NVH robust optimization of gear macro and microgeometries using an efficient tooth contact model

This paper presents a methodology for the multi-objective optimization of both gear macro and microgeometry parameters in order to minimize the Static Transmission Error (STE) and the mesh stiffness fluctuations generated by the meshing process. The optimization is performed using a genetic algorithm which allows testing of a high number of gears. As a fast evaluation of the gear excitation sources is required, a analytical tooth bending model is introduced. It computes the gear compliance with an analytical thick plate model evaluating the tooth strain energy and a Ritz-Galerkin approximation evaluating the tooth deflection. For each gear design analyzed, the robustness to manufacturing errors is evaluated by performing Monte Carlo simulations for a thousand random manufacturing errors samples. The Probability Density Functions describing the RMS values of the mesh stiffness and STE fluctuations of each gear are estimated, and their average values are the two objectives of each gear. Standard deviations and maximum values describing the dispersion of results are also evaluated. Finally, the methodology provides a range of gears and a decision help tool, illustrated with a reverse gear.