Realization Mechanism and Development of Permanent Magnetic Levitation: A Review

doi:10.3901/JME.2023.17.189

Abstract

Abstract: Permanent magnetic levitation technology uses the force between magnet and magnet or ferromagnet to achieve contactless support, which has the outstanding characteristics of no friction and low energy consumption. With the development of rare earth permanent magnet materials, the high remanence, high coercivity and high magnetic energy product improve the load-bearing performance of the permanent magnetic levitation system, which causes scholars have carried out many researches. China has the most reserves of rare earth resources in the world, and the development of permanent magnetic levitation technology has natural advantages and great significance. First of all, the mechanism and characteristics of permanent magnetic levitation technology are clarified. Secondly, the development history of passive levitation and active levitation is systematically reviewed. The magnetic circuit structure, levitation characteristics, and research status of three kinds of permanent magnet active levitation with air gap adjustment, magnetoresistive modulation and magnetic source regulation are described in detail. Thirdly, the technical difficulties such as magnetic circuit design and optimization, magnetic force accurate modeling, performance and control methods are analyzed, and the corresponding solutions are presented. Finally, the future application prospect and development trend of permanent magnetic levitation technology in gravity compensator, light load micro bearing, low frequency vibration isolation and other fields are prospected.

Key words: permanent magnetic levitation, magnetic circuit design, mechanism, development, review

CLC Number:

ZHAO Chuan, SUN Feng, PEI Wenzhe, JIN Junjie, XU Fangchao, OKA Koichi, YU Suyuan. Realization Mechanism and Development of Permanent Magnetic Levitation: A Review[J]. Journal of Mechanical Engineering, 2023, 59(17): 189-207.

References

[1] BLEULER H. A survey of magnetic levitation and magnetic bearing types[J]. JSME International Journal,Series III,1992,35(3):335-342.
[2] MASLEN E H,SCHWEITZER G,BLEULER H,et al. Magnetic bearings-theory,design,and application to rotating machinery[M]. Berlin/Heidelberg:Springer,2009.
[3] MASLEN E H,SCHWEITZER G,BLEULER H,等. 磁悬浮轴承:理论,设计及旋转机械应用[M]. 徐旸,张凯,赵雷译. 北京:机械工业出版社,2012. MASLEN E H,SCHWEITZER G,BLEULER H,et al. Magnetic bearings:theory,design,and application to rotating machinery[M]. XU Yang,Zhang Kai,Zhao Lei Trans.. Beijing:China Machine Press,2012.
[4] 王家素,王素玉. 高温超导磁悬浮列车研究综述[J]. 电气工程学报,2015,10(11):1-10. WANG Jiasu,WANG Suyu. High temperature superconducting maglev train[J]. Journal of Electrical Engineering,2015,10(11):1-10.
[5] DENG Zigang,ZHANG Weihua,ZHENG Jun,et al. A high temperature superconducting maglev ring test line developed in Chengdu,China[J]. IEEE Transactions on Applied Superconductivity,2016,26(6):1-8.
[6] 徐园平,周瑾,金超武,等. 抗磁悬浮研究综述[J]. 机械工程学报,2019,55(2):214-222. XU Yuanping,ZHOU Jin,JIN Chaowu,et al. Diamagnetic levitation:a review[J]. Journal of Mechanical Engineering,2019,55(2):1-10.
[7] XU Yuanping,CUI Qingwen,KAN R, et al. Realization of a diamagnetically levitating rotor driven by electrostatic field[J]. IEEE/ASME Transactions on Mechatronics,2017,22(5):2387-2391.
[8] LONG Zhiqiang,HE Guang,XUE Song. Study of EDS & EMS hybrid suspension system with permanent-magnet halbach array[J]. IEEE Transactions on Magnetics,2011,47(12):4717-4724.
[9] 马卫华,罗世辉,张敏,等. 中低速磁浮车辆研究综述[J]. 交通运输工程学报,2021,21(1):199-216. MA Weihua,LUO Shihui,ZHANG Min,et al. Research review on medium and low speed maglev vehicle[J]. Journal of Traffic and Transportation Engineering,2021,21(1):199-216.
