate the effect of stiffeners location, number of stiffeners, boundary
conditions and plate dimensions on the buckling parameters. The proposed results can be used to develop
an improved design for ESP cone structure along with best suited stiffener arrangement.
2.PROBLEM STATEMENT
The problem investigated in present paper is the determination of deformation of entire ESP cone structure
with the use of FEA tool. The study is done for different stiffener arrangement which includes cross to axis
of cone, parallel to axis of cone and hybrid of both arrangements. The stiffeners are equally spaced and are
of equal cross section and having material properties same as that of cone structure. The cone is subjected
to suction pressure which is acting in the direction of gas flow.
Fig.1 Model- Cone Structure
3.PROPOSED FORCE TERMINOLOGY
Main body is supported with the help of columns and cones are suspended in a cantilever arrangement to
it. This arrangement is itself a difficult one to implement and also cause the cone structure to be under
tremendous pressure. It causes cone structure to rely on main body for support.
Fig. 3 Kirchhoff’s Plate
The Kirchhoff–Love theory (Classical Plate Theory) is an extension of Euler–Bernoulli beam theory to
thin plates. The theory was developed by Love using assumptions proposed by Kirchhoff. It is assumed
that there a mid-surface plane can be used to represent the three-dimensional plate in two dimensional
form.
Mindlin's theory assumes that there is a linear variation of displacement across the plate thickness and but
the plate thickness does not change during deformation. This implies that the normal stress through the
thickness is ignored; an assumption which is also called the plane stress condition. On the other hand,
Reissner's theory assumes that the bending stress is linear while the shear stress is quadratic through the
thickness of the plate. Details of field equations for above stated theories are briefly available in Steele and
Balch (2009)
2) Model B: In this model stiffeners are arranged in the direction of gas flow. These stiffeners are
enclosed by channel section at small ends and by single plates at big end. Channel sections at small
end are also connected by arrangement same as that in model A.
Fig. 5 Model B: Vertical Stiffener
3) Model C: This is the combination of first two models. This arrangement provides more stiffness as
compare to previous two models. Inner vertical stiffeners are enclosed at both ends by single plates
only.
Table 1
Boundary conditions:
Fix Edges & Faces: All edges & faces at big end are kept fix.
Pressure: 0.023 Mpa in the direction of flow.
7.RESULTS& CONCLUSION
Comparative study of nonlinear buckling analysis has been done for three different arrangements of
stiffeners on the cone structure of Electrostatic Precipitator. Deflections & weights for all three models are
as listed in table.
Weight, W (kg) Max Deflection
Model NO.
δ (mm)
36123 kg
A (Stiffener Across Axis ) 31.751
20016 kg
B (Stiffener Parallel to Axis ) 19.258
39470 kg
C (Hybrid Arrangement) 15.511
Table 2
Model A Model B
Model C
Fig. 7 Results
After observing above results some conclusions can be made that Model C i.e Hybrid arrangement of
stiffeners gives minimum deflection as compare to other two models. So thinking toward safety
perspective model C is safer as compare to other two models whereas weight of model 3 is more as
compare to other two models. So model C will require more material and it will cause increase in cost.
Model B presents the optimum combinational balance between weight and deflection so is more preferable
as compare to other two models. Also it is interestingly noted that maximum deflection region in each
case of model is at centre of face having maximum surface area. The reason behind this is extended
portion on this face which kept fixed as per boundary condition requirements & deflection distribution in
all cases is nearly symmetric.
REFERENCES
Chad Balch and Charles Steele “Introduction to the Theory of Plates” Stanford University.
Dr. D. Dinev , “Plate analysis For Floor and deck slabs”, Theory of Elasticity and Plasticity,
Department of Structural Mechanics.
G. Grondin, A. Elwi, J. Cheng, “Buckling of stiffened steel plates—a parametric study”, University
of Alberta, August 1998.
J. Turner, P. Lawless, T.Yamamoto, D. Coy, W. Vatavuk, G.Greiner ,J. McKenna, “Electrostatic
Precipitator”, December 1995.
N. Taysi, “Determination of thickness and stiffener locations for optimization of critical buckling
load of stiffened plates”, University of Gaziantep, April 2010.
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
PapeID-CAME2013-S2/O3
DESIGN OF A SELF REGULATED PRESSURE VALVE BY FINITE ELEMENT ANALYSIS
Nilesh Jadhav
Sunil Bhat
M.Tech. (CAD-CAM) Vinay Patil
Professor
student FEA Consultant
Vellore Institute of
Vellore Institute of Vaftsy CAE
Technology
Technology Pune, India
Vellore, India
Vellore, India vinaay.patil@vaftsycae.com
snlbhat@rediffmail.com
nilesh_jadhav@yahoo.com
ABSTRACT
This paper deals with a pressure system in which the flow is required to be regulated when the
pressure reaches the permissible value in the storage chamber. The objective is to design a mechanical,
spring controlled, pressure valve with a feedback mechanism to regulate the flow without failing under the
effect of flow loads. Other supporting components namely flow pipes, springs, jacket etc. are also
designed to meet the operational requirements. Structural integrity of the assembly is finally checked
under transient loads by finite element method.
Keywords- Pressure valve, FEA, flow, transient analysis, feedback pressure loop
NOMENCLATURE
A - Area of solid cylinder C - Weisback constant D - Inner diameter of pipe
d- Mean diameter of spring E′- Equivalent elastic modulus F-Axial force on face plate
K-Stiffness of spring Lf -Free length of spring P-Flow pressure
t - Time tp - Thickness of pipe σ - Yield strength
δmax- Maximum spring compression
1. INTRODUCTION
Flow processes in the industry need to be controlled to prevent accidents. Protection of pressure vessel
against excessive pressure without feedback system is often achieved through the use of mechanical self-
actuated devices like safety relief valve or bursting disc. In the feed-back system, a spring controlled valve
is used that is operated by the feedback pressure. When the vessel or chamber pressure reaches the
maximum allowable value, feedback loop operates causing the valve plate to move up, against the spring
force, in the inlet flow pipe to restrict the flow. The valve and springs are housed in the jacket. Basic block
diagram of a feedback system is given at Fig. 1
Fig. 1 Feedback based pressure regulating system
2. DESIGN PARAMETERS
Table 1. Operating conditions
Flow pressure 0.1 MPa Permissible chamber pressure 0.32 MPa
Desired valve movement 42 mm Flow temperature 70 C(Min)-3500C(Max)
0
3. DESIGN
The whole assembly is first conceptualised which is followed by preliminary modelling and analysis of
system components. The valve consists of, rectangular, face and restrictor plates joined in the form of a
“T” configuration. Suitable dimensions of the plates are assumed. Springs are replaced by solid cylinders.
Elastic modulus of solid cylinders, equivalent to actual springs, is determined theoretically to achieve the
desired compression during valve movement. A start up finite element analysis is undertaken under
maximum static inlet (bending) and feedback (axial) pressures on restrictor and face plates respectively to
optimise the thickness of the plates and to verify the spring parameters. Thickness of the inlet and
feedback pipes is found from the conventional principles. Geometry of the jacket that depends upon the
valve, spring and pipe dimensions is then finalised. Lastly the assembly is subjected to complete finite
element analysis under realistic transient loads with appropriate boundary conditions to confirm i) Desired
valve travel in the given time and ii) Structural integrity of the assembly.
i) Conceptualization
The conceptual model of the assembly and its sectional view are shown in Fig. 2 and Fig. 3 respectively.
The valve geometry is shown in Fig. 4.
Fig. 2 Conceptual model Fig. 3 Sectional view Fig. 4 Valve geometry
Fig. 5 Valve plate dimensions Fig. 6 Spring compression
Since axial force exerted on the face plate of the valve is responsible for spring compression, its value is
obtained as
F = Maximum pressure * Area of face plate = 0.32 MPa * 35 mm * 45 mm = 504 N (1)
For the purpose of theoretical analysis, springs are replaced by solid cylinders. Equivalent elastic modulus
of a cylinder is written as [1]
∗ π
E′ = ∗δ
= ( ∗ )∗
= 7.945 MPa where A = d (2)
′
Spring stiffness = K = = 2999.6 N/m (3)
ANSYS workbench [2]is used for finite element modelling of valve and springs at the topmost (extreme)
position of the valve when flow pressure of 0.32 MPa is acting over both the valve plates. SOLID186, a
higher order 20 node hexahedron structural solid element as shown in Fig. 7, is used for meshing. The top
of solid cylinders is fixed as the boundary condition. The loads and the boundary condition are shown in
Fig. 8.
9.
Fig. 7 SOLID186 element Fig. 8 Loads and boundary condition Fig. 9 Equivalent
stress
At 1 mm plate thickness, maximum equivalent stress is found to be beyond the yield strength of 160 MPa
of valve material. Hence, plate thickness is increased from 1mm to 2mm. At 2 mm thickness (Fig. 9), the
maximum equivalent stress developed is 89.875 MPa which is less than the yield strength. Factor of safety
is 1.78 that is sufficient to account for thermal stress induced in the valve body due to flow at high
temperature which is not considered in the analysis.
b) Design of pipes
The thickness of pipe (tp) to withstand the flow pressure is obtained by thin cylinder formula [1, pp.262-
266] given by t = σ + C (4)
Maximum flow pressure, P, is 0.32 MPa. Constant C is taken as 3 to account for possibility of pipe
corrosion due to the flow at high temperatures. For inlet pipe of 40 mm diameter,
. ∗
t = ∗ + 3 = 3.03 mm
Similarly for feedback pipe of 30 mm diameter, tp is 3.023 mm.
c) Design of jacket
The geometry of the jacket is decided by the dimension of valve plates. A lubricated, low friction, high
temperature resistant, oil seal is circumferentially fitted over the grove in the rim of the valve face plate to
minimise the escape of flow gases from the feedback pipe into the jacket. Similarly the gases from inlet
pipe shall be prevented from leaking inside the jacket with the help of seals.
Fig. 10 Contact between valve and jacket Fig.11 Transient feedback pressure curve
iii) Transient analysis
The designed assembly is finally subjected to time dependant finite element analysis to check the desired
valve travel in the given time and to obtain the stress distribution in the components. Axial feedback
pressure time curve acting over the face plate is shown in Fig. 11. On the other hand, the bending load on
the restrictor plate also varies with time as more and more area of the plate is exposed to flow pressure in
the inlet pipe with upward movement of the valve. Increase in restrictor plate area that is exposed to inlet
flow with time is computed in the software. The mesh model of the assembly is shown in Fig. 12.
SOLID186 element is used for meshing. The number of nodes and elements are 156095 and 37948
respectively. No separation contact is used between valve and jacket. Springs are replaced by solid
cylinders. Since variation of inlet pipe pressure vs time is not available, the pressure is assumed to be
constant at 0.32 MPa. The feedback pressure time curve is divided into 45 load steps. At each load step
and time, the valve system experiences different loads over the face and the restrictor plates.
4. RESULTS
Fig.12 Mesh model t =10s t = 20s t = 30s t = 45s
Fig.13 Valve displacement vs. time
t =10s t = 20s t = 30s t = 45s
Fig.14 Equivalent stress plots in assembly at different instants of valve travel
Fig.15 Valve displacement vs time Fig.16 Valve stress vs time
Transient simulations shown in Fig.13 confirm the valve travel of 42mm in 45s. Maximum stress of
50.514 MPa develops in the restrictor plate of the valve at its topmost position (45s), which is safe.
Variations of valve displacement and stress in valve with time are presented in Fig.15 and Fig.16
respectively. Stress values in springs, pipes and jacket body are also well within the limits.
4. CONCLUSIONS
The valve configuration is finalised with the help of Design by Analysis approach such that the valve
travels by the desired distance in stipulated time and the stress values developing in it under axial and
bending flow loads are well within the limits. Spring stiffness and dimensions of other assembly
components are also established to support the valve operation ii) Frictional effects produced during
sliding motion of the valve against the inner surface of the jacket are neglected in the analysis. Inclusion of
such effects shall reduce the valve velocity or increase the time of travel of the valve. These parameters
shall be checked during experimentation. Springs of lower stiffness may have to be used to obtain the
desired valve velocity iii) Thermal effects have been ignored in the stress analysis. The results shall
improve by undertaking thermo-mechanical analysis.
REFERENCES
1. R.S.Khurmi and J.K.Gupta, “A text Book of Machine Design” Eurasia Publishing House
Ltd. Delhi, pp.821-827, (2003)
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID – ICAME2013 S2/O6
PREDICTION OF PRESSURE DROP COEFFICIENTS AND HEAT TRANSFER
COEFFICIENTS OF TURBULIZER BY CFD ANALYSIS
ABSTRACT
Turbulizers are widely used in compact heat exchangers for enhancement of heat transfer rate, but at the
same time they also cause an additional pressure drop in the heat exchanger passage. The shape of
turbulizer needs to be optimized for obtaining higher heat transfer and lower pressure drop in heat
exchanger flow passage. The current work focuses on developing a methodology to conduct test, analyze
the turbulizers using CFD methodologies to obtain the porous as well as the heat transfer co-efficients.
With the developed method results are validated with test data. The simulation results suggest that this
methodology can be used for design and optimization the turbulizer flow and heat transfer characteristics.
Keywords: turbulizer, heat transfer coefficient, porous media, CFD, heat exchanger.
1.INTRODUCTION
The plate heat exchanger is an essential component of modern industries. It has various applications such
as engine oil coolers, transmission oil coolers, exhaust coolers etc. The turbulizer is used in coolers for
enhancing the heat transfer rate. The turbulizers are brazed with the cooler plates. Figure (A) shows
schematic arrangement of the turbulizer inside a cooler. The turbulizers are of different types and in this
work wavy offset fin as shown in Fig. (B) is considered for study.
Modeling the turbulizer is the most challenging part while performing CFD analysis on any cooler mainly
because of the small size and complex shape of turbulizer. Also, the brazing process during assembly of
turbulizer adds some change to its shape which cannot be captured and another reason is the uncertainty of
actual flow inside the domain i.e. the phase (laminar, transitional or turbulent) cannot be predicted. The
solution is to model the turbulizer as porous media for which the porous coefficients are obtained by
laboratory tests. This work aims in developing a methodology to calculate the porous media coefficients
and heat transfer coefficients of turbulizer using CFD methods along the high pressure direction of
turbulizer.
2.METHEDOLOGY
Two types of analyses are carried out at various mass flow rates, firstly flow analysis to determine the
Darcy friction factor, compare it with the friction factors available from test and then calculate the porous
coefficients. Then carry out heat transfer analysis to calculate the average heat transfer coefficients and the
Nusselts number. For testing two types of fluids are used, namely Paratherm OR™ and Paratherm LR™.
These are standard test fluids used for all laboratory tests on heat exchangers because they cover the entire
range of fluids practically used in coolers. OR and LR have properties similar to that of oil and coolant
respectively. Initially simulations are carried out using OR and LR fluid properties for four different flow
rates with both laminar and turbulent models, and then results are studied for selection of suitable flow
model for the respective fluids.
3.DATA REDUCTION
Flow analysis is carried out on domain at different flow rates to obtain the pressure drop, then Darcy
friction factor is calculated using Eq. (1) at each flow rate (Frank M. white, 4th edition). A graph is plotted
for Darcy friction factor at different Re values and compared with the test data. Then the porous
coefficients are calculated.
flv 2
dP (1)
2 Dh g
The generalized porous coefficients Ri(inertial) and Rv (viscous), as shown in Eq. (2), are independent of
fluid properties. In this work initially the porous coefficients dependent on fluid properties ie, Pi and Pv are
obtained as in Eq. (3), then Ri and Rv are calculated. (J. Geertsma and Koninklijke, 1974)
dP 1 2 (2)
R i v R V v
l 2
This is rearranged to obtain fluid dependent viscous and inertial coefficients as,
dP
i P v2 P v
(3)
V
l
Where,
Pi Inertial resistance
Pv Viscous resistance
The average heat transfer coefficient at different Re values is calculated using the LMTD approach
(Donald A.Nield and Adrain Bejan, 2006) shown in Eq. (4). It is assumed that the overall turbulizer
temperature and fluid inlet temperature remains constant for both OR and LR fluids.
havg As ( LMTD ) m c p T (4)
Where,
T Tinlet Tout
T T
LMTD A B
T
ln A
TB
TA Tinlet Twall
TB Toutlet Twall
Then the Nusselts number value is calculated using Eq. (5) (Ali Hashmi et al., 2012),
hl
Nu
(5)
k
The heat transfer coefficients calculated from simulation results are compared with the heat transfer
coefficients calculated from test data. The test data is obtained by measuring temperatures at a various
points in a single plate of cooler tested alone and then generating a modified Wilsons plot (John W. Rose,
2004; Jose´ Ferna´ndez et al., 2007), test data in Fig. (H) & (I).
4.COMPUTATIONAL MODEL
The flow and heat transfer analyses is carried out using StarCCM+ in which periodic boundary condition
is used, this reduces the size of turbulizer domain and aids in obtaining solution faster.
Geometry
The geometry of the turbulizer is shown in Fig. (B). Due to the small size and complex shape of the
turbulizer, it would require a very fine mesh size to resolve flow in the fluid domain which may result in
impractical cell count in the fluid domain. Therefore, only a single channel of turbulizer is considered with
five full convolutions of the turbulizer as shown in Fig. (C). The inlet and outlet were extended in order to
reduce the entry effects and flow reversals at the outlet.
Grid Independence Study
The selection of optimum mesh size is very critical for any CFD simulation, as selection of a coarser mesh
size may result in an inaccurate solution and refining the mesh size too much makes the analysis compute
intensive. Therefore four different mesh sizes were analyzed, shown Fig. (D) and it was found that the
solution with basic mesh size, smaller that 0.035 mm, did not bring about any considerable change in the
results. Therefore mesh size of 0.035 mm was considered for further analysis.
Model Setup and Analysis
The sides of the turbulizer where modeled as periodic boundaries, inlet as mass flow inlet and outlet as
pressure outlet. The extended inlet and outlet were applied with slip wall condition so as to avoid frictional
losses in them. Segregated flow model was used for flow analysis and segregated fluid temperature model
was used for the heat transfer analysis. Flow analysis was carried out considering the flow to be both
laminar and turbulent. The turbulence model used is k-ε model with all walls standard y+ treatment. The
flow pattern at various sections and the pressure drop is monitored to predict convergence of the solution.
The results of the analysis are validated by comparing the Darcy friction factor calculated from analysis
results to the actual friction factors of the turbulizer which were calculated theoretically from pressure
drop values at different flow rates.(Frank M. white, 4th edition).
The results of initial laminar and turbulent flow simulations on the turbulizer domain, show that for the OR
fluid solution converges with both laminar and turbulent models, but convergence is much slower with
turbulent model, thus it can be assumed that fluid is some where between laminar and transitional phase,
shown in Table 1. Also from data in Table 2 it can be concluded that for LR fluid, solution converges only
when the turbulent fluid model is used. This gives an idea that though the Reynolds number (calculated
using the hydraulic diameter of single turb channel) values are less than one thousand, fluid flow exhibits
turbulent nature.
Table 1.Convergence with OR fluid properties. Table 2. Convergence with LR fluid properties
The Darcy friction factor is a property of the domain which is dependent on geometry features as seen
from Eq. (1) and independent of fluid properties. Ideally it should remain flat for entire range of Reynolds
number for both OR and LR. The results in Fig. (E) show a similar trend. The results overlap with the test
data as well. This confirms that the methodology adopted can accurately predict the pressure drop in
turbulizer. Figure (F) & (G) shows the calculation of porous coefficients by fitting a polynomial curve to
the pressure drop per unit length curve for OR and LR respectively. This graph shows an increase in
pressure drop with increase in velocity as expected theoretically. Equations (6) & (7) are obtained from
polynomial curve fit on data in Fig. (F) & (G) .Comparing Eq. (6) & (7) with Eq. (3), Pi and Pv values are
obtained for OR and LR respectively.
y 3E 6 x 2 75 E 3x (6)
y 2.1E 6 x 2 9.8 E 3x (7)
Table (3).Calculated values of porous coefficients.
Then Ri and Rv are calculated using Eq. (2), since these are coefficients independent of fluid properties
therefore they should remain same for any kind of fluid flowing through the domain. Table 3 shows the
calculated values for porous coefficients. The results show that Ri values for both OR and LR are in the
same range where as Rv values are slightly different. This slight variation in Rv can be neglected since Ri is
the most sensitive towards pressure drop results.
The heat transfer analysis of OR fluid shows a good match with test data for higher Reynolds number
values but it over predicts the value of Nusselts number at lower Reynolds number values, shown in Fig.
(H). Analysis of LR fluids shows that for all ranges of Reynolds number values, the results match with the
test data in Fig (I). It is also observed that for both the cases the Nusselts number value increases with
increase in Reynolds number, which clearly suggests that at higher Reynolds number values, with increase
in turbulence in the fluid, the heat transfer coefficient also increases considerably and as value of Reynolds
number increases the slope of the curve also increases. The over prediction of Nusselts number at lower
Reynolds number for OR needs to be examined in detail.
Using this methodology analysis is again carried out on a different turbulizer and the Darcy friction factor
were calculated as shown in Fig. (J), here it was observed that for Reynolds number values above 50 the
Darcy friction remains constant. This again confirms that the above methodology can accurately predict
the flow and heat transfer characteristics for Reynolds number values above 50(Frank M. white, 4th
edition).
6.CONCLUSIONS
From the initial analysis it can be concluded that for OR range of fluids laminar models shall be used for
better results and faster convergence and incase of LR range of fluids turbulent models are to be used.
Also the good agreement of the calculated Darcy friction factor with the ones obtained from tests confirms
that the methodology adopted can be implemented for obtaining the porous coefficients. This method can
be used in both high pressure and low pressure directions of turbulizer, eliminating the need for laboratory
testing to obtain porous coefficients. Further for the heat transfer coefficients though the results show
good agreement with test data at higher Reynolds number values, the deviation of analysis results from test
data at lower Reynolds number needs to be inspected thoroughly and adds to the further scope of this
work.
7.ACKNOWLEDGMENTS
Authors would like to acknowledge Amit Kumar Gupta and team from DITC for their valuable support
and co-operation extended during the entire course of this work.
NOMENCLATURE
As total surface area of the turbulizer channel (top and bottom)
cp specific heat at constant pressure (coolant/oil)
Dh hydraulic diameter
dP pressure drop across inlet and outlet of turbulizer
f Darcy friction factor
g acceleration due to gravity
havg average heat transfer coefficient
k thermal conductivity of fluid
l length of turbulizer channel
LMTD log mean temperature difference
LR Paratherm LR™, standard test fluid with properties similar to coolants
m˙ mass flow rate of coolant/oil
Nu Nusselts number
OR Paratherm OR™, standard test fluid with properties similar to oils
Ρ density of fluid
Re Reynolds number
Tinlet temperature of coolant or oil at inlet
Toutlet temperature of coolant or oil at outlet
μ dynamic viscosity
v velocity
Enumerations
Fig. (B) CAD Fig. (C) flow domain with 5
model of turbulizer convolutions
Fig. (A) Detailed assembly of a plate heat
exchanger. (Courtesy DANA Holding Corp.)
Fig (D). pressure drop at various mesh size
Fig (E). Darcy friction factor Vs Re for both OR Fig (F). Curve fit for obtaining Pi and Pv form
and LR combined for both test and CFD. pressure drop length Vs. velocity for OR
Fig (G).Curve fit for obtaining Pi and Pv form Fig (H). Nusselts number at different flow rates
pressure drop length Vs. velocity for LR. from test and CFD for OR fluid.
Fig (I). Nusselts number at different flow rates from Fig (J). CFD analysis result for another turbulizer
test and CFD for LR fluid. (only oil).
REFERENCES
1. Ali Hashmi,Fraaz Tahir, Umair Hameed “Empirical Nusselts Number Correlation for Single
Phase Flow through a Plate Heat Exchanger”, Recent Advances in Fluid Mechanics, Heat &
Mass Transfer and Biology, ISBN: 978-1-61804-065-7 (2012).
2. Donald A.Nield and Adrain Bejan, “Convection in Porous Media”, Springer Publishing co., pp
4-9 (2006).
3. Frank. M. White, “Fluid Mechanics”, 4th Edition, McGraw Hill Publishers, pp 338-340, 357-
362.
4. John W. Rose, “Heat-transfer coefficients, Wilson plots and accuracy of thermal
measurements”, Experimental Thermal and Fluid Science Journal, 28 (2004).
5. Jose´ Ferna´ndez-Seara, Francisco J. Uhı´a, Jaime Sieres, Antonio Campo “A general review of
theWilson plot method and its modifications to determine convection coefficients in heat
exchange devices”, Applied Thermal Engineering Journal, 27 (2007).
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID : ICAME2013 S2/O8
ABSTRACT
Large number of efforts have been made in past to analyses the vibration spectrum obtained from
marine gearbox to identify defects at incipient stage. This was to avoid long layoff of the ship / machinery
due to intricacies involved in gearbox repairs, shipping-unshipping route etc. Efforts were also made to
develop finite element model of gearbox and analyse vibration signatures. Mostly all efforts involved use
of some other dynamic simulation technique to cater for non-linearity.
In the present work, efforts were made to simulate the gearbox with and without defect using finite
element analysis. A model of simple spur gear box was modeled in solid works and imported to ANSYS
environment for analysis. Mid surface criterion was used to contain no. of nodes and thereby calculation
time. A transient analysis was undertaken considering non-linear phenomena associated with the gearbox
operation. Acceleration was measured along Z axis on a node near input shaft bearing. Vibration
signatures obtained from finite element analysis was compared with the signatures obtained from the
gearbox experimentally.
Keywords : Finite Element Analysis (FEA), Gearbox Signature, Vibration Spectrum
1.INTRODUCTION
Fault diagnosis of gearbox is highly complex phenomena. Most modern techniques for gear diagnostics
are based on the analysis of vibration signals picked up from the gearbox casing. The common target is to
the detect presence and type of fault at an early stage of development and to monitor its evolution, in order
to estimate the machine’s residual life and choose an adequate plan of maintenance. The simple spectral
analysis is generally unable to detect gear failures at an early stage; for this reason, many researchers have
proposed the application of other vibration analysis techniques for the early detection of fault / symptoms
[1,2]. This paper attempts to bring a practical solution to identify the gearbox faults at an incipient stage.
During literature survey, it has been observed that similar efforts made in the past, used dynamic
environment softwares like simulink [3] to cater for non-linearity associated with meshing of gears.
Further, most studies are related to contact stress analysis of gears in mesh [4], modal analysis of gearbox
casing [5], vibration analysis of single stage reduction gearbox with 1:1 gear ration [3,6].
In the present work, FE model is used to obtain simulated vibration signatures. These signatures are
compared with experimental signatures acquired from a Gearbox Dynamic Simulator. The equipment is
capable of generating various types of defective gear signatures including for spur and helical gears. Real
time vibration signatures of good and defective gears could be acquired with the help of accelerometers
using Data Acquisition System (DAS).
2.EXPERIMENTAL SETUP
Experimental set up comprises of a variable speed AC motor, driving a two stage reduction gear box. The
gearbox consists of three shafts (input, intermediate and output), each shaft is rested on two single row,
deep groove ball bearings. Gear with 32 in no. teeth is fitted on input shaft on drive end. This gear is
meshed with 80 teeth gear. Two gears, 80 teeth and 48 teeth, are fitted on intermediate shaft. The 48 tooth
gear is meshed with 64 teeth gear which is fitted on out shaft, at driven end. The Gear under analysis (32
teeth gear) is fitted on input shaft at drive end side for ease of replacement. The load on the system can be
adjusted by electronically controlled magnetic brake. The types of faults include chipped gear, missing
gear and surface wear gear. Figure 1 illustrates various components of experimental setup.
Fig 1: Experimental setup
2.DEVELOPMENT OF MODEL
2.1Geometry and Configuration of gearbox
The Physical model was developed using Solid Works software. A method of assembly by part was used
to develop model of actual Gear Box. In this method, various parts viz gears, gear box body, shafts,
bearing, bearing covers etc were modelled in part file separately and subsequently assembled in assembly
file. No. of mates for example gear mates between two meshing gears were used to enable proper transfer
of motion between gears based on gear ratio. Parallel mates were used between the shafts to keep them at
centre distance of gears. The solid model of the gearbox is shown in figure 2.
Fig 2 Gear box model developed in Solid Works
2.2 FEM Model
Carmignani et al [3], developed a FE model of gear box having two gear of same diameter. The same
concept was used in the present work. Spur gears were modelled with shell elements of constant thickness
as disks with diameter equal to gear base diameter. The casing was modelled with shell elements having
six holes for fitment of bearings. The shafts were modelled with pipe elements capable of transmitting
both bending and torsion loads.
The bearing effects were modelled by connecting the shafts and the gear box with links. Such elements are
able to transmit flexural loads to the housing by means of their connectivity. The contacts between the
gears were modelled by a spring element connecting the gears along the line of action.
All the material properties were not available with supplier of experimental model, materials were
therefore assumed for shafts and gearbox casing. Post assigning the materials, a mid surface criterion was
used to decrease of no. of nodes and their by calculation time. Visual representation of gearbox in
workbench and class is as shown in figure 3.
Fig 3 Gearbox developed workbench and Classic
3.RESULTS AND DISCUSSIONS
3.1Experimental Results
Gear vibration signatures were acquired at different loads viz 0%, 50% and 75% using all types of gears
(good and defective)). The vibrations were recorded at set rpm of 1200 corresponding to 20 Hz frequency.
Time domain signature for duration of 5 sec with sampling frequency of 51.2 Ks/s was collected through
the accelerometer and Oros-data acquisition module. It was observed that although the set frequency was
20 Hz (1200 rpm) at 0% loading condition, the actual frequency was 19.88 Hz (1187 rpm). The same
could be due to gearing load.
Initially, it was decided to model good gear and one defective gear (missing tooth) in order to contain the
modeling efforts and FEM analysis. The screen shots of the Time and frequency domain vibration
signatures recorded are as appended below in figures 4 and 5.
Fig 4: Frequency Domain Signatures for Good Gear
Fig 5: Frequency Domain Signatures for Missing Tooth Gear
3.2 Simulation Results
Various values of meshing stiffness, bearing spring constant, moments etc used are as mentioned in table 1
below. Meshing stiffness was calculated based previous work by Kiekbuschand Howard [4]. Bearing
spring constant was assumed as details were not available. The brake torque was calculated based on the
graph provided by manufacturer of the experimental setup and given in table 1.
Table 1 Values of various constants used for Calculation
Sl. Quantity Test Trial Conditions Remarks
No. Conditions
1 Shaft RPM 1200 1200 -
2 Mesh Stiffness 1 28414 N/mm 14207 N/mm Calculated
3 Mesh Stiffness 2 194311 N/mm 97155 N/mm Calculated
4 Bearing Spring Constant 35030N/mm 70000 N/mm Assumed
5 Brake Torque 18000 Nmm 18000 Nmm Calculated
Simulation trials were carried out for 0.2 sec due to limitation of computer system. No. of solutions were
carried out with change in meshing stiffness, bearing spring constant values etc. Details of trial conditions
are as shown in table 1. Various graphs obtained from the FE model in frequency domain are as shown in
figures 6 to 8. These graphs are generated in MATLAB using a small program generated for conversion of
time domain data obtained from simulation model to frequency domain.
Fig 6: Accn vs Frequency graph at Test Conditions
Fig 7
n
Acc vs. Frequency graph for Bearing Spring Constant at Trial Condition and remaining parameters at Test
Conditions
Fig 7 Accn vs. Frequency graph for Meshing Stiffness at Trial Conditions and remaining parameters at
Test Conditions
In the frequency domain graphs obtained from experimental results, a peak is observed at 640 Hz
frequency with side bands spaced at 20Hz on lower and upper sides. This is the gear mesh frequency
(rotation frequency (20) x no. of teeth (32)). In case of defective gear (missing tooth), along with gear
mesh frequency (640 Hz), it’s harmonics are also observed to be excited at higher amplitude of
acceleration of 1280 Hz and 1920 Hz with side bands.
Graphs obtained from the simulation result have shown peaks at 636Hz with unevenly spaced side bands.
Further, More peaks are observed at frequencies viz 511Hz, 536Hz. The peak observed at 636 Hz for is
associated with the gear mesh frequency. However, remaining peaks could not be compared with available
data. This deviation might be due to no. of assumption made in terms of material properties of gear box
body, bearing spring constant, shaft material etc.
Efforts were made to input the meshing stiffness as variable to cater for non-linearity associated with
meshing stiffness and gear angular position. Various spring elements were tried to enable tabular input for
real constant (k - stiffness) leading to un-converging solutions.
4.CONCLUSION
Comparison of experimental and simulated results has shown equivalence to a certain extent. Solutions in
the present work have been obtained by using constant meshing stiffness. Accordingly, the model
developed here doesn’t consider the non-linearity related to meshing of gears. This could be one of the
reasons for deviation of simulated graphs from experimental. Further, the reasons for divergence can be
attributed to the no. of assumptions made regarding material properties and spring constants of bearing.
The results would have been more comparable with consideration of non-linear effect related to meshing
stiffness. The basic theory envisaged in the present research concerning application of finite element
analysis techniques for development of actual model of gear box and obtaining vibration spectrum for
analysis has been achieved to large extent.
REFERENCES
1. Lt Cdr V Sharma. ‘Pattern Recognition Architecture for Warship Propulsion Transmission Fault
Identification ’. M Tech Dissertation topic, 2011-12. DIAT(DU), Pune-25
2. Lt P. Suresh ‘Gearbox Fault Diagnosis using Vibration Analysis’. M Tech Dissertation topic
Dissertation topic, 1997. DIAT(DU), Pune-25
3. C Carmignani, P Forte and G Melani ‘Component modal synthesis modelling of a gearbox for
vibration monitoring simulation’. Sixth International Conference on Condition Monitoring and
Machinery Failure Prevention Technologies. 23-25 June 2009, Dublin, Ireland
4. Kiekbuschand Howard ‘A Common Formula For The Combined Torsional Mesh Stiffness Of Spur
Gears’. 5th Australasian Congress on Applied Mechanics, ACAM 2007 10-12 December 2007,
Brisbane, Australia.
5. M. Sofian D. Hazry K. Saifullah M. Tasyrif K.Salleh and I.Ishak ‘A study of Vibration Analysis
for Gearbox Casing Using Finite Element Analysis’. Proceedings of International Conference on
Applications and Design in Mechanical Engineering, 11-13 Oct 2009, Batu Ferringhi, Penang,
Malaysia.
6. L Deshpande, N Sawalhi and RB Randall ‘ Gearbox bearing fault simulation using a finite element
model reduction technique.’ 25th International Congress on Condition Monitoring and Diagnostic
Engineering. 18-20 Jun 2012, University of Huddersfield, UK
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID – ICAME2013 S2/09
USING FEATURES FOR GENERATION OF MIDSURFACE
ABSTRACT
Data provided by CAD (Computer Aided Design) models is often not suitable for CAE (Computer
Aided Engineering) operations like meshing. Some geometric-topological features are irrelevant and
suppression of them does not harm accuracy of the analysis-result to a large extent, but in turn provides
significant leverage in terms of processing time-space. Thus CAD models are often simplified-abstracted-
idealized to suit needs of CAE analysis. One of the prominent simplification techniques is called
Midsurface which is highly suitable for thin walled parts prevalent in plastics and sheet metal domain.
Thin portions of the model are idealized to surface along with thickness data later to be used for modeling
Shell elements. Midsurfacing techniques have been researched for past few decades. Many commercial
CAD-CAE applications have midsurfacing capability. Apart from CAE, midsurface has found applications
in Visualization, Animation, Feature Recognition etc. as well.
This paper proposes a framework for generating connected-midsurface in the feature-based modeling
environment. The proposed framework will be based on non-manifold topology and will cater to features
prominent in thin wall parts typically used in Sheet Metal CAD applications.
1.INTRODUCTION
Midsurface is an abstraction for thin-walled portions. Shell elements, based on midsurface, will give
sufficiently close analysis results compared to that of 3D Solid elements. ’Thin Wall’ is an inherent
characteristic of the Sheet Metal parts and thus this work will cater to features prominent in Sheet Metal
CAD applications. Midsurface can be used in thin portions of usual/mixed-dimensional/thick-thin parts
also, but there, one needs to work out treatment of interfaces/joints/couplings which is considered out-of-
scope for the current research. Midsurface is expected to have proper connectivity (no gaps) and it should
follow shape of the base part. As midsurface is generated Face-Pair wise, it needs to be stitched together to
form a continuous shape. In midsurfacing techniques, there are two broad categories namely ’Medial Axis
Transform (MAT)’ and ’Midsurface Abstraction (MA)’.
MAT is locus of the center of an inscribed disc of maximal diameter as it rolls around the object interior.
The associated radius function gives radius of the inscribed circle at every point on the skeleton, and
makes the original 2D object recoverable from the medial axis. In 2D it’s called Medial Axis Curve
(Figure 1) whereas in 3D it is called Medial Surface. Major drawback of this method is that it creates
unnecessary branches and its shape is smaller than the original corresponding faces. Plus there is major
issue of perturbations, meaning slight change in the base geometry forces re-computation of MAT and the
result could very well be different than the original.
Instead of basing the construction on the
information contained in the feature
model, the geometry as a whole is
analyzed and then a global abstracted
shape is derived, commonly based on the
medial surface, medial axis, or a similar
skeletal structure. In this process,
however, the connection of the analysis
geometry with the features, the
corresponding semantics, and the
Figure 1: Midsurface Extraction methods constraints that define the design model,
is lost [2].
Both the above mentioned techniques are based on extraction where algorithm is applied on the final
share. Many a times, due to complexity in recognizing forms, and due to complex interactions between
them, midsurface of the part does not follow its form and is not fully connected [3, 4]. Solution could be,
to create midsurface while building the model itself.
In Features-based Solid Modeling, input feature-parameters are used to build tool-bodies and the whole
part gets built using direct or indirect boolean of base and tool bodies. Creating midsurface for individual
tool bodies appears to be a more deterministic problem than recognizing the feature forms. With well-
defined boolean operations, correct midsurface connectivity can be ensured. To the best of author’s
knowledge and during the literature review done so far, such system was not found either in the academic
research or in the commercial applications.
2.LITERATURE REVIEW
Good amount of research has been done in both approaches MAT and MA, but for different application
domains. Midsurface is commercially available in many CAD/CAE packages. What’s lacking in them is
the usage of feature information. Various reasons for not using the feature-information are access-
restrictions to the proprietary feature information, unsuitable non-manifold structure, as well as
impracticality to include CAE structures in CAD software. There has been some work using M-Rep
(Medial Representation similar to B-rep) which uses Medial entities as data model. But it has very basic
data model and is mainly for medical visualization and not in the domain of Feature-based Modelers [5].
Another related effort generates mid-curves in sketch and then sweeps to form midsurface [1]. This work
is in Mix-Dimensional modeling, limited to sweep and does not seem to do feature interactions.
Lee et al. suggested a conversion method from a sheet model to a solid model for the efficient solid
modeling of thin-walled plastic or sheet metal parts. This method shows a great potential for degenerate
solids in the representation of thin-walled parts. However, because this method adopts non-manifold
boundary representation, it is difficult to represent the exact adjacency relations between topological
entities in a sheet model and to describe a mixture of wire and sheet objects that appear in the intermediate
steps of sheet modeling operations. In order to overcome these problems, Lee et al. [6] introduced a non-
manifold boundary representation as a topological framework and proposed a sheet thickening algorithm
by presenting variations to a general non-manifold offset algorithm that is based on the mathematical
definition of offsets. In addition, to facilitate sheet-modeling operations, they provided a set of generalized
Euler operators for non-manifold models as well as sheet modeling capabilities including adding, bending,
and punching functions with two dimensional curve editors. However, in these algorithms, all of the holes
that lay on thickness faces cannot be removed automatically and topological irregularity of an offset face
caused by self-intersection is not yet considered [6].
Thus research so far does not deal with the major problems of midsurface, that of connectivity and
simplification. Gaps and extraneous features in midsurface render it useless for meshing operation.
Proposed research is planning for improved and robust generation and connectivity of midsurface [4].
3.PROPOSAL
In the proposed approach, midsurface is generated at each feature operation level which has known face
pairs, known boolean operands, so it’s more deterministic to compute extension and then trim individual
Midsurface patches.
Figure 2: Feature-wise Midsurface
At each feature step, shapes are relatively simple than final shape, thus creation of mid-surfaces at each
stage is far simpler (Figure 2). After development of boolean of the non-manifold shapes this method can
build well connected, isomorphic mid-surfaces better than the extraction way. Making midsurface as the
core data model will significantly improve connectivity and ensure more accurate analysis result. The
main crux is that understanding of the sub-shapes/face-pairs and their interactions is far more in-
deterministic problem in case of final-body/shape’. Even in simple shapes like ’T’, ’K’ one needs to
formulate rules for grouping face-pairs so that common connection/junction gets created. In a more
complex part, situation becomes more difficult whereas if you start creating midsurface as part is being
built, at-least one operand in the boolean, called tool body, typically can be deterministic (not simpler).
There as the interaction and the boolean type, is known they can be leveraged to arrive at well-connected
midsurface. Also, procedure of creating midsurface in existing MA approach and in the newly proposed
approach would be different. In case of, say, simple plate, in the existing approach it would guess face
pairs, get their surface geometry /sample points and create/fit average/offset surface between the paired
faces. In the newly proposed approach, this would correspond to an Extrude feature. It would have, say,
elongated rectangle as a sketch-profile which then gets extruded by some distance in the normal direction.
Here the mid-curve (a line) corresponding to the midsurface is created in the sketch profile itself. This
mid-curve will get extruded similarly as that of parent/original profile thus mimicking shape well. This
tool body when will get boolean-ed to the base part, it will know the boolean type and the interaction, thus
it would do the boolean of midsurface-patches as well. A non-manifold (surface/sheet) modeler will be
proposed for the thin wall modeling in which the data-model will have all the information related to the
midsurface. The devised data model will be able to switch itself to the corresponding solid model for the
purpose of visualization.
4.CONCLUSION
This paper proposes a new approach of building midsurface using feature information. In this approach
midsurface is concurrently built as part gets created (called forward create). Or this approach can also
work on feature based model which can be played back. At each feature step, shapes are relatively simple
than final shape, thus creation of mid-surfaces at each stage is far simpler. After development of boolean
of the non-manifold shapes, this method can build well connected, isomorphic mid-surfaces better than
extraction.
REFERENCES
1. T T Robinson, C G Armstrong, G McSparron, A Quenardel, H Ou, and R M McKeag, “Automated
mixed dimensional modeling for the finite element analysis of swept and revolved cad features,” in
SPM ’06: Proceedings of the 2006 ACM symposium on Solid and physical modeling, New York,
USA, 2006, pp. 117–128, ACM.
2. M. Sypkens Smit, Efficient remeshing and analysis views for integration of design and analysis,
Ph.D.thesis, TU Delft, 2011.Dong-Pyoung Sheen; Tae geun Son; Dae-Kwang Myung; Cheolho
Ryu; Sang Hun Lee; Kunwoo Lee;
3. Tae Jung Yeo, “Solid deflation approach to transform solid into mid-surface,” Proceedings of the
TMCE,2008.
4. Andrew Lewis Thall, Deformable solid modeling via medial sampling and displacement
subdivision,Ph.D. thesis, 2004, Director-Pizer, Stephen M.
5. Lee S. H.; Kim H. S., “Sheet modeling and thickening operations based on nonmanifold boundary
representations,” Proceedings of DETC01, ASME2001 Design Engineering Technical
Conferences, 2001.
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S2/P3
Steady State Thermal and Static Structural Analysis of Piston Valve Body
G.M.Chendke Prof.M.M.Mirza, Prof.S.N.Jalwadi
Mechanical Dept., Rajarambapu Institute of Professor, Mechanical Dept., Rajarambapu
Technology, Islampur, Maharashtra, India Institute of Technology, Islampur,
gmchendke@gmail.com Maharashtra, India
1.INTRODUCTION
A 'piston valve' is a device used to control the motion of a fluid along a pipe by means of the linear motion
of a piston within a chamber or cylinder. Piston valve is a zero leak on-off valve. Valve body (Fig.1)
contains the other components which arrest the leak. Valve body is the castcomponent (Cast Steel) which
is machined to achieve machined dimensions & surface finishfor assembly and proper function.
Fig.1 Valve Body (Isometric View) Fig.2 Valve Body Boundary
conditions
So it important to check the model for both static structural analysis and steady state thermal analysisto
finalize/modify the design.
2. STATIC STRUCTURAL ANALYSIS
Fig.3ANSYS ‘SOLID 187’ ElementFig.4 Mesh (Element size - 6mm, No. of Elements:523917)
Mesh Sensitivity Analysis is carried out to obtain the optimum element size. The results obtained are given
below which shows 6 mm element size is best, as the results are converging at this element size. The
element size 5mm will not only consume more time for meshing, solving but the results are also same
when element size 6 mm is used.This element size is used for further analysis to obtain the results at
various design conditions and to obtain the maximum possible pressure that can be sustained by the valve
body.
Table 1. Mesh Sensitivity analysis
Fig.5- Maximum Von Mises stress location at 83 Bar g pressureFig.6- Maximum Total deformation
location at 83 Bar g pressure
Fig.8 Procedure for Steady State Thermal and Static Structural Analysis
4.1 Analysis for Maximum Operating Pressure Condition - 41.5 bar g @ 2530 C
First the Steady State thermal analysis of the valve is done at 2530C and the results of the analysis are
carried forward for the Static structural analysis at the 41.5 bar g pressure so as to simulate the real
situation. This is the Maximum Operating Pressure Condition. The same procedure is followed for other
two conditions-
Maximum Operating Temperature 4250 C @ 28.8 bar g
Maximum Allowable Pressure 51 bar g @ 38 0C
5.RESULT
The results of the analysis for the Designed Condition are given in Table2.
Table 2- Result Table (with 6mm element size)
Max. Total Max. Von
Sr. Designed Condition for Factor of Temperature
deformation , Misses stress ,
No. Analysis Safety at outer side
mm Mpa
Maximum Allowable
1. Pressure 0.155 122.07 2.08 37.3230C
51 bar g @ 380C
Maximum Operating
2. Pressure- 1.2657e-7 99.33 2.52 243.220C
41.5 bar g @ 2530C
Maximum Operating
3. Temperature 8.7837e-8 68.94 3.62 407.90C
4250C @ 28.8 bar g
6.CONCLUSION -From above results, it is concluded that
1. The locations for maximum Von Misses Stress and maximum total deformation are same for all
designed conditions.
2. The valve body can sustain all these designed conditions safely as the values of Maximum Von Misses
Stress are much below the yield stress and the total maximum deformation values are also negligible.
3. The location of maximum Von Misses Stress is near to the outlet section and maximum total
deformation occurs near to the base of valve body which is far away from mating flanges. Both these
locations will not arise any functional issue.
4. In further work, the analysis will be done by reducing the minimum thickness of the component.
Fig. 9 - Piston Valve Body with locations of Maximum value of Von Misses Stress and Maximum total
Deformation
ACKNOWLEDGEMENT
I wish to thank Forbes Marshall Pvt. Ltd., Pune for giving me an opportunity to work in this
field. The guidance, cooperation, practical approach & inspiration given by company especially by
Mr.M.M.Pingale (R & D Manager) provided me the much needed impetus to hard work.
REFERENCES
1. ASME SEC.II Part D, 2004 Edition, pp.301
2. Nitin S. Gokhale, Sanjay S. Despande, Dr. Anand N. Thite ,Practical Finite Element Analysis, 1st
Edition, Finite to Infinite, Pune
3. Ansys, Element Reference, Release12.0, April 2009, pp. 1357
4. Ansys, Element Reference, Release12.0, April 2009, pp 649
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID - ICAME2013S2/P7
A REVIEW ON POCKETING TOOLPATH OPTIMIZATION IN CNC MILLING
ABSTRACT
Today's manufacturing industries augment their production lines with modern machining centers
backed by CAM softwares. Several attempts are being made to cut down the programming time for
machining complex geometries. Special programs/softwares have been developed to generate the digital
numerical data and to prepare NC programs by using suitable post-processors for different machines. By
selecting the proportional tools and manufacturing process plan; the tool paths and NC program are
generated.More and more complex mechanical parts that earlier were being cast and
assembled/manufactured by other processes are now beingmachined. Majority of these parts require lots of
pocketing operations and find their applications in die and mold, turbomachinery, aircraft, nuclear, defense
etc. Pocketing operations involve removal of large quantity of material from the metal surface. In today’s
rapid manufacturing concept, application of proper simulation, modeling and optimization strategies in
metal cutting is essential to improve the machining and the overall productivity.This paper presents an
exhaustive review on the work done in this area by researchers worldwide. Pocketing operation has been
specifically chosen for toolpath optimization. Amongst many methods of toolpath generation, there are
two strategies for toolpath optimization. The first strategy communicates with MasterCAM® software for
reduction in machining time by optimization of tool path using CAD/CAM simulation. The second
strategy requires selection of optimal cutting parameters such as feed rate, depth of cut, cutting speed and
stepover for pocket milling process.
Keywords: toolpath, part program, optimization, pocket
1.INTRODUCTION
In today’s fast growing manufacturing sector, applications of proper simulation, modeling and
optimization strategies in metal cutting is essential to improve the machining and overall productivity. End
milling process is widely used in industry including the aerospace and automotive sectors because of its
versatility and efficiency. Most of the CAD/CAM systems are not able to provide machining time
automatically like MasterCAM® (Jayswaland Taufik, 2011). CAM module makes universal, standard NC
code, which is further translated (post-processed) into a form, which is understood by specific machine
controllers. Each machine controller has specific post-processor, which transforms different code formats
(Krajnik and Kopac, 2004).
The advantages produced by the use of solid modeling instead of surfaces must be considered. Thus, a part
modeled as a solid closes a certain volume, so that the zones in which material may be present can be
easily defined. On the other hand, a first radius can be easily introduced. There are three stages in the
generation of CAM cutting paths, according to the type of operation: (a) roughing, (b) semifinishing and
(c) finishing (Lamikiz et al., 2005).More than 80% of all mechanical parts which are manufactured by
milling machines can be cut by NC pocket machining. This is based on the fact that most mechanical parts
consist of faces parallel or normal to a single plane and that free-form objects are usually produced from a
raw stock by 2.5D roughing and 3D-5D finishing. In order to generate optimum tool paths for pocket
milling, cutting forces and radial depth of cut maintained under reference values must be required in the
entire machining area (Hyun, 2007).
The pocketing operation particularly relates to the manufacturing industry. The main objective is to reduce
the toolpath length ultimately to reduce the machining time. It is possible to either decrease the length of
the tool path or increase the instantaneous feedrate of the tool. The tool path presents a set of circle arcs
(continuities) at each corner in tangency located at the radial tool path linking. NC toolpath should be
smooth and steady as possible to guarantee the machining quality and to protect the spindle (Zhenyu et al.,
2009).Today, many approaches that take into account one or several criteria (production cost, production
time, productivity, machining accuracy, etc.) are being developed to optimize certain cutting parameters
(cutting speed, feed rate, depth of cut, etc.)(Bouaziz andZghal, 2008).
2.POCKETING OPERATIONAND TYPES
Definition:
A pocket machining can be defined as any machining which removes all the material located inside a
preset boundary between two horizontal planes (Zhenyu et al., 2009).
Pocket types:
A machining feature of a pocket can be classified by the inclination of its wall to be simple or complex. As
seen in Fig.1(a), the simple pocket has a perpendicular wall to the XY-plane and the island in the pocket is
also perpendicular. The machining area of a simple pocket is removed layer by layer with a constant
cutting depth. The complex pocket (Fig.1(b)) differs from the simple pocket in that it has a slope in the
wall.
After roughing, the machining feature needs semi-finishing because its stair shape causes the irregular
cutting load in finishing (Heo et al., 2011).
(a) Simple Pocket (b) Complex Pocket
Figure1:Two types of pocket shape
Tool Selection:
On a 3-axis CNC machining centre, pocketing operations are typically performed using a flat end-mill, and
finish-machining of sculptured surface cavities is performed using a ball-nose end-mill (Veeramani and
Gau, 1997).
Characteristics for Toolpath:
The time required for machining a desired feature on a computer numerically controlled (CNC) machining
centre depends on a number of factors including the machine characteristics, machining strategy, the
chosen cutting-tool types and sizes, the geometry of the feature and tolerance specifications, and
machining process parameters (Veeramani and Gau, 1997).The cutters are selected according to the part
geometry, the machining method, the number of operations as well as the technological conditions. A
sequence of the optimum tool work takes into account at the same time the minimum number of tool
changing and the minimum cutting time.The important factors in process planning for pocket machining
are: cutting-tool diameter selection, tool-path planning, the distance between tool-paths called the
stepover. Also worth noting is machining time calculation, as well as other things such as: spindle speed
and feed rate. From the above factors, cutting-tool diameter is the most important factor because the other
factors depend on it (Soepardiet al., 2010).
3.TOOLPATH GENERATION METHODS
Ideally, toolpath should be formed by connecting the cutter trajectories continuously without non-cutting
moves. However, this is often impossible for the cases with complex part geometry or islands. Hence, it is
necessary to plan the toolpath. There are two toolpath that satisfying minimum machining time (Tawfik et
al., 2006).
Although there are many possible ways of planning a tool path in pocket-milling operation, direction
parallel (or zig-zag or staircase) and contour parallel (spiral) milling, have been the two standard
procedures practiced(Selvaraj and Radhakrishnan, 2006). The contour-parallel toolpath comprises of a
series of contours that are parallel to the boundary of the 2D cross-section.
Figure 2:Toolpath Generation Methods: (a) Direction - parallel and (b) Contour – parallel
(a) normal zigzag (b) smooth zigzag (c) normal spiral(d) smooth spiral (e) fishtail spiral
Figure 3: Toolpath patterns
Whereas, direction-parallel path is the path segments correspond to back and forth motion in a fixed
direction within the boundary of the 2D cross-section (Tawfik et al., 2006). Fig. 2(a) illustrates direction
parallel (zig-zag) method and Fig. 2(b) explains that of contour parallel milling method. The further
classified toolpath patterns are shown in Fig. 3. They are normal zigzag, smooth zigzag, normal spiral,
smooth spiral and fishtail spiral(Tawfik et al., 2006).
3.OPTIMIZATION TECHNIQUES
1) Automatic Tool-Change:The mind-set of single tool selection has been reinforced by the fact that
many early generation CNC machines require manual time consuming loading and set-up of cutting-
tool in the spindle. Butwith the availability of automatically tool change mechanism in modern CNC
machining centre called automatic tool-change (ATC) that is capable of rapid turnover cutting-tool,
then the above objectives become irrelevant. In fact, the use of single cutting-tool will result in a
longer processing time and high production cost, especially when the pocket has a narrow bottleneck
areas and a small angle radius of curvature (Soepardi et al., 2010).
2) Feedrate Optimization:Software modules like dynamic feed rate optimization and high speed
machining can shorten the NC program and reduce machining time. Dynamic feed rate optimization
module (Fig. 4(a)) enables the feed decrease as the tool cuts more material and increases as the tool
cuts less material.This helps keep a constant chip load on the cutter for longer tool life and more
efficient cutting. Similar to federate optimization is smart cornering (Fig. 4(b)), which adjusts the feed
rate around corners and small radii for smooth transition in tight areas based on the part and machine
tool characteristics.In order to improve a machining process at low performance machine tools, we
developed an optimization software G-optim. It eliminates the bottleneck of insufficient Look-ahead
function, problem of long cycle time of CNC controller and the problem of weak data connection
between computer and machine tool. The program works as off-line optimizing software which adjusts
the feed rate function to pre-generated standard G-code (Krajnik and Kopac, 2004).
(a) (b)
Figure 4: Feedrate Optimization
Figure 5: Rapid Movement Figure 6: Cusp
3) Rapid Movement:In actual machining, the tool is moving rapidly when there is no feedrate needed
(Fig. 5).
4) Reducing Cusp:Direction parallel tool paths, also commonly referred to as Zig-zag machining, are not
preferred for features with hard boundaries because cusps are left behind along the hard edges during
rough machining (Fig. 6); the removal of these cusps requires an extra pass thus increasing the total
tool path length. They identified a corner uncut area occurring at a sharp corner, a centre uncut area
occurring at the centre of an innermost contour parallel offset curve, and a neck uncut area occurring in
a region where the next level tool paths split.
4.SIMULATION AND EXPERIMENTAL RESULTS
The pocket machining time by using a single cutter, which must be the smallest cutting-tool with diameter
of 2.54cm, amounted to 1201.4 seconds. The pocket machining time using cutting-tool combination (6.35,
2.54), amounted to 715.6 seconds. The time saving is 1201.4 – 715.6 = 485.3 seconds (Table 1)
(Soepardiet al., 2010).
Table 1: Simulation Results of pocket machining
Sr.No. Tool Dia. (cm) Machining Time (seconds)
1 2.54 1201.4
2 (6.35, 2.54) 715.6
Time Saving 485.3
The pocket under study is taken from a plastic injection mould proposed by a collaborating manufacturing
company. In both cases of research of a roughing tool and of an under roughing tool, the optimization
algorithm utilizes the diameter of the tools in the limits of 12mm to 36mm. The simulation results show
that the pocket machining with only one tool C0(Φ 10 mm) requires a cutting time equal to 313.5min.
Whereas, use of two tools (C0, C1) minimize the cutting time to 103.5minutes. Finally, the use of three
tools (C0, C1, C2) greatly minimizes the cutting time to 100.75min (Table 2).Unlike the under roughing
with only one tool (Φ 10 mm) which requires a machining time equal to 72.05min, the use of two tools
(Φ10 and 16 mm) minimizes the machining time to 55.75min(Table 3) (Bouaziz andZghal, 2008).
Table 2: Simulation Results of roughing Table 3: Simulation Results of under
roughing
Sr Tool Dia. Machining Time Sr.No. Tool Dia. Machining Time
No (mm) (minute) (mm) (minute)
1 C0 313.5 1 10 72.05
2 (C0,C1) 210.0 2 (10, 16) 16.3
3 (C0,C1,C2) 109.25 Time Saving 55.75
5.CONCLUSION
It has been observed that the cycle time can be improved by reducing machining time by selection of
proper tool path strategy and modifying some of the design parameters of cyclic time such as spindle
speed, feed rate, depth of cut and stepover. There have been use multiple tools for optimization of
toolpath. The larger diameter tool is used to save time for rough machining, after that the smaller diameter
tool is used for finishing. Also the tool traverses rapidly when there is no feedrate needed at movement in
air.
REFERENCES
1. Bouaziz Z and Zghal A, “Optimization and selection of cutters for 3D pocket Machining”,
International Journal of Computer Integrated Manufacturing, Vol. 21, No. 1, 73 – 88 (2008)
2. ChungangZhuang, ZhenhuaXiong and Han Ding, “High speed machining tool path generation for
pockets using level sets”, International Journal of Production Research, Vol. 48, No. 19, 5749–
5766 (2010)
3. Eun-Young Heo, DorukMerdol, Yusuf Altintas, “High speed pocketing strategy”, CIRP Journal of
Manufacturing Science and Technology, 3, 1–7 (2010)
4. Eun-Young Heo, Dong-Won Kim, Jong-Young Lee, Cheol-Soo Lee, F. Frank Chen , “High speed
pocket milling planning by feature-based machining area partitioning”, Robotics and Computer-
Integrated Manufacturing, 27, 706–713 (2011)
5. Hyun Chul Kim, “Tool path modification for optimized pocket milling,” International Journal of
Production Research, Vol. 45, No. 24, 5715–5729 (2007)
6. Krajnik P and Kopac J, “Modern machining of die and mold tools”, Journal of Materials
Processing Technology, 157–158, 543–552 (2004)
7. Lamikiz A, López De Lacalle LN, Sánchez JA, Salgado MA, “Cutting force integration at the
CAM stage in the high-speed milling of complex surfaces”, International Journal of Computer
Integrated Manufacturing , Vol. 18, No. 7, 586 – 600 (2005)
8. MoncefHbaieb, RadhouaneOthmani&WassilaBouzid, “Time modeling in high-speed machining of
mold pocket,” Int J AdvManufTechnol, 53, 113 – 120 (2011)
9. Salman M, Mansor A, Hinduja S, Owodunni O, “Voronoi diagram-based tool path compensations
for removing uncut material in 2*1⁄2 D pocket machining,” Computer-Aided Design, 38, 194–
209(2006)
10. S.C. Jayswal and Mohammad Taufik, “Cutting Strategies for Optimization of Tool Path and Cyclic
Time in the CNC End Milling Process”, Int J of Engg. R&T, Vol. 4(5), pp.493-505 (2011)
11. Selvaraj P andRadhakrishnan P, “Algorithm for Pocket Milling using Zig-zag Tool Path”,Defence
Science Journal, Vol. 56, No. 2, pp. 117-127(2006)
12. Soepardi A, Chaeron M, Aini F L, “Optimization Problems Related to Triangular Pocket
Machining”, IEEE (2010)
13. Sotiris L Omirou and Andreas C Nearchou, “An epitrochoidal pocket—A new canned cycle for
CNC milling machines”, Robotics and Computer-Integrated Manufacturing, 25, 73 – 80 (2009)
14. Tawfik T EL-Midany, Ahmed Elkeran, HamdyTawfik, “Toolpath pattern comparison – contour
parallel with direction parallel”, IEEE, (2006)
15. Veeramani D and Gau YS, “Selection of an optimal set of cutting-tools for a general triangular
pocket,” International Journal of Production Research, Vol.35, No.9, 2621-2637, 1997(2010)
16. Vincent Pateloup, Emmanuel Duc, Pascal Ray, “Bspline approximation of circle arc and straight
line for pocket machining,” Computer-Aided Design, 42, 817-827(2010)
98
17. ZHAO Zhenyu, LIU Bai, ZHANG Meng, ZHOU Houming,YUSongsen, “Toolpath Optimization
for high speed milling of pockets”, IEEE, (2009)
99
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S2/P8
Keywords: Drive shaft, Composite Materials, Torsional buckling, Analysis;
1 INTRODUCTION
We can define a composite as 'a multiphase material from a combination of materials, differing in
composition or form, which remain bonded together, but retain their identities and properties, without
going into any chemical reactions.' The components do not dissolve or completely merge. They maintain
an interface between each other and act in concert to provide improved, specific or synergistic
characteristics not obtainable by any of the original components acting singlyconstitute of composite
material:- i)Reinforcement: Reinforcement material which basically gives strength, stiffness and other
mechanical properties to the composite material. It is generally in the form of fibers, whiskers, filaments
and includes 1) Glass fiber, 2) Carbon fiber, 3) Kevlar fiber, 4) Boron filament/ fiber, 5) Asbestos fiber,
etc. On the other hand, fillers are in the form of flakes or fine particlesii) Matrix: Matrix is also known as
binder material. It provides shape to the composite material, Makes the composite material generally
resistant to adverse environments andProtects reinforcement material from adverse environments.The
materials which constitute matrix of composite materials are plastics, metals, ceramics and rubber.
100
Fig 1. Layout of three piece propeller shaft in automobile
The three piece steel drive shaft consists of four universal joints, two center supporting bearing and a
bracket, which increases the total weight of a vehicle and decrease fuel efficiency. In automobile, thumb
rule is that 17-22% of the power generated by the engine is lost to rotating mass of the drive train system
used in automobile. The power is lost because it takes more energy to spin heavier parts. This energy loss
can be reduced by decreasing the amount of rotating mass. Power transmission can be improved through
the reduction of inertial mass and light weight. Substituting composite structures for conventional metallic
structures has many advantages because of higher specific stiffness and higher specific strength of
composite materials. Composite materials can be tailored to efficiently meet the design requirements of
strength, stiffness and composite drive shafts weight less than steel or aluminum
101
i) Torsional analysis ii) Buckling Analysis ii) Model Analysis
A drive shaft has to be design to meet the design requirements for automobiles. Comparative studies of
three different composite materials were conducted to choose the best "suited materials”. Steel was chosen
for reference and the rest of three composites were analyzed at ± 45o ply orientation. The material
properties of all materials considered from design considerations. The numerical analysis carried out by
using commercial software ANSYS 12.0
2. DESIGN OF STEEL & COMPOSITE DRIVE SHAFT DRIVVE SHAFT:-
(1) The shearing stress( τxy ) is defined and given by Equation no. 1
Τxy = = ( ……………….. (equation no.1)
)
Where , J = polarmoment of inertia, T = Applied torque, R = Outer radius, r = Inner radius of the shaft
(2) The critical torsional buckling torque, Tb is given by Equation no. 2
= (2r m2 t)(0.272) (Ex ×E3y)0.25 ( )1.5 ………… (equation no 2)
Where, t = the overall wall thickness, rm = mean radius, Ex,Ey=average in-plane elastic moduli in the
axial and transverse directions respectively.
(3) The drive shaft is idealized as a pinned-pinned beam. The lowest natural frequency is calculated using
the Equation
………………………… (equation no 3)
102
2.2.2 Assumptions
1). The shaft has a uniform, circular cross section 2). The shaft rotates at a constant speed about its
longitudinal axis. 3)The shaft is perfectly balanced, 4). All damping and nonlinear effects are excluded.
5). The stress-strain relationship for composite material is linear & elastic; hence, Hooke’s law is
applicable for composite materials.
2.2.3Selection of Cross-Section
In case of solid drive shaft the stress distribution is zero at the center it varies linearly from center to the
outer fiber of shaft and it becomes maximum at the outer fiber of the shaft in hollow shaft stress variation
is similar it shows that material at the center of solid shaft is not utilised fully hence Here hollow circular
cross-section was chosen because, The hollow circular shafts are stronger in per kg weight than solid
circular.
Table no.2 Material properties calculated from design consideration used for analysis are listed
below
103
3. RESULTS
3.1 FEA Analysis of steel & Composite Drive Shaft
Finite Element Analysis (FEA) is a computer-based numerical technique for calculating the strength and
behavior of engineering structures.
3.1.1. steel result :-
Fig no.2 Total deformation in steel shaft Fig no.3 Shear stress value of steel shaft
3.1.2. Boron /epoxy Result:-
Fig no.4 Total deformation in boron/epoxy shaft Fig no.5 Shear stress value of boron/epoxy shaft
104
Fig
no.5 Total deformation in kelvar/epoxy shaft Fig no.6 Shear stress value of kelvar/epoxy shaft
3.1.4 E-glass/ polyester resign :-
Fig no 7 Total deformation in E-glass/polyester resign shaft Fig no.8 Shear stress value E-glass shaft
fig no:-
9 buckling of steel fig .no . 10 buckling of boron/epoxy
105
Fig11. :- 6th vibration mode shape of steel
4.CONCLUSION
1) The usage of composite material has resulted to inconsiderable amount of weight saving in the range of
75% when compared to conventional steel shaft
2) Taking into considerations the weight saving , Kelvar /Epoxy composite has the most encouraging
properties to act as replacement for steel out of the considered two materials .2) Taking into considerations
the shear stress induced and deformation steel is better than any other composite considered here
3) The presented work was aimed to reduce the fuel consumption of the automobile in the particular or any
machine, which employs drive shafts; in general it is achieved by using light weight composites like
Kelvar /Epoxy
4) The presented work also deals with design optimization i.e converting two piece drive shaft
(conventional steel shaft) in to single piece light weighted composite drive shaft.
REFERENCES
1. Ever J. Barberao,”finite element analysis of composite material”, 1st Indian reprint, 2011
Thesis
2. Gummadi sanjay Akula jagadeesh kumar,” optimum design and analysis of composite driveshaft
for an automobile”, M.S degree thesis ,Dept of Mechanical Engineering Belkinee institute of
Technology KarlsKrona, Sweden 2007
3. M.A.K. Chowdhuri , R.A. Hossain ,” Design Analysis of an Automotive Composite Drive Shaft”
International Journal of Engineering and Technology Vol.2(2), 2010, 45-48
106
SUB THEME 3
Composite Materials
1
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID: ICAME2013 S3/O1
FINITE ELEMENT ANALYSIS OF NANOCOMPOSITE PLATELET STRUCTURE
ABSTRACT
Polymer composites are manufactured commercially for many diverse applications. In the last 20
years, there has been a strong emphasis on the development of polymeric nanocomposite where at least
one of the dimensions of the filler material is of the order of a nanometre. Particularly in automobile
components such as car bonnet & doors, we can manufacture polymeric nanocomposite sheet which is
strong enough compare to steel sheet by which we can contribute to reduce weight of vehicle. In
nanocomposite platelet structure, the mechanical properties are depending on the arrangement of the
platelets in the matrix material. Carbon-nanoplatelets are expected to be an excellent choice for the
reinforcement phase of composites. While carbon-nanotubes provide reinforcement in just one direction,
carbon nanoplatelets is effective in two directions. Thus platelets will yield a higher degree of stiffening
and strengthening in most applications.
In the present paper, Finite element analysis was carried out for a Graphene crystal of layered
structure, when added to polymer matrix is analyzed to investigate the effect of platelet structure. When
the reinforcement volume fraction is kept constant, the analysis result clearly shows the co-relation
between platelet structure and response i.e. deformation and stresses shown by the composite. The
preferred tool for this is ANSYS classic APDL. The results are discussed with a view toward developing
guidelines on the platelet structure of graphene for maximum reinforcement efficiency.
Keywords: Nanocomposite; Polymer matrix composite (PMCs); Finite element analysis by ANSYS
classic APDL; Graphene platelets.
1. INTRODUCTION:
Nanocomposites have lately attracted considerable attention because of the possibility of
performance of lightweight, energy-efficient and multifunctional systems. The characteristic of
nanocomposites depends on the choice of reinforcement phase and the distribution of reinforcement. As a
reinforcement of nanocomposites, carbon nanotubes have drawn attention due to their high potential to
increase the load carrying capability of structural composites. While the benefits of continuous nanotubes
are obvious, their production still lies far into the future. As a compromise, discontinuous nanotubes could
be used to reinforce the matrix. Although being short, on the order of 1 micron or so, these nanotubes are
still efficient in reinforcing the matrix due to their high aspect ratio reaching 100 to 1000. According to
2
micromechanical predictions, an aspect ratio of 1000 enables discontinuous fibres to perform almost like
continuous fibres as far as the modulus is concerned.
Assuming that the continuum mechanics is applicable, the longitudinal composite modulus E1 is calculated
as follows:
⁄
= , = ⁄
Where, Er is the Young’s Modulus of the reinforcement, Em is the Young’s Modulus of the matrix; Vr is
the reinforcement volume content, and is a parameter depending on the reinforcement geometry. For a
fibre of length l and diameter d, the reinforcement parameter is given by
=2⁄ +
For carbon nanotubes, the mechanical properties have not been fully explored. But, the base of the atomic
study shows following values reasonable.
Er=1TPa, vr =0.2
Where, vr is the Poisson’s ratio. For a polymer polyethylene used for matrix, the typical mechanical
properties are
Em =1.2GPa, vm =0.46
For carbon nanotubes having a diameter of d= 1nm, the aspect ratio can easily reach 1000 or more and the
longitudinal modulus can be as high as above 10 times the matrix modulus for volume content Vr = 0.04.
In practice, nanotubes cannot be aligned perfectly in nanocomposites. In the extreme case of two-
dimensional random orientation, the composite modulus can be calculated using the laminated theory.
Because of the poor stiffening efficiency in the two transverse directions-, the quasi-isotropic composite
modulus becomes much lower than the longitudinal modulus.
In the case of nanoplatelets that consist of a few graphene sheets, the thickness of a nanoplatelet is
on the same order as the diameter of a carbon nanotube. When the nanoplatelet has the same side
dimensions as the nanotubes length, its aspect ratio is almost the same as that of the nanotube. Thus the
nanoplatelets will yield the same composite modulus in their two planar directions as the longitudinal
modulus of a nanotube reinforced composite. That is, the quasi-isotropic modulus of the nanoplatelet
composite is the same as the longitudinal modulus of the nanotube composite.
Nanoplatelets are thus ideally suited for reinforcing the matrix phase considering the stiffening
efficiency. When graphite nanoplatelets are introduced into fibre-reinforced composites, the resulting
composites will exhibit higher stiffness and strength in the transverse directions. In general, nanoplatelets
are micron-size graphite crystals and the level of nanoplatelet structure in matrix component directly has
an influence on the mechanical properties of nanocomposites. So the study is required to investigate the
relation between the level of arrangement of nanoplatelets and the mechanical properties such as the
stiffness and the strength because the distribution of reinforcement is directly determined from the level of
arrangement of nanoplatelets.
In this paper, finite element simulation was carried out to investigate the effect of distribution of
nanoplatelets on the mechanical properties. Nanocomposites were modelled by a layered structure of
graphite nanoplatelets embedded in a matrix. Analysis was carried out for the variation of layer spacing
among nanoplatelets with the constant value of the reinforcement volume fraction. Further the analysis
models of nanocomposites are extended to a random distribution of graphite nanoplatelets in order to
provide the guideline of distribution quality required to improve the mechanical properties.
3
The first model is the one in that the nanoplatelet is regularly distributed at the centre of matrix.
The distribution depends on the distance between the nanoplatelets. Fig. 1 shows a schematic diagram of
the regular model for the analysis of nanocomposites. Each nanoplatelet reinforcement has a length L’ =
100 nm and a width w’=1nm, thus the aspect ratio reaches to 100 and their volume fraction with respect to
the matrix is 1/90. The material used in the reinforcement is carbon nanographite and the matrix used is
polyethylene.
Table 1: shows the material properties of the Fig. 1: schematic diagram of a nanocomposite
reinforcement and the matrix for finite element regularly distributed.
analysis.
Material Young’s Poison’s
Modulus Ratio
Reinforcement 1000 GPa 0.1
(Graphene)
Matrix 1.2 GPa 0.46
(Polyethylene)
4
MODEL 2: Random distribution of nanoplatelets
In the previous analysis, nanoplatelets are regularly distributed at the centre of matrix. But not all
nanoplatelets are expected to be aligned perfectly uniform in practice. In reality, nanoplatelets are
randomly distributed in the matrix. Fig. 5 shows partially distributed graphite nanoplatelets. An analysis
model needs to be extended for consideration of the random distribution of nanoplatelets in order to show
the effect of exfoliation and to provide the guideline of exfoliation quality required to improve the
mechanical properties. But the distribution of nanoplatelets is so random in nanocomposites that it is
necessary to simplify the distribution in the model.
Fig.2: Distribution of the von Mises stress of Fig.3: Stiffness of nanocomposites with respect
nanocomposites with respect to the distribution to the distribution of nanoplatelets
of nanoplatelets
Fig.4: Mechanical efficiency of nanocomposite with respect to spacing between nanoplatelets
In this paper, simplified nanocomposite models are proposed to consider the case of randomly
distributed nanoplatelets. Fig. 6 shows the two simplified random distribution models. These models may
be regarded as a portion of randomly distributed nanoplatelets in the matrix. Different nanocomposites
randomly distributed were modelled by layered structure of carbon graphite nanoplatelets embedded in the
polyethylene matrix. The distribution of nanoplatelets can take variation in two directions. A spacing in
5
the horizontal direction is indicated as a symbol ‘H’ and in the vertical direction is indicated as a symbol
‘V’ on both models. Analysis was carried out to show the effect of random distribution on the stiffening
and stress distribution.
Fig6: Schematic diagrams of random distributed nanocomposites
Fig.5: partially distributed graphite
platelets.
Finite Element analysis of the random distributed models
Finite element analysis was carried out for the variation of the spacing in the vertical and
horizontal direction. Two values in the vertical and horizontal spacing are taken to indicate distribution of
nanoplatelets. Analysis models are listed in Table 2. The uniform displacement boundary condition was
applied on the one side of nanocomposites while the other side was fixed. The results are compared with
the variation of the horizontal spacing and the vertical spacing. The reaction force and the stress
distribution in the matrix are obtained to investigate the effect of the distribution of nanoplatelets.
Table 2: Variation of spacing in the simplified random distributed model
Model 2 Horizontal Vertical space Model 3 Horizontal Vertical space
space (H) (nm) (V) (nm) space (H) (nm) (V) (nm)
M2-H1V20 1 20 M3-H1V20 1 20
M2-H3V20 3 20 M3-H3V20 3 20
M2-H1V40 1 40 M3-H1V50 1 50
M2-H3V40 3 40 M3-H3V50 3 50
In the case of Model 2, the von Mises stress distribution in the matrix at the extension of 10 nm is
shown in Fig. 7 and Fig.8. The distribution of von Mises stress tends to be uniform as the horizontal
spacing is increased in the regular model. The tendency is still persists in Model 2. But the analysis results
of Model 2 shown in Fig. 7 and Fig. 8 indicate that the distribution of von Mises stress becomes more
uniform as the vertical spacing is decreased more. Those results are due to the decrease of the portion
occupied by nanoplatelets in the nanocomposites. Fig. 9 and Fig. 10 show the stiffness of the
nanocomposites with respect to the variation of the vertical spacing. Each figure shows the improvement
of the stiffening efficiency in nanocomposites with increase of the vertical spacing at a constant horizontal
spacing. Figures also indicate that random distribution of nanoplatelets increase the stiffness of
nanocomposites.
Nanoplatelets in the Model 3 are more randomly embedded in the matrix. It can be regarded as a
mixed formation of vertical and horizontal distribution. The von Mises stress distribution in the matrix at
the extension of 10 nm is shown in Fig. 11 and Fig. 12. The reaction force of nanocomposites during the
6
extension is plotted in Fig. 13 and Fig. 14. Comparing with the case of Model 2, similar results are
obtained for the distribution in the vertical and horizontal direction. The increase of the vertical spacing in
Model 3 induces the stress concentration in a matrix, but stiffening the nanocomposites. Based on the
analysis results, it is possible to estimate the distribution quality required for the maximum nanoplatelets
efficiency.
Fig. 7: Distribution of the von Mises stress in Fig. 8: Distribution of the von Mises stress in
Model 2 with respect to the variation of V=20 Model 2 with respect to the variation of V=20
&40 at H=1nm. & 40 at H=3 nm.
Fig. 9: Stiffness of nanocomposites in Model 2 Fig. 10: Stiffness of nanocomposites in Model 2
with respect to the variation of V at H=1nm. with respect to the variation of V at H=3nm.
Fig. 11: Distribution of the von Mises stress in
Model 3 with respect to the variation of V=20
& 40 at H=1nm.
7
Fig. 12: Distribution of the von Mises stress in
Model 2 with respect to the variation of V=20
& 40 at H=3 nm.
Fig. 13: Stiffness of nanocomposites in Model 3
With respect to the variation of V at H=1nm.
Fig. 14: Stiffness of nanocomposites in Model 3
With respect to the variation of V at H=3nm
.
8
3. CONCLUSION
Finite element simulation has been carried out to investigate the effect of the distribution of
nanoplatelets on the mechanical properties. The analysis models represent the model of regularly or randomly
distributed at the centre of the matrix. Analysis results clearly demonstrate the improvement of the stiffening
efficiency in nanocomposites and the reduction of the stress concentration in the matrix proportional to
distribution of nanoplatelets. Models are extended to have random distribution of graphite nanoplatelets. Two
simplified models regarded as a part of practice nanocomposites are proposed for the analysis. The vertical and
horizontal spacing is considered to denote the distribution of nanoplatelets. Analysis results show that the
increase of the vertical spacing in Model 3 induces the stress concentration in a matrix, but stiffening the
nanocomposites. These results can be utilized as the guideline of distribution quality required to improve the
mechanical properties.
4. REFERENCES
1. Hurang Hu, Landon Onyebueke , Ayo Abatan, ‘Characterizing and modeling mechanical properties of
nanocomposites review and evaluation ’ , 2010; jmmce.org275-319.
2. X.X. Yu, W.B. Lee, ‘The design and fabrication of an alumina reinforced aluminum composite material’
, 2000; elsevier.com;composites part A 31; 245-258.
3. T.D.Fornes, D.R.Paul. ‘Modeling properties of nylon 6/clay nanocomposites using conposite theories’, ;
elsevier.com, Polymer 44(2003)4993-5013.
4. E. W. Wong, P. E. Sheehan and C. M. Lieber, ‘Nanobeam mechanics: Elasticity, strength, and
toughness of nanorods and nanotubes,’ Science, 277, 1971-1975 (1997).
5. L. Dai, A. W. H. Mau, ‘Controlled synthesis and modification of carbon nanotubes and C60: Carbon
nanostructures for advanced polymeric composite materials,’ Advanced Materials, 13, 899-913 (2001).
6. Narita and K. Shintani, ‘Atomistic Study of Mechanical Properties of Carbon Nanotubes,’ Mat.
Res. Soc. Symp. Proc., 706, Z.9.7.1, Z.9.7.6. (2001).
7. E.T. Thostenson, Z. Ren, and T.W. Chou, ‘Advanced in the Science and Technology of Carbon
Nanotubes and their composites: a Review,’ Composites science and Technology, 61, 1899-1912(2001).
9
Proceedings of International Conference on Advances in Mechanical Engineering
ABSTRACT
This paper focuses on design of hybrid composite leaf spring for a multi utility vehicle. A hybrid composite leaf spring
consists of a steel master leaf & leaf no.2 to leaf no. 6 of composite material. This enables ease of fitment on the vehicle.
Reduction in the un-sprung mass of vehicle reduces the amount vibrations transferred. Present steel multi leaf spring
set-up weighs 24 kg. After replacement by hybrid composite leaf spring arrangement, a weight reduction of about 60% is
obtained. Change in the vertical stiffness of spring affects the dynamic behavior of vehicle. It also changes the natural
frequency of rear suspension changing the front to rear suspension frequency ratio which is important for flat-ride
criteria. Hence it is necessary that the load deflection curves for steel & hybrid arrangements should be similar and
therefore load deflection curves of steel & hybrid leaf spring are compared. Fatigue life of the hybrid arrangement is
predicted a theoretically & validated by FEA.
A manufacturing process called Vacuum assisted Resin Transfer molding process which is an efficient way for mass
production of composite leaves is also discussed. The process has a cycle time of 0.5 hours. Solid modeling and Finite
Element analysis is done using commercial software packages. Analytical & FEA results for the deflection & stress are
validated under identical loading conditions.
1. INTRODUCTION
Many attempts have been made in the past to replace the conventional steel multi-leaf spring. Advantages of composite
leaf spring are the high strength to weight ratio, high specific strain energy and reduction in un-sprung mass of vehicle.
However, there are areas of improvement for the composite leaf spring, driven by the ease of fitment on vehicle (with
no cost addition), better fatigue life and cost efficient manufacturing techniques. In the present work, a Hybrid approach
will provide cost efficient fitment on the vehicle. Material selection is influenced by a goal of fatigue life of 200,000
cycles. The fatigue life will be predicted by Hawang-Han relation [1]. Also fatigue analysis is carried out by commercial
software. Resin transfer molding is a moderate volume production technique which will be discussed for its influence.
2. MAIN SECTION
STEEL MULTI-LEAF SPRING–
20000
18011
15000
13508
10000
5000 4500
2200
0 0
0 50 100 150 200 250
HYBRID COMPOSITE MULTI-LEAF SPRING –
Hybrid Concept - This approach comprises of a steel master leaf and leaf 2 to 6 made up of carbon fiber-epoxy.
This enables ease of fitment, compared to other composite set-ups, since the master leaf which is connected to
the chassis does not change, hence preventing additional costs.
Material Selection-
Fiber selection- Carbon fiber has been selected based on strength, fatigue life and density. Fiber orientation
selected is unidirectional (0degree). The Direction of fiber is along the longitudinal direction of vehicle to
support the vertical loading.
Resin Selection – The inter-laminar shear strength in carbon fiber is controlled by the matrix system used. Since
these fibers are reinforced along the thickness, fibers do not influence inter-laminar shear strength. Therefore
the matrix system should have good inter-laminar shear strength and compatibility with the fiber. Hence epoxy
resin is selected with a compatible hardener.
The failure of composite material [2] is driven by fiber dominated failure (breakage, micro-buckling), bulk
matrix dominated failures (voids, crazing) & interface failure (delamination).The lamina is considered to be
specially orthotropic lamina whose principal material axes are aligned with the axes of body on which load is
applied. Tsai-Wu Failure theory is applied to predict the failure of the unidirectional lamina.
Design Calculations – The hybrid multi-leaf spring is designed for the same data in Table 1, as the vertical
stiffness has to remain same. The length and thickness of each leaf is calculated using SAE spring design
manual [3]. Width of the leaf spring is same as that for the original steel set- up.
=
32 × 1.1 ×
ℎ
=2 × ℎ + +
∑ 2
12
6 16 390 436 826
20000
15000
Steel
10000
5000
Hybrid
0
0 50 100 150 200 250
Figure 2 – Comparison of Load (N)-Deflection (mm) for steel and Hybrid composite set-up
Installation Effects [2] - As the spring deflects the length of the cord changes and the shackle will swing and
change its angle. In swinging, the shackle may lift or lower the eye of the spring and with it the point of load
application. This is the first shackle effect. When the shackle is not perpendicular to the datum line of spring the
shackle load will have a longitudinal component either compressing or stretching the spring between the eyes.
Compressing will decrease the rate of the spring, while stretching will increase the rate. This is the second
shackle effect. The rate of the installed spring with shackle may easily be 50% higher/lower than the nominal
rate. In this particular application due to vertical loading the shackle will tend to stretch the leaf spring and
hence will increase the installed rate of leaf spring. This effect is also validated through the results of FEA
analysis.
Finite Element Analysis –
Selection of type of analysis[3] – Linear static analysis assumes that the geometric parameters do not change
when the structure is loaded, while non-linear analysis takes into consideration the changes in geometric
parameters as load is applied to the structure. These changes are associated into the analysis by re-building of
the stiffness matrix. Hence non-linear analysis is selected. The solution given by the solver is driven by
convergence criteria in non-linear analysis.
13
Hybrid model is meshed with solid hex element. Load is applied through inactive seat length and is uniformly
distributed along the concerned nodes. Fixed end and shackle is modeled using RBE2 and CGAP elements.
Travel of shackle for the given load is calculated. A CGAP element of calculated length is used to account for
the effect of shackle. CGAP element is also used to simulate contact between the leaves. The center bolt is
modeled using 1D bar element. Mesh quality check up for hex elements:
Warp angle Acceptable ≤10o
Jacobian Acceptable ≥ 0.7
Quad Face included angle 30 o≤ θ ≤ 135o
Figure 4 – Finite element analysis model
3. RESULTS –
14
Figure 5 – Displacement and Stress distribution at 9756N load
Figure 6 – Displacement and Stress distribution at design load
Figure 7- stress in spring eye region at design load
Results obtained for various loads are plotted as below.
20000
15000
10000
5000
0
0 50 100 150
15
20000
15000
10000
5000
0
0 200 400 600 800
Figure 9 – Load (N) - maximum Stress (N/mm2) chart
The critical area was observed near the centre bolt region & spring eye. The shackle effect discussed earlier was
validated by load-deflection graph as shown in figure 8. Weight reduction obtained is 58.33%
Modal Analysis [3] – When the excitation frequency is close to natural frequency of component, there would be
a significant difference in static and dynamic results. Static analysis shows stress within the yield strength but
practically it may fail. For this purpose modal analysis is carried out with given constraints and contacts. 1st 12
modes are as follows.
The modes obtained can be illustrated as below:
16
Fatigue Analysis – Fatigue life cycle goal is 200,000 cycles. Hawang-Han [1] relation is used to predict the life
theoretically.
= (1 − )
N- Number of cycles before failure.
B- 10.33
C- 0.14012
r- σmax/σuts
The number of cycles obtained from this relation is 1.88 x 106 considering the maximum stress at design load
given by finite element analysis.
Also fatigue life is estimated using commercial software for the entire hybrid arrangement. Alternating type
load is selected with maximum load 1100 kg and minimum load of 200 kg as it is similar to the loading
conditions on the steel set-up. The surface finish considered was 60 micron with shot peening as the surface
treatment. The critical area was observed on the steel master leaf near the centre bolt region. Number of cycles
to failure was 5.332 x 107 cycles exceeding the required target of 200,000 cycles
17
Figure 11 –Fatigue life (Critical area)
1. 4. MANUFACTURING
Resin Transfer Molding (RTM) - is a low pressure closed molding process for moderate volume production
quantities, filling the gap between the slow, contact molding processes and the faster, compression molding
processes, which have higher tooling costs. Continuous strand mats and woven reinforcement is laid up dry
in the bottom mould half. Preformed glass reinforcements are often used for complex mould shapes. The
mould is closed and clamped, and a low viscosity, catalyzed resin is pumped in, displacing the air through
strategically located vents. Metered mixing equipment is used to control resin/catalyst ratios that are mixed
through a motionless static mixer and injected into the mould port. Common matrix resins include polyester,
vinyl ester, epoxy and phenolics. Advantages of RTM over contact molding methods are a uniform
thickness, two finished sides and low emissions.
Preparation of Mold- Patterns were prepared using carpentry tools, thick rubber liners, laminates and metal inserts.
These patterns were used to make the male half of the molds of Glass Reinforced Plastic. The female molds were
prepared from plywood and were covered with laminates for proper surface finish.
Three layers of a release agent were applied to the molds. This is done to prevent the resin from sticking to the mold
surfaces and facilitate easy removal of job.
18
The pasted mats were placed in the female mold cavity. The vaccum pump was connected to the two suction ports. This
clamped the two molds together due to vaccum. The pump was also connected to the riser port so that air from the job
region was extracted creating the vaccum. Hence the two outer suction ports contribute to the clamping while the riser
port creates the actual vaccum responsible for inflow of resin. The two inner resin ports were connected to a reservoir
that contained the mixture of the resin and hardener. The cycle time for the process is 0.5 hours.
5.EXPERIMENTAL VALIDATION –
A sample module of same stiffness was tested for static deflection against varying load. The spring assembly was
supported on rollers at both ends. Maximum load applied was 3000N through the inactive seat length. The spring
assembly was deflected up to maximum deflection of 120 mm 3 times before plotting the load-deflection
characteristics. The testing was carried at the Automotive Research Association of India (ARAI). The results obtained
were as follows.
19
Figure 16 – Test set-up
Remark – The testing of the sample module indicates that the leaf spring is 50% less stiff than predicted. It can be
concluded that, carbon fiber, being an anisotropic material, shear extension coupling takes place when load applied is in
normal direction[5][6].
Figure 14 shows linear and continuous nature of graph, which indicates that no lamina failure occurred during the
loading. Hence the Tsai-Wu failure criteria [5] [6] is also validated by static load deflection test at the given load.
Figure 15 shows that hysteresis for the hybrid composite leaf spring. The Deviation between the deflection values during
compression & release are shown in figure 16.
6. CONCLUSIONS
1. To account for coupling between normal stress and shear deformation, the staking sequence should be
altered. +45 /-45 degree orientations of layers should be added to account for coupling.
20
2. Fatigue life, both estimated theoretically and by FEA satisfies the 200,000 cycles goal.
3. Overall weight reduction obtained is 58.33%
4. RTM can be used as a moderate volume production technique for the cost efficient products.
5. Hybrid approach is the cost efficient approach for commercial application of composite leaf spring with
durability goal of 200,000 cycles.
REFERENCES
1. Hawang W and Han K S, “Fatigue of composites- Fatigue modulus concept and life prediction”, J Com
Materials, 20(1986)154-165.
2. Mukhopadhyay Madhujit, “Mechanics of Composite materials & Structures”
3. SAE spring design manual (1996)
4. Gokhale Nitin S., “Practical Finite Element Analysis”.
5. Jones, Robert M., “Mechanics of Composite Materials”, Second edition.
6. Mallick, P.K., “Fiber reinforced composites, materials, manufacturing and design”, Second Edition.
ACKNOWLEDGEMENTS
.D DEFINITIONS/ABBREVIATIONS
L Length between eye
centers of spring
t Thickness of leaf in
mm
σmax Maximum stress in
composite leaf spring
in N/mm2
σuts Ultimate Tensile
Strength of composite
material in N/mm2
coeff coefficient
Gpa 103 N/mm2
21
Mpa N/mm2
22
Page 23 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID
ICAME2013_S3/O4
OPTIMAL DESIGN FOR PATCH REINFORCEMENT IN NOTCHED COMPOSITE PLATE
Keywords: Composite material, patch, FEM
1. INTRODUCTION
Composite materials are commonly used in structures that demand a high level of mechanical
performance. Their high strength to weight and stiffness to weight ratios has facilitated the development of
lighter structures. In addition to this, due to high strength and safety requirements in automotive and
aviation industry,composites are extensively used.
For the convenience in manufacture or transportation and limitations on material size,it is rarely
possible to produce a construction without joints. All connections or joints are potentially the weakest
points in the structures so can determine its structural efficiency [1].For facilitating mounting of various
members or fasteners requirement usually is to create holes in composite members [1-3].These holes
significantly reduce the load carryingcapacity of composites due to the stress concentrationin the vicinity
of the boundary of the hole and in many cases are the causes of failure [4,5].Correlation between failure
stress and hole diameter of composite material was performed. Also, Position of hole in laminate
influences the strength of plate and mode of failure [6-7] .Hence width, end distance, hole diameter and
laminate thickness are the key parameter in failure hypothesis [6]. One more influencing key parameter on
strength of composite plate is orientation of fibers with respect to loading direction [4,8].The
reinforcement of notches has been another area of interest in recent years. Commonly used, metal spacers
(fig.1) increase complexity of manufacturing process as well as total weight of the products [10]. Light
weight composite adhesive patches provide an effective reinforcement and require relatively simple
process with low skill level[11]. However, there is lack of general investigations and design rules in this
area. The solution presented over here is to cover these holes with a patch of composite lamina and effect
Page 24 of 89
of reinforcing patch is quantified. Because of the anisotropic and heterogeneousnature, the joint problem in
composites is more difficult to analyze than the case withisotropic materials.
Fig 1.schematic diagram for spacer in bolted Fig. 2:Plate with hole indicating boundary
composite plate condition
Table 1.Material property of plate and patch
3. ANALYSIS
The joint problem considered is more difficult to analyze as the composites are of the anisotropic and
heterogeneous nature than the case with isotropic materials. The ANSYS finite element package is used to
evaluate the stress distributions in plate. Ten-noded three dimensional structural solid element, SOLID 187
were selected to model the plate and patch. It is a tetrahedron with mid-side nodes which gives accurate
result than 4-node element. The plate and patch are in contact with each other, hence Contact between
plate and patch is considered to be rigid and define as perfectly bonded. To get the accurate results and less
time for solution, fine meshing at the vicinity of hole is created with sphere of influence in fig 3.
Page 25 of 89
Fig 3.Fine meshing at the vicinity of hole
Also, Plate thickness in varied from 1 to 5 mm to find suitable combination of patch-plate thickness.
Plate without patch and plate with patch of varying plate thickness in studied. From fig 5 it indicates that
increase in plate thickness for constant patch thickness will decreases stresses developed in plate. It is
noticeable that patching of less thickened plates reduces stresses more effectively.
Table 2: Stress reduction in different optimal patch shapes
Page 26 of 89
(a) Circular patch (b) Kite Patch
(c) Rectangular patch along width variation (d) Rectangular patch along length variation
(e) Elliptical patch along length variation (f) Elliptical patch along width variation
Page 27 of 89
(g)Hexagonal Patch
Fig4.Effect of different types of patches on stress and deformation of plate
Fig 5.Effect of plate thickness on patching.
5. CONCLUSIONS
The study presented in this paper outlines the importance of patch repair of notched composite plates;
which helps in regaining loading capacity of plate.The most influencing constrains; shape of patch and
plate thickness are consideredin designing of patch.From the results, the followingconclusions are drawn:
i. Patching of notched composite plate reduces stresses developed in vicinity of hole which is
the major cause of failure.
ii. Kite shaped patch is best suitable on account of stresses developed and weight along with
cost optimization.
iii. Increasing dimension of patch in width direction of plate will generates good result than
along length.
iv. Patching effect is inversely proportional to the plate thickness.
REFERENCES
Page 28 of 89
1. A.G. Magalha esa, J.P.M. Gonc-alves, M.F.S.F. de Mourab, “Evaluation of stress concentration
effects in single-lapbonded jointsof laminate composite materials”, International Journal of
Adhesion & Adhesives, 313–319,25 (2005)
2. Álvaro Olmedo and Carlos Santiuste, “On the prediction of bolted single-lap composite
joints”,Composite Structures , 2110–2117,94 (2012)
3. Joseph D. Melograna and Joachim L. Grenestedt, “Improving joints between composites and steel
using perforations”, Composites,1253–1261,Part A 33 (2002)
4. Bernard Lorrain, Lotfi Toubal, Moussa Karama “Stress concentration in a circular hole in
composite plate”, Composite Structures, 31–36,68 (2005)
5. MarinSandu,Nicolae Constantin, Stefan Sorohan, “Restoration of the mechanical performance of
damaged Al panels using bonded composite repair patches”, International Journal of Adhesion &
Adhesives, 69–76,42 (2013)
6. Bulent Murat Icten ,Cihan Rıza Calıs Ckan,Mehmet Aktas S, Ramazan Karakuzu,“Failure behavior
of laminated composite plates with two serial pin-loaded holes”, Composite Structures, 225–234,82
(2008)
7. Ignaas Verpoest,Kazuaki Nishiyabu,Surya D. Pandita, “Strain concentrations in woven fabric
composites with holes” , Composite Structures,361–368,59 (2003)
8. C.Soutis, N.A.fleck, P.T.Curtis, “Hole hole interaction in carbon fibre/epoxy laminates under
uniaxial compression”, Composites,22(1991)
9. Ever J. Barbero, “Finite element analysis of composite materials”, CRC press,New York.(2008)
10. “Composites”, ASM handbook, Volume 21, (2001)
11. R. Jones, “A scientific evaluation of the approximate 2D theories for composite repairsto cracked
metallic components”, Composite Structures ,151–160,87 (2009)
Page 29 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID S3
ICAME2013S3/O5
Impact and slurry erosion resistance of polymer matrix glass fibre reinforced
Composite material
S. G.Kulkarni, A. R. Khatavkar, D. R. Deokar,
Research scholar, Student, S.K.N.S.C.O.E. Student, S.K.N.S.C.O.E.
