Automated multilevel nested FE meshing and loaded tooth contact analysis of complex gear geometries

This study presents an automated methodology for loaded tooth contact analysis of complex gear geometries based on the finite element method (FEM). Due to large stress/strain gradients, non-conformal contact analysis on 3D gear geometries requires numerous elements and high computational costs. The proposed method defines a candidate contact region for each active tooth surface and generates solid meshes with multiple discretization levels. This allows us to model the near-contact region with a mesh size of tens of microns, while adopting a much coarser mesh for the rest of the geometry. We investigate different strategies to manage the transition between the different mesh levels. This is a key challenge because smooth transition ensures numerical accuracy. As a solution, we employ internal contact elements to assemble nested mesh levels of mapped hexahedral elements. We analyze, as a test case, a variable-ratio rack-and-pinion drive used in steering systems. Convergence studies on contact pressure and sub-surface stress validate the accuracy of the results. Although the procedure was implemented using MATLAB scripts and Ansys APDL codes, it is applicable to various general-purpose FEM platforms. Its fully automated implementation makes it a versatile stand-alone module suitable for closed-loop gear design optimization.