变极永磁同步电动机研究
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摘要
目前，变极调速技术在感应电动机中应用广泛，只需改变定子绕组的极数即可改变电机转速，但功率因数较低。普通永磁同步电动机具有高效、高功率因数和经济运行范围宽的特点，但为防止出现不可逆去磁，永磁体用量较多，导致电机成本较高，并且永磁磁极的极性难以改变，电机在制成之后极数是固定的，不能实现变极。若能将二者的优点相结合，开发变极永磁同步电动机，具有重要的理论意义和现实意义。
2001年德国的Vlado Ostovic率先提出了变极永磁同步电动机，并进行了相关研究，设计制造了一台样机并进行了试验研究。Vlado Ostovic的样机定子绕组与变极感应电动机相同，转子采用切向充磁的铝镍钴永磁和软铁相互叠加而成的“Sandwich”结构，变极时以定子绕组为充磁绕组。试验表明：该电机能够实现变极，且效率高于同功率等级的感应电动机。但其研究只是验证了变极永磁同步电动机的可行性，缺乏系统深入的研究，并且采用的转子结构复杂，加工困难，结构强度低，充磁时充磁绕组与转子相对位置对充磁结果有较大影响，作者推导了变极充磁电流和变极后每极磁通与电机结构参数和永磁体性能的关系，推导变极充磁电流时忽略了铁心磁压降，推导每极磁通时假设充磁后永磁体都被饱和切向磁化了，与永磁体的实际磁化状态有较大误差，没有给出永磁体充磁后磁化状态的确定方法。
本课题针对上述不足进行了进一步的研究，主要研究内容如下：
1．提出了变极永磁同步电动机的表面式转子结构，采用环形永磁体。Vlado Ostovic样机采用的“Sandwich”转子结构复杂，加工困难，结构强度较低，充磁时充磁绕组与转子相对位置对充磁结果有较大影响。为此，本文提出了表面式转子结构，采用环形永磁体。表面式转子结构在永磁直流电机、无刷直流电机和表面式永磁同步电动机中得到了广泛的应用，生产和加工工艺已经非常成熟，具有结构简单可靠、机械强度高、充磁与定转子相对位置无关等优点，能够保证电机运行的可靠性，降低了成本。
2．研究了变极充磁时永磁体磁化状态确定方法。Vlado Ostovic推导了变极充磁电流和变极后每极磁通与电机结构参数和永磁体性能的关系，推导变极充磁电流时时忽略了充磁过程中的铁心磁压降，推导每极磁通时假设充磁后永磁体都被饱和切向磁化了，与实际情况有较大误差，没有给出永磁体充磁后磁化状态的确定方法。由于变极永磁同步电动机以定子绕组为充磁绕组，充磁磁场比较复杂，本文建立了永磁体的初始磁化模型和重新磁化模型，引入饱和系数，解析法计算了考虑铁心饱和时的充磁磁场强度，将两者相结合得到了考虑永磁体原磁化状态的永磁体磁化状态确定方法和饱和充磁电流确定方法。
3．研究了变极永磁同步电动机的性能计算方法。由于变极永磁同步电动机中永磁体的磁化状态由充磁决定，磁化状态比较复杂，以往气隙磁密的计算方法不再适用，本文采用有限元法计算得到了气隙磁密，据此得到了空载反电动势，其他计算步骤与普通永磁同步电动机相同。研究了提高永磁同步电动机效率和功率因数、扩大经济运行范围的技术措施，研究表明保持空载反电动势小于并接近于外加电压，可以获得接近于1的功率因数，空载反电动势满足这一要求还可使永磁同步电动机在不同的负载下效率最高，获得较宽广的经济运行范围。
4．对永磁电机的共性问题——齿槽转矩进行了研究，主要工作包括：
(1)基于能量法得到了表面式永磁电机齿槽转矩的解析表达式，该表达式体现了电机结构参数对齿槽转矩的影响，为齿槽转矩削弱方法研究提供了依据。
(2)分析了永磁体极弧系数对齿槽转矩的影响。现有的极弧系数确定方法得到的都是近似值，很难在实际中应用。本文分析了平行充磁永磁直流电机极弧系数对齿槽转矩的影响，得到了极弧系数的确定方法。
(3)分析了不等槽口宽配合削弱齿槽转矩的方法。改进了Sang-Moon Hwang提出的Teeth Pairing法，得到了槽口宽度计算方法和该方法的适用范围。
(4)分析了磁极偏移削弱齿槽转矩的方法。现有关于磁极偏移削弱齿槽转矩的文献都是基于削弱永磁体对称时存在的齿槽转矩谐波，但是磁极偏移后会引进新的齿槽转矩谐波，本文得到了削弱永磁体对称时存在的和磁极偏移后引进谐波的磁极偏移角度计算方法。
(5)分析了永磁体极弧系数组合削弱齿槽转矩的方法，得到了相邻永磁体极弧系数的计算方法。
(6)分析了不等厚永磁磁极削弱齿槽转矩的方法。研究表明：随着偏心距的增大，有些极数和槽数组合的永磁电机齿槽转矩会减小，但是也有些情况下会增大。
(7)研究了定子齿开辅助槽削弱齿槽转矩的方法。现有文献得到的辅助槽数确定方法对于每极整数槽的情况不适用，本文将辅助槽法和永磁体极弧系数选择相结合，得到了辅助槽数确定方法。
(8)推导了内置式永磁同步电动机齿槽转矩的解析表达式，并对齿槽转矩的组成分量和斜槽的影响进行了分析。
Pole-changing induction motors are widely used in many applications. The number of poles can be changed by changing the pole number of stator windings. But the power factor of pole-changing induction motor is low. The power factor and efficiency of permanent magnet synchronous motor are high, but the pole number of permanent magnet can not change in common permanent magnet synchronous motor, pole-changing can not achieved. It has great significance to develop pole-changing permanent magnet synchronous motor which can combine the characteristic of pole-changing and high power factor and high efficiency.