S.V.N.I.T. Surat Pandharpur. Pandharpur.
swanand29@rediffmail.com
ABSTRACT
Surface erosion of materials by impact of solid particle present in the liquid is a major problem in many
types of industrial equipment involving multiphase flow. Erosion causes pitting resulting in holes leads to
functional failure, though the remainder of the equipment is relatively undamaged. Erosion phenomenon
has been studied for conventional material but very less work is available in case of polymer matrix
composite. In current work the erosive wear of Polytetrafluoroethylene (PTFE) and PTFE matrix glass
fiber reinforced composite in pure water has been studied. The factorial design method is used to predict
the erosion of pure PTFE and PTFE glass fiber composite. The erosive wear (Y) can be expressed in terms
of coded values of velocity, impact angle, reinforcement of the sample with respect to their direction of
rotation in the pure water(x2) and reinforcement(x3) by the following regression equation:-
Keywords: - Polytetrafluorethylene, Glass fiber(GF), Factorial design, erosion, composite .
1. INTRODUCTION
Surface erosion of materials by impact of solid particle present in the liquid is a major problem in
many types of industrial equipment involving multiphase flow. Erosion causes pitting and/or holes leads to
functional failure, though the remainder of the equipment is relatively undamaged. This may be
achieved by altering the flow geometry, impact direction, suitable impinging velocity within the
equipment such that the fluid flow field, and in turn the particle impact dynamics are changed. As the
erosion rate is considered as function of the local particle impact rate, velocity and impact angle these
parameters are studied for different materials.Slurry erosion is common phenomenon occurring in various
places such as impeller of pump, blades of water turbine, pipes carrying mud, sewerage pipes etc.
Generally a suspended solid particle present in liquid makes impact on surface of target material to give
rise to removing material from surface resulting in erosion. In recent years number of articles dealing in
erosion of polymer and metal matrix composites are available but exhaustive study on vital aspect is
hardly found. In the present work, polymer matrix and metal reinforced composite material is selected.
Various compositions of these materials are produced. Polymer material is in the form of
polytetrafluorethylene is used as it is tough, wear resistant and sustains comparatively at high temperature.
Reinforcement in the form of metals is used. The metal reinforcement is also selected in the form of wear
resistant properties at various configurations and their impact and erosion resistance is checked in slurry
erosion apparatus.
Page 30 of 89
Polytetrafluoroethylene (PTFE) matrix composite have been proved useful in variety of engineering
application. PTFE is used as a non-stick coating for pans and other cookware. It is often used in containers
and pipe work for reactive and corrosive chemicals. PTFE reduces friction, wear, and energy consumption
of
Sr.No. Specimen Angle Velocity Initial Final Erosion(mg)
machinery. Though limited studies have been carried out in this direction wherein the effect of different
factors like rate of impact of local particle, velocity and impact angle for different composite material.
Composite material has found their potential as substitute metal where corrosion/erosion is major
problem/condition. In study empirical equation with factorial design have been presented to calculate
erosion/corrosion rate at different input parameters like (velocity ,Impact angle, reinforcement). This kind
of approach is already being adopted in areas like process metallurgy, mineral processing, etc. however
such an approach does not adopted so far as the influence of various actors on the wear response of
material is concerned. An attempt has been made to develop a linear regression equation for a calculation
of erosive-corrosive wear rate of PTFE with GF particulates taking into consideration factors like rate of
impact of local particle, velocity and impact angle for different composite material and their effect on wear
properties of material. Theoretically calculate values of wear rate have been checked through
experimentally observed ones.
Objective of the experiment are to study the effect of different angle, velocities on test specimen .To
study the type of erosion with its erosion characteristics of composite materials and compare it with pure
metals and to check the feasibility of material.
2. EXPERIMENTAL WORK
Slurry Erosion test rig is developed to study the erosive wear characteristics of composite materials as
well as metals. Test rig is constructed as shown in figure 1. A slurry erosion apparatus is developed to
check the effect of impact angle and velocity on target material. In present work effect of pure water
particles is studied in order to find the erosion of composite material in pure water. It has been found that
due to rotation of target material in pure water erosion happens. It may be due to water particles or very
small size particles present in the water.
Material:- The erosion testing is carried on different material and it is given in Table 1to Table 4 as
below
Table 1. Erosion (mg) for pure PTFE
Sr.No. Specimen Angle Velocity Initial Final Erosion(mg)
1 A1 90 15 3.524 3.522 2
2 A2 90 30 4.045 4.043 2
3 A3 90 45 3.733 3.73 3
4 A4 60 15 3.577 3.577 0
5 A5 60 30 3.666 3.664 2
6 A6 60 45 3.598 3.596 2
7 A7 30 15 3.798 3.798 0
8 A8 30 30 3.538 3.537 1
9 A9 30 45 3.813 3.811 2
Table 2. Erosion (mg) for PTFE + 15% Glass fibre
Page 31 of 89
1 B1
90 15 4.083 4.082 1
2 B2 90 30 4.002 4 2
3 B3 90 45 3.947 3.945 2
4 B4 60 15 4.293 4.292 1
5 B5 60 30 4.243 4.242 1
6 B6 60 45 4.19 4.188 2
7 B7 30 15 4.351 4.351 0
8 B8 30 30 4.312 4.311 1
9 B9 30 45 4.271 4.269 2
Table 3. Erosion (mg) for PTFE + 25% Glass fibre
Sr.No. Specimen Angle Velocity Initial Final Erosion(mg)
1 C1 90 15 3.965 3.963 2
2 C2 90 30 4.139 4.136 3
3 C3 90 45 4.523 4.519 4
4 C4 60 15 3.998 3.997 1
5 C5 60 30 4.19 4.189 1
6 C6 60 45 4.252 4.25 2
7 C7 30 15 4.64 4.64 0
8 C8 30 30 4.37 4.369 1
9 C9 30 45 4.23 4.228 2
Table 4. Erosion (mg) for PTFE + 35% Glass fibre
Sr.No. Specimen Angle Velocity Initial Final Erosion(mg)
1 D1 90 15 4.44 4.437 3
2 D2 90 30 4 3.995 5
3 D3 90 45 4.267 4.262 5
4 D4 60 15 4.187 4.185 2
5 D5 60 30 4.221 4.219 2
6 D6 60 45 3.95 3.947 3
7 D7 30 15 4.296 4.296 0
8 D8 30 30 4.078 4.077 1
9 D9 30 45 4.13 4.128 2
3. EROSION TESTS
Erosion tests were carried out by rotating sample test method as discussed. Fig.1 shows schematic
view of test apparatus. The medium used for testing the sample is pure water. The specimen having size 25
mm X 25 mm surface area & 3 mm thickness were used for study. The linear velocity of rotation of
Page 32 of 89
sample in slurry is given in table. The experimental parameters whose effects on wear behaviour of sample
were studied including velocity, impact angle, reinforcement with respect to direction of rotation in pure
water.
1 Disc 5 Double wall container
2 sample holder 6 Spindle
3 sample 7 Driving motor
4 slurry media 8 Column
9 Machine base
Fig.1. schematic view of the erosion tester
4. FACTORIAL DESIGN OF EXPERIMENT
A full factorial design of experiment of type p was used in present study where n corresponds to
number factors and p represents no of levels. Here n=3(velocity, impact angle, reinforcement) and p=2.
Thus the minimum no of trials needed for investigation is 2=8.If response variable (i.e wear rate) is
represented by Y, the linear regression equation for experiment may be expressed as
Y=a0 + a1X1 + a2X2 + a3X3 + a4X1X2 + a5X2X3 + a6X1X3 + a7X1X2X3 (1)
Where a0 is the response variable at the base level and a1,a2,a3 are coefficients of representing the
effect of variables x1,x2 and x3(i.e coded values of velocty, impact angle and reinforcement) respectively;
a4, a5 and a6 represent interaction coefficient of variables X1-X2, X1-X3, and X2-X3, respectively; and a7
represent the interaction coefficient among the variables X1, X2 and X3 within selected levels of each
variable. The methodology for calculating the values of each regression coefficient using the coded value
of each factor is described. The positive value of Y in in equation 1 indicate weight loss while a negative
value of a same means weight gain. Further a negative value of any term in equation signifies reduced rate
of material loss. It may also be noted that weight gain as well as weight loss can take place during the kind
of tests adopted in investigation depending on whether the cutting and eroding action of the erodent
particles and liquid droplets (both causing weight loss) are predominant by the entrapment of corrosion
product as well as erodent particles in cavities (formed during erosion) in successive passes or not.
5. RESULT AND DISCUSSION
The upper and lower values of each factor along with their coded value in investigation are shown in
Table 5. the factorial of the experiment and the values of response variable corresponding to each trial are
reported in Table 6. The values of each coefficient of Eq (1) were calculated using the methodology as
discussed. The matrix design equation for calculating each coefficient of Eq.(1) is shown in Table 7.
Table 5. Levels of different factors and their coded values (within brackets)
Factor level an code Factors
Angle (θ) (0) Velocity (V)(m/s) Reinforcement (%)
Page 33 of 89
Upper level 90 45 15
Code value (+1) (+1) (+1)
Lower level 60 30 25
Code value (0) (0) (0)
Base level 30 15 35
Code value (-1) (-1) (-1)
Table 6. Selected trials as per model
Trial no Angle Velocity Reinforcement Wear rate
1 90 45 35 5
2 90 45 15 2
3 90 15 35 3
4 90 15 15 1
5 30 45 35 2
6 30 45 15 2
7 30 15 35 0
8 30 15 15 0
Table 7 Selected trials with coding and wear rate.
Trial X1 X2 X3 X1X2 X1X3 X2X3 X1X2X3 Wear
no rate
1 1 1 1 1 1 1 1 2
2 1 1 -1 1 -1 -1 -1 5
3 1 -1 1 -1 1 -1 -1 1
4 1 -1 -1 -1 -1 1 -1 3
5 -1 1 1 -1 -1 1 -1 2
6 -1 1 -1 -1 1 -1 1 2
7 -1 -1 1 1 -1 -1 1 0
8 -1 -1 -1 1 1 1 -1 0
The final linear regression equation in this study shown as Eq. (2)
Y=1.875 + 0.875X1 + 0.875X2 + 0.625X3 - 0.125X1X2 + 0.625X2X3 + 0.125X1X3 + 0.125X1X2X3
(2)
Where the multiplication factor is calculated as per annexure and X1, X2,X3 are coded values of
velocity ,Impact angle(θ),reinforcement ,respectively. The value a0 is the mean response value of eight
trials.
6. CONCLUSION
[1]. It has been found that due to rotation of target material in pure water erosion happens. It may
be due to water particles or very small size particles present in the water.
[2]. It is also observed that as velocity increases erosion also increases.
[3]. One critical value of velocity comes above which erosion happens.
[4]. It is found that this critical value is different for different material.
[5]. Wear rate was decreased with increasing angle.
Page 34 of 89
[6]. The result indicate that erodent size, fibre loading, impingement angle, impact velocity,
volume fraction, reinforcement type have the significant effect on erosion rate.
[7]. Increase in reinforcement percent of glass fibre in PTFE erosion decreased upto 15 percent
increment of glass fibre.
[8]. Erosion of PTFE matrix glass reinforced composite increases after 15 percent increment in
glass fibre reinforcement.
[9]. Mathematical modeling based on multiple regression analysis is done based on experimental
results which is valid.
APPENDIX
Calculation of coeffient of regression equation.
a 0 = (ΣYi)/n;
a1 = (Σ(X1)iYi)/n;
a2 = (Σ(X2)iYi)/n;
a3 = (Σ(X3)iYi)/n;
a4 = (Σ(X1X2)iYi)/n;
a5 = (Σ(X1X3)iYi)/n;
a6 = (Σ(X2X3)iYi)/n;
a7 = (Σ(X1X2X3)iYi)/n;
1. REFERENCES
1. Barkoula NM and Karger-Kocsis J., “Solid particle erosion of unidirectional GF reinforced EP
composites with different fibre/matrix adhesion”. Journal of Reinforced Plastics and composites,
19, 1-12 (2000)
2. Hager A. et. al., “Study of erosion wear of advanced polymer composites”, Conference
Proceedings, Whistler, BC, Canada. Cambridge.
3. Hawthorne H.M. et. al., “A study of single particle–target surface interactions along a specimen in
the Coriolis slurry erosion tester” Wear. 253, 403–410 (2002).
4. Miyazaki N and Hamao T. “Effect of interfacial strength on erosion behaviour of FRPs”. Journal of
Composite Materials. 30, 35-50 (1996).
5. Pool KV et. al., “Erosive wear of composite materials”, Wear. 107, 1-12(1986)
6. S. Das et. al., “Erosive–corrosive wear of aluminum alloy composites: Influence of slurry
composition and speed”, Wear. 261, 2, (2006).
7. Walley SM et. al., “Single solid particle impact erosion damage on polypropylene”. Wear. 100,
263-280 (1984).
8. Wang YQ et. al., “The blast erosion behaviour of ultrahigh molecular weight polyethylene”. Wear
218, 128-133 (1998).
Page 35 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
ICAME2013 S3/O6
ABSTRACT
CFRP composites are considered as emerging material in a variety of engineering fields (mainly in aerospace and
automobile sector) because of their excellence properties such as high toughness, low weight-to-volume ratio,
high rigidity, strength, etc. However, the machinability of such composites is seemed quite difficult to form desired
shape and hence, it becomes indeed necessary to determine the most favorable machining environment towards
satisfactory yield (quality and productivity) in composite machining. This paper presents a novel integrated multi-
objective optimization method based on Desirability Function (DF), Principal Component Analysis (PCA) coupled
with Grey Relation Theory and Taguchi approach for parametric optimization of carbon fiber reinforced polymer
composites.
Keywords: CFRP, Desirability Function, Principal Component Analysis, Grey Relation Theory.
1. INTRODUCTION
In today’s world, CFRP composites are gaining wide research interest because of inherent advanced properties like
low weight-to-volume ratio, high strength, fracture toughness as well as stiffness. Therefore, researchers have
become more concerned towards assessing favorable process parameters while machining of those composites.
Fung and Kang (2005) utilized Taguchi method and PCA analysis for optimizing the injection-molding process for
understanding friction properties of fiber-reinforced polybutylene terephthalate composites. Palanikumar et al.
(2006) attempted to assess the influence of machining parameters on the machining of GFRP composites by
utilizing the fuzzy logic concept. Rajasekaran et al. (2011) investigated the influence of machining parameters to
obtain a good surface finish in turning of CFRP and to predict the surface roughness values using fuzzy linguistic
modeling. Although considerable extent of research has been carried out to study the machining and machinability
aspects of composites with a variety of prediction-modeling/optimization techniques; an attempt has also been
made in this paper to evaluate optimal machining process environment in machining of CFRP composites by
Page 36 of 89
developing a novel multi-objective efficient optimization module integrating Desirability Function, PCA, Grey
Relation theory in combination with Taguchi’s optimization philosophy.
2. EXPERIMENTATION
2.1 Work piece and tool material
Sample of carbon fibered reinforced polymer (CFRP) bars having dimension of diameter 50 mm and
length of 150 mm has been used as work-piece material. Single point HSS tool of 3-X 10% cobalt has
been used during experiments.
3. PROPOSED METHODOLGY
Page 37 of 89
r
yˆ y min
d i Higher-is-Better (HB)
y max y min
r
yˆ y max
d i Lower-is-Better (LB) (2)
y
min y max
Here y min denotes the lower tolerance limit of ŷ , the y max represents the upper tolerance limit of ŷ and r
represents the desirability function index (Datta and Mahapatra, 2010). Table 3 represents individual
desirability values corresponding to each performance characteristics.
Assess the Eigen value k and the corresponding Eigen vector k k 1, 2,3,......... .n from the correlation matrix
formed by all the quality characteristics (Table 4) and also compute principal component scores of the normalized
reference sequence and comparative sequences (Table 5) using the equation shown below:
n
Yi (k ) X i* ( j ) kj , i 0,1,2.........,m, k 1,2,3.............., n (3)
j 1
*
Here, Yi (k ) is the principal component score of the kth element in the ith series. Let, X i ( j ) be the normalized
value of the jth element in the ith sequence, and kj is the jth element of the Eigen vector k .
Step 4: Application of grey analysis for evaluating overall grey relation grade
Individual grey coefficient has been assessed by using as:
mx
ij min (4)
0i j max
Here, 0i ( j ) y 0 ( j yi ( j )) , min mini min j 0i j , max maxi max j 0i j , i 1,2,........,m
j 1,2,.......n 0,1 the distinguishing coefficient, usually, 0.5
Table 6 presents the individual grey coefficient and computed overall grey relation grade.
Page 38 of 89
Finally, Taguchi method has been adopted for evaluating the optimal machining condition as N2 f 2 d1O3 . It
has been observed that predicated S/N ratio corresponds to the highest value amongst all computed S/N
ratios. Therefore, quality (as well as productivity) has been improved (optimized) by this method.
4. CONCLUSIONS
In order to attain best quality characteristics and satisfactory process performance yield during turning of
CFRP composites it is indeed essential to optimize the machining parameters. The present study proposed
an integrated multi-objective optimization philosophy for assessing the optimal parametric combination in
machining of CFRP composites. PCA is a method for reducing the space dimension of samples and delete
redundant information and grey relative degree has been introduced here to deal with small sample data
instead of relative coefficient method. The aforesaid approach can effectively be used for continuous
quality improvement and offline quality control in any manufacturing/production process involving
multiple performance evaluation indices.
REFERENCES
1. Fung C.P. and Kang P.C., “Multi-response optimization in friction properties of PBT composites using
Taguchi method and principle component analysis”, Journal of Materialsand Process Technology170,
602 (2005).
2. Palanikumar K., Karunamoorthy L., Karthikeyan R., Latha B., “Optimization of machining parameters
in turning GFRP composites using a carbide (K10) tool based on the Taguchi method with fuzzy
logics”, Metals and Materials International12, 483 (2006).
3. Li Z. L., Chu P. L., Zheng H. Y., Lim G. C., “Process development of laser machining of carbon fibre
reinforced plastic composites”, SIMTech technical reports 10, 10 (2009).
4. Rajasekaran T., Palanikumar K., Vinayagam B. K., “Application of fuzzy logic for modeling surface
roughness in turning CFRP composites using CBN tool”, Production Engineering and
ResearchDevelopment5, 191(2011).
5. Datta S. and Mahapatra S. S., “Use of desirability function and principal component analysis in grey-
Taguchi approach to solve correlated multi-response optimization in submerged arc welding”, Journal
of Advanced Manufacturing Systems9, 117 (2010).
ACKNOWLEDGEMENT
The research has been supported by DST funded Fast track Project. [Sanction Ref. No.:
SR/FTP/ETA-0140/2011 Dated 21 November 2011]
Table 1. Process parameters and Domain of experiment
Sl. No. Process parameters Notation Unit Level 1 Level 2 Level 3
1 Spindle Speed N RPM 605 787 1020
2 Feed rate f mm/rev. 0.06 0.07 0.08
3 Depth of cut d mm 0.9 1.2 1.5
4 Orientation o degree 45 60 90
Table 2. Design of experiment (L9 OA) and Experimental Data
Page 39 of 89
N f d O MRR Ra Fx Fy Fz
(mm3/min) (µm) (kgf) (kgf) (kgf)
605 0.06 0.9 45 2412.851 3.092333 0.61 0.57 0.83
605 0.07 1.2 60 9318.136 5.606 2.93 3.97 2.78
605 0.08 1.5 90 9304.806 8.166667 6.08 8.21 3.98
787 0.06 1.2 90 4452.443 5.320667 1.87 2.67 1.53
787 0.07 1.5 45 8451.643 4.785667 2.78 4.1 2.11
787 0.08 0.9 60 10037.99 7.147667 4.36 5.15 2.74
1020 0.06 1.5 60 39112.18 10.049 10.61 13.25 3.98
1020 0.07 0.9 90 3425.981 7.446 2.31 2.17 1.04
1020 0.08 1.2 45 11864.29 9.440667 6.99 8.51 2.49
Table 3. Normalized Experimental Data
N mrr N Ra N Fx N Fy N Fz
0 1 1 1 1
0.188158 0.638668 0.768769 0.731861 0.380952
0.187795 0.27058 0.453453 0.397476 0
0.055576 0.679684 0.874875 0.834385 0.777778
0.164548 0.756588 0.783784 0.721609 0.593651
0.207773 0.417058 0.625626 0.638801 0.393651
1 0 0 0 0
0.027606 0.374173 0.830831 0.873817 0.933333
0.257537 0.087446 0.362362 0.373817 0.473016
Table 4. Eigen values and Eigen vector
Table 5. Major Principal Components and corresponding Quality loss
Page 40 of 89
0.690122 -0.42364 -0.44454 1.405878 0.536360298 1.40946
1.867879 -1.44728 -1.72652 0.228121 0.48728037 0.127476
1.720313 -1.19022 -1.44952 0.375687 0.230218508 0.404482
1.189436 -0.83302 -1.03779 0.906564 0.126979954 0.816214
-0.323 0.886 0.331 2.419 1.845999941 2.185
1.648544 -1.42706 -1.77953 0.447456 0.467062575 0.074472
0.589319 -0.39972 -0.72569 1.506681 0.560284378 1.128314
Table 6. Grey relation coefficients and corresponding S/N ratios
Grey 1 Grey 2 Grey 3 Overall grey SNRA1 PSNRA1
0.870765 0.525496 0.804445 0.733569 -2.6912 2.27847
0.656033 1 0.652441 0.769491 -2.2759
0.351826 0.665153 0.441487 0.486155 -6.2645
0.999999 0.690929 0.952174 0.881034 -1.1001
0.812458 0.866874 0.761773 0.813702 -1.7907
0.48514 0.965628 0.587234 0.679334 -3.3583
0.225881 0.333333 0.333333 0.297516 -10.5298
0.744547 0.702137 1 0.815562 -1.7709
0.333333 0.653273 0.500337 0.495648 -6.0965
Page 41 of 89
Fig. 1. Evaluation of optimal parametric combination
Page 42 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
Paper ID
ICAME2013 S3/07
ABSTRACT
Recently, the use of natural fibers as reinforcement for composites is drawing more and more research attention.
Over hundreds of years jute has been used for preparing bags, ropes and beds etc. In developing countries, the
diversification of jute fibers from their traditional markets to other potential sectors like furniture and building has
gained interest as a substitute of wood. The objective of the present work is to investigate the physical and
mechanical behaviour of needle-punched nonwoven jute fiber reinforced composites. The composites were
fabricated by simple hand lay-up technique. Effect of fiber loading on the properties like density, hardness, tensile,
flexural, inter laminar shear and impact strength the composites is studied. The experimental result reveals that
mechanical properties are significantly influenced by the fiber content. It has been observed that mechanical
properties of the composites increase with the increase in fiber loading.
1. INTRODUCTION
An essential condition for most of the engineering material is that, they must possess good strength and stiffness
along with sufficient toughness. This necessity can be full-filled by the man-made composites as they show crack-
stopping capability which makes them very attractive for structural and semi-structural applications (Stocchi et al.,
Page 43 of 89
2007). However, various ecological concerns and government regulations limits the use of synthetic fibers like glass
and carbon (Vilaseca et al., 2007, Tao et al., 2009, Jústiz-Smith et al., 2008). The synthetic fibers not only require
more energy for production but are also expensive than the natural fibers. Renewable fibers like flax, hemp, jute
and sisal has good mechanical properties and can compete with the glass fiber in terms of specific strength and
modulus (Seki, 2009). The natural fibers possess numerous advantages over the synthetic fibers like low density,
low cost, high toughness, competitive specific mechanical properties, low abrasiveness, biodegradability and ease
of separation (Lee and Wang, 2006, González et al., 2011).
Jute also called as the golden fiber from eastern India and Bangladesh is one of the largely available agro-fibers has
high tensile strength and low elongation at break (Mohanty et al., 2000). It has been used for hundreds of years for
many applications such as bags, ropes and bed etc. Now-a-days the diversification of the jute fibers from their
traditional markets to other prospective sectors like furniture and building has gained interest as a substitute of
wood in developing countries (Singh et al., 2000). Fibers like jute and sisal are renewable, non-timber based
materials could reduce the use of traditional materials such as minerals, woods and plastics for some applications
and has great potential of producing jobs in the rural sector (Alves et al., 2010).
Nonwoven fabrics are sheet or web of directional or randomly oriented fiber which are bonded by cohesion,
friction or adhesion. They provide low-cost reinforcement for composites. Needle-punching technique involves an
array of the barbed needles which are pushed or penetrated through the nonwoven web to form fiber
entanglements and 3D fiber orientation (Hao et al., 2012). Some fibers are hold by barbs and their orientation is
changed as they transfer into the vertical plane of the ensuing fabric (Senguta et al., 2008). The needle-punching of
the fibrous web leads to the formation of a coherent and self-locking material (Tejyan et al., 2012). Needle-
punched nonwoven composites offer good compressive, shear and interlaminar properties (Wang, 1999).
To this end, the present work is undertaken to study the effect of fiber loading on the physical and mechanical
behaviour of the needle-punched nonwoven jute fiber reinforced epoxy composite.
2. EXPERIMENTAL DETAILS
Needle-punched nonwoven jute fiber mats were used as a reinforcing material for the present study. Epoxy LY556,
chemically belonging to the ‘epoxied’ family was used as a binding agent. The epoxy resin (density 1.15 gm/cm3)
and the corresponding hardener were mixed in the ratio of 10:1 as recommended. The composites with five
different compositions (fiber content of 0–48 wt.-% in steps of 12 wt.-% complemented by resin material) were
prepared using simple hand lay-up technique. The specimens were kept for curing under a load of 50 kg at room
temperature for approximately 24 h. After proper curing these composites were cut into required dimension for
physical and mechanical tests.
Page 44 of 89
The theoretical density of the composite in term of weight fraction was evaluated by the relation proposed by
Agarwal and Broutman (1990), shown in Eq. (1).
1
ct
f f Wm / m
W /
(1)
where, W and ρ denotes the weight fraction and density, respectively. The suffix ct, f and m represent the
composite, fiber and matrix, respectively. The actual density (ρex) of the composite can be determined
experimentally by simple water immersion technique. The void fraction ( v ) of the composites is calculated by
using the Eq. (2):
ct ex
v (2)
ct
Hardness (HR-B) measurement is done using a Rockwell hardness tester. Tensile test is performed using universal
testing machine Instron 1195 as per the ASTM D 3039-76 test standards. During the test uniaxial load is applied
through both the ends. A three point bend test was carried out to determine the flexural strength and modulus of
the composites using universal testing machine Instron 1195 at a crosshead speed of 10 mm/min. Interlaminar
shear strength (ILSS) of the nonwoven composites is obtained by conducting experiment on same equipment at a
crosshead speed of 10 mm/min. Low velocity impact tests as per the ASTM D256 test standards were performed
in order to obtain the impact strength of the prepared composites.
The theoretical density, experimental density and the corresponding void fraction of the composites is represented
in Table 1. The presence of voids in composites significantly affects its physical and mechanical properties. It is
observed that the void fraction of the composite increases with increase in fiber content. The similar trend is also
observed by previous researchers (Dhal and Mishra, 2013, Gangil et al., 2012).
Theoretical Expt.
g/cm3 g/cm3
Page 45 of 89
NJFE -3 Epoxy + 24 wt.-% Jute Fiber (NP) 1.162 1.124 3.270
The measured hardness value of the composites with different fiber loading is shown in Figure 1. The test result
shows that with increase in fiber loading the hardness of the composites increases. The increase in hardness is due
to brittle nature of lignocellulosic fiber (Chand and Jhod, 2008). Similar observation of improvement in the
hardness of composites with the inclusion of viscose fiber based needle-punched nonwovens in the epoxy matrix
has been reported by researchers (Patnaik and Tejyan, 2012). The composite with 48 wt.-% fiber loading exhibit
maximum hardness of 82 HRB among all set of composites under the study.
85
80
75
Hardness (HRB)
70
65
60
55
50
45
40
0 12 24 36 48
Needle-punch fiber loading (wt.-%)
The variation of the tensile strength and modulus of needle-punched nonwoven jute composites with different
fiber loading is shown in Figure 2. It is clearly visible that both tensile strength and modulus are improving with
increase in fiber loading. This shows an effective and uniform stress transfer within the composite after the
incorporation of fibers into matrix. Similar observations have also been made by John and Anandjiwala (2009) in
case of nonwoven flax reinforced polypropylene composites. It has been reported in their study that the tensile
modulus depends mainly on the fiber volume fraction and not on the physical structure of the fibers. It is also
observed that the composite with 48 wt.-% fiber loading exhibits better tensile strength and modulus as compared
to other composites.
Page 46 of 89
6.4 3.5
135 55
5.6
120 50 3.0
4.8
Tensile strength (MPa)
Tensile modulus(GPa)
Figure 3 illustrates the effect of fiber loading on flexural behaviour of composites. The flexural strength and
modulus of composite decreased at 12 wt.-% fiber loading but further addition of fiber in the matrix result in
improved flexural properties, as it increased in case of NJFE-3, NJFE-4 and NJFE-5. Similar trend is also observed by
White and Ansell (1983) in case of straw-reinforced polyester composites. The initial reduction in flexural
properties may be due to the weak interfacial bonding. But, the further addition of fiber improves the flexural
strength of composite. This may be due to favorable entanglement of the polymer chain with reinforcement which
has overcome the weak fiber matrix adhesion with increase in fiber loading (Rahman et al., 2009). Composite with
48wt.-% fiber loading has maximum flexural strength and modulus as compared to all the other set of composites
under the present study.
Effect of fiber loading in ILSS of composites is shown in Figure 4. It is observed from the figure that composite with
12 wt.-% fiber loading exhibit low ILSS as compared to other samples. Further addition of fibers in the matrix
results in improvement of ILSS of the composites. It is found that NJFE-4 composite exhibit slight improvement in
ILSS, however the ILSS of NJFE-5 composites improved by 29 % when compared to neat epoxy. Cheon and Lee
(1999) also reported a slight decrease and then increase in ILSS property of silane treated glass reinforced
polyester composites with the increase in fiber volume fraction. Figure 5 depicts the effect of needle-punch jute
fiber loading on the impact strength of composites. It is observed from the figure that the impact strength of
needle-punched nonwoven jute composite increased with increase in fiber loading. Similar trend of increase in
impact strength with increase in needle-puched nonwoven fiber loading has also been reported by few researchers
(Patnaik and Tejyan, 2012, Hargitai and Rácz, 2005). The impact failure of composites occurs mainly by factors such
as fiber pull out, fiber and/or matrix fracture and fiber/matrix debonding. Fiber pullout dissipates more energy
compared to fiber fracture. The fiber fracture is common in composites with strong interfacial bonding, whereas
occurrence of fiber pullout is a sign of weak bond. The load applied on composite, transfers to the fibers by shear
may exceed the fiber-matrix interfacial bonding strength and debonding occurs. When the stress level surpasses
Page 47 of 89
the fiber strength, fiber fracture takes place (Özturk, 2010). The fractured fibers may be pulled out of the matrix,
resulting in energy dissipation.
5.0
Inter-laminar shear strength (MPa)
64
4.5
56 4.0
3.0
40
2.5
32
2.0
24 1.5
1.0
16
0 12 24 36 48 0 12 24 36 48
Needle-punch fiber loading (wt.-%) Needle-punch fiber loading (wt.-%)
Figure 4. Effect of needle-punch jute fiber loading on Figure 5. Effect of needle-punch jute fiber loading on
inter-laminar shear strength of composites impact strength of composites
4. CONCLUSIONS
From the study of physical and mechanical behaviour of needle-punched nonwoven jute fiber reinforced epoxy
composites following conclusion can be drawn:
1. The significant effect of fiber loading on physical and mechanical behaviour of composites.
2. The void fraction of composites increases with increase in fiber loading.
3. The tensile strength and modulus increases with increase in fiber loading of the composites.
Composites with 48 wt.-% fiber loading shows better tensile strength and modulus.
4. With the incorporation of fibers, improvement in the flexural properties of needle-punched
nonwoven composite is observed. Composite with 48 wt.-% fiber loading exhibit maximum
flexural strength and modulus as compared to other composites under present study.
5. Short beam shear test revealed an increase of 29 % in interlaminar shear strength of NJFE-5
composites (i.e. 48 wt.-% fiber loading) as compared to neat epoxy resin.
6. Improvement in impact strength of the composite is also observed with the increase in fiber
loading.
REFERENCES
5. Agarwal B.D., Broutman L.J., “Analysis and performance of fiber composites”, John Wiley and Sons, New
York, pp. 58-59 (1990)
6. Alves C., Ferrão P.M.C., Silva A.J., Reis L.G., Freitas M., Rodrigues L.B., Alves D.E., “Ecodesign of automotive
components making use of natural jute fiber composites”, Journal of Cleaner Production, 18, 313 (2010)
7. Chand N., Jhod B. D., “Mechanical, electrical, and thermal properties of maleic anhydride
modified rice husk filled pvc composites”, Bioresources, 3, 1228 (2008)
Page 48 of 89
8. Cheon S. S., Lee D. G., “Impact properties of glass fiber composites with respect to surface treatment and
fiber volume fraction”, Proceedings ICCM-12, Europe, (1999)
9. Dhal J. P., Mishra S.C., “Processing and properties of natural fiber-reinforced polymer composite”,
Journal of Materials, 2013, 1 (2013)
10. Gangil B., Patnaik A., Kumar A., Kumar M., “Investigations on mechanical and sliding wear behaviour of
short fibre-reinforced vinylester-based homogenous and their functionally graded composites”, Journal of
Materials Design and Applications, 226, 300 (2012)
11. González D., Santos P., Parajó J. C., “Manufacture of fibrous reinforcements for biocomposites and
hemicellulosic oligomers from bamboo”, Chemical Engineering Journal, 167, 278 (2011)
12. Hao A., Zhao H., Jiang W., Yuan L., Chen J. Y., “Mechanical properties of kenaf/polypropylene nonwoven
composites”, Journal of Polymers and the Environment, 20, 959 (2012)
13. Hargitai H., Rácz I., “Development of hemp fibre-PP nonwoven composites”, Proceeding of the 8th
Polymers for Advanced Technologies International Symposium, Budapest, Hungary, 13-16 September
(2005)
14. John M. J., Anandjiwala R. D., “Chemical modification of flax reinforced polypropylene composites”,
Composites: Part A, 40, 442 (2009)
15. Jústiz-Smith N. G., Virgo G. J., Buchanan V.E., “Potential of Jamaican banana, coconut coir and bagasse
fibres as composite materials”, Materials Characterization, 59, 1273 (2008)
16. Lee S., Wang S., “Biodegradable polymers/bamboo fiber biocomposite with bio-based coupling agent”,
Composites: Part A, 37, 80 (2006)
17. Mohanty A.K., Khan M.A., Hinrichsen G., “Influence of chemical surface modification on the properties of
biodegradable jute fabrics—polyester amide composites”, Composites: Part A, 31, 143 (2000)
18. Özturk S., “Effect of fiber loading on the mechanical properties of kenaf and fiberfrax fiber-reinforced
phenol-formaldehyde composites”, Journal of Composite Materials, 44, 2265 (2010)
19. Patnaik A., Tejyan S., “Mechanical and visco-elastic analysis of viscose fiber based needlepunched
nonwoven fabric mat reinforced polymer composites: Part I”, Journal of Industrial Textiles, 0, 1 (2012)
20. Rahman M. R., Huque M. M., Islam M. N., Hasan M., “Mechanical properties of polypropylene composites
reinforced with chemically treated abaca”, Composites: Part A, 40, 511 (2009)
21. Seki Y., “Innovative multifunctional siloxane treatment of jute fiber surface and its effect on the
mechanical properties of jute/thermoset composites”, Materials Science and Engineering A, 508, 247
(2009)
22. Senguta S., Chattopadhyay S.N., Samajpati S., Day A., “Use of jute needle-punched nonwoven fabric as
reinforcement in composite”, Indian journal of Fibre & Textile Research, 33, 37 (2008)
23. Singh B., Gupta M., Verma A., “The durability of jute fibre-reinforced phenolic composites”, Composites
Science and Technology, 60, 581 (2000)
24. Stocchi A., Lauke B., Vázquez A., Bernal C., “A novel fiber treatment applied to woven jute fabric/vinylester
laminates”, Composites: Part A, 38, 1337 (2007)
25. Tao Y., Yan L., Jie R., “Preparation and properties of short natural fiber reinforced poly (lactic acid)
composites”, Transactions of Nonferrous Metal Society of China, 19, 651 (2009)
26. Tejyan S., Patnaik A., Rawal A., Satapathy B. K., “Structural and mechanical properties of needle-punched
nonwoven reinforced composites in erosive environment”, Journal of Applied Polymer Science, 123, 1698
(2012)
27. Vilaseca F., Mendez J.A., Pèlach A., Llop M., Cañigueral N., Gironès J., Turon X., Mutje P., “Composite
materials derived from biodegradable starch polymer and jute strands”, Process Biochemistry, 42, 329
(2007)
28. Wang Y., “Effect of consolidation method on the mechanical properties of nonwoven fabric reinforced
composites”, Applied Composite Materials, 6, 19 (1999)
29. White N. M., Ansell M. P., “Straw-reinforced polyester composites”, Journal of Materials Science, 18, 1549
(1983)
Page 49 of 89
Page 50 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
Paper ID
ICAME2013 S3/O16
S. D. Kulkarni
Department of Civil Engineering, College of Engineering Pune, Pune 411005, India
sdk.civil@coep.ac.in
ABSTRACT
In this work the four node quadrilateral element DKZIGT developed earlier by the author based on third order
zigzag theory for the analysis of composite plates is tested for its performance for the static analysis of the
moderately thick to thick functionally graded plates. The element DKZIGT has seven degrees of freedom per node.
The plates have isotropic, two-constituent material distribution through the thickness. The modulus of elasticity is
assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents.
Poisson’s ratio is assumed to be constant. In finite element mesh, the number of layers in the thickness direction is
considered to simulate the variation of the material properties. The material properties are constant in a layer but
vary from layer to layer. The finite element results for various values of the volume fraction exponent for
deflection and stresses are compared with the available results. It is observed that the performance of the DKZIGT
element is quite satisfactory. Additional results for all-round clamped plates with different span to thickness ratios
are also presented.
1. INTRODUCTION
In recent years use of functionally graded materials is increasing in many engineering fields. Functionally graded
materials are preferred because of the gradual change of material properties through the thickness. Many
researchers have investigated the behaviour of the functionally graded plates and shells using analytical as well as
finite element models. The analytical and finite element solutions for the static response of functionally graded
rectangular plates based on third-order shear deformation plate theory are presented by Reddy (Reddy, 2000).
Zenkour presented generalized shear deformation theory for bending analysis of functionally graded plate plates
(Zenkour, 2006). Mantari et al. have obtained the bending response of functionally graded plates by using a new
higher order shear deformation theory developed by them (Mantari et al., 2012). Wu et al. have used RMVT-based
Page 51 of 89
meshless collocation and element-free Galerkin methods for the quasi-3D analysis of multilayered composite and
FGM plates and obtained solutions that are in excellent agreement with 3D solutions (Wu et al., 2011). Recently
Neves et al. have analysed functionally graded plates using a quasi-3D higher-order shear deformation theory and
a meshless technique (Neves et al., 2013).
In the present paper for the first time the finite element solution is obtained for the static response of functionally
graded plates using a four-node improved discrete Kirchhoff quadrilateral (DKZIGT) element developed earlier by
the author (Kapuria and Kulkarni, 2007) based on third order zigzag theory by successfully circumventing the
problem of C1 continuity which is encountered in the FE formulation. This element (DKZIGT) has seven degrees of
freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at
the mid-surface and can be used for plates other than rectangular shape. In this work moderately thick and thick
functionally graded plates, are analysed for static response using the DKZIGT element. It is assumed that the plate
has isotropic, two-constituent material distribution through the thickness. The modulus of elasticity is assumed to
vary according to a power-law distribution in terms of the volume fractions of the constituents. Poisson’s ratio is
assumed to be constant. In finite element mesh, the number of layers in the thickness direction is considered to
simulate the variation of the material properties. The material properties are constant in a layer but vary from
layer to layer. The finite element results for various values of the volume fraction exponent for deflection and
stresses are compared with the available results based on various theories for thick and moderately thick plates.
Additional results for all-round clamped boundary condition with different span to thickness ratios are also
presented which would act as reference for future research. It is observed that the performance of the DKZIGT
element is quite satisfactory.
where Rk(z) is a 2 × 2 matrix of layer-wise function of z, and
u x u0 x w0, x 0 x
u , uo , w0d , 0 . (2)
u
y u
oy
w0, y
0 y
A quadrilateral plate element with four physical nodes each having seven kinetic degrees of freedom (DOF) namely
u0 x , u0 y , 0 x , 0 y , 0 x , 0 x is developed based on the above theory is shown in Fig. 2.
y
Ceramic
Page 52 of 89
h
3
4
z
Metal y
Lth Layer
x
ξ
x
b
1st Layer 1
a 2
The requirement of C1 continuity of the interpolation functions of the deflection is circumvented by using the
improved discrete Kirchhoff quadrilateral (IDKQ) functions, originally proposed for isotropic thin Kirchhoff plate by
(Jeychandrabose et al., 1987) and successfully applied by the author (Kapuria and Kulkarni, 2007) to ZIGT of (Shu
and Sun, 1994) for elastic anisotropic plates.
3. NUMERICAL RESULTS
The present FE formulation based on third order zigzag theory of (Shu and Sun, 1994) is assessed by comparing the
results with the available analytical results available in the literature based on various theories for an all round
simply supported square plate of functionally graded material consisting of aluminum and alumina with Young’s
modulus for aluminum 70 GPa and that for alumina 380 GPa. The given plate is considered to be made of 50 layers
with each layer of equal thickness. The functional relationship between Young’s modulus E and z for ceramic and
metal FGM plate is assumed as
k
2z h
E E ( z ) Em ( Ec Em )
2h
where Ec and Em are the corresponding properties of the ceramic and metal, respectively, and k is the volume
fraction exponent. Poisson’s ratio is taken as constant equal to 0.3. For each layer the Young’s modulus is
calculated at the centre of the layer and assumed to be constant for that layer. The results obtained using a
Page 53 of 89
100h3 Ec b 10h3 Ec a b h a b
ux 4
u x 0, , z , w 4
w , , z , x x , , z ,
a q0 2 a q0 2 2 aq0 2 2
h a b h h b
y y , , z , xy xy 0, 0, z , zx zx 0, , z .
aq0 2 2 aq0 aq0 2
A square simply-supported plate is analysed for different values of k for two loading cases namely; a uniformly
distributed load of intensity q0 and a sinusoidal loading equal to q0 sin (Лx/a) sin (Лy/b). The results for the
uniformly distributed loading case are presented in Table 1 for displacements and stresses and are compared with
the results given in (Zenkour, 2006). The results are quite close to those given in (Zenkour, 2006).
h h h h
k Theory ux ( ) w (0) x ( ) xy ( ) zx ( )
4 3 3 6
The results for sinusoidal loading case are given in Table 2 and are compared with those given in (Zenkour, 2006),
(Wu et al., 2011), (Mantari et al., 2012) and (Neves et al., 2012). It is observed that for this case also the results are
in close agreement with the results given in the references mentioned above.
Page 54 of 89
h h h h
k Theory ux ( ) w (0) x ( ) xy ( ) zx ( )
4 3 3 6
Fig. 3 shows the variation of stresses under sinusoidal loading through the thickness of an all-round simply-
supported, square plate with S = 5 and k = 4. The results are compared with the quasi 3D results of (Wu et al.,
2011) and show excellent agreement with those results for in-plane and transverse stresses.
Page 55 of 89
Fig. 3: Variation of stresses through the thickness for a square plate
The variation of stresses under uniformly distributed loading through the thickness of a rectangular simply
supported plate with various aspect ratios (a/b) and for k = 2 is presented in Fig. 4. The results are compared with
the results of (Zenkour, 2006) and show good agreement with those results except for transverse shear stress zx .
This may be due to the fact that the present results are close to quasi 3D results of (Wu et al., 2011) indicating the
superiority of ZIGT.
Additional results for an all-round clamped plate for deflection w and normal stress x are presented in
Table 3 for sinusoidal loading case. These results can be quite useful to the researchers working in this area.
Page 56 of 89
K Entity S=5 S = 10 S = 20
4. CONCLUSIONS
The DKZIGT element formulated for the analysis of composite plates earlier by the author has been used for the
analysis of functionally graded plate by considering it as a layered plate. The results for in-plane displacement,
central deflection and in-plane normal and shear stresses as well as transverse shear stresses for an all-round
simply-supported square plate are compared with those available in the literature for two loading cases namely;
uniformly distributed loading and sinusoidal loading. The results are particularly quite close to the quasi 3D results
which are considered to be very accurate. It is also observed that the variation of stresses through the thickness
obtained using DKZIGT element for an all-round simply supported thick plate closely match with that obtained by
quasi 3D theory available in literature thus indicating the excellent performance of the DKZIGT element for thick
and moderately thick plates. Additional results for an all-round clamped square plate with different span to
thickness ratios are also presented which will be useful for further research.
ACKNOWLEDGMENTS
Page 57 of 89
This research is financially supported by Department of Civil Engineering, Government College of Engineering
Pune.
REFERENCES
5. Jeychandrabose C., Kirkhope J., Meekisho L. “An improved discrete Kirchhoff quadrilateral thin-plate
bending element”, Int. J. Numer. Methods Engg. 24, 635–654 (1987).
6. Kapuria S. and Kulkarni S. D. “An improved discrete Kirchhoff quadrilateral element based on third-order
zigzag theory for static analysis of composite and sandwich plates”, Int. J. Numer. Methods Engg. 69, 1948–
1981 (2007).
7. Mantari J. L., Oktem A. S., Soares C. G. “Bending response of functionally graded plates by using a new
higher order shear deformation theory”, Compos. Struct. 94, 714–723 (2012).
8. Neves A. M. A., Ferreira A. J. M., Carrera E., Cinefra M., Roque C. M .C., Jorge R. M. N., Soares C. M. M.
“Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a
quasi-3D higher-order shear deformation theory and a meshless technique”, Compos. Part B. 44, 657-674
(2013)
9. Reddy J. N. “Analysis of functionally graded plates”, Int. J. Numer. Methods Engg. 47, 663-664 (2000).
10. Shu X. and Sun L. “An improved simple higher-order theory for laminated composite plates”, Comput.
Struct. 50, 231-236 (1994).
11. Wu C. P., Chiu K. H., Wang Y. M. “RMVT-based meshless collocation and element free Galerkin methods for
the quasi-3D analysis of multilayered composite and FGM plates”, Compos. Struct. 93, 923-943 (2011).
12. Zenkour A. M. “Generalized shear deformation theory for bending analysis of functionally graded plates”,
Appl. Math. Modl. 30, 67-84, (2006).
Page 58 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S3/O13
ABSTRACT
In this study Taguchi approach is used to predict the optimum parameters that influence the wear rate of Al5083
composite reinforced with Silicon carbide (SiC). Taguchi approach is an efficient and effective experimental
method in which a response variable can be optimized, given various control and noise factors, using fewer
experiments than a factorial design. Present study uses sliding speed, load, sliding distance and percentage of SiC
as control factors. An orthogonal array of L9 was used; signal-to-noise ratio and Analysis of Variance (ANOVA)
analysis were carried out to identify the significant factors affecting the wear rate and the optimal condition owing
to lower wear rate. The liquid metallurgical technique has been selected for preparation of composite specimens.
The cast prepared composite specimen is later compared with unreinforced Al5083 alloy. Finally, confirmation
tests verified that the Taguchi approach was successful in predicting optimum parameters that influence the wear
rate.
Keywords: Metal matrix composites, Liquid metallurgy techniques, Dry sliding wear, Taguchi technique,
1. INTRODUCTION
Aluminium alloys are preferred engineering material for automobile, aviation industries for various high
performance components that are being used for various applications owing to lower weight and excellent thermal
Page 59 of 89
conductivity properties. Aluminium alloy reinforced with ceramic particles exhibit superior mechanical properties
to unreinforced Al alloys and hence are candidate for engineering applications. Basavarajappa et al., 2006,
prepared SiCp reinforced with Al2219 (Al-Cu-Mg alloy) by Liquid metallurgy technique- stir casting method and
wear results showed SiCp reinforced in MMC exhibited reduced wear loss than unreinforced alloy. Dhokey and
Rane, 2011, synthesized Al-based composites containing 2% by wt copper reinforced with 2.5 and 5wt% TiB2
composites were made in induction furnace by in situ synthesis process using simultaneous addition of halide
fluxes (K2TiF6 and KBF4). It was observed that overall wear behavior gave reasonably good correlation with
mechanical properties of composites as compared to gray cast iron. Hemanth Kumar et al., 2011, dry sliding wear
and frictional force of the composite material under different loads and Sliding velocities was successfully analyzed
using Taguchi design of experiment. Veeresh Kumar et al., 2011, they presented a review paper and consolidate
some of the aspects of mechanical and wear behavior of Al-MMCs and the prediction of the Mechanical and
Tribological properties of Aluminum MMCs. Mishra et al., 2012, have studied tribological behaviour of aluminium
alloy Al-6061 reinforced with SiC and found that sliding distance has the highest influence followed by load and
sliding speed. Reddy et al., 2012, studied the wear properties of as-cast metal matrix composite of AA7075
reinforced with fly ash particulates of 200 microns in different compositions. An attempt in the present
investigation is to find the influence of wear parameters on dry sliding wear of the composites and to establish
correlation between sliding speed, load, sliding distance and percentage of SiC on dry sliding wear of the
composites.
2. TAGUCHI TECHNIQUES
Taguchi method is a powerful tool for the design of high quality system, Taguchi and Konishi, 1987 .It
provides a simple, efficient and systematic approach to optimize designs for performance characteristics
through the setting of design parameters and reduce the sensitivity of the system performance to source of
variation. This technique is multi-step process, which follows a certain sequence for the experiments to
yield an improved understanding of product or process performance. The Taguchi approach to
experimentation provides an orderly way to acquire data and to analyse the effects of process and material
parameters over some specific response. Thus this method combines experimental and analytical concepts
to determine the parameter with the strongest influence on the resulting response for a significant
improvement in the overall performance. The plan of experiments is generated in Taguchi method by the
use of standard orthogonal arrays, Taguchi, 1993. The experimental results are then analysed by using
analysis of mean and analysis of variance of the influencing factors.
3. EXPERIMENTAL PROCEDURE
3.1 Materials
The matrix material for the present study is Al5083. The chemical composition of the base alloy as found out
by Spectro analysis was 0.0960 wt.% Si, 0.161 wt.% Fe, 0.0270 wt.% Cu, 0.600 wt.% Mn, 3.92 wt.% Mg, 0.0790
wt.% Cr, 0.00080 wt.% Ni, 0.0270 wt.% Zn, 0.0660 wt.% Ti, 0.002 wt.% Sb, 0.001 wt.% Sn, balance was Aluminum.
SiC is used as reinforcement material in the preparation of composites. The particles size of the reinforcing
material was about 25 μm. The SiC particle reinforcement was done by 3, 5 and 7 wt pct.
Page 60 of 89
The liquid metallurgy technique was used to prepare composite
specimens as shown in fig.1. This method is most economical to fabricate
composites with discontinuous fibers or particulates. In this process, matrix
alloy (Al- 5083) was firstly superheated over its melting temperature and
then temperature was lowered gradually below the liquids temperature to
keep the matrix alloy in the semi-solid state. At this temperature, the
preheated (800°C) SiC particles were introduced into the slurry and
mixed. The composite slurry temperature was increased to fully liquid state
and stirring was continued for 10 mins at an average stirring speed of 500 rpm. The melt was then superheated
above liquidus temperature (760°C) and finally poured into preheated permanent metallic moulds which were C-
clamped mould. The pouring temperature was maintained at 7000C. The melt was then allowed to solidify the
moulds.
Page 61 of 89
Fig.2 DUCOM pin-on-disc sliding wear testing apparatus
The experiments were conducted as per orthogonal array and the wear results obtained are shown in table 2.
The analyses of the experimental data were carried out using MINITAB 16 software, which is specially used for DOE
applications. The experimental results were transformed into signal-to-noise (S/N) ratios.
Table 2 Orthogonal array of Taguchi for wear rate and experimental results
Page 62 of 89
4 0.942 9.81 1000 7 0.111 19.09
5 0.942 29.43 1500 3 2.160 -6.68
6 0.942 49.05 500 5 0.100 20
7 1.570 9.81 1500 5 0.050 26.02
8 1.570 29.43 500 7 0.453 6.87
9 1.570 49.05 1000 3 0.141 17.01
The signal to noise ratio measures the sensitivity of the quality investigated to those uncontrollable factors in
the experiment. The higher value of S/N ratio is always desirable because greater S/N ratio will result in smaller
product variance around the target value (table 3). As mentioned earlier the quality characteristic used in this
study was “Smaller the better”. Based on main effects of S/N ratio, from the fig.3 the optimal combination of
parameters and their levels for achieving minimum wear rate is A3B1C2D2 i.e. sliding speed at level 3 (1.57 m/s),
load at level 1 (9.81 N), sliding distance at level 2 (1000 m) & wt% of SiC at level 2 (5 wt%).
Rank 1 3 4 2
10
0
Mean of SN ratios
-10
-20
0.314 0.942 1.570 9.81 29.43 49.05
Sliding distance wt % of SiC
20
10
-10
-20
500 1000 1500 3 5 7
Page 63 of 89
Fig.3 Main Effect Plot for S/N ratios
4.2 Analysis of Variance and Mathematical model
ANOVA is used to determine the design parameters significantly influencing the wear rate (response). Table 4
shows the results of ANOVA for wear rate. This analysis is evaluated for a confidence level of 95%, i.e. for
significance level of α = 0.05. The results show that the sliding speed (84.46%) has major influence on wear rate,
load (4.65%) & wt% of SiC (8.31%) has moderate influence on wear rate & sliding distance (2.39%) has negligible
influence on wear rate. The ANOVA has resulted in zero degree of freedom for error term, it is necessary to pool
the factor having less influence, for correct interpretation of results. In table 5 shows F-test, if F > 4, then it means
that the change of the design parameter has significant effect on quality characteristic. Table 5 shows pooled
ANOVA table, shows that the pooled error is 2% were important factors are not omitted from experiments.
Multiple linear regression equation is obtained using “MINITAB R16”.
Error 0 - -
Total 8 93.294
The terms that are statistically significant are included in the model. The regression coefficient of the model is
0.82. The equation obtained is as follows
W = 12.4 - 5.22* Sliding speed - 0.0395* Load - 0.00102* Sliding distance -0.539* wt % of SiC (1)
Page 64 of 89
Load 2 4.341 2.171 1.94 4.65
Total 8 93.294
In order to validate the regression model, confirmation wear tests were conducted with parameter levels that
were different from those used for analysis. Optimal combination of parameter and their levels A3B1C2D2
experiment was conducted on pin-on-disc machine. The value of wear rate obtained from experiment was
compared with estimated value from the regression model equation 1 as shown in Table 6. It can be seen from this
Table 9 the difference between experimental results and the estimated results is 0.009. This indicates that the
experimental result of wear rate is close to the estimated value. This verifies that the experimental results are
strongly correlated with the estimated result, as the error is 8.1%.
Table 6 Confirmation wear result and their comparison with regression model
5. CONCLUSION
From the analysis on the results of dry sliding wear of the SiC reinforced metal matrix composites, the following
conclusions can be drawn from the study:
a) Sliding speed is the wear factor that has the highest physical properties as well as statistical influence on
the dry sliding wear of the composites (84.46%), the load (4.65%) & wt% of SiC (8.31%) has moderate
influence on wear rate & sliding distance (2.39%) has negligible influence on wear rate.
b) The coefficient of regression obtained with the multiple regression value of 0.82 shows that the
satisfactory correlation was obtained.
c) The confirmation tests verify that the experimental results are strongly correlated with the estimated
result, as the error is 8.1%.
Page 65 of 89
REFERENCES
1. Basavarajappa S., Chandramohan G., Subramanian R., Chandrasekar A., “Dry sliding wear
behavior of Al2219/SiC metal matrix composites”, Material Science-Poland, 24,357 (2006).
2. Mishra A. Kr., Sheokand R., Dr. R K Srivastava, “ Tribological Behaviour of Al-6061 / SiC Metal
Matrix Composite by Taguchi’s Techniques”, Int. J of Sci. and Res. Pub., 2, (2012).
3. Reddy M. S., Chetty S. V., Sudheer P. , Khaleel A. N. A., “Wear Properties of Aluminium (7075)-Based Metal
Matrix Composites Reinforced with Fly Ash Particulates”, Indian Foundry Journal, 58 , (2012).
4. Veeresh Kumar G. B., Rao C. S. P., Selvaraj N., “Mechanical and Tribological Behavior of Particulate
Reinforced Aluminum Metal Matrix Composites – a review”, J. of Min. & Mat. Cha. & Eng., 10, 59 (2011).
5. Hemanth Kumar.T.R., Swamy.R.P. and Chandrashekar T.K., “Taguchi Technique for the Simultaneous
Optimization of Tribological Parameters in Metal Matrix Composite”, J. of Min. & Materials Cha. & Eng., 10,
1179 (2011).
6. Dhokey N. B. and Rane K. K., “Wear Behavior and Its Correlation withMechanical Properties of TiB2
Reinforced Aluminium-Based Composites, Adv. in Trib.,(2011).
7. Taguchi G., Konishi S., “Taguchi methods, orthogonal arrays and linear graphs, tools for quality
engineering”, Dearborn, MI: American Supplier Institute; pp. 35-38 (1987).
8. Taguchi G., “Taguchi on robust technology development methods”, New York, NY: ASME Press,
pp. 1-40 (1993).
Page 66 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
ICAME2013__S3/O15
A REVIEW PAPER ON FABRICATION OF PARTICULATE ALUMINUM METAL MATRIX
COMPOSITE (PAMC) REINFORCED WITH ALUMINA, SILICON CARBIDE AND GRAPHITE
PARTICLES
ABSTRACT
Piston ring and liner made of particulate aluminum alloy metal matrix composite (PAMC) having
reinforcements of alumina (Al2O3) and silicon carbide (SiC) has shown improvement in the dimensional
stability, mechanical and thermal properties at elevated temperature and strength to weight ratio[1, 13, 15].
Increase in the frictional forces by the addition of reinforcements can be counteracted by addition of 4% to
6% graphite particles by volume [7, 8]. PAMC’s are fabricated from liquid state (LSPT) and solid state
(SSPT) processing techniques. LSPT are simple, flexible, and economic while SSPT are complex, costly,
time consuming but can produce composites with better properties than LSPT [2, 13, 14]. In the present
work, various processing techniques are compared on the basis of cost, product properties and process
parameters. It aims at manufacturing PAMC with graphite particles and studying the effect of composition
on the mechanical, tribological and metallurgical properties of the manufactured composite. It has been
found that stir casting process is the most suitable for the fabrication of composite under study, because
stir casting is simple, flexible, most economic, and can be used for low volume contribution of
reinforcement from 0 to 30%. Stir casting results in homogeneous distribution of the reinforcement
particles in the matrix, which leads to better mechanical and tribological property of the composite
material [2, 10].
Keywords: Piston ring, Particulate aluminum metal matrix composite (PAMC’s), Fabrication of
particulate composite, Stir casting, Tribology.
1. INTRODUCTION
Frictional, inertial and exhaust losses in automobile engine and transmission components contribute almost
50% of the total power distribution [18]. Use of components made of PAMC’s in automobile has shown
about 5% fuel economy by reducing the automotive component weight by about 10% [5]. It makes
component light weight and durable making engine efficient, environment friendly and less costly [18,
19]. Piston ring materials have been continuously evolving to meet the ever-increasing demand of the
performance in modern IC engines. At present, piston rings are made of cast iron, stainless steel and metal
matrix composites (MMC) reinforced with Saffil fiber [18, 19]. Cast iron has lowest coefficient of friction
and wear. It works efficiently at dry lubricating conditions. Stainless steel has high strength, toughness,
elasticity, corrosion resistance than cast iron but has large specific gravity and high coefficient of friction
and wear [19]. MMC’s have high strength, low inertia and wear but its performance is poor at dry
conditions [15, 18]. In quest of manufacturing material having advantages of all the above mentioned
Page 67 of 89
materials, a PAMC with reinforcements such as graphite, SiC and Al2O3 is thought of. It is expected to
have high strength, toughness, elasticity and corrosion resistance along with low coefficient of friction and
wear. Graphite in PAMC acts as dry surface lubricant at elevated temperature, thus reducing lubricating oil
consumption and toxic emissions [2, 8, 18]. Fabrication of the PAMC is affected by low wetability and
varying density of reinforcements which results in weak interfacial bonding, particle segregation, non-
homogeneous distribution and weak composite property [10]. Selection of manufacturing process,
therefore, becomes a challenge in this case. For example In- situ fabrication has limitations due to
uncontrolled interfacial chemical reactions and particle segregation, Infiltration processes and all solid
state processes require large external forces to enhance the wetability between reinforcement particles and
matrix material. Many of the above processes require costly equipments and complex systems.
Comparatively stir casting is simple, flexible most economic and can produce composite with good
interfacial bonding [2].
2. MATERIAL SELECTION
PAMC under study consist of matrix material of aluminum alloy Al6061 whose chemical composition is
shown in the Table 1. Particles of Al2O3, SiC and graphite of mesh size 320 are used as reinforcement.
Table 2 shows various properties of the constituents of PAMC. Wetability is inversely proportional to
contact angle. These particles have low wetability in molten aluminum. Due to density variation light
weight graphite particles float on the molten matrix and comparatively heavy Al2O3 and SiC particles sink
at the bottom of the crucible.
Table 1: Chemical composition (wt.%) of the Al-alloy (Al6061) used in the study.
Si Fe Cu Mn Mg Cr Zn Ti Other Al
0.20 -0.60 0.00-0.35 0.00-0.10 0.00-0.10 0.45-0.90 0.0-0.10 0.00-0.10 0.00-0.10 0.00-0.15 Remainder
Table 2: Properties of various materials
Property Unit Al6061 [3] Al2O3 [1] SiC [1] Graphite [1]
−3
Density (at Room Temperature) g·cm 2.70 3.97 3.22 2.09–2.23
Melting / Sublimation point K 923 2,288 2973 3915
Coefficient of thermal expansion µm/m OC 23.6 7.1 4 2-6
Thermal conductivity W/mK 180 35.6 126 85
Young's modulus GPa 69 370 410 10
Coefficient of friction with self 0.35 [1] 0.30 – 0.50 0.30 – 0.90 0.18
with Steel 0.25 [1] 0.20 – 0.60 0.29 0.18
Wettability with Molten Al Contact angle in 0 ≈100 [14] ≈136 [15] ≈156 [15]
1100OC degree
Page 68 of 89
actions such as mechanical stirring, eddy current, heat convection, magnetic stirring and vibratory stirring
etc. Composite casting having homogenous distribution of reinforcement is obtained by solidification of
molten matrix. Secondary processes such as forging, machining, and extrusion etc. can be used for further
processing due to isotropic behavior of PAMC’s. Following processes fall under this category [2].
In Situ processing: There are several different processes that would fall under this category including
liquid-gas, liquid-solid, liquid-liquid and mixed salt reactions [13]. Reinforcement particles are generated
by allowing these chemical reactions. Gases such as CH4, water vapor, air etc. are used as reactant. Solid
and liquid reactant consists of metals such as Mg, Ti, Br, Cu, Si, Al etc. Quantity, geometry and
distribution of the reinforcement particles are uncontrolled due to uncontrolled rate of chemical reaction.
EX.: 3H2O (Vapor) +2 Al ==) Al2O3 +6H. C+Ti+Al==)TiC+Al [2, 14]
Stir Casting [2, 10]: Figure 1 shows, the matrix material is melted in insulated crucible above its liquid
temperature by using heater. Pretreated reinforcements are poured through hopper. Mechanical stirrer is
used to achieve wetability. Compo-casting is a type of stir casting in which reinforcements are poured into
semisolid matrix to achieve high wetability and to reduce settling time of the particles. High temperature,
motion of matrix, mechanical force and high viscosity are used to increase the wetability of the
reinforcement.
Infiltration [2, 12, 14, 6]: PAMC’s are manufactured by infiltrating molten aluminum alloy through
porous preform made of 30% to 70% reinforcements by volume. Actions such as capitations, vacuum, gas
pressure and die pressure are used to overcome the opposing forces produced by the low wetability and the
micro-pores due to which the melt does not mix with the reinforcement spontaneously. Infiltration process
is known by the method of application of the pressure. Figure 2 shows that the pressure less infiltration is
carried by the capillary action of the molten aluminum alloy into porous preform. Squeeze Casting
Infiltration: Figure 3 shows a porous preform is being infiltrated by molten aluminum alloy by applying
pressure on the inert gas atmosphere with the help of mechanical punch. Gas Pressure Infiltration: Figure 4
shows a constant gas pressure of inert gases such as N2 or Ar gas is applied with the help of the pneumatic
means or mechanical punch. This process is faster, simple and can produce parts with refined
microstructure and with less porous structure
Spray Co-deposition [2, 9, 14]: Figure 5 shows that preheated molten matrix is diffused into small
droplets by using atomizer. Together with the fine powder of the reinforcement it is sprayed on the
substrate with a high velocity. Due to limited movement and time chemical reaction during mixing is less.
This process is mainly used to coat the component with composite coating.
3.2. Solid State Processing Techniques (SSPT)[6, 14]
Matrix and the reinforcement are heated to solidus temperature of the matrix. High viscosity and
secondary processes such as degassing and external forces results in the fabrication of the composite with
non porous structure, homogeneously distributed reinforcement and with close tolerances.
Powder Metallurgy (PM): Figure 6 shows that the powder metallurgy process starts with preparation of
fine powder of the matrix and reinforcement materials. These powders are thoroughly mixed with wetting
agent by blending process. A green dense compact is prepared by the sintering process followed by the
vacuum degassing to remove air bubbles. Secondary processes like hot pressing, extrusion, machining etc.
are applied to prepare the final product.
4. DISCUSSION
Material properties of PAMC depend on the type of fabrication method. The fabrication method selected
depends on desired properties of component. In general selection of fabrication method is governed by
quantity and size of reinforcement particles, size and shape of component, metallurgical, mechanical and
tribological properties required to component and cost. Present study compares the fabrication processes
on the basis of above mention parameters.
Page 69 of 89
Volume of component: SSPT’s are generally suitable for small size components such as sintered bearings
[5]. Size and shape of component is governed by pressure and machine size availability. It is unsuitable to
fabricate component with complex shape [2, 5, 10]. LSPT’s manufacture components with varying size
depending upon the type of process. In-situ process manufactures smaller size components such as
electronic parts [2]. Its major limitation is uncontrolled shape, size and volume fraction of reinforcement
[14]. Infiltration techniques fabricate medium size components such as piston, connecting rod with 30 to
70% volume fraction of reinforcement [14]. Stir casting method is suitable to manufacture the components
from small to large size like shock absorber cylinder [2]. At present in India the maximum quantity
processed by stir casting is 40 Kg/batch [5]. It is also suitable to fabricate component with complicated
shape. Spray co-deposition process do not manufacture 3D component but only used to develop composite
coat on components such as piston ring and liner. This technique is capable of producing high deposition
rates (10 kg/min) with 30 to 70% of reinforcement by volume. The reinforcement size is up to 2-10μm [5].
Metallurgical properties: SSPT works at re-crystallization temperature of matrix, resulting in refined
grain structure, low porosity and homogeneous distribution of the reinforcements. This process fabricates
components having reinforcement particle size of wide range (nano to a few hundred microns) as well as
high percentage of reinforcement by volume (up to 60%). Metallurgical properties in LSPT depend on
type of fabrication method. In-situ process has uncontrolled rate of chemical reaction which results in non-
homogeneous distribution of reinforcement. Stir casting produces component with 30% porosity but it can
be reduced to 5% by mechanical agitation at semisolid stage [10]. The addition of magnesium particles
enhances wetability between reinforcements and matrix material [2, 10]. Faster cooling rates, keep the
matrix cell size small (equal to particle size) resulting in a much more homogeneous distribution of
particles [14]. The microstructure of the composite during infiltration depends on the local solidification
and cooling processes within the preform [14].
Mechanical properties: Less porosity and increased wetability in SSPT’s gives good mechanical
properties to material [6]. Mechanical strength of LSPT component varies with fabrication method. In-situ
process results in poor strength due to varying reinforcement size and high porosity [2]. Stir casting results
in good mechanical properties by controlling porosity and reinforcement quantity. Specific strength in
squeeze casting is superior as compared to that obtained in any another fabrication process [5]. Strength of
component increases with increase in volume fraction of reinforcement in preform.
Tribological properties: SSPT components, powder metallurgy components in particular, have smooth
surface finish which reduces friction and wear [6, 14]. In-situ process has weak bonding between substrate
and the composite which results in poor wear properties to material [2, 14]. In stir casting wear resistance
and coefficient of friction increases with increase in quantity of ceramic reinforcement. Squeeze casting
gives high wear resistance and low thermal expansion to material because of high percentage of
reinforcement.
Cost: High cost of the infrastructure in SSPT limits its commercialization [6, 14]. Initial cost in in-situ
processing is minimal because of few processing components. Stir casting handles tones of material per
batch which reduces overhead and process cost. It can produce large quantity of components in near net
shape. Automation of the stir casting process is simple as a few parameters need to be controlled [2].
Infiltration techniques require preform and continuous constant pressure which makes it costlier. The spray
deposited composites require further consolidation which adds up to the cost [5].
Page 70 of 89
Other parameters to be considered while selecting fabrication process: A major limitation of in-situ
technique is related to the thermodynamic restrictions on the composition and nature of the
reinforcement phase that can form in a given system, and the kinetic restrictions on the shape,
size and volume fraction of the reinforcement that can be achieved through chemical reactions
under a given set of test conditions.[2] Uncontrolled rate of reaction in In-situ processing
techniques makes it unfit for the fabrication of the composite under study. It also requires precise
maintenance of reactant quantity throughout the process. Infiltration process is only one process
among all fabrication methods where porous preform made of reinforcement is required. Preform
requires minimum 30% of reinforcement by volume to withstand the high pressure [6]. Spray Co-
deposition process is unsafe for human health due to high processing temperature and fine spray.
It has to be carried out in sealed chamber [2]. Disadvantage of the process include, formation of
residual porosity, high cost and quantity of the inert gas and waste of material during the
deposition [14]. Stir casting process is simple, economic and flexible. It efficiently works upto 30
% of reinforcement by volume. Reinforcements with very low wettability (contact angle > 100O)
are processed. Table 3 shows comparison of the processes on the basis of various parameters
such as volume % of reinforcement, working temperature, porosity %, post processing, cost etc.
Table 3: Comparison of fabrication processes
In Situ Stir Spray Powder
Parameter Infiltration
Processing Casting Co-deposition Metallurgy
Preform Not Required Not Required Not Required Not Required
Required
Volume % of Uncontrolled <30 30 to 70 10 To 70 30 To 70
Reinforcement
Working Temperature Liquid Liquid Liquid Liquid Solidus
Ease in Operation No Simplest No Yes No
Automation Simple Simple Required Required Required
Complexity of shape Possible Possible Not Not Possible Not Possible
Possible
Porosity % < 70 5 to 30 < 20 7 to 10 2 to 10
Chemical Interaction Uncontrolled Possible Possible Possible Minimum
Post Processing Required Required Depends Not Required Required
Near Net Shape Possible Possible Possible Possible Possible
production
Cost Lowest Lowest High Medium High
Page 71 of 89
Figure 4: Gas Pressure Figure 5: Spray Co-deposition Figure 6: Powder metallurgy
Infiltration
5. CONCLUSION
In present study the aim is to reinforce aluminum alloy with SiC, Al2O3 and graphite particles to
get better mechanical, metallurgical and tribological properties of PAMC. Stir casting is the only
method suitable to manufacture PAMC under study. Stir casting process is simple and cost
effective. Homogeneous distribution of reinforcement in the matrix material which is possible by
controlling process parameters leads to better mechanical and tribological property of the
composite material. It can fabricate components with variable size and complex shape. The
process is simple to automate for mass production.
Infrastructure and machinery required to fabricate composite material by solid state processing
techniques is expensive. In-situ process consists of uncontrolled rate of chemical reaction
between matrix material and reactant which affects the material properties. Infiltration processes
are not suitable because of multi reinforcements in present study. Spray co-deposition is
applicable to develop composite coat on component.
REFERENCES
1. ASM Metal handbook, Volume 18, Friction, Lubrication, and Wear Technology, ASM
International, The Materials Information Company, (1992)
2. ASM Metal handbook, Volume 21, Composite, ASM International, The Materials
Information Company, (2001), Page No. 1359 to 1372,
3. ASM Metal handbook, Volume 2, Properties and selection: Nonferrous Alloys and
Special Purpose Materials, ASM International, The Materials Information Company,1990
4. A. Ramesh, J. N. Prakash, A. S. Shiva Shankare, Comparison of the Mechanical
Properties of AL6061/Albite and AL6061/Graphite Metal Matrix Composites, Journal of
Minerals & Materials Characterization & Engineering, Vol. 8, No.2, pp 93-106, 2009
5. B.C. Pai, R.M.Pillai and K.G.Satyanarayana, Light metal matrix composites - present
status and future strategies, RegionalResearch Laboratory, Thiruvananthapuram, Trans.
Indian Inst. Metals, 55(3) (2002), pp. 115-130
6. CA Mitchell, A study of the powder processing, tribological performance and metallurgy
of aluminum based, discontinuously reinforced metal matrix composites, thesis submitted
in partial fulfillment of the requirements of Napier University for the degree of Doctor of
Philosophy, 2002
7. Dunia Abdul Saheb, Aluminum silicon carbide and aluminum graphite particulate
composites, ARPN Journal of Engineering and Applied Sciences,vol. 6, no. 10, october
2011
8. F. Akhlaghi∗, A. Zare-Bidaki, Influence of graphite content on the dry sliding and oil
impregnated sliding wear behavior of Al 2024–graphite composites produced by in situ
powder metallurgy method, Wear 266 (2009) 37–45,
9. Hui Lu, Xianping Wang, Tao Zhang, Zhijun Cheng and Qianfeng Fang, Design,
Fabrication, and Properties of High Damping Metal Matrix Composites—A Review,
Materials 2009, 2, 958-977
Page 72 of 89
10. J. Hashim, L. Looney, M.S.J. Hashmi, Particle distribution in cast metal matrix
composites—Part I, Journal of Materials Processing Technology 123 (2002) 251–257
11. J.W. Kaczmara,K. Pietrzakb, W.WosinÂskic, The production and application of metal
matrix composite materials, Journal of Materials Processing Technology 106 (2000) 58-
67
12. L.A. Dobrzañski a, M. Kremzer a, A.J. Nowak a, A. Nagel b, Aluminium matrix
composites fabricated by infiltration method, Archives of materials science and
engineering, volume 36, Issue 1, March 2009, Pages 5-11
13. M K Surappa, Aluminium matrix composites: Challenges and opportunities, S¯adhan¯a
Vol. 28, Parts 1 & 2, February/April 2003, pp. 319–334.
14. N. Chwala, K. Chawala, Metal matrix composite, Springer Science, 2006
15. Peter Andersson, Piston ring Tribology A literature survey, Espoo 2002. VTT Tiedotteita
– Research Notes 2178. 105 p.
16. Sarina bao, Kai Tang, Anne Kvithyld, Wettability of Aluminum on Alumina, The
Minerals, Metals & Materials Society and ASM International 2011,
17. Sarina Bao, Anne Kvithyld, Wettability of aluminium with sic and graphite in aluminium
filtration, TMS (The Minerals, Metals & Materials Society), 2011
18. Simon C. Tung , Michael L. McMillan, Automotive tribology overview of current
advances and challenges for the future, Tribology International 37 (2004) 517–536
19. Teruo Onozaki, Compression ring, united state patent and trademark office, Patent No.
4,344,634 ,dated August 17,1982
Page 73 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID:
ICAME2013/S3/O17
IMPROVISATION OF INTERFACIAL BONDING STRENGTH IN SHAPE MEMORY
ALLOY HYBRID POLYMER MATRIX COMPOSTES.
ABSTRACT
Fibre-reinforced composites with thermosetting polymeric matrices have found many uses in
structural applications because of their excellent in-plane properties and high specific strength.
Despite above mentioned properties, they are particularly prone to damage from out-of-plane
impact. Although fibre damage is usually localized at the site of impact, matrix damage in the
form of delaminations and transverse cracks can be more widespread. Delaminations in particular
can significantly reduce compressive strength and grow in response to fatigue loading. Recent
studies in the area of hybrid composites coined a very promising concept of composite
hybridization using Shape Memory Alloy (SMA) to withstand damage under conditions of
repeated load application. This has been attributed to unique property of SMA called Super
elasticity (SE) or Pseudo elasticity (PE) which allows them to absorb huge amount of elastic
energy. Full potential of SMA cannot be utilized until an efficient load transfer mechanism at
SMA and Matrix interface has been established. This paper presents different methodologies
such as surface roughening and chemical etching of SMA wire which has been adopted for
improvisation of interfacial bonding strength between SMA and Matrix phases. A pull-out test
has been performed to find out the improvement in load transfer between SMA and host matrix.
260% improvement in load transfer in case of specimens with chemically etched wire has been
observed over the untreated SMA wire specimens.
Key words: Shape Memory Alloy, Hybrid composites, Interfacial bond strength, Pull-out test.
1. INTRODUCTION
Page 74 of 89
Today Shape Memory Alloys finds wide application in different areas due to their unique
properties of pseudo elasticity and shape memory effect. SMA materials also find application in
damage tolerant composite structures due to their unique mechanical and thermal properties
compared with conventional materials. Many studies have shown that shape memory alloy wires
can absorb a lot of energy during loading due to their super-elastic and hysteretic behaviour [4].
The super-elastic effect is due to reversible stress induced transformation from austenite to
martensite. If a stress is applied to the alloy in the austenitic state, large deformation strains (8%)
can be obtained and stress induced martensite is formed. Upon removal of the stress, the
martensite reverts to its austenitic parent phase and the SMA undergoes a large hysteresis loop
and a large recoverable strain is obtained. This large strain energy absorption capability can be
used to improve the impact tolerance of composites [6]. By embedding SMA in the form of wire
or strips into a composite structure to produce Shape Memory Alloy Hybrid Composites
(SMAHC), impact damage can be reduced quite significantly, provided load transfer between
matrix and SMA is achieved efficiently [7]. Effectiveness of using SMA in composites is limited
by interfacial bonding strength between matrix material and SMA.
Interfacial bonding between SMA and matrix:
Maximum interfacial adhesion between the SMA fibres or foils and the matrix is desirable in the
SMAHC to get efficient load transfer. A strong interfacial bond also ensures the structural
integrity of the final composites. Due to oxide layer formation on the surface of the SMA wires
proper adhesion between matrix and wires is not achievable. Surface treatments of the SMA
fibres can be used to improve the interfacial bonding. These surface treatments are normally
conducted in order to achieve different SMA-Epoxy surface interactions. In this study different
possible methods for the improvement of interfacial bond strength between SMA-epoxy
inte
rfac
es
has
bee
n identified and compared with
base level strength. For this a
testing methodology called Pull-
out test has been used [2]. Also a
Scanning Electron Microscopy
(SEM) has been done to study the surface morphology of SMA wires.
EXPERIMENTAL PROCEDURE:
For determination of interfacial bonding strength between SMA wires and Epoxy a Pull-out test
have been performed on Bangalore Integrated System Solution (BISS) make Universal testing
machine (UTM) machine. Cylindrical test specimens were prepared by embedment of 0.3mm
diameter SMA wires (Ni-Ti alloy wire) within epoxy matrix as shown in fig.1 and a Pull-out test
has been performed on these specimens by applying tensile load. Schematic of Pull-out testing is
as shown in fig. 2.
(b)
Page 75 of 89
(c) (d)
Fig.1 (a) Images of Pull-out test specimens (b) Image showing SMA wire coming out of epoxy
cylinder (c) and (d) Specimen inserted into the holding fixture.
Fixture to hold the epoxy matrix is
fabricated in the form of hollow
cylinder from Acrylic Butadiene
Styrene (ABS) plastic of size: ID
10.5 mm; OD = 15mm; Length =
100mm.This hallow cylinder is used
to hold the epoxy part of the
specimen inside one of the grips of
UTM. SMA wire is pulled by
gripping them in to movable grip of
the UTM. Dimensions of test
specimen are: epoxy cylinder
diameter = 10mm; Epoxy cylinder
length = 30mm; SMA wire diameter
= 0.3mm.
Test has been performed on three types of specimens which are:
Type-i specimens: These are made up of untreated SMA wire cleaned with acetone to remove
dust, oil
particle etc. from surface of wire.
Type-ii specimen: In case of these specimens the surface oxide layer on wire is broken at
multiple
locations by polishing wire across the length using emery paper. A emery
paper of 600grade is used to polish wire along circumference at right angle to
the length of wire so as to produce scratches at right angle to the loading
direction to produce mechanical anchoring effect.
Type-iii specimen: For this type surface of the wire is chemically etched to remove the oxide
layer to
improve adhesion between SMA and Epoxy. Wires were kept in concentrated
H2SO4 for 20 minutes under ultrasonic bath. Then wire is degreased by using
solvent (Isopropyl alcohol) for 20
minutes. Finally wires were rinsed
thoroughly by distilled water to clean
the surface.
The interfacial strength for each type
can be determined by calculating
shear stress between SMA-Epoxy
interfaces using equation (1) and
Tensile stress on SAM wire can be
found out by using equation (2),
τ= (1)
Where; τ = Interfacial shear stress (MPa)
Page 76 of 89
P = De-bonding load (N)
d = diameter of SMA wire (mm)
l = length of the specimen (mm)
σ=
(2)
Where; σ = Tensile Stress on SMA wire (MPa)
P = De-bonding load (N)
r = Radius of SMA wire (mm) [0.15mm]
40
Load (N)
30
20
10
0
0 5 10 15 20 25 30 35
Elongation (mm)
Fig.3 Graph showing Load Vs Elongation behaviour of all three types of specimens under pullout
test
From pullout test results in Table (2) we can see that there is significant improvement in amount
of stresses, both tensile as well as interfacial shear, that can be transferred between SMA and
Epoxy. It can be concluded from the test results that deboning load and hence the interfacial
shear strength has been increase from type (i) to type (iii) specimen. From type (i) to type (ii)
Page 77 of 89
specimen there is increase of 133% in interfacial bonding strength whereas 266% increase is
observed in type (iii) over type (i) specimen. This can be attributed to the removal of oxide layer
(NiO and TiO) from the Ni-Ti wire surface due to chemical etching and surface roughing
processes. This is also evident from the Scanning Electron Microscopic (SEM) images of the
three types shown in fig.4.
Table (1): Specifications of materials used to prepare Pullout test specimen:
Material Composition Manufacturer Mechanical property
Resin-LY 1564 Tesile strength=60MPa
Epoxy Huntsman, USA
Hardener-XB3486 Young’s Modulus=3GPa
Tensile
Nickel-56%
Shape Memory Alloy NAL, Bangaluru strength=1300MPa
Titanium-balance
Young’s modulus=35GPa
Table (2): Pullout test results tree type of specimen:
Specimen type De-bond load Maximum Tensile stress on Maximum Interfacial
(N) SMA wire shear strength
(MPa) (MPa)
Type(i) 15 212.20 0.530
Type(ii) 35 495.14 1.237
Type(iii) 55 778.09 1.945
(Note: De-bond load shown in table is average value of 5 specimens of each type)
300 um
(a) (b)
(c) (d)
Page 78 of 89
Page 79 of 89
Fig.4 Scanning Electron Microscope images of SMA wires embedded within Type-i specimen-
(a)and(b); Type-ii specimen-(c)and(d); and Type-iii specimen-(e)and(f)
[Note: all images of wires are taken before embedment in specimen]
Fig. 4 (a) and (b) shows 1KX and 2KX SEM images of the untreated SMA wire surface. The
surface of the wire is smooth with neutral oxide layer due to which there is poor adhesion
between SMA and Epoxy. Fig.4 (c) and (d) shows 1KX and 2KX SEM images of Surface
roughened SMA wires. In these images we can clearly observe that there is removal of material
from the surface at microscopic level, due to which the oxide layer has been broken at multiple
locations exposing the reactive metal surface inside. This allowed the Epoxy to penetrate and
establish better adhesion with metal surface. Fig.4 (e) and (f) shows 1KX and 2KX SEM images
of chemically etched wire surface. In these images we can observe that the oxide layer has been
completely removed due to etching, exposing full wire surface for Epoxy to adhere and hence
shown substantial improvement in the interfacial strength. Also the surface of wire became rough
due to chemical etching which have also effected in increased surface area which further assisted
the adhesion between two. Significance of calculating tensile stress on SMA wire as shown in
table (2) is to know whether the transformation stress for SMA has been reached. Transformation
stress is nothing but the stress value at which transformation from Austenite phase to Martensite
phase takes place within the SMA. Pseudo elastic behaviour of SMA can only be seen above this
stress level. SMA wire used for this experiment has 550MPa transformation stress. From Table
(2) it is evident that only type-iii specimens have reached stress level above 550 MPa which is
778 MPa and hence only type-iii will experience a stress induced transformation of SMA. This is
also evident from fig. 3, where Load Vs Elongation curve of chemically etched wire specimen
shows some amount of energy absorption at around 40N load for deformation of wire during
Page 80 of 89
pullout testing. This shows that stress induced transformation has been achieved only in case of
type-iii specimen.
3. CONCLUSION:
Experimental study shows that the efficiency of load transfer between interface of SMA and
Epoxy can be substantially improved by performing chemical etching of the wire with
concentrated Sulphuric acid. The improvement in interfacial shear strength is nearly 260% from
that of base level. If this type of surface treatment is done on SMA wires to be used in SMA
hybrid composites then Pseudo elastic character of SMA can be utilised more effectively in
improving the out of plane loading response of the composite materials.
4. FUTURE WORK:
Effectiveness of surface treated SMA in product level needs to be studied experimentally. This
can be done by embedding chemically etched SMA wires inside a Carbon-Epoxy or Glass-Epoxy
composite laminates. Low velocity impact test can be performed on the specimens prepared out
of these laminate and energy absorption behaviour can be studied to quantify overall
improvement in the toughness property of the composite products.
5. ACKNOWLEDGMENT:
Authors would like to acknowledge Research and Development Establishment (Engineers),
Dighi, Pune for the financial support and allowing the utilisation of infrastructure for performing
the experimental work. The authors acknowledge National Aeronautical Laboratory, Bangaluru
for supplying Nitino (SMA) wires of required specifications.
REFERENCES
1. DiFrancia C., Ward T.C., Claus R.O., “The single-fibre pull-out test. 1: Review and
interpretation,” Composites Part A: Applied Science and Manufacturing, 27, Issue 8, pp
597-612 (1996)
2. Fu SY, Yue CY, Hu X, Mai YW. “Analyses of the micromechanics of stress transfer in
single- and multi-fibre pull-out tests”, Composites Science and Technology, 60, pp569-
579 (2000)
3. Futch David B. “Investigation of interfacial strength of shape memory alloy embedded
composites” Ph.D thesis, University of Florida (2012)
4. Huang W.M. et. al, Shape Memory Materials, Materials Today, 13, Issue 7-8, pp. 54-61
(2010)
5. Marfia S., Micro–macro analysis of shape memory alloy composites. International
Journal of Solids and Structures, 42, 3677–3699 (2005)
6. Tsoi K., “Impact damage behaviour of shape memory alloy composites”, Mater. Sci.
Eng., pp. 207–215 (2003)
7. Wei Z.G., Sandstrom R., Miyazaki S., “Shape-memory materials and hybrid composites
for smart systems,” Journal of Materials Science, 33, Issue 15, pp 3743-3762 (1998)
Page 81 of 89
Proceedings of International Conference on Advances in Mechanical Engineering
Paper ID
ICAME2013 S3/P1
ABSTRACT
Gears are toothed components which transmit power between two shafts by meshing without any
slip. The MMC materials are having good properties like tensile strength, thermal strength,
corrosion resistance and light in weight. High temperature and local stresses are developed in the
gear due to continuous contact, fretting fatigue and non uniform load distribution. This paper
describes the development of a finite element analysis (FEA)model based on stress analysis
results that is capable of predicting structural failure. The FEA results were compared with
experimental data and found to be in good agreement within an error of 15%.The developed
model avoided the structural failure, improved operating conditions, reduced product
development time and cost for testing Al matrix composite gear materials.
Keywords: CAE, FEA, Failure.
1. INTRODUCTION
Gearing is one of the most critical components in mechanical power transmission systems.
Contact problems are highly nonlinear and require significant computer resources to solve.
Contact nonlinearities occur when two or more components come into or out of contact with
each other. In engineering applications, most contact processes are dynamic in a restrictive
sense. Many of them can, however, be regarded as static for simplicity. By nature, contact
phenomena always involve friction phenomena. However, friction effect may be neglected for
simplicity in situations where frictional forces are sufficiently small. One may argue that the
subject of contact mechanics started in 1882 with the publication of the classical work by Hertz.
The Hertz theory is however restricted to frictionless contact and perfectly elastic solids. Finite
element analysis of meshing gear pairs will be subject to non-linear contact analysis. In this
situation, JIANDE WANG (Jiande Wang) investigated numerical methods for modeling the
contact stresses of involutes spur gears in mesh, over the mesh cycle, which forms the major
part of this work. Zeping Wei (Zeping Wei) investigated the characteristics of an involutes
gear system including contact stresses, bending stresses, and the transmission errors of gears in
mesh. The characteristics of involutes spur gears are analyzed by using the finite element
Page 82 of 89
method. C H Wink and A. L. Serpa (C. H. Wink and A. L. Serpa). Tooth contact deviations from
the plane of action and their effects on gear transmission error are investigated. Tooth contact
deviations come from intentional modification of involutes tooth surfaces such as tip and
root profile relief; manufacturing errors such as adjacent pitch error ,profile errors,
misalignment and lead errors; and tooth elastic deflections under load, for example, bending and
local contact deflections. Those deviations are usually neglected on gear tooth contact models. A
procedure to calculate the static transmission error of spur and helical gears under loading is
proposed. In our model we have taken Aluminum composite Material(MMC) for investigating
the above scenario with better performance criterion.
2. EXPERIMENTATION
The finite element method of contact analysis:-
The finite element general equation can be described by:
[Μ]{Α}+ [Κ] {U} = {F} ---------- (1)
Where [M] is the mass matrix, [K] is the stiffness; {U} is the displacement vector. {A} is the
acceleration vector,
and {F} is the external load vector as in the standard finite element procedure.
It can be taken as the primary unknowns to be solved for Denoting the contribution of' contact
forces to the load vector by {Fc}, we can write,
[M]{A}+ [K] {U} = {F} + { Fc } ---------- (2)
In eq. (2), { Fc } is unknown and is to be calculated under the constraint given in eq. (3). With
the finite element discretization, the kinematics constraint on contacting nodes can be put into the
form,
[Q]{U}+ {G} =0 ---------- (3)
Where {G} is calculated from initial gaps of contacting nodes and [Q] is a coefficient matrix
resulting from the finite element discretization.
In order to solve equations (2, 3), first determine the total number of contacting nodes, which are
unknown until the solution is found. Thus, trial contacting nodes need to he used and iterations
need to be carried out to find the true contacting nodes, at the same time, the contact condition
must been forced to solve the unknown contact force, which necessitates a constraint method. If
frictional effects are to be considered, a friction law governing the tangential contact force is
required. Furthermore, both displacements and accelerations are unknowns in equations (2, 3).
Therefore, a time integration method is also required for the solution.
3D contact element decription:-
The element of three dimensions to be used from ANSYS library is SOLID186. SOLID186 is a
higher order 3-D 20-node solid element that exhibits quadratic displacement behavior. The
element is defined by 20 nodes having three degrees of freedom per node: translations in the
nodal x, y, and z directions. The element supports plasticity, hyper elasticity, creep, stress
stiffening, large deflection, and large strain capabilities. It also has mixed formulation capability
for simulating deformations of nearly incompressible elastoplastic materials, and fully
incompressible hyper elastic materials.
Page 83 of 89
The geometry, node locations, and the element coordinate system for this element are shown in
Figure. (1). the contact algorithm of FEM computer program (ANSYS program) requires
definition of contacting surface. To define a contact pair completely, contact and target element
have to be referred to same characteristic parameters. The contact element 174 and target 170
with three nodes are used as a contact surface-to-surface in the present analysis as shown in
Figure (2)
Figure 1. Geometry of
SOLID186
Figure 2. 3D Contact Gear
Contact174 3-D 8-Node Surface-to-Surface Contact:-
CONTA174 is used to represent contact and sliding between 3-D "target" surfaces (TARGE170)
and a deformable surface, defined by this element. The element is applicable to 3-D structural
and coupled field contact analyses. This element is located on the surfaces of 3-D solid or shell
elements with midside nodes (SOLID87, SOLID90, SOLID92, SOLID95, SOLID98, SOLID122,
SOLID123, SOLID186, SOLID187, SOLID191, SOLID226, SOLID227, SOLID231,
SOLID232, VISCO89, SHELL91, SHELL93, SHELL99, SHELL132, SHELL281, and
Page 84 of 89
MATRIX50). It has the same geometric characteristics as the solid or shell element face with
which it is connected (see Figure 174.1: "CONTA174 Geometry" below). Contact occurs when
the element surface penetrates one of the target segment elements (TARGE170) on a specified
target surface. Coulomb and shear stress friction is allowed. This element also allows separation
of bonded contact to simulate interface delimitation. element is defined by eight nodes (the
underlying solid or shell element has midside nodes). It can degenerate to a six node element
depending on the shape of the underlying solid or shell elements. If the underlying solid or shell
elements do not have mid side nodes, use CONTA173 (you may still use CONTA174 but you
must drop all mid side nodes).
Target 170 3-D Target Segment:-
TARGE170 is used to represent various 3-D "target" surfaces for the associated contact elements
(CONTA173, CONTA174, CONTA175, CONTA176, and CONTA177). The contact elements
themselves overlay the solid, shell, or line elements describing the boundary of a deformable
body and are potentially in contact with the target surface, defined by TARGE170. This target
surface is discretized by a set of target segment elements (TARGE170) and is paired with its
associated contact surface via a shared real constant set. You can impose any translational or
rotational displacement, temperature, voltage, and magnetic potential on the target segment
element. You can also impose forces and moments on target elements. For rigid target surfaces,
these elements can easily model complex target shapes. For flexible targets, these elements will
overlay the solid, shell, or line elements describing the boundary of the deformable target body.
The geometry and node locations are shown in Fig. (4).
Figure 4. Geometry of target 170
Page 85 of 89
Figure 5. Contact stress (Von Mises),with
different contact position.
1 20 (30-30) 4
2 20 (25-50)-48 2
3 20 (20-60) 3
Also, this section contains comparisons of the numerical and theoretical results obtained from
the available published results and with the results of ANSYS package, Ver. (13), and this
section investigates the characteristics of an involutes gear system including contact stresses.
The material used for models is Metal Composites AMC225XE T4 Aluminum/Silicon Carbide
MMC Extruded Bar with modulus of elasticity (E), yield stress (σy ), ultimate stress (σu ),
material density (ρ) and Poisson’s ratio (υ) as follows:-
E = 1.2 *109 ( N / m 2 ) ,
σy = 48 *106 ( N / m 2 ) ,
σu =69 *106 ( N / m 2 )
v = 0.3,ρ =2.88 g/cc
One case of table (1) has been accomplished in Fig. (5) To represent the sample of the nodal
solution stress (Von Mises), with different contact position, were plotted using ANSYS package,
the von Mises criterion is best applied and best understood when used to predict the onset of
yielding in a structure where the material behaves in a ductile fashion.
Table 2. Comparison of contact stress between experimental and ANSYS result.
Contact Stress Percentage Error (%)
Experimental result ANSYS result
Page 86 of 89
28.9 25.3 12.95
4. CONCLUSIONS
The main conclusions obtained from the present work can be summarized as follows: -
Table. (2) Shows that a FEA model (surface to surface) could be used to simulate contact
between two bodies accurately by verification of contact stresses between two gears in contact
and comparison between these results with experimental result. The diffrence between FEA and
experimental result is very small and equal to 12.95 % and maximum go up to appx. 15%
considering inaccuracies into consideration. The present work can be utilised for fast analysis of
gear to check stresses and factor of safety for aluminium based metal matrix composite.
REFERENCES
1. ANSYS 13, Structural Analysis Guide.
2. C. H. Wink and A. L. Serpa. (2005). Investigation of Tooth Contact Deviations from the
Plane of Action and Their Effects on Gear Transmission Error, State University of
Campinas, Brazil, I. Mech. E. Vol. 219 Part C: J. Mechanical Engineering Science,
PP.501-509.
