volume | PIER Journals

Abstract

This paper presents a general analytical formulation for calculating the three-dimensional magnetic field distribution produced by Halbach structures with radial or axial polarization directions. Our model allows us to study tile permanent magnets of various magnetization directions and dimensions. The three magnetic field components are expressed in terms of analytical and semi-analytical parts using only one numerical integration. Consequently, the computational cost of our model is lower than 1 s for calculating the magnetic field in any point of space. All our expressions have been checked with previous analytical models published in the literature. Then, we present two optimized permanent magnet structures generating sinusoidal radial fields.

1. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Magnetic field in MRI yokeless devices: Analytical approach," Progress In Electromagnetics Research, Vol. 94, 327-341, 2009.
doi:10.2528/PIER09061205 Google Scholar

2. Halbach, K., "Strong rare earth cobalt quadrupoles," IEEE Trans. Magn., Vol. 26, No. 3, 3882-3884, 1979. Google Scholar

3. Marble, A. E., "Strong, stray static magnetic fields," IEEE Trans. Magn., Vol. 44, No. 5, 576-580, 2008.
doi:10.1109/TMAG.2008.918278 Google Scholar

4. Chang, W., K. Chen, and L. Hwang, "Single-sided mobile NMR with a halbach magnet," Magnetic Resonance Imaging, Vol. 24, No. 8, 1095-1102, 2006.
doi:10.1016/j.mri.2006.04.005 Google Scholar

5. Chen, J. and C. Xu, "An improved discrete configuration of a cylinder magnet for portable nuclear magnetic resonance instruments," J. Appl. Phys., Vol. 101, No. 12, 2007. Google Scholar

6. Marble, A. E., I. V. Mastikhui, B. G. Colpitts, and B. J. Balcom, "Designing static fields for unilateral magnetic resonance by a scalar potential approach," IEEE Trans. Magn., Vol. 43, No. 5, 1903-1911, 2007.
doi:10.1109/TMAG.2006.889538 Google Scholar

7. 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 Google Scholar

8. Ryu, J. S., Y. Yao, C. S. Koh, and Y. J. Shin, "Development of permanent magnet assembly for mri devices," IEEE Trans. Magn., Vol. 42, No. 4, 1351-1353, 2006.
doi:10.1109/TMAG.2006.871563 Google Scholar

9. Thompson, M. R., R. W. Brown, and V. C. Srivastava, "An inverse approach to the design of mri main magnets," IEEE Trans. Magn., Vol. 30, No. 1, 108-112, 1994.
doi:10.1109/20.272522 Google Scholar

10. Baran, W. and M. Knorr, "Synchronous couplings with SmCo5 magnets," 2nd Int. Workshop on RECo Permanent Magnets and Their Applications, 140-151, Dayton, Ohio, USA, 1976. Google Scholar

11. Furlani, E. P., "Analysis and optimization of synchronous couplings," J. Appl. Phys., Vol. 79, 4692-4694, 1996.
doi:10.1063/1.361872 Google Scholar

12. Elies, P. and G. Lemarquand, "Analytical study of radial stability of permanent magnet synchronous couplings," IEEE Trans. Magn., Vol. 35, No. 4, 2133-2136, 1999.
doi:10.1109/20.774183 Google Scholar

13. Ravaud, R. and G. Lemarquand, "Magnetic couplings with cylindrical and plane air gaps: Influence of the magnet polarization direction," Progress In Electromagnetics Research B, Vol. 16, 333-349, 2009.
doi:10.2528/PIERB09051903 Google Scholar

14. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Permanent magnet couplings: Field and torque three-dimensional expressions based on the coulombian model," IEEE Trans. Magn., Vol. 45, No. 4, 1950-1958, 2009.
doi:10.1109/TMAG.2008.2010623 Google Scholar

15. 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

16. Furlani, E. P., "Computing the field in permanent-magnet axialfield motors," IEEE Trans. Mag., Vol. 30, No. 5, 3660-3663, 1994.
doi:10.1109/20.312734 Google Scholar

17. 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

18. Marinescu, M. and N. Marinescu, "New concept of permanentmagnet excitation for electrical machines," IEEE Trans. Magn., Vol. 28, 1390-1393, 1992.
doi:10.1109/20.123952 Google Scholar

19. 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, 3125-3127, 2000.
doi:10.1109/20.908707 Google Scholar

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

21. 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 Google Scholar

22. 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 Google Scholar

23. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Magnetic field produced by a tile permanent magnet whose polarization is both uniform and tangential," Progress In Electromagnetics Research B, Vol. 13, 1-20, 2009.
doi:10.2528/PIERB08121901 Google Scholar

24. 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 Google Scholar

25. 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

Dr. Romain Ravaud

Prof. Guy Lemarquand

Prof. Valerie Lemarquand