永磁同步电机转子偏心磁场解析计算
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摘要
为了快速准确计算两极平行充磁实心圆柱式永磁同步电机(SCPMSM)各种转子偏心参数下的磁场分布,提供研究转子偏心对电机性能影响的有效方法,利用子区域法和摄动法,在二维极坐标平面内建立了考虑定子齿槽效应时的SCPMSM转子偏心磁场解析模型;将求解场域划分为永磁体、气隙和定子槽3类子区域,分别用对应的控制函数来表达,各区域之间用边界条件连接,利用边界条件求出控制方程通解的各个谐波系数。根据摄动理论,将磁场的0阶分量和1阶分量叠加获得相应子域转子偏心磁场分布,利用麦克斯韦应力张量法计算了转子静态偏心以及动态偏心引起的不平衡磁拉力。以一台2极12槽平行充磁SCPMSM为例,将转子偏心磁场以及静态偏心和动态偏心不平衡磁拉力的解析计算结果与有限元计算结果进行对比,验证了解析模型的正确性。
An analytical model for magnetic field of solid cylindrical permanent magnet synchronous motor(SCPMSM)with rotor eccentricity,considering the stator slotting effect,is developed based on subdomain and perturbation methods in 2Dpolar coordinates to quickly and accurately calculate the magnetic field distribution in two-pole parallel magnetised SCPMSM with rotor eccentricity with various parameters and to provide an effective method of studying the influence of rotor eccentricity on motor performances.The analysis is performed by dividing the solution domain into three subdomains,viz.permanent magnet,air gap and stator slots.Those subdomains are expressed by corresponding governing equations,and are connected by boundary conditions.The harmonic coefficients in the general solutions of these governing equations are determined by the boundary conditions.The magnetic field distributions of corresponding subdomains in the motor with rotor eccentricity are obtained by superposing the first-order component of the magnetic field onto the zeroth-order component according to the perturbation theory.The unbalanced magnetic pulls under both rotor static and dynamic eccentricity modes arecalculated using Maxwell stress tensor method.A 2-pole and 12-slot parallel magnetised SCPMSM is taken as an example,and its rotor eccentric magnetic field and unbalanced magnetic pulls under two eccentricity modes are calculated by the proposed model and are compared with those by a finite element method.Result verifies the correctness of the analytical model.
An analytical model for magnetic field of solid cylindrical permanent magnet synchronous motor(SCPMSM)with rotor eccentricity,considering the stator slotting effect,is developed based on subdomain and perturbation methods in 2Dpolar coordinates to quickly and accurately calculate the magnetic field distribution in two-pole parallel magnetised SCPMSM with rotor eccentricity with various parameters and to provide an effective method of studying the influence of rotor eccentricity on motor performances.The analysis is performed by dividing the solution domain into three subdomains,viz.permanent magnet,air gap and stator slots.Those subdomains are expressed by corresponding governing equations,and are connected by boundary conditions.The harmonic coefficients in the general solutions of these governing equations are determined by the boundary conditions.The magnetic field distributions of corresponding subdomains in the motor with rotor eccentricity are obtained by superposing the first-order component of the magnetic field onto the zeroth-order component according to the perturbation theory.The unbalanced magnetic pulls under both rotor static and dynamic eccentricity modes arecalculated using Maxwell stress tensor method.A 2-pole and 12-slot parallel magnetised SCPMSM is taken as an example,and its rotor eccentric magnetic field and unbalanced magnetic pulls under two eccentricity modes are calculated by the proposed model and are compared with those by a finite element method.Result verifies the correctness of the analytical model.
引文
[1]KIM U,LIEU D K.Magnetic field calculation in permanent magnet motors with rotor eccentricity:without slotting effect[J].IEEE Transactions on Magnetics,1998,34(4):2243-2252.
[2]KIM U,LIEU D K.Magnetic field calculation in permanent magnet motors with rotor eccentricity:with slotting effect considered[J].IEEE Transactions on Magnetics,1998,34(4):2253-2266.
[3]RAHIDEH A,KORAKIANITIS T.Analytical opencircuit magnetic field distribution of slotless brushless permanent-magnet machines with rotor eccentricity[J].IEEE Transactions on Magnetics,2011,47(12):4791-4808.