Vlado Ostovic first proposed pole-changing permanent magnet motor. In his paper, the rotor is built following the sandwich of permanent magnets, soft iron, all of them being mechanically fixed to a non-magnetic shaft, and the stator is the same as that of pole-changing induction motor. Magnetic equivalent circuit is used to get the current to magnetize the PM and the flux per pole. A prototype is designed and tested at last. The test results verify the author's design. The efficiency and power factor of pole-changing permanent magnet motor is higher than that of induction motor. But the configuration of the rotor is complicated, and construction strength is low. When the permanent magnet is magnetized, the position between stator and rotor has effect on the magnetized state of permanent magnet. Based on Vlado Ostovic's research, the main study works of this dissertation are as follows.
1. In order to solve the shortcomings of sandwich configuration rotor, the surfaced-mounted permanent magnet rotor is applied. The configuration of surface-mounted permanent magnet rotor is widely used in permanent magnet direct current machine, brushless direct current machine and permanent magnet synchronous motor. The configuration is very simple, and mechanical strength is good. When the permanent magnet is magnetizing, the position between rotor and stator winding has no effect on the magnetization of permanent magnet.
2. The initial magnetization model and remagnetization model of permanent magnet are suggested. In Vlado Ostovic's research, magnetic equivalent circuit is used to get the current to magnetize the PM and the flux per pole on the assumption that all the permanent magnets in the rotor are saturation magnetized. But in fact, it is impossible to make all the permanent magnets be saturation magnetized. In this paper, the magnetic field strength in permanent magnet is calculated by analytical method and finite element method. The magnetized state of permanent magnet is got by combining magnetization model and magnetic field strength result.
3. The performance calculation of pole-changing permanent magnet synchronous motor is studied. The technical measures to improve the efficiency and power factor, to broaden the economical operation of permanent magnet synchronous motor are studied.
4. Cogging torque of permanent magnet motor is studied. The research work is shown as follows.
(1) The analytical expressions of cogging torque of surface-mounted permanent magnet motor and self starting permanent magnet synchronous motor are got by energy method. This analytical expression can be used to study the reduction method of cogging torque.
(2) The reduction method of cogging torque by pole arc coefficient of permanent magnet is studied. The pole arc coefficient of PM got in reference is approximation value. In this paper, the method to calculate the pole arc coefficient is got.
(3) The reduction method of cogging torque by different slot width pairing is studied. The range of application of this method and the calculation of slot opening with are studied.
(4) The reduction method of cogging torque by PM shifting is studied. The research works of PM shifting in references are based on eliminating the harmonics of cogging torque with PM symmetry. When PM shifting is adopted, new lower harmonics of cogging torque are inevitably introduced. In this paper, the PM shifting angles calculation is studied to reduce both the lower original harmonics and newly introduced harmonics of cogging torque.
(5) The reduction method of cogging torque by pole arc combination is studied, and the calculation method of pole arc coefficient of PM is got.
(6) The reduction method of cogging torque by eccentricity PM is studied.
(7) The reduction method of cogging torque by notches is studied. It is very important to select the number of notches in one stator tooth. It is not easy to decide the number when the slot number per pole is an integer. In this paper, the method of notch and pole arc coefficient is combined to reduce the cogging torque.
(8) The analytical expression of cogging torque of self starting permanent magnet synchronous motor. The influence factor of cogging torque is studied.
