volume | PIER Journals

Abstract

We have developed a simple method to calculate the axial force between concentric thin walled solenoids. To achieve this, we mapped the force between them as a function of their geometrical relations based on separation to diameter ratios. This resulted in an equation and a set of data. We used them together to calculate the axial forces between two coaxial thin walled solenoids. With this method, direct evaluation of elliptical integrals was circumvented, and the forces were obtained with a simple expression. The results were validated against existing semi-analytical solutions and measurements of force between high coercivity permanent magnets.

1. Beleggia, M., D. Vokoun, and M. De Graef, "Forces between a permanent magnet and a soft magnetic plate," IEEE Magn. Lett., Vol. 3, 0500204, 2012.
doi:10.1109/LMAG.2012.2214027

2. Robertson, W., B. Cazzolato, and A. Zander, "A simplified force equation for coaxial cylindrical magnets and thin coils," IEEE Trans. Magn., Vol. 47, No. 8, 2045-2049, 2011.
doi:10.1109/TMAG.2011.2129524

3. Ravaud, R., G. Lemarquand, S. Babic, V. Lemarquand, and C. Akyel, "Cylindrical magnets and coils: Fields, forces, and inductances," IEEE Trans. Magn., Vol. 46, No. 9, 3585-3590, 2010.
doi:10.1109/TMAG.2010.2049026

4. Ravaud, R., G. Lemarquand, V. Lemarquand, S. Babic, and C. Akyel, "Mutual inductance and force exerted between thick coils," Progress In Electromagnetics Research, Vol. 102, 367-380, 2010.
doi:10.2528/PIER10012806

5. 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.

6. 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

7. Yang, Z. and R. Hull, "Forces and torques between two square current loops," Int. J. of Applied Electromagnetics and Mechanics, Vol. 10, No. 1, 63-76, 1999.

8. Babic, S., C. Akyel, and N. Boudjada, "The simplest formulas for self inductance, mutual inductance and magnetic force of coaxial cylindrical magnets and thin coils," Recent Researches in Circuits and Systems, 44-4, WSEAS Press8, Kos Island, Greece, 2012.

9. Babic, S., C. Akyel, Y. Ren, and W. Chen, "Calculation of the mutual inductance and the magnetic force between a thick circular coil of the rectangular cross section and a thin wall solenoid (integro-differential approach)," Progress In Electromagnetics Research B, Vol. 33, 221-237, 2011.
doi:10.2528/PIERB11062111

10. Babic, S. and C. Akyel, "Magnetic force between inclined circular loops (Lorentz Approach)," Progress In Electromagnetics Research B, Vol. 38, 333-349, 2012.
doi:10.2528/PIERB12011501

11. Babic, S., C. Akyel, Y. Ren, and W. Chen, "Magnetic force calculation between circular coils of rectangular cross section with parallel axes for superconducting magnet," Progress In Electromagnetics Research B, Vol. 37, 275-288, 2012.
doi:10.2528/PIERB11110508

12. Shiri, A. and A. Shoulaie, "A new methodology for magnetic force calculations between planar spiral coils," Progress In Electromagnetics Research, Vol. 95, 39-57, 2009.
doi:10.2528/PIER09031608

13. Shiri, A., M. R. Alizadeh Pahlavani, H. A. Mohammadpour, and A. Shoulaie, "Electromagnetic force distribution on cylindrical coils’ body," PIERS Proceedings, 1102-1105, Xi'an, China, March 22-26, 2010.

14. Iwasa, Y., Case Studies in Superconducting Magnets, 2nd Ed., 88-89, Springer, 2009.

15. Garrett, M. W., "Calculations of fields, forces, and mutual inductances of current systems by elliptic integrals," J. Appl. Phys., Vol. 34, No. 9, 2567-2573, 1963.
doi:10.1063/1.1729771

16. Maxwell, J., A Treatise on Electricity and Magnetism, 3rd Ed., Vol. 2, Arts. 615 and 833, Oxford University Press, London, U.K., 1891 (Reprinted 1954, Dover, New York).

17. Pérez-Loya, J. J. and U. Lundin, "Optimization of force between cylindrical permanent magnets," IEEE Magn. Lett., Vol. 5, 1-4, 2014.
doi:10.1109/LMAG.2014.2363438

18. Hultman, E., B. Ekergard, T. Kamf, D. Salar, and M. Leijon, "Preparing the Uppsala University wave energy converter generator for large-scale production," 5th International Conference on Ocean Energy, Halifax, Canada, 2014.

19. Robertson, W., B. Cazzolato, and A. Zander, "Maximizing the force between two cuboid magnets," IEEE Magn. Lett., Vol. 1, 9000102, 2010.
doi:10.1109/LMAG.2010.2081351

20. Cooper, R., V. Neil, and W. Woodruff, "Optimum permanent-magnet dimensions for repulsion applications," IEEE Trans. Magn., Vol. 9, No. 2, 125-127, 1973.
doi:10.1109/TMAG.1973.1067575

21. Kinouchi, Y., T. Ushita, H. Tsutsui, and Y. Yoshida, "Optimization and design of permanent magnet devices for retaining dental prosthetic appliances," IEEE Trans. Biomed. Eng., Vol. 30, No. 4, 201-207, 1983.
doi:10.1109/TBME.1983.325218

Dr. Jesus Jose Perez-Loya

Dr. Claes Urban Lundin