Semi-FEM dynamic meshing impact forecasting model for spiral bevel and hypoid gear transmission

Focusing on the accurate size, direction and position of dynamic meshing impact, an innovative semi-finite element method (semi-FEM) forecasting model is proposed for spiral bevel gear transmission under both high speed and heavy load conditions. To distinguish with the traditional rotor dynamic analysis focusing on vibration effect for global system, a new dynamic loaded tooth contact analysis (DLTCA) focusing on loaded contact effect for local contact area is proposed for the geometric boundary forecasting. Where, DLTCA shows a systematically time-varying characteristics including the dynamic loaded contact pattern, pressure, transmission error. Considering tooth flank flexural behaviors, data-driven tooth flank simulation and finite element modeling is developed by using universal motion concept (UMC) machine settings. At each finite element in a local geometric boundary, the dynamic compatibility and equilibrium equations are established as a semi-FEM dynamic meshing impact forecasting model. Moreover, for a dynamic transmission system, a basic judgement criterion is firstly developed. Then, the improved simplex method is applied to solve the established model for the dynamic meshing impact size evaluations including transmission error, torque, angular velocity, and acceleration. Finally, numerical and test instances are provided to verify the proposed method.