非线性永磁体分布参数模型及其在桥式磁系统中的应用
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摘要
铁铬钴、铝镍钴等合金永磁材料具有非线性的去磁曲线，被称为非线性永磁体；该类永磁体具有较高的温度系数及良好的加工性能，被广泛应用于军事、航天及民用领域的继电器等微小型含永磁电磁机构中。
含非线性永磁体电磁机构的参数设计、容差设计过程中，电磁系统吸力计算是关键的一环；目前使用有限元等数值方法耗时较长，而等效磁路法精度又较低；针对我国含非线性永磁体电磁设备，尤其是航天电磁极化继电器可靠性设计基础薄弱、电磁系统计算效率低的现状，通过对永磁体等效解析模型的基础研究，建立一种更适合非线性永磁体单体及含该类永磁体的磁系统等效模型，解决模型的基本微元、建模方法以及电磁机构建模等问题；从而在计算基础上提高含非线性永磁体电磁继电器的可靠性设计水平。
首先，本文基于永磁体基本物理量关系以及磁通管的基本概念，建立了开路长方形非线性永磁体分布参数模型微元，推导了模型微元间的关系；对开路长方形永磁体漏磁导进行分类，推导了几类漏磁导的计算方法；提出基于磁力线划分的长方形非线性永磁体微元划分方法；以某牌号长方形非线性永磁体为例，建立了开路长方形永磁体分布参数模型，分析了模型的求解过程，求解了各分段起始工作点及截面磁通值，并与有限元模型及实测数据进行比较，验证了模型的正确性。
其次，针对另外一种常见的规则形状非线性永磁体——扇形永磁体单体的分布参数模型进行研究；提出了永磁体截面磁力线的获取方法，建立了适合扇形永磁体的单层和多层分布参数模型；以某牌号开路扇形非线性永磁体为例，采用磁力线划分的方法建立了扇形永磁体分布参数模型，求解了各分段起始工作点及截面磁通值，与有限元模型相比，该方法较为接近三维有限元方法计算结果。
然后，在开路长方形非线性永磁体分布参数模型的基础上，分析了某型号含长方形非线性永磁体的电磁继电器磁系统，该继电器为具有典型桥式极化磁系统的电磁继电器，将分布参数模型应用于桥式极化磁系统的建模计算过程中；建立了磁系统模型微元；确定了永磁体的分界面，提出了区域细分的灵活建模方式，建立了桥式极化磁系统分布参数模型，分析了模型中永磁衔铁的静态吸力求取方法，提出了基于牛顿法与遗传算法的桥式极化磁系统分布参数模型方程求解方法；分别计算磁系统在零安匝及吸合安匝下，不同转角的静态吸力，以及永磁体各分段磁场强度、截面磁通等物理量；对比传统集中参数模型和有限元法结果，验证了该模型的准确性，对比计算时间，考察了模型的计算效率。
最后，针对分布参数模型研究过程中的实际需要，提出了针对长方形永磁体的磁通测试方法；提出了针对扇形永磁体截面磁通综合测试的方法；实测了多种形状永磁体的截面磁通，并与有限元模型进行对比，测试结果与有限元仿真结果吻合度较好；针对开路永磁体及磁系统中分布参数模型研究的需要，提出磁场图景测试系统的设计思路，搭建了基于可编程逻辑控制器（PLC）及伺服控制器的磁场图景测试系统；并实测了长方形永磁体中心截面的磁场图景，实现了磁场图景的自动化测试。
本研究对于提高含非线性永磁体极化继电器的设计、分析和优化水平具有重要的理论意义和实用价值，其关键技术与理论思想可推广至其它电磁机构的分析与设计中。
Nonlinear permanent magnet (NPM), such as FeCrCo and AlNiCo, has a nonlinear hysteresis curve (2nd quadrant). The NPM is often used in minitype electromagnetic devices for its high temperature coefficient and good machinability, for example electromagnetic relay (EMR). It is widely used in military, aerospace field etc.
In the process of parameters design and optimization process for electromagnetic devices which have polarized magnetic system and contain NPM, the accurate and efficient calculation of attractive force is a basic and important step. There are mainly two popular ways: finite element method (FEM) and magnetic equivalent circuit method (MEC). FEM has a high level accuracy but often costs a lot of time. MEC has the superiority in its calculation speed but disadvantages in accuracy. The design and electromagnetic system (EMS) calculation ability is on a low level. The basic foundation of NPM modeling method in MEC needs to be improved. Forces on the basic calculation infinite block and the modeling method, the method which has a fast calculation speed and acceptable accuracy will be meaningful for the reliability design of EMR.
Firstly, based on the pricinple of magnetic flux tube, a distributed parameter calculation model (DPM) was established. The infinite block was built for rectangle NPM. The relationship between infinite blocks was deduced. The solution procedure as well as verification condition of this model was given; By a case study of the single rectangle NPM, the method of magnetic field lines division (MFLB) was present and adopted to build the permanent magnet DPM, the whole DPM model of rectangle NPM was built, the starting point and section magnetic flux of each subsection were solved; compared with FEM and test data this model proves to be of acceptable calculation accuracy and high calculation speed.
Secondly, for the other typical shape of NPM—sector NPM, the distribution parameter model for sector NPM was researched; the gathering method for section flux distribution was present; a improved model for sector NPM were present based on the MFLB method the whole DPM model of sector NPM was built, the starting point and section magnetic flux of each subsection were solved; the calculation results of sector NPM were similar to FEM calculation data. This model was verified by FEM data.
Thirdly, based on the research of open circuit NPM, the electromagnetic structure of a type of bridge polarized magnetic system (BPMS) was analized; the MFLB distribution parameter model was used to build the calculation model of BPMS; the finite block was built; the interface of rectangle NPM in BPMS was determined; a local region fine division method was present; the whole distribution parameter model of EMR was built; the leakage permeance calculation formulas were deduced; the static attractive force calculation method was analyzied; the newton method and the genetic algorithm method were used to calculate the force under different ampere-turn of0and±120At and different rotation angle of armature; compared with3D-FEM calculation data; the other parameters such as magnetic flux density and section magnetic flux were also calculated; the calculation accuracy was higher than2D-FEM and MEC, and the calculation time consumption was far less than3D-FEM.
At last, according to the practical need in the research of distribution parameter model, the section magnetic flux test method for rectangle NPM was present; the test equipment was manufactured; the test for cylinder and annulus NPM were also realized at the same time; the test method for sector NPM was present too; cooperating with the servo control system the test equipment for sector NPM was manufactured for the special need of sector NPM; compared with the FEM test data, the equipment achieved the task accurately; the test method and the design thought for the section magnetic field image test of NPM were present; the control strategy for2D motion platform based on PLC was studied; the software and hardware of test system were realized based on the motion control platform; the automatic test of magnetic field image for rectangle NPM was realized.
The research proposed in this paper are of important theoretical significance and practical value for the design, analysis and optimization of EMR which contain NPM, the basic thought and relevant key technology can be extended to other electromagnetic devices.
