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2009-10-28

Magnetic Field Produced by a Parallelepipedic Magnet of Various and Uniform Polarization

By Romain Ravaud and Guy Lemarquand
Progress In Electromagnetics Research, Vol. 98, 207-219, 2009
doi:10.2528/PIER09091704

Abstract

This paper deals with the modeling of parallelepipedic magnets of various polarization directions. For this purpose, we use the coulombian model of a magnet for calculating the magnetic potential in all points in space. Then, we determine the three components of the magnetic field created by a parallepiped magnet of various polarization direction. These three components and the scalar magnetic potential are also expressed in terms of fully analytical terms. It is to be noted that the formulas determined in this paper are more general that the ones established in the literature and can be used for optimization purposes. Moreover, our study is carried out without using any simplifying assumptions. Consequently, these expressions are accurate whatever the magnet dimensions. This analytical formulation is suitable for the design of unconventional magnetic couplings, electric machines and wigglers.

Citation


Romain Ravaud and Guy Lemarquand, "Magnetic Field Produced by a Parallelepipedic Magnet of Various and Uniform Polarization," Progress In Electromagnetics Research, Vol. 98, 207-219, 2009.
doi:10.2528/PIER09091704
http://jpier.org/PIER/pier.php?paper=09091704

References


    1. Babic, S. I., 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, 3125-3217, 2000.
    doi:10.1109/20.908707

    2. Babic, S. I. 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.

    3. 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

    4. Yonnet, J. P., Rare-earth Iron Permanent Magnets, Ch. Magnetomechanical devices, Oxford science publications, 1996.

    5. Ravaud, R., 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

    6. 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

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

    8. 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

    9. 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

    10. Jian, L. and K. T. Chau, "Analytical calculation of magnetic field distribution in coaxial magnetic gears," Progress In Electromagnetics Research, Vol. 92, 1-16, 2009.
    doi:10.2528/PIER09032301

    11. Huang, S. M. and C. K. Sung, "Analytical analysis of magnetic couplings with parallelepiped magnets," Journal of Magnetism and Magnetic Materials, Vol. 239, 614-616, 2002.
    doi:10.1016/S0304-8853(01)00683-7

    12. 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

    13. Yonnet, J. P., et al., "Analytical calculation of permanent magnet couplings," IEEE Trans. Magn., Vol. 29, No. 6, 2932-2934, 1993.
    doi:10.1109/20.280913

    14. 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

    15. Conway, J., "Noncoaxial inductance calculations without the vector potential for axisymmetric coils and planar coils," IEEE Trans. Magn., Vol. 44, No. 4, 453-462, 2008.
    doi:10.1109/TMAG.2008.917128

    16. Babic, S. I., F. Sirois, and C. Akyel, "Validity check of mutual inductance formulas for circular filaments with lateral and angular misalignments," Progress In Electromagnetics Research M, Vol. 8, 15-26, 2009.
    doi:10.2528/PIERM09060105

    17. 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, Vol. 88, 307-319, 2008.
    doi:10.2528/PIER08112708

    18. Perigo, E., R. Faria, and C. Motta, "General expressions for the magnetic flux density produced by axially magnetized toroidal permanent magnets," IEEE Trans. Magn., Vol. 43, No. 10, 3826-3832, 2007.
    doi:10.1109/TMAG.2007.904708

    19. 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

    20. Varga, E. and A. Beyer, "Magnetic field of a uniformly magnetized hollow cylinder," IEEE Trans. Magn., Vol. 34, No. 3, 613-618, 1998.
    doi:10.1109/20.668053

    21. Zhilichev, Y., "Calculation of magnetic field of tubular permanent magnet assemblies in cylindrical bipolar coordinates," IEEE Trans. Magn., Vol. 43, No. 7, 3189-3195, 2007.
    doi:10.1109/TMAG.2007.894636

    22. Selvaggi, J. P., et al., "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

    23. Selvaggi, J. P., et al., "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

    24. Selvaggi, J. P., et al., "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

    25. Ravaud, R. and G. Lemarquand, "Comparison of the coulombian and amperian current models for calculating the magnetic field produced by arc-shaped permanent magnets radially magnetized," Progress In Electromagnetics Research, Vol. 95, 309-327, 2009.
    doi:10.2528/PIER09042105

    26. Xia, Z., Z. Q. Zhu, and D. Howe, "Analytical magnetic field analysis of Halbach magnetized permanent-magnet machines," IEEE Trans. Magn., Vol. 40, No. 4, 1864-1872, 2004.
    doi:10.1109/TMAG.2004.828933

    27. 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

    28. Ravaud, R. and G. Lemarquand, "Discussion about the magnetic field produced by cylindrical Halbach structures," Progress In Electromagnetics Research B, Vol. 13, 275-308, 2009.
    doi:10.2528/PIERB09012004

    29. Ravaud, R. and G. Lemarquand, "Mechanical properties of a ferrofluid seal: Three-dimensional analytical study based on the coulombian model ," Progress In Electromagnetics Research B, Vol. 13, 385-407, 2009.
    doi:10.2528/PIERB09020601

    30. Ravaud, R. and G. Lemarquand, "Design of ironless loudspeakers with ferrofluid seals: Analytical study based on the coulombian model," Progress In Electromagnetics Research B, Vol. 14, 285-309, 2009.
    doi:10.2528/PIERB09031904

    31. Bancel, F. and G. Lemarquand, "Three-dimensional analytical optimization of permanent magnets alternated structure," IEEE Trans. Magn., Vol. 34, No. 1, 242-247, 1998.
    doi:10.1109/20.650248