Research Overview on Field Modulated Magnetic Gear

doi:10.3901/JME.2024.14.347

Abstract

Abstract: Transcending the topology of the traditional magnetic gears, the field modulated magnetic gears(FMMGs) adopts the coaxial topology and have a high utilization of permanent magnets. FMMGs have the advantages of no contact, no wear, no lubrication, low noises and overload protection, and can provide a larger torque and a higher torque density. So, FMMGs can be widely used in the navigation, wind turbine systems, petrochemical engineering and other fields. Based on a brief history review of the traditional magnetic gear and outline of the working principle of FMMGs, kinds of radial, axial and intersecting axes FMMGs are introduced, and the torque characteristics of them are compared. The calculation methods and optimization methods of related researches about FMMGs are summarized. The performance indexes of different types of FMMGs such as torque density, cogging torques, losses and temperature rises are compared and analyzed. Finally, the applications and prospects of FMMGs in magnetic geared machines, polar and other environments are summarized. The future research areas of FMMGs are predicted.

Key words: filed modulation, magnetic gear, topological structure, evaluation index, research method

CLC Number:

TH132

YUAN Xiaoming, PANG Haodong, GAO Hongfa, HOU Shubo, HAO Xiuhong. Research Overview on Field Modulated Magnetic Gear[J]. Journal of Mechanical Engineering, 2024, 60(14): 347-363.

References

[1] 宁文飞，包广清，王金荣. 磁齿轮拓扑分析及其应用综述[J]. 机械传动，2012，36(2)：91-96. NING Wenfei，BAO Guangqing，WANG Jinrong. A review of the topological analysis and application of magnetic gear[J]. Journal of Mechanical Transmission，2012，36(2)：91-96.
[2] 王虎生，侯云鹏，程树康. 无接触永磁齿轮传动机构发展综述[J]. 微电机，2008，41(2)：71-73. WANG Husheng，HOU Yunpeng，CHENG Shukang. Development and prospect of non-contact permanent magnetic gear transmission[J]. Micromotors，2008，41(2)：71-73.
[3] LI Xianglin，CHAU K T，CHENG Ming，et al. Comparison of magnetic-geared permanent-magnet machines[J]. Progress in Electromagnetics Research，2013，133：177-198.
[4] WANG Yawei，FILIPPINI M，BIANCHI N，et al. A review on magnetic gears：Topologies，computational models，and design aspects[J]. IEEE Transactions on Industry Applications，2019，55(5)：4557-4566.
[5] 汲柏良，秦清海. 磁性传动齿轮研究综述[J]. 微特电机，2022，50(2)：59-66. JI Bailiang，QIN Qinghai. Review of research on magnetic transmission gear[J]. Small & Special Electrical Machines，2022，50(2)：59-66.
[6] 付兴贺，王标，林明耀. 磁力齿轮发展综述[J]. 电工技术学报，2016，31(18)：1-12. FU Xinghe，WANG Biao，LIN Mingyao. Overview and recent developments of magnetic gears[J]. Transactions of China Electrotechnical Society，2016，31(18)：1-12.
[7] FAUS H. Magnet gearing：US，2243555[P]. 1942-12-27.
[8] ATALLAH K，HOWE D. A novel high-performance magnetic gear[J]. IEEE Transactions on Magnetics，2002，37(4)：2844-2846.
[9] UPPALAPATI K K，CALVIN M，WRIGHT J，et al. A magnetic gearbox with an active region torque density of 239Nm/L[J]. IEEE Transactions on Industry Applications，2017，54(2)：1422-1428.
[10] MEZANI S，ATALLAH K，HOWE D. A high-performance axial-field magnetic gear[J]. Journal of Applied Physics，2006，99(8)：08R303.
[11] ATALLAH K，WANG Jiabin. A high-performance linear magnetic gear[J]. Journal of Applied Physics，2005，97(10)：1-3.
[12] 程明. 电机气隙磁场调制统一理论及其应用[M]. 北京：机械工业出版社，2021. CHENG Ming. General airgap field modulation theory for electrical machines and its applications[M]. Beijing：China Machine Press，2021.
