Browse > Article
http://dx.doi.org/10.5370/JEET.2018.13.6.2158

Calculation of Magnetic Field for Cylindrical Stator Coils in Permanent Magnet Spherical Motor  

Li, Hongfeng (Dept. of Electrical and Information Engineering, Tianjin University)
Ma, Zigang (Dept. of Electrical and Information Engineering, Tianjin University)
Han, Bing (State Grid Tianjin Power Maintenance Company)
Li, Bin (Dept. of Electrical and Information Engineering, Tianjin University)
Li, Guidan (Dept. of Electrical and Information Engineering, Tianjin University)
Publication Information
Journal of Electrical Engineering and Technology / v.13, no.6, 2018 , pp. 2158-2167 More about this Journal
Abstract
This paper analyzed the magnetic field produced by the cylindrical stator coils of permanent magnet spherical motor (PMSM). The elliptic equations about the vector magnetic potential were given. Given that the eddy current effects are neglected, the magnet field of the PMSM is regarded as irrotational field, which can be calculated by scalar magnetic potential. The current density of cylindrical stator coil was proposed based on the definition of current density. The expression of current density of stator coil was obtained according to the double Fourier series decomposition and spherical harmonic functions. Then the magnetic flux density for scalar magnetic potential was derived. Further, the influence of different parameters on radial flux density was also analyzed. Finally, the results by the analytical method in this paper were validated by finite element analysis (FEA).
Keywords
Current density; Double Fourier series decomposition; PMSM; Scalar magnetic potential; Spherical harmonic functions; Vector magnetic potential;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Z. Belli and M. R. Mekideche, "Investigation of Eddy Current Losses Reduction in Permanent Magnets Machines with Slots Skew Optimization and Demagnetization Effect Analysis," Int. J. Appl. Electromagn. Mech., vol. 43, no. 4, pp. 337-346, Jan. 2013.   DOI
2 P. Silvester and M. V. K. Chari, "Finite Element Solution of Saturable Nagnetic Field Problems," IEEE Trans. Power Appl. System, vol. 89, no. 7, pp. 1642-1651, Jan. 1970.
3 W. Liu, "3D Magnetic Field Analysis and Magnetic Circuit Equivalent of Hybrid Excitation Wind Generator," Electrical Engineering, vol. 1, no. 1, pp. 1-5, Jan. 2010.
4 J. Li, "FEM Analysis on Eddy Current Losses in the Permanent Magnets and Its Influence on the Machines' erformance," M.S. thesis, School of electrical and Automation Engineering, Tianjin Univ, Tianjin, China, 2013.
5 S. L. Shen, "Analysis of Electromagnetism in DDPMG and Research on Eddy-current Loss of Permanent Magnet," M.S. thesis, School of electrical and Automation Engineering, Tianjin Univ, Tianjin, China, 2013.
6 N. Huang, "Design and Loss Analysis of Mw-level High Speed Permanent Synchronous Machine," M.S. thesis, Shenyang University of Technology, Shenyang, China, 2013.
7 Y. Ni, Y. Huang, and L. Zhao, "Analysis of 3-Dimensional Field and Calculation of Inductance for A New Structure of A Permanent Magnet Canned Motor," Transactions of China Electrotechnical Society, vol. 30, no. 1, pp. 98-104, Jun. 2015.
8 J. Chen, B. Zhang, Y. Ding, et al, "Field Analysis of A Sinusoidal-edged Halbach Magnet Array Using the Differential Quadrature Finite Element Method," Int. J. Appl. Electromagn. Mech., vol. 50, no. 1, pp. 63-80. Jan. 2016.   DOI
9 S. H. Lee, Y. J. Kim, K. S. Lee, et al, "Prediction of Dynamic Characteristics of Permanent Magnet Motor Using Numerical Analysis Coupled with Motion Equation," Int. J. Appl. Electromagn. Mech., vol. 50, no. 3, pp. 503-510, Mar. 2016.   DOI
10 Z. Li, Y. Zhang, X. X. Wang, et al, "Design and Comparison of A Novel 3-DOF Deflection Type Permanent Magnet Actuator," Int. J. Appl. Electroagn. Mech., vol. 46, no. 1, pp. 229-242, Jan. 2014.
11 L. J. Wu and Z. Q. Zhu, "Analytical Model for Predicting Magnet Loss of Surface-mounted Permanent Magnet Machines Accounting for Slotting Effect and Load," IEEE Trans. Magn., vol. 48, no. 1, pp. 107-117, Jan. 2012.   DOI
12 S. T. Zhu, "Transient Characteristics Analysis of PM Spherical Motor Based on the Finite Element Method," M.S. thesis, School of electrical and Automation Engineering, Tianjin University, Tianjin, China, 2012.
13 S. Y. Guo, "Analytical Solution of Magnetic Field in Permanent Magnet Machines: Theory and Application," Ph.D. Dissertation, Wuhan University of Technology, Wuhan, China, 2014.
14 L. J. Wu, Q. J. Wang, S. J. Du, et al, "Integral Equation Method for Simulation of Magnetic Field of Permanent Magnetic Spherical Stepper," Proeedings of the CSEE, vol. 24, no. 9, pp. 192-197, Sep. 2004.
