Nonlinear dynamic modeling and analysis of helical gear system with time-varying backlash caused by mixed modification

When the helical gear contains mixed modification, the backlash will vary along the tooth width and tooth profile, which will lead to uneven contact of the meshing tooth pairs and meshing impact on both sides of the gear teeth, and deeply affect the dynamic characteristics of the system. In this paper, each meshing excitation with time variation is analyzed based on the function of the meshing surface, and the quantitative calculation model of the meshing force and friction torque considering the meshing state and the contact state is developed. The nonlinear dynamic model of helical gear pair with time-varying backlash caused by mixed modification is established, and the influence mechanism of each modification amount on the bifurcation characteristics of the system is analyzed. Through optimizing the multi-modification parameters, the vibration amplitude of the chaotic motion is significantly weakened, and the obtained modification parameters are also generally applicable to the vibration suppression of other high-speed motions. Furthermore, a strong advantage of this work is that although the method is proposed for modified tooth surfaces, it is also suitable for other unconventional tooth surfaces that can be described by functions.