Tooth contact analysis of spur and helical gears with crowned profile for pinion

Abstract

The paper presents tooth contact analysis (TCA) of modified gears using semi-analytical methods (SAMs). The semi-analytical methods use Love’s analytical formulation for Boussinesq equation of linear half-space theory and Hartnett approach for numerical formulation. The linear contact between two teeth has a finite length and during meshing process the edge effect appears, with a harmful influence on the gear reliability. To eliminate this, some tooth profile modifications are needed. To turn a line contact into a point contact, the crowned lead profile surface is considered. The ways used to obtain the matrices of separation are discussed for both spur and helical cylindrical gears. The large pressures’ systems of equations were solved using the method of conjugate gradients and fast Fourier transform. For validation, in cases of hertzian geometries the SAM results have been compared with results obtained analytically, while for non-hertzian geometries, the SAM results have been compared with FEM results as presented in the specific literature. The developed SAM proved to be an accurate, robust and very fast tool for TCA of spur and helical cylindrical gear.