Analytical models for thermal deformation and mesh stiffness of spur gears under steady temperature field

• A thermal expansion model of tooth profile under the steady bulk temperature field is established. • An analytical method for calculating mesh stiffness of spur gear considering thermal effect is proposed. • The proposed models are verified by the finite element method. • The effects of temperature on mesh stiffness, load sharing ratio and loaded static transmission error are analyzed . • The difference between uniform and non-uniform temperature field on mesh stiffness are discussed. Thermal effect is an important cause of engineering failure of gear system. However, the lack of accurate model limits the research on the thermal behavior of gear transmission system. Here, based on the linear thermal expansion theory, involute profile theory and energy method, the thermal expansion model, the mesh stiffness model, the load sharing ratio model and the loaded static transmission error model of spur gears are proposed which comprehensively consider the thermal changes of material properties, theoretical involute, thermal profile error and actual contact positions. The corresponding finite element models are established to verify the accuracy of the proposed model and published models. The results indicate that the proposed model is accurate enough. The increase of temperature leads to the decrease of mesh stiffness, the unevenness of load sharing ratio and the increase of loaded static transmission error, accompanied by the phenomenon of earlier meshing. The hub bore radius has obvious influences on the thermal profile error and mesh stiffness, and the load torque also has apparent influences on mesh stiffness. The research provides supports for gear thermal effect analysis and gear system design.