中文摘要：

考虑时变啮合刚度、齿侧间隙等因素的影响，建立了单对齿轮系统纯扭转非线性动力学模型。将齿轮综合传递误差波动和外部载荷作为随机变量，利用数值仿真方法对系统模型进行了求解，通过统计分析得到了系统各响应量和动态啮合力的统计特征。结果表明：外部激励的随机性对齿轮系统振幅和动态啮合力的影响比综合传递误差波动随机时明显；综合传递误差及外部激励随机波动离散程度的增加会导致系统振幅和动态啮合力不稳定性加剧。

英文摘要：

A nonlinear dynamic model of spur gear pair system was aevetopeu wlu, consideration of time-varying mesh stiffness and backlash. The fluctuation of transmission error and external load were treated as random variables, then, the nonlinear dynamic model of spur gear pair system was solved using the numerical emulation method. The statistical properties of vibration displacement and dynamic engaging force of gear pairs were obtained through the statistics analysis of the simulation resuits. The statistic analyses show that. the random fluctuation of external excitation have a greater impact on the dynamic response of gear system than the random fluctuation of transmission error. The instability of vibration amplitude and dynamic meshing force of the system increases with the increase of the degree of dispersion of transmission error and external excitation.