A new method for accurate gear tooth contact determination for hypoid bevel gears using automatic differentiation

Based on a mathematical model of a virtual machine tool we develop necessar y and sufficient conditions for a pair of generated gear tooth flanks to be in contact. The approach allows the direct computation of the path of cont act as the singular solution set of a nonlinear operator equation using a m inimally augmented defining system. As a byproduct we obtain curvature prop erties of the gear tooth panics, the reduced curvatures, and contact ellips es at the contact points in a convenient way. By the use of automatic diffe rentiation all geometric quantities are calculable with machine accuracy of the computer.