中文摘要：

为揭示多间隙作用下Ravigneaux型复合行星齿轮传动系统的非线性动力学行为,建立考虑时变啮合刚度、齿侧间隙与综合啮合误差的系统纯扭转强非线性动力学模型。将齿侧间隙非线性函数表达为描述函数的形式,运用谐波平衡法（Harmonic balance method,HBM）将方程组转化为非线性代数方程组,使用逆Broyden秩1法进行迭代求解,得到系统的基频稳态响应。通过改变时变啮合刚度、齿侧间隙与综合啮合误差的大小,分析参数变化对系统非线性动态特性的影响。研究发现,由于齿侧间隙的影响,系统动态特性曲线出现幅值跳跃与多值解等典型非线性特征,系统出现复杂的冲击现象;齿侧间隙、啮合刚度波动与误差波动的耦合使系统的非线性程度得以强化。基于描述函数的HBM法可用于求解更加复杂模型的基频稳态响应,为深入研究复合行星齿轮系统的动态特性提供了一种方法。

英文摘要：

A purely rotational model of Ravigneaux compound planetary gear train sets including time-varying mesh stiffness,synthetic mesh errors and gear backlashes is developed to show the nonlinear dynamic behavior of the system with the action of multi-clearances.The gap function is expressed as describing function and harmonic balance method（HBM） is used to convert the differential equations to nonlinear algebraic equations,which is solved iteratively by single rank inverse Broyden method.The steady state response of fundamental frequency is obtained.The influences of gear backlashes,time-varying mesh stiffness and synthetic mesh errors are analyzed by changing the value of the parameter.It is showed from the research that multiple value and amplitude jump discontinuities are presented on the dynamic curves,there the impact phenomenon is reflected.Meanwhile the nonlinearity degree of the system is increased by the coupling of stiffness fluctuation,mesh errors and backlashes.The HBM based on describing function can be used for more complicated model to obtain the steady state response of fundamental frequency,which provides a method for deeply researching the dynamic behavior of compound planetary gear train sets.