关键词: Lyapunov指数, 齿轮, 非线性动力学, 随机

Abstract: One set of one-stage gear pair, whose assembling backlash meets normal distribution, is taken as an example, and the dynamic analysis of a set of gear pair with stochastic assembling backlash is presented. Based on nonlinear dynamic theories, the nonlinear dynamic model of the gear pair with stochastic assembling backlash is established. The bifurcation diagram and the maximum Lyapunov index of the gear system with stochastic assembling backlash are presented. The chaos index and critical variance are introduced in the analysis. The relationship between the instability index and variance of assembling backlash, and the relationship between the mean value and critical variance of assembling backlash are discussed. It shows that the dynamic stability of the system can be achieved not only by minimizing the backlash, but also by well matched mean value of the backlash and its variation, which provides theoretical basis for determination of precision level in the design of gear system, selection of machining method, and mounting precision of gear pair.

Key words: Gear, Lyapunov exponent, Nonlinear dynamics, Stochastic