Free vibration characteristics of compound planetary gear train sets
Free vibration characteristics of compound planetary gear train sets
复制标题
DOI：
10.1243/09544062jmes870
复制
发表时间：
2008-08-01
影响因子：
2
通讯作者：
Haddar, M.
中科院分区：
文献类型：
--
作者：
Dhouib, S.;Hbaieb, R.;Haddar, M.
为了研究复合行星轮系的自由振动特性，建立了复合行星轮系的平面模型。对于CPGT的每个元素(太阳、载体、环-1、环-2和行星)，考虑两次平移和一次自转。啮合齿之间的接触由具有刚度的线性弹簧模拟，称为齿轮啮合刚度。考虑了这些刚度之间的阶段性。利用拉格朗日公式，推导出运动方程。从系统的特征值问题出发，研究了行星个数和位置的影响以及陀螺现象对CPGT自由振动的影响。自然模式分为三组：平移(载体、环1和太有纯模式平移偏转而不旋转)、旋转(载体、环1和太有纯模式旋转偏转而不平移)和行星模式(仅行星具有模式偏转)。研究发现，行星角位置的变化不会影响这种分类。另一方面，对载体转速影响的研究表明，陀螺效应将重复的平移模式分离成不同的模式。所获得的结果在设计过程中非常重要，以避免导致不期望的振动的临界运行条件。
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-1, 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' number 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 rotation), rotational (the carrier, ring 1, and sun have pure modal rotational 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.