volume | PIER Journals

Abstract

We present in this paper an analytical model for the calculation of the electromagnetic field in a slotless surface mounted permanent magnet machines. This model takes into account the two essential directions of magnetization of the magnets, namely tangential magnetization and radial magnetization. It especially accounts for the parallel form of the magnetization direction. The model uses equivalent currents on the surfaces of the magnets, and in an original way, it uses currents in all volume of the magnet. The model is validated by numerical results obtained with a free software of calculation of the electromagnetic fields (FEMM: Finite Element Method Magnetics) which uses the finite elements method and by an existing experimental structure. The model is extended to the magnets segmented in bars and separated. It is then extended to the shape of magnets close to parallepiped forms which are really used in large machines.

1. Warnick, K. F. and P. H. Russer, "Differential forms and electromagnetic field theory," Progress In Electromagnetics Research, Vol. 148, 83-112, 2014.
doi:10.2528/PIER14063009

2. Mahmoudi, A., S. Kahourzade, N. A. Rahim, H. W. Ping, and N. F. Ershad, "Slot-less torus solid- rotor-ringed line-start axial-flux permanent-magnet motor," Progress In Electromagnetics Research, Vol. 131, 331-355, 2012.
doi:10.2528/PIER12070308

3. Chen, M., K.-T. Chau, C. H. T. Lee, and C. Liu, "Design and analysis of a new axial-field magnetic variable gear using pole-changing permanent magnets," Progress In Electromagnetics Research, Vol. 153, 23-32, 2015.
doi:10.2528/PIER15072701

4. Rahideha, A. and T. Korakianitis, "Analytical calculation of open-circuit magnetic field distribution of slotless brushless PM machines," Intern. Journ. of Electrical Power & Energy Systems, Vol. 44, No. 1, 99-114, Jan. 2013.
doi:10.1016/j.ijepes.2012.07.030

5. Tiegna, H., Y. Amara, and G. Barakat, "Overview of analytical models of permanent magnet electrical machines for analysis and design purposes," Mathematics and Computers in Simulation, Vol. 90, 162-177, 2013.
doi:10.1016/j.matcom.2012.12.002

6. Boules, N., "Prediction of no load flux density distribution in permanent magnet machines," IEEE Trans. on Ind. Appl., Vol. 21, 633-643, Jul.-Aug. 1985.

7. Zhu, Z. Q., D. Howe, and C. C. Chan, "Improved analytical model for predicting the magnetic field distribution in brushless permanent magnet machines," IEEE Trans. on Magnetics, Vol. 38, No. 1, 229-238, Jan. 2002.
doi:10.1109/20.990112

8. Dubas, F. and C. Espanet, "Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect: No-load vector potential and flux density calculation," IEEE Trans. on Magnetics, Vol. 45, No. 5, 2097-2109, May 2009.
doi:10.1109/TMAG.2009.2013245

9. Holm, S. R., H. Polinder, and J. A. Ferreira, "Analytical modeling of a permanent-magnet synchronous machine in a flywheel," IEEE Trans. on Magnetics, Vol. 43, No. 5, May 2007.
doi:10.1109/TMAG.2007.892791

10. Boughrara, K., D. Zarko, R. Ibtiouen, O. Touhami, and A. Rezzoug, "Magnetic field analysis of inset and surface mounted permanent magnet synchronous motors using Schwarz-Christoffel transformation," IEEE Trans. on Magnetics, Vol. 45, No. 8, 3166-3178.
doi:10.1109/TMAG.2009.2016559

11. Chikouche, B. L., K. Boughrara, and R. Ibtiouen, "Cogging torque minimization of surface- mounted permanent magnet synchronous machines using hybrid magnet shapes," Progress In Electromagnetics Research B, Vol. 62, 49-61, 2015.
doi:10.2528/PIERB14112302

12. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Magnetic field created by a uniformly magnetized tile permanent magnet," Progress In Electromagnetics Research B, Vol. 24, 17-32, 2010.
doi:10.2528/PIERB10062209

13. Bellara, A., Y. Amara, G. Barakat, and B. Dakyo, "Two-dimensional exact analytical solution of armature reaction field in slotted surface mounted PM radial flux synchronous machines," IEEE Trans. on Magnetics, Vol. 45, No. 10, 4534-4538, Oct. 2009.
doi:10.1109/TMAG.2009.2021527

14. Lubin, T., S. Mezani, and A. Rezzoug, "Exact analytical method for magnetic field computation in the air-gap of cylindrical electrical machines considering slotting effects," IEEE Trans. on Magnetics, Vol. 46, No. 4, 1092-1099, Apr. 2010.
doi:10.1109/TMAG.2009.2036257

