volume | PIER Journals

Abstract

This study presents a novel three-degree-of-freedom (3-DOF) axial-enhanced hybrid magnetic bearing (AEHMB), which introduces an axial auxiliary electric excitation to break the inherent proportional constraint between radial and axial maximum suspension forces in conventional 3-DOF HMBs. This configuration enables independent design of radial and axial bearing performance, satisfying diverse application demands of transmission systems while effectively enhancing the axial load-bearing capability. This study first elaborates the structural topology of the proposed 3-DOF AEHMB, along with its primary bias magnetic circuit and axial compensation bias magnetic circuit. Mathematical models for the axial and radial suspension forces are subsequently established based on equivalent magnetic circuit analysis. Based on the maximum design requirements of the radial and axial suspension forces, key structural parameters were optimized and determined. Finally, the finite element method was adopted to validate the rationality of the magnetic circuit configuration and suspension working mechanism through systematic calculations of the air-gap bias flux density, control flux density, force-current characteristics, and force-displacement characteristics. Simulation results verified the feasibility of the proposed structure, accuracy of the magnetic circuit design method and mathematical models, and reliability of the overall design scheme for the 3-DOF AEHMB.

1. Mancuzo, M. V., R. M. Finzi Neto, A. A. Cavallini Jr., and V. Steffen Jr., "Design and implementation of a low-cost active magnetic bearing," Journal of Vibration Engineering & Technologies, Vol. 12, No. 3, 2851-2864, 2024.
doi:10.1007/s42417-023-01018-z Google Scholar

2. Huang, Zhihang, Changhe Li, Zongming Zhou, Bo Liu, Yanbin Zhang, Min Yang, Teng Gao, Mingzheng Liu, Naiqing Zhang, Shubham Sharma, Yusuf Suleiman Dambatta, and Yongsheng Li, "Magnetic bearing: Structure, model, and control strategy," The International Journal of Advanced Manufacturing Technology, Vol. 131, No. 5, 3287-3333, 2024.
doi:10.1007/s00170-023-12389-8 Google Scholar

3. Laldingliana, Jonathan, Sukanta Debnath, Pabitra Kumar Biswas, and Upama Das, "Design and speed control of U-type 3-coil active magnetic bearing," Electrical Engineering, Vol. 106, No. 2, 1135-1145, 2024.
doi:10.1007/s00202-023-01838-y Google Scholar

4. Yu, Chunmiao, Yuanwen Cai, Weijie Wang, Wenjing Han, Zengyuan Yin, and Wenting Han, "Analysis and compensation of Lorentz force magnetic bearing magnetic flux density uniformity error," Sensors, Vol. 24, No. 9, 2683, 2024.
doi:10.3390/s24092683 Google Scholar

5. Li, Binglin and Li Zeng, "Position decoupling control of rigid rotor of active magnetic bearing," Mechanika, Vol. 29, No. 4, 292-301, 2023.
doi:10.5755/j02.mech.31642 Google Scholar

6. Ahad, Muhammad Abdul and Sarvat M. Ahmad, "Marine rotor supported by frictionless 3-DOF active magnetic bearings," Journal of Vibration Engineering & Technologies, Vol. 13, No. 4, 254, 2025.
doi:10.1007/s42417-025-01815-8 Google Scholar

7. Zhong, Yunlong, Lijian Wu, Youtong Fang, and Xiaoyan Huang, "Investigation of cross-coupling effect of a 3-DOF magnetic bearing using magnetic circuit method," 2017 20th International Conference on Electrical Machines and Systems (ICEMS), 1-6, Sydney, NSW, Australia, 2017.
doi:10.1109/ICEMS.2017.8056254

8. Sun, Jinji, Ziyan Ju, Cong Peng, Yun Le, and Hongliang Ren, "A novel 4-DOF hybrid magnetic bearing for DGMSCMG," IEEE Transactions on Industrial Electronics, Vol. 64, No. 3, 2196-2204, 2017.
doi:10.1109/tie.2016.2626238 Google Scholar

9. Wu, Leitao, Dong Wang, Zhenzhong Su, Kang Wang, and Xianbiao Zhang, "Analytical model of radial permanent magnet biased magnetic bearing with assist poles," IEEE Transactions on Applied Superconductivity, Vol. 26, No. 7, 1-5, 2016.
doi:10.1109/tasc.2016.2594820 Google Scholar

10. Zhu, Runze, Wei Xu, Caiyong Ye, Jianguo Zhu, Gang Lei, and Xiang Li, "Design optimization of a novel heteropolar radial hybrid magnetic bearing using magnetic circuit model," IEEE Transactions on Magnetics, Vol. 54, No. 3, 1-5, 2018.
doi:10.1109/tmag.2017.2749759 Google Scholar

11. Wang, Zixin, Tao Zhang, and Shasha Wu, "Suspension force analysis of four-pole hybrid magnetic bearing with large radial bearing capacity," IEEE Transactions on Magnetics, Vol. 56, No. 8, 1-4, 2020.
doi:10.1109/tmag.2020.3003983 Google Scholar

12. Singh, Nisha and Praveen Kumar Agarwal, "Self-tuned optimum control of hybrid foil magnetic bearing," Journal of Vibration Engineering & Technologies, Vol. 13, No. 6, 419, 2025.
doi:10.1007/s42417-025-01977-5 Google Scholar

