5自由度磁悬浮轴承—转子系统非线性动力学研究

Research on Nonlinear Dynamics of Five-DOF Active Magnetic Bearings-rotor System

为了探讨磁悬浮轴承—转子系统的稳定性,从非线性多自由度的角度对5自由度主动磁悬浮轴承—转子系统的非线性动力学特性进行研究。在考虑电磁力、重力和不平衡力周期性影响的情况下,建立5自由度磁浮轴承—转子系统的动力学模型,通过泰勒公式对其进行非线性展开,运用多尺度法的基本原理对5自由度非线性微分方程进行复数处理。通过Matlab软件编程,借助庞加莱映射图和相图对系统的运动形态进行分析,得到在复数领域中的倍周期运动、拟周期运动和混沌运动的相图及庞加莱映射截面图。在试验过程中也发现,随着转速的增加,磁悬浮轴承—转子系统的轴心轨迹由有规律的稳定运动状态进入无规律的失稳运动状态。数值模拟和试验结果都表明:磁悬浮轴承—转子系统中存在丰富的非线性动力学现象,在不同参数条件下,系统存在稳定的倍周期运动、临界的拟周期运动和失稳的混沌运动现象。

To investigate the stability of rotor-active magnetic bearing（AMB） system,the nonlinear dynamic characteristics of the five-DOF AMB-rotor system is researched from the perspective of nonlinear multi-degree of freedom.With consideration of the cyclical impact of electromagnetic force,gravity and unbalanced force,a dynamics model of the five degree freedom AMB-rotor system is established.The five-DOF nonlinear differential equations are processed by using the basic principle of multi-scale complex number method using expansion of Taylor＇s formula.The Poincare section maps and phase diagrams of the double periodic,quasi-periodic and chaotic motion are obtained and analyzed by software Matlab in complex number field.In the experiment,it is also discovered that with the increase of rotating speed,the axes orbit of rotor-AMB system becomes irregular instability state of motion from a regular steady state of motion.Numerical simulation and experimental results show that there are abundant nonlinear dynamics phenomena in AMB-rotor system.There exists the phenomenon of stable periodic motion,critical quasi-periodic motion and instable chaotic motion when system is under different parameter conditions.