含非线性永磁体电磁机构的参数设计、容差设计过程中，电磁系统吸力计算是关键的一环；目前使用有限元等数值方法耗时较长，而等效磁路法精度又较低；针对我国含非线性永磁体电磁设备，尤其是航天电磁极化继电器可靠性设计基础薄弱、电磁系统计算效率低的现状，通过对永磁体等效解析模型的基础研究，建立一种更适合非线性永磁体单体及含该类永磁体的磁系统等效模型，解决模型的基本微元、建模方法以及电磁机构建模等问题；从而在计算基础上提高含非线性永磁体电磁继电器的可靠性设计水平。
首先，本文基于永磁体基本物理量关系以及磁通管的基本概念，建立了开路长方形非线性永磁体分布参数模型微元，推导了模型微元间的关系；对开路长方形永磁体漏磁导进行分类，推导了几类漏磁导的计算方法；提出基于磁力线划分的长方形非线性永磁体微元划分方法；以某牌号长方形非线性永磁体为例，建立了开路长方形永磁体分布参数模型，分析了模型的求解过程，求解了各分段起始工作点及截面磁通值，并与有限元模型及实测数据进行比较，验证了模型的正确性。
其次，针对另外一种常见的规则形状非线性永磁体——扇形永磁体单体的分布参数模型进行研究；提出了永磁体截面磁力线的获取方法，建立了适合扇形永磁体的单层和多层分布参数模型；以某牌号开路扇形非线性永磁体为例，采用磁力线划分的方法建立了扇形永磁体分布参数模型，求解了各分段起始工作点及截面磁通值，与有限元模型相比，该方法较为接近三维有限元方法计算结果。
然后，在开路长方形非线性永磁体分布参数模型的基础上，分析了某型号含长方形非线性永磁体的电磁继电器磁系统，该继电器为具有典型桥式极化磁系统的电磁继电器，将分布参数模型应用于桥式极化磁系统的建模计算过程中；建立了磁系统模型微元；确定了永磁体的分界面，提出了区域细分的灵活建模方式，建立了桥式极化磁系统分布参数模型，分析了模型中永磁衔铁的静态吸力求取方法，提出了基于牛顿法与遗传算法的桥式极化磁系统分布参数模型方程求解方法；分别计算磁系统在零安匝及吸合安匝下，不同转角的静态吸力，以及永磁体各分段磁场强度、截面磁通等物理量；对比传统集中参数模型和有限元法结果，验证了该模型的准确性，对比计算时间，考察了模型的计算效率。
最后，针对分布参数模型研究过程中的实际需要，提出了针对长方形永磁体的磁通测试方法；提出了针对扇形永磁体截面磁通综合测试的方法；实测了多种形状永磁体的截面磁通，并与有限元模型进行对比，测试结果与有限元仿真结果吻合度较好；针对开路永磁体及磁系统中分布参数模型研究的需要，提出磁场图景测试系统的设计思路，搭建了基于可编程逻辑控制器（PLC）及伺服控制器的磁场图景测试系统；并实测了长方形永磁体中心截面的磁场图景，实现了磁场图景的自动化测试。
本研究对于提高含非线性永磁体极化继电器的设计、分析和优化水平具有重要的理论意义和实用价值，其关键技术与理论思想可推广至其它电磁机构的分析与设计中。
Nonlinear permanent magnet (NPM), such as FeCrCo and AlNiCo, has a nonlinear hysteresis curve (2nd quadrant). The NPM is often used in minitype electromagnetic devices for its high temperature coefficient and good machinability, for example electromagnetic relay (EMR). It is widely used in military, aerospace field etc.
In the process of parameters design and optimization process for electromagnetic devices which have polarized magnetic system and contain NPM, the accurate and efficient calculation of attractive force is a basic and important step. There are mainly two popular ways: finite element method (FEM) and magnetic equivalent circuit method (MEC). FEM has a high level accuracy but often costs a lot of time. MEC has the superiority in its calculation speed but disadvantages in accuracy. The design and electromagnetic system (EMS) calculation ability is on a low level. The basic foundation of NPM modeling method in MEC needs to be improved. Forces on the basic calculation infinite block and the modeling method, the method which has a fast calculation speed and acceptable accuracy will be meaningful for the reliability design of EMR.
Firstly, based on the pricinple of magnetic flux tube, a distributed parameter calculation model (DPM) was established. The infinite block was built for rectangle NPM. The relationship between infinite blocks was deduced. The solution procedure as well as verification condition of this model was given; By a case study of the single rectangle NPM, the method of magnetic field lines division (MFLB) was present and adopted to build the permanent magnet DPM, the whole DPM model of rectangle NPM was built, the starting point and section magnetic flux of each subsection were solved; compared with FEM and test data this model proves to be of acceptable calculation accuracy and high calculation speed.
Secondly, for the other typical shape of NPM—sector NPM, the distribution parameter model for sector NPM was researched; the gathering method for section flux distribution was present; a improved model for sector NPM were present based on the MFLB method the whole DPM model of sector NPM was built, the starting point and section magnetic flux of each subsection were solved; the calculation results of sector NPM were similar to FEM calculation data. This model was verified by FEM data.
Thirdly, based on the research of open circuit NPM, the electromagnetic structure of a type of bridge polarized magnetic system (BPMS) was analized; the MFLB distribution parameter model was used to build the calculation model of BPMS; the finite block was built; the interface of rectangle NPM in BPMS was determined; a local region fine division method was present; the whole distribution parameter model of EMR was built; the leakage permeance calculation formulas were deduced; the static attractive force calculation method was analyzied; the newton method and the genetic algorithm method were used to calculate the force under different ampere-turn of0and±120At and different rotation angle of armature; compared with3D-FEM calculation data; the other parameters such as magnetic flux density and section magnetic flux were also calculated; the calculation accuracy was higher than2D-FEM and MEC, and the calculation time consumption was far less than3D-FEM.
At last, according to the practical need in the research of distribution parameter model, the section magnetic flux test method for rectangle NPM was present; the test equipment was manufactured; the test for cylinder and annulus NPM were also realized at the same time; the test method for sector NPM was present too; cooperating with the servo control system the test equipment for sector NPM was manufactured for the special need of sector NPM; compared with the FEM test data, the equipment achieved the task accurately; the test method and the design thought for the section magnetic field image test of NPM were present; the control strategy for2D motion platform based on PLC was studied; the software and hardware of test system were realized based on the motion control platform; the automatic test of magnetic field image for rectangle NPM was realized.
The research proposed in this paper are of important theoretical significance and practical value for the design, analysis and optimization of EMR which contain NPM, the basic thought and relevant key technology can be extended to other electromagnetic devices.
引文
[1]谢勇,梁慧敏等.军用电磁继电器结构分类和比较[J].低压电器,2013,10:14-18.
[2]严密,彭晓领.磁学基础与磁性材料[M].杭州:浙江大学出版社,2006:22-23.
[3] Helmut Kronmüller, Stuart Parkin. Handbook of advanced magnetic materials[M]. Germany: Springer Publisher,2006:117-118.
[4] K. H. J. Buschow, F. R. De Boer. Physics of Magnetism and Magnetic Materials[M]. Netherlands: Kluwer Academic/Plenum Publishers,2003:47-49.