[10] SU Yixin,GU Yongpeng,KEOGH P S,et al. Nonlinear dynamic simulation and parametric analysis of a rotor-AMB-TDB system experiencing strong base shock excitations[J]. Mechanism and Machine Theory,2021,155:104071.
[11] 朱熀秋,王绍帅. 六极径向-轴向主动磁轴承电磁特性分析及实验研究[J]. 中国电机工程学报,2020,40(5):1653-1663. ZHU Huangqiu,WANG Shaoshuai. Electromagnetic characteristics analysis and experiment study of six-pole radial-axial active magnetic bearing[J]. Proceedings of the CSEE,2020,40(5):1653-1663.
[12] SAWA Y. Current status of third-generation implantable left ventricular assist devices in Japan,Duraheart and HeartWare[J]. Surg Today,2015,(45):672-681.
[13] 董宝田,王坤,韩邦成,等. 高速磁悬浮鼓风机涡轮锁紧装置设计分析及试验[J]. 机械工程学报,2019,55(3):154-161. DONG Baotian,WANG Kun,HAN Bangcheng,et al. High-speed maglev blower turbine locking device design analysis and experiment research[J]. Journal of Mechanical Engineering,2019,55(3):154-161.
[14] 杨杰,高涛,邓永芳,等. 永磁磁浮空轨系统的研究与设计[J]. 铁道学报,2020,42(10):30-37. YANG Jie,GAO Tao,DENG Yongfang,et al. Study and design on suspended permanent maglev rail transit system[J]. Journal of the China Railway Society,2020,42(10):30-37.
[15] MONTGOMERY D B. Overview of the 2004 Magplane design[C]//18th International Conference on Maglev Levitated Systems and Linear Drives,October 26-28,2004,Shanghai.
[16] SUN Feng,PEI Wenzhe,ZHAO Chuan,et al. Permanent maglev platform using a variable flux path mechanism:stable levitation and motion control[J]. IEEE Transactions on Magnetics,2022,58(7):1-10.
[17] SON D H,UGURLU M C,SITTI M. Permanent magnet array-driven navigation of wireless millirobots inside soft tissues[J]. Science Advance,2021,7(43):eabi8932.
[18] 钱坤喜,许自豪,王颢,等. 新型永磁悬浮轴承在透平机及心脏泵中的应用[J]. 江苏大学学报,2011,32(6):663-666+677. QIAN Kunxi,XU Zihao,WANG Hao,et al. Applications of novel permanent maglev bearings in turbinemachines and heart pumps[J]. Journal of Jiangsu University,2011,32(6):663-666+677.
[19] 周立山. 永磁阵列式大载荷磁悬浮重力补偿器的基础研究[D]. 哈尔滨:哈尔滨工业大学,2021. ZHOU Lishan. Basic research on a large-load magnetic levitation gravity compensator with permanent magnet array[D]. Harbin:Harbin Institute of Technology,2021.
[20] FANG Jiancheng,WANG Xi,WEI Tong,et al. Homopolar 2-Pole radial permanent-magnet biased magnetic bearing with low rotating loss[J]. IEEE Transactions on Magnetics,2012,48(8):2293-2303.
[21] 严博,马洪业,韩瑞祥,等. 可用于大幅值激励的永磁式非线性隔振器[J]. 机械工程学报,2019,55(11):169-175. YAN Bo,MA Hongye,HAN Ruixiang,et al. Permanent magnets based nonlinear vibration isolator subjected to large amplitude acceleration excitations[J]. Journal of Mechanical Engineering,2019,55(11):169-175.
[22] EARNSHAW S. On the nature of molecular forces which regulate the constitution of luminiferous ether[J]. Transactions of the Cambridge Philosophical Society. 1842(7):97-112.
[23] BASSANI R. Earnshaw (1805-1888) and passive magnetic levitation[J]. Meccanica,2006,41(4):375- 389.
[24] HARRIGAN R M. Levitation device:U.S. Patent,4382245[P]. 1983-05-03.