[4]FU J J,ZHU C S.Subdomain model for predicting magnetic field in slotted surface mounted permanentmagnet machines with rotor eccentricity[J].IEEETransactions on Magnetics,2012,48(5):1906-1917.
[5]周晓燕,李琛,仇志坚,等.基于摄动法的交替极永磁电机偏心磁场解析计算[J].电工技术学报,2013,28(9):321-331.ZHOU Xiaoyan,LI Chen,QIU Zhijian,et al.Magnetic field calculation for consequent-pole motor with rotor eccentricity based on perturbation method[J].Transactions of China Electrotechnical Society,2013,28(9):321-331.
[6]刘蓉晖,章跃进,李琛,等.永磁电动机转子偏心空载气隙磁场矢量位解析法[J].微特电机,2013,41(6):6-9.LIU Ronghui,ZHANG Yuejin,LI Chen,et al.Analytical method with vector magnetic potential for opencircuit air-gap magnetic field computation in permanent magnet motors with rotor eccentricity[J].Small&Special Electrical Machines,2013,41(6):6-9.
[7]LI J T,LIU Z J,NAY L H A.Effect of radial magnetic forces in permanent magnet motors with rotor eccentricity[J].IEEE Transactions on Magnetics,2007,43(6):2525-2527.
[8]DORRELL D G,HSIEH M F,GUO Y G.Unbalanced magnet pull in large brushless rare-earth permanent magnet motors with rotor eccentricity[J].IEEETransactions on Magnetics,2009,45(10):4586-4589.
[9]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[J].IEEE Transactions on Magnetics,2010,46(7):2675-2685.
[10]张冉,王秀和,杨玉波,等.基于等效剩磁法的永磁电动机转子偏心磁场解析计算[J].电工技术学报,2009,24(5):7-12.ZHANG Ran,WANG Xiuhe,YANG Yubo.Analytical prediction of magnetic field in permanent magnet motors with rotor eccentricity based on the method of equivalent remanence[J].Transactions of China Electrotechnical Society,2009,24(5):7-12.
[11]XIANG C L,LIU F,LIU H,et al.Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull[J].Journal of Sound and Vibration,2016,371:277-294.
[12]左曙光,高丽华,吴旭东,等.电动车用永磁同步电机转子偏心对电磁力影响分析[J].佳木斯大学学报(自然科学版),2014,32(2):166-170,175.ZUO Suguang,GAO Lihua,WU Xudong,et al.The analysis of electromagnetic force in permanent magnet synchronous motors with rotor eccentricity in electric vehicles[J].Journal of Jiamusi University(Natural Science Edition),2014,32(2):166-170,175.
[13]KIM U,LIEU D K.Effects of magnetically induced vibration force in brushless permanent-magnet motors[J].IEEE Transactions on Magnetics,2005,41(6):2164-2172.
[14]KIM D,NOH M D,PARK Y W.Unbalanced magnetic forces due to rotor eccentricity in a toroidally wound BLDC motor[J].IEEE Transactions on Magnetics,2016,52(7):8203204.
[15]WANG J P,LIEU D K.Magnetic lumped parameter modeling of rotor eccentricity in brushless permanentmagnet motors[J].IEEE Transactions on Magnetics,1999,35(5):4226-4231.
[16]岳二团,甘春标,杨世锡.气隙偏心下永磁电机转子系统的振动特性分析[J].振动与冲击,2014,33(8):29-34.YUE Ertuan,GAN Chunbiao,YANG Shixi.Vibration characteristics analysis of a rotor for a permanent magnet motor with air-gap eccentricity[J].Journal of Vibration and Shock,2014,33(8):29-34.
[17]CHENG W J,SUN Y H,YU L,et al.Analytical solution to magnetic field distribution of a parallel magnetised rotor with cylindrical or ring-type permanent magnet[J].IET Electric Power Applications,2015,9(6):429-437.
[18]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.
[2]KIM U,LIEU D K.Magnetic field calculation in permanent magnet motors with rotor eccentricity:with slotting effect considered[J].IEEE Transactions on Magnetics,1998,34(4):2253-2266.
