A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears

Tooth contact analysis with errors (ETCA) has been widely applied to simulate the meshing process of a pair of spiral bevel or hypoid gears. In the computation of ETCA, all contact points of the meshing process are calculated based on application of numerical methods. To start the computation procedure, an initial contact point should be firstly calculated, and the result of ETCA is sensitive to this initial contact point. In this paper, a new systematic methodology using a novel operation strategy and an optimization algorithm is proposed to accurately identify the initial contact point for ETCA. First, the nonlinear equations of ETCA are established by a universal model of the real tooth flank using universal machine settings. Second, the matching strategy of candidate points on the discrete tooth flank is proposed to determine the target points with the minimum distance. And then the discretization optimization based on the subdivision rule and the numbering of target matching points is described to perform an accurate and effective matching. After the target points are obtained as the initial values, the BFGS algorithm is applied to solve the initial contact point, as well as ETCA results. Finally, numerical examples are provided to verify the accuracy and efficiency of the proposed systematic method.