基于PD控制的电磁轴承-转子系统非线性振动研究

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摘要针对PD控制下轴向电磁轴承-转子系统，运用多尺度法详细研究了控制器比例增益、微分增益以及扰动力对系统软硬弹簧特性的影响，并根据骨架线方程推导出判别软硬弹簧特性的条件；使用四阶Runge-Kutta方法探究转子非线性振动及分岔。研究结果表明：扰动力对软硬弹簧特性没有影响；无量纲比例增益"K" _"p" 增大时系统会在软弹簧与硬弹簧特性之间切换，"K" _"p" 大于2时表现为软弹簧特性；微分增益较大时幅频特性曲线发生分裂，稳态解不再具有多值现象；随着扰动频率的增加，发生二次Hopf分岔，转子振动由周期-1变为拟周期振动，拟周期情况下振动形式为拍振，在基频"f" _"0" 附近存在相近的频率"f" _"0" "±" "f" _"b" 。

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	张国荣
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	邹瀚森

关键词 ：电磁轴承, 非线性振动, 软硬弹簧特性, 多尺度法

Abstract：For the axial magnetic bearing-rotor system with PD control, the effects of proportional gain, differential gain and disturbance force on the soft-spring or hard-springs characteristics were studied using the multi-scale method. The conditions for judging the soft-spring or hard-springs characteristics were also derived according to the skeleton line equation. The nonlinear vibration and bifurcation was investigated using the 4th order Runge-Kutta method. The results show that the disturbance force has no effect on the soft-spring and hard-springs characteristics and the system switches between the soft-spring and hard-spring characteristics as the dimensionless proportional gain "K" _"p" increases. It behaves soft-spring characteristics when "K" _"p" is greater than 2. When the differential gain is large, the resonance curve will split, and the steady solution will no longer have multiple values. A second Hopf bifurcation occurs, and the rotor vibration changes from period-1 to quasi-period as the disturbance frequency increases. In the quasi-periodic case, the form of vibration is the beat vibration. There are frequency "f" _"0" ±"f" _"b" near the fundamental frequency "f" _"0" .

Key words： magnetic bearing nonlinear vibration soft and hard spring characteristics multi-scale method

收稿日期: 2020-12-08 出版日期: 2022-05-28

引用本文:

张国荣，张鹏飞，王志恒，席光，邹瀚森. 基于PD控制的电磁轴承-转子系统非线性振动研究[J]. 振动与冲击, 2022, 41(10): 99-105.
ZHANG Guorong，ZHANG Pengfei，WANG Zhiheng，XI Guang，ZOU Hansen. Nonlinear vibration of a magnetic bearing-rotor system based on PD control. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(10): 99-105.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I10/99

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