组合磁极结构的永磁电机解析法建模与分析
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摘要
磁极结构直接影响永磁电机气隙磁场的分布。提出一种组合双层Halbach阵列结构。利用叠加原理,采用标量磁位法对该结构电机中的气隙磁场进行了解析计算。同时,对于有齿尖结构的定子槽,通过改进的卡特系数对气隙长度进行等效。为了比较,同时分析得到了单层Halbach结构气隙磁密的最优值。在此基础上,通过改变双层结构磁极上下层的厚度比、上下层中间磁极极弧系数以及边磁磁化角度等参数变量,分析优化电机的气隙磁密,并计算优化后的双层结构永磁电机的气隙磁密、感应电动势和电磁转矩。计算结果表明,在永磁用量相等的前提下,双层Halbach结构永磁电机的电磁性能优于单层结构。最后,通过有限元法验证了解析计算的正确性。
The magnetic pole structure directly influences the air-gap magnetic field distribution for permanent magnet( PM) machines. The air-gap magnetic fields for combination double-layer Halbach magnet structure were analyzed using a scalar magnetic potential. Besides,the air-gap flux densities in the slotted PM machine were calculated by a modified Carter's coefficient. For comparison,the optimal airgap flux densities for single-layer Halbach structure were also derived. On this basis,in terms of the magnet thickness ratio,pole embrace of middle magnet and magnetization angle of side magnets,the airgap flux densities for the double-layer structure were optimized. In addition,the back electromotive force( EMF) and electromagnetic torque were also obtained. The results show that the PM machine with double-layer Halbach structure exhibits a better electromagnetic performance for the equal usage of magnets.Finally,the correctness of the analytical model was verified by a finite element method.
The magnetic pole structure directly influences the air-gap magnetic field distribution for permanent magnet( PM) machines. The air-gap magnetic fields for combination double-layer Halbach magnet structure were analyzed using a scalar magnetic potential. Besides,the air-gap flux densities in the slotted PM machine were calculated by a modified Carter's coefficient. For comparison,the optimal airgap flux densities for single-layer Halbach structure were also derived. On this basis,in terms of the magnet thickness ratio,pole embrace of middle magnet and magnetization angle of side magnets,the airgap flux densities for the double-layer structure were optimized. In addition,the back electromotive force( EMF) and electromagnetic torque were also obtained. The results show that the PM machine with double-layer Halbach structure exhibits a better electromagnetic performance for the equal usage of magnets.Finally,the correctness of the analytical model was verified by a finite element method.
引文
[1]王秀和.永磁电机[M].北京:中国电力出版社,2007.
[2]周渊深.电力电子技术与Matlab仿真[M].北京:中国电力出版社,2005.
[3] SHEN Yang,ZHU Ziqiang. Investigation of permanent magnetbrushless machines having unequal-magnet height poles[J]. IEEETransactions on Magnetics,2012,48(12):4815.
[4] SHEN Yang,ZHU Ziqiang. Analysis of electromagnetic perform-ance of Halbach PM brushless machines having mixed grade andunequal height of magnets[J]. IEEE Transactions on Magnetics,2013,49(4):1461.
[5]范坚坚,吴建华.计及齿槽极间隔断Halbach型磁钢的PMSM气隙磁场解析分析[J].中国电机工程学报,2010,30(12):98.FAN Jianjian,WU Jianhua. Analytical solution and analysis ofair-gap magnetic field of PMSM with partition-between-poles Hal-bach magnet considering effect of slotting[J]. Proceedings of theCSEE,2010,30(12):98.
[6]范坚坚,吴建华.极间隔断Halbach型磁钢的永磁同步电机气隙磁场解析计算及参数分析[J].电工技术学报,2010,25(12):40.FAN Jianjian,WU Jianhua. Analytical calculation and parameteranalysis of air-gap magnetic field distribution in permanent magnetsynchronous motor with partition-between-poles Halbach magnet[J]. Transactions of China Electrotechnical Society,2010,25(12):40.