2001年德国的Vlado Ostovic率先提出了变极永磁同步电动机，并进行了相关研究，设计制造了一台样机并进行了试验研究。Vlado Ostovic的样机定子绕组与变极感应电动机相同，转子采用切向充磁的铝镍钴永磁和软铁相互叠加而成的“Sandwich”结构，变极时以定子绕组为充磁绕组。试验表明：该电机能够实现变极，且效率高于同功率等级的感应电动机。但其研究只是验证了变极永磁同步电动机的可行性，缺乏系统深入的研究，并且采用的转子结构复杂，加工困难，结构强度低，充磁时充磁绕组与转子相对位置对充磁结果有较大影响，作者推导了变极充磁电流和变极后每极磁通与电机结构参数和永磁体性能的关系，推导变极充磁电流时忽略了铁心磁压降，推导每极磁通时假设充磁后永磁体都被饱和切向磁化了，与永磁体的实际磁化状态有较大误差，没有给出永磁体充磁后磁化状态的确定方法。
本课题针对上述不足进行了进一步的研究，主要研究内容如下：
1．提出了变极永磁同步电动机的表面式转子结构，采用环形永磁体。Vlado Ostovic样机采用的“Sandwich”转子结构复杂，加工困难，结构强度较低，充磁时充磁绕组与转子相对位置对充磁结果有较大影响。为此，本文提出了表面式转子结构，采用环形永磁体。表面式转子结构在永磁直流电机、无刷直流电机和表面式永磁同步电动机中得到了广泛的应用，生产和加工工艺已经非常成熟，具有结构简单可靠、机械强度高、充磁与定转子相对位置无关等优点，能够保证电机运行的可靠性，降低了成本。
2．研究了变极充磁时永磁体磁化状态确定方法。Vlado Ostovic推导了变极充磁电流和变极后每极磁通与电机结构参数和永磁体性能的关系，推导变极充磁电流时时忽略了充磁过程中的铁心磁压降，推导每极磁通时假设充磁后永磁体都被饱和切向磁化了，与实际情况有较大误差，没有给出永磁体充磁后磁化状态的确定方法。由于变极永磁同步电动机以定子绕组为充磁绕组，充磁磁场比较复杂，本文建立了永磁体的初始磁化模型和重新磁化模型，引入饱和系数，解析法计算了考虑铁心饱和时的充磁磁场强度，将两者相结合得到了考虑永磁体原磁化状态的永磁体磁化状态确定方法和饱和充磁电流确定方法。
3．研究了变极永磁同步电动机的性能计算方法。由于变极永磁同步电动机中永磁体的磁化状态由充磁决定，磁化状态比较复杂，以往气隙磁密的计算方法不再适用，本文采用有限元法计算得到了气隙磁密，据此得到了空载反电动势，其他计算步骤与普通永磁同步电动机相同。研究了提高永磁同步电动机效率和功率因数、扩大经济运行范围的技术措施，研究表明保持空载反电动势小于并接近于外加电压，可以获得接近于1的功率因数，空载反电动势满足这一要求还可使永磁同步电动机在不同的负载下效率最高，获得较宽广的经济运行范围。
4．对永磁电机的共性问题——齿槽转矩进行了研究，主要工作包括：
(1)基于能量法得到了表面式永磁电机齿槽转矩的解析表达式，该表达式体现了电机结构参数对齿槽转矩的影响，为齿槽转矩削弱方法研究提供了依据。
(2)分析了永磁体极弧系数对齿槽转矩的影响。现有的极弧系数确定方法得到的都是近似值，很难在实际中应用。本文分析了平行充磁永磁直流电机极弧系数对齿槽转矩的影响，得到了极弧系数的确定方法。
(3)分析了不等槽口宽配合削弱齿槽转矩的方法。改进了Sang-Moon Hwang提出的Teeth Pairing法，得到了槽口宽度计算方法和该方法的适用范围。
(4)分析了磁极偏移削弱齿槽转矩的方法。现有关于磁极偏移削弱齿槽转矩的文献都是基于削弱永磁体对称时存在的齿槽转矩谐波，但是磁极偏移后会引进新的齿槽转矩谐波，本文得到了削弱永磁体对称时存在的和磁极偏移后引进谐波的磁极偏移角度计算方法。
(5)分析了永磁体极弧系数组合削弱齿槽转矩的方法，得到了相邻永磁体极弧系数的计算方法。
(6)分析了不等厚永磁磁极削弱齿槽转矩的方法。研究表明：随着偏心距的增大，有些极数和槽数组合的永磁电机齿槽转矩会减小，但是也有些情况下会增大。
(7)研究了定子齿开辅助槽削弱齿槽转矩的方法。现有文献得到的辅助槽数确定方法对于每极整数槽的情况不适用，本文将辅助槽法和永磁体极弧系数选择相结合，得到了辅助槽数确定方法。
(8)推导了内置式永磁同步电动机齿槽转矩的解析表达式，并对齿槽转矩的组成分量和斜槽的影响进行了分析。
Pole-changing induction motors are widely used in many applications. The number of poles can be changed by changing the pole number of stator windings. But the power factor of pole-changing induction motor is low. The power factor and efficiency of permanent magnet synchronous motor are high, but the pole number of permanent magnet can not change in common permanent magnet synchronous motor, pole-changing can not achieved. It has great significance to develop pole-changing permanent magnet synchronous motor which can combine the characteristic of pole-changing and high power factor and high efficiency.
