Decomposition methodology for gear tooth contact analysis

A methodology for gear tooth contact analysis was proposed. The conventional approach of tooth contact analysis was used to solve a system of five nonlinear equations for each contact point, but the numerical stability of the algorithm was weak. In addition, the mathematical models for tooth surface contact and edge contact were not the same; therefore, different systems of five nonlinear equations were required for different mathematical models, causing complex computing process and too many parameters involved therein. This decomposition methodology defined and utilized a concept called instantaneous conjugate contact curve. By constructing instantaneous conjugate contact curve, the transmission errors can be separated effectively and then the contact point and instantaneous contact curve can be located effortlessly. The number of nonlinear equations for searching contact point was reduced from 5 to 2.This mathematic model was also applied to edge contact analysis. So the decomposition methodology was simple, effective and adaptable. At the end, the decomposition methodology was applied to a pair of spiral bevel gears to demonstrate its effectiveness compared with the conventional method. For tooth surfaces contact, contact patterns were identically calculated by the two methods, and the relative difference for the magnitude of transmission errors was about 03″. In the case of edges contact, there were relatively few differences for patterns.