9.1 INTRODUCTION

Computerized simulation of meshing and bearing contact is a significant achievement that could substantially improve the technology and quality of gears. Computer programs known as tooth contact analysis (TCA) programs are directed at the solution of the following basic problem:

The equations of pinion and gear tooth surfaces, the crossing angle, and the shortest distance between the axes of rotation are given. The pinion and gear tooth surfaces are in point contact. It is necessary to determine (i) the transmission errors, (ii) the paths of contact points on the gear tooth surfaces, and (iii) the bearing contact as the set of instantaneous contact ellipses.

In the case of determination of the bearing contact, it is considered that due to the elasticity of gear tooth surfaces their contact is spread over an elliptic area, and the center of the contact ellipse is the theoretical point of contact. It is also considered that the surface elastic approach is known (for instance, from the experimental data), and the problem of bearing contact can be solved as a geometric problem (see Section 8.7).

The main idea of TCA is based on simulation of tangency of tooth surfaces that are in mesh. The determination of the instantaneous contact ellipse requires knowledge of the principal directions and curvatures of the tooth surfaces that are in tangency. A substantial simplification for the solution to this problem has been achieved due to the expression of principal curvatures and directions for the generated surface by the principal...