潜油电机机械损耗及隔磁段电磁参数计算分析
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摘要
潜油电机作为潜油电泵机组的动力部分,是一种立式三相异步电动机,工作于数千米井下的特殊环境中,定转子采用分段的细长结构,气隙中充满专用润滑油。转子由同轴的若干个独立的笼型转子单元组成,每两个单元之间装有扶正轴承;与扶正轴承相对应的定子铁心处装有隔磁段。显然,普通三相感应电动机的通用设计方法不再完全适合潜油电机,但是目前国内外还没有一种完善的充分考虑其特殊结构和工作环境的设计方法,多数仍是采用传统普通异步电机设计方法,这在工程实践中很难满足实际准确度需求,误差很大。
本文根据国内外潜油电机设计的研究现状,分析了目前设计中所存在的问题。针对设计中的关键技术问题,结合其结构特点运用电磁场理论、流体理论等技术理论对潜油电机的设计方法进行了深入具体的研究,形成了具有高准确度的设计方法。
首先研究了气隙中充满专用润滑油后对潜油电机机械损耗的影响,着重分析了电机高速旋转时润滑油对转子形成的油摩损耗,采用流体力学的原理并结合潜油电机稳态运行时止推轴承动块、静块及扶正轴承的摩擦损耗的经验公式得到了潜油电机机械损耗的准确计算方法,通过对实例的计算、实验对比,证明了该方法的有效性。
分析了潜油电机隔磁段处漏磁对电机性能参数的影响,定义了潜油电机特有的隔磁段漏抗。建立了隔磁段三维有限元模型,通过求解其中的磁场储能来获得该漏抗值,实验证明隔磁段漏抗对电机的性能参数有较大的影响,在电机的设计中必须考虑。
同时利用有限元模型,在保证计算结果正确的前提下,对定转子铁心磁导率的非线性做了简化后计算了转子扶正轴承中的附加涡流损耗。分析了采用现有钢外套扶正轴承的潜油电机其附加损耗对电机效率的影响,并研究了采用新型具有大电阻率而又不导磁的合金材料制造扶正轴承外套时,可将该损耗显著降低,对电机效率影响可忽略不计。
结合潜油电机直径很小长度很大难以采用传统斜槽,文中通过将转子槽中心线与键中心线设计成某一定特定角度,转子铁心叠压时分别采用冲片的正反面,形成不同的转子铁心,安装在扶正轴承的两侧,在整个电机中起到了等效斜槽的作用。
研制了两台模拟实验样机,样机设计时考虑了既能够反映所要研究的问题又要结构简单易于制造。两台实验样机采用相同的电磁设计方案,不同的结构设计。样机由两段组成,输出功率6 kW,电压290 V,总装完成后电机的长度是1.6 m。样机中一台定转子之间装有隔磁段和扶正轴承;另一台样机没有扶正轴承,转子分段处用卡簧固定。
样机制造完成后,首先应用前文所述方法对样机的扶正轴承附加涡流损耗及其机械损耗进行了理论计算。购置了相关实验设备并分别对两台样机进行了实验,分析两组实验数据,得到了扶正轴承附加涡流损耗和机械损耗的实验值。最后对比相关参数的计算值与实验值表明,考虑本文所提出的参数后的计算结果更加接近实验值,直接验证了研究内容的正确性。对样机的定子隔磁段漏抗进行了间接验证,证明了文中所述理论计算方法具有很高的准确度。
在上述研究基础上,对潜油电机隔磁段漏抗做了应用研究,深入研究了隔磁段漏抗随电机功率等级、隔磁段宽度、隔磁段数量以及扶正轴承与相邻两段转子相对位置的变化,对现有各功率等级潜油电机在不同隔磁段宽度下的隔磁段漏抗做了大量的计算,得到潜油电机漏抗曲线族,为今后潜油电机的设计提供了可靠的依据。
论文的研究成果为潜油电机的设计提供了参考,并考虑到今后产品的批量生产,提出了电机结构中的通用性、适应性和可靠性的设计。所提出的方法和研究成果不仅具有理论意义,而且具有较高的实用价值。
As the drive part of submersible pump set, submersible motor is a kind of vertical three-phase asynchronous motor, working in very special situation , the bottom of oil well , thousands of meters under ground. The stator and rotor are slender and separated; the gap is full of special lube oil. The rotor includes several cage-type rotor units; there is bearing between every two units; corresponding to the rotor bearing, there are magnetic isolated segments in the stator core. Obviously, common calculation method for general three-phase asynchronous motor is not completely suitable for submersible motor, but till now there is not a design method inside or outside of China that can perfectly consider the special structure and working situation. Traditional design method for general asynchronous motor is used in most occasions, the error is big and the practical accuracy requirement is hard to be satisfied in engineering practice.
