中文摘要：

建立了随机齿侧间隙的单自由度齿轮系统的非线性动力学模型，利用变步长 Runge-Kutta 法对系统在确定齿侧间隙和随机齿侧间隙两种情况下的运动微分方程分别进行了数值求解，结合系统随量纲-间隙平均值变化的分岔图、相图及 Poincar＆#233;映射图，分析了系统在确定齿侧间隙和随机齿侧间隙两种情况下的动力学特性，在此基础上研究了随机干扰对齿轮系统的动力学影响，发现随机干扰对系统的周期运动影响较大，对系统的倍化分岔过程影响显著，而对系统的混沌运动影响较小。

英文摘要：

The nonlinear dynamic model of the single-stage gear system with stochastic backlash is established.The nonlinear differential equations with determinate backlash and stochastic back-lash are solved by employing variable step size Runge-Kutta integration method.The nonlinear dynamic characteristic of the system with determinate backlash and stochastic backlash is discussed based on bifurcation diagram of system via average value of dimensionless clearance,phase portraits and Poincare maps.The influence of the stochastic disturbance on the system is researched and the effect of the stochastic disturbance on periodic motion and chaotic motion is found.