[25] HONES E W,HONES W G. Magnetic levitation device and method:U.S. Patent,5404062[P]. 1995- 04-04.
[26] JONES T B,WASHIZU M. Simple theory for the Levitron[J]. Journal of Applied Physics,1997,82(2):883-888.
[27] GENTA G, DELPRETE C,RONDANO D. Gyroscopic stabilization of passive magnetic levitation[J]. Meccanica,1999,34:411-424.
[28] KIM K B,IM S H,UM D Y,et al. Comparison of magnetic levitation systems using ring-shaped permanent magnets[J].IEEE Transactions on Magnetics,2019,55(7):1-4.
[29] AZUKIZAWA T,YAMAMOTO S,MATSUO N. Feasibility study of a passive magnetic bearing using the ring shaped permanent magnets[J].IEEE Transactions on Magnetics,2008,44(11):4277-4280.
[30] 钱坤喜,曾培,茹伟民,等. 永磁体磁浮叶轮血泵的研制和试验研究[J]. 机械工程学报,2002,38(5):86-88. QIAN Kunxi,ZENG Pei,RU Weimin,et al. Prototype design and experimental study of a permanent maglev impeller blood pump[J]. Chinese Journal of Mechanical Engineering,2002,38(5):86-88.
[31] QIAN Kunxi,XU Hongxia. Gyro-effect and Earnshaw's theorem:Stable and unstable equilibrium for rotary and stationary permanent magnetic levitators[C]//2nd International Conference on Bioinformatics and Biomedical Engineering,May 16-18,2006,Shanghai. Computer Society,United States:IEEE,2008:1323-1325.
[32] 张钢,孟庆涛,钟永彦,等. 五自由度全永磁轴承系统的稳定悬浮特性分析[J]. 机械工程学报,2015,51(5):56-63. ZHANG Gang,MENG Qingtao,ZHONG Yongyan,et al.Stable levitation performance analysis of five degrees of freedom all permanent magnetic bearing system[J].Journal of Mechanical Engineering,2015,51(5):56-63.
[33] 张钢,张坚,张海龙,等. 基于等效磁荷法用蒙特卡洛法计算永磁轴承磁力[J]. 轴承,2013(10):1-4. ZHANG Gang,ZHANG Jian,ZHANG Hailong,et al.Calculation on magnetic force for permanent magnetic bearings by monte carlo method based on equivalent magnetic charge method[J].Bearing,2013(10):1-4.
[34] MUKHOPADHYAS S C,OHJI T.Design,analysis and control of a new repulsive-type magnetic bearing system[J].IEE Proceedings,Part B,1999,146(1):33-40.
[35] RODRIGUEZ E,SOTELO G G,OLIVEIRA J D,et al.Designing,simulations and experiments of a passive permanent magnet bearing[J].International Journal of Applied Electromagnetics & Mechanics,2016,51(2):131-149.
[36] 李奕良,戴兴建,张小章. 储能飞轮永磁卸载设计及试验[J]. 清华大学学报,2008(8):1268- 1271. LI Yiliang,DAI Xingjian,ZHANG Xiaozhang. Design and testing of a permanent magnetic bearing for an energy storage flywheel[J]. Journal of Tsinghua University,2008(8):1268- 1271.
[37] 汤双清,周东伟,李庆东,等. 基于遗传算法的飞轮储能系统用径向永磁轴承的优化设计[J]. 中国农机化学报,2016,37(8):101-105,131. TANG Shuangqing,ZHOU Dongwei,LI Qingdong,et al. Optimization design of the radial permanent magnet bearings of the flywheel energy storage systems based on genetic algorithm[J]. Journal of Chinese Agricultural Mechanization,2016,37(8):101-105+131.
[38] 张锦光,胡业发,王念先. 小型低风速风力发电机永磁轴承的设计与分析[J]. 机械制造,2010,48(5):20-23. ZHANG Jinguang,HU Yefa,WANG Nianxian. Design and analysis of permanent magnetic bearings in small-sized low-speed wind power generator[J]. Machinery,2010,48(5):20-23.
