共轴对转封闭差动轮系固有特性及灵敏度分析

基于共轴对转封闭差动轮系的扭转动力学集中参数模型,求解了系统的固有频率和振型。理论分析了频率对刚度和质量的参数灵敏度,及频率变化轨迹中的模态跃迁现象。分析结果表明:根据振动特征可将系统振型分为扭转振动模式、行星轮振动模式和星轮振动模式,分别对应于系统的单根、L(行星轮数)-1和N(星轮数)-1重根频率;行星轮的个数对重根频率数值无影响;刚度变化率为正时,固有频率变化率为正,转动惯量变化率为正时,固有频率变化率为负;同种振动模式下的两条频率轨迹在接近时会发生模态跃迁。通过实例计算验证了理论分析的正确性,为共轴对转封闭差动轮系的固有特性分析与优化设计提供了依据。 

Natural characteristics and sensitivity analysis of a coaxial contra-rotating encased differential gear train

Based on the torsional vibration lumped-parameter model of the coaxial contra-rotating encased differential gear train, the natural frequencies and vibration modes of the system were solved. The results showed that all vibration modes of the planetary gear train can be categorized into three classes: rotational mode, stepped planet mode and planet mode, corresponding to the distinct frequency, L (Number of planet gear)-1 and N (Number of star gear)-1 multiple frequency respectively. The number of planets had no effect on the magnitude of the multiple frequency. When the change rate of stiffness was positive, the change rate of natural frequency was positive, and the change rate of natural frequency was negative when the change rate of moment of inertia was positive. Frequency loci veering occurred when two frequencies in the same vibration mode were approaching. The correctness of the theoretical analysis was verified by an example, providing a basis for the analysis and optimization of the natural characteristics design of the coaxial contra-rotating encased differential gear train.