Application of Finite Elements to the Analysis of Gear Tooth Stresses

Abstract

This paper explains the application of the analytical method of finite elements to the analysis of gear tooth stresses. The details necessary for simulating a two-dimensional tooth shape with finite elements are outlined and a technique for determining stress values at the tooth surface in the root fillet is given. The remainder of the paper uses the finite element method to analyze tensile fillet stress in generated tooth shapes incorporating either symmetric or asymmetric profiles. Special attention has been given to the asymmetric profiles (used in Hypoid gears) since no reliable formulas are available. Stress data thus obtained are used to develop a new simplified stress formula that gives tensile fillet stress as a function of geometric tooth shape and general loading conditions. The accuracy and wide range of applicability of the new stress formula is shown by comparing the new formula to other previously accepted formulas for a variety of tooth shapes and loading conditions.