Modeling and Dynamics Analysis of High-Temperature Magnetic Bearing-Rotor System
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摘要:
在多电航空发动机中，主动磁悬浮轴承因其耐高温、非接触等特性可以突破温度对支承部位的限制，使支承部位能够更靠近燃烧室. 为探究温度对磁悬浮轴承转子系统动态特性的影响规律，提出一种高温磁悬浮轴承转子系统动力学建模方法. 通过仿真得到转子在不同温度下的温度分布，并使用多项式拟合转子轴向温度分布；基于有限元方法推导柔性转子单元的动力学模型，引入温度影响，建立考虑温度影响的磁悬浮轴承转子系统整体动力学模型，并通过模态试验验证模型的准确性；基于理论动力学模型分析系统的动态特性. 结果表明：温度升高会导致转子的前三阶支承模态频率下降，增大各阶幅频响应幅值；当温度从常温升至450 ℃时，转子的前三阶弯曲支承模态频率分别降低了3.818%、5.670%、3.183%，前三阶弯曲模态幅频响应幅值分别升高了83.4%、34.4%、24.1%.
Abstract:In the multi-electric aircraft engine, an active magnetic bearing can break through the limitation of temperature on the support part due to its high temperature resistance and non-contact characteristics, which enables its support part to be closer to the combustion chamber. In order to investigate the influence of temperature on the dynamic characteristics of the magnetic bearing-rotor system, a dynamics modeling method for a high-temperature magnetic bearing-rotor system was proposed. The temperature distributions of the rotor at different temperatures were obtained through simulation, and the axial temperature distribution of the rotor was fitted using polynomials. Based on the finite element method, the dynamics model of the flexible rotor unit was derived. The temperature influence was introduced, and the overall dynamics model of the magnetic bearing- rotor system considering the temperature influence was established. The accuracy of the model was verified by a modal test. The dynamic characteristics of the system were analyzed based on the theoretical dynamics model, and the results show that an increase in temperature leads to a decrease in the first three orders of the support modal frequency of the rotor and an increase in the amplitude of the amplitude frequency response of each order. When the temperature increases from room temperature to 450 ℃, the first three orders of the bending support modal frequency of the rotor decrease by 3.818%, 5.670%, and 3.183%, respectively, and the amplitudes of the first three orders of the bending modal amplitude frequency response increase by 83.4%, 34.4%, and 24.1%, respectively.
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图 1 高温磁悬浮轴承模拟转子试验台
Figure 1. Simulated test bench of high-temperature magnetic bearing-rotor
图 2 仿真温度区域设置与温度采样点说明
Figure 2. Simulated temperature region setting and temperature sampling point description
图 5 不同热源工况下的转子轴向温度数据
Figure 5. Axial temperature data of rotor under different heat source conditions
图 9 随温度变化的转子单元刚度矩阵示意
Figure 9. Diagram of rotor unit stiffness matrix variation with temperature
图 10 软磁合金在25 ℃和450 ℃的B-H曲线
Figure 10. B-H curves of magnetically soft alloy at 25 ℃ and 450 ℃
图 11 单自由度电磁力与参数示意
Figure 11. Single degree of freedom electromagnetic force and parameters
图 13 温度变化对转子支承模态频率的影响
Figure 13. Influence of temperature variation on support modal frequency of rotor
表 1 机械系统所使用的材料
Table 1. Materials used in mechanical systems
序号 所用材料 1，2，3，4，6，8 1Cr11Ni2W2MoV 5 GH4169 7，10 高温软磁合金（1J22） 9，11 38 黄铜 
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表 2 数学模型拟合的R2值
Table 2. R2 by mathematical model fitting
m 150 ℃ 300 ℃ 450 ℃ 1 0.799 123 0.815 718 0.824 486 2 0.993 046 0.993 757 0.993 782 3 0.996 804 0.995 234 0.994 565 4 0.998 708 0.998 45 0.998 344 5 0.999 406 0.999 188 0.999 120 6 0.999 495 0.999 374 0.999 328
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表 3 磁悬浮轴承的结构参数和电控参数
Table 3. Structural parameters and electrical control parameters of magnetic bearing
参数 取值 参数 取值 转子半径/mm 89.4 比例系数 kp 1 磁极面积 As/mm2 200 积分系数 ki 1 磁极夹角 θ/（°） 22.5 微分系数 kd 0.0 005 单边气隙 sa/mm 0.3 偏置电流 I/A 2 定子齿数 8 线圈匝数 N/匝 240
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表 4 支承模态频率对比
Table 4. Comparison of support modal frequency
温度/℃ 阶次 计算频率/Hz 试验频率/Hz 误差/% 25 1 994.490 994.375 0.0 115 2 1506.200 1506.250 0.0 033 3 2437.090 2494.380 2.2 960 150 1 990.606 983.750 0.6 900 2 1471.570 1496.880 0.0 169 3 2421.910 2477.610 2.3 000 300 1 982.417 976.250 0.6 300 2 1450.280 1450.990 0.0 493 3 2404.800 2460.590 2.2 320 450 1 968.743 958.750 1.0 000 2 1412.160 1413.460 0.0 922 3 2374.860 2391.080 2.6 830
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