2009-03-05
Analytical Expression of the Magnetic Field Created by Tile Permanent Magnets Tangentially Magnetized and Radials Current in Massive Disks
By
Progress In Electromagnetics Research B, Vol. 13, 309-328, 2009
Abstract
In this paper, we present new expressions for calculating the magnetic field produced by either tile permanent magnets tangentially magnetized or by radial currents in massive disks. These expressions are fully analytical, that is, we do not use any special functions for calculating them. In addition, they are three-dimensional and can be used for calculating the magnetic field for all regular points in space. The expressions commonly used for calculating the magnetic field produced by radial currents in massive disks are often based on elliptic integrals or semi-analytical forms. We propose in this paper an alternative analytical method that can also be used for tile permanent magnets. Indeed, by using the analogy between the coulombian model and the amperian current model, radial currents in massive disks can be represented by using the fictitious magnetic pole densities that are located on two faces of a tile permanent magnet tangentially magnetized. The two representations are equivalent and thus, the shape of magnetic field produced is the same for all points in space, with a smaller value in the case of it is produced by radial currents in massive disks. Such expressions can be used for realizing easily parametric studies.
Citation
Romain Ravaud, and Guy Lemarquand, "Analytical Expression of the Magnetic Field Created by Tile Permanent Magnets Tangentially Magnetized and Radials Current in Massive Disks," Progress In Electromagnetics Research B, Vol. 13, 309-328, 2009.
doi:10.2528/PIERB09012704
References

1. 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

2. Babic, S. and M. M. Gavrilovic, "New expression for calculating magnetic fields due to current-carrying solid conductors," IEEE Trans. Magn., Vol. 33, No. 5, 4134-4136, 1997.
doi:10.1109/20.619687        Google Scholar

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

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, "The three exact components of the magnetic field created by a radially magnetized tile permanent magnet," Progress In Electromagnetics Research, PIER 88, 307-319, 2008.        Google Scholar

6. 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

7. 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

8. 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

9. 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

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

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

12. Furlani, E. P. and M. Knewston, "A three-dimensional field solution for permanent-magnet axial-field motors," IEEE Trans. Magn., Vol. 33, No. 3, 2322-2325, 1997.
doi:10.1109/20.573849        Google Scholar

13. 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

14. 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

15. 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

16. Elies, P. and G. Lemarquand, "Analytical optimization of the torque of a permanent-magnet coaxial synchronous coupling," IEEE Trans. Magn., Vol. 34, No. 4, 2267-2273, 1998.
doi:10.1109/20.703865        Google Scholar

17. Lemarquand, V., J. F. Charpentier, and G. Lemarquand, "Nonsinusoidal torque of permanent-magnet couplings," IEEE Trans. Magn., Vol. 35, No. 5, 4200-4205, 1999.
doi:10.1109/20.799068        Google Scholar

18. Lang, M., "Fast calculation method for the forces and stiffnesses of permanent-magnet bearings," 8th International Symposium on Magnetic Bearing, 533-537, 2002.        Google Scholar

19. Babic, S. and C. Akyel, "An improvement in the calculation of the magetic field for an arbitrary geometry coil with rectangular cross section," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 18, 493-504, November 2005.        Google Scholar

20. 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

21. Babic, S., C. Akyel, and M. M. Gavrilovic, "Calculation improvement of 3d linear magnetostatic field based on fictitious magnetic surface charge," IEEE Trans. Magn., Vol. 36, No. 5, 3125-3127, 2000.
doi:10.1109/20.908707        Google Scholar

22. Selvaggi, J. P., S. Salon, O. M. Kwon, M. V. K. Chari, and M. DeBortoli, "Computation of the external magnetic field, near-field or far-field from a circular cylindrical magnetic source using toroidal functions," IEEE Trans. Magn., Vol. 43, No. 4, 1153-1156, 2007.
doi:10.1109/TMAG.2007.892275        Google Scholar

23. Selvaggi, J. P., S. Salon, O. M. Kwon, and M. V. K. 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

24. Selvaggi, J. P., S. Salon, O. M. Kwon, and M. V. K. Chari, "Calculating the external magnetic field from permanent magnets in permanent-magnet motors --- An alternative method," IEEE Trans. Magn., Vol. 40, No. 5, 3278-3285, 2004.
doi:10.1109/TMAG.2004.831653        Google Scholar

25. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Ironless loudspeakers with ferrofluid seals," Archives of Acoustics, Vol. 33, No. 4, 3-10, 2008.        Google Scholar

26. 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

27. 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

28. Zhu, Z., G. W. Jewell, and D. Howe, "Design considerations for permanent magnet polarised electromagnetically actuated brakes," IEEE Trans. Magn., Vol. 31, No. 6, 3743-3745, 1995.
doi:10.1109/20.489757        Google Scholar

29. 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

30. Baran, W. and M. Knorr, "Synchronous couplings with sm co5 magnets," 2nd Int. Workshop on Rare-Earth Cobalt Permanent Magnets and Their Applications, 140-151, Dayton, Ohio, USA, 1976.        Google Scholar

31. Remy, M., G. Lemarquand, B. Castagnede, and G. Guyader, "Ironless and leakage free voice-coil motor made of bonded magnets," IEEE Trans. Magn., Vol. 44, No. 11, 2008.
doi:10.1109/TMAG.2008.2003401        Google Scholar

32. Berkouk, M., V. Lemarquand, and G. Lemarquand, "Analytical calculation of ironless loudspeaker motors," IEEE Trans. Magn., Vol. 37, No. 2, 1011-1014, 2001.
doi:10.1109/20.917185        Google Scholar

33. Blache, C. and G. Lemarquand, "High magnetic field gradients in flux confining permanent magnet structures," Journal of Magnetism and Magnetic Materials, Vol. 104, 1111-1112, 1992.
doi:10.1016/0304-8853(92)90510-U        Google Scholar

34. 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

35. Charpentier, J. F. and G. Lemarquand, "Optimization of unconventional p.m. couplings," IEEE Trans. Magn., Vol. 38, No. 2, 1093-1096, 2002.
doi:10.1109/20.996280        Google Scholar

36. Lemarquand, G., "Ironless loudspeakers," IEEE Trans. Magn., Vol. 43, No. 8, 3371-3374, 2007.
doi:10.1109/TMAG.2007.897739        Google Scholar