Engineering Transactions, 72, 3, pp. 343–363, 2024
10.24423/EngTrans.3230.2024

Unbalanced Response Analysis and Experiment of Magnetic Levitation Rotor Based on the State-Space Method

Shuyue ZHANG
Chuzhou University
China

Yahu ZHANG
Chuzhou University
China

Xiaolian LV
Chuzhou University
China

Songling JIN
Anhui Ming Hui Electric Company Limited
China

Magnetic levitation compressors are critical for producing large flow rates of superfluid helium. The steady operation of these compressors depends heavily on the unbalanced response characteristic of their rotors. Previous research, utilizing traditional unbalance response calculation methods, primarily focused on displacement response while neglecting current response. This paper transforms the finite element model of the magnetic levitation rotor into a statespace
representation. It then investigates the influence of vital parameters on both displacement and current responses. The results of speed-up experiment carried out on the compressor prototype test rig agree with the simulation results. The study indicates that adjusting control parameters can suppress vibration and simultaneously reduce control current. This work is essential for the application of compressors in the superfluid helium system.
Keywords: electromagnetic bearing; displacement response; current response; state-space method
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Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).

References

Kuendig A., Schoenfeld H., Voigt Th., Kurtcuoglu K., Yoshinaga S., Saji N., Shimba T., Honda T., Chapter 247: The cold-compressor systems for the LHC cryoplants at CERN, Proceedings of the Twentieth International Cryogenic Engineering Conference (ICEC20), pp. 1043–1046, 2005, doi: 10.1016/B978-008044559-5/50250-7.

Schweitzer G., Maslen E.H. [Eds], Magnetic Bearings: Theory, Design, and Application to Rotating Machinery, Springer, Berlin, 2009.

Zhang S.Y., Pan W., Wei C.B., Wu J.H., Structure design and simulation research of active magnetic bearing for helium centrifugal cold compressor, IOP Conference Series: Materials Science and Engineering, 278: 012162, 2017, doi: 10.1088/1757-899X/278/1/012162.

Huynh V.V., Tran M.H.Q., Integral sliding mode control approach for 3-pole active magnetic bearing system, Applied Mechanics and Materials, 829: 128–132, 2016, doi: 10.4028/www.scientific.net/AMM.829.128.

Pesch A.H., Sawicki J.T., Active magnetic bearing online levitation recovery through μ-synthesis robust control, Actuators, 6(1): 2, 2017, doi: 10.3390/act6010002.

Zhang S.Y., Wei C.B., Yang S.Q., Jia Q.M., Dong X.B., Wu J.H., Robust control of active magnetic bearing systems for helium centrifugal cold compressors, IOP Conference Series: Materials Science and Engineering, 502: 012055, 2018, doi: 10.1088/1757-899X/502/1/012055.

Park C.H., Choi S.K., Ham S.Y., Design of magnetic bearings for turbo refrigerant compressors, Mechanics & Industry, 15(4): 245–252, 2014, doi: 10.1051/meca/2014032.

Zhang S.Y., Chen Z.B., Lva X.L., Yan H.L., Wu J.H., Zhou Y.L., Dynamic characteristics analysis of magnetic levitation rotor considering unbalanced magnetic pull, Applied Computational Electromagnetics Society Journal (ACES), 37(10): 1096–1109, 2022, doi: 10.13052/2022.ACES.J.371010.

Wei C., Söffker D., Optimization strategy for PID-controller design of AMB rotor systems, IEEE Transactions on Control Systems Technology, 24(3): 788–803, 2016, doi: 10.1109/TCST.2015.2476780.

Wang Z., Mao C., Zhu C., A design method of PID controller for active magnetic bearings-rigid rotor systems [in Chinese], Proceedings of the Chinese Society of Electrical Engineering, 38(20): 6154–6163, 2018, doi: 10.13334/j.0258-8013.pcsee.171472.

Du G., Shi Z., Zuo H., Zhao L., Sun Z., Analysis of unbalanced response of rigid rotor supported by AMBs under coupling dynamic and control methods, Applied Computational Electromagnetics Society Journal, 34(4): 512–519, 2019.

Wang D., Wang, N., Chen K., Ye C., Dynamic characteristics of magnetic suspended dual-rotor System by RICCATI transfer matrix method, Shock and Vibration, 2019(1): 9843732, 2019, doi: 10.1155/2019/9843732.

Tang E., Fang J., Han B., Active vibration control of the flexible rotor in high energy density magnetically suspended motor with mode separation method, ASME Journal of Engineering for Gas Turbines and Power, 137(8): 082503, 2015, doi: 10.1115/1.4029372.

Wang D., Wang N., Chen K., Unbalance response of a magnetic suspended dual-rotor system, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 233(15): 5758–5772, 2019, doi: 10.1177/0954410019858011.

Gao H., Meng X., Qian K., The impact analysis of beating vibration for active magnetic bearing, IEEE Access, 7: 134104–134112, 2019, doi: 10.1109/ACCESS.2019.2932723.

Liu Y., Ming S., Zhao S., Han J., Ma Y., Research on automatic balance control of active magnetic bearing-rigid rotor system, Shock and Vibration, 2019(1): 3094215, 2019, doi: 10.1155/2019/3094215.

Lei S., Palazzolo A., Control of flexible rotor systems with active magnetic bearings, Journal of Sound and Vibration, 314(1–2): 19–38, 2008, doi: 10.1016/j.jsv.2007.12.028.

Numanoy N., Srisertpol J., Vibration reduction of an overhung rotor supported by an active magnetic bearing using a decoupling control system, Machines, 7(4): 73, 2019, doi: 10.3390/machines7040073.

Skogestad S., Postlethwaite I., Multivariable Feedback: Control Analysis and Design, John Wiley & Son, Chichester, 2001.

Becker F.B., Sehr M.A., Rinderknecht S., Vibration isolation for parameter-varying rotor systems using piezoelectric actuators and gain-scheduled control, Journal of Intelligent Material Systems and Structures, 28(16): 2286–2297, 2017, doi: 10.1177/1045389X17689933.

Gu H., Zhao L., Shi L., Diao X., Controller design for a flexible rotor supported by active magnetic bearing passing the critical rotational speed, Journal of Tsinghua University, 45(6): 821–823, 2005.

Maslen E.H., Knospe C.R., Zhu L., An enhanced dynamic model for the actuator/amplifier pair in AMB systems, Proceedings of the 10th International Symposium on Magnetic Bearings, Martigny, 2006.

Wang Y., Fang J., Zheng S., Optimal phase compensation control and experimental study of flexible rotor supported by magnetic bearing, [in:] Proceedings of the 2012 8th IEEE International Symposium on Instrumentation & Control Technology, London, 2012, pp. 314–319, doi: 10.1109/ISICT.2012.6291635.

Fang J., Tang E., Zheng S., Optimum damping control of the flexible rotor in high energy density magnetically suspended motor, ASME Journal of Engineering for Gas Turbines and Power, 137(8): 082505, 2015, doi: 10.1115/1.4029393.




DOI: 10.24423/EngTrans.3230.2024