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2010-03-16
Mutual Inductance and Force Exerted Between Thick Coils
By
Progress In Electromagnetics Research, Vol. 102, 367-380, 2010
Abstract
We present exact three-dimensional semi-analytical expressions of the force exerted between two coaxial thick coils with rectangular cross-sections. Then, we present a semi-analytical formulation of their mutual inductance. For this purpose, we have to calculate six and seven integrations for calculating the force and the mutual inductance respectively. After mathematical manipulations, we can obtain semi-analytical formulations based on only two integrations. It is to be noted that such integrals can be evaluated numerically as they are smooth and derivable. Then, we compare our results with the filament and the finite element methods. All the results are in excellent agreement.
Citation
Romain Ravaud, Guy Lemarquand, Valerie Lemarquand, Slobodan Babic, and Cevdet Akyel, "Mutual Inductance and Force Exerted Between Thick Coils," Progress In Electromagnetics Research, Vol. 102, 367-380, 2010.
doi:10.2528/PIER10012806
References

1. Costa, E. M. M., "Responses in transformers built with plana coils inner ring coils excited by square waves," Progress In Electromagnetics Research B, Vol. 18, 43-58, 2009.
doi:10.2528/PIERB09082003

2. Costa, E. M. M., "Planar transformers excited by square waves," Progress In Electromagnetics Research, Vol. 100, 55-68, 2010.
doi:10.2528/PIER09110103

3. Yang, Z. J. and J. R. Hull, "Magnetic field of cylindrical coils," Int. J. of Applied Electromagnetics and Mechanics, Vol. 10, No. 4, 351-367, 1999.

4. Grover, F. W., Inductance Calculations, Dover, 1964.

5. Kamon, M., M. J. Tsuk, and J. White, "Fast-henry: A multiple-accelerated 3D inductance extraction program," IEEE Trans. Microwave Theory Tech., Vol. 42, 1750-1758, 1994.
doi:10.1109/22.310584

6. Yu, D. and K. S. Han, "Self-inductance of air-core circular coils with rectangular cross section," IEEE Trans. Magn., Vol. 23, No. 6, 3916-3921, 1987.
doi:10.1109/TMAG.1987.1065777

7. Fawzi, T. H. and P. E. Burke, "The accurate computation of self and mutual inductances of circular coils," IEEE Trans. PAS, Vol. 97, No. 2, 464-468, 1978.

8. Bunin, A. G. and M. Y. Vinogreev, "A method for calculating the inductance circular rings of rectangular cross section," Elektromehanika, Vol. 2, 77-85, 1985.

9. Koledintseva, M. Y., et al. "Method of edge currents for calculating mutual external inductance in a microstrip structure," Progress In Electromagnetics Research, Vol. 80, 197-224, 2008.
doi:10.2528/PIER07101504

10. Koledintseva, M. Y., et al. "Mutual external inductance in stripline structures," Progress In Electromagnetics Research, Vol. 80, 349-368, 2008.
doi:10.1109/TMAG.2008.920251

11. Babic, S. I. and C. Akyel, "Calculating mutual inductance between circular coils with inclined axes in air," IEEE Trans. Magn., Vol. 44, No. 7, 1743-1750, 2008.
doi:10.1109/TMAG.2007.915292

12. Babic, S. I. 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.2006.888565

13. Conway, J., "Inductance calculations for noncoaxial coils using bessel functions," IEEE Trans. Magn., Vol. 43, No. 3, 1023-1034, 2007.
doi:10.2528/PIER09042105

14. 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:10.1109/TMAG.2008.917128

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.2007.892275

16. 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:10.1109/20.179441

17. 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.

18. Ravaud, R., et al. "Ironless loudspeakers with ferrofluid seals," Archives of Acoustics, Vol. 33, No. 4S, 3-10, 2008.
doi:10.1109/20.104612

19. Lemarquand, G. and V. Lemarquand, "Annular magnet position sensor," IEEE. Trans. Magn., Vol. 26, No. 5, 2041-2043, 1990.
doi:10.1109/TMAG.2009.2016088

20. Ravaud, R., G. Lemarquand, and V. Lemarquand, "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.2009.2025315

21. Ravaud, R., G. Lemarquand, and V. Lemarquand, "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:10.2528/PIER09021104

22. Ravaud, R. and G. Lemarquand, "Modelling an ironless loudspeaker by using three-dimensional analytical approaches," Progress In Electromagnetics Research, Vol. 91, 53-68, 2009.
doi:10.1109/20.231636

23. Furlani, E. P., "Formulas for the force and torque of axial couplings," IEEE Trans. Magn., Vol. 29, No. 5, 2295-2301, 1993.

24. Kim, K., et al. "Restoring force between two noncoaxial circular coils," IEEE Trans. Magn., Vol. 32, No. 32, 478-484, 1996.

25. Lang, M., "Fast calculation method for the forces and stiffnesses of permanent-magnet bearings," 8th International Symposium on Magnetic Bearing, 533-537, 2002.
doi:10.1109/20.45327

26. Azzerboni, B., E. Cardelli, and A. Tellini, "Computation of the magnetic field in massive conductor systems," IEEE Trans. on Magn., Vol. 25, No. 6, 4462-4473, 1989.

27. Kajikawa, K. and K. Kaiho, "Usable ranges of some expressions for calculation of the self inductance of a circular coil of rectangular cross section," Cryogenic Engineering, Vol. 30, No. 7, 324-332, 1995.

28. http://www.sc.kyushu-u.ac.jp/»kajikawa..