This paper presents the exact analytical formulation of the three components of the magnetic field created by a radially magnetized tile permanent magnet. These expressions take both the magnetic pole surface densities and the magnetic pole volume density into account. So, this means that the tile magnet curvature is completely taken into account. Moreover, the magnetic field can be calculated exactly in any point of the space, should it be outside the tile magnet or inside it. Consequently, we have obtained an accurate 3D magnetic field as no simplifying assumptions have been used for calculating these three magnetic components. Thus, this result is really interesting. Furthermore, the azimuthal component of the field can be determined without any special functions. In consequence, its computational cost is very low which is useful for optimization purposes. Besides, all the other expressions obtained are based on elliptic functions or special functions whose numerical calculation is fast and robust and this allows us to realize parametric studies easily. Eventually, we show the interest of this formulation by applying it to one example: the calculation and the optimization of alternate magnetization magnet devices. Such devices are commonly used in various application fields: sensors, motors, couplings, etc. The point is that the total field is calculated by using the superposition theorem and summing the contribution to the field of each tile magnet in any point of the space. This approach is a good alternative to a finite element method because the calculation of the magnetic field is done without any simplifying assumption.
1. Babic, S. and C. Akyel, "Improvement of the analytical calculation of the magnetic field produced by permanent magnet rings," Progress In Electromagnetics Research, Vol. 5, 71-82, 2008.
2. 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
3. Selvaggi, J., 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
4. 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
6. Rakotoarison, H. L., J. P. Yonnet, and B. Delinchant, "Using coulombian 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
7. Durand, E., "Electrostatique," Masson Editeur, Paris, France, Vol. 1, 248-251, 1964.
8. 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
9. 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
10. 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, 497-500, 2002. doi:10.1109/20.996131
11. 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
12. 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
13. 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
14. 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
15. Furlani, E., "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
16. Furlani, E. and M. Knewston, "A three-dimensional field solution for permanent-magnet axial-field motors," IEEE Trans. Magn., Vol. 33, No. 1, 2322-2325, 2008.
17. Furlani, E. P., Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications, 235-245, Academic Press, 2001.
18. 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
19. 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
20. 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
21. 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
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
24. Yonnet, J. P., Rare-earth Iron Permanent Magnets, Ch. Magnetomechanical devices, Oxford Science Publications, 1996.
25. Blache, C. and G. Lemarquand, "Linear displacement sensor with hight magnetic field gradient," Journal of Magnetism and Magnetic Materials, Vol. 104, 1106-1108, 1992. doi:10.1016/0304-8853(92)90508-L
26. 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
27. 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
28. 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
30. 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
31. 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
32. 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
33. 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
34. Yong, L., Z. Jibin, and L. Yongping, "Optimum design of magnet shape in permanent-magnet synchronous motors," IEEE Trans. Magn., Vol. 39, No. 11, 3523-4205, 2003. doi:10.1109/TMAG.2003.819462
35. Lemarquand, G. and V. Lemarquand, "Annular magnet position sensor," IEEE. Trans. Magn., Vol. 26, No. 5, 2041-2043, 1990. doi:10.1109/20.104612