行星齿轮传动固有频率的统计特性分析

建立了2K-H直齿行星齿轮传动平移-扭转耦合模型,分析了行星传动的固有特性。基于传动系统的三种典型的振动模式(扭转振动模式、平移振动模式和行星轮振动模式),以及有关的特征敏感度计算方法,引入随机参数,以解析形式给出了三种振动模式固有频率的统计量计算方法,并对模态跃迁造成的方差突变现象做了初步研究。指出在发生模态跃迁的参数敏感位置,参数的随机性导致了行星齿轮传动的动态特性不稳定,在动态设计中应小心避开。仿真结果证明了所得结论的正确性。

Statistical Analysis of the Eigenvalue of Planetary Gears

A model for simulating the free vibration of 2K-H spur planetary gears is established. The three-dimensional model includes two rigid body and one rotation motions of the gears and the carrier. The natural frequencies and vibration modes are investigated. Based on the three typical vibration modes: rotational modes, translation modes and planet modes, the eigenvalue-sensitivity are calculated and expressed in simple formulae. Random parameters are included and the statistics expressions of the three types of frequencies are given. The phenomenon of the statistics mutation caused by loci veering is investigated. The instability of the dynamic characteristics caused by the randomness of parameters in the sensitive region is obvious, which should be avoided in the dynamic design. The conclusions are demonstrated by simulation result.