According to nowadays international study status of submersible motor, the problems exist in present design method are analyzed. For the pivotal technology problems in design, combined with its structure character, electromagnetic field theory, liquid theory and etc. are applied to thoroughly and concretely study the design method of submersible motor, and the high accuracy design method is formed.
When the gap is full of special lube oil, the influence to the mechanical loss of the submersible motor is studied; the oil friction loss formed by lube oil with rotor as the motor revolves with high speed is analyzed emphatically; hydromechanical theory and empirical formula for friction loss of thrust bearing shoe, static block and rotor bearing under working condition of the motor are adopted, the accurate calculation method of mechanical loss of submersible motor is acquired, and the effectiveness of this method has been proved by experiments and calculations of example.
The leak magnet influence of magnetic isolated segment to the performance parameter of submersible motor is analyzed, and the concept of leakage reactance in magnetic isolated segment is defined. The 3D FEM model of magnetic isolated segment is set up, and the leakage reactance is achieved by solving the stored energy of the model. It is proved by experiment that the influence of leakage reactance in magnetic isolated segment to the performance parameter of the motor is clear and must be considered in the design of the motor.
Meanwhile, under the premise of guaranteeing the calculation result is right, the nonlinearity of magnetic conductivity of the stator core and rotor core is simplified and the additive loss in rotor bearing is calculated by FEM model. For the submersible motor with steel outer space rotor bearing, the influence of additive loss to the efficiency of motor is analyzed. It is studied that, when new type alloy material with big resistivity and without magnetic permeability is used to produce the outer space rotor bearing, the loss is reduced obviously and the influence to the motor efficiency can be ignored.
As the characteristic of submersible motor with small diameter and big length that traditional skewed slot is hard to be adopted. In this dissertation, the angle between the line of rotor slot centre and the line of key centre is designed with some special degree. Front and back of iron sheet are used separately when making the rotor iron core, and different rotor cores are formed and installed at the two sides of the rotor bearing, so the function of skewed slot is attained for the whole motor.
Two sets of simulated experiment simulated model are developed, not only the studied problems are considered when designing the sample motor, but also the structure shall be easy to be manufactured. For the two sets of model, the same electro-magnetic design scheme but different structure designs are used. The sample has two sections, output power 6kW, voltage 290V, the length of the whole assembled motor is 1.6m. For one sample, magnetic isolated segment and rotor bearing are installed at the subsection of the stator and rotor; for the other one, no rotor bearing is installed at the subsection but circlip to fix.
After the samples are completed, the additive loss in rotor bearing and mechanical loss are theoretically calculated by the method stated above. The related experiment equipments are purchased and the experiments are carried out for the two samples, two groups of test data are analyzed and the experimental values of additive loss in rotor bearing and mechanical loss are acquired. At last, comparing the calculation value with the experimental value of the related parameters, it shows that, the calculation result which considers the parameters raised in this dissertation can reach the experimental values closer. The correctness of the study content is proved directly. The theoretical calculation method is testified with very high accuracy by indirect experiment of leakage reactance in magnetic isolated segment of samples.
Based on the reserch above, the universality research of leakage reactance in magnetic isolated segment of submersible motor is carried out. It is studied profoundly that how the leakage reactance in magnetic isolated segment changes with the motor power rate, the width of magnetic isolated segment, the quantity of magnetic isolated segment and the relative position of rotor bearing and the near two section of rotors. For each power rate of now available submersible motor, large amount of calculations of leakage reactance in magnetic isolated segment under different width of magnetic isolated segment have been done, and the leakage reactance curve group of submersible motor is achieved, which will provide reliable foundation for submersible motor design in future.
Research achievement of this dissertation provided the reference for the design of submersible motor. Considering batch production of the product in future, the universal property, flexibility and reliability design of the motor structure is provided. The provided method and study achievement not only have theoretical significance but also very high practical value.Submersible Motor.