Vlado Ostovic first proposed pole-changing permanent magnet motor. In his paper, the rotor is built following the sandwich of permanent magnets, soft iron, all of them being mechanically fixed to a non-magnetic shaft, and the stator is the same as that of pole-changing induction motor. Magnetic equivalent circuit is used to get the current to magnetize the PM and the flux per pole. A prototype is designed and tested at last. The test results verify the author's design. The efficiency and power factor of pole-changing permanent magnet motor is higher than that of induction motor. But the configuration of the rotor is complicated, and construction strength is low. When the permanent magnet is magnetized, the position between stator and rotor has effect on the magnetized state of permanent magnet. Based on Vlado Ostovic's research, the main study works of this dissertation are as follows.
1. In order to solve the shortcomings of sandwich configuration rotor, the surfaced-mounted permanent magnet rotor is applied. The configuration of surface-mounted permanent magnet rotor is widely used in permanent magnet direct current machine, brushless direct current machine and permanent magnet synchronous motor. The configuration is very simple, and mechanical strength is good. When the permanent magnet is magnetizing, the position between rotor and stator winding has no effect on the magnetization of permanent magnet.
2. The initial magnetization model and remagnetization model of permanent magnet are suggested. In Vlado Ostovic's research, magnetic equivalent circuit is used to get the current to magnetize the PM and the flux per pole on the assumption that all the permanent magnets in the rotor are saturation magnetized. But in fact, it is impossible to make all the permanent magnets be saturation magnetized. In this paper, the magnetic field strength in permanent magnet is calculated by analytical method and finite element method. The magnetized state of permanent magnet is got by combining magnetization model and magnetic field strength result.
3. The performance calculation of pole-changing permanent magnet synchronous motor is studied. The technical measures to improve the efficiency and power factor, to broaden the economical operation of permanent magnet synchronous motor are studied.
4. Cogging torque of permanent magnet motor is studied. The research work is shown as follows.
(1) The analytical expressions of cogging torque of surface-mounted permanent magnet motor and self starting permanent magnet synchronous motor are got by energy method. This analytical expression can be used to study the reduction method of cogging torque.
(2) The reduction method of cogging torque by pole arc coefficient of permanent magnet is studied. The pole arc coefficient of PM got in reference is approximation value. In this paper, the method to calculate the pole arc coefficient is got.
(3) The reduction method of cogging torque by different slot width pairing is studied. The range of application of this method and the calculation of slot opening with are studied.
(4) The reduction method of cogging torque by PM shifting is studied. The research works of PM shifting in references are based on eliminating the harmonics of cogging torque with PM symmetry. When PM shifting is adopted, new lower harmonics of cogging torque are inevitably introduced. In this paper, the PM shifting angles calculation is studied to reduce both the lower original harmonics and newly introduced harmonics of cogging torque.
(5) The reduction method of cogging torque by pole arc combination is studied, and the calculation method of pole arc coefficient of PM is got.
(6) The reduction method of cogging torque by eccentricity PM is studied.
(7) The reduction method of cogging torque by notches is studied. It is very important to select the number of notches in one stator tooth. It is not easy to decide the number when the slot number per pole is an integer. In this paper, the method of notch and pole arc coefficient is combined to reduce the cogging torque.
(8) The analytical expression of cogging torque of self starting permanent magnet synchronous motor. The influence factor of cogging torque is studied.
引文
[1] V. Ostovic, Pole-changing permanent-magnet machines, IEEE Trans. Industry Applications, vol. 38, pp. 1493-1499, 2002.
[2] V. Ostovic, Memory motors, IEEE Industry Applications Magazine, vol. 9, pp. 52-61, 2003.
[3] V. Ostovic, Memory motors: a new class of controllable flux PM machines for a true wide speed operation, Third-sixth IAS annual meeting, vol. 4, pp. 2577-2584, 2001.
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[14] 王兴华等，永磁无刷直流电机磁阻转矩的解析计算方法，中国电机工程学报，Vol．22，no．10．2002．
[15] Xiuhe Wang et al., Study of cogging torque in surface-mounted permanent magnet motors with energy method, Journal of Magnetism and Magnetic Materials, 267(2003), pp. 80-85.
[16] I. Takeo et al., A method of reducing ripple torque in permanent magnet motors without skewing, IEEE Trans. Magnetism, vol. 29, pp. 2028-2031, 1993.
[17] Touzhu et al., Reduction of cogging torque in permanent magnet motors, IEEE Trans. Magnetics, vol. 24, pp. 2901-2903, 1988.
[18] N. Bianchi and S. Bolognani, Reducing torque ripple in PM synchronous motors, in Proc. Int. Conf. Electrical Machines, ICEM 2000, Helsinki, Finland, Aug. 28-30, pp. 1222-1226.
[19] Nicola Bianchi and Silverio Bolognani, Design techiniques for reducing the cogging torque in surface-mounted PM motors, IEEE Trans. Magnetism, vol. 38, pp. 1259-1265, 2002.
[20] C. Breton et al., Influence of machine symmetry on reduction of cogging torque in permanent magnet brushless motors, IEEE Trans. Magnetics, vol. 36, pp. 3819-3823, 2000.
[21] D. C. Hanselman, Effect of skew, pole count and slot count on brushless motor radial force, cogging torque and back EMF, IEE Pro.-Electr. Power Appl., vol. 144, No. 5, 1997.
