A general contact stiffness model for elastic bodies and its application in time-varying mesh stiffness of gear drive

As a critical element of time-varying mesh stiffness (TVMS), contact stiffness of a gear drive has been defined based on simplified Hertzian contact stiffness or semi-empirical nonlinear Hertzian contact stiffness in previous works. This study proposes a general contact stiffness model for elastic bodies through piecewise linear interpolation of contact pressure. The TVMS of a spur gear drive is determined through potential energy method and proposed contact stiffness model verified by Hertzian contact theory and finite-element method. Then, the influence of applied load on contact stiffness is studied, and the differences among proposed contact stiffness, simplified Hertzian contact stiffness, and nonlinear Hertzian contact stiffness are analyzed. Results show that contact stiffness increases with the applied load, and the TVMS based on the proposed contact stiffness model is the smallest among the three contact stiffness models. Effects of tooth width and input torque on the TVMS are further discussed. The TVMS becomes bigger with increased tooth width and input torque, but the increase rate decreases as tooth width or input torque increases. These findings indicate that reasonable matching of design parameters is beneficial for increasing load capacity and optimizing the dynamic performance of gear systems.