A new iterative method for calculating the time-varying meshing stiffness of orthogonal face gear pairs

Time-varying meshing stiffness (TVMS) plays a critical part in the dynamic analysis of gear systems. This paper introduces a new iterative method for calculating the TVMS of orthogonal face gear pairs. Initially, the tooth surface equations are derived based on the shaping process. A contact coordinate system for the gear pair is subsequently established. The initial values for the equations are determined through a traversal search method, which facilitates the calculation of contact ellipse parameters and the load distribution function across the tooth surface. Subsequently, the surfaces are further analyzed by slicing along the radial direction and tooth profile. Using the potential energy method, the deflection of an equivalent cantilever beam under working conditions is derived. Load distribution coefficients are iteratively assigned and refined, with the TVMS recalculated until convergence criteria are satisfied. Finally, a case study examines the effects of pressure angle and external loads on the calculated results. The proposed model is validated through finite element analysis, demonstrating its accuracy and reliability.