[22] Sang-Moon Hwang et al., Cogging torque and acoustic noise reducing in permanent magnet motors by teeth pairing, IEEE Trans. Magnetics, vol. 36, pp. 3144-3146, 2000.
[23] Sangmoon Hwang, et al., Design techniques for reduction of reluctance torque in brushless permanent magnet motors, IEEE Trans. Magnetics, vol. 30, no. 6, pp. 4287-4289, 1994.
[24] Ki-jin Han, et al., Core shape optimization for cogging torque reduction of BLDC motor, IEMD' 99, pp. 416-418, 1999.
[25] K. J Han, et al., Optimal core shape design for cogging torque reduction of BLDC motor using algorithm, Proc. Compumag'99, pp. 332-333, 1999.
[26] T. M. Jahns, et al., Pulsating torque minimization techniques for permanent magnet AC motor drives-a review, IEEE Trans. Industrial Electronics, vol. 43, pp. 321-330, 1996.
[27] M. Lukaniszyn, et al., Optimization of permanent magnet shape for minimum cogging torque using a genetic algorithm, IEEE Trans. Magnetics, vol. 40, no. 2, 2004.
[28] Sang-Moon Hwang, et al., Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors, IEEE Trans. Magnetics, vol. 37, pp. 2806-2809, 2001.
[29] A. Nakahata, et al., 3-D finite-element analysis of electromagnets with permanent magnet taking into account magnetizing process, IEEE Trans. Magnetics, vol. 33, pp. 2057-2060, 1997.
[30] T. Nakata, et al., Numerical analysis of transient magnetic field in a capacitor-discharge inpulse magnetizer, IEEE Trans. Magnetics, vol. 22, pp. 526-528, 1986.
[31] Yoshihiro Kawase, et al., Analysis of magnetization process using discharge current of capacitor by 3-D finite element method, IEEE Trans. Magnetics, vol. 38, pp. 1145-1148, 2002.
[32] Chang Seop Koh, et al., Finite element analysis of magnetizer using Preisach model, IEEE Trans. Magnetics, vol. 35, pp. 1227-1230, 1999.
[33] Edward Della Torre, et al., Preisach modeling and reversible magnetization, IEEE Trans. Magnetics, vol. 26, pp. 3052-3058, 1990.
[34] I. D. Mayergoyz, et al., Generalized preisach model of hysteresis, IEEE Trans. Magnetics, vol. 24, pp. 212-217, 1988.
[35] C. K. Lee, et al., Analysis of magnetization of magnet in the rotor of line start permanent magnet motor, IEEE Trans. Magnetics, vol. 39, pp. 1499-1503, 2003.
[36] Ann Reimers, et al., Fast Preisach-based vector magnetization model, IEEE Trans. Magnetics, vol. 37, pp. 3349-3352, 2001.
[37] Ann Reimers, et al., Implementation of Preisach DOK magnetic hysteresis model in a commercial finite element package, IEEE Trans. Magnetics, vol. 37, pp. 3362-3365, 2001.
[38] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅰ: open-circuit field, IEEE Trans. Magnetics, vol. 29, pp. 124-135, 1993.
[39] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅱ: armature-reaction field, IEEE Trans. Magnetics, vol. 29, pp. 136-142, 1993.
[40] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅲ: effect of stator slotting, IEEE Trans. Magnetics, vol. 29, pp. 142-151, 1993.
[41] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅳ: magnetic field on load, IEEE Trans. Magnetics, vol. 29, pp. 152-158, 1993.
[42] Do Hyun Kang, Paul Curiac, Yeon Ho Jeong, and Soo Jin Jung, Prospects for magnetization of large PM motors: conclusions from a development case study, IEEE Trans. Energy Conversion, vol. 18, no. 3, pp. 409416, 2003.
[43] H. G. Brachtendorf and R. Laur, A hysteresis model for hard magnetic core materials, IEEE Trans. Magnetics, vol. 33, no. 1, Jan. 1997, pp. 723-727.
[44] K. H. Carpenter, A differential equation approach to minor loops in the Jiles-Atherton hysteresis model, IEEE Trans. Magnetics, vol. 27, Nov. 1991.
[45] D. C. Jiles and D. L. Atherton, Ferromagnetic hysteresis, IEEE Trans. Magnetics, vol. 19, pp. 2183-2185, Sept. 1983.
[46] D. C. Jiles and D. L. Atherton, Theory of the magnetization process in ferromagnets and its application to the magnetomechanical effect, J. Phys., D: Appl. Phys., vol. 17, pp. 1265-1281, 1984.
[47] D. C. Jiles and D. L. Atherton, Theory of ferromagnetic hysteresis, Magnetism Magn. Mater., vol. 61, pp. 48-60, 1986.
[48] D. C. Jiles and D. L. Atherton, Theory of ferromagnetic hysteresis(invited), J. Appl. Phys., vol. 55, pp. 2115-2120, Mar. 15, 1984.