本文根据国内外潜油电机设计的研究现状,分析了目前设计中所存在的问题。针对设计中的关键技术问题,结合其结构特点运用电磁场理论、流体理论等技术理论对潜油电机的设计方法进行了深入具体的研究,形成了具有高准确度的设计方法。
首先研究了气隙中充满专用润滑油后对潜油电机机械损耗的影响,着重分析了电机高速旋转时润滑油对转子形成的油摩损耗,采用流体力学的原理并结合潜油电机稳态运行时止推轴承动块、静块及扶正轴承的摩擦损耗的经验公式得到了潜油电机机械损耗的准确计算方法,通过对实例的计算、实验对比,证明了该方法的有效性。
分析了潜油电机隔磁段处漏磁对电机性能参数的影响,定义了潜油电机特有的隔磁段漏抗。建立了隔磁段三维有限元模型,通过求解其中的磁场储能来获得该漏抗值,实验证明隔磁段漏抗对电机的性能参数有较大的影响,在电机的设计中必须考虑。
同时利用有限元模型,在保证计算结果正确的前提下,对定转子铁心磁导率的非线性做了简化后计算了转子扶正轴承中的附加涡流损耗。分析了采用现有钢外套扶正轴承的潜油电机其附加损耗对电机效率的影响,并研究了采用新型具有大电阻率而又不导磁的合金材料制造扶正轴承外套时,可将该损耗显著降低,对电机效率影响可忽略不计。
结合潜油电机直径很小长度很大难以采用传统斜槽,文中通过将转子槽中心线与键中心线设计成某一定特定角度,转子铁心叠压时分别采用冲片的正反面,形成不同的转子铁心,安装在扶正轴承的两侧,在整个电机中起到了等效斜槽的作用。
研制了两台模拟实验样机,样机设计时考虑了既能够反映所要研究的问题又要结构简单易于制造。两台实验样机采用相同的电磁设计方案,不同的结构设计。样机由两段组成,输出功率6 kW,电压290 V,总装完成后电机的长度是1.6 m。样机中一台定转子之间装有隔磁段和扶正轴承;另一台样机没有扶正轴承,转子分段处用卡簧固定。
样机制造完成后,首先应用前文所述方法对样机的扶正轴承附加涡流损耗及其机械损耗进行了理论计算。购置了相关实验设备并分别对两台样机进行了实验,分析两组实验数据,得到了扶正轴承附加涡流损耗和机械损耗的实验值。最后对比相关参数的计算值与实验值表明,考虑本文所提出的参数后的计算结果更加接近实验值,直接验证了研究内容的正确性。对样机的定子隔磁段漏抗进行了间接验证,证明了文中所述理论计算方法具有很高的准确度。
在上述研究基础上,对潜油电机隔磁段漏抗做了应用研究,深入研究了隔磁段漏抗随电机功率等级、隔磁段宽度、隔磁段数量以及扶正轴承与相邻两段转子相对位置的变化,对现有各功率等级潜油电机在不同隔磁段宽度下的隔磁段漏抗做了大量的计算,得到潜油电机漏抗曲线族,为今后潜油电机的设计提供了可靠的依据。
论文的研究成果为潜油电机的设计提供了参考,并考虑到今后产品的批量生产,提出了电机结构中的通用性、适应性和可靠性的设计。所提出的方法和研究成果不仅具有理论意义,而且具有较高的实用价值。
As the drive part of submersible pump set, submersible motor is a kind of vertical three-phase asynchronous motor, working in very special situation , the bottom of oil well , thousands of meters under ground. The stator and rotor are slender and separated; the gap is full of special lube oil. The rotor includes several cage-type rotor units; there is bearing between every two units; corresponding to the rotor bearing, there are magnetic isolated segments in the stator core. Obviously, common calculation method for general three-phase asynchronous motor is not completely suitable for submersible motor, but till now there is not a design method inside or outside of China that can perfectly consider the special structure and working situation. Traditional design method for general asynchronous motor is used in most occasions, the error is big and the practical accuracy requirement is hard to be satisfied in engineering practice.
According to nowadays international study status of submersible motor, the problems exist in present design method are analyzed. For the pivotal technology problems in design, combined with its structure character, electromagnetic field theory, liquid theory and etc. are applied to thoroughly and concretely study the design method of submersible motor, and the high accuracy design method is formed.
