Influence of system parameters on dynamic behavior of gear pair with stochastic backlash

The influence of stochastic backlash on nonlinear dynamic behavior of spur gear pair with stochastic assembling backlash is discussed. Bifurcation diagram and maximum Lyapunov exponent diagram of the system are presented to evaluate the influences of load ratio, damping ratio, and backlash on the dynamic behavior of the system. The results show that backlash has great contribution to light-loaded gear pair. Therefore, dynamic behavior with stochastic assembling backlash is analyzed. Two novel indexes are introduced to evaluate the dynamic behavior of the system, dynamic instability exponent and critical variance. In addition, the relationship between the dynamic instability exponent and variance of the backlash, and the relationship between the critical variance and the mean value of the backlash are studied. The results show that it is not the unique way to improve the dynamic behavior of the system by minimizing the assembling backlash, which provide a novel way to determine the machining precision requirements, tolerance for assembling, and etc.