近极槽表贴式永磁力矩电机转矩性能研究
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摘要
数控机床直接驱动数控转台解决了以往间接传动引起的弹性变形、摩擦和存在反向间隙等问题,可以提高系统的动态性能。与此同时,高性能直接驱动数控转台对旋转进给永磁力矩电机也提出了更高的要求：一是电动机必须有足够的转矩输出能力,能够满足机床低速重切削和快速响应的要求；二是转矩波动要小,特别是在低速时仍能平稳运行,满足机床高精度加工和高精度定位的要求。可见,力矩电机的转矩性能直接关系到直接驱动系统的优劣,本文针对近极槽表贴式永磁力矩电机,为提高其转矩性能进行了如下研究。
采用解析法推导了基于定、转子全谐波磁动势的电磁转矩表达式。引入虚拟电机概念,推导出平均电磁转矩和纹波电磁转矩与定、转子磁动势各次时间和空间谐波间的定量关系,为消除和削弱近极槽表贴式永磁力矩电机的转矩脉动提供了理论依据。仿真分析了正弦电流供电时转子磁场正弦和非正弦分布时的电磁转矩性能,研究了槽口的大小对纹波转矩的影响,以及单层和双层绕组对转矩性能的影响。
针对近极槽永磁力矩电机重载运行时磁路易饱和的局限性,分析了隔齿隔相绕组电机的磁场分布特点,指出隔齿隔相绕组电机适合采用不等齿宽和齿顶宽结构降低电枢齿的磁通密度,提高电机的转矩输出能力。理论分析了隔齿隔相绕组电机极槽配合规律以及齿顶宽和齿宽的不同匹配影响转矩输出的规律。利用该方法设计了一台60槽50极表贴式永磁电机样机,测试结果与仿真结果相一致。
研究了齿顶漏磁引起的纹波转矩以及不等齿顶宽电机的齿槽转矩。解析法推导了近极槽永磁电机的单齿齿顶漏磁表达式,分析了全齿顶漏磁的特点,将周期的齿顶漏磁通函数通过傅里叶级数分解,运用法拉第电磁感应定律计算了各相绕组的反电动势谐波,进而分析其引起的纹波转矩。不等齿顶宽对气隙磁导的调制不同于等齿顶宽电机,利用气隙相对磁导简化模型推导了不等齿顶宽电机齿槽转矩的解析表达式,提出了调整辅助齿齿顶宽削弱齿槽转矩的方法。
为了进一步提高转台电机转矩输出能力和削弱纹波转矩,研究了双三相近极槽单元电机的极槽数组合规律和非正弦供电的有效性。双三相电机的每套三相绕组互差120°,两套绕组之间移30°。利用ANSOFT仿真比较了正弦电流供电下的96槽88极电机和96槽80极电机在三相和双三相接法时,以及双三相电机在正弦电流供电和非正弦电流供电时的平均转矩和纹波转矩,验证了双三相电机非正弦供电的可行性和有效性。
设计制造了一台60槽50极不等齿宽和齿顶宽永磁力矩伺服电机试验样机验证本文所提出的理论分析和方法的正确性和有效性。
Numerical control (NC) direct drive rotary table solves the elastic distortion, friction, backlash and other problems resulted from previous indirect drive, and can improve the dynamic performance of the system. At the same time, higher requirement is proposed for rotating feed permanent magnet (PM) torque servo motor:one is that the motor must have enough torque output capability to meet the requirements of low-speed heavy cutting and fast response; the other is that the torque ripple must be small, especially still running smoothly at low speed, in order to satisfy the requirements of high machining accuracy and high precision positioning. Thus, the torque performance of the torque servo motor is directly related to the quality of the direct drive system. The researches as follows are performed to enhance the torque performance of surface-mounted PM torque servo motor with similar number of poles and slots in this dissertation.
The electromagnetic torque expression based on the whole harmonic magnetic motive force (MMF) of stator and rotor is derived by analytical method. The quantitative relationship between the average torque, ripple torque and all the time and space harmonics of MMFs of stator and rotor is deduced by introducing the concept of virtual motor, in order to provide the theoretical basis for eliminating and weakening the torque ripple of surface-mounted PM torque motor with similar number of poles and slots. The torque performance is simulated and analyzed when the distribution of rotor magnetic field is sinusoidal and non-sinusoidal under sinusoidal current supply. The influences of the slot width size on the ripple torque and single and double layer winding on torque performance are studied.
For the limitation of the easy-saturation magnetic circuit of PM torque motor with similar number of poles and slots when overload running, the structure of unequal teeth width and unequal teeth tops width is suitable for the motor with different phase windings wound on alternate teeth through analyzing the magnetic field distribution characteristics of the motor, in order to reduce the flux density of armature tooth and to enhance the torque output capability. The law of the influences of the pole-slot coordination rule and the different matching of teeth tops width and teeth width of the motor with different phase windings wound on alternate teeth on torque output is theoretically analyzed. A prototype of60-slot50-pole surface-mounted PM motor is designed through using the method. Test results and simulation results are consistent.
The ripple torque caused by tooth top leakage flux and the cogging torque resulted from unequal teeth width are studied. The single zigzag leakage flux expression of PM motor with similar number of poles and slots is derived by analytical method, and the characteristics of whole zigzag leakage flux is analyzed. Also, the cycle zigzag leakage flux function is decomposed by Fourier series and the back electromotive force (EMF) harmonics of each phase winding are calculated by Faraday's law to further analyse the ripple torque. Unequal teeth tops width motor modulates the air gap permeance in the different way with equal teeth tops width one. The analytical expression of cogging torque in unequal teeth tops width motor is derived from the simplified model of air gap relative permeance. The method that the cogging torque is reduced by adjusting the assistant teeth tops width is put forward.
In order to further improve the torque output capability and to reduce the ripple torque of rotary table motor, the pole and slot number combining rule of dual three-phase unit motor with similar number of poles and slots and the validity of non-sinusoidal supply are studied. In each three-phase winding, the three windings are120°phase shifted with each other, and the two three-phase windings are30°phase shifted one from another. The average torques and ripple torques of96-slot88-pole motor and96-slot80-pole motor in two different situations are simulated and compared by using ANSOFT. One situation is that the motor windings are respectively connected to be three-phase winding and dual three-phase winding under sinusoidal current supply. The other is that the motor windings are connected to be dual three-phase winding under sinusoidal current and non-sinusoidal current supply respectively. The feasibility and validity of the dual three-phase motor under non-sinusoidal supply are verified.
A60-slot50-pole PM torque servo motor with unequal teeth width and unequal teeth tops width is designed and manufactured to prove the correctness and effectiveness of the proposed theoretical analysis and method.
