Analytical calculation models for mesh stiffness and backlash of spur gears under temperature effects

The temperature has a great contribution to the mesh stiffness and backlash of the gear pair. Presence of thermal deformation caused by temperature will complicate the gear teeth interaction. In this paper, the thermal time-varying stiffness model and thermal time-varying backlash model are proposed with the consideration of tooth profile error and total thermo-elastic deformation consists of the teeth deformation, teeth contact deformation, and gear body-induced deformation. The key parameters of thermo-elastic coupling deformation affected by temperature are calculated. Based on the proposed models, the influencing mechanism of temperature on the tooth profile error, mesh stiffness, total deformation, and backlash are revealed. The effects of shaft radius and torque load on the thermal stiffness and thermal backlash are studied. The proposed thermal stiffness and backlash calculation model are proven to be more comprehensive and the correctness is validated.