Abstract：The dynamic capacity of the active magnetic bearing (AMB) system changes due to its channel failure. The accurate calculation of dynamic capacity is required to determine AMB system operation conditions. However, the AMB system model with partial channel failure in existing studies greatly deviates from reality. In order to improve the model accuracy for calculating the dynamic capacity of the AMB system, considering the external load and initial unbalance mass from the rotor, this paper establishes the four degrees of freedom (DOF) AMB system models with or without channel failure. Based on the system model, dynamic capacity can be calculated with the relations between external load, rotor displacements, and channel current. Firstly, based on the single DOF AMB system model, this paper elaborates on two critical states related to rotor mass: rotor displacement critical state and channel current critical state. Then, the 4-DOF model is established considering external load and initial unbalance mass from the rotor. Secondly, the initial unbalance mass from the rotor is calculated according to the rotor displacement amplitude, which changes by placing various external loads on the rotor. Finally, according to the two critical states, the dynamic capacity of the system with or without partial channel failure is calculated, and the influence of control parameters is analyzed for the AMB system with partial channel failure. By changing the external load value or rotor mass on a single DOF AMB system, we find that the rotor displacement amplitude reaches the critical value (collision value) for the low-mass rotor, and the channel current reaches the critical value (saturation value) for the big-mass rotor. The ratio of rotor displacement amplitude at the stretch side and non-stretch side is related to the load axial position. Therefore, the axial position sign of the load can be determined according to the ratio value. The rotor displacement amplitude can be obtained by substituting the dynamic load into the model, and the error of dynamic load of calculated and set value is less than 1.5 %. The dynamic load calculated by rotor displacement amplitude at 4-DOF from experiment data can also be mutually verified, proving the method of calculating dynamic load from rotor displacement amplitude works. Experiments at different rotor speeds and additional extern loads are conducted. The result shows that the maximum amplitude error in rotor displacement from the experiment and simulation does not exceed 3.9 %. By changing the proportional and differential coefficient value in a limited range of the AMB system with lower channel failure, the maximum displacement amplitude error of the simulation and experiments does not exceed 3.5 %. Since the rotor mass of the experiment platform is relatively small, the dynamic capacity of the AMB system with or without failure can be calculated from the rotor displacement amplitude. The dynamic capacity of the AMB system with/without failure is 3 600 N/5 100 N. The following conclusions can be drawn through simulation analysis and experiments: (1) As the dynamic load changes, the AMB system has two critical states. That is, rotor displacement amplitude and channel current reach a critical value. According to the critical states, the dynamic capacity of the AMB system can be calculated. The value of the dynamic capacity increases first and then decreases in the process of rotor mass increases. (2) The error of the maximum displacement amplitude of simulation and experiments does not exceed 3.9 % without channel failure, and the error does not exceed 3.9 % with channel failure. It indicates that the model can be used to calculate the dynamic capacity of AMB systems with or without channel failure. (3) The dynamic capacity of the AMB system is associated with the proportional and differential coefficient values, but the adjustment range is limited.
刘奇, 苏振中, 姜豪, 吴超, 晏明. 考虑部分通道故障的磁轴承系统动态承载力分析[J]. 电工技术学报, 2023, 38(10): 2625-2636.
Liu Qi, Su Zhenzhong, Jiang Hao, Wu Chao, Yan Ming. Dynamic Capacity Analysis of Active Magnetic Bearing System with Partial Channel Failure. Transactions of China Electrotechnical Society, 2023, 38(10): 2625-2636.
