行星齿轮装置轴系的扭转振动模型分析

Analysis of models for torsional vibration of shaft system with epicyclic gear trains

行星轮机构几何运动关系较复杂，如何建立有效的动力学模型一直深得关注。剖 析了用于扭转振动的单惯量轴系模型和常规回转振动模型，推荐了作者所建立的两种 新模型──抽象平面杆系模型和等效轴系模型。通过分析比较，说明单惯量轴系模型 与常规回转模型均有一定的局限性。抽象平面杆系模型虽形式不直观，但可全面体现 行星齿轮装置内部的几何与动力学关系，并易于联接轴系；等效轴系模型经过了深入 地数学加工，是最具实用价值的扭转振动计算模型。

The kinematics of the epicyclic gearings are complex, and it is difficult to erect a dynamic model which is effective. In this paper, the single-mass model for the calculations of the torsional vibration and the general model for the rotary vibration calculations are analysed, and two new models, (a) ficti- tious co-planar model and (b) equivalent shaft model, built by authors are proposed. The results from the calculation and the analyses on above models indicate that: a) the single-mass model and the general rotary model are limited to some extent, either in mathematics or in graphics; b) the fictitious co-planar model includes all of the geometric and dynamic parameters as the general rotary model, and it can connect with the shaft, although it is fictitious in form; c) by means of mathematic treatment, the equivalent shaft model is the most useful and the most effective model for the calculation of the torsional vibration of the shaft system with epicyclic gear train.