2 Marks QA MOM
2 Marks QA MOM
2 Marks QA MOM
1.
What are the conditions for a body to be in static and dynamic equilibrium?
Necessary and sufficient conditions for static and dynamic equilibrium are
1. Vector sum of all forces acting on a body is zero.
2. The vector sum of the moments of all forces acting about any arbitrary point or axis is
zero.
First condition is the sufficient condition for static equilibrium together with
second condition is necessary for dynamic equilibrium.
2. Define static force analysis.
If components of a machine accelerate, inertia is produced due to their masses.
However, the magnitudes of these forces are small compared to the externally applied
loads. Hence inertia effect due to masses are neglected. Such an analysis is known as
static force analysis.
3. Define force and applied force.
Force is a push or pull, which acts on a body changes or tends to change, the state
of rest or of uniform motion of the body. A force is completely characterized by its point
of application, its magnitude and direction.
The external force acting on a system of body from outside the system are called
applied force. The applied forces are classified as active and reactive force.
4. Rate of change of momentum of a body is directly proportional to Force acting on it.
5. Which law helps to measure a force quantitatively?
Newtons second law helps us to measure a force quantitatively.
6. When will the two force member is in equilibrium?
The member under the action of two force will be in equilibrium if,
1. The two forces are of same magnitude,
2. The forces act along the same line, and
3. The forces are in opposite direction
8. Give any three advantages of free body diagram.
1. Free body diagram assist in seeing and understanding all aspects of problem.
2. They help in planning the approach to the problem.
3. They make mathematical relations easier to the problem.
9. When will the three force member is in equilibrium.
A body or member will be in equilibrium under the action of three forces if,
1. the resultant of the forces is zero, and
2. the line of action of the forces intersect at a point.
10. Differentiate between static force analysis and dynamic force analysis.
If components of a machine accelerate, inertia forces are produced due to their
masses. If the magnitude of these forces are small compared to the externally applied
loads, they can be neglected while analyzing the mechanism. Such an analysis is known
as static force analysis.
11. What do you mean by inertia?
The property of matter offering resistance to any change of its state of rest or of
uniform motion in a straight line is known as inertia.
UNIT V - BALANCING
1. Write the importance of Balancing?
If the moving part of a machine are not balanced completely then the inertia
forces are set up which may cause excessive noise, vibration, wear and tear of the
system. So balancing of machine is necessary.
2. Why balancing of dynamic forces is necessary?
If dynamic force are not balanced, they will cause worse effects such as war and
tear on bearings and excessive vibrations on machines. It is very common in cam shafts,
steam turbine rotors, engine crank shafts, and centrifugal pumps, etc.,
3. Write the different types of balancing?
VIBRATIONS
50. What are the causes of vibration?
The causes of vibration are unbalanced forces, elastic nature of the system, self
excitations, winds and earthquakes.
1. A petrol engine has a stroke of 120 mm and connecting rod is 3 times the crank length.
The crank rotates at 1500 rpm clockwise direction. Determine 1. Velocity and
acceleration of the piston and 2. Angular velocity and angular acceleration of the
connecting rod, when the piston has traveled one-fourth of its stroke from I.D.C.
(Ans. Refer Prob. No. 2.3, Page No. 2.15 Dynamics of Machines by V. JAYAKUMAR)
2. The ratio of the connecting rod length to crank length for a vertical petrol engine is 4:1.
The bore/stroke is 80/100 mm and mass of the reciprocating part is 1 kg. The gas pressure
2
on the piston is 0.7 N/mm when it has moved 10 mm from TDC on its power stroke.
Determine the net load on the gudgeon pin. The engine runs at 1800 rpm At what engine
speed will this load be zero.
(Ans. Refer Prob. No. 2.14, Page No. 2.36 Dynamics of Machines by V. JAYAKUMAR)
3. The turning moment diagram for a four stroke gas engine may be assumed for simplicity
to be represented by four triangles, the areas of which from the line of zero pressure are
2
2
as follows: Expansion stroke = 3550 mm ; Exhaust stroke = 500 mm ; Suction stroke =
2
2
2
350 mm ; and compression stroke = 1400 mm . each mm represents 3 N-m. Assuming
the resisting moment to be uniform, find the mass of the rim of a fly wheel required to
keep the mean speed 200 rpm within 2%. The mean radius of the rim may be taken as
0.75 m. Also determine the crank positions for the maximum and minimum speeds.