[5]朱永庆,吴世湘.军用继电器的发展态势[J].电子科学技术评论,2005(1):55-56.
[6]金峻.世界继电器市场回顾及展望[J].机电元件,2005,25(2):56-58.
[7] Rhesa, Nathanael. Nano-Electro-Mechanical (NEM) Relay Devices andTechnology for Ultra-Low Energy Digital Integrated Circuits [R]. USA,Technical Report No. UCB/EECS-2013-45,2013:5-6.
[8] Werner Johler. The Design Challenges Involved in Miniaturization ofElectromechanical Relays[C]. IEEE52th International Conference on ElectricalContacts.2006:151-152.
[9] P. Meredith, C. J. Bettinger, M. Irimia-Vladu, A. B. Mostert and P. E. Schwenn.Electronic and optoelectronic materials and devices inspired by nature[R]. USA,Reports On Progress In Physics,2013:2-3.
[10]杨文英.电磁继电器功能模块的电磁敏感性研究[D].哈尔滨工业大学博士论文,2009:2-5.
[11]王容华.直流继电器电性能测试系统及实验研究[D].华中科技大学硕士论文,2012:3-4.
[12]许志红.电器理论基础[M].北京:机械工业出版社,2014:10-11.
[13]李昕.电磁继电器触头相关参数的测量研究[D].河北工业大学硕士论文,2012:1-2.
[14]余琼.航天继电器可靠性评价及寿命试验方法的研究[D].哈尔滨工业大学博士论文,2011:3-5.
[15]变形铁铬钴永磁合金(YB/T5261-1993)[M].中国标准出版社,1993:2-3.
[16]朱中平,薛剑峰.中外磁性材料实用手册[M].中国物资出版社,2004:78-79.
[17]李文军,凌铨.半硬磁性FeCrCo合金的热处理工艺及其对性能的影响[J].磁性材料及器件,2010,3:56-62.
[18]王子生,李冬云,吴琼,胡秀坤等.铝镍钴永磁材料磁参数测量不确定度评定[J].电工材料,2012,4:47-51.
[19] Pecht M, Gu J. Physics-of-failure-based Prognostics for Electronic Products[J].Transactions of the Institute of Measurement and Control,2009(31):309-322.
[20] A. S. S. Vasan, B. Long, M. Pecht. Diagnostics and Prognostics Method forAnalog Electronic Circuits[J]. IEEE Transactions on Industrial Electronics,2013,60(11):5277-5291.
[21]梁慧敏,叶雪荣,翟国富,刘茂恺,郝燕玲.极化继电器判别准则的研究与应用[J].电机工程学报,2007,27(27):62-69.
[22]邓杰.航天电磁继电器稳健性设计研究[D].哈尔滨工业大学,硕士学位论文,2010:30-32.
[23] Zhai Guofu, Zhou Yuege, Ye Xuerong, Hu Bo. A method of multi-objectivereliability tolerance design for electronic circuits[J]. Chinses Journal ofAeronautics,2012,26(1):161-170.
[24] Han Hu, Xin Qi, Chang-song Wang. Finite element analysis on magnetic fieldin the actuator of giant magnetostrictive linear motor with Ansoft[C].2008IEEE International Conference on Industrial Technology,2008:1-5.
[25] Choi Jong-Hyun, Kim Jung-Hoon, Kim Dong-Ho, Baek Yoon-Su. Design andparametric analysis of axial flux PM motors with minimized cogging torque[J].IEEE Transactions on Magnetics,2009,45(6):2855-2858.
[26]王其亚.航天电磁继电器动态特性及其优化方法的研究[D].哈尔滨工业大学博士学位论文,2011:5-7.
[27]郑永成,王洋.基于磁场分割的磁导计算与磁路设计[J].机械与电子,2006(7):11-13.
[28]刘荣林.航空同步发电机的等效磁路模型[J].中国民航学院学报,2004,22(3):18-20.
[29]佟为明,李凤阁,赵志衡.单永磁极化磁系统的永磁工作点图解法统一模型与分析[J].中国电机工程学报,2005,25(6):129-133.
[30]游一民,陈德桂,罗文科,张敬菽.关于永磁机构中永磁工作点的讨论[J].高压电器,2002,38(4):39-41.
[31]李景天,宋一得,郑勤红,刘剑虹.用等效磁荷法计算永磁体磁场[J].云南师范大学学报(自然科学版),1999,19(2):33-36.
[32] Compter J C, Janssen J L G, Lomonova E A. Ampere's circuital3-D model fornoncuboidal magnets[J]. IEEE Transactions on Magnetics,2010,46(12):4009-4015.
[33] Ives Lawrence, Bui Thuc, Vogler William, Bauer Andrew, Shephard Mark,Beall Mark. Three-dimensional magnetostatic analysis using structured meshand nodal elements[J]. IEEE Transactions on Magnetics,2011,47(2):198-202.
[34] Li G J, Ojeda J, Hoang E, Gabsi M. Thermal-electromagnetic analysis of afault-tolerant dual-star flux-switching permanent magnet motor for criticalapplications[J]. IET Electric Power Applications,2011,5(6):503-513.
[35] Vuxuan H, Lahaye D, Ani S O,Polinder H, Ferreira J A. Effect of designparameters on electromagnetic torque of PM machines with concentratedwindings using nonlinear dynamic FEM[C].2011IEEE International ElectricMachines and Drives Conference IEMDC,2011:383-388.
[36] Tamitani Satoshi, Takamatsu Tomoaki, Otake Asuka, Wakao Shinji, KameariAkihisa, Takahashi Yasuhito. Finite-element analysis of magnetic field problemwith open boundary using infinite edge element[J]. IEEE Transactions onMagnetics,2011,47(5):1194-1197.
[37]姚振汉.边界元法[M].高等教育出版社,2010:5-15.
[38] A. Buchau, W. Hafla, and W. M. Rucker, Accuracy investigations of boundaryelement methods for the solution of laplace equations[J]. IEEE Transactions onMagnetics,2007,43(4):1225-1228.
[39] A. Buchau, S. M. Tsafak, W. Hafla, and W. M. Rucker, Parallelization of a fastmultipole boundary element method with cluster openMP[J]. IEEE Transactionson Magnetics,2008,44(6):1338–1341.
[40] C. Scheiblich, R. Banucu, V. Reinauer, J. Albert, and W. Rucker, Parallelhierarchical block wavelet compression for an optimal compression of3-DBEM problems[J]. IEEE Transactions on Magnetics,2011,47(5):1386–1389.
[41] I. Ciric, F. Hantila, and M.Maricaru, A new vector potential BEM for magneticfields bounded by perfect conductors[J]. IEEE Transactions on Magnetics,2011,47(5):1350–1353.
[42] P. T. While, L. K. Forbes, S. Crozier,3-D Gradient Coil Design—InitialTheoretical Framework[J]. IEEE Transactions on Biomedical Engineering,2009,56(4):1169-1183.
[43] M. Enokizono, T. Todaka, and K. Hayakawa. Three dimensional magnetic fieldanalysis of permanent magnet by boundary element method[J]. IEEETransactions on Journal of Magnetics Jappn,1990,5(9):749–754.