[13] ZHU Ziqiang，EVANS D. Overview of recent advances in innovative electrical machines-with particular reference to magnetically geared switched flux machines[C]//2014 17th International Conference on Electrical Machines and Systems. Hangzhou：IEEE，2014：1-10.
[14] CHEN Mu，CHAU K T，LI Wenlong，et al. Development of non-rare-earth magnetic gears for electric vehicles[J]. Journal of Asian Electric Vehicles，2012，10(2)：1607-1613.
[15] TEMPER C. Magnetic gear and gear train configuration：US，5569967A[P]. 1996-10-29.
[16] JORGENSEN F T，ANDERSEN T O，RASMUSSEN P O. Two dimensional model of a permanent magnet spur gear[C]//Fourtieth IAS Annual Meeting. Conference Record of the 2005 Industry Applications Conference. Hong Kong：IEEE，2005：261-265.
[17] YAO Y D，HUANG D R，HSIEH C C，et al. The radial magnetic coupling studies of perpendicular magnetic gears[J]. IEEE Transactions on Magnetics，1996，32(5)：5061-5063.
[18] MURUGANANDAM G，PADMA S，SELVAKUMAR P. Design and implementation of a novel magnetic bevel gear[J]. Control Engineering and Applied Informatics，2013，15(2)：30-37.
[19] KIKUCHI S，TSURUMOTO K. Design and characteristics of a new magnetic worm gear using permanent magnet[J]. IEEE Transactions on Magnetics，1993，29(6)：2923-2925.
[20] TSURUMOTO K，KIKUCHI S. A new magnetic gear using permanent magnet[J]. IEEE Transactions on Magnetics，1987，23(5)：3622-3624.
[21] HUANG Chengchi，TSAI M，DORREL D G，et al. Development of a magnetic planetary gearbox[J]. IEEE Transactions on Magnetics，2008，44(3)：403-412.
[22] XU Lizhong，ZHU Xuejun. Magnetic planetary gear drive[J]. Proceedings of the Insitution of Mechanical Engineers Part C：Journal of Mechanical Engineering Science，2009，223(9)：2167-2181.
[23] RENS J，ATALLAH K，CALVERLEY S，et al. A novel magnetic harmonic gear[J]. IEEE Transactions on Industry Applications，2010，46(1)：206-212.
[24] JORGENSEN F，ANDERSEN T，RASMUSSEN P. The cycloid permanent magnetic gear[J]. IEEE Transactions on Industry Applications，2008，44(6)：1659-1665.
[25] 郑大周，许立忠，李雯，等. 机电集成超环面传动的驱动原理[J]. 机械设计与研究，2008，24(3)：43-45. ZHENG Dazhou，XU Lizhong，LI Wen，et al. Driving principle of electromechanical integrated toroidal drive[J]. Machine Design & Research，2008，24(3)：43-45.
[26] TSURUMOTO K. Power transmission of magnetic gear using common meshing and insensibility to center distance[J]. IEEE Translation Journal on Magnetics in Japan，1988，3(7)：588-589.
[27] TLALI P M，WANG R J，GERBER S. Magnetic gear technologies：A review[C]//2014 International Conference on Electrical Machines (ICEM). Berlin：IEEE，2014：544-550.
[28] ATALLAH K，CALVERLEY S，HOWE D. Design，analysis and realisation of a high-performance magnetic gear[J]. IEE Proceedings-Electric Power Applications，2004，151(2)：135-143.
[29] JIAN Linni，CHAU K T，GONG Yu，et al. Comparison of coaxial magnetic gears with different topologies[J]. IEEE Transactions on Magnetics，2009，45(10)：4526-4529.
[30] SHEN Jianxin，LI Huayang，HAO He，et al. A coaxial magnetic gear with consequent-pole rotors[J]. IEEE Transactions on Energy Conversion，2017，32(1)：267-275.
[31] PENG Shan，FU Weinong，HO S L. A novel high torque-density triple-permanent-magnet-excited magnetic gear[J]. IEEE Transactions on Magnetics，2014，50(11)：1-4.
[32] MIZUANA Y，NAKAMURA K，SUZUKI Y，et al. Development of spoke-type IPM magnetic gear[J]. International Journal of Applied Electromagnetics and Mechanics，2020，64(1-4)：771-778.