[39] LI Songsheng,MAO Huawei,CHEN Ping,et al. Dynamic performance of the bearing-rotor system in the ultra-high speed electric spindle with a additional supporting system make up of the permanent magnetic bearings[J]. Advanced Materials Research,2011,295-297:2294-2299.
[40] MARTH E,JUNGMAYR G,AMRHEIN W. A 2-D-based analytical method for calculating permanent magnetic ring bearings with arbitrary magnetization and its application to optimal bearing design[J]. IEEE Transactions on Magnetics,2014,50(5):1-8.
[41] MARTH E,JUNGMAYR G,PANHOLZER M. Optimization and realization of a multi-pole permanent magnetic bearing with rotating magnetization[J]. Proceedings of the Institution of Mechanical Engineers,2016,230(i4):320-329
[42] OHJI T,ICHIYAMA S,AMEI K,et al. Conveyance test by oscillation and rotation to a permanent magnet repulsive-type conveyor[J]. IEEE Transactions on Magnetics,2004,40(4):3057-3059.
[43] 胡坤,王爽,李德永,等. 一种永磁磁垫式带式输送机的气隙特性研究[J]. 煤炭学报,2015,40(3):701-706. HU Kun,WANG Shuang,LI Deyong,et al. Research on air gap characteristics of permanent magnetic cushion belt conveyor[J]. Journal of China Coal Society,2015,40(3):701-706.
[44] 胡坤,王爽,郭永存,等. 永磁悬浮带式输送机侧向力与跑偏仿真分析[J]. 系统仿真学报,2016,28(5):1173-1178. HU Kun,WANG Shuang,GUO Yongcun,et al. Analysis of lateral force and deviation of permanent magnetic levitation belt conveyor[J]. Journal of System Simulation,2016,28(5):1173-1178.
[45] WANG Shuang,HU Kun,LI Deyong. Analysis and experimental research on air gap characteristics of permanent magnet low-resistance belt conveyor[J]. IET Science Measurement Technology,2018,12(4):472-478.
[46] 王仲勋,郭永存,胡坤. 永磁悬浮带式输送机悬浮力特性分析[J]. 煤炭技术,2019,38(05):133-135. WANG Zhongxun,GUO Yongcun,HU Kun. Analysis on suspension force characteristics of permanent magnet suspension belt conveyor[J]. Coal Technology,2019,38(05):133-135.
[47] CHO H W,HAN H S,LEE J M,et al. Design considerations of EM-PM hybrid levitation and propulsion device for magnetically levitated vehicle[J]. IEEE Transactions on Magnetics,2009,45(10):4632- 4635.
[48] Toshiro H,OKA K. Reluctance control magnetic suspension system with permanent magnet and linear actuator[J]. IEEJ Transactions on Industry Applications,1993,113(8):988-994.
[49] OKA K,TOSHIRO H. A three-degrees-of-freedom Maglev system with actuators and permanent magnets[J]. Electrical Engineering in Japan,1996,116(5):138-147.
[50] OKA K,Toshiro H,Takuya S. Hanging type Mag-lev system with permanent magnet motion control[J]. IEEJ Transactions on Industry Applications,1999,119(3):291-297.
[51] Morita T,Shimizu K,Hasegawa M,et al. A miniaturized levitation system with motion control using a piezoelectric actuator[J]. IEEE Transactions on Control Systems Technology,2002,10(5):666-670.
[52] SUN Feng,Oka K. Zero power non-contact suspension system with permanent magnet motion feedback[J]. Journal of System Design & Dynamics,2009,3(4):627-638.
[53] 孙凤,王亚刚,李东生,等. 悬挂式永磁悬浮系统的悬浮特性研究[J]. 组合机床与自动化加工技术,2012(11):25-28. SUN Feng,WANG Yagang,LI Dongsheng,et al. Characteristics analysis of a hanging type permanent magnetic suspension system[J]. Modular Machine Tool & Automatic Manufacturing Technique,2012(11):25-28.
