Mesh stiffness model of a spur gear pair with surface roughness in mixed elastohydrodynamic lubrication

The calculation of time-varying mesh stiffness for gear meshing in mixed EHL regime is of great importance to the accurate evaluation of tooth damage, contact fatigue life and wear performance of a gear transmission system. In this work, the mesh stiffness of a spur gear pair in mixed elastohydrodynamic line (EHL) contact is established in conjunction with a revised contact stiffness to include the effect of surface roughness and oil film. The revised contact stiffness of gear tooth surface in EHL contact is developed by combining the stiffness of both the rough gear tooth and liquid film based on the load-sharing concept, which is used to replace the Hertzian contact stiffness of ideal smooth cylinders in traditional gear mesh stiffness. To include the effect of tooth curvature on the asperity distribution at the gear tooth surface, the cylindrical contact coefficient is introduced and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to derive the stiffness of rough curved gear tooth contact. The film thickness equation for mixed EHL line contact is employed together with the lubricant bulk modulus to predict the liquid film stiffness at different mesh positions. Effects of surface roughness, input torque, rotating speed and lubricant on the contact stiffness and EHL mesh stiffness are analyzed. Results show that the lubricant film stiffness is much higher than the solid part, especially at tip or root position. The fluctuation of mesh stiffness in single-to-double teeth contact is smaller than that calculated using Hertzian contact model, indicating a better transmission stationarity.