采用解析法推导了基于定、转子全谐波磁动势的电磁转矩表达式。引入虚拟电机概念,推导出平均电磁转矩和纹波电磁转矩与定、转子磁动势各次时间和空间谐波间的定量关系,为消除和削弱近极槽表贴式永磁力矩电机的转矩脉动提供了理论依据。仿真分析了正弦电流供电时转子磁场正弦和非正弦分布时的电磁转矩性能,研究了槽口的大小对纹波转矩的影响,以及单层和双层绕组对转矩性能的影响。
针对近极槽永磁力矩电机重载运行时磁路易饱和的局限性,分析了隔齿隔相绕组电机的磁场分布特点,指出隔齿隔相绕组电机适合采用不等齿宽和齿顶宽结构降低电枢齿的磁通密度,提高电机的转矩输出能力。理论分析了隔齿隔相绕组电机极槽配合规律以及齿顶宽和齿宽的不同匹配影响转矩输出的规律。利用该方法设计了一台60槽50极表贴式永磁电机样机,测试结果与仿真结果相一致。
研究了齿顶漏磁引起的纹波转矩以及不等齿顶宽电机的齿槽转矩。解析法推导了近极槽永磁电机的单齿齿顶漏磁表达式,分析了全齿顶漏磁的特点,将周期的齿顶漏磁通函数通过傅里叶级数分解,运用法拉第电磁感应定律计算了各相绕组的反电动势谐波,进而分析其引起的纹波转矩。不等齿顶宽对气隙磁导的调制不同于等齿顶宽电机,利用气隙相对磁导简化模型推导了不等齿顶宽电机齿槽转矩的解析表达式,提出了调整辅助齿齿顶宽削弱齿槽转矩的方法。
为了进一步提高转台电机转矩输出能力和削弱纹波转矩,研究了双三相近极槽单元电机的极槽数组合规律和非正弦供电的有效性。双三相电机的每套三相绕组互差120°,两套绕组之间移30°。利用ANSOFT仿真比较了正弦电流供电下的96槽88极电机和96槽80极电机在三相和双三相接法时,以及双三相电机在正弦电流供电和非正弦电流供电时的平均转矩和纹波转矩,验证了双三相电机非正弦供电的可行性和有效性。
设计制造了一台60槽50极不等齿宽和齿顶宽永磁力矩伺服电机试验样机验证本文所提出的理论分析和方法的正确性和有效性。
Numerical control (NC) direct drive rotary table solves the elastic distortion, friction, backlash and other problems resulted from previous indirect drive, and can improve the dynamic performance of the system. At the same time, higher requirement is proposed for rotating feed permanent magnet (PM) torque servo motor:one is that the motor must have enough torque output capability to meet the requirements of low-speed heavy cutting and fast response; the other is that the torque ripple must be small, especially still running smoothly at low speed, in order to satisfy the requirements of high machining accuracy and high precision positioning. Thus, the torque performance of the torque servo motor is directly related to the quality of the direct drive system. The researches as follows are performed to enhance the torque performance of surface-mounted PM torque servo motor with similar number of poles and slots in this dissertation.
The electromagnetic torque expression based on the whole harmonic magnetic motive force (MMF) of stator and rotor is derived by analytical method. The quantitative relationship between the average torque, ripple torque and all the time and space harmonics of MMFs of stator and rotor is deduced by introducing the concept of virtual motor, in order to provide the theoretical basis for eliminating and weakening the torque ripple of surface-mounted PM torque motor with similar number of poles and slots. The torque performance is simulated and analyzed when the distribution of rotor magnetic field is sinusoidal and non-sinusoidal under sinusoidal current supply. The influences of the slot width size on the ripple torque and single and double layer winding on torque performance are studied.
For the limitation of the easy-saturation magnetic circuit of PM torque motor with similar number of poles and slots when overload running, the structure of unequal teeth width and unequal teeth tops width is suitable for the motor with different phase windings wound on alternate teeth through analyzing the magnetic field distribution characteristics of the motor, in order to reduce the flux density of armature tooth and to enhance the torque output capability. The law of the influences of the pole-slot coordination rule and the different matching of teeth tops width and teeth width of the motor with different phase windings wound on alternate teeth on torque output is theoretically analyzed. A prototype of60-slot50-pole surface-mounted PM motor is designed through using the method. Test results and simulation results are consistent.
The ripple torque caused by tooth top leakage flux and the cogging torque resulted from unequal teeth width are studied. The single zigzag leakage flux expression of PM motor with similar number of poles and slots is derived by analytical method, and the characteristics of whole zigzag leakage flux is analyzed. Also, the cycle zigzag leakage flux function is decomposed by Fourier series and the back electromotive force (EMF) harmonics of each phase winding are calculated by Faraday's law to further analyse the ripple torque. Unequal teeth tops width motor modulates the air gap permeance in the different way with equal teeth tops width one. The analytical expression of cogging torque in unequal teeth tops width motor is derived from the simplified model of air gap relative permeance. The method that the cogging torque is reduced by adjusting the assistant teeth tops width is put forward.
In order to further improve the torque output capability and to reduce the ripple torque of rotary table motor, the pole and slot number combining rule of dual three-phase unit motor with similar number of poles and slots and the validity of non-sinusoidal supply are studied. In each three-phase winding, the three windings are120°phase shifted with each other, and the two three-phase windings are30°phase shifted one from another. The average torques and ripple torques of96-slot88-pole motor and96-slot80-pole motor in two different situations are simulated and compared by using ANSOFT. One situation is that the motor windings are respectively connected to be three-phase winding and dual three-phase winding under sinusoidal current supply. The other is that the motor windings are connected to be dual three-phase winding under sinusoidal current and non-sinusoidal current supply respectively. The feasibility and validity of the dual three-phase motor under non-sinusoidal supply are verified.
A60-slot50-pole PM torque servo motor with unequal teeth width and unequal teeth tops width is designed and manufactured to prove the correctness and effectiveness of the proposed theoretical analysis and method.
引文
[1]梁铖,刘建群.五轴联动数控机床技术现状与发展趋势多.机械制造,2010,48(1)：5-7.
[2]刘士玉.五轴联动龙门加工中心现状与发展策略.制造技术与机床,2008,(8)：37-40.
[3]高莹,赵宏安,董建军.VHT系列五轴联动立式车铣复合加工中心的设计.组合机床与自动化加工技术,2010,(11)：80-82.
[4]赵宏安,张然,董建军等.直驱转台技术在立式车铣复合加工中心上的应用.制造技术与机床,2011,(4)：37-39.
[5]张文博,李焱,高秀峰等.几种数控机床回转进给机构的传动形式.机械传动,2011,35(5)：76-80.
[6]冯长征.电机现代控制技术CAD/CAM与制造业信息化,2011,(6)：71-73.
