Dynamic characteristic analysis of S-type profile herringbone gear system considering time-varying friction under mixed elastohydrodynamic lubrication

This study systematically investigates the influence of the time-varying friction under mixed elastohydrodynamic lubrication (EHL) on the dynamic response of S-type profile herringbone gears through theoretical modeling and numerical simulation. A high-precision 3D mesh model is constructed based on the tooth profile and meshing line equations. The time-varying meshing stiffness (TVMS) is obtained through finite element analysis and the relative sliding and coiling velocities are determined. Considering nonlinear factors such as TVMS, tooth side backlash and comprehensive meshing errors, an ordinary dynamic model is established to calculate the initial dynamic meshing force (DMF). The friction under mixed EHL is then introduced, and a dynamic model incorporating friction is coupled with the mixed EHL model for iterative solving of the time-varying friction. Through numerical simulation, the variations of the friction coefficient under different operating conditions and its influence on the dynamic response of the gear system are explored. The results indicate that the S-type profile herringbone gear exhibits lower vibration amplitudes compared to the conventional involute gear under identical conditions. Furthermore, friction significantly affects not only the vibration amplitude but also the frequency-domain characteristics and dynamic stability of the S-type herringbone gear system. Notably, within high-frequency ranges, the presence of friction causes the system to enter chaos earlier, while simultaneously suppressing chaotic motion.