A three-dimensional nonlinear dynamic model of gear transmission system was developed, considering the time-varying meshing stiffness, tooth surface friction and backlash. Based on the contact point location, the expressions of meshing stiffness and tooth surface friction coefficient with respect to time were deduced, considering the distribution of dynamic load. It is difficult to solve the strongly non-linear variant differential equation, so a method was proposed which changes the variant differential equation to ordinary differential equation by increasing the dimension of differential equations. The differential equations were solved numerically by using 4 to 5 th order adaptive variable steps Runge-Kutta method. The effects of teeth surface friction, web damping and web stiffness on the nonlinear dynamic behaviors of gear were analysed systematically. The study provides the theoretical basis and directions for in-depth research of gear transmission systems.%在考虑齿轮副时变啮合刚度、齿面摩擦、齿侧间隙及辐板刚度和阻尼的情况下,建立了齿轮传动系统的三维非线性动力学模型.根据啮合点位置推导出啮合刚度、齿面摩擦系数与时间的关系,并考虑了齿轮动载荷在各齿轮副之间的实际分配情况.针对强非线性变微分方程组求解困难的问题,提出了利用添加方程组维数的方法将变系数微分方程组转化成常微分方程组,并采用4 ～5阶自适应变步长的龙格库塔法求解微分方程组的数值解.系统地分析了辐板刚度、阻尼以及齿面摩擦对齿轮副和辐板振动性能的影响,为更深入研究齿轮的阻尼减振提供了理论基础和研究方向.
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