Dynamic study of anti-backlash gears and angle-contact ball bearing based on a simplification of the Hertz contact theory

Abstract

The contact stiffness of a mechanical joint surface has a significant influence on the assembly resonance frequency by affecting the stiffness matrix of the kinetic equation. The Hertz contact theory is improved and facilitated to found a mapping relationship between the assembly process parameters and contact stiffness, which is applied in the anti-backlash gear and the angle-contact ball bear to establish reduced model of transmission system. The anti-backlash gear can be simplified using a contact of two cylinders in reduced model, and the rotational resonance frequency of the transmission system can be increased through torsional spring preloading, while the angle-contact ball bearing can be facilitated into a contact of two spheres in reduced model, and the translational resonance frequency of the transmission system can be enhanced through axial preloading. The contact stiffness in anti-backlash gear is calculated and converted considering the driving torque and gear preloading, while the contact stiffness in angle-contact ball bearing is improved and merged by multiplying a correction factor [Formula: see text] in axial preloading. By adding corresponding non-massive rigid auxiliary elements, the transmission system model composed by the anti-backlash gear and the angle-contact ball bear is established to simulate the dynamic performance in ADAMS software. The frequency response values of the transmission system agree well with the theoretical value. Thus, the complex theoretical calculation formulas can be replaced by the simplified model.