3. Faydor L. Litvin, Alfonso Fuentes, J. Matthew Hawkins and Robert F.handschuh. (2001).
Design, Generation and Tooth Contact Analysis (TCA) of Asymmetric Face Gear Drive
With Modified Geometry, NASA Center for Aerospace Information.
4. Jiande Wang. (2003). Numerical and Experimental Analysis of Spur Gears in Mesh, PhD
Curtin University of Technology September.
5. K. L. Johnson. (2003). Contact Mechanics, Cambridge University Press, Ninth prints.
6. M., Amabili and A. Rivola. (June 2008). Dynamic Analysis of Spur Gear Pairs: Study-
State Response and Stability of the SDOF Model with Time-Varying Meshing Damping,
University of Bologna, Italy, Mechanical Systems and Signal Processing, PP.375-390.
7. Nilanjan Sarkar, Randy E. Ellis, Thomas N. Moore. (2006). Backlash Detection in
Geared Mechanisms: Modeling, Simulation, and Experimentation, Queen's University,
Kingston, Canada, I. Mech. E. Vol. 220 Part K: J. Multi-body Dynamics, PP.273-282.
8. Ramamurti, V., and Ananda, M. (1988). Dynamic Analysis of Spur Gear Teeth, Indian
Institute of Technology, India, Journal of Computers and Structures, Vol.29, No.5,
PP.831-843.
9. Spitas. G. A. Papadopoulos. C. Spitas and T.Costopoulos. (2009), Experimental
Investigation of Load Sharing in Multiple Gear Tooth Contact Using the Stress-Optical
Method of Caustics, Journal Compilation, doi:10.1111/j.PP.1475-1305.2008.00558.x.
10. V. Atanasiu, I. Doroftei. (2009). Dynamic Contact Loads of Spur Gear Pairs with
Addendum Modifications, Technical University of Lasi, Romania, Journal of Mechanical
and Environmental Engineering.
Page 87 of 89
11. Zeping Wei. (2004). Stresses and Deformations in Involutes Spur Gears by Finite
Element Method, M.Sc,University of Saskatchewan, Canad
Page 88 of 89
Page 89 of 89
SUB THEME 4
107
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/01
IMAGING ANALYSIS AND MICRO-PIV OF SINGLE MENISCUS INSIDE SQUARE
CAPILLARY
Ajay Tripathi* S. K. Agrawal
Department of Mechanical Engineering Department of Mechanical Engineering
Motilal National Institute of Technology Allahabad Motilal National Institute of Technology
(UP), 208016 India Allahabad (UP), 208016 India
*Tel: +91-7544-267-312; Fax: +91-7544-267-312
E-mail: ajay.tripathi@juet.ac.in
ABSTRACT
With the current emergence of energetic challenges, the opportunities to make use of new and
innovative devices are upcoming. Advancement in interface capturing techniques from macro to molecular
level has drawn the attention of many researchers towards the single-phase and two-phase flows in mini
and micro channels. A multiphase flow in micro channels is considered to be most suitable for heat and
mass transfer processes because of their high surface to volume ratio and small diffusion paths which
provides large interfacial area enhancing the performance of such devices [1, 2].
In the present study we focus on gas-liquid two-phase slug flows which are commonly encountered in
many types of process equipment from boilers and condensers to heat exchangers and even fuel cells. Two
different methods have been used: an imaging method, through the use of a video recorder and the micro-
PIV method (Particle Image Velocimetry). Dynamic apparent contact angles inside square capillaries were
measured by video recording for different Capillary Numbers and results demonstrate that Tanner’s Law is
valid in square capillaries but with a dependence on the Bond Number; more systematic data will be
acquired to identify the exact relation. Micro-PIV was done to see the hydrodynamics behind moving
menisci, and a thorough study showed that the flow behind the meniscus departs from parabolic profiles
(Hagen-Poiseuille equation) as we move closer to the meniscus.
108
1. INTRODUCTION
Many systems do not involve the flow of a single homogenous material (phase) such as gas, liquid or
solid. Instead complex combinations of two or more of these phases predominate; with gas-liquid, gas-
solid, liquid-solid, liquid-liquid, gas-liquid-liquid and even gas-liquid-solid flows frequently occurring in
both nature and technology. For example, clouds are droplets of liquid moving in a gas. Oil, gas and water
can coexist in rock. Near the surface of the Earth, particles are moved by interacting with air or water,
resulting in the shaping of geological features. In the realm of human endeavors, boiling heat transfer is
the workhorse of the energy industry, involving gas bubbles nucleating, growing, and coalescing.
Chemical processing involves mixing, emulsifying, and catalysis in a myriad of flow scales, and finally,
we drink carbonated beverages from soda water to champagne.
The widespread presence of these multi-fluid systems suggests the utility of a general technique of
description to understand their behavior. However, each of these systems has distinguishing characteristics
that keep any particular multiphase model from being generally applicable. The result is that many disjoint
modeling communities use their own specific formulation and approximations, slowing our progress in
better understanding these complex flows. They are commonly encountered in many types of process
equipment from boilers and condensers to heat exchangers and even fuel cells. They are also prevalent in
hydrocarbon recovery onshore and offshore where oil and gas are currently transported through pipelines.
In addition to being the most common of the two-phase cases, gas-liquid slug flow is also the most
complex since it combines the characteristics of a deformable interface with those of a compressible phase.
This means that for a specified channel design and inclination, and for a given fluids flow-rate fed into the
system, the gas-liquid interface can arrange itself into a large variety of forms. As a result many
investigators have concluded that, although theoretically possible, it is simply too difficult to solve this
two-phase flow problem using the classic Navier-Stokes equations of fluid dynamics. This has led to the
adoption of a phenomenological approach in which the flow distributions are classified into several
distinct “patterns” enabling the main characteristics of each group to be studied separately.
Slug flow is one of two phase flow patterns which achieve, as the gas flow rate increases in liquid, resulted
in Taylor flow forms. These flow patterns consists of elongated bubbles with equivalent spherical
diameter, almost filling the tube, usually many times that of the channel diameter, separated from the wall
of the tube with a liquid film and also from each other with liquid plugs as shown in Figure 2.2 (b).
Whereas, Figure 2.2 (a) represents an instant in the motion of Taylor bubbles through a stagnant or
flowing liquid. As bubbles move upward, the liquid is forced to flow around them in a thin annular film,
whose weight is totally supported by the shear forces at the column wall (a free-falling film). The
thickness of that film varies from millimeter scale to micro scale depending upon the dimensions,
geometry, flow velocity, orientation of the channel and the thermo physical property of the fluid and the
channel used. The presence of bubbles in front and at the back of the slugs, modifies the flow field in the
liquid slug compared with single-phase flow and toroidal vortices extending the length of the slug can
form [Figure 2.2 (c)] [3].
109
Figure 2.1 critical conditions for zero terminal velocity of a cylindrical bubble rising through stagnant
liquid contained inside channel. [7]
A bubble rises through the denser liquid because of its buoyancy. The velocity v∞ with which a single
cylindrical bubble rises through stagnant liquid in a duct is governed by interaction between buoyancy and
other forces acting on the bubble because of its shape and motion as shown in Figure 2.1
As the liquid film drains past the tail of the Taylor bubble it penetrates the liquid slug creating a relatively
confined flow, the bubble wake, with forms varying from a closed well-defined recirculation region to an
open random-like circulation region (laminar and turbulent wakes, respectively). The entrainment of small
gas bubbles at the Taylor bubble wake contributes to the more or less aerated nature of the liquid slug
region. Slug flow pattern has often been addressed on the basis of the “unit cell” concept, developed by
Fernandes et al. [4] for vertical slug flow. The intrinsically complex structure of such flow is taken as a
series of unit cells, each consisting of a Taylor bubble and the liquid slug below, rising along the column at
different velocities. Following on from this idea, the slug flow pattern is said to be undeveloped when
there is relative motion between consecutive unit cells (i.e. Taylor bubbles interacting, approaching and
eventually coalescing). This condition is associated with strong changes in the flow pattern characteristics
(e.g. bubble lengths, velocities and frequency). As the distance between consecutive bubbles escalates, the
relative motions dissipate and the flow reaches its fully developed condition.
Figure 2.2 Gas-liquid Taylor flow inside capillary, showing,
(a) Liquid Slugs and Taylor bubbles in vertical channels
(b) Images taken from High speed camera (c) Streamline patterns in the liquid slug
(See online version for colours), [3]
110
Knowledge of hydrodynamic characteristics during Taylor/slug flow inside mini/micro systems is
necessary for understanding the behavior and improving the performance of systems in which this type of
flow exists. An interesting feature of slug flow in small capillaries is that, it exists in horizontal as well as
vertical orientation, because of the predominance of the surface tension forces over the gravitational
forces. Also, flow is essentially laminar and predominantly viscous; the liquid plugs are free of smaller
bubbles and breakage and coalescence of air slugs is virtually absent. The film surrounding the bubbles is
the only means of communication between two successive slugs and in the majority of cases its thickness
is only a very small percentage of the tube diameter. The recirculation within the liquid slugs improves
heat and mass transfer from the liquid to wall and interfacial mass transfer from gas to liquid. The
combination of good radial mass transfer and low axial mass transfer in the liquid makes Taylor flow
suitable for two-phase applications that involve the mass transfer or single-phase liquid applications which
suffer from large back-mixing. The enhanced heat and mass transfer rates possible in micro-channels
would enable a kinetically controlled operating regime to be established that allows evaluation of reaction
kinetics. As a result of the modification of the flow field in the slugs, Taylor flow offers many advantages
for carrying out reactions compared with other patterns and also single-phase laminar flow [5].
Recently, Angeli and Gavriilidis [3] reviewed the work done to understand the hydrodynamics of Taylor
flow (two phase flow occurring in minichannel) in capillary. They have clearly distinguished the circular
and non circular capillaries and studied all aspects separately. The hydrodynamic characteristics reviewed
were, thickness of film that surrounds the bubbles, contact angle, bubble shape and velocity, bubble and
slug length, flow patterns in the liquid slug, and pressure drop in the system. They clearly mentioned that
the two-phase flow characteristics of capillaries/mini-channels are known to be significantly different from
the characteristics of larger channels, and consequently the existing vast literature associated with the
phenomenology of change-of-phase heat transfer and two-phase flow hydrodynamic processes generally
do not apply to capillaries. The surface tension is predominant in capillaries and significantly reduces the
slip velocity, and renders the flow characteristics independent of channel orientation with respect to
gravity.
3. EXPERIMENTAL SETUP, INSTRUMENTATION AND DATA ANALYSIS:
The experiments were first performed using high speed camera (HSV) to determine dynamic contact
angle and then PIV of the flow was done to see the flow pattern behind moving meniscus.
3.1 Experimental setup:
The schematic of experimental setup is shown in Figure 3.1. The glass capillary is set horizontally with
the help of capillary stand. The capillary was connected to syringe containing test fluid with the help of
plastic tubing. The equipments which were used during experimentation are CCD camera -Imperx IPX-
VGA210-L, Square capillaries (1x1mm and 2x2mm), syringe pump with syringes (diameters: 1.50cm and
0.5cm), diffused light source and different Fluids (distilled water, ethanol, glycerin). During
experimentation syringe was placed in single-syringe infusion pump provided by Cole Parmer (model
number EW-74900-00) and the piston of syringe was pushed different fluid with different speeds by the
pump depending on the flow rate set in the pump so as to get different velocity of flow. Piston pushed the
fluid into capillary with a calibrated flow rate. The capillary is linked to the syringe through a plastic tube
and placed on the support. Once the focus has been made and the lighting on the area is correct using 150
W diffused light source, the syringe pump was started. The interface was viewed and captured through a
111
Figure 3.1: Experimental setup for capturing advancing liquid-air meniscus in a capillary.
3.2 Experimental procedure in imaging analysis:
Four different fluids water, ethanol, glycerin and silicone oil were used for the experiment. The
experimental and physical parameters of the fluids are given in Table 3.1. Proper cleaning treatment of
capillary channel was carried out to avoid contamination. The sonication was done using ultrasonic cleaner
provided by Cole Parmer (EW-08895-22 series). In case of glycerin and silicone oil it was difficult to
remove the stuck liquid from inside the tube wall. So to remove stuck liquid, the capillary was dipped for
5-10 minutes in piranha solution – mixture of sulfuric acid (H2SO4) and hydrogen peroxide (H2O2) in the
ratio 1:3 before sonication. In literature use of chromic acid (H2CrO4) is also mentioned to clean the
capillary but we have not made use of it. It was made sure that before each run the capillary is dry. Each
fluid was tested for different sets of capillary number ranging from very low to high capillary number (as
mentioned in Table 3.1). The maximum capillary number which could be obtained was limited by the
syringe diameter and the fluid viscosity. Flow rate was given as input to the syringe pump and it pushed
the fluid with calibrated flow rate. The syringe pump was calibrated by setting specific volume in pump,
and then measuring this volume in a measuring cylinder. The liquid-air interface was captured at the
location where there was no further change in contact angle for given velocity. Moving meniscus was
captured for each velocity using high speed camera. The frame rate during image capturing varied from
200 fps to 2000 fps depending on the velocity of flow and type of fluid. The captured images were then
processed in software like Adobe Photoshop and dynamic contact angle was measured by drawing tangent
to the three phase contact line. The actual velocity of interface was calculated by measuring the pixel
distance moved by interface in a particular time gap. By measuring the pixel distance moved by interface
and dividing it by time difference between two frames, actual velocity of interface can be calculated.
112
Bond no.
Velocity Range
Fluid μ (Pa-s) γ (N/m) Ca (max)
(cm/s) 1x1 mm 2x2 mm
Table 3.1: Experimental parameters and physical properties of fluids used in the experiment
3.3 Experimental procedure in PIV measurement:
PIV measurement was done for water and ethanol in 1x1 mm2 capillary. The capillary was mounted in a
capillary stand and this assembly was then mounted in a PIV platform. Figure 3.4 shows the schematic
representation of μ-PIV setup used and position of velocity measurement in the present work.
A micro PIV system was used to study the flow behind moving meniscus. PIV is a non-intrusive technique
which measures the movement of small tracer particles by means of camera and pulsed laser light. The
region of interest in microchannel is placed on the platform provided just above the camera lens.
Depending on flow tracer size, magnification and camera sensitivity optical sources of illumination like
laser or bright field illumination is employed for imaging. Experimental parameters in present work are
displayed in chart below (Figure 3.5). Velocity behind air-water and air-ethanol interface was obtained for
three different flow rates of each fluid.
The acquired PIV images for three different velocities were processed using Dantec dynamic software
package to obtain the vector plots and velocity profiles. Due to the frequency limitation in bright field
mode the maximum average velocity achieved was 0.27 mm/s (with the current experimental condition).
There were no frequency limitations for the fluorescence mode as such. The acquired PIV images were
masked so as to exclude the unusable portion of the image. The vector plots were obtained from masked
images using adaptive correlation technique in two stages. In first stage the vector plots are obtained and in
second stage the obtained vector plots were filtered to get the final plot. From the vector plots obtained the
numerical value of velocity (U) profile was acquired at meniscus and various other locations away from
meniscus as shown in Figure 3.8.
Two different capillaries have been used. For each fluid, different velocities have been studied. For each of
these velocities, two contact angles have been measured: the lower one and the upper one, in order to study
the impact of gravity on the fluid. These contact angles have been measured on 3 different pictures and an
average has been calculated, in order to avoid marginal errors. The purpose of these experiments was to be
able to compare the behavior of a fluid for different Capillary Numbers (Ca) but same Bond Number (Bo)
which resulted in a qualitative analysis of the results and a quantitative one through excel plotting of the
different formulations of the Tanner’s Law and for different Bo but same Ca
113
Figure 3.4: (a) Schematic of μ-PIV setup for velocity measurement inside capillary.
(b) Various locations at which U-velocity profile was extracted
Figure 3.5: Schematic showing PIV experimental condition during two different modes.
4.1Static Meniscus:
The results of the experiments were extremely surprising because they did not fit in with the expected
outcome drawn from the literature. The contact angle was expected to be less than 90 degrees, and the
meniscus shape was supposed to be symmetrical but the meniscus is not symmetric and the contact angles
(lower and upper ones) and not only different but also superior to 90 degrees as shown in Figure 4.1.
4.2Dynamic Meniscus:
Four different fluids water, ethanol, glycerin and silicone oil were used for the experiment. Each fluid was
tested for different sets of capillary number ranging from very low to high capillary number. Flow rate was
given as input to the syringe pump and it pushed the fluid with calibrated flow rate. The liquid-air interface
was captured at the location where there was no further change in contact angle for given velocity. Moving
meniscus was captured for each velocity using high speed camera. The captured images were then
processed for getting various hydrodynamic properties near three phase contact line. The static contact
angle came out to be different for all cases because of the different boundary conditions. Static contact
114
angle in a 2x2 mm2 is different from that in 1x1 mm2 channel for all the fluids. As with the increase in
tube diameter the effect of gravity comes into play and surface tension no more dominates, similarly due to
change in bond number the contact angle is different for different size capillary.
2 2
Figure 4.1: Static meniscus of different fluids inside (a) 1x1cm (b) 2x2 cm glass tubes.
As soon as the liquid inside the capillary is set in motion increase in advancing contact angle occurs until it
reaches the dynamic contact angle value θd corresponding to the imposed velocity. From experiments it
was observed that the shape of moving meniscus is a strong function of Ca. Depending on the viscosity of
fluid there is enormous difference in the shape of advancing meniscus at different Ca. This leads to
increase in dynamic contact angle with increase in capillary number. Similarly bond number is also
playing role in changed shapes as at low bond number (1x1 mm2 capillary) the meniscus shape is almost
symmetric whereas it is not so in case of higher bond number (2x2 mm2 capillary). This asymmetry was
not due to pinning problems, as described in Jean Berthier [6] as whatever the orientation of the capillary
the results are the same; hence for this size of capillary there are no pinning effect. Then the effect of
gravity was checked and it was observed that when the capillary is vertical the meniscus shape is indeed
symmetric. Thus it can be concluded that for a square capillary gravity played an important role that was
not yet described in the literature.
Through the many plotting configurations that It was found that the first relation between θ and Ca was the
most appropriate, though the coefficient found barely resembled the one of the literature. Therefore, this
relation on a log scale was tried for all three fluids to find a pattern linking Ca and Bo, plot that one can
observe in the figure below [Figure 4.2]. The coefficient A here fits perfectly the literature but only for
Glycerin.
It is therefore obvious that the Bond Number plays a role in Tanner’s law, and that gravity shall maybe be
taken into account. For the smaller capillary, the results were those expected: the meniscus was
symmetrical with an angle of less than 90°. However, this time the problem encountered was the
phenomenon of hysteresis, which had barely appeared for the Capillary 3x3. This hysteresis tends to blur
the results. For the capillary 1x1mm I also performed an excel analysis in which I was able to show that
Tanner’s Law is valid for every fluid. However, the Tanner coefficients are not the same for every fluid (or
Bond Number), which contradicts the theory (according to which the Bond number has no influence). This
115
shows us even more that the Bond number shall be taken into account. Glycerin once again is the only
fluid for which Jean Berthier’s Tanner’s Law is valid [6]. Water and Ethanol both follow another Tanner’s
Law, as described inError! Reference source not found..
5
θd3 – θs3
Ca
0
0.000001 0.00001 0.0001 0.001 0.01 0.1 1
Figure 4.2: Contact Angle and Capillary Numbers for the Capillary 2x2 mm
The PIV equipment and lasers
The acquisition and post-processing software
A square capillary (0.5x0.5mm)
A syringe pump and syringe (0.5cm)
Distilled water
The PIV is a very precise technique that naturally triggers a need for a precise set-up. During
experimentation the capillary had to be fixed to the support of the microscope without any problems of
116
parallelism, the focus had to be made so that at least half of the capillary was visible. Eventually, the
following setting gave relatively good results:
Settings of PIV
Time between pulses: 80000 microseconds
Trigger rate: 4 Hz
No of images: 400
Flash 1 to Q-switch 1 delay 160 microseconds
Flash 2 to Q-switch 2 delay 170 microseconds
Q-switch 1 activation delay 0.18 microseconds
4.3.1 Results of PIV
Only one type of capillary has been used for this type of experiments which is 0.5x0.5mm. Two different
speeds have been tested (U=5.55E-04m/s and U=7.77E-04m/s) and for each speed two measurements have
been taken.
(a) Qualitative Discussion
For each measurement three pictures of the meniscus have been taken and after masking the areas of non-
interest a vector map has been created. Below is an example of the results it gave.
Figure 4.3 Vector Map for Q=0.5mL/h and U=5.55E-04 Image #10
The results of the PIV were good, as we can see in the vector maps that were generated by post-
processing. One can clearly see the advancing meniscus, the prewetting fluid and the velocity of the
fluorescent particles (through each of the velocity vectors). The fluid is moving uniformly; as it is
described in the early study by Taylor describing possible streamlines [8]. It is possible to see a pattern of
a vortex in some of the measurements taken with PIV (see Error! Reference source not found. and
Error! Reference source not found.). Indeed, more recent studies and PIV measurements by Taha and
Cui [9] have confirmed that together with a constant velocity; when Ca is small (less than 0.5) toroidal
vortices appear. However, the resolution of our findings was too narrow to be able to clearly see those, and
this issue shall be revised in the future.
(b) Quantitative Discussion on the Velocity profiles
For Q = 0.7 mL/h and U = 7.77E-04 m/s one will found below the analysis made on the results of the PIV.
The capillary number was 1.05E-05 and there were no prewetting effects.
117
As one can see, the Poiseuille profile is well respected, especially when the velocity is measured not quite
on the meniscus but a little further away. For the Image #10, the experiments fitted very well the theory at
0.075mm away for the meniscus, hence 15% of the edge R (0.5mm). This is also true for a smaller flow
Q=0.5mL/h. We can therefore consider that at 0.15R from the meniscus, the velocity profile follows the
Hagen-Poiseuille equation.
Figure 4.4 Velocity profile at the meniscus (Image #10)
Dynamic apparent contact angles inside square capillaries were measured by videography for different
Capillary Numbers and for different Bond Numbers (through the use of different fluids and different
capillary sizes). In addition, micro-PIV was done to see the hydrodynamics behind moving menisci.
Results show that Tanner’s Law is valid in square capillaries but with a dependence on the Bond Number;
more systematic data will be acquired to identify the exact relation between the dynamic apparent contact
angle and the non-dimensional numbers. PIV demonstrated that the flow behind the meniscus followed the
parabolic profiles (Hagen-Poiseuille equation) until close to the meniscus (about 0.15R) where it departed
from the theory. Further on, it will become necessary to study the influence of heat on the behavior of the
slug flow in order to find out the exact hydrodynamics behind a pulsating heat pipe.
ACKNOWLEDGMENTS
The author wishes to acknowledge the invaluable assistance given by Dr. Sameer Khandekar and Dr.
P.K.Panigrahi (Professor, Mechanical Engineering Department, I.I.T. Kanpur, India) who provides all the
facilities, perfect logistic support for conduction of experiments.
118
Figure 4.5 Velocity profile far from the meniscus (Image#18)
REFERENCES
1. Gupta, R., Fletcher, and D.F., Haynes, B.S., 2009, “On the CFD Modelling of Taylor Flow in
Microchannels,” Chemical Engineering Science, 64, pp.2941-2950.
2. Gunther, A., and Jensen, K.F., 2006, “Multiphase Microfluidics from Flow Characteristics to
Chemical and Material Synthesis,” Lab on a Chip, 6, pp.1487-1503.
3. Angeli P. and Gavriilidis, A., 2008 "Hydrodynamics of Taylor flow in small channels: a review”,
Int.J. Mechanical Engineering Sci.,222(5), pp.737-751.
4. Fernandes, R. C., Semiat, R. and Dukler, A. E., 1983. “Hydrodynamic model for gas-liquid slug
flow in vertical tubes” AIChE J. 29(6), pp.981-989.
5. Tripathi A., Agrawal S.K., 2012, “Hydrodynamics of oscillating slug flow inside mini channels: a
state of art review”,Int. J. of Theoretical and Applied Multiscale Mechanics, 2(3), pp.225 – 254.
6. Berthier, Jean, 2008, “Microdrops and digital microfluids” s.l. : William Andrew.
7. Khandekar, S., 2004 “Thermohydrodynamics of closed loop pulsating heat pipes”, PhD thesis.
8. Taylor, G.I., 1961, “Deposition of a viscous fluid on the wall of a tube”, Journal of Fluid
Mechanics”, 10(2), pp.161-165.
9. Taha, T. and Cui, Z.F., 2004, “Hydrodynamics of slug flows inside capillaries”, Journal of
Chemical Engineering Sciences, Vol. 59, pp.1181-1190.
119
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/02
CFD SIMULATION OF UNDEREXPANDED SUPERSONIC JET STRUCTURE
ABSTRACT
The present work analyzes underexpanded supersonic jet characteristics for various nozzle pressure
ratios at steady state. For this purpose commercial Computational Fluid Dynamics (CFD) software (Ansys
Fluent 14.5) is used. In the simulation the working fluid used is Argon as an ideal gas; the type of nozzle
used is straight contoured converging one with length to throat diameter ratio of 2:1 and the turbulence
model used is v2-f. Pressure, temperature and nozzle diameter are kept such that the clustering and
condensation will not occur inside the jet, according to Hagena’s scaling law. The effect of variation of
pressure ratio on the shock wave structure formed inside the jet and flow properties variation inside the
shock structure is studied by comparing simulation results with previous jet studies using experiments or
Method of Characteristics (MOC) and a good match is noticed. Numerical model of the present study can
be used for analyzing shock structure and variation of properties in strongly underexpanded supersonic
jets.
Keywords: CFD, Method of Characteristics, underexpanded supersonic jet, zone of silence, v2–f model
1. INTRODUCTION
Supersonic jet analysis can be useful in large number of applications and events where it is predominant,
e.g. Studies of jet-jet \ jet-surface interactions, jet propelled vehicles, laser jet machining, leakage of a gas
through vents of pressure vessels, flow through choked valves, volcanic eruption studies, studies of cluster
formation, , extraction of molecular \ atomic \ cluster beams, molecular beam epitaxy, molecular
spectrometry, mass spectrometry, plasma studies etc.
The jet is formed when a free stream of a gas comes out of the nozzle from a gas reservoir maintained at a
pressure Po to discharge chamber at pressure Pb< Po and if the region within the jet is supersonic (Mach
number M > 1), it is called as a supersonic jet. For a convergent nozzle, pressure ratio PR =Po / Pb must be
greater than critical pressure ratio G [Eq. (1)] to obtain supersonic jet (Miller, 1988).
In case of a supersonic jet the gas travels at speed grater than speed of sound but the information about
flow properties in background can only travel with the speed equal to speed of sound, hence the flow can
not acquire background conditions. This makes pressure at exit plane Pe not equal to back pressure Pb. This
condition initiates the Prandtl-Mayer (compression or expansion) waves, oblique shock waves (barrel
120
shock) and normal shock waves (Mach disk shock) to make the down stream of flow to acquire
background conditions (Miller, 1988).
If Pe> Pb (i.e. jet has not yet expanded to back pressure, hence called underexpanded jet), the lower
magnitude backpressure expands the free jet boundary and expansion waves are set up. When these waves
reach jet boundary the region inside the jet is expanded to a pressure P < Pb (overexpansion), therefore
higher magnitude back pressure compresses the jet boundary and compression waves are set up. Again
when these waves reach jet boundary the region inside the jet becomes underexpanded with pressure
greater than Pb. This pattern repeats itself until the viscous forces disturb the pattern. If the under
expansion is strong enough (i.e. at high pressure ratios), these simple waves unite to form oblique shock
and normal shock and the region surrounded by these shocks is called ‘zone of silence’ (Sannaand
Tomassetti, 2005).
2. COMPUTATIONAL DOMAIN
Fig. 1 Domain geometry, discretization and boundaries
2.1Domain extent
Domain geometry used in the simulation has three major regions; reservoir, nozzle and discharge chamber.
Inlet diameter and length of the nozzle are 100 micron, while the throat diameter D is 50 micron. The
subdomains, reservoir and discharge chamber, extends three times D in the y direction from x-axis. In the
x direction the discharge chamber extends to 10 times D from nozzle exit, while reservoir extends 2 times
D from inlet of domain to inlet of nozzle.
Domain is discretized so as to obtain optimum between, computational expense for meshing, accuracy,
convergence and stability. Since axisymmetric domain minimizes number of cells and hence
computational time of solver, it is used for the simulation. Brikby and Page, 2001, Matsuo et al, 2004 have
employed such a domain in their simulations of supersonic air jets. Domain is discretized in 6100 cells
using the meshing shown in fig. 1. Structured meshing scheme with quadrilateral elements is used, because
it permits the flow to be aligned with grid. Aligning the flow with grid minimizes false (numerical)
diffusion caused due to truncation errors that are a consequence of representing the fluid flow equations in
discrete form. For aligning the flow with grid and making grid fine at jet formation region to capture
gradients of flow properties, proper aspect ratio is used for edge meshing where ever required. Aspect ratio
at edges also improves smoothness of grid, which avoids rapid changes in cell volume between adjacent
cells, one of the reasons for truncation errors and reduces computational time by coarsening the grid at
121
regions where the jet is not forming. The cell shapes in the grid are examined in terms of cell skewness,
cell squish index, aspect ratio and maximum values of them found to be 0.156, 0.0293, 13.728
respectively. As general rule of thumb grid cells with skewness and squish index values (varying from 0
to1) closer to 0 and aspect ratio not exceeding 5:1 are considered better for convergence and stability
including the grid with triangular cells. Since quadrilateral cells are used in the grid they permitted a larger
aspect ratio without producing, high value of skewness, instability and convergence difficulties, which is
not possible for grids with triangular cells (Fluent users guide).
2.3 Domain boundaries
Boundary types used for the domain are: wall with no slip and no heat transfer conditions, axis at
centerline of axisymmetric geometry, pressure inlet and pressure outlet with total temperature 300 K. Total
pressure at inlet is kept to be 2 bar, while static pressure conditions at outlet are varied for analysis
purpose. To avoid condensation inside the jet, D is kept to 50 micron so that Hagena’s parameter Ѓ < 200
[Eq. (7)] (Hagena, 1992). Relevant turbulent intensity and hydraulic diameter specified at inlet and outlet
are 0.1 % and 0.0003 m respectively. In the fluid zone condition argon gas is used as working fluid with
following assumptions: argon behaves as an ideal gas, specific heats are constant, thermal conductivity
varies according to kinetic theory equation, dynamic viscosity varies with temperature according to three
coefficients Sutherland law.
3. NUMERICAL MODEL
Fevre time averaged conservation equations are solved in axisymmetric coordinate system (x = axial
distance, y = radial distance) with four additional differential equations (for turbulent kinetic energy k,
turbulent rate of dissipation ε, velocity variance scale v2 and elliptic relaxation function f) of v2-f
turbulence model (based on k-ε-v2 model by Durbin, 1995), to provide necessary closure (Eqns. Fluent
users guide).The v2-f model is an extension of the classical k-ε model, obtained by including transport
equations for quantities representative of the Reynolds stress anisotropy induced by wall blockage. It is a
general low-Reynolds-number turbulence model that is valid all the way up to solid walls and therefore
does not need to make use of wall functions. Other necessary equations to be considered are equations of
ideal gas, sound velocity, dynamic viscosity variation, thermal conductivity variation, gas constant in
terms specific heats, enthalpy and internal energy with assumption of calorically perfect gas (Eqns. Fluent
users guide and Sannaand Tomassetti, 2005). No equations are needed for specific heats because they are
assumed invariable.
Diffusion terms and viscous terms in the equations are descretized using second order central differencing
scheme, convective terms descretized using second order upwind schemes because second order schemes
minimize numerical diffusion and provide more accurate results. For gradients evaluation least square cell
based scheme is used. For solution of the discretized equations, density-based implicit approach is used
because it provides more accuracy and better shock resolution in case of compressible flows compared to
pressure based solver (Fluent users guide). It also provides preconditioning that avoids numerical stiffness
that results in poor convergence rates at low Mach number flows. It provides point implicit linear equation
scheme with an algebraic multigrid method to solve the system of linear equations for all dependent
variables in each cell. The inviscid flux vector that contains characteristic information propagating through
the domain with speed and direction according to the eigen values of the system is evaluated by a standard
upwind, flux-difference splitting (Roe, 1986).
122
Fig. 2 Density contour at PR=25 showing key features of jet structure
Fig.2 provides the necessary visual information about the jet structure. In side the jet a region exists that is
surrounded by barrel shock and Mach disk shock called ‘zone of silence’. This is the region mainly
focused in the present study.
a) b)
Fig. 3 Mach number variation along x-axis from nozzle inlet to Mach disk shock
The Mach number variation on y-axis vs. position in x direction (non-dimensionalized by D) on x-axis at
centerline of zone of silence is plotted in fig. 3b. Such graphs are useful in molecular beam research.
Current CFD solution agrees with MOC fit for centerline of zone of silence given in Miller, 1988 [Eq. (3)
& [Eq. (4)]. MOC solutions are found to be well agreed with experiments for many gases (Owen and
Thornhill, 1952, Reis and Fenn, 1963) so such comparison is useful. Vertical dotted line in fig. 3b
indicates discontinuity (Mach disk shock Location) which makes the flow downstream to be subsonic.
Theoretical area ratio equation [Eq. (2)] for Mach number at centerline of nozzle is also compared with
CFD solution in fig. 3a. Mach number at exactly outlet plane of nozzle in case of CFD solution is not
equal to 1. This is because of slight curvature of sonic plane in downstream direction.
a) b)
123
c) d)
Fig. 4 Density variation along y-axis at various planes parallel to y-axis
Fig. 4 compares off axis density variation up to barrel shock location inside zone of silence for PR = 30
between CFD and MOC fit given by Ashkenas and Sherman, 1966 [Eq. (5)] on various planes parallel to
y-axis at X = 0.000075, 0.0001, 0.000125, 0.00015. These locations are chosen for comparison because
the fit equation predicts well with experiments where flow inclination is lower, as per graph given in paper
by Ashkenas and Sherman, 1966. The discontinuities that can be seen in the figures are due to barrel
shock and Jet boundary. The strength of barrel shock could be seen to increase in x-direction. Also the
curved density profile becomes flat as one proceeds in x- direction (also see fig. 2). These graphs are
useful in plasma research.
a) b)
Fig.5 Features of Mach disk shock varying with pressure ratio
Empirical equation derived from experiments for Mach disk shock location [Eq. (6)], valid for PR ≥ 15,
(Ashkenas and Sherman, 1966) is compared (fig. 5a) and ratio of Mach disk diameter to its location to be
almost constant (approximately 0.336 for Argon or monoatomic gases) proposed from the experiments by
Bier and Schmidt, 1961 and Ashkenas and Sherman, 1966, for PR > 20, is confirmed (fig. 5b). These are
measured using density plots and contours.
5. CONCLUSION
Predictions of flow properties variation inside zone of silence are found to be very accurate. Shock
dimensions and locations are also well agreed with empirical relations. In general, various characteristics
of underexpanded supersonic jet are studied and it is concluded that geometrical and numerical model used
in the simulation is appropriate to analyze underexpanded jets that are used in many applications.
124
EQUATIONS
γ+1 (1)
G=( )
2
A 1 2 γ−1 (2)
= [ 1+ M ]( )⁄[ ( )]
A∗ M γ+1 2
M=ξ (3.232 − 0.7563ξ + 0.3937ξ − 0.0729ξ ) for ξ = x/D > 0.5 (3)
M = 1 + 3.337ξ − 1.541ξ for 0 < ξ < 1 (4)
ρ(y, x) = ρ(x)cos θ. cos ( ) where θ = tan (5)
.
Xm = 0.67D√PR (6)
Po(mbar)D(μm) . (7)
Ѓ = 1646.
To(K) .
If Ѓ< 200: No cluster formation , 200 < Ѓ< 1000: Onset of condensation ,1000 < Ѓ: Massive clustering
NOMENCLATURE
125
10. Owen, P. L., and Thornhill, C. K. (1948), Aero. Res. Council, R and M 2616, Great Britain Reis Victor
H. and Fenn John B., Separation of gas mixtures in supersonic jets, the journal of chemical physics,
vol. 39, no.12, 1963, 3240-3250
11. Roe, P. L. Characteristic based schemes for the Euler equations, Annual Review of Fluid Mechanics,
18:337-365, 1986
126
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/03
1. INTRODUCTION
During engine operations, heat release from the explosion of the charge, increases temperature on the
cylinder walls, piston and area surrounding the valve. In normal working conditions, peak temperature of
the gases inside the cylinder is of the order of 2500 K. At such a high temperature lubrication is
impossible, unless provisions are made for cooling. Also, these high temperature and heat fluxes lead to
thermal expansion and stresses, which can destroy the clearance fits between parts and escalate the
distortions and fatigue cracking of parts. As the demand for the more powerful engines grows day by day,
there is need to have more efficient cooling jacket which match to the design goals. Growth in
computational technology enables us to use more accurate numerical tool for the numerical simulation.
Present work aims to have numerical study of cooling of engine block head using conjugate heat transfer
and optimization technique. Fluid flow and heat transfer analysis is being carried out in engine head block
using multi-physics capability of Abaqus/CAE called co-simulation. Co-simulation integrates the coupled
response of fluid flow with heat transfer in structure.
1.1Geometric and Numerical Modeling
Cylinder block head assembly used in present work is shown in Fig.1a. In order to get better results in
CFD analysis, we have extracted synonymous geometry as actual system, refined mesh at important
locations, identified and defined proper boundary conditions. Fluid domain is extracted by closing all holes
in fluid path using multiple extract option in ExSight tool (Fig. 1b). Mesh generation is the most important
and time consuming part of any numerical analysis. An Octree tetrahedron mesh of appropriate size is
generated over the solid structural domain. Total 3,72,129 cells were generated on structural part and
1,93,482 cells were generated on fluid domain as shown in following figure.
Abaqus/CFD is used for the fluid flow simulation and Abaqus/Standard for the solid heat transfer
simulation of engine head block assembly. The SIMULIA co-simulation Engine (CSE) is the tool in
Abaqus, which allows the two different solvers to interact and exchange the desired variable values at the
specified location, irrespective of mesh density and element types. Present numerical study is carried out
in fully coupled flow-thermal analysis. Fluid and solid heat transfer solvers start at the same time and
exchange the data after every time step in fully coupled analysis. In present study, fluid considered as
water which is incompressible. Three dimensional, unsteady RANS equations are solved. Two equation k-
127
Outflow
Inflow
(a) Engine Structural Part (b) Fluid part (Cooling Jacket)
Fig.1 Mesh generation (Exsight Tool).
REFERENCES
128
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/04
Mr. Pankaj Ghatage Prof. Durgeshkumar Chavan Prof. Ashok .T. Pise
Student M.Tech. Professor Rajarambapu Institute Professor Government
(CAD/CAM/CAE) of Technology, Rajaramnagar, College of Engineering, Karad
Rajarambapu Institute of Islampur 415409. Dist Satara. India 415110
Technology, Rajaramnagar, dkumar.c@rediffmail.com ashokpise@yahoo.com
Islampur 415409.
pankajghatage@gmail.com
ABSTRACT
With the demand for energy continues to grow globally, there is a need to make heat transfer
equipment more energy efficient. At one hand, the exponential growth of electronics, communication and
computer technology and their choice to go for miniaturization has put added pressure on the designer to
create efficient thermal management devices for these systems. Particularly thermal conductivity of a
fluid plays a vital role in the development of energy-efficient heat transfer equipment. An innovative idea
is to suspend nano-sized solid particles in the fluid to improve heat transfer characteristics of the fluid.
Nanofluids are the suspension of nanometer-sized particles in base fluids such as water and ethylene
glycol. In convective heat transfer, number of other factors along with thermal conductivity affects heat
transfer performance, so careful examination of convective heat transfer using nanofluid is required. For
optimum condition of nanofluids, some experimentation is required for better result. As experimentation
is time consuming process, nanofluids are analyzed by using CFD (computational fluid dynamics)
approach. In this work, a systematic computational fluid dynamic investigation with constant wall
temperature boundary condition will be carried out adopting single phase and two phase approach and
the results are compared with experimental results.
Keywords: Nanofluid, convective heat transfer, CFD.
1. INTRODUCTION
The thermal management of many applications like transportation, manufacturing and micro-electronics
is very important, to maintain their desired performance and durability. The improvement to make heat
transfer equipment more energy efficient can be made by focus on reduces the size on one hand and huge
increase in heat flux on the other. Heat transfer fluids such as water, mineral oil and ethylene glycol are
used in many industrial processes. The poor heat transfer properties of these common fluids compared to
most solids is a primary obstacle to the high compactness and effectiveness of heat exchangers. As the
thermal conductivity of a fluid plays a vital role in the development of energy efficient heat transfer
equipment, there is need to find new heat transfer fluid with has higher thermal properties and an
advanced cooling techniques. To overcome above problems, new class of heat transfer fluid called
129
nanofluid can be used. Nanofluid is heat transfer fluid in which nanometer sized solid particles are
dispersed in traditional heat transfer fluid. These fluids exhibit significantly higher thermal properties, in
particular, thermal conductivity, than those base fluids. For optimum condition of nanofluids, some
experimentation is required for better result. As experimentation is time consuming process, nanofluids
are analyzed by using CFD (computational fluid dynamics) approach. The CFD approach has attracted
the attention of researchers in past decade, though the mechanism is not fully understood yet.
A lot of experimental work has been done recently on the forced convective heat transfer of nanofluids in
pipe flow but only few has attempted CFD approach. S.M. Fotukian and M. Nasr Esfahany [1]
investigated turbulent convective heat transfer and pressure drop of Al2O3/water nanofluid inside a
circular tube experimentally. Experimental results were compared with existing correlations for
nanofluid convective heat transfer coefficient in turbulent regime. Results indicated that addition of small
amounts of nanoparticles to the base fluid augmented heat transfer remarkably. M. Haghshenas Fard et
al. [2] studied laminar convective heat transfer of nanofluid in circular tube under constant wall
temperature condition by using CFD approach. They compared two phase and single phase models for
prediction of laminar heat transfer in tube with constant wall temperature for Cu/water nanofluid. They
have concluded that two phase model is more precise than the single phase model for prediction of heat
transfer rate. Akbari et al. [3] has carried out forced convective heat transfer studies in pipe flow with
systematic investigation of computational fluid dynamic with constant wall temperature boundary
condition covering both laminar and turbulent regimes. They found that Single-phase and two-phase
models predict almost identical hydrodynamic fields but very different thermal ones. P.Kumar [4] has
studied the heat transfer enhancement by computational fluid dynamic modeling of the nanofluid flow
adopting single phase approach. He found that both the experimental values and the numerical
predictions show that heat transfer enhancement in the laminar regime were not as significant as in the
turbulent regime. Model predictions in the turbulent regime agree very well with experimental values
than laminar regime so more research needs to be done for conclusion on the efficacy of single phase for
laminar flow heat transfer prediction.
A closer look at all the available literature reveals that very few works has been done on forced
convective heat transfer studies with constant wall temperature boundary condition in turbulent regime
by using computational fluid dynamics adopting two phase approach. So in this work, a systematic
computational fluid dynamic investigation with constant wall temperature boundary condition has been
carried out adopting the single phase and two phase approach in the turbulent regime and the results are
compared with the experimental results available in the literature.
2. EXPERIMENTAL BACKGROUND
Experimental investigation of turbulent convective heat transfer of dilute -Al2O3/water nanofluid
inside a circular tube are reported by S.M. Fotukian &M. Nasr Esfahany. [1]
The experimental set-up is shown in Fig. 1 and consisted of 1100 mm annular tube, which was
constructed of 5 mm diameter inner cupper tube with 0.5 mm thickness, and 32 mm diameter outer
stainless steel tube. The nanofluid flows inside the inner tube while saturated steam enters the annular
section, which created constant wall temperature condition. The effect of Reynolds number and
nanoparticle volume fraction on heat transfer of nanofluid has been studied.
130
Fig.1 Experimental set-up [1]
3. CFD MODELLING
Fig.2 Grid Independence study
It can be observed that the Nusselt number for water increases linearly till an optimum number of
cell volumes is reached. Beyond this, any further increase in the number of cell volumes only increases
the computational time, without any significant improvement in the Nusselt number. Similar trend was
also observed with the nanofluids. So this “optimum” mesh size was selected for further study with both
water and the nanofluids.
131
B. Boundary Condition:-
The following boundary conditions are used for single and two phase modelling
1. Inlet Boundary Condition: -
At the tube inlet, “velocity inlet” boundary condition was used. The magnitude of the inlet velocity is specified
and the direction is taken to be normal to the boundary. Turbulent intensity, I and the hydraulic diameter, Dh
were specified for an initial guess of turbulent quantities (k and ε). The turbulent intensity was estimated for
each case based on the formula I = 0.16(Re)-1/8. [4] At this boundary, the appropriate value for the velocity
components and inlet temperature has specified.
For two-phase modelling DPM boundary conditions used along with above boundary conditions.
C. Numerical solution strategy:-
The commercial CFD solver FLUENT was used to perform the simulations based on finite volume
approach to solve the governing equations, based on finite volume approach to solve the governing
equation with segregated solver. The DPM model with two-way coupling was used for two phase model.
The first and second order scheme was used for discretization. The SIMPLE algorithm was used to
resolve coupling between velocity and pressure fields. The convergence criterion is based on the residual
value of calculated variables such as mass, velocity components, turbulent kinetic (k), turbulent
dissipation energies (ε), energy and volume fraction. In the present calculations, the initial residual values
were set to 10-3 for all variables, except for energy for which 10-6 is used. The under-relaxation factors
used for the stability of the converged solutions are set at their default values. The numerical simulation
was decided as converged when the sum of normalized residuals for each conservation equation and
variables was less than the set residual values. However, the residual for the continuity equation reached
a minimum plateau before the value of 10-4, thus additionally, the mass balance and temperature outlet
are monitored on the flux report and was used as a secondary indicator of convergence when the net
imbalance is less than 1% of the inlet flux through the domain boundary. [4]
D. Data Reduction:-
The area weighted average temperature was noted at the inlet and outlet surfaces of the pipe. The heat
transfer coefficients were calculated as follows.
q = h A (T – Tf ) (1)
Where,
q = heat transfer rate. T = surface temperature
h = heat transfer coefficient. Tf = fluid temperature
A = surface area
132
The fig. 3 show that heat transfer coefficient verses Reynolds number of water which are carried
out by CFD techniques and S.M. Fotukian and M. Nasr Esfahany [1] experimental results. It is clear from
figure the CFD predictions closely agreement with experimental results and heat transfer coefficient
increases with Reynolds number.
Fig. 3 Comparison of CFD prediction of heat transfer coefficient of water with experimental results.
The Fig. 4 show that heat transfer coefficient verses Reynolds number of water and two different
volume fraction of nanofluid. It is clear from figure at constant Reynolds number heat transfer coefficient
of nanofluid is more than water and it also increases with increase in volume fraction and Reynolds
number.
133
Fig. 4 Reynolds number verses heat transfer coefficient.
The Fig. 5 show the heat transfer coefficient of Al2O3/Water nanofluid with 0.03% volume concentration
versus Reynolds number under two phase and single phase models. It can be seen that the CFD
predictions single phase and two phase results show good agreement with experimental with
experimental data but two phase results slightly closer to the experimental results than single phase
results. So two phase model can be used for prediction of heat transfer coefficient.
Fig. 5 Comparison between CFD predictions (based on single-phase and two-phase models) and
available experimental data in Al2O3/Water nanofluid with 0.03% volume fraction.
4.CONCLUSION
In the present work, the computational Fluid Dynamics models has been developed to predict the
convective heat transfer coefficient of nanofluid with different volume fraction in circular pipe. The
effects of some important parameter such as Reynolds number, particle volume fraction and phase model
type on heat transfer coefficient have been investigated under turbulent conditions. It has been observed
that heat transfer coefficient of nanofluid increases with an increase in the volume fraction of nanofluid
and Reynolds number. Both the single phase and two phase CFD results closely agreements with S.M.
Fotukian and M. Nasr Esfahany [1] experimental results. Two phase results slightly closer to
experimental results compared to single phase results. The average relative error of single phase model
was 14.90 % and for two phase model it was 14.70%. As pointed out by M. Haghshenas Fard et al [2],
the average relative error between experimental data and CFD results based on single phase model was
16% while for two phase model was 8%. Contradictorily, Mostafa Keshavarz Moraveji et al [6] observed
maximum error was around 10% for single phase model, so more research needs to be carried out to
arrive at definite conclusion on the capacity of single phase and two phase approach for heat transfer
prediction of nanofluid.
134
REFERENCES
1. S.M. Fotukian, M. Nasr Esfahany, Experimental investigation of turbulent convective heat transfer of
dilute -Al2O3/water nanofluid inside a circular tube, International Journal of Heat and Fluid Flow, 31
(2010) 606–612.
2. M. Haghshenas Fard, M. Nasr Esfahany, M.R. Talaie, “Numerical study of convective heat transfer of
nanofluids in a circular tube two-phase model versus single-phasemodel”, International,Communications
in Heat and Mass Transfer, 37 (2010) 91–97.
3. M. Akbari, N. Galanis, A. Behzadmehr, “Comparative analysis of single and two-phase models for
CFD studies of nanofluid heat transfer”, International Journal of Thermal Sciences, 50 (2011)
1343e1354
4. P.Kumar, “A CFD Study of Heat Transfer Enhancement in Pipe Flow with Al2O3 Nanofluid”, World
Academy of Science, Engineering and Technology, 57 2011.
5. Perumal Kumar, Rajamohan Ganesan, “A CFD Study of Turbulent Convective Heat Transfer
Enhancement in Circular Pipeflow”, International Journal of Civil and Environmental Engineering, 6-
2012.
6. Mostafa Keshavarz Moraveji, Mehdi Darabi, Seyyed Mohammad Hossein Haddad, Reza Davarnejad,
“Modeling of convective heat transfer of a nanofluid in the developing region of tube flow with
computational fluid dynamics”, International Communications in Heat and Mass Transfer, xxx (2011)
xxx–xxx.
135
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/05
136
Recently, many investigators have developed mathematical model of the paper drying process. An
experimental investigation of paper drying done by Lu and Shen, 2007 measured relative humidity of air
in gas pocket on a running paper machine. Widlund et al., 1997 used LDV measurements and CFD
simulations to obtain distributions of velocity and turbulence level around the boundary layers of moving
felts. Hashemi and Douglas, 2003 reported the experimental investigation about the effect of drying
intensity, initial moisture content, sheet formation and paper weight on local moisture non-uniformity.
Bhutani et al., 2012 presented energy efficiency improvement through energy assessment of paper
machines. Mostly in paper industry the challenge is to find out where energy is wasted and how energy
savings are possible. Measuring and improving energy performance is of course not a new idea, as by
Kuvalekar, 2007 and Reese, 2009 different ways for improving energy performance are presented.
Research attention has been often directed towards the moisture boundary layer formation near paper
surface and their physical behaviour with respect to moving paper at different working conditions. A
very less information is available on energy consumption and energy saving in paper drying machine as
reported by Manninen, 2002.
The present work proposes computational model of paper drying process in a paper industry. The
simulation of the drying behaviour of the web is included. The heat and mass transfer within the web was
assumed to occur so quick that no moisture content develops in the direction of thickness. The web is
treated as a water film passing through the dryer section.
The main objective of the current work is to quantify the moisture boundary layers formed near paper
surface and estimate distribution of this moisture inside dryer pocket after saturation.
I. SYSTEM DESCRIPTION OF PAPER DRYING PROCESS
The most common drying system used in paper industry is a multi-cylinder dryer section. It consists of a
series of cylindrical cast iron dryer drums (1.5m diameter); the proposed computational model for the
paper drying process of each dryer pocket was divided into following four phases and as shown in
figure1a.
Phase I: - The paper sheet is in contact with outer surface of the cylinder but it is not covered with the
felt. (AB)
Phase II: - The paper sheet not in contact with dryer cylinder and it is in an open draw, where moisture
can evaporate from both sheet surfaces. (BC)
Phase III: - Similar to Phase-II; but on the opposite side. (DE)
Phase IV: - similar to Phase- I; but on the opposite side. (EF)
(a) (b)
137
Fig.1.Schematic of paper drying system in dryer section
These phases in the model were defined as;
I, IV: - contacting drying period
II, III: - Free movement drying period.
In phases I and IV, which are small parts of the whole drying period, one side of the paper sheet is in
contact with cylinder. It is considered that 35% (Reardon et al., 2000) evaporation occurs in this region
and it limits to vapor diffusion. Similarly phases II and III are defined as free movement drying period
which demonstrates that 65% (Reardon et al., 2000) moisture evaporation occurs in free draw region.
This forms the basis in modelling cell zone mass source condition.
II. DETAILS OF COMPUTATIONAL MODELLING
The proposed Computational model consists of differential equations that govern the behavior of
the physical system and the associated boundary conditions shown in figure 2 a.
(a) Computational domain with boundary conditions (b) structured mesh
Fig. 2.Computational domain for dryer pocket in dryer section.
The grid generation shown in figure 2b was carried out using commercially available software ICEM
CFD to obtain a surface and volume mesh. Since the area of concentration was near paper surface, finer
mesh density was maintained in that region.In order to capture both the humidity and velocity boundary
layers near paper wall surface, the entire model was discretized using structured mesh.
The various parameters used to develop the model of the paper drying process and simulations, are listed
in Table 1.
Table 1. Details of parameters used in modeling of paper drying process
138
Cover angle of paper contacting the cylinder, α 240 ˚
Water evaporation from paper, mevp 0.05 kg/s
Deckle length across CD profile,l 3.6 m
Total number of cylinders, N 43
(a) Before moisture saturation inside pocket (b) After moisture saturation inside pocket
Fig.3.Relative Humidity contour near paper surface (10mm from Paper).
The contour plot has shown in figure 3a reveals that the relative humidity is comparatively high near
bottom of pocket. This is due to continuous increase in the evaporation of moisture from paper surface.
As a result of which moisture layer near paper surface also moves in the direction of paper. There is
continuous extraction of moisture from paper surface which subsequently goes into pocket. This leads to
saturation of pocket volume by moisture at a certain stage. This situation leads to higher energy
consumption.
139
Contours for relative humidity shown in figure 3a and 3b shows that there is a significant difference in
relative humidity, especially in the region near paper surface, after saturation of moisture inside pocket.
Also at the end of both edges, the humidity is comparatively less than the middle in the cross direction
(CD) of machine. This is because edge regions are open to the surrounding air. Therefore, it is necessary
to give due attention to the middle region of pocket for uniform distribution of moisture and identifying
energy saving potential.
Fig.4.velocity of air distribution inside pocket
From the contour plot shown in figure 4, velocity of outer wall surface is noticed to be higher than
velocity of air inside pocket. This is because of rotational speed of surfaces such as paper, felt and dryer
surface, which are defined as moving walls. The low velocity inside the pocket causes poor exchange
with atmospheric air. Thus, it hampers drying rate. This is well understood from the velocity variation
along CD inside dryer pocket shown in figure 5.
Fig.5. Variation of air velocity along CD inside pocket
140
Fig. 6.Variation of relative Humidity inside pocket.
The Variation in the relative humidity with distance along CD profile is shown in figure 6.It was noticed
that moisture content is maximum in the middle of pocket towards CD profile than at edges. The middle
portion of paper web therefore dries more slowly. This causes the faster drying edges to strain when they
shrink resulting in stretched edges, wrinkles and even web breaks; it also causes non uniform moisture
profile along CD. Therefore, the correct way to avoid the uneven drying of paper is to create uniform
drying conditions at the middle and edge sections.
V. CONCLUSION
A Computational model was developed to investigate the Relative humidity profile near paper surface
and moisture distribution inside the pocket in the dryer section of paper industry. After validation of the
model with experimental data and numerical results from open literature, the results obtained in this work
helps to conclude as following.
During contact drying period, moisture moves from paper surface into pocket due to vapor
transport. In free movement drying period, average drying rate is higher.
Moisture content is higher in the middle of pocket along CD profile than at the edges due to which
non uniform moisture profiles were formed near paper surface.
The correct way to avoid the uneven drying of paper is to create uniform drying conditions at the
middle and edge sections.
Balancing the moisture condition is natural solution for uneven drying hence if dry compensation
air enters the pocket in a controlled manner, uniform drying conditions, can be achieved.
Hence, application of various blow box or Pocket ventilation box design and optimization of air
movement is recommended for the moisture removal and control.
141
REFERENCES
[1] Kuvalekar D., “Reducing specific steam consumption through Automation in steam
systems”, Proceedings of PAPAEREX 2007, New Delhi, India, December 7-9, 2007.
[2] Manninen J. et al.,“Energy aspects in paper mills utilizing future technology”, Applied
Thermal Engineering 22 (2002), 929–937.
[3] Naveen Bhutani et al.,“Energy assessment of paper machines”, Energy Procedia 14(2012)
955-963.
[4] Reese D. “Measuring paper Machine Energy Performance”, Proceedings of paper Con’09,
st.Louis, USA, 2009.
[5] S.J.Hashemi, W.J.Murray Douglas.“Moisture nonuniformity in drying paper: measurement
and relation to process parameters”, Drying Technology 21 (2) (2003) 329-347.
[6] Shaun Reardon et al., “Computational modelling of paper drying machines”, September
2000, TAPPI Journal peer reviewed paper.
[7] T. Lu, S.Q. Shen.“Numerical and experimental investigation of paper drying: Heat and mass
transfer with phase change in porous media”, Applied Thermal Engineering 27(2007) 1248–1258.
[8] Widlund ONG, Ragvald HS, Halldin CBH, Lindqvist NLO: Aerodynamics of high-speed
paper machines. TAPPI J 1997; April: 113-8.
142
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/06
VERIFICATION OF PRESSURE DROP ESTIMATION AND FLOW RATE BY TEST FOR AIR
STORAGE AND SUPPLY SYSTEM
Nitinkumar Pol P K Chattopadhyaya
R&DE(E), Pune R&DE(E), Pune
pnitin@rde.drdo.in pkchattopadhyaya@rde.drdo.in
ABSTRACT
1. INTRODUCTION
143
144
with ratio controllersare used to operate the dome loaded pressure regulator remotely. Quick opening and
closing pneumatic ball valves are used to control the air supply duration for the system. The high
pressure delivery hoses are used to connect the output lines to the combustor.
2.1 Required Flow Rate and Delivery Pressure
The system is required to deliver a total of 40 kg/s flow to the combustor. Such high flow can’t be
handled safely by one single delivery line.Hence multiple delivery lines are designed to meet the flow
requirements. Eight delivery lines are configured for the system inclusive of two active redundant lines.
Hence piping system is designed for minimum capacity of 6.67 kg/s mass flow rate for each line
considering at least six operational lines. The delivery pressure of air at hose end is required to be in
range of 4.0 to 5.0 MPa pressure as per the mission requirements.
3. PRESSURE DROP ESTIMATION
145
3.1 PipingLength
The parts causing pressure drop in a fluid system include not only the straight pipe, but also components
such as fittings, valves etc. The pressure drop across a valve or fitting can be considered as being equal to
the pressure drop through a length of pipe. An equivalent length of pipe representing the fittings and
valves is estimated as per procedure laid down in literature [5], which gives nomograph for common type
and size of fittings and valves. Table 1 lists the details of complete piping and fittings for the delivery
lines from dome regulator to hose end.
Table 1 – Details of Piping and Fittings
Nomenclature Length / Equivalent Length, m Quantity Total Length, m
45 degree elbow
Contraction 0.35
Enlargement 0.35 1.05
Straight pipe
lexible Hose
Total Length of Piping 19.85 (say 20 m)
3.2 Effective Gas Pressure
An effective pressure is assumed to initiate the process of calculation of the air flow velocity because, to
deliver a given amount of air expressed in cubic meter at standard atmospheric pressure, an increase in
system pressure will reduce the required air velocity. Since the system requires a high flow rate and the
number and types of, fittings are known, a pressure drop equal to 20 to 40 % is assumed. The effective
system pressure is made equal to (P1+P2)/2, where P1 is pressure at supply i.e., dome regulator outlet and
P2 is pressure at delivery i.e.hose end.Having been known the required air flow in standard cubic meter
per second, the required flow at the effective air pressure can be estimated.
3.3 Estimation of Pressure Drop from Dome Regulator to Delivery Hose End
The pressure drop estimation in one delivery line designed for minimum mass flow of 6.67 Kg/s is
carried out. The required delivery hoseend pressure (P2) is 4.5 MPa. Since the length of pipe and types of
components are known and a high air velocity is desirable, pressure drop equal to 40% of supply pressure
is been assumed and tentative supply pressure is determined. Hence followings can be noted.
Tentative Supply Pressure, (P’1) = 7.5 MPa
Delivery Hose End Pressure (P2) = 4.5 MPa
Tentative Effective Pressure (P’E) = 6.0 MPa
Weight density of air at P’E = 74.43 Kg/m3
146
Volumetric flow rate at P’E = 0.088 m3/s
The empirical pressure drop table [4] is available for 0.69 MPa (100 psi) effective pressure. Referring the
compressed air pressure drop table comparison of pressure drop for various sizes can be done. Selecting
50 NB pipe size, pressure drop of 0.056 Mpa is estimated for pipe length of 20 m.The weight density of
air at P’E is 8.92 times to weight density of air at 0.69 MPa. Because of increased density of air, the
0.056MPa must be multiplied by 8.92 to give an effective pressure drop. It is again corrected for 160
schedule pipe. Hence, the estimated pressure drop equals to 1.375MPa, for 20 m of pipe length. Since
this is less than the assumed pressure drop of 40 %, a lower supply pressure (P1) can be used.
With the size of the pipe known and the pressure conditions approximated, it is now possible to obtain a
closer approximation by using Equation (1). Now a supply pressure of 6.0 Mpa and 50 NB 160 Sch. pipe
size is considered. Hence,
Supply Pressure (P1) = 6.0 MPa
Delivery hose end pressure (P2) = 4.5 MPa
Effective Pressure (PE) = 5.25 MPa and
Weight density at PE, (ρ) = 65 Kg/m3.
Table – 2 : Pressure Drop Estimation
Flow diameter Pressure drop
Piping Section Friction factor [4] Length (m) Velocity (m/s)
(m) (MPa)
Metallic Pipe
0.018 0.0429 0.34
(stainless steel)
Flexible Hose 0.035 0.0508 0.86
The delivery line consist of two sections, first of metallic pipe & fittings; second having flexible hose.
The pressure drop in both the sections is estimated using Equation (1) as summarized in Table - 2.
Hence, the total pressure drop from dome regulator to delivery hose end is estimated to be 1.2MPa.
147
The nozzle was calibrated at NABL accredited test house, Fluid Control and Research Institute, Pallakad
and calibration certificate was obtained. A turbine flow meter with high degree of repeatability and better
uncertainty than required calibration was used as reference meter. The nozzle was mounted downstream
of the reference meter and both were mounted in series. To eliminate the effect of moisture in calibration,
the air having relative humidity of zero percent was used. The flow nozzle was calibrated under the
148
stable, fully developed flow conditions achieved by passing the air through a straight, smooth bore pipe
of sufficient length. The calibration range was 30 to 186 m3/h and Reynolds number ranging from 52500
to 1380440. As per the results of calibration [6], the mean coefficient of discharge, C = 0.9813.
5. TEST SETUP
After the realization of system, experimentation testing was carried out on
the actual system. The pressure drop and mass flow rate from each delivery
line were measured. The flow rate was measured using the flow nozzle
assembly in the system. The flow nozzle assembly was fitted at the end of
hose on suitable platform and supported with anchoring. The absolute
pressure sensors and temperature sensor were fitted onto the flow nozzle
assembly as shown in the Figure - 3. The pressure of air at entry to
nozzleassembly was measured using separate pressure transducer. The
pressure and temperature data were recorded using data acquisition system.
The flow rate is calculated using following equation [2].
= 2∆ … … … … … … . . (2)
1− 4
Where, Qm is measured flow rate in Kg/s, C is coefficient of
discharge (0.9813), β is diameter ratio (0.51), ε is expansion factor (0.80),
d is diameter at throat in m., Δp is differential pressure across nozzle in Pa,
ρ1 is density of air at entry in Kg/m3.
6. VERIFICATION
6.1 Measured Pressure Drop from Dome Regulator to Delivery Hose End
Table – 3 : Actual Pressure Drop
Dome regulator supply pressure
Hose end delivery Measured pressure drop in
Test No.
(MPa) pressure (MPa) delivery line (MPa)
Test 1
Test 2
Test 3
149
Mass flow rate from the delivery lines was measured in the experimentation setup. The differential
pressure across the nozzle, pressure of air at entry of nozzle and temperature of air was measured during
the firings. Three firings test were carried out for each line. Data recorded for first delivery line testing is
shown in Table -4.
Table 4 – Data Recorded during Air Flow Measurement
Dome Reg. Supply Nozzle Entry Nozzle Pressure, MPa(a) Temp. of air,
Test No. Discharge Time
Pressure, MPa Pressure, MPa Upstream (PDownstream (P
1) 2)
7 sec 4.45 4.25 3.07
7 sec 4.48 4.27 3.10
7 sec 4.55 4.34 3.12
The flow measurement calculations were carried out using Equation 2. The results of flow measurement
are given in Table – 5.
The average flow rate in delivery lines is 6.80 Kg/s.
TABLE – 5 : Flow Measurement Result
Density of air at nozzle entry,
Differential pressure across Measured mass flow rate,
Test No. 3
ρ (Kg/m ) nozzle, ΔP (MPa) (Kg/s)
Test 1 54.84 1.18 6.75
Test 2 55.21 1.17 6.75
Test 3 56.09 1.22 6.92
7. CONCLUSION
In this study a high pressure compressed air flow of air storage and supply system is analyzed. The
pressure drop estimation in the piping system from dome loaded pressure regulator to delivery hose end
is carried out. The results of the reported estimation are then verified with experimental results for the
system. It has been revealed that the reportedestimation is fairly accurate to determine the pressure drop
in high flow &pressure air delivery systems. The measured pressure drop is at the higher side than the
estimated drop which may be due to fact that flexible hose have variation in friction factor value over
long length. The mass flow rate from the system is also measured using pressure differential device and it
has been established that the delivery lines are capable to deliver the required air flow. The system is
verified by testing and qualified for the intended application.
ACKNOWLEDGEMENT
The authors are grateful to Dr. S Guruprasad, Director R&DE(Engrs), Pune for his valuable guidance and
kind permission to publish this paper.
150
REFERENCES
[1] NAVFAC DM-39, “Hyperbaric Facilities Design Manual 39”, Department of the Navy, Naval
Facilities Engineering Command, pp 223-240 (1982).
[2] ISO 5167-1, “Measurement of Fluid Flow by means of Pressure Differential Devices inserted in
circular cross-section conduits running full”.
[3] Benard C.J., “Handbook of Fluid Flowmetering”, first ed.The Trade & Technical Press Limited,
England, pp.
[4] Dr. Swierzawski T.J., “Flow of Fluids in :Nayyar M.L., Piping Handbook”, seventh ed., McGraw-
Hill Book Company, New York, pp. B.351-B414.
[5] Technical Paper No. 410, “Flow of Fluids through Valves, Fittings, and Pipe”, Crane Company,
Chicago, USA.
[6] “Calibration Report No. CAH 319 1105 018 on Flow Nozzle”, Fluid Control Research Institute,
Pallakad.
151
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/07
EXPERIMENTAL & NUMERICAL ANALYSIS OF JET IMPINGEMENT HEATING ON
CYLINDRICAL BODY
Ranjit J. Singh V. R. Kalamkar
M-Tech student Associate Professor,
Heat Power Engineering Mechanical engineering Department
VNIT – NAGPUR VNIT - NAGPUR
ABSTRACT
Jet impingement technology is used to attain high temperature distribution over the target body in the
short operating duration. Both cooling and heating air jets can be used, where precise and rapid thermal
control is required .In this paper the heat transfer predictions of hot air jets impinging on circular
cylinders was investigated experimentally & by using computational fluid dynamics (CFD). The
distribution of local Nusselt numbers and temperature around the cylinders for different Reynolds
numbers (8,000-100,000), variation of distances between the jet and cylindrical body (H/D ratio) from 1
to 3 was analyzed. The k-ε and k-ω turbulence model is used separately. The validation of the CFD
results is carried out by experiment with the help of Resistance Temperature Detectors (RTDs) to find
out the temperatures at various points on cylinder, blower and heater to get hot air at different velocities.
The flow characteristics and the heat transfer and temperature distribution around the cylinders are found
to be dependent on the H/D ratio with different Reynolds number. Heat transfer increases for higher
Reynolds number and temperature reduces for higher H/D ratio.
Keywords:Jet impingement, Resistance temperature detector, Nusselt number, cylinder, CFD,
Experiment
1. INTRODUCTION
Impinging jet heat transfer has been established as an effective technique for heating, cooling, or drying a
target surface and has a variety of engineering applications. Many previous investigations have been
carried out to understand the heat and mass transfer characteristics of impinging jet through experiments
and numerical calculation. Heating and cooling are important processes in the food industry. By using
computational fluid dynamics (CFD), the fluid flow, turbulence, heat transfer and temperature
distribution from the impinging jets to the cylindrical product can be predicted. CFD modeling is a
powerful tool in studying complicated flow and heat transfer. It can be used to investigate the effect of
various parameters on the flow pattern and the heat-transfer distribution on the surface of the product,
leading to a reduction in process time in the experimental tests required. Rapid heat-transfer methods can
be used to shorten the process time and increase the production rate. Jet Impingement is a swift
convective heat-transfer method, which consists of directed jets that impinge on the surface of the
product. It can be used to speed up thermal processes in the food industry as well as in other applications.
Impinging jets have been widely used and developed to increase heat & mass transfer in areas such as
152
cooling gas turbines, drying paper and textiles, and cooling electronic components, heating and cooling
of food, melting chocolates etc.
E E.M. Olsson, and others [1, 5, 7], carried out at domain pressure 0.1 MPa and 2 o C, by keeping solid
food product at 35o C; they reported that the heat transfer around the cylinder increases with increasing
Reynolds numbers. The heat transfer at the Reynolds numbers investigated does not seem to depend
significantly on the jet-to-cylinder distance (H/d). Arnab Sarkar, R. Paul Singh [2] studied the effect of
constrictions in a jet for an array of multiple jets, effect of the roughness of the impingement surface on
the flow characteristics. E E.M. Olsson and others [3], pointed out that the highest average heat transfer
is found for cylinders under two impinging jets with a shared distance of H/d=2. For longer and shorter
distances (H/d=1 and 4), the heat transfer is reduced. For a jet distance of H/d = 4, the heat transfer is
highest for the smallest opening (d/D=1). Larger openings reduce the heat transfer significantly. Carmela
Dirita, and others [4] studied that the heat transfer rate is altered by the conduction in the food. Chougule
N.K and others [6] studied the effect of H/d ratio on heat sink flat plate by jet impingement. While
GoriandBossi [8]studied the effect of impinged free cylinders, with no inference on the effect of
surrounding limiting walls. Downs and James [9] reviewed the characteristics of heat transfer from round
and slot impinging jets, where they summarized the impact of geometric and temperature effects,
interference and cross flow, turbulence levels, incidence and surface curvature.
1.1 Problem definition
In this paper experimental & CFD analysis of the heat transfer between a cylindrical body and hot air
from single round jet is carried out. The primary objectives of this paper can be summarized as below.
1) To analyze the heat transfer rates along the jet impingement area for close nozzle to jet spacing over
cylindrical body.
2) To monitor the heat transfer at a reference temperature (480 c) for varying Reynolds Numbers.
3) To study the effect of potential core jet impingement on local heat transfer rates.
4) To study the effect of jet height to cylindrical diameter ratio (H/D ratio).
5) To study the effect of jet diameter to cylindrical diameter ratio (d/D ratio).
2. EXPERIMENTAL SET UP
The layout of experimental set up is shown in Fig 1.It consists of 1 hp blower, by pass valve, orifice
meter, heater (Nichrome wired), and Resistance temperature detectors.The air is supplied through
centrifugal blower, which draws air from the atmosphere and delivers it along a pipe through by pass
valve to the heating pipe. After adjusting the H/D ratio make heater on to heat pipe and simultaneously
start the blower to impinge the hot air on the cylindrical body. The heat is supplied by adjusting dimmer
stat attached to the heating coil in the range of 135 watts. The amount of heat (Q) by digital voltmeter (90
V) and digital ammeter (1.5 A) and flow air is measure by digital anemometer placed normal to the flow
of jet.
153
Fig1. General layout experimental set up of jet impingement.
3.NUMERICAL ANALYSIS.
The boundary conditions used in the simulation are tabulated below.
Sr No Zone name Zone Type Temperature Velocity
Jet Inlet Inlet c 70 m/s
154
Fig 3.Triangular unstructured grid (H/D = 1).
3.2.1 Governing equations
The standard governing Reynolds-averaged Navier–Stokes and energy equations are used in conservative
form and for primitive variables, to find out velocity components and pressure and temperature to solve
155
flow and heat-transfer problems, the governing equations used are transport equations for momentum and
energy, developed from the conservation laws of physics.
Continuity Equation:
+ = 0
р
(ρu) + (ρuu) + (ρvu) = - + {(2ρ( v + v t )) }+ {ρ( v+vt)( + )}
р
(ρv) + (ρuv) + (ρvv) = - + {(ρ( v + v t )( + )}+ {2ρ ( v+vt ) )}
Energy Equation :
156
Fig 7. Grid independence test for H/D = 2 at Re = 8000.
4.2 Validation of simulation.
Validations has been carried out at fixed temperature and Reynolds number, and for H/D = 1,
H/D = 2 & H/D = 3. The Reynolds number was taken as 8000 at 48o c, after being validated from
Experimental set up. The further analysis is carried out and graphs has been taken by varying the
Reynolds number from 10,000 to 100,000 at fixed temperature in ANSYS software using fluent as
solver.
Fig 4 Validation of CFD by Experimental results Fig 5 Validation of CFD by Experimental Results
for
For H/D = 1 Re = 8000. H/D = 2, Re= 8000.
The graphs shown in fig 4 to 6 was the comparison between experimental results and CFD results,
showing close relation between CFD and Experimental results up to H/D = 2 shown in fig 4 & 5, beyond
this if we increases the ratio of H/D then temperature achievement is slope down in both the CFD &
experimental cases as shown in graph H/D = 3 in fig 6.
157
Fig 6. Validation of CFD & experimental result for H/D = 3, at Re = 8000.
The main objective of this work was to study the temperature distribution at various H/D ratios by
varying the Reynolds number at fixed temperature, as the H/D ratio increases the temperature
distribution over the surface reduces significantly as shown in fig 6.
Fig 8. Heat transfer variation at Re = 10000, Fig 9. Heat transfer variation at Re = 20000
For different H/D ratios (1, 2 & 3) for different H/D ratios (1, 2 & 3)
The potential core of jet was found to be short, about 1 to 2 height of jet to diameter of target body. Other
authors had found the potential core to be longer, about 4 slot jet widths [1, 3, and 8]. The degree of
confinement influences the flow entrainment in the jet. The nozzle in the impingement system in Figure
8 to11 was constructed as unconfined jet, which resulted in a flow entrainment of air different from those
158
in other investigations, and may explain the observed difference. As expected, the turbulence intensity
was high in the shear layers, the jet lost kinetic energy to the surroundings before impinging on the
cylinder.
Fig 10. Heat transfer variation at Re = 50000 Fig 11. Heat transfer variation at Re=100000
For different H/D ratios (1, 2 & 3).For different H/D ratios (1, 2 & 3).
4.4 Effect of surface curvature (d/D ratio) on heat distribution
The effect of the curvature of the surface (ratio of jet diameter to cylinder diameter) was also
investigated. It was found that the Nusselt number distribution around the cylinder and in the stagnation
point was affected by the surface curvature. The Nusselt number increases with increasing surface
curvature, shown in Fig. 12, the Nusselt number and the Reynolds number are based on the jet diameter
(d), which was constant and velocity of jet was varied to get different Reynolds number & diameter of
cylinder was also varied to get different surface curvature . The height of the cylinder are kept constant
(H = 50 mm).
159
Fig12. Heat transfer around the cylinder for
different d/D ratio, at Re = 10000 and H/D = 2. Fig 13.Velocity vector around the surface.
4.4 Jet flow characteristics
The thickness of the boundary layer determines the heat transfer see Fig. 13. It shows the flow pattern of
jet over surface of cylinder, High velocity creates a thin boundary layer, and a thin boundary layer has a
high rate of heat transfer.
A turbulent boundary layer increases the rate of heat transfer as compared to a laminar boundary layer.
The flow in the stagnation point has a high degree of turbulence, which causes high heat transfer in the
stagnation region. The heat transfer decreases over the curved surface, the turbulence level is probably
reduced by the locality of the wall. The heat transfer is low in the separation region. The recirculation
creates an increase in velocity and heat transfer. The flow on the back at the cylinder (Θ = 180O) is zero
indicating zero heat transfer.
5.CONCLUSION
The heat transfer from a circular jet impinging on a circular cylinder placed on a solid surface has been
studied using CFD simulations with the K-ε & K-ω turbulence models. Validation of the simulation has
been carried out by experimental results & using K-ε turbulence model. The simulations predicted the
heat transfer well on the upper part of the cylinder, but with some deviation in the non-isotropic region in
the wake. Heat transfer increases as Reynolds number increases. Heat transfer around the cylindrical
body is better if the H/D ratio is more than 2 to 4. Though the heat distribution is more but the
temperature distribution over the surface of cylinder decreases when H/D increases beyond H/D = 3. This
is due to entrainment of fresh air from surrounding into the path of hot air jet impinged on the body
160
which reduces the temperature of jet. To get better result of temperature distribution, H/D ratio must lie
in the range of 1 to 3.
6.ACKNOWLEDGEMENTS
This work is funded by Visvesvaraya National Institute of Technology, Nagpur. And guided by Professor
V. R. Kalamkar, Mechanical engineering department (VNIT-Nagpur).
NOMENCLATURE.
Cp specific heat (J/(kgoC)) d diameter of jet (mm)
d/D surface curvature D diameter of cylinder (mm)
h heat transfer coefficient (W/(m2oC) H/d jet-to-cylinder distance
ν velocity in y- direction K turbulent kinetic energy (m2/s2)
Nu Nusselt number (Nu = h d/k) P pressure (Pa)
T temperature (o C) u velocity (m/s) in x- direction
Re Reynolds number (Re = ρvd/μ ) t time (s)
Greek symbols
ε turbulent dissipation rate ( m2/s2) Θ angle on cylinder (o)
μ dynamic viscosity ( Pas) ν kinematic viscosity ( m2/s)
ρ density ( Kg/m3) ω specific dissipation rate (s-1)
REFERENCES
1. E.E.M. Olsson, L.M. Ahrne, and A.C. Tragardh. Heat transfer from a slot air jet impinging on a
circular cylinder. Journal of Food Engineering 63: 393–401, 2004.
2. Arnab Sarkar, R. Paul Singh. Air impingement technology for food processing: visualization studies,
Swiss Society of Food Science and Technology, 37, 873–879, 2004.
3. E.E.M. Olsson, L.M. Ahrens, and A.C. Tragardh. Flow and heat transfer from multiple slot air jets
impinging on circular cylinders. Journal of Food Engineering 67: 273–280, 2005.
4. Carmela Dirita, Maria Valeria De Bonis, Gianpaolo Ruocco, CFD turbulent modeling of jet
impingement and its validation by particle image Velocimetry and mass transfer measurements,
Journal of Food Engineering 81 (2007) 12–20,2006
5. Eva E.M. Olsson, Christian Tragardh, CFD Modeling of Jet Impingement during Heating and
Cooling of Foods, Computational Fluid Dynamics in Food Processing, 2007
6. Chougule N.K, Parishwad G.V, Gore P.R, Pagnis S, Sapali S.N,CFD Analysis of Multi-jet Air
Impingement on Flat Plate, Proceedings of the World Congress on Engineering 2011 Vol III,2011.
7. E.E.M. Olsson, L.M. Ahrens, and A.C. Tragardh. Prediction of optimal heat transfer from slot air
jets impinging on cylindrical food products using CFD. In: Proceedings of the 9th International
Congress on Engineering and Food (ICEF 9), Montpellier, France, 2004.
8. F. Gori and L. Bossi. On the cooling effect of an air jet along the surface of a cylinder. International
Communications in Heat and Mass Transfer 27 (5): 667–676, 2000.
161
9. Downs, S. J., & James, E. H. Jet impingement heat transfer – a literature survey. American
Society of Mechanical Engineers (Paper), 87-HT-35, 1–11, 1987.
162
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/09
BIFURCATION ANALYSIS OF A SINGLE GAS BUBLE RISING IN A LONG VERTICAL
CHANNEL
Shantanu Ghatnekar C. M. Sewatkar*
Department of Mechanical Engineering, Department of Mechanical Engineering,
College of Engineering Pune, India - 411005. College of Engineering Pune, India – 411005.
ghatnekarshantanu@yahoo.co.in cms.mech@coep.ac.in
ABSTRACT
The dynamics of a single gas bubble rising in a long vertical channel is discussed in this work.
The solution of this problem is obtained using Volume of Fluid method (VOF) coupled with finite
volume method solution of Navier-Stokes equations. The effects of governing parameters have been
numerically studied for 10 ≥ Re ≥ 2000 and 0.27 ≥ B ≥ 2. Elementary results show that after the bubble
reaches maximum rise velocity above a certain Reynolds number the bubble starts oscillating in the
vertical channel. Thus it is concluded that the bifurcation occurs at a critical Reynolds number. The
problem is solved to find values of critical Reynolds Number for different values of Bond Number using
bifurcation analysis. It is found that critical Reynolds number decreases with increase in Bond number.
The rise velocity of the bubble is affected by both Reynolds number and Bond number.
Keywords: Bubble dynamics, Vertical channel, Numerical analysis, VOF, Bifurcation.
1. INTRODUCTION
The dynamics of gas bubble is a problem having many applications in various fields and processes such
as biological systems, nuclear power plants, heat exchangers etc. Examples are multiphase flow in pipes,
porous media and motion of gas bubbles through bloodstream. Hence it is important to understand and
predict the behavior of these bubbles to understand complex real life processes. The present focuses on
the effect of gas bubbles rising in a liquid vertical channel. It is important that the vertical channel is long
enough so that the dynamics of the bubble can be clearly understood as the flow will be completely
developed by the time the bubble moves out of the channel.
In an early experiment by Zukoski (1965) on long bubbles in closed tubes the rise velocity of the bubble
was found to be varying with respect to the angle of inclination, with maximum rise velocity at the
critical angle at 45˚. This critical angle was found to be varying with Bond number (B ~ 1 – 4). In a
similar study by Maxworthy (1991) the critical angle was found to be at 50˚ where the rise velocity of the
bubble was maximum. On the contrary in an experimental study by Masliyah (1993) the rise velocity of
the bubble decreased with the inclination of channel from vertical for spherical bubbles. Their
experiments involved very small bubbles with an effective radius of 0.085 cm to 0.145 cm resulting in a
range of Reynolds number from 10 to 575 and Bond numbers less than 1. Similar results were noted by
Debisschop (2001) and Norman (2005a) where the rise velocity increases with angle of inclination with
maximum velocity at vertical position. This is true for small Bond numbers (B < 1) but not at large Bond
numbers.
163
The rise velocity of the bubble is also found to be affected by Bond number. Zukoski (1965), Chen
(2000) and Norman (2005a) reported that the rise velocity increased monotonically with increase in Bond
number. Chen (2000) compared the rise velocities for different bubble regimes and it was concluded that
the rise velocity decreased with Bond number where the Bond number is varied with large intervals. This
was observed due to change in shape of the bubble. Debisschop (1999) and Norman (2005a) also
observed the effects of Bond number on bubble shapes termed as shape oscillation. Desbisschop (1999)
reported steady shapes at lower Bond numbers (B ~1 – 4) and unsteady at higher Bond numbers, while
Norman (2005a) reported steady bubble shapes at B < 2 and Re < 1000. Further increase in Bond number
(B > 2) caused the bubble shape to oscillate. Hopf bifurcation occurred when the oscillations changed
from damped to steady state with rupture of bubble at the bifurcation point (B ≈ 4).
The Reynolds number affects the shapes of the bubble as well as the path of the rise of bubbles termed as
path oscillation as suggested by Chen (2000) and Norman (2005a) in their numerical analysis. An
increase in Reynolds number caused the bubble shapes to change from steady shapes to steady
oscillations. Aspect ratio of the bubble was found to be increasing with increase in Reynolds number.
Norman (2005a and 2005b) observed for inclined channel the bubbles repeatedly bounce off the channel
wall for higher Reynolds number. Masliyah (1993) also noted that the rise velocity was also found to be
increasing with respect to increase in viscosity (decrease in Reynolds number) while Chen (2000)
suggested that viscosity ratio did not have any significant effect. Masliyah (1993) suggested that large
bubbles were found to rise faster than smaller bubbles. Here the bubbles were in spherical cap regime.
The spherical cap regime is defined as the region where flow regime is 'inviscid'. This regime occurs for
Bond number greater than 40 and Reynolds number greater than 150. Chen (2000) reported the rise
velocity of the bubbles increased with increase in density ratio (80 to 1000).
Thus, it is noticed that the bubble dynamics has to be understood as a function of different governing
parameters such as Reynolds number, Bond number, angle of inclination etc. The prediction of the
critical Reynolds number beyond which the oscillations of the bubble starts is still a characteristic
problem. The present work adopts bifurcation technique to obtain the values of critical Reynolds number
for different Bond number. The simulations are further carried out to understand the behavior of bubble
at different Reynolds number beyond the critical value.
∇. =0 … (1)
164
∇ ∇ ∇F
=− + − − … (2)
The Reynolds Number and Bond number are defined as below,
σrρ
= , = … (3)
In Eq. (1) and (2), the interface between the fluids moves with the fluid, hence the Volume fraction (F)
evolves by the equation
+ .∇ = 0 … (4)
The values of the density (ρ) and viscosity (µ) are not constant in the neighborhood of the interface, but
rather depend on volume fraction (F). Far from the interface, each of these parameters is constant and
equal to the value in the liquid (i.e., each are equal to 1) or gas (ρB/ρLand µB/µL). These viscosities and
densities are modified using the mean viscosity Eq. (2) and density equation Eq. (3) given by,
= + [1 − ] … (5)
= + [1 − ] … (6)
The curvature of the interface ĸ is determined from the volume fraction equation,
∇F
= ( ) = ∇. … (7)
|∇F|
Here the characteristic velocity is defined as (σ /µL) and the characteristic time as (WµL /σ). The
equations Eq. (1) to Eq. (7) were solved using ANSYS Fluent 12. The geometry and mesh was generated
using ANSYS ICEM CFD. The geometry was generated in rectangular co-ordinates and the mesh type
was quadrilateral throughout the domain. The cell lengths were taken to be equal in both x and y
directions. The case was defined as pressure based solver with SIMPLE as pressure – velocity coupling,
PRESTO as pressure correction algorithm, QUICK scheme for momentum equations and finally Geo-
Reconstruct algorithm for Volume fraction equation. All the above schemes were chosen after referring
to the ANSYS Fluent manuals.
The boundary conditions are defined as shown in Fig. 1(b). The no slip condition is applied to the left
and right channel walls. The bottom boundary is taken as inlet while top boundary is taken as outlet. The
inlet and outlet conditions are provided so as to stimulate an infinite vertical channel where the primary
phase is liquid. This takes care of the possibility of effects due to outside conditions. The bubble is
assumed to be circular with effective radius (ξ = r / W) of 0.1425 and the bubble is placed at the center of
the channel and 0.5 units from the bottom boundary. The distance 0.5 is selected in such a way that the
bubble is sufficiently away from the bottom boundary (greater than diameter of the bubble) to avoid any
interaction with it. The study is carried for bubble with radius (r) of 0.1425 only.
The problem was solved for quadrilateral grids only. The effect of bubble shape and Reynolds number
were studied for grid sizes N = 32, 64, 128 and 256. For small grid sizes (N = 32, 64) the bubble shape
was distorted and the diffused interface was thick thus reducing the accuracy of the problem. As of for
165
grid sizes N = 128 and N = 256 the diffused interface is smooth and thin. For grid independence study
other parameters were also considered. The results were validated with the results by Norman (2005a)
and Hysing (2009). After considering all the parameters the grid with N = 128 was chosen for the study.
(a) (b)
Fig.1. (a) Geometry of the problem; (b) Boundary conditions for the problem.
In this literature the governing parameters are Reynolds number and Bond number. The Bond number is
varied from B = 0.27, 1, 2. The Reynolds number is varied in such a way that at first the approximate
location of the critical Reynolds number is located. Here the difference between values of Reynolds
number varies from 10 to 50. After the location of the range between which the critical Reynolds number
exits the values are varied with a difference of 2 to 4. The exact critical Reynolds number cannot be
determined via computations as the value can exists between a very short range (0.2 to 1).
3. RESULTS AND DISCUSSION
In the bubble dynamics problem it has been observed that flow patterns for the bubble vary according to
viscosity ratio of the fluids and the surface tension existing between them. In this problem these
parameters are being governed by the Reynolds number and Bond number respectively. Careful
observation of the equation for Reynolds number shows that the only variable parameter is viscosity and
that in Bond number is surface tension. Thus variation in these two parameters results in variation in the
flow patterns.
3.1 Effect of Reynolds number
The variation in Reynolds number results in variation in viscosity of the both the fluids for constant
density ratio within the fluids. It has been observed that with increase in Reynolds number causes the
steady bubble shapes to deform. This deformation is very low over a large range of Reynolds number.
The deformation in shapes is such that they become flatter on the top and round at the bottom with
increase in Reynolds number, as shown in Fig. 2(a). This effect was reported by Norman (2005a).
Further increase in Reynolds number causes the bubble to oscillate for lower Bond numbers (B = 0.27 to
B = 2). This effect was observed in studies by Chen (2000) and Norman (2005a). Figure 2(b). shows the
166
position of the variation of center of bubble along the channel length for different values of Reynolds
numbers. It is observed that with increase in Reynolds number there is no significant change in the wave
length of the oscillations also they appear to be steady with further increase. The amplitude of
oscillations increases with the increase in Bond number. Due to introduction of errors in numerical
computation it is difficult to determine the critical Reynolds number as it becomes difficult to separate
error curve from the oscillation curve.
(a) (b)
Fig.2. (a) Effect of Reynolds number on shape of bubble (B = 1); (b) Effect of Reynolds number on
the center of bubble (B = 1).
The bubble starts oscillating after a particular length in the channel. This length can be identified as
critical length of oscillation. As the Reynolds number is increased beyond the critical Reynolds number
the critical length decreases. Figure 3 shows the change in critical length of oscillation for B = 1 with
respect to Reynolds number. It is observed that as the bubble starts oscillating the rise velocity of the
bubble drops and oscillates, as shown in Fig. 3. This amplitude of oscillation increases with the increase
in Reynolds number.
167
(a) (b)
Fig.3. Effect of Reynolds number on the rise velocity of the bubble (a) B = 0.27; (b) B = 1.
The normalized rise velocity of the bubble reduces with increase in Reynolds number, as shown in Fig. 3.
This result is valid as the Reynolds number increases the viscosity of the fluids increases and hence the
rise velocity decreases. Though the change is rise velocity in this case is not large. Chen (2000) observed
no significant change in the rise velocity with respect to change in viscosity ratio.
3.2 Bifurcation Analysis
As stated earlier the bubble oscillates above a critical Reynolds number for a constant Bond number,
where bifurcation occurs. This critical Reynolds number decreases with increase in Bond number. After
calculations based on the results obtained by numerical analysis it is found that the nature of bifurcation
of the results is Hopf bifurcation. Using the formulae for Hopf bifurcation ∝ ( − ) . the
bifurcation curve was plotted along with the numerical values obtained by numerical analysis. The
critical Reynolds number obtained from bifurcation analysis matches the results from numerical analysis.
This critical Reynolds number is found to be decreasing with increase in Bond number. For B = 0.27 the
critical Reynolds number by bifurcation analysis was observed at Recr = 1465, while that for B = 1, it
was observed to be Recr = 285.6. For B = 2 the critical Reynolds number was observed within the range
of Re = 80 to Re = 90. Figure 4 (a, b) shows the bifurcation curve for Bond numbers 0.27 and 1
respectively.
168
(a) (b)
Fig.4. Hopf bifurcation for (a) B = 0.27; (b) B = 1.
3.3 Effect of Bond number
The variation in Bond number results in variation in surface tension between both the fluids. As Bond
number increases the surface tension decreases. It has been observed that as the Bond number is
increased keeping the Reynolds number constant the viscosity of the fluids reduces. In a study by
Maxworthy (1991) for Bond number above 40 and Reynolds number above 150 the flow becomes
“inviscid”.
For lower Bond numbers (B = 0.27) the steady bubble shape is spherical. For B = 2 the bubble shape
changes such that it is flatter at top and bottom, as shown in Fig. 5. This was observed by Chen (2000)
and Norman (2005a). Thus we can conclude that aspect ratio of the bubble increases as the Bond number
is increased. Here the aspect ratio is defined as the ratio of the difference of the maximum and minimum
extent of the bubble interface in the x direction to the difference of the maximum and minimum extent in
the y direction.
169
Fig.5. Effect of Bond number on bubble shapes
The normalized rise velocity increases with respect to increase in Bond number when the Reynolds
number was kept constant. Figure 6(a) shows that for B = 1 normalized rise velocity is higher than that of
B = 0.27. This effect was confirmed by Zukoski (1965) in his experiments. In the work by Norman
(2005a) it was concluded that as the Reynolds number based on the rise velocity of the bubble decreased
with decrease in Bond number while Chen (2000) reported that there is an increase in the rise velocity in
the radial direction of the channel as Bond number is increased.
(a) (b)
Fig.6. (a) Effect of variation of Bond number keeping Reynolds number constant on normalized rise
velocity of the bubble (Re = 500); (b) Effect of Bond number on normalized x direction velocity
There is change in amplitude of oscillation velocity of the bubble center with respect to change in Bond
number. Increase in Bond number increases the amplitude of oscillations of the bubble. Figure 6(b)
170
shows the different amplitudes of oscillation for respective change in Bond numbers. Also change is
observed in the wave length of oscillations. The wave lengths of the oscillating wave increases with
respect to decrease in Bond number.
4. CONCLUSION
In this literature numerical simulations were carried out for a single bubble in a long vertical channel.
The effect for the flow governing parameters mainly Reynolds number and Bond number are studied.
The density ratio, viscosity ratio of the fluids, the channel length and width, initial radius of circular
bubble along with its initial position in the channel are kept constant throughout the study. The results are
studied over a small range of Bond numbers (B = 0.27 to B = 2). The Reynolds number is varied for a
particular case of Bond number such that the density of the numbers is near the critical Reynolds number.
It can be seen that the rise velocity of the bubble is steady and has reached a maximum value long before
the oscillations start. The wakes are developed below the bubble as it rises due to buoyancy. These wakes
become unsteady for higher Reynolds number. Due to these wakes the bubble experiences oscillations.
From the observations the effect of wakes is also the cause for the deformation of the bubble during
oscillations. This was observed by Esamaeeli (2005). Thus it can be implied that the phenomenon of
bubble dynamics is complicated for a flow in a long vertical channel.
REFERENCES
1. CHEN, L., GARIMELLA, S. V., REIZES, J. A. & LEONARDI, E. 2000 The development of bubble rising in
a viscous liquid. J. fluid Mechanics, 387, 61- 96.
2. DEBISSCHOP, K. M., MIKSISA, M. J., ECKMANN, D. M. 2002 Bubble rising in an inclined channel.
Phys. Fluids14, 93-107.
3. ESAMAEELI, A. & TRYGVASON, G. 2005 A direct simulation study of buoyant rise of bubbles at O
(100) Reynolds number. Phys. Fluids17, 093303.
4. HIRT, C. W. & NICHOLS, B. D. 1981 Volume of Fluid (VOF) Method for the Dynamics of Free
Boundaries. J. Comput. Phys. 39, 201-225.
5. HYSING, S., TUREK, S. KUZMIN, D. PAROLINI, N. BURMAN, E. GANESAN, S. TOBISKA, L, 2009
Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Numer. Meth.
Fluids. 60, 1259–1288.
6. MASLIYAH, J., JAUHARI, R. & GRAY, M. 1993 Drag co-efficients for air bubbles rising on an inclined
surface. Chem. Engg. Science, 49, 1905-1911.
7. MAXWORTHY, T. 1991 Bubble rise in an inclined plane. J. fluid Mechanics, 229, 659-674.
8. NORMAN, C. E & MIKSISA, M. J. 2005a Dynamics of a gas bubble rising in an inclined channel at
finite Reynolds number. Phys. Fluids17, 022102.
9. NORMAN, C. E & MIKSISA, M. J. 2005b Gas bubble with a moving contact line rising in an inclined
channel at finite Reynolds number. Physica D 209, 191-204.
10. TSAO, H. K. & KOCH, D. L. 1997 Observations of high Reynolds number bubbles interacting with a
rigid wall. Phys. Fluids 9, 44.
171
11. ZUKOSKI, E. E. 1966 Influence of viscosity, surface tension, and inclination angle on motion of long
bubbles in closed tubes. J. Fluid Mech. 25, 821-837.
172
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/010
STUDY OF THE POCKET VENTILATION SYSTEM IN DRYER SECTION OF PAPER
INDUSTRY
Bharat Patil1 Dr. M. K. Nalawade2
bharatmtech.vit@gmail.com mukundnalawade@gmail.com
Vishwakarma Institute of Technology, Bibwewadi, Pune.Maharashtra, India 411 037.
