A Unified Transient EHL-Based Framework for Determining Contact Stiffness and Damping for Application in Spur Gear Dynamics

Abstract

Time-varying mesh stiffness (TVMS) is a primary contributor to gear noise, vibration and harshness (NVH). Accurate implementation of the lubrication effect on the TVMS is often neglected. This work presents a numerical lubricated contact stiffness extraction method by combining the lubricant film and elastic compliances through rigid-body separation for spur gears. A deformation datum for infinite line contacts is defined using Weber’s local elastic deformation of gear teeth, resolving inconsistent treatments in the literature. A novel apparent transient damping coefficient is extracted using transient multigrid elastohydrodynamic (EHL) simulations. At high load and low speed, the EHL contact stiffness approaches the analytical local elastic stiffness, whereas at low load and high speed, it deviates by up to an order of magnitude. The stiffness linearisation is compared directly against fixed-separation EHL solutions, and force reconstruction confirms recovery of the full transient contact force. The results show that lubricant film compliance can significantly alter the EHL contact stiffness under low-load/high-speed conditions, which is relevant to dynamic mesh force fluctuations in high-speed transmissions. Thus, accurate lubricant effects must be included for reliable NVH predictions in such cases.