Articles

Analytic calculation of magnetic force between two current-carrying coils

Expand
  • College of Mechanics and Materials, Hohai University, Nanjing 210098, China

Received date: 2014-05-09

  Revised date: 2014-08-07

  Online published: 2015-04-01

Supported by

Project supported by the National Natural Science Foundation of China (No. 11372096) and the Program for Research Fund for the Doctoral Program of Higher Education of China

Abstract

Current-carrying coils are basic elements in electromagnetic equipments, for example, in high field magnets from high temperature superconducting wires or tapes. In the assembly of these systems and their current-carrying operation, unavoidable mis-alignment and shift from the original position can be induced by disturbances such as the imbalance of magnetic force due to safety problems. For two current-carrying coils with non-coplanar axes, the analytic expression of the magnetic force between the two coils is presented according to the rule of Ampere circulation and the Biot-Savart law. Based on the expression, the dependence of the magnetic force on the size and the relative position of each other is further investigated, and the variation of the magnetic force is obtained with the above parameters.

Cite this article

Xiaofan GOU;Jian QIN . Analytic calculation of magnetic force between two current-carrying coils[J]. Applied Mathematics and Mechanics, 2015 , 36(4) : 475 -486 . DOI: 10.1007/s10483-015-1924-9

References

[1] Lee, J. J., Jo, Y. S., Hong, J. P., and Kwon, Y. K. Design of field coil for 100 hp class HTS motor considering operating current. IEEE Transactions on Applied Superconductivity, 13(2), 2214-2217 (2003)
[2] Zheng, X. J., Wang, X. Z., and Zhou, Y. H. Magnetoelastic analysis of non-circular superconduct-ing partial torus. International Journal of Solids and Structures, 37(4), 563-576 (2000)
[3] Friend, C. M., Miao, H. P., Huang, Y. B., Melhem, Z., Domptail, F., Meinesz, M., Hong, S., Young, E. A., and Yang, Y. F. The development of high field magnets utilizing Bi-2212 wind & react insert coils. IEEE Transactions on Applied Superconductivity, 20(3), 583-586 (2010)
[4] Nomura, S., Ohata, Y., Hagita, T., Tsutsui, H., Tsuji-Iio, S., and Shimada, R. Helically wound coils for high field magnets. IEEE Transactions on Applied Superconductivity, 14(2), 709-712 (