ABSTRACT
In this work, computational model of pocket ventilator along with dryer pocket were proposed. Use of
CFD simulation model to optimize pocket ventilation (PV) system in a dryer section of paper machine
can be a useful tool to improve drying efficiency of paper machine. In conventional paper machines, the
primary reason for uneven drying across the deckle length was uneven distribution of pocket air humidity
between the edges and middle region of the dryer pocket. Balancing of the moisture condition is a natural
solution to eliminate the problem. Improving ventilation in the dryer pocket can accomplish this.
Ventilating air through the dryer fabric is the most functional pocket ventilation system, which requires
fabrics with sufficient air permeability characteristics. Development and use of dryer fabrics with PV
systems has proved to be an appropriate solution to the problem. Therefore, any improvement or even a
better understanding of the dryer pocket ventilation (PV) can significantly reduce the paper making
operation cost. This work addresses the issues such as velocity and humidity distribution inside the dryer
pocket and flow of dry air through moving porous material. Computational results were found to be in
good agreement with the experimental counterpart.
Keywords: Porous medium; Mass transfer; Dryer pocket; Paper drying; Paper machines.
1. INTRODUCTION
In conventional paper machines, wet paper sheet was conveyed through a series of dryers from which the
residual water gets vaporized. The paper is threaded around each dryer, which were heated by
condensing steam with conduction as the major mode of heat transfer to the paper sheet. The drying felt
is a highly porous material whose main purpose is to hold the paper sheet in close contact with dryer
cylinder. This increases the heat transfer between dryer drum and paper sheet. Also it prevents shrinkage
and deformation of paper sheet, enhances the stability of the moving paper. In a conventional double
felted dryer section paper, dryer fabrics, paper lead rolls and dryers can create pockets that exhaust moist
air mainly at edges. The moisture content is higher in the middle of machine than at edges. High air
humidity in the dryer pockets and everywhere in the surrounding of web gives reduced drying rate.The
pockets of a double felted dryer section have low natural air exchange. The high air humidity occurs in
the pocket without ventilation.The moist air trapped in these pockets retards the drying rate of the sheet
173
in the open draw regions and further causes non uniform moisture distribution across the width of the
sheet. However, conditions in the pockets can be improved by introducing hot, dry air evenly across the
width by the addition of PV system.
The main objective of paper machine ventilation is to keep the surroundings of the web well ventilated
and keep air humidity at optimum level. There are different designsto achieve ventilation in the dryer
pockets which can increase the drying efficiency approximately by 20%.In PV system; Hot air is
introduced into the pocket through the perforated shell of the felt roll. The application of very high–
permeability dryer felt in the paper industry made it possible to introduce air through the felt. Also these
systems provide better cross flow ventilation, which in turn results in more uniform and higher mass-
transfer rates. Thus, pocket ventilators keep the humidity at optimum level with uniformity in cross
direction (CD) profile.
Mostly, design of dryer pocket and pocket ventilation box were formulated with trial and error approach.
The spontaneous air flow through moving porous medium reported by Mou et al., 2003 addressed the use
of induced pressure difference to drive the air through the moving porous material. Computational
modelling of paper drying machines done by Reardon et al., 2000 demonstrates that 65% of the moisture
evaporation occurs in the free draw region.Theoretical study of paper drying process reported by
Etemoglu et al., 2005suggest that during the drying period, the vapor pressure of the evaporating liquid
on the drying surface remains at a quasi-saturated value corresponding to the liquid temperature.
According to Kong and liu, 2012, the supply of hot air, transfers heat and mass to the paper web
primarily by convection. Also Reese, 1988, addressed that the exhausted moist air leaving the web
evaporation surface is diluted by leakage air before leaving the dryer hood.
The purpose of current work is to quantify the spontaneous air flow through moving porous medium
(felt) along with pocket ventilation system. Velocity distribution inside dryer pocket through moving
porous material and humidity profile along cross direction inside the dryer pocket is also addressed.
2. DESCRIPTION OF POCKET VENTILATION SYSTEM
In two-tier paper dryer section as shown in figure 1, individual pocket is separated by a dryer felt, dryer
surface, guide roll and paper web. The paper is threaded around each dryer and is heated by condensing
steam inside the dryers. The heat and mass transfer processes differ in contact drying period from those
in free movement drying period. Thus results in gradients of drying parameters such as moisture content,
temperature of paper sheet etc. In pocket, majority of moisture evaporation occur from the paper web.
For the efficient drying of paper, it is extremely important to remove the water vapor from around the
web as suggested by Karlson, 2000.
174
Schematic of pocket ventilation system in dryer section
Water evaporated from the web was removed from the pockets by using hot and dry air coming from PV
system. Two separate PV boxes named as upper and lower PV box were installed to remove the moisture
between two sequential pockets. If the movements of air in the pockets is too low or too close to
stagnation, higher temperature in the pockets does not help in improving drying rate. There should be
sufficient airflow in the pockets from PV Box for efficient drying conditions inside the pocket; which
proves the importance of pocket ventilation system in hood and dryer section as reported by
Panchapakesan, 1991.
3. DETAILS OF COMPUTATIONAL MODELLING
The most common drying system used in paper industry is a multi-cylinder dryer section. This consists
of a series of cylindrical cast iron dryer drum (1.5m diameter of dryer); in proposed computational model
for the paper drying process, each dryer pocket was divided in different phases as recommended by Patil
et al., 2013.
Computational domain with boundary conditions (b)Structured mesh
Fig. 2.Computational domain for pocket ventilation in dryer section
175
Figure 2a shows the computational domain for dryer pocket along with pocket ventilation box and
associated boundary conditions. The grid generation shown in figure 2b was carried out using
commercially available software ICEM CFD. Since the area of focus was near the paper surface, finer
mesh density was maintained there.In order to capture both the humidity and velocity boundary layers
near paper wall surface, the entire model was discretized using structured mesh.
In addition to the parameters given in Patil et al., 2013, the additional parameters used to develop the
model in this work are listed in Table 1.
Table 1. Details of parameters used in modeling of paper drying process
Type and Symbol
Mass flow rate of dry air, Q 3000 kg/hr
Width of slot for PV box,w 5 mm
Di Diaameter of pipe for air inlet on PV box,d 150 mm
T Temperature of dry air,T 110 ˚c
Length of PV box across machine direction,þ 3.6 m
Density of dry air, ρ 1.22 kg/m3
Dynamic viscosity of air,μ 1.78e-05
I. BOUNDARY CONDITIONS
Flow simulation was done by using a commercially available software FLUENT. To satisfy the physics
of the problem, flow turbulence, energy and species transport models was selected.RANS two equation
standard k-ε turbulence model with standard wall function was used for simulation. The species selected
were air and water vapor with density as volume weighted mixing law to make the solution simpler.
Paper was moving along with the dryer, hence in boundary condition both are defined as moving wall
with speed 500mpm. In cell zone condition, water evaporation rate of 50gm/s from paper surface to
surrounding air was taken. Both pressure outlets were open to atmosphere, therefore defined as
atmospheric pressure boundary conditions. The mass flow rate of dry air supplied from hood was
3000kg/hr at 1100c and was defined in terms of velocity at the inlet of pocket ventilation box. Felt is a
porous medium through which dry air supply is provided into dryer pocket. In simulation, inertial and
viscous resistance obtained from experiment discussed in section V was defined in porous cell zone
conditions. The initialization of value was computed from velocity inlet of dry air. It was also necessary
to select the appropriate approximation required in the residual command under monitors and check in
plot to visualize the progress of iteration. After describing every parameter the iteration was performed
till the value gets converged to required approximation.
176
were carried out by pressure transmitters and anemometer respectively. Porous coefficients were
obtained from the plot between pressure drop and velocity, shown in figure 3b.
Experimental set up (b) Porous coefficients
Fig.3. Deriving the Porous Coefficients based on experimental data
The details of calculations for the porous coefficient are as follows.
Y = + = 0.277 + 9.0473 …… (i)….Equation of curve shown in figure 3b
.·. a = 0.277 and b = 9.0473
Inertial Resistance Factor is given by [9];
= ∆ ……………………………………… (ii)
.·. = 197.856945
Similarly,Viscous resistance factor, 1/α is given by [9];
= …………………………………… (iii)
∝ ∆
.·. 1/α = 2.033e+08
4. RESULTS AND DISCUSSION
The humidity boundary layers formed near the paper surface and velocity distribution of air inside the
dryer pocket were investigated.
Variation of velocity at outlet of PV box.
177
Pocket ventilation box has velocity outlet slot of width 5 mm along the length. Figure 4 reveals that the
use of PV box offers uniform velocity distribution of drying air in the middle region of PV box outlet.
This leads to uniform moisture content along the CD profile. Hence, it improved drying efficiency.
Velocity distribution inside pocket through moving felt.
As seen from figure 5, due to the resistance of moving felt, there is reduction in velocity of air before it
gets distributed inside the pocket. Therefore, the effect of felt was considered in computational modelling
of PV system.
Fig.6. Relative Humidity contour near paper surface (10mm from Paper).
Figure 5 and 6 shows that relative humidity is high near the bottom of the pocket. This is due to the
insufficient flow of dry air in this region. Therefore, for efficient drying of paper there should be
sufficient airflow in the pockets.
178
Fig.7. Comparison of relative humidity near paper surface with and without PV box.
The relative humidity variation with and without pocket ventilation system, shownin figure 7 reveals that
the relative humidity with pocket ventilation system is low than without PV box. This is due to uniform
distribution of velocity in CD profile. Thus, pocket ventilation system helps in maintaining uniform
moisture profile over the paper web.
5. VALIDATION OF RESULTS
To validate the CFD results with experimental values, six locations inside the dryer pocket were selected.
The variations in relative humidity measured and obtained from simulations at these selected locations
have shown in figure 9.
Comparison of CFD and experimental results of relative humidity inside dryer pocket.
It is observed that the results are in agreement with a deviation less than 10%.Hence, the proposed
model can be used to simulate the pocket ventilation system in dryer section.
6. CONCLUSION
In paper industry, the heat and mass transfer during paper drying process generally accelerates
evaporation from paper surface when the paper sheet moves into open draw region. This work
presents a computational model for paper drying process along with pocket ventilation system in a
dryer section. The CFD and experimental results obtained show that:
Pocket ventilation system helps to create and maintain a controlled and favorable environment for
the drying process in a dryer section.
Paper machine equipped with pocket ventilator, will have low and uniform relative humidity profile
across the width of the dryer pocket.
Pocket ventilation systems can increase the drying efficiency approximately by 20%.
To enhance the circulation of hot air inside the dryer pocket via the moving permeable felt,
optimization of air distribution is necessary to increase the drying efficiency of Pocket ventilation
system.
179
ACKNOWLEDGEMENT
The authors acknowledge the support and facilities extended to carry out the work by “Andhra
Pradesh paper mill, Rajahmundry”.
REFERENCES
1. A. B. Etemoglu et al.,“Theoretical study of combined heat and mass transfer process during paper
drying”, Heat Mass Transfer 41 (2005): 419–427.
2. Bharat Patil et al., “Analysis of humidity inside pocket in dryer section of paper industry”,
communicated to International Conference on Advances in Mechanical Engineering, May 29-31,
2013.
3. Jianyao Mou et al., “A study of the spontaneous air flow through a moving porous medium”,
Advances in Engineering Software 34 (2003) 507–514.
4. Karlson, M. Papermaking science and Technology: papermaking part 2, drying, (ed), published by
Finnish Engineers’ Association and Tappi, chapter 9 (2000).
5. Lingbo Kong, Huanbin Liu, “A Static Energy Model of Conventional Paper Drying for
Multicylinder Paper Machines”, Drying Technology, 30: 276–296, 2012.
6. Panchapakesan, B., “Enclosed PM Hood operating at high humidity conserves energy”, pulp paper
133, April (1991).
7. Reese, J.R.“High humidity hoods conserve energy and improve runnability”, Tappi Engineering
conference, p653 (1988).
8. Shaun Reardon et al., “Computational modelling of paper drying machines”, September 2000,
TAPPI Journal peer reviewed paper.
9. Ansys 14.0 help manual (Fluent users guide 7.2.3.6.11).“Deriving the Porous Coefficients Based on
Experimental Pressure and Velocity Data”.
180
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/011
DYNAMICS OF TWO BUBBLES RISING IN A VERTICAL CHANNEL
ABSTRACT
The current industrial scenario indicates that multiphase flows are of great engineering relevance
and hence are being studied. In the present work, the dynamics of two bubbles rising in a stagnant fluid
contained in a vertical channel is being investigated as a function of spacing between two bubbles and
Bond number at fixed Reynolds number of 250. The bubbles are oriented vertically one below the other.
The physical interaction between two bubbles is studied for fixed Reynolds number by varying the
spacing between the bubbles for s/d = 17, 14, 10, 7, 3.5 and 1 at Bo=1 and 2 (where Bo is Bond number).
The computational domain is solved by ‘VOF’ multiphase model of the Ansys Fluent solver. The fluid is
stagnant and is considered to be viscous and incompressible. Driven by the buoyancy forces the bubbles
rise up in the channel and affect the fluid continuum.
The threshold s/d ratio is identified as 14, beyond which the bubble interaction does not occur.
Various bubble flow behaviour regimes are identified for different s/d spacing range. These regimes are
identified on the basis of bubble motion (adhering to shape/path oscillations), coalescence and
acceleration of the bubble. Thus, an attempt has been made here to understand the dynamics of two
bubbles rising in a vertical channel as a function of spacing and Bond number.
1. INTRODUCTION
The physics related to the multiphase flow is being explored experimentally and numerically. The
domain of the problem was solved using the commercial software. The present study involves rise of
bubbles in a channel. The problem finds it relevance in fields like nuclear physics, hydraulics, and blood
circulation system in human body and many more. The bubble dynamic study is intensely rich. Studies
on the motion of single bubble and a pair of bubbles are very limited. It is obvious that the flow structure
of gas-liquid bubbling. The computations based on transient flow are being employed presently as many
evidences suggested that the time-averaged computations cannot provide rational explanation of the
transport process of mass, momentum and energy transfer between the bubbles and the liquid..
2. LITERATURE SURVEY
The study of bubble dynamics was being conducted by different numerical methods with various
physical perspectives. The dynamics of homogeneous bubbly flows at low to moderate Reynolds number
is fairly well understood with regard to the physical aspects concerning the fully resolved flow around
181
bubble, viscosity inertia and surface tension. Bubbles at high Reynolds number frequently exhibit at
hand/or shape oscillations, depending on their size. Different mechanisms have been suggested for this
onset of wobbly motions, but it is now commonly believed that wobbling is the result of wake instability.
Norman and Mikis (2005) presented the behaviour of a single bubble as a function of Reynolds number
(Re), Bond number and angle of inclination. Steadily rising bubbles are found for small values of both
the Reynolds and Bond number. With increasing Reynolds number, the steady solution first bifurcates to
a time periodic oscillation, and then the numerical results imply period doubling. Large values of
Reynolds or Bond number cause the bubble to either detach from the wall or to rupture. Smolianski et al.
(2004) conducted the study of wobbling-bubble regime characterized by the non-symmetric vorticity
pattern in the wake and further discussed the results on the bubble coalescence phenomena, emphasizing
the main differences in the merger process for diverse bubble-shape regimes
Coalescence of bubbles being an interesting phenomenon, it was addressed by many researchers,
such as Muccucci (1969), Chi and Leal (1989) and Basaran (1992). Limited theoretical and experimental
studies of gas bubble coalescence were done by Narayanan et al (1974), Bhaga and Weber (1980),
Oolman and Blanch (1986), Egan and Tobias (1994) and Stover et al (1997). Most of their studies
focused on the experimental investigation. Chen et al. (1996) studied gas bubble coalescence using our
modified VOF method associated with a semi-implicit algorithm for Navier-Stokes equations. The
effects of liquid viscosity and surface tension force on the coalescence were also investigated.
Objective of the present work is to study the effect of Reynolds number, Bond number and s/d
ratio on the bubble rise flow pattern. The study of physics related bubble motion and the coalescence of
bubble phenomenon is also another objective of the present thesis.
3. NUMERICAL AND PHYSICAL DETAILS OF THE PROBLEM
The two dimensional computational domain consists of a vertical channel as described below in the
figure-1.A channel length of 30 units and width of 1 unit is considered. The fluid is stagnant and is
considered to be viscous and incompressible. A ‘No slip condition’ exists along each of the walls. Two
bubbles are introduced into the computational space at the positions. The physics of the bubbles is
influenced by non-dimensional parameters like Reynolds number, Bond Number and the ratio of the
spacing between the two centres of the bubbles and the diameter of the bubble (s/d ratio) observed just as
the problem is initialised.
= 0, =0, = 0
u = 0
u = 0
v=0 v=0
= 0 = 0
Bubbles
Spacing
Vertical channel 182
Stagnant fluid
u = 0 v =0
The domain of the problem is modelled in ICEM CFD and is meshed in unstructured manner.
The case is set up in FLUENT for the same boundary conditions as described and the solution is
obtained. The multiphase model employed in the software utilizes the finite volume based ‘Volume of
Fluid Method’ which is actually associated with the domain Computational Fluid Dynamics.
4. GOVERNING EQUATIONS
The interface moves with the fluid, hence the Volume fraction evolves by the equation
+ .∇ = 0 … (1)
The viscosities and densities are modified using the mean viscosity given by,
σ ρ
Reynolds Number Re = & Bond Number Bo =
Normalised time = t/t*, where t is real time and t* is characteristic time = wµL /σ (w - width of
channel)
The Continuity and Navier – Stokes equations using the above defined variables are,
∇. =0 … (5)
∇ ∇ ∇F
=− + − − . … (6)
183
(a) N x = 32 (b) N x = 64 (c) N x = 128
Fig 5.1: Grid Independent study for grids (a) Nx = 32 (b) N x = 64 & (c) Nx = 128
6. VALIDATION
The computational fluid dynamics has its own shortcomings when it comes to the authenticity of the
results obtained from the simulations. The correctness of the solution procedure is validated against a
paper presented by Li Chen, Yuguo Li and Richard Manasseh on “The Coalescence of Bubbles - A
Numerical Study” in Third International Conference on Multiphase flow in June 1998. The parameters
were defined as:
. .
Re = , Bo = & Mo = (where Ro is the bubble radius)
The problem is simulated for the following case:
Re=12, Bo=5,M=4.1 ×10-3, ρl/ρg =1000, μf /μg=100,Ro=0.15.
(a) (b)
184
The bubble shapes observed for the given case show that they are in good agreement with the
results presented in the paper Chen et al (1998). Thus the problem is validated and now simulations can
be conducted for different Reynolds number, Bond number and spacing between two bubbles.
7. RESULTS& DISCUSSION:
EFFECT OF s/d RATIO ON FLOW BEHAVIOUR FOR Bo = 1 & 2
The Reynolds number was fixed as 250, initially Bond No was set to 1, it was noted, that significant
bubble interaction initiates at s/d = 14, beyond this s/d no noteworthy interactions was observed. This
interaction occurs for 14 > s/d > 7.0. Occurrence of coalescence of bubbles was reported s/d = 7. For s/d
= 17.0 no interaction between the bubbles was observed within the simulation time. The wake behind the
leading bubble does not affect the motion of the following bubble.
Within the range 14> s/d >7.0, the magnitude of bubble interaction increases as the s/d ratio is reduced.
(a) = 280.41 (b) = 291.63 (c) = 299.11 (d) = 306.58 (e) = 314.06 (f) = 321.54
Figure 7.1: Re = 250, Bo = 1, ρl/ρg = 100, μf /μg =1, r = 0.1425, s/d = 14
185
The frames above capture the phenomenon of initiation of oscillatory motion of the following
bubble for s/d = 14. Initially bubbles rise steadily but at some point in the channel, oscillations arise due
to transient nature of wake left behind the leading bubble in the path of the following bubble. A wave
like pattern in the stream traces of the leading bubble is observed, forming eddies in the wake, which
induce oscillations in the following bubble. As the bubble rises in the channel vortices are being
developed at the interface due to the circulation of fluid around the bubble. These vortices are highly
unstable in nature as they form and dissipate in the fluid as the bubble rises. The following bubble sheds
hairpin like vortices in its wake as it oscillates and moves upwards thus following a spiral trajectory. The
vortex shedding occurs in alternate manner resulting in vortices having opposite sense of rotation. For the
rest of the time the leading bubble rises steadily however simultaneously the leading bubble (although
it’s oscillating) is being accelerated towards the leading bubble. The acceleration occurs due to the
presence of a low pressure region in the wake of the leading bubble; also flow separation also contributes
to this phenomenon by some extent. However the acceleration phenomenon observed is very subtle. No
coalescence was recorded.
A very much similar behaviour was observed for s/d = 10.5. The following bubble starts
oscillation at a certain point of time owing to the reasons as described in the previous case (s/d =14). This
motion continues for certain time. However due to the viscous forces experienced by the bubble interface
causes the leading bubble to oscillate.
(a) = 351.45 (b) = 358.93 (c) = 366.41 (d) = 373.88 (e) = 381.36 (f) = 388.84
Figure 7.2: Re = 250, Bo = 1, ρl/ρg = 100, μf /μg = 1, r = 0.1425, s/d = 10.5
The s/d was further reduced to 7. Owing to the instable nature of the wake of the leading bubble,
the following bubble starts oscillating. However for lower the s/d ratio, as the following bubble
accelerates its vortices locks on to those of leading bubbles inducing oscillations onto the leading bubble.
186
So the leading bubble along with following bubble starts oscillate with certain phase difference. As time
progresses the following bubble approaches leading bubble, while both being in an oscillatory state. Just
before the coalescence occurs there is a small elongation in the shape of the following bubble, then the
interface between the bubbles break and they collapse into one another forming a larger bubble. As this
occurs, the individual vortices of each bubble gradually terminate and a larger vortex is formed
encompassing the larger bubble. Since the coalescence occurred while bubbles in oscillatory state the
coalesced bubble continues the oscillations. This phenomenon is accompanied by shedding of vortices
along the path of the bubble. Along with path oscillations, the coalesced bubble also experiences shape
oscillations. This state of motion continues for the rest of the time
(a) = 306.58 (b) = 314.06 (c) = 321.54 (d) = 329.02 (e) = 336.49 (f) = 343.79
sec
Figure 7.3: Re = 250, Bo = 1, ρl/ρg = 100, μf /μg = 1, r = 0.1425, s/d = 7
The coalescence phenomenon for the case of s/d = 3.5 remains identical as described in the
previous case (s/d = 7). However the coalescence in this case occurs early in the time flow due to lower
s/d ratio (refer figure 7.4).
(a) = 44.86 (b) = 52.34 (c) = 59.82 (d) = 67.29 (e) = 74.77 (f) = 82.25
Figure 7.4: Re = 250, Bo = 1, ρl/ρg = 100, μf /μg = 1, r = 0.1425, s/d = 3.5
187
For s/d = 1 bubbles are so closely oriented that they share a part of their interfaces. This
culminates into immediate coalescence. However as the coalescence occurs in the equilibrium position of
the bubble, no oscillations occur and the coalesced bubble moves steadily through the channel without
any path oscillations. This shows that the surface of the coalesced bubble can sustain the normal viscous
forces. The nature of vortex shedding is uniform i.e. identical shape of vortices are shed along the either
sides of the wall.
(a) = 3.73 (b) = 7.47 (c) = 14.95 (d) = 22.43 (e) = 29.9 (f) = 37.38
Figure 7.5: Re = 250, Bo = 2, ρl/ρg = 100, μf /μg = 1, r = 0.1425, s/d = 1
Further, the simulations were carried out for Bo = 2.0 to understand its effect on the flow
behaviour as a function of s/d. For all the values of s/d it is noticed that the shape of the bubble becomes
ellipsoidal as the Bond number is increased (surface tension force is reduced).
(a) = 211.50 (b) = 216.79 (c) = 222.07 (d) = 227.36 (e) = 232.65 (f) = 237.94
188 f /μg = 1, r = 0.1425, s/d = 14
Figure 7.6: Re = 250, Bo = 2, ρl/ρg = 100, μ
The frames above capture the phenomenon of initiation of oscillatory motion of the following bubble
for s/d = 14. Initially bubbles rise steadily in the channel. At a certain point in the channel, the
leading bubble starts oscillating. This behaviour is totally opposite to the case of Bo = 1 (for the
same Reynolds number and s/d ratio), wherein the following bubble starts oscillating first. This
occurs as the surface tension force of the bubble is reduced thus compromising the stability of the
bubble, thus the interface of the bubble is not strong enough to sustain the shear viscous .The
vortices of opposite sense of rotation are shed as the leading bubble moves in the channel. Now as
the following bubble rises along the channel, as it reaches the length at which the leading bubble had
started oscillating formerly, the following bubble also starts oscillating with the shedding of vortices.
It was also observed that the oscillations early in the flow time at = 137.47 instead of = 280.41
(for the case Bo= 1), the reason being the weaker interface of the bubble. Thus both the bubbles keep
oscillating in the channel for the rest of the flow time. The vortex shedding phenomenon occurs in
the similar manner as for the same case but Bo = 1.
(a) = 142.76 (b) = 148.05 (c) = 153.33 (d) = 158.62 (e) = 163.91 (f) = 169.20
For s/d = 10, both the bubbles start their respective oscillations almost at the same time instant
Figure 7.7: Re = 250, Bo = 1, ρl/ρg = 100, μ f /μg = 1, r = 0.1425, s/d = 10
(refer figure 7.7) and continue to oscillate for the rest of the time. In this case also the oscillations
initiate early in flow at = 163.91 instead of = 388.84 (for Bo =1). This occurs due to instable nature of
bubbles due to lesser surface tension.
189
(a) = 121.61 (b) = 126.90 (c) = 132.18 (d) = 137.47 (e) = 142.67 (f) = 148.05
Figure 7.8: Re = 250, Bo = 2, ρl/ρg = 100, μf /μ g = 1, r = 0.1425, s/d = 7
For s/d = 7, the coalescence of bubbles occur as the oscillating following bubble collapses into to
somewhat steady leading bubble. The coalescence was recorded early in the flow at = 153.33 instead
of: = 321.54 (for Bo = 1).
For s/d = 3.5, the coalescence of bubbles occur as the bubbles move steadily but after collapsing to one
another somewhat wobbling of the bubble occurs after a certain time. In this case also the coalescence
occurs early in the flow at = 47.58 instead of = 74.77 (for Bo = 1)
(a) = 31.72 (b) = 37.01 (c) = 42.30 (d) = 47.58 (e) = 52.87 (f) = 58.16
Figure 7.9: Re = 250, Bo = 2, ρl/ρg = 100, μ f /μg = 1, r = 0.1425, s/d = 3.5
The frames below describe the motion of bubbles for s/d = 1. The bubbles immediately coalesce
without any path oscillations for the rest of the time.
190
(a) = 2.64 (b) = 7.93 (c) = 13.21 (d) = 18.50 (e) = 23.79 (f) = 29.08
Figure 7.10: Re = 250, Bo = 2, ρl/ρg = 100, μf /μg = 1, r = 0.1425, s/d = 1
Similar behaviour of the bubble was also noticed for Bo = 2.0 with regard to the hairpin vortex shedding
phenomenon and acceleration of the following bubble towards leading bubble were also noted.
Conclusion
The physical and numerical structure of problem was understood followed by a discussion of the
solution technique used. The physics of the bubble motion and coalescence of two bubbles was explored
.The problem was validated successfully followed by a grid independent study, thus laying down a valid
foundation for further investigation of the dynamic study. The dynamics of two bubbles rising in a
channel was investigated for Re = 250 for Bo = 1 and 2.
191
REFERENCES
1. CHEN, L., GARIMELLA, S. V., REIZES, J. A. & LEONARDI, E. 2000, The development of bubble rising
in a viscous liquid. J. fluid Mechanics, 387, 61- 96.
2. ASGHAR ESMAEELI & GRÉTAR TRYGGVASON 2005,A direct numerical simulation study of the buoyant
rise of bubbles at O(100) Reynolds number . Phys. Fluids 17, 093303.
3. LI CHEN, YUGUO LI AND RICHARD MANASSEH 1998, The coalescence of bubbles - a numerical study.
Third International Conference on Multiphase Flow, ICMF’98.
4. T. HONG, C. ZHU, P .CAIAND LS FAN Numerical modelling of basic modes of formation and
interaction of bubbles in liquids.
5. GADA, VINESH H. AND SHARMA ATUL 2008 Comparisons of Volume of Fluid (VOF) and Level Set
Method For Two-Fluid Flow Simulations,19th National & 8th ISHMT-ASME Heat and Mass
Transfer conference January 3 - 5, JNTU Hyderabad, India.
6. C. W. HIRT AND B. D. NICHOLS 1981, Volume of Fluid (VOF) Method for the Dynamics of Free
Boundaries, J. Computational. Phys., vol. 39, pp. 201–225.
7. S. W. J. WELCH AND J. WILSON 2000, A Volume of Fluid Based Method for Fluid Flows with Phase
Change, J. Computational. Phys., vol. 160, pp. 662–682, 2000.
8. ASGHAR ESMAEELIAND GRETAR TRYGGVASON1998,Direct numerical simulations of bubbly flows Part
1. Low Reynolds number arrays, J. Fluid Mech, vol. 377.
9. NORMAN C. E . AND MIKIS M. J., ‘Gas bubble with a moving contact line rising in an inclined channel
at finite Reynolds number’. Physica D 209 191–204 (2005).
10. ANTON SMOLIANSKI, HEIKKI HAARIOB AND PASI LUUKKAB, Vortex Shedding Behind a Rising Bubble
and Two-Bubble Coalescence: a Numerical Approach, Institute of Mathematics, Zurich University,
CH-8057 Zurich, Switzerland (2004).
11. ANTOINE WILHELMUS GERARDUS DE VRIES, ‘Path and wake of rising bubble, ISBN 9036525262.
12. TSAO, H. K. & KOCH, D. L. 1997 Observations of high Reynolds number bubbles interacting with a
rigid wall. Phys. Fluids 9, 44.
13. ZUKOSKI, E. E. 1966 Influence of viscosity, surface tension, and inclination angle on motion of long
bubbles in closed tubes. J. Fluid Mech. 25, 821-837.
14. HYSING, S., TUREK, S. KUZMIN, D. PAROLINI, N. BURMAN, E. GANESAN, S. TOBISKA, L, 2009
Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Numer. Meth.
Fluids. 60, 1259–1288.
192
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/012
ABSTRACT
A series of Runs were performed on fluent 14 to study the effect of canards and its position on the
downstream flow field over the wing surface. A 2-Dimensional Analysis of two Airfoils placed at certain
distances from each other was run, in order to investigate various Aerodynamic Parameters. The Flow
interactions between the airfoils E423 (forward surface with chord 33 cm) and S1223 (aft surface with
chord 38 cm) were studied at a velocity of 20 m/s using the turbulence model k-kl-omega by varying the
horizontal & vertical distance with respect to each other. From the analysis performed it is observed that
a canard configuration can give good lift characteristics provided the spacing of the surfaces is well taken
care of and a position is chosen which instead of making the wing lose on lift energizes the flow and
improves the Aerodynamic efficiency.
Keywords: K-Kl-omega, Turbulence Intensity, Turbulence length Scale, Cl, Cd.
1. INTRODUCTION
With the growing reliability and sustainability of Monoplanes, the once in vogue Canards began to
lose their rage. Canards at one point of time were considered to be that discovery by mankind that
set wings to the human aspirations of catching it to the skies! Not to mention, the first Flying
machine built by the Wright was a canard and this gave rise to design and fabrication of many more
Canards with the Burt Rutan’s Designs This Evolution Continued until several of the complexities of
this Configuration were discovered. An additional lifting surface ahead of the wing guided people to
think that it would increase the effective lift and offer better efficiency. But the loses due to vortex
interactions between the two surfaces lead to the net decrease in lift and simply added to the weight
of the Aircraft without offering any aerodynamic advantages. A more in depth study leads one to
193
think that if these two surfaces are placed in optimum positions, the flow may get reenergized at a
point and effective lead to increase in the effective lift. The Paper works out the same thought.
2. METHODOLOGY
With the advent of powerful computers and advanced numerical algorithms, computational
fluiddynamics (CFD) has revolutionised the aerodynamic design of Aerospace vehicles all over the
world. CFD code Ansys fluent 14 has been used in the present analysis. The investigations were
carried out with chord lengths of 33 cm (E423) for the canard and 38 cm (s1223) for the wing. The
models were meshed with GAMBIT using a Quad-Map and Quad pave type structured mesh.
The Comparative study on Fluent is based on the Following 3 cases:
Case 1:
The Horizontal distance between the two foils is varied (25cm, 35cm, 40cm) while the vertical separation
and angle of incidence remains same for each of the cases.
Case 2:
The Canard is placed below the wing and the vertical distance is varied (0cm, 10cm, 30cm) while the
horizontal separation and angle of incidence remains same.
Case 3:
The Canard is placed above the wing and the vertical distance is varied (0cm, 20cm, 30cm) while the
horizontal separation and angle of incidence remains same.
A total of about 16 lakh grid points were formed for the Canard Wing Geometry. The meshed airfoil
models were then exported into FLUENT 14 to set the boundary conditions and to solve the
equation. The simulation was carried out at 20 m/s turbulence intensity 0.2 and Turbulence length
Scale 0.00417 m.
Both the Mach number and the Reynolds number for the given are considerably low. Hence the k-kl-
w model is used for Reynolds-average simulation of incompressible flows with a boundary layer that
undergoes a transition from laminar to turbulent flow. The airfoil is given the boundary type of wall
as air would not pass through it. The inlet and side inlet boundaries have a velocity inlet boundary
type while the outlet has Pressure outlet boundary. This is because we give the inlet conditions in
terms of velocity components of free stream air velocity and we expect results in terms of forces
194
(pressure).In the Specification method for boundary layer, the values of turbulence intensity, Length
Scale and Laminar Kinetic Energy are mentioned.
4.RESULTS AND DISCUSSION:
The Main reason due to which an Aircraft flies is Lift, which is produced due to a Pressure Gradient
Formed between the upper and Lower Surfaces of the Airfoil. As can be observed in figure 1, The
Contours in the lower region of front surface are high as compared to that of the aft surface. Similarly the
upper surface of the Airfoil has Lower Pressure in contrast to the lower surface. This Pressure Gradient
can be also studied through Figure 2, which shows the change in Pressure at each and every point on the
Airfoil. From both the figures if the Pressure Gradient is compared for canard and wing, it is clearly
observed that this Lift Producing Gradient has reduced in case of the wing. The reason behind this is
primarily the interaction of vortices emerging from canard and interacting with the Wing Thereby
Reducing the effective lift of the Configuration. The understanding of this thought becomes clearer from
the contours of velocity as shown in figure 3, where contours are higher on upper region of frontal
surface as compared to that of aft. This is well supported by the Bernoulli’s Equation which States that
the Net Head over a system remains constant thereby implying that the Kinetic Head must be inversely
proportional to the pressure head.
Case 1:
The Horizontal distance between the two foils is varied (25cm, 35cm, 40cm) while the vertical separation
and angle of incidence remains same for each of the cases. As the distance Increases the contours on the
lower region of aft surface go higher thereby increasing the lift.
Figure 1: Horizontal distance between the two surfaces is 25 cm while vertical is 20cm
195
Figure 2: Plot of Static Pressure with respect to Positions on the Airfoils
Figure 3: Horizontal distance between the two surfaces is 25 cm while vertical is 20cm
The Canard is placed above the wing and the vertical distance is varied (0cm, 10cm, 30cm) while the
horizontal separation and angle of incidence remains same.
196
The interpretation of the Contours and Plots is Explained in the above figures, the figures 4 depict change
in the Pressure gradient a the Vertical Distance between the Two surfaces increase. With increase in
Vertical Separation the effect of vortices from canards on wing reduces and there isn’t a significant loss
of lift after a certain limit where the wing is well away from the canard.
Figure 4 Canard is above the wing by 10 cm
5. CONCLUSIONS:
Case1:
Angle Vertical
of Spacing Horizontal Coefficient of lift
Coefficient Coefficient
of of
Incidence (αi)
(cm) Spacing (cm) (Cl) drag (Cd) Pressure (Cp)
197
When the Wing and the canard are at same levels i.e. Coplanar the Effects of vortices are Best Results
are obtained when Canard is above the wing.
198
Coefficie
nt of lift
Cl vs Horizontal Coefficient of Drag
Lift, Cl Distance 2.02E-02
8.85E-01 2.00E-02
8.80E-01
1.98E-02
8.75E-01 Coefficie
8.70E-01 nt of 1.96E-02
Drag,Cd
8.65E-01 1.94E-02
8.60E-01
1.92E-02
8.55E-01
8.50E-01 1.90E-02
8.45E-01 0 20 40 60
0
Horizontal 20 between
Distance 40 the two
60
Horizontal Distance between the two
surfaces surfaces
Graph1: Cl vs HorizontalSeparation Graph2: Cd vs Horizontal Separation
Coefficien
Coefficient of lift (Cl) t of drag Coefficient of drag (Cd)
8.80E-01 (Cd)
2.25E-02
8.70E-01
8.60E-01 2.20E-02
8.50E-01 2.15E-02
8.40E-01 2.10E-02
Coefficient
8.30E-01
of lift (Cl) 2.05E-02
8.20E-01
8.10E-01 2.00E-02
8.00E-01 1.95E-02
7.90E-01 1.90E-02
7.80E-01
0 20 40
0 20 40 Vertical Distance between the two
Vertical Distance between the two Surfaces Surfaces
Graph 4: Cl vs Vertical Separation Graph 5: Cd vs Vertical Separation
ACKNOWLEDGEMENT
The authors would like to thank the Director, Veermata jijabai technological institute and the head of
Mechanical department for their support and access to the computational fluid dynamics laboratory
which proved to be a great help in obtaining significant conclusions.
199
REFERENCES
1) Raghav Mahalingam and Narayanan Komerath“Fundamental studies of Vortex interactions”, Army
Research Office / Joint Project with Ohio State University
2) Thomas Holbrook, Dana Morris Dunham, and George C. Greene “Vortex Wake Alleviation Studies With
a Variable Twist Wing”
4)Z. Husain, M. Z. Abdullah (corresponding author) and T. C. Yap School of Mechanical Engineering,
University Sains Malaysia, Penang, Malaysia “Two-dimensional analysis of tandem/staggered airfoils
using computational fluid dynamics”, International Journal of Mechanical Engineering.
200
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/013
ABSTRACT
Most flows encountered in engineering practice are turbulent flow. However, turbulent flow is a
complex mechanism dominated by fluctuations, the paths of individual particles of fluid are no longer
everywhere straight but are sinuous, intertwining and crossing one another in a disorderly manner so that
a thorough mixing of the fluid takes place. The theory of turbulent flow remains largely undeveloped and
relies on experiments and the empirical or semi-empirical correlations developed for various situations.
The widespread use of turbo-machinery calls for the design of more efficient and more reliable machines,
which directly translates into cost savings and better productivity. Experimental investigations are very
difficult because the flow is particularly sensitive to unavoidable and often unknown disturbing
influences which can decisively change the transition behavior.
The design of the Centrifugal pump has reached to a stage where improvements could only be achieved
through thorough understanding of internal flow. The prediction of internal flow is quite tedious and
complicated in such equipments on account of rotation and 3-D curved shaped of the impeller.
Withtheaid of computational fluid dynamics (CFD), the complex internal flows in water pump impellers
can be well predicted, thus facilitating the design ofpumps.The blade number of impeller is an important
design parameter of pumps, which affects the characteristics of pump heavily. Centrifugal pump
technology involves a wide spectrum of flow phenomenon and various methods of impellers design,
fabrication and number of blades, which has a profound impact on its performance. Numerical
simulations can provide quite accurate information on the complicated fluid behavior inside the machine
for various number of blade necessary for performance evaluation of a particular design of pump.
The current investigation is aimed to simulate the complex internal water flow in a Centrifugal
pumps impellers of low specific speed (6- & 7- number of blade, semi-shrouded) by solving (3-D)
Navier-Stokes equation for various turbulences models and comparing the results with experimental
201
results. The numerical solution of the deiscretized (3-D), incompressible Navier-Stokes equations over a
structured/unstructured grid is accomplished with CFD package Ansys-CFX.
Keywords:--Navier-Stokes equation, Centrifugal pump, impeller, Model, blade angle, CFD, turbulent
flow
202
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/P1
Email: suniliitd2003@gmail.com
ABSTRACT
Gas turbine blades are cooled internally and externally and one widely used blade cooling
technique is film cooling. In this type of cooling, relatively cool air is injected from the inside of the
blade to the outside surface which forms a protective layer between the blade surface and hot gas
streams. The present study is an attempt to establish the effect of blowing ratio and pressure ratio
numerically on film cooling effectiveness in a typical nozzle guide vane with single hole on both
pressure and suction surface of the vane. The commercially available CFD code “FLUENT 6.2.18” has
been used after validating it against the experimental results reported in literature. Pressure ratio was
varied from 1.1 to 1.2 with density ratio 2.0. Results obtained from the numerical investigation show that
with increase in pressure ratio at constant blowing ratio, there was an increase in film cooling
effectiveness. It is found that film spread is more on the pressure side as compared to suction side.
Keywords: Film cooling, Blowing ratio, Pressure ratio, CFD.
203
REFERENCES
1. Ravitej, M., Kesavan, V., Krishnamoorthy, V., Felix, J. and Deepak, J., “Cooling Effectiveness
Measurements Of Film Cooling Configuration of the Suction and Pressure Surface of the Nozzle
Guide Vane,” International Conference on Aerospace Science and Technology, No. 36, June 2008.
2. Mayhew, James E., Baughn, James W., Byerley and Aaron R., “The Effect Of Free Stream
Turbulence on Film Cooling Adiabatic Effectiveness,” GT-2002-30172 ASME Turbo Expo 2002.
3. Ligrani, P. M., Wigle, J. M., Ciriello, S. and Jackson, S. M., “Film Cooling from Holes with
Compound Angle Orientations: Part 1- Result downstream of two staggered row of Holes with 3D
Spanwise Spacing,” Journal Of Heat Transfer, Vol. 116, May 1994, pp. 341–352.
4. Ammari, H. D., Hay, N. and Lampard, D., “The Effect of Density Ratio on the Heat Transfer
Coefficient from a Film-Cooled Flat Plate,” ASME journal of heat transfer, Vol. 112, July 1990, pp.
444–450.
204
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India.
Paper ID – ICAME2013 S4/P3
CFD ANALYSIS WITH TEMPERATURE EFFECT ON THE PERFORMANCE OF A FINITE
LENGTH HYDRODYNAMIC JOURNAL BEARING SYSTEM
ABSTRACT
The present work aims to numerically study the thermal effect on the performance of hydrodynamic journal
bearing. Hydrodynamic journal bearings have been receiving wide importance in order to overcome the
adverse effect of temperature on the performance characteristics. When a bearing operates at high speed, then
heat is generated and raises the temperature of lubricant and affects the performance of hydrodynamic journal
bearing. Excessive temperature may lead to the bearing damage. This paper is aimed to study the thermo
hydrodynamic effect on a finite length journal bearing using a CFD package (ANSYS- Gambit, Fluent) to
predict accurately the performance characteristics of a hydrodynamic journal bearing. This 3-D analysis takes
into account the temperature variation along the circumference of the journal. The temperature distributions
on the bearing wall are plotted along with the eccentricity ratio at different speeds. Also temperature variation
at different clearance values have been studied where the dependence of temperature on clearance is clearly
perceptible. Temperature profile around the journal in mid-plane of hydrodynamic journal bearing is
generated and comprehensive CFD analysis is provided to examine the published theoretical results and
experimental data. An agreement between published results and CFD results is satisfactory.
Keywords: Thermohydrodynamic (THD), Journal bearing, temperature effect
205
1. INTRODUCTION
Since the perception of hydrodynamic journal bearing, it is being the prime juncture of researchers and
scholars in the field of thick film hydrodynamic lubrication to predict the bearing performance.
Conventionally, the isothermal form of Reynold’s equation is used to study the characteristics of journal
bearing. However, today, the inclination toward the “Optimization” necessitates the better tools to determine
the operating characteristics accurately. As there is strong dependence of lubrication viscosity on temperature,
the thermal effects must be taken into account. This has been confirmed by various experimental studies
Ferron et al (1983), Paranjape and Han (1994) and Huges and Osterle (1958). Several methods have been
proposed to take these into account.
Using numerical techniques Raimondi (1996) obtained an adiabatic solution for the finite slider
bearing. A more elaborate investigation was proposed by Dowson (1962) in which a generalized Reynold’s
equation was obtained. This equation considered the variation of the lubricant properties both along and
across the film. This equation led Dowson and Hudson Part I-II (1963) to study both one dimensional slider
bearing and the one dimensional parallel surface bearing. This study included heat flow across the boundary
between the film and the fixed pad bearing. It showed that the temperature effect on the density variation is
negligible as compared to that of the absolute viscosity. For calculating the effective temperature and the
corresponding effective viscosity through an evaluation of the dissipated power using isothermal theory was
proposed by Cameron (1966). Khonsari et al (1985) formed an analytical model of journal bearings for
analyzing the thermal effects and the boundary condition at the shaft oil interface. The thermal effects in
hydrodynamic journal bearings and the pressure distribution at the inlet by assuming parabolic variation was
investigated by Boncompain et al (1986). Using finite volume method, Han and Paranjape (1990) analyzed
the THD (Thermo hydrodynamic) performance of a circumferential groove journal bearing and the effects of
boundary condition the shaft, oil supply and reverse flow were discussed in depth. THD analysis of a journal
bearing using CFD as a tool is performed by Sahu et al (2012). Further CFD has been used in the analysis of
the performance characteristics of a hydrodynamic journal bearing lubricated with a Bingham fluid by
Gertzos et al (2008). The FLUENT software package is used to calculate the hydrodynamic balance of the
journal using the so-called ‘‘dynamic mesh’’ technique. The results obtained from the developed 3-D CFD
model are found to be in very good agreement with experimental and analytical data from previous
investigations on Bingham fluids. The effects of variable density and variable specific heat on maximum
pressure, maximum temperature, bearing load, frictional loss and side leakage in high-speed journal bearing
operation are examined by Chun (2004), in this investigation the influences of variable density and variable
specific heat on a high-speed journal bearing are compared with those using constant density and constant
specific heat.
However there is a dearth of comparative studies between theory and experiments. Feron et al (1983)
performed a THD performance study of a plain journal bearing for comparison of theory and practice.
This paper presents a comprehensive CFD analysis to examine the published theoretical results and
experimental data.
206
2. THEORETICAL BACKGROUND
One early idea to model thermal effects is approach of effective viscosity (Raimondi and Boyd, 1958).
This method employs an empirical equation to calculate effective temperature. From the effective
temperature, an an effective viscosity is determined and used in Reynolds equation. While this simple idea
recognizes the viscosity reduction due to temperature rise, its effectiveness is very limited and it fails to give
the maximum pad temperature, which is an important parameter.
Fig. 1 Hydrodynamic journal bearing system
Fig. 1 shows the geometry of the hydrodynamic lubrication system. Temperature rise takes place in
lubrication zone due to viscous shearing. Temperature effect is critical for accurate bearing performance
predictions. Energy equation is the governing equation. To accurately model the thermal effects, temperature
distribution must be solved from the governing critical energy equation. The energy equation for bearing
analysis has been substantially simplified because of small film thickness. The three-dimensional energy
equation for laminar flow is usually written in the form of-
∁ + + = + + + +
As shown in above equation, the steady state temperature is determined by three terms. The dissipation term
describes the internal heat generation due to viscous shearing. The heat convection term describes the rate of
heat transfer due to the lubricant’s motion. The conduction term determines the heat transfer between the
lubricant and surrounding surfaces. It can be shown by dimensional analysis the heat convection term is
usually much larger than the conduction term. Thus the film physically constitutes a heat source; while some
of that heat is conducted away through solid surfaces, the majority of it is carried away by the flowing
lubricant.
207
To achieve better computational efficiency, a simplified form of energy equation considering it as adiabatic,
that is obtained by neglecting the conduction term is used. The adiabatic equation implies that no heat is
transferred to the solids and the film temperature is constant radially.
In this paper CFD analysis has been performed by applying boundary conditions for those used by Feron et
al (1983) for experimental investigation.
3. METHODOLOGY
Three-dimensional modeling of the lubricant fluid film thickness has been done in GAMBIT, where
dimensions are referred from Feron et al. Operating conditions and dimensions of bearing are given below in
Table 1.
Table 1. Operating conditions
208
set as X=0,Y=0, Z= -1 (for an anticlockwise rotation of journal). The journal is modeled as a ‘moving wall’
with absolute motion at an angular speed of required rpm. Lubricant inlet temperature and bearing
temperature is set as 40 0C. Side boundaries of Fluid zone are set as pressure outlet zone to the atmospheric
pressure at the outflow boundary. In fluid cell zone condition define motion type as a moving reference frame
for journal with a rotational velocity of required rpm and direction of rotation is as rotation of journal. The
translational velocity in all three coordinate directions is set equal to zero.
Various parameters like fluid density, viscosity, specific heat constant associated with the solution method
used in the calculation are specified. The segregated solver is used for finding the solution and the flow is
assumed to be laminar and steady. The discretization used is ‘PRESTO’ for pressure, ‘second order’ for
momentum, ‘second order’ for energy and ‘simple’ for the P-V coupling.
3-D temperature distribution across the fluid film is presented in the form of contour Fig.7.
4. RESULTS AND DISCUSSION
Temperature variation is significant at different speeds with an eccentricity ratio. For comparison purpose
theoretical and experimental results for the same operating conditions are presented along with CFD results.
exp 4000 RPM exp 3000 RPM
CFD 4000 RPM CFD 3000 RPM
65 Theory 4000 RPM Theory 3000 RPM Theory
54
60 CFD
52
55 50
TEMP 0C
TEMP 0C
48
50
46
45 44
40
42
209
60
c =145µm
59 64
c=152µm L/D=1
58
62 L/D=0.8
57 c=166µm
60 L/D=0.5
56
TEMP 0C
55
TEMP. 0C
58
54
56
53
52 54
51 52
50
50
0.2 0.4 0.6 0.8
ECCENTRICITY RATIO 0.1 0.3 0.5 0.7 0.9
ECCENTRICITY RATIO
Fig.6 Mesh generation Fig.7 Temperature contour
210
5. CONCLUSION
Temperature variation in the fluid film of hydrodynamic journal bearing have been studied at different speeds
and different geometric conditions. Results determined using CFD numerical analysis are in good agreement
with those found out experimentally.
Through above CFD results the following conclusions are drawn:
i. Dependence of temperature on eccentricity ratio at different journal speeds has been proved.
ii. At constant eccentricity ratio, if radial clearance is increased, fall in temperature value is observed.
iii. If L/D ratio increases at constant eccentricity ratio, rise in temperature happens.
NOMENCLATURE
c Radial clearance, m p Pressure, Pa
Cp Specific Heat, J/kg 0C N Journal speed, rpm
e Eccentricity, m T Temperature 0C
ɛ Eccentricity ratio (e/c) u,v,w Fluid velocity components
dj Journal diameter, m x, y, z Cartesian coordinates
d Bearing diameter, m µ Dynamic Viscosity, Pa.s
F Force, N ρ Density, kg-m-3
h Fluid film thickness, m ϴ Bearing angular coordinate, deg.
K Thermal conductivity, W/m°C Ø Attitude angle, deg
L Bearing length, m
REFERENCES
JOURNAL ARTICLES
211
10. Boncompain R.,Fillon M. and Frene J. “Ananlysis of thermal effects in hydrodynamic bearings,”ASME J.
Tribology, 108,219-225,(1986).
11. Ferron J., Frene J., Boncompain R. A Study of the thermohydrodynamic performance of a plain journal
bearing comparison between theory and experiments, ASME Journal of Lubrication Technology., 105, 422-
428, (1983).
12. Gertzos K.P., Nikolakopoulos P.G., Papadopoulos C.A., “CFD analysis of journal bearing hydrodynamic
lubrication by Bingham lubricant,” Tribology International, 41, 1190–1204, (2008).
13. Sahu Mukesh, Giri A.K., Das A., “Thermohydrodynamic analysis of a journal bearing using CFD as a
tool,” IJSRP Vol.2, Issue 9, (2012)
BOOKS
1. Cameron A., "The Principles of Lubrication," Longmans Greens & Co., pp. 397-411, 1966.
212
SUB THEME 5
Design Optimization
1
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O1
ABSTRACT
The present work deals with the investigation and mathematics behind the strength of a specialized
chassis mounted platform/structure designed to carry concentrated load. This work deals w ith the
mathematics behind the load transfer during the gradient travel of a vehicle, through shea r and bending
diagrams analysis processes. The perce ptible loading case in the present analysis c omprises gradient load
and its effect on the platf orm/structure by usage of simple shear force & bending moment diagrams. T hese
diagrams reveal the distribution of shearing force during gradient travel for typical chassis mounted
platform. Present analysis accentuates on the des ign stage aspects of the platform as this research is a step
in doctoral study. Effect of load during gradient travel for an atypical type of combination of longitudinal
and cross members in platform/frame des ign is formulated. This paper provides a new technique for
computation of strength using shear and bending diagrams. Peculiarity of this analysis is the usage of
combined section modulus of three members for c omputation of stress.
Keywords: Gradient Load, Horizontal L oad, Shear Stress, Structural Strength, Shear force and bending
moment diagram.
1. INTRODUCTION
The secure and consistent use of a road vehicle necessitates the incessant adjustment of its speed and
distance in response to change in traffic conditions. Prese nt scenario postulates transportation as one of the
promising parameter for any country’s economic development. In today’s era of design optimization a nd
cost cutting with multiplied output, classical methods, computer based methods of des ign and analysis
provide a vital tool to the research and development process in any industry. Any truck/transportation
vehicle is subjected to innumerable types of static and dynamic loads during its travel. P resent rese arch
focuses on the structural strength of a platform/structure which is subjected to a conce ntrated load during
its travel on a gradient. The structure under consideration is especially designed for concentrated loading.
The structure is comprised of a combination of c hannel and tapered channel sections and their properties.
These members are termed as longitudinal and cross members of the platform. S pecial arrangement is
made for subjecting the platform/structure to concentrated load. T he longitudinal and c ross members are
light weight channel sections selected from a vailable Indian Standard IS 808:1989.
2
The cross members are designed w ith a taper angle of 5.720 from the central axis channel of total length of
one metre. This taper is provided only on one side of the cross member in order to have cantilever effect
for the section which rests on vehicle c hassis. The orientation and intermediate distance between the cross
members is postulated using computer aid. Bum Suk Kim et.al, 2009 proposed a first order analysis
method to design a vehicle sub-frame using a n equivale nt model of vehicle sub-frame consisting simply
beam elements. He further studied the modal properties shown by this model and compared them with the
full scale finite element model. Chul-Goo Ka ng, 2007 built hardware in loop system for braking scheme of
a high velocity train and analyzed its characteristics via real-time simulations. Deulgaonkar V.R. et.al,
2012 a nalyzed the structure/platform using shear force and bending moment calculations and worked out
stress for braking condition, this technique used classical method of calculation of combined section
modulus from which the stress values were evaluate d. L.Li, J., et.a l, (2009) developed a new approach for
non linear asymptotic observers base d on cascade observer system with a fusion of sensor signals which
reduced/diminished errors in observation of vehicle velocity, by considering the vehicle dynamic system
characteristics. Matani A.G. et.al, 2013 stipulated a similar structure for braking load, using classical
method of stress computation and found that stress values were within acceptable limits. Ilki and Kyongsu,
2002 developed and implemented a control scheme consisting of vehicle to vehicle distance control
algorithm and brake control algorithm for tracking acceleration. Seong, 2004 developed a methodology for
establishing rutting performance based load limits in conventional flexible pavements. The intent of this
present structure is to carry maximum payload with optimum self-we ight and dimensions from the
available materials. C lassical method of computation of section properties is applied to calculate the
properties of combined sections.
The present structure is designed for the concentrated nature of load. The individual members of the
structure are C-channels preferred over the conventional T , I and other round sections. The section
properties viz moment of inertia, section modulus, centroidal distance etc form both X and Y a xes a re of
each individual mem ber of the structure are studied and these members are so oriented that the
combination gives maximum amount of strength to withstand the load. T he outer two C- channels of
125X75X6 mm are called as outer longitudinal members, and eight tapered channels of 150X100X8 mm
are called a s cross members. The individual members of the structure are joined by we lding process a nd
then the whole c ombination of the longitudinal and cross members is again welded to main longitudinal
members which are of 125X75X5 mm. These main longitudinal members are either continuous or
discontinuous and are mounted on vehicle chassis with suitable number of U-bolts at suitable locations
over the length of chassis. These main longitudinal members provide as strong base and separation to cross
members. The cross-members are also either continuous or discontinuous depending upon the nature of
cargo transported or the locations of other various components of the load carrying vehicles. T he rear
portion of the structure is overhanging depending upon the wheel base of the vehicle, and hence one or
two cross members are left overhanging. Small channels of 50x50x5 mm a nd suitable length are welded
at front, middle and rear portion of the structure, in-order to provide a support to the plate w hich is later
welded to the outer longitudinal member a nd this small channel.
The locations of these plates are front, mid and rear of the structure and are placed at each corner of the
structure. These corners are called as ISO corners a t which the structure is subjec ted to concentrated load
and, all these longitudinal & cross members are shown in fig.1. The c ontainer or shelter is mounted on the
platform using locking arrangement. The freight we ight present in the shelter transferred through a dummy
platform on the structure and the nature of the load w hich acts on the structure becomes c oncentrated. In
order to strengthen the structure, triangular gusse t plates of 5mm thickness are we lded to the structure at
3
the points w here the cross member is attached to the main longitudinal member. At each cross member
four gusset plates are we lded. The thickness of these plates varies according to the payload carrying
capacity of the vehicle.
As the platform is a rigid structure the outer longitudinal members are recognized as long cylindrical or
prismatic bodies. T hese members are subjected to concentrated loads/forces that are perpendicular to
longitudinal elements and invariable along the length. D imension a long z-direction is e xtremely governing
as compared with the dimensions in x & y directions. Microanalysis of forces acting on the body shows
that surface traction and body forces also exist. F undamental assumption of the body being rigid, imitates
the fact that re lative distance between any two points on it is a lways constant. T he components of small
displacements parallel to x, y & z axis are u, v & w respectively. Then the components of normal and
shearing strain along x, y & z axes are given by Eq.(1) & Eq.(2). The intend of considering complete
differentials rather that partial ones is that it gives complete strain in the pres umed plane, as already known
that length is the dominant dimension in present a nalysis.
Applying the above equations to the longitudinal member of the platform we get c omponents u and v of
the displacement functions are x and y & being independent of the z c o-ordinate. He nce the longitudinal
displacement of the outer member is zero. We get the following equations as in Eq.(3). F urther using
Hooke’s law the normal stress is computed.
When the vehicle travels on a gradient or slope, the distribution a nd nature of forces acting on the structure
gets changed. In such situations, the major and prominent component of load gets transferred to rear
portion of the structure a nd hence the rear portion of the structure is subjected to severe loading a nd stress.
The nature and distribution of forces when the vehicle travels on a gradient is shown in fig 2 below. In
present analysis a maximum gradient value of 300 is used to distribute the components of loads/weights
acting on the structure. When the load carrying vehicle travels on a slope, the load distribution on the
structure is shown in fig.2. The key contributing force for the vehicle stability on the gradient is the
friction force between the rolling wheels/tires and the road surface. R oad surface undulation, nature of
4
road surface, wet roads, are also promising factors that has great influence on the friction force. The load
on the platform gets resolved into two directions one parallel and the other perpendicular to the plane of
the structure or platform. T he parallel component of load on the structure acts in the opposite direction of
friction force so as to keep the structure in horizontal plane equilibrium. The normal force and the
perpendicular force component of force on the structure keeps the structure in vertical equilibrium.
Equations (5) and (6) in Appendix 1, re present the relationship between these forces.
Further the calculation and characteristics of shear force and bending moment on the structure is done
using clas sical approach in strength analysis of materials. Shear force and bending moment analysis for
both para llel a nd perpendicular load components on the structure during gradient travel are shown in fig.3
(a) & (b) respectively.
(a) (b)
Fig. 3. She ar force and bending mome nt analysis for both load components
Figure 3 shows that although the magnitudes of forces/loads acting on the ISO corners are different in both
the planes , the nature of shear force variation is similar in both the planes. Form table 1, in Appendix 2
comparing the magnitude of shear force in parallel plane of action of forces and perpendicular one, the
para llel component is found dominant. This shows that the horizontal component of load is major
causative factor in design of such structure subjected to concentrated load on gradient travel. Similar
characteristics are observed in bending behavior of the structure. The magnitude of bending moment is
dominant in load along the plane of the structure. The resultant bending moment is computed by using
vector sum of moments in horizontal and vertical planes which is found to be 26.76447 kN-m. Further
5
using the value of combined sec tion modulus of the vehicle chassis, main longitudinal member and cross
member of the structure the stress value is computed for gradient loading, which is found to be 27.73MPa.
5. CONCLUSION
For the design of platform/structure against dynamic loading condition, the fundamental bending theory is
applied. Computation of stress value through numeric technique is accomplished. Plane stress and plane
strain concepts are utilized to have thorough insight of the stress and strains along the dominant parameter
i.e. length of the main longitudinal member. Applying the identical modus operandi for working out the
dynamic load behavior of structure on main longitudinal and cross member as employed for estimating
stress at various locations on the structure pr ovides us the novel way of determining the stress values and
hence the strength/efficie ncy of combined sections.
APPENDIX 1
Equations of e quilibrium
x = du/dx; y = dv/dy and z = dw/dz --(1)
γxy = (du/dy) + (dv/dx); γxz = (du/dz) +(dw/dx); γ yz = (dv/dz)+(dw/dy) --(2)
γxy = γxz = z = 0 --(3)
W =mg --(4)
∑F x = mg sinθ - F f --(5)
∑F y = mg c osθ - F N --(6)
6
APPENDIX 2
Tables
Table 1: Shear force and be nding moment values in horizontal and ve rtical planes of structure
REFERENCES
1) BAKKER, E., P ACEJKA , H.B AND LINDER , L., A new tire model with an application in vehicle
dynamics studies, SAE 890087 (1989)
2) BUM S UK K IM , MAKSYM S PIRYAGIN , B ONG SOO KIM, HON G HEE YOO, Analysis of the effects of
main des ign parameters variation on the vibration characteristics of vehicle sub frame, J.Mech. Sci.
& Tech. 23 960 (2009).
3) CHO , D ., AND HEDRICK , J.K., Automotive Power train modeling for control, ASME transactions on
dynamic system, measurements and c ontrol, (1989)
4) CHOI,S.J., RA RK ,J.W., AND JEON , K.K., Extreme driving characteristics estimation for ESP
equipped passenger car, Int. J. Automotive Technology 07, 816 (2006)
5) CHOI, S., AND D EVLIN , P., Throttle and brake combined control for intelligent vehicle highway
systems, SAE 951897 (1995)
6) CHUL-GOO KANG, Analysis of Braking S ystem of the Korean High-S peed train using real time
simulations, J.Mech. Sci. & Tech. 21, 1048 (2007)
7) DEULGAONKAR V.R., DR. MAT ANI A.G., DR. KALLURKA R S.P., Advanced Mathematical A nalysis
for chassis integrated platform designed for unconventional loading by using simple technique for
static load, Int. J.Engg. & Innovative Tech., 1, 26 (2012).
8) DEULGAONKAR V.R., PROF. DR. KALLURKAR S.P., PROF. DR. MAT ANI A.G., Mathematical
Analysis of Section properties of P latform Integrated with Vehicle chassis, Int. J.Sci. and Res.
Pub., 2, 87 (2012)
9) DEULGAONKAR V IKAS RADHAKRISHNA, SHI VANG BHAT NAGAR, A SHI SH K ARVE AND V ARUN K ELKAR,
Development a nd Design Validation of Pneumatic Tool for Stem Seal
& Collet Fitment of SL-90 Engine Cylinder Head, Int.J.Mfg.Sci. & Engg. 2, 53 (2011)
10) D EULGAONKAR V.R., P ROF. DR. KALLURKAR S.P., PROF. DR. MATANI A.G., Review and
Diagnostics of Noise a nd V ibrations in automobiles, In t.J. Mod.Engg.Res. 1, 242 (2011)
11) D HANDAPANI N.V., DR. M OHAN KUMAR G., DR. D EBANATH K.K., Static analysis of off-highway
vehicle chassis support for the effect of various stress distributions, Int. J. Adv. Res. in Tech. 2, 1
(2012).
7
12) DUGOFF,H., F RANCHER , P .S . AND S EGAL ,L. A n a nalysis of tire traction properties and their influence
on vehicle dynamic performance , SAE 700377 (1970)
13) GYU HA KIM, KYU ZONG CHO, IN BUM C HYUN , GI SEOB CHOI, Dynamic stress a nalysis of vehicle
frame using a non linear finite eleme nt method, KSME Int. J. 17, 1450 (2003)
14) Hyung-Sub Bae and Myeong-Kwan Park, “A Study of Torque characteristics of small disk brake
using magnetic fluid”, J.Mech. Sci. and Tech. 25, 349 (2011)
15) ILKI MOON., KYONGSU YI., Vehicle tests of a longitudinal control law for application to stop-and-go
cruise control, KSME Int. J. 16 1166 (2002)
16) KAT O, I.,TE RUMICHI , Y., A DACHI, M. AND S OGABE,K., Dynamics of track/wheel systems on high
speed vehicles, J.Mech. Sci. and Tech. 19,1328 (2005).
17) KUNSOO HUH , KYUNGYOUNG JHANG, JAEEUN G OH, JOONYOUNG KIM AND JAEHEE H ONG,
Development of a simulation tool for the c ornering performance analysis of 6WD/6WS vehicles,
KSM E Int. J. 13, 211 (1999).
18) L. LI, J. SONG, L. KONG, Q. HUANG, Ve hicle velocity estimation for real-time dynamic stability
control, Int. J. Au to. Tech. 10, 675 (2009).
19) LEE, H.C, Reliability indexed sensor fusion and its applica tion to vehicle velocity estimation,
ASME, 128, 236 (2006)
20) MAT ANI A.G, P ROF.DEULGAONKAR V.R, P ROF.DR. KALLURKAR S.P, An investigation of structural
integrity of chassis Mounted platform subjected to concentrated load during braking, 4 115(2013)
21) SCHIEHLEN ,W, W., Recent developme nts in multi-body dynamics, J.Mech.S ci. Tech. 19, 227
(2005)
22) SEONG –WAN PARK , L oad Limits based on Rutting in pavement foundations, KSCE J. Civil Engg.
8, 23 (2004).
23) CROLLA D.A, Automotive engineering power train, chassis system and vehicle body Butterw orth-
Heinemann, (2009).
24) TIMO SHENKO S.P ., GOODIER J.N., Theory of Elasticity, T hird Edition, Tata Mc-Graw Hill Edition
New Delhi (2010)
8
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O2
ABSTRACT
Comm unities residing in island(s) and geographically remote areas which are not integrated
with the electric grid have a high energy demand. Wind power is an attractive option for onsite
power generation at such locations. High magnitude of demand mandates the use of multiple
wind mac hines. This paper presents a methodology to des ign multiple wind turbine system-
battery storage by taking into consideration the uncertainty of wind availability. T he inputs to
the methodology are the load profile, w ind speed profile, c haracteristics of various components.
From time step simulation of the e ntire system, the complete set of feasible s olutions in terms of
the power rating of the turbine, rotor blade diameter and size of the storage for a given number
of wind machines can be determined. T he solution space depicting the relation between the wind
turbine rating and storage s ize as a function of number of wind machines is the design space for
the problem. From the design space depiction, it is found that there exists minimum and
maximum limit to the values of generator rating and battery size within which a feasible design
is possible.
Keywords: Design space; isolated wind-battery systems; multiple wind turbine systems.
1. INTRODUCTION
Constraints on diesel fuel a vailability, its cost as well as restrictions on environmental emissions
(Senjyu et al., 2007) poses a threat to the energy security of isolated islands which are not
connected to the main grid. Wind power is a clean source of energy and the most utilized
renewable source as most islands have a good wind regime. Knowing that the e nergy demand at
such locations is substantially high (of the order of several MWh/day), it is evident that a single
wind machine will not be able to supply the entire demand. This necessitates the deployment of
multiple wind turbines. There a re a number of a lternatives w hen choosing the number of wind
machines. A designer may prefer few numbers of relatively higher rated machines or ma ny
machines of small rating. T he design space approach for solving this particular problem is
presented in this paper.
Design of systems consisting of multiple wind turbines integrated w ith storage requires the
determination of the optimum number of wind turbines, the rating and diameter of each machine
9
as well as the size of storage for a specified system reliability requirement. In system design
problems consisting of multiple objectives and constraints, the solution space can be explored
prior to system optimization. Design space is a method that identifies the space occupied by all
feasible s olutions to a particular problem. T his paper inves tigates the interrelationship between
different design variables of an isolated multiple w ind turbine-battery system by the use of the
design space philosophy. The method is dem onstrated by the help of an illustrative example.
2. MATHEMATICAL MODEL
The sc hematic of a system containing multiple generators along with a battery storage operating
in an autonomous mode is illustrated in F igure 1. A number of wind generators represented by
WT1, WT 2 ….WTn are connected to the AC bus. Each of these generators has the same rating
and rotor diameter and is completely identical to each other in every res pect. The model of
power generation as detailed in Roy et a l. (2011)
P1(t)
W T1
P2(t)
W T2
f
Pn(t)
QB(t)
W Tn Bi-d irectional
Converter & Battery
L(t ) Charge cont roller bank
AC Load
A C Bus DC Bus
Figure 1. Schematic of a n isolated wind battery system with multiple wind generators.
As seen in Figure 1, the components comprise of a wind turbine, battery bank, bi-directional
converter and charge controller are arranged in a parallel interconnection system between an AC
and DC bus. At any instant of time, when generated power exceeds the demand, the surplus
charges the battery or if the battery is fully c harged it is sent to dump loads. When generation is
insufficient to meet the demand, e nergy is drawn from the battery, provided the battery has not
reached its depth of discharge (DOD ). A loss of load occurs if at any instant there is no or less
generation from the w ind turbine and the battery bank is fully drained. (Arun et al., 2008). For a
small period of time (Δt), if P(t) is the power coming from a single wind turbine and L(t) is the
demand, then power available in the battery bank at the end of this time interval QB(t+ Δt) is
given by following energy balance equation:
N
QB (t t ) QB (t ) [ P (t ) L (t ) Pdu (t ) ft (1)
2
Where, Q B(t) is the energy available in the battery in the previous time interval, Pdu(t) is power
dumped, and f represents the losses during the charging a nd discharging of the battery bank.
Chance constraint programm ing has been utilized to portray the uncertainty of wind speed
availability at a given time step of simulation (Charnes and Cooper, 1959). Wind speed and
10
hence wind power is considered as random variables following a Weibull distribution while the
load is assumed to be deterministic. A chance constraint specifies that due to uncertainty
associated with one or more variables, there is a probability associated with the satisfying a
design constraint. In this study, the major design constraint is fulfillment of energy requirement
at all time steps of simulation. Therefore, the probability that N identical generators along with
battery storage would meet the demand with pre-specified reliability (probability) of χ is given
mathematically as:
N dQ B (2)
Prob Pn ( t ) L(t )
2 dt
The term dQB dt relates to the power supplied from the battery bank while the first term
represents the power coming from N number of wind generators. It must be pointed out that as,
there is no power output for wind speeds less than the cut-in (V c) and greater than the cut-off (Vf )
wind spee d of the turbine, the periods when these w ind speeds a re encountered must be suitably
accounted in calculating the system reliability. Alternatively, an effective value of reliability
(χeff) which includes the probability of occurrence of wind speed lowe r than the cut-in (αc) and
greater than cut-off (α f) should be included. Hence, equation (2) is modified as:
N
dQB
Prob[ Pn (t ) L(t)] eff where eff c f (3)
2 dt
The values of α c and α f can be readily calculated from the Weibull cumulative probability
distribution function of wind speed for the site under consideration. Under the assumption that
all the wind machines are identica l and neglecting the non-uniformity in the spatial distribution
of turbulence as we ll as the wa ke effects of one wind machine on the other, power generation
from a cluster of N identica l machines can be expressed as:
N
P (t ) P (t ) P (t ) ....... P (t ) NP (t )
n 1 2 n N 2
2 (4)
Where, P(t) is the power generated by one wind machine. S ubstituting (4) in (3) and isolating
the random variable P(t) to the left hand side of the inequality inside the square bracket:
L (t ) Q B (t t ) Q B (t )
Prob P (t )
N
Nf (t )t 1 eff
(5)
The probabilistic re lation given by equation (5) represents the cumulative distribution function
of w ind power and can be converted into a deterministic form as given below by taking an
inverse of (5) a nd expressing in the form of battery energy values:
Q B (t t ) Q B ( t ) [ N F P1 (1 eff ) L (t ) Pdu (t ) f t
(6)
The term NF P-1(1-χeff) is the power generated by N wind machines corresponding to the
reliability requirement of χ. F P-1(1-χeff) is the power output model of a single w ind turbine under
the consideration of resource uncertainty a nd is found form the follow ing (Roy et al., 2011):
3
FPw1(1 eff ) P (t) aVe Vc Ve Vr
Pr Vr Ve Vf
0 Vc Ve and Ve V f
(7)
11
Where, V e is the estimated wind speed at a given time step obtained from chance constraint
programming and wind speed probability distribution (Roy et al., 2011). It is the wind speed
corresponding to which, the system will be a ble to give a reliability of χ.
Ve c ln( eff ) k
1
(8)
Given a generator rating and rotor diameter of the wind turbine, the storage capacity
requirement is obtained by solving E quation (6) at each time step in the entire time horizon (T).
The battery bank capacity (Br) is then obtained using e quation (9).
max{Q B (t )}
Br (9)
DOD
For each value of generator rating and rotor diameter considered, the associate d minimum
battery bank capacity is obtained by minimizing the storage capacity equation (9). The
optimization variables are the initial battery energy, QB (t = 0) and the power dumped at each
time step (P du(t)), subject to the constraint of equality of the battery energy at the start and end
of the time horizon (Q B (t= 0) = Q B (t=T)). Additional c onstraints of non-negativity of the battery
state of energy (Q B (t) ≥ 0) as we ll as the dump (P du(t)≥ 0), ensure that these varia bles alwa ys
assume a positive value. The methodology is described by taking an illustrative example.
3. ILLUSTRATIVE EXAMPLE
The example considered here, pertains to the Indian Sundarban region which consists of a group
of 102 islands out of which 54 are inhabited. T he island of Gangasagar in this region possesses a
favorable wind climate. The hourly mean and standard deviation of wind speed for a
representative day at a hub height of 25 m is shown in Figure 1 (Rangarajan, 1998). The mean
wind spee d over the entire day is 4.9 m/s. Average values of shape and scale parameters at the
site are 2.05 and 5.55 m/s respectively. The variation of load over a typical day is shown in
Figure 2. The load as well as w ind speed is assumed to remain constant over the time step of one
hour. T he time step of simulation is 1h and the time horizon considered is 1 day. The battery –
converter system net charging a nd discharging efficiency is ta ken to be 85%, while DOD of the
battery is 70%. The turbine has a hub-height of 25m and the power law index for the site is 0.31.
Total energy demand of the community is 1037.8 kWh w hile the average (over six hours) power
demand is 172 kW.
Methodology for the generation of des ign space corresponding to a reliability requirement of
60% to be achieved with two w ind generators (N=2) and battery storage is first discussed. It is
found from system simulations that a minimum rating of 59.2 kW (individual machine rating =
59.2/2 = 29.6 kW) along w ith a battery bank size of 1147.3 kWh ensures a feasible design. This
point is designated as Pmin and its position is marked on a plot of battery capacity vs. generator
rating as shown in Figure 3. For values of generator rating greater than Pmin , the locus of design
points corresponding to minimum battery size forms the sizing curve and is shown in F igure 3.
12
6 mean wind speed 200
5.5
5 Average speed = 4.9
150
4.5
Wind speed, m/s 4
Lo ad (kW )
100
3.5
3
2.5 50
2
1.5 0
0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 24
Time (h our of th e day)
Time of day,h
Fig. 1. D iurnal wind speed profile on a typical day Fig. 2. H ourly average daily demand
at a height of 25 m above ground at Gangasagar. for the island of Gangasagar.
400
Pr =184 kW
200
0
10 100 Generator rating, kW
1000 10000
Figure 3. S izing curves for χ = 0.6 with different numbers of wind turbine.
A design point in the region enveloped by the sizing curve is guarantee d to satisfy the demand accor ding
to the reliability requirement. Thus the region above the sizing curve is the feas ible design region or
‘des ign space’ while the shaded area in F igure 3 shows the infeasible design region. When generator size
is increased from P min , the battery bank requirement reduces indicating availability of surplus energy. The
decrease in storage requirement with increase in rating continues up to a point where the battery capacity
reaches to a global minimum value. Such an option is indicated by the point marked B mi n in F igure 3. The
corresponding total generator capacity is 140 kW. In the current example, the hub height of the wind
turbine being 40 m, the maximum diameter is limited to 60 m considering h 0 = 10 m. For generator ratings
greater than 140 kW, the part load energy loss is higher than the incremental energy available due to a
higher rating. On increasing the rating furthermore, a point is reached where, loss due to part load
operation is so high that it is not compensated by further higher generator capacity. T his imposes a
restriction on the maximum possible generator rating (Pmax). T he maximum generator rating is 196 kW for
the present case. Therefore, there exists a range of generator ratings w hich will meet the load as per the
reliability requirement.
13
By varying the number of generators from 2 to 15, the sizing curve for each value of N may be generated
(F igure 3). It is seen that the minimum generator rating is the same irrespective of the number of wind
turbines used. However, the demand energy being fixed, an increase in the number of wind turbines
requires a reduce d generation capacity from a n individual machine. Hence, with increase in N, the rating
of each generator required to support the demand reduces. Figure 3 also illustrates that when generator
rating is raised from P min , battery bank size reduces. Because of the prevalence of surplus energy
availability over the energy loss due to part load operation in the region from 55 kW to 184 kW, the
mismatch betwee n generation and demand over the time horizon remains constant, independent of the
number of wind generators e mployed. Consequently, the battery storage requireme nt for a specific rating
is also the same across differe nt number of w ind generators.
4. CONCLUSION
A method for selecting the optimum number and size of wind generators w hen more than one wind turbine
is employed is demonstrated. For a specific number of w ind turbines, the design space indicates that there
are upper and lowe r bounds to the values of rotor diameter, generator rating and battery bank size that can
serve the demand. Based on the above investigation, following conclusive remarks may be draw n:
(i) In order to fulfill a particular reliability, the minimum rating and the corresponding battery
bank size remains the same irrespective of the number of wind generators.
(ii) There exists a design corresponding to m inimum storage requirement for every given reliability
level.
(iii) For a given reliability level, it ma y be possible to meet the load with a wind turbine only
configuration.
In the pres ent study, the array eff ects on the pow er output have been neglected. Also there may be restrictions
on c apital availability, land us e and o peration and maintenance expenditure. A more r ealistic scenario c an be
generated by the inc lus ion of these parameters.
REF ERENCES
1. ARUN P, BANERJEE R, AND BANDYOPADHYAY S., Optimum sizing of battery integrated dies el
generator for remote e lectrification through design space approac h, Energy 33, 1155(2008).
2. CHARNES A. AND COOPER W.W., Chance-constrained programming, Management Science, 6,
73(1959).
3. RANGARA JAN S., Wind energy resource survey in India: Volume- V, Allied Publishers, New Delhi,
1998.
4. ROY A, KEDARE S.B. AND BANDYOPADHYAY S., Application of design space methodology for
optimum sizing of wind-battery systems, Applied Energy, 86, 2690 (2008).
5. ROY A., KEDARE S.B. AND BANDYOPADHYAY S, P hysical design space for isolated wind- battery
system incorporating resource uncertainty, Journal of Power and Energy: Proceedings of the
Institution of Mechanical Engineers, Part –A., 225, 421(2011).
6. SENJYU T., HAYASHI D., YONA A., URASAKI N., F UNABASHI T. Optimal configuration of power
generating systems in isolated island with renewable energy, Renewable Energy; 32, 1917 (2007).
14
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O3
ANALYSIS AND DESIGN OPTIMISATION OF REAR GAURDS
OF HEAVY DUTY TRUCKS
AB STRACT
Truck underride is when a passe nger vehicle crashes into and penetrates beneath, or
"underrides", the taller rear of a large truck or trailer. The top of the car is crushed or ripped off, and the
occupants suffer severe with injuries. Rear guards on trucks and trailers were initially required in 1953,
and are known as ICC bumpers (Interstate Commerce Commission), but such rear bumper devices are
typically defective, too high a bove the road, too narrow across the truck's rear, and too weak to prevent the
underride hazard.
To minimize the number of deaths a nd serious injur ies associated with underride collisions, in the United
States, NHTSA issued a safety standard to require safer guards as per their roadway regulations still truck
guards are not strong enough to absorb impact forces, and may we ll be defectively designed and
ineffective. As per work carried out by NHTSA , without compromising w ith the proved out designs of
rear truck underride , some amount des ign optimization has been looked in to the existing design to suit
the Indian perspective. The pres ent investigation is carried out by providing the flexibility & by varying
height of the guards, a concerted has been made optimize existing design & conduct the crashworthy
analysis. Apart from adopting credible analysis software tools such as Hyper Mesh & LS- DYNA has been
used to carry out cre dible investigation and find optimized solution. Without compromising the bas ic
design new avenues have been probed to improve the strength properties as well as shocking absorbing
capacity of large truck underride guards to suit varied Indian road conditions.
Keywords: Optimization, Design Variables, L inear analysis, Nonlinear Analysis, Impact, Dynamic
Analysis
1. INTRODUCTION
Regardless of what ca uses a passenger vehicle to crash into the rear or side of a large truck or trailer –
driver misjudgment, a lack of conspicuousness that leaves the trailer less visible in the dark of night,
inclement weather, or some other reason – the rear and sides of the truck or trailer must have sufficient
15
underride prevention guards so that the collision does not result in severe or fatal injuries to the occupants
of the impacting passe nger vehicle.
When a passenger vehicle collides w ith the rear end or side of trucks, trailers or buses not equipped with
effective guards (bumpers), it continues to travel beneath the taller chassis of the larger vehicle, i. e. , the
passenger vehicle "rides under" the larger one. The invasion of the passenger compartment that follows the
underriding ca uses severe head and upper body injuries in the car occupants and consequently results in a
very high rate of fatality. Often the car passengers are decapitated, when occurs the so called "guillotine
effect".
Truck underride is preventable. The prevention of the truck-underride hazard is accomplished with guard
devices designed into or attac hed to the rear or side of large trucks or trailers. When a passenger vehicle
makes contact with a guard of sufficient strength, that guard prevents the vehicle from underriding,
thereby sa fely maintaining the occupants’ survival space.
About 40-percent of all rear underride fatalities involve the rear corners of the truck or trailer. Therefore,
an effective guard should have a dditional vertical support members at the corners to help prevent the main
horizontal bar from breaking away and failing
Byron Bloch discovers the importance of rear and side guards for trucks and trailers in preventing truck
underride tragedies, and how much more there is to do in the name of safety.
According to the Fatality Analysis Reporting S ystem (FARS), about 10 percent of passenger vehicle
occupant fatalities occur in cras hes involving large trucks. Two recent studies limited to frontal crashes of
vehicles designed to perform well in crash test programs found that large truck crashes are a common
source of fatality or serious injur y for belted frontseat occupants [1,2]. T he only US regulations a ddressing
the structural incompatibility between passenger vehicles and large trucks are Federal Motor Ve hicle
Safety Standards (FMVSS) 223 and 224, which require rear underride guards on some tractortrailers [3].
Both standards became effective in 1998, with FMVSS 224 outlining the types of trailers required to have
underride guards as w ell as dimensional requirements for the guards, and FMVSS 223 describing strength
and energy absorption requirements in quasi-static tests at three locations on the guard. T he National
Highway Traffic Safety Administration (NHTSA) issued this rule to “reduce the number of deaths and
serious injuries occurring when light duty vehicles impact the rear of trailers a nd semitrailers with a gross
vehicle weight rating of 4,536 kg or more” [4].
Brumbelow and B lanar’s [5] findings confirmed that the problems with FMVSS-compliant guards
identified in a previous series of crash tests were indicative of field crash performance. The crash tests,
conducted by NHTSA in support of the rulemaking, illustrated how an underride guard could meet all of
the requirements of both standards yet still produce severe underride due to attachment failure or
deformation of the trailer chassis [6]. The tested guard design was able to prevent severe underride of a
1992 H onda C ivic in a 48 km/h full-width test only a fter the attac hment hardware was upgraded and the
trailer structure was reinforced. Elias and Monk [6] stated that compliance with FMVSS 223 was
insufficient to ensure good crash performance if the “attachment hardware or the trailer sub-system to
which the guard is attached is not of sufficient strength.” Howe ver, the final rule that later was issued
allowe d guards to be tested independently of trailers and contained no provision for evaluating the strength
of the trailer or attachment. NHTSA did state that adequate guard performance could not be assured at
crash spee ds a bove 45 km/h (61 FR 2010).
16
This paper primarily focuses on T o establish minimum requirements for the manufacture and installation
of rear guards to be attached to trucks, trailers and semi-trailers with gross vehicle we ight rating (GVWR)
above 4,600 kg. Evaluate the effectiveness of the new rear impact guard safety standard.
Compare the crash performance of guards on trailers meeting the NHTSA standard and/or TTMA
recomme nded practice to the smaller "pre-TTMA" guards on trailers meeting only the 1952 FMSCR
standard. Compare the striking vehicle (car, pickup truck, SUV, or van) passe nger compartment intrusion
(P CI) underride rate of the "pre-TTMA" guard and the P CI underride rate of the new NHTSA and/or
TTMA guard for trailers. Examine the crash performance of the rear-end structures of single-unit trucks.
Estimate the cost per vehicle for the initial installation and subsequent maintenance of the rear impact
guard. Examine the durability and reliability of the rear impact guard.
2. METHODOLOGY
The frame is attached to the truck chassis beams by means of tw o Articulations and device on truck have
full-width structural supports across the rear of the trailer. The material and all other properties of the
guard are given while analysis in Ls-Dyna.
Figure 1 Relevant de tails pe rtain ing to the U.S. reg ulation FMVSS 223 & 224
The dimensions of the guard are varied as per FMVSS 223& 224 a nd NHTSA regulations. The rear guard
is modeled in CATIA.
17
Fig2.
FMVSS 223 and CMVSS 223 test locations of re ar guard.
The meshing of the model is carried out by hyper-mesh. The mixed mode element is used in this a nalysis.
This model is a linear beam and has a complex geometry hence translation as we ll as rotation is not
possible in a ll the three directions. The chose n element should have six degrees of freedom at e ach node.
The displacement has been arrested at hanging hole radius in the directions X, Y and Z, rotation in
directions X and Y where as the rotation in Z direction is allowe d which is required for easy hitting of the
rear guard.
The solved model is stored as log file a nd retrieved in the probabilistic des ign module. Then the
probabilistic analysis is done. Here the major steps included are Specification of random input varia bles,
Specification of random output variables, Proess of solving problem using Post-Processing.
18
2.3.2 Specification of random input variables
The first step involved in ANSYS PDS is the specification of input random variables. Input parameter
namely density is characterized by the lower and upper bounds. Force, Young’s modulus and Poisson’s
ratio are specified with the mean and standard deviation. Table 1 shows the mean, standard deviation,
minimum, maximum values as we ll as the distribution types of random input varia bles.
The output parameter defined is Maximum forces(MAXFRC). Rear guard is designed for the maximum
allowa ble forces and the deflection should also be w ithin the limit for the input random variable variations
and the effect of these input random varia bles on the output variables are to be observed and decision has
to be made acc ordingly.
The res ults of the dynamic model are grabbed using Ls-Dyna, post processing a nd they are run in Ls-
manager.
The energy absorption and strength test requirements are defined at the locations as shown in the
figure,and the results are btained w hen the velocity is taken as 35 to 40 m/s
– The guard shall resist a force of 50,000 N at points P1 and P 2 without deflecting more than
125mm.
– The guard shall resist a force of 100,000 N at point P3 without deflecting more than 125mm.
19
– The guard shall absorb energy of 5,560 J w ithin the first 125mm of deflection at each P3
location.
4. CONCLUSIONS
New novel methods of design has to be incorporate d to absorbed varied energy level at the time of impact,
new breed of materials needs utilized w ith changing operating conditions.The analysis reveal the rear
guard design considered certainly matc hs the NHTSA regulations and for fixed velocity of the vehicle, but
the des ign needs to modified to suit the Indian road conditions and traffic management. The work carried
out has revealed with change design parameters better res ults can be obtained.
REFERENCES
1. BRUMBELOW ML, Z UBY DS. 2009. Impact and injury patterns in frontal crashes of vehicles with
good ratings for frontal crash protection. Proceedings of the 21st ESV Conference (CD-ROM),
Washington, DC:National Highwa y Traffic Safety Administration.
2. RUDD RW, BEAN J, C UENT AS C, K AHANE CJ, MYNATT M, WIACEK C. 2009. A study of the factors
affecting fatalities of air bag and belt-restrained occupants in frontal crashes. Proceedings of the
21st ESV Conference (CD-ROM). Washington, DC: National Highway
3. Traffic Safety Administration.
4. Office of the Federal Register. 1996. Federal Register, vol. 61, no. 16, pp. 2004-2036. NHTSA –
Final rule. Docket no. 1-11, Notice 11; 49 CFR P art 571 – FMVSS, Rear Impact Guards, Rear
Impact Protection. Washington, DC: National Archives and Records Administration .
5. National Highway Traffic Safety Administration. 2009. Title 49 Code of Federal Regulations
(CFR) Part 571, rear impact protection. Washington, DC: Office of the Federal Register.
6. BRUMBELOW ML, BLANAR L. 2010. Evaluation of US rear underride guard regulation for large
trucks using real-world crashes. Proceedings of the 54 th Stapp Car Crash Conference, 119-31.
Warrendale, PA: Society of Automotive Engineers.
7. ELIAS JC, MONK MW. 1993. Heavy truck rear underride protection. Report no. D OT-HS-808-081.
Washington, DC: National Highway Traffic Safety Administration.
20
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O4
Not Received
21
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O5
ABSTRACT
The primary objective of this paper is to optimize the des ign of a roll ca ge frame structure for SAE
standard based small segment ca r. A small segment vehicle is a small, off road vehicle powered by a four
stroke engine, thus large part of vehicle performance depends on acceleration which is proportional to the
weight of the roll ca ge and hence chassis. to ac hieve greater performance of the vehicle, a balance must be
found between strength and we ight of the roll cage to ensure safety of the driver. S o roll cage part of the
chassis is the primary protection for the driver. He nce roll cage must be structurally rigid and its des ign
becomes very important in the vehicle performa nce. Since small segment car are designed for high
accelerations, they can reach very high speeds in ideal test conditions. During such high speed conditions,
the stiffness of the roller cage structure is measured in terms of the torsional and bending stiffness. B ut
however torsional stiffness predominates, since deflection due to bending will not affect traction loads on
whee ls. T he design optimization of roll cage is based on position, location and orientation of associated
links. He nce a multi-body dynamic analysis is carried out to study performance of the roll cage.
Established tec hniques of modeling have been implemented to distribute the mass of the vehicle over its
frame members, so as to simulate dynamic analysis. F inite element mode of analysis has been carried out
to decipher the existing problems and using existing and widely use d software pac kage LS-DYNA. The
paper e laborates on some of the pressing issues such as selec tion of material of roll cage was safety, cost
and durability. A s incere attempt has been made by using LS-DYNA to analyze the non-linear dynamic
response of the three dimension structures.
Keywords: Roll Cage Structure, Stiffness, Optimization, Design Variables, N onlinear analysis
1. INTROD UCTION
The objective of this paper is to simulate rea l-world engineering design projects and their related
challenges. The engine cannot be enhanced in any way to ensure uniform comparison of overall vehicle
design. Thus, a large part of vehicle performance depends on the drive train and the maneuverability of the
vehicle. By improving drive-tra in effic iency, the vehicle will accelerate faster and achieve a higher top
speed. The other contributing factor for the vehicle performa nce is acceleration a nd maneuverability. T he
total weight of the vehicle including the driver we ight has significant impact on performance. Overall, a
22
light vehicle should perform better since the engine capac ity is fixed. Driver safety is an important c oncern
in the design of the vehicle. The rollcage part of the chassis is the primary protection for the driver. So to
ensure driver safety, the rollcage must be structurally rigid. As weight is critical in a vehicle powered by a
small engine, a balance must be found between the strength and weight of the vehicle. Thus the chassis
design becomes very important in the vehicle performance. The frame design discussed in this report is in
compliance with the 2009 Ba ja SAE Rules [1].
The design is heavily influenced to address new safety concerns. These rules define the frame design in
two wa ys. First, the rules set specific requirements on minimum frame cross-section flexural strength. This
flexural strength can be achieved by any combination of material and cross-section geometry. Smaller
members can be used with stronger materials. They also define the specific requirements of the frame
geometry, s uch a s maximum length, width and height as well as minimum clearance between driver a nd
frame members. A thorough review of the different types of chassis designs and rules were made at the
end of the design stage before fabrication [2, 3, 4].
The requirements were referenced when making decisions regarding the material selection, des ign
geometry and any additional modifications to the design.
The scope of present inves tigation revolves around the design of, A four-w heel vehicle w ith a roll cage
with appropriate bracing. S ome of the prerequisites are to allow eas y driver e ntrance and exit, aesthetically
pleas ing a nd be rugged, dependable, and easy to maintain.
Optimization of strength/weight ratio for the entire vehicle to enhance performance parameters. A frame
constructe d of either steel tubing or material having equivalent strength and bending modulus is to be
considered.
In this paper issues re lated to roll cage of a SAE (Small segment car) has been discussed, the frame has
been designed by incorporating continuous lengths of tubing, which reduces welding zones and hence
improves strength. By adopting this design it has been possible optmize strength, we ight, durability and
facilitate eas y fabrication, the use of geometric modeling and Finite Element Analysis (FEA) techniques
are e xtremely useful in addition to conventional analysis
2. METHODLOGY
Before beginning the des ign of the frame it was important to make several global design decisions. T hese
include such details as intended steering and suspension des ign and also intended fabrication methods.
While these decisions are not important to the analysis of the frame, they are important to understanding
the design. The rules regarding the frame geometry and driver safety must be considered a s we ll.
2.2 Materials
For each component in FEM, a mathematical material needs to be assigned to simulate the
behavior of the component. T he chassis frame is a of alloy steel 1020 and other components of the vehicle
are constructed with different materials. T he material behavior and properties of eac h material is different
from others. LS-DYNA has over 100 material models to choose from but due to simplicity of the vehicle
model only one of these are selected for the a nalysis.
23
2.3 Geometry Development
A preliminary design was developed as per the rules and guidelines laid by SAE. Since (CATIA)model is
the basis to create a complex FEA model, there began a quest to develop a CATIA model. With the
reference dimensions, a CATIA m odel was developed . CATIA drawings w ere made from the developed
model .F igure represents the solid model of the chassis developed for the preliminary design. Upon
completion of CATIA m odel of the frame, the P ro/Engineer part model is imported into the Hyper Mesh
environment which is a part of the A ltair Hyper Works software package. Altair Hyper Mesh was used as
the finite element meshing utility in preparation for the optimization study. It is made sure that all the
surfaces are imported into Hyper Mesh properly without any geometry pr oblems. The next step is
extracting the midsurfaceof the solid pipe model. Hyper Mesh can automatically generate amid-surface
from a symmetrical cross section. T he surface editing tools would allow morphing the generated
midsurface to be convenient for the quadratic meshing.
Once the geometry was fine tuned, the surfaces of the frame member were e dited for proper mes hing. that
the joints can be meshed first followed by adjacent tube members. In this way mesh quality can be
improved. The design space volume was filled with quadrilateral elements using the auto-mesh features of
HyperMesh (Refer Figure 1). The mesh size is selected depending upon the requirement. To ensure model
accuracy and efficiency, the mesh of the model needs to meet a mesh quality criterion. The quality of the
mesh w ill affect the time step calculations of the simulations a nd thus the computation time. T he time step
is directly re lated to the characteristic length of the elements so the minimum element size is of particular
importance. Severe ly distorted elements w ill affect the accuracy of the results due toan increase in
stiffness of the element due to the distortion. The percentage triangular elements should be less than 5% of
the number of elements in the component because the triangular elements impart an artificial stiffness into
parts modeled with them.
