平行不对中转子系统的非线性动力学行为

在几个基本假设如刚性转子、轴承各向同性等条件下，考虑转子的不对中和圆盘的不平衡等因素后，建立平行不对中转子系统的动力学模型。首先通过一个坐标变换消除不对中转子间的约束关系，然后根据Lagrange方程推导系统的运动微分方程，分析表明不对中转子系统是一个具有自激振动特征的强非线性系统。最后采用Runge-Kutta法进行数值积分，分析不对中转子系统的非线性动力学行为。数值结果发现，当系统参数变化时，转子系统的轴心轨迹时而表现为周期运动，时而又呈现出准周期特性。当系统作准周期运动时，转子的稳态横向振动中明显存在着多个频率成分，其中包含转子转速的同频以及多种组合频率。

NONLINEAR DYNAMIC BEHAVIOR OF PARALLEL-MISALIGNED ROTOR SYSTEM

Under some assumptions such as rigid rotors and isotropic bearings etc., the dynamic model of rotor system is developed after considering the parallel misalignment of rotors and unbalance of disk. Firstly the constraint equation, which describes the relationship of motion of the misaligned rotors, is eliminated by a coordinate transformation. Then the motion equations are derived on Lagrange's approach, and it presents that the misaligned rotor system is a parametric excited one with strongly nonlinear characteristics. The nonlinear dynamic behavior of the system is analyzed by Runge-Kutta method at last. The results show that the orbits of the rotors may be periodic or quasi-periodic when the parameters of the system are varied, and in the latter case there exists several frequencies components such as the synchronous and combined ones in the steady state response.