Research on synchronous damping around the critical bending speed of magnetic bearings

doi:10.19799/j.cnki.2095-4239.2021.0258

Abstract

Abstract:

Recently, magnetic bearing systems have undergone development to induce higher speed and better reliability in such systems. This has led to the rotor speed exceeding the first-order bending critical speed. However, due to insufficient damping at a critical frequency, magnetic bearing systems face instability risks. In order to adapt the system's performance and stability around the first-order critical speed, this paper proposes a synchronous damping method to provide the damping required for the rotor to cross the critical speed and to support it in reaching a higher yet stable speed. With a rotor modal constructed using the classic finite element method and combining the modal separation method and mass discretization, the suppression of unbalanced vibration around the first-order critical speed using the synchronous damping method was verified in detail. This result can serve as a foundation for the practical application of the synchronous damping method. Finally, with the addition of the synchronous damping module in the existing magnetic bearing equipment in a laboratory setting, the rotor steadily transited the first-order bending speed of 45,000 r/min, which verified the effectiveness of the synchronous damping method in supporting the flexible rotor to pass through the critical speed.

Key words: magnetic bearing, unbalance control, flexible rotor, critical speed, synchronous damping

CLC Number:

TH 133

Yating LIU, Kai ZHANG, Yang XU. Research on synchronous damping around the critical bending speed of magnetic bearings[J]. Energy Storage Science and Technology, 2021, 10(5): 1656-1666.

Figures/Tables 30

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Table 2

Fig. 16

Table 3

Fig. 17

Table 4

Fig. 18

Fig. 19

Fig. 20

Fig. 21

Fig. 22

Fig. 23

Fig. 24

Fig. 25

Fig. 26

References 18

1	GUO Z L, WANG Y J, SHULTZ R, et al. Application and configuration of high power motor-compressor units equipped with active magnetic bearings[J]. Chinese Journal of Turbomachinery, 2019, 61(6): 79-85, 5.
2	张文亮, 丘明, 来小康. 储能技术在电力系统中的应用[J]. 电网技术, 2008, 32(7): 1-9.
	ZHANG W L, QIU M, LAI X K. Application of energy storage technologies in power grids[J]. Power System Technology, 2008, 32(7): 1-9.
3	张维煜, 朱熀秋. 飞轮储能关键技术及其发展现状[J]. 电工技术学报, 2011, 26(7): 141-146.
	ZHANG W Y, ZHU H Q. Key technologies and development status of flywheel energy storage system[J]. Transactions of China Electrotechnical Society, 2011, 26(7): 141-146.
4	李万杰, 张国民, 王新文, 等. 飞轮储能系统用超导电磁混合磁悬浮轴承设计[J]. 电工技术学报, 2020, 35(S1): 10-18.
	LI W J, ZHANG G M, WANG X W, et al. Integration design of high-temperature superconducting bearing and electromagnetic thrust bearing for flywheel energy storage system[J]. Transactions of China Electrotechnical Society, 2020, 35(S1): 10-18.
5	HERZOG R, BUHLER P, GAHLER C, et al. Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings[J]. IEEE Transactions on Control Systems Technology, 1996, 4(5): 580-586.
6	钟一谔. 转子动力学[M]. 北京: 清华大学出版社, 1987.
	ZHONG Y E. Rotor dynamics[M]. Beijing: Tsinghua University Press, 1987.
7	杨静, 虞烈. 电磁轴承过临界转速的非线性极点配置[J]. 轴承, 2002(11): 1-4.
	YANG J, YU L. Non-linear polar configuration of rotor system over critical for electromagnetic bearing speed[J]. Bearing, 2002(11): 1-4.
8	张剀, 赵雷, 赵鸿宾. 电磁力超前控制在磁悬浮飞轮中的应用[J]. 机械工程学报, 2004, 40(7): 175-179.
	ZHANG K, ZHAO L, ZHAO H B. Application of magnetic forcelead control on a flywheelsuspended by ambs[J]. Chinese Journal of Mechanical Engineering, 2004, 40(7): 175-179.
9	谷会东, 赵雷, 石磊, 等. 电磁轴承支承挠性转子过临界控制器设计[J]. 清华大学学报(自然科学版), 2005, 45(6): 821-823.
	GU H D, ZHAO L, SHI L, et al. Controller design for a flexible rotor supported by active magnetic bearing passing the critical rotational speed[J]. Journal of Tsinghua University (Science and Technology), 2005, 45(6): 821-823.
10	牟伟兴. 磁悬浮轴承柔性转子系统的变参数控制研究[D]. 南京: 南京航空航天大学, 2010.
	MU W X. Research on varying parameter control of flexible rotor system supported by active magnetic bearings[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2010.
11	张剀, 戴兴建, 张小章. 磁轴承超临界高速电机系统控制器设计[J]. 清华大学学报(自然科学版), 2010, 50(11): 1785-1788.
	ZHANG K, DAI X J, ZHANG X Z. Controller design of a supercritical high speed motor system suspended by active magnetic bearings[J]. Journal of Tsinghua University (Science and Technology), 2010, 50(11): 1785-1788.
12	SCHWEITZER G, MASLEN E H. 磁悬浮轴承: 理论、设计及旋转机械应用[M]. 徐旸, 张剀, 赵雷译. 北京: 机械工业出版社, 2012.
13	OKADA Y, NAGATA T, TANI J J, et al. Vibration analysis and active control of flexible-shell-structured rotor supported by magnetic bearings[J]. JSME International Journal Ser C, Dynamics, Control, Robotics, Design and Manufacturing, 1994, 37(3): 488-493.
14	SHIAU T N, SHEU G J, YANG C D. Vibration and control of a flexible rotor in magnetic bearings using hybrid method and H^∞ control theory[J]. Journal of Engineering for Gas Turbines and Power, 1997, 119(1): 178-185.
15	TAMISIER V, FONT S, LACOUR M, et al. Attenuation of vibrations due to unbalance of an active magnetic bearings milling electro-spindle[J]. CIRP Annals, 2001, 50(1): 255-258.
16	TAMISIER V, CARRÈRE F, FONT S. Synchronous unbalance cancellation across critical speed using a closed-loop method[C]//Eighth International Symposium on Magnetic Bearings, Mito, Japan, 2002: 399-404.
17	KNOSPE C R, HOPE R W, FEDIGAN S J, et al. New results in the control of rotor synchronous vibration[C]//Fourth International Symposium on Magnetic Bearings, 1994.
18	LARSONNEUR R. Modeling and analysis of dynamic mechanical systems: With a special focus on rotordynamics and active magnetic bearing (AMB) systems[R]. 2006.

