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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)
  • Received : 2017.08.23
  • Accepted : 2018.06.18
  • Published : 2018.11.01

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).

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. 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. https://doi.org/10.3233/JAE-140192
  2. 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.
  3. 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.
  4. 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. https://doi.org/10.3233/JAE-2005-697
  5. 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. https://doi.org/10.1109/TIA.2009.2036666
  6. 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. https://doi.org/10.1109/TMAG.2011.2157351
  7. 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. https://doi.org/10.1109/TMAG.2011.2155042
  8. 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.
  9. 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. https://doi.org/10.3233/JAE-131659
  10. 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. https://doi.org/10.3233/JAE-131720
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. N. Huang, "Design and Loss Analysis of Mw-level High Speed Permanent Synchronous Machine," M.S. thesis, Shenyang University of Technology, Shenyang, China, 2013.
  16. 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.
  17. 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. https://doi.org/10.3233/JAE-150069
  18. 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. https://doi.org/10.3233/JAE-150136
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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. https://doi.org/10.1109/TMAG.2011.2165321
  24. 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. https://doi.org/10.1109/TMAG.2005.854337
  25. 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.
  26. 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. https://doi.org/10.1109/TMECH.2011.2159238
  27. 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. https://doi.org/10.1016/j.sna.2007.02.018
  28. 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. https://doi.org/10.5370/JEET.2016.11.1.093
  29. 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.
  30. 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.
  31. 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.
  32. 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. https://doi.org/10.1109/TEC.2015.2419636