3. DYNAMIC ANALYSIS
The major steps involved in the design process for dynamic analysis.
a. From the existing design, additional geometry members that would be mounted on the chassis like
engine, suspension, transmission, driver with seating system and other auxiliary components are
24
modeled a s equivalent mass e lements for mass distribution of the vehicle to simulate the design for
real world dynam ic analysis problem.
b. A finite element (FE) model was created using QUAD AND TRIAC using Hyper Mesh, on which
dynamic analysis was performed. The element quality has been ensured for optimum FE analysis
results.
c. The next step in the analysis was setting the boundary conditions for simulation. The parameters
include material properties, section properties, contacts constraints, creating rigid wa lls, defining
initial velocity and other simulation related parameters.
d. After setting the parameters, the simulation was run using LSDYN A solver for the cras h analysis.
e. The results of the simulation were interpreted in Hyper View/Ls-P ost. The analysis determines the
velocity profile, rigid wa ll forces or reaction forces, total a nd absorbed energy and Acceleration at
any desired location that the frame members are subjected for the applied loading condition
For each c omponent in FEM, a mathematical material needs to be assigned to simulate the behavior of the
component. The chassis frame is ade of alloy steel 1020 and other components of the vehicle are
constructe d with different materials. The material behavior and properties of each material is different
from others. LS-DYNA has over 100 material models to c hoose from but due to simplicity of the vehicle
model only one of these are selected for the analysis. T he presumptions taken into consideration for the
analysis are;
*MAT_PLASTIC_KINEMATIC
This model is suited to model isotropic and kinematic hardening plasticity with the option of including rate
effects. It is a very c ost efficient material a nd can be used with beam, shell and solid.
Most of the multi body systems involve contact between differe nt components. In this case contacts are
25
defined between the chassis and engine, chassis and suspension, chassis and seating (including driver
weight) and chassis and bumper members. In actual case all these components are either welded to the
frame or fixed through re liable joints to prevent the motion of the components with respect to the chassis.
*CONTACT_TIED_SURFACE_TO_SURFACE
LS-DYNA provides an automatic contact formulation between each individual component of the crash
model. As currently implemented, one surface of the interface is identified as the master surface and the
other as a slave. In tied contact types, the slave nodes are constrained to move with the master surface.
This contact type should generally only be used w ith solid e lements since rotational degrees-of-freedom of
the slave node are not constrained.
REFERENCES
26
4. MARK, WAN ., Different Types of Chassis. Autozine. 2000. Autozine T echnical School. 21 Mar. 2006
27
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtr a, India
Paper ID-ICAME2013 S 5/O6
THE NUMERICAL ANALYSIS AND STRCTURAL OPTIMIZATION OFHEAVY
TRUCK VEHICLE CHASSIS FOR BETTER
TORSIONAL STABILITY
AB STRACT
A chassis structure is an important part of an automobile. The chassis serves as a back bone. T he
chassis structure subjected to deflections, torsion loads and payloads during its operation. So it should be
rigid enough to w ithstand the torsion loads and other payloads during its operations. Therefore the strength
and torsion stiffness are the two important design parameters. In the prese nt study, work focused towards
the optimization of chassis frame structures of truck vehicles for localized system with respect to torsion
handling characteristics. The nonlinear analysis is done to the model using the finite element techniques.
The 3D parametric model the chassis structure by using UN IGRAP HICS software, a nd non-linear analysis
done on the modeled chassis structure in LS-DYNA environment. The res ults from the analysis are
correlated w ith the ca lculated values for an articulated model. T hus the results a nd the analysis approach
are proved to be stable, reliable and repeatable and useful for linear and nonlinear analysis.
1. INTRODUCTION
Automobile chassis usually refers to the lower body of the vehicles including the tires, engine, frame,
drivelines and suspension. Out of these, the frame provides necessary support to the vehicle components
placed on it. Also the frames should be strong enough to withstand shock, twist, vibrations, bending loads
and other stresses. T he chassis frame consists of side members attac hed with a series of cross members.
Along with strength a n important consideration in the chassis design is to increase the stiffness (bending
and torsion) characteristics. Adequate torsional stiffness is required to have good handling characteristics.
Normally the chassis are designed on the basis of strength and stiffness. In the conventional design
procedure the design is bas ed on the strength and emphasis is then given to increase the stiffness of the
chassis, w ith very little c onsideration to the we ight of the chassis. One such des ign procedure involves the
adding of structural cross member to the e xisting chassis to increase its torsional a nd bending stiffness. As
a result weigh to the chassis increases. This increase in weight reduces the fuel efficiency and increase the
cost due to extra materials. The design of chassis with adequate stiffness, strength and lower weight
provides the motivation for this project.[1]
28
During service, a ny vehicle is subjected to loads that cause stresses, vibrations a nd noise in the different
component of its structure. This requires appropriate strength, stiffness and fatigue properties of the
component to a ble to stand these loads. On top of that, quality of the structure a s a system, which includes
efficient e nergy c onsumption, safety, and provision of comfort to user are highly desired.
All the largely demand refined and complex design and ma nufac turing proce dures involved during the
production stage. This in turn, requires good understanding of internal system of vehicle and the
characteristics of differe nt body structure in reaction to static a nd dynam ic loads.[2]
Vehicle dynamics, a disc ipline of broader significance, is an area where the basics of analyses on vehicle
structures are dealt with. Force or loads acting on structures can be categorized as impact loads, self-loads
and gravity loads. Of all thes e, F orces and moments generated by tires at the ground are significant in
controlling motion of vehicle. The res ponse of vehicle structure to these loads is dealt with in vehicle
dynamics. The responses of vehicle structure are defined in terms of deflections, stress, and strains, natural
frequencies so on. Evaluation of the above is what puts the basis on which robustness of structure or
design is as certain in terms of its mec hanical behavior. S imulation of structure largely conce ntrates on
determination of the above.[3]
Different research have been carried out regarding the performance, the res ponse of components to static
and dynamic loads, crashworthiness, safety and other by different institutions and a utomotive companies.
Particularly, w ith the grow ing simulation capability using computers, researches are facilitated that are
aimed at achieving better quality products. This prompts implementation of existing knowledge and
facilities towards addressing the problem in the area of truck chassis structures.
Analysis of chass is structure of heavy duty truck and optimization of m odel for reduction of we ight is an
area on w hich different researches have been carried out. Different people at institutional and individua l
level involved in the area produced findings which a re relevant in the automotive industry. In nearly a ll the
literature reviewed it is observed that most of the researches constitute development of virtual or prototype
models and all the analyses are performed on these models. Verification of the results is accomplished by
comparison made w ith experimental or analytical results. Listed below are some of the literatures surveyed
that a re deemed to be significant to this study that is conducted on analysis of chassis structure of the truck
vehicles.[4]
Akash Lodhi, Kushal Gawande, Udbhav Singh Chetan, J.Choudhari[4] developed the model for chassis
structure of TATA-407 vehicle using the tool P RO-E after meshing process same model imported into
ANSYS for conducting the static linear analysis. FEA consists of a computer model of a material or design
that is stressed and analyzed for specific results. It is used in new product design, and existing product
refinement. FEA has become a solution to be task predicting failures due to unknown stresses by showing
problem areas in the material and a llowing designers to see all of the theoretical stress within. This method
of product design and testing is far superior to the manufacturing costs.
This paper encompasses all the pressing issues,T he objective of the study is to produce the res ults which
may help to rectify the problems associated with chassis structures of commercial truck vehicle and which
also may be of significance during design of chassis structure of the vehicle after carrying out static and
dynamic analysis, c ombining existing theoretical knowledge and advance d analytica l methods. Preferably
finite e lement model of chass is structure of commercial truck vehicle w hich includes two side rails, cross
members and stiffeners and carry out linear and nonlinear analysis of structure. Based on the analysis, the
29
identified points and sections are stressed due to applied loads by means of which the overall intensity of
loading in structure is assessed Arrive at conclusions and propose recommendations.
2. METHODOLOGY
2.1 Materials
The materials used in the cage must meet certain requirements of geometry as set by SAE, and other
limitations. The main criteria we took into consideration when choosing the material for the roll cage are
safety,cost and durability. A method of adaptive designing was use d wherever possible and considerations
were made for the ergonomics of the dr iver. These members were included in the preliminary des ign a nd
the minimum possible section was taken Material: ASTM LOW ALLOY STEEL,YEILD STRENGTH
=552MPA,TENSILE STRENGTH=620MPA..
THE model is imported into the HyperMesh environment which is a part of the software package.
HyperMesh was used as the finite element meshing utility in preparation for the optimization study. It is
made sure that all the surfaces are imported into HyperMesh properly w ithout any geometry problems..
30
HyperMesh can automatically generate a mid-surface from a symmetrical cross se ction. The surface
editing tools would allow morphing the generated mid-surface to be convenient for the quadratic meshing.
The design space volume was filled with quadrilateral elements using the auto-mesh features of
HyperMesh. The mesh size is selected depending upon the requirement.The QI optimization criterion was
selecte d to optimize the mesh quality as per the preset condition. to meet a mesh quality criterion. T he
quality of the mesh will affect the To ensure model accuracy and efficiency, the mesh of the model needs
time step calculations of the simulations and thus the c omputation time. The time step is directly related to
the characteristic length of the elements so the minimum element size is of particular importance. Severely
distorted elements will affect the accuracy of the results due to an increase in stiffness of the element due
to the distortion. The percentage triangular elements should be less than 5% of the number of elements in
the component because the triangular elements impart an artificia l stiffness into parts modeled with them.
31
Figure 3:Meshed Model – Elements Handle On
LS-DYNA is a genera l purpose explicit and implicit finite element program used to analyze the nonlinear
dynamic res ponse of three dimensional structures [10]. Its fully automated contact analysis capability a nd
error checking features have enabled users w orldwide to solve successfully many complex crash and
forming problems. LS-DYNA is one of the premier software’s to study automotive crash and has many
defa ult input parameters tailored for crash simulations. F or cras h simulations, the explicit time integration
is used due to advantage over implicit integration method. In the explicit integration method, the solution
is advanced without c omputing the stiffness matrix thus dramatically reducing the time of the simulation.
Due to these savings, complex geometries and large deformations can be simulated. LS-DYNA supports a
very extensive library of material models. Over one hundred metallic and non metallic material models
able to simulate elastic, elastoplastic, elasto-viscoplastic, B latzko rubber, foams, glass and composite
materia ls. LS-DYNA supports a fully automated c ontact analysis that is simple to use, robust a nd has been
validated. It uses the constraint and penalty method to simulate contact conditions. T hese methods have
been shown to work particularly well in full vehicle crashworthiness studies , systems/component analysis
and occupant safety studies. safety studies. LS-DYNA supports over twe nty-five c ontact formulations to
treat contacts between deformable objects and rigid bodies.
As it can be seen, numerous types of simulations or analyses can be carried out regarding behavior of
chassis structure of truck vehicle. In this study, as stated, linear and nonlinear analysis of optimized chassis
structure of commercial truck vehicle are carried out. The nonlinea r analysis includes impact loads (c rash
analysis) of structure. Nonlinear behavior which component could experie nce is dealt with and, linear and
isotropic material models are used for linear analysis. The a nalys is is carried out for self-we ight of vehicle
and gravity loads and main loads due installed components of vehicle i.e., chassis side frame rails and
cross members, the effect of engine loads and cabin loads and dynamic loads . Effect of tires, joints
(welding and riveting) are not dealt w ith.
32
REFERENCES
33
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O7
Not Received
34
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O8
LOAD-DEFLECTION ANALYSIS OF FLAT AND CORRUGATED
STAINLESS STEEL DIAPHRAGMS.
Swapnil Gawade Durgeshkumar Chavan Prashant R anade Nitin Panase
Rajarambapu Institute Rajarambapu Institute of Forbes Marshall P vt. Forbes Marshall Pvt.
of Technology, Technology, Ltd, P impri, P une. Ltd, P impri, Pune.
Rajaramnagar, Dist – Rajaramnagar, Dist – Dist – P une. Dist – P une.
Sangli. Ma harashtra, Sangli. Maharashtra, Maharashtra, India Maharashtra, India
India 415414. India 415414. 411018. 411018.
AB STRACT:
In this study analytical m odel for flat and corrugated stainless steel (SS-304, ASTM A-
240) diaphragm has bee n proposed. T he load-deflection analyses of flat and corrugated stainless steel
diaphragms are performed to compare the sensitivity of the flat a nd corrugated diaphragm.
The application of corrugated diaphragms offers the possibility to control the se nsitivity of thin
diaphragms by geometrical parameters. Depth of corrugations, thickness of diaphragms, and number of
corrugations plays an important role to increase the mechanical sensitivity of the corrugated diaphragm.
Verification of results for load-deflection obtained by analytica l formulae compared with finite element
analysis a nd experimental results.
1. INTRODUCTION
Flat diaphragms show a nonlinear relation between the deflection and the applied pressure. F or relatively
small deflections, this relation is a pproximately linear. The nonlinearity for large deflections is cause d by
stress due to stretching of the diaphragm. It has been experimentally shown that corrugated diaphragms
have a larger linear range than flat diaphragms, because of the achieved reduction of the radial stress in the
diaphragm. The larger linear range compared with flat diaphragms; make the corrugated diaphragms
attractive for specific application with improved sensitivity. The design of corrugated diaphragms may
offer the possibility to control the mechanical sensitivity of the diaphragm by means of the geometric
parameters of the diaphragms, such as depth of corrugations, thickness of diaphragm and number of
corrugations.
The diaphragms used in this experime nt are of two types. One is flat (planer) diaphragm and other is
corrugated one. The material used for both the diaphragms is stainless steel (SS 304 ASTM-240). F lat
circular diaphragm the size is 190 mm in diameter and 0.25 mm in thickness. For the corrugated
diaphragms depth, pitch and number of corrugations are 2mm, 18 mm and 2 respectively. The solidity
ratio used for both the diaphragm is 0.50.
35
3. THEORY
The pressure - deflection relationship for a pressure loaded diaphragm is linear for only small deflections
as already indicated. When diaphragm rigidly c lamped at the edge, is deflected even 10 % of its thickness,
tensile stresses begin to appea r. As the load continues to increase, the deflection increases at a slower ra te
and load - deflection relationship becomes nonlinear.
Where P is applied pressure, E is Modulus of e las ticity of material h is thickness of diaphragm, a is radius
of diaphragm, Y is center deflection, Ap is Stiffness coefficient for the linear term which depends upon
solidity ratio (b/a) and Bp is Stiffness coefficient for nonlinear term which depends upon solidity ratio
(b/a).
The characteristic equation for the corrugated diaphragm with rigid center is different from flat
diaphragms; the Crosssection of a circular corrugated diaphragm is as shown in fig.1.
36
In above equation the values of constants Ap & Bp which are bending a nd tension c oefficie nt respectively
depends upon the profile factor (q). T he values of constants Kp & Lp which are bending and tension
stiffness coefficients respectively depends on the profile fa ctor (q) & solidity ratio (b/a). Va lues of these
constants are taken from graphs. P is applied pressure, E is Modulus of elasticity of material h is thickness
of diaphragm, a is radius of diaphragm, Y is center deflection.
4. SIMULATION:
The load-deflection analyses are performed to obtain load-deflection relationship of both flat and
convoluted diaphragms. FE analysis is necessary in order to model and simulate the flat and corrugated
diaphragm in order to validate the results obtained from the theoretica l load deflection analysis. T he
commerc ial finite eleme nt simulation software ANSYS is used for the simulation.
5. EXPERIMENT
The experimental setup for measuring load deflection of a diaphragm is as shown in Figure 2. The
diaphragm is mounted in between two pressure chambers and clamped w ith bolts. These diaphragms are
tested under various pressures and then the corresponding deflection is measured using mec hanical dial
gauge. The dial gauge has least count of 0.01 mm. The applied pressure is monitored by a pressure gauge
as shown in figure 2.
37
Figure.2. Layout of Test se t up for pressure deflection analysis diaphragms.
6. RESULTS
Above graph shows that good agreement of theoretical a nd F. E. analysis results of loaddeflection for flat
diaphragm. Base d on res ults, the convoluted diaphragms a re more se nsitive than flat diaphragms of same
size. Sensitivity can be controlled by changing geometric parameters such as depth of corrugations &
thickness of diaphragms.
38
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O9
AB STRACT
The use of high strength steels in automotive production contributes significantly to lightweight
construction. T his increases the efficiency of the vehicle. However, large spring backs occ ur when forming
high strength steel. The current meas ures to control the dime nsional deviations have some disadvantages.
A new research approach checks the deliberate modification of the pre drawing stage using forming
simulation in order to thereby integrate spring back reducing design notes. Below, the results of variational
calculations w ith respect to radii, blank holder forces and distances between the punch and die are
represented for the end of the pre draw ing stage process.
1. INTRODUCTION
The automotive industry is making enormous efforts to promote lightweight construction. This type of
construction makes it possible to reduce a vehicle's fuel consumption and CO2 emissions. As the largest
mass proportion is present in the chas sis, on average, there is special potential for optimization in this area.
One possibility is to replace traditional deep draw ing steels with high strength materials. Therefore, with
constant crash requirements, the steel thicknesses can be reduced. Consequently, the vehicle can achieve a
lower chassis a nd total weight.
The problem with this development is that the spring back of the formed metal parts increases as the metal
strength decreases and the sheet thickness increases [1]. However, there are several meas ures in industrial
practice designed to control the dime nsion a nd shape deviations. In order to increase the expansion of the
components and to correspondingly reduce the spring back, geometric and process engineering
applications are implemented. In doing so, the manufacturability of the components is often degraded.
Another measure is the spring back compensation [2]. T his measure also has limits, as the over extension
of formed parts is only possible to a certain degree without creating an undercut [3]. A ll spring back
reducing measures are primarily limited to the final shaping stage.
39
A new research appr oach tests whether the deliberate modification of the pre drawing stage offers
opportunities to improve the dimensional and shape stability. As the forming simulation and the spring
back prediction have been established in the meta l forming field [4], a numerical simulation using a n FE M
analysis will follow.
2. RESEARCH APPROACH
An industrial structural component is used to check the new researc h approach, which includes a
multistage forming proce ss (F igure 1 above). T his a ddres ses the backrest side beam of a car seat structure.
As the manufacture of the industrial component from high strength material cannot achieve dimensional
stability in accordance with current procedures, this component is suitable for exam ination. In order to
simplify the analysis, a demonstrator has been designed on the basis of the complex structure. T he
production method was adopted from the backrest side beam (Figure 1, center). T he circuit board is
preferred in OP 20. H ere, the inner contour and a part of the outer edge are re formed. After trimming in
OP 30, the outer edge is turned off in the second draw ing stage (OP 40). A new state of stress is created in
the component after the forming tools are opened [5]. T he deformation in the form of the spring back is
show n in OP 50.
There are several ways to modify the pre-draw ing stage, thereby influencing the spring back. As a
geometric measure, the radii of the pre-drawing stage should be varied. A n advantage is that there are
modification options that do not require changing the design specifications of the final geometry. As a
process engineering measure, the blank holder force of the first draw ing stage is varie d. A n additional
modification option exists in the distance between the punch and die and the process end of the first
draw ing stage (Figure 1, bottom left).
40
After all variants have been calculated with the forming simulation (PAM STAMP 2G), a comparison of
the spring back geometry will follow. F or this purpose, a center section will be defined by the
demonstrator and the distance betwee n the side walls is measured (Figure 1, bottom right). In addition, the
tensions in the components must be a nalyzed as they have a direct influence on the spring back
3. RESULTS
A sensitivity a nalysis is carried out to check the influence of the radii variations in the first drawing stage
on the spring back after the second draw ing stage. The demonstrator should display an overall radius of 8
mm after production. Accordingly, this radius is already marked in the pre-draw ing stage according to the
state of the technology. In the following analysis, the ra dii of the pre-draw ing stage (r1 , r2 , r3, r4 ) w ith 6
mm (smaller) or with 10 mm (larger) are preferred. In order to obtain a comparison of the dimensional
stability according to the total formation, the avera ge distance of the frame is measured according to the
spring bac k. The res ults are shown in (F igure 2).
.
The reference varia nts (r1= r2=r 3=r4=8mm) display a frame distance of 177.5 mm. It can be seen that all
modification options for the radii demonstrate smaller frame distances and therefore has lower springbac k.
The variation of the die radius (r4 ) in particular has very low s pring back. The potential of a spring back
reducing modification of the pre drawing stage thereby becomes apparent. In order to analyze this
situation more precisely, the die radius (r4) was varied between 4 mm -12 mm in 1 m m steps in the Pre-
draw ing stage. T he results show that smaller as we ll as larger radii can function as spring back reducing
radii. T his behavior is also confirmed in further studies with high strength steels [1]. In addition, the
potential can be estimated, as all spring back variations show higher dimensional accuracy than the
reference.
Furthermore, the blank holder force was varied in the first drawing stage in order to check its influence on
the spring back after the second draw ing stage (Figure 3).
41
A blank holder force of 200 kN was defined as a reference. T he observed variation range lies between
100kN and 300kN. The increment size is 20kN. The results show that a lower blank holder force in the
first drawing stage tends to have a spring back reducing effect after the total forming process. P reviously,
an increase in the blank holder force has been preferred in the second drawing stage, as this resulted in
larger extension and therefore achieved higher dimensional stability. It is notew orthy that the behavior is
contrary to that in the pre-draw ing sta ge.
(F igure 4) shows the results evaluation of the variation of different distances between punch and die at the
end of the first drawing stage. It can be seen that, with the presence of a small distance between the tool
elements and the process e nd of the first drawing stage, lower spring back is also achieved after the total
forming process. The influence of the stop criterion is greater than expected, as large deviations regarding
the spring back results had alrea dy been determined with small changes in distance. Accordingly, the stop
criterion of the forming simulation has also been viewed critically. A pinch tes t can be used as a stop
criterion. In doing so, calculation is aborted after a contact point of the circuit board simultaneously
contacts the tool active surface of the punch and the die. However, as the pinch test is triggered at different
points in time, the distances between the tool elements are correspondingly different. Accordingly, using a
pinch test is not recommended for a better comparison of the results. Instead, a fixed distance should be
given as a stop criterion in the forming simulation.
42
After the spring back results have been compared and evaluated, the stresses of the component are
analyzed in more detail. If the main stresses of the upper and lower fibers are c onsidered, it can be seen
that opposite voltage states are prevailing in the radii area in particular. Therefore, there are tensile stresses
on the one side and compressive stresses on the other side (Figure 5 left). In order to make the differences
in the principal stresses visible, a new function is defined in the forming s imulation PAM-STAMP. The
results in post-processing will be those areas w hich demonstrate a large difference in principal stresses. If
the differences in the principal stresses are determined after unloading, it will be seen that these principal
stress differences disappear almost entirely. Therefore, the intensity of these areas represents an indicator
for the impending dimensional deviation before an actual spring back calculation has been performed.
The reference variants (8_8_8_8) demonstrate that a large spring back occurs. The frame distance is 177.5
mm. The principal stress differences, according to the second drawing stage, show strong red areas in the
radii. T herefore, high principal stress difference s occur here as well. For the forming varia nt 8_8_8_12, the
die radius r 4 w ith 12 mm in the pre-drawing stage is preferred larger. As can be seen in the diagram, the
frame distance as a measurement for the spring back is sma ller with 176 mm. The intensity of the a reas of
the principal stress differences is also low, resulting in a connection betwee n principal stress differences
and spring back.
In summary, it can be sa id that knowledge of the resilience of high-strength structural sheet metal
components occupies an important place in automotive production. C urrent measures to ensure the
accuracy of the dimensions and shape are usually limited to the last draw ing stage. However, the
deliberate modification of the pre-draw ing stage has immense potential to achieve further spring back
reducing effects.
The geometric m odification of the radii in the first drawing stage dem onstrated that the die radius has a
great influence. The radii should be selected to be smaller or larger than the reference radius. In a ddition,
optimized dimensional stability can be achieved if the blank holder force is reduce d in the first draw ing
stage. In addition, at the process end of the first draw ing stage, the tools should be closed if possible. F or
43
enhanced comparability, a fixed distance is used as a stop criterion. The evaluation of the principal stress
difference enables the initial assessment of the upcoming spring back before it is calculated.
As the results are obtained numerically, the next step is the production of the forming tool for the
demonstrator. This is intended to validate the res ults from the forming s imulation. The experience based
method planning will be helpfully supplemented with spring back reducing des ign notes. This c ontributes
to the progress of lightweight construction and to control of the spring back
ACKNOWLEDGMENTS
The research project OP TISTUF is funded by the BMBF as part of the FhprofUnt line of funding. T he
authors w ould like to thank the BMBF for funding the researc h project.
BIBLIOGRAPHY
3. ROLL K., L EMKE T., WIE GAND K., Simulationsgestützte Kompensation der Rückfederung, LS-
DYNA Anwen derforum, Bamberg, pp. A-I-1 –A-I-13 (2004)
4. KAULICH C.,WENZLAFF M., IndiForm Eine intuitive Be dienoberfläc he für die industrielle
Umformsimulation, 9. LS-DYNA Forum, Bamberg pp. C-III-1 1–C-III-18 (2010)
44
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID-ICAME2013 S 5/O10
Modeling and Simulation of Suspensio n System Using Bond Graph Approach
Kumbhar R. P Jaybhaye M. D
MTech Mechatronics, COEP P rod. De pt. COEP, Pune
ravishpk@gmail.c om mdj.prod@coep.ac.in
ABSTRACT
The Bond Graph (BG) is a graphical language of modeling, in w hich component energy ports are
connected by bonds that s pecify the transfer of energy between system components. In the present paper
Energy Based B ond Graph (B G) modeling tec hnique is applied for Passive and Active S uspension
systems. The paper discusses the Quarter Vehicle response resulted from road disturbance like bump input
in BG modeling environment. Sprung mass was well isolated from road disturbance and its acceleration
was reduced thereby increasing the ride comfort upto some extent, but the vehicle handling capability was
affecte d. P-I-D controller was used for an active suspension system models. Results of BG model were
discussed. 20S im is used for modeling BG System model.
1. INTRODUCTION
System Level approach is playing a vital role is upgrading the existing systems to be more efficient. Hence
multidomain modeling features are needed to be considere d while developing the system. As a step
towards it, bond graph modeling method is a dopted in most of literature [A. Alabakhshizadeh et. al, 2011]
to model the mechatronics systems in different modeling environments. Fig 1 shows a Quarter-vehicle
model of Passive Suspens ion system and beside it Systems Active element implementation [Nemat Changizi et.
al, 2011 a nd M. D. Donahue e t. al, 2007]
Fig. 1 A Quarter-vehicle model of Passive S uspens ion system and its Active element implementation
2. SUSPENSION SYSTEMS
The sprung mass Ms represent the vehicle chassis, while the unsprung mas s Mu represent the wheel
assembly along with spring and damper mass lumped together. The spring, Ks, and damper, Bs, represent a
45
passive spring and shock absorber that are placed between the vehicle body a nd the wheel assembly, while
the spring Kt serves to model the compressibility of the pneumatic tire.
3. BOND GRAPHS
Bond graphs are a graphical tool used to describe and model subsystem interactions involving power
exchange. A bond graph can be generated from the physical structure of the system. This formulation can
be used in hydraulics, mechanical, and thermodynamic and electrical systems along with electronic
circuits. The bond graph is proven effective for the modeling and simulation of multidomain systems
including automotive systems [P eter J. Gawthrop et al., 2007].
Bond graph being a multidomain modeling environment, one should understand the feasibility of system
modeling in said modeling environment using sa id modeling strate gy before indulging high fidelity
dynamics in present system. There exists a need to model the system in more than one modeling
environment with more than one modeling method. Hence, this work is been initiated for active
suspension system with simple structure as discussed in below section. Also, since the bond graph
representation is unambiguous, a computer can be utilized to carry out these transformations. In a ddition,
the bond graph methodology is equation based rather than assignment based. T his reduces the need for
multiple models of a single physical system [A. A labakhshizadeh et al., 2011].
Bond graphs are a graphical tool used to describe and model subsystem interactions involving power
exchange. It can be generated from the physical structure of the system. This formulation can be used in
hydraulics, mechatronics , and thermodynamic and electrical systems. T he bond graph is pr oven effective
for the modeling and simulation of multidomain systems including automotive systems.
4.1 Bond Graph Modeling Technique
Key vectors of Bond graphs are shown in Fig.4. The storage a nd dissipater are bi-directional e lements and
the energy flow occ urs through junctions to which they are connected with. The detector is like a sensor,
46
which extracts the flow a nd effort variable values to output. T he Source element is the one, through which
the flow or e ffort source is let into the system.
There are four elementary one port components: O ne source/se nsor (SS), one energy dissipater (R) and
two energy storage ports, (C a nd I). T he SS component is used to interface bond graph subcomponents and
define boundary conditions. Moreover, SS components are used as source elements to supply power to a
system.
A source component holds one of the power variables (effort e (t) or flow f (t)) constant or is some pre–
defined function of time. The value of the co–variable is determined by the system the source supplies.
The half arrow of a bond points in the direction of positive power flow, and hence when f (t).e (t) is
positive, e nergy flows from the source into the system. The C and I components are known as the flow and
effort stores respectively. I n the mechanical domain the C c omponent is as sociate d with potential e nergies
and I component with kinetic energies.
Each component has an associated energy variable: generalized displaceme nt (q), for the C component,
and generalized momentum (p), for I component. The two junction elements (0 and 1) are used to
interconnect bonds. T he 0 junction, also known as the comm on effort or parallel junction and T he 1
junction, also known as the common flow or series junction compliments, the 0 junction. Causality is a
key conce pt w ithin the bond graph methodology. Causality determines which variable, effort or flow, is
the input and hence w hich is the output of a bond [Gilberto Gonzalez et. al, 2008]. The end of the bond
with the causal stroke denotes the direction in which the effort variable is directed. Alternative software
programs include Bondlab, CAMBAS, Camp-G/ALSL, Dymola, a Java Applet program, Hyber Sim,
MS1, 20-sim. For this paper 20-Sim has been use d.
The first step of bond graph modeling is analysing the physical relationship among the sub-domains. F or
each sub-domain, determine the 0-junction, 1-junction, corres ponding C-element, R-element and suitable
47
connection plugs. A full arrow head indicates an active bond whose influence on the system from its
environment occurs at essentially zero power flow. Bond graph will be arranged in form of Newton’s
linear dynamic equation. The bond graph model of Active suspension system is s hown below in Fig. 4 and
equation derived is identical to Newton’s equation and hence validates bond graph model. The controller
used is P -I-D Controller which is manually tuned. For better good acceleration reduction in order to
achieve ride comfort a nd vehicle stability one may go to robust c ontrol or adaptive robust control sc hemes.
Results plotted in bond graph modeling environment are further discusse d.
Fig. 4: Bond graph model for Quarter Vehicle Active Suspension system
5. RESULTS
Road disturbance is applied to system which follows below equation (3), where, ra =0.08 meter. This
input results in below response of passive suspension system. System parameters are taken from [Dwi
Nusa ntoro et. a l, 2011].
Zr = ra (1- cos (8 п t))/2 for 1.25 < t < 1.50 and Zr =0, for others (3)
48
Fig. 5: Bump Input as disturbance sprung mass displacement res ponse in BG Modeling e nvironment for
both active and passive systems
10 ddZs_Ac…
5 ddZs_Pa…
0
-5
-10
10.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
Fig. 6 Comparison of Active and Passive Suspension system sprung Mass acceleration
Table 3. Comparison of Passive and Active Suspension system using Bond Graph Approach
The responses for Active suspension system having parameters mentioned in Table no. 2, subjected to
bump input are shown in Fig. 5 and Fig. 6. The Sprung mass displac ement to 0.08 meter is achieved in 3.5
sec. T he maximum displacement is 0.0934 m in mathematical modeling environme nt which shows
comfort level is achieved upto some extend and which is appreciable. Also settling time is reduced by
introducing active element in active suspension system. While for unsprung mass, the maximum
displacement is 0.0985 which is more than bump input amplitude, thus vehicle handling is not appreciably
achieved and ride c omfort is improved merely.
6. CONCLUSION
Sprung mass was well isolated from road disturbance a nd its acceleration was reduced thereby increasing
the ride comfort upto some extent, but the vehicle handling capability was affected. P-I-D controller was
used for an active suspension system models. Results of BG model were discussed. 20Sim is used for
modeling BG S ystem model. Bond graph modeling technique is efficiently adopted to model the active
suspension system with bump input. The methods presented here ca n be applied generally to dynamic
49
engineering systems, but are es pecially useful in a multi-energy domain, where an entire system can be
modelled and a nalyzed in a single simulation environment.
ACKNOWLEDGMENTS
Authors would like to acknowledge Dr. B.B Ahuja, College of Engineering, P une. Sandeep Na me and
Staff of Data Centre for setting up the required software. Authors are also thankful to Manish Jaiswa l for
technical guidance.
NOMENCLATURE
REFERENCES
1. ALABAKHSHIZADEH , Y. I SKANDARANI, G. HOVLAND , O. M. MIDT GARD , Analysis, Modeling and
Simulation of Mechatronic Systems using the Bond Graph Method, Modeling, Identification and
Control, Vol. 32, No. 1, pp. 35-45 (2011)
2. P.E. WELLST EAD , Appleyard,Active Suspensions: Some Background, IEE Proc.-Control Theory
Appl., Vol. 142, No. 2, (1995)
3. DWI N USANTORO , GI GIH P RIYANDOKO, P ID State Feedback Controller of a Quarter Car active
Suspension System, Journal of Basic and Applied Scientific Research (2011)
6. NEMAT C HANGIZI , MODJTABA R OUHANI, Comparing P ID and F uzzy Logic Control a Quarter Car
Suspension System, The Journal of Mathematics and Computer S cience Vol .2 No.3, P g.559-564
(2011)
8. ZHEN LIU , CHENG LUO, DEWEN H U, Active S uspension Control Design Using a C ombination of
LQR and Backstepping, Proceedings of the 25th Chinese Contro l Conference, Harbin,
Heilongjiang, August (2006)
50
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S 5/P1
M. K. Botre Dr.V.M.Phalle
M.Tech CAD/CAM Student Head a nd Associate P rofessor,
VJTI, Mumbai, India. Mechanical Department, VJTI, Mumbai
Mail id-botremanoj@gmail.com Mail id-vmphalle@vjti.org.in
ABSTRACT
Last two decades, growth of FEA in the field engineering is significant. Industries from
mechanical, aerospace etc. getting considerable benefit from it in terms of time, reliability, des ign
modification etc. Failure analysis and fatigue life prediction are very important in the design procedure to
assure the safety and reliability of components of aircraft. T his article is deals with study of linear and
nonlinear characteristics of a component for failure analysis and design of experiments for optimization of
design parameter. The component is se lected for study is critical single point failure item (CSPFI) from
maneuvering asse mbly whose function to control wing flapper motion of aircraft.
In maneuvering assembly, subassemblies are connected in parallel connection avoiding failure of whole
assembly on the failure of one of the subassemblies. These subassemblies are connected to common
component. Such component’s failure results in failure of all subassemblies. S uch component is selected
as CSP FI component of maneuvering as sembly.
Different Materials with linear and nonlinear characteristics are studied individually for failure analysis
and fatigue life. S imultaneously analysis is done for weight reduction. T itanium sleeve is used at
maximum s tress region for a nalysis. Design of e xperiment is carried out to optimize the results of des ign
parameters.
1. INTORDUCTION
Disastrous incidents in aircraft with result loss of life can happen due to failure of an aircraft structural
component. The investigation of defects and failures in aircraft structures is, thus, of vital importance in
preventing further incidents. In general, fa ilures occur when a component or structure is no longer able to
withstand the stresses imposed on it during operation. C ommonly, failures are associated with stress
concentrations, w hich can occur for several reasons including:
• Design errors, e.g. the presence of holes, notches, a nd tight fillet radii;
• The microstructure of the material may c ontain voids, inclusions etc;
• Corrosive attack of the material, e.g. pitting, can also generate a local stress concentration.
Percentage possibility of failure of aircraft component due to overload is 14% and 55% due to fatigue. [1]
51
Many research works has been done regarding computational fluid dynamics study of the wing design of
aircraft to improve performance of aircraft using time-accurate aerodynamic, aero-elastic and flight -
mechanics calculations to achieve objective.[2-6] Similarly for micro aeria l vehicle are also studied for
flapper mechanism performance improvement through design modification.[7-11]
The failure of the vital parts of a manoeuvring assembly can result in the aircraft manoeuvrability lost, an
accident causing serious crew injuries or death and the damage of the aircraft. Unfortunately, the results
of the investigation concerning the failures of manoeuvring assembly components of aircraft are not
widely presented in scientific papers.In maneuvering assembly of aircraft, motors navigate the w ings of
the aircraft to alter the direction of the aircraft. These motors are connected to the w ing through a
mechanism. The linkages in this mechanism are c ritical as their failure would mean a failure to c ontrol the
aircraft. [2]
In machine design, reliability is one of the most important factors, especially more important in aircraft
maneuvering. I n aircraft maneuvering a ssembly, different asse mblies are c onnected in parallel connection.
Possibility of failure of maneuvering assembly is reduced due to this parallel connection. There are some
components w hich are used to connect parallel assembly together. Such components are selected as critical
single point failur e item (CSPFI). Failure of this component result of total mechanism. In this article, such
component is selected for study failure analysis and fatigue life as CSPFI component.
52
2.2 External load
Due to aerodynamic forces, the lever is predominantly subjected to ultimate load on the surface as s hown
in Fig.2, The prescribed ultimate load (F = 400 N) was taken into the consideration for the charac teristic
load case structural steel.
The uniaxial stress fields obtained according to the Von Mises hypothesis, for the charac teristic
load case Structural steel, are show n in Figs. 3-4
Based on the results of finite element analysis (FEA) for the structure of the lever, it was concluded
that:
1. The pronounced stress conce ntration occurs in two zones: the zone of the corner region of lever
and the zone of the pin.
2. The maximum deformation is 0.49978mm for ultimate load case Structural steel material. F ig.
3
3. The maximum stress is 0.49978mm for ultimate load case Structural steel material appears at
the middle region of the lever, Figs. 4.
4. The maximum value of stress (for ultimate load case Structural steel) is 250 MPA.
5. Fatigue life of component is 10 6 cycles.
3. DESIGN CHANGES
Based on results of finite element analysis (FEA) for the structural of the lever, it is analysed for
linear and non-linear analysis. Practically all analyses are nonlinear in nature. Performing linear analysis
simulation is less time c onsuming than non-linear analys is. We perform the linear analysis where error is
in between acceptable limit. Acceptable Limit is depends on type the application. Nonlinear analysis is
done by reca lculating stiffness matrix [k] by using series of linear a nalysis as sub-steps. [12-14]
There a re 3 types of nonlinearity incurred in Non-Linear analysis.
1. Material nonlinearity
2. Geometric nonlinearity
3. Contact nonlinearity.
53
500
450
400
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Fig 5.Results comparing Linear & Nonlinear analysis characteristics
Based on the results of non-linear FEA of the lever (Fig.5), for a voiding failure, lever material is
varie d. Here Structural steel, Ma gnesium a lloy and Aluminium a lloy is c onsidered for variation. The lever
is analysed for a ll 3 materials w ith and w ithout Titanium alloy sleeve. Simultaneously it is a lso a nalysed
for with and without material removal from the region, where stress are less for weight reduction purpose.
Effect of parameter calculated as follow s using ANNOVA. Minimum value of maximum stress is desired.
Table No. 2 ANNOVA Table
54
Sum of
Factors DOF Variance (V) F(Vf/Ve) Percentage(%)
Square (SS)
A 1 59250.59 59250.59 17.386 77.46
B 1 5739.49 5739.49 1.684 7.53
C 2 21438.85 10719.425 3.1453 14.06
Total 7 76195.07 100
Error 3 -10223.9 -3407.97 -4.47
The lever of maneuvering assembly of a ircraft is analyzed with finite element method using FEA software.
Lever material is optimized for material variation, with and w ithout titanium sleeve and, with and without
material removal. The best result can be getting with material Magnesium alloy and with titanium sleeve.
Titanium sleeve has maximum effect on the maximum stress (Von Mises) developed in lever.
Simultaneously material removal does n’t increase the maximum stress effectively. The lever is also
analyzed for fatigue analysis as the component is subjected to cyclic loading life w ith magnesium material
gives maximum fatigue life.
REFERENCES
1. FINDLAY S. J. AND HARRI SON N. D., Why a ircraft fail, QinetiQ Ltd, Hampshire, UK
2. DRA GAN TRI FKOVIC , S LO BODAN ST UPAR, S RDJAN BOSNJAK, MILO RAD MILO VANCEVI C, BRANIMIR
KRST IC , Z ORAN R AJIC, MOMCILO DUNJI C , Failure analysis of the combat jet aircraft rudder shaft,
Engineering Failure Analysis, 18, (2011)
55
3. IN -JOOJEONG, L IVIU LI BRESCU , S UNGSOO N A, MYUNG-H YUN KIM, P IER MARZO CCA ,
“R obustaeroelastic control of flapped w ing systems using a sliding mode observer”, Aerospace
Science and Technology, 10, (2006)
4. LIVIU L IBRE SCU , SUNGSOO NA, P IERGIO VANNI MARZOCCA , CHANHOON CHUNG, MOON K. KWAK,
Active aero elastic control of 2-D w ing-flap systems operating in a n incompressible flow-field and
impacted by a blast pulse , Journal of Sound a nd V ibration, 283, (2005)
5. MAZAHERI AND E BRAHIMI, Experimental investigation on aerodynamic performa nce of a flapping
wing vehicle in forward flight, Elsevier, Journal of Fluids and Structures, 27, (2011)
6. SCHÜTT E, A., E INARSSON, G., SCHÖNING, B.; MADRANE A., MÖNNICH, W., K RÜ GE R, W.,
Numerical simulation of maneuvering aircraft by aerodynamic and flight mechanic coupling. RTO
AVT-Symposium Paris, 22.-25. April 2002
7. M. J. P AT IL AND D. H. HODGES, F light dynamics of highly flexible flying wings, in International
Forum on Aeroelasticity and S tructural Dynamics IFASD-2005, (Munich, Germany), June 28 –
July 1 2005.
8. QUOC VIET NGUYEN, QUANG T RI T RUON G, HOONCHEOL P ARK, NAM S EO GOO, DOYOUNG B YUN,
Measurement of F orce Produced by an Insect-Mimicking Flapping-Wing System, Jou rnal of
Bionic Engineering 7 Suppl. (2010) S 94–S102
9. MICHAEL A.A. FENELON, TOMONARI FURUKAWA, Design of an active flapping w ing mechanism and
a micro aerial vehicle using a rotary actuator, Mechanism and Machine Theory, 45, (2010)
10. HUIHUA, A NAND GOPA KUMAR, GREGG A BAT E, R OBERTO ALBE RT ANIC, An experimental
investigation on the aerodynamic performances of flexible mem brane wings in flapping flight,
Aerospace Science and Technology, 14, (2010)
11. SHIGLEY , Mechanical Engineering, McGraw Hill Publication
12. KHOT N S AND KAMAT M P. Minimum weight design of structures w ith geometric nonlinear
behavior., AIAA Paper 83-0937,AIAA /ASME/ASCE/AHS 24th Structures, Stru ctural Dynamics
and Material Conference, 1983, 383-391
13. WENYAN TANG, YUANXIANGU., Research and Application of Genetic Algorithm in Structural
Optimization., Advances in M echanics, Vol.32, NO.1, pp26-40, 2002.
14. C.C. WU AND J.S. A RORA . Design sensitivity analysis and optimization of nonlinear structural
response using incremental procedure. AIAA Journal, 1987, 25(8): 1118-1125
15. R. JEYAPAUL, P. S HAHABUDEEN, K. K RI SHNAIAH, Simultaneous optimization of multi-response
problems in the Taguchi method using genetic algorithm, In ternational Journal of Advanced
Manufacturing Technology, Vol. 30, 2006, 870-878.
16. RAMA RAO.S, P ADMANABHAN . G, Application of Taguchi methods and ANO VA in optimization of
process parameters for metal removal rate in electrochemical machining of Al/5% SiC composites.,
IJERA, ISSN:2248-9622 , Vol. 2 , Issue 3, May-Jun 2012, pp. 192-197
17. ABBAS AL-RE FAIE, TAI-H SI WU , MIN G-H SIEN LI, A n Effective Approach for Solving T he Multi-
Response P roblem in Taguchi Method, JJMIE Volume 4 , Number 2, March. 2010 ISSN 1995-
6665 P ages 314 – 323.
56
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
P aper ID
ICAME2013- S 5/P2
Not Received
57
P roceedings of International Confere nce on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S 5/P3
AB STRACT
Helmet protection to vulnerable two wheeler riders presents many challenges including those of
weight, ergonomics a ppearance and convenience. Safety provided to a two wheeler riders head is mainly
dependent on the level of shock getting propagated to the brain during the accident situations and therefore
the design of the layer of shock absorbing padding assumes great importance. This padding, generally
made of expanded polystyrene (EPS) or of state of art materia ls needs to be optimized. Our paper here
presents an em pirically arrived Optimization function of the thickness of the shock absorption padding to
arrive a t a minimum weight of the helmet with its constituent assemblies.
Helmets prototypes using an external hard shell ma de of F iber Reinforce d P las tic (FRP) were built to the
different EPS thicknes ses to near usable practical c onditions. Impact absorption tests on different types of
helmets samples were conducte d. Helmets were built with distinct features and Theoretical Simulations of
impact during accident situations for helmet prototype were done using the FEM tools (RADIOSS
software) and HYPERMESH.
Dynamic model of impact absorption test was prepared and solved to obtain the values of the shock
propagated to the human brain. These values are compare d with experime ntal values , for validating the
models to arrive at an optimized weight and thickness.
Keywords: EPS Protective padding, Optimization function, He lmet prototype, Impact absorption tes ting,
RADIOSS and HYPERMESH.
1. INTRODUCTION
In today’s India a person has to travel to work places which are mostly 15-20 km away from house,
depending on the transportation available, m ost favorite option is a two wheeler. An ever rising economic
growth with the middle class has see n a huge sale of two wheelers across the nation. With the continual
growth of two wheelers riding come the possibilities of road accidents, for which lighter we ight helmets
are necessary.
The present work is to e mpirically arrived Optimization function of the thickness of the shock absorption
padding to arrive at a minimum we ight of the helmet w ith its c onstituent as semblies.
Statistic shows that head injuries are fatal in m ore than 60% road accident cases, makes a safety of a two
whee ler rider a social issue [2]. Helmet is the most preferre d protective device used by two whee ler riders.
58
2. LITERATURE SURVEY
Chia –Y uan chang has worked upon the business model of helmet manufacturing plants; he proposes the
optimization equation to reduce the weight of existing helmets. Assumptions made by him are mostly
dependent on the existing helmet standards like SNELL B-95, ASTM F 1447.Crash helmet testing and
design
specifications by P rof.J.H.M.Wisma ns discuss various hea d injury criteria based on translational
accelerations of the head’s centre of gravity and injury criterion based on stress and strains inside the
brain.
Helmets prototypes using an external hard shell made of Fiber Reinforced P lastic (FRP) [4][6] were built to
the different thicknesses and impact absorption tests on different types of test rigs were conducted.
Dynamic model of impact absorption test was prepared and solved to obtain the values of the shock
propagated to the human brain. These values are compared with experimental values, for validating the
models. Theoretica l Simulations of impact during accident situations for helmet prototype has been done
using the FEM tools (RADIOSS software) and HYPERMESH. Conclusions of the experime ntation give
rise to the new c ommercial novelty model of helmet having tremendous market potential.
Assumptions:
1) Mass of helmet (M) a nd Head acceleration (G) is depend on
a) Density of material of protective padding (qf)
b) Thickness of the protective padding (Material-EPS) (t f)
c) Density of material of FRP shell (q s)
d) Thickness of protective FRP shell (ts)
The optimization function for we ight of the helmet is given by [9]
M=126.629 t f3q f+ 25338.05ts3 qs ---------------------------------------- (1)
G=-211.136t f-3.267qf+3.5326v+226.95 -------------------------------------- (2)
Subjects to the c onditions like
0<=M<= 1kg, 0g<=G<=300g
50kg/m3<=qf<=68Kg/m 3 , 650Kg/m3<=qs<=750kg/m 3, 2.5mm<=ts<=2.8mm.
After solving this model the realtion between Head acceleration and Mass of helmet is obtained which is
as shown in figure 1[9]
59
The function indicate that the major contributing factor in we ight of helmet is the density and thickness of
outer FRP shell but according to Mills[8] to maintain the stiffness of the helmet assembly it can not be
reduced below 2.8mm hence we ight of helmet is to be reduced then thickness and density of EPS
protective padding need to be targeted also optimization function need to be experimentally varified by
actually testing the helmet models.
Impact absorption test for Trac k1 type of helmet is simulate d using RADIOSS. P roblem geometry is
imported from a CAD package in to Hypermesh. Following observations are noted.
1) Type of mesh used: Tet mesh gives the best possible res ults[1][5] , 2) Type of Element used: Tetrahedral,
3) Master and slave body: Master body is Anvil and slave body is helmet, 4) T ype of contact: Point to
point contact, 5) Method of constraining: Kinematics constraints method, 6) Time step used in explicit
analysis:1.5e-2 second Courant stability condition Time step <(length/Elastic wa ve speed) is obeyed[3] ,7)
Von misses stress maximum value is 1.764e4N/m 2 less than E value for EPS material, 8) Maximum
displacement value is 1.542 mm at the node of accelerometer, 9) Maximum Accelerometer reading 425g
Conclusion from this simulation is that the Track1 helmet w ill propagate the shock to the ce ntre of gravity
of the human brain which would be a bove the permissible limit of 275g
500
Acceleration at G
400
300
200
Tim
100 e…
0
106
141
176
211
246
281
316
351
1
36
71
Fig. 2 Problem formulated and Acceleration v/s Time curve obtained by using RADIOSS
Models used for the present study are developed by cutting EPS to the desired sizes and then layering FRP
(F iber reinforced plastic) layer on to it. After observing feedback from market w e concluded that storage
space, cost are the critica l parameters w hich make a two wheeler riders reluctant to wear the helmets hence
prototypes which accommodate less space are used in this experimentations. F irst a wooden pattern is
manufactured from w hich the Basic shape made as per IS4151 [1 0]. With the wooden pattern different
models of helmets were made as e numerated in the table 1.
60
2 Mark models By sectioning Basic shape at various locations
the Mark models are manufactured
As per the existing standard norms, The impact energy transferred to the head should be less than 100J
[7][10]
The present work mainly focuses on testing of the helmets according to the IS4151: Protective helmet for
two w heeler rider. The criterion used while testing of the helmet is Head injury criterion 2400 or
Maximum acceleration induced at the centre of gravity of head should be less than 275g [10] .Both the
criterions are based on the Wayne status tolerance curve [7]
Attempt 1.1: E xperimentation of Track1 type of Helmet with test rig in to which helmet remains
stationary and impact hammer is dropped from specific height and force sensor placed at the centre of
gravity of the head form measures the force .Interface software w ill give output of F-t curve and energy of
impact
Fig. 3 Schematic diagram of the test rig and Force Vs time curve obtained from attempt 1.1
Table 2. Different type of impact hammer used for testing of the Model M of Track1 type of helmet and
experime ntal results
61
Model Mass of Impact Falling Dwell Area under Work done in
Sr. Hammer
Trake1 Indenter force velocity time in F-t curve J=Area*dwell
No type
Type Kg KN m/s ms ( m2) time
1 M 3 spherical 4.8 5.128 8.314 19.92 165
2 M 5 conical 3.9 5.115 9.4 19.17 181.45
1) Energy of impact transformed from the EPS of density more than 65 Kg/m 3 is not under permissible
limit. Hence EPS density should be less than 65 K g/m3
Attempt 1.2: Experimentation on Trac k 2 type of helmets having variable thickness of Protective padding
(EPS) the test rig used is as per IS4151 in which helmet with head form freely falls on the anvil w ith the
velocity of 7.2 m/s and the acce leration levels at the center of gravity of headform are measured.
Fig 4. Tes t window for Impac t absorption test on Model B of Trac k1 type of helmet as per IS 4151
Table 3 Results of Attempt1.2: Track1 m odels tested as per IS4151 on impact absorption test rig
Sr Track 1 Thick ness Anvil Type Acc1 Acc2 Acc3 Tri Falling T1 T2 HIC
no Mode l Of EPS Axial ve locity ms ms
padding accn m/s
mm
1 A 25 Flat 291.7 361.2 271 537.6 7.71 11.3 15.3 8851
2 B 25 Flat 366.4 166.3 139.9 425.8 7.71 10.8 15.1 9159
3 C 28 Flat 366.4 133.4 49.4 390.8 7.71 9.4 14.9 10256
4 D 22 Hemispherical 366.5 299.5 185.5 434.4 7.71 10.7 15 1314
5 E 28 Hemispherical 366.5 294.1 109.5 415.1 7.71 11.5 15.9 2358
6 I 18 Hemispherical 366.5 334.2 226.6 477.4 7.71 13.4 14.6 4185
7 M 35 Hemispherical 366.5 335.1 229.6 479.1 7.71 11.8 16 2118
62
8 J 18 Hemispherical 357.1 223.3 264.3 372.6 7.71 11.4 15.1 1816
1) S quare models will provide the space benefit and can get fit into 130mm height space but the shock
propagated to the wearers head during the accidental condition is exceeding maximum permissible limit
2) B y observing readings obtained for m odel M which has bee n teste d in both the attempt, it is clear that
during Attempt 1.2 it has propagated shock above permissible limit hence helmet undergone heavy impact
once should not be used again.
Attempt 2: Track 2 type of helmet tested as per IS 4151 on impact absorption test rig
Fig 5. Test window for Impact absorption test of Track 2 type of helmet as per IS4151
Conclusion of Attempt 1.2: Track2 helmets developed have EPS padding thickness of 22 mm and density
55K g/mm3 and has minimum optimized weight of 850 gms and has potential to pass the safety norms as
per IS4151
Table 4 summarizing Attempt1.1 and Attempt 1.2 in tabular form
Sr No Model Thickness of Thickness Weight of Density of Maximum Head acce leration
Name Protective of FRP Helmet EPS (g)
Padding shell assembly padding FEA Experimental
‘mm’ ‘mm’ Kg Kg/m3
1 Track1 26 2.8 1.2 65 425 537
2 Track2 22 2.6 0.85 55 230 267
63
7. CONCLUSIONS
1) Theoretically helmet mass can be optimize up to 700gms; but without compromising safety
practically
the mass of the total helmet assembly having EPS protective padding can’t be reduced below
850gms.
2) P ractically FRP shell thickness can be reduced below 2.6 mm without c ompromising safety.
ACKNOWLEDGEMENT
We acknow ledge the support provided by BCUD Pune University for sponsoring the project and to
Ms.Badve He lmets India Pvt. Ltd, Aurangabad and Ms. DAK systems Mumbai for providing helmet
testing facilities. We also acknowledge help provided by several Rapid Prototyping vendors such as Ms.
Imaginarium Mumbai and to several faculty members of VIT Pune.
REFERENCES
1. AFSHARI A. , RAJAAI S., F inite element simulations investigating the role of the helmet in reducing
head Injuries, J. International Journal of simulation and modeling pp 42-51(2008)-ISSN 1726-
4529
2. CHAWLA A., KADAM S., SIN GH S. P. ,”Dynamic Modeling Base d Optimal Design of a Crash
Helmet”, J. Computer Aided Design & Applications, 3, Nos 1-4, 425-435 (2006).
3. ROYCHOWDHURY A., MAJUMDER S., S ARKA R S. Response of Human head under static & dynamic
load using F inite Element Method, J.Trends Biomaterial & Artificial organs, 17(2), 130-134(2004)
4. GILCHRIST A., ROWLAND F., MILLS N, M odeling of impact response of motorcycle helmets, J.
International Journal of Impact Engineering, 15, 201-218 (1994)
5. BOWMAN, LAWRENCE M., P AUL R., MOHAN D, S imulation of head/neck impact responses for
helmeted and unhelmeted motorcyclists, SAE Paper No.811029, 3318-3343 (1982)
6. DANIEL I.M AND ORI I SHAI, Engineering Mechanics of composite materials, O xford University
press (First edition),1994.
7. WISMANS J.H.M., Cras h He lmet Testing and Design Specifications, university press, Eindhoven,
Netherlands PP 135-139(2006) ISBN No: 10:9038628781
8. GILCHRIST A., ROWLAND F., MILLS N., Mathematical Modeling of Effectiveness of helmets in head
Protection, Proceedings of IRCOBI, Conference on Biomechanics of impact, pp 215-226 (1988)
9. CHIA -Y UAN CHANG, C HIH-H SIAN G HO, SAN-YI CHANG, Design Of a helmet, ME Thesis, Un iversity
of Michigan. USA (2003).
10. Indian sta ndard P rotective Helmets for Scooter and Motorcycle riders-specification
IS4151:1993(Third revision)-Published report.
64
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S 5/P4
ABSTRACT
L&T, a leading pressure vessels manufacturing industry, has taken step to optimize, redesign and
automate the nozzle we lding machine for higher sagitta nozzle. The complex three dimensional profile
formed by nozzle to shell joint is difficult to trace by ordinary welding machine using SAW method.
Ordinary SAW machines have large and heavy boom on which machine is mounted. These machines
consume time in set up a nd are usable for smaller sagitta.
With the studies of existing machine and comparing those from available in markets, a new
conceptual design is made for a utomatic SAW welding of nozzle to shell joint. The approach started with
design and synthesis of mechanism to mount the machine on nozzle itself. A lso the mechanism is designed
to trace the Sagitta profile. F or this the vertical motion of welding arm and rotary motion of machine is
synchronized.
This paper also includes the geometric analysis of acc uracy of the mechanism to trace the profile
and optimization of the design to minimize error. Conce ptual 3D model is prepare d. The analysis s hows
limitations and areas to improve accuracy.
Sagitta: Sagitta of a circular arc is the distance from the center of the arc to the center of its base.
SAW: Submerged Arc Welding.
1. INTRODUCTION
Larsen and Toubro ltd. is taking a step to automate the process of nozzle to shell we lding having higher
sagitta. P resently it is manual we lding using SMAW (S hielded metal arc welding) process. T he
automation is to be done for SAW process. T he existing machines for automatic SAW are mounted on
heavy sized boom. To eliminate boom, the machine is re quired to mount on nozzle itself. For that a proper
holding chuck is required to design. Another important requirement is that there must be mec hanism to
trace the nozzle-shell joint profile. After studying various alternatives it is found that slider crank
mechanism is best to have the desired kind of motion. After analysis, these mechanisms are implemented
in machine and 3-D conceptual model is prepared.
The 3D model below (Fig. 1) shows how machine is mounted on nozzle with the help of
chuck. The machine is rotated by means of motor and fixed. The slider crank mechanism gives up-down
movement to we lding torch synchronize d with circular m otion given by motor.
65
Fig.1. 3-D model of automatic SAW mac hine for nozzle to shell joint.
Next sections include structural analyses of chuck and detail geometric analysis of slider
crank mechanism to follow nozzle-shell joint profile.
2. CHUCK DESIGN
Requirements for the chuck are-
1. Chuck must be self centering type, so that locating centerline of machine with centerline of nozzle
can be easy.
2. Assembling a nd dissembling should be simple.
3. Chuck must be rigid enough to take the machine weight load and hold machine firmly.
4. Weight of chuck should be minimum possible.
2.1 Mechanism
Considering listed factors and surveying many industrial work holding c hucks, a 3-Jaw chuck
best suits the application. 3-Jaw chuck is best to locate centerline of nozzle.
There is a ce ntral leadscrew rod and two bosses are mounted on it (Fig.2). Lower boss is
having internal threads and mates w ith leadscrew threads. Upper boss is not having internal threads a nd is
fixed with bush bearing on lea dscrew shaft. The leadscrew is fixed with the upper flange on which
machine flange will be bolted.
As lea dscrew rotates, the lower boss moves up or down. The jaws are connected to bosses by
means of links as shown in fig. Hence as boss moves up or down, links pushes the jaws to expand or
contract so as to adjust in ID of nozzle.
2.2Dimensional synthesis
66
For closer most position,
′
=√ −ℎ
…………………………. (1)
′′
is the distance of jaw from boss at any
Hence minimum ID of nozzle required to
mount the we lding machine on it is,
′
= 2 ′ + 140 …………... …….(3)
140 added is the approximate consideration for
offset distance of pin joint on boss to centerline
of boss.
Chuck is to be checked for its sustainability in c arrying the machine weight of 3ooKg approx.
The analysis is carried out in Solidw orks w here meshing a nd solver are inbuilt in it. L oad 300Kg is a pplied
on top of chuck and fixture is provided at three holding legs. Material selected is plane carbon steel. The
effect of such loading is buckling of links.
67
3. MECHANISM FOR SAGITTA PROFILE
For vertical m otion along height a nd depth of Sagitta; the options available are; Slider crank
mechanism, P roximity sensor (distance mea suring), Voltage sensing and controlling, Cam and follower
mechanism etc.
P roximity sensor and voltage controlling are e lectrical c ontrol mechanism; senses the distance
between torch and workpiece with a feed back control system. But there is limitation of weld profile and
the curvature of surface. Also the flux spread in SAW method may become barrier for sensor. In both
cases, there is lack of proper control over motion.
Cam and follower is a well known mechanical linkage and seems applicable here. But for eac h
level of sagitta the different sizes of cam is not possible.
68
.
Path trace d by slide r crank me chanism
Consider a slider crank mechanism which is to be used on machine to follow Sagitta profile. (F ig.
6)
Let, = crank length
L = connecting rod length
Where is equal to half of actual maximum Sagitta.
= /2 ..……… (6)
For one revolution of machine, there must be two revolutions of crank, hence,
Ѳ = 2×Ѳ …………. (7)
Ѳ
Ѳ = sin ...………. (8)
∴ ′=( Ѳ − Ѳ + ) − … (9) Fig.6. Mechanism De pth Variation
∴ Difference/error in actual profile a nd the profile traced by mechanism at the same location is,
= − ′ ..……………… (10)
The quarter of the profile i.e. 0º to 90⁰ is taken for analysis as this profile re peats four times. The initial
values taken for shell ID are 2000mm, for nozzle OD is 1000mm and c onnecting rod length as 390mm.
Using Eq. (5), (9) and (10), the difference/error ‘x’ is calculated for each degree of rotation ‘Ѳ ’. The
sagitta for c onsidered ID a nd OD is 134mm. The data for error variation w.r.t. angle of rotation of machine
is represented graphica lly in Fig. 7 below.
4.0
3.5
3.0
DIFFERENCE
2.5
2.0
1.5
1.0
0.5
0.0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91
Ѳ
Fig.7. Mechanism error at 0 to 90 degrees of rotation
The graph shows that at 40º to 50º of any quarter profile, the difference/error is maximum. F or above
selecte d diameters of shell and nozzle the maximum error occurred is 3.4mm. The wire feeder mechanism
in SAW can have the limited speed c ontrol. By increasing or decreasing the speed, it can take care of the
extra gap (error) occurring due to mechanism. The maximum permissible error is 8-10 mm.
69
The repea ted analysis according to Eq. (5), (9) and (10) shows that if we increase the connecting rod
length then error gets reduced (Table 1). The final model assembly limits the length to 350-450mm. More
length increases overall machine height which makes it unstable. In this range the error is 4.1 to 2.6mm
which is much less than permissible error (8-10mm). Hence optimum is selected accordingly.
L (mm) 250 300 350 400 450 500 550 600 650
Max. error (mm) 6.7 5.2 4.1 3.2 2.6 2.1 1.7 1.4 1.1
Table 1: Error variation for varying lengths of connecting rod.
1. Chuck analysis shows Von mises stresses are maximum at links joints. He nce links and joints must
be rigid enough.
2. The path traced by slider mechanism follows perfectly at peak points of crest and trough of nozzle-
shell joint profile but differs slightly at intermediate portion.
3. The difference depends upon connecting rod length. Maximum is the rod length, minimum is the
difference. (Selected optimum is 400mm).
4. The difference of 8 to 10mm can be a utomatica lly compensated by wire feeder motor by increasing
or decreas ing wire feed speed through feed back c ontrol system.
ACKNOWLEDGMENT
I am very grateful to M/S Larsen and Toubro Ltd. Powai, for giving me opportunity to learn
and innovate the idea and for letting the industrial exposure to me. I am indebted to the production
department and the staff for their help.
I am also thankful to my institute V.J.T.I. Matunga and my professors for their support and
motivation.
REFERENCES
Books
R. S. H ART ENBERG AND J. DENA VIT , Kinematic synthesis of linkages, New York , McGraw-Hill., pp.
294 (1964).
Pate nt
ALBE RT W. N UCCEL , Nozzle Welder, Teledyne, Inc., York , Pa. Appl. No. 100,040. (1970)
Inte rnet
www.bugo.c om
www.atlantagmbh.de
www.esab.com
www.rbcbearings.com
70
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S 5/P5
AB STRACT
In the field of hydrodynamic lubrica tion, the operating conditions of the machines are becoming very
stringent, exact and more demanding. T he pressure developed along the circumference of the journal plays
a vital role to improve performance of the lubricated hydrodynamic journal bearings. The aim of this paper
is to model and simulate the pressure distribution around the circumference of hydrodynamic journal
bearing using the numerical simulation method, Computational F luid Dynamic (CFD) software package
ANSYS. A journal of diameter 100 mm and a length-to-diameter (L/D) ratio 0.5 is considered and
influence of other operating parameters such as speed, load and eccentricity ratio are evaluated for
pressure distribution in a hydrodynamic journal bearing. T he simulated results have been presented for a
wide range of speed, eccentricity ratio and varying clearance. The results suggest that the clearance space
in the bearing makes significa nt changes in the performance of the bearings at different speed of the
journal. F urther the results reveal that the lesser the clearance, higher the load carrying ca pacity of
hydrodynam ic journal bearing.
1.INTRODUCTION
Cylindr ical hydrodynamic journal bearings have been widely used in industrial applicationspredominantly
with heavy machines such as steam turbines, turbo-alternators and other high-dimension shafts for more
than a century.When a bearing operates at high speed, then heat is generated and raises the temperature of
the lubricant and affects the performance of hydrodynamic journal bearing then it is necessary to see the
thermal effect on bearing performance.The film pres sure is created by the moving surface itself pulling the
lubricant into a we dge-shaped zone at a velocity sufficiently high to create the pressure necessary to
separate the surfaces against the load on the bearing which prevent meta l-to-metal contact. There are
several important operating and geometric parameters in hydrodynamic lubrication which directly
influence the design stage of journal bearing along with the therma l effect.
Petroffand Tower (1883) carried out an extensive e xperimental investigation a nd showe d the dependence
of friction on viscosity of the lubricant, load and dimensions of the journal bearing.The experimental
investigations by Petroff and Tower formed the background for the hydrodynamic lubrica tion theory.Later
Osborne Reynolds (1886)conducte d experiments and published the findings in the form of the present day
Hydrodynamic T heory of lubrication. K. Mahala et al. and Gertzos etal. (2008) investigated journal
bearing performance characteristics w ith a Non-Newtonian fluid i.e. Bingham fluid considering the
71
thermal effect for several (L/D) ratios.Ferron et al. (1983) studied the pressure and temperature
distribution on bearing wall and meas ured along with the eccentricity ratio at different speeds
Nomenclature
c Radial c learance at 400C, mm To Ambient temperature, K
cp Specific heat of lubrica nt, J.Kg-1.k-1 Tshaft Temperature of the shaft, K
e Journal Eccentricity, mm ε Eccentricity ratio
h Film thickness, mm θ Bearing angular coordinate, deg.
hk Convection heat transfer coefficient, W.m-2.k-1 μ Dynamic viscosity of lubricant, N .s. m-2
K Thermal conductivity, W.m-1. k -1 ρ Density of lubrica nt, Kg.mm -3
K a Thermal conductivity of the air, W.m-1. k-1 Φ Attitude/pressure a ngle, deg.
K b Thermal conductivity of the bush, W.m-1.k -1 f Friction force, N
K o Thermal conductivity of the lubrica nt, W.m-1. k-1 ωj Journal rotational speed, rad. s-1
K s Thermal conductivity of the shaft, W.m-1.k -1 Wr Radial load, N
L Bearing length, mm X,Y,Z Cartesian c oordinates
R b Radius of bearing, mm Rj Radius of journal, mm
p Pressure, N.mm -2 Ro Bearing outer radius, mm
P in Inlet lubricant pressure, N.mm-2
and loads using theoretical and e xperimental method for a plain journal bearing.
Bouyer and F illon (2011) and Monmousseau and Fillon (2000) estimated the operating conditions during
start-up which allow for a safe running ofa plain journal bearing and a tilting-pad journal bearing to
analyze the inf luence of se veral operating conditions (rotational speed, radial bearing clearance, fee ding
temperature) to predict safe operating c onditions.D ufrane et al. (1983) and Hashimoto et al. (1986)made a
mathematica l model for the wear geometry and the steady-state characteristics of the bearings such as film
pressure, attitude angle and Sommerfeld number are analyzed by a semi analytical finite e leme nt method
for various wear depth parameters at low operating speed and normal operating conditions including
turbulent regime.
Rahmatabadi etal.(2000) also studied the steady-state performance of circular and noncircular three-
lobe journal bearings of finite length, lubricated with Newtonian and micropolar fluids. Aziz Ouadoud et
al.(2012) studied the thermoelastohydrodynamic study for a nalysis of elliptical journal bearing (Tw o-lobe)
operating with Newtonian lubricant.Rahmatabadi et al.(2010),investigated effect of the size of material
characteristic length and the coupling number on the static performanceof two, three and four lobed
bearings using micropolar fluid theory . Phalle et al.(2011) presented an analytica l study concerning the
influence of wear on the performance of a membrane compensated 2-lobe four-pocket hybrid journal
bearing system and also studied aligned and misalignment conditions of journal on the bearing
performance characteristics.
Through many research workshave been reported on the performance of plain hydrodynamic journal
bearing w ith different effects and a nalysis by FEM and FDM there are few work where CFD used as a tool
in the study of hydrodynam ic journal bearing.In the prese nt work we have studied theoretical prediction of
pressure distribution in journal bearing based on mathematical solutions and CFD as a tool to find a
pressure distribution profile around the hydrodynamic journal bearing.
72
2. ANALYSIS
Reynolds equation governs the pressure generated around the circumference of the journal in
hydrodynam ic film lubrication. Reynolds equation forms the basis for the hydrodynamic fluid film theory
and Pressure profile is plotted using the Reynolds equation. The coordinate system and the geometry of
journal bearing are shown in figure 1. The journal rotates at an angular velocity ωj in an equilibrium
position between the external load and the pressure generate d by the lubricant film.
2.1 Assumption
A rigid aligned bearingwith the steady state condition is assumed. The flow is assumed
Newtonian,inviscous,incompressible, isothermal, laminar and inertia is neglected. Journal and bearing
surfaces are
smoothand a constant vertical load is assumed to be applied at journal ce nter.
μ
+ μ
= (1)
There have been proposed several analogies, mathematical solutions, relaxation methods, numerical and
graphical methods to obtain a solution for Reynolds equation.
To proceed with this a nalysis,first a 3-dimensional a nnular fluid film thickness in the bea ringhas been
modeled in GAMBIT by using the following dimensions as reffered in Ferron J. (1883) and
SalmiahKasolang (2012).
Table 1Operating parameters for bearinganalysis Table 2Name and types of boundaries of the flow regime
Length of the bea ring(L) 50 mm Sr. Geometrical boundary CFD boundary type
Diameter of the journal(D) 50 mm 1 Journal surface Wall
Radial clearance(c) 52 µm 2 Bearing surface Wall
Lubricant viscosity 68 cSt @400C 3 Fluid zone side 1 P ressure outlet
Journal spee d(N) 600RPM 4 Fluid zone side 2 P ressure outlet
After Modeling of the lubricant in the clearance space of journal bearing, this geometry is meshed in
gambit.After generating meshed volume in GAMBIT boundary conditions have beenapplied a s given in
Table 2.T hen we specifies continuum type as FLUID to the film thickness,and as SOLID to the bearing
inner wall a nd shaft surface of above geometry.
73
The mesh file (.msh) created from gambit has bee n imported to the ANSYS Fluent software for CFD
simulation.In fluent after conforming quality of the mesh, data related to chemical and physical properties
of the lubricant oil used is applied.The bearing is m odeled as a ‘moving wa ll’ with absolute motion at an
angular spee d of 0 rpm. The rotational axis origin of the journal is set at the origin which is x= 0, y= 0,
z= 0).The rotation axis direction is set as X= 0, Y=0, Z= -1 (for an anticlockwise rotation of journal). T he
journal is modeled as a ‘moving wall’ with absolute motionat an angular speed of 4000 rpm.
Side boundaries of F luid zone set the pressure outlet zone to the atmospheric pressure at the outflow
boundary. In fluid cell zone condition define motion type as a m oving reference frame for a journal w ith a
rotational velocity 4000rpm and direction of rotation is as rotation of the jour nal.The translational velocity
in all three coordinate directions was set equal to zero.
Specify various parameters associated with the solution method to be use d in the calculation .T he
segregated solver is used for finding the solution a nd the flow is assumed to be laminar a nd steady. T he
discretisation use d is ‘P RESTO’ for pressure, ‘second order’ for momentum, ‘second order’ for energy
and ‘simple’ for the P-V coupling.
After simulation 3-dime nsional pressure distribution around the journal surface is presented in the form of
contour.T he above pressure distribution on the Journal surface of a Journal Bearing has bee n generated
with considering the effect of temperature. The above result is very much in compliance with the work of
J. Ferron presented in his work. In this work simulation has been done in 3-Dimensional flow region
representing the 3-Dimensional lubricant flow of inside the bearing. So, the w ork presented in this paper
depicts more acc urate pressure distribution.
CFD results for pressure profile are plotted. The theoretical values obtained from Raimondi and Boyd
charts are shown on the pressure profile. At the same operating conditions the predicted maximum
pressure location from Raimondi and Boyd chart is at 197.50while in the CFD analysis, the maximum
pressure position is located at 2010 is in agreement.
Figure 2C FD pressure profile around the journal Figure 3CFD pressure profile around the journal
at 600 rpm and 6kN lo ad at 600 rpm and 8kN
74
Also the maximum pressure obtained from CFD is 2.99 MPa is very close to the predicted value from
Raimondi and Boyd chart is 2.93 MPa. By squeezing action, the converging and diverging sections are
defined from the minimum film thickness. In the diverging section, the pressure drop is observed and it
takes negative values.
Corres ponding pressure profiles for fluid lubrication at 8 kN is shown below. Theoretica lly as the load
increases, the position of minimum fluid film thickness will displace to a new position. However, the
position of maximum pressure remains the same a s predicted from Ra imondi and Boyd chart.
2000000 10000000
CFD 9000000 L/D=1
1800000
Maximum Pressure (Pa)
1600000
Theoretical 7000000 L/D=0.5
1400000
1200000 6000000
1000000 5000000
800000 4000000
600000 3000000
400000 2000000
200000 1000000
0 0
0 30 60 90 120 150 180 210 240 270 300 330360 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Degrees Eccentricity ra tio (ε)
75
0.9 9000000
0.8
N=1500 rpm
0.6 6000000
0.5 5000000
4000000
0.4
3000000
0.3 Theory
CFD 2000000
0.2
exp eriment 1000000
0.1
0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 10002000300040005000600070008000900010000
Load (N) Ecentricity Ratio (ε)
6000000 2500000
C= 0.145mm
Maximum Pressure (Pa)
5000000 2000000
C= 0.152mm
4000000
Pressure (Pa )
C= 0.166mm
1500000
3000000
1000000
2000000
1000000 500000
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 10 20 30 40 50 60 70 80
Eccentricity ratio (ε) Axia l position (mm )
5. CONCLUSION
A CFD model is developed in order to simulate and find the maximum pressureand the pressure
distribution around the circumference of hydrodynamic journal bearing.It is found that the ma ximum
pressure value obtained from CFD study is closer to the theoretical ma ximum pressure value w ith 2%
76
variation. It is also noticed even though the position of minimum film thicknes s varie d clearly with
changes in loads, the location (i.e. angle) of the maximum pressure has not changed significa ntly with
loads.We observe the good agreement between the res ults obtained for the pressure profiles plotted using
CFD package and theoretical profiles from Raimondi and Boyd as well as e xperimental results for a plain
journal bearing in hydrodynamic lubrication.
REFERENCES
Journal articles
Aziz Ouadoud, Ahmed Mouchtachi, NoureddineBoutammachte, “Thermoelastohydrodynamic
Analysis of E lliptical Journal Bearing (Tw o-Lobe)”, European Journal of Scientific Research,Vol.76
No.1, pp. 108-116, (2012).
Bouyer J., Fillon M., “Experimental measurement of the friction torque on hydrodynamic plain journal
bearings during start-up”, Tribology In ternational, 44 , pp. 772–781, (2011).
Dowson D. “A generalized Reynolds equation for fluid-film lubrication”, International Journal of
Mechanical S ciences Volume 4 , pp.159–170, (1962).
Ferron J., Frene J., Boncompain R., "A Study of the Thermohydrodynamic P erformance of a Plain
Journal Bearing Comparison Between Theory and Experiments" ,Tran sactions of the ASME, 422/Vol.
105, (1983).
Gertzos K.P ., Nikolakopoulos P.G. , P apadopoulos C.A., “ CFD analysis of journal bearing
hudrodynamic lubrication by Bingham lubrica nt”, Tribology International,vol.4 1,pp. 1190– 1204,
(2008),.
Hashimoto Hiromu, Sanae Wada, Katsuhiro Nojima”performance characteristic of worn journal
bearings in both laminar and turbulent regime Part 1: steady-state characheristics” Tribology
Transactions,29: 4,565-571, (1986).
MahalaK.,“Evolution of the Lubrication Regime of a cylindrica l journal bearing in the starting phase,”
Wiley Lubrication Science, ID:LS-12-0072-RA-LS.
Minhui He , C loud C. H unter, Byrne James M.,“Fundamentals of Fluid Film Journal Bearing Operation
and Modeling”, Proceedings of the thirty-fourth Turbo machinery Symposium-2005 US, pp. 155-
175,(2005).
Monmousseau P., Fillon M., “Transient thermoelastohydrodynamic analysis for safe operating
conditions of a tilting-pad journal bearing during start-up”, Tribology International 33, pp.225–231,
(2000).
Nair K. Prabhakaran, Na ir V.P . Sukumaran, JayadasN.H.,“Static and dynamic analysis of
elastohydrodynamic elliptica l journal bearing with micropolar lubricant”, T ribo logy International, 40,
297–305, (2007).
Nuruzzaman D. M., Khalil M. K. , Chowdhury M. A. , Rahaman M. L.,“S tudy on Pressure Distribution
and L oad Capacity of a Journal Bearing Using F inite Element Method and Analytical Method,”
IJM ME-IJENS Vol: 10 No: 05.
Osborne Reynolds,“Theory of Lubrication, Part I,” Phil. Tran. Roy. Soc. London ,1886
P halle Vikas M., Sharma Satish C., Jain S.C., “Combined influence of wear and Misa lignmnet of
jour nal on the Performance Analysis of Three-Lobe Three-Pocket Hybrid Journal Bearing
Compensated with ca pillary Restrictor”
P halle Vikas M., Sharma Satish C., Jain S.C., “Influence of wear on the performance of a 2-lobe
multirecess hybrid journal bearing system compensated with mem brane restrictor”, Tribology
International,vol. 44 , pp. 380–395, (2011).
77
Rahmata badi A.D., MehrjardiM.Zare, Fazel M.R., “P erformance analysis of micropolar lubricated
jour nal bearings using GDQ method”, Tribology In ternational,vol. 43pp.2000–2009,(2010).
Rahmata badi A.D., Ne koeimehr M., Rashidi R., “Micropolar lubricant effects on the performance of
noncircular lobed bearings”, Tribology International, vol.4 3, pp 404–413,(2010).
SalmiahKasolang, Mohamad Ali Ahmad, Rob-Dwyer Joyce, C heFaridah Mat Taib,“Preliminary study
of Pressure P rof ile in Hydrodynamic Lubrication Journal Bearing”, Procedia Engineering 41, pp1743
– 1749, ( 2012 ).
Sharma R.K., P andey R.K., “E xperimental studies of pressure distributions in finite s lider bearing with
single continuous surface profiles on the pads”, Tribo logy International 42, pp.1040–1045, (2009).
Tower B.,“First report on Friction E xperiments,” Proc. Inst. Mech. Eng., pp.632-666,(1883)
BOOKS
Alastair Cameron, Basic Lubrication Theory, 3rd E dit ion, Wiley Easter n Ltd.
78
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S 5/P6
AB STRACT
This paper describes the use of 1-D F luid Flow S imulation Software (AMESim) Model to simulate
different aspects of a Engine Lubrication Systems. A 1-D computer model was developed to study the pr-
essure variations in the lubr ication system. T he study carrie d out on a six-cylinder air cooled diesel engine
is presented in this paper. Theoretical values of the nature of oil flow through the oil galleries, hydraulic
tappet, T- joints and plain journal bearings were also obtained using hand calculations. The flow from oil
pump & the flow re sistance through the oil filter a nd oil cooler are considered at a standard temperature.
Various design guidelines and certain assumptions are applied in the analysis. The flow and pressure
distributions a nd the pressure data obtained from the simulation are compared with experimental data at
various locations w ithin the engine lubrication system. This new computer model was thus validated &
can be used to facilitate the engine lubrication system design process.
The other major aspect of this paper is to carry out the sensitivity study. It mainly includes examining the
effect of changing various parameters such as viscosity, length & diameter of pipe, bearing clearance,
bend angles, etc on variation of the pressure and ultimately on the e fficiency of the lubrication system. T he
model has lead to selection of optimum combination of all this parameters w hich was then validated with
actual testing.
1.INTRODUCTION
The quality of engine lubrication depends upon how much oil is supplied and how the lubricant is
pressurized to the lubricated components. These varia bles strongly affect the safe operation and the
lifetime of an engine. During the conce ptual design stage of an engine, the engine lubrication system
cannot be verified experimentally and the use of analytical methods aiming a t optimizing the lubrication
system is often required. Various methods have been developed by several researcher and the flow
characteristics in most lubricated engine components have bee n successfully modelled analytically.
However, this method is very tiring a nd time consuming.
The AMEsim model offers the user the opportunity to build 1- D F luid Flow Simulation Models in an easy
manner via a Graphical User Interface. In this a lubrication system is represe nted as a system of
components desc ribing the hydrodynamic and thermodynamic behaviour of system elements. These
components are c onnected to form a network consisting of pipes, joints, bends, bearings e tc.
79
This paper includes a description of general flow network theory and flow characteristics for each
lubricated component. T he flow network elements are systematically structured and modelled in software
in order to simulate the engine lubrication system. The flow and pressure distributions res ults which are
obtained along various engine elements are then analysed and the pressure data is compare d to
experime ntal data for a few locations in the e ngine lubr ication system, thus validating the model.
Sensitivity study is of vital importance for optimizing the performance of lubricating system. Components
of which dimensions were varied for checking the sensitivity mainly include bearing clearance, gallery
diameter, viscosity & engine rpm. Conclusions were drawn after varying each parameter which led to
selection of most optimized combination of these parameters.
2. AMEsim
AMESim stands for A dvanced Modelling Environment for performing S imulations of engineering
systems. It is based on an intuitive graphical interface in which the system is displayed throughout the
simulation proces s.
AMESim uses symbols to represent individual components within the system which are based on the
standard symbols used in the engineering field such as ISO symbols for hydraulic components or block
diagram symbols for control systems; or w hen no such standard symbols exist symbols which give an
easily recognizable pictorial representation of the system.
Using AMESim you build sketches of engineering systems by adding symbols or icons to a drawing area.
When the sketch is complete, a simulation of the system proceeds in the follow ing stages:
• Mathematical descriptions of c omponents are associated with the icons.
• The features of the components are set.
• A simulation run is initiated.
• Graphs are plotted to interpret the system behaviour.
Model of the system: the set of equations defining the dynamic behaviour of the e ngineering system a nd
its implementation as computer code.
Sub model: the equations and corresponding code for each component within the system. AMESim
contains large libraries of icons and sub models of components
Ports: The points at which icons are c onnected together. If a component icon has no ports then it cannot be
connected to any other component (it can communicate though).A port c an only be connected to another
port of precisely the same type. (Exce ption: signal ports can be attached to any other port.)
Flow resistance has a strong influence on the design of fluid power circuits in which pressures are
relatively low but flow rates are high. The Hydraulic Resistance Library comprises a set of components
from which it is easy to model large hydraulic networks, evaluate the pressure drops through the elements
and, if required, modify the design of the system.
80
2.1 The four AMESim work ing modes
With AMESim, you can build a sketch, affect sub models to the components and lines , set up the
parameters of the sub models and then launch a simulation. Each step is performed in a specific working
mode in AMESim:
• Sketch mode
• Sub model mode
• Parameter mode
• Simulation mode
The Modes toolbar changes depending on the mode you a re working in.
In Sketch mode, you can build your sketch using the components that are available in the
categories. The categories are displayed in a vertica l toolbar on the left of the main window
of AMES im.
In Sub model mode, you can c hoose the sub models you want to attach to each c omponent.
In Parameter mode, you can set the parameters of the sub models. You can save the parameters from one s
Simulation mode enables you to run a simulation and to analyze the results of the
simulation.
81
Fig 1: Actual amesim model for the given engine
The model does not take in account the cooling of engine parts by the lubrication oil.
The sump tem perature is assumed to be c onstant at 100deg. C.
The friction due to roughness of pipe is neglected.
The friction factor for bends and T joint are assumed as default values given in software.
The Rocker bush and Turbo Bearing are simulated as restrictions.
Flow of oil over inlet and exhaust valve is neglected as their function is only c ooling of valves.
In order to determine the flow rate and pressure drop through the oil network, the theory of mass
conservations imposed at each junction of the network. The algebraic summation of all flows entering a
junction must be zero.F or incompressible flows, at a node, the c ontinuity
equation is,
∑ (Q ) = 0 (1)
The principle of energy conservation per unit mass is then applied. It states that the energy potential
between two nodes (e.g. nodes a and b) in a pipe is conserved.
For an incompressible flow, on the same streamline, the energy balance equation is
(2)
where
82
Pa, Pb, and Va, Vb, and Za, Zb represent pres sure, velocity and elevation at points a and b, hfis friction
alhea d loss, γ is the specific gravity of the fluid, and g is the acceleration of gravity.
The evaluation of pressure dr ops and friction factors in every hydraulic resistance library component are
based on Idel'c ik's formulation and assumptions.
In a network, part of the total energy is expended overcoming the resistance forces created by real viscous
fluids. Therefore, the term fluid resistance or hydraulic loss represents the irreversible loss of total energy
over a given system length. Here we are w orking with total pressure which is the sum of the static pressure
(potential energy) a nd the dynamic pressure (kinetic e nergy). The fundamental re lation used to evaluate a
pressure drop in the hydraulic resistance library is based on Bernoulli's we ll known e quation (4) :
However, working with total pressures and assuming that z1 = z2, this e quation becomes :
with
where
Δptottotal pressure drop;
ζ total friction factor;
ζloc local friction factor (local pressure drops);
ζfr frictional drag factor (pressure drops due to equivalent straight pipe segments of length l,
diameter D);
ρ density of the fluid;
wmax maximum stream velocity.
From equation (5) we can e xpress the total pressure drop as a function of the volumetric flow rate:
Where
Q - volumetric flow rate;
83
A - min sma llest cross-sectional area of the c onsidered element.
where
ptottotal pressure ;
pstatstatic pressure ;
1/2 ρw2 dynamic pressure.
All submodels use the follow ing units :
The oil pump pumps the lubricant from the oil pan through a suction pipe with a strainer welded at the
front. The lubricant passes through the cooler and then through the oil filter, then it enters the main oil
gallery and distributed to the main and big end bearings, and continues to flow in jets on the connecting
rods. After supplying oil to the main bearing the sub-branch further extends up to the cam bearing. The oil
from cam bearing then moves up into the push rod through tappet. The oil from push rod is then supplied
84
to rocker arm & rocker bush bearing through internal drill. the oil from rocker arm returns back to the
sump through push rod c over.
7
6
Cooler In Pr (bar)
5
4
3
2
Cooler IN Pr. (A MEsim)
1
Cooler IN Pr.(Expt.)
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Time (hrs.)
85
7
6
5
Filter In Pr (bar)
2
Filter In Pr. (Amesim)
1 Filter In (Expt.)
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Time (hrs.)
86
7
6
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Time (hrs.)
Amesim
Expt
7
5
Pressure
0
Cooler In Cooler out Filter In Main Gallery
Location
The above graphs shows overa ll comparison of the results obtained by experimentation a nd simulations
across various elements. The results are very well matched with very little deviation.
87
9. SENSITIVITY ANALYSI
Sensitivity analysis is of vital importance so as predict the engine performance by varying various
parameters at the design stage itself. In Sensitivity Study the effect of parameters like Bearing
Clearances, Gallery Diameter, Temperature and Engine rpm are investigated to make the present
lubrication circuit more efficient and optimal. The following table summarises parameters that are
varie d to carry out the analysis.
Table 2
9.1 Bearing Clearance
In this paper bearing clearances have been varied to have a proper understanding of the behaviour of the
engine during his e ntire life span. When the engine is new its bearing c learances (c) are kept according to
the design, but most of the time these designs are done on the thump rule that nominal clearance should be
approximately 1 micron per diameter (d) of bearing. T hus an analysis is done by reducing the bearing
clearance by 20% w.r.t nominal c learance, by reducing the c learances we are providing an allowance for
unexpected wear and tear that if takes place ,will at most increase the clearance to nominal clea rance.
Analysis has also been done on behaviour of the engine with nominal cleara nce and its effect when
clearance increases due to prolonged use, as it w ill cause wear and tear of the bearing surface. T o study
this e ffect we have increase d the bearing clea rance by 40% w.r.t nominal c learance.
By performing the above cases, we have simulated the circuit to find the pressure and flow variation
across various components of the oil circuit.
Firstly, all bearing c learances were considered; therefore to find the result we simulated the circuit with
increased and reduced value of c learances for a ll the bearings.
88
7 c=0.0008d
6 c=0.001d
c=0.0014d
5
Pressure (Bar)
4
0
Pump Cooler In C ooler F ilt er In Main Main C onrod Cam
Out out Gallery Bearing Bearing Bearing
60 c=0.0008d
c=0.001d
50
c=0.0014d
Flowrate (Lpm)
40
30
20
10
0
Pump Cooler In Cooler F ilter In Main M ain C onrod C am
Out out Gallery Bearing Bearing Bearing
From the simulated result of pressure show n,it is observed that when the clearances of all bearings are
reduced by 20% w.r.t nominal clearance, there is an increase in the output pressure of pump by 7%
(0.37388 bar) and also pressure gain of 25.64% (0.75618 bar) in main oil gallery, 26.66% (0.76798 bar) in
main bearing, and 23% (0.77988 bar) and 27% (0.76997 bar) in conrod and cam bearing respectively when
compared w ith the results of standard oil circuit .i.e. with nominal clearance. The other observation made
was, that the pressure drop across the cooler decreases from 1.81bar a t nominal clearance to 1.5 bar i.e.
7.3% (0.2858 bar) decrease in the pressure drop across cooler and 4% (0.078 bar) decrease in pressure
drop across filter.
Similarly, it is observed that when the clearances of all the bearings are increase d by 40% w.r.t nominal
clearance, there is a decline in the pump output pressure by 8.8% (0.47194 bar) and a lso pressure drop of
32% (0.94159 bar) in main oil gallery, 33% (0.95783 bar) in main bearing, and 29% (0.9816 bar) and
89
33.6% (0.95713 bar) in conrod and cam bearing res pectively when compare d with the results of standard
oil circuit. And pressure drop across cooler and filter increases by 10.84% (0.35707 bar) and 8.35%
(0.0958 bar) respectively.
From the simulated result of flow variation as shown, it is observed that the output flow rate from the
pump changes considerably, flow rate increases by 9% (4.629 lpm) and decreases by 8% (4.1127 lpm)
and also flow to the main-bearing increases by 36.5% (1.22 lpm) and decreases by 28%(0.95 lpm). And
there is no considerable difference in the flow rate through the conrod and cam bearings. When the bearing
clearance is increased by 40% and decreased by 20% w.r.t nominal clearance.
After changing clearance of all the bearing, the next sensitivity analysis was done by keeping the
connecting rod bearing clearance constant at standard value and varying the main bearing clearance. To
study the effect we followed the same procedure of increasing and decreasing the clearance by 40% a nd
20% respectively w.r.t nominal clearance.
7 c=0.0008d
6 c=0.001d
5
c=0.0014d
Pressu re (Bar)
0
Pump Out C ooler In C ooler out F ilter In Main M ain Conrod C am
Gallery Bearing Bearing Bearing
90
60 c=0.0008d
c=0.001d
50
c=0.0014d
Flowrate (L/min)
40
30
20
10
0
Pump Cooler In Cooler F ilter In Main Main C onrod C am
Out out Gallery Bearing Bearing Bearing
In this sensitivity analys is con-rod bearing clearances were varied keeping the main bearing clearances
constant.
6 c=0.0008d
c=0.001d
5
c=0.0014d
4
Pr essure
0
Pump Cooler In Cooler F ilter In Main Main C onrod C am
Out out Gallery Bearing Bearing Bearing
From the simulated result of pressure as s hown, it is observed that when main-bearing clearance is reduced
by 20% there no considerable durable improvement in pump (only 0.5%) and also the improvement in all
91
bearing is not more than 2% when compared with the corres ponding value with nominal bearing
clearance.
Similarly, when clearance increased by 40% the obtained results are shown, pump output pressure
decreases by only 1%(0.05945 bar) ,pressure drop of 4% (0.123 bar) in main oil gallery, 4.4% (0.1262 bar)
in main bearing, and 4.46% (0.15 bar) and 4.45% (0.1268 bar) in conrod and cam bearing respectively
when compared with the results of standard oil circuit. And pressure drop across cooler a nd filteris very
negligible in both the cases.
c=0.0008d
60
c=0.001d
50
c=0.0014d
Flowrate (Lpm)
40
30
20
10
0
Pump Out Cooler In C ooler out Filter In Main Main Conrod Cam
Gallery Bearing Bearing Bearing
From the simulated result of flow variation, as shown , we observe that there no considerable change in
flow rate of oil to different locations. S o, we can conclude that conrod bearing is not very sensitive
parameter w hile considering the oil flow.
9.2 VISCOSITY
The operating condition for engine changes with the change in country for variety of customers. T he
engine may have to perform in diverse climatic condition. Thus in order to map the performance of engine
in such changing climate and to know the effect of change in temperature on lubrica nt’s viscosity the
sensitivity analysis is done. It would help to predict engine performance at design sta ge itself. The a nalysis
is done at four different temperatures viz; 40deg, 60 deg, 100deg & 120deg
92
At 40de g At 60deg
At 120deg At 100deg
7
5
Pressure
0
Pump Out Cooler In Cooler Filter In Main Main Conrod Cam
out Gallery Bearing Bearing Bearing
During the design stage of an engine the gallery diameter are mostly selected either from the earlier design
or from a benchmark value and are very rare ly changed. Thus in order to study the effect of change in the
diameter of main oil gallery on pressure drop across the engine this sensitivity analysis is done. It is done
by varying diameter by +6mm a nd -6mm i.e viz 14mm, 20mm & 26mm. the results obtained are shown in
graph below.
93
d= 14mm d= 26mm
d=20mm
6
4
Pressure
0
Pump Out Cooler In Cooler Filter In Main Main Conrod Cam
out Galle ry Bearing Bearing Bearing
We have done the case study on the Constant S peed, Six cylinders, Air-cooled D iesel E ngine used for
Genset application. But the same engine is also used for industrial purposes w here it is used at different
speeds, so to study its pressure variation a t different locations according to application; we have simulated
the model at differe nt engine rpm. viz 1500prm, 2000rpm, 2300rpm, & 2700rpm
94
7 1500rpm
2000rpm
6
2300rpm
5 2700rpm
Pressure
4
0
Pump Out Cooler In C ooler out F ilter In M ain Gallery Main C onrod Cam Bearing
Bearing Bearing
From the simulated result of engine rpm, as shown in Fig.7, it is observed that with increase in engine rpm
the pressure also increases. when the engine rpm is reduced from its rated speed of 2300rpm to 2000
rpm,there is an improvement in the pressure output of the pump by around 3.6% (0.196 bar), inlet to main
gallery by 3.43% (0.10137 bar), main bearing, conrod and cam bearing pressure by 3.44% (0.09917
bar),3.17% (0.1.667 bar) and 3.44% (0.09807 bar) respectively.
Similarly, w hen rpm was further reduce d to 1500rpm, as shown in F ig.7, it is observed that there is more
pressure gain as the pressure output of the pump increases by around 15.5% (0.83205 bar) ,inlet to main
gallery by 13% (0.38438 bar), main bearing ,conrod and cam bearing pressure by 16.4% (0.47304 bar),
11.6% (0.393 bar) and 13% (0.36759 bar) respectively.
Then to study the effect of high engine speed we simulated the model at 2700rpm ,as shown in Fig.7,and
observed that output pressure of pump decreases by 3% (0.168 bar), inlet to main oil gallery by 3.38%
(0.09967 bar), main-bearing ,conrod and cam bearing by 3.41% (0.09831 bar), 3.21% (0.10809 bar) a nd
3.4% (0.09731 bar).
10. CONCLUSIONS
Simulation model of this e ngine lubrication system using 1-D fluid flow methods has lea d to good results
and now can be used for various design processes. The simulation model should be build up with most
relevant data and should be problem oriented for higher success rate.