[33] RASMUSSEN P O，ANDERSEN T O，JORGENSEN T，et al. Development of a high-performance magnetic gear[J]. IEEE Transactions on Industry Applications，2005，41(3)：764-770.
[34] LI Xianglin，CHAU K T，CHENG Ming，et al. An improved coaxial magnetic gear using flux focusing[C]//International Conference on Electrical Machines & Systems. Beijing：IEEE，2011：1-4.
[35] JOHNSON M，GARDNER M C，TOLIYAT H A. Analysis of axial field magnetic gears with Halbach arrays[C]//2015 IEEE International Electric Machines & Drives Conference. Coeur d'Alene：IEEE，2016：108-114.
[36] ACHARYA V M，CALVIN M，BIRD J Z. A low torque ripple flux focusing axial magnetic gear[C]//IET International Conference on Power Electronics. Britain：Manchester，2014：1-6.
[37] JOHNSON M，SHAPOURY A，BOGHRAT P，et al. Analysis and development of an axial flux magnetic gear[C]//2014 IEEE Energy Conversion Congress and Exposition (ECCE). Pittsburgh：IEEE，2014：5893-5900.
[38] LI Yong，XING Jingwei，PENG Kerong，et al. Principle and simulation analysis of a novel structure magnetic gear[C]//11th International Conference on Electrical Machines and Systems. Beijing：World Publishing Corporation，2008：3845-3849.
[39] LI Kang，BIRD J Z. A review of the volumetric torque density of rotary magnetic gear designs[C]//2018 XIII International Conference on Electrical Machines (ICEM). Alexandroupoil：IEEE，2018：2016-2022.
[40] BOMELA W，BIRD J，ACHARYA V. The performance of a transverse flux magnetic gear[J]. IEEE Transactions on Magnetics，2014，50(1)：1-4.
[41] YIN Xin，PFISTER P，FANG Youtong. A novel magnetic gear：Toward a higher torque density[J]. IEEE Transactions on Magnetics，2015，51(11)：1-4.
[42] LIU Yulong，HO S L，FU Weinong. A novel magnetic gear with intersecting axes[J]. IEEE Transactions on Magnetics，2014，50(11)：1-4.
[43] HAO Xiuhong，ZHU Hongqian，GUAN Xuemei，et al. Magnetic gear with intersecting axes and straight stationary pole-pieces[J]. Advances in Mechanical Engineering，2018，10(11)：1-10.
[44] ATALLAH K，CALVERLEY S D，HOWE D. High-performance magnetic gears[J]. Journal of Magnetism and Magnetic Materials，2004，272-276：1727-1729.
[45] PERCEBON L A，FERRAZ R，DA LUZ M V F. Modelling of a magnetic gear considering rotor eccentricity[C]//2011 IEEE International Electric Machines and Drives Conference. Niagara Falls：IEEE，2011：1237-1241.
[46] MOGHIMI A，ALIABADI M H，FARAHANI H F. Torque sensitivity analysis for triple-speed coaxial magnetic gear using finite element method[J]. IET Electric Power Applications，2021，15(4)：405-414.
[47] PARK E J，JUNG S Y，KIM Y J. Comparison of magnetic gear characteristics using different permanent magnet materials[J]. IEEE Transactions on Applied Superconductivity，2020，30(4)：1-4.
[48] MATEEV V，TODOROVA M，MARINOVA I. Eddy current losses of coaxial magnetic gears[C]//2018 XIII International Conference on Electrical Machines (ICEM). Alexandroupoli：IEEE，2018：1157-1162.
[49] CHEN Yiduan，FU Weinong. A novel hybrid-flux magnetic gear and its performance analysis using the 3-d finite element method[J]. Energies，2015，8(5)：3313-3327.
[50] DENG Zhangxian，NAS I，DAPIN M J. Torque analysis in coaxial magnetic gears considering nonlinear magnetic properties and spatial harmonics[J]. IEEE Transactions on Magnetics，2019，55(2)：1-11.
[51] ZHU Ziqiang，HOWE D. Instantaneous magnetic field distribution in brushless permanent magnet dc motors，part III：Effect of stator slotting[J]. IEEE Transactions on Magnetics，1993，29(1)：143-151.
