A novel two-variable optimization algorithm of TCA for the design of face gear drives

Abstract

Tooth contact analysis (TCA) is a crucial step in evaluating the working performances of gear designs. According to the meshing process, or the equation of meshing, TCA is usually numerically implemented to find contact points on tooth surfaces with a highly nonlinear model, which contains five independent equations and five variables. It is computationally expensive to solve this model, especially for spatial gears with a complicated tooth geometry such as face gears. To solve this problem, we propose a novel method to simplify the optimization model to two variables. Specifically, the rotation relationship between the face gear and pinion is analyzed in a kinematic view to mathematically eliminate three parameters in the meshing equation. The geometric characteristic of face gear drives is also studied to constrain the parameter range at a reasonable computation cost. Furthermore, this optimization model is solved by a two-stage algorithm with high stability and efficiency, realized by the particle swarm optimization (PSO) algorithm and the Quasi-Newton method, respectively. Examples are given to verify the efficiency and stability of the proposed method.