volume | PIER Journals

Abstract

This paper presents the exact 3D calculation of the magnetic field produced by a tile permanent magnet whose polarization is both tangential and uniform. Such a calculation is useful for optimizing magnetic couplings or for calculating the magnetic field produced by alternate magnet structures. For example, our 3D expressions can be used for calculating the magnetic field produced by a Halbach structure. All our expressions are determined by using the coulombian model. This exact analytical approach has always proved its accuracy and its usefulness. As a consequence, the tile permanent magnet considered is represented by using the fictitious magnetic pole densities that are located on the faces of the magnet. In addition, no simplifying assumptions are taken into account for calculating the three magnetic field components. Moreover, it is emphasized that the magnetic field expressions are fully three-dimensional. Consequently, the expressions obtained are valid inside and outside of the tile permanent magnet, whatever its dimensions. Such an approach allows us to realize easily parametric studies.

1. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Improvement of the analytical calculation of the magnetic field produced by permanent magnet rings," Progress In Electromagnetics Research, PIER 88, 307-319, 2008. Google Scholar

2. Babic, S. and C. Akyel, "Improvement of the analytical calculation of the magnetic field produced by permanent magnet rings," Progress In Electromagnetics Research C, Vol. 5, 71-82, 2008. Google Scholar

3. Furlani, E. P., Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications, Academic Press, 2001.

4. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Analytical calculation of the magnetic field created by permanent-magnet rings," IEEE Trans. Magn., Vol. 44, No. 8, 1982-1989, 2008.
doi:10.1109/TMAG.2008.923096 Google Scholar

5. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Discussion about the analytical calculation of the magnetic field created by permanent magnets," Progress In Electromagnetics Research B, Vol. 11, 281-297, 2009.
doi:10.2528/PIERB08112102 Google Scholar

6. Selvaggi, J. P., S. Salon, O. M. Kwon, and M. Chari, "Computation of the three-dimensional magnetic field from solid permanent-magnet bipolar cylinders by employing toroidal harmonics," IEEE Trans. Magn., Vol. 43, No. 10, 3833-3839, 2007.
doi:10.1109/TMAG.2007.902995 Google Scholar

7. Azzerboni, B. and G. Saraceno, "Three-dimensional calculation of the magnetic field created by current-carrying massive disks," IEEE Trans. Magn., Vol. 34, No. 5, 2601-2604, 1998.
doi:10.1109/20.717601 Google Scholar

8. Azzerboni, B. and E. Cardelli, "Magnetic field evaluation for disk conductors," IEEE Trans. Magn., Vol. 29, No. 6, 2419-2421, 1993.
doi:10.1109/20.280997 Google Scholar

9. Azzerboni, B., E. Cardelli, M. Raugi, A. Tellini, and G. Tina, "Magnetic field evaluation for thick annular conductors," IEEE Trans. Magn., Vol. 29, No. 3, 2090-2094, 1993.
doi:10.1109/20.211324 Google Scholar

10. Rakotoarison, H. L., J. P. Yonnet, and B. Delinchant, "Using colombian approach for modeling scalar potential and magnetic field of a permanent magnet with radial polarization," IEEE Trans. Magn., Vol. 43, No. 4, 1261-1264, 2007.
doi:10.1109/TMAG.2007.892316 Google Scholar

11. Durand, E., Electrostatique, Vol. 1, 248-251, Masson Editeur, Paris, France, 1964.

12. Babic, S. and C. Akyel, "Magnetic force calculation between thin coaxial circular coils in air," IEEE Trans. Magn., Vol. 44, No. 4, 445-452, 2008.
doi:10.1109/TMAG.2007.915292 Google Scholar

13. Babic, S., C. Akyel, and S. Salon, "New procedures for calculating the mutual inductance of the system: Filamentary circular coilmassive circular solenoid ," IEEE Trans. Magn., Vol. 39, No. 3, 1131-1134, 2003.
doi:10.1109/TMAG.2003.810550 Google Scholar

14. Babic, S., C. Akyel, S. Salon, and S. Kincic, "New expressions for calculating the magnetic field created by radial current in massive disks," IEEE Trans. Magn., Vol. 38, No. 2, 497-500, 2002.
doi:10.1109/20.996131 Google Scholar

15. Babic, S., S. Salon, and C. Akyel, "The mutual inductance of two thin coaxial disk coils in air," IEEE Trans. Magn., Vol. 40, No. 2, 822-825, 2004.
doi:10.1109/TMAG.2004.824810 Google Scholar

16. Conway, J., "Noncoaxial inductance calculations without the vector potential for axisymmetric coils and planar coils," IEEE Trans. Magn., Vol. 44, No. 10, 453-462, 2008.
doi:10.1109/TMAG.2008.917128 Google Scholar