[3]RAHIDEH A,KORAKIANITIS T.Analytical opencircuit magnetic field distribution of slotless brushless permanent-magnet machines with rotor eccentricity[J].IEEE Transactions on Magnetics,2011,47(12):4791-4808.
[4]FU J J,ZHU C S.Subdomain model for predicting magnetic field in slotted surface mounted permanentmagnet machines with rotor eccentricity[J].IEEETransactions on Magnetics,2012,48(5):1906-1917.
[5]周晓燕,李琛,仇志坚,等.基于摄动法的交替极永磁电机偏心磁场解析计算[J].电工技术学报,2013,28(9):321-331.ZHOU Xiaoyan,LI Chen,QIU Zhijian,et al.Magnetic field calculation for consequent-pole motor with rotor eccentricity based on perturbation method[J].Transactions of China Electrotechnical Society,2013,28(9):321-331.
[6]刘蓉晖,章跃进,李琛,等.永磁电动机转子偏心空载气隙磁场矢量位解析法[J].微特电机,2013,41(6):6-9.LIU Ronghui,ZHANG Yuejin,LI Chen,et al.Analytical method with vector magnetic potential for opencircuit air-gap magnetic field computation in permanent magnet motors with rotor eccentricity[J].Small&Special Electrical Machines,2013,41(6):6-9.
[7]LI J T,LIU Z J,NAY L H A.Effect of radial magnetic forces in permanent magnet motors with rotor eccentricity[J].IEEE Transactions on Magnetics,2007,43(6):2525-2527.
[8]DORRELL D G,HSIEH M F,GUO Y G.Unbalanced magnet pull in large brushless rare-earth permanent magnet motors with rotor eccentricity[J].IEEETransactions on Magnetics,2009,45(10):4586-4589.
[9]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[J].IEEE Transactions on Magnetics,2010,46(7):2675-2685.
[10]张冉,王秀和,杨玉波,等.基于等效剩磁法的永磁电动机转子偏心磁场解析计算[J].电工技术学报,2009,24(5):7-12.ZHANG Ran,WANG Xiuhe,YANG Yubo.Analytical prediction of magnetic field in permanent magnet motors with rotor eccentricity based on the method of equivalent remanence[J].Transactions of China Electrotechnical Society,2009,24(5):7-12.
[11]XIANG C L,LIU F,LIU H,et al.Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull[J].Journal of Sound and Vibration,2016,371:277-294.
[12]左曙光,高丽华,吴旭东,等.电动车用永磁同步电机转子偏心对电磁力影响分析[J].佳木斯大学学报(自然科学版),2014,32(2):166-170,175.ZUO Suguang,GAO Lihua,WU Xudong,et al.The analysis of electromagnetic force in permanent magnet synchronous motors with rotor eccentricity in electric vehicles[J].Journal of Jiamusi University(Natural Science Edition),2014,32(2):166-170,175.
[13]KIM U,LIEU D K.Effects of magnetically induced vibration force in brushless permanent-magnet motors[J].IEEE Transactions on Magnetics,2005,41(6):2164-2172.
[14]KIM D,NOH M D,PARK Y W.Unbalanced magnetic forces due to rotor eccentricity in a toroidally wound BLDC motor[J].IEEE Transactions on Magnetics,2016,52(7):8203204.
[15]WANG J P,LIEU D K.Magnetic lumped parameter modeling of rotor eccentricity in brushless permanentmagnet motors[J].IEEE Transactions on Magnetics,1999,35(5):4226-4231.
[16]岳二团,甘春标,杨世锡.气隙偏心下永磁电机转子系统的振动特性分析[J].振动与冲击,2014,33(8):29-34.YUE Ertuan,GAN Chunbiao,YANG Shixi.Vibration characteristics analysis of a rotor for a permanent magnet motor with air-gap eccentricity[J].Journal of Vibration and Shock,2014,33(8):29-34.
[17]CHENG W J,SUN Y H,YU L,et al.Analytical solution to magnetic field distribution of a parallel magnetised rotor with cylindrical or ring-type permanent magnet[J].IET Electric Power Applications,2015,9(6):429-437.
[18]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.