二自由度电磁轴承转子系统的动力学分析  

Dynamic analysis of rotor system of two-DOF active magnetic bearing

作　　者：陈淑婕 李欣业[1] 张华彪 张利娟[1] CHEN Shujie;LI Xinye;ZHANG Huabiao;ZHANG Lijuan(School of Mechanical Engineering,Hebei University of Technology,Tianjin 300401,China;School of Mechanical Engi-neering,Tianjin Commercial University,Tianjin 300134,China)

机构地区：[1]河北工业大学机械工程学院,天津300401 [2]天津商业大学机械工程学院,天津300134

出　　处：《河北工业大学学报》2021年第5期61-66,共6页Journal of Hebei University of Technology

基　　金：国家自然科学基金(10872063,11302223)。

摘　　要：根据麦克斯韦电场理论得到的电磁力模型并结合PD控制理论,在差动激磁方式下建立了二自由度电磁轴承转子系统的动力学方程。基于多尺度法对泰勒展开后的方程进行摄动分析,求得了关于系统振幅和相位的平均方程。利用同伦延拓法对平均方程进行求解,得到了系统的幅频特性曲线,发现幅频特性曲线表现出明显的滞后现象,在升速和降速通过共振区域时都会发生跳跃,利用数值仿真对解析计算的正确性进行了验证。分析了电流及控制参数对幅频特性曲线的影响,研究表明共振区域的最大振幅及其对应转速随着电流的增大而增大,随比例系数的增大而减小。According to the electromagnetic force model obtained by Maxwell's electric field theory and PD control theo⁃ry,the dynamic equation of the two-degree-of-freedom electromagnetic bearing rotor system is established under differen⁃tial excitation mode.The perturbation analysis of Taylor's expanded equations is based on the method of multiple scales,and the average equations for the amplitude and phase of the system are obtained.Using the homotopy continuation meth⁃od to solve the average equation,the amplitude-frequency characteristic curve of the system is given.It is found that the amplitude-frequency characteristic curve shows obvious hysteresis,and jumps occur when the speed is increased and the speed is reduced.The simulation verified the correctness of the analytical calculation.The influence of current and con⁃trol parameters on the amplitude-frequency characteristic curve is analyzed.The results show that the maximum ampli⁃tude of the resonant region and its corresponding rotational speed increase with the increase of current,and decrease with the increase of the proportional coefficient.

关 键 词：电磁轴承转子系统 非线性动力学 PD控制 多尺度法 数值仿真 

分 类 号：O322[理学—一般力学与力学基础]