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Effect of Rim Thickness on Bending Stresses in
Low Addendum Large Spur Gears

Yesh P. Singh
Department of Mechanical Engineering
The University of Texas at San Antonio
San Antonio, TX 78249-0670
Ravichandra Patchigolla
Department of Mechanical Engineering
The University of Texas at San Antonio
San Antonio, TX 78249-0670

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Abstract
A finite element based approach is used for determining the effect of gear rim thickness on tooth bending stresses in
low addendum large spur gears. These gears are used in cement plants, sugar mills, ball mills, coal mills, kilns,
grinding mills, copper converters, and anode furnaces, etc. A program is developed using ANSYS Parametric
Design Language (APDL) to generate 1, 3, and 5 tooth segments of a large spur gear. A controlled meshing
approach is developed using free and mapped meshing capabilities of ANSYS to generate two-dimensional and
three-dimensional finite element models of the gear tooth segments. The controlled meshing approach employed
here has the following advantages: it prevents high stresses at load location, avoids too many elements in the low
stressed region, and generates a fine mesh in the fillet regions of the loaded gear tooth. The finite element models
are analyzed in the position of Highest Point of Single Tooth Contact (HPSTC). The two and three-dimensional
models of 1, 3 and 5 tooth segments are analyzed by varying β, which is the ratio of rim thickness to tooth height of
the gear. The effect of web on stresses is studied in the 3-D models. Equivalent (von Mises) and bending stresses are
obtained for different values of β in various models. Using a program written in APDL the gear tooth profile and rim
surface bending stresses are arranged in the form of tables using Microsoft Excel and plots are generated using the
capabilities of MATLAB program. Maximum bending and maximum von Mises stress plots are generated for
varying values of β in two and three-dimensional models. Also, plots are generated to compare maximum stresses in
1, 3 and 5 teeth models.
Introduction
A number of researchers have worked on gear tooth failure and used experimental, analytical and numerical
techniques to determine the stresses in the gear tooth. Most commonly used experimental techniques include
photoelastic and strain gages, and finite element method was the mostly used numerical technique.
Photoelastic technique was widely used for many years. Baud and Timoshenko1 introduced the photoelastic
technique to examine the stress concentration effect at the gear tooth fillets. Sopwith and Heywood2 used
photoelastic technique to develop a fillet stress formula that accounted for some pressure angle unbalance. Kelly and
Pederson3 improved this formula by employing more realistic tooth shapes in their photoelastic models. Drago and
Luthans4 conducted experiments using 2 and 3 dimensional photo elastic techniques to evaluate the combined
effects of rim thickness and gear pitch diameter on tooth root and fillet stresses. They calculated stresses for the load
applied at LPSTC, HPSTC and Pitch point along the tooth profile. The main drawback of this method is that the
experimental investigation is time consuming and it is very difficult to construct and prepare the models for
investigation.
Many investigators have used different finite element approaches in evaluation of the gear tooth stresses for a long
time. Wilcox and Coleman5 used analytical method of finite elements in analyzing the gear tooth stresses.
Quadrilateral elements have generally been used in two dimensional models. They developed a new stress formula,