[7]Hendershot J R, Miller T J E. Design of brushless permanent-magnet motors. Oxford:Clarendon press,1994.
[8]Cros J, Viarouge P. Synthesis of high performance PM motors with concentrated windings. IEEE Transactions on Energy Conversion,2002,17(2):248-253.
[9]Spooner E, Williamson A C, Sci Lab, et al. Direct coupled, permanent magnet generators for wind turbine applications. IEE Proceedings on Electric Power Applications,1996,143(1):1-8.
[10]Florence Libert. Design, optimization and comparison of permanent magnet motors for a low-speed direct-driven mixer(PhD thesis). Sweden, Royal Institute of Technology,2004.
[11]谭建成.三相无刷直流电动机分数槽近极槽槽极数组合规律研究(连载之一).微电机,2007,40(12)：70-86.
[12]谭建成.三相无刷直流电动机分数槽近极槽槽极数组合规律研究(连载之二).微电机,2008,41(1)：52-56.
[13]董婷.直接驱动数控转台永磁环形力矩电机及其控制策略的研究(博士学位论文).沈阳：沈阳工业大学,2010.
[14]EL-Refaie A M, Shah M R, Qu R., et al. Effect of number of phases on losses in conducting sleeves of high speed surface PM machine rotors.42nd IEEE IAS Annu. Meeting on Industry Applications, New Orleans, LA,2007:1522-1529.
[15]EL-Refaie A M, Shah M R, Qu R, et al. Effect of number of phases on losses in conducting sleeves of surface PM machine rotors equipped with fractional-slot concentrated windings. IEEE Transactions on Industry Applications,2008,44(5):1522-1532.
[16]Meier F. Permanent-magnet synchronous machines with non-overlapping concentratedwindings for low-speed direct-drive applications(PhD thesis). Sweden, Royal Institute of Technology,2008.
[17]Magnussen. F, Sadarangani C. Winding factors and joule losses of permanent magnet machines with concentrated windings. IEEE International Conference on Electric Machines and Drives,2003, 1:333-339.
[18]谭建成.三相无刷直流电动机分数槽近极槽槽极数组合规律研究(连载之三).微电机,2008,41(1)：52-56.
[19]Skaar S E, Krφvel Φ, Nilsen R. Distribution, coil-span and winding factors for PM machines with concentrated windings. International Conference on Electrical Machines (ICEM), Chania,Greece, 2006.
[20]Bianchi N, Bolognani S, Grezzani G. Design considerations for fractional-slot winding configurations of synchronous machines. IEEE Transactions on Industry Applications,2006,42(4): 997-1006.
[21]Bianchi N, Dai Pre M. Use of the star of slots in designing fractional-slot single-layer synchronous motors. IEE Proceedings on Electric Power Applications,153(3):997-1006.
[22]Ishak D, Zhu Z Q, Howe D. Comparative study of permanent magnet brushless motors with all teeth and alternative teeth windings. Second International Conference on Power Electronics, Machines and Drives,2004,2:834-839.
[23]Ishak D, Zhu Z Q, Howe D. Comparison of PM brushless motors, having either all teeth or alternate teeth wound. IEEE Transactions on Energy Convers,2006,21(1):95-103.
[24]Popescu M, Dorrell D G, Ionel D, et al. Single and double layer windings in fractional slot-per-pole PM machines-effects on motor performance.34th Annual Conference of IEEE, Industrial Electronics, Orlando, FL,2008:2055-2060.
[25]Hwang C C, Cheng S P, Chang C M. Design of high-performance spindle motors with single-layer concentrated windings and unequal tooth widths. IEEE Transactions on Magnetics,2005,41(2): 971-973.
[26]Germishuizen J J, Kamper M J. IPM traction machine with single layer non-overlapping concentrated windings. IEEE Transactions on Industry Applications,2009,45(4):1387-1394.
[27]D. Ishak, Z Q Zhu, D Howe. Permanent magnet brushless machines with unequal tooth widths and similar slot and pole numbers. IEEE Transactions on Industry Applications,2005,41(2):584-590.
[28]EL-Refaie A M, Jahns T M. Impact of winding layer number and magnet type on synchronous surface PM machines designed for wide constant-power speed range operation. IEEE Transactions on Energy Conversion,2008,23(1):53-60.
[29]Reddy P B, Jahns T M, El-Refaie A M. Impact of winding layer number and slot/pole combination on ac armature losses of synchronous surface PM machines designed for wide constant-power speed range operation. IEEE, Industry Applications Society Annual Meeting, Edmonton, Alta,2008:1-8.
[30]Cistelecan M V, Ferreira F J T E, Popescu M. Three phase tooth-concentrated interspersed windings with low space harmonic content.2010 XIX International Conference on Electrical Machines, Rome,2010:1-60.
[31]Cistelecan M V, Ferreira F J T E, Three phase tooth-concentrated multiple-layer fractional windings with low space harmonic content.2010 IEEE on Energy Conversion Congress and Exposition, Atlanta, GA 2010:1399-1405.
[32]Reddy P B, EL-Refaie A M, Kum-Kang Huh. Effect of number of layers on performance of fractional-slot concentrated-windings interior permanent magnet machines.2011 IEEE 8th International Conference on Power Electronics and ECCE Asia,2011:1921-1928.
[33]Alberti L, Bianchi N. Theory and design of fractional-slot multilayer windings.2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ,2011:3112-3119.
[34]Atallah K, Howe D, Mellor P H, et al. Rotor loss in permanent-magnet brushless AC machines. IEEE Transactions on Industry Applications,2000,36(6):1612-1618.
[35]Toda H, Xia Z, Wang J, et al. Rotor eddy-current loss in permanent magnet brushless machines. IEEE Transactions on Magnetics,2004,40(4):2104-2106.
[36]Ishak D, Zhu Z Q, Howe D. Analytical prediction of rotor eddy current losses in permanent magnet brushless machines with all teeth and alternate teeth windings-Part I:Polar co-ordinate model.7th International Conference on Electrical Machines and Systems,2004.
[37]Ishak D, Zhu Z Q, Howe D. Analytical prediction of rotor eddy current losses in permanent magnet brushless machines with all teeth and alternate teeth windings-Part II:Rectangular co-ordinate model.7th International Conference on Electrical Machines and Systems,2004.
[38]Zhu Z Q, Ng K, Schofield N, et al. Improved analytical modeling of rotor eddy current loss in brushless machines equipped with surfacemounted permanent magnets. IEE Proceedings-Electric Power Applications,2004,151(6):641-650.
[39]Nakano M, Kometani H, Kawamura M. A study on eddy-current losses in rotors of surface permanent-magnet synchronous machines. IEEE Transactions on Industry Applications,2006,42(2), 429-435.