[49] D. C. Jiles, J. B. Thoelke, and M. K. Devine, Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis, IEEE trans. Nagnetics, vol. 28, no. 1, pp. 27-35, Jan. 1992.
[50] H. G. Brachtendorf, and R. Laur, A hysteresis model for hard magnetic core materials, IEEE Trans. Magnetics, vol. 33, no. 3, pp. 723-727, Jan. 1997.
[51] 曹淑瑛,王博文,闫荣格等,超磁滞伸缩致动器的磁滞非线性动态模型,中国电机工程学报,2003年23卷11期．
[52] D. C. Jiles, A self consistent generalized model for the calculation of minor loop excursions in the theory of hysteresis, IEEE Trans. Magneticis, vol. 28, no. 5, pp: 2602-2604.
[53] Sergey E. Zirka, and Yury I. Moroz, Hysteresis modeling based on similarity, IEEE Trans. Magnetics, no. 4, vol. 35, pp.2090-2096, 1999.
[54] S. E. Zirka, and Yu. I. Moroz, Hysteresis modeling based on transplantation, IEEE Trans. Magnetics, no. 6, vol. 31, pp. 3509-3511, 1995.
[55] David L. Atherton, and Markus Schonbachler, Measurements of reversible magnetization componet, IEEE Trans. Magnetics, no. 1, vol. 24, pp. 616-620, 1088.
[56] Der-Ray Huang, Tai-Fa Ying, Shyh-Jier Wang, and etc., Cogging torque reduction of a single-phase brushless DC motor, IEEE Trans. Magnetics, vol. 34, No. 4, pp2072077, 1998.
[57] C. C. Hwang, S.B.John and S.S.Wu, Reduction of cogging torque in spindle motors for CD-ROM drive, IEEE Trans.,Magnetics, vol. 34, No. 2, pp 468-470, 1998.
[58] Z. Q. Zhu, D. Howe, Analytical prediction of magnet brushless motors, IEEE Trans., Magneics, vol. 28, No. 2, pp468-470,1992.
[59] 冀溥，王秀和，王道涵，杨玉波，转子静态偏心的表面式永磁电机齿槽转矩研究，中国电机工程学报，2004，24(9)：188-191．
[60] 王兴华，励庆孚，永磁无刷直流电机空载气隙磁场和绕组反电势的解析计算，中国电机工程学报，2003，23(3)：126-130．
[61] 杨玉波，王秀和，陈谢杰，冀溥，基于不等槽口宽配合的永磁电动机齿槽转矩削弱方法，电工技术学报，2005，20(3)：40-44．
[62] 宋伟，王秀和，杨玉波，削弱永磁电机齿槽转矩的一种新方法，电机与控制学报，2004，8(3)：214-217．
[63] 杨玉波，王秀和，张鑫，贺广富，磁极偏移削弱永磁电机齿槽转矩方法，电工技术学报，2006，21(10)：22-25．
[64] 王秀和，杨玉波，丁婷婷，朱常青，王道涵，基于极弧系数选择的实心转子永磁同步电动机齿槽转矩削弱方法，中国电机工程学报，2005，15(15)：147-149．
[65] Yubo Yang, Xiuhe Wang, Rong Zhang, Tlngting Ding, Renyuan Tang, The optimization of pole arc coefficient to reduce cogging torque in surface-mounted permanent magnet motors, IEEE Trans. Magnetics, vol. 42, No. 4, pp.1135-1138, 2006.
[66] 杨玉波，王秀和，丁婷婷，张鑫，张冉，朱常青，极弧系数组合优化的永磁电机齿槽转矩削弱方法，中国电机工程学报，27(6)，pp．7-11，2007．
[67] 邹俊杰，鼠笼式拖动电机变极调速原理及分析，船电技术，2006年4期，28-30．
[68][68] 唐文忠，李高，4／8极绕线型变极调速感应电动机的研究，电机电器技术，2001年第3期，11-13．
[69] 李宁，贾堂刚，交流异步电动机调速方式分析，矿山机械，33(3)，2005，70-72．
[70] 郭羽，浅谈三相异步电动机的调速，农村电工，2005年10期．
[2] V. Ostovic, Memory motors, IEEE Industry Applications Magazine, vol. 9, pp. 52-61, 2003.
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[13] Z. Q. Zhu et al., Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines, IEEE Trans. Magnetics, vol. 38, pp. 229-238, 2002.
[14] 王兴华等，永磁无刷直流电机磁阻转矩的解析计算方法，中国电机工程学报，Vol．22，no．10．2002．
[15] Xiuhe Wang et al., Study of cogging torque in surface-mounted permanent magnet motors with energy method, Journal of Magnetism and Magnetic Materials, 267(2003), pp. 80-85.
[16] I. Takeo et al., A method of reducing ripple torque in permanent magnet motors without skewing, IEEE Trans. Magnetism, vol. 29, pp. 2028-2031, 1993.
[17] Touzhu et al., Reduction of cogging torque in permanent magnet motors, IEEE Trans. Magnetics, vol. 24, pp. 2901-2903, 1988.