参数	数值
转子总质量m/kg	3.5
转子总长度l/mm	440
临界转速/(r·min^-1)	45000
径向电磁气隙/mm	0.3
径向保护气隙/mm	0.1

[1]	Junze GAO, Yibing LIU, Chuandi ZHOU, Haiting HE, Xin WU. Magnetic circuit design and magnetic analytical model of permanent magnet suspension bearing for flywheel [J]. Energy Storage Science and Technology, 2022, 11(5): 1437-1445.
[2]	Suhang YU, Wenyong GUO, Yuping TENG, Wenju SANG, Yang CAI, Chenyu TIAN. A review of the structures and control strategies for flywheel bearings [J]. Energy Storage Science and Technology, 2021, 10(5): 1631-1642.
[3]	Chunyi WANG, Kai ZHANG, Yang XU. Reactive power compensation technology for the inductive sensors of magnetic bearings [J]. Energy Storage Science and Technology, 2021, 10(5): 1650-1655.
[4]	Dongxu HU, Xinran WANG, Wen LI, Xingjian DAI, Xing WANG, Hucan HOU, Haisheng CHEN, Zhitao ZUO. Vibration of double-cantilever shafting structure passing through critical speed [J]. Energy Storage Science and Technology, 2021, 10(5): 1536-1543.
[5]	PENG Long, LI Guangjun, CUI Yadong, WANG Fang. Analyses and experimental validation testing of rotor dynamics of a flywheel [J]. Energy Storage Science and Technology, 2019, 8(3): 595-601.
[6]	ZHANG Kai, XU Yang, DONG Jinping, ZHANG Xiaozhang. Application of active magnetic bearings in flywheel systems [J]. Energy Storage Science and Technology, 2018, 7(5): 783-793.
[7]	HAN Yongjie, LI Chong, WANG Haoyu, REN Zhengyi, WU Bin. Analysis of the dynamic load operating envolope for E-core radial magnetic bearings in flywheel energy storage system [J]. Energy Storage Science and Technology, 2018, 7(5): 804-809.
[8]	REN Zhengyi, ZHOU Yuanwei, MA Yanqin, HUANG Tong. Critical speed analysis of disc and column flywheel rotor system [J]. Energy Storage Science and Technology, 2018, 7(5): 821-827.
[9]	LI Zehui, TENG Wanqing, LI Chong. Finite element analysis of a magnetic circuit of radial magnetic bearing for magnetically suspended flywheels [J]. Energy Storage Science and Technology, 2014, 3(4): 308-311.