An improved model for time-varying meshing stiffness of straight bevel gears based on potential energy method and elastohydrodynamic lubrication

Abstract

Based on the potential energy method (PEM) and elastohydrodynamic lubrication (EHL) theory, this paper proposes an approximate solution for the time-varying meshing stiffness (TVMS) of straight bevel gears that accounts for the actual tooth cross-section and lubrication conditions. By introducing the influence of tooth surface roughness, the tooth surface lubrication status is characterized as full-film, mixed, or boundary lubrication. Additionally, the effects of varying torque, rotational speed, and surface roughness on the TVMS and contact stiffness of straight bevel gears under these three lubrication regimes are examined. The results indicate that the meshing stiffness under the actual cross-section is higher than that under the approximate cross-section, yet the stiffness variation trends for both cross-sections are consistent. During the transition of lubrication regimes, both contact stiffness and time-varying meshing stiffness are highest under full-film lubrication and lowest under boundary lubrication. As surface roughness or rotational speed increases, the contact stiffness and time-varying meshing stiffness decrease across all three lubrication regimes; whereas, with an increase in torque, both stiffness values increase.