[1] 姜豪, 苏振中, 王东. 运动平台上磁轴承-转子系统的动力学建模[J]. 电工技术学报, 2019, 34(23): 4880-4889. Jiang Hao, Su Zhenzhong, Wang Dong.Dynamic modeling of magnetic bearing-rotor system on moving platform[J]. Transactions of China Electro- technical Society, 2019, 34(23): 4880-4889. [2] 黄威, 邓智泉, 李克翔, 等. 一种磁悬浮轴承支承刚性转子现场动平衡方法[J]. 电工技术学报, 2020, 35(22): 4636-4646. Huang Wei, Deng Zhiquan, Li Kexiang, et al.A filed dynamic balancing method for rigid rotor supported by magnetic bearings[J]. Transactions of China Electrotechnical Society, 2020, 35(22): 4636-4646. [3] 胡烽, 孙宏博, 蒋栋, 等. 基于四相全桥的磁悬浮轴承开关器件开路故障容错控制策略[J]. 电工技术学报, 2022, 37(9): 2295-2305. Hu Feng, Sun Hongbo, Jiang Dong, et al.Fault- tolerant strategy of four-phase full-leg for active magnetic bearing in case of open circuit fault of switching device[J]. Transactions of China Electro- technical Society, 2022, 37(9): 2295-2305. [4] 李志, 苏振中, 胡靖华, 等. 磁轴承复合位移传感设计与实验研究[J]. 电工技术学报, 2021, 36(7): 1425-1433. Li Zhi, Su Zhenzhong, Hu Jinghua, et al.Design and experimental research of magnetic bearing compound displacement sensor[J]. Transactions of China Electrotechnical Society, 2021, 36(7): 1425-1433. [5] Jiang Dong, Li Tian, Hu Zaidong, et al.Novel topologies of power electronics converter as active magnetic bearing drive[J]. IEEE Transactions on Industrial Electronics, 2020, 67(2): 950-959. [6] Cheng Xin, Cheng Baixin, Lu Meiqian, et al.An online fault-diagnosis of electromagnetic actuator based on variation characteristics of load current[J]. Automatika, 2020, 61(1): 11-20. [7] 钟一谔, 何衍宗. 转子动力学[M]. 北京: 清华大学出版社, 1987. [8] Wang Xiping, Yu Liang, Wan Jingui, et al.Analysis on stiffness and damping performance of active magnetic bearing system[J]. Journal of Shanghai University (English Edition), 1998, 2(3): 221-225. [9] 汪希平, 朱礼进, 于良, 等. 主动磁轴承转子系统动力学特性的研究[J]. 机械工程学报, 2001, 37(11): 7-12. Wang Xiping, Zhu Lijin, Yu Liang, et al.Investi- gation on dynamic performance of active magnetic bearing rotor system[J]. Chinese Journal of Mecha- nical Engineering, 2001, 37(11): 7-12. [10] 田拥胜, 孙岩桦, 虞烈. 高速永磁电机电磁轴承转子系统的动力学及实验研究[J]. 中国电机工程学报, 2012, 32(9): 116-123, 18. Tian Yongsheng, Sun Yanhua, Yu Lie.Dynamical and experimental researches of active magnetic bearing rotor systems for high-speed PM machines[J]. Proceedings of the CSEE, 2012, 32(9): 116-123, 18. [11] 张舒月, 李青, 伍继浩. 磁悬浮冷压缩机转子的动力学分析和试验研究[J]. 湖南大学学报(自然科学版), 2021, 48(10): 57-66. Zhang Shuyue, Li Qing, Wu Jihao.Dynamic analysis and experiments on cold compressor research of magnetic suspension rotor[J]. Journal of Hunan University (Natural Sciences), 2021, 48(10): 57-66. [12] 李胜远, 郑龙席. 磁轴承激励下转子系统动力学特性[J]. 中国机械工程, 2021, 32(8): 901-907. Li Shengyuan, Zheng Longxi.Dynamics characteristics of rotor systems under magnetic bearing excitation[J]. China Mechanical Engineering, 2021, 32(8): 901-907. [13] 杨作兴, 赵雷, 赵鸿宾. 电磁轴承动刚度的自动测量[J]. 机械工程学报, 2001, 37(3): 25-29. Yang Zuoxing, Zhao Lei, Zhao Hongbin.Automatic measurement of dynamic stiffness for active magnetic bearings[J]. Chinese Journal of Mechanical Engin- eering, 2001, 37(3): 25-29. [14] 吴海同, 周瑾, 纪历. 基于单相坐标变换的磁悬浮转子不平衡补偿[J]. 浙江大学学报(工学版), 2020, 54(5): 963-971. Wu Haitong, Zhou Jin, Ji Li.Unbalance compensation of magnetically suspended rotor based on single phase coordinate transformation[J]. Journal of Zhejiang University (Engineering Science), 2020, 54(5): 963-971. [15] 周天豪, 陈磊, 祝长生, 等. 基于自适应变步长最小均方算法的磁悬浮高速电机不平衡补偿[J]. 电工技术学报, 2020, 35(9): 1900-1911. Zhou Tianhao, Chen Lei, Zhu Changsheng, et al.Unbalance compensation for magnetically levitated high-speed motors based on adaptive variable step size least mean square algorithm[J]. Transactions of China Electrotechnical Society, 2020, 35(9): 1900-1911. [16] Rao D K, Brown G V, Lewis P, et al.Stiffness of magnetic bearings subjected to combined static and dynamic loads[J]. Journal of Tribology, 1992, 114(4): 785-789. [17] Maslen E, Hermann P, Scott M, et al.Practical limits to the performance of magnetic bearings: peak force, slew rate, and displacement sensitivity[J]. Journal of Tribology, 1989, 111(2): 331-336. [18] 巩磊, 祝长生. 基于变角度搜索算法的磁悬浮高速电机刚性转子系统的不平衡补偿方法[J]. 中国电机工程学报, 2021, 41(19): 6769-6778. Gong Lei, Zhu Changsheng.Unbalance compensation method of an active magnetic bearings-rigid rotor system for high-speed motors based on variable angle seeking algorithm[J]. Proceedings of the CSEE, 2021, 41(19): 6769-6778. [19] Bornstein K R.Dynamic load capabilities of active electromagnetic bearings[J]. Journal of Tribology, 1991, 113(3): 598-603. [20] Maslen E H, Meeker D C.Fault tolerance of magnetic bearings by generalized bias current linearization[J]. IEEE Transactions on Magnetics, 1995, 31(3): 2304-2314. [21] 何海婷, 柳亦兵, 巴黎明, 等. 基于BP神经网络的飞轮储能系统主动磁轴承非线性动力学模型[J]. 中国电机工程学报, 2022, 42(3): 1184-1198. He Haiting, Liu Yibing, Ba Liming, et al.Nonlinear dynamic model of active magnetic bearing in flywheel system based on BP neural network[J]. Proceedings of the CSEE, 2022, 42(3): 1184-1198. [22] 汤继强, 隗同坤, 宁梦月, 等. 基于反馈线性化的MSCMG转子稳定控制[J]. 北京航空航天大学学报, 2020, 46(6): 1063-1072. Tang Jiqiang, Wei Tongkun, Ning Mengyue, et al.Stable control of MSCMG rotor based on feedback linearization[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(6): 1063-1072. [23] 王忠博, 毛川, 祝长生. 主动电磁轴承-刚性转子系统PID控制器设计方法[J]. 中国电机工程学报, 2018, 38(20): 6154-6163. Wang Zhongbo, Mao Chuan, Zhu Changsheng.A design method of PID controller for active magnetic bearings-rigid rotor systems[J]. Proceedings of the CSEE, 2018, 38(20): 6154-6163.
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