Fea of Helical Gear Using 3D Model
Fea of Helical Gear Using 3D Model
Fea of Helical Gear Using 3D Model
ISSN: 2277-9655
Impact Factor: 1.852
IJESRT
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH
TECHNOLOGY
babitavishwakarma18@gmail.com
Abstract
Gears are one of the most critical components in mechanical power transmission systems. The bending and
surface strength of the gear tooth are considered to be one of the main contributors for the failure of the gear in a
gear set. Thus, analysis of stresses has become popular as an area of research on gears to minimize or to reduce the
failures and for optimal design of gears. This paper investigates finite element model for monitoring the stresses
induced of tooth flank, tooth fillet during meshing of gears. The involute profile of helical gear has been modeled
and the simulation is carried out for the bending and contact stresses and the same have been estimated. To estimate
bending and contact stresses, 3D models are generated by modeling software CATIA V5 and simulation is done by
finite element software package ANSYS 14.0. Analytical method of calculating gear bending stresses uses Lewis
and AGMA bending equation. For contact stresses Hertz and AGMA contact equation are used. Study is conducted
by varying the face width to find its effect on the bending stress of helical gear. It is therefore observed that the
maximum bending stress decreases with increasing face width. The stresses found from ANSYS results are
compared with those from theoretical and AGMA values.
Keywords: Helical Gear, Stress Calculation, Bending Stress, Contact Stress, Finite Element Analysis.
Introduction
Gears are use to transmit power and motion
from one shaft to another. Helical gears are currently
being used increasingly as a power transmitting gear
owing to their relatively smooth and silent operation,
large load carrying capacity and higher operating
speed. Helical gears have a smoother operation than
the spur gears because of a large helix angle that
increases the length of the contact lines. Designing
highly loaded helical gears for power transmission
systems that are good in strength and low level in
noise necessitate suitable analysis methods that can
easily be put into practice and also give useful
information on contact and bending stresses [1].
Gears are used to change the speed, magnitude, and
direction of a power source. Gears are being most
widely used as the mechanical elements of power
transmission. When two gears with unequal numbers
of teeth are combined, a productive output is realized
with both the angular speeds and the torques of the
two gears differing through a simple relationship.
AGMA [1] and ISO [2] standards generally are being
used as the strength standard for the design of spur,
helical, and worm gears. The strength determined
from the AGMA and ISO standards is valid under the
ISSN: 2277-9655
Impact Factor: 1.852
b
deflection and stress distribution for various gear
F m Y .(1.1)
drives. Several researchers have analyzed line-contact
Where, = Root bending stress (N/m2), Wt =
involute helical gears using three-dimensional (3-D)
Transmitted tangential Load (Newton), F = Face
Finite element (FE) stress analysis [10],[11].
width (m or mm), m = Module (m or mm), Y = Lewis
However, these researchers applied loads directly to
form Factor. Y is the function of number of teeth,
the contact ellipses and contact lines obtained from
pressure angle and an in volute depth of the gear,
tooth contact analysis (TCA). FE contact analysis for
2x
deformable bodies is complex and non-linear. Most
Y
early 3-D FE contact analyses were performed using
3m
gap elements [14]. Now, due to the progress of
It
is
fact
that, when teeth mesh, the load is delivered
computer technology and computational techniques,
to
the
teeth
with some degree of impact. If
some FEA packages can deal with contact analysis
we
go
with
simply to calculate bending stress, the
without using gap elements. Some researchers have
velocity factor is should be used in calculation. Now
begun to apply these FEA softwares to contact
Lewis equation becomes,
problems of gear surfaces [15],[8]. The authors have
presented a generation method for the modi_ed
helical gear, possessing double crowning effects in
the profile and lengthwise directions [16]. A
http: // www.ijesrt.com(C)International Journal of Engineering Sciences & Research Technology
[1952-1958]
Wt
b
Kv F m Y
Where, K v is the Velocity Factor.
AGMA Bending Stress Equaction
Equation (1.1) is known as Lewis equation,
which considers only static loading and doesnt take
the dynamics of meshing teeth into account. The
above stress formula must be modified to account
different situations like stress concentration and
geometry of the tooth. Therefore, Equation (1.2) that
is shown below is the modified Lewis equation
recommended by AGMA for practical gear design to
account for variety of conditions that can be
encountered in service.
The AGMA equation for bending stresses given by,
Ft
K v K o K s 0.93K m
bmn J
..(1.2)
Where,
mn Normal Module
J Geometry factor
K v Dynamic factor
K o Overload factor
K s Size factor
K m Load distribution factor.
ISSN: 2277-9655
Impact Factor: 1.852
machine design, problems frequently occurs when
two members with curved surfaces are deformed
when pressed against one another giving rise to an
area of contact under compressive stresses. Of
particular interest to the gear designer is the case
where the curved surfaces are of cylindrical shape
because they closely resemble gear tooth surfaces.
The surface compressive stress (Hertzian stress) is
found from the equation
1 1
Ft
r1 r2
c
B cos 1 v12 1 v2 2
E1
E2
Where,
where
r1
and
r2
r1
d p sin
2
r2
d g sin
2
c Cp
Where,
cos
Ft
K v K o 0.93K m
0.95CR
bdI
Cp
N / mm2
is
an
elastic
coefficient
2
Cp
2
2
1
v
1
v
1
2
E1
E2
C p 190.3 (MPa) for steel (Bhandari, 2012)
Where
CR
r1 a
rb12
rb2 2 r1 r2 sin
m cos
r2 a
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sin cos i
2
i 1
14.
15.
16.
17.
18.
Parameters
Pinion
Gear
Number of teeth
Pressure
angle,
normal
Helix angle
18
36
40
Material
Input speed (rpm)
(A)
Input power (KW)
(A)
Input speed (rpm)
(B)
Input power (KW)
(B)
Diameter of pitch
circle (mm)
Diameter of base
circle (mm)
Diameter
of
Addendum circle
(mm)
Diameter
of
Dedendum circle
(mm)
Circular
Pitch
(mm)
Youngs modulus
(MPa)
Poissons ratio
Torque (N-m)
200
150(RH)
150(LH)
4
Grade
Steel
Grade
Steel
720
1500
35
72
144
67.4
135.2
80
152
62.8
134
12.56
2.1105
0.3
663.48
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Table 2 : Comparison of Values of the Root
Bending Stresses by Considering Different Face
Width
Root Bending Stresses (MPa)
Face
Width (b)
(mm)
LEWIS
AGMA
ANSYS
36
30.97
29.41
26.12
40
28.78
28.06
25.3
44
26.17
26.58
23.47
48
23.98
24.95
21.43
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AGMA
ANSYS
36
107.47
102.15
93.86
40
96.71
94.31
83.72
44
87.93
88.37
75.69
48
80.61
80.83
68.62
Contact Stress
Hertz Equation
-470.64 MPa
548.66 MPa
FEA
510.48 MPa
Comparison
In this section the modeled helical gear is
analyzed to study the effect of face width on bending
under static load with different parameters.
Throughout the analysis each gear is studied for four
different face widths (b = 36 mm, 40 mm, 44 mm, 48
mm). All the rest parameters and the applied load are
kept constant.
AGMA results
ANSYS results
And all results are closer as shown in graphs.
ISSN: 2277-9655
Impact Factor: 1.852
Conclusions