复杂非线性转子—轴承系统动力特性数值分析

研究非线性高维复杂转子－轴承系统的动力特性。针对系统的局部非线性特征，给出了一种降阶及配套动力积分方法。降阶系统仍保持局部非线性特征，非线性响应数值积分所需的迭代只需在局部非线性的维数上执行。对于油膜力无封闭解的实际轴承，采用变分不等方程有限元法求解Reynolds边值问题，使得油膜力及其Jacobian矩阵的计算变得非常简单明了且与具有协调一致的精度。应用上述方法计算分析了一双跨、椭圆轴承－转子系统的不平衡响应，数值结果展现了系统丰富复杂的非线性现象。

NUMERICAL ANALYSIS FOR THE DYNAMIC ACTIONS OF A COMPLEX NONLINEAR ROTOR-BEARING SYSTEM

The dynamic behaviors of a high order of complex rotor-bearing system are analyzed in this paper. According to the local nonlinearities of the system, an order reduction and corre-sponding integral method for the dynamic responses is presented. The reduced system keeps the local nonlinearities, therefore the iterations for the nonlinear responses only need be performed on the dimensions of the local nonlinearities. For the practical bearings, since non-closed form of the oil forces can be available, the finite element method based on variational inequality is used to calculate the Reynolds boundary problem. By means of this method the bearing forces and their Jacobians are easily calculated with the compatible precision. The numerical schemes of this study are applied to a two spans of rotor system with elliptical bearing supports. The numerical results of unbalanced responses reveal rich and complex nonlinear behavior of the system.