Analytical Model of Gear Thermal Stiffness Based on the Potential Energy Method

Stiffness is the main internal excitation of gear system vibration and is the basis for studying the static and dynamic characteristics of the system. Based on the relationship between thermal stress and strain in plane strain theory and combined with the potential energy method, a novel gear thermal stiffness model is proposed in this paper. The model deduces more general analytical formulas for gear thermal mesh stiffness and time-varying thermal mesh stiffness. The results show that the gear thermal stiffness decreases as a whole compared with the elastic stiffness. The decrease in stiffness is nonuniform along the line of action. The effects of temperatures, temperature distributions and thermal stress on gear thermal stiffness are investigated. The accuracy of the model is verified by comparisons with existing methods and references.