[7]范坚坚,吴建华,沈磊,等.极间隔断Halbach型磁钢的永磁同步电机多目标优化设计[J].电工技术学报,2009,24(9):53.FAN Jianjian,WU Jianhua,SHEN Lei,et al. Multi-objective op-timization of permanent magnet synchronous motor with partitionbetween poles Halbach magnet[J]. Transactions of China Electro-technical Society,2009,24(9):53.
[8]王爱元,朱建国,商雨青.三段Halbach磁铁阵列永磁同步电机铁心的优化设计[J].电机与控制学报,2017,21(4):37.WANG Aiyuan,Zhu Jianguo,SHANG Yuqin. Optimization of i-ron core design for permanent-magnet synchronous machines withthree-segment Halbach magnet array[J]. Electric Machines andControl,2017,21(4):37.
[9]寇宝泉,曹海川,张晓晨.新型结构高速无槽永磁同步电机研究[J].电机与控制学报,2016,20(6):77.KOU Baoquan,CAO Haichuan,ZHANG Xiaochen. Research onhigh speed slotless permanent magnet synchronous motor with a no-vel structure[J]. Electric Machines and Control,2016,20(6):77.
[10]曹海川.电感集成式高速无槽永磁同步电机的研究[D].哈尔滨:哈尔滨工业大学,2015.
[11]寇宝泉,曹海川,李伟力,等.新型双层Halbach永磁阵列的解析分析[J].电工技术学报,2015,30(10):68.KOU Baoquan,CAO Haichuan,LI Weili,et al. Analytical anal-ysis of a novel double layer Halbach permanent magnet array[J].Transactions of China Electrotechnical Society, 2015, 30(10):68.
[12] LEONG Tiang Tow,ISHAK Dahaman,JAMIL Mohamad KamarolMohd. Complete subdomain model for surface-mounted perma-nent magnet machines[C]. IEEE Conference on Energy Conver-sion,Johor Bahru,Malaysia,2014:140-145.
[13] ZHU Ziqiang,HOWE David. Instantaneous magnetic field distri-bution in brushless permanent magnet dc motors. PartⅢ:Effectof stator slotting[J]. IEEE Transactions on Magnetics,1993,29(1):143.
[14]周羽,李槐树,周石,等.考虑开槽时永磁无刷直流电机气隙磁场的解析计算[J].中国电机工程学报,2014,34(20):182.ZHOU Yu,LI Huaishu,ZHOU Shi,et al. Analytical method forcalculating air-gap magnetic field of brushless dc motor account-ing for slots[J]. Proceedings of the CSEE,2014,34(20):182.
[15]方勇.闭口槽潜水电机卡特系数计算及定子端部绕组电磁振动研究[D].合肥:合肥工业大学,2015.
[16] LALDIN O,SUDHOFF S D,PEKAREK S. Modified Carter’scoefficient[J]. IEEE Transactions on Magnetics,2015,30(3):1133.
[17] ZHU Ziqiang,HOWE David,CHAN C C. Improved analyticalmodel for predicting the magnetic field distribution in brushlesspermanent-magnet machines[J]. IEEE Transactions on Magnet-ics,2002,38(1):229.
[2]周渊深.电力电子技术与Matlab仿真[M].北京:中国电力出版社,2005.
[3] SHEN Yang,ZHU Ziqiang. Investigation of permanent magnetbrushless machines having unequal-magnet height poles[J]. IEEETransactions on Magnetics,2012,48(12):4815.
[4] SHEN Yang,ZHU Ziqiang. Analysis of electromagnetic perform-ance of Halbach PM brushless machines having mixed grade andunequal height of magnets[J]. IEEE Transactions on Magnetics,2013,49(4):1461.