[40]Ede J, Atallah K, Jewell, G, et al. Effect of axial segmentation of permanent magnets on rotor loss in modular permanent-magnet brushless machines. IEEE Transactions on Industry Applications, 2007,43(5):1207-1213.
[41]Wang J, Atallah K, Chin R, et al. Rotor eddy-current loss in permanent-magnet brushless AC machines. IEEE Transactions on Magnetics,2010,46(7):2701-2707.
[42]Bianchi N, Fornasiero. Impact of mmf space harmonic on rotor losses in fractional-slot permanent-magnet machines. IEEE Transactions on Energy Conversion,2009,24(2):323-328.
[43]Bianchi N, Fornasiero. Index of rotor losses in three-phase fractionalslot permanent magnet machines. IET, Electric Power Applications,2009,3(5):381-388.
[44]Polinder H, Hoeijmakers M, Scuotto M. Eddy-current losses in the solid back-iron of PM machines for different concentrated fractional pitch windings. IEEE International Electric Machines & Drives Conference,2007,1:652-657.
[45]Cheng Y S, Zhu Z, Howe D. Vibration of PM brushless machines having a fractional number of slots per pole. IEEE Transactions on Magnetics,2002,42(10):3395-3397.
[46]Zhu Z, Ishak D, Howe D, et al. Unbalanced magnetic forces in permanent-magnet brushless machines with diametrically asymmetric phase windings. IEEE Transactions on Industry Applications,2007,43(6):1544-1553.
[47]Wang J, Xia Z, Long S, et al. Radial force density and vibration characteristics of modular permanent magnet brushless ac machine. IEE Proceedings-Electric Power Applications,2006, 53(6):793-801.
[48]Zhu Z, Xia Z, Wu L, et al. Influence of slot and pole number combination on radial force and vibration modes in fractional slot PM brushless machines having single-and double-layer windings. IEEE, Energy Conversion Congress and Exposition,2009:3443-3450.
[49]Zhu Z, Xia Z, Wu L, et al. Analytical modeling and finite element computation of radial vibration force in fractional-slot permanentmagnet brushless machines. IEEE Transactions on Industry Applications,2010,46(5):1908-1918.
[50]Wu L J, Zhu Z Q, Chen J T, et al. An analytical model of unbalanced magnetic force in fractional-slot surface-mounted permanent magnet machines. IEEE Transactions on Magnetics, 2010,46(7):2686-2700.
[51]Wu L J, Zhu Z Q, Chen J T, et al. An analytical model of unbalanced magnetic force in fractional-slot surface-mounted permanent magnet machines. IEEE Transactions on Magnetics, 2010,46(7):2686-2700.
[52]杨浩东,陈阳生.分数槽永磁同步电机电磁振动的分析与抑制.中国电机工程学报,2011, 31(24)：83-89.
[53]Krotsch J, Ley T, Piepenbreier B. Reduction of torque and radial force fluctuation in permanent magnet synchronous motors by means of multi-objective optimization.1st International, Electric Drives Production Conference,2011:40-48.
[54]Krotsch J, Piepenbreier B. Radial forces in external rotor permanent magnet synchronous motors with non-overlapping windings. IEEE Transactions on Industrial Electronics,2012,59(5): 2267-2276.
[55]Dorrell D G, Popescu M, Ionel D M. Unbalanced magnetic pull due to asymmetry and low-level static rotor eccentricity in fractional-slot brushless permanent-magnet motors with surface-magnet and consequent-pole rotors. IEEE Transactions on Magnetics,2010,46(7):2675-2685.
[56]Fujishiro Satoshi,Ishikawa Kazumi,Kikuchi Shinki,et al.Design of outer-rotor-type multipolar switched reluctance motor for electric vehicle. Journal of Applied Physics,2006,99(8):324-326.
[57]Ando Kazumasal,Yamada Atsushi1,Miki Ichirol,et al.Study on improvement of efficiency for outer rotor type of interior permanent magnet synchronous motor. International Symposium on Power Electronics,Electrical Drives,Automation and Motion,Ischia,2008:599-602.
[58]Ben Hamadou, G., Masmoudi, A., Abdennadher, I. et al.. Design of a Single-Stator Dual-Rotor Permanent-Magnet Machine. IEEE Transactions on Magnetics,2009,45(1):127-132
[59]徐衍亮,王法庆,冯开杰等.双转子永磁同电机电感参数、永磁电势及齿槽转矩.电工技术学报,2001,22(9)：40-44
[60]Ronghai Qu; Lipo, T.A.. Dual-rotor, radial-flux, toroidally wound, permanent-magnet machines. IEEE Transactions on Industry Applications,2003,39(6):1665-1673.
[61]曹江华,杨向宇,肖如晶.双转子径向永磁电机的设计与有限元分析.电机与控制应用,2010,37(1)：8-12.
[62]王峥.拼块式和铰链式无刷直流电动机.微特电机,2010,38(5)：16-21.
[63]Libert F., Soulard J.. Manufacturing methods of stator cores with concentrated windings. The 3rd IET International Conference on Power Electronics, Machines and Drives,2006:676-680.
[64]A. G. Jack, B. C.Mecrow, P. G. Dickinson, et al. Permanent magnet machines with powdered iron cores and pressed windings. IEEE Transactions on Industry Applications,2000,30(4):1077-1084.
[65]J. Cros, P. Viarouge, C. Gelinas. Design of PM brushless motors using iron-resin composites for automotive applications, the 33th IAS Annual Meeting, St. Louis, MO, USA.1998,1:5-11.
[66]H. Akita, Y. Nakahara, N. Miyake, et al. New core structure and manufacturing method for high efficiency of permanent magnet otors. the 38th IAS Annual Meeting, Salt Lake City, UT,2003, 1:367-372.
[67]J. Cros, P. Viarouge, R. Carlson, et al. Comparison of brushless DC motors with concentrated winding and segmented stator. in Proc. ICEM,2004, p.761.
[68]黄先进.采用集中绕组和高强度冷却的高转矩密度永磁电机.电力电子,2008,(1)：17-21.
[69]赵品志,杨贵杰,李勇.三次谐波注入式五相永磁同步电机转矩密度优化.中国电机工程学报,2010,30(33)：71-77.
[70]Parsa L., Toliyat H.A.. Five-phase permanent-magnet motor drives. IEEE Transactions on Industry Applications,2005,41(1):30-37.
[71]Ishak, D., Zhu, Z.Q., Howe, D.. Permanent-magnet brushless machines with unequal tooth widths and similar slot and pole numbers. IEEE Transactions on Industry Applications,2005, 41(2):584-590.
[72]王成元,王贵子,夏加宽.机床转台直接驱动力矩电机的转矩优化设计.沈阳工业大学学报,2008,30(1)：6-10.