(Ans. Refer Prob. No. 3.11, Page No. 3.25 Dynamics of Machines by V. JAYAKUMAR)
4. The equation of the turning moment diagram for the three crank engine is given by: T(Nm) = 25000 7500 sin 3, where radians is the crank angle from inner dead centre.
2
The moment of inertia of the flywheel is 400 kg-m and the mean engine speed is 300
rpm. Calculate,
1. The power of the engine, and
2. The total fluctuation of speed of the flywheel when
a) The resisting torque is constant, and
b) The resisting torque is (25000 + 3600 sin ) N-m.
(Ans. Refer Prob. No.3.16, Page No. 3.36 Dynamics of Machines by V. JAYAKUMAR)
5. A steam engine runs2at 150 rpm. Its turning moment diagram gave the following area
measurements in mm taken in order above and below the mean torque line: 500, -250,
270, -390, 190, -340, 270, -250. The scale for the turning moment is 1 mm = 500 N-m,
o
and for crank angle is 1 mm = 5 . If the fluctuation of speed is not to exceed 1.5 % of
the mean, determine a suitable diameter and cross-section of the rim of the flywheel
assumed with axial dimension (i.e., width of the rim) equal to 1.5 times the radial
dimension (i.e., thickness of the rim). The hoop stress is limited to 3 Mpa and the density
3
of the material of the flywheel is 7500 kg/m .
(Ans. Refer Prob. No.3.19, Page No. 3.43 Dynamics of Machines by V. JAYAKUMAR)
6. Three masses are attached to a shaft as follows: 10 kg at 90 mm radius, 15 kg at 120 mm
radius and 9 kg at 150 mm radius. The masses are to be arranged so that the shaft is in
complete balance. Determine the angular position of masses relative to 10 kg mass. All
the masses are in the same plane.
(Ans. Refer Prob. No.5.2, Page No. 5.9 Dynamics of Machines by V. JAYAKUMAR)
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7. A shaft has tree eccentrics, each 75 mm diameter and 25 mm thick, machined in one
piece with the shaft. The central planes of the eccentric are 60 mm apart. The distance of
the centers from the axis of rotation are 12 mm,18 mm and 12 mm and their angular
o
3
positions are 120 apart. The density of metal is 700 kg/m . Find the amount of out-ofbalance force and couple at 600 rpm. If the shaft is balanced by adding two masses at a
radius 75 mm and at distance of 100 mm from the central plane of the middle eccentric,
find the amount of the masses and their angular positions.
(Ans. Refer Prob. No.5.8, Page No. 5.21 Dynamics of Machines by V. JAYAKUMAR)
o
8. The cranks of a three-cylinder locomotive are set at 120 . The reciprocating masses are
450 kg for the inside cylinder and 390 kg for each outside cylinder. The pitch of the
cylinder is 1.2 m and the stroke of each piston 500 mm. The planes of rotation of the
balance masses are 960 mm from the inside cylinder. If 40% of the reciprocating masses
are to be balanced, determine
1. The magnitude and the position of the balancing masses required at a radial
distance of 500 mm; and
2. The hammer blow per wheel when the axle rotates at 350 rpm.
(Ans. Refer Prob. No.6.5, Page No. 6.17 Dynamics of Machines by V. JAYAKUMAR)
9. An air compressor has four vertical cylinders 1, 2, 3 and 4 in line and the driving cranks
o
at 90 intervals reach their upper most positions in this order. The cranks are of 150 mm
radius, the connecting rods 500 mm long and the cylinder centre line 400 mm apart. The
mass of the reciprocating parts for each cylinder is 22.5 kg and the speed of rotation is
400 rpm. Show that there are no out-of-balance primary or secondary forces and
determine the corresponding couples, indicating the position of No.1 crank for maximum
values. The central plane of the machine may be taken as reference plane.
