中文摘要：

综合考虑由扭矩波动引起的低频外激励和齿轮阻尼比、齿侧间隙、啮合频率、啮合刚度的随机扰动等因素，基于牛顿定律建立了单对三自由度直齿齿轮系统的随机振动方程，利用Runge-Kutta法对运动微分方程进行了求解，采用系统的分岔图、相图、时间历程图和Poincar＆#233;映射图分析了齿轮系统在啮合频率变化下的分岔特性与稳定性，并分析了啮合频率的随机扰动对系统分岔特性的影响．数值仿真表明：随机非光滑齿轮系统存在丰富的倍周期分岔现象，随着齿轮啮合频率的减小，齿轮系统通过周期倍化分岔从周期运动通向混沌运动；通过剔除6处不稳定转速区段，可获得无量纲啮合频率在0．1～6．0之间的稳定速度区段；系统的运动对啮合频率的随机扰动极其敏感，建模时要考虑其大小的影响．

英文摘要：

By considering the random disturbances caused by the low-frequency internal excitation of torque fluctua-tion,damping ratio,gear backlash,meshing frequency and meshing stiffness,the random vibration equations of a single pair of spur gear system with three degrees of freedom are established based on Newton＆#39;s law.Then,the mo-tion differential equations are solved by means of the Runge-Kutta method,and the bifurcation and stability of the gear system with varying gear meshing frequency are analyzed according to the bifurcation diagram,phase diagram, time course diagram and Poincar＆#233; mapping graph of the system.Finally,the effect of the random disturbance of meshing frequency on the system dynamics is investigated.Numerical simulation results show that （1 ）there exists abundant period-doubling bifurcation in the random non-smooth gear system;（2）with the decrease of meshing fre-quency,the periodic motion of gear system becomes chaotic via the period-doubling bifurcation;（3）by eliminating 6 unstable speed sections,a stable speed section can be obtained in a dimensionless meshing frequency range from 0.1 to 6.0;and （4）as the system motion is extremely sensitive to the random disturbance of meshing frequency, the influence degree should be taken into consideration during the system modeling.