[52] LEE J I，SHIN K H，SEO S W，et al. Electromagnetic performance analysis and experimental verification considering the end effect of linear magnetic gears using subdomain-based analytical method[J]. IEEE Transactions on Magnetics，2021，57(2)：1-5.
[53] HOLEHOUSE R C，ATALLAH K，WANG Jiabin. A linear magnetic gear[C]//2012 XXth International Conference on Electrical Machines. Marseille：IEEE，2012：563-569.
[54] BENLAMINE R，HAMITI T，VANGRAEFSCHEPE F，et al. Modeling of a coaxial magnetic gear equipped with surface mounted PMs using nonlinear adaptive magnetic equivalent circuits[C]//2016 XXII International Conference on Electrical Machines (ICEM). Lausanne：IEEE，2015：1888-1894.
[55] FUKUOKA M，NAKAMURA K，ICHINOKURA O. Dynamic analysis of planetary-type magnetic gear based on reluctance network analysis[J]. IEEE Transactions on Magnetics，2011，47(10)：2414-2417.
[56] FUKUOKA M，NAKAMURA K，ICHINOKURA O. A method for optimizing the design of SPM type magnetic gear based on reluctance network analysis[C]//2012 XXth International Conference on Electrical Machines. Marseille：IEEE，2012：30-35.
[57] THYROFF D，MEIER S，HAHN I. Modeling integrated magnetic gears using a magnetic equivalent circuit[C]//IECON 2015-41st Annual Conference of the IEEE Industrial Electronics Society. Yokohama：IEEE，2016：002904-002908.
[58] MATTHEW J，MATTHEW C，TOLIYAT H. A parameterized linear magnetic equivalent circuit for analysis and design of radial flux magnetic gears-part I：Implementation[J]. IEEE Transactions on Energy Conversion，2017，33(2)：784-791.
[59] MATTHEW J，MATTHEW C，TOLIYAT H. A parameterized linear magnetic equivalent circuit for analysis and design of radial flux magnetic gears-part II：Evaluation[J]. IEEE Transactions on Energy Conversion，2017，33(2)：792-800.
[60] BOULES N. Two-dimensional field analysis of cylindrical machines with permanent magnet excitation[J]. IEEE Transactions on Industry Applications，1984(5)：1267-1277.
[61] BOLTE E，OBERRETL K. Three-dimensional analysis of linear motor with solid iron secondary[C]// International Conference on Electrical Machines，1981：68-75.
[62] WANG Xinhua，LI Qingfu，WANG Shuhong，et al. Analytical calculation of air-gap magnetic field distribution and instantaneous characteristics of brushless DC motors[J]. IEEE Transactions on Energy Conversion，2003，18(3)：424-432.
[63] DUBAS F，ESPANET C. Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect：No-load vector potential and flux density calculation[J]. IEEE Transactions on Magnetics，2009，45(5)：2097-2109.
[64] ZHU Ziqiang，WU Lijian，XIA Z P. An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent-magnet machines[J]. IEEE Transactions on Magnetics，2010，46(4)：1100-1115.
[65] RAHIDEH A，KORAKIANITIS T. Analytical magnetic field calculation of slotted brushless permanent-magnet machines with surface inset magnets[J]. IEEE Transactions on Magnetics，2012，48(10)：2633-2649.
[66] BOUGHRARA K，IBTIOUEN R，LUBIN T. Analytical prediction of magnetic field in parallel double excitation and spoke-type permanent-magnet machines accounting for tooth-tips and shape of polar pieces[J]. IEEE Transactions on Magnetics，2012，48(7)：2121-2137.
[67] LUBIN T，MEZANI S，REZZOUG A. Analytical computation of the magnetic field distribution in a magnetic gear[J]. IEEE Transactions on Magnetics，2010，46(7)：2611-2621.
[68] JIAN Linli，CHAU K T. Analytical calculation of magnetic field distribution in coaxial magnetic gears[J]. Progress in Electromagnetics Research，2009，92(4)：1-16.
[69] FILIPPINI M，ALOTTO P. An optimization tool for coaxial magnetic gears[J]. Compel International Journal for Computation & Mathematics in Electrical & Electronic Engineering，2017，36(5)：1526-1539.
