计入齿圈柔性的直齿行星传动动力学建模

为揭示齿圈柔性对传动系统动态性能的影响，在系杆随动坐标系下建立计入齿圈柔性的直齿行星传动精细化动力学模型，建模中计入时变啮合刚度、支承刚度、陀螺效应和齿圈柔性等诸多影响因素。采用有限段单元的离散化建模方法，将连续体的柔性齿圈离散成由等效虚拟弹簧连接的刚性齿圈段，并推导齿圈段与行星轮的啮合判据。通过分析各构件间的相对位移关系及其受力，最终建立系统的运动微分方程。以三行星轮的NGW型直齿行星传动为例对其进行固有特性分析，得出系统的低阶固有频率分布及相应的振动模式，并进一步分析齿圈柔性和安装方式对系统固有特性的影响。研究结果表明，直齿行星传动的振型可归结为中心构件(太阳轮、系杆)扭转振动和中心构件平移振动两种模式，两种模式下齿圈和行星轮均做复杂平面振动；齿圈的柔性会降低系统的低阶固有频率，且其影响程度与齿圈安装方式有关，齿圈完全固定时其影响最小，径向浮动或周向转动时影响较明显。

Dynamic Modeling for Spur Planetary Gear Transmission with Flexible Ring Gear

An elasto-dynamic model for spur planetary gear transmission (SPGT) is presented, in which the flexibility of ring gear, time-varying mesh stiffness, bearing stiffness, gyroscopic effect are accounted in. The continuous flexible ring gear is discreted into a serial of rigid ring gear segments connected with each other through equivalent virtual springs. The flexibility of ring gear is represented by the stiffness of proposed virtual springs. The mesh condition between ring gear segments and planetary gear is derived and the relative displacements among each component are analyzed. By combining the motion equations of each component, the governing equations of the planetary system are obtained. By solving the eigenvalue problem of system governing equations, the natural frequencies and corresponding mode shapes can be classified. Finally, the effects of ring gear flexibility as well as mounting conditions on system inherent characteristics are discussed. The simulation results reveal that there are two categories of vibration modes in SPGT, i.e. the rotational mode and the translational mode, in which the ring gear and the planetary gears undergo complex planar vibrations. In addition, the system lower natural frequencies are affected by ring gear flexibility and mounting conditions. The flexibility of ring gear will decrease the lower natural frequencies and this effect is more obvious when ring gear is floating radially or circumferentially rather than it is fixed.