[54] SUN Feng,OKA K. Noncontact spinning mechanism using rotary permanent magnets[J]. IEEJ Transactions on Industry Applications,2010,130(7):913-919.
[55] 孙凤,韦伟,金嘉琦,等. 永磁悬浮非接触回转驱动系统[J]. 机械工程学报,2017,53(20):192-201. SUN Feng,WEI Wei,JIN Jiaqi,et al. Non-contact rotation driving system using permanent-magnetic suspension[J]. Journal of Mechanical Engineering,2017,53(20):192-201.
[56] Oka K,Yamamoto K,Harada A. Magnetic suspension mechanism using rotary permanent magnets[J]. International Journal of Applied Electromagnetics and Mechanics,2020,64(1-4):977-983.
[57] 水野毅,関口秀樹,荒木獻次. 永久磁石の運動制御を利用した反発形磁気軸受に関する研究:アキシャル方向の安定化制御[J]. 日本機械学会論文集C編,1998,64(628):4717-4722 MIZUNO T,SEKIGUCHI H,ARAKI K. Repulsive magnetic bearing using motion control of permanent magnets (stabilization in the axial direction)[J]. Transactions of the Japan Society of Mechanical Engineers Series C,1998,64(628):4717-4722.
[58] Eirich M,Ishino Y,Takasaki M,et al. Development of a repulsive magnetic bearing device with an adjustability function of radial stiffness[C]//Ulbrich H and Ginzinger L,Motion and vibration control:selected papers from MOVIC 2008. The international conference on motion and vibration control,September 15-18,2008,Technical University of Munich,Munich,Germany. Berlin:Springer Netherlands,2009:63-70.
[59] 关勇,李红伟,刘淑琴. 轴流式磁悬浮人工心脏泵磁悬浮轴承系统设计[J]. 山东大学学报,2011,41(1):151-155. GUAN Yong,LI Hongwei,LIU Shuqin. System design of magnetic bearings in an axial-flow artificial blood pump[J]. Journal of Shandong University,2011,41(1):151-155.
[60] 李红伟,范友鹏,张云鹏,等. 轴流式人工心脏泵混合磁悬浮系统的耦合特性[J]. 电机与控制学报,2014,18(5):105-111. LI Hongwei,FAN Youpeng,ZHANG Yunpeng,et al. Coupling in hybrid magnetic levitation system of axial-flow blood pump[J]. Electric Machines and Control,2014,18(5):105-111.
[61] Mizuno T,Ishino Y,Takasaki M. Force compensation for anti-collision in placing a magnetized component on ferromagnetic plate[C]//European Control Conference (ECC),June 29-July 1,2016,Aalborg,Denmark. New York:IEEE,2017:1556-1561.
[62] 上野敏幸,裘進浩,谷順二. 超磁歪材料を用いた新しい磁気力制御方法[J]. 日本機械学会論文集C編,2000,66(644):1180-1185. UENO T,QIU J,TANI J. New magnetic force control method using giant magnetostrictive material[J]. Transactions of the Japan Society of Mechanical Engineers Series C,2000,66(644):1180-1185.
[63] UENO T,QIU J,TANI J. Magnetic circuit design method for magnetic force control systems using inverse magnetostrictive effect:Examination of energy conversion efficiency depending on ΔE effect[J]. Electrical Engineering in Japan,2002,140(1):8-15.
[64] UENO T,QIU J,TANI J. Magneto-electric composite element and its application to magnetic levitation system[C]//Proceedings of the SPIE 4327,Smart Structures and Materials 2001:Smart Structures and Integrated Systems,March 5-8,2001,California,USA. SPIE,2001:533-540.
[65] Ueno T,Qiu J,Tani J. Magnetic force control based on the inverse magnetostrictive effect[J]. IEEE Trans on Magnetics,2004,40(3):1601-1605.
[66] Ueno T,Higuchi T. Novel composite of magnetostrictive material and piezoelectric actuator for coil-free magnetic force control[J]. Sensors & Actuators A Physical,2006,129(1-2):251-255.