[73]Xia Jiakuan, Dong Ting, Wang Chengyuan, et al. Low speed high torque PMSM design based on unequal teeth structure. International Conference on Electrical Machines and Systems, Wuhan, China,2008:3274-3277.
[74]董婷,黄伟,王成元.不等齿顶宽间隔绕组对直接驱动转台电机转矩特性的影响.电工技术学报,2010,25(8)：12-17,30.
[75]Senol Seray, Ustun, Ozgur. Design, analysis and implementation of a subfractional slot concentrated winding BLDCM with unequal tooth widths.37th Annual Conference on IEEE Industrial Electronics Society,2011:1807-1812.
[76]Ben Hamadou G, Masmoudi A, Abdennadher I. Design of a single-stator dual-rotor permanent-magnet machine. IEEE Transactions on Magnetics,2009,45(1):127-132.
[77]Kazmin E V, Lomonova E A, Paulides J J H. Brushless traction pm machines using commercial drive technology,Part Ⅰ:design methodology and motor design. International Conference on Electrical Machines and Systems,2008:3801-3809.
[78]Kazmin E V, Lomonova E A, Paulides J J H. Brushless traction PM machines using commercial drive technology,Part II:comparative study of the motorconfigurations. International Conference on Electrical Machines and Systems,2008:3772-3780.
[79]Wrobel R, Mellor P H. Design considerations of a direct drive brushless machine with concentrated windings. IEEE Transactions on Energy Conversion,2008,23(1):1-8.
[80]Ombach G, Junak J. Two rotors designs'comparison of permanent magnet brushless synchronous motor for an electric power steering application. European Conference on Power Electronics and Applications,2007:1-9.
[81]Ombach G, Junak J. Comparison of double-layer interior permanent magnet synchronous motor design with two different pole numbers.18th International Conference on Electrical Machines,2008: 1-6.
[82]Feng Guihong, Wang Lifeng, Zhang Bingyi, et al. Analysis of magnetic field for low speed and high torque permanent magnet synchronous machine. Sixth International Conference on Electrical Machines and Systems,2003,2:778-781.
[83]Scuiller F, Charpentier J, Semail E. Multi-star multi-phase winding for a high power naval propulsion machine with low ripple torques and high fault tolerant ability.2010 IEEE, Vehicle Power and Propulsion Conference,2010:1-5.
[84]Yang Yee Pien, Yang Shih Chin, LIU Jieng Jang. Optimal design and control of a torque motor for machine tools. J. Electromagnetic Analysis& Applications,2009,1:220-228.
[85]Feng Guihong, Wang Lifeng, Zhang Bingyi, et al. Multi-star multi-phase winding for a high power naval propulsion machine with low ripple torques and high fault tolerant ability. Sixth International Conference on Electrical Machines and Systems,2003,2:778-781.
[86]许实章.交流电机的绕组理论.北京：机械工业出版社,1985.
[87]陈益广,潘玉玲,贺鑫.永磁同步电机分数槽集中绕组磁动势.电工技术学报,2010,25(10)：30-36.
[88]许善椿,金波,李春廷等.交流电机定子分数槽绕组的谐波磁势问题.大电机技术,1999,3：1-5.
[89]Proca A B, Keyhani A, EL-Antably A, et al. Analytical model for permanent magnet motors with surface mounted magnets. IEEE Transactions on Energy Conversion,2003,18(3):386-391.
[90]Germishuizen J J. Kamper M J. IPM traction machine with single layer non-overlapping concentrated windings. IEEE Transactions on Industry Applications,2009,45(4):1387-1394.
[91]Hwang C C, Cheng S P, Chang C M. Design of high-performance spindle motors with single-layer concentrated windings and unequal tooth widths. IEEE Transactions on Magnetics,2005.41(2): 971-973.
[92]王兴华,励庆孚,王曙鸿.永磁无刷直流电机空载气隙磁场和绕组反电势的解析计算.中国电机工程学报,2003,23(3)：126-130.
[93]Shih-Chin Yang, Suzuki T, Lorenz R D, et al. Surface-permanent-magnet synchronous machine design for saliency-tracking self-sensing position estimation at zero and low speeds. IEEE Transactions on Industry Applications,2011,41(5):2103-2116.
[94]Qu R H, Lipo T A. Analysis and modeling of air gap & zigzag leakage fluxes in a surface mounted-PM machine. IEEE Transactions on Industry Applications,2004,40(1):121-127.
[95]Hwang S. M., Eom J. B., et al. Cogging torque and acoustic noise reduction in permanent magnet motors by teeth pairing. IEEE Transactions on Magnetics,2000,36(5):3144-3146.
[96]Hwang S. M., Eom J. B., Jung Y. H., et al. Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors. IEEE Transactions on Magnetics,2001, 37(4):2806-2809.
[97]杨玉波,王秀和,陈谢杰等.基于不等槽口宽配合的永磁电动机齿槽转矩削弱方法.电工技术学报,2005,20(3)：40-44.
[98]Barcaro M, Bianchi N, Magnussen F. Six-phase supply feasibility using a PM fractional-slot dual winding machine. IEEE Transactions on Industry Applications,2011,47(5):2042-2050.
[99]Barcaro M, Bianchi N, Magnussen F. Analysis and tests of a dual three-phase 12-slot 10-pole permanent magnet motor. IEEE Transactions on Industry Applications,2010,46(6):2355-2362.
[100]齐歌.双三相永磁同步电动机交互饱和模型与特性研究(博士学位论文).武汉：华中科技大学,2010.
[101]El-Refaie A M, Shah M R, Ronghai Qu, et al. Effect of number of phases on losses in conducting sleeves of surface pm machine rotors equipped with fractional-slot concentrated windings. IEEE Transactions on Industry Applications,2008,44(5):1522-1532.
[102]杨金波,李铁才,杨贵杰.一相开路双三相永磁同步电机建模与控制.电工技术学报,2011,26(10)：167-173,187.
[103]袁飞雄,黄声华,龙文枫.六相永磁同步电机谐波电流抑制技术.电工技术学报,2011,26(9)：31-36.
[104]韩光鲜,程智,王宗培.永磁同步电动机齿槽定位转矩的研究.伺服控制,2006,2：21-24.
[105]程树康,宫海龙,柴凤等.永磁轮毂电机齿槽转矩研究.中国电机工程学报,2009,29(30)：47-51.
[2]刘士玉.五轴联动龙门加工中心现状与发展策略.制造技术与机床,2008,(8)：37-40.
[3]高莹,赵宏安,董建军.VHT系列五轴联动立式车铣复合加工中心的设计.组合机床与自动化加工技术,2010,(11)：80-82.
