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.