It is very important to validate the test result with the simulated model result. Ha ving done so, the model
becomes powerful to be applied early in the design process, eliminating problems before prototype build
and enabling to build better products. Here the validation was carried out by comparing the experimental
and simulated results at various locations such as filter, cooler, gallery etc across the engine. T he results
95
are very we ll matched and the deviation between the results is less than 10% at all stages. Thus the model
is fine tuned to felicitate various design processes
From the se nsitivity analysis, bearing clearance was found to be most se nsitive. it was obse rved that
reduction in the main bearing clearance by about 20 % there is a pressure gain of about 20-25% in all
components. A lso varying the engine rpm has lead to the conclusion that, as the engine rpm is decreased
from the rated speed of 2300 rpm to 1500 rpm maximum gain in pressure is observed, output of the pump
increases by a round 15.5% ,inlet to main gallery by 13% , main bearing ,conrod and cam bearing pressure
by 16.4% , 11.6% and 13% res pectively. Thus at higher speeds the pressure drops are reduced
considerably. Variation in temperature has lead to the conclusion that at lower temperature
Pressure drops are less than at higher temperature. T hus the engine can work efficiently in cold conditions.
However it was found that changing oil gallery diameter doesn’t cause considerable changes in the
pressure values and hence it not much sensitive.
Thus as greater variations of operating conditions can be explored with simulation than w ith actual testing,
the risk of problems that would appear during actual performance are greatly reduce d. A lso it provides
designer a spectrum to work with and has a potential to sa ve the manufacturer a great dea l of cost, time
and bad publicity.
REFERENCES
96
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S 5/P7
Not Received
97
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S5/P8
ABSTRACT
The present work mainly focuses on designing a shell and tube heat exchanger as a
condenser (one side fluid condensing and other side fluid in single-phase). Thermal design is
done by KERN method for calculation of heat transfer coefficient and pressure drop. Bell-
Delaware method is used in this paper to compute the shell side heat transfer coefficient and
pressure drop. Thermal design is also done by CHEM-CAD (CC THERM) software (6.5.0). The
results are compared with analytical method, CHEM-CAD (CC THERM) software (6.5.0) for
smooth tube and corrugated tube heat exchanger. The analysis of 3-D smooth and corrugated
tube by CFD (Ansys fluent 12.0) software is done. The variations of the fluid temperature and
total pressure drop along tube length are shown. It is proved that the corrugated tube gives higher
heat transfer rate and it reduces heat transfer length, so that number of corrugated tubes required
is less compared to smooth tubes.
Keyword−Shell and tube heat exchanger, Heat transfer coefficient, Pressure drop, CFD, Smooth
tube, Corrugated tube.
1. INTRODUCTION
Shell-and-tube exchangers have main four components: a bundle, a shell (with nozzles)
enclosing the bundle, a stationary channel with nozzles, and the return head or its equivalent, U-
tubes. Tubes are arranged within a circular area and rolled or welded into tube sheets. Shell-side
baffles are positioned at intervals along the tubes to control flow, to act as tube supports, and to
minimize vibration. Their function is to maximize the heat transfer rates within the allowable
pressure drop. Meeting these conditions is not always possible in a given shell diameter. When it
exceeds the same, the shell diameter or tube pitch or both can be increased. In that case, divided
flow or the use of two or more units in parallel is adapted.
Shell and tube heat exchanger is widely used in many industrial power generation plants as well
as chemical, petrochemical, and petroleum industries. In thermal design , the heat exchanger is
sized, which means that all the principal construction parameters such as shell type and diameter,
number of tubes, tube OD and thickness, tube length, tube pitch, number of tube passes, baffle
spacing and cut are determined [1] .The LMTD method is used to design the shell and tube heat
98
exchanger. The shell and tube exchanger can be reasonably easily cleaned and those components
which are most subjected to failure-gaskets and tubes-can be easily replaced.
CFD is a science that can be helpful for studying fluid flow, heat transfer, chemical reactions
etc. by solving mathematical equations with the help of numerical analysis. It is equally helpful
in designing a heat exchanger system from scratch as well as in troubleshooting/optimization by
suggesting design modifications. CFD employs a very simple principle of resolving the entire
system in small cells or grids and applying governing equations on these discrete elements to
find numerical solutions regarding pressure distribution, temperature gradients, flow parameters,
etc. in a shorter time at a lower cost because of reduced required experimental work [2].
Table 1 describes the parameters towards the analysis of the following case study :
Hot stream Cold stream
Fluid Water vapour Cooling water
Mass flow rate (kg/sec) 0.166 18.76
Inlet temperature (⁰C) 60 32
Outlet temperature(⁰C) 60 37
Stream Allocation Shell side Tube side
A selected shell and tube heat exchanger must satisfy the process requirements with the
allowable pressure drops till the next cleaning of plant is scheduled. The methodology to
evaluate thermal parameters is explained with suitable assumptions. The following are the major
assumptions made for the thermal design and analytical calculations:
1. Flow is steady and fluid properties are independents of time.
2. Fluid properties do not vary with temperature.
3. Pressure at a point in the fluid is independent of direction.
6. Friction factor is considered to be constant with passage flow length.
Heat transfer or the size of heat transfer exchanger can be obtained from equation,
Q = U A ∆T ….(1)
For preliminary design, shell with any even number of tube side passes, heat load can be
estimated from the heat balance as [3]:
Q = (m ) T , − T , = (m ) (T , − T , ) …. (2)
If phase change takes place in one stream,
Q=mh …. (3)
Number of tubes of diameter (do ), shell diameter (Ds) to accommodate the number of tubes (Nt),
with given tube length (L) can be estimated
A = πd N L …. (4)
99
The tube side pressure drop can be calculated by knowing the number of tube passes (Np) and
length (L) of heat exchanger. The change of direction in the passes introduces an additional
pressure drop due to sudden expansions and contractions that the tube fluid experiences during a
return, accounted for allowing velocity head per pass. The total pressure drop of the side
becomes [3,4]:
∆P = 4f + 4N …. (6)
McAdams [3] suggested the following correlation for the shell-side heat transfer coefficient:
. μ . μ .
= 0.36 ….(7)
μ μ
where h is the shell-side heat transfer coefficient, D is the equivalent diameter on the shell side,
and G is the shell-side mass velocity.
The shell side pressure drop depends on the number of tubes, the number of times the fluid
passes the tube bundle between the baffles and the length of each crossing. The pressure drop on
the shell side is calculated by the following expression [3,4]:
( )
∆p = ∅
…. (8)
Bell-Delaware method is also employed to compute the shell side heat transfer coefficient and
pressure drop in form of [5]:
h = α o Jc JL JB …. (10)
where α o is the heat transfer coefficient for the ideal exchanger with pure cross flow stream over
tube bundle, Jc is the correction factor for baffle configuration (baffle cut and spacing) and takes
into account the heat transfer in the window, JL is the correction factor for baffle leakage effects
and takes into account both the shell-to-baffle and tube-to-baffle hole leakages, JB is the
correction factor for bundle and pass partition bypass streams w hich depends on the flow bypass
area and number of sealing strips.
The total shell side pressure drop is computed as the sum of three terms including
crossflow pressure drop (∆P cr), inlet and outlet pressure drop (∆P i-o) and window section pressure
drop (∆P w) as follows [1,5]:
∆P s = ∆P cr + ∆P i-o + ∆P w …. (11)
100
5. CORRUGATED TUBE
Corrugated tube induces turbulence on both the tube side and shell side fluids, which
results in significant enhancement over smooth tubes, with the resulting advantages of lower size
and space, reduced fouling and uniform temperature distribution, even for viscous liquids [6,7].
101
smooth tubes. These variations between Kern and Bell-Delware method is due to following
factor [4]:
1. Leakage through the gaps between the tubes and the baffles as well as baffle and the shell.
2. Bypassing the flow around the gap between the tube bundle and shell.
The difference between CHEM-CAD software output and anlytical solution is due to following
reason:
1. Change in fluid thermal properties with temperature.
2. In CHEM-CAD software all clearance like baffle to shell, tube to baffle etc. are considered.
102
Fig. 4 Temperature x-y P lot for Smooth and Corrugated Tube along Axis.
Fig.5 Tempersture Distribution of Smooth and Corrugated Tube along the different Lengths
Fig.6 Total Pressure x-y Plot for Smooth and Corrugated Tubes
Fig.5 shows that smooth tube achieves 309 K temperature at 1.5 m length, however under
the same conditions, corrugated tube requires only 1.25 m, resulting in reduction in length by
0.25 m. It conclued that corrugated tube saves 16 % length compared to smooth tube at same
mass flow rate 0.24 kg/sec and same heat flux 44000 W/m2. Fig.6 shows that pressure drop
obtained for smooth and corrugated tube is 1.2 kPa and 13 kPa repectively, which is attributed to
the absence of any spiral angle.
103
ACKNOWLEDGMENTS
My sincere thanks go to Mr. Piyush Gomase for his constant support and encouragement in
completing this work. I am highly indebted to my close colleagues who helped me in analysis
with CFD software.
Nomenclature :
Greek symbols
∆P pressure drop, Pa
∆Tm logarithmic mean temperature difference, oC
ρ fluid density, kg/m3
Subscripts
s shell side
t tube side
REFERENCES
[1] HA SSAN HAJABDOLLAHI, SEPEHR SANAYE, Multi-Objective Optimization of Shell and Tube
Heat Exchangers, Applied Thermal Engineering, 30, (2010), 1937e1945.
[2] AHMER RAI S KHAN, A SLAM BHUTTA MUHAMMAD MAHMOOD, KANWAR NAVEED AHMAD ,
MUHAMMAD HASSAN BA SHI R, NA SIR HAYAT , SARFARAZ KHAN, CFD Applications in Various
Heat Exchangers Design: A Review, Applied Thermal Engineering, 32, (2012), 1e12.
[3] SADIK KAKAC, Heat Exchangers Selection, Rating and Thermal Design, Second ed., pp. 283-
348.
[4] SANDEEP K. P AT EL, P ROFESSO R ALKESH M. MA VANI , Shell & Tube Heat Exchanger Thermal
Design with Optimization of Mass Flow Rate and Baffle Spacing, International Journal of
Advanced Engineering Research and Studies, E-ISSN 2249–8974.
[5] BOTT T.R., HEWITT G.F., SHIRES G.L., Process Heat Transfer, pp. 263-295.
[6] MUKHERJEE R., Practical Thermal Design of Shell and Tube Heat Exchanger, Ch.1,2,5,7,13.
104
[7] AHMET SELIM DALKILIC, FAT IH KANTAS, HAKAN DEMIR, OZDEN A GRA , OZGU R AT AYILMAZ,
“Numerical Investigation of Heat Transfer and Pressure Drop in Enhanced Tubes”,
International Communications in Heat and Mass Transfer, 38, (2011), 1384–1391.
[8] COULSON AND RICHARDSON S, Chemical Engineering Design, Fourth ed., Vol. 6, pp. 634-705.
[9] DONALD Q. KERN, Process Heat Transfer, International Ed., pp. 127-174, (1965).
[10] Standards of Tubular Exchangers Manufacturers Association (TEMA), Eighth Ed.
[11] TABO REK , Heat Exchanger Design Handbook, pp 3.3.5.
105
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S5/P9
ABSTRACT
The Roll cage or Frame of a Baja vehiclemust be capable of supporting all components and
the driver and shouldabsorb all loads fed into it without deflecting unduly.The main objective
while designing the roll cage was to ensure drivercomfortand safety even under the worst
possible conditions. Moreover, to enhance the overall performance of the vehicle, low weight
andgreater stiffness of the roll cage are essential. The scope of the project was to optimise the
load paths to ensure maximum stiffness of roll cage and using a tube section having lesser weight
per unit length.
The FEA results showed acceptable values of factor of safety even for worst case conditions and
thus a lightweight and sturdy roll cage design was accomplished.
1. INTRODUCTION
Mini Baja is an international competition wherein the engineering college students are expected
to design and fabricate themselves an All-Terrain Vehicle that can effectively negotiate highly
challenging terrain.The Roll cage (Frame) is a bracket that holds the driver and all the other
vehicle components together.
Such a vehicle (race-car) is expected to have quick response during cornering, acceleration and
braking in order to have the least lap time. If the frame (roll cage) members deflect under the
dynamic loads, the vehicle response is sluggish. Thus, the roll cage is expected to be rigid in
bending and torsion-that is it should neither sag nor twist. Stiffness can be imparted to it by
avoiding putting bending loads into members and always loading the joints in tension or
compression. Being a means of connecting mounting brackets, it shall be designed by locating
106
and orienting the members in such a way that they serve to the greatest advantage, and the loads
involved can be effectively absorbed with least deflection. Moreover, to have lower vehicle
weight, the roll cage has to be extremely lightweight and compact. But designing a very sturdy
roll cage which has low weight is no walk in the park. The roll cage design is always a trade-off
between high stiffness and low weight.
2. DESIGN METHODOLOGY
The roll cage design started with the cockpit by considering the measurements of the largest
driver. Emphasis was given on driver ergonomics by suitable placement of pedals, steering
wheel and gear shifter so as to have angles at elbows and knees within the driver’s comfort zone.
The cockpit members were placed strictly adhering to the Baja competition rulebook. The rest
members were placed according to sub-system (suspension, power train and steering) mountings.
The triangulation members were so placed and oriented as to optimise all the loads paths.Nodal
geometries were created everywhere such that the loads must be fed into joints to avoid
deflection and thus obtain maximum stiffness.To have lower weight, the total number of
members was kept to a minimum.Fig. 1 shows part of the roll cage structure with nodal
geometry.
On completion of the initial roll cage design, its FEA was done in ANSYS APDL. It was
analysed under the worst case front, side and roll-over impact conditions. Design modifications
were carried out according to the results of preliminary FEA and it was again analysed under the
same conditions until adequate values of factor of safety were obtained. Subsequently, position
and orientation of members was modified to increase its stiffness and it was later analysed for
bump conditions to obtain the value of torsional stiffness. Alternate analysis and modifications
continued till a high stiffness value was achieved.
After acceptable stiffness value was achieved, weight reduction strategies were applied. Initially,
the roll cage was designed with a 1 inch OD and 3mm thickness tube. According to the rulebook,
any material having a bending stiffness and bending strength equal or greater than the 1 inch OD
107
3mm thickness tube can be used for the roll cage. Both bending stiffness and strength depend on
moment of inertia of the tube and hence we decided to use a tube having a greater OD but the
same moment of inertia. A tube with 1.125 inch OD and 1.8mm thickness was found to be apt.
This tube had 30% lesser weight per unit length than the previously mentioned tube. Thus, a 30%
weight reduction in roll cage was achieved without decreasing its total tubing length. FEA of roll
cage with changed tube dimensions was carried out to obtain the values of factor of safety and
stiffness.
The roll cage consists of primary, secondary and triangulation members. There was still scope of
weight reduction in secondary and triangulation members. Thus, for further weight reduction, a
tube with a very low thickness could be used. But tubes with low thickness were found to form
insufficient weld pools and melting of tubes was observed during welding. Thus, taking
manufacturing feasibility into consideration, a 1 inch OD 1.6mm thickness tube was found to be
apt for the secondary and triangulation members. The final roll cage with a combination of 1.125
inch OD 1.8mm thickness tubes for primary and heavily loaded members and 1 inch OD 1.6mm
thickness tubes for the rest was analysed in ANSYS. This final FEA yielded results that included
satisfactory values of factor of safety and torsional stiffness under the same worst case scenarios.
3. FEA OF ROLLCAGE
The FEA of roll cage included frontal, side and roll over impacts, a torsional analysis and a
modal analysis. The first three analyses give us the values of factor of safety under worst case
impact scenarios. The stiffness of vehicles is given in terms of torsional stiffness of the frame
(roll cage) and is obtained from the torsional analysis.
FEA being a prediction, the conventional procedure of using conversion plots was adopted for all
the analyses. The roll cage was analysed for the same load conditions but with different mesh
sizes. Initially the mesh size was taken to be 20mm and it was gradually decreased till the error
was less than 5% as compared to result w ith previous mesh size. The values were finally used to
create conversion plots for all the analyses. Fig. 2 shows the conversion plot of frontal impact
analysis.
108
3.1 Impact Analyses
Table 1 below shows the conditions considered for the various impact analyses while
table 2 shows their results. Adequate values of factor of safety were obtained for the analyses
and the deformation values were also within the required limits.
In torsional analysis of the roll cage 3g cross bump forces were taken at the front and rear
suspension points.Fig. 3 shows the results of torsional analysis.
After obtaining the results, the torsional stiffness of the roll cage was calculated. The
value of the torsional stiffness is 1276 Nm/deg for the final roll cage with the combination of
tubes for different members.
The high value of torsional stiffness is due to the following reasons:
The torsional moments do not add up as they act about different axes due to the presence
of double wishbone in the front and trailing arm in the rear.
109
The distance between both spring mountings is less owing to the rear trailing arm
suspension.
The rear shocks are mounted on the RRH which is the stiffest part of the structure.
Modal analysis or vibrational analysis was done to ensure that the natural frequency of
the roll cage does not match the frequency of vibration of the engine in its working range i.e.
from 1700 rpm to 3800 rpm. The modal analysis was done finally with the roll cage having tube
combination.
In the working range, the frequency of vibration of the engine is from 14.16 Hz to 31.67
Hz. The result ofmodal analysis implies that the entire range of vibration of the engine lies
between the 3rd and 4th mode natural frequencies of the roll cage and hence there is no resonance.
Fig. 4 shows the results of modal analysis.
4. OPTIMISATION
Finite Element Analyses was done for various tubes with different cross sections. Weight,
minimum factor of safety and torsional stiffness for the different tubes were obtained which were
then plotted in a single graph (fig. 5) by using appropriate division factor. This plot puts a clear
picture of the relative changes in all the parameters and their slopes imply the rates of change.
The plot helps to know if the relative decrease in stiffness and factor of safety is greater than that
of weight or not. Deciding the tube configuration for the roll cage becomes effortless after
observing the plot.
110
Fig. 5 Graph
It is evident from the graph that the weight reduction due to change in tube is substantial.
It can also be observed that the slopes of blue lines are greater than those of red and green lines.
This implies that reduction is weight is greater as compared to that of stiffness or factor of safety.
Even if the values of factor of safety and stiffness are least for the combination of tubes, these
values are above the required limit which ensures a very safe and sturdy roll cage design. Table 2
shows the actual values of the three parameters for different tubes and the percentage change in
the value of parameter.
In the above table, the fourth column gives the value of percentage change in parameter
when tube was changed from 1 inch OD 3mm thickness to 1.125 inch OD 1.8mm thickness.
While the rightmost column shows the percentage change of the parameters when the
configuration was changed from only 1.125 inch OD 1.8mm thickness tubes to the combination
of two tubes.
Two different tubes were used for the roll cage which exceeded the strength requirements as per
the Baja regulations and also provided an advantage in weight reduction. A roll cage design with
the unprecedented combination of torsional stiffness of 1276 Nm/deg. and just 36 kg weight was
accomplished.On completion of manufacturing, the vehicle was subjected to brutal testing that
111
consisted of various bumps jumps, logs etc., to validate the FEA results. The vehicle was
successfully tested for 250 km without any structural failure.
The goal of designing a compact, lightweight and sturdy roll cage was successfully achieved.
Since there is limited power, the overall low weight resulted in increased acceleration in a
straight line as well as in the corners.
ACKNOWLEDGEMENTS
We would like to thank Dr. A.D. Sahasrabudhe, Dr. B. B. Ahuja, Dr. D. W. Pande and
Dr. S. N. Sapali for their immense support to all our endeavors.
We would also like to thank Mr. SiddharthAmondikar and Mr. Rohan Patel for their
continual guidance and support.
REFERENCES
(1) COST IN MICHAEL AND P HIPPS DA VID, Racing and sports car chassis design, 1966.
(2) REIMPELL J. AND ST OLL H., Automotive Chassis Engineering Principles, Second Edition,
2001.
(3) ADAMS HERB, Chassis Engineering, 1993.
(4) TEBBY ST EVEN , E SMAILZADEHEBRAHIM AND BARARI AHMAD . “Methods to determine
torsional stiffness of an automotive
chassis”,http://www.cadanda.com/CAD_PACE_1__67-75.pdf.
(5) ABRAM S, RYAN. “Formula SAE Race Car
Analysis.”http://www.fisita.com/education/congress/sc08papers/f2008sc005.pdf
112
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013- S5/P10
ABSTRACT
The objective of the performance modelling was to obtain the best possible combination
of gear ratios and tyre size to have optimum acceleration, top speed and gradeability. This paper
presents a vehicle dynamics model for estimating maximum vehicle acceleration levels based on
vehicle’s tractive effort and rolling resistance, aerodynamic and gradient forces, rotational
inertia, simulated with a time interval of 0.01 seconds.
Earlier, gear and tyre calculations were done only on the basis of maximum gradeablity and top
speed required. This type of method was not able to completely simulate the vehicle’s
acceleration levels during the entire acceleration run of 45.7 meters. There are many variables
like shift points, weight transfer, shifting time, rotational inertia and rpm drop during gear shift
which need to be understood and optimized.
The modelling not only gave a thorough understanding of these parameters but also helped in
selecting a tyre size of 23” (diameter) and corresponding optimum gear ratios. The modelling
results were validated during vehicle testing and the change in performance was significantly
noticeable as compared to the previous vehicle.
1. INTRODUCTION
Baja is a national level competition wherein the engineering college students are expected to
design and fabricate themselves a single seat four wheeled All-Terrain Vehicle that can
effectively negotiate a highly challenging terrain in the least possible time.
The Baja SAE provides all the teams with a single cylinder 10 HP OHV Briggs and Stratton
engine. As all the teams being at the same power level, the challenge was to harness the engine’s
10 horsepower in the most efficient way.
113
Apart from the engine the teams are free to design and implement their own drivetrains. Thus the
modelling helped in understanding the various drivetrain design parameters which affect the
vehicle performance. These parameters were nothing but the drivetrain inertia, tyre size, gear
ratio, weight transfer, slip ratio. Apart from this it also helped the driver to understand the shift
points, launch rpm and optimum gears for different grades.
The study first presents the proposed vehicle dynamics model and recommended parameters for
the model. Next the paper describes how the model was calibrated/validated using field data
collected during testing and the actual event held in Pretoria, South Africa and Indore, India.
Finally the conclusions of the paper and recommendations for further research are presented.
2. MATHEMATICAL MODEL
The model calculates the tractive effort as function of the torque curve of the engine. As the
torque of the engine varies with the rpm, so does the effort. This makes the model very accurate
as the acceleration is instantaneous and not average.
19.5
19
18.5
Torque in Nm
18
17.5
17
16.5
16
2000 2500 3000 3500 4000
Engine Rpm
The equation of the torque curve was found by polynomial curve fitting. The equation is as
follows.
T=6.443 + 0.009393Rp - 0.000001756Rp2 (1)
The Eq.(1) is used to calculate the instantaneous torque provided by the engine depending
on its rpm. The tractive effort was calculated as follows.
Ft = (T x Gr x ηt )/r (2)
Where, T: Engine Torque,
Rp: Engine rpm,
Gr: Gear ratio,
η t: Transmission efficiency,
r: Tyre radius (m)
114
2.2 Resistance Forces
The model considers three major types of resistance forces, including aerodynamic, rolling, and
grade resistance as was proposed in previous models (Fitch, 1994). The total resistance force is
computed as the sum of the three resistance components, as summarized in Eq.(3)
R Ra Rr Rg (3)
Where, R: total resistance (N),
Ra: aerodynamic resistance (N),
Rr: rolling resistance (N);
Rg: grade resistance (N).
The aerodynamic resistance, or air drag, is a function of the vehicle frontal area, the drag
coefficient, and the square of speed of the vehicle, as indicated in Eq.(4)
Ra = 0.5 x ρ x CD x A x v2 (4)
3
Where ρ: Air density(Kg/m ),
CD: Drag coefficient,
A: Frontal Area(m2 ),
v: Velocity (m/s)
2.4 Rolling Resistance
It is the resistance to the rolling motion of the wheels caused by the friction between rubber and
the surface. The Eq.(5) gives the rolling resistance.
Rr = Cr x W (5)
Where, Cr: Rolling resistance coefficient
W: Weight of the vehicle (N)
The grade resistance is a constant that varies as a function of the vehicle’s total mass and the
percent grade that the vehicle travels along, as indicated in Eq.(6). The grade resistance accounts
for the proportion of the vehicle weight that resists the movement of the vehicle:
Rg = W x sin(θ) (6)
Where , θ: Inclination of the surface
The maximum acceleration is a function of the forces acting on the vehicle and can be computed
using the Eq.(7).
a = (Ft - R) / M (7)
2
Where, a = acceleration (m/s )
M = Mass of the vehicle (Kg)
From Eq.(3),(4),(5) and (7) we get Eq.(8) which will be the basis for the modelling.
115
a = ((T x Gr x ηt ) – (Cr x W) – (0.5 x ρ x CD x A x v2 ))/(r x M) (8)
Given that the acceleration is the second derivative of distance with respect to time, Eq.(8)
resolves to a second-order Ordinary Differential Equation (ODE) of the form indicated in Eq.(9).
The ODE is a function of the first derivative of distance (vehicle speed) because the
tractive effort and aerodynamic resistance forces are all functions of the vehicle speed. In
addition, the ODE may be a function of the distance traveled if the roadway grade changes along
the acceleration section distance. But it is assumed that the grade remains zero along the entire
length of the acceleration track.
It should be noted at this point that because the tractive effort includes a minimum
operand, the derivative of acceleration becomes a non-continuous function.
a = f (v,s) (9)
Equation (9) is second order differential equation such that Velocity (v) is the first
derivative of the distance travelled (s) and acceleration is the second derivative of distance
travelled and first derivative of the velocity.
The Eq.(9) can be converted into two separate single order differential equations. These
equations then can be solved by Euler’s method of numerical integration.
v = v + dt x a (10)
s = s + dt x v (11)
Where dt: duration of time interval used for solving the ODE (in this case 0.01 seconds)
116
3. MODEL ANALYSIS
Launch /Engine
rpm
Computation of Corresponding
Engine rpm torque from
Eq.(1).
Calculation of Calculation of
wheel rpm from Tractive effort
velocty Eq.(2)
Computation of
acceleration from
Eq.(7)
The procedures for solving the ODE are best described by illustrating how the various
parameters were computed for the first 0.02 seconds of a test run.
Initially the launch rpm was considered to be 2000 rpm. Then from Eq.(1) the corresponding
engine torque was calculated and from Eq.(2) the tractive effort was computed..
Using the initial condition of speed equal to zero i.e.(v = 0 for t = 0), the tractive force,
aerodynamic resistance, and rolling resistance were estimated using Eq.(2),(4), and (5). Then the
acceleration of the vehicle at that instant was calculated using Eq.(7)
Considering that the vehicle is under this acceleration for 0.01 seconds the velocity gained and
distance travelled during this time are computed using Eq.(10),(11). As we know the velocity of
the vehicle, the angular speed of the wheel can be calculated. During this calculation it is
considered that the wheel is under a slip ratio of 2%. (Fitch,1994). This is done to accurately
compute the engine rpm.
As a positive drive is connected to the wheel through the engine the engine rpm is calculated by
multiplying the corresponding gear ratio by the wheel rpm. Therefore at t=0.01 seconds we know
117
the engine rpm and thus the effort and in this way the cycle goes on until the engine reaches its
maximum rpm.
After the engine has reached the maximum rpm, the driver changes gear (Only in this case, as the
max power occurs at max rpm). When the gear is changed the engine rpm drops and vehicle
velocity is unaffected. This is considered as the momentum of the vehicle is very large as
compared to the engine. The shifting time was considered to be 0.5 seconds. The engine rpm
drop is calculated from the Eq.(12) given below.
Rp2= (Gr2 / Gr1 ) x Rp1 (12)
Where, Rp1 and Rp2 are old and new engine rpm
Gr1 and Gr2 are old and new gear ratios (e.g Gr2 = second gear and Gr1 = first gear)
With the new engine rpm computed the cycle repeats until the next gear.
Parameter Value
Max Power 10 Hp @ 3600 rpm
Max torque 19.2 Nm @ 2700 rpm
Aerodynamic drag coefficient 0.75(Fitch, 1994)
Rolling resistance coefficient (dry earth road) 0.1 (Fitch, 1994)
Vehicle weight (GVW) 320 kg
Frontal Area 0.44 m2
The above parameters in Table (1) were used to simulate the vehicle performance for tyre sizes
of 23” and 25” diameter and different stock gear boxes. It should be noted that increase in inertia
of the rotating parts was converted into equivalent weight and was added to the gvw to simulate
increase in rotational inertia.
The results of the simulation are compiled in the table (2) below
The Mahindra Alfa gear box with 23” tyre diameter proves to be the optimum choice. It is seen
that the Mahindra Alfa gear ratios match the engine requirements as the rpm drops fairly near the
maximum torque range. Also the overall rotational inertia of the 23” tyre and the gearbox is less
due to which vehicle acceleration is higher. The above simulation is done for a dry earth road.
118
Simulating on concrete or asphalt gives improved times as the rolling resistance is decreased and
initial slip is eliminated.
The simulation for different gradients was done by finding a polynomial equation of the grade
with respect to distance travelled. This helped in finding the optimum gear ratio for different
grades.
The modelling results were successfully implemented on the vehicle and the vehicle was
tested for it’s acceleration and top speed.
Figure 9 - South Afirca car during testing Figure 8 - India car during testing
The above table gives the timing actually tested on Vbox(GPS) and the theoretical timing from
the modelling in the brackets. The modelling time and tested time is well within agreement.
119
6. CONCLUSION
Based on the field tests that were conducted with the Vbox test facility it can be concluded that
the proposed model and proposed model input parameters provide results that are consistent with
field observations, presenting errors less than 10%.
As in any research effort, further investigations are required to better establish the accuracy of
the proposed models. These investigations will include:
1) Develop simple linear dynamic model of the wheel slip during initial acceleration.
2) Dynamic model of the engine and clutch during powershifting.
ACKNOWLEDGEMENTS
We would like to thank Dr. A.D. Sahasrabudhe, Dr. B. B. Ahuja, Dr. D. W. Pande, Dr. S.
N. Sapali and members of Team Nemesis Racing for their immense support to all our endeavors.
REFERENCES
3. SAE Procedure J2188 (1996), Commercial truck and bus SAE recommended procedure
for vehicle performance prediction and charting, Society of Automotive Engineers,
Warren dale, PA.
120
SUB-THEME 6
Fatigue and Fracture
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O1
ICAME2013 S6/O2
ABSTRACT
Crack path propagation in plate structure depends upon crack length, crack inclination angle to load
applied, load applied, biaxiality factor, and thickness. Crack propagation includes parameters such as stress
intensity factor, crack opening angle and plastic zone size. In this paper we have discussed the effect of crack
inclination angle to load applied, biaxiality factor and thickness on stress intensity factor, crack opening angle.
We have considered plate with crack at center and inclination of crack with x-axis. We are using finite
element method with ANSYS software where displacement extrapolation method is used for finding stress
intensity factor. Finite element results are in well agreement with analytical result. Opening stress intensity
factor (KI) reduces with increasing inclination of crack and for biaxiality factor 1 KI is higher and constant.
Sliding stress intensity factor (KII) is higher for biaxial factor -1. It increases for crack inclination 0 to 45 and
then reduces up to 90 degree, for all biaxial factors. With increase in thickness KI and KII reduces.
The plate structure is general element used in industry and locomotives . It takes different loding with
presence of some flaws, inclined crack and loading on different axis due to which mixed modes of fracture
can be seen. Crack path propagation depends upon crack length, crack inclination angle to load applied, load
applied,biaxiality factor and thickness.Crack propagation includes parameters such as stress intensity factor,
crack opening angle and plastic zone size.
V.N. Shlyannikov discussed about modeling of crack growth trajectories for the inclined through thickness
central cracks and the part-through surface flaw. He found that the crack paths strongly depend on mode
mixity, nominal stress biaxiality, initial flaw configuration and material properties. Gdoutos and
Papakaliatakis have investigated the influence of load biaxiality on the stress field and fracture behavior of
cracked plate.Theocaris and Papadopoulos studied initially inclined crack and its propagation. They found
there is great importance of loading angle and biaxiality factor. In general the influence of biaxiality factor is
always stronger than angle of inclination of crack. P. C. Gope et al studied the crack initiation angle under
biaxial loading by finite element method. They use higher order four node quadrilateral element for analysis
of stress. They give large literature survey for use of finite element method for analysis of crack problem. The
optimum size of element is about 0.005 times crack length near crack tip which gives error within 1%.
A rectangular plate of size 200 mm ×200 mm with varying thickness and inclined crack to x- axis is
considered for 2- dimensional analysis.the material properties of C35 are used for this analysis, younds
modulous (E) is 2.06 × 105 N/mm and poissons ratio(ν) is 0.3. The biaxiality factor is the ratio of load appled
in x-direction to load applaed in y-direction.
σx
2W
σy
2a
2W
2a= crack length =20mm
β = angle of inclination with x- axis.
σx= load applied din x-direction, σy= load applied in y- direction.
B= biaxiality factor =
We considered biaxiality factors are 1, 0.5, 0, -0.5and -1 also the angle of inclination from 0 to 90
degree with difference of 10 degree. For study of effect of thickness we use 10 degree inclination of crack to
x-axis and thickness from 1mm to 6 mm with increment of 1mm. For study of crack initiation we use Strain
Energy Density’ (SED) theory [4] for angle of inclination 10, 20, 30 degree with biaxiality factor zero.
We can use shell93 or solid 83- four node quadrilateral elemement for stress analysis in ANSYS
software. Shell 93 element allwos addition of thichness so we used same for all models.
In ANSYS stress intensity factor can be calculated in three steps:
I. First make the model with specific crack point and loading arrangement:
In ANSYS we can solve full model and if symmetrical crack are there then half model also. Stress and
deformation fields around the crack tip generally have high gradients. The precise nature of these fields
depends on the material, geometry, and other factors. To capture the rapidly varying stress and
deformation fields, use a refined mesh in the region around the crack tip. The stresses and strains are
singular at the crack tip, varying as 1 ⁄ (√r). To produce this singularity in stresses and strains, the crack
tip mesh should have certain characteristics:
The crack faces should be coincident.
The elements around the crack tip should be quadratic, with the midsize nodes placed at the
quarter points.
II. Solve this model for stress and displacement of each node.
III. Calculation of stress intensity factor :
To calculate stress-intensity factors using the displacement extrapolation method, follow these steps
within the POST- postprocessor:
Step 1: Define a Local Crack-Tip or Crack-Front Coordinate System
Step 2: Define a Path along the Crack Face: for half crack model define 3 nodes, at crack opening and
one crack face. For full crack model define 5 nodes, at crack opening and upper and lower face of
crack
Step 3: Calculate KI and KII: KCALC is used for calculation of stress intensity factor. We have to
provide the problem is in plane stress or in plane strain. Here ‘displacement extrapolation method’ is
used for stress intensity factor.
error(%)ki error(%)kii
0 0
0 50 100 0 50 100
-1 -0.2 -1
-0.2
-0.5 -0.4 -0.5
%
%
-0.4 0 0
-0.6
0.5 0.5
-0.6 -0.8
ANGLE Angle
Graph 1 Graph 2
3.1 Biaxiality factor = zero:
At 0 degree inclination of crack KI is higher and KII is zero. And at 90 degree inclination of crack both KI
and KII is zero.KI reduces with increase in angle of inclination of crack while KII is increases up to 45 degree
and then reduces.KII is symmetrical curve about 45 degree. KI is more than KII i.e. opening mode dominates
up to 45 degree after this sliding mode of fracture dominates. (graph3)
The KI is reducing as angle of inclination changes from 0 to 90 degree. The KII is having symmetrical curve
about 45 0 of inclination. In this case opening mode always dominates sliding mode of fracture. (graph4)
Graph 3 Graph 4
BF= -0.5 BF= -1
600 600
400 400
SIF
SIF
200 ki 200 ki
0 0
kii kii
0 10 20 30 40 45 50 60 70 80 90 0 10 20 30 40 45 50 60 70 80 90
ANGLE ANGLE
Graph 5 Graph 6
Graph 7 Graph 8
Both curves of K and KII are symmetrical about 45 degree inclination of crack. At 0 and 90 degree KI
is maximum& KII is zero. At 45 degree KII is maximum and equal to KI at 0. Opening mode of fracture
dominates from 0 to 22.5 degree and 77.5 to 90degree.between 22.5 to 77.5sliding mode dominate. At 45
degree load in y-direction and x-direction are same but one is tensile and other is compressive so that pure
shearing occurs i.e. only sliding mode of fracture is present (graph 6)
Stress intensity factor for mode I (KI) is constant for all angles for biaxiality factor 1 and is always higher for
all angles for biaxiality factor -1,-0.5,0 and0.5. KI decreases from biaxiality factor 1 to -1 in the range of 0 to
45 degree inclination of crack then for biaxiality factor -0.5 and -1 it increases. (Graph 7)
Sliding mode is not avilable at biaxial factor 1.for all angles Stress intensity factor for mode II (KII) reduces
from -1 to1 biaxial factor and is symmetrical about 45 degree inclination of crack. At 45 degree inclination of
crack KII is high because of tension-compression lading and pure shearing takes place at axis of crack.(graph
8).
With avilable values of stess intensity factor of opening and sliding mode we calcutate the crack
initiaon angle for biaxiality factor zero. We use formulae for SED criteria given by Gope[4]
500
400
300
SIF
200 KI
100 KII
0
1 2 3 4 5 6
TICKNESS (mm)
Graph 9
4. CONCLUSION
Accuracy of Stress intensity factor by ANSYS depends on size of element and type. As error is below 1%
results by ANSYS are acceptable.
Stress intensity factor for opening mode is higher at biaxial factor 1 and for sliding mode at biaxiality
factor -1.
For positive biaxiality factor KI is reducing with increase in inclination of angle. For negative biaxiality
factor KI reduces up to some inclination then again increases.
KII increases for all angle from biaxiality factor 1 to -1
Crack initiation angles by SDE criteria up to 300 are matching with values given by Gope[4]
With increase in thickness KI and KII reduces.
5. REFERENCES
1. E.E.Gdoutos and G.Papakali-Atkis “The Effect of Load Biaxiality on Crack Growth in Non- Linear
Material” Theoretical and Applied Fracture Mechanics 5 (1986)133-140.
2. P.S. Theocaris And G. A. Papado-Poulos “Crack-Propagation Trajectories Under Biaxial Loading,
Based On Fracture Criteria”, Department Of Theoretical And Applied Mechanics, The National
Technical University Of Athens, 5, Heroes Of Polytechnion Avenue, Gr157- 73 Athens, Greece.
3. Ngo Huong Nhu and Nguyen Truong Giang,”Calculation of Fracture Mechanic Parameter via Fem for
Some Cracked Plates Under Different Loads.” Vietnam Journal of Mechanics, Vast, Vol.28, No.2
(2006) 83-93.
4. P.C.Gope,S.P.Sharma And A.K.Srivastava,” Prediction Of Crack Initiation Direction For Inclined
Crack Under Biaxial Loading By Finite Element Method”, Journal Of Solid Mechanics
Vol.2no.3(2010)257-266
5. Elements of Fracture Mechanics by Prashant Kumar.
6. Ansys Mechanical APDL Structural Analysis Guide, Release13.0, Nov.2010
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O3
Not Received
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O4
ABSTRACT
This paper drive a methodology for the study of thermal stress intensity factor in a thermal barrier
coated plate. The energy release criteria is used for calculation of SIF and the history of stress intensity factor
of the cracked body for different crack lengths. This can be obtained by a closed-form integration of the stress
field, using Duhamel’s theory with the principle of superposition for boundary conditions and appropriate
weight functions. The obtained results are compared with numerical simulations performed with ABAQUS,
both mathematical method and FEM method give the same results. In this paper the stainless steel AISI 304L
is taken as a base or substrate metal with a crack in the middle of the plate and coating is done on the plate.
Keywords: Stress intensity factor, temperature, thermal stress, thermal barrier coating.
1. INTRODUCTION
Thermal barrier coatings (TBC) are highly advanced material systems usually applied to protect turbine blades
from the high temperature of the process gas inside a turbine.The most commonly used TBC materials for
turbine engines are oxide ceramics, specifically yttria-stabilized zirconia (YSZ). However, other materials
can and have been used for thermal barrier coatings, even metal alloys. Usually, two coats are done one is top
coat for providing thermal resistance whose thermal conductivity is very low and the second one is bond coat
on the substrate which has high corrosive and wear resistant to prevent from corrosion and oxidation. A very
thick layer is form between top coat and bond coat due to oxidation called thermally grown oxide (TGO)
layer. The substrate, usually a stainless steel AISI 304L, is first coated with a bond coat that improves
adhesion of the ceramic top coat and that also serves as oxidation and corrosion protection layer. Oxidation of
the bond coat leads to the formation of a thermally grown oxide layer (TGO) between the bond coat and the
top coat (Baker, 2012).
Experimentally, it is known that these layers fail by spallation due to a complex interplay of
microcrack formation driven by thermal stresses and oxide growth (Stöver et al.,1999), (Trunova et al., 2008).
The reliability and durability problems of the coating/substrate systems are arisen largely from high thermal
and residual stresses and poor bonding strengths of the interfaces between coating and substrate (Wang et al.,
2010).Experiments were conducted to determine the thermal shock resistance of thermal coatings (Chen et al.,
2011), (Chen et al., 2010). A computational fatigue analysis was made for cyclic thermal shock in notched
specimens (Wang et al., 2007). Thermal cycling test has been conducted for the thermal shock resistance
prediction and adhesion strength analysis of coating/substrate system (Chen et al., 2003). Cracking behavior
in a thermal barrier coating upon thermal shock loading was numerically analyzed (Zhou et al., 2002).
Theoretical predictions and experimental observations suggested that multiple cracks may develop in any
homogeneous or nonhomogeneous material systems subjected to rapid temperature changes (Wang et al.,
2010).
Calculating the service- life of the structure often involves an analysis of fatigue crack growth and requires
accurate stress intensity factor (SIF) solution to predict both the crack propagation rate and the fracture
strength of the crack body. When a structure is subjected to thermal transient load, the corresponding SIFs can
be efficiently found out with the help of weighted function method (WFM). The weighted function separates
the influences of geometry and loading. Once the Weighted function for the geometry is known, the SIFs for
the other loading cases can be easily determined (Lee et al., 1999).The computation of SIFs of ceramics
coated cracked body subjected to a thermal transient loading by the finite element method requires step-by-
step computation for the entire time range, and the procedure should be repeated for such step of the crack
growth (Lee et al., 1999).
In this paper, an energy release criterion is used for calculation of SIF and the history of stress intensity factor
of the cracked body for different crack lengths. This can be obtained by a closed-form integration of the stress
field, using Duhamel’s theory with the principle of superposition for boundary conditions and appropriate
weight functions. The obtained results are compared with numerical simulations performed with ABAQUS,
both mathematical method and FEM method give the same results. Weighed function approach is used for the
analysis of crack propagation has been presented under thermal transient loading.
For the study of failure mechanism of thermal barrier ceramic coating system, operating at a high temperature
co-ordinate condition the physical map of temperature field related thermal stress field should be the
concerned. Generally, models should be three dimensional but for simplicity two dimensional models are
considered.
Plate
Bond coat
TGO
Top
C coat
o
n
v Y
e Convection
c X
ti
o
n
3. TEMPERATURE FIELD
Here we first determine the temperatures at the interfaces between layers and represent intra-layer
temperatures by those interface temperatures without solving an eigenvalue problem. Further an asymptotic
temperature solution for small times is obtained.In this paper Taylor Transformation is used to solve
differential equation to find the time dependent temperature field.
In determining the temperature field following assumptions are taken:
Energy is generated in layers (i=1,2….M) at rate of gi (x,t) which may be induced by plastic
work. where M=4 for interested problem as schemed inFig. 1.
Thermal deformation is infinitesimal so that the temperature distribution can be solved based on
initial configuration rather than on deformed ones.
Continuity of heat flux is across the interface and contact conduction hi at interfaces x=xi (i=1,
2…. M) exist.
Governing equation: One dimensional heat conduction equation for transient temperature field Ti (x,t) in
layers (here each layer is assumed as homogeneous layer) (i=1,2......M) is given by
k (T ) + g (x, t) = ρ c x < <x (1)
Equation (1) is subjected to boundary conditions
Equation (2) and equation (5) present heat supply or loss with convection from outer boundary surface x=xm+1
in temperature fM+1(t) and inner boundary surface x=xi in temperature fi(t) with heat transfer co-efficient hM+1
and h i respectively.
Here all the parameter such as thermal conductivity mass density and specific heat are temperature dependent
on other hand thermal conductivity is more temperature dependent parameter than other physical parameter.
In order to consider the effect of temperature dependent data we have to require using of a transformation
method.
Taylor Transformation θ (x, t) = ( ) ∫ k () d (7)
where T0 is room temperature.
By using Taylor Transformation we can modify all above temperature field governing equations from (1) to
(6) are
ρ (T )c (T ) = k (T ) + g (x, t) (8)
( )
= α (T ) + ( )
g (x, t) (9)
Equation (9) subject to boundary condition with modify form
In outer most layer due to conduction and convection
−k (T ) + h (T )θ = h (T ) f (t) (10)
At the interface between to layer
−k (T ) = h (θ − θ ) (i=1, 2.....M-1) (11)
( )
ϑ (x, t) = ∑ ∫ G {x , t, , τ} ϑ ()d + ∫ ∂τ ∫ G {x , t, , τ} ( )
g (, t) d (16)
By putting boundary condition in equation (14) and after solving it the temperature field is given by new form
of equation.
T(x, τ) = ∑ exp + ∫ exp [T (τ ) − (−1) T (τ ) dτ ]
0< x < hi (17)
Equation (17) of the temperature field cannot be used in equation (13) to determine the unknowns Tm(t)as the
right hand side series does not converge uniformly in the interval considered. Thus the following alternative
form for the temperature is used:
∗ ∗ ∗
sin nπx ∗
T(x , τ) = (1 − x )T (τ) + x T (τ) − 2 T (τ) − β exp −β (τ − τ )T (τ ) dτ
nπ
∗
+2 ∑ (−1) T (τ) − β ∫ exp −β (τ − τ )T (τ ) dτ (18)
4. THERMAL STRESS:
The temperature and mechanics analyses are uncoupled in this work, i.e. the temperature analysis is
performed first, and the stress analysis is conducted afterwards. In the present study of thermal stresses, the
TBCs layers and TSIFs at the tip of an edge crack shown in Fig. 1, a special kind of TBCs is considered in
which the Young’s modulus and Poisson’s ratio are constant. This assumption will limit the applications of
the present analysis, however, there do exist some TBCs systems, especially ceramic/ceramic TBCs, for
which Young’s modulus may be approximately assumed as constant. The ad-vantage of assuming a
constant Young’s modulus is that the crack analysis is simplified.
The TBCs layers are assumed to undergo plane strain deformations and are free from constraints at the far
away ends as shown in Fig. 1. The only nonzero in-plane stress YYis given by
−Eα(x)
σ (x, τ) = T(x, τ)
1−ϑ
+( (A − xA ) ∫ T(x , τ)dx − (A − xA ) ∫ T(x , τ)dx (19)
)
where Aij and A0 is given by
=∫ ( )
=( )
= =∫ ( )
= ( )
=∫ ( )
= ( )
= −
By substituting the temperature solution in equation (19) we obtain the normalized thermal Stress in the TBCs
layer
( , )=
( )
( , )+ 4−6 ∑ ( ) −
( )
− 6 − 12 ∑ ( )+ ( )
(20)
wherei (i=1,2......M) are the coefficients of thermal expansion in the ith layer and Hn1(t) and Hn2(t) are
= ∫ ( ∗, ) ∗ = ∫ ( ∗, ) ∗ ∗
The failure of cracked components is governed by the stresses in the vicinity of the crack tip. The singular
stress contribution is characterized by the stress intensity factor. Stress intensity factor depends on the
boundary conditions (thermal, bending, torsion) and geometry of the components. The procedure for their
determination is the weight function technique where the weight functions are only depends on the crack
geometry.
The unique feature of weight function is that, once the weight function of a particular cracked body is
determined, the stress Intensity factor for any loading system applied to that body can be calculated. The
stress intensity factor for the applied temperature dependent loading can be calculated by the integral of
multiplication of thermal stresses and weight function and is given by:
SIF = K (t) = ∫ m(x, a) σ (x, t) (21)
Where σyy(x, t) is the calculated thermal stress which is induced due to temperature dependent boundary
conditions and m(x, a) is weight function and is given by
( )
m(x, a) = (22)
Where u is the crack opening displacement and is given by
u(x) = √a − x D whereD = 1.452 − 0.72 + 0.618 − 0.24
(23)
4σ
u(0) = (1.452a)
E
5.83
u(0) = (σa)
E
.
and m(x, a) = σ (24)
By substituting the value of weight function we get:
.
m(x, a) = (25)
.
finally K =∫ σ (x, t) dx (26)
350
Temperature (°C))
300
250
200
150
0 20 40 60 80 100
time (sec)
Fig. 2.Temperature evolutions in the specimen when convective medium of cyclic temperature is applied
with T i=350 oC
Heat flow within the solid induces the cyclic temperature and cyclic stresses. The cyclic stresses calculation is
done in third chapter and from equation (20) the induced stresses are shown in Fig. 3 at the edge and at heart
respectively. The delay in the stresses is due to the conduction phenomena.
200
Fig. 3 Stresses induced of cracked Body submitted to sinusoidal Fluctuation of temperature at x=0 and x=L
2.0
3
1.5
2 1.0
1 0.5
0.0
SIF
0 -0.5
SIF
-1 -1.0
-1.5
-2 -2.0
-3 0 20 40 60 80 100
0 20 40 60 80 100
time (sec) Time (sec)
Fig. 5 SIF in TBCs coated cracked plate Fig. 6 SIF when thickness is increase of TBCs
With the increase in thickness, the SIF value becomes less due to further decrease in conductivity.
7. CONCLUSIONS
A multi-layered material model is employed to solve the temperature field in a layer of a Thermal barrier
ceramic material subjected to transient thermal loading conditions. The TBCs is assumed to have constant
Young’s modulus and Poisson’s ratio, but the thermal properties of the material vary along the thickness
direction of the strip.SIF decrease with an increase thickness of TBCs up to an optimum value.The obtained
results are compared with numerical simulations performed with ABAQUS, both mathematical method and
FEM method give the same results.
REFERENCES
1. Baker M., “Finite Element Simulation of Interface Cracks in Thermal Barrier Coatings” Comput.
Mater. Sci. (2012)
2. Chen, Z.B., Wang, Z.G. and Zhu, S.J., “Tensile Fracture Behavior of Thermal Barrier Coatings on
Super Alloy.” Surf.Coat Technol.,. 205, pp. 3931–3938 (2011)
3. Chen X.L., Zhang Y.F., Zhong X.H., Xu Z.H., Zhang J.F., Cheng Y.L., Zhao Y., Liu Y.J., Fan X.Z.,
Ying Wang, Ma H.M. and Cao X.Q.,”Thermal Cycling Behaviors of the Plasma Sprayed Thermal
Barrier Coatings of Hexaluminates with Magnetoplumbite Structure.”J. Eur. Ceram. Soc., 30,
pp.1649–1657 (2010)
4. Chen H., Zeng Y. and Ding C.X., “Microstructural Characterization of Plasma-Sprayed
Nanostructured Zirconia Powders and Coatings” J. Eur. Ceram. Soc., 23, pp. 491–497(2003)
5. Chen H., Zeng Y. and Ding C.X., “Investigation of the Thermo-mechanical Properties of a
Plasma-Sprayed Nanostructured Zirconia Coating.”J. Eur. Ceram. Soc., 23, pp. 1449–1455 (2003)
6. Gong W.B., Sha C.K., Sun D.Q. and Wang W.Q., “Microstructures and Thermal Insulation Capability
of Plasma-Sprayed Nanostructured Ceria Stabilized Zirconia Coatings” Surf. Coat. Technol., 201, pp
3109–3115 (2006)
7. Lee H.Y., Kim J.B. and Yoo B., “Green's Function Approach for Crack Propagation Problem
Subjected to High Cycle Thermal Fatigue Loading” Int. J. Press. Ves.Pipin.,76, pp.487–494 (1999)
8. Lima R.S., Kucuk A. and Berndt C.C., “Bimodal Distribution of Mechanical Properties on Plasma
Sprayed Nanostructured Partially Stabilized Zirconia” Mater. Sci. Eng.-A, 327, pp. 224–232 (2002)
9. Lalit M. J., “Heat Conduction in Metals”
10. Stöver D. and Funke C.,“Directions of the Developments of Thermal Barrier Coatings in Energy
Applications.” J. Mater. Process.Technol., 92–93, pp.195-202 (1999)
11. Saeedi B., Sabour A. and Khoddami A.M., “Study of Microstructure and Thermal Shock Behavior of
Two Types of Thermal Barrier Coatings.” Mater.Corros.,60, pp.695–703 (2009)
12. Trunova O., Beck T., Herzog R., Steinbrech R.W. and Singheiser L., “Damage Mechanisms and
Lifetime Behavior of Plasma Sprayed Thermal Barrier Coating Systems for Gas Turbines—Part I:
Experiments.” Surf.Coat. Technol., 202, pp.5027–5032 (2008)
13. Wang N., Zhou C.G., Gong S.K., and Xu H.B., “Heat Treatment of Nanostructured Thermal Barrier
Coating” Ceram. Int., 33, pp. 1075–1081 (2007)
14. Wang B.L., Han J.C. and Du S. Y., “Thermal Shock Resistance Analysis Methodology of Ceramic
Coating/Metal Substrate Systems” Eng. Frac. Mech., 77, pp. 939-950 (2010)
15. Zhou Y.C., Tonomori T., Yoshida A. Liu L., Bignall G. and Hashida T., “Fracture Characteristics of
Thermal Barrier Coatings after Tensile and Bending Tests” Surf. Coat. Technol., 157, pp. 118–127
(2002)
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O5
ICAME2013 S6/O6
ABSTRACT
Sheet forming processes are among the most important processes in manufacturing. Particularly these
processes are important in the field of car body and auto components manufacturing, due to the fact that the
tools are very expensive and any failure or redesign procedure dramatically increases the price of the
products. Fracture phenomenon is one of the main obstacles affecting sheet metal forming as accurate
prediction of fracture initiation is difficult in the forming processes. In order to find out the fracture limits,
fracture test and finite-element (cohesive zone model) simulation tool are used. After successive experimental
attempts, ‘load drop technique’ is verified and used as a fracture criterion. Critical CTOD is used as a fracture
toughness parameter. An alternative constant traction separation law is used to account for maximum load and
large load line displacements. Experimental findings as well as CZM shows that the strain rate has no
significant effect on fracture toughness till the strain rate is 0.4 mm/min at room temperature; however, there
is a sharp decrease in fracture toughness beyond 0.4 mm/min. Thus, it is concluded that the forming of the
EDD steel sheet should be done at lower strain rates for high formability.
Keywords: EDD steel sheets, CZM, CTOD.
1. INTRODUCTION
Extra deep drawn (EDD) steel sheet is widely used in industrial applications. EDD steel has superior
formability and non–ageing characteristics. These steels are low carbon, Al–killed steels. Exterior
components such as car body, starter, end-covers, petrol tanks, etc. are made of EDD grade steel sheets. Apart
from automobile industries, the EDD steel sheets are extensively used in enameling applications such as bath
sink units, kitchenware, cooker, washing machine and refrigerator bodies, etc. Presently, EDD steel sheets are
characterized with the help of mechanical properties correlating to formability indices. The particular class of
mechanical components is manufactured using deep drawn (DD) or extra deep drawn (EDD) steel sheets and
by forming processes (like bending, stretching, drawing etc.). The efforts have been taken to predict accurate
fracture limits of sheet metals by using formability approach however even today the crack formation during
forming process is a challenging task. The phenomena of crack initiation and crack propagation are dealt
within the discipline of fracture mechanics. There is an increasing demand from industrial users for an
accurate assessment of crack initiation load and forming rate. Present study aims to study the effect of strain
rate on fracture toughness of EDD steel sheets using fracture mechanics approach to predict critical load
accurately which will be beneficial to both, sheet metal manufacturer and their industrial users (product
manufacturers).
2. EXPERIMENTAL PROCEDURE
Earlier research work published by Kulkarni et al (2008) and Chaudhari et al (2009, 2010 and 2011) shows
the experimental procedure involved in the testing of EDD steel sheets using compact tension (CT) type
specimens. The dimensions of the CT specimens used in the present work are chosen from the recommended
design standard given in ASTM E1820 (2011). Specimens were fabricated by the wire electric discharge
machine to maintain the exact relationship among all the dimensions. The configuration of the test specimen
is shown in Fig. 1 (Specimen dimensions are W = 24 mm, a0 = 10.5 mm, B = 1.4 mm and = 0.125 mm).
Eight specimens were tested at different strain rates (i.e. 0.1, 0.2, 0.3, 0.4, 0.6, 1.0, 1.5 and 2.5 mm/min.). The
chemical composition of the investigated EDD steel is given in Table 1.
For mechanical properties of material, tensile tests are carried out using specimens machined as per ASTM
standard E8M (2011). The specimens are tested along three directions, with the tensile axis being parallel (0 o),
diagonal (45 o) and perpendicular (90o) to the rolling direction of the sheet on 100 kN capacity Universal
Testing Machine. The value of E and YS are obtained as 210 GPa and 245.05 MPa, respectively. The fracture
tests were carried out at the room temperature (300 K) using a Universal Testing Machine with a loading rate
corresponding to the different cross head displacement (i.e. 0.1, 0.2, 0.3, 0.4, 0.6, 1.0, 1.5 and 2.5 mm/min.).
CMOD gauge is used to measure load–line displacement. Anti-buckling fixtures are used to avoid out-of-
plane buckling. The experimental set up is shown in Fig. 2. During such tests, the magnitude of load (P) and
load–line displacement (Vll) were recorded together with time. The ‘load drop technique’, mentioned by Ray
et al (2010) and Kulkarni et al (2008) is used as a fracture criterion to measure fracture parameters. According
to this criterion, the load drops at a particular instant when crack is initiated. This load is considered as a
critical load (Pc). At that instance of time, the loading of a specimen is discontinued and the specimen is taken
out for subsequent measurement of CTOD. As the plastic load-line displacement is high in case of EDD steel
sheets, crack flank opening angle (CFOA) method proposed by Chaudhari et al (2011) is used to find plastic
CTOD, in addition to existing plastic hinge model (PHM) and FE analysis.
Cohesive zone model is formulated with the help of finite element analysis software ABAQUS 6.7 to verify
experimental results. The fracture model (CZM) for the compact tension (CT) specimen is used to study the
effect of the type of softening (i.e. linear, exponential and constant traction) on the load versus load line
displacement response. This model includes mesh, boundary conditions and special features such as the
cohesive elements on the expected crack path (Fig. 3) and a nonlinear step definition to solve the nonlinear
fracture problem. As shown in Fig. 3, the CT specimen model has a bulk section made with two dimensional
plain stress elements (CPS4R) defined by its elastic–plastic properties (2916 nodes and 2704 four nodded
quadrilateral continuum elements). The crack path is modeled using cohesive elements (COH2D4) defined by
a traction-separation law (272 nodes and 135 cohesive elements). Cohesive elements are taken to be square of
side 0.1 mm. Plane stress elements around cohesive zone are taken to be squares of side 0.5 mm. A true stress-
strain curve up to breaking-strain point is used with multi-linear isotropic hardening to incorporate non-linear
material properties. The loading pins are modeled as rigid pins to avoid any severe local deformation at the
contact points. The contact between loading pins and plane stress elements is considered smooth.
The ‘load drop technique’, mentioned by Ray (2010), Kulkarni (2008) is used as a fracture criterion to
measure the fracture parameters. Fig. 4 shows the crack profile for the specimens unloaded just before the
load drop point and at the load drop point. It is verified from Fig. 4 that the crack is initiated only at load drop
point.
Fig. 4Crack profile on surface of a specimen unloaded before and at the load drop point
Specimen S1 was first analyzed. The commonly adopted approach assumes certain law of the traction–
separation relation for the cohesive zone and the cohesive parameters are treated as modeling constants which
are determined by fitting the CZM simulation results to a set of experimental data. The key features of a
cohesive zone model include the shape of the traction-separation curve and the value of the cohesive
parameters. Fig. 5 shows the representative cohesive law shapes. Among the various forms of cohesive laws,
there is one common feature, i.e. the magnitude of the cohesive traction usually increases with accrued
separation between the cohesive surfaces, and after a critical peak value is reached, the traction drops towards
zero with further separation. For the ductile materials literature suggests [e.g., Jadhav and Maiti (2010),
Scheider and Brocks (2006, 2003a)] use of exponential or constant variation of normal traction with the
relative normal displacement.
In the present case, the material used is high ductile material with load maxima is fracture criteria. The
constant traction law is chosen with δ2= δf(Fig. 5 (d)). The analysis is done using linear, exponential and
proposed constant traction law and results are compared with the experimental load vs. load line displacement
curve (Fig 6).
1.2
0.6 EXPT
CZM (Traction seperation law)
0.4
Proposed
0.2 Linear
Exponential
0
0 0.5 1 1.5 2 2.5 3 3.5 4
LLD (mm)
Fig. 6 Comparison of load–LLD curves based on three cohesive laws with experimental data.
From Fig. 6 it is observed that linear traction separation law (Fig. 5 (a)) underestimates the maximum load and
it is suitable for brittle material/ linear elastic analysis. Exponential law (Fig. 5 (b)) is used for ductile
materials but in present case it underestimates load line displacement. For example experimentally the
maximum load observed at 3.59 mm load line displacement where as exponential law gives maximum load at
2.9 mm. The results from proposed constant traction separation law are found to be close to the experimental
observations; the maximum load is over–estimated only by 2.66% and corresponding J value at crack
initiation i.e. Ji, based on load vs LLD is 3.85% more than experimental value. Thus the proposed constant
traction- separation law is considered for the further study.
The remaining specimens i.e. S2 – S8 were studied using proposed constant traction separation law and 0.5
mm element size. The percentage difference between peak load from experimental data and peak load
calculated from CZM is found to be within 4%, thus the values of peak loads calculated from CZM are
acceptable. The percentage difference between Ji from experimental data and J i calculated from CZM for all
cases is found to be within 5%, thus the values of Ji calculated from CZM are acceptable.
The results on critical CTOD for different strain rates are presented in Fig. 7. It shows the variation of critical
CTOD with strain rate (0.1- 2.5 mm/ min.). It is observed that the fracture toughness is almost constant up to
the strain rate 0.4 mm/ min. Furthermore it is observed that there is a sharp decrease in fracture toughness
with increase in strain rate beyond 0.4 mm/min.
1.6
1.4 CZM
PHM
1.3
1.2
1.1
1.0
0 0.5 1 1.5 2 2.5 3
The reason may be same as in case of strain rate effects on strength and ductility. According to Heet al (2012),
Verleysen et al (2011) as strain rate increases, the tensile strength of steel and other alloys increases, however,
the ductility values tend to diminish. With high strain rate, plastic deformation becomes a difficult process, as
dislocation motion is restricted. Dislocation movements through crystal lattice involve atomic diffusion and
displacements under the applied stress. When the strain rate increases, the atomic diffusion vis-à-vis the
dislocations motion becomes difficult because of short duration. In other words, process of deformation
becomes limited resulting in reduced plasticity and toughness. Therefore, it is concluded that for higher
formability, the forming of the EDD steel sheet should be done at lower strain rates. The strain rate 0.4
mm/min is found to be critical strain rate in case of EDD steel sheet. Beyond the critical strain rate, the results
found are not good for the forming operations.
5. CONCLUSIONS
In order to study effect of strain rate on fracture toughness of EDD steel sheets, fracture criterion (critical load
at which crack initiates) and critical CTOD (as fracture toughness parameter) are used. Cohesive zone models
are suitable tool for the characterization of fracture behaviour in the materials of interest. An alternative
constant traction separation law is used to account for maximum load and large load line displacements. The
results from proposed constant traction separation law are found to be close with the experimental findings.
Experimental findings as well as CZM shows that the strain rate has no significant effect on fracture
toughness till the strain rate is 0.4 mm/min at room temperature; however, there is a sharp decrease in fracture
toughness beyond 0.4 mm/min. This may be because of the dislocation motion restricted with high strain rate.
Therefore, in order to have high formability, the forming of the EDD steel sheets should be done at lower
strain rates.
REFERENCES
1 ASTM E1820-11: Standard test method for measurement of fracture toughness. American Society of
Testing and Materials, Philadelphia; (2011).
2 ASTM E8M-11: Standard test methods for tension testing of metallic materials. American Society of
Testing and Materials, Philadelphia; (2011).
3 Chaudhari V.V., Kulkarni D.M., Prakash R., “Determination of critical CTOD using crack flank
opening angle method in general yield regime”,FATIGUE FRACT ENG Mat. 34,260 (2011).
4 Chaudhari V.V., Kulkarni D.M., Prakash R., “Study of Influence of Notch Root Radius on Fracture
Behaviour of Extra Deep Drawn Steel Sheets”, FATIGUE FRACT ENG Mat. 32, 975 (2009).
5 Chaudhari V.V., Kulkarni D.M., Prakash R., “Three- dimensional finite element analysis of fracture
behavior in general yielding fracture mechanics”, J Mech Eng. Strojnίcky Casopis. 61(c. 3), 131
(2010).
6 He Z, He Y, Ling Y, Wu Q, Gao Y, Li L. Effect of strain rate on deformation behavior of TRIP steels.
J Mater Process Tech. 212, 2141 (2012).
7 Jadhav D.N., and Maiti S.K., “Characterization of stable crack growth through AISI 4340 steel using
cohesive zone modeling and CTOD/CTOA criterion”, Nucl Eng Des. 240, 713 (2010).
8 Kulkarni D.M., Chaudhari V.V., Prakash R., Kumar A.N., “Effect of thickness on fracture criterion in
general yielding fracture mechanics”, Int J Fracture. 151,187 (2008).
9 Ray K.K., Patra1 A., Bhattacharjee D. A., “New methodology for estimating fracture criterion of thin
sheets”, Key Eng Mat. 417, 305 (2010).
10 Scheider I., Schodel M., Brocks W., Schonfeld W., “Crack propagation analyses with CTOA and
cohesive model: Comparison and experimental validation”, Eng Frac Mech. 73, 252 (2006).
11 Scheider I., and Brocks W., “The effect of the traction separation law on the results of cohesive zone
crack propagation analyses”, Key Eng Mat. 313 (2003a).
12 Verleysen P., Peirs J., Slycken J.V., Faes K., Duchene L., “Effect of strain rate on the forming
behaviour of sheet metals”, J Mater Process Tech. 211, 1457 (2011).
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O7
P. K. Sarkar P. Kumar
Indian School of Mines, College of Engineering Pune
Dhanbad prkumar@iitk.ac.in
ABSTRACT
For the determination of fracture toughness, JIc (critical J-Integral) of thin aluminum alloy 6061-T6
plates, a single-edge notch tension (SENT) specimen with appropriate screw tabs was designed. An
experimental-cum-numerical methodology was developed in which the critical load was obtained from an
experiment, and the stress field in the specimen was determined, through a finite element analysis using
ANSYS or ABACUS, using non-linear elastic-plastic stress-strain curve of the specimen. The stress field
yielded critical J-integral (JIc).
The JIc of thin aluminum alloy 6061-T6 sheets of 1.0 mm and 1.6 mm thickness was determined in both
rolling and transverse direction. The JIc of 1.0 mm thick specimen was found to be 84.3 kJ/m2and 74 kJ/m2 in
rolling and transverse direction respectively, and for 1.6 mm thick specimen it was found to be 106.3
kJ/m2and 84.4 kJ/m2in rolling and transverse direction respectively. It was observed that the results of J-
integral obtained from ABAQUS and ANSYS analysis were consistent. The JIc was also found by Begley and
Landes approach and the results matched well with that of experimental- cum- numerical technique.
Keywords: Fracture toughness, J- Integral, thin plates, Aluminium alloy 6061-T6.
1. INTRODUCTION
The plastic zone size near the crack tip is large in thin plates with respect to thick plates. Hence, the fracture
toughness; critical J-Integral (JIc) of thin sheets in Mode I is substantially higher than the corresponding plane
strain toughness of thick sheets and, therefore, its value is more relevant for many applications. However, it is
difficult to determine the thin sheet fracture toughness as their specimen tends to buckle. Extensive
applications of fracture mechanics methods via fracture toughness in structural integrity and assessment are
documented in a set of eleven-volume comprehensive books compiled by Milne et al, 2007. Begley and
Landes, 1972 were among the pioneers who first successfully measured the J- integral and its critical value JIc
at the crack initiation. Extensive experimental investigations on the J-Integral testing were conducted with a
target to develop effective test methods for evaluating the critical J-integral (JIc) for plane strain opening
cracks of thick specimen, where the applied fracture work is predominantly in mode- I loading and elastic-
plastic conditions (Xian et. al, 2012). Schwalbe et al, 2007 presented an updating review of classic fracture
mechanics methods involving fracture test techniques and experimental analysis.
Evaluation of plane strain fracture toughness is well developed and standardized as per ASTM E1823-10a,
2011. In recent years, efforts are on to develop effective test methods for determination of plane stress fracture
toughness. Several studies have been made on double edge notched tensile (DENT) specimen to determine
fracture toughness of thin plates. Paradon et al,1999 and Paradon et al.,2002conducted some experiments to
study the effect of thickness on the critical values of J integral (Jc) and crack tip opening displacement, CTOD
(δc) of aluminium thin plates of 1-6 mm thickness using double edge notched tension (DENT) specimens.
Their research showed that with increase in thickness, Jc and δc increases linearly for thinner specimens and
nonlinearly for larger thicknesses. They attended almost same results by testing sixteen different alloys of
aluminium, brass, stainless steel, bronze, Zinc and lead (Paradon et al,2004). In a DENT specimens used by
several investigators, the tensile load in the un-cracked ligament is high. It tends to make the specimen fail in
localised yielding and thus stress concentration due to the crack tip is subdued which leads to necking
formation at crack tip, making it difficult to isolate the fracture toughness from such a test. Over the years, J-
integral is also determined using a compact tension (CT) specimen applying combined bending and tension
load (Kaiser, 1985 and Sonnerlind et al, 1986). If a compact tension specimen is employed, guide plates, one
on the side of each face of the specimen, are required to avoid buckling of the thin specimen (Shahani et al,
2010). This makes the technique cumbersome and there is always a doubt on the role of friction between
guides and the specimen. A study was conducted by Kuang et al, 1996 to characterize J-integral within the
plastic zone for different strain hardening materials of 7075-T651 aluminium alloy and HY 130 steel.
The aim of the present study was to develop a simple and effective experimental-cum-numerical technique to
determine the fracture toughness (i.e critical J-Integral (JIc)) of thin metallic sheets. A single-edge crack
tension (SENT) specimen with appropriate screw taps as load fixture was designed and developed to avoid the
yielding of the specimen at the load point during the loading. In this experimental-cum-numerical technique,
the critical load was obtained from experiment. The numerical analysis determined the stress field in the
specimen by employing the nonlinear stress-strain behavior of monotonic loading of the specimen material.
This stress field was used to determine critical J-Integral. The fracture toughness obtained by experimental-
cum-numerical technique was further compared with the results obtained through Begley and Landes
approach.
2. SPECIMEN
Thin sheet of thickness ranging from 0.7 to 2.0 mm is extensively used vehicle construction material. This
investigation is focused on evaluating J-Integral (Jc) of thin plates made up of aluminum alloy 6061-T6; which
is a solutionized and artificially aged aluminium alloy. Specimens were prepared both in rolling direction and
transverse direction of sheet. The specimen plates of 1.0 mm and 1.6 mm thickness were chosen, which were
purchased from two different sources. Stress-strain relations of these sheets were determined as per ASTM-
E8, 2008 using a 100 KN Universal Testing Machine with a cross-head speed of 0.1 mm/min. The material
behavior was found to follow Ramberg-Osgood relation.
= + α (1)
where α is a coefficient and n is an exponent of the power hardening material, σo and εo are the flow stress and
flow strain, respectively. α and n are found by fitting the curve of the Ramberg-Osgood equation on the
original stress-strain curve (pendola et al, 2000) and they are listed in Table 1 along with other experimentally
obtained material properties.
Table 1: Mechanical properties of aluminum alloy 6061-T6 specimens tested as per ASTM-E8
Sheet thickness Modulus Yield stress Ultimate strength
(mm) (GPa) (MPa) (MPa) n α
1.6 69.8 ± 1.5 277.6 ± 8.3 319.8 ± 16.2 22 0.223 x 10 -3
1.0 70.4 ± 1.5 267 ± 5.3 294.9 ± 2 32 0.524
While designing the specimen of the thin aluminum alloy sheets, an approximate estimation was made. The
plastic zone size (rp) was estimated using the following Irwin’s formula (Kumar P, 2009) for plane stress:
rp= (2)
whereK is the critical stress intensity factor and σ is the yield stress. When available value of toughness of
aluminum alloy is used for plane stain as K = 25 Mpa√m, rp was found to be 2.6 mm. The actual plastic zone
size was much larger as the toughness of the thin sheets, determined through this investigation, was found to
be much greater than plane strain toughness. Thus the specimens of this study were definitely loaded in plane
stress.
A SENT specimen was designed and developed to enhance the stress field near the crack tip and thus, it
increased the chances of failure through fracture growth. Figure 1 presents the geometry of the specimen. The
specimens of size 220 mm × 60 mm, were cut on a conventional milling machine. The length of specimen was
chosen to be large so that the concentrated load at the load point developed uniform tensile stress at a
reasonable large distance from the crack plane. The tip of the crack, prepared through a wire - EDM machine,
was not sharp enough. It was required to be extended to obtain a sharp initial pre-crack. A suitable fixture was
developed to hold a fresh razor blade and apply a reasonable large force to extend the crack by about 2 mm.
The radius of curvature at crack tip was monitored through a shadow-graph (LEICA) and was found to be of
the order of 11µm. Pardoen et al, 1999 also used the similar technique to sharpen a crack. Four specimens
each were tested in both rolling and transverse direction.
3. EXPERIMENTAL-CUM NUMERICAL TECHNIQUE
The objective of this study was to develop a suitable experimental-cum-numerical methodology for the
determination of fracture toughness of aluminium alloy 6061-T6 made of thin sheet with thickness 1.0 mm
and 1.6 mm. In this technique the critical load was obtained from an experiment which was used as loading
boundary conditions to obtain the stress field in the specimen, through a finite element analysis using ANSYS
or ABACUS. Using the stress field, J-Integral (Jc) was determined. The non-linear elastic plastic stress-strain
relation of the specimen was used in the numerical analysis. However, only monotonically increasing loading
was considered to determine the stress field and then the J-Integral.
4. EXPERIMENTATION
Experimental tests were performed on the SENT specimens defined in Section 2, by pulling the specimen in a
10-ton Universal Testing Machine at the very slow speed of 0.1 mm/min, till the critical load at which crack
occurred. The specimen was loaded through pin joints at its ends. A suitable fork-specimen-holder were
designed to make sure that only tensile load passes through the specimen and no bending or twisting moment
were developed. To suppress plastic deformation around pin joint, screwed metal tabs of mild steel were used
on both faces of the specimen as shown in Figure 2. To measure the displacement accurately, a plunger type
dial gauge with least count of 10 µm was used. The displacement was measured over a gauge length of 90 mm
(Figure 1). A suitable fixture was designed to mount dial gauge on the surface of the specimen under loading.
The detection of crack initiation was done by closely monitoring the crack-tip with the help of magnifying
glass and simultaneously observing the run-time load-displacement curve. The critical load obtained from
experiments was used as loading boundary conditions in a nonlinear numerical analysis to obtain stress-strain
fields.
To compare the results of J-integral obtained from experimental-cum-numerical technique, Begley and
Landes, 1972 approach was used. To evaluate J-integral through this approach, load displacement curves were
generated experimentally for identical specimens with different initial crack lengths. The specimens with
crack lengths a= 27 mm, 30 mm and 33 mm were used in both rolling and transverse direction for
experimentation. For each specimen the energy was determined at four different displacements. Energy was
measured at the same four displacement values for each specimen to obtain the plot of energy verses crack
length curves. The slope of these curves provided J-integral at a constant displacement. JIc was determined for
the critical displacement.
5. NUMERICAL ANALYSIS
The stress field in the specimen was determined for the critical load obtained experimentally which was then
post processed to determine the critical J-integral. In this study, a two-dimensional, plane stress, numerical
analysis of the single-edge crack specimen was done using two software packages, ABAQUS 6.10 and
ANSYS 13.0, so as the results could be compared and validated. To validate the stress field determined by the
numerical analysis, the displacement at the 90 mm distance was found through both the ABAQUS 6.10 and
ANSYS 13.0 software. It was then compared with the displacement measured at 90 mm distance on dial
gauge during experimentation. The measured displacement was found to be matching with that of the
numerical prediction. Since thin plates were used in this study, a 2D plane stress model was analyzed using
these softwares. Due to symmetry of the specimen geometry and loading, only the top half of the specimen
was modeled. To obtain quality mesh, the geometry was partitioned into several areas. The complete model
was meshed with CPS8R elements in ABAQUS 6.10. CPS8R is an iso-parametric 8-noded biquadratic plane
stress quadrilateral element having two degrees of freedom at each node. To attain singularity at the crack tip
8-noded triangular quarter point elements were used. The use of quarter point elements in improving the
accuracy of the solution around the crack tip was suggested by Hensel and shaw25 and Barsoum26. The
meshing of the 2D FE model in ABAQUS is shown in Figure 3. The global element size of 1 mm was used to
mesh entire region. The elasto-plastic material properties for the specimen made of aluminium 6061-T6 were
used for the analysis in which elastic properties are E=70 GPa, ν=0.33. In ABAQUS analysis, a contact was
established between the rigid pin and the specimen by applying a small displacement (1x10-5mm) in the
vertical direction at the reference point (rigid body reference node) and then a concentrated force was applied
at that reference point.
In this study, numerical analysis was also done using ANSYS software to compare with the results obtained in
ABACUS. A 2D plane stress model was analyzed in ANSYS. For analyzing in ANSYS, PLANE 183 element
was used. It is an iso-parametric 8-noded quadrilateral element, having two degrees of freedom at each node.
A massless element, MASS21, was defined at the center of the pin. Because of the symmetry of the specimen
with respect to the crack plane, only half specimen was again modeled for the analysis. The crack-tip was
modeled using quarter-point element. The load on the specimen was applied on a mass-less element at the pin
center of the hole. The results obtained from the converged nonlinear analysis were used to calculate the
fracture parameter, J-Integral, by a subroutine written in ANSYS’s scripting language.
Figure 3: 2D Meshing of Specimen in ABAQUS
Four specimens each in rolling and transverse direction were tested for each thickness ‘B’ (1.0 mm and 1.6
mm). It was found that in the thin plate of aluminum alloy 6061-T6, significant plastic deformation took place
prior the crack growth at the region close to the crack-tip. A dimple was formed prior to the crack growth on
each face of the specimen. At the critical load the crack grew suddenly along one of the two edges of the
dimple, and the load on the specimen started dropping. The critical load at crack-initiation and the
corresponding displacement was noted down during experiment for each specimen. The critical load obtained
was used as loading boundary condition in a numerical analysis done with the help of ABACUS and ANSYS.
In ABAQUS, J-integral output was requested for 25 contours. The scatter in J-integral values over all the
requested contour paths was found to be 1.57%. Since this scatter is very small, the J-integral was found to be
path independent. In ANSYS the numerical solution was post processed with the help of a code to calculate
the J-integral on at least 12 paths. The scatter in the J-integral values over all the contour paths was found to
be small, within 1.3% of difference and, therefore, J-integral was considered to be path independent. The
critical J-integral values obtained by ABACUS and ANSYS were found to be consistent and uniform.
The fracture toughness of thin aluminium sheets for the specimens mentioned earlier was also evaluated
through Bagley and Landes approach to compare the results of experimental-cum-numerical technique
obtained using ABACUS and ANSYS software. The load displacement curves for three crack lengths; a = 27,
30 and 33 mm were considered for the analysis. The J-integral values obtained by Begley and Landes
approach were compared with those obtained from experimental-cum-numerical technique through ABACUS
and ANSYS. The determination of J-integral through Begley and Landes was considered to be 1ess rigorous
when compared with Experimental-cum-numerical technique, because the Begley and Landes procedure is
complicated and multiple specimen tests are required to obtain a single experimental result of J-integral (Xian
et al, 2012).
Figure 4 presents the average critical J-Integral (JIc) of four specimens each for 1.6 mm and 1.0 mm thick
sheets of aluminum alloy 6061-T6 along rolling and transverse direction. The average value of critical J-
Integral (JIc) obtained from the experimental-cum-numerical technique for thickness of 1.0 mm in the rolling
direction of the specimen was 84.3 kJ/m2 and 74 kJ/m2 in the transverse direction whereas the average JIc
obtained for thickness of 1.6 mm was 106.3 kJ/m2 in the rolling direction of the specimen and 84.4kJ/m2 in
the transverse direction. It was found that the J-integral values obtained for 1.6 mm thick sheet was higher
than JIc obtained for 1 mm thick sheets. Paradon T et al, 2004 investigated from experimental
load/displacement curve using Rice’s analytical formula corrected with the numerical factor, the fracture
toughness of aluminium alloy-6082 T0 thin plates of 1-6 mm thickness and obtained J-Integral (Jc) as 50
kJ/m2 for 1.0 mm thickness and 80kJ/m2for 1.6 mm thickness. As shown in Figure 4, it was observed that the
results of J-integral obtained from ABAQUS and ANSYS analysis were consistent.
Figure 4: J-integral for 1 mm and 1.6 mm thickness along rolling and transverse direction
7. CONCLUSIONS
A simple and effective experimental-cum-numerical technique was developed to determine the fracture
toughness; critical J-integral of thin sheets made of aluminium alloy 6061-T6. A single-edge crack tension
specimen with appropriate screw tabs was used to conduct the experiments. The critical load obtained from
the experiments was used as loading boundary conditions in numerical analysis to obtain stress-strain field in
the specimen by employing the nonlinear stress-strain behavior of monotonic loading of the specimen
material. The numerical analysis was done in both ABAQUS and ANSYS softwares. The fracture toughness
obtained by experimental-cum-numerical technique was further compared with the results obtained through
Begley and Landes approach.
It was found that in thin plate of aluminium alloy 6061-T6, significant plastic deformation took place prior the
crack growth at the region close to the crack tip. In this study the fracture toughness was determined along the
rolling and transverse direction of specimen sheet of 1.0 mm and 1.6 mm each. The average value of critical J-
Integral obtained from the experimental-cum-numerical technique for thickness of 1.0 mm was 84.3 kJ/m2 in
the rolling direction of the specimen and 74 kJ/m2 in the transverse direction; whereas critical J-Integral for
thickness of 1.6 mm was 106.3 kJ/m2 in the rolling direction of the specimen and 84.4kJ/m2 in the transverse
direction. The results obtained from ABACUS and ANSYS were found to be consistent.
ACKNOWLEDGEMENT
The project was sponsored by Aeronautics Research and Devlopment Board (ARDB),
DefenceResearch and DevlopmentOrganisation (DRDO), New Delhi.
REFERENCES
Journal articles
1. Barsoum R, “Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements”,
International Journal for numerical methods in Engineering, 11(1), 85-98, (1977).
2. Begley J A and Landes J D, “The J-integral as a fracture criterion”, Fracture Mechanics ASTM STP
514. American Society for Testing and Materials, 1-23, (1972)
3. Henshel R D and Shaw K G, “Crack tip elements are unnecessary”, International Journal of
Numerical methods,9, 495-509, (1975).
4. Kaiser S, “The J-Integral and tearing modulus for a SEN specimen under bending and tension”,
Engineering Fracture Mechanics, 22 (5), 737–749 (1985)
5. Kuang J H and Chen Y C, “The values of the J-integral within the plastic zone”, Engineering Fracture
Mechanics, 55 (6), 869-981, (1996).
6. Pardoen T, Marchal Y., Delannay F, “Thickness dependence of cracking resistance in thin aluminium
plate”, Journal of the Mechanics and Physics of Solids, 47(10), 2093-2123, (1999)
7. Pardoen T, Marchal Y, Delannay F, “Essential work of fracture compared to fracture mechanics
towards thickness independent plane stress toughness”, Engineering Fracture Mechanics, 69 (5), 617-
631, (2002)
8. Pardoen T, Hacheza F, Marchionia B, Blythb P, Atkinsb A, “Mode I fracture of sheet metal”, Journal
of the Mechanics and Physics of Solids, 52 (2), 423-452, (2004)
9. Pendola M, Mohamed A, Lemaire M, Hornet P, “Combination of finite element and reliability
methods in nonlinear fracture mechanics”, Reliability Engineering & System Safety,70 (1), 15-27,
(2000).
10. Shahani A.R, Rastegar M, Dehkordi M, Kashani H, “Experimental and numerical investigation of
thickness effect on ductile fracture toughness of steel alloy sheets”, Engineering Fracture Mechanics,
77 (4), 646–659, (2010)
11. Sonnerlind H and Kaiser S, “The J-integral for a SEN specimen under non-proportionally applied
bending and torsion”, Engineering Fracture Mechanics, 24 (5), 637-646, (1986)
12. Xian-Kui Zhu and James A, “Joyce Review of fracture toughness (G, K, J, CTOD, CTOA) testing and
standardization”, Engineering fracture mechanics, 85, (2012)
Books
1. ASTM standard E8, “Standard Test Methods of Tension Testing of Metallic Materials”, American
Society for Testing and Materials, (2008).
2. ASTM E1823-10a, “Standard terminology relating to fatigue and fracture testing”, American Society
for Testing and Materials, (2011)
3. Kumar P, “Elements of Fracture Mechanics”, Tata McGraw-Hill, New Delhi, Chapters 5, 6, 8, (2009).
4. Milne I, Ritchie R O, Karihaloo B., “Comprehensive structural integrity”, Elsevier ,1-11online
version, (2007).
5. Schwalbe K H, Landes J D, Heerens J, “Classic fracture mechanics methods”, In: Milne I, Ritchie R
O, Karihaloo B, editors. Comprehensive structural integrity, 11, Elsevier, (2007)
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O8
ABSTRACT
The integrity assessment of the piping components needs to be demonstrated under cyclic loadings,
during the normal operation and the design basis accidents such as earthquake. In order to understand
material’s cyclic plasticity and failure behavior, systematic analytical investigations were carried on
specimens of SA333 Gr.6 low carbon manganese steel material. The material specifications of this steel are
same as Primary Heat Transport (PHT) piping material of Indian Pressurized Heavy Water Reactor (PHWR).
The axial-torsion fatigue tests were conducted on tubular specimens for different phase shifts in order to
quantify the fatigue damage under multiaxial and non-proportional loading. The current work mainly aims at
the investigations of material behavior under different loading combinationsof axial and shear strain
amplitudes pertaining to proportional and non-proportional loading for different equivalent strain
amplitude.The effect of Relative Strain Amplitude Ratio (RSAR), that is the ratio of shear to axial strain
amplitude, was studied in conjunction with phase shift angle. The multiaxial non-proportional response of
material helps in identifying the critical ranges of RSAR and phase shift.
1.INTRODUCTION
Engineering components in conventional power plant as well as in Nuclear Power Plant (NPP) may be
subjected to cyclic loading during their service life. It includes normal operation loading, loading during the
accident events such as earthquake loads generally considered in design. In case of earthquakes, cyclic
loading may induce large amplitude stress reversals, which exceed the elastic limit of the material. Under
cyclic loading conditions, the material mainly fails due to the fatigue damage and the components are required
to be designed for it. Generally the fatigue damage is evaluated according to the design codes procedures in
which fatigue design curves are generated from uniaxial fatigue tests at specimen level. However in actual
situation, the state of induced stress/strain is multiaxial due to complex geometry of components and / or
loadings itself. This complexity may lead to cyclic loading with non-zero mean and /or varying principle
directions that is generally termed as non-proportional loading. In addition to this, ratcheting phenomenon
could occur due to progressive accumulation of strain under sustained (or primary) loading along with cyclic
inelastic loading. This ratcheting phenomenon adds to fatigue damage under cyclic loading and causes
reduction in the fatigue life of components which lead to premature failure of components.
Boussaa, 1994 and Xia, 1996 have shown significant influence of ratcheting interaction on fatigue life of
component. In view of this, safety and integrity of high energy pressurized piping system is of main concern
and many researchers [1, 2, 4, and 8] have carried out experimental and analytical investigations. The
investigations have shown that the fatigue-ratcheting synergy, leading to crack initiation and rupture in few
cycles only, is the likely mode of failure. Large numbers of proposals for multiaxial fatigue analyses were
developed in past and are available in literature reported by Diarmid, 1991, and Chu 1995. The state of the art
of various fatigue models has been investigated which varies mainly as a function of the fatigue life and is
different for low-cycle fatigue (LCF) and high-cycle fatigue regions.
In view of above, to develop rational piping design methods for the failure mechanisms, accurate prediction of
stress-strain response is required. Therefore, there is a need of a robust cyclic plasticity model which can
predict cyclic stress strain responses accurately and leads to improved design methodology against such
failure mechanisms. To understand the material’s response under multiaxial and non-proportional loading,
systematic experimental and analytical investigations were carried on tubular specimen of SA333Gr.6 carbon
steel by Bhabha Atomic Research Center (BARC), Mumbai.The current work aims to investigate the behavior
of material under different loading combinations of RSAR and phase shift angle pertaining to proportional
and non-proportional loading using Chaboche model.
2.SPECIMEN DETAILS
The axial-torsion fatigue tests were conducted on tubular specimens of SA333 Gr.6 carbon manganese steel as
recommended by Arora et. al., 2011.The chemical composition of the material chosen for testing is given in
Table 1. The figure 1 shows the details of specimens.
Table 1: Chemical composition of SA333 Gr.6 (in weight %) [Arora et. al., 2011]
Material C Mn Si P S Al Cr Ni N
SA333 Gr.6 0.14 0.9 0.25 0.016 0.018 <0.1 0.08 0.05 0.01
Figure 1: Details of tubular specimen used in axial-torsion cyclic tests [Arora et. al., 2011]
A 3-D gauge section (middle region) of the tubular specimen is modeled with gauge length equal to 30 mm.
The stress distribution is uniform in the gauge region. In order to apply combined shear as well as axial strain
loading, a 20 noded brick element is used. Figure 2 shows the Finite Element (FE) model of tubular specimen
with outer diameter of 25.4mm and thickness as 1.7mm. For the FE analysis, a fine meshed model is
developed with 3 elements along the length whereas 2 elements along the thickness direction as shown in
figure 2.
Shear
0 Phase
_0
-0.2
Phase
-0.4 _90
-0.6 Phase
_45
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Axial Strain (%)
Before putting in use for the case under consideration, this model was validated under elastic loading with the
results from mechanics calculations under pure axial and pure shear loading conditions. The same validated
model is then used for further elastic-plastic analysis under combined axial strain () and shear strain (
loading magnitudes. This combined loading leads to axial-torsion fatigue in tubular specimens. A systematic
parametric variation is carried out to investigate the effect of RSAR (λ = and phase shift angles () on
the multiaxial and non-proportional response of material. It is observed that RSAR (λ) helps in evaluating the
effect of dominance of one strain over other and phase shift angle (leads to different amount of non-
proportionality, for a given axial strain and shear strain amplitude. The different strain controlled loading
paths considered for analysis purpose are shown in figure 3. The phase angle between the axial and shear
strain cycle, was varied in the range, In-Phase (i.e. 0° Phase-Shift), 90°, 45°,135°and 180° phase shifts for 4
different strain equivalent loading stations. Typical loading of axial and shear strain with respect to phase
angle for 900 out of phase shift are shown in figure 4.
1
0.75 900_Out of Phase Shift
Axial and Shear Strain(%)
0.5
0.25
0
-0.25
-0.5
Axial strain
-0.75
Shear strain
-1
0 90 180 270 360 450 540 630 720
Phase Angle
Figure 4: Typical loading of axial and shear strain for 90 0 out of phase shift
The variation of Phase angle (0) and relative strain amplitude ratio i.e. RSAR () for different strain
equivalent loading is given in Table 2. The equivalent strain in percent (eqv) was calculated using equation
(iv).
Table 2: Variation of Phase angle () and relative strain amplitude ()
eqv Phase angle () = a/3*a
Mpa (%)
159 0.35 0, 45, 90, 135, 180 0.5, 0.75, 1, 1.25, 1.732
169 0.5 0, 45, 90, 135, 180 0.5, 0.75, 1, 1.25, 1.732
185 0.75 0, 45, 90, 135, 180 0.5, 0.75, 1, 1.25, 1.732
201 1 0, 45, 90, 135, 180 0.5, 0.75, 1, 1.25, 1.732
yield strength of material
For cyclic plasticity modeling purpose, Chaboche 3-decomposed material model was used. Chaboche et. al.,
1986 proposed a ‘decomposed’ nonlinear kinematic hardening rule in the form given below:
M
In the above equation, ‘dp’ is the accumulated plastic strain which can be expressed as follows:
Chaboche et. al., 1986 recommended the use of three decomposed hardening rules, i.e M= 3 in equation (i), to
improve the hysteresis loops in three segments obtained through simulation.The various Chaboche material
model parameter constants were borrowed from the work reported by Arora et. al., 2010. These constants
were evaluated from uniaxial LCF test data for the same material. Table 3 gives the details of Chaboche three
decomposed model.
Out of various cases considered in the FE analysis, typical axial and shear stress-strain response is shown in
figures 5a and 5b respectively for different values of phase shifts (. It shows response against 0.75%
equivalent strain loading and identified as CA53S92 case. In this case values used are axial strain
and shear strain which is corresponding to (λ = 1). It reveals that in comparison to
proportional loading (material shows extra hardening in case of non-proportionality, as here
( in both axial as well as shear response. The results presented in figure 5a and 5b clearly
shows that there is significant difference in the stress response due to the phase shift angle. Under 90o out of
phase and for = 1 case, the area of hysteresis loops and the maximum stresses are higher than that of
proportional loading ( = 0 0). This may lead to a higher fatigue damage in material under non-proportional
loading and hence shorten the fatigue life.
CA53S92: Different Phase angle () CA53S92: Different Phase angle ()
400 200
300 150
Shear stress (Mpa)
200 100
Axial stress (Mpa)
100 50
0 0
-100 -50
-200 -100
-150
-300
-400 -200
-1 -0.5 0 0.5 1
-0.6 -0.3 0 0.3 0.6
Axial strain (%) Shear strain (%)
Figure 5a: Axial stress-strain response under Figure 5b: Shear stress-strain response
different phase shifts under different phase shifts
Further, the FE studies predict the maxima and minima of stress and strain components to exist at same time
instant for proportional load condition indicating the synchronous behaviour between axial stresses and strains
as seen from figure 5a. However, the maxima and minima of shear stress and strain do not occur at the same
time instant under non-proportional loading condition as seen from figure 5b. This signifies that the stress and
strain are not synchronous to each other viz. there occurs independent rotation of principal stress and strain
axes. This reveals the complex nature of damage occurring under non-proportional load condition.
Stress-strain hysteresis loop area as evaluated from FE analysis is considered as the measure of the fatigue
damage parameter as suggested by Chu, 1995. Figure 6 shows the response of normalised area (A/A=00)
against phase angle for various values of () at 0.75% equivalent strain loading. It is clear that () = 900 and
(is the most critical case as hysteresis loop area is maximum in this case.
stres(Mpa)
1.05
1.04 300
1.03
200
1.02
1.01 100
1
0
0.99
0 0.25 0.5 0.75 1 1.25
0 45 90 135 180
Von mises equivqlent strain (%)
Phase Angle (
Figure 6: Response of normalized area against Phase Figure 7: Response of Von-Mises stress-strain for
angle () = 1
The variation of Von-Mises equivalent stress amplitude vs. strain amplitude is plotted in figure 7 with
different phase angles () for = 1. The von- Mises equivalent stress and strain was evaluated using equations
(iii) and (iv) respectively. The figure 7 also shows that stress induced in the material is highest for 900 phase
shift as compared to other phase shifts at same equivalent strain loading station.
eqv = [(xa)2 + 3 ( axy)2]1/2 (iii)
eqv = [(xa)2 + (a2xy/3)]1/2 (iv)
The axial and shear stress-strain response of actual test results for CA25S43 (i.e. 0.35% equivalent strain
loading) is plotted against FE simulation results for proportional and non-proportional loading in figures 8 and
9 respectively.
300 150
CA25S43PO CA25S43PO
200 100
100 50
0
0
-50
-100
-100 FE_Chaboche
-200 FE_Chaboche
TEST
TEST -150
-300 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
-0.4 -0.2 0 0.2 0.4
Axial strain (% ) Shear strain (%)
450 200
CA25S74NPO_90
CA25S43NPO_90 150
300
Axial stress (Mpa)
100
150 50
0 0
-50
-150
-100
FE_Chaboche
FE_Chaboche
-300 TEST -150
TEST
-450 -200
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-0.4 -0.2 0 0.2 0.4
Axial strain (%) Shear strain (%)
From the in phase (i.e. proportional) multiaxial loading comparisons shown in figure 8, it is clear that shear
stress-strain response of FEA with Chaboche model shows closer matching with test results. However, there is
a deviation in the axial stress-strain response in the region of lowest and highest values of axial stresses. From
the out of phase (i.e. non-proportional) multiaxial loading comparisons shown in figure 9, it is clear that, both
the experimental and FEA results are able to support the mechanics of the non-proportional loading, however,
deviation is noticed in the axial and shear responses predicted by FEA and test results. The engineering
quantification of the extra strain hardening due to non-proportionality to predict real damage in material is
difficult. Therefore, there is a need of further improvements in the cyclic material modeling to account for
extra strain hardening which occurs under non-proportional loading condition and depends on the parameters
() and ().
