Mesh Stiffness Calculation and Error Analysis: Hypoid Gear Pair and System

Accurate mesh stiffness calculation is crucial for developing reliable dynamic models and analyzing vibratory behavior in hypoid gears. Current studies often use a hypoid gear pair, incorporating the misalignment effects of the hypoid gear system model, as a substitute for the full hypoid gear system model to reduce simulation costs. However, this simplification overlooks the boundary problem, particularly the influence of housing on the hypoid gear system. This discrepancy can lead to deviations in mesh stiffness calculation and affect the accuracy of dynamic response predictions. To address this issue, we established a three-dimensional static mesh model to calculate the mesh stiffness under different boundary conditions, i.e., the gear pair model constrained at the base and the gear system model constrained at the housing, based on finite element results. Then, we introduce a 14-degree-of-freedom dynamic model to examine the influence of mesh stiffness differences on system dynamics. Finally, a numerical case study evaluates key factors, including unloaded and loaded transmission error, mesh points, line of action, and static mesh force, to assess their impact on mesh stiffness and the resultant impact on dynamic behavior. The findings provide insights into the selection of an appropriate calculation model for accurate gear design and simulation.