15 Z. Q. Zhu and D. Howe, "Eddy-current Loss in the Rotor Magnets of Permanent-magnet Brushless Machines Having A Fractional Number of Slots Per Pole," IEEE Trans. Magn., vol. 41, no. 9, pp. 2462-2469, Sep. 2005.   DOI
16 L. F. Ju, Q. J. Wang, and G. L. Li, "Parameter Optimization for Support Vector Machine Model of Permanent Magnet Spherical Motors," Transactions of China Electrotechnical Society, vol. 29, no. 1, pp. 85-90, Jan. 2014.
17 L. Yan, I. M. Chen, K. M. Lee, et al, "Modeling and Iron-Effect Analysis on Magnetic Field and Torque Output of Electromagnetic Spherical Actuators with Iron Stator," IEEE/ASME Trans. Mechatron., vol. 17, no. 6, pp. 1080-1-87, Dec. 2012.   DOI
18 Y. Oner, "A Permanent Magnet Spherical Rotor Design and Three Dimensional Static Magnetic Analysis," Sens. Actuators A, vol. 137, no. 2, pp. 200-208, Jul. 2007.   DOI
19 Y. Oner and S. Kesler, "3D Magnetic Analysis of Permanent Magnets in Spherical Configuration," J. Electr. Eng. Technol., vol. 11, no. 1, pp. 93-99, Jan. 2016.   DOI
20 X. Chen, J. Hu, Z. Peng, and K. Chen, "Nonlinear Torsional Vibration Characteristics of PMSM for HEV Considering Electromagnetic Excitation," Int. J. Appl. Electromagn. Mech., vol. 49, no. 1, pp. 9-21, Sep. 2015.   DOI
21 Y. S. Kim, D. W. Kang, and L. Ju, "Methodology of Prediction the Rotor Position of Spherical Permanent Magnet Synchronous Motor," ICEMS, Pattaya City, Thailand, pp. 958-961, Oct. 2015.
22 B. Li, C. Liu, H. F. Li, et al, "Permanent Magnetic Model and Magnetic Field Analysis for Stator Coil of Permanent Magnetic Spherical Motor," Journal of Tianjin University, vol. 45, no. 11, pp. 1024-1029, Nov. 2012.
23 H. F. Li and Y. B. Shen, "Eddy Current Loss Analysis in the Rotor Magnets of Permanent Magnet Spherical Motor," Transactions of China Electrotechnical Society, vol. 30, no. 12, pp. 267-275, Jun. 2015.
24 H. F. Li and Y. B. Shen, "Thermal Analysis of the Permanent-magnet Spherical Motor," IEEE Trans. Energy Convers., vol. 30, no. 12, pp. 991-998, Sep. 2015.   DOI
25 N. Zhao, Z. Q. Zhu, and W. Liu, "Rotor Eddy Current Loss Calculation and Thermal Analysis of Permanent Magnet Motor and Generator," IEEE Trans. Magn., vol. 47, no. 10, pp. 4199-4202, Oct. 2011.   DOI
26 P. Chen, R. Tang, W. Tong, J. Jia, and Q. Duan, "Permanent Magnet Eddy Current Loss and Its Influence of High Power Density Permanent Magnet Synchronous Motor," Transactions of China Electrotechnical Society, vol. 30, no. 6, pp. 1-9, Mar. 2015.
27 R. Tang, P. Chen, W. Tong, and X. Han, "Analytical Calculation of Eddy Current Loss Accounting for Eddy Current Reaction," Transactions of China Electrotechnical Society, vol. 30, no. 24, pp. 1-10, Dec. 2015.
28 M. W. Waszak, "Efficient Method for Eddy Current Analysis in Permanent Magnets of Electric Motors," Int. J. Appl. Electromagn. Mech., vol. 22, no. 3, pp. 133-139, Jan. 2005.   DOI
29 S.-H. Han, T. M. Jahns and Z. Q. Zhu, "Analysis of Rotor Core Eddy-current Losses in Interior Permanentmagnet Synchronous Machines," IEEE Trans. Ind. Appl., vol. 46, no. 1, pp. 196-205, Jan/Feb. 2010.   DOI
30 L. J. Wu, Z. Q. Zhu, D. Staton, M. Popescu, and D. Hawkins, "Analytical Modeling and Analysis of Open-circuit Magnet Loss in Surface Mounted Permanent Magnet Machines," IEEE Trans. Magn., vol. 48, no. 3, pp. 1234-1247, Mar. 2012.   DOI
31 H. Li, Y. Shen, and S. Zhu, "Permanent Magnet Eddy Current Loss Analysis of the Permanent Magnet Spherical Motor," Proceedings of the ICMS, pp. 481-485, Aug. 2014.
32 P. Lindh, T. Vaimann, A. Kallaste, J. Pyrhonen, D. Vinnikov, and V. Naumanen, "Influence of Slot Wedge Material on Permanent Magnet Losses in a Traction Motor with Tooth Coil Windings," Int. J. Appl. Electromagn. Mech., vol. 42, no. 2, pp. 227-236, Jan. 2013.   DOI