2K-H行星传动的修正扭转模型建立与固有特性分析

MODIFIED TORSIONAL MODEL DEVELOPMENT AND NATURAL CHARACTERISTICS ANALYSIS OF 2K-H EPICYCLIC GEARING

建立了2K-H均布行星传动的修正扭转模型,以揭示系统的固有频率与振动模态特性。该模型在纯扭转模型的基础上,进一步计入了行星轮轴心沿系杆切向的位移与行星轮轴的轴承支承刚度对系统动力学性能的影响。无阻尼固有特性分析表明,2K-H均布行星传动中存在三种典型的振动模式,即中心构件扭转振动模式、行星轮扭转振动模式与行星轮平移振动模式。求解相应的子特征值问题,获得了两种行星轮振动模式所对应的系统固有频率的封闭解析表达式。固有频率的参数灵敏度分析表明,行星轮轴的轴承支承刚度是影响2K-H均布行星传动的一阶固有频率的关键因素。固有频率敲击试验表明,与纯扭转模型相比,修正扭转模型更具工程应用价值,可用以指导2K-H均布行星传动的动态设计。

A modified torsional model of planetary gear trains with equally-spaced pinions is developed and used to identify unique properties of natural frequencies and vibration modes. Compared with the purely torsional model, tangential displacements and bearing stiffness of the pinions are included in the governing equation of motion. On the basis of natural characteristics analysis, vibration modes of the undamped system are classified into three types, which are named rotational mode of the central members, rotational mode of the pinions and translational mode of the pinions, respectively. For each type of vibration modes the associated reduced-order eigenvalue problems are derived and closed-form analytical expressions of natural frequencies are presented for the pinion modes. Natural frequency sensitivities to system parameters are rigorously investigated, which reveals that pinion bearing stiffness affects the first natural frequency of the system significantly. Through a comparison of natural frequencies experimentally collected and numerically computed, the modified torsional model is proved to be more accurate than the purely torsional model and may be applied to dynamic design of epicyclic gearing with equally-spaced pinions.