17. Furlani, E. P., S. Reznik, and A. Kroll, "A three-dimensional field solution for radially polarized cylinders," IEEE Trans. Magn., Vol. 31, No. 1, 844-851, 1995.
doi:10.1109/20.364587 Google Scholar

18. Furlani, E. P., "Field analysis and optimization of NDFEB axial field permanent magnet motors ," IEEE Trans. Magn., Vol. 33, No. 5, 3883-3885, 1997.
doi:10.1109/20.619603 Google Scholar

19. Furlani, E. P. and M. Knewston, "A three-dimensional field solution for permanent-magnet axial-field motors," IEEE Trans. Magn., Vol. 33, No. 1, 2322-2325, 1997.
doi:10.1109/20.573849 Google Scholar

20. Furlani, E. P., "A two-dimensional analysis for the coupling of magnetic gears," IEEE Trans. Magn., Vol. 33, No. 3, 2317-2321, 1997.
doi:10.1109/20.573848 Google Scholar

21. Mayergoyz, D. and E. P. Furlani, "The Computation of magnetic fields of permanent magnet cylinders used in the electrophotographic process," J. Appl. Phys., Vol. 73, No. 10, 5440-5442, 1993.
doi:10.1063/1.353709 Google Scholar

22. Yonnet, J. P., "Passive magnetic bearings with permanent magnets," IEEE Trans. Magn., Vol. 14, No. 5, 803-805, 1978.
doi:10.1109/TMAG.1978.1060019 Google Scholar

23. Abele, M., J. Jensen, and H. Rusinek, "Generation of uniform high fields with magnetized wedges," IEEE Trans. Magn., Vol. 33, No. 5, 3874-3876, 1997.
doi:10.1109/20.619600 Google Scholar

24. Aydin, M., Z. Zhu, T. Lipo, and D. Howe, "Minimization of cogging torque in axial-flux permanent-magnet machines: Design concepts," IEEE Trans. Magn., Vol. 43, No. 9, 3614-3622, 2007.
doi:10.1109/TMAG.2007.902818 Google Scholar

25. Marinescu, M. and N. Marinescu, "Compensation of anisotropy effects in flux-confining permanent-magnet structures," IEEE Trans. Magn., Vol. 25, No. 5, 3899-3901, 1989.
doi:10.1109/20.42470 Google Scholar

26. Akoun, G. and J. P. Yonnet, "3d analytical calculation of the forces exerted between two cuboidal magnets," IEEE Trans. Magn., Vol. 20, No. 5, 1962-1964, 1984.
doi:10.1109/TMAG.1984.1063554 Google Scholar

27. Yong, L., Z. Jibin, and L. Yongping, "Optimum design of magnet shape in permanent-magnet synchronous motors," IEEE Trans. Magn., Vol. 39, No. 11, 3523-420, 2003.
doi:10.1109/TMAG.2003.819462 Google Scholar

28. Lemarquand, G. and V. Lemarquand, "Annular magnet position sensor," IEEE. Trans. Magn., Vol. 26, No. 5, 2041-2043, 1990.
doi:10.1109/20.104612 Google Scholar

29. Yonnet, J. P., "Permanent magnet bearings and couplings," IEEE Trans. Magn., Vol. 17, No. 1, 1169-1173, 1981.
doi:10.1109/TMAG.1981.1061166 Google Scholar

30. Zhu, Z. and D. Howe, "Analytical prediction of the cogging torque in radial-field permanent magnet brushless motors," IEEE Trans. Magn., Vol. 28, No. 2, 1371-1374, 1992.
doi:10.1109/20.123947 Google Scholar

31. Wang, J., G. W. Jewell, and D. Howe, "Design optimisation and comparison of permanent magnet machines topologies," IEE Proc. Elect. Power Appl., Vol. 148, 456-464, 2001.
doi:10.1049/ip-epa:20010512 Google Scholar

32. Yonnet, J. P., Rare-earth Iron Permanent Magnets, Ch. Magnetomechanical devices, Oxford Science Publications, 1996.

33. Blache, C. and G. Lemarquand, "New structures for linear displacement sensor with hight magnetic field gradient," IEEE Trans. Magn., Vol. 28, No. 5, 2196-2198, 1992.
doi:10.1109/20.179441 Google Scholar

34. Halbach, K., "Design of permanent multiple magnets with oriented rec material," Nucl. Inst. Meth., Vol. 169, 1-10, 1980.
doi:10.1016/0029-554X(80)90094-4 Google Scholar

35. http://www.univ-lemans.fr/∼glemar, , .

Dr. Romain Ravaud

Prof. Guy Lemarquand

Prof. Valerie Lemarquand

Dr. Claude Depollier