Quantitative Research on Misalignment Magnitude of Rotor-Magnetic Bearing System with Axis Misalignment under Shock Excitation
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摘要:
为研究和识别转子系统在轴承处发生的平行角度混合不对中，提出一种频谱辨识转子-磁轴承系统固有不对中量大小的方法. 采用动量矩定理将圆盘不平衡力对转轴的影响等效到转子轴向力上，建立考虑轴向径向耦合效应的刚性双偏置圆盘转子-磁轴承系统的动力学模型；通过SIMULINK仿真得到系统时域下的位移和电流响应，分析不对中条件下转子系统动力学特性，并利用快速傅里叶变换将时域响应转换为频域响应，基于频域下最小二乘算法得到转子系统不对中量大小. 结果表明：在冲击激励影响条件下，采用该方法计算的不对中量大小误差均在5.0%以内，当转子受到外界扰动力时，该算法能够准确定量识别转子的不对中量，可为不对中转子-磁轴承系统故障诊断及自修复提供理论参考.
Abstract:A spectral identification method for calculating the magnitude of inherent misalignment in a rotor-magnetic bearing system was proposed to study and identify mixed parallel misalignment of the rotor system occurring at the bearing. The momentum moment theorem was used to equate the effect of the disc unbalance force on the rotating shaft to the axial force of the rotor and establish a dynamics model of the rigid double offset disc rotor-magnetic bearing system considering the axial and radial coupling effects. The SIMULINK simulation was used to calculate the displacement and current response of the system in the time domain, and the dynamics characteristics of the rotor system under the misalignment condition were analyzed. Furthermore, the fast Fourier transform was utilized to convert the response in the time domain into that in the frequency domain. The magnitude of the misalignment of the rotor system was then calculated based on the least squares algorithm in the frequency domain. The results show that the error in the calculated magnitude of misalignment by using this method is within 5.0% under the influence of shock excitation, indicating that even if the rotor is affected by external disturbance forces, the algorithm can accurately quantify the rotor’s misalignment. This provides a theoretical reference for fault diagnosis and self-repair of misaligned rotor-magnetic bearing systems.
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图 1 刚性双偏置圆盘转子-磁轴承系统模型
Figure 1. Model of a rigid double offset disc rotor-magnetic bearing system
图 2 圆盘1形心和重心位置关系
Figure 2. Relationship between shape center and gravity center for disc 1
图 5 不同转速下径向磁轴承处位移、电流稳态响应
Figure 5. Steady-state response of displacement and current at radial magnetic bearing at different rotational speeds
图 6 不同转速下混合磁轴承处位移、电流稳态响应
Figure 6. Steady-state response of displacement and current at hybrid magnetic bearing at different rotational speeds
图 7 不同噪声影响下计算的不对中量误差百分比
Figure 7. Percentage of misalignment error calculated under different noise interferences
表 1 系统结构参数与仿真参数
Table 1. System structure parameters and simulation parameters
参数 大小 参数 大小 M/kg（l/m） 3.910（0.400） s0/ mm 0.400 md1/ kg 1.065 δx1，δx2/ mm 0.140，0.150 md2/ kg 2.081 δy1，δy2/ mm 0.160，0.145 e1/μm 80 δz2，Δx1/ mm 0.130，0.100 e2/μm 100 Δy1，Δx2/ mm 0.130，0.120 $ {e_{{\textit{z}}1}}，{e_{{\textit{z}}2}} $/μm 8，10 Δy2，Δz2/ mm 0.110，0.150 β1，β2/ deg 20，30 KP/（A.m−1） 5500 Id/（ kg·m2） 0.0455 KI/ （A.（m.s）−1） 8000 a1/ mm 0.226 mm KD/（A.s.m−1） 3 a2/ mm 0.174 mm R, t /ms 20,6 b1/ mm 0.126 b2/ mm 0.074 Ip1/（ kg·m2） 0.0019 Ip2/（kg·m2） 0.0059 
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表 2 频域下的径向磁轴承处转子位移和控制电流响应
Table 2. Rotor displacement and control current response at radial magnetic bearing in frequency domain
频率 （i） 位移 电流 幅值/A 相位/（°） 幅值/m 相位/（°） 30 Hz 0 3.69 × 10−9 −16.09 0.929 −132.73 1 1.36 × 10−4 −32.43 0.754 152.99 35 Hz 0 1.13 × 10−9 112.79 0.930 −133.20 1 1.83 × 10−4 −61.97 1.016 124.49
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表 3 无噪声影响下不对中量实际值和估计值比较
Table 3. Comparison of actual and estimated values of misalignment without noise interference
不对中量 实际设定值/mm 估计值/mm 误差/% δx1 0.140 0.1388 −0.857 δy1 0.160 0.1575 −1.563 δx2 0.150 0.1439 −4.067 δy2 0.145 0.1456 0.414 δz2 0.130 0.1285 −1.154
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