Efficient analytical method to obtain the responses of a gear model with stochastic load and stochastic friction

Abstract

The friction, which is widely existed in practical, is seldom considered when modelling the gear system with stochastic load. Due to the variation of the temperature and lubrication condition, friction is a stochastic factor to a gear model. In this paper, a gear model with stochastic load, stochastic friction, and some other deterministic factors is considered. Due to the effects of stochastic factors (i.e., load and friction), the gear system faces more vibration and noise than the case with all deterministic factors. Thus, to analyse the variation of responses in the gear dynamical model, the corresponding dynamic equation needs to be solved. However, the statistic characteristics of dynamic responses are hard to obtain by numerical methods. Thus, an efficient analytical method is proposed, and then, an approximate analytical solution of the dynamic equation can be obtained in this paper. By the obtained solution, the vibration and noise of gear systems can be well investigated. Simulation results are provided to demonstrate the superior performance of the proposed method.