[70] LUBIN T，MEZANI S，REZZOUG A. Development of a 2-D analytical model for the electromagnetic computation of axial-field magnetic gears[J]. IEEE Transactions on Magnetics，2013，49(11)：5507-5521.
[71] ZHANG Xiaoxu，XIAO Liu，SONG Zhanfeng，et al. Fast calculation of magnetic field distribution in magnetic gear for high torque application[C]//22 nd International Conference on Electrical Machines (ICEM). Lausanne：IEEE，2016：1742-1748.
[72] DESVAUX M，TRAULLE B，LATIMIER R L G，et al. Computation time analysis of the magnetic gear analytical model[J]. IEEE Transactions on Magnetics，2017，53(5)：1-9.
[73] DEVILLERS E，LE BESNERAIS J，LUBIN T，et al. A review of subdomain modeling techniques in electrical machines：Performances and applications[C]//2016 XXII International Conference on Electrical Machines (ICEM). Lausanne：IEEE，2016：86-92.
[74] DESVAUX M，SIRE S，HLIOUI S，et al. Development of a hybrid analytical model for a fast computation of magnetic losses and optimization of coaxial magnetic gears[J]. IEEE Transactions on Energy Conversion，2018，34(1)：25-35.
[75] PENG Shan，FU Weinong，HO S L. A novel triple-permanent-magnet-excited hybrid-flux magnetic gear and its design method using 3-D finite element method[J]. IEEE Transactions on Magnetics，2014，50(11)：1-4.
[76] TSAI M，KU L. 3-D printing-based design of axial flux magnetic gear for high torque density[J]. IEEE Transactions on Magnetics，2015，51(11)：1-4.
[77] AISO K，AKATSU K，AOYAMA Y. A novel reluctance magnetic gear for high-speed motor[J]. IEEE Transactions on Industry Applications，2019，55(3)：2690-2699.
[78] JING Libing，ZHANG Ting，GAO Yuting，et al. A novel HTS modulated coaxial magnetic gear with eccentric structure and Halbach arrays[J]. IEEE Transactions on Applied Superconductivity，2019，29(5)：1-5.
[79] NIGUCHI N，HIRATA K. Cogging torque analysis of magnetic gear[J]. IEEE Transactions on Industrial Electronics，2011，59(5)：2189-2197.
[80] JUNGMAYR G，LOEFFLER J，WINTER B，et al. Magnetic gear：Radial force，cogging torque，skewing and optimization[J]. IEEE Transactions on Industry Applications，2016，52(5)：3822-3830.
[81] ZAYTOON H，ABDEL-KHALIK A S，AHMED S，et al. Torque ripple alleviation of a radial magnetic gearbox using step skewing approach[C]//2014 International Conference on Electrical Machines (ICEM). Berlin：IEEE，2014：648-653.
[82] ABDELHAMID D Z，KNIGHT A M. The effect of modulating ring design on magnetic gear torque[J]. IEEE Transactions on Magnetics，2017，53(11)：1-4.
[83] MATEEV V，MARINOVA I. Loss estimation of magnetic gears[J]. Electrical Engineering，2020，102(1)：387-399.
[84] KIM S Y，LEE T W，CHUN Y D，et al. Performance analysis of magnetic gear with Halbach array for high power and high speed[J]. International Journal of Applied Electromagnetics and Mechanics，2020，64(1-4)：959-967.
[85] 罗帅，周钰峰，鲁仰辉，等. 永磁体分块对永磁变速机涡流损耗的影响研究[J]. 机械设计与制造，2022，377(7)：139-142，148. LUO Shuai，ZHOU Yufeng，LU Yanghui，et al. Influence of permanent magnet partition on eddy current loss of permanent magnet transmission[J]. Machinery Design & Manufacture，2022，377(7)：139-142，148.
[86] 鲁仰辉，罗帅，吴素君. 调磁环材料性能对永磁齿轮损耗的影响研究[J]. 机械工程学报，2022，58(22)：269-275. LU Yanghui，LUO Shuai，WU Sujun. Influence of material properties of magnetic adjusting ring on the loss of magnetic gear[J]. Journal of Mechanical Engineering，2022，58(22)：269-275.