5.CONCLUSION
From the investigations for multiaxial fatigue on SA333 Gr.6 material it is concluded that under non-
proportional loading condition material is showing extra strain hardening which is in line with test results.
Also, stress-strain hysteresis loop area is maximum for RSAR (=1) and phase shift angle () leading to
increase in fatigue damage.
REFERENCES
[1] Boussaa D., Van, K.D., Labbe, P., Tang, H.T., “Fatigue–Seismic Ratcheting Interactions in
pressurized Elbows”, Journal of Pressure Vessel Technology, Vol. 116, pp. 396-402 (1994)
[2] C C Chu, “Fatigue damage calculations using the critical plane approach”, Journal of Engineering
Materials and Technology, (1995).
[3] Chaboche, J. L. “Time-Independent Constitutive Theories for Cyclic Plasticity. Int. J. Plasticity”,
Vol- 2, P. 149-188, (1986).
[4] D.L. Mc Diarmid, “A general criterion for high cycle multiaxial fatigue failure”, Fatigue of
Engineering Materials, (1991)
[5] Punit Arora, Suneel. K. Gupta, V.Bhasin, K.K. Vaze, S. Sivaprasad and S. Tarafdar, “Multi-axial
Fatigue Studies On Carbon Steel Piping Material of Indian PHWRs”, SMiRT-21, Paper 479, New
Delhi, India, (2011)
[6] P. Arora, S. Goyal, S. K. Gupta, M. A. Khan, V. Bhasin, S. Sivaprasad, S. Tarafdar, K. K. Vaze, A.
K. Ghosh, H. S. Kushwaha, “Multiaxial Non-Proportional Fatigue and Ratcheting Studies on PHT
Piping Material of Indian PHWRs”,36th MPA Seminar, Stuttgart, Germany, October 6-7, (2010)
[7] Suneel K. Gupta, Sumit Goyal, Vivek Bhasin, K. K. Vaze, A.K. Ghosh, H. S. Kushwaha,
“Ratcheting-Fatigue Failure of Pressurized Elbows made of Carbon Steel”, SMiRT 20, Division-II,
Paper 1861 Espoo, Finland, (2009).
[8] Xia, Z., Kujawski, D. and Ellyin, F, “Effect of mean stress and ratcheting strain on fatigue life of
steel”’ Int. J. Fatigue.18, 335-341, (1996)
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O9
ICAME2013 S6/O10
ABSTRACT
Dynamic analysis of stationary cracks is investigated in the framework of the extended finite element
method. The Generalized-α (G-α) method is adopted for solving the dynamic equation as the time integration
scheme. The G-α method has shown to provide better numerical dissipation characteristics, smaller period and
lower displacement errors compared with other time integration methods such as the Newmark algorithm.
Finally, numerical examples are solved using the extended finite element method and the predicted dynamic
intensity factors for stationary cracks are verified by available analytical solutions.
1.INTRODUCTION
The Extended Finite Element Method (XFEM) has been widely utilized for analysis of crack stability and
propagation, with satisfactory results and high degree of precision compared with other methods. They
include stationary cracks (Motamedi and Mohammadi, 2010), quasi-static crack growth (Sukumar and
Prevost, 2003), and cohesive crack propagation (Moes and Belyschko, 2002). In dynamic finite element
modeling, different time integration methods such as the Wilson-θ Method (Wilson, 1968), the HHT-α
method (Hilber et al., 1977), the Bazzi and Anderheggen-ρ Method (Bazzi and Anderheggen, 1982), and the
Genaralized-α method (Chung and Hulbert, 1993) have been developed for solving dynamic equations.
Unfortunately, all these methods use some sort of artificial damping in solving the motion equations.
In this paper, the dynamic fracture analysis is performed in the framework of the extended finite element
method, using the Generalized- α method as the time integration technique.
The XFEM approach extends the conventional finite element method by enriching the displacement solutions
with discontinuous functions. Enrichments can beused for increasing the order of solution precision that can
be achieved, which results in higher accuracy of the approximation. The choice of the enriched functions
depends on the a priori analyticalsolution of the problem (Mohammadi, 2008). XFEM allows for generation
of the finite element mesh of the entire domain without considering the interface geometry, and avoids
remeshing of the domain, as the interface propagates. In this technique, arbitrary discontinuities are taken into
account by adding proper functions into the standard FEM approximation. The additional functions are used
to enrich the displacement field in order to reproduce the discontinuity of strain and displacement fields
(Mohammadi, 2008).
In contrast to the conventional finite element that the discontinuity line has to conform to the element
boundaries for representing the interface surfaces, XFEM is mesh independent because of using the
enrichment function to model the discontinuity. An arbitrary discontinuity within an independent FEM mesh
is shown inFig. (1).
3.Basics of XFEM
As mentioned before, finite elements in XFEM are generated regardless of the existence and location of any
discontinuities. Then, by using the level set methods the exact location of the crack path (or any other
discontinuity) with respect to the FEM mesh is determined. Afterwards, corresponding degrees of freedom are
added to the classical FE model in selected nodes around the discontinuity. The displacement field can be
written in terms of the classical finite element approximation and the XFEM enriched fields (Belytschko et al.,
1999),
( )= ∅( ) + ∅( ) ( ) + ∅ ( ) ( ) (1)
where the first term of Eq. (1) represents the conventional FEM displacement field. and are the vector of
additional degrees of freedom related to the modeling crack faces and crack tips, respectively. ∅ ( ),∅ ( ),
and ∅ ( ) are the shape functions related to FEM degrees of freedom, crack faces, and crack tips,
respectively. ( )is the Heaviside enrichment function, as shown in Eq. (2):
∗ ). (2)
+1 ( − >0
( )=
−1 ℎ
{ ( , )} = √ ,√ ,√ ,√ , (3)
2 2 2 2
The point x usually represents a Gauss integration point and x* is the nearest point on the crack interface to
the point x. , are both calculated in the crack tip local coordinate system.
(a) (b)
Fig. (2): (a).Crack tip enrichment functions are calculated in the tip local coordinate system. (b).x* is the nearest point on the crack
interface to the point x.
The Generalized-α method has proved to provide better numerical dissipation characteristics, smaller period,
and lower displacement errors compared with other numerically dissipative schemes (Chung and Hulbert,
1993). The basic form of the Generalized-α method is given as,
(4)
= +∆ ̇ +∆ − ̈ + ̈
̇ = ̇ + ∆ (( − ) ̈ + ̈ ) (5)
M ̈ + ̇ + = ( ) (6)
Where:
= − + (7)
̇ = − ̇ + ̇ (8)
̈ =( − ) ̈ + ̈ (9)
= − + (10)
where nis the current time step number and ∆tis the time increment size. Other parameters are described as,
β=( , =
, =
, = (11)
) ( )
There are two noticeable advantageous related to the G-α method: First, the optimal G-α method permits high
frequency dissipation to vary from the no dissipation case ( = 1) to the so-called asymptotic annihilation
case ( = 0). Second, other dissipative algorithms can be reproduced by this method. For instance, by
putting = = 0, the Newmark method is obtained.
5.NUMERICAL EXAMPLES
In this section, a numerical example is studied. The dynamic stress intensity factor is used for verifying the
proposed approach. The predicted dynamic stress intensity factors and other results are compared with
available analytical solution (Chen, 1975).
5.1-2-D isotropic plate with a stationary central crack under the tensile stress loading
An isotropic plate under the tensile stress loading (Figure (4)) is studied. The size of the plate is D =
20(mm), L = 40(mm), and the crack length is 4.8(mm). Material properties are considered to be =
200 , = .3 and = 5000 .Considering the symmetry of the geometry and loading, half of the plate
can be simulated by applying the appropriate boundary conditions.
Fig. (3):Anisotropic plate with a central crack under the tensile stress loading
This problem is modeled with three different FEM mesh sizes of 12 40, 24 80, and 48 160 (Fig. (5a)). The
Problem is also solved with different time steps of 0.25 and 0.5 micro seconds and different J-integral
computation radii of 0.2a and 0.4a (Figures 5(b) and 5(c)). The total time of the analysis is 15 Micro seconds.
It is obvious that by using a finer mesh and a smaller time step, more accurate results are obtained. The little
difference between the analytical and numerical results is caused by the numerical errors and the way the
stress intensity factor is computed. All mode I intensity factors are normalized by √ . Fig. (5d) illustrates
the difference of predicted frequency dissipation between the Newmark and G-α methods. The Generalized-α
method provides results with optimized frequency dissipation. This is noticeable that due to lack of a contact
constraint, unrealistic negative intensity factors appear whenever the relative displacement of crack faces
becomes negative.
3.5 3
(Chen, 1975) (Chen, 1975)
3 12 X 40 2.5 J radius=0.2a
2.5 24 X 80 J radius=0.4a
2
Normalized KI
Normalized KI
1.5
1.5
1
1
0.5
0.5
0
0
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16 -0.5
-0.5
-1 -1
Time (μs) Time (μs)
(a) (b)
3.5 3
(Chen, 1975)
3 ∆t=0.25 μs 2.5 G-α Method G-α Method
2.5 ∆t=0.5 μs
2
Normalized KI
Normalized KI
2
1.5
1.5
1
1
0.5
0.5
0 0
0 2 4 6 8 10 12 14 16
-0.5 0 5 10 15 20 -0.5
(c) (d)
Fig. (4): (a). Comparison of the predicted mode I intensity factor (KI) with the analytical solution provided by (Chen, 1975) for
different FEM mesh sizes. (b). Comparing the numerical results for different J integral radii. (c). Results fordifferent time steps. (d).
Comparing the Newmark and G-α methods
In Figs. (5) and (6), the stress contours and deformed shape configurations at different time steps are
presented.
Fig. (5): Stress and displacement contours at 5 Micro seconds
6.CONCLUSION
In this paper, the G-α method, as an improved numerical dissipation time integration algorithm for dynamic
analysis of structures, is used for modeling the dynamic fracture problem by XFEM. Various capabilities of
XFEM for solving the dynamic fracture modeling with minimal meshing have been studied. Also it is shown
that by using the G-α method high frequency effects in numerical results can be partly or completely
annihilated. The acceptable agreements demonstrate the efficiency of the proposed method for modeling the
dynamic fracture problems.
REFERENCES
1. Motamedi D. and Mohammadi S., “Fracture analysis of composites by time independent moving-
crack orthotropic XFEM”, Int. J. Mech. Sci., 2012. 54(1): p. 20-37.
2. Sukumar N. and J.H. Prévost, “Modeling quasi-static crack growth with the extended Finite Element
Method Part I: Computer implementation”, Int. J. Solids. Struc., 2003. 40(26): p. 7513-7537.
3. Moës N. and Belytschko T., “Extended finite element method for cohesive crack growth”, Eng.
Fract.Mech., 2002.69(7): p. 813-833.
4. Wilson E. L., “A computer program for the dynamic stress analysis of underground structures”, SESM
report No. 68-1, Div. Struc. Eng. Stru.Mech., University of California, Berkeley, CA, U.S.A., 1968.
5. Hilber H. M., Hughes T. J. R., Taylor R. L., “Improved numerical dissipation for time integration
algorithms in structural dynamics”, Earthq.Eng. Struct. D., 1977; 5: p. 283-292.
6. Bazzi G. and Anderheggen E., “The ρ-family of algorithms for time-step integration with improved
numerical dissipation”, Earthq.Eng. Struct. D., 1982; 10:537-550.
7. Chung J. and Hulbert G. M., “A time integration algorithm for structural dynamics with improved
numerical dissipation: The generalized-α method”, J. Appl. Mech., 1993; 60:371-375.
8. Mohammadi S., “Extended Finite Element Method: For Fracture Analysis of Structures”,
Wiley/Blackwell, 2008.
9. Belytschko T. and Black T., “Elastic crack growth in finite elements with minimal remeshing”, Int. J.
Numer. Meth. Eng., 1999; 45:601–20.
10. Chung J. and Hulbert G. M., “A time integration algorithm for structural dynamics with improved
numerical dissipation: The generalized-α method”, J. Appl. Mech., 1993, 60: p. 371-375.
11. Chen Y.M., “Numerical computation of dynamic stress intensity factors by a Lagrangian finite-
difference method (the HEMP code)”. Eng. Fract.Mech., 1975.7(4): p. 653-660.
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/O11
ABSTRACT
Numerical modeling of tensile cracking in quasi-brittle materials is one of the important topics in
computational failure mechanics. In order to have a realistic analysis of failure in a structure, it is necessary to
find the location and initiation time of damage and the way damage is transformed into a macro crack. In this
study, the XFEM technique is applied for modeling crack propagation in quasi-brittle fracture using the
elastic-damage model. First, a continuous elastic-damage analysis is carried out. When the criterion of crack
initiation is satisfied, a crack is introduced in the element by the extended finite element technique. Finally, in
order to demonstrate the capabilities of the proposed method, a mixed mode beam test is simulated.
Keywords: elastic-damage, quasi-brittle materials, strain localization, XFEM, mixed mode loading
1.INTRODUCTION
Cracking analysis of structures has been a big challenge for the researchers in the field of computational
mechanics. In order to have a correct analysis of cracking, it is required to know the location and initiation
time of damage in structures as well as the way damage is transformed into a macro crack. A full analysis of
the failure process by the continuum damage mechanics theory can be performed in two steps. The first step is
a continuous solution of the domain to anticipate creation of the crack, and the second step is the
discontinuous solution of the cracked domain.
The first step of continuous solution of the domain is based on the softening behavior of material. In fact, the
behavior of many quasi-brittle materials is such that micro cracks are spread in a small region which is called
the fracture process zones. In this region, the strain and damage are concentrated. The size of this region
depends on the size and spacing of heterogeneities in the structure. By increasing the amount of loading,
generated micro cracks propagate in this region and coalescence of the micro cracks leads to the formation of
a discontinuity in the displacement field.
Numerical and theoretical models for quasi-brittle fracture have to provide a correct interpretation of energy
dissipation in the fracture process zone. The numerical results usually suffer from a mesh dependency where
the loading capacity of the structure varies by the size of elements. Mesh refinement may lead to a decrease in
the dissipated energy in the numerical model, and in the limiting case, becomes zero when the size of
elements approaches to zero. In order to overcome the challenge of mesh dependency, a number of techniques
have already been proposed:
1) the cohesive crack model: This model removes the mesh dependency by considering a discontinuity in the
displacement field (strong discontinuity) and using the traction-separation law (Hillerborg et al., 1976).
2) crack band model: This model simulates the process zone with a band of localized strains separated from
the neighbor points with weak discontinuities. In this model, the tangent of the softening curve is related to the
size of the finite element and the fracture energy of material (Bazant and Oh, 1983).
3) nonlocal model: In this model, concentration of strain in a small region is prevented by defining the width
of the process zone and distributing the strain in it. The main challenge of the model is defining an appropriate
width for the process zone (Bazant and Pijaudier-Cabot, 1988).
In this paper, the crack band model is adopted to overcome the mesh dependency. Also, a continuous-
discontinuous model of cracking analysis in quasi-brittle materials is presented using the damage mechanics.
The extended finite element method is a combination of conventional finite element method and some of the
basic ideas of meshless methods (Moës et al., 1999). In the extended finite element method, first, the usual
finite element mesh is generated without considering the existing discontinuities such as a crack or hole. Then,
for considering the effect of discontinuities, some additional degrees of freedom are defined near the
discontinuities and are associated with the enrichment functions obtained from the analytical solution. The
theoretical description of the model is presented as follows.
The domain which contains a crack is considered, as depicted in Figure 1. c represents the boundary of
the crack, and t and u are the prescribed tractions f t and displacement u boundaries, respectively.
∗ .
.
1
if x x .n 0 (2)
Pj x H x
0 otherwise
where x is the nearest point to x on c and n is the normal vector to c at the point x . It can be easily
observed that the value of the Heaviside function is positive if the considered point is above the crack and vice
versa.
2.1Elastic-damage model
Damage mechanics is an appropriate method for modeling of micro cracks. In this paper, the constitutive
model is considered based on the continuum damage mechanics theory.
The constitutive relation for the local form of the damage model is defined as:
1 d 1 d C : (3)
where is the effective stress and d is the damage variable, which varies between 0 and 1. Also, is
the strain tensor and C is the isotropic linear-elastic stiffness tensor. The conditions of loading-
unloading for this damage model is defined as,
f , eq 0, 0, f , 0 (4)
where f is the damage loading function, eq is the scalar equivalent strain and is related to the
maximum equivalent strain experienced so far by the material from the start of the loading. The
equivalent strain( eq ) is defined as:
:C : (5)
eq
E
where E is the Young’s modulus. It can be easily observed that for a one dimensional case, the
equivalent strain becomes equal to the longitudinal strain.
(6)
0 0
d 1 exp 2 H dis
0
where H dis 0 is the softening parameter which is related to the size of the element and the tensile
fracture energy of material.
In order to avoid undesired mesh dependency in materials with strain softening, the crack band model
is adopted (Bazant and Oh, 1983). First, consider the following equation:
g f lc GF (7)
where g f is the area under the local stress-strain curve, lc is the characteristic length and GF is the
tensile fracture energy of material which has a constant value. Based on the results of reference(Rots,
1988), lc for quadrilateral elements can be defined as,
l 2A (8)
c
Implementation of the extended finite element method with the damage mechanics approach can be performed
by the following steps:
1- Generate the mesh for geometry of the model and detect the nodes that have to be enriched.
2- Include the effect of enrichment on approximation of the displacement field in the extended finite
element method by imposing of the discontinuity to the enriched nodes. Then, analyze the problem
based on the continuum damage mechanics theory.
3- Detect the zones in which the value of damage reaches to its critical value ( d cr 0.9999 1) and then
extend the crack.
4.NUMERICAL RESULT
In this section, the mixed mode bending beam test is simulated. Figure 2 represents the geometry of the
model, previously tested by Denarié et al., 2001. This problem is analyzed in the plane strain state. The type
of loading and the geometry of the problem lead to the mixed mode crack propagation. This problem is loaded
until the crack opening CMOD = 0.48 mm . Also the value of d cr 0.9999 is considered for the crack
initiation. The material parameters are assumed as: Young’s modulus E 38000 Mpa ; tensile strength
f0 3 Mpa ; mode I fracture energy G F = 69 J m 2 ; Poisson’s ratio 0.2 .
The computational domain for analysis of this problem is discretized by 1517 quadrilateral elements and 1575
nodes. Figure 3 represents the deformed shape of the beam at the final stage ( CMOD = 0.48 mm ). As can be
observed, the crack is initiated from the tip of the notch and propagates in mixed mode towards the top edge
of the beam.
Figure 3. Numerical deformed shape (× 80) at the final stage and details of crack.
Figure 4 demonstrates the comparison between the crack tracks obtained from the proposed numerical method
and the experimental results, which shows an excellent agreement.
Figure 4. Comparison between the crack tracks obtained from the proposed numerical method and the experimental results.
Figure 5 represents the load-CMOD curve for the two cases of numerical analysis with and without macro
crack propagation, in comparison with the experimental results. It can be observed that the numerical and
experimental results are in a good agreement. Figure 6 shows the evolution of fracture process zone, where
the damage contour and traction-free discontinuity created in the damaged zone are presented at the final stage
( CMOD = 0.48 mm ).
Figure 6.Damage distribution at the final stage and traction-free discontinuity.
5.CONCLUSION
In this research, the extended finite element method is applied for modeling crack propagation in quasi-brittle
material using the elastic-damage model. For crack propagation, the damage variable is computed and the
crack is propagated when the damage reaches to its critical value of d 1 . Finally, it is demonstrated that the
damage mechanics can provide an appropriate criterion for crack propagation in the framework of the
extended finite element method.
REFERENCES
1. Bazant Z. P. and Oh B.-H., “Crack band theory for fracture of concrete”, Mater. Struct, 16, 3, pp. 155-
177 (1983)
2. Bazant, Z. P. and Pijaudier-Cabot G., “Nonlocal continuum damage, localization instability and
convergence,” J. Appl. Mech, 55, 2, pp. 287-293 (1988)
3. Cervera M., Pela L., Clemente R., Roca P., “A crack-tracking technique for localized damage in quasi-
brittle materials", Eng. Fract. Mech, 77, 13, pp. 2431-2450 (2010)
4. Denarié E., Saouma V. E., Iocco A., Varelas D., “Concrete fracture process zone characterization with
fiber optics”, J. Struct. Eng-ASCE, 127, 5, pp. 494–502 (2001)
5. Hillerborg A., Modeer M., Peterson P. E., “Analysis of crack propagation and crack growth in
concrete by means of fracture mechanics and finite elements”, Cement. Concrete. Res, 6, 6, pp. 773-
782 (1976)
6. Moës N., Dolbow J., Belytschko T., “A finite element method for crack growth without remeshing”,
Int. J. Numer. Meth. Engng, 46, 1, pp. 131–150 (1999)
7. Mohammadi S., “Extended Finite Element Method”, Wiley/Blackwell, United Kingdom (2008)
8. Rots J. G., “Computational modeling of concrete fracture” PhD Thesis, Technische Hogeschool Delft
(1988)
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/P1
ABSTRACT
In several areas of mechanical engineering and structures as well, real challenges that arises are
concerned with diagnostic identification of damages. For this reason, nondestructive testing, now a day, is of
great interest, because it can provide a direct assessment of machine part or structure during service or can be
employed to assess the structure after the occurrence of strong seismic event.
The damage or cracks are developed mainly due to fatigue loading. Such cracks affect static and dynamic
characteristics of machine part or structure. Hence, vibration analysis draws a great attention of researchers to
identify and to locate such cracks. In present work, the focus is given on the research which has been carried
out on vibration analysis of healthy as well as cracked beam. The previous study has drawn some conclusion
from experimental work. Hence, in this work, more emphasize is given on the methodologies used for
analytical as well as experimental assessment of cracked beams. The literature which involves new
approaches for such work, such as FEA approach, irregularity based analysis and others also covered.
Keywords: Vibration analysis, crack detection, multiple cracks, FEA approach, FFT analyzer.
1.INTRODUCTION
The mechanical systems or their structure consists of many components and elements. These parts of system,
many times treated as, simple structural elements like beams, columns, rods, cylinders, tubes, cubes etc. These
parts of system experiences many types of physical and chemical loadings. Such loading affects the parts in a
way like impact, fatigue, corrosion, welding, etc. All these effects can result in flaws or damage that leads to
the alteration of the dynamic behavior of machines and structures.
The machines are the heart of fast growing industrialized world. For mass production, machines are running
continuously even for 24 hours also. For consistent quality product, health of machine is an important factor.
The safe working assessment of machine or structure depends on the health of its critical component. To
assess such health of machine, its static and dynamic behavior is important. Based on such behavior, its
overall performance, criticality in failure can be judged.
Fracture is a natural reaction of solids to relieve stress and shed excess energy. Fragility of solids is a constant
threat to our survival as we drive over a bridge, go through a tunnel, or live inside a building. We accept
fracture as a way of life and admire solids for what they provide. Fragility is not always perceived as a baneful
threat because if all solids were unbreakable, we would not be able to break things when we want to.
Thus, in a way, fracture, like fire and wind, is both a foe and a friend of mankind – friend if controlled, foe
otherwise. Prediction, prevention, control and treatment of fractures represent a big bulk of engineering and
medical practice today. Hence the exact identification of these changes is significantly important. Such
identification gives us an idea about extent of failure, working life period, of the element, and its overall effect
on the system. As we know, crack is the unavoidable failure phenomenon, in beams also, we have to analyze
the beam when crack generates and how it affects the beam working. The presence of a crack in beams brings
a potential risk of destruction or collapse of the beam element, which forms fundamental parts of critical
structures. This produces high cost of production and maintenance.
Nowadays, the procedure often used for crack detection is the direct type of procedure such as ultrasonic, X-
rays etc. However these methods are not suitable for few cases. Also they require very minute detailed
periodic inspections which are very costly. There are several other methods with which we can monitor the
defects in the component. Here, by word monitoring, I mean to say that the location of defect and its severity.
Among these, the vibration based monitoring of components consisting of cracks or crack like defects in
service is important. And the study of vibrations of a component with crack is now-a-days, very widely used.
In order to avoid the costs, during the last decades, people have searched for more efficient procedure in crack
detection through vibration analysis whether by FFT analysis or by the time – domain response of the system
and also by studying the changes on natural frequencies and modes of shape that the crack introduces.
2.REVIEW OF PAPERS
In the early years of 1960’s and 1970’s, power generation is one of the critical issues in foreign countries. The
turbo machineries are used for power generation, like steam turbine, hydraulic turbine. The commissioning of
power equipments, used in power stations was done at 1960’s and a design life was finalized of about 30
years. So in the decades 1990 and 2000, the power equipments were in the third and last decade of their life.
During commissioning, erection, inspection it was observed that the major cause of machine failures is
initiation of cracks due to fatigue loading. This problem brought the attention of scientists and engineers to
detect the crack and its monitoring. Then several methods came out from their work. But again they found that
all these methods are of ‘off-site’ nature. It was obvious thing that the power equipments, such as turbine
blades, turbine rotors, shafts were heavy machine parts. It was difficult to disassemble them, bring them to the
site of inspection and testing, and again put them into working. This problem again forces the scientist to think
about ‘on site’ damage detection.
The development of methods for on-line (or in-situ) crack detection and monitoring started in the 1970’s in
the power industries. The vibration based methods were firstly reported by Andrew D. Dimarogonas
[Dimarogonas, 1970]. He submit his two reports to General Electric Co., Turbine department. These two
reports were related to the theory of vibration of cracked shaft and turbine blades. After his work, so many
researchers follow his study line and up to 1980’s a substantial research work has been compiled on this
subject.
Number of reports describing field experience as well as analytical approach related to vibration of cracked
structure, were developed by Pafelias, Schmerling and Hammonds, Jack and Patterson. Pafelias [Pafelias,
1971] represent an extensive laboratory and field experiments to develop a methodology for crack detection
based on harmonic behavior. He further reported on the development of an on-line electronic instrument for
monitoring and early warning of crack rotors to be used as a turbine supervisory instrument. The fact was
observed that a crack or local defect affects the dynamic response of a structural member. The first attempts to
quantify local defects were by Kirmsher [Kirmsher, 1944] and Thomson [Thomson, 1943]. They found the
effect of crack on component flexibility by using the concept of local bending moment of reduced section.
Also they found its magnitude by experimental estimations. The analysis of the local flexibility of a cracked
region of structural element was quantified in the 1950’s by Irwin [Irwin, 1957], Westmann and Yang
[Westmann and Yang, 1967] by relating local flexibility to the crack stress intensity factor (SIF). Based on
this principle, a method was developed for the computation of the SIF based on the local bending stiffness of a
cracked beam. This formulation was helpful in 1960’s by Liebowitz and Claus and many other investigators
for their work.
Fine-mesh finite element techniques were used to compute local flexibilities by many investigators such as
Chen and Wang, Ostachowicz and Krawczuk [Ostachowicz and Krawczuk, 1991]. Afterwards a number of
finite element analyses were developed and reported on the same subject by many people.
3.FORMULATION AND FORWARD PROBLEM
It has been observed that the occurrence of cracks in machines has potential effect on their static as well as
dynamic behavior. As a result of this, there are variations in stiffness of such elements. Frequencies of natural
vibration, amplitude of forced vibration and dynamic stability also get affected due to existence of cracks. An
analysis of these changes makes it possible to identify the magnitude and the location of the crack. Using
vibration analysis for early detection of cracks has gained popularity over the years. The material faults can be
detected, especially in steel beams, which are very important construction elements because of their wide
spread usage.
When a machine element suffers from damage, its dynamic properties can change. Specifically crack or
damage can cause a stiffness reduction, with an inherent reduction in natural frequencies and a change in the
mode shapes. From these changes the crack position and magnitude can be identified. Since the reduction in
natural frequencies can be easily observed, most researchers use this feature.
Many investigators use the finite element equation for beam element based on Euler-Bernoulli theory
as,
4.EXPERIMENTAL STUDIES
Ruotolo and Surace [Ruotolo and Surace, 2005] conducted the experiment on cantilever beam. Tests were
carried out on both, untracked and cracked beams. Cantilever beam made up of C 30 steel has cross section of
0.02 m X 0.02 m with the length of 0.8 m. The crack depth ratios were 0.2 and 0.3 resp. while the location
ratios were 0.3182 and 0.6812 resp. The cracks were generated by wire erosion method. The Young’s
modulus as 181 GPA is used throughout the study.
Owolabi et al [Owolabi et al, 2003] perform the testing on aluminum beams. The cross section was 25.4 mm x
25.4 mm with the length of 650 mm and Young’s modulus is 70 GPA. Some authors perform the experiments
on simply supported beams and fix-fix beams. Also we can observe the study on rectangular beams with steel
and aluminum material. Thus many combinations can be formed with cross section, material, boundary
conditions which will be suited to the actual application areas in mechanical as well as structural industries.
The different methodologies can be used in the analysis of beams such as FEA approach. In this case, the
element type referred to as ‘solid 95’ is employed. However a good approximation to exact result requires
frequent meshing in the vicinity of any discontinuities. Smaller mesh elements near the cracks are generated
by using ‘smartsize’ command in free meshing procedure. As a result the natural frequencies are found by the
analysis type called modal analysis in the program.
In forward analysis, we come to know that both the crack location and the crack depth influence the
changes in the natural frequencies of a cracked beam. Thus a particular frequency could correspond to
different crack locations and crack depths, hence to identify the presence of multiple cracks we have to
measure a sufficient number of natural frequencies of the beam.
For a beam having crack with unknown parameters, the following sequence is used to predict the crack
location and depth.
1) Measurement of natural frequency, mode shapes in forward analysis and create the data base.
2) Generating a graphical representation on axes coordinate systems.
3) Perform the testing for unknown parameters and execute the same analysis.
4) Then point(s) of intersection of the different contour lines are located. These points indicate the
crack location and crack depth.
Thus a simple way to locate the crack which is commonly adopted, is to prepare a sufficient number of
readings from the forward problem analysis. And then first, use the data to locate known crack. For unknown
crack, we plot the same contour lines with first three natural frequencies or mode shapes. On x-axis the crack
depth is located while on y-axis crack location is plotted. When we plot all three modes or more, then we get a
common intersection point, which indicate the crack location and the crack depth.
Fig. 3 : Crack identification technique by using frequency contours
6.CONCLUSION
The working life of many machine components depends on their health and any fault or damage is
disturbing their performance. Hence detecting such damage and curing them can save the system elements.
Beams are the vital part of mechanical systems. The existence of crack reduces the natural frequency of
vibration of beams, as shown in the table in forward analysis. A large database is created with many
combinations of materials, cross section, boundary conditions of beams as seen in experimental studies. With
these readings, a contour representation is generated. For inverse analysis, the above data is used to analyze
known crack and to ensure the reliability of method. Then the similar data is used to locate the crack whose
position is unknown.
ACKNOWLEDGEMENT
I would like to express my deepest gratitude to Dr. A. G. Thakur and the institute SRES COE, Kopargaon, all
my friends and family members.
REFERENCES
1] Andrew D. Dimarogonas, “Dynamic response of cracked rotors”, General Electric Co., Internal report,
Schenectady, NY, U.S.A. 1970.
2] Pafelias T., “Dynamic behavior of a cracked rotor”, General Electric co., Technical Information Series,
NY, U.S.A. 1971.
3] Ostachowicz W. M. and Krawczuk M., “Analysis of the effect of the cracks on the natural frequencies of a
cantilever beam”, Journal of Sound and Vibration, 150, 1991.
4] Kirmsher P. G. “The effect of discontinuities on the natural frequency of beams”, Proc. American Society
of Testing and Materials, 94, 1944.
5] Thomson W. J. “Vibration of slender bars with discontinuities in stiffness”, Journal of Applied Mechanics,
17, 1943.
6] Irwin G. R., “Analysis of stresses and strains near the end of crack traversing a plate “, Journal of Applied
Mechanics, 24, 1957.
7] Westmann R. A. and Yang W. H., “Stress analysis of cracked rectangular beams”, Journal of Applied
Mechanics, 32, 1967.
8] Jinhee Lee, “Identification of multiple cracks in a beam using vibration amplitudes”, Journal of Sound and
Vibration, 326, 2009.
9] D. P. Patil and S. K. Maiti, “Experimental verification of a method of detection of multiple cracks in beams
based on frequency measurements”, Journal of Sound and Vibration, 281, 2005.
10] S. Chinchalkar, “Determination of crack location in beams using natural frequencies”, Journal of Sound
and Vibration, 247, 2001.
11] R. Ruotolo, C. Surace, “Damage assessment of multiple cracked beams: numerical results and
experimental validation”, Journal of Sound and Vibration, 206, 4, 2005.
12] G. M. Owolabi, A. S. J. Swamidas, R. Seshadri, “Crack detection in beams using changes in frequencies
and amplitudes of frequency response function”, Journal of Sound and Vibration, 265, 4, 2003.
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S6/P2
ICAME2013 S6/P3
ICAME2013 S6/P4
ICAME2013 S6/P5
1.INTRODUCTION
Fracture mechanics deals with the measurement and analysis of crack. Fracture toughness is used as a term for
measuring the resistance of a material to extension of a crack. Fracture toughness play an important role in
application of fracture mechanics. This is used in the life prediction for a structure that contains the crack,
damage tolerance design, oil and gas pipe line industries, and residual strength analysis for different
engineering components and structures. The fracture toughness values may also use as in material properties
against crack propagation, performance evaluation, and quality assurance for typical engineering structures,
pressure vessels and petrochemical vessels and tanks and automotive, ship and aircraft structures and also in
the railways. Therefore, fracture toughness testing and evaluation has been a very important subject in
development of fracture mechanics method and its engineering applications. The terms K, J and CTOD are
used as the evaluation for fracture toughness of materials.
2.LITERATURE SURVEY
2.1Brief History of Fracture Mechanics
According to Anderson, 2005 the causes for failure of structure is the ignorance during the design,
manufacturing and the new design methods and new materials for replacement for old materials. The
application of new design method and materials cause the catastrophic failure because the designer ignores
some problems that are with them. So, testing and evaluation is become more important for new materials and
design. Some of the historical failure which needs the fracture mechanics is given.
During the Second World War in 1943, the liberty ships are made which are cheaper and less time consuming
because they uses welding in ships instead of welding. Nearly about 2700 ships are made and one half were
damaged. The main causes of failure are the lack of toughness in steels, improper welds which contains cracks
and the local stress concentration on the deck. After this some researchers at Naval Research Laboratory
studied the fracture in detail and the field of fracture mechanics was born.
In 1983 polyethylene is used for gas pipe line in U.S. There are for maintenance the pinch clamping process
was used. After the 6 years the flaw will grow that is generated from this process and gas will leak from this
spread near the residential area and there were severe damage of houses were take place.
In 2003 the failure of the Space Shuttle Columbia was takes place. The reason was that foam insulation from
external tank was strike with the left wing and the temperature was reached about 1450 oC.
There are many incidents which are in the form of catastrophic failure and many accidents were prevented
from the use of fracture mechanics in design.
According to Zhu and Joyce, 2012 a long history of more than 50 years in the development of fracture
mechanics theory. Different fracture toughness parameters have been proposed, and various fracture
toughness test methods and experimental technologies have been developed and revised incrementally over
the years. In the 1950s and 1960s, fracture mechanics focused on linear elastic materials testing using G and
K. In the 1970s and 1980s, it was concentrated on the J-integral and on the CTOD testing for Elastic–plastic
materials. In the 1990s, the ductile to brittle transition of ferritic steels and In the 2000s, the attention was on
the crack tip opening angle (CTOA) testing for stable crack extension of thin-walled materials in low-
constraint conditions.
2.2Fracture Toughness Testing
A fracture toughness test measures the resistance of a material to crack extension. Such a test may yield either
a single value of fracture toughness or a resistance curve, where a toughness parameter such as K, J, or CTOD
is plotted against crack extension.
Linear elastic fracture mechanics (LEFM) is used for linear elastic materials. The KIC based testing is comes
under LEFM. But it is applicable to materials which having lower toughness values and also because the
materials have a sufficient amount of plasticity near the crack tip. So, an alternative fracture mechanics model
is Elastic-plastic fracture mechanics (EPFM) is used to materials which having high fracture toughness and
behaves like non-linear (i.e., plastic deformation). Crack-tip-opening displacement (CTOD) and the J contour
integral that is associated with EPFM. Both parameters describe crack-tip conditions for elastic-plastic
materials. Critical values of CTOD or J give nearly size-independent measures of fracture toughness, even for
relatively large amounts of crack-tip plasticity.
KIC can be determined by using the standard procedure of ASTM E 399. This test method covers the
determination of fracture toughness (KIC) of metallic materials under linear-elastic, plane-strain conditions.
The fatigue precracking of specimens is required. The specimen having a thickness of 1.6 mm or greater is
subjected to slowly, or in special cases rapidly, increasing crack-displacement force. Although plane strain is a
necessary condition for a valid KIC test and a specimen must also behave in a linear elastic manner.
With the help of autograph recorder we get the graph of any type like in Figure1. There are three types of
load-displacement curves are shown in Figure1. The critical load PQ is defined in one of several ways,
depending on the type of curve. Then the construction of a 5% secant line i.e., a line drawn from the origin
with a slope equal to 95% of the initial elastic loading slope equal to (initial force/initial displacement near to
origin) to determine P5.
The ratio Pmax/PQ shall be calculated. If this ratio does not exceed 1.10, then one must proceed to calculate KQ
as the specimen configuration with respect to Annexure that are given in the ASTM E 399. If Pmax/PQ does
exceed 1.10, then the test is not a valid KIC test and the user is referred to Test Method ASTM E 1820 on
The value 2.5 ⁄ , where is the 0.2 % offset yield strength in tension according to ASTME8/E8M
shall be calculated. If this is less than the specimen ligament (W–a) then KQ is equal to KIC. Otherwise, the test
is not a valid KIC test.
It is difficult to perform a valid KICtest on most materials at ambient temperatures. Material could meet the
validity requirements with a reasonable section thickness because the materials show some amount of
plasticity or because of at the temperature probably materials are sufficiently ductile for showing plasticity.
When linear elastic test methods are invalid, fracture toughness must be quantified by an elastic-plastic
parameter such as J or CTOD.
2.4 According to ASTM E 1737
J-integral is a mathematical expression, a line or surface integral over a path that encloses the crack front from
one crack surface to the other, used to characterize the local stress-strain field around the crack front as
describe in ASTM E 1737, 1996. ASTM E 813 is the first standard for JIC Testing. According to this single
specimen test via unloading compliance technique is used instead of multiple specimen test technique. ASTM
E 1737 is the combined version of E 813 and E 1152. J-integral can be described as the potential energy
difference between two identically loaded specimens which have slightly different crack lengths. That means
for this multiple specimens are used. By idealizing elastic-plastic deformation as nonlinear elastic, Rice, 1968
gives the extension of fracture mechanics methodology that is beyond the LEFM. The loading behaviour for
the two materials is identical, but the material responses differ when each is unloaded. The elastic-plastic
material follows a linear unloading path with the slope equal to Young’s modulus, while the nonlinear elastic
material unloads along the same path as it was loaded. According to Anderson, 1986 there is a unique
relationship between stress and strain in an elastic material, but a given strain in an elastic-plastic material can
correspond to more than one stress value if the material is unloaded or cyclically loaded. Consequently, it is
much easier to analyse an elastic material than a material that exhibits plasticity. J integral is the path
independent integral of non-linear energy release rate and also shows the crack tip stresses and strain in the
materials. Thus the J integral can be viewed as both an energy parameter and a stress intensity parameter.
According to ASTM E 1737 fatigue precracked specimens and determination of J as a function of crack
growth. Load versus load-line displacement is recorded. The J-integral is determined and plotted against
estimated or physical crack growth within specified limits of crack growth. The resulting data reflect the
material's resistance to crack growth. The fatigue precracking load PM is given by Eq. (1) and Eq. (2)
For SE (B) specimen
.
= Eq. (1)
Where S = span of specimen.
For C(T) and DC(T) specimen
.
= ( )
Eq. (2)
Where W = specimen width, B = specimen thickness and b = width W – ap (physical crack front).
The loading rate of the specimen is such that the time taken to reach the load PM is between 0.1 to 10.0 min.
and the unloading rate should be as slow as the required accuracy to measure the crack length. The J-integral
shall be determined from load, load line displacement curves. At a given deflection, the area under the load-
displacement curve shall be evaluated for J-integral testing. For J-R curve determination, crack extension
should be measured in a manner such that the data points are evenly spaced over the prescribed test region.
Two J-∆a data points are required in the space between the ordinate of the plot and the secant line defined by
= (4/3) ∆ as shown in Figure2. Eight J-∆a data points are required between the secant line and the box
defined by the ∆a and Jmax from the Eq. (3) and Eq. (4).
∆ = 0.1 Eq. (3)
And
= Eq. (4)
Where b0 = W- a0 (original crack size).
The value of J-integral can be calculated from the given annexure according to the type of specimen
from the ASTM E 1737.
2.5 According to ASTM E 1290
The CTOD Test method ASTM E 1290 characterizes the fracture toughness of materials. The values of CTOD
may be affected by specimen dimensions. There are commonly single edge notched bend SE(B) specimens
and compact tension C(T) specimens are generally used. The value of CTOD can be differ by type of
specimen and dimensions of specimen. For example CTOD determined on SE(B) specimens using the square
section may be differ from the rectangular section, and may differ from C(T) specimens. The force vs clip
gauge displacement is may be five types as shown in Figure3. The construction lines drawn parallel to the
elastic loading slope to give vp, the plastic component of total displacement, vg.
According to ASTM E 1290, 2008 the value of CTOD is determined by Eq. (5)
= + ( )( ( )) Eq. (5)
( . . )
Where =
And Y, m, differs as the specimen changes. i.e. the type of specimen SE(B), C(T), A(T) etc.
The value of KIC obtained by ASTM E 399 test method may be used to estimate the relation between failure
stress and crack size in plane strain. KIC Plane-strain critical fracture toughness value obtained at slow loading
rates and the fracture is sudden and unstable with a little deformation. The J-integral values measured by
ASTM E 1737 characterize the toughness of ductile materials that lack sufficient size and thickness to be
tested for KIC in accordance with the requirements of Test Method E 399. Critical crack tip opening
displacement obtained by ASTM E 1290 and used to characterize the resistance of a material to crack
initiation and early crack extension at a given temperature. These test is done for the materials which have a
fatigue precracked notch. The use of ASTM E 1820 is for finding the all three fracture toughness parameter in
a single test and If the specimen does not fulfil the requirement of specimen size under ASTM E 399 then it is
invalid result. But in ASTM E 1820 it can be useful by some statistical approaches.The use of fracture
toughness in design is very essential and vast. On the other hand the brittle fracture is very dangerous than
ductile fracture. So, according to the Barsom and Rolfe, 1999 for minimize the possibility of brittle fracture in
a given structure, the one has three factors that can control it. First is Material fracture toughness at the
particular service temperature and loading rate and second is nominal stress and third is the crack size that is
already present in the material. General relationship among material fracture toughness (KC), nominal stress
( ), and flaw size (a) is shown schematically in Figure4. It is clear that the material having higher value of
fracture toughness is having the more values of combination of flaw size and nominal stress. For the design
point of view the Figure5 shows the clear relationship. In short if the particular combinations of stress and
flaw size in a structure reach the KC level, fracture can occur. There are many combinations of stress and flaw
size that may cause fracture in a structure that is fabricated from a structural material having the particular KC
Figure 4: Stress-flaw-size relation for a through- Figure5: Relation among stress, flaw size, and
thickness crack showing effect of higher KIC (100 material toughness
ksi√in.).
value at a particular service temperature and loading rate. Conversely, there are many combinations of stress
and flaw size, for example, and ao that will not cause failure of a particular material. So KI can increase
throughout the life of a structure because of crack growth by fatigue.
REFERENCES
1. ASTM E 8/E 8M – 08.“Standard Test Methods for Tension Testing of Metallic Materials”, ASTM,
2008.
2. ASTM E 399 – 08.“Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of
Metallic Materials”, 2008.
3. ASTM E813-81.“Standard test method for JIC, a measure of fracture toughness.American Society for
Testing and Materials”; 1982.
4. ASTM E 1290 – 08.“Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture
Toughness Measurement”, 2008.
5. ASTM E 1737-96. “Standard Test Method for J-integral Characterization of Fracture Toughness.
ASTM”, 1996.
6. ASTM E 1820 – 08a.“Standard Test Method for Measurement of Fracture Toughness”, 2008.
7. John M. Barsom and Stanley T. Rolfe. “Fracture and Fatigue Control in Structures: Applications of
Fracture Mechanics”, ASTM Manual Series: MNL41 ASTM, 1999.
8. Rice JR. “A path independent integral and the approximate analysis of strain concentration by notches
and cracks”, Journal of Applied Mechanics 1968; Volume 35:379–386.
9. Ted L. Anderson. “Ductile and Brittle Fracture Analysis of Surface Flaws Using CTOD”, Symposium
on the Surface Crack. ASTM 1986.
10. Ted L. Anderson. “Fracture mechanics – fundamentals and applications”, 3rd edition; CRC Press;
2005.
11. Xian-Kui Zhu and James A. Joyce.“Review of fracture toughness (G, K, J, CTOD, CTOA) testing and
standardization”, Engineering Fracture Mechanics; 2012 Volume 85, 1–46.
SUB-THEME 7
Frontier Areas of Research in Heat Transfer
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S7/O1
M. J. Gurav V.N.Kapatkar
G.S.Moze College of Sinhgad College of
Engineering Balewadi, Pune Engineering Vadgoan, Pune
Mmokashi04@gmail.com vnkapatkar@ rediffmail.com
ABSTRACT
The enhancements of heat transfer characteristics in a uniform heat flux circular tube fitted with inserts
creating annular blockages are experimentally investigated in this paper. This paper is outcome of
experimental study conducted to compare the rate of heat transfer with annular blockages in a tube. Blockages
are created by using insert rings of aluminum of various inner diameter creating 22%, 44% 48% and 64% of
blockage in the tube. It can be attributed that the use of ring inserts can cause the turbulence and uniformity of
temperature and pressure gradient in radial direction. The boundary layer along would be thinner with the
increase of turbulent flow and pressure resulting in more heat flow through fluid. In addition to this due to the
contact of six rings with hot inside tube wall there would be better heat transfer due to conduction. It is found
that each application of the % blockages can help to increase considerably the heat transfer rate over that of
the plain tube by about 20% - 40%. Nusselt number, Heat transfer rate, Reynolds number is determined with
the experimental data. It was found that the use of the annular blockage of 48% leads to a maximum heat
transfer rate that is up by 30 to 40% than plain tube.
1. INTRODUCTION
Heat transfer augmentation techniques (passive, active or a combination of passive and active methods) are
commonly used in areas such as process industries, heating and cooling in evaporators, thermal power plants,
air-conditioning equipment, refrigerators, radiators for space vehicles, automobiles, etc. Passive techniques,
where inserts are used in the flow passage to augment the heat transfer rate, are advantageous compared with
active techniques, because the insert manufacturing process is simple and these techniques can be easily
employed in an existing heat exchanger. In design of compact heat exchangers, passive techniques of heat
transfer augmentation can play an important role if a proper passive insert configuration can be selected
according to the heat exchanger working condition (both flow and heat transfer conditions,
Heat exchangers have several industrial and engineering applications. The design procedure of heat
exchangers is quite complicated, as it needs exact analysis of heat transfer rate and pressure drop estimations
apart from issues such as long-term performance and the economic aspect of the equipment.
The major challenge in designing a heat exchanger is to make the equipment compact and achieve a high heat
transfer rate using minimum pumping power. Techniques for heat transfer augmentation are relevant to
several engineering applications. In recent years, the high cost of energy and material has resulted in an
increased effort aimed at producing more efficient heat exchange equipment. Furthermore, sometimes there is
a need for miniaturization of a heat exchanger in specific applications, such as space application, through an
augmentation of heat transfer. Therefore, an increase in the efficiency of the heat exchanger through an
augmentation technique may result in a considerable saving in the material cost. The heat transfer rate can be
improved by introducing a disturbance in the fluid flow (breaking the viscous and thermal boundary layers),
but in the process pumping power may increase significantly and ultimately the pumping cost becomes high.
Therefore, to achieve a desired heat transfer rate in an existing heat exchanger at an economic pumping
power, several techniques have been proposed in recent years.
The science and engineering of air-side heat transfer enhancement plays a critical role in the design of various
engineering equipments. In the past researches, Royds (4) was the first to prove the useful effects of
turbulence flow generators on heat transfer in 1921 with many experiments and types of turbulators. Kreith
and Margolis (5),Kreith and sonju(6) proposed that heat transfer can be enhanced by introducing swirl flow in
the heat exchanger with tangential injection of the fluid at various locations along the tube axis. Marner and
bergles(7) reported experimental data for laminar flows of ethylene glycol and polybutene with twisted tape in
an isothermal tube. In general twisted tape insert can help to generate the swirl flow and stronger turbulence in
the tubes. The straight tape twisted in geometry form of helical tape with similar geometry of the screw tape,
called the helical tape was introduced in a research study (8).
The swirl flow generator is also used in augmenting heat transfer in many engineering applications. Filament
inserts are widely used for enhancing heat transfer rate. The Filaments inserts with holes, twisted tapes etc are
the examples. Inserts when placed in the path of the flow of the liquid, create a high degree of turbulence
resulting in an increase in the heat transfer rate and the pressure drop. The present work includes the
determination of friction factor and heat transfer coefficient with inserts having different annular blockages.
After extensive literature reviewed, the use of annular blockages inserts replacing the filament inserts is
discussed in the paper. To verify the enhancement in heat transfer experimentations is done.
2. EXPERIMENTATION
An experimental setup of circular tube with blockages is developed and discussed below
(fig 1).
Figure 1 shows the setup of Forced convection Heat transfer from circular tube with annular blockages.
Fig.1 Experimental set up
The MS tube has a test section length of L=500mm, with 25mm inner diameter and 28mm outer diameter. The
tube was heated by continually winding flexible electrical wire provided a uniform heat flux boundary
condition.
The outer surface of the test tube was well insulated with glass wool to minimize convective heat loss to
surroundings and necessary precautions were taken to prevent leakage from the system. The inner and outer
temperatures of bulk air were measured at certain points with multi-channel temperature measurement unit in
conjunction with the copper-constantan thermocouples.
The annular ring inserts as shown in Fig. 2 are made of aluminum. The rings are placed at equal intervals of
90mm.The inserts are fitted inside the test tube. Thermocouples T1 and T8 are placed in air stream before and
after the test section. Thermocouples T2, T3, T4, T5, T6 and T7 are embedded in the pipe wall to measure the
pipe wall temperatures. Manometer and Micro manometer are used to measure the pressure drop across the
orifice and test tube.
2.2 Test Procedure
The test procedure was started with 0% blockage ie.plain tube and gradually increased blockages were
introduced with aluminum ring inserts. The maximum blockage percentage attempted was 64% with the inner
diameter of 1.5mm.The plain circular tube without blockages was supplied with heater input 25, 50, 75 and
100 Watt and flow from blower and the temperature are recorded at each thermocouple. The same procedure
is repeated with various blockages of 22%, 44%, 48% and 64%.
Using the data obtained from experiments, rate of heat transfer, heat transfer coefficient, Nusselt Number and
ratio of Nusselt number to base line Nusselt Number for different heat input and for different mass flow rates
of air are discussed in the following subsections.
Enhancement of heat transfer has been studied for different ring inserts made of aluminum. Performance
graphs have drawn for Heat transfer coefficient and mass flow rates. The contact between rings and circular
tube wall from inside is inevitable and consequently heat transfer will exist due to heat conduction through
some contacted insert rings. It can be attributed that the use of ring inserts can cause the turbulence and
uniformity of temperature and pressure gradient in radial direction.
Theoretically the Nusselt number should be more as the Reynolds number increases with the % of blockages
but for 64% blockage the Nusselt number is decreasing as the flow gets blocked disturbing turbulent flow.
25W 50W
60 60
Nusselt Number Nu (AU)
Nusselt Number Nu (AU)
40 40
20 20
Nu Exp Nu Exp
0 0
Nu Analy Nu Analy
10915
12604
6302
8912
6172
8912
10915
12600
Fig. 3.1 (a)- Verification of Nusselt number for Plain tube for reading for 25 & 50 watts.
75W 100W
Nusselt Number Nu (AU) 60 70
6173
8913
10916
12604
Reynolds Number Re Reynolds Number Re
Fig 3.1 (c ) - Verification of Nusselt number for Plain tube for reading for 75 & 100 watts.
22.56% 42.24%
120 200
Heat Transfer Coefficient
160
80 75W 120 100W
80
(Expt) h-w/m²k
(Expt) h-w/m²k
40 25W 40 75W
0
0
50W 50W
1.92
2.74
3.36
2.5 4.3 3.87
100W 25W
Mass (gms/s) Mass (gms/s)
Fig. 3.2 Enhancement of heat transfer for 22.56% and 42.24% blockages
With increase in turbulence the Nusselt number increase cause enhancement in heat transfer coefficient than
plain tube.
The maximum Nusselt number observed is 97 at the Reynolds number 13286. Whereas for Plain tube 57.16.
The maximum Nusselt number observed with this blockage is 125 at the Reynolds number 15286.
48.16% 64%
200 200
(Expt) h-w/m²k
(Expt) h-w/m²k
40 50W 40 75W
0 0
75W 50W
2.217
3.163
3.874
4.473
1.445
2.092
2.575
2.959
100W 25W
Mass (gms/s) Mass (gms/s)
Fig 3.4 Enhancement of heat transfer for 48.16% and 64% blockages
The maximum Nusselt number observed is 161 at the Reynolds number 190925.
25W 50W
200
200
Nusselt Number Nu
Nusslet Number Nu
150
150 PT PT
100 100
50 2.2 50 2.2
0 1.9 0 1.9
1.8 1.5
1.5 1.8
Reynolds Number Re Reynolds Number Re
Fig. 3.6 (a) – 25W Curve Fig. 3.6 (b) – 50W Curve
75W 100W
200 200
Nusselt Number Nu
Nusselt Number Nu
150 PT 150 PT
100 100
50 2.2 50 2.2
0 1.9 0 1.9
1.8 1.8
1.5 1.5
Reynolds Number Re Reynolds Number Re
Fig. 3.6 (c) – 75W Curve Fig. 3.6 (a) – 100W Curve
4. CONCLUSIONS
REFERENCES
1 Bergles, A. E., Jensen, M. K., Shome, B., 1995, Bibliography on enhancement of convective heat and mass
transfer, Rensselaer Polytechnic Institute Heat Transfer Laboratory Report HTL-23; Introduction in J.
Enhanced Heat Transfer, 4, 1-6.
2.Bergles, A. E., 1997, Heat transfer enhancement – the encouragement and accommodation of high heat
fluxes, J. Heat Transfer 119, 8-19.
3.Bergles, A. E., 1998, Techniques to enhance heat transfer, in Handbook of Heat Transfer, Rohsenow, W.
M., Hartnett, J. P.,Cho, Y. I., eds., McGraw-Hill, New York, 11.1-11.76.
3.Bergles, A. E., 1997, Heat transfer enhancement – the encouragement and accommodation of high heat
fluxes, J. Heat Transfer 119, 8-19.
4.Q.liao,M.D.Xin, 2000,Agumentation of Convective heat transfer inside tubes with three dimensional
internal extended surfaces and twisted tape inserts., Chemical Engineering Journal 78(2000) 95-105
5. Kreith,F.and Margolis. 1959 Heat transfer and friction in turbulent vortez flow.Applied science
Resource,vol.8.no.6,pp 457-473
6. Smith Eiamsa –ard, Chinaruk Thianpong, Petpices Eiamsa, Pongjet Promvonge.2009, Convective heat
transfer in a circular tube with short length twisted tape insert., International communication in Heat and Mass
Transfer 36, 365-371
7 Kreith,F.and Sonju,O.K. 1965 The decay of a turbulent swirl flow in a pipe.Journal Fluid
mechanics,vol.22(part2),pp.257-271
8.BetulAyhan Sarac,Tulin Bali.,2007 An experimental study on heat transfer and pressure drop characteristics
of decaying swirl flow through a circular pipe with a vortex generator., Experimental Thermal and Fluid
Science 32,158-165
9. Eiamsa-ard, S.and Promvonge, P.2007.Enhancement of heat transfer in a tube with regularly spaced helical
tape swirl generators. Internal energy Journal 8, 29-36
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S7/O4
B.B.Pandit V.S.Kulkarni
, Department of Mathematics, Nagpur University Department of Mathematics
Nagpur-440033 Mumbai University
Maharashtra, India. Mumbai- 400098
panditbhagwat51@gmail.com vinayakskulkarni1@rediffmail.com
ABSTRACT
This manuscript deals with the heat transfer analysis of a rectangular isotropic plate subjected to
sinusoidal temperature distribution at initial edge (x = 0) along vertical axis. The convection due to dissipation
takes place at parallel extreme edge (x = a). The initial and extreme edges (y = 0 and y = b) along horizontal
axis are thermally insulated. Initially the rectangular plate is kept at zero temperature. Due to sinusoidal
temperature along the vertical axis the heat conduction takes place within rectangular plate. The heat transfer
analysis is done by finite difference method. The convergence and stability analysis of results obtained by
finite difference method are done. The results obtained by finite difference method are presented graphically
and interpreted technically.
Livne E. et al. [7] applied symmetric semi-implicit difference scheme for the formulation of heat conduction
equation. Hemkar P.W. et al. [6] considered Dirichlet problem for partial differential equation with
discontinuous initial conditions and applied finite difference method to obtain the solution of f parabolic
partial differential equations. Tony et al. [8] developed two dimensional finite difference scheme for solving
convection- diffusion problem also applied alternating direction implicit scheme of Polezhaev to solve for the
Helmholtz equation. Benito J.J. et al [1] solved parabolic and hyperbolic equations by generalized finite
difference method to obtain explicit solution, he also studied the convergence and truncation errors over
irregular grids. Faruk Yigit[4] studied approximate analytical solution of a two-dimensional heat conduction
problem with phase-change on a sinusoidal mold using a linear perturbation method. Recently Bin Shen et al.
[2] developed a heat transfer model based on finite difference method for grinding.
2.MATHEMATICAL MODEL:
Consider a rectangular plate with its dimensions 0 ≤ x ≤ a, 0 ≤ y ≤ b with initially at zero temperature. The
boundary value problem for heat conduction of a homogeneous isotropic solid is given as,
2 2
T T 1 T
(1)
2 2 t
x y
T
0 at y b
y
T f ( y) T
T 0 at t 0 hT 0 at x a
at x 0 x
T
0 at y 0
y
T
hT 0 at x a (3)
x
T
0 at y b (4)
y
T
0 at y 0 (5)
y
and initial condition
T 0 at t 0 (6)
where, T T ( x, y )
f ( y) T0 sin(2 y)
T0 is Temperature Strength.
3.MATHEMATICAL SOLUTION:
The finite difference method is applied [9] to solve the boundary value problem defined by (1) to (6).
One can divide the x, y, t domain into small intervals x, y , t such that
x ix i 0,1,.....N ( N x a)
y jy j 0,1,2,........
t nt n 0,1,2,........
The temperature at the nodal point (ix, jy ) at the time n.t is denoted by
Using the forward difference in time domain, time derivative of temperature is given as
n1 n
T Ti, j Ti, j
O( t )
t t
Finite difference expressions for the partial derivatives with respective to the space variables are given as
2 n n n
T Ti1, j Ti 1, j 2Ti, j 2
2 2 O (x)
x (x)
and
2 n n n
T Ti, j 1 Ti , j 1 2Ti, j 2
2 2 O (y )
y (y )
Substituting these values in the one dimensional heat equation, one gets the recursive relation as,
n1 n n n n n
Ti , j (1 4r )Ti , j rTi1, j +rTi 1, j rTi, j 1 +rTi, j 1
t
i 1, 2,....., j 1, 2,..........., n 0,1, 2,..... (7) where, r and
2
( x )
2
truncation error of order O ( t ) O ( x )
Substituting these values in the initial and boundary conditions, one gets the recursive relations as
0
Initially at t = 0 Ti, j 0 (8)
n
at initial edge (x = 0) T0, j T0 sin(2 jy ) (9)
n 1 1 n 1
at parallel extreme edge (x = a) Ti, j T (10)
1 hx i 1, j
n1 n 1
The initial and extreme edges (y = 0 and y = b) along horizontal axis Ti , j Ti , j 1 (11)
Equation (8) gives the initial temperature at each grid point of the plate (at t = 0).
Equation (7) gives the temperature at each internal node and equations (9) to (11) gives the temperature at all
the boundary points (at x = 0, x = a, y = 0, y = b).
The MATLAB has been used to determine the temperature at all the nodal points for different time intervals .
t 1 and
is stable for 0 r
2 4
( x )
Theorem 2: Due to Lax [10], the explicit finite difference scheme is stable if and only if it is convergent.
The above theorems have been used for the stability and convergence of solution obtained.
4.NUMERICAL CALCULATIONS:
For better accuracy of results obtained 200 iterations has been performed for each time step of t =17.8
seconds. The plate is divided in equal grids of x y =0.1 meters. For convergence and stability we have
used r = 0.2.
Dimensions:
Material Properties:
The numerical calculation has been carried out for a copper (pure) thin plate with the material properties
Temperature at grid points equally spaced with x y = 0.1 and at time t = 200x17.8 =3560 seconds is
given in the following table.
- - - - - - - - - - - - - - - - - - - -
0.0000 319.82 174.01 94.686 51.52 28.03 15.25 8.299 4.51 2.45 1.33 0.72 0.39 0.21 0.11 0.06 0.03 0.01 0.00 0.00 0.00
17 92 2 00 27 30 3 58 71 69 74 58 53 71 36 44 84 94 39 20
- - - - - - - - - - - - - - - - - - - - -
587.78 319.82 174.01 94.686 51.52 28.03 15.25 8.299 4.51 2.45 1.33 0.72 0.39 0.21 0.11 0.06 0.03 0.01 0.00 0.00 0.00
53 17 92 2 00 27 30 3 58 71 69 74 58 53 71 36 44 84 94 39 20
- - - - - - - - - - - - - - - - - - - - -
951.05 517.48 281.56 153.20 83.36 45.35 24.67 13.42 7.30 3.97 2.16 1.17 0.64 0.34 0.18 0.10 0.05 0.02 0.01 0.00 0.00
65 24 90 54 11 79 98 86 67 57 32 70 04 84 95 29 57 98 52 64 32
- - - - - - - - - - - - - - - - - - - - -
951.05 517.48 281.56 153.20 83.36 45.35 24.67 13.42 7.30 3.97 2.16 1.17 0.64 0.34 0.18 0.10 0.05 0.02 0.01 0.00 0.00
65 24 90 54 11 79 98 86 67 57 32 70 04 84 95 29 57 98 52 64 32
jΔy - - - - - - - - - - - - - - - - - - - - -
587.78 319.82 174.01 94.686 51.52 28.03 15.25 8.299 4.51 2.45 1.33 0.72 0.39 0.21 0.11 0.06 0.03 0.01 0.00 0.00 0.00
53 17 92 2 00 27 30 3 58 71 69 74 58 53 71 36 44 84 94 39 20
0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.0000 0.0000 0.0000 0.0000
0 0 0 0 00 00 00 00 00 00 00 00 00 00 00 00 00
587.78 319.82 174.01 94.686 51.52 28.03 15.25 8.299 4.51 2.45 1.33 0.72 0.39 0.21 0.11 0.06 0.03 0.01 0.00 0.00 0.00
53 17 92 2 00 27 30 3 58 71 69 74 58 53 71 36 44 84 94 39 20
951.05 517.48 281.56 153.20 83.36 45.35 24.67 13.42 7.30 3.97 2.16 1.17 0.64 0.34 0.18 0.10 0.05 0.02 0.01 0.00 0.00
65 24 90 54 11 79 98 86 67 57 32 70 04 84 95 29 57 98 52 64 32
951.05 517.48 281.56 153.20 83.36 45.35 24.67 13.42 7.30 3.97 2.16 1.17 0.64 0.34 0.18 0.10 0.05 0.02 0.01 0.00 0.00
65 24 90 54 11 79 98 86 67 57 32 70 04 84 95 29 57 98 52 64 32
587.78 319.82 174.01 94.686 51.52 28.03 15.25 8.299 4.51 2.45 1.33 0.72 0.39 0.21 0.11 0.06 0.03 0.01 0.00 0.00 0.00
53 17 92 2 00 27 30 3 58 71 69 74 58 53 71 36 44 84 94 39 20
319.82 174.01 94.686 51.52 28.03 15.25 8.299 4.51 2.45 1.33 0.72 0.39 0.21 0.11 0.06 0.03 0.01 0.00 0.00 0.00
0.0000
17 92 2 00 27 30 3 58 71 69 74 58 53 71 36 44 84 94 39 20
ix
900.0000
x=0
x=0.1
400.0000
x=0.2
x=0.3 x=0.5
Temperature
x=2 x=0.4
-600.0000
-1100.0000
Y
1000.0000
800.0000
y=0.2
600.0000
y=0.1
400.0000
Temperature
200.0000
y=0
0.0000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
-200.0000
-400.0000 y=1
-600.0000 y=0.6
-800.0000 y=0.7
-1000.0000
X
The sinusoidal temperature distribution can be observed by graph plotted of the temperature
along y axis. The convection due to dissipation takes place at parallel extreme edge can be
observed.
This type of work has a wide scope of application in industry for material design, structural
design etc.
REFERENCES
Journal articles
1. Benito J.J. et al., “Solving parabolic and hyperbolic equations by the generalized finite
difference method”, Journal of Computational and Applied Mathematics, pp 208 –
233(2007).
2. Bin Shen et al., “A Heat Transfer Model Based on Finite Difference Method for Grinding”,
Journal of Manufacturing Science and Engineering, Vol. 133(2011).
5. Harinaldi et al., “Flow and Heat Transfer Characteristics of an Impinging Synthetic Air Jet
under Sinusoidal and Triangular Wave Forcing”, International Journal of Engineering &
Technology IJET-IJENS Vol: 11(2011).
6. Hemkar P.W. and Shishkin G.I., “Approximation of parabolic PDEs with discontinues
initial condition”, East-West Journal of Numerical Mathematics, Vol.1, No.4, pp 287-
302(1993).
7. Livne E. and Glasner A., “A Finite Difference Scheme for the Heat Conduction Equation”
Journal of Computational Physics,pp 59-66(1985).
Books
9.Ozisik M.N., “Boundary value problem of heat conduction”, International Text book
Company, Scranton, Pennsylvania, pp84-87, 1968.
10.Thomas J.W. “Numerical Partial Differential Equation: Finite Difference Methods”,
Springer-Verlag, New York, 1995
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S7/O5
ABSTRACT
Micro-convection is a strategic area in transport phenomena, since it is the basis for a
wide range of miniaturized high-performance heat transfer applications. Surface area is one
of the most important parameter for high flux heat transfer in microchannels. This
experimental study deals with heat transfer using triangular microchannel having hydraulic
diameters of 321μm and 428μm. The diffrent microchannels made up of Copper with 29
microchannels each having length of 50mm, 70mm and 90mm and tip angles of 500 and 600
with width of 30mm each are analyzed numerically. Spacing between microchannel is also
varied and 300μm and 400μm spacing are considered for the analysis. The flow rate of water
is changed from 1 lpm to 8 lpm. It is observed that as hydraulic diameters increase from
321μm to 428μm the heat transfer coefficient decreases. Water side pressure drop increases
from 0.05 KPa to 0.45 KPa with decreases in hydraulic diameter from428μm to 321μm
respectively. As the heat input to microchannel increases from 10 Watt to 100 Watt the
temperature drop across varies from 20C to 220C as water flow rate.increases from 1 lpm to 8
lpm respectively. In this experiment microchannel configuration is divided into two sets. First
set consists of channel spacing and depth being kept constant and lengths of microchannel
and tip angles are varied.In the second set channel length and tip angle is kept constant and
channel spacing and depths are varied. The numerical analysis is done using C programming.
Experimental result shows variation with theoretical for tempreture drop is 10% to 20%
because assuming there is no heat loss. It is also observed that in all triangular microchannel
its geometry i.e. tip angle and hydraulic diameters are dominant parameters which influences
on rate of heat transfer.With increase in channel depth ,the flow passage area increases and
therefore resulting into heat transfer rate enhancement which is established through
experiments carried out in this study.
Keywords- Forced convection, Triangular microchannels, Pressure drop, Heat transfer etc.
1. INTRODUCTION
The microchannels find important research interest due to rapid growth of applications in
microelectronics for effective heat transfer. One of the emerging cooling approaches that
addresses the increased miniaturization of electronic component, is the microchannel based
heat sink. High heat transfer rate is the need of many systems in today’s world in order to
improve their performance by maintaining their operating temperature below acceptable
levels.For example in case of high performance computer chips and microelectronic
equipments surface temperature should be below 100 ºC. This can be achieved both by direct
geometry advantage of “higher heat transfer area” and “higher heat transfer coefficient”.As
the computer industry continues to make rapid advances in processor speed, thermal
management plays a more important role. The developments in microelectromechanical
devices naturally require heat removal systems that are equally small. Forced convection
boiling in microchannel is recognized as an enabling heat transfer mode that can be
efficiently exploited to dissipate heat for further ultra high power density electronic
components such as integrated Circuits (IC’s).Due to increased packaging density and
performance of microelectronic devices, IC chip power has significantly risen in last two
decades.All such other devices need to use microchannels for efficient heat transfer
phenomenon.
2.EXPERIMENTAL PROCEDURE
The experimental test piece consists of Copper block having dimensions of 30mm×50mm×4
mm.On this block triangular microchannel are formed on one side.The test set up has
microchannel provided with catridge heater on back side of the copper chip, two tanks for
storage of water, rotameter for measuring flow rate of water, two pumps for circulation of
water over microchannel, acrylic enclosure.Water is used as a working fluid. The acrylic
manifold has two ports, one at the inlet and other at the outlet. On the rear face, two K- type
thermocouples one on the right and other on the left side at inlet and outlet ports are installed
for measuring temperatures of water at respective points.Various parameters namely aspect
ratio, hydraulic diameters, outlet water temperature, heat flux transfer coefficient, pressure
drop etc.are theoretically determined and these values are validated by experimental obtained
values. The experiment were conducted in following cases.
1. Keeping flow rate constant and heat input vary from 10 Watt to 100 Watt
2 Keeping heat input constant and flow rate vary from 1 lpm to 8 lpm.
2.MICROCHANNEL CONFIGURATION
The reading are recorded during the experiment and the graphs are plotted.Figure 3 shows the
variation in pressure drop with respect to change in water flow rate at two different hydraulic
diameters. It is observed that as the hydraulic diameter increases from 321 μm to 428 μm, the
pressure drop decreases at all the water flow rates,this is due to increased flow area of
microchannel. As the height to width ratio also decreases with decrease in hydraulic diameter
which tends to decrease in flow area opening results into increase pressure drop across the
microchannel. As the analysis is done for 29 and 23 microchannels with water as medium.
0.45
0.4
0.35
0.3
Pressure 0.25
Drop(Kpa) 0.2
Hy.Dia - 321 µm
0.15
0.1 Hy.Dia - 428 µm
0.05
0
0 2 4 6 8 10
Flow Rate (lpm)
Pressure drop observed for hydraulic diameter of 321μm and 428 μm microchannel is 0.05
KPa to 0.35 KPa. Higher the range of hydraulic diameter less will be the pressure drop
observed. For minimum pressure drop 3 lpm to 7 lpm is best suitable flow rate for different
hydraulic diameter configurations.
In this study heat input is varied from 10 Watt to 100 Watt. A graph of heat input V/s
temperature drop across the microchannels under various hydraulic diameters is shown in a
fig 4. Temperature drop for hydraulic diameter 321μm to 428μm is 2 K to 6 K. As the heat
input to the microchannel increases the temperature drop across the microchannel is also
increases under forced convection heat transfer condition.
30
25
20
temp drop 0 K 15
321 µm
10
428 µm
5
0
0 50 100 150
heat input (watt)
After analysis of graphs plotted in this study certain conclusions are drawn and are as
mentioned below.
1) From nature of curve it is found that for 321μm, 428μm hydraulic diameter the
temperature drop is found to be optimum at a flow rate of 3 lpm to 7 lpm with a heat
input of 20 to 80 watt.
2) As flow rate increase the temperature drop across the microchannel is also decreases
with same heat input condition.
3) In future work microchannels are actually manufactured and inserted in a manifold for
testing. The test result with theoretical analysis is compared with available literature
for triangular microchannel configuration.
REFERENCES
ICAME2013 S7/O8
1.INTRODUCTION
This paper deals with experimental and CFD analysis of Thermosyphon to determine its
performance at various operating conditions. An experimental setup was created to test it
under various operating conditions similarly the performance was predicted byusing CFD
under same conditions. Test rig was versatile and was able to impose desired conditions on
heat pipe. The objective of the research is to investigate the effect of working fluid fill
volume, heat input and inclination angle on the performance of the two phase thermosyphon
through CFD as well as experimentation.
Various equations were used to simulate the flow pattern inside thermosyphon by using CFX.
Details of every aspect of analysis is explained in following paper, along with testing
procedure and Software simulation.
=− + + + +
1.2 Notations
= heat input to heaters
= heat carried by cooling water
= mass flow rate of cooling water
=shear stress in x direction
= normal stress in y direction
= normal stress in z direction
= Temperature of water at inlet
= Temperature of water at outlet
= Specific heat of water
ℎ = latent heat of vapourization
= Density of steam
2.EXPERIMENTAL SET-UP
The setup consists of two overhead tanks placed one over the other. Top/Auxiliary tank (of
variable head) was used to maintain constant head on the Main tank. The main tank supplied
water at constant head to the flow meter which provided metered flow into condenser jacket
with less variations. Torricelli’s equation was basic principle behind constant head. Flow
meter was able to regulate water discharge over wide range.
Condenser jacket consisted of two inlets i.e. provision for inlet and outlet of water. The
sensors were placed at inlet and outlet to measure the temperatures of incoming and outgoing
water.
Evaporator section consisted of eight 125W clamp on mica heaters with sensors placed
between them for measuring temperature on evaporator surface. One temperature sensor was
placed on adiabatic section. Asbestos wool was wounded over the heaters and sensors
covering entire evaporator and adiabatic section thus preventing heat loss by convection and
radiation from the surface.
A provision was made on test rig for tilting heat pipe, this was achieved by drilling holes over
specified angles on main frame (Stationary). Secondary frame (rotating) had provision to
clamp heat pipe, the whole assembly was bolted to the main frame via these holes.
3.TEST PROCEDURE
Clamp on mica heaters were mounted on evaporator section in parallel. Input to heaters was
provided by dimmerstat to control power. Single phase A.C wattmeter was used to measure
the input power to heaters. A constant water discharge was passed through the condenser
which carried the heat transmitted by heat pipe two temperature sensors were placed at inlet
and outlet measuring the temperatures.
Sensors were mounted along the length of heat pipe to plot temperature profile. After steady
state was achieved the temperature sensors didn’t show deflection in temperatures. The heat
pipe was then tilted at an angle with respect to vertical by nut and bolt arrangement and
further analysis was found in tilted position.
Flow was kept constant throughout the analysis, graphs were simultaneously plotted and the
effect of inclination was thus studied. After one pipe was completely tested heat input was
increased and further reading were carried out along with graphs.
4.RESULTS
The flow pattern was simulated in Ansys CFX flow solver for 14cc heat pipe for heat input of
1000W it was observed that the temperature along the surface of pipe was higher than 28cc.
The pipe worked at high temperature because of low quantity of working fluid. The pressure
also varies its maximum at bottom and minimum at the top.
Fig.1 Fig.2
The steady state temperature profiles of 28cc heat pipe were plotted for various heat inputs
and angle of inclination with vertical. The load on condenser was kept constant throughout
the experiment.
Temperature profile-440Watts
100
90
80
70
TEMPERATURE
60
0 deg
50
40 10 deg
30 20 deg.
20
40 deg.
10
0
0.085 0.17 0.255 0.34 0.4 0.485 0.57 0.63 0.715 0.8
LENGTH
Fig.3
Temperature profile-600Watts
90
80
TEMPERATURE 70
60
50 0 deg
40 10 deg
30
20 deg
20
10 30 deg
0
0.085 0.17 0.255 0.34 0.4 0.485 0.57 0.63 0.715 0.8
LENGTH
Fig.4
Temperature profile-800Watts
120
100
TEMPERATURE
80
60 0 deg
40 10 deg
20 deg
20
0
0.085 0.17 0.255 0.34 0.4 0.485 0.57 0.63 0.715 0.8
LENGTH
Fig.5
Temperature profile-1000Watts
180
160
TEMPERATURE 140
120
100 0 deg.
80 10 deg.
60
20 deg
40
20 30 deg
0
0.085 0.17 0.255 0.34 0.4 0.485 0.57 0.63 0.715 0.8
LENGTH
Fig.6
Flow inside 28cc heat pipe was simulated for 600W heat input, the velocity of flow
was maximum at bottom of evaporator section and decreases at the top. Flow took place at
subsonic velocity.
Fig.7
5.CONCLUSIONS
From graphs it was concluded that the temperature of heat pipe at evaporator section
increases with increase in angle of inclination, this was due to formation of liquid film on one
side of heat pipe. The heat transfer rate increases with increase in angle of inclination and
was maximum at 10° .
Thermal efficiency of pipe was measured by using simple calorimeter. It was found that
efficiency of pipe was 95% for =440W; 97.69% for =600W; 92.1% for
=1000W; 94.2% for =800W.Hence it was concluded that efficiency first increases
and then decreases. The main reason for low efficiency was high heat loss at elevated
temperatures for high values of heat input.
In Ansys CFX, pipe having less fill volume operated at higher temperature than pipe having
greater fill volume. As the fill volume decreases the velocity of flow increases and flow takes
place at higher velocities for fast transportation of heat.
REFERENCES
1) Yunus. A. Cengel, Heat and mass transfer a practical approach, Tata McGraw Hill
Education, 2007
2) J. P. Holman adapted by Souvik Bhattacharyya, Heat transfer, Tata McGraw Hill
Education, 2008
3) David Reay and Peter kew, Heat pipes theory design and application, B H publications,
Fifth edition John Anderson, Computational Fluid Dynamics
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013 S7/O9
ABSTRACT
This paper presents the computational study for predicting the influence of design
parameters on the overall thermal performance of the elliptical pin fin heat sink, subjected to
mixed convection. The design parameters include the heat sink geometry parameters as pin
aspect ratio, longitudinal and transverse pitches, fin bundle void fraction and axis ratio. Also
the influence of fin layout, approach velocity in the mixed convection range and input heat
flux are studied. A comprehensive analytical model is formulated having capability of
predicting influence of various geometrical, thermal and flow parameters on the thermal
resistance of the heat sink. The L25 orthogonal array of design of experiments is used to
minimise the computational runs. The ANSYS-CFX 13 is used for computational analysis of
elliptical pin fin heat sink. The data is analysed by using ANNOVA based JMP 3.14
statistical software. The Pareto charts are plotted to study the influence of various design
parameters. The regression analysis has provided the platform for deciding the selection and
omission of parameters for further experimentation by studying the Pareto charts. The Pareto
charts shown that input heat flux is having a very weak function with the air side performance
of heat sink, i.e. the thermal resistance. Hence, the further experimentations can be performed
at a constant heat input.
Keywords:heat sink, elliptical pin fins, mixed convection, heat transfer, design of experiment.
1.INTRODUCTION
The continuing increase of power densities in microelectronics and the simultaneous drive to
reduce the size and weight of electronic products have led to the increased importance of
thermal management issues in this industry. The temperature at the junction of an electronics
package (chip temperature) has become the limiting factor determining the lifetime of the
package (Kristiansen, 2001). The process industries and electronic industries are taking great
amount of efforts over the years to reduce the size of the devices. Advanced thermal
architectures are required to meet the future requirements of cooling.
In most of the cooling applications, natural convection and radiation is desirable because of
its simplicity and associated low cost of system. Electronic circuits with low power
consumptions and dissipation up to 5 W can be cooled very effectively by natural convection
(Scott, 1974). Yu and Joshi, 2002 investigated the enhancement of combined natural
convection, conduction, and radiation heat transfer from pin–fin heat sinks. The experimental
investigations were carries out by Sahray et al., 2010 to study the effects of fin height and fin
population density and provided further insight in heat transfer from horizontal-base pin fin
heat sinks in free convection of air.
Chapman et al., 1994 experimentally investigated the pin fin heat sinks with square, circular
and elliptical cross-section and found that elliptical pin fins are superior on air side
performance. Khan et al., 2006 analytically developed a model for determining heat transfer
from in-line and staggered pin-fin heat sinks used in electronic packaging applications and
examined the effect on overall thermal/fluid performance associated with different fin
geometries, including, rectangular plate fins as well as square, circular, and elliptical pin fins.
An experimental study was performed by Yang et al., 2007 for pin fin heat sinks having
circular, elliptic, and square cross-section with inline and staggered arrangements to study the
effect of fin density on the heat transfer performance. The work on numerical investigations
for elliptical pin fin heat sinks was reported by Seyf and Layeghi, 2010. Elliptical cross
section pin fins provide more general geometrical configuration than circular pins. In the
limiting cases, they represent a horizontal plate fin when the axis ratio, ϵ→ 0 and a circular
pin fin when, ϵ→ 1.
At low velocities, the presence of temperature gradient in a fluid in a gravity field always
gives rise to natural convection currents. Therefore, forced convection is always accompanied
by natural convection both being strong function of fluid velocity. The error involved in
ignoring natural convection is negligible at high velocity but may be considerable at low
velocities. In the open literature, very few studies are observed dealing with this kind of
mixed convection where forced convection is accompanied by natural convection in pin fin
heat sink applications. Kobus and Oshio, 2005 carried out a comprehensive theoretical and
experimental study on the thermal performance of a circular pin-fin heat sink under combined
natural and forced convection with jet impingement. Deshmukh and Warkhedkar, 2011 has
documented a comprehensive literature review on thermal performance of pin fin heat sinks
covering all modes of heat transfer, including mixed convection, up to 2011.
The purpose of current research is to study the influence of design parameters on the air side
thermal performance of elliptical pin fin heat sink subjected to mixed convection.
A theoretical model for predicting the thermal performance of a pin-fin array heat sink
is formulated by considering the heat sink to be made up of a number of individual pin-fins
operating in parallel.
2.1Theoretical Model
The shape of the elliptical pin fin is selected in such a way that the mass of the elliptical
and circular fin is same. Assuming the material and volume same for both the fins:
( ) =( )
(1)
= √4
(2)
The aspect ratio (ϒ) and axis ratio (ϵ) for the elliptical pin fin can be defined as,
Aspect ratio, ϒ = H/d, and Axis Ratio, ϵ = a/b
The total rate of heat transfer from the heat sink, , which contains n fins, can be
expressed as,
= + (3)
The effective thermal resistance of the heat sink, , , can be modeled as ,
, = [ℎ( − )+ ( tanh )] (4)
For doing the experimental investigation to evaluate the performance of elliptical pin fin heat
sink in terms of thermal resistance, the parameters like longitudinal pitch, SL, transverse
pitch, ST, fin bundle void fraction, α and aspect ratio, ϒ, need to be varied in some specific
interval along with the approach velocity, U∞.
A change in diameter has relatively little influence on the effective thermal resistance for the
air velocities in the mixed convection region. For very less velocities where natural
convection starts to dominate the heat transfer mechanism, a 25% change in diameter has 6%
change in thermal performance [10]. The fin height has a significant effect on air side
performance of heat sink with a limitation on aspect ratio. Fins that are too short can’t be
modelled with an adiabatic tip which may lead to poor performance and overheating of the
sink surface. Fins that are too long will have compromised fin efficiency since fin efficiency
is a strong function of fin height. Therefore, the variation in aspect ratio was done by varying
the height of the pin fin with fin efficiency close to 90%.
The parameters, longitudinal pitch, SL and transverse pitch, ST (and hence the fin bundle void
fraction, α) has a strong effect on the pin density. Too wide spacing in longitudinal and
transverse directions will lead to less dense structure resulting in less number of pins on base
plate, both in inline and staggered arrangement, which may have poor effect on air side
performance. The selection and variation in approach velocity was the most critical parameter
in view of the current study of mixed convection. A careful selection of velocity and its
variation should result in providing room for both natural convection and forced convection.
The mixed convection parameter, Gr/Re2, should be in the range of 0.1<Gr/Re2<10 so that
neither natural convection nor the forced convection would dominate the flow field.
For selection and variation of the parameters like longitudinal pitch, SL, transverse pitch, ST,
fin bundle void fraction, α, aspect ratio, ϒ, and approach velocity, U∞, the Taguchi,
1987method of an orthogonal array was used with five levels of parameters as represented in
Table. 1. Note that the void fraction, α, is a function of SL and ST.
As per Taguchi method of orthogonal array, for four independent parameters with five levels,
L25 orthogonal array method was used to arrange the input data in 25 combinations.
The data was analyzed by using statistical analysis software JMP 3.14. This software
analyzes the data by using analysis of variance (ANNOVA). The outcome is presented in
Figs. 2 – 5. The Pareto chart in Fig. 6 show the significant contribution of approach velocity
on the air side performance of heat sink. In mixed convection, with assisting flow, the
approach velocity has a significant role to play. Also it is observed that thermal resistance as
a response has a weak function with input heat flux (see Fig. 5) and aspect ratio (see Fig. 4).
The regression analysis has provided the platform for deciding the selection and omission of
parameters for further experimentation by studying the Pareto charts. The Pareto charts revels
the weak function of input heat flux with the air side performance of heat sink, i.e. the
thermal resistance. Hence, the further experimentation can performed at a constant heat input.
(a) Inline (b) Staggered
Fig. 4Influence of aspect ratio, ϒ, on thermal resistance.
The main objective of numerical simulation was to provide a physical insight of the mixed
convection mechanism and to study the influence of number of independent parameters on
the air side performance of elliptical pin fin heat sink both in inline and staggered
arrangement. The regression analysis has provided the platform for deciding the selection and
omission of parameters for further experimentation by studying the Pareto charts. The Pareto
charts shown that input heat flux is having a very weak function with the airside performance
of heat sink, i.e. the thermal resistance. Hence, the further experimentation can be performed
at a constant heat input. Also, it is revelled from the Pareto charts that, the aspect ratio, both
in inline and in staggered arrangement is having a little influence. But from the point of view
of natural convection assisting the forced convection, the fin height and its variation can’t be
ignored.
REFERENCES
1) Deshmukh, P. A., Warkhedkar, R. M., "Thermal Performance of Pin Fin Heat Sinks-A
Review of Literature", Int. Review of Mechanical Engineering, V. 5. N. 4, 726 (2011).
2) Kai-Shing Yang, Wei-Hsin Chu, Ing-Yong Chen, Chi-Chuan Wang, "A comparative
study of the airside performance of heat sinks having pin fin configurations", Int. J. Heat and
Mass Transfer, 50, 4661 (2007).
3) Khan, W. A., Culham, J. R., Yovanovic ,M. M., "The Role of Fin Geometry in Heat Sink
Performance", J. Heat Transfer, 128, 324 (2006).
4) Kobus, C.J., Oshio, T., "Development of a theoretical model for predicting the thermal
performance characteristics of a vertical pin-fin array heat sink under combined forced and
natural convection with impinging flow", Int. J. Heat and Mass Transfer, 48, 1053 (2005).
5) Kobus, C.J., Oshio, T., "Predicting the thermal performance characteristics of staggered
vertical pin fin array heat sinks under combined mode radiation and mixed convection with
impinging flow", Int. J. Heat and Mass Transfer, 48, 2684 (2005).
6) Sahray, D., Shamuell, H., Ziskind, G., Letan, R., "Study and Optimization of Horizontal-
Base Pin-Fin Heat Sinks in Natural Convection and Radiation", J. Heat Transfer, 132,
012503-1-12 (2010).
7) Sahray, D., Ziskind, G., Letan, R., "Scale-Up and Generalization of Horizontal-Base Pin-
Fin Heat Sinks in Natural Convection and Radiation", J. Heat Transfer, 132, 112502-1-10
(2010).
8) Seyf H. R., Layeghi M., "Numerical Analysis of Convective Heat Transfer From an
Elliptic Pin Fin Heat Sink With and Without Metal Foam Insert", J. Heat Transfer, 132,
071401-1-9 (2010).
Yu, E., Joshi, Y., "Heat transfer enhancement from enclosed discrete components using pin–
fin heat sinks", Int. J. Heat and Mass Transfer, 45, 4957 (2002).
9) Chapman, C. L., Lee, S., Schmidt, B. L., "Thermal Performance of An Elliptical Pin Fin
Heat Sink" , Tenth IEEE SEMI-THERM, 24 (1994).
10) Kristiansen, H., "Thermal management in electronics", Chalmers University of
Technology, Sweden (2001)
11) Scott, W. A., "Cooling of electronic equipment", John Wiley and Sons, New York, USA
(1974).
Taguchi, G., "System of Experimental Design", Quality Resources, 2, pp. 1173 (1987).
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013_S7/O10
ABSTRACT
The present work involves a numerical investigation of the effects of large-scale heating
on heat transfer characteristics in two-dimensional forced convective flow past a square
cylinder. To account for the effects of large-scale heating, a low-speed fully compressible
flow model of a thermally perfect gas with temperature dependent molecular transport and
thermophysical properties is considered. Numerical integration of the strong conservation
form of the governing equations, transformed into body–fitted coordinates, is carried out via
a two-step, predictor-corrector, flux-based Particle Velocity Upwind (PVU-M+) scheme.
Computations are carried out at Re = 60, 100 and 140 for 0 TW T T 1 in steps of
0.2 for different free-stream orientations, α = 0o, 15o, 30o and 45o while the remaining
parameters are kept fixed. At all parameter combinations the flow is found to be unsteady
due to periodic vortex-shedding. It is shown that the data obtained for the Nusselt number at
different Re and ε can be transformed into appropriate scaling parameters, namely, Effective
Nusselt number (Nueff) and Representative Reynolds number (Rep) that yield a complete
collapse of the data at different Re and ε for a fixed free-stream orientation. A procedure for
achieving the best collapse is also proposed.
1.INTRODUCTION
Studies carried out for bluff body flows with heat transfer have revealed that heat exchange
can significantly alter the flow dynamics It is also known that the thermal buoyancy can lead
to suppression of the vortex shedding for supercritical Reynolds numbers (Chang and Sa
(1990), Hasan and Ali (2013)). In comparison to the isothermal scenario, the scenario
involving heat exchange involves more complicated physics owing to the possibilities of
various thermal effects like:
i) Significant variations in density across different fluid particles (stratification) giving
rise to buoyancy forces.
ii) Large temperature variations leading to significant volumetric straining effects in
individual fluid particles
iii) Large temperature variations leading to variations in molecular transport properties,
thermo-physical properties etc.
Most of the studies on non-isothermal flows have focused only on the effects of stratification
and the buoyancy forces in the presence of an external force field like gravity (Sharma and
Eswaran (2004), Bhattacharyya and Mahapatra (2005), Singh et al. (2007), Ranjan et al.
(2008), Sahu et al. (2009)). Very little attention has been given to the large-scale heating
scenario in which the heating is large enough to cause significant volumetric straining in the
fluid particles and significant variations in transport and thermophysical properties. In fact,
there are a few studies involving a circular cylinder (both experimental and numerical)
subjected to large heating (Sabanca and Durst (2003), Shi et al. (2004), Wang and Travnicek
(2001)). However, the problem of flow past a heated square cylinder with large-scale heating
remains to be investigated both in the forced and the mixed convection regimes.
Figure 1 shows the generic configuration for the problem of two-dimensional non-
y
TW≠T
d
g
U T
,T
2.MATHEMATICAL FORMULATION
The flow is to be modeled as unsteady, compressible flow in order to capture the effects of
large-scale heating. Therefore, the equations representing the basic conservation laws must
be supplemented with the various equations of state in order to achieve closure for laminar
flows. The dimensionless governing equations together with the boundary conditions and the
various dimensionless parameters involved are described in brief in the following sub-
sections.
0
0
J (1- ) / Fr 2 , (2)
2
-1 (1- ) M v - -1 .V
Fr
where F ( 1)M 2 pu DF , G ( 1)M 2 pv DG .
Re Re
F G
In the terms , of the flux vectors F, G, respectively, the quantities DF& DG are:
2 v 2u v u 2 u 2v v u
DF u v , DG v u . (3)
3 y x x y 3 x y x y
In Eqs. (1)-(3), the symbols t, x and y represent the dimensionless time and the space
coordinates (Fig. 1). The quantities ρ, u, v and E appearing in the solution vector U, are the
dimensionless density, x-velocity, y-velocity and total energy. The remaining flow variables
occurring in the flux vectors F, G are the dimensionless pressure, coefficient of viscosity and
thermal conductivity symbolically represented as p, μ and k, respectively.
The thermodynamic state equations for a thermally perfect gas are expressed in
dimensionless form as,
3
γ(γ 1) 2 2 1 + γ M2 p 2
1+
E e M u v , ρ =
2
, μ = T , k = A + BT + CT 2 ,
2 T T +
C 2 C 3 C 4
e = T + 1 T - 1 + 2 T - 1 + 3 T - 1 . (4)
2 3 4
Symbols e, and σ (= S / T ) in the thermodynamic state relations are dimensionless
internal energy and the dimensionless Sutherland Law constant, respectively. The various
constants in Eq. (4) are given as,
These constants are obtained by curve-fitting the experimental data obtained from
literature (Holman, 1989). The data from Eq. (4) over the range 1 T 3 is utilized to obtain
the inverse curve-fit relation given as,
T = - 0.04921+1.08234 e - 0.03404 e 2 - 2.8819 × 10-4 e3 . (6)
Equations (1)-(4) have been converted into dimensionless forms using size of the cylinder
‘d’, residence time ‘(d / U∞)’ and free-stream velocity U∞ as the length, time and velocity
scales. Except for pressure, all the thermodynamic and transport properties are scaled with
respect to their free-stream values.
For the present problem involving forced convection, the effects of gravity have been
neglected i.e the terms in source vector J containing Fr have been dropped.
At the surface of the square cylinder, the conditions in non-dimensional form are expressed
as,
u = v = 0, TW 1 , (7)
where ε is the overheat ratio defined as TW T T . The symbols TW and T represent
the dimensional uniform cylinder surface and uniform free-stream temperatures, respectively.
For pressure, the normal momentum equation is utilized and density is updated via equation
of state.
At infinitely large distance from the cylinder the free-stream conditions must exist.
Mathematically,
V sin ˆi cos ˆj, T 1.0, 1.0 (8)
For the purpose of numerical computations, the infinite domain is truncated by introducing
an artificial circular boundary concentric with square cylinder and enclosing it. Characteristic
boundary conditions are imposed on this boundary within the framework of local one-
dimensional flow approximation along the normal direction to the artificial boundary (Hirsch,
1990). At the inflow portion, the density and the tangential velocity component are fixed
equal to their free-stream values. At the outflow portion, density is updated using a
convective boundary condition and the tangential velocity component is obtained via
vorticity extrapolation from the interior.
The undisturbed free-stream conditions are specified in the entire flowfield as initial
conditions.
In the present investigation, except for the Over-heat ratio, all the dimensionless control
parameters are kept fixed at values given as, Re = 100, M = 0.1, Pr = 0.7, γ = 1.4, = 0, α = 0
and σ = 110 / 298 = 0.369. The Over-heat ratio is varied in the range [0, 1] in steps of 0.2.
The free-stream Mach number is deliberately kept small to avoid any significant
compressibility effects.
3.METHODOLOGY
The infinite physical domain surrounding the cylinder is truncated by an artificial boundary
in the form of a circle whose center is coincident with that of the square cylinder. The
truncated doubly connected physical x-y domain is mapped on the simply connected
rectangular domain in the ξ-η computational plane using well established techniques of
generating O-type grids in doubly connected domains (Warsi (1999)).
F G,
F x F y G, G x y
The PVU-M+ scheme is utilized to carry out the computations (Shameem, 2011). The PVU-
M+ is a flux-based, two-step time integration scheme that is shown to be quite accurate and
stable for a wide range of flow Mach numbers ranging from 0.1 to 10. The scheme is an
extension of the PVU scheme given by Qamar et al. (2006). The main idea of the scheme is
to split the total fluxes into a convective and a non-convective part. The convective
components along x and y directions are Fc = u U and Gc = v U, respectively. The non-
convective components Fnc, Gnc can be readily determined by subtracting the convective
components from the total flux vectors F and G. Using Eq. (13), the convective flux vectors
along ξ and η directions are F c u U and G
c u U, respectively. For details of the scheme,
the reader is referred to the work of Hasan, Mujaheed and Shameem (2011).
Before proceeding to validate the numerical methodology along with the computer code,
various numerical issues / aspects are given due consideration. The presence of sharp corners
poses numerical difficulties in the application of the normal momentum equation for
pressure. A new procedure which involves distance weighted interpolation of corner values
of pressure from eight neighboring points on either side of the corner has been employed
which yields good results.
For determining a suitable position / distance for the artificial boundary from the center of the
cylinder as well as a suitable grid, convergence tests are carried out. In these tests, numerical
simulations for the case of an unheated cylinder (ε = 0) with (α = = 0), are carried out. In
each of these tests the global output flow parameters like time mean Drag coefficients, CD ,
r.m.s fluctuations of Lift coefficient and vortex-shedding frequency observed from the lift
oscillation cycle are recorded. A dimensionless distance of 60 for the artificial boundary and
a grid having 241 325 points are found to be appropriate for the present study.