15. Holm, S. R., H. Polinder, and J. A. Ferreira, "Analytical modeling of a permanent-magnet synchronous machine in a flywheel," IEEE Trans. on Magnetics, Vol. 43, No. 5, May 2007.
doi:10.1109/TMAG.2007.892791

16. Gysen, B. L. J., K. J. Meessen, J. J. H. Paulides, and E. A. Lomonova, "General formulation of the electromagnetic field distribution in machines and devices using Fourier analysis," IEEE Trans. on Magnetics, Vol. 46, No. 1, 39-52, Jan. 2010.
doi:10.1109/TMAG.2009.2027598

17. Lubin, T., S. Mezani, and A. Rezzoug, "Two-dimensional analytical calculation of magnetic ¯eld and electromagnetic torque for surface-inset permanent-magnet motors," IEEE Trans. on Magnetics, Vol. 48, No. 6, 2080-2091, Jun. 2012.
doi:10.1109/TMAG.2011.2180918

18. Li, W. and K.-T. Chau, "Analytical field calculation for linear tubular magnetic gears using equivalent anisotropic magnetic permeability," Progress In Electromagnetics Research, Vol. 127, 155-171, 2012.
doi:10.2528/PIER12030301

19. Yan, L., L. Zhang, T. Wang, Z. Jiao, C.-Y. Chen, and I.-M. Chen, "Magnetic field of tubular linear machines with dual halbach array," Progress In Electromagnetics Research, Vol. 136, 283-299, 2013.
doi:10.2528/PIER12110302

20. Rasmussen, K. F., "Analytical prediction of magnetic field from surface mounted permanent magnet motor," Proc. IEEE IEMDC, Seattle, WA, May 9-12, 1999.

21. Boutora, Y., R. Ibtiouen, and N. Takorabet, "Analytical model of magnet bars of surface permanent magnet slotless machine," 13th International Conference on Electrical Machines, ICEM 2012, 2772-2778, Marseille, Sep. 4-6, 2012.

22. Nogarede, B., Etude de moteurs sans encoches a aimants permanents de forte puissance a faible vitesse, Doctorat. Thesis, INP Toulouse, France, 1990.

23. Nogarede, B., M. Lajoie-Mazenc, and B. Davat, "Modelisation analytique des machines a aimants a induit sans encoches," Revue de Physique Appliquee, No. 25, 707-720, Paris, 1990.
doi:10.1051/rphysap:01990002507070700

24. Zhu, Z. Q., L. J. Wu, and Z. P. Xia, "An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent magnet machines," IEEE Trans. on Magnetics, Vol. 46, No. 4, 1100-1115, Apr. 2010.
doi:10.1109/TMAG.2009.2038153

25. Bentouati, S., Z. Q. Zhu, and D. Howe, "Influence of design parameters on the starting torque of a single-phase PM brushless DC motor," IEEE Trans. on Magnetics, Vol. 36, No. 5, 3533-3536, May 2000.
doi:10.1109/20.908890

26. Jung, J.-W. and T. H. Kim, "A study on the effect of the magnetization direction on the iron loss characteristics in brushless DC motors," Journal of Magnetics, Vol. 15, No. 1, 40-44, 2010.
doi:10.4283/JMAG.2010.15.1.040

27. Ferraris, L., P. Ferraris, E. Po·skovic, and A. Tenconi, "Evaluation of the magnetization direction effects on ferrite PM brushless fractional machines," IECON 2012, 38th Ann. Conf. on IEEE Indust. Electron. Society, 6194-6199, Alessandria, Italy, Oct. 25-28, 2012.

28. Ferraris, L., P. Ferraris, E. Po·skovic, and A. Tenconi, "Comparison between parallel and radial magnetization in PM fractional machines," IECON 2011, 37th Ann. Conf. on IEEE Indust. Electron. Society, 1776-1782, Turin, Italy, Nov. 7-10, 2011.

29. Jang, S.-M., H.-I. Park, J.-Y. Choi, K.-J. Ko, and S.-H. Lee, "Magnet pole shape design of permanent magnet machine for minimization of torque ripple based on electromagnetic field theory," IEEE Trans. on Magnetics, Vol. 47, No. 10, 3586-3589, Oct. 2011.
doi:10.1109/TMAG.2011.2151846

30. Meeker, D., Manual of femm4.2, available http://www.femm.info/wiki/HomePage.

Dr. Youcef Boutora

Dr. Noureddine Takorabet

Dr. Rachid Ibtiouen