When the gap is full of special lube oil, the influence to the mechanical loss of the submersible motor is studied; the oil friction loss formed by lube oil with rotor as the motor revolves with high speed is analyzed emphatically; hydromechanical theory and empirical formula for friction loss of thrust bearing shoe, static block and rotor bearing under working condition of the motor are adopted, the accurate calculation method of mechanical loss of submersible motor is acquired, and the effectiveness of this method has been proved by experiments and calculations of example.
The leak magnet influence of magnetic isolated segment to the performance parameter of submersible motor is analyzed, and the concept of leakage reactance in magnetic isolated segment is defined. The 3D FEM model of magnetic isolated segment is set up, and the leakage reactance is achieved by solving the stored energy of the model. It is proved by experiment that the influence of leakage reactance in magnetic isolated segment to the performance parameter of the motor is clear and must be considered in the design of the motor.
Meanwhile, under the premise of guaranteeing the calculation result is right, the nonlinearity of magnetic conductivity of the stator core and rotor core is simplified and the additive loss in rotor bearing is calculated by FEM model. For the submersible motor with steel outer space rotor bearing, the influence of additive loss to the efficiency of motor is analyzed. It is studied that, when new type alloy material with big resistivity and without magnetic permeability is used to produce the outer space rotor bearing, the loss is reduced obviously and the influence to the motor efficiency can be ignored.
As the characteristic of submersible motor with small diameter and big length that traditional skewed slot is hard to be adopted. In this dissertation, the angle between the line of rotor slot centre and the line of key centre is designed with some special degree. Front and back of iron sheet are used separately when making the rotor iron core, and different rotor cores are formed and installed at the two sides of the rotor bearing, so the function of skewed slot is attained for the whole motor.
Two sets of simulated experiment simulated model are developed, not only the studied problems are considered when designing the sample motor, but also the structure shall be easy to be manufactured. For the two sets of model, the same electro-magnetic design scheme but different structure designs are used. The sample has two sections, output power 6kW, voltage 290V, the length of the whole assembled motor is 1.6m. For one sample, magnetic isolated segment and rotor bearing are installed at the subsection of the stator and rotor; for the other one, no rotor bearing is installed at the subsection but circlip to fix.
After the samples are completed, the additive loss in rotor bearing and mechanical loss are theoretically calculated by the method stated above. The related experiment equipments are purchased and the experiments are carried out for the two samples, two groups of test data are analyzed and the experimental values of additive loss in rotor bearing and mechanical loss are acquired. At last, comparing the calculation value with the experimental value of the related parameters, it shows that, the calculation result which considers the parameters raised in this dissertation can reach the experimental values closer. The correctness of the study content is proved directly. The theoretical calculation method is testified with very high accuracy by indirect experiment of leakage reactance in magnetic isolated segment of samples.
Based on the reserch above, the universality research of leakage reactance in magnetic isolated segment of submersible motor is carried out. It is studied profoundly that how the leakage reactance in magnetic isolated segment changes with the motor power rate, the width of magnetic isolated segment, the quantity of magnetic isolated segment and the relative position of rotor bearing and the near two section of rotors. For each power rate of now available submersible motor, large amount of calculations of leakage reactance in magnetic isolated segment under different width of magnetic isolated segment have been done, and the leakage reactance curve group of submersible motor is achieved, which will provide reliable foundation for submersible motor design in future.
Research achievement of this dissertation provided the reference for the design of submersible motor. Considering batch production of the product in future, the universal property, flexibility and reliability design of the motor structure is provided. The provided method and study achievement not only have theoretical significance but also very high practical value.Submersible Motor.
