有限长轴承支撑的转子系统非线性动力学分析

基于π油膜假设，运用变分约束原理和分离变量法求得了有限长动压轴承非线性油膜力的近似解析表达式。通过计算比较可知，该方法和有限元法的计算结果非常接近，而且可以节约大量计算时间。在此基础上，以转子的角速度、圆盘处的偏心量及转轴的刚度为控制参数，运用Newmark法分析了轴承-转子系统的非线性动力学行为。数值结果揭示系统具有周期运动、倍周期运动、准周期运动、六周期运动、十周期运动等复杂丰富的非线性动力学特征。

Analysis of Nonlinear Dynamics of Rotor System Supported by Finite Long Bearing

Based on the assumption of π oil film, an approximation expression of nonlinear oil film force of finite hydrodynamic bearing was obtained by variational constraint principal and the separation of variables. The results calculated by the proposed method are in good agreement with the oil film forces by the finite element method, and the computing cost is reduced greatly. Based on the nonlinear oil film force, the speed of rotor, eccentricity of disk and stiffness of shaft were taken as control parameters, nonlinear dynamic behaviors of bearing-rotor system were analyzed by Newmark method. Numerical results reveal periodic, double-periodic, quasi-periodic, 6-periodic, 10-periodic of rich and complex nonlinear behaviors of the system.