复式行星齿轮传动装置的自由振动特性（二）

Free Vibration Characteristics of Compound Planetary Gear Train Sets

本文为研究其自由振动特性而推荐了一个复式行星齿轮传动（CPGT）的平面模型。该CPGT的各个元件（太阳轮、行星架、齿圈1、齿圈2和一些行星齿轮）有二个移动和一个转动。啮合中轮齿间接触所谓齿轮啮合刚度模拟为线性弹性，考虑这些刚度之间的相位，采用Lagrarge公式，导出运动方程式。从系统的固有值问题起步，研究行星齿轮的数目和位置的影响，以及陀螺现象对CPGT自由振动的影响。典型的固有模式有三：其一为移动（行星架，齿圈1和太阳轮具有无转动的纯典型的移动偏移），其二为转动（行星架、齿圈1和太阳轮具有无移动的典型的纯偏转），其三为行星齿轮模式（仅行星齿轮具有的一个典型的变形）。可以发现行星齿轮角度位置的改变不影响这种分类。另一方面，行星架转动速度的影响的研究表示陀螺影响区别于反复移动为一个不同点。获得了许多重要的结果，以便在设计过程避免导致不希望的振动危险工作状况。

In this study,a plane model of a compound planetary gear train（CPGT） is proposed in order to study its free vibration characteristics. Two translations and one rotation are considered for each element （sun,carrier,ring-l,ring-2,and planets） of the CPGT. The contact between the teeth in mesh is modelled by linear springs with stiffness called gearmesh stiffness. The phasing between these stiffness is taken into account. Using Lagrange formulation,the equation of motion is derived. Starting from the eigenvalue problem of the system, the influence of the planets＇umber and position, and the effect of the gyroscopic phenomena on the free vibration of the CPGT are studied. The natural modes are classified into three groups. translational（the carrier, ring 1, and sun have pure modal translational deflection with no translation）, rota- tional （the carrier,ring 1,and sun have pure modal totational deflection with no translation）, and planets＇ modes（only the planets have a modal deflection）. It was found that the change of the planets ＇ angular position does not affect this classification, on the other hand, the study of the influence of the carrier rotation speed show that the gyroscopic effect separates the repeated translational modes into distinct ones. The obtained results are much important in the design process in order to avoid critical operating conditions which lead to undesirable vibrations.