[4]赵宏安,张然,董建军等.直驱转台技术在立式车铣复合加工中心上的应用.制造技术与机床,2011,(4)：37-39.
[5]张文博,李焱,高秀峰等.几种数控机床回转进给机构的传动形式.机械传动,2011,35(5)：76-80.
[6]冯长征.电机现代控制技术CAD/CAM与制造业信息化,2011,(6)：71-73.
[7]Hendershot J R, Miller T J E. Design of brushless permanent-magnet motors. Oxford:Clarendon press,1994.
[8]Cros J, Viarouge P. Synthesis of high performance PM motors with concentrated windings. IEEE Transactions on Energy Conversion,2002,17(2):248-253.
[9]Spooner E, Williamson A C, Sci Lab, et al. Direct coupled, permanent magnet generators for wind turbine applications. IEE Proceedings on Electric Power Applications,1996,143(1):1-8.
[10]Florence Libert. Design, optimization and comparison of permanent magnet motors for a low-speed direct-driven mixer(PhD thesis). Sweden, Royal Institute of Technology,2004.
[11]谭建成.三相无刷直流电动机分数槽近极槽槽极数组合规律研究(连载之一).微电机,2007,40(12)：70-86.
[12]谭建成.三相无刷直流电动机分数槽近极槽槽极数组合规律研究(连载之二).微电机,2008,41(1)：52-56.
[13]董婷.直接驱动数控转台永磁环形力矩电机及其控制策略的研究(博士学位论文).沈阳：沈阳工业大学,2010.
[14]EL-Refaie A M, Shah M R, Qu R., et al. Effect of number of phases on losses in conducting sleeves of high speed surface PM machine rotors.42nd IEEE IAS Annu. Meeting on Industry Applications, New Orleans, LA,2007:1522-1529.
[15]EL-Refaie A M, Shah M R, Qu R, et al. Effect of number of phases on losses in conducting sleeves of surface PM machine rotors equipped with fractional-slot concentrated windings. IEEE Transactions on Industry Applications,2008,44(5):1522-1532.
[16]Meier F. Permanent-magnet synchronous machines with non-overlapping concentratedwindings for low-speed direct-drive applications(PhD thesis). Sweden, Royal Institute of Technology,2008.
[17]Magnussen. F, Sadarangani C. Winding factors and joule losses of permanent magnet machines with concentrated windings. IEEE International Conference on Electric Machines and Drives,2003, 1:333-339.
[18]谭建成.三相无刷直流电动机分数槽近极槽槽极数组合规律研究(连载之三).微电机,2008,41(1)：52-56.
[19]Skaar S E, Krφvel Φ, Nilsen R. Distribution, coil-span and winding factors for PM machines with concentrated windings. International Conference on Electrical Machines (ICEM), Chania,Greece, 2006.
[20]Bianchi N, Bolognani S, Grezzani G. Design considerations for fractional-slot winding configurations of synchronous machines. IEEE Transactions on Industry Applications,2006,42(4): 997-1006.
[21]Bianchi N, Dai Pre M. Use of the star of slots in designing fractional-slot single-layer synchronous motors. IEE Proceedings on Electric Power Applications,153(3):997-1006.
[22]Ishak D, Zhu Z Q, Howe D. Comparative study of permanent magnet brushless motors with all teeth and alternative teeth windings. Second International Conference on Power Electronics, Machines and Drives,2004,2:834-839.
[23]Ishak D, Zhu Z Q, Howe D. Comparison of PM brushless motors, having either all teeth or alternate teeth wound. IEEE Transactions on Energy Convers,2006,21(1):95-103.
[24]Popescu M, Dorrell D G, Ionel D, et al. Single and double layer windings in fractional slot-per-pole PM machines-effects on motor performance.34th Annual Conference of IEEE, Industrial Electronics, Orlando, FL,2008:2055-2060.
[25]Hwang C C, Cheng S P, Chang C M. Design of high-performance spindle motors with single-layer concentrated windings and unequal tooth widths. IEEE Transactions on Magnetics,2005,41(2): 971-973.
[26]Germishuizen J J, Kamper M J. IPM traction machine with single layer non-overlapping concentrated windings. IEEE Transactions on Industry Applications,2009,45(4):1387-1394.
[27]D. Ishak, Z Q Zhu, D Howe. Permanent magnet brushless machines with unequal tooth widths and similar slot and pole numbers. IEEE Transactions on Industry Applications,2005,41(2):584-590.
[28]EL-Refaie A M, Jahns T M. Impact of winding layer number and magnet type on synchronous surface PM machines designed for wide constant-power speed range operation. IEEE Transactions on Energy Conversion,2008,23(1):53-60.
[29]Reddy P B, Jahns T M, El-Refaie A M. Impact of winding layer number and slot/pole combination on ac armature losses of synchronous surface PM machines designed for wide constant-power speed range operation. IEEE, Industry Applications Society Annual Meeting, Edmonton, Alta,2008:1-8.
[30]Cistelecan M V, Ferreira F J T E, Popescu M. Three phase tooth-concentrated interspersed windings with low space harmonic content.2010 XIX International Conference on Electrical Machines, Rome,2010:1-60.
[31]Cistelecan M V, Ferreira F J T E, Three phase tooth-concentrated multiple-layer fractional windings with low space harmonic content.2010 IEEE on Energy Conversion Congress and Exposition, Atlanta, GA 2010:1399-1405.
[32]Reddy P B, EL-Refaie A M, Kum-Kang Huh. Effect of number of layers on performance of fractional-slot concentrated-windings interior permanent magnet machines.2011 IEEE 8th International Conference on Power Electronics and ECCE Asia,2011:1921-1928.
[33]Alberti L, Bianchi N. Theory and design of fractional-slot multilayer windings.2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ,2011:3112-3119.
[34]Atallah K, Howe D, Mellor P H, et al. Rotor loss in permanent-magnet brushless AC machines. IEEE Transactions on Industry Applications,2000,36(6):1612-1618.
[35]Toda H, Xia Z, Wang J, et al. Rotor eddy-current loss in permanent magnet brushless machines. IEEE Transactions on Magnetics,2004,40(4):2104-2106.
[36]Ishak D, Zhu Z Q, Howe D. Analytical prediction of rotor eddy current losses in permanent magnet brushless machines with all teeth and alternate teeth windings-Part I:Polar co-ordinate model.7th International Conference on Electrical Machines and Systems,2004.
[37]Ishak D, Zhu Z Q, Howe D. Analytical prediction of rotor eddy current losses in permanent magnet brushless machines with all teeth and alternate teeth windings-Part II:Rectangular co-ordinate model.7th International Conference on Electrical Machines and Systems,2004.