[44] G. Shou, L. Xia, F. L., M. Zhu, Y. Li, and S. Crozier, MRI coil design usingboundary-element method with regularization technique: A numericalcalculation study[J]. IEEE Transactions on Magnetics,2010,46(4):1052–1059.
[45] Atef Elsherbeni, Veysel Demir. The Finite Difference Time Domain Method forElectromagnetics: With MATLAB Simulations[M]. SciTech Publishing,2009:12-18.
[46] Ramli, K. N. Abd-Alhameed, R. A.; See, C. H., Atojoko, A., Noras, J. M.,Excell, P. S. Electromagnetic Field Computation for Power Transmission LinesUsing Quasi-Static Sub-Gridding Finite-Difference Time-Domain Approach[J].Eectromagnetics,2014,34(1):47-65.
[47] Yao Chenguo, Wu Hao, Mi Yan. Finite Difference Time Domain Simulation ofLightning Transient Electromagnetic Fields on Transmission Lines[J]. IEEETransactions on Dielectrics and Electrical Insulation,2013,20(4):1239-1246.
[48] Capoglu, Ilker R., Taflove Allen, Backman Vadim. Angora: A Free SoftwarePackage for Finite-Difference Time-Domain Electromagnetic Simulation[J].IEEE Antennas and Propagation Magazine.2013,55(4):80-93
[49]金建铭.电磁场有限元方法[M].西安电子科技大学出版社,2001:12-15.
[50]李景涌.有限元法[M].北京邮电大学出版社,1999:18-22.
[51]龙驭球.新型有限元论[M].清华大学出版社,2005:2-8.
[52] Jian-Ming Jin. The Finite Element Method in Electromagnetics(SecondEdition)[M], Wiley-IEEE Press,2002:13-14.
[53] J. Sibué, J. Ferrieux, G. Meunier, and R. Périot. Modeling of lossesand currentdensity distribution in conductors of a large air-gap transformer usinghomogenization and3-D FEM[J]. IEEE Transactions on Magnetics,2012,48(2):763–766.
[54] K. Hwang, H. Lin, S. Rhyu, and B. Kwon. A study on the novel coefficientmodeling for a skewed permanent magnet and overhang structure for optimaldesign of brushless DC motor[J]. IEEE Transactions on Magnetics,2012,48(5):1918–1923.
[55] T. Chan, W. Wang, and L. Lai. Magnetic field in a transverse-and axial-fluxpermanent magnet synchronous generator from3-D FEA[J]. IEEE Transactionson Magnetics,2012,48(2):1055–1058.
[56] Z. Mouton, M. J. Kamper. Modeling and Optimal Design of an Eddy CurrentCoupling for Slip-Synchronous Permanent Magnet Wind Generators[J]. IEEETransactions on Industrial Electronics,2014,61(7):3367-3376.
[57] Ross A. Howard, Xiao Yimin, Steven D. Pekarek. Modeling and Testing of anArmature-Reaction-Compensated (PM) Synchronous Generator[J]. IEEETransactions on Energy Conversion,2013,28(4):793-804.
[58] J. S. Jiang, S. D. Bader, Rational design of the exchange-spring permanentmagnet[J]. Journal of Physics-Condensed Matter,2014,26(6):1-9.
[59] P. Jin, S. Fang, H. Lin, Z. Zhu, Y. Huang, and X. Wang, Analytical magneticfield analysis and prediction of cogging force and torque of a linear and rotarypermanent magnet actuator[J]. Transactions on Magnetics,2011,47(11):3004–3007.
[60] Lee Sujin, Kim Kyuseob, Cho Sugil, Jang Junyong, Lee Taehee, Hong Jungpyo.Optimal design of interior permanent magnet synchronous motor consideringthe manufacturing tolerances using Taguchi robust design[J]. IET ElectricPower Applications.2014,8(1):23-28.
[61] Ye Xuerong, Deng Jie, Ma Yue, Zhai Guofu, Yan Jihong. A robust solution forhesitate phenomenon in pick up process of aerospace electromagnetic relay[J].Chinese Journal of Aeronautics,2013,26(3):697-704.
[62]王其亚,陈庆,谭忠华,翟国富.基于拍合式磁路结构的磁保持型继电器设计研究[J].机电元件,2013,33(5):23-30.
[63] Amrhein Marco, Krein Philip T. Magnetic equivalent circuit simulations ofelectrical machines for design purposes[J]. IEEE Electric Ship TechnologiesSymposium,2007:254-260.
[64] Amrhein Marco, Krein Philip T.3-D Magnetic equivalent circuit framework formodeling electro--mechanical devices[J]. IEEE Transactions on EnergyConversion,2009,24(2):397-405.
[65] Amrhein Marco, Krein Philip T. Force calculation in3-D magnetic equivalentcircuit networks with a Maxwell stress tensor[J]. IEEE Transactions on EnergyConversion,2009,24(3):587-593.
[66] Gyselinck J, Dular P, Legros W, Grenier D. Hybrid magnetic equivalent circuit-finite element modelling of transformer fed electrical machines[C]. COMPEL-The International Journal for Computation and Mathematics in Electrical andElectronic Engineering,2003,22(3):643-658.
[67] Sabariego R V, Geuzaine C, Dular P and Gyselinck J. H-and A-time-domainformulations for the modeling of thin electromagnetic shells[J]. IET ConferencePublications,2008(537):106-107.
[68] J Owens, P Chapman. Reduced fea-state space modeling of stationary magneticdevices[C]. IEEE34th Power Electronics Specialist Conf,2003(1):265–271.
[69] S Rutenkroger, B Deken, S Pekarek. Reduction of model dimension innonlinear finite element approximations of electromagnetic systems[C]. IEEEWorkshop on Computers in Power Electronics,2004:20-27.
[70] Zhai Guofu, Wang Qiya and Ren Wanbin. An Output Space-Mapping Algorithmto Optimize the Dimensional Parameter of Electromagnetic Relay[J]. IEEETransactions on Magnetics,2011,47(9):2194-2199.
[71] William H. Hayt, John A. Buck. Engineering Electromagnetics (8th Revisededition)[M]. McGraw Hill Higher Education Press,2011:12-13.
[72] S. Paul, D. Bobba, N. Paudel, and J. Bird, Source field modeling in air usingmagnetic charge sheets[J]. IEEE Transactions on Magnetics,2012,48(11):3879–3882.
[73] J. Yonnet and H. Allag,“Three-dimensional analytical calculation of permanentmagnet interactions by “magnetic node” representation[J]. IEEE Transactionson Magnetics,2011,47(8):2050–2055.
[74] C. Akyel, S. Babic and MM. Mahmoudi, Mutual inductance calculation for non-coaxial circular air coils with parallel axesrogress[J]. In ElectromagneticsResearch,2009,91:287–301.
[75] Gysen Bart L. J., Ilhan Esin, Meessen Koen J., Paulides Johannes J. H.,Lomonova Elena A. Modeling of Flux Switching Permanent MagnetMachines With Fourier Analysis[J]. IEEE Transactions on Magnetics,2010,46(6):1499-1502.
