中文摘要：

采用动态子结构法建立计入内齿圈柔性的行星传动刚柔耦合动力学模型，将内齿圈视为弹性连续体，导出内外约束条件下的运动微分方程，并将其与刚体构件的集中参数方程相结合，构建出系统的运动微分方程。基于所建模型，进行柔性齿圈直齿行星齿轮系的自由振动分析和相关试验验证。理论分析揭示出此类系统的振型可归结为4类：中心构件扭转振动模式、中心构件平移振动模式、行星轮振动模式和内齿圈振动模式，并给出每类振动模式的特征和降阶计算公式。数值仿真表明，内齿圈柔性使系统低阶固有频率降低，且新呈现的内齿圈振动模式对应的固有频率位于整个系统固有频率的中低频段，故在后续行星轮系的动态设计中应计及齿圈柔性的影响。振动试验则表明，内齿圈柔性对系统振动特性存在一定影响，除啮频激励和箱体结构共振外，行星传动中还存在低阶谐振现象；对于中低速工况下且太阳轮浮动的行星传动而言，减小齿圈柔性有利于降低系统振动。

英文摘要：

A discrete-continuum dynamic model for spur planetary gear trains （SPGTs） is developed by using the sub-structure synthesis method. By combining the equation of motion of an elastic continuum ring subjected to internal and external constraints with lumped parameter equations of motion of rigid bodies, the system governing equations are obtained. A modal analysis is conducted to reveal the modal properties of spur planetary gear trains. The free vibration characteristics of the system are classified into four distinct modes： rotational, translational, planet and ring. For each vibration mode, the properties and reduced-order formulae are derived. The effect of ring elasticity on system natural characteristics is then discussed. The simulation results show that the elastic ring gear decreases the lower order natural frequencies and introduces a new vibration mode i.e. the ring mode. And the natural frequencies of the ring mode locate at the middle and low region of the overall system frequencies. The simulation indicates that the elasticity of ring gear must be considered during the dynamic design of planetary gear trains. A back-to-back test rig is constructed and some vibration tests are conducted. The experimental results agreed well with the theoretical and numerical analysis.