Research on the stiffness of spur gear pairs based on the improved energy method under multiple influencing factors

Abstract

To investigate the effects of axial misalignment, lead crown relief, and temperature on the meshing stiffness of gears, this study aims to derive high-precision gear stiffness values that are more aligned with practical engineering applications. Based on the thermal expansion theory, slice coupling effect, and involute profile theory, a thermal stiffness model for meshing spur gear pairs under multiple influencing factors has been established, integrating the improved potential energy method and the nonlinear contact stiffness calculation approach. A calculation method for the thermal stiffness of meshing spur gear pairs, considering the impacts of axial misalignment and lead crown relief, has been developed. Furthermore, the mechanisms by which varying temperature, modification amounts, and misalignment affect the meshing stiffness of spur gear pairs have been explored. The results indicate that both lead crown relief and axial misalignment alter the load distribution across the tooth width, leading to a relative load concentration and consequently affecting the deformation of the gears under external loading, thereby influencing their meshing stiffness. It was found that the meshing stiffness decreases with an increase in axial misalignment and lead crown relief amounts. Additionally, with the introduction of temperature effects, an increase in temperature further reduces the meshing stiffness of the gear pair. The thermal deformation induced by temperature variations results in profile errors, affecting the actual meshing positions of the gears and altering the dimensions of single and double tooth intervals along the meshing line. This research establishes a theoretical foundation for the design of gear systems and the study of gear transmission system dynamics.