[67] Ueno T,Keat C S,Higuchi T. Linear step motor based on magnetic force control using composite of magnetostrictive and piezoelectric materials[J]. IEEE Transactions on Magnetics,2007,43(1):11-14.
[68] Ueno T,Higuchi T. Zero-power magnetic levitation using composite of magnetostrictive/piezoelectric materials[J]. IEEE Transactions on Magnetics,2007,43(8):3477-3482.
[69] Ueno T,Higuchi T. Magnetic circuit for stress-based magnetic force control using iron-gallium alloy[J]. IEEE Transactions on Magnetics,2007,43(6):2594-2596.
[70] Xu Aiqun,Gu Qianxing,Yu Haikuo. Mechanism of controllable force generated by coupling inverse effect of piezoelectricity and magnetostriction[J]. International Journal of Precision Engineering and Manufacturing-Green Technology,2020(8):1-11.
[71] Mizuno T,Hirai Y,Ishino Y,et al. Flux path control magnetic suspension:development of a system using voice coil motors[J]. Transactions of the Japan Society of Mechanical Engineers,Part C,2006,72(721):2869-2876.
[72] Takabayshi A,Mizuno T,Takasaki M,et al. Development of flux-path control magnetic suspension system using flux concentration[J]. Transactions of the Japan Society of Mechanical Engineers,2013,79(801):1483-1494.
[73] Mizuno T,Hirai Y,Ishino Y,et al. Magnetic suspension system using three flux path control modules[J]. IFAC Proceedings Volumes,2006,39(16):554-558.
[74] Mizuno T,Hirai Y,Ishino Y,et al. Flux-path control magnetic suspension system using voice coil motors[J]. Journal of System Design & Dynamics,2007,1(2):147-158.
[75] Furutachi M,Inaba S,Ishino Y,et al. Three-dimensional force measurement and control of a flux-path control magnetic suspension[J]. Journal of System Design & Dynamics,2008,2(6):1239-1249.
[76] Mizuno T,Nagano Y,Ishino Y,et al. Flux-path control module using a single actuator[C]//The Society of Instrument and Control Engineers,2009 ICCAS-SICE,August 18-21,2009,Fukuoka,Japan. New York:IEEE,2009:4407-4410.
[77] Sun Feng,Jin Junjie,Oka K. Noncontact magnetic suspension of an iron ball using flux path control mechanism[J]. Advanced Materials Research,2011,230-232:573-577.
[78] Sun Feng,Oka K, Saibara Y. Magnetic suspension system by flux path control using rotary actuator[J]. International Journal of Applied Electromagnetics and Mechanics,2010,33(1-2):769-776.
[79] Oka K,Okazaki T,Morimitsu T. 2 DOF non-contact magnetic suspension system:A feasibility study[J]. International Journal of Applied Electromagnetics and Mechanics,2014,45(1-4):627-632.
[80] Jin Junjie,Duan Zhenyun,Sun Feng,et al. Model identification and analysis for parallel permanent magnetic suspension system based on ARX model[J]. International Journal of Applied Electromagnetics & Mechanics,2016,52(1-2):145-152.
[81] 孙兴伟,路英园,孙凤,等. 可变磁路式永磁悬浮系统的动力学特性研究[J]. 中国机械工程,2014,25(20):2782-2787. SUN Xingwei,LU Yingyuan,SUN Feng,et al. Research on dynamics performance of permanent magnet suspension system with variable magnetic circuit[J]. China Mechanical Engineering,2014,25(20):2782-2787.
[82] 孙凤,韦伟,金俊杰,等. 可控磁路式并联型永磁悬浮系统[J]. 仪器仪表学报,2017,38(7):1714-1722. SUN Feng,WEI Wei,JIN Junjie,et al. Parallel permanent magnetic suspension system with flux path control[J]. Chinese Journal of Scientific Instrument,2017,38(7):1714-1722.
[83] ZHAO Chuan,SUN Feng,JIN Junjie,et al. Research of permanent magnetic levitation system:Analysis,control strategy design,and experiment[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2022,236(14):7617-7628.
