This paper is the third part of a series dealing with permanent magnet passive magnetic bearings. It presents analytical expressions of the axial force and stiffness in radial passive magnetic bearings made of ring permanent magnets with perpendicular polarizations: the inner ring polarization is perpendicular to the outer ring one. The main goal of this paper is to present a simple analytical model which can be easily implemented in Matlab or Mathematica so as to carry out parametric studies. This paper first compares the axial force and stiffness in bearings with axial, radial and perpendicular polarizations. Then, bearings made of stacked ring magnets with alternate polarizations are studied for the three kinds of polarizations, axial, radial and perpendicular. The latter correspond to Halbach structures. These calculations are useful for identifying the structures required for having great axial forces and the ones allowing to get great axial stiffnesses.
2. Ravaud, R., et al., "Force and stiffness of passive magnetic bearings using permanent magnets. Part 1: Axial magnetization," IEEE Trans. Magn., Vol. 45, No. 7, 2996-3002, 2009.
doi:10.1109/TMAG.2009.2016088
3. Ravaud, R., et al., "Force and stiffness of passive magnetic bearings using permanent magnets. Part 2: Radial magnetization," IEEE Trans. Magn., Vol. 45, No. 9, 3334-3342, 2009.
doi:10.1109/TMAG.2009.2025315
4. Azzerboni, B., E. Cardelli, and A. Tellini, "Computation of the magnetic field in massive conductor systems," IEEE Trans. Magn., Vol. 25, No. 6, 4462-4473, 1989.
doi:10.1109/20.45327
5. 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
6. Kim, K., et al., "Mutual inductance of noncoaxial circular coils with constant current density," IEEE Trans. Magn., Vol. 33, No. 5, 4303-4309, 1997.
doi:10.1109/20.620439
7. Babic, S., et al., "Analytical calculation of the 3d magnetostatic ¯eld of a torroidal conductor with rectangular cross section ," IEEE Trans. Magn., Vol. 24, No. 6, 3162-3164, 1988.
doi:10.1109/20.92368
8. Ravaud, R. and G. Lemarquand, "Comparison of the coulombian and amperian current models for calculating the magnetic field produced by radially magnetized arc-shaped permanent magnets," Progress In Electromagnetics Research, Vol. 95, 309-327, 2009.
doi:10.2528/PIER09042105
9. 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
10. 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.
11. Ravaud, R., et al., "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
12. Ravaud, R., , G. Lemarquand, and V. Lemarquand, "Magnetic field created by tile permanent magnets," IEEE Trans. Magn., Vol. 45, No. 7, 2920-2926, 2009.
doi:10.1109/TMAG.2009.2014752
13. 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
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. Azzerboni, B., et al., "Analytic expressions for magnetic field from finite curved conductors," IEEE Trans. Magn., Vol. 27, No. 2, 750-757, 1991.
doi:10.1109/20.133288
16. 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
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
18. Lang, M., "Fast calculation method for the forces and stiffnesses of permanent-magnet bearings," 8th International Symposium on Magnetic Bearing, 533-537, 2002.
19. Ohji, T., et al., "Performance of repulsive type magnetic bearing system under nonuniform magnetization of permanent magnet," IEEE Trans. Magn., Vol. 36, No. 5, 3696-3698, 2000.
doi:10.1109/20.908944
20. Samanta, P. and H. Hirani, "Magnetic bearing configurations: Theoretical and experimental studies," IEEE Trans. Magn., Vol. 44, No. 2, 292-300, 2008.
doi:10.1109/TMAG.2007.912854
21. Hussien, A., et al., "Application of the repulsive-type magnetic bearing for manufacturing micromass measurement balance equipment," IEEE Trans. Magn., Vol. 41, No. 10, 3802-3804, 2005.
doi:10.1109/TMAG.2005.854929
22. Mukhopadhyay, S. C., et al., "Fabrication of a repulsive-type magnetic bearing using a novel arrangement of permanent magnets for vertical-rotor suspension," IEEE Trans. Magn., Vol. 39, No. 5, 3220-3222, 2003.
doi:10.1109/TMAG.2003.816727
23. Janssen, J., et al., "Three-dimensional analytical calculation of the torque between permanent magnets in magnetic bearings," IEEE Trans. Mag., Vol. 46, No. 6, 1748-1751, 2010.
doi:10.1109/TMAG.2010.2043224
24. Azukizawa, T., S. Yamamoto, and N. Matsuo, "Feasibility study of a passive magnetic bearing using the ring shaped permanent magnets," IEEE Trans. Magn., Vol. 44, No. 11, 4277-4280, 2008.
doi:10.1109/TMAG.2008.2001490
25. Hijikata, K., et al., "Behavior of a novel thrust magnetic bearing with a cylindrical rotor on high speed rotation," IEEE Trans. Magn., Vol. 45, No. 10, 4617-4620, 2009.
doi:10.1109/TMAG.2009.2022178
26. Filatov, A. and E. Maslen, "Passive magnetic bearing for flywheel energy storage systems," IEEE Trans. Magn., Vol. 37, No. 6, 3913-3924, 2001.
doi:10.1109/20.966127
27. Moser, R., J. Sandtner, and H. Bleuler, "Optimization of repulsive passive magnetic bearings," IEEE. Trans. Magn., Vol. 42, No. 8, 2038-2042, 2006.
doi:10.1109/TMAG.2005.861160
28. 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
29. 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
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