[87] 葛研军，王彪，牛志，等. 同心式永磁齿轮损耗分析及结构优化[J]. 大连交通大学学报，2016，37(4)：61-66. GE Yanjun，WANG Biao，NIU Zhi，et al. Loss analysis and structure optimization of coaxial magnetic gear[J]. Journal of Dalian Jiaotong University，2016，37(4)：61-66.
[88] DESVAUX M，BILDSTEIN H，MULTON B，et al. Magnetic losses and thermal analysis in a magnetic gear for wind turbine[C]//13th International Conference on Ecological Vehicles and Renewable Energies. Monte Carlo：IEEE，2018：1-7.
[89] SHIN H，CHANG J，HONG D. Design and characteristics analysis of coaxial magnetic gear for contra-rotating propeller in yacht[J]. IEEE Transactions on Industrial Electronics，2019，67(9)：7250-7259.
[90] EVANS D J，ZHU Ziqiang. Influence of design parameters on magnetic gear's torque capability[C]//2011 IEEE International Electric Machines and Drives Conference. Niagara Falls：IEEE，2011：1403-1408.
[91] JIAN Linni，XU Guoqing，SONG Jianjian，et al. Optimum design for improving modulating-effect of coaxial magnetic gear using response surface methodology and genetic algorithm[J]. Progress in Electromagnetics Research，2011，116(116)：297-312.
[92] ZHAO Hang，LIU Chunhua，SONG Zaixin，et al. A fast optimization scheme of coaxial magnetic gears based on exact analytical model considering magnetic saturation[J]. IEEE Transactions on Industry Applications，2020，57(1)：437-447.
[93] WANG Yawei，FILIPPINI M，BACCO G，et al. Parametric design and optimization of magnetic gears with differential evolution method[J]. IEEE Transactions on Industry Applications，2019，55(4)：3445-3452.
[94] NIU Shuangxia，CHEN Ningning，HO S L，et al. Design optimization of magnetic gears using mesh adjustable finite-element algorithm for improved torque[J]. IEEE Transactions on Magnetics，2012，48(11)：4156-4159.
[95] JIAN Linni，XU Guoqing，GONG Yu，et al. Electromagnetic design and analysis of a novel magnetic-gear-integrated wind power generator using time-stepping finite element method[J]. Progress in Electromagnetics Research，2011，113：351-367.
[96] TALLERICO T F，CAMERON Z A，SCHEIDLER J J. Design of a magnetic gear for NASA's vertical lift quadrotor concept vehicle[C]//2019 AIAA/IEEE Electric Aircraft Technologies Symposium (EATS). Indianapolis：IEEE，2019：1-21.
[97] CHAU K T，ZHANG Dong，JIANG Jianzhong，et al. Design of a magnetic-geared outer-rotor permanent-magnet brushless motor for electric vehicles[J]. IEEE Transactions on Magnetics，2007，43(6)：2504-2506.
[98] ATALLAH K，WANG Jiabin，CALVERLEY S D，et al. Design and operation of a magnetic continuously variable transmission[J]. IEEE Transactions on Industry Applications，2012，48(4)：1288-1295.
[99] WANG Jiabing，ATALLAH K，CARVLEY S D，et al. A magnetic continuously variable transmission device[J]. IEEE Transactions on Magnetics，2011，47(10)：2815-2818.
[100] BAI Jingang，ZHENG Ping，TONG Chengde，et al. Characteristic analysis and verification of the magnetic-field-modulated brushless double-rotor machine[J]. IEEE Transactions on Industrial Electronics，2015，62(7)：023-4033.
[101] WANG Lili，SHEN Jianxin，WANG Yunchong，et al. A novel magnetic-geared outer-rotor permanent-magnet brushless motor[C]//4th IET International Conference on Power Electronics，Machines and Drives. York：IET，2008，33-36.
[102] ZHENG Ping，BAI Jingang，TONG Chengde，et al. Investigation of a novel radial magnetic-field-modulated brushless double-rotor machine used for HEVs[J]. IEEE Transactions on Magnetics，2012，49(3)：1231-1241.