引文
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35 Erdelyi E A, Ahmed S V. Flux Distribution in Saturated D.C. machines. IEEE Trans PAS, 1965, 84(6):1315~1322
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38 Pabot J L.Study on The Electromagnetic Field of Windings of Turbogenerator. IEEE Trans. PAS, 1975, 94(4):519~528
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45 Frederic bcuillault, Adel razek. Dynamic Model for Eddy Current Calculation inSaturated Electric Machines. IEEE IEEE Trans.MAG, 2005, 19(6):2639~2642
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47 Kurt Preis, Oszkár Bíró, Igor Ti?car. FEM Analysis of Eddy Current Losses in Nonlinear Laminated Iron Cores. IEEE Trans.MAG, 2005, 41(5),1412~1415
48严登俊,刘瑞芳,胡敏强,李训铭.鼠笼异步电机启动性能的时步有限元计算.电机与控制学报,2003,7(3):177~181
49 M.A.Choudhury, M.Azizur Rahman. Determination of Operation Conditions of Submersible Induction Motors. IEEE Trans.APPL, 2002, 38(3):680~684
50谢德馨,姚缨英,白保东,李锦彪.三维涡流场的有限元分析.北京:机械工业出版社,2001:14~25
51 Silvester P P,Chari M V K. Finite Element Solution of Saturable Magnetic Field Problems. IEEE Trans. PAS, 1970, 89(12):1674~1685
52 Christian Kaehler and Gerhard Henneberger. Transient 3-D FEM Computation of Eddy-Current Losses in the Rotor of a Claw-Pole Alternator. IEEE Transactions on magnetics, 2004, 40(2),1362~1365
53 Karl Hollaus and Oszkár Bíró. A FEM Formulation to Treat 3D Eddy Currents in Laminations. IEEE Transactions on magnetics, 2000, 36(4),1289~1292
54 Harrington R F. Field Computation by the Moment Method. New York: Macmillan.2005:33~52
55 Dudley R F, Burke P E. The Prediction of Current Distribution in Induction Heading Installations. IEEE Trans. Ind. Appl. 2006, 42(8):1632~1638
56 Ishibashi K. Nonlinear Eddy Current Analysis by Volume Integral Equation Method. IEEE Trans. MAG, 1997, 23(6):927~933
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65 M.V.K Chari,P.Silvester,A.Konrad,Z.J.Csendes,M.A.Palmo. Three-Dimensional Magnetostatic Fields Analysis of Electrical Machinery by the Finite-element Method. IEEE Trans, 2006 (100):4007~4017
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35 Erdelyi E A, Ahmed S V. Flux Distribution in Saturated D.C. machines. IEEE Trans PAS, 1965, 84(6):1315~1322
36 Ahamed S V, Erdelyi E A. Nonlinear Theory of Salient Pole Machines. IEEE Trans. PAS, 1965, 84(4):1165~1167
37 Erdelyi E A,Ahmed S V. Nonlinear Theory of Synchronous Machines on Load. IEEE Trans. PAS, 1965, 84(4):1347~1353
38 Pabot J L.Study on The Electromagnetic Field of Windings of Turbogenerator. IEEE Trans. PAS, 1975, 94(4):519~528
39 Molinari G,Viviani.A. Grid and metric optimization procedures in finite difference and finite element method. Proc of IEE PES Winter meeting,New York, A78,289-1,1-9(1978):243~247
40赵光,陈永校.一种计算笼型异步电机稳态特性的有限元模型.中小型电机,2001,28(3):26~29
41 Martic H C,Carey G.Introduction to Finite Element Analysis Theory and Applications. New York:McGraw-Hill,1973:79~88
42 Hildebrand F B. Advanced Calculus for Applications. Englewood Cliffs,N.J. :Prentice-Hall,1962:141~153
43 Winslow A A. Numerical Solution of The Quasi-linear Poisson Equation in a Non-uniform Triangular Mesh. J. Comput. Phys.,1971,1:385~389
44王坚.基于有限元法的电机铁心涡流损耗分析.大电机技术,2004,(4):5~9
45 Frederic bcuillault, Adel razek. Dynamic Model for Eddy Current Calculation inSaturated Electric Machines. IEEE IEEE Trans.MAG, 2005, 19(6):2639~2642
46闫照文,李朗如.电磁场有限元分析的优秀软件.微电机,2002,27~29
47 Kurt Preis, Oszkár Bíró, Igor Ti?car. FEM Analysis of Eddy Current Losses in Nonlinear Laminated Iron Cores. IEEE Trans.MAG, 2005, 41(5),1412~1415
48严登俊,刘瑞芳,胡敏强,李训铭.鼠笼异步电机启动性能的时步有限元计算.电机与控制学报,2003,7(3):177~181
