FEA Stress Analysis and Durability Study of Spur Gear

International Journal of Advanced Research in Technology, Engineering and Science (A Bimonthly
Open Access Online Journal) Volume2, Issue2, March‐April, 2015. ISSN: 2349‐7173(Online).
All Rights Reserved©2015 IJARTES Visit: www.ijartes.org Page 8

Stress Analysis on Spur Gear and Durability
Study by FEA
V.Thirumalairaj1*
K.Chandrasekaran2
, R.Ahamed Meeran3
, R.Radhakrishnan4
,
A.Vambathurajesh5
. _________________________________________
Abstract:
Gears are widely used in transmission system which
undergoes cyclic loads in service. But still the gears for
the specific transmission will be having a limit working
load which is the maximum load carried by the gear.
The maximum stress induced on the gear tooth when it
meshes with other gear should be less than its
capability so that it will be lasting. Repeated cycles of
stress on the gears are considerably changing the
fatigue life of gears. In order to get good durability it is
necessary to understand the maximum stress induced
in its tooth. Prior to the study of durability it is
necessary to analyze the load acting on the tooth while
transmission and the corresponding induced stress on
the gear tooth. Based on the above said analysis the
induced stress is predicted on the tooth. Also the Finite
Element Analysis play vital role on the durability
studies since the prediction of life and location of
damage are critical. The force and stress analysis can
be made to justify the result by analytically and using
FEA tools.
_________________________________________
Keywords: gear, stress analysis, FEA tools
_________________________________________
I. Introduction:
Gearing is one of the most critical components in a
mechanical power transmission system, and in most
industrial rotating machinery. It is possible that gears
will predominate as the most effective means of
transmitting power in future machines due to their high
degree of reliability and compactness. In addition, the
rapid shift in the industry from heavy industries such as
shipbuilding to industries such as automobile
manufacture and office automation tools will necessitate
a refined application of gear technology [1].
________________________________________
Authors Address: Assistant Professor, Department of
Mechanical Engineering, Nadar Saraswathi College of
Engineering and Technology, Theni, Tamilnadu,
India.
______________________________________________________________________
A gearbox as usually used in the transmission system is
also called a speed reducer, gear head, gear reducer etc.,
which consists of a set of gears, shafts and bearings that
are factory mounted in an enclosed lubricated housing.
Speed reducers are available in a broad range of sizes,
capacities and speed ratios. Their job is to convert the
input provided by a prime mover (usually an electric
motor) into an output with lower speed and
correspondingly higher torque. In this thesis, analysis of
the characteristics of involutes spur gears in a gearbox
was studied using nonlinear FEM [2].
The increasing demand for quiet power transmission in
machines, vehicles, elevators and generators, has created
a growing demand for a more precise analysis of the
characteristics of gear systems. In the automobile
industry, the largest manufacturer of gears, higher
reliability and lighter weight gears are necessary as
lighter automobiles continue to be in demand. In
addition, the success in engine noise reduction promotes
the production of quieter gear pairs for further noise
reduction. Noise reduction in gear pairs is especially
critical in the rapidly growing field of office-automation
equipment as the office environment is adversely
affected by noise, and machines are playing an ever
widening role in that environment. Ultimately, the only
effective way to achieve gear noise reduction is to
reduce the vibration associated with them [3]. The
reduction of noise through vibration control can only be
achieved through research efforts by specialists in the
field. However, a shortage of these specialists exists in
the newer, lightweight industries in Japan mainly
because fewer young people are specializing in gear
technology today and traditionally the specialists
employed in heavy industries tend to stay where they
are. Designing highly loaded spur gears for power
transmission systems that are both strong and quiet
requires analysis methods that can easily be
implemented and also provide information on contact
and bending stresses, along with transmission errors.
The finite element method is capable of providing this
information, but the time needed to create such a model
is large. In order to reduce the modeling time, a
preprocessor method that creates the geometry needed
for a finite element analysis may be used, such as that
provided by Pro/Engineer. Pro/Engineer can generate
models of three-dimensional gears easily. In Pro/E, the


