A unified computational framework for meshing stiffness of spur gears incorporating lubrication and thermal effects

Gear transmissions typically operate under lubrication conditions, and the frictional heat generated during meshing is inevitable. To more accurately describe the gear meshing characteristics, this paper proposes a time-varying meshing stiffness calculation system for spur gears that considers different contact states, and investigates the mechanisms through which lubrication and thermal effects influence gear stiffness. The system integrates thermal elastohydrodynamic lubrication and heat transfer analysis, local contact stiffness calculations, tooth profile thermal deformation deviations based on the bulk temperature, and uses a load distribution model as the iterative core. The proposed method is applied to an industrial turbine spur gear pair to study the influence of operating conditions and lubrication parameters on contact stiffness, bulk temperature, and meshing stiffness. In addition, the impact of different contact states and the consideration of thermal effects on meshing stiffness are compared. The results show that under lubricated contact, the tooth surface temperature significantly decreases and is more evenly distributed, with the meshing stiffness being noticeably lower under light-load, high-speed conditions compared to dry contact. The thermal effects on meshing stiffness under lubricated contact are more complex, and the coupled influence of lubrication and thermal effects on gear meshing characteristics should not be overlooked.