[84] 孙凤,夏鹏澎,孙兴伟,等.可控磁路式永磁悬浮系统的鲁棒控制[J]. 振动与冲击,2019,38(10):65-70. SUN Feng,XIA Pengpeng,SUN Xingwei,et al.Robust control of a permanent magnetic suspension system using the variable flux path control method[J]. Journal of Vibration and Shock,2019,38(10):65-70.
[85] 李强,唐敬虎,孙凤,等. 可变磁路式永磁悬浮系统的防跌落防吸附控制[J]. 仪器仪表学报,2019,40(3):246-254. LI Qiang,TANG Jinghu,SUN Feng,et al. Anti-fall and anti-adsorption control of permanent magnetism levitation system with flux path control[J]. Chinese Journal of Scientific Instrument,2019,40(3):246-254.
[86] 孙凤,唐敬虎,李强,等. 可变磁路式永磁悬浮系统刚度特性分析及变刚度控制[J]. 振动与冲击,2020,39(7):132-139. SUN Feng,TANG Jinghu,LI Qiang,et al. Stiffness characteristics analysis and variable stiffness control for a permanent magnetic levitation system with variable magnetic circuit[J]. Journal of Vibration and Shock,2020,39(7):132-139.
[87] Zhao Chuan,Sun Feng,Jin Junjie,et al.Analysis of quasi-zero power characteristic for a permanent magnetic levitation system with a variable flux path control mechanism[J]. IEEE-ASME Transactions on Mechatronics,2021,26(1):437-447.
[88] ZHOU Ran,YAN Mingyin,GUO Yongquan,et al. Suspension characteristics of a zero-power permanent magnetic suspension system with flux path control[J]. International Journal of Applied Electromagnetics and Mechanics,2020,63(01):187-198.
[89] Sun Feng,Zhou Ran,Jin Junjie,et al. Optimal design for quasi-zero power performance of a permanent magnetic suspension system[J]. International Journal of Applied Electromagnetics and Mechanics,2019,59(2):607-616.
[90] 金俊杰,段振云,孙凤,等. 永磁悬浮无尘传送系统的悬浮特性及解耦控制仿真分析[J]. 中国机械工程,2016,27(4):518-525. JIN Junjie,DUAN Zhenyun,SUN Feng,et al. Simulation analysis on suspension characteristics and decoupling control for dust-free transit system using permanent magnetic suspension[J]. China Mechanical Engineering,2016,27(4):518-525.
[91] Stoica M. Casting and characterization of Fe-(Cr,Mo,Ga)-(P,C,B) soft magnetic bulk metallic glasses[D]. Dresden,Germany:Technische Universität Dresden,2005.
[92] Tumanski S. Modern magnetic materials-the review[J]. Przeglad Elektrotechniczny,2010,86(4):1-15.
[93] 中华人民共和国国家质量监督检验检疫总局,国家标准化管理委员会. GB/T 13560-2017烧结钕铁硼永磁材料[S]. 北京:中国标准出版社,2017. General Administration of Quality Supervision,Inspection and Quarantine of the People's Republic of China,Standardization Administration. GB/T 13560-2017 Sintered neodymium iron boron permanent magnets[S]. Beijing:Standards Press of China,2017.
[94] 中华人民共和国国家质量监督检验检疫总局,中国国家标准化管理委员会. GB/T 21219-2007磁性材料分类[S]. 北京:中国标准出版社,2007. General Administration of Quality Supervision,Inspection and Quarantine of the People's Republic of China,Standardization Administration. GB/T 21219- 2007 Magnetic materials[S]. Beijing:Standards Press of China,2007.
[95] 王进. 低损耗复合结构铁基软磁材料的制备及性能研究[D]. 广州:华南理工大学,2016. WANG Jin. Preparation and properties of low loss iron-based soft magnetic materials with composite structures[D]. Guangzhou:South China University of Technology,2016.
