FE-Analytical Contact Modeling for the 3D Simulation of Bevel Gear Dynamics

Abstract The numerical prediction of spiral bevel gear contact dynamics is often hampered by the complexity of the gear tooth geometry and the three-dimensional (3D) nature of the motion transfer, which forms a major challenge for efficient contact detection and accurate contact force calculation. This works proposes a novel spiral bevel gear contact force element that enables the accurate prediction of 3D bevel gear contact force distributions in flexible multibody system dynamics simulations (MBDS). An efficient contact detection strategy, based on the surface of action, is used, while the accurate contact force calculation is obtained by inclusion of a new semi-analytical bevel gear contact stiffness model. This stiffness model relies on model order reduction (MOR) of finite element method (FEM)-based models to describe the bevel gear tooth and blank deformation, and analytical modeling to predict the tooth contact deformation. The solution can be used to model and analyze lightweight bevel gear dynamics. The method is validated against high-fidelity nonlinear finite element analysis-based contact simulations to evaluate the predicted transmission error, contact pattern, and contact pressure distribution. Finally, a use case is presented to demonstrate how the methodology enables detailed insights in spiral bevel gearbox dynamics, and noise and vibration (NVH) performance.