[38]Zhu Z Q, Ng K, Schofield N, et al. Improved analytical modeling of rotor eddy current loss in brushless machines equipped with surfacemounted permanent magnets. IEE Proceedings-Electric Power Applications,2004,151(6):641-650.
[39]Nakano M, Kometani H, Kawamura M. A study on eddy-current losses in rotors of surface permanent-magnet synchronous machines. IEEE Transactions on Industry Applications,2006,42(2), 429-435.
[40]Ede J, Atallah K, Jewell, G, et al. Effect of axial segmentation of permanent magnets on rotor loss in modular permanent-magnet brushless machines. IEEE Transactions on Industry Applications, 2007,43(5):1207-1213.
[41]Wang J, Atallah K, Chin R, et al. Rotor eddy-current loss in permanent-magnet brushless AC machines. IEEE Transactions on Magnetics,2010,46(7):2701-2707.
[42]Bianchi N, Fornasiero. Impact of mmf space harmonic on rotor losses in fractional-slot permanent-magnet machines. IEEE Transactions on Energy Conversion,2009,24(2):323-328.
[43]Bianchi N, Fornasiero. Index of rotor losses in three-phase fractionalslot permanent magnet machines. IET, Electric Power Applications,2009,3(5):381-388.
[44]Polinder H, Hoeijmakers M, Scuotto M. Eddy-current losses in the solid back-iron of PM machines for different concentrated fractional pitch windings. IEEE International Electric Machines & Drives Conference,2007,1:652-657.
[45]Cheng Y S, Zhu Z, Howe D. Vibration of PM brushless machines having a fractional number of slots per pole. IEEE Transactions on Magnetics,2002,42(10):3395-3397.
[46]Zhu Z, Ishak D, Howe D, et al. Unbalanced magnetic forces in permanent-magnet brushless machines with diametrically asymmetric phase windings. IEEE Transactions on Industry Applications,2007,43(6):1544-1553.
[47]Wang J, Xia Z, Long S, et al. Radial force density and vibration characteristics of modular permanent magnet brushless ac machine. IEE Proceedings-Electric Power Applications,2006, 53(6):793-801.
[48]Zhu Z, Xia Z, Wu L, et al. Influence of slot and pole number combination on radial force and vibration modes in fractional slot PM brushless machines having single-and double-layer windings. IEEE, Energy Conversion Congress and Exposition,2009:3443-3450.
[49]Zhu Z, Xia Z, Wu L, et al. Analytical modeling and finite element computation of radial vibration force in fractional-slot permanentmagnet brushless machines. IEEE Transactions on Industry Applications,2010,46(5):1908-1918.
[50]Wu L J, Zhu Z Q, Chen J T, et al. An analytical model of unbalanced magnetic force in fractional-slot surface-mounted permanent magnet machines. IEEE Transactions on Magnetics, 2010,46(7):2686-2700.
[51]Wu L J, Zhu Z Q, Chen J T, et al. An analytical model of unbalanced magnetic force in fractional-slot surface-mounted permanent magnet machines. IEEE Transactions on Magnetics, 2010,46(7):2686-2700.
[52]杨浩东,陈阳生.分数槽永磁同步电机电磁振动的分析与抑制.中国电机工程学报,2011, 31(24)：83-89.
[53]Krotsch J, Ley T, Piepenbreier B. Reduction of torque and radial force fluctuation in permanent magnet synchronous motors by means of multi-objective optimization.1st International, Electric Drives Production Conference,2011:40-48.
[54]Krotsch J, Piepenbreier B. Radial forces in external rotor permanent magnet synchronous motors with non-overlapping windings. IEEE Transactions on Industrial Electronics,2012,59(5): 2267-2276.
[55]Dorrell D G, Popescu M, Ionel D M. Unbalanced magnetic pull due to asymmetry and low-level static rotor eccentricity in fractional-slot brushless permanent-magnet motors with surface-magnet and consequent-pole rotors. IEEE Transactions on Magnetics,2010,46(7):2675-2685.
[56]Fujishiro Satoshi,Ishikawa Kazumi,Kikuchi Shinki,et al.Design of outer-rotor-type multipolar switched reluctance motor for electric vehicle. Journal of Applied Physics,2006,99(8):324-326.
[57]Ando Kazumasal,Yamada Atsushi1,Miki Ichirol,et al.Study on improvement of efficiency for outer rotor type of interior permanent magnet synchronous motor. International Symposium on Power Electronics,Electrical Drives,Automation and Motion,Ischia,2008:599-602.
[58]Ben Hamadou, G., Masmoudi, A., Abdennadher, I. et al.. Design of a Single-Stator Dual-Rotor Permanent-Magnet Machine. IEEE Transactions on Magnetics,2009,45(1):127-132
[59]徐衍亮,王法庆,冯开杰等.双转子永磁同电机电感参数、永磁电势及齿槽转矩.电工技术学报,2001,22(9)：40-44
[60]Ronghai Qu; Lipo, T.A.. Dual-rotor, radial-flux, toroidally wound, permanent-magnet machines. IEEE Transactions on Industry Applications,2003,39(6):1665-1673.
[61]曹江华,杨向宇,肖如晶.双转子径向永磁电机的设计与有限元分析.电机与控制应用,2010,37(1)：8-12.
[62]王峥.拼块式和铰链式无刷直流电动机.微特电机,2010,38(5)：16-21.
[63]Libert F., Soulard J.. Manufacturing methods of stator cores with concentrated windings. The 3rd IET International Conference on Power Electronics, Machines and Drives,2006:676-680.
[64]A. G. Jack, B. C.Mecrow, P. G. Dickinson, et al. Permanent magnet machines with powdered iron cores and pressed windings. IEEE Transactions on Industry Applications,2000,30(4):1077-1084.
[65]J. Cros, P. Viarouge, C. Gelinas. Design of PM brushless motors using iron-resin composites for automotive applications, the 33th IAS Annual Meeting, St. Louis, MO, USA.1998,1:5-11.
[66]H. Akita, Y. Nakahara, N. Miyake, et al. New core structure and manufacturing method for high efficiency of permanent magnet otors. the 38th IAS Annual Meeting, Salt Lake City, UT,2003, 1:367-372.
[67]J. Cros, P. Viarouge, R. Carlson, et al. Comparison of brushless DC motors with concentrated winding and segmented stator. in Proc. ICEM,2004, p.761.
[68]黄先进.采用集中绕组和高强度冷却的高转矩密度永磁电机.电力电子,2008,(1)：17-21.
[69]赵品志,杨贵杰,李勇.三次谐波注入式五相永磁同步电机转矩密度优化.中国电机工程学报,2010,30(33)：71-77.
[70]Parsa L., Toliyat H.A.. Five-phase permanent-magnet motor drives. IEEE Transactions on Industry Applications,2005,41(1):30-37.