49 M.A.Choudhury, M.Azizur Rahman. Determination of Operation Conditions of Submersible Induction Motors. IEEE Trans.APPL, 2002, 38(3):680~684
50谢德馨,姚缨英,白保东,李锦彪.三维涡流场的有限元分析.北京:机械工业出版社,2001:14~25
51 Silvester P P,Chari M V K. Finite Element Solution of Saturable Magnetic Field Problems. IEEE Trans. PAS, 1970, 89(12):1674~1685
52 Christian Kaehler and Gerhard Henneberger. Transient 3-D FEM Computation of Eddy-Current Losses in the Rotor of a Claw-Pole Alternator. IEEE Transactions on magnetics, 2004, 40(2),1362~1365
53 Karl Hollaus and Oszkár Bíró. A FEM Formulation to Treat 3D Eddy Currents in Laminations. IEEE Transactions on magnetics, 2000, 36(4),1289~1292
54 Harrington R F. Field Computation by the Moment Method. New York: Macmillan.2005:33~52
55 Dudley R F, Burke P E. The Prediction of Current Distribution in Induction Heading Installations. IEEE Trans. Ind. Appl. 2006, 42(8):1632~1638
56 Ishibashi K. Nonlinear Eddy Current Analysis by Volume Integral Equation Method. IEEE Trans. MAG, 1997, 23(6):927~933
57 Koizumi M, Onizawa M. Computational Method of Three Dimensional Eddy Current by Using Volume Integral Equation Method. IEEE Trans. MAG, 1991, 17(4):487~495
58 Gimignani M, Musolino A,Raugi M. Integral Formulation for Nonlinear Magnetostatic and Eddy Currents Analysis. IEEE Trans. MAG, 1994, 20(4):1471~1479
59 Fawzi T H, Burke P E. Use of surface integral equations for the analysis of TM-induction problem. Proc. IEE, 1974, 31(5):991~1007
60 Mayergoyz. Boundary Integral Equations of Minimum Order for Calculation of Three Dimensional Eddy Current Problems. IEEE Trans. MAG, 2006,32(3):369~374
61 Lowther D A, Silvester P P. Computer Aided Design in Magnetics. Berlin: Springer. 2003:17~31
62 Zienkiewicz O C. Taylor R L. The Finite Element Method(4th edition).New York: Mc Graw-Hill.2006:94~103
63 Reece A B J, Preston T W. Finite Element Methods in Electrical Power Engineering. London: Oxford,2005:3~12
64 K.Preis,H.Stogner,K.R.Richter. Calculation of Eddy Current Losses in Air Coils by Finite Element Method. IEEE Trans. MAG, 2002, 18(6),1064~1066
65 M.V.K Chari,P.Silvester,A.Konrad,Z.J.Csendes,M.A.Palmo. Three-Dimensional Magnetostatic Fields Analysis of Electrical Machinery by the Finite-element Method. IEEE Trans, 2006 (100):4007~4017
66 Toshiya Morisue. Magnetic Vector Potential and Electrical Scalar Potential in Three Dimension Eddy Current Problem. IEEE Trans Magnetics, 2000, 18(2),531~533
67 N.A.Demerdash, O.A.Mohammed, T.W.Nehl, F.A.Found,R.H.Miller. Solution of Eddy Current Problems Using Three Dimension Finite Element Complex Magnetic Vector Potential. IEEE Trans, 2006, (100):3038~3043
68 O.A.Mohammed, N.A.Demerdash,T.W.Nehl. Validity of Finite Element Formulation an Solution of Three Dimension Magnetic Problems in Electrical Device with Applications to Transformers and Reactors.IEEE Trans, 2005, 99(7):1846~1853
69黄学良,胡敏强,杜炎森,周鹗.汽轮发电机端部似稳涡流场数学模型.东南大学学报,1995,(2):90~97
70阮江君,陈贤珍,周克定.大型汽轮发电机端部三维瞬态涡流场数值分析.大电机技术,1997,(5):1~4
71 Ballisti R, Hafner C. The Multipole Method in Electro and Magnetostatic Problems. IEEE Trans. MAG, 2004, 30(4):2309~2317
72 Meng H Lean. Application of Boundary Integral Equations to Electromagnetics. IEEE Trans. MAG, 2005, 31(5):856~869
73 Lalaichelvan S, Lavers J D. On the Implementation of a Boundary Element Method for 3-D Multiply Connected EM Field Problems. IEEE Trans. MAG, 2004, 30(7):1979~1990
74 Shao K R, et al. Boundary Element Analysis Method for 3-D Eddy Current Problems Using the Second Order Vector Potential. IEEE Trans. MAG, 2003, 29(6):1857~1861
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