geometry is saved as a file and then it can be transferred
from Pro/E to ANSYS. In ANSYS, one can click File >
Import > IGES > and check No disfeaturing and Merge
coincident key points [4].
The prime source of vibration and noise in a gear system
is the transmission error between meshing gears.
Transmission error is a term used to describe or is
defined as the differences between the theoretical and
actual positions between a pinion (driving gear) and a
driven gear. It has been recognized as a main source for
mesh frequency excited noise and vibration. With prior
knowledge of the operating conditions of the gear set it
is possible to design the gears such that the vibration and
noise is minimized. Transmission error is usually due to
two main factors. The first is caused by manufacturing
inaccuracy and mounting errors. Gear designers often
attempt to compensate for transmission error by
modifying the gear teeth [5]. The second type of error is
caused by elastic deflections under load. Among the
types of gearbox noise, one of the most difficult to
control is gear noise generated at the tooth mesh
frequency. Transmission error is considered to be one of
the main contributors to noise and vibration in a gear
set. This suggests that the gear noise is closely related to
transmission error. If a pinion and gear have ideal
involutes profiles running with no loading torque they
should theoretically run with zero transmission error [6].
However, when these same gears transmit torque, the
combined tensional mesh stiffness of each gear changes
throughout the mesh cycle as the teeth deflect, causing
variations in angular rotation of the gear body. Even
though the transmission error is relatively small, these
slight variations can cause noise at a frequency which
matches a resonance of the shafts or the gear housing,
causing the noise to be enhanced. This phenomenon has
been actively studied in order to minimize the amount of
transmission error in gears.
Gears analyses in the past were performed using
analytical methods, which required a number of
assumptions and simplifications. In general, gear
analyses are multidisciplinary, including calculations
related to the tooth stresses and to tribological failures
such as like wear or scoring. In this thesis, static contact
and bending stress analyses were performed, while
trying to design spur gears to resist bending failure and
pitting of the teeth, as both affect transmission error. As
computers have become more and more powerful,
people have tended to use numerical approaches to
develop theoretical models to predict the effect of
whatever is studied. This has improved gear analyses
and computer simulations. Numerical methods can
potentially provide more accurate solutions since they
normally require much less restrictive assumptions. The
model and the solution methods, however, must be
chosen carefully to ensure that the results are accurate
and that the computational time is reasonable. The finite
element method is very often used to analyze the stress
state of an elastic body with complicated geometry, such
as a gear. There have been numerous research studies in
the area as described. In this thesis, first, the finite
element models and solution methods needed for the
accurate calculation of two dimensional spur gear
contact stresses and gear bending stresses were
determined. Then, the contact and bending stresses
calculated using ANSYS 7.1 were compared to the
results obtained from existing methods. The purpose of
this thesis is to develop a model to study and predict the
transmission error model including the contact stresses,
and the torsion mesh stiffness of gears in mesh using the
ANSYS 7.1 software package based on numerical
method. The aim is to reduce the amount of transmission
error in the gears, and thereby reduce the amount of
noise generated [7,8].
From the literature review the contact stress refers to the
localized stresses that develop as two curved surfaces
come in contact and deform slightly under the imposed
loads. The amount of deformation is dependent on the
modulus of elasticity of the material in contact. Hertzian
contact stress forms the foundation for the equations for
load gear capabilities and fatigue life in bearings, gears,
and other bodies where two surfaces are in contact.
Failure from contact stresses generally falls into two
categories:
o Localized deformations by yielding
or distortions, and
o Fracture by progressive spreading of
a crack (fatigue)
II. Contact Stress Analysis
The objective of the contact stress analyses was to gain
an understanding of the modeling and solution
difficulties in contact problems and examine the contact
stresses in the gears. In order to verify the FEM contact
model procedure, contact between two cylinders was
modeled. To reduce computer time, only half cylinders
were meshed in the model .The fine meshed rectangular
shaped elements were generated near contact areas .The
dimensions of the elements are based on the half width
of the contact area. The contact conditions are sensitive
to the geometry of the contacting surfaces, which means
that the finite element mesh near the contact zone needs
to be highly refined. Finer meshing generally leads to a
more accurate solution, but requires more time and
system resources. It is recommended not to have a fine
mesh everywhere in the model to reduce the
computational requirements. The edge length dx of the
rectangular shaped fine mesh elements: dx = 2 * a /
Num. Num is the number of elements in the contact zone


