Direct gear tooth contact analysis for hypoid bevel gears Original Research Article

A new methodology for tooth contact analysis based on a very general mathematical model of the generating process is proposed. Considering the line of action as a first order singularity of a certain operator equation we develop first and second order conditions for a pair of generated gear tooth flanks to be in contact. The constructive approach allows the direct computation of the paths of contact as the solution of a nonlinear equation system including the exact determination of the bounds of the paths of contact. The transmission error as well as curvature properties in the contact points are obtained in a convenient way. The resulting contact ellipses approximate the bearing area. Through the use of automatic differentiation all the geometric quantities are calculable within the machine accuracy of the computer.