[76] K. Meessen, J. Paulides, and E. Lomonova, Analysis of3-D effects insegmented cylindrical quasi-Halbach magnet arrays[J]. IEEE Transactions onMagnetics,2011,47(4):727–733.
[77] C. L. W. Sonntag, Contactless energy transfer platform using aircored planarinductors[D]. Ph.D. dissertation, Eindhoven University of Technology,Eindhoven, The Netherlands,2010:6-7.
[78] Tiegna Huguette, Amara Yacine, Barakat Georges. Overview of analyticalmodels of permanent magnet electrical machines for analysis and designpurposes[J]. Mathematics and Computers in Simulation,2013,90:162-177.
[79]朱剑.复杂电磁问题的有限元、边界积分及混合算法的快速分析技术[D].南京理工大学,博士学位论文,2011:2-5.
[80] Ilhan E., Gysen B. L. J., Paulides J. J. H., Lomonova E. A. Analytical HybridModel for Flux Switching Permanent Magnet Machines[J]. IEEE Transactionson Magnetics,2010,46(6),1762-1765.
[81] C. B. Rasmussen, E. Ritchie. A Magnetic Equivalent Circuit Approach forPredictiing PM Motor Performance[C]. IEEE Industry Applications SocietyAnnual Meeting,1997:10-17.
[82] J K Kim,S W Joo, S C Hahn, J P Hong, D H Koo. Static Characteristics ofLinear BLDC Motor Using Equivalent Magnetic Circuit and FEM[J], IEEETransactions on Magnetics,2004,40(2):742-745.
[83]赵阳,陈美娟,孙雨施.电磁场计算中一种特殊边界条件及其在波阵解中应用[J].南京航空航天大学学报,1994,26(6):745-751.
[84]梁慧敏,叶雪荣,翟国富,刘茂恺,郝燕玲.极化磁系统判别准则的研究与应用[J].中国电机工程学报,2007,27(27):56-60.
[85]张冠生.电器理论基础[M].机械工业出版社,1989:238-243.
[86]毕刘新,王善铭,夏永洪.表贴式永磁电机漏磁导的解析计算[J],清华大学学报,2010,50(4):525-528.
[87] Guo Yujing, Lin Heyun, Jin Ping, Yan Jianhu, Wang Jian, Jia Zhou. AnalyticalModeling of Air-Gap Field Distributions in Permanent Magnet EmbeddedSalient Pole Wind Generator[J]. IEEE Transactions on Magnetics,2013,49(12):5756-5760.
[88]白保东,郭志楠,谢德馨.强磁场下永磁机构的优化设计及磁力分析[J].沈阳工业大学学报,2008,30(1):19-24.
[89]李斌,刘超,李洪凤,李桂丹.永磁球形电机定子绕组的永磁体模型及磁场分析[J].天津大学学报,2012,45(11):1025-1029.
[90] H R Bolton, Y Shakweh. Performance prediction of Laws’s relay actuator[J].Electric Power Applications IEE Proceedings B,1990,137(1):1-13.
[91] Manz B, Benecke M, Volke F. A simple, small and low cost permanent magnetdesign to produce homogeneous magnetic fields[J]. Journal of MagneticResonance,2008,192(1):131-138.
[92]梁慧敏,由佳欣,叶雪荣,翟国富.基于三维磁场仿真分析的含永磁继电器等效磁路模型的建立[J].电工技术学报,2011,26(1):46-50.
[93]徐俊.条形永磁分段回复线模型的研究[D].哈尔滨工业大学,硕士学位论文,2009:11-20.
[94]张荣岭,郑艳明,崔浩,梁慧敏,翟国富.条形永磁开路漏磁导磁场仿真计算方法[J].机电元件,2008,28(4):24-27.
[95]梁慧敏,张荣岭,徐俊,刘茂恺,翟国富.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.
[96] Cale J, Sudhoff S D, Tan Li-Quan. Accurately modeling el core inductors usinga high-fidelity magnetic equivalent circuit approach[J]. IEEE Transactions onMagnetics,2006,42(1):40-46.
[97] Shakirov M A. An analysis of the nonuniformity in the distribution of magneticloads and losses in transformers using magnetoelectric equivalent circuits[J].Elektrichestvo,2005(11):15-27.
[98]吴迪,辜承林.新型横向磁通永磁电机三维磁路分析[J].中国电机工程学报,2010,30(33):91-96.
[99] Jagadeesh K Tangudu, Thomas M Jahns, Ayman EL-Refaie, Z Q Zhu. Lumpedparameter magnetic circuit model for fractional-slot concentrated-windinginterior permanent magnet machines[C].2009IEEE Energy ConversionCongress and Exposition ECCE,2009(9):2423-2430.
[100]佟为明,张荣岭,刘茂恺.永久磁铁的等效处理[J].机电元件,1997,17(3-4):37-41.
[101]佟为明,刘宁宾,刘茂恺,姜守旭.极化磁系统永磁工作点的求解[J].低压电器,2000,4:12-16.
[102]向洪岗,陈德桂,李兴文,吴锐,刘洪武,耿英三.基于三维磁场分析建立电磁铁等效磁路的研究[J].西安交通大学学报,2003,37(8):807-811.
[103]梁慧敏,任万滨,王思民,翟国富.基于三维有限元法的极化磁系统静态吸力特性分析[J].机电元件,2005,25(3):3-7.
[104] Liang Huimin, You Jiaxin, Ye Xuerong and Zhai Guofu. A type of attractiveforce calculation model of polarized relay based on nonlinear permanentmagnet bar subsection model[C]. IEEE58th Holm Conference on ElectricalContacts,2012:300-304.
[105] You Jiaxin, Liang Huimin, Ye Xuerong and Zhai Guofu. The Effect of Coil onCombined Three-Subsection Permanent Magnet in Close Magnetic CircuitModel[C]. IEEE57th Holm Conference on Electrical Contacts,2011:175-178.
[106]叶雪荣.基于动态特性的航天电磁继电器可靠性容差设计技术研究[D].哈尔滨工业大学工学博士学位论文,2009:42~47.
[107]刘志刚,杜娟.一种求解非线性方程组的量子粒子群算法[J].微计算机应用,2011,32(2):31-36.
[108]姜智鹏,赵伟,屈凯峰.磁场测量技术的发展及其应用[J].电测与仪表,2008,45(4):1-5.
[109]梁慧敏,崔浩,张荣岭,翟国富.磁钢内部磁通测量装置的研制[J].机电元件,2008,6:25-28.
[110]崔浩.基于有限元法的极化磁系统等效磁路模型的研究[D].哈尔滨工业大学,硕士学位论文,2009:16-18.
[111] Xiaotao Han, Zhiwei Song. The Development of Measurement and ControlSoftware Applied To Small Pulsed High Magnetic Field Facility[C].Proceedings of2009Chinese Control and Decision Conference,2009(3):4470-4474.
[2]严密,彭晓领.磁学基础与磁性材料[M].杭州:浙江大学出版社,2006:22-23.
[3] Helmut Kronmüller, Stuart Parkin. Handbook of advanced magnetic materials[M]. Germany: Springer Publisher,2006:117-118.
