基于PD控制的电磁轴承-转子系统非线性振动研究  

Nonlinear vibration of a magnetic bearing-rotor system based on PD control

作　　者：张国荣 张鹏飞[1] 王志恒[1] 席光[1] 邹瀚森 ZHANG Guorong;ZHANG Pengfei;WANG Zhiheng;XI Guang;ZOU Hansen(School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学能源与动力工程学院,西安710049

出　　处：《振动与冲击》2022年第10期99-105,共7页Journal of Vibration and Shock

基　　金：国家重点研发计划项目(2018YBF0606102)。

摘　　要：针对比例-微分控制(proportional-derivative,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)>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)。For an axial magnetic bearing-rotor system with proportional-derivative(PD)control,the effects of proportional gain,differential gain and disturbance force on the soft-spring or hard-spring characteristics were studied using the multi-scale method.The conditions for judging the soft and hard spring characteristics were also derived according to the skeleton line equation.The nonlinear vibration and bifurcation were investigated using the 4th order Runge-Kutta method.The results show that the disturbance force has no effect on the soft and hard spring characteristics and the system switches between the soft-spring and hard-spring characteristics as the dimensionless proportional gain K_(p) increases.The system 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 states as the disturbance frequency increases.In the quasi-periodic state case,the form of vibration is beat vibration.There are components of frequency f_(0)±f_(b) near the fundamental frequency f_(0).

关 键 词：电磁轴承 非线性振动 软硬弹簧特性 多尺度法 

分 类 号：TH133.3[机械工程—机械制造及自动化]