[96] 梁慧敏,张荣岭,徐俊,等. 组装式永磁体分段回复线模型的研究[J].中国电机工程学报,2009,29(27):133-138. LIANG Huimin,ZHANG Rongling,XU Jun,et al. Modeling of combined permanent magnet subsection recoil line[J]. Proceedings of the CSEE,2009,29(27):133-138.
[97] 严密,彭晓领. 磁学基础与磁性材料[M]. 2版. 杭州:浙江大学出版社,2006. YAN Mi,PENG Xiaoling. Magnetic foundation and magnetic material[M]. 2nd ed. Hangzhou:Zhejiang University Press,2006.
[98] 田录林,李鹏. 锥形永磁轴承磁力解析模型[J]. 中国机械工程,2014,25(3):327-332. TIAN Lulin,LI Peng. Magnetic force analytic model of conic permanent magnetic bearings[J]. China Mechanical Engineering,2014,25(3):327-332.
[99] Bachovchin K D,Hoburg J F,Post R F. Magnetic fields and forces in permanent magnet levitated bearings[J]. IEEE Transactions on Magnetics,2012,48(7):2112-2120.
[100] 杨欢,赵荣祥,祝长生. 基于电流片模型的永磁推力轴承优化设计[J]. 电工技术学报,2010,25(10):51-58. YANG Huan,ZHAO Rongxiang,ZHU Changsheng. Optimum design of permanent magnet thrust bearings based on current sheet model[J]. Transactions of China Electrotechnical Society,2010,25(10):51-58.
[101] 孙立军,张涛,赵兵. 永磁磁轴承数学模型的研究[J]. 机械工程学报,2005,41(4):69-74. SUN Lijun,ZHANG Tao,ZHAO Bing. Study of mathematical model of permanent magnet bearings[J]. Chinese Journal of Mechanical Engineering,2005,41(4):69-74.
[102] 王洪昌,蒋书运,梁玉飞. 基于分子电流法轴向永磁轴承轴向刚度的分析[J]. 机械工程学报,2009,45(5):102-107. WANG Hongchang,JIANG Shuyun,LIANG Yufei. Analysis of axial stiffness of permanent magnet bearings by using the equivalent surface currents method[J]. Chinese Journal of Mechanical Engineering,2009,45(5):102-107.
[103] 李群明,万梁,段吉安. 一种永磁轴承的设计和磁场分布的解析计算[J]. 中南大学学报,2006,37(5):970-975. LI Qunming,WAN Liang,DUAN Ji'an. Design of a new radial permanent magnet bearing and analytical calculation of its magnet field[J]. Journal of Central South University,2006,37(5):970-975.
[104] 张海波,邱玉江,蒋书运. 永磁轴承承载能力分子电流模型的积分定义求解方法[J]. 机械工程学报,2016,52(7):54-59. ZHANG Haibo,QIU Yujiang,JIANG Shuyun. Analysis of the equivalent surface current model for the permanent magnet bearing by using the integral definition[J]. Journal of Mechanical Engineering,2016,52(7):54-59.
[105] Cho H W,Yu J S,Jang S M,et al. Equivalent magnetic circuit based levitation force computation of controlled permanent magnet levitation system[J]. IEEE Transactions on Magnetics,2012,48(11):4038-4041.
[106] TAQAVI O,TAGHAVI N. Development of a mixed solution of Maxwell's equations and magnetic equivalent circuit for double-sided axial-flux permanent magnet machines[J]. IEEE Transactions on Magnetics,2021,57(4):1-11.
[107] SUN Feng,JIN Junjie,OKA K. Permanent magnetic suspension system:principle,model,simulation and experiment[M]. Beijing:Science Press,2019.
[108] WU Huachun,ZHOU Jian,XIE Chunhu,et al. Two-dimensional time series sample entropy algorithm:Applications to rotor axis orbit feature identification[J]. Mechanical Systems and Signal Processing,2021,147:107123.
[109] ZHOU Jian,WU Huachun,WANG Weiyu,et al. Online unbalance compensation of a maglev rotor with two active magnetic bearings based on the LMS algorithm and the influence coefficient method[J]. Mechanical Systems & Signal Processing,2022,166:108460.