(Ans. Refer Prob. No.6.9, Page No. 6.31 Dynamics of Machines by V. JAYAKUMAR)
10. The firing order of a six cylinder, vertical, four-stroke, in-line engine is 1-4-2-6-3-5. The
piston stroke is 80 mm and length of each connecting rod is 180 mm. The pitch distances
between the cylinder centre lines are 80 mm, 80 mm, 120 mm, 80 mm and 80 mm
respectively. The reciprocating mass per cylinder is 1.2 kg and the engine speed is 2400
rpm. Determine the out-of-balance primary and secondary forces and couples on the
engine taking a plane mid-way between the cylinders 3 and 4 as the reference plane.
(Ans. Refer Prob. No.6.14, Page No. 6.41 Dynamics of Machines by V. JAYAKUMAR)
11. Determine the equivalent spring stiffness and the natural frequency of the following
vibrating systems when
a) the mass is suspended to a spring
b) the mass is suspended at the bottom of two springs in series
c) the mass is fixed in between two springs
d) the mass is fixed to the mid point of a spring
(Ans. Refer Prob. No. 18.1, Page No. 598 Theory of Machines by S.S. RATTAN)
12. A vibrating system consists of a mass of 50 kg, a spring of stiffness 30 kN/m and a
damper. The damping provided is only 20 % of the critical value. Determine
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1.
2.
3.
4.
5.
(Ans. Refer Prob. No. 18.5, Page No. 609 Theory of Machines by S.S. RATTAN)
13. The machine mounted on springs and fitted with a dashpot has a mass of 60 kg. There are
three springs, each of stiffness 12 N/mm. The amplitude of vibrations reduces from 45 to
8 mm in two complete oscillations. Assuming that the damping force varies as the
velocity, determine
i)
the damping coefficient,
ii)
the ratio of frequencies of damped and undamped vibrations, and
iii)
the periodic time of damped vibrations.
(Ans. Refer Prob. No. 18.8, Page No. 611 Theory of Machines by S.S. RATTAN)
14. A single cylinder vertical diesel engine has a mass of 400 kg and is mounted on a steel
chassis frame. The static deflection owing to the weight of the chassis is 2.4 mm. The
reciprocating masses of the engine amounts to 18 kg and the stroke of the engine is 160
mm. A dashpot with a damping coefficient 2 N/mm/s is also used to dampen the
vibrations. In the steady-state of the vibrations, determine
1. the amplitude of the vibrations if the driving shaft rotates at 500 rpm.
2. the speed of the driving shaft when the resonance occurs.
(Ans. Refer Prob. No. 18.12, Page No. 619 Theory of Machines by S.S. RATTAN)
15. A machine supported symmetrically on four springs has a mass of 80 kg. The mass of the
reciprocating parts is 2.2 kg which move through a vertical stroke of 100 mm with
simple harmonic motion. Neglecting damping, determine the combined stiffness of the
th
springs so that the force transmitted to the foundation is 1/20 of the impressed force.
The machine crank shaft rotates at 800 rpm
If under actual working conditions, the damping reduces the amplitudes of
successive vibrations by 30 %, find,
1. the force transmitted to the foundation at 800 rpm,
2. the force transmitted to the foundation at resonance, and
3. the amplitude of the vibrations at resonance.
(Ans. Refer Prob. No. 18.15, Page No. 624 Theory of Machines by S.S. RATTAN)
16. A shaft supported freely at the ends has a mass of 120 kg placed 250 mm from one end.
Determine the frequency of the natural transverse vibrations if the length of the shaft is
2
700 mm, E = 200 GN/m and shaft diameter is 40 mm.
(Ans. Refer Prob. No. 18.16, Page No. 626 Theory of Machines by S.S. RATTAN)
17. A shaft 40 mm diameter and 2.5 m long has a mass of 15 kg per meter length. It is
simply supported at the ends and carries three masses 90 kg, 140 kg and 60 kg at 0.8 m,
2
1.5 m and 2 m respectively from the left support. Taking E = 200 GN/m , find the
frequency of the transverse vibrations.
