Finite Element Stress Analysis of Spur Gear and Evaluation …€¦ · · 2013-02-12Finite Element Stress Analysis of Spur Gear and ... plane elements is considered for analysis.
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International Conference on Challenges and Opportunities in Mechanical Engineering, Industrial Engineering and Management Studies 55
Abstract--- In spite of the number of investigations devoted to gear research and analysis there still remains to
be developed, a general numerical approach capable of predicting the effects of variations in gear geometry,
contact and bending stresses, and transmission errors. One of the primary objectives is to use a numerical approach
to develop theoretical models of the behavior of spur gears in mesh, to help to predict the effect of gear tooth
stresses and transmission error.
The main focus is to develop and to determine appropriate models of contact elements, to calculate contact
stresses using ANSYS and compare the results with Hertzian theory and also to generate the profile of spur gear
teeth and to predict the effect of gear bending using a three dimensional model and two dimensional model and
compare the results with those of the Lewis equation and also determines the static transmission errors of whole
gear bodies in mesh.
This work investigates characteristics of an involute gear system using Finite Element (FE) Methods. Bending
and contact stresses are evaluated using nonlinear FE methods and then compared against AGMA standards to
establish an accurate design procedure. The study started with evaluation of contact stress using ANSYS code for
simulating a pair of cylinders in contact. The results obtained are in good agreement with Hertz’s equation. A single
tooth model was then analyzed for arriving at the bending stress. Forces were applied at different radii of the tooth
and peak stresses obtained at the root were compared with AGMA standard evolved out of basic Lewis formula with
several corrections taken into account.
The results of 2D and 3D FE models of complete pinion and gear are also presented. It is shown that AGMA
standards provide a very conservative approach with a single tooth analysis and FE approach provides a more
accurate result for the bending and contact stress. Finally, transmission error arising from deformations in the
pinion and gear due to variations in stiffness in one meshing period is evaluated. Different positions within the
meshing cycle are analyzed and investigated and the results are reported.
I. INTRODUCTION
EARING 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, automobile manufacture and office automation tools
will necessitate a refined application of gear technology.
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 are performed, while trying to design spur gears to resist bending failure and pitting of the teeth, as both
affect transmission error.
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
S. Puttaswamaiah, Assistant Professor and Research Scholar, Department of Mechanical Engineering, EWIT, Bangalore
Dr.J.N. Prakash, Professor, Department of Mechanical Engineering, EWIT, Bangalore K.B. Kiran, Research Scholar, Department of Mechanical Engineering, EWIT, Bangalore
PAPER ID: MED10
Finite Element Stress Analysis of Spur Gear and
Evaluation of Transmission Error S. Puttaswamaiah, Dr. J.N. Prakash and K.B. Kiran
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International Conference on Challenges and Opportunities in Mechanical Engineering, Industrial Engineering and Management Studies 56