Analysis of the mesh characteristics of hypoid gear pair dynamics

Most of the current models employed in analyzing the dynamics of hypoid or bevel gear pair systems are based on approximate representations of the tooth meshing kinematics. The approximate gear mesh representations that account for tooth contact position and load line of action vector are normally derived from experimental observations or semi-empirical considerations. Moreover, the resultant dynamic model is often linear with time-invariant coefficients. The fundamental behavior of the time-varying mesh points and load line of action vectors, which can be important characteristics of the hypoid gear pair system, have not been fully explored. To address this issue more in-depth, the current study examines the inherent spatial and time-varying tooth meshing positions and normal load vectors of typical hypoid gear pairs applied in automotive systems. Numerical results of the quasi-static gear tooth contact analysis using 3-dimensional finite element models are compared to the theoretical data produced by a set of analytical tooth contact analysis equations based strictly on gear geometry formulation. The potential effects of gear meshing characteristics on dynamic transmission error as well as torsional vibration response are also discussed.