Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics

The microscopic topography of tooth surface affects the nonlinear dynamic characteristics of the gear system. However, few studies have fully taken into account the effects of microscopic topography on time-varying meshing stiffness (TVMS) and backlash in gear dynamics. In this context, this study derives TVMS and time-varying backlash with fractal characteristics based on fractal theory and introduced them into a 6-DOF nonlinear dynamic model. With various nonlinear dynamics analysis tools, the dynamic characteristics of the gear system under different fractal parameters are investigated. The results indicate that the increase in the fractal dimension or the decrease in the characteristic scale coefficient leads to a smoother tooth surface, larger TVMS, and smaller amplitude of backlash. The effect of fractal dimension is more sensitive than characteristic scale coefficient. Furthermore, in the low-speed region, the increase in fractal dimension has a positive effect on the dynamic response of the system and can reduce the amplitude of dynamic transmission error. In the high-speed region, the opposite is true. It is worth pointing out that the influence of fractal dimension on gear dynamic characteristics is nonlinear. Considering the machining cost and dynamic response of gear, the fractal dimension of 1.5 is the best choice. The influence of characteristic scale coefficient on system dynamics is similar to that of fractal dimension, but the intensity is much weaker.