(Ans. Refer Prob. No. 18.17, Page No. 633 Theory of Machines by S.S. RATTAN)
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= 1.2 m
= 14,
= 16 kg,
= 0.4 mm
2
= 200 GN/m
6
2
= 70 X 10 N/m
speed over which it is
(Ans. Refer Prob. No. 18.20, Page No. 636 Theory of Machines by S.S. RATTAN)
19. The following data refer to the transmission gear of a motor ship:
2
= 4800 kg m
Moment of inertia of flywheel
2
= 3200 kg m
Moment of inertia of propeller
9
2
Modulus of rigidity of shaft material
= 80 X 10 N/m
2
= 400 kg m
Equivalent MOI per cylinder
Assuming the diameter of the torsionally equivalent crankshaft to be 320 mm and
treating the arrangement as a three rotor system, determine the frequency of free torsional
vibrations.
(Ans. Refer Prob. No. 18.27, Page No. 656 Theory of Machines by S.S. RATTAN)
20. A reciprocating IC engine is coupled to a centrifugal pump through a pair of gears. The
shaft from the flywheel of the engine to the gear wheel has a 48 mm diameter and is 800
mm long. The shaft from the pinion to the pump has a 32 mm diameter and is 280 mm
long. Pump speed is four times the engine speed. Moments of inertia of flywheel, gear2
2
2
2
wheel, pinion and pump impeller are 1000 kg m , 14 kg m , 5 kg m and 18 kg m
respectively. Find the natural frequency of the torsional oscillation of the system. G = 80
2
G N/m .
(Ans. Refer Prob. No. 18.28, Page No. 660 Theory of Machines by S.S. RATTAN)
21. Each arm of a Porter governor is 250 mm long. The upper and lower arms are pivoted to
links of 40 mm and 50 mm respectively from the axis of rotation. Each ball has a mass of
5 kg and the sleeve mass is 50 kg. The force of friction on the sleeve of the mechanism is
40 N. Determine the range of speed of the governor for extreme radii of rotation of 125
mm and 150 mm.
(Ans. Refer Prob. No. 16.3, Page No. 540 Theory of Machines by S.S. RATTAN)
22. The mass of each ball of a Proell governor is 7.5 kg and the load on the sleeve is 80 kg.
Each of the arms is 300 mm long. The upper arms are pivoted on the axis of rotation
whereas the lower arms are pivoted to links of 40 mm from the axis of rotation. The
extensions of the lower arms to which the balls are attached are 100 mm long and are
parallel to the governor axis at the minimum radius. Determine the equilibrium speeds
corresponding to extreme radii of 180 mm and 240 mm/
(Ans. Refer Prob. No. 16.4, Page No. 543 Theory of Machines by S.S. RATTAN)
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23. In a spring loaded Hartnell type of governor, the mass of each ball is 4 kg and the lift of
the sleeve is 40 mm. The governor begins to float at 200 rpm when the radius of the ball
path is 90 mm. The mean working speed of the governor is 16 times the range of speed
when friction is neglected. The lengths of the ball and roller arms of the bell-crank lever
are 100 mm and 80 mm respectively. The pivot centre and the axis of governor are 115
mm apart. Determine the initial compression of the spring, taking into account the
obliquity of arms.
Assuming the friction at the sleeve to be equivalent to a force of 15 N, determine
the total alteration in speed before the sleeve begins to move from the mid- position
(Ans. Refer Prob. No. 16.6, Page No. 548 Theory of Machines by S.S. RATTAN)
24. The controlling force curve of a spring controlled governor is a straight line. The weight
of each governor ball is 40 N and the extreme radii of rotation are 120 mm and 180 mm.
If the values of the controlling force at the above radii be respectively 200 N and 360 N
and the friction of the mechanism is equivalent to 2 N at each ball. Find a) the extreme
equilibrium speeds of the governor, b) the equilibrium speed and the coefficient of
insensitiveness at a radius of 150 mm.
(Ans. Refer Prob. No.10.32, Page No. 10.68 Dynamics of Machines by V. JAYAKUMAR)
25. In a Porter governor, each arm is 200 mm long and is pivoted at the axis of rotation. The
mass of each ball is 5 kg and the load on the sleeve is 30 kg. The extreme radii of rotation
are 80 mm and 140 mm. Plot a graph of the controlling force vs. radius of rotation and set
off a speed scale along the ordinate corresponding to a radius of 160 mm.
(Ans. Refer Prob. No. 16.10, Page No. 563 Theory of Machines by S.S. RATTAN)