[18] N. Bianchi and S. Bolognani, Reducing torque ripple in PM synchronous motors, in Proc. Int. Conf. Electrical Machines, ICEM 2000, Helsinki, Finland, Aug. 28-30, pp. 1222-1226.
[19] Nicola Bianchi and Silverio Bolognani, Design techiniques for reducing the cogging torque in surface-mounted PM motors, IEEE Trans. Magnetism, vol. 38, pp. 1259-1265, 2002.
[20] C. Breton et al., Influence of machine symmetry on reduction of cogging torque in permanent magnet brushless motors, IEEE Trans. Magnetics, vol. 36, pp. 3819-3823, 2000.
[21] D. C. Hanselman, Effect of skew, pole count and slot count on brushless motor radial force, cogging torque and back EMF, IEE Pro.-Electr. Power Appl., vol. 144, No. 5, 1997.
[22] Sang-Moon Hwang et al., Cogging torque and acoustic noise reducing in permanent magnet motors by teeth pairing, IEEE Trans. Magnetics, vol. 36, pp. 3144-3146, 2000.
[23] Sangmoon Hwang, et al., Design techniques for reduction of reluctance torque in brushless permanent magnet motors, IEEE Trans. Magnetics, vol. 30, no. 6, pp. 4287-4289, 1994.
[24] Ki-jin Han, et al., Core shape optimization for cogging torque reduction of BLDC motor, IEMD' 99, pp. 416-418, 1999.
[25] K. J Han, et al., Optimal core shape design for cogging torque reduction of BLDC motor using algorithm, Proc. Compumag'99, pp. 332-333, 1999.
[26] T. M. Jahns, et al., Pulsating torque minimization techniques for permanent magnet AC motor drives-a review, IEEE Trans. Industrial Electronics, vol. 43, pp. 321-330, 1996.
[27] M. Lukaniszyn, et al., Optimization of permanent magnet shape for minimum cogging torque using a genetic algorithm, IEEE Trans. Magnetics, vol. 40, no. 2, 2004.
[28] Sang-Moon Hwang, et al., Various design techniques to reduce cogging torque by controlling energy variation in permanent magnet motors, IEEE Trans. Magnetics, vol. 37, pp. 2806-2809, 2001.
[29] A. Nakahata, et al., 3-D finite-element analysis of electromagnets with permanent magnet taking into account magnetizing process, IEEE Trans. Magnetics, vol. 33, pp. 2057-2060, 1997.
[30] T. Nakata, et al., Numerical analysis of transient magnetic field in a capacitor-discharge inpulse magnetizer, IEEE Trans. Magnetics, vol. 22, pp. 526-528, 1986.
[31] Yoshihiro Kawase, et al., Analysis of magnetization process using discharge current of capacitor by 3-D finite element method, IEEE Trans. Magnetics, vol. 38, pp. 1145-1148, 2002.
[32] Chang Seop Koh, et al., Finite element analysis of magnetizer using Preisach model, IEEE Trans. Magnetics, vol. 35, pp. 1227-1230, 1999.
[33] Edward Della Torre, et al., Preisach modeling and reversible magnetization, IEEE Trans. Magnetics, vol. 26, pp. 3052-3058, 1990.
[34] I. D. Mayergoyz, et al., Generalized preisach model of hysteresis, IEEE Trans. Magnetics, vol. 24, pp. 212-217, 1988.
[35] C. K. Lee, et al., Analysis of magnetization of magnet in the rotor of line start permanent magnet motor, IEEE Trans. Magnetics, vol. 39, pp. 1499-1503, 2003.
[36] Ann Reimers, et al., Fast Preisach-based vector magnetization model, IEEE Trans. Magnetics, vol. 37, pp. 3349-3352, 2001.
[37] Ann Reimers, et al., Implementation of Preisach DOK magnetic hysteresis model in a commercial finite element package, IEEE Trans. Magnetics, vol. 37, pp. 3362-3365, 2001.
[38] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅰ: open-circuit field, IEEE Trans. Magnetics, vol. 29, pp. 124-135, 1993.
[39] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅱ: armature-reaction field, IEEE Trans. Magnetics, vol. 29, pp. 136-142, 1993.
[40] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅲ: effect of stator slotting, IEEE Trans. Magnetics, vol. 29, pp. 142-151, 1993.
[41] Z. Q. Zhu et al., Instantaneous magnetic field distribution in brushless permanent magnet dc motors, part Ⅳ: magnetic field on load, IEEE Trans. Magnetics, vol. 29, pp. 152-158, 1993.
[42] Do Hyun Kang, Paul Curiac, Yeon Ho Jeong, and Soo Jin Jung, Prospects for magnetization of large PM motors: conclusions from a development case study, IEEE Trans. Energy Conversion, vol. 18, no. 3, pp. 409416, 2003.
[43] H. G. Brachtendorf and R. Laur, A hysteresis model for hard magnetic core materials, IEEE Trans. Magnetics, vol. 33, no. 1, Jan. 1997, pp. 723-727.