as specified in the input file. It was hoped that the
number of elements in the Hertz contact zone could be
related to the solution accuracy, independent of the
specific force or cylinder sizes considered. Num is equal
to 10 here.
III. Result and Discussion
One of the predominant modes of gear tooth failure is
pitting. Pitting is a surface fatigue failure due to many
repetitions of high contact stress occurring on the gear
tooth surface while a pair of teeth is transmitting power.
In other words, contact stress exceeding surface
endurance strength with no endurance limits or a finite
life causes this kind of failure. Contact failure in gears is
currently predicted by comparing the calculated Hertz
stress to experimentally determine allowable values for
the given material. The details of the subsurface stress
field usually are ignored. This approach is used because
the contact stress field is complex and its interaction
with subsurface discontinuities is difficult to predict.
However, all of this information can be obtained from
the ANSYS model. Since a spur gear can be considered
as a two-dimensional component, without loss of
generality, a plane strain analysis can be used. The
nodes in the model were used for the analysis. The
nodes on the bottom surface of the gear were fixed. A
total load is applied on the model. It was assumed to act
on the two points. There are two ways to get the contact
stress from ANSYS. Figure 4.5 shows the first one,
which is the same method as one in chapter 3 to create
the contact element COCNTA 48 and the rectangular
shape fine mesh beneath the contact surfaces between
the contact areas. The enlarged-area with a fine meshes
which is composed of rectangular shapes.
Fig 1 Single Teeth Mesh Model Fig 2 Fine Mesh Model in Single Teeth Model
Fig 3 contact stress Fig 4 equivalent stress

International Journal of Advanced Research in Technology, Engineering and Science (A Bimonthly Open
Access Online Journal) Volume2, Issue2, March‐April, 2015. ISSN: 2349‐7173(Online).

Fig 5 contact pressure
Fig 6 contact status
Fig 7 Initial status contact pressure Fig 8 total deformation
Fig 9 equivelent stress Fig 10 contact status

International Journal of Advanced Research in Technology, Engineering and Science (A Bimonthly Open Access
Online Journal) Volume2, Issue2, March‐April, 2015. ISSN: 2349‐7173(Online).

S.No Parameter Design Value Ansys values
1 Bending stress 220.35N/mm2
205.576N/mm2
2 Compressive
Stress
150.303
N/mm2
139.076/mm2
3 Von-misses
stress
2000 N/mm2
260.92 N/mm2
4 Deflection 0.058752mm
Table7.1 Comparison of theoretical and ANSYS design
values
IV.Conclusion:
Theoretical design is carried out using standard design
formulae as per carried out analyses by ANSYS and analysis
carried out using ANSYS .The following
• Bending, compressive, Vonmisses stresses were
obtained by theoretical and ANSYS software for
Aluminum alloy. The obtained stresses by ANSYS
are less than that of the theoretical calculations.
• From the results, it is observed that the bending and
compressive stresses of aluminum alloy (ceramics)
are less than that of the other material like steel.
• Aluminum alloy reduces the weight up to 5567%
compares to the other materials
• Aluminum is having unique property (i.e. corrosive
resistance), good surface finishing, hence it permits
excellent silent operation.
• Weight reduction is a very important criterion, in
order to minimize the UN balanced forces setup in
the marine gear system, there by improves the
system performance.
• Hence aluminum alloy is best suited for marine gear
in the high speed applications.
• The designed gear set have been manufactured using
gear hobbling technique and finished by gear
shaving operation and tested for the strength of the
gear teeth.
REFERENCES
[1] Baass, K. G, The use of clothed templates in highway design,
Transportation Forum 1984; 1, 47 52.
[2] Walton, D. J.and Meek, D. S, PlanarG2 transition between two circles
with a fair cubic Bezier curve,J. Computer Aided Design 1999; 31, 857 866.
[3] Walton, D. J and Meek, D. S, The use of cornu spirals in drawing planar
curves of controlled curvature, J. Computational and Applied Mathematics
1989 ; 25, 69 78.
[4] Walton, D. J., Meek, D. S. and Ali, J. M., Planar G2 transition curves
composed of cubic Bezier spiral segments, J. Computational and Applied
Mathematics2003; 157, 453 476.
[5] Walton, D. J. and Meek, D. S., Curvature extrema of planar parametric
cubic curves, J. Computational and Applied Mathematics2001; 134, 69 83.
[6] Walton, D. J. and Meek, D. S., A planar cubic Bézier spiral, J.
Computational and Applied Mathematics 1996; 72, 85 100.
[7] Habib, Z. and Sakai, M., G2 planar cubic transition between two circles,
Int. J. Computer Mathematics 2003; 80, 959 967.
[8] Juhász, I., Cubic parametric curves of given tangent and curvature, J.
Computer Aided Design 1998; 25, 1 9.

FEA Stress Analysis and Durability Study of Spur Gear

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (15)

Similar to FEA Stress Analysis and Durability Study of Spur Gear

Similar to FEA Stress Analysis and Durability Study of Spur Gear (20)

More from IJARTES

More from IJARTES (20)

Recently uploaded

Recently uploaded (20)

FEA Stress Analysis and Durability Study of Spur Gear