Improved Analytical model for mesh stiffness of helical gears considering the relationship of friction and flash temperature under steady temperature field

Abstract In the transmission process, thermal deformation of gears due to external factors, coupled with the thermal expansion of the tooth profile induced by flash temperature from surface friction, significantly impacts the time-varying mesh stiffness (TVMS) characteristics. Therefore, this paper proposes a novel analytical model for the TVMS of helical gears that considers these factors. In this model, the thermal deformation of gear foundation under a bulk temperature field is first determined using the displacement method. Blok's theory is then applied to establish the relationship between tooth surface friction and flash temperature, leading to the derivation of the actual tooth profile expansion equation under steady-state conditions. After that, based on this equation and considering the friction force in tangential, radial, and axial directions, the gear tooth and foundation stiffness of helical gear in transverse and axial directions under steady-state temperature field are accurately established. Finally, the proposed model is obtained by coupling each stiffness. By comparing with the FE result, the model is validated, and the influence of friction coefficient, bulk temperature, and gear parameters on TVMS is studied. The analytical model and findings provide valuable insights for optimizing gear parameter design.