Spur gear tooth root stress analysis by a 3D flexible multibody approach and a full-FE contact-based formulation

This paper proposes an original method to determine the gear tooth root stresses from a 3D finite element (FE) flexible multibody approach and a full-FE contact-based formulation. The contact problem is dealt with an augmented Lagrangian formulation whereas the analysis is performed by a preconditioned gradient solver (PCG). Tooth flank modifications are directly introduced within the 3D model. This one is thus able to take into account straightforwardly tooth bending and Hertzian-like deformations as well as the micro-geometry effect. Simulations are performed for several mesh periods, without making any assumptions about load distribution, tooth and gear blank flexibilities, and possible premature or delayed contacts between tooth pairs in quasi-static conditions. A precise distribution of tooth root stresses associated with instantaneous contacts conditions is then computed. For this study, a single stage spur gear with micro-geometry modifications corresponding to an arc-shaped profile crowning is modeled. Several output torques are considered. The obtained results are compared to those obtained using a 2D FE ISO-based model, where external forces are applied along the theoretical line of action.