[4] K. H. J. Buschow, F. R. De Boer. Physics of Magnetism and Magnetic Materials[M]. Netherlands: Kluwer Academic/Plenum Publishers,2003:47-49.
[5]朱永庆,吴世湘.军用继电器的发展态势[J].电子科学技术评论,2005(1):55-56.
[6]金峻.世界继电器市场回顾及展望[J].机电元件,2005,25(2):56-58.
[7] Rhesa, Nathanael. Nano-Electro-Mechanical (NEM) Relay Devices andTechnology for Ultra-Low Energy Digital Integrated Circuits [R]. USA,Technical Report No. UCB/EECS-2013-45,2013:5-6.
[8] Werner Johler. The Design Challenges Involved in Miniaturization ofElectromechanical Relays[C]. IEEE52th International Conference on ElectricalContacts.2006:151-152.
[9] P. Meredith, C. J. Bettinger, M. Irimia-Vladu, A. B. Mostert and P. E. Schwenn.Electronic and optoelectronic materials and devices inspired by nature[R]. USA,Reports On Progress In Physics,2013:2-3.
[10]杨文英.电磁继电器功能模块的电磁敏感性研究[D].哈尔滨工业大学博士论文,2009:2-5.
[11]王容华.直流继电器电性能测试系统及实验研究[D].华中科技大学硕士论文,2012:3-4.
[12]许志红.电器理论基础[M].北京:机械工业出版社,2014:10-11.
[13]李昕.电磁继电器触头相关参数的测量研究[D].河北工业大学硕士论文,2012:1-2.
[14]余琼.航天继电器可靠性评价及寿命试验方法的研究[D].哈尔滨工业大学博士论文,2011:3-5.
[15]变形铁铬钴永磁合金(YB/T5261-1993)[M].中国标准出版社,1993:2-3.
[16]朱中平,薛剑峰.中外磁性材料实用手册[M].中国物资出版社,2004:78-79.
[17]李文军,凌铨.半硬磁性FeCrCo合金的热处理工艺及其对性能的影响[J].磁性材料及器件,2010,3:56-62.
[18]王子生,李冬云,吴琼,胡秀坤等.铝镍钴永磁材料磁参数测量不确定度评定[J].电工材料,2012,4:47-51.
[19] Pecht M, Gu J. Physics-of-failure-based Prognostics for Electronic Products[J].Transactions of the Institute of Measurement and Control,2009(31):309-322.
[20] A. S. S. Vasan, B. Long, M. Pecht. Diagnostics and Prognostics Method forAnalog Electronic Circuits[J]. IEEE Transactions on Industrial Electronics,2013,60(11):5277-5291.
[21]梁慧敏,叶雪荣,翟国富,刘茂恺,郝燕玲.极化继电器判别准则的研究与应用[J].电机工程学报,2007,27(27):62-69.
[22]邓杰.航天电磁继电器稳健性设计研究[D].哈尔滨工业大学,硕士学位论文,2010:30-32.
[23] Zhai Guofu, Zhou Yuege, Ye Xuerong, Hu Bo. A method of multi-objectivereliability tolerance design for electronic circuits[J]. Chinses Journal ofAeronautics,2012,26(1):161-170.
[24] Han Hu, Xin Qi, Chang-song Wang. Finite element analysis on magnetic fieldin the actuator of giant magnetostrictive linear motor with Ansoft[C].2008IEEE International Conference on Industrial Technology,2008:1-5.
[25] Choi Jong-Hyun, Kim Jung-Hoon, Kim Dong-Ho, Baek Yoon-Su. Design andparametric analysis of axial flux PM motors with minimized cogging torque[J].IEEE Transactions on Magnetics,2009,45(6):2855-2858.
[26]王其亚.航天电磁继电器动态特性及其优化方法的研究[D].哈尔滨工业大学博士学位论文,2011:5-7.
[27]郑永成,王洋.基于磁场分割的磁导计算与磁路设计[J].机械与电子,2006(7):11-13.
[28]刘荣林.航空同步发电机的等效磁路模型[J].中国民航学院学报,2004,22(3):18-20.
[29]佟为明,李凤阁,赵志衡.单永磁极化磁系统的永磁工作点图解法统一模型与分析[J].中国电机工程学报,2005,25(6):129-133.
[30]游一民,陈德桂,罗文科,张敬菽.关于永磁机构中永磁工作点的讨论[J].高压电器,2002,38(4):39-41.
[31]李景天,宋一得,郑勤红,刘剑虹.用等效磁荷法计算永磁体磁场[J].云南师范大学学报(自然科学版),1999,19(2):33-36.
[32] Compter J C, Janssen J L G, Lomonova E A. Ampere's circuital3-D model fornoncuboidal magnets[J]. IEEE Transactions on Magnetics,2010,46(12):4009-4015.
[33] Ives Lawrence, Bui Thuc, Vogler William, Bauer Andrew, Shephard Mark,Beall Mark. Three-dimensional magnetostatic analysis using structured meshand nodal elements[J]. IEEE Transactions on Magnetics,2011,47(2):198-202.
[34] Li G J, Ojeda J, Hoang E, Gabsi M. Thermal-electromagnetic analysis of afault-tolerant dual-star flux-switching permanent magnet motor for criticalapplications[J]. IET Electric Power Applications,2011,5(6):503-513.
[35] Vuxuan H, Lahaye D, Ani S O,Polinder H, Ferreira J A. Effect of designparameters on electromagnetic torque of PM machines with concentratedwindings using nonlinear dynamic FEM[C].2011IEEE International ElectricMachines and Drives Conference IEMDC,2011:383-388.
[36] Tamitani Satoshi, Takamatsu Tomoaki, Otake Asuka, Wakao Shinji, KameariAkihisa, Takahashi Yasuhito. Finite-element analysis of magnetic field problemwith open boundary using infinite edge element[J]. IEEE Transactions onMagnetics,2011,47(5):1194-1197.
[37]姚振汉.边界元法[M].高等教育出版社,2010:5-15.
[38] A. Buchau, W. Hafla, and W. M. Rucker, Accuracy investigations of boundaryelement methods for the solution of laplace equations[J]. IEEE Transactions onMagnetics,2007,43(4):1225-1228.
[39] A. Buchau, S. M. Tsafak, W. Hafla, and W. M. Rucker, Parallelization of a fastmultipole boundary element method with cluster openMP[J]. IEEE Transactionson Magnetics,2008,44(6):1338–1341.
[40] C. Scheiblich, R. Banucu, V. Reinauer, J. Albert, and W. Rucker, Parallelhierarchical block wavelet compression for an optimal compression of3-DBEM problems[J]. IEEE Transactions on Magnetics,2011,47(5):1386–1389.
[41] I. Ciric, F. Hantila, and M.Maricaru, A new vector potential BEM for magneticfields bounded by perfect conductors[J]. IEEE Transactions on Magnetics,2011,47(5):1350–1353.
[42] P. T. While, L. K. Forbes, S. Crozier,3-D Gradient Coil Design—InitialTheoretical Framework[J]. IEEE Transactions on Biomedical Engineering,2009,56(4):1169-1183.