The Nusselt number data obtained for low heating levels (ε = 0.2, α = = 0) for Re = 60, 100
and 140 is compared with the numerical data reported by Sahu et al. (2009) in Table 1. The
differences observed in the values of Nu W obtained from the present model and those
reported by them is predominantly owing to the temperature dependence of thermal
conductivity considered in the present compressible model. This is further confirmed by
removing the effect of increase of thermal conductivity over and above the free stream value
and defining the mean free-stream Nusselt number as, Nu k W k Nu W . The values of
mean free-stream Nusselt number are in much closer agreement (within 4%) to the values
reported by Sahu et al. (2009).
Table 1: Comparison of Nusselt number data with the numerical data reported by
Sahu et al. (2009)
The various scaling laws for Nusselt number for forced convective flows past heated bluff
bodies for fixed Pr can be written in a generic form as,
Nu W func(Re, TW T , ) (13)
It is in general difficult to obtain reliable curve-fit scaling laws involving two or more
independent variables from the data obtained from either numerical or physical experiments.
In order to overcome the difficulty, Wang and Travnicek (2001) demonstrated that for a
circular cylinder, excellent data collapse could be achieved by combining the heating effects
with inertia and viscous effects in a manner so as to transform Eq. (13) as,
Nu eff func(Re p ) , (14)
where the quantities Nu eff , Rep are termed as ‘Effective Nusselt number’ and ‘Representative
Reynolds number’, respectively. These transformed variables are defined as,
m
Nu eff (k W k eff )Nu W , Re p Reeff TW T . (15)
The quantity Reeff in Eq. (15) is defined as,
Reeff (eff ) (eff ) Re . (16)
The properties eff , eff and k eff must be evaluated at a temperature ‘ Teff ’, termed as
‘Effective Temperature’, that lies in the range [ T , TW ] and given as,
Teff T 1 c (TW T ) T 1 c , c [0, 1] . The values of (c, m) that yield the best
collapse of a given data set must be found so that the relation expressed via Eq. (13) can be
transformed into the functional relation given by Eq. (14).
In the present work, the numerical data obtained for Nu W at different Re and over-heat ratios
or TW T for different free-stream orientations is collapsed using the above ideas. For this
purpose, a new mathematical procedure is proposed that employs the minimization of a scalar
L1-norm, that is a measure of data collapse in the Nu eff Re p plane, defined as,
n
(m, c) (Zi 1 Zi ) (Re p i 1 Re p i ) (Zi Zi 1 ) (Re p i Re p i 1 ) , (17)
1
where Z = Nu eff and n is the total number of data points across different Re and TW T or ε.
The global minimum of the norm χ is found by varying m, c in steps of 0.05 in the range [0,
1] for both m and c and carrying out a linear search over the set of values of the norm. Small
values of indicate a good collapse of the data with respect to the representative Reynolds
number Rep.
A typical variation of with respect to the temperature parameter ‘c’ for m = 0.15 obtained
by utilizing the Nusselt number data at (α = 45o) is shown in Fig. 3. It is interesting to
observe that exhibits a minimum at c = 0.25 for m = 0.15. The
Fig. 3 Variation of norm χ with the parameter c at m = 0.15 for the heat transfer data
obtained for different combinations of (Re, TW T ) at α = 45o
minimum value of observed for m = 0.15 is 0.0537. Interestingly, the norm exhibits a
highly non-monotonic trend with several local minima. A strong local minimum also exists
for c 0.6 which is often utilized for estimating effective temperature for scaling
characteristics of forced convection flow past a heated circular cylinder. Therefore, the
proposed procedure and the norm allow precise quantitative determination of the
‘Effective temperature’ which results in the best possible collapse for a given data set. For
other values of m in the range [0, 1], the minimum values of observed are higher than the
one observed at m = 0.15 as shown in Table 2. Therefore for the data obtained at α = 45o, the
combination of (m = 0.15, c = 0.25) yields the best collapse of the ( Nu W Re TW T ) data.
Table 2: Values of χ for different combinations of m and c for the case of Nusselt number at
α = 45o
S. No m cmin
Table 3 provides the global minimum points (m, c) and the corresponding minimum values
min observed for the data recorded at different free-stream orientations α. It is quite
interesting to observe that at all orientations the global minimum occurs at m = 0.15
α m cmin
These curve-fit relations can thus be utilized for the prediction of heat transfer rates within
the range of parameters considered in the present study.
5.CONCLUSIONS
The present study highlights the role of a compressible flow model to investigate
theoretically / numerically the large-scale heating effects in forced convective flow of air past
a heated square cylinder. The compressible model accounts for the effects of; a) thermal
volumetric straining and the density variations of individual fluid particles, b) the variations
of transport and thermophysical properties.
The heat transfer data obtained from the numerical solution of the model at different
combinations of Re and Over-heat ratio ε at different free-stream orientations is utilized to
develop heat transfer scaling laws utilizing the concept of Effective temperature ‘ Teff ’ and a
set of appropriately derived variables termed as Effective Nusselt number, Nu eff and
Representative Reynolds number, Rep defined as,
m
Nu eff (k W k eff )Nu W , Re p Reeff TW T .
These transformed variables are defined in terms of fluid properties evaluated at Teff = 1+cε.
The scaling parameters (m, c) that yield the best collapse of the Nu W Re TW T
numerical data on the parametric space of the transformed variables Nu eff and Rep are
estimated through a novel procedure involving the minimization of a scalar measure or norm
that indicates the extent of the data collapse. This new procedure is shown to yield estimates
of Teff as 1+0.25ε and m = 0.15 for all free-stream orientations considered in the present
study.
REFERENCES
ICAME2013-S7/P2
ABSTRACT
Extended surfaces, commonly known as fins. Extended surfaces are used in variety of
engineering applications with different shapes.In present work, a one dimensional Cylindrical
fin is used for the thermal analysis .The problem was to find out the temperature distribution
on different points along the length of fin and heat flow rate. The results obtained by
Experimental method are compared with analytical and Ansys results. The results are also
studied by increasing the air flow rate and by changing the fin material.
1.INTRODUCTION
Heat transfer is a phenomenon which occurs due to the existence of the temperature
difference within the system or between two different systems, in physical contact with each
other. The heat generated may be dissipated to another body or to the surrounding through
conduction, convection and radiation which are collectively termed as ‘modes of heat
transfer’. Heat transfer by convection is given by Newton’s law of cooling which states that,
“The rate of heat transfer by convection between a surface and a surrounding is directly
proportional to the surface area of heat transfer and also to the temperature difference
between them.
There are only two ways by which the rate of heat transfer can be increased, i.e., one by
increasing the heat transfer coefficient h and the other by increasing the surface area As.
When the available surface is found to be inadequate to transfer the required quantity of heat
the surface area exposed to the surroundings is frequently increased by attachment to
protrusions to the surfaces. These protrusions are called extended surfaces or fins.
Extended surfaces are used with various types of materials and simple shapes, such as
rectangular, square, cylindrical, annular, tapered or pin fins, to a combination of different
geometries. The extended surfaces are widely used in Convectors for steam and hot-water
heating systems, Economizers for steam power plants, Radiators of automobile etc.
2.LITERATURE SURVEY
R.Karthikeyan and R.Rathnasamy [1]has been conducted experiment for various flow
rates and clearance ratios with cylindrical and square cross-sections pin-fin attached with
duralumin flat plate. Their experimental result shows the Effect of Clearance Ratio, Area,
Pin-fin shape, Pin-fin arrangements on heat transfer rate. They concluded that square cross-
section fins may lead to better heat transfer.
Young Min Han et al [3] had done Analysis of a one-dimensional fin using the analytic
method and the finite difference method.Theirresults show that the relative error between the
analytic method and the finite difference method decreases as the numbers of nodes for finite
difference method increase.
Manpreet Singh Brar, Sunil Kumar[4] carried outAnalysis of Steady State Heat
Conduction Problem Using Element free gelerkin method to obtain the temperature
distribution on different points across the thickness of a plane wall. The results obtained by
EFG method are compared with analytical and FEM results to validate the proposed
MATLAB codes.
N.Nagarani and K.Mayilsamy[5] carried out experimental heat transfer analysis on annular
circular and elliptical fins. Their experimental results shows that Fin efficiency is higher for
elliptical fin than circular fin and it could be a better choice if space restriction is along one
particular direction, while the perpendicular direction is relatively unrestricted.
Thermal analysis is used to determine the temperature distribution and related thermal
quantities in the model.
Basic steps in Thermal analysis
a) Defining the element type and material properties.
b) Modeling of geometry of pin-fin and meshing.
c) Applying load and boundary condition.
d) Temperature Distribution along the length and heat transfer rate.
Brass fin with cylindrical Cross-section having diameter 12.7mm and length 141mm is used
for thermal analysis. By applying boundary condition Temperature distribution and Heat
transfer rate is calculated
Fig 1.Fin model
4.MATLAB PROGRAMMING
For the analytical method Matlab software is used. Analytical method gives heat transfer rate
through the fin.
5.EXPERIMENTAL ANALYSIS OF FIN
Experimental Setup
5.1Experimental Procedure
5.2 Specifications
1. Duct size=14.5cm*9.8cm.
2. Length of fin= 14.1cm.
3. Diameter of fin=12.7mm.
4. Diameter of orifice=2.6cm.
5. Coefficient of discharge (cd) =0.65
6. Diameter of delivery pipe=3.6cm
7. No. of thermocouples=7.
5.3 Calculation
6.VALIDATION OF RESULTS.
70 70
60 60
ansys ansys
50 50
40 40
30 matlab 30 matlab
20 20
10 experiment 10 experimenta
al 0 l
0
0 0.05 0.1 0.15
0 0.05 0.1 0.15
80 80
70 70
60 ansys 60
50 50
ansys
40 matlab 40
30 30 matlab
20 20 experimental
10 experiment 10
al
0 0
0 0.05 0.1 0.15 0 0.05 0.1 0.15
2.5 4
2 ansys 3 ansys
1.5
matlab 2 matlab
1
0.5 1
experimenta experimenta
0 l 0 l
0 10 20 30 0 10 20 30
Aluminum Brass
7.CONCLUSION
1) Temp. Distribution along the length of fin is obtained by analytical, Ansys and
Experimental method for different material at different air flow rate.
2) The Results obtained from Experimental, analytical and Ansys method, it is found
that heat transfer rate of Brass fin is more as compared to the Aluminum.
NOMENCLATURE
0
Tm - Average fin temp (0 c)
0
Tmf - Mean film temperature (0 c)
Ka- Thermal conductivity of air (W/mk)
ρa- Density of air (Kg/m3)
υa- Kinematic viscosity of air (m2/s)
a1- Area of delivery pipe (m2)
a2- Area of orifice (m2)
Q- Air flow rate (m3/s)
A- Area of cross-sectional of duct, (m2)
Va- Velocity of air at ambient temperature (m/s)
Vmf - Velocity of air, (m/s)
Re - Reynolds No,
Nu - Nusselts No,
h- Heat transfer coefficient (W/ m2k)
Af - Area of cross-section of fin, (m2)
P- Perimeter of fin, (m)
m- Fin parameter
REFERENCES
1. R. karthikeyen and R. Rathnasamy “Thermal performance of pin-fin arrays”
International journal of advanced engineering sciences and technologies vol.10, issue
1,125-138.
2. H. Yuncu and G.Anbar. “An experimental investigation on performance of
rectangular fins on a horizontal base in free convection heat transfer”. Heat and Mass
Transfer 33 (1998) 507-514.
3. Manpreet Singh Brar,Sunil Kumar “Analysis of Steady State Heat Conduction
Problem Using EFGM” International Journal of Engineering and Management
Research,ISSN No.: 2250-0758Vol.-2, Issue-6, December 2012.
4. Young Min Han ,Joo Suk Cho , Hyung Suk Kang “Analysis of a one-dimensional fin
using the analytic method and the finite difference method”J. KSIAM Vol.9, No.1,
91-98, 2005.
5. N.Nagarani and K.Mayilsamy“Experimental heat transfer analysis on annular circular
and elliptical fins”.International Journal of Engineering Science and Technology.
Vol. 2(7), 2010, 2839-2845.
6. M. Sudheer, G. VigneshShanbhag, Prashanth Kumar and ShashirajSomayaji “Finite
element analysis of thermal characteristics of annular fins with different
profiles”.ARPN Journal of Engineering and Applied Sciences.ISSN 1819-6608 VOL.
7, NO. 6, JUNE 2012.
7. Nitin.S.Gokhale,Sanjay.S.Deshpande,Sanjeev.V.Bedekar,Anand.N.Thite.Finite to
Infinite “Practical Finite Element Analysis”.1edn.ISBN978-81-906195-0-9.
Proceedings of International Conference on Advances in Mechanical Engineering
ICAME2013-S7/P2
ABSTRACT
Heat pipes are essentially a means of transferring high rates of heat even with very
small temperature gradients, and as such may be considered thermal “superconductors”.In the
case of heat pipes for HVAC purposes, refrigerants such as R22 and R134a have traditionally
been used as working fluids. Use of water as working fluid for Heat pipes, not only provides
a greener solution but it would also allow improvements in its efficiency. When refrigerant is
replaced by water in heat pipe then the associated carbon penalty significantly decreases.
Also water is harmless to the environment and has an ozone depletion and global warming
potential of zero.
In spite of all above, open literature reveals very fewer efforts towards use of water as a
working fluid in Heat Pipes. Therefore, the current work is dedicated to design and
investigate the performance of a water type wraparound heat pipe for low humidity condition.
The performance was investigated for the working conditions of inlet air temperature 22.5 0C,
outlet air temperature 16.1 0C, with air flow rate of 2000 CFM at 12 fins per inch (FPI). The
theoretical performance was validated with that obtained using commercially available
software FLUENT for the same operating conditions of Heat pipe.
Keywords: wraparound heat pipe; evaporation section; condensation section.
I. INTRODUCTION:
Air cooling solution which comprises a fan and heat sink is employed to remove heat
generated by electronic device for stability and enhanced performance and life. Heat pipes are
two-phase heat transfer devices with high effective thermal conductivity. Due to high heat
transport capacity, heat pipe has become much smaller than traditional heat exchangers in
handling high heat fluxes. Heat pipe technology has found increasing applications in
enhancing the thermal performance of cooling devices in microelectronics, energy saving in
HVAC systems, surgery centres, hotels, clean rooms as reported in X. Yang et al., 2012. Heat
pipe is an evaporation-condensation device for transferring heat in which the latent heat of
vaporization is exploited to transport heat over long distances with a corresponding small
temperature difference. Closed circulation of the working fluid is maintained by capillary
action. In many applications, the heat transport rate is typically limited by the capillary
pressure that can be generated by the wick structure, reported in R. Kempers et al., 2006. A
number of investigations showed that heat transfer in the condenser section does appear due
to conduction, and most cases assume the same is true in the evaporator even reported in A.J.
Robinson et al., 2008. Several measurement techniques have been used to describe the flow
pattern in verticaland horizontal pipe flows reported by Meysam Rahmat et al., 2010, R.
Kempers et al., 2008.Recent work conducted by using nano-fluids to investigate the heat
transfer characteristics of various geometries were reported by Jocelyn Bonjour et al., 2009.
In the current work; the inside water temperature of tube recorded as 17.55 0C in evaporation
section and 16.32 0C in condensation section. It was observed that, the mass flow rate of
water decreases and mass flow rate of vapour increases continuously from the condensation
inlet to the evaporation outlet. (The performance of wraparound heat pipe were investigated
using water, R-134A etc, for the inlet temperatures of 22.5 0C and 22.2 0C.)
The heat transfer from the air to the surface of the heat pipe by convection (i.e. at the
evaporation section) was obtained by Newton law of cooling expressed as;
Q = h.A. ( Ti - T s ) (2)
The surface temperature (Ts) of tube after heat transfer by convection was found to be 18.1
0
C. The total heat transfer area in presence offin was estimated as;
A = Ab + η . N. Af(3)
The heat transfer rate by conduction through the tube wall thickness was obtained as,
× × { }
Q= (4)
From the properties of water at the saturation temperature of 17.04 0C, the type of flow inside
the tube was noticed to be turbulent. The heat transfer coefficient of water inside the pipe was
calculated using Dittus Boelter equation,
The Convection heat transfer to the working medium ‘water’ from inner surface of pipe was
obtained by the following equation;
Figure 2: Single tube heat pipe Figure 3: Heat pipe analysis at different section
Figure 4a: Mass flow rate of water and vapour Figure 4b: Mass flow rate of water and vapour
along the condensation section along the evaporation section
The latent heat involved in calculation of mass flow rate at each part along the condensation
section was obtained by addition of hf at water temperature and qconv across that part. The
variation in the mass flow rates so obtained in condensation and evaporation section is shown
in figures 4a and 4b respectively.
From the above graphs, we can observe that the mass flow rate of water decreases
continuously whereas mass flow rate of vapour continuously increases from the start of
condensation section, which is in accordance with natural behaviour.
The effect of working fluid on the effectiveness of heat pipe was verified with water and R-
134 A as working fluids for the inlet temperatures of 22.5 0C (set-I) and 22.2 0C (set-II).
From the heat transfer calculations with R-134 A, the temperatures of refrigerant inside the
evaporation and condensation section for set-I were found to be 17.77 0C and 16.32 0C
respectively. For the inside temperature 17.77 0C, the preheat temperature was 18.86 0C. The
effectiveness of Heat pipe was obtained using following equation;
Effectiveness = (8)
The effectiveness of Heat pipe with water and R-134A for the inlet air temperatures of 22.5
0
C and 22.2 0C are shown in Table 1.
Table 1: Effectiveness of Heat Pipe
V.COMPUTATIONAL MODELLING:
In the analysis of wraparound heat pipe, single tube with fins was considered. The geometry
contains 420 numbers of fins on both evaporation and condensation section. Due to very
small thickness (0.15 mm) and large number of fins on both the sections of heat pipe, it was
difficult to mesh the geometry and run the simulation. To overcome this difficulty and
simplify the problem, the geometry was divided into two parts without affecting the nature
and accuracy of the results.
The first part deals with the temperature analysis of a single fin, from which the pipe surface
temperature was obtained. The geometry created and meshed is shown in figure 5. In the second part
geometry considered was a plain Heat pipe (i.e. without fins) which is as shown in figure 6. This is
based on the fact that the temperature of air flowing over the heat pipe equals to the surface
temperature obtained from the analysis of first part.
Figure 5: Geometry of fin with hole Figure 6: Geometry of single Heat pipe
The contour plot for temperature variation of a single fin is shown in figure 6. The highest
temperature of 20.5 0C was noticed at the outer edge of the fin. The surface temperature around the
hole was approximately 18.5 0C.
The contour plots of temperatures of heat pipe for evaporator and condenser sections are shown in
figures 8a and 8b. The temperature for the evaporation and condensation section varies from 17 0C to
17.55 0C and 17.03 0C to 16.5 0C respectively.
The mass flow rate of water and vapour obtained from simulation is shown in fig 9(a) and 9(b). It was
observed that, the mass flow rate of water decreases and mass flow rate of vapour increases
continuously from the condensation inlet to the evaporation outlet, similar to that recorded in
theoretical analysis. The deviations in the results were within 7%.
Figure 8a: Temperature contour plot for Figure 8b: Temperature contour plot for
evaporation section condensation section
Figure 9a: Computational results for mass flow Figure 9b: Computational results for mass flow
rate of water rate of vapour
VII. CONCLUSIONS:
The effectiveness of heat pipe with water is higher than refrigerant R-134 A.
The temperature of water and water vapours continuously increases from the
condensation inlet.
The mass flow rate of water decreases rapidly and the mass flow rate of vapour
increases slowly from the condensation inlet.
NOMENCLATURE:
A = Total heat transfer area, m2 r1 = Inside radius of heat pipe, mm
Ab = Tube surface bare area, m2 r2 = Outside radius of heat pipe, mm
Af = Area of section for single fin, m2 Ti = Inlet temperature (temp.) of air, 0C
Aw = Base surface area, m2 Tp = Preheat temperature of air, 0C
hw = Heat transfer coefficient of water, w/m2k Tr = Reheat temperature of air, 0C
k = Thermal conductivity of copper, w/mk Ts = Outer surface temp. of heat pipe, 0C
ka = Thermal conductivity of air, w/mk Tinside = Inner surface temp. of heat pipe, 0C
L = Length of heat pipe, mm Tw = Temp. of water in theHeat pipe 0C
η = Fin efficiency, % Tsat = Saturation temperature, 0C
N = Number of fins
REFERENCES
ABSTRACT
Hydraulic turbines, slurry pumps, valves and pipelines carrying mixture of solid
liquid particles often used in industries, are associated with problems involving erosion,
which hence causes loss of material at the surface due to erosive wear. To improve the
service life of the component/equipment one can either change the design of component or
change in material selection or improve the surface properties. Surfacing is one of the
fabrication technique used as an alternative to improve erosion resistance properties of
functional surfaces. Development of metal-ceramic composite and cladding the same on
tough metallic substrates can bring about significant changes in engineering functional
surfaces. In the recent years, microwave processing of metallic materials is growing
significantly because of some intrinsic processing advantages including volumetric heating
and selective heating. In the present work, microwave energy was used to develop metal
based ceramic composite cladding on austenitic stainless steel (SS-316).
The present paper discusses development of cladding consisting of tungsten carbide
(WC10Co2Ni) based reinforcing particles in a Ni-based matrix. The cladding was developed
through exposure of microwave irradiation at 2.45 GHz frequency for an average duration of
6 minutes. The composite clad were characterized through field emission scanning electron
microscope (FESEM) equipped with EDAX detector, X-ray diffraction (XRD), and
measurement of microhardness. The clad cross sections show good metallurgical bonding
with substrate by partial dilution of cladding material. The back scattered image of clad cross
section shows that the reinforced particles are well embedded and uniformly distributed in the
Ni matrix indicating superior erosive wear resistance. The XRD pattern reveals the detected
phases in the composite clad contains metallic carbides of chromium, W, and Ni. The XRD
patterns confirm presence of free tungsten.
1.INTRODUCTION
Erosive wear is the major problem leading to replacement of tribological components in the
industry. Surfacing is used to produce a composite material i.e. base material which has good
mechanical properties such as strength, toughness and a surface coating that can withstand
abrasion, corrosion and impact. Surfacing is a process of depositing a material layer over a
base metal or substrate to improve surface characteristics like corrosion resistance, wear
resistance, etc. For hard and wear resistant materials, the improvement in surface properties is
achieved through microwave cladding.Cladding materials such as cobalt, iron and nickel base
alloys along with hard carbide particles (WC) are used in gas turbines, steam turbines and
aerospace engines to improve the resistance to wear [1-3]. Ni-based alloy is extensively used
for wear resistance application in order to increase the working life of tribological
components subjected to wear.The proportion of carbide particles in the nickel alloy matrix
increases the microhardness of the clad, with the nickel matrix providing the desired
toughness. The hardness of the nickel base alloy cladding also depends on microstructural
parameters, size and shape of carbide particles and their stability, etc. [4]. Recently
investigators have reported on different processes and developments in the microstructure,
microhardness, bonding strength and wear behavior of Ni-Cr alloy coating/cladding with and
without chromium carbide particles. [4]
In the recent years, microwave processing of materials has emerged as one of the advanced
and fastest material processing techniques. Microwave processing of materials is different
from the conventional thermal processing methods. Microwave energy heats the material at
molecular level, which leads to uniform bulk heating. In the conventional heating systems,
however, the material gets heated from the surface to interior with thermal gradient [5], [6].
Microwave processing was mainly confined in the domain of ceramics because of the fact
that microwave radiation at 2.45GHz is well absorbed by the ceramics at elevated
temperature. On the other hand, microwave radiation gets reflected by bulk metals at ordinary
conditions, owing to which metals cannot directly interact with microwave radiation.
Application of microwave energy processing in metallic materials is quite challenging owing
to which microwave absorption for metals at 2.45GHz radiation, this frequency is commonly
used for industrial use and is less than room temperature. [7] Several authors have reported
sintering of metallic and ceramic materials through microwave heating. [8-11] Sharma et al.,
(2009) [12] reported joining of bulk metallic materials using microwave irradiation.
2. EXPERIMENTAL PROCEDURE
Composite cladding has been developed in order to enhance surface properties and increase
life of the tribological component. In the present work the wear resistant cladding is
developed on austenitic stainless steel as metallic substrate through microwave energy used
as a heating source. The following sections briefly describe the development and
characterization of cladding.
Ni-based alloy is used as matrix and chromium carbide as reinforcement for development of
composite clad in order to enhance surface hardness for wear resistant and corrosion
resistance on austenitic stainless steel. In the current study, spherical shaped Ni- based alloy
powder and irregular shaped chromium carbide (as seen through FE-SEM) were having grain
size less than 40 μm used. Typical morphology of powder used in cladding is as illustrated in
the Fig.1 (a) and Fig.1 (b). Austenitic steel (SS-316) plates machined to dimensions 35mm
×12mm ×6mm were used as substrate materials. Chemical composition of SS-316 used as
substrate is as shown in Table 1.
Table 1.Elemental weight composition of the substrate material (SS-316).
SS-316 C Si Mn Ni Cr Mo Fe P,S,Cu,Zn
Wt.% 0.08 0.75 2 14 17 2 Balance 1
Fig.1 (a) Morphology of Ni-based alloy powder Fig.1 (b) Morphology of WC powder
In the present work hardfacing composite clad developed with different composition (Ni-
WC). Substrates were cleaned with alcohol in an ultrasonic bath prior to deposition of
powder. Developed clad consisting of tungsten carbide (WC) based reinforcement particles in
Ni- matrix were having average grain size of less than 40 μm intermixed properly and
preheated at 100°C for 24 hours in a conventional muffle furnace. Preheating removes
possible moisture in the powder. The powder was preplaced manually on SS-316 substrate
maintaining an approximately uniform thickness of 2 mm.
The absorption of microwave energy dependent on powder particle size, properly mixed
powder particles cannot directly interact with microwave radiation at room temperature,
instead, will tend to reflect microwaves. In order to overcome the problem of microwave
being reflected by Ni-based and WC powder (80%wt. and 20% wt.), claddings were
developed by microwave hybrid heating (MHH) technique using suitable susceptor. The
susceptor material which absorbs microwave energy and then transfers heat source to the
powder particles on the substrate. In order to avoid possible contamination of cladding by
susceptor powder used in the MHH, a 99% pure graphite sheet was used as a separator
between the susceptor and powder as shown in the Figure 2. The figure shows a schematic
view of the MHH arrangement. The optimized processing parameters for composite clad as
shown in Table 2.
Parameters Description
Applicator Multimode(Make:LG,Model:Solar DOM)
Frequency 2.45GHz
Exposure time 360sec
Exposure power 900W
Results along with the discussion are presented in this section for the experiments. The
results presented accordingly in line to the objectives mentioned.
In the present work, microwave cladding of Ni based alloy as matrix, WC reinforcement
particle powder has been successfully carried out on austenitic stainless steel (SS-316)
substrate using a multimode domestic microwave oven, operated at 900W and 2.45GHz.
Fig.3.1:A typical XRD spectrum of the Ni based-WC composite cladding (radiation: Cu-Kα).
3.1.2 Microstructure of the Composite Clad
The microstructure of the composite clad Ni-WC studied through FE-SEM. The Back
scattered electron image of transverse section of microwave composite clad is illustrated in
the fig.3.2, the uniformly distribution of reinforcement particles in the tough ductile matrix
Ni- based matrix. It shows average thickness of clad ~500 m and good metallurgical
bonding to the substrate from the clad and clad to substrate.
The back scattered electron (BSE) image of a typical transverse section of the Composite
cladding is illustrated in Fig. 3.2. The cladding with an average thickness of ~500 m shows
good metallurgical bonding with substrate through partial mutual diffusion of elements like
iron (Fe), from the substrate to clad and from clad to substrate. The developed clad is free
from interfacial and the porosity of developed clad .The crack free clad and significantly less
porosity is indicative of uniform heating associated with microwave processing.
4. CONCLUSION
(1) The clad of thickness ~500 m have been developed by the exposure of microwave
radiation at 2.45GHz and power 900W for the duration of 360s.
(2) The clad is metallurgical bonded with the substrate by partial mutual diffusion of
elements.
(3) The WC particles are reinforced in a metallic (mainly nickel) tougher and ductile
matrix.
(4) The average microhardness of developed clad are ~520Hv in Ni -WC and.
(5) The developed clad through microwave radiation can be effectively used in wear
resistant applications.
REFERENCES:
1. WONG TT, LIANG GY, HE BL, WOO CH 2000 Wear resistance of laser-clad Ni-Cr-B-Si
alloy on aluminium. Materials Processing Technology100,142–146
2. RODRIGUEZ J, MARTIN A, FERNANDEZ R, FERNANDEZ JE, 2003 An experimental study of
the wear performance of NiCrBSi thermal spray coatings. Wear255,950–955
3. SKULEV H, MALINOV S, SHA W, BASHEER PAM 2005Microstructural and mechanical
properties of nickel-base plasma sprayed coatings on steel and cast iron substrates. Surf
CoatTechnology197,177–184
4. SKULEV H, MALINOV S, B ASHEER PAM, SHA W 2004 Modifications of phases,
microstructure and hardness of Ni-based alloy plasma coatings due to thermal treatment.
Surf Coat Technology185,189
5. SHARMA A. K., ARAVINDHAN S. & KRISHNAMURTHY R. 2001 Glazing of alumina–titania
ceramic composite coatings. Materials Letter50, 295–301.
6. SHARMA APURBBA KR. and KRISHNAMURTHY R 2002 Microwave processing of sprayed
alumina composite for enhanced performance. Journal of European Ceramic Society22,
2849–2860.
7. GUPTA, M. & WONG, W.L.E. 2005 Enhancing overall mechanical performance ofmetallic
materials using two-directional microwave assisted rapid sintering. Scripta Materialia52,
479–483.
8. S.S. PANDA, V. SINGH, A. UPADHYAYA & D. AGRAWAL 2006 Sintering response of
Austenitic (316L) and ferritic (434L) stainless steel consolidated in conventional and
microwave furnaces, Scr.Mater. 54, 2179–2183.
9. K. SAITOU 2006 Microwave sintering of iron, cobalt, nickel, copper and stainless steel
powders, Scr.Mater54,875–879.
10. P. CHHILLAR, D AGRAWAL, J. H.ADAIR 2008 Sintering of molybdenum metal powder
usingmicrowave energy, Powder Metallurgy51-2,182-187.
11. A. MONDAL, A. UPADHYAYA and D. Agrawal 2009 Microwave Sintering of W-18Cu and
W- 7Ni3CAlloys, J. Microwave Power Electromagn. Energy (JMPEE)43-1, 11-16.
12. A. K. SHARMA, M.S. SRINATH& PRADEEP KUMAR 2009 Microwave Joining of Metallic
Materials, Indian Patent 1994/Del/2009.
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID
ICAME2013 S9/O2
1.INTRODUCTION
The need to observe device behaviour at nanoampere (nA) levels is being driven by the
ongoing reduction in the geometric size of MOSFET devices to increase circuit density,
facilitate higher speeds and reduce power consumption [3]. Decreasing the scale of the circuit
can help provide the aforementioned improvements; however, tradeoffs in performance will
also occur. For this reason, it is necessary to have the tools available to observe the new
operating characteristics for comparison with the predicted values. Micropositioner is one
such popular device. A micropositioner probe makes a physical and electrical connection
between a test point or signal sourceand an oscilloscope. This necessitates the building of an
accurate device to comply with the functional obligations. The foremost challenge is to retain
its cost within affordable limits. The objective of this work is to design and manufacture the
three axes micropositioner at low cost without much compromise in the operation of the
electrical probing. This paper gives the design of the micropositioner, based on the principle
of the sliding drive to achieve long travel range with fine step motion for two of the three
axes by means of micrometer. The third axis motion is achieved by fine screw in screw
arrangement and a tailored lever arm.
2.DESIGN CONSIDERATION
The ideal probe is to be designed in such a way that it will offer the key attributes such as
connection ease and convenience, absolute signal fidelity, zero signal source loading,
complete noise immunity. Accordingly, the micropositioner has some design
considerations.All the motion involved at every stage is in microns. Any instability at the
base would introduce haphazard movement at each stage resulting into non-precise motion.
Magnetic as well as vacuum base are found to provide the required clamping force. But the
magnetic base is economical over vacuum chuck with required level of performance. To take
care of the discrepancies in the assembly and the incompatibility between the mating
components it is necessary to establish a mechanism which will reduce backlash. It can be
minimized with the provision of the spring. In addition to this, the spring restores the initial
position of the slider. The main objective of the micropositioner is to obtain the controlled
precise motion of the probe at the working site .The resolution of the instrument required is
10 µm. Dovetail groove, linear motion guide and linear motion bearings are the available
mechanisms which can give the desired motion.
3.DESIGN METHODOLOGY
From the market survey linear bearings are found to be best complying with the design
considerations out of available mechanisms. Micrometers are opted as the suitable actuating
mechanism. DFMA principle is effectively employed in this phase to achieve the optimum
design contributes so as to conquer project objective.The design work mainly consists of the
modeling of springs, X-Y stage components, Z case and rocker arm. Since there is very low
load on the components hence load is not criterion while deciding dimensions. They are
decided on the basis of the dimensions of the standard components like bearing, shaft,
fasteners etc. Geometric relations between assembly of parts and their dimensions are
established. Size of individual part and assembly are optimized with the aid of CAD software
(CATIA V5). Fits provided for all the mating parts in the assembly are very vital. The slight
variation of the fit selection from the ideal mating fit, results into substantial deviation of the
results from the desired standard output.
The assembly consists of X Y Z stages arranged one over the other as shown in fig (1).X and
Y stage are designed in modular fashion to achieve effective operating mechanism along with
great ease of manufacturing and packaging. The X and Y stages are exactly alike with their
axes held perpendicular in assembly to deliver precise movement of 10-12 mm in respective
direction. Each of them consists of a frame for shaft housing, micrometer, linear bearing-shaft
set, an H-shaped slider and a helical spring as shown in fig (2). For obtaining a jerk free
motion at the slider, a point contact between micrometer spindle and slider is established by
embedding in slider a ball with high press fit.
The X movement is achieved by actuating corresponding micrometer; this in turn makes Y
and Z stage to move in the direction as the X-slider. Y motion is obtained by micrometer
actuation resulting into the relative motion of the Y frame with its slider. Geometric
relationship is imparted which keeps Y slider in same position with facilitating only Y frame
movement.
The operating principle employed at Y stage demands integrity of both sliders, which is
achieved by providing a fastener in vertical manner. The optimum gap is maintained between
two sliders to avoid the interference in motion at two stages. The snug fit between the dowel
and slider prevent any angular movement of the sliders about vertical axis. Helical spring
employed with reliable stiffness ensure zero backlash during actuation.
Design of the Z stage is shown in fig (3). Z case has to perform its intended function along
with the critical electrical routing. Reduction of electrical noise is very important aspect
influencing the Z stage design as this noise may add up substantial error in the measured IV
characteristic. The noise at the nanoampere level is difficult or impossible to see in real time,
the best measure against this source of error is prevention. So the material employed for
rocker has to be essentially non conductive in nature to insulate the electrical signal in collet
from body of the device. This facilitates the elimination of probable signal interference
resulting into excellent output. The available choice for rocker material is nylon and acrylic,
but from manufacturing consideration acrylic is opted for the purpose.
Z case is designed to accommodate the rocker, a screw in screw assembly and a torsion
spring. Bell crank rocker is pivoted about the dowel pin placed in hole provided in the Z case
with appropriate fit selection. The role of the torsion spring is identical to that of helical
compression spring in X and Y stages. The precision angular movement of lever from 0°-10°
is achieved by incorporating the screw assembly.
Torsional spring is designed for obtaining sufficient stiffness to restore lever arm against
frictional resistance between Z case and lever arm. Spring is mounted on z dowel and groove
is made in lever itself for packaging the spring. These space limitations govern the
dimensions of the spring. It is exclusive property of torsional spring, that its diameter reduces
with deflection due to which spring intrudes into shaft and further motion is restricted.
Compensating clearance must be provided on shaft to avert this.
After deciding dimensions, number of turns is selected, so as to give minimum reduction in
diameter and maximum stiffness. But this stiffness is insufficient to store energy in 10° of
deflection to act against frictional torque. Frictional torque is obtained experimentally and
corresponding required initial deflection is found out to be 35°. Fig (4) depicts geometry,
dimensions and mounting of the spring.
Helical spring is used to provide motion to slider in reverse direction. The major parameter
for designing spring is solid length which is constrained by space limitations. Wire diameter
and no. of turns are selected so as to have solid length less than constrained one and to
provide enough stiffness for avoiding backlash.
Providing magnet at the base is best viable solution for achieving objective of firm base. Two
magnets with opposite poles placed alongside results in concentric channelization of flux to
enhance magnetic force. Space restrictions and availability determines the dimensions of the
magnet. Each magnet block of 30mm*20mm*6mm provides clamping force of
approximately 2 kg. So collectively more than 4 kg holding force is obtained which is
sufficient for stability of device during operation and also ensures easy maneuverability of
device if required.
7.MANUFACTURING
The testing of the wafer coating involves measurement of current of the range of
nanoampere. The design considerations are achieved by concurrent design and manufacturing
approach along with incorporation of DFMA principle. Efforts are taken on aesthetic and
packaging of the device so as to launch it as a commercial product in near future.
Assembly of the device essentially consist the procured and manufactured parts. Building the
device with these building blocks having excellent mating relationship is the key prerequisite.
Choice of machining processes is compromise between cost, availability and accuracy of the
machine. Material selection has played a vital role from manufacturing aspect. Selection of
aluminium ensured ease of machining of the critical parts and light weight assembly. The
magnetic base too is of aluminum to get the improved clamping force by directing maximum
magnetic lines into the metallic platform. Modularity in the design of X and Y stage
deliberately reduces the manufacturing efforts for each stage and ensures interchangeability
during the assembly. Components which are essentially procured include micrometer head,
linear ball bearing-shaft assembly, dowels, collet and magnets. The machines with high
operational flexibility and accurate machining are employed for precision manufacturing of
the parts. It comprises of milling machine, CNCs, M1TR drilling center, grinding machine
and lathe machine.
The acrylic is found to perform superior than nylon as a rocker material. The reason is, in
case of nylon machining processes results in the loss of close designed tolerances, which is of
shear importance for the controlled and jerk free Z movement. The acrylic rocker has a recess
for accommodation of torsion spring and routing of the electrical connection. Maintaining
close tolerances of torsion spring for its mounting at pivot point with provision of such trivial
space is foremost challenge to be tackled. The tailored bell crank lever pivoted at fulcrum
point complies with all these requirements.
The micropositioner is fabricated and assembled for experimental evaluation. Activating the
micrometer by one division produces an ideally linear motion of 10µm in both the X and Y
direction with an accuracy of 2µm. The motion in the vertical Z direction is approximated by
the screw having pitch of 1mm. Thus the device has been manufactured giving reliable
service in positioning. Ease of operation and modular design are additional appealing features
of the design. Moreover, the response of an electronic device in terms of current carried is
recorded for increasing voltage. The following graphs show the I-V characteristics of the
device connected across the probes.
a b
Figure: 4- (a) I-V Characteristics with no device connected (b) Linear I-V characteristics of a
1.2 MΩ resistor (c) I-V characteristics of an electronic sensor held between the probes of
device
The fig(4.a) shows that the range of the current detected with no device connected amid the
probes is of a few nanoamperes, which is a pure electrical noise present in the lab during
experimentation. Whereas the values from the fig (4.b) and fig(4.c) show that such a low
noise interfere negligibly in the desired characteristics. The cost of the device is reduced to
about 70 percent of the original cost by employing the devised design.
9.CONCLUSION
Special thanks to Mr. Narendra Pitale, Engineering consultant, for sharing his knowledge,
experience and time.
REFERENCES
BIBLIOGRAPHY
1. Compression springs handbook, 17.0 series, End coil closed and ground by Lee Spring.
2. Catalogue of linear bearing, INA bearings ltd.
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID
ICAME2013 S9/O3
Dr M L Kulkarni R R Honkalas
MIT Alandi, Pune COE, Pandharpur and NBNSCOE,Solapur
mrmlkulkarni@gmail.com rahul.honkalas@gmail.com
ABSTRACT
Table movement of micro milling is in microns. Most of Micro milling table consist
of slides/guides, recirculating ball screw and air bearing. The linear motion guides are used
for accurate linear movements. Study of linear guide used in micro-milling within frame
work of FEA. FE simulations of such linear guide system were not reported before in the
literature. By getting the FEA result can optimize the design of existing micro milling table
and this study gives a complete testing procedure of design and analysis of table of micro
milling (linear guide) using FEA tool and some of its important performance affecting
parameters.
Keywords: Micro, Milling, Micron, FEA etc.
1. INTRODUCTION
The continuing quest for smaller, more reliable consumer and industrial product is
pushing current limits in miniaturization technology .Micromilling is one of the emerging
fabrication technologies. While studying the literature available on Micro Milling, there was
very few scope are given to the mechanical structure required for the machine. The
mechanical structure like machine frame, machine bed / table, required housing to support the
structure. Machine table is one of the important components of every machine, here also it is
major. So there is a need of detail study of the tableespecially for micro milling. Most of
micromilling table concerns slide/guide, recirculating ball screw, air bearing. With this study
a basic testing procedure of design and analysis of table (linear guide) for micromilling
machine by using Finite Element Method can be established and optimization can be
possible.
CNC milling machines are usually assembled with five modular components: a
machine base, saddle, table, vertical column, and head stock with a spindle tool unit.
In the table/spindle system, the feedingmechanism of the control axis is constructed
in various configurations using linear guides, ball screws, and supporting bearings,
see fig.
In this study by using the machine catalogue available of Hepco machine tools are used for
making the cad model with the all specification of slide of table.
2.4. Geometric Input for Linear Guide System
Hepco Simple-Select offers four useful sizes of spacer slides complete with carriages
assembled ready for installation. All units are fitted with double row bearings and cap seals to
ensure a long and trouble-free life. Their general purpose spacer slide precision cold drawn
and hardened on the Vee running surfaces provides good accuracy and long life, even in the
most hostile environment. Fig shows typical linear guide from Hepco.
Finite element method is an excellent tool to analyze complex structures like Linear Guide
System by using computer which can help to reduce time and cost required for prototyping.
Additionally, computer based designs can
provide better solutions.
Fig. 5 Structure of 10 node solid tetrahedron element Fig.6 3D CAD Model of Linear Guide
Imported in ANSYS
3.1. Mesh Generation
Fig 7 shows meshed model of assembly. Meshing is nothing but converting a whole
geometry into number of elements and these elements are connected by nodes. Both screw
rotors are meshed with tetrahedral solid elements of ANSYS. Fig.5 shows tetrahedral element
used in meshing of the linear guide in Ansys.Table 3 shows mesh statistics for the complete
model.
Fig.5 shows a SOLID element which is tetrahedral element used in meshing of linear guide
system. It has a quadratic displacement behavior and is well suited to modeling irregular
meshes (such as those produced from various CAD/CAM systems). The element is defined
by 10 nodes having three degrees of freedom at each node: translations in the nodal x, yand z-
direction.
To carry out FE analysis of linear guide used in micro-milling table, slide ends are fixed, see
blue color in Fig. Fx and Fy are applied on carriage Fig.8 shows typical arrangement of loads
and boundary conditions on linear guide in ANSYS.
Fig.8 Model with loads and boundary condition
3.3. Solution
The given configuration of micromilling table linear guide system is solved using ANSYS
with inputs discussed in above.
3.4. Post-processing
Post processing involves the review of various results such as stresses and deformations.
Fig.9 shows stresses inlinear guide used in micromilling table. From results it appears that
maximum stress is around1MPa. This stress is much below yield limit of material.
Fig.10 shows the deformation in micromilling table linear guide. The maximum deformation
is 0.6 m which is below the accuracy limit of table.
4.1 Results
4.2 Discussion
Successfully validated design of micromilling table which uses linear guide system subjected
Fx and Fy.
1. Successfully used commercial FEA tool ANSYS in the design validation of linear guide
system used in micromilling table.
2. Stresses obtained by ANSYS are lower than allowable limit and deformation is also lower
than accuracy limit of table.
3. Testing procedure of design and analysis of micromilling table (linear guide) established.
4. Optimization of micromilling table can be possible; the result of FEA is much lower than
than the material yield limit. Can reducing FOS for slide material to achieving the exact
optimization.
5. With the help of FEM analysis will try to find out the vibration present in existing
micromilling table from the design catalogue of a manufacturer. And will create a new
optimized design for table which gives less amplitudes and more accuracy.
6. Through optimization material and overall cost of table may reduce.
ACKNOWLEDGEMENT
We are very much thankful to our management, principal, HOD for boosting and
promoting us for the research oriented works.
REFERENCES
1. DEHONG HUO, 2009 A holistic integrated dynamic design and modelling approach applied
to the development of ultraprecision micro-milling machines. International Journal of
MTM 50, (2010)
2 . SHIH-M ING WANG et al.A New Cutting Force Model for Micro-milling and
Determination of Optimal Cutting Parameters.National Taiwan University.
3. JAY PRAKASH PATHAK, 2003 Design, Assembly, and Testing of an Ultra High Speed
Micro-Milling Spindle, University of Florida.
4. JOHANNES SCHNEIDER, 2010 Mechanical Design of a Desktop Milling Machine for
Fabrication in an Introductory Machining.Massachusetts Institute of Technology.
5. S K BASU, D K PAL, Design of Machine Tools, pp38-40.
6. G C SEN, A BHATTACHARAYA, Principles of Machine Tool, pp44-46.
7. N K Mehta, Machine Tool Design and Numerical Control, pp178-181.
8 .http://www.hepcomotion.com/
Proceedings of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME2013S9/P1
ABSTRACT
This paper presents a design of single-bit RF MEMS phase shifter. RF MEMS series
resistive switches are used extensively in the frequency range of DC-40 GHz. These switches
exhibit low insertion loss and better isolation at sufficiently high frequencies. The switch is
optimized by considering different trade-offs between these parameters. These switches,
operated individually, provide minimal phase shifts of 30-40 degrees. Hence, single-bit phase
shifters have been designed by cascading several similar RF MEMS switched capacitors so as
to exhibit considerable amount of phase shift. Mechanical and Electromechanical analysis of
the designed miniaturized phase shifter is conducted using COVENTOR which primarily
consists of Static Analysis, Modal Analysis and Transient Analysis respectively. Analysis
yields an actuation voltage of 13.6V and a solution for switching time reduction is discussed.
Keywords: Static Analysis, Modal Analysis, Transient Analysis. RF MEMS series resistive
switch, cantilever beam, Insertion loss, Isolation.
1. INTRODUCTION
(ii) The value of the mechanical resonant frequency (in MHz) of vibration of the beam and its
various deformed shapes,
(iii) The value of the switching time (in nsec) required by the miniaturized beam to undergo
full up and down state transition once. An actuation voltage of 13.6V with a switching time
of 600microsec is achieved.
Fig 1: Ohmic contact series switch
2. QUALITY FACTOR
Quality factor plays important role .It is directly proportional to air gap .therefore we can
reduce the switching time of switch by increasing the air gap which intern reduces the
required pull in voltage.
Static Analysis refers to the plot of displacement vs. voltage applied to a switch when it is
being subjected to an externally applied electrostatic actuation. It aids in obtaining the
amount of actuation voltage required to achieve the down (actuated) state configuration from
the up (un-actuated state). For simplified theoretical analysis, the governing equations of the
problem have been enumerated as under.
V= 8k g ⁄27εWw … (1)
K= 2Ew(t/l)3/3 … (2)
Modal Analysis [6] or rather, the Eigen frequency analysis refers to the calculation of natural
frequencies of vibration of the beam. Modal analysis is the study of the dynamic properties of
structures under vibrational excitation. The Eigen values are used to determine the natural
frequencies (or Eigen frequencies) of vibration, and the eigenvectors determine the shapes of
these vibrational modes. Modal Analysis aids in computing the values of these mechanical
resonant frequencies of vibration of the beam. FEM simulations employing COMSOL
Multiphysics provides the deformed shapes of the beam when subjected to the various modes
of vibration. The simplified governing equation has been written as under-
0 = 1⁄2π k⁄m…(3)
m=0.35(lwt) …(4)
Fig 6: Displacement in micrometers vs time in sec.Time required for switching is found out
to be 600microseconds practically
Transient Analysis refers to the curve of displacement (nm) vs. time (nsec) so as to obtain the
required switching time of operation. Transient Analysis is also known as the dynamic
response of a system and it employs a non-linear equation called D’ Alembert’s principle [1]
as the primary governing equation. The equation has been written as under for convenience-
z Pull in voltage
Length (μm) VP (v)
210 17.3
220 14.7
230 12.7
240 11.2
250 10
Air gap plays very important role in the performance of switch.
Now will vary aig gap and observe the change.
Table 1. Air gap in microns and Voltage required in volts
3. CONCLUSION
The performance of RF MEMS ohmic series switch in the frequency range of 1 - 40 KHz has
been studied. The switch cantilever beam is connected to anchor at only one end. The effect
of different geometrical parameters is studied and simulated using Coventorware. This paper
shows that varying anchors length improves the contact force thereby reducing the insertion
loss.
REFERENCES
1. GABRIEL M. REBEIZ, 2003 RF MEMS: Theory, Design, and Technology, John Wiley &
Sons Ltd. Chapters 1, 9 and 10, pp.1-20, 259-324.
2. Benjamin Lacroix, Arnaud Pothier, Aurelian Crunteanu Pierre Blondy 2008 Phase
Shifter
Design Based on Fast RF MEMS Switched Capacitors. IEEE 3rd European Microwave
Integrated Circuits Conference, pp. 478-481.
3. http://www.ansoft.com/products/hf/hfss
4. http://www.comsol.com/
5. VARADAN V K, VINOY K J and JOSE K A 2003 RF MEMS and Their Applications. New
York: Wiley.
SUB THEME 10
Nano and Micro-fluids
Proceedings of International Conference on Advances in Mechanical Engineering
V. G. Kasbe G. S. Lathkar
Asst. Professor, M.S.Bidve Engineering College Director & Principal, MGM College of Engineering,
Latur, Nanded.
vgkasbe@rediffmail.com principalmgmcen_gsl@yahoo.com
ABSTRACT
Newly emerging technologies are not being effectively served by the conventional heat transfer fluids. To
serve these emerging technologies, nanofluids are found to be better alternatives to the conventional heat
transfer fluids. In this study, experimental investigation of heat transfer between a Zinc Oxide–Water
nanofluid and a horizontal hot Copper Tube surface is carried out. Behavior of convective heat transfer
coefficient (CHTC) for laminar flow regime of nanofluid at steady state condition is investigated. Different
flow rates and different concentrations of nanoparticles are used. The experimental results indicate that, the
heat transfer process can be enhanced using nanofluid as a heat transfer carrier. Dispersion of the
nanoparticles into the base liquid increases the thermal conductivity and viscosity of nanofluids which further
enhances heat transfer coefficient. Using Zinc Oxide–Water nanofluid a sufficient increase in the convective
heat transfer is obtained as compared to De-ionized (DI) water. The enhancement in increment of Convective
heat transfer coefficient also increases with increasing axial distance. Few higher concentrations of particles
depicted a lower heat transfer coefficient. In some exceptional cases lower than DI water too. This nonlinear
behavior indicates the need for more intensive study to explain the comprehensive phenomenon of heat
transfer by nanofluids.
Keywords:Zinc Oxide-WaterNanofluid, Convective heat transfer coefficient, Laminar flow regime, Steady
state.
1. INTRODUCTION
Water, oil and ethylene glycol are mostly used heat transfer fluids in many industrial applications such as
power generation, microelectronics, heating processes, cooling processes and chemical processes. Today’s
heat transfer fluids used in these thermal systems have inherently poor heat transfer properties. More efficient
heat transfer fluids are the great need of many industries from transportation to energy supply to electronics.
To fulfill the requirement of efficient heat transfer, attempts are being made to enhance the heat transfer
properties of conventional working fluids by adding small particles of high thermal conductivity material in
these fluids. Many studies had been carried out in the past on thermal behavior of suspensions of particulate
solids in liquids. In those studies suspensions of millimeter or micrometer sized particles were used, which
although showed some enhancement, experienced problems such as abrasion and channel clogging due to
poor suspension stability (02). The clogging problem can be a serious problem for systems using micro or mini
channels.
New Technology being well reputed as nanotechnology gives extended opportunities to process and produce
materials with average crystallite sizes below 100 nm. These nanoparticles have superior thermal properties
compared to conventional heat transfer fluids, as well as fluids containing micro-sized metallic particles.
Nanofluids are nothing but nanometer-sized particles (less than 100 nm) dispersed in convectional fluids like
water, oil or ethylene glycol. Larger surface to volume ratios of these particles provide significantly improved
heat transfer capabilities and the stability of the suspensions. The presence of these high thermal conductivity
nanoparticles enhances thermal conductivities of the nanofluids. Several theoretical and experimental
researches are carried out by different scientists to check the thermal behavior of nanofluids. Hrishikesh Patel
et al., 2005; presented a micro-convection based model for wide range of particle sizes, particle
concentrations and particle materials (metal particles as well as metal oxides) and did not find significant
enhancement in heat transfer for metal particles. F. Rashidi and N. MosavariNezamabad, 2005; measured heat
transfer coefficient of CNT nanofluid in laminar flow regime and showed enhancement in convective heat
transfer is a function of axial distance.Yurong He et al., 2007; attempted to show that in case of laminar and
turbulent flow of aqueous TiO2 nanofluids thermal conduction increases with increasing particle
concentration and decreasing particle (agglomerate) size. While developing an empirical correlation for
CuO/water nanofluid in laminar regime Lazarus Godson Asirvatham et al., 2009; found that chaotic
movement of ultrafine particles is the important factors for an increase in heat transfer rate for a very low
volume fraction. H. Almohammadi et al., 2012; presented a study on the effect of different volume
concentrations of Al2O3/water nanofluid in laminar regime on convective heat transfer coefficient and
friction factor. Their study draws the conclusion that increase of particle volume concentration leads to
enhance convective heat transfer coefficient. The study also emphasizes the enhancement in convective heat
transfer coefficient of nanofluid with increase in heat flux. Further the study clears that enhancement in heat
transfer coefficient with respect to concentrations and heat flux is without significant increase in friction
factor. For fully developed laminar flow regime, AbdulhassanAbd. K et al., 2012; found that increase in heat
transfer coefficient for aluminium metal nanoparticles is comparatively more than aluminium oxide and
comparatively poor in copper oxide nanoparticles.
TiO2 (05),CNT(06),CuO(7) , Al2 O3 (08), Au(09),SiC(10)particlesare frequently used with water, oil or ethylene
glycolfor the thermal investigation in different research works. Their enhanced thermal conductivities and
efficient heat transfer properties are well established and proved in many research works. But higher cost of
these nanofluids is one of the important factors which limit their usage in commercial applications. Zinc
Oxide nanoparticles are comparatively cheaper and can be dispersed in basic fluids like water to use as
nanofluid. In this experimental study an attempt is made to investigate the thermal behavior of Zinc Oxide-
Water nanofluid with different concentrations of ZnO particles.
2. EXPERIMENTATION
2.1. Preparation of Nanofluid
Dry zinc oxide and De- ionized water were used to prepare nanofluids. The nanoparticles were
Purchased from Nanoshell LLC Wilmington DE Delaware - 19808, USAand used as received. Fig.1. (a)
shows the nanoscale image of particles before dispersed in liquid. Particles had an average size of 80- 200 nm
diameter with purity of 99% and Specific surface area more than 90m2 /g (21). The zinc oxide nanoparticles
were added in the DI water and stirred with high speed mechanical stirrer. The mixture of DI was agitated
only with high speed mechanical stirrer for more than half an hour without any further process for
homogeneity, like ultrosonication. Four samples were prepared with particle concentrations as 0.25 wt %,
0.50 wt %, 0.75 wt %, and 1.00 wt %. Fig.1. (b) shows the images of prepared samples before use.
Figure 1: (a) Nanoparticles Image before dispersed in water. (b) ZnO-Water Nanofluid samples with different
concentrations
If ‘q’ is heat flux, s( ) is measured wall temperature at a distance ′ ′ from the inlet, and ( ) is
the fluid bulk temperature at a distance ′ ′ from the inlet then the convective heat transfer coefficient h( )can
be given by an equation as:
ℎ( ) = ( ) ( )
(01)
The heat flux supplied to the fluid (q) can be found using:
( )
= (02)
Where ‘Tbo’ and ‘Tbi’ are the outlet and inlet fluid bulk temperature respectively; whereas ‘A’ is convective
heat transfer area of the test section.
In steady state condition, heat flow rate remains constant. Energy balance at an axial distance ′ ′ can be used
for determining the bulk temperature of the fluid at distance ( )
( )= ( )+ (03)
Where ‘m’ is mass flow rate of fluid, ‘c’ is specific heat, ‘p’ is a perimeter and ‘x’ is distance where the bulk
temperature of fluid is calculated.
In the form of Nusselt number (Nu(x)) the convective heat transfer coefficient, h(x), in Eq. (1) is usually
expressed as:
( )
( )= (04)
Where ‘k’ and ‘di’ are the thermal conductivity of the test fluid and the inside diameter of the copper tube,
respectively.
2.4. Properties of ZnO-Water Nanofluid
(3)
The effective density of the nanofluid containing suspended particles can be evaluated by the Pak and Cho
correlations equation:
= + (1 − ) (05)
Where , , and are volume fraction, the nanofluid density, density of ZnO particles, and density of
base fluid.
Thermal equilibrium between the particle and surrounding fluid is considered by Xuan and Roetzel(19), to
suggest the following equation for determining the specific heat of nanofluid:
( )
= (06)
Where and are the specific heat of nanoparticle and base fluid respectively.
For determining the effective dynamic viscosity of nanofluids Einstein’s equation (20) for a viscous fluid
containing a dilute suspension ( ≤ 2%) of small, rigid, spherical particles is mostly used. As very dilute
suspensions were used in this work ( ≤ 1%); the Einstein equation used to estimate the viscosity of
nanofluids was.
µ = µ (1 + 2.5 ) (07)
Where ‘µ’ and ‘µ ′are the dynamic viscosity of nanofluid and the base fluid respectively.
Since the analysis is obtained in weight percent (w); so it is necessary to have a conversion between weight
and volume fraction which can be obtained using:
= ( )
(08)
Experimental set up is fabricated and designed for Forced convective heat transfer. In the beginning of
investigation, experiments were performed with DI water to establish the reliability and accuracy of
experimental measurements. The experimental set up is validated by comparing the experimental convective
heat transfer coefficient for different flow rates of DI water with the results of the Shah equation (16) in laminar
regime.
Shah equations are as: (09)
= 1.302 −1 ≤ 0.00005
= 1.302 − 0.5 0.0005 ≤ ≤ 0.001
.
= 4.3641 + 8.68(10 ) ( ) ≥ 0.001
ℎ( ) /
Where = =
The heat transfer coefficient in laminar region for DI water is shown in Fig.3. For most of the
650
Theoritical 'hx'
600
Experimental 'hx’
CHCT, (hx), (W/m 2 K)
550
500
450
400
350
300
30 50 70 90 110 130 150
x/di
tests, error in theoretical values (predicted from the Shah equation) and experimental values of convective
heat transfer coefficients for DI water is around 7.5%. This seems to be acceptable range of error as shah’s
Equations are derived for large channels.
The variation of local convective heat transfer coefficient for particle concentration of 0.75w% along the axial
distance from the entrance of the test section at three Reynolds numbers are shown in fig.4. There is
increment in the local heat transfer coefficient, ℎ( ), with increase in the Reynolds number.
Fig.5 shows the effect of variation in concentration of ZnO nanoparticle on the local convective heat transfer
coefficient at various axial distances under Reynolds number of 1591. Obviously it is clear that all nanofluid
suspensions have remarkable enhancement in convective heat transfer coefficient than the DI water.
Dispersion of the nanoparticles into the base liquid increases the thermal conductivity and viscosity of
nanofluids which further enhances heat transfer coefficient. Effect of different factors given in researches [12]
, [16], [18]; like Brownian motion of Particles, thickness, delay in boundary layer development and mixing
effects of particles near the wall can be taken in to account to justify this enhancement. Another indication is
that for all concentrations local CHTC reduces with ‘x’ from the entry section. The gain in CHTC with
reference to water increases towards the exit section of the test length. For nanofluid of 0.50% concentration
at the length of test section where ‘x/di’ is 120, there is a maximum gain in CHTC by 48.3% under the
Reynolds number of 1591. Whereas there is a reduction of 4.75% in CHTC for the concentration of 0.25% at
a length of ‘x/di’ as 44.66 under the same Reynolds number, whose explanation requires more detail study of
the heat transfer phenomenon by nanofluids.
At the same time fig.5 shows that there is no linear enhancement in the convective heat transfer coefficients
with particle concentrations. ZnO-Water nanofluid with 0.5w% concentration shows
700
Re=1194
650
Re=1500
CHCT, (hx), (W/m 2 K)
600 Re=1591
550
500
450
400
350
300
30 50 70 90 110 130 150
x/di
relatively more enhancement than the concentrations of 0.75w% and 01.00w%. For the clarification of non
linear relation between CHCT, particle concentration and flow rates; more detail study is necessary. One
possible reason for this is that the thermal conductivity is highly dependent on some important factors such as
the structure of the nanoparticle, clustering,temperature, etc(15). Selection of Small volume fraction (11) and
absence of ultrasonication process in the sample preparation may be another reason for the nonlinearity.
Fig.6 shows almost gain in CHTC compared to DI water at 0.25% of weight concentration for all Reynold
numbers, but the gain at this lower concentration does not found in any discipline with reference to rise in
Reynolds numbers.
700
0.25%w
650
0.50%w
CHCT , (hx), (W/m2 K) 600
0.75%w
550
01.00%w
500
water
450
400
350
300
30 50 70 90 110 130 150
x/di
On the other hand Fig.7 is a display of the enhancement of convective heat transfer coefficient, with reference
to DI water versus axial distance for nanofluid of 01.00w %, at different Reynolds numbers. For flow of all
Reynolds number the enhancement in CHTC with reference to water is almost positive except for Reynolds
number of 1194. Under this Reynolds number with reference to DI water there is reduction of convective heat
transfer coefficient all most for all
0.60 Re = 1061
0.50 Re = 1194
Re = 1248
0.40 Re = 1500
0.30 Re = 1591
∆hx/hf
0.20
0.10
0.00
30 50 70 90 110 130 150
-0.10
-0.20
x/di
Fig. 6 Enhancement of convective heat transfer coefficient versus axial distance for 0.25w% at Re =1061, Re =1194, Re
=1248, Re =1500, and Re =1591.
concentrations of nanoparticles. For suspension of 01.00w%, the maximum enhancement in CHTC with
reference to DI water is found 30% under the Reynolds number of 1591, where as the investigation shows the
maximum reduction of 7.45% in CHTC for the same concentration under the Reynolds number of 1194
This investigation shows maximum enhancement by 59% and 30% in local CHTC for concentration of 0.50%
and 1.0% under the Reynolds numbers of 1061 and 1591 respectively. This mean at higher concentration and
higher Reynolds number the nanofluid is showing lower gain in heat transfer. This nonlinear behavior of the
nanofluid with reference to particle concentration and flow rates (Reynolds number) requires more intensive
study.
4. CONCLUSION
This paper presents the experimental investigation of heat transfer performance of ZnO-water nanofluid for
0.25%, 0.50%, 0.75%, and 1.00% weight concentration for laminar flow regime under constant heat flux
conditions.Findings of this investigations are:
1. The Nano fluid has larger heat transfer (CHTC) than pure water under the same Reynolds number.
2. In aggregate, under the same Reynolds number, Heat transfer enhances with increasing Nanoparticle’s
concentration, where as for some concentration (0.5%) it is exceptionally more which is a matter of
further investigation.
0.35
Re = 1061
0.30 Re = 1194
0.25 Re = 1248
0.20 Re = 1500
Re = 1591
0.15
Δhx/hf
0.10
0.05
0.00
30 50 70 90 110 130 x/di 150
-0.05
-0.10
-0.15
Fig.7 Enhancement of convective heat transfer coefficient versus axial distance for 01.0W% at Re =1061, Re =1194, Re
=1248, Re =1500, and Re =1591.
3. For all concentrations of nanoparticles in the study, the Convective heat transfer coefficient enhancement
increases with increasing axial distance. The maximum increase in enhancement of CHTC across axial
distance is about 518% for concentration of 0.25% under Reynolds number of 1248.
4. The enhancement increases with increasing Reynoldsnumber for 01.0% weight concentrations. For this
concentration maximum enhancement of heat transfer coefficient is 29% under Reynoldsnumber of 1591.
Whereas the response of CHTC is nonlinear to different Reynolds number at lower weight concentration.
5. Investigation of Zno-Water nanofluid with higher concentrations (more than 01.00%) and well prepared
homogeneous suspension under the flow of higher Reynolds numbers (more than 1500) can be an
alternative to avoid the nonlinearity in this investigation.
REFERENCES
1. ABDULHASSAN ABD. K, SATTAR AL-JABAIR, KHALID SULTAN ; Experimental Investigation of Heat
Transfer and Flow of Nano Fluids in Horizontal Circular Tube; World Academy of Science,
Engineering and Technology 61 2012.
2. A.S. AHUJA , Augmentation of heat transport in laminar flow of polystyrene suspension: I –
experiments and results, J. Appl. Phys. 46 (1975) 3408–3416.
3. B.C. PAK , Y.I. CHO , Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic
oxide particles, Exp. Heat transfer, 11(1998)151.
4. C.Y. TSAI, H.T. CHIEN, P.P. DING , B. CHAN, T.Y. LUH and P.H. CHEN, Effect of structural character of
gold nanoparticles in nanofluid on heat pipe thermal performance, Materials Letters 58 (2004) (9), pp.
1461–1465.
5. DREW, D.A., PA SSM AN , S.L. Theory of Multicomponent Fluids. Springer: Berlin, 1999.
6. F. RASHIDI, N. MOSAVARINEZAMABAD, Experimental Investigation of Convective Heat Transfer
Coefficient of CNTs Nanofluid under Constant Heat Flux, Proceedings of the World Congress on
Engineering 2011 Vol III.
7. H. ALMOHAMMADI, SH. NASIRIVATAN , E. ESM AEILZADEH, A. MOTEZAKER, A. NOKHOSTEEN,
Experimental Investigation of Convective Heat Transfer and Pressure Drop of Al2O3/Water
Nanofluid in Laminar Flow Regime inside a Circular Tube, World Academy of Science, Engineering
and Technology 68 2012.
8. H.C. BRINKM AN , The viscosity of concentrated suspension and solution, J. Chem. Phys., 20 (1952)
571-581.
9. JOOHYUN LEE, PATRICIA E. GHARAGOZLOO, BABAJIDEKOLADE, JOHN K. EATON , KENNETH E. GOODSON,
Nanofluid Convection in Microtubes , Journal of Heat Transfer, SEPTEMBER 2010, Vol. 132.
10. LAZARUS GODSON ASIRVATHAM , NANDIGANA VISHAL, SENTHIL KUMAR GANGATHARAN and DHASAN
MOHAN LAL, Experimental Study on Forced Convective Heat Transfer with Low Volume Fraction of
CuO/Water Nanofluid, Energies 2009, 2, 97-119; doi:10.3390/en20100097.
11. M.S.LIU, M.CHING-CHENG LIN, I.T.HUANG , C.-C. WANG, Enhancement of thermal conductivity with
carbon nanotube for nanofluids, International Communications in Heat and Mass Transfer 32 (9)
(2005) 1202–1210.
12. RISHIKESH E PATET, T SUNDARARAJAN , T PRADEEP, A DASGUPTA, N DASGUPTA and SARIT K DAS, A
micro-convection model for thermal conductivity of nanofluids, Pramana, journal of physics
November 2005,Vol. 65, No. 5, pp. 863-869.
13. S.A. PUTNAM, D.G. CAHILL, P.V. BRAUN, Z. GE, R.G. SHIMM IN, Thermal conductivity
of nanoparticle suspensions, Journal of Applied Physics 99 (8) (2006) 084308.
14. VASSALLO, P., R. KUM AR, and S. D'AM ICO. Pool Boiling Heat Transfer Experiments in Silica-Water
Nano-Fluids. International Journal of Heat and Mass Transfer 47 (2004), pp. 407-411.
15. WANG, X., XU, X., and CHOI, S. U. S. Thermal conductivity of nanoparticle-fluid mixture. Journal of
Thermophysics and Heat Transfer, 13, no. 4, 474–480 (1999).
16. XUAN, Y. and LI, Q. Heat transfer enhancement of nanofluids. International Journal of Heat and Fluid
Transfer, 21, 58–64 (2000).
17. YURONG HE A, YI JIN B, HAISHENG CHEN C, YULONG DING A,*, DAQIANGCANG B, HUILIN LU D, Heat
transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing
upward through a vertical pipe; International Journal of Heat and Mass Transfer 50 (2007) 2272–2281.
18. Y. XUAN, Q. LI, investigation on convective heat transfer and flow features of nanofluids, J. Heat
Transfer, 125(2005)151-155.
19. Y. XUAN, W. ROETZEL, Conceptions for heat transfer correlation of nanofluid, Int. J. Heat Mass
Transfer, 43(2000) 3701-3707.
20. A. BEJAN , A.D. KRAUS, Heat Transfer Handbook, John Wiley and Sons, 2003.
21. www.nanoshel.com
Proceedings of International Conference on Advances in Mechanical Engineering
Not received
Proceedings of International Conference on Advances in Mechanical Engineering
Not received
Proceedings of International Conference on Advances in Mechanical Engineering
ABSTRACT
Nanotechnology has attracted the attention of the researchers due to their surface area to volume ratio.
Addition of any nano materials in form of nanoparticle,fibers,tubes,flakesetc has enhanced the material
properties. Here we have review the parameters which affects the dimension and properties of the nano fiber.
The polymer nano fibers can be produced by using various processing techniques like drawing, self assembly,
template synthesis, phase separation, electrospinning etc. Out of these processing techniques electrospinning
is a best way to produce a polymer nano fibers with small diameter (10 nm to 1500nm). Due to large length to
diameter ratio and small mass to volume ratio these nano- size fibers has many application in industry. The
parameters affecting fiber diameter and properties can be varied by adjusting the concentration of the
polymer solution, distance from tip to collector, applied electric field , flow rate, viscosity, surface tension,
electrical conductivity of solution and temperature of solution, Ionic salt addition, Molecular weight etc.
1. INTRODUCTION
Drawing, Template Synthesis, Phase Separation and Self assembly are the methods useful for developing 1-D
nano structures but these methods have limitations of scalability [1]. In contrast, Electro spinning is a simple
and versatile process to generate uniform diameter fibers in random, as well as aligned fashion from wide
variety of polymer, ceramic or composite solutions in cost effective manner. Low cost, scalability for mass
manufacture, several areas of applications, wide variety of materials are the parameters that make
electrospinning very popular process among research community associated with One Dimensional (1-D)
nanostructures. Figure 1 demonstrates wide variety of applications of electro spunnan fibers. Currently, over
one hundred polymers, mainly in dissolved form and some in melt form have been successfully
electrospun[20].
There are fundamental four components associated with the electro spinning process viz. spinneret, voltage
supply, and collector and dispensing pump as seen in the schematic of Figure 1. There are basically three
parts 1) A high voltage supplier, 2) A capillary tube with a pipette or needle of small diameter, and 3) Metal
collecting screen. One electrode is placed into the polymer solution/melt and the other attached to the metal
collector as indicated in Fig. 1. The electric field produces surface tension on the polymer, which induces a
charge on the surface of the polymer. Further with increasing the electric field, a critical value is attained at
which the repulsive electrostatic force overcomes the surface tension and the charged jet of the fluid is ejected
in form of polymer nanofibers. Also, for the quality and variety of nanofibers produced by electro spinning,
certainly cost associated is very-very low.
Fig 1. Schematic of Electrospinning Setup for . a) Aligned Fiber Deposition and b) Actual Setup for Electrospinning
Process at BVUCOE,Pune [2]
Cellulose Viscosity above 10.2 poises could not be electro spun into fibers
acetate (1.2 - Fluid jet broke up to droplets due to too low viscosity increased after
10.2 poises) solgel aging
[20]
Surface Poly ethylene Beads –Surface tension increases the beads formation increase and
tension [3] oxide (35-55 vice versa
dyne /cm) Diameter –Surface tension increase diameter increase and vice versa.
Electric Poly ethylene Beads-Electric field increases the beads formation increases and vice
oxide(5kv -
Field 7kv) versa .
Diameter-Electric field increase diameter decreases and vice versa.
[3,10]
Concentratio PDLA (20%- Beads- Higher the concentration, less the beads
n [10,11] 40%) Diameter –Power law relationship with exponent of about 0.5 and 0.3
is observed.
Ionic salt PDLA (1wt% Beads- Addition of ionic salt reduces the beads.
addition salt ) Diameter –Addition of ionic salt gives the uniform diameter ,also
[10,11] helps in reducing the diameter .Fiber diameter depends on the radius
of the ions.
Molecular PS solution 40- Beads –Higher the molecular weight less the beads formation
weight 200 mg/ml for Diameter –As molecular weight increase the diameter also increases.
[3,12] PMMA fibers
Feed rate 20-70 Beads –As feed rate increases the beads increases.
[12] Diameter –Higher the feed rate larger the diameter.
Following Nylon-6 nanofibe rs are spun to optimize the diameter with the three parameter i.e Distance
between spinne ret and collector, voltage and flow rate of solution.
Fig.4 SEM of Nylon 6 (40-50nm) –Distance- Fig.5 SEM of Nylon 6 (40-50nm) –Distance-
15cm,Voltage 20KV Flow rate-0.2ml/hr 15cm,Voltage 20KV Flow rate-0.2ml/hr
Fig.6 SEM of Nylon 6 (20-30nm) –Distance- Fig.7 SEM of Nylon 6 (20-30nm) –Distance-
15cm,Voltage 20KV Flow rate-0.1ml/hr 15cm,Voltage 20KV Flow rate-0.1ml/hr
Fig.8 SEM of Nylon 6 (40--50nm) –Distance- Fig.9 SEM of Nylon 6 (40-50nm) –Distance-
15cm,Voltage 15KV Flow rate-0.2ml/hr 15cm,Voltage 15KV Flow rate-0.2ml/hr
Fig.10 SEM of Nylon 6 (30-40nm) –Distance- Fig.11 SEM of Nylon 6( 30-40nm) –Distance-
15cm,Voltage 15KV Flow rate-0.1ml/hr 15cm,Voltage 15KV Flow rate-0.1ml/hr
3. CONCLUSION:
1. Electrospinning is found to be really cost effective method to synthesis 1-D nanostructures from wide
variety of polymers, ceramics,composite solutions.
2. Due to reduction in diameter of the fiber there is exponential improvement in surface area of the fiber
mesh. this Character tics make eletro spunnanofibers very effective for medical ,automobile, defense
,aerospace, sensory etc. applications.
REFERENCES
1. D. LI, Y. XIA” Electro spinning of Nanofibers: Reinventing the Wheel? Advanced Materials Volume
16, Issue 14, pages 1151–1170, July, 2004
2. D.H. RENEKER, A.L. YARIN , E. ZUSSM AN , H. XU “Electro spinningof Nanofibers from Polymer
Solutions and Melts”Advances in Applied Mechanics Volume 41, 2007, Pages 43–195, 345–346
3. SACHIN SHENDOKAR,AJIT KELKAR ,RAM MOHAN,RONBOLICK “Parameter investigation on the effect of
electro spinning process variables on the macroscopic properties of hybrid composites IMECE 2009-
12188.
4. SCOPELIANOS AG. US patent, 5522879, 1996.
5. SODANO HA, INM AN DJ, PARK G. A review of power harvesting from vibration using piezoelectric
materials. Shock Vib Digest 2004;36(3):197–205.
6. SUN L, GIBSON RF, GORDANINEJAD F, SUHR J. Energy absorption capability of nanocomposites: a
review. Compos SciTechnol 2009;69:2392–409.
7. TAYLOR G. Electrically driven jets. Proceedings of the Royal Society of London. Series A,
Mathematical and Physical Sciences, vol. 313, 1969. pp. 453-475.
8. WILLIAM GACITUA E, ALDO BALLERINI A, JINWENZHANG ,“ Polymer Nanocomposites: Synthetic And
Natural Fillers A Review”, Maderas. Ciencia y tecnología 7(3): 159-178, 2005.
9. WU DY, MEURE S, SOLOMON D. Self-healing polymeric materials: a review of recent developments.
ProgPolymSci 2008;33(5):479–522.
10. XINHUA ZONG, KWANGSOK KIM , DUFEIFANG , SHAFENGRAN, BENJAM INS. HSIAO , BENJAMIN CHU, ”
Structure and process relationship of electrospun bio absorrablenanofibermembranes”,Polymer
43(2202)4403-4412.
11. J.M DEITZEL, JKLEINM EYER, D.HARRI S,N.C BECK TAN “The effect of processing variables on the
morphology of the electrosunnanofibers and textile” ,Polymer 42(2001)261-272.
12. S.M.SHENDOKAR .A.A.KELKAR, “Comparative study of eletrospiningnanofibervs E-glass microfibers
infused with Epon 862-W resin”,Proceeding of SAMPE 2010,Confernce and exhibition,Washington
State Convention Center ,Seattle ,Washinton ,May 18-20,2010.
13. BRIAN P. SAUTTER, “Continuous Polymer Nanofibers Using Electrospinning” NSF-REU Summer 2005
Program, University of Illinois at Chicago August 5, 2005.
14. NASIMAM IRALIYAN , MAHDI NOURI, and MOHAMM AD HAGHIGHAT KISH, “Electrospinning of Silk
Nanofibers. I. An Investigation of Nanofiber Morphology and Process Optimization Using Response
Surface Methodology” ,Fibers and Polymers 2009, Vol.10, No.2, 167-176.
15. ASHRAF A. ALI, M.A. EL-HAM ID, “Electro-spinning optimization for precursor carbon nanofibers”,
Composites: Part A 37 (2006) 1681–1687.
16. S.Y. GU, J. REN, G.J. VANCSO, “Process optimization and empirical modelling for
electrospunpolyacrylonitrile (PAN) nanofiber precursor of carbon nanofibers”, European Polymer
Journal 41(2005) 2559–2568.
17. HOM AHOMAYONI, SEYED ABDOLKARIMHOSSEINIRAVANDI, MASOUMEHVALIZADEH,
“Electrospinning of chitosan nanofibers: Processing optimization”, Carbohydrate Polymers 77 (2009)
656–661.
18. PENG YE, ZHI-KANG XU, JIAN WU, CHRISTOPHE INNOCENT , PATRICK SETA, “Nanofibrous
poly(acrylonitrile-co-maleic acid) membranes functionalized with gelatin and chitosan for lipase
immobilization”, Biomaterials 27 (2006) 4169–4176.
19. SANG KYOO LIM , SUNG-HO HWANG , DAEIC CHANG , SOONHYUN KIM, “Preparation of mesoporous
In2O3 nanofibers by electrospinning and their application as a CO gas sensor”, Sensors and Actuators
B 149 (2010) 28–33.
20. XINYINGGENG, OH-HYEONG KWON, JINHO JANG, “Electrospinning of chitosan dissolved in concentrated
acetic acid solution”, Biomaterials 26 (2005) 5427–5432.
Proceeding of International Conference on Advances in Mechanical Engineering
May 29-31, 2013, COEP, Pune, Maharashtra, India
Paper ID ICAME 2013 S10/O5
ABSTRACT
In this paper the stability of Al2 O3 nano particles in Paraffin is investigated. Homogeneous nanofluid is
prepared with stability measuring techniques and different concentration of oleic acid (C18 H34O2 ) dispersant.
The stability of Al2 O3 (20 nm size) nano suspension in paraffin is explained with the help of flow chart and
experimental procedure. The stability results are observed by sedimentation photograph capturing technique.
The optimizing concentration of oleic acid in the ratio of 1:25 which has the best disperses results for the
nanofluid stability of 1% Al2 O3 – paraffin wax nano suspension.
1. INTRODUCTION:
Nanofluids are solid- liquid composite materials consisting of solid nanoparticles or nanofibers with sizes
typically of 1-100 nm suspended in liquid [1]. Compared to conventional heat transfer fluids, nanofluids
show a superior potential for increasing heat transfer rates and are thought to be the next-generation heat
transfer fluids proposed for various uses in important fields such as electronics, transportation, medicine,
and HVAC (heating, ventilating, and air-conditioning heating) [2-4]. Researchers have demonstrated that
oxide ceramic nanofluids consisting of CuO or Al2 O3 nanoparticles in water or ethylene glycol exhibit
enhanced thermal conductivity [5]. A maximum increase in thermal conductivity of approximately 20%
was observed in that study, having 4% vol, CuO nanoparticles with mean diameter 35 nm dispersed in
ethylene glycol. Furthermore, the effective thermal conductivity of metallic nanofluid increased by up to
40% for the nanofluid consisting of ethylene glycol containing approximately 0.3% vol. Cu nanoparticles
of mean diameter less than 10 nm [6]. And the effective thermal conductivity of nanofluid consisting of
carbon nanotube (1 vol %) in oil exhibit 160% enhancement [7]. However, preparation of homogeneous
21
suspension remains a technical challenge since the nanoparticles always form aggregates due to very
strong van der Waals interactions. Therefore, controlling the coagulation of nanoparticles in the nanofluid
becomes a common factor in the current technological limitations for their potential benefits and
applications [8].
In the physical or chemical treatment such as the addition of surfactant, surface modification of the
suspended particles or applying strong force on the clusters of the suspended particles can change the
suspension stability [9, 10]. Donggeun Lee [11] studied the stability of nanofluids by changing pH of the
solution systematically to control surface charge density and surface potential, they found that the surface
charge states directly affected the suspension stability and presented the strong correlation between
hydrodynamic size of particles and stability coefficient. Ultra Violate spectrophotometric measurements
have been used to quantitatively characterize colloidal stability of the dispersions [10]. Although the
stability of nanofluid is very important for its applications, there is a little study on estimating the stability
of suspension.
2. STABILITY OF NANOPARTICLE:
To provide better cooling using nanofluids in industry, they are expected to possess long-term stability
which should be noted during preparation and synthesis of nanofluids. Indeed, to utilization of
nanofluids in practice, stability might be one key issue. Therefore, reasons for fast sedimentation of
nanoparticles or nanotubes should be recognized and dispelled. Therefore, in preparation both issues
should be taken into account to make a balance between stability and thermal conductivity, having a
stable thermal conductive nanofluid. Those three common techniques for making stable nanofluid are
stated below: 2.1 Addition of Surfactant.
2.2 PH control.
2.3 Ultrasonic agitation (vibration).
Addition of surfactant and pH control is two techniques to prevent clustering and agglomeration while
ultrasonic vibration is applied to break down agglomeration.
Surfactants can be defined as chemical compounds added to nanoparticles in order to lower surface
tension of liquids and increase immersion of particles. Several literatures talk about adding surfactant to
nanoparticles to avoid fast sedimentation; however, enough surfactant should be added to particle at any
particular case. In researches, several types of surfactant had been utilized for different kinds of
nanofluids. The most significant ones could be listed as below:
a) Sodium dodecyl sulfate (SDS).
b) Sodium dodecyl benzenesulfonate (SDBS).
22
c) Salt and oleic acid.
d) Cetyltri methyl ammonium bromide (CTAB).
e) Dodecyl tri methyl ammonium bromide (DTAB) and sodium octanoate (SOCT).
f) Hexade cyltrim ethyl ammonium bromide (HCTAB).
g) Poly vinyl pyrrolidone (PVP).
h) Gum Arabic.
2.2 pH Control
Stability of nanofluid is directly related to its electro-kinetic properties; therefore, pH control of them can
increase stability due to strong repulsive forces. General speaking, two types of behavior including
attraction and rejection occurs among particles due to van der Waals and electrostatic forces and it is
possible to control these forces by means of pH control. Lee et al. [12] investigated various pH values for
Al2 O3 nanofluid and observed decrease or increment of agglomeration by changing pH Moreover, Lee
studied change of size particle and pH value for Al2 O3 /DI nanofluid containing some other additives to
keep pH constant in a particular test case. Finally, it should be noted that optimized pH value is different
from one sample to another. For instance, suitable pH value for alumina, copper and graphite dispersed in
water are around 8, 9.5 and 2, respectively.
In the sonification treatment the ultrasonic sound waves are passes from the bottom side which will help
to prepare a mixture in a homogeneous form; this will be used for the further experimentation. The
sonification process is done for the normal atmospheric condition. After preparation of nanofluids,
agglomeration might occur over the time which results in fast sedimentation of nanoparticles due to
enhancement of downward body force. As it was mentioned before, all three methods might be used for
one specific sample during synthesis and preparation; yet, it is difficult to make stable nanofluid and rare
to maintain nanofluids synthesized by the traditional methods in a homogeneous stable state for more than
30 minutes to up to 24 hrs depending on the material to be prepared and the time period for stable mixture.
Among limited number of studies on stability of nanofluids, evaluation of them has been considered by
some researchers and six different methods were utilized which can be listed as below:
3.1 UV-Vis spectrophotometer.
3.2 Zeta potential test.
3.3 Sedimentation photograph capturing.
3.4 TEM (Transmission Electron Microscopy) and SEM (Scanning Electron Microscopy).
3.5 Sedimentation balance method.
23
3.6 3ω method.
It is one of the most common methods used to investigate stability of nanofluids due to its ease of use and
fast analysis. It has been utilized to magnitude stability of suspensions in nanofluids; viscosity of base
fluid would be known as one constraints of this method. This method is based on different wavelengths of
light in which it can be scattered or absorbed by other materials. It is known when light is passing through
fluids, intensity of it changes by absorption and scattering.
Stabilization theory states that increasing zeta potential, scientific term for electrokinetic potential in
colloidal system, results in high stability of the suspension. It is also well known that electrostatic
repulsion between the particles would be increased in high absolute value of zeta potential. Vandsburger
tabulated different values of zeta potential in mV and stated stability situation of the Suspension in any
specific zeta potential value which can be observed in Table 1.
0 Little or no stability
30 Moderate stability
It can be introduced as a basic method to evaluate stability of nano suspensions inside the fluid. After
preparation of nanofluid, it would be kept in a stationary standing condition inside glass tubes and
settlement of particles would be recorded continuously by capturing photos. Waiting time for capturing
photos links up with quality of nanofluid during preparation and well use of applied methods to make a
stable nanofluid. For instance, Wei et al. [13] tested their samples within 24 hours after preparation. Wang
et al. [14] investigated sedimentation of Al2 O3 inside water after 7 days capturing using this method as
well.
24
3.4 TEM (Transmission Electron Microscopy) and SEM (Scanning Electron Microscopy)
These two are known as suitable tools for study and determination of microstructures. Shape, size and
distribution of nanoparticles can be distinguished using them. Moreover, their aggregation which is related
to stability of nanofluid could be monitored also. They are capable to capture photos in small sizes to
reveal suspension situation of nanoparticles inside the fluid after preparation.
In this method, accurate balance with tray, which is able to collect nanoparticles while sedimentation,
would be immersed inside nanofluid immediately after preparation phase. Monitoring weight of
nanoparticles, suspension fraction of them is calculated by following formula:
−
=
Where Fs is suspension ethylene glycol fraction at an accepted time; WT is total weight of nanoparticles
inside the base fluid and W is weight of settled nanoparticles at an accepted time.
3.6 3ω Method
In this method, stability of suspensions can be evaluated considering thermal conductivity growth caused
by the nanoparticle sedimentation in a wide nanoparticle volume fraction range.
In this paper, preparation and stability of Al2 O3 nano-particles in water and Al2 O3 – Paraffin wax were
investigated with stability techniques and different concentration of dispersant used for the nano
suspension.
In this work, Al2 O3 of 20 nm size and 99% pure particles were purchased from a commercial company are
chosen as a source material for a nanofluid. It can be seen that the primary Al2 O3 nanoparticles are
spherical and their size is widely distributed in a range of 20-30 nm. The BET surface area of the powder
is found to be (30-50) m2/g, and Al2 O3 nanofluids were prepared by the two-step method. Distilled water
was used as the host liquid and SDBS (sodium dodecylbenzene- sulfonate) was used as dispersant to
inhibit Al2 O3 nanoparticles aggregation and break up clusters. The Al2 O3 -H2 O nanofluids suspension was
vibrated for 1 h in an ultrasonic vibrator. At the same time, the Al2 O3 suspension without SDBS dispersant
25
was also vibrated for 1 h in the ultrasonic vibrator for comparison. It shows that the stabilization of the
suspension with dispersant can last about 1 week in the stationary state and no sediment was found, while
the suspension without dispersant exhibited weaker dispersion and aggregatation quickly occurring. The
experimental results show that for SDBS there is an optimizing concentration in the nanofluids which can
induce high zeta potential and high absorbency, and that in 0.1% Al2 O3 -H2O nano-suspensions the
optimizing concentration of SDBS is 0.09%, which has the best disperse results of the nanofluids [ 15 ].
In the preparation of Al2 O3 - paraffin wax nanofluid there is difficult to directly add the dispersant in
paraffin wax due to its non polar functioning. We have to firstly to functionalize Al2 O3 nano material with
respect to base material. In this work, Al2 O3 of 20 nm size and 99% pure particles were purchased from a
commercial company (Nanoshel By Intelligent Material Pvt. Ltd.) are chosen as a source material for a
nanofluid.
In the preparation of Nanofluid by using Al2 O3 the main problems is settlement of Al2 O3 at the bottom of
container that is solved by addition of functional group on Al2 O3 is commonly made by immersing it in
Oleic Acid in the range 1:25. Functionalization is a chemical process that inserts functional groups on the
sidewall of Al2 O3 . The introduction of this procedure can also be helpful to obtain better dispersion of
Al2 O3 material into Paraffin Wax of Commercial grade.
26
The following treatments are done while preparing a synthesized Nano Al2 O3 :
This treatment is done at normal atmospheric temperature range. For polar nano materials the acid
treatment is essential to became its as non-polar in base material. This is done with nanomaterials which
have composites of metals; this will be done mainly with Oxides of nanomaterial like Al2 O3 , CuO, metals
Al, Cu and also with Carbon nanotubes (CNT), Graphite. For Different Nanomaterial the acid treatment
will be different as per the base fluid is used. We have to use a Paraffin Wax as a base fluid and Al2 O3 of a
20nm size and 99% pure as an enhancing material in base material for improving the thermal conductivity
of paraffin.
The mixture prepares for two gram of a nano Al2 O3 of 20 nm with addition of 50 ml Oleic Acid Pure
(C18 H34O2 ) and 250 ml Methanol (CH4 O), the mixture is prepared as the ratio of 1:25:125 by weight
concentration. The methanol is added for the dissolving of surfactant i. e. oleic acid for the proper
functioning of nano Al2 O3 nanomaterial.
27
4.2.2 Ultrasonic Agitation (Vibration)
The prepared mixture is kept on sonification bath at normal atmospheric temperature for the time period of
45 minutes. During this process the mixture homogeneous mixture is formed which is used for the further
experimentation.
This treatment is done for at 800C and 700-1200 rpm speed. The magnetic needle is added into the mixture
which is helpful for stirring the mixture well. The main purpose of this is to completely remove the effect
of methanol from the mixture, the time taken for that is 3 hrs.
4.2.4 Filtration
After complete removal of Methanol from the mixture we have to proceed for the filtration, by using filter
paper we filter the homogeneous mixture of Al2O3 and Oleic acid for the complete removal of oleic acid
from the mixture, to complete the filtration process for separation of nanomaterial it has to take time
period of 24 hrs.
28
4.2.5 Washing
After complete filtration the next step to wash the nanomaterial for the removal of acid and methano l
effect from the functionalized nano material. For the washing process use Acetone [(CH3)2CO)] as washer.
The quantity of acetone used for each wash is 20 ml. The functionalized nano Al2O3 wash with acetone at
three to four times for the complete removal of acid and methanol effect. Finally the mixture of acetone
and nanomaterial is kept on a sonification bath for the homogeneity of nanomaterial and separate the
material from each other the time period for this is 30 minutes.
For the complete removal of acetone from the mixture we have to keep the mixture in atmospheric air for
20 to 30 minute along with complete vaporization of acetone. Finally the nanomaterial is kept on a Hot
Air Oven for the temperature at 650C - 700 C for the time period of 15 minutes.
Fig 4.4 Washing with Acetone Fig 4.5 Mixtures of Al2O3 & Acetone
In Ultrasonic Bath
4.2.6 Drying:
After complete the Functionalization process the synthesized Al2O3 Nanomaterial is kept in
atmospheric condition for 24 hrs. Finally synthesized Al2O3 nanopowder is used for the experimentation.
29
Fig 4.8 Synthesized Al2O3 Nanopowder after 24 Hrs.
In this work, Al2O3 of 20 nm size and 99% pure particles were purchased from a commercial
company (Nanoshel By Intelligent Material Pvt. Ltd.) are chosen as a source material for a nanofluid.
The nanoparticles were used as received, which were produced by a physical vapour deposition
technique. It can be seen that the primary Al2O3 nanoparticles are spherical and their size is widely
distributed in an average range of 20 nm and Al2O3 nanofluids were prepared by the two-step method.
The mixture of Synthesized Al2O3-Paraffin Wax nanofluids suspension was vibrated for 10 minute in
an ultrasonic vibrator. At the same time, the plain Al2O3 suspension with base Paraffin Wax was also
vibrated for 10 minute in the ultrasonic vibrator for comparison. Their sedimentation photographs
were shown in Figure 5.1 which shows that the stabilization of the suspension with synthesized Al2O3
nanopowder in the stationary state and no sediment was found, while the suspension with plain Al2O3
nanopowder exhibited weaker dispersion and aggregatation occurred.
30
Figure 5.1 Photographs of Nano Al2O3 -Paraffin Wax suspensions before and after enhancement of
synthesized material by 1% weight Concentration.
6. CONCLUSION
Based on the work done in this research, the following conclusion can be drawn.
Proper addition of dispersant to nano- Al2O3 suspension exhibits an enhanced dispersion and stability
compared to the suspension without dispersant. The experimental results show that for SDBS there is
an optimizing concentration in the nanofluids in 0.1% Al2O3 -H2O nano-suspensions, the optimizing
concentration of SDBS is 0.09% and Stability for 1% Al2O3 – paraffin wax nano suspension the
optimizing concentration of oleic acid in the ratio of 1:25 which has the best disperses results for the
nanofluid.
REFERENCES
1. CHOI S.U. “Enhancing thermal conductivity of fluids with nanoparticles,” ASME, FED, 231,
99(1995).
2. EASTM AN J.A., “Anomalously increased effective thermal conductivities of ethylene glycol-based
nanofluids containing copper nanoparticles,” Applied Physics Lett., 78(6): 718-7209(2001).
3. WANG S. W., ZHU D. S., “Adsorption heat pump using an innovative coupling refrigeration cycle,”
Adsorption, 10(1): 47-55(2004).
4. HE L., ZHU D. S., “Heat transfer augmentation for the flow of highly viscous fluids in the tubes using
cross trapezoid wave tape inserts,” Journal of Heat Transfer, 11(4):371-377(2004).
5. NGUYEN C. T., ROY G., GAUTHIER C., GALANIS N., “Heat transfer enhancement using Al2O3–water
nanofluid for an electronic liquid cooling system,” Applied Thermal Engineering 27, 1501–
1506(2007).
31
6. MURSHED S. M., LEONG K. C., YANG C., “Enhanced thermal conductivity of TiO2 –water based
nanofluids,” Int. J. Thermal Sci. 44, 367–373(2005).
7. XUE Q. Z., “Model for thermal conductivity of carbon nanotube-based composites,” Physics B 368,
302–307(2005).
8. LI X. F., and X .J. WANG, “Evaluation on dispersion behavior of the aqueous copper nano-
suspensions,” Colloid Interface Sci. 310456 (2007).
9. ANA . R. J. DAR, ANTONIO M. R, JUAN L. and ORTEGA V., “Effect of the ionic surfactant concentration
on the stabilization/destabilization of polystyrene Colloidal particles,” Journal of Colloid and Interface
Science, 298, 248-252 (2006).
10. JIANG, L. and SUN J., “Production of aqueous colloidal dispersions of carbon nanotubes” Journal of
Colloid and Interface Science, 26089-26094(2003).
11. LEE D. and KIM B. G., “A New Parameter to Control Heat Transport in Nanofluids: Surface Charge
State of the Particle in Suspension,” J. Phys. Chem. B, 110:4323-4328(2006).
12. LEE H., FO VET Y., TOUM ELIN-CHEM LA F., “Influence of pH and fluoride concentration on titanium
passivating layer: stability of titanium dioxide”, Talanta 53 (5) 1053-1063 (2001).
13. WEI X., ZHU H., KONG T., “Synthesis and thermal conductivity of Cu2 O nanofluids”, International
Journal of Heat and Mass Transfer 52 4371-4374 (2009).
14. LI X.F., ZHU D.S. and WANG X.J. “Thermal conductivity enhancement Dependent pH and chemical
surfactant for Cu-H2 O nanofluids”, Thermochim. Act 469, 98-103 (2008).
15. XIAN -JU, WANGAPI, and XIN-FANG LI, “Influence of SDBS on stability of Al2 O3 nano-Suspensions”,
Proc. of SPIE Vol. 6831, 683113, (2007).
32
Proceedings of International Conference on Advances in Mechanical Engineering
Not received
33