电动汽车永磁轮毂电机磁场非线性解析计算方法
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摘要
针对传统解析法通常假设铁磁材料磁导率为无穷大、忽略了磁饱和效应的问题,提出一种考虑铁磁材料磁导率非线性影响的磁场解析建模方法。利用复数形式的傅里叶级数和柯西乘积将材料磁导率嵌入到静磁场求解中,将永磁轮毂电机分为定子齿槽、气隙和永磁体3个求解域,以矢量磁位为求解变量,根据激励源的不同在各求解域建立拉普拉斯方程或泊松方程,联立边界条件求得各域矢量磁位。根据材料非线性B-H曲线,利用迭代算法得到了各工况下定子齿上的相对磁导率分布,计算了空载、电枢、负载磁场分布及输出转矩,并通过有限元法验证了该非线性解析法较传统解析法更准确。
A magnetic field analytical modeling method that considers the nonlinear influence of magnetic permeability of ferromagnetic materials is proposed to solve the problem that traditional analytical methods usually assume that the permeability of ferromagnetic materials is infinite and ignore the effect of magnetic field saturation.The material permeability is embedded into the static magnetic field by using the complex Fourier series and the Cauchy product,and the permanent magnet hub motor is divided into three domains:the stator tooth/slot,air gap and permanent magnet.The vector magnetic potential is used as a solution variable,Laplace equations or Poisson equations are established in each solution domain according to difference of excitation sources,and the vector magnetic potential of each domain is obtained by simultaneous boundary conditions.According to the nonlinear B-H curve of the material,an iterative algorithm is used to obtain the relative permeability distribution on the stator teeth under various working conditions.The no-load,armature,load air gap flux density and output torque are calculated.A finite element method is used to verify that the nonlinear analytical method is more accurate than the traditional analytical methods.
A magnetic field analytical modeling method that considers the nonlinear influence of magnetic permeability of ferromagnetic materials is proposed to solve the problem that traditional analytical methods usually assume that the permeability of ferromagnetic materials is infinite and ignore the effect of magnetic field saturation.The material permeability is embedded into the static magnetic field by using the complex Fourier series and the Cauchy product,and the permanent magnet hub motor is divided into three domains:the stator tooth/slot,air gap and permanent magnet.The vector magnetic potential is used as a solution variable,Laplace equations or Poisson equations are established in each solution domain according to difference of excitation sources,and the vector magnetic potential of each domain is obtained by simultaneous boundary conditions.According to the nonlinear B-H curve of the material,an iterative algorithm is used to obtain the relative permeability distribution on the stator teeth under various working conditions.The no-load,armature,load air gap flux density and output torque are calculated.A finite element method is used to verify that the nonlinear analytical method is more accurate than the traditional analytical methods.
引文
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[16]DJELLOUL-KHEDDA Z,BOUGHRARA K,DU-BAS F,et al.Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines[J].IEEE Transactions on Magnetics,2017,53(7):1-11.
[2]仇志坚,李琛,周晓燕,等.表贴式永磁电机转子偏心空载气隙磁场解析[J].电工技术学报,2013,28(3):114-121.QIU Zhijian,LI Chen,ZHOU Xiaoyan,et al.Analytical calculation of no-load air-gap magnetic field in surface-mounted permanent magnet motors with rotor eccentricity[J].Transactions of China Electrotechnical Society,2013,28(3):114-121.
[3]郭思源,周理兵,曲荣海,等.基于精确子域模型的游标永磁电机解析磁场计算[J].中国电机工程学报,2013,33(30):71-80.GUO Siyuan,ZHOU Libing,QU Ronghai,et al.Analytical magnetic field calculation of vernier permanentmagnet machines based on sccurate dubdomain model[J].Proceedings of the CSEE,2013,33(30):71-80.
[4]李琛,章跃进,仇志坚.无轴承交替极永磁电机空载气隙磁场全局解析模型[J].电工技术学报,2012,27(11):104-110.LI Chen,ZHANG Yuejin,QIU Zhijian.Exact analytical model for the no-load air-gap magnetic field calculation in consequent-pole permanent magnet bearingless motor[J].Transactions of China Electrotechnical Society,2012,27(11):104-110.
[5]ZARKO D,BAN D,LIPO T A,et al.Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance[J].IEEE Transactions on Magnetics,2006,42(7):1828-1837.
[6]ZARKO D,BAN D,LIPO T A.Analytical solution for cogging torque in surface permanent-magnet motors using conformal mapping[J].IEEE Transactions on Magnetics,2008,44(1):52-65.
[7]ZARKO D,BAN D,LIPO T A.Analytical solution for electromagnetic torque in surface permanent-magnet motors using conformal mapping[J].IEEE Transactions on Magnetics,2009,45(7):2943-2954.
[8]ZHU Z Q,WU L J,XIA Z P.An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent-magnet machines[J].IEEETransactions on Magnetics,2010,46(4):1100-1115.
[9]WU L J,ZHU Z Q,STATON D.An improved subdomain model for predicting magnetic field of surfacemounted permanent magnet machines sccounting for tooth-tips[J].IEEE Transactions on Magnetics,2011,47(6):1693-1704.
[10]WU L J,ZHU Z Q,STATON D,et al.Comparison of analytical models of cogging torque in surfacemounted PM machines[J].IEEE Transactions on Industrial Electronics,2012,59(6):2414-2425.
[11]郭思源,周理兵.表面埋入式永磁电机磁场解析[J].中国电机工程学报,2015,35(3):710-718.GUO Siyuan,ZHOU Libing.Analytical solution of magnetic field in surface-inset permanent magnet machines[J].Proceedings of the CSEE,2015,35(3):710-718.
[12]杨金歌,邓兆祥.车用永磁轮毂电机解析建模与齿槽转矩削弱[J].西安交通大学学报,2017,51(1):84-91.YANG Jinge,DENG Zhaoxiang.Analytical modeling and cogging torque weakening of permanent magnet inwheel motor for electric vehicles[J].Journal of Xi’an Jiaotong University,2017,51(1):10-19.
[13]WU L J,LI Zhaokai,HUANG Xiaoyan.A hybrid field model for open-circuit field prediction in surfacemounted PM machines considering saturation[J].IEEE Transactions on Magnetics,2018,54(6):1-12.
[14]LAZHAR R,KAMEL B.New subdomain technique for electromagnetic performances calculation in radialflux electrical machines considering finite soft-magnetic material permeability[J].IEEE Transactions on Magnetics,2018,54(4):1-15.
[15]SPRANGERS R L J,PAULIDES J J H,GYSEN B LJ.Magnetic saturation in semi-analytical harmonic modeling for electric machine analysis[J].IEEETransactions on Magnetics,2016,52(2):1-10.
[16]DJELLOUL-KHEDDA Z,BOUGHRARA K,DU-BAS F,et al.Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines[J].IEEE Transactions on Magnetics,2017,53(7):1-11.