Influences of stochastic perturbation of parameters on dynamic behavior of gear system

Gear systems are commonly used in vehicles, and the vibration of the gear system was paid more attention in recent years. In this paper, the dynamic behavior of gear system with stochastic perturbation of system parameters was analyzed. A stochastic nonlinear dynamic model of gear system, with consideration of the stochastic perturbation of system parameters, was established. The influences of stochastic perturbation of system parameters, such as excitation frequency, damping ratio, and backlash, on the dynamic behavior of the system were discussed. It was found that when the perturbation intensity is weak, the topological structure of the system solutions will not change, and there is no transition of the attractors. But if the perturbation intensity increases further, there will be transition between the attractors. In general, for single-DOF gear system, the multi-periodic attractor will jump to the quasi-period-1 attractor. But the quasi-period-1 attractor will not jump to other attractors. If the perturbation intensity is considerable great, bi-directional transition will occur. Yet, the probability of transition from multi-periodic attractor to quasi-period-1 attractor is greater than the probability of transition from multi-periodic attractor to other attractors. Which provide theoretical basis for effective vibration control of gear system.