13. Boutra, N., R. Mehasni, and M. Feliachi, "Modeling and analysis of a proposed AC-DC C-core heteropolar radial hybrid magnetic bearing," Applied Computational Electromagnetics Society Journal, Vol. 39, No. 9, 814-822, 2024.
doi:10.13052/2024.aces.j.390907 Google Scholar

14. Wu, Mengyao, Huangqiu Zhu, Hao Zhang, and Weiyu Zhang, "Modeling and multilevel design optimization of an AC-DC three-degree-of-freedom hybrid magnetic bearing," IEEE Transactions on Industrial Electronics, Vol. 70, No. 1, 233-242, 2023.
doi:10.1109/tie.2022.3148744 Google Scholar

15. Lu, Jing, Yutong Yan, Jintao Ju, and Huangqiu Zhu, "Decoupling control of neural network inverse system based on improved online learning Levenberg-Marquardt for 3-DOF hybrid magnetic bearing," Electrical Engineering, Vol. 108, No. 1, 30, 2026.
doi:10.1007/s00202-025-03382-3 Google Scholar

16. Wang, Chun'e, Jiancheng Fang, Jiqiang Tang, and Jinji Sun, "Structure and coupling analysis of a novel 3-DOF conical magnetic bearing," International Journal of Applied Electromagnetics and Mechanics, Vol. 43, No. 4, 389-401, 2013.
doi:10.3233/jae-131725 Google Scholar

17. Li, K. X., Z. Q. Deng, C. Z. Liu, et al. "Design of disturbance rejection control system for 5-DOF magnetic bearing," Journal of Aerospace Power, Vol. 30, No. 4, 1016-1024, 2015.
doi:10.13224/j.cnki.jasp.2015.04.031 Google Scholar

18. Sun, J. J., "Research on structure and design method of a new type of permanent magnet biased active magnetic bearing for magnetic levitation flywheel," Beihang University, Beijing, China, 2012.

19. Fang, J. C. and J. J. Sun, "New permanent magnet biased radial magnetic bearing in magnetic suspending flywheel application," Journal of Beijing University of Aeronautics and Astronautics, Vol. 32, No. 11, 1304-1307, 2006.
doi:10.3969/j.issn.1001-5965.2006.11.010 Google Scholar

20. Han, Xue, Gang Liu, Baodong Chen, and Shiqiang Zheng, "Surge disturbance suppression of AMB-rotor systems in magnetically suspension centrifugal compressors," IEEE Transactions on Control Systems Technology, Vol. 30, No. 4, 1550-1560, 2022.
doi:10.1109/tcst.2021.3112765 Google Scholar

21. He, Jiaxi, Zhiquan Deng, Cong Peng, and Kexiang Li, "Reduction of the high-speed magnetically suspended centrifugal compressor harmonic vibration using cascaded phase-shifted notch filters," IEEE Sensors Journal, Vol. 21, No. 2, 1315-1323, 2021.
doi:10.1109/jsen.2020.3017953 Google Scholar

22. Uzhegov, Nikita, Alexander Smirnov, Cheol Hoon Park, Ji Hun Ahn, Janne Heikkinen, and Juha Pyrhönen, "Design aspects of high-speed electrical machines with active magnetic bearings for compressor applications," IEEE Transactions on Industrial Electronics, Vol. 64, No. 11, 8427-8436, 2017.
doi:10.1109/tie.2017.2698408 Google Scholar

23. Filatov, Alexei and Larry Hawkins, "Comparative study of axial/radial magnetic bearing arrangements for turbocompressor applications," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Vol. 230, No. 4, 300-310, 2016.
doi:10.1177/0959651815593649 Google Scholar

24. Han, Bangcheng, Qinjie Xu, and Qian Yuan, "Multiobjective optimization of a combined radial-axial magnetic bearing for magnetically suspended compressor," IEEE Transactions on Industrial Electronics, Vol. 63, No. 4, 2284-2293, 2016.
doi:10.1109/tie.2015.2509905 Google Scholar

25. Zhong, Yunlong, Lijian Wu, Xiaoyan Huang, and Youtong Fang, "Modeling and design of a 3-DOF magnetic bearing with toroidal radial control coils," IEEE Transactions on Magnetics, Vol. 55, No. 7, 1-7, 2019.
doi:10.1109/tmag.2019.2914510 Google Scholar

26. Zhong, Yunlong, Lijian Wu, Youtong Fang, and Xiaoyan Huang, "Investigation of cross-coupling effect and its restraining methods of a 3-DOF hybrid magnetic bearing," COMPEL, Vol. 37, No. 6, 2195-2210, 2018.
doi:10.1108/compel-01-2018-0037 Google Scholar

27. Zhong, Yunlong, Lijian Wu, Xiaoyan Huang, Youtong Fang, and Jian Zhang, "An improved magnetic circuit model of a 3-DOF magnetic bearing considering leakage and cross-coupling effects," IEEE Transactions on Magnetics, Vol. 53, No. 11, 1-6, 2017.
doi:10.1109/tmag.2017.2708102 Google Scholar

28. Le, Yun, Jinji Sun, and Bangcheng Han, "Modeling and design of 3-DOF magnetic bearing for high-speed motor including eddy-current effects and leakage effects," IEEE Transactions on Industrial Electronics, Vol. 63, No. 6, 3656-3665, 2016.
doi:10.1109/tie.2016.2530778 Google Scholar

Dr. Xiaoting Ye

Dr. Xianhai Yu

Dr. Zirui Chen

Dr. Tao Zhang