[71]Ishak, D., Zhu, Z.Q., Howe, D.. Permanent-magnet brushless machines with unequal tooth widths and similar slot and pole numbers. IEEE Transactions on Industry Applications,2005, 41(2):584-590.
[72]王成元,王贵子,夏加宽.机床转台直接驱动力矩电机的转矩优化设计.沈阳工业大学学报,2008,30(1)：6-10.
[73]Xia Jiakuan, Dong Ting, Wang Chengyuan, et al. Low speed high torque PMSM design based on unequal teeth structure. International Conference on Electrical Machines and Systems, Wuhan, China,2008:3274-3277.
[74]董婷,黄伟,王成元.不等齿顶宽间隔绕组对直接驱动转台电机转矩特性的影响.电工技术学报,2010,25(8)：12-17,30.
[75]Senol Seray, Ustun, Ozgur. Design, analysis and implementation of a subfractional slot concentrated winding BLDCM with unequal tooth widths.37th Annual Conference on IEEE Industrial Electronics Society,2011:1807-1812.
[76]Ben Hamadou G, Masmoudi A, Abdennadher I. Design of a single-stator dual-rotor permanent-magnet machine. IEEE Transactions on Magnetics,2009,45(1):127-132.
[77]Kazmin E V, Lomonova E A, Paulides J J H. Brushless traction pm machines using commercial drive technology,Part Ⅰ:design methodology and motor design. International Conference on Electrical Machines and Systems,2008:3801-3809.
[78]Kazmin E V, Lomonova E A, Paulides J J H. Brushless traction PM machines using commercial drive technology,Part II:comparative study of the motorconfigurations. International Conference on Electrical Machines and Systems,2008:3772-3780.
[79]Wrobel R, Mellor P H. Design considerations of a direct drive brushless machine with concentrated windings. IEEE Transactions on Energy Conversion,2008,23(1):1-8.
[80]Ombach G, Junak J. Two rotors designs'comparison of permanent magnet brushless synchronous motor for an electric power steering application. European Conference on Power Electronics and Applications,2007:1-9.
[81]Ombach G, Junak J. Comparison of double-layer interior permanent magnet synchronous motor design with two different pole numbers.18th International Conference on Electrical Machines,2008: 1-6.
[82]Feng Guihong, Wang Lifeng, Zhang Bingyi, et al. Analysis of magnetic field for low speed and high torque permanent magnet synchronous machine. Sixth International Conference on Electrical Machines and Systems,2003,2:778-781.
[83]Scuiller F, Charpentier J, Semail E. Multi-star multi-phase winding for a high power naval propulsion machine with low ripple torques and high fault tolerant ability.2010 IEEE, Vehicle Power and Propulsion Conference,2010:1-5.
[84]Yang Yee Pien, Yang Shih Chin, LIU Jieng Jang. Optimal design and control of a torque motor for machine tools. J. Electromagnetic Analysis& Applications,2009,1:220-228.
[85]Feng Guihong, Wang Lifeng, Zhang Bingyi, et al. Multi-star multi-phase winding for a high power naval propulsion machine with low ripple torques and high fault tolerant ability. Sixth International Conference on Electrical Machines and Systems,2003,2:778-781.
[86]许实章.交流电机的绕组理论.北京：机械工业出版社,1985.
[87]陈益广,潘玉玲,贺鑫.永磁同步电机分数槽集中绕组磁动势.电工技术学报,2010,25(10)：30-36.
[88]许善椿,金波,李春廷等.交流电机定子分数槽绕组的谐波磁势问题.大电机技术,1999,3：1-5.
[89]Proca A B, Keyhani A, EL-Antably A, et al. Analytical model for permanent magnet motors with surface mounted magnets. IEEE Transactions on Energy Conversion,2003,18(3):386-391.
[90]Germishuizen J J. Kamper M J. IPM traction machine with single layer non-overlapping concentrated windings. IEEE Transactions on Industry Applications,2009,45(4):1387-1394.
[91]Hwang C C, Cheng S P, Chang C M. Design of high-performance spindle motors with single-layer concentrated windings and unequal tooth widths. IEEE Transactions on Magnetics,2005.41(2): 971-973.
[92]王兴华,励庆孚,王曙鸿.永磁无刷直流电机空载气隙磁场和绕组反电势的解析计算.中国电机工程学报,2003,23(3)：126-130.
[93]Shih-Chin Yang, Suzuki T, Lorenz R D, et al. Surface-permanent-magnet synchronous machine design for saliency-tracking self-sensing position estimation at zero and low speeds. IEEE Transactions on Industry Applications,2011,41(5):2103-2116.
[94]Qu R H, Lipo T A. Analysis and modeling of air gap & zigzag leakage fluxes in a surface mounted-PM machine. IEEE Transactions on Industry Applications,2004,40(1):121-127.
[95]Hwang S. M., Eom J. B., et al. Cogging torque and acoustic noise reduction in permanent magnet motors by teeth pairing. IEEE Transactions on Magnetics,2000,36(5):3144-3146.
[96]Hwang S. M., Eom J. B., Jung Y. H., et al. Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors. IEEE Transactions on Magnetics,2001, 37(4):2806-2809.
[97]杨玉波,王秀和,陈谢杰等.基于不等槽口宽配合的永磁电动机齿槽转矩削弱方法.电工技术学报,2005,20(3)：40-44.
[98]Barcaro M, Bianchi N, Magnussen F. Six-phase supply feasibility using a PM fractional-slot dual winding machine. IEEE Transactions on Industry Applications,2011,47(5):2042-2050.
[99]Barcaro M, Bianchi N, Magnussen F. Analysis and tests of a dual three-phase 12-slot 10-pole permanent magnet motor. IEEE Transactions on Industry Applications,2010,46(6):2355-2362.
[100]齐歌.双三相永磁同步电动机交互饱和模型与特性研究(博士学位论文).武汉：华中科技大学,2010.
[101]El-Refaie A M, Shah M R, Ronghai Qu, et al. Effect of number of phases on losses in conducting sleeves of surface pm machine rotors equipped with fractional-slot concentrated windings. IEEE Transactions on Industry Applications,2008,44(5):1522-1532.
[102]杨金波,李铁才,杨贵杰.一相开路双三相永磁同步电机建模与控制.电工技术学报,2011,26(10)：167-173,187.
[103]袁飞雄,黄声华,龙文枫.六相永磁同步电机谐波电流抑制技术.电工技术学报,2011,26(9)：31-36.
[104]韩光鲜,程智,王宗培.永磁同步电动机齿槽定位转矩的研究.伺服控制,2006,2：21-24.
[105]程树康,宫海龙,柴凤等.永磁轮毂电机齿槽转矩研究.中国电机工程学报,2009,29(30)：47-51.