[5]范坚坚,吴建华.计及齿槽极间隔断Halbach型磁钢的PMSM气隙磁场解析分析[J].中国电机工程学报,2010,30(12):98.FAN Jianjian,WU Jianhua. Analytical solution and analysis ofair-gap magnetic field of PMSM with partition-between-poles Hal-bach magnet considering effect of slotting[J]. Proceedings of theCSEE,2010,30(12):98.
[6]范坚坚,吴建华.极间隔断Halbach型磁钢的永磁同步电机气隙磁场解析计算及参数分析[J].电工技术学报,2010,25(12):40.FAN Jianjian,WU Jianhua. Analytical calculation and parameteranalysis of air-gap magnetic field distribution in permanent magnetsynchronous motor with partition-between-poles Halbach magnet[J]. Transactions of China Electrotechnical Society,2010,25(12):40.
[7]范坚坚,吴建华,沈磊,等.极间隔断Halbach型磁钢的永磁同步电机多目标优化设计[J].电工技术学报,2009,24(9):53.FAN Jianjian,WU Jianhua,SHEN Lei,et al. Multi-objective op-timization of permanent magnet synchronous motor with partitionbetween poles Halbach magnet[J]. Transactions of China Electro-technical Society,2009,24(9):53.
[8]王爱元,朱建国,商雨青.三段Halbach磁铁阵列永磁同步电机铁心的优化设计[J].电机与控制学报,2017,21(4):37.WANG Aiyuan,Zhu Jianguo,SHANG Yuqin. Optimization of i-ron core design for permanent-magnet synchronous machines withthree-segment Halbach magnet array[J]. Electric Machines andControl,2017,21(4):37.
[9]寇宝泉,曹海川,张晓晨.新型结构高速无槽永磁同步电机研究[J].电机与控制学报,2016,20(6):77.KOU Baoquan,CAO Haichuan,ZHANG Xiaochen. Research onhigh speed slotless permanent magnet synchronous motor with a no-vel structure[J]. Electric Machines and Control,2016,20(6):77.
[10]曹海川.电感集成式高速无槽永磁同步电机的研究[D].哈尔滨:哈尔滨工业大学,2015.
[11]寇宝泉,曹海川,李伟力,等.新型双层Halbach永磁阵列的解析分析[J].电工技术学报,2015,30(10):68.KOU Baoquan,CAO Haichuan,LI Weili,et al. Analytical anal-ysis of a novel double layer Halbach permanent magnet array[J].Transactions of China Electrotechnical Society, 2015, 30(10):68.
[12] LEONG Tiang Tow,ISHAK Dahaman,JAMIL Mohamad KamarolMohd. Complete subdomain model for surface-mounted perma-nent magnet machines[C]. IEEE Conference on Energy Conver-sion,Johor Bahru,Malaysia,2014:140-145.
[13] ZHU Ziqiang,HOWE David. Instantaneous magnetic field distri-bution in brushless permanent magnet dc motors. PartⅢ:Effectof stator slotting[J]. IEEE Transactions on Magnetics,1993,29(1):143.
[14]周羽,李槐树,周石,等.考虑开槽时永磁无刷直流电机气隙磁场的解析计算[J].中国电机工程学报,2014,34(20):182.ZHOU Yu,LI Huaishu,ZHOU Shi,et al. Analytical method forcalculating air-gap magnetic field of brushless dc motor account-ing for slots[J]. Proceedings of the CSEE,2014,34(20):182.
[15]方勇.闭口槽潜水电机卡特系数计算及定子端部绕组电磁振动研究[D].合肥:合肥工业大学,2015.
[16] LALDIN O,SUDHOFF S D,PEKAREK S. Modified Carter’scoefficient[J]. IEEE Transactions on Magnetics,2015,30(3):1133.
[17] ZHU Ziqiang,HOWE David,CHAN C C. Improved analyticalmodel for predicting the magnetic field distribution in brushlesspermanent-magnet machines[J]. IEEE Transactions on Magnet-ics,2002,38(1):229.