[44] K. H. Carpenter, A differential equation approach to minor loops in the Jiles-Atherton hysteresis model, IEEE Trans. Magnetics, vol. 27, Nov. 1991.
[45] D. C. Jiles and D. L. Atherton, Ferromagnetic hysteresis, IEEE Trans. Magnetics, vol. 19, pp. 2183-2185, Sept. 1983.
[46] D. C. Jiles and D. L. Atherton, Theory of the magnetization process in ferromagnets and its application to the magnetomechanical effect, J. Phys., D: Appl. Phys., vol. 17, pp. 1265-1281, 1984.
[47] D. C. Jiles and D. L. Atherton, Theory of ferromagnetic hysteresis, Magnetism Magn. Mater., vol. 61, pp. 48-60, 1986.
[48] D. C. Jiles and D. L. Atherton, Theory of ferromagnetic hysteresis(invited), J. Appl. Phys., vol. 55, pp. 2115-2120, Mar. 15, 1984.
[49] D. C. Jiles, J. B. Thoelke, and M. K. Devine, Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis, IEEE trans. Nagnetics, vol. 28, no. 1, pp. 27-35, Jan. 1992.
[50] H. G. Brachtendorf, and R. Laur, A hysteresis model for hard magnetic core materials, IEEE Trans. Magnetics, vol. 33, no. 3, pp. 723-727, Jan. 1997.
[51] 曹淑瑛,王博文,闫荣格等,超磁滞伸缩致动器的磁滞非线性动态模型,中国电机工程学报,2003年23卷11期．
[52] D. C. Jiles, A self consistent generalized model for the calculation of minor loop excursions in the theory of hysteresis, IEEE Trans. Magneticis, vol. 28, no. 5, pp: 2602-2604.
[53] Sergey E. Zirka, and Yury I. Moroz, Hysteresis modeling based on similarity, IEEE Trans. Magnetics, no. 4, vol. 35, pp.2090-2096, 1999.
[54] S. E. Zirka, and Yu. I. Moroz, Hysteresis modeling based on transplantation, IEEE Trans. Magnetics, no. 6, vol. 31, pp. 3509-3511, 1995.
[55] David L. Atherton, and Markus Schonbachler, Measurements of reversible magnetization componet, IEEE Trans. Magnetics, no. 1, vol. 24, pp. 616-620, 1088.
[56] Der-Ray Huang, Tai-Fa Ying, Shyh-Jier Wang, and etc., Cogging torque reduction of a single-phase brushless DC motor, IEEE Trans. Magnetics, vol. 34, No. 4, pp2072077, 1998.
[57] C. C. Hwang, S.B.John and S.S.Wu, Reduction of cogging torque in spindle motors for CD-ROM drive, IEEE Trans.,Magnetics, vol. 34, No. 2, pp 468-470, 1998.
[58] Z. Q. Zhu, D. Howe, Analytical prediction of magnet brushless motors, IEEE Trans., Magneics, vol. 28, No. 2, pp468-470,1992.
[59] 冀溥，王秀和，王道涵，杨玉波，转子静态偏心的表面式永磁电机齿槽转矩研究，中国电机工程学报，2004，24(9)：188-191．
[60] 王兴华，励庆孚，永磁无刷直流电机空载气隙磁场和绕组反电势的解析计算，中国电机工程学报，2003，23(3)：126-130．
[61] 杨玉波，王秀和，陈谢杰，冀溥，基于不等槽口宽配合的永磁电动机齿槽转矩削弱方法，电工技术学报，2005，20(3)：40-44．
[62] 宋伟，王秀和，杨玉波，削弱永磁电机齿槽转矩的一种新方法，电机与控制学报，2004，8(3)：214-217．
[63] 杨玉波，王秀和，张鑫，贺广富，磁极偏移削弱永磁电机齿槽转矩方法，电工技术学报，2006，21(10)：22-25．
[64] 王秀和，杨玉波，丁婷婷，朱常青，王道涵，基于极弧系数选择的实心转子永磁同步电动机齿槽转矩削弱方法，中国电机工程学报，2005，15(15)：147-149．
[65] Yubo Yang, Xiuhe Wang, Rong Zhang, Tlngting Ding, Renyuan Tang, The optimization of pole arc coefficient to reduce cogging torque in surface-mounted permanent magnet motors, IEEE Trans. Magnetics, vol. 42, No. 4, pp.1135-1138, 2006.
[66] 杨玉波，王秀和，丁婷婷，张鑫，张冉，朱常青，极弧系数组合优化的永磁电机齿槽转矩削弱方法，中国电机工程学报，27(6)，pp．7-11，2007．
[67] 邹俊杰，鼠笼式拖动电机变极调速原理及分析，船电技术，2006年4期，28-30．
[68][68] 唐文忠，李高，4／8极绕线型变极调速感应电动机的研究，电机电器技术，2001年第3期，11-13．
[69] 李宁，贾堂刚，交流异步电动机调速方式分析，矿山机械，33(3)，2005，70-72．
[70] 郭羽，浅谈三相异步电动机的调速，农村电工，2005年10期．