[103] SUN Le，CHENG Ming，JIA Hongyun. Analysis of a novel magnetic-geared dual-rotor motor with complementary structure[J]. IEEE Transactions on Industrial Electronics，2015，62(11)：6737-6747.
[104] QU Ronghai，LI Dawei，WANG Jin. Relationship between magnetic gears and vernier machines[C]//International Conference on Electrical Machines & Systems. Beijing：IEEE，2011，1-6.
[105] WANG Yunchong，HO S L，FU Weinong，et al. A Novel brushless doubly fed generator for wind power generation[J]. IEEE Transactions on Magnetics，2012，48(11)：4172-4175.
[106] CHEN Yiduan，FU Weinong，WENG Xu. A concept of general flux-modulated electric machines based on a unified theory and its application to developing a novel doubly-fed dual-stator motor[J]. IEEE Transactions on Industrial Electronics，2017，64(12)：9914-9923.
[107] ATALLAH K，RENS J，MEZANI S，et al. A novel “pseudo” direct-drive brushless permanent magnet machine[J]. IEEE Transactions on Magnetics，2008，44(11)：4349-4352.
[108] 李祥林，程明，邹国棠. 聚磁式场调制永磁风力发电机输出特性改善的研究[J]. 中国电机工程学报，2015，35(16)：4198-4206. LI Xianglin，CHENG Ming，ZOU Guotang. Research on improvement of output characteristics of the flux-concentrating field-modulated permanent-magnet wind power generator[J]. Proceedings of the CSEE，2015，35(16)：4198-4206.
[109] 袁晓明，罗成，王溪堃，等. 一种旋转阀芯式电磁滑阀：中国，ZL201611203428.1[P]. 2018-10-16. YUAN Xiaoming，LUO Cheng，WANG Xikun，et at. The utility model relates to a rotating spool type el-ectromagnetic slide valve：China，ZL201611203428.1[P]. 2018-10-16.
[110] JOHNSON M，GARDNER M C，TOLIYAT H A，et al. Design，construction，and analysis of a large-scale inner stator radial flux magnetically geared generator for wave energy conversion[J]. IEEE Transactions on Industry Applications，2018，54(4)：3305-3314.
[111] MCGILTON B，CROZIER R，MCDONALD A，et al. Review of magnetic gear technologies and their applications in marine energy[J]. IET Renewable Power Generation，2018，12(2)：174-181.
[112] PUCHHAMMER G. Magnetic gearing versus conventional gearing in actuators for aerospace applications[C]//The 42nd Aerospace Mechanism Symposium. Maryland：NASA Goddard Space Flight Center，2014：175-181.
[113] PEREZ-DIAZ J L，DIEZ-JIMENEZ E，VALIENTE-BLANCO I，et al. Contactless mechanical components：Gears，torque limiters and bearings[J]. Machines，2014，2(4)：312-324.
[114] PFISTER P D，YIN Xin，FANG Youtong. Slotted permanent-magnet machines：General analytical model of magnetic fields，torque，eddy currents，and permanent-magnet power losses including the diffusion effect[J]. IEEE Transactions on Magnetics，2016，52(5)：1-13.
[115] QAZALBASH A A，SHARKH S M，IRENJI N T，et al. Rotor eddy loss in high-speed permanent magnet synchronous generators[J]. IET Electric Power Applications，2015，9(5)：370-376.
[116] RUOHO S，SANTA-NOKKI T，KOLEHMAINEN J，et al. Modeling magnet length in 2-D finite-element analysis of electric machines[J]. IEEE Transactions on Magnetics，2009，45(8)：3114-3120.
[117] HAO Xiuhong，ZHU Xuejun，ZHANG Hongfei. Free vibration of the electromechanical integrated magnetic gear system[J]. Journal of Vibroengineering，2015，17(3)：1120-1132．
[118] FRANK N W，PAKDELIAN S，TOLIYAT H A. Passive suppression of transient oscillations in the concentric planetary magnetic gear[J]. IEEE Transactions on Energy Conversion，2011，26(3)：933-939.
[119] MONTAGUE R，BINGHAM C，ATALLAH K. Servo control of magnetic gears[J]. IEEE/ASME Transactions on Mechatronics，2012，17(2)：269-278.