[43] M. Enokizono, T. Todaka, and K. Hayakawa. Three dimensional magnetic fieldanalysis of permanent magnet by boundary element method[J]. IEEETransactions on Journal of Magnetics Jappn,1990,5(9):749–754.
[44] G. Shou, L. Xia, F. L., M. Zhu, Y. Li, and S. Crozier, MRI coil design usingboundary-element method with regularization technique: A numericalcalculation study[J]. IEEE Transactions on Magnetics,2010,46(4):1052–1059.
[45] Atef Elsherbeni, Veysel Demir. The Finite Difference Time Domain Method forElectromagnetics: With MATLAB Simulations[M]. SciTech Publishing,2009:12-18.
[46] Ramli, K. N. Abd-Alhameed, R. A.; See, C. H., Atojoko, A., Noras, J. M.,Excell, P. S. Electromagnetic Field Computation for Power Transmission LinesUsing Quasi-Static Sub-Gridding Finite-Difference Time-Domain Approach[J].Eectromagnetics,2014,34(1):47-65.
[47] Yao Chenguo, Wu Hao, Mi Yan. Finite Difference Time Domain Simulation ofLightning Transient Electromagnetic Fields on Transmission Lines[J]. IEEETransactions on Dielectrics and Electrical Insulation,2013,20(4):1239-1246.
[48] Capoglu, Ilker R., Taflove Allen, Backman Vadim. Angora: A Free SoftwarePackage for Finite-Difference Time-Domain Electromagnetic Simulation[J].IEEE Antennas and Propagation Magazine.2013,55(4):80-93
[49]金建铭.电磁场有限元方法[M].西安电子科技大学出版社,2001:12-15.
[50]李景涌.有限元法[M].北京邮电大学出版社,1999:18-22.
[51]龙驭球.新型有限元论[M].清华大学出版社,2005:2-8.
[52] Jian-Ming Jin. The Finite Element Method in Electromagnetics(SecondEdition)[M], Wiley-IEEE Press,2002:13-14.
[53] J. Sibué, J. Ferrieux, G. Meunier, and R. Périot. Modeling of lossesand currentdensity distribution in conductors of a large air-gap transformer usinghomogenization and3-D FEM[J]. IEEE Transactions on Magnetics,2012,48(2):763–766.
[54] K. Hwang, H. Lin, S. Rhyu, and B. Kwon. A study on the novel coefficientmodeling for a skewed permanent magnet and overhang structure for optimaldesign of brushless DC motor[J]. IEEE Transactions on Magnetics,2012,48(5):1918–1923.
[55] T. Chan, W. Wang, and L. Lai. Magnetic field in a transverse-and axial-fluxpermanent magnet synchronous generator from3-D FEA[J]. IEEE Transactionson Magnetics,2012,48(2):1055–1058.
[56] Z. Mouton, M. J. Kamper. Modeling and Optimal Design of an Eddy CurrentCoupling for Slip-Synchronous Permanent Magnet Wind Generators[J]. IEEETransactions on Industrial Electronics,2014,61(7):3367-3376.
[57] Ross A. Howard, Xiao Yimin, Steven D. Pekarek. Modeling and Testing of anArmature-Reaction-Compensated (PM) Synchronous Generator[J]. IEEETransactions on Energy Conversion,2013,28(4):793-804.
[58] J. S. Jiang, S. D. Bader, Rational design of the exchange-spring permanentmagnet[J]. Journal of Physics-Condensed Matter,2014,26(6):1-9.
[59] P. Jin, S. Fang, H. Lin, Z. Zhu, Y. Huang, and X. Wang, Analytical magneticfield analysis and prediction of cogging force and torque of a linear and rotarypermanent magnet actuator[J]. Transactions on Magnetics,2011,47(11):3004–3007.
[60] Lee Sujin, Kim Kyuseob, Cho Sugil, Jang Junyong, Lee Taehee, Hong Jungpyo.Optimal design of interior permanent magnet synchronous motor consideringthe manufacturing tolerances using Taguchi robust design[J]. IET ElectricPower Applications.2014,8(1):23-28.
[61] Ye Xuerong, Deng Jie, Ma Yue, Zhai Guofu, Yan Jihong. A robust solution forhesitate phenomenon in pick up process of aerospace electromagnetic relay[J].Chinese Journal of Aeronautics,2013,26(3):697-704.
[62]王其亚,陈庆,谭忠华,翟国富.基于拍合式磁路结构的磁保持型继电器设计研究[J].机电元件,2013,33(5):23-30.
[63] Amrhein Marco, Krein Philip T. Magnetic equivalent circuit simulations ofelectrical machines for design purposes[J]. IEEE Electric Ship TechnologiesSymposium,2007:254-260.
[64] Amrhein Marco, Krein Philip T.3-D Magnetic equivalent circuit framework formodeling electro--mechanical devices[J]. IEEE Transactions on EnergyConversion,2009,24(2):397-405.
[65] Amrhein Marco, Krein Philip T. Force calculation in3-D magnetic equivalentcircuit networks with a Maxwell stress tensor[J]. IEEE Transactions on EnergyConversion,2009,24(3):587-593.
[66] Gyselinck J, Dular P, Legros W, Grenier D. Hybrid magnetic equivalent circuit-finite element modelling of transformer fed electrical machines[C]. COMPEL-The International Journal for Computation and Mathematics in Electrical andElectronic Engineering,2003,22(3):643-658.
[67] Sabariego R V, Geuzaine C, Dular P and Gyselinck J. H-and A-time-domainformulations for the modeling of thin electromagnetic shells[J]. IET ConferencePublications,2008(537):106-107.
[68] J Owens, P Chapman. Reduced fea-state space modeling of stationary magneticdevices[C]. IEEE34th Power Electronics Specialist Conf,2003(1):265–271.
[69] S Rutenkroger, B Deken, S Pekarek. Reduction of model dimension innonlinear finite element approximations of electromagnetic systems[C]. IEEEWorkshop on Computers in Power Electronics,2004:20-27.
[70] Zhai Guofu, Wang Qiya and Ren Wanbin. An Output Space-Mapping Algorithmto Optimize the Dimensional Parameter of Electromagnetic Relay[J]. IEEETransactions on Magnetics,2011,47(9):2194-2199.
[71] William H. Hayt, John A. Buck. Engineering Electromagnetics (8th Revisededition)[M]. McGraw Hill Higher Education Press,2011:12-13.
[72] S. Paul, D. Bobba, N. Paudel, and J. Bird, Source field modeling in air usingmagnetic charge sheets[J]. IEEE Transactions on Magnetics,2012,48(11):3879–3882.
[73] J. Yonnet and H. Allag,“Three-dimensional analytical calculation of permanentmagnet interactions by “magnetic node” representation[J]. IEEE Transactionson Magnetics,2011,47(8):2050–2055.
[74] C. Akyel, S. Babic and MM. Mahmoudi, Mutual inductance calculation for non-coaxial circular air coils with parallel axesrogress[J]. In ElectromagneticsResearch,2009,91:287–301.
[75] Gysen Bart L. J., Ilhan Esin, Meessen Koen J., Paulides Johannes J. H.,Lomonova Elena A. Modeling of Flux Switching Permanent MagnetMachines With Fourier Analysis[J]. IEEE Transactions on Magnetics,2010,46(6):1499-1502.
[76] K. Meessen, J. Paulides, and E. Lomonova, Analysis of3-D effects insegmented cylindrical quasi-Halbach magnet arrays[J]. IEEE Transactions onMagnetics,2011,47(4):727–733.
[77] C. L. W. Sonntag, Contactless energy transfer platform using aircored planarinductors[D]. Ph.D. dissertation, Eindhoven University of Technology,Eindhoven, The Netherlands,2010:6-7.
[78] Tiegna Huguette, Amara Yacine, Barakat Georges. Overview of analyticalmodels of permanent magnet electrical machines for analysis and designpurposes[J]. Mathematics and Computers in Simulation,2013,90:162-177.
[79]朱剑.复杂电磁问题的有限元、边界积分及混合算法的快速分析技术[D].南京理工大学,博士学位论文,2011:2-5.
[80] Ilhan E., Gysen B. L. J., Paulides J. J. H., Lomonova E. A. Analytical HybridModel for Flux Switching Permanent Magnet Machines[J]. IEEE Transactionson Magnetics,2010,46(6),1762-1765.
[81] C. B. Rasmussen, E. Ritchie. A Magnetic Equivalent Circuit Approach forPredictiing PM Motor Performance[C]. IEEE Industry Applications SocietyAnnual Meeting,1997:10-17.
[82] J K Kim,S W Joo, S C Hahn, J P Hong, D H Koo. Static Characteristics ofLinear BLDC Motor Using Equivalent Magnetic Circuit and FEM[J], IEEETransactions on Magnetics,2004,40(2):742-745.
[83]赵阳,陈美娟,孙雨施.电磁场计算中一种特殊边界条件及其在波阵解中应用[J].南京航空航天大学学报,1994,26(6):745-751.
[84]梁慧敏,叶雪荣,翟国富,刘茂恺,郝燕玲.极化磁系统判别准则的研究与应用[J].中国电机工程学报,2007,27(27):56-60.
[85]张冠生.电器理论基础[M].机械工业出版社,1989:238-243.
[86]毕刘新,王善铭,夏永洪.表贴式永磁电机漏磁导的解析计算[J],清华大学学报,2010,50(4):525-528.
[87] Guo Yujing, Lin Heyun, Jin Ping, Yan Jianhu, Wang Jian, Jia Zhou. AnalyticalModeling of Air-Gap Field Distributions in Permanent Magnet EmbeddedSalient Pole Wind Generator[J]. IEEE Transactions on Magnetics,2013,49(12):5756-5760.
[88]白保东,郭志楠,谢德馨.强磁场下永磁机构的优化设计及磁力分析[J].沈阳工业大学学报,2008,30(1):19-24.
[89]李斌,刘超,李洪凤,李桂丹.永磁球形电机定子绕组的永磁体模型及磁场分析[J].天津大学学报,2012,45(11):1025-1029.
[90] H R Bolton, Y Shakweh. Performance prediction of Laws’s relay actuator[J].Electric Power Applications IEE Proceedings B,1990,137(1):1-13.
[91] Manz B, Benecke M, Volke F. A simple, small and low cost permanent magnetdesign to produce homogeneous magnetic fields[J]. Journal of MagneticResonance,2008,192(1):131-138.
[92]梁慧敏,由佳欣,叶雪荣,翟国富.基于三维磁场仿真分析的含永磁继电器等效磁路模型的建立[J].电工技术学报,2011,26(1):46-50.
[93]徐俊.条形永磁分段回复线模型的研究[D].哈尔滨工业大学,硕士学位论文,2009:11-20.
[94]张荣岭,郑艳明,崔浩,梁慧敏,翟国富.条形永磁开路漏磁导磁场仿真计算方法[J].机电元件,2008,28(4):24-27.
[95]梁慧敏,张荣岭,徐俊,刘茂恺,翟国富.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.
[96] Cale J, Sudhoff S D, Tan Li-Quan. Accurately modeling el core inductors usinga high-fidelity magnetic equivalent circuit approach[J]. IEEE Transactions onMagnetics,2006,42(1):40-46.
[97] Shakirov M A. An analysis of the nonuniformity in the distribution of magneticloads and losses in transformers using magnetoelectric equivalent circuits[J].Elektrichestvo,2005(11):15-27.
[98]吴迪,辜承林.新型横向磁通永磁电机三维磁路分析[J].中国电机工程学报,2010,30(33):91-96.
[99] Jagadeesh K Tangudu, Thomas M Jahns, Ayman EL-Refaie, Z Q Zhu. Lumpedparameter magnetic circuit model for fractional-slot concentrated-windinginterior permanent magnet machines[C].2009IEEE Energy ConversionCongress and Exposition ECCE,2009(9):2423-2430.
[100]佟为明,张荣岭,刘茂恺.永久磁铁的等效处理[J].机电元件,1997,17(3-4):37-41.
[101]佟为明,刘宁宾,刘茂恺,姜守旭.极化磁系统永磁工作点的求解[J].低压电器,2000,4:12-16.
[102]向洪岗,陈德桂,李兴文,吴锐,刘洪武,耿英三.基于三维磁场分析建立电磁铁等效磁路的研究[J].西安交通大学学报,2003,37(8):807-811.
[103]梁慧敏,任万滨,王思民,翟国富.基于三维有限元法的极化磁系统静态吸力特性分析[J].机电元件,2005,25(3):3-7.
[104] Liang Huimin, You Jiaxin, Ye Xuerong and Zhai Guofu. A type of attractiveforce calculation model of polarized relay based on nonlinear permanentmagnet bar subsection model[C]. IEEE58th Holm Conference on ElectricalContacts,2012:300-304.
[105] You Jiaxin, Liang Huimin, Ye Xuerong and Zhai Guofu. The Effect of Coil onCombined Three-Subsection Permanent Magnet in Close Magnetic CircuitModel[C]. IEEE57th Holm Conference on Electrical Contacts,2011:175-178.
[106]叶雪荣.基于动态特性的航天电磁继电器可靠性容差设计技术研究[D].哈尔滨工业大学工学博士学位论文,2009:42~47.
[107]刘志刚,杜娟.一种求解非线性方程组的量子粒子群算法[J].微计算机应用,2011,32(2):31-36.
[108]姜智鹏,赵伟,屈凯峰.磁场测量技术的发展及其应用[J].电测与仪表,2008,45(4):1-5.
[109]梁慧敏,崔浩,张荣岭,翟国富.磁钢内部磁通测量装置的研制[J].机电元件,2008,6:25-28.
[110]崔浩.基于有限元法的极化磁系统等效磁路模型的研究[D].哈尔滨工业大学,硕士学位论文,2009:16-18.
[111] Xiaotao Han, Zhiwei Song. The Development of Measurement and ControlSoftware Applied To Small Pulsed High Magnetic Field Facility[C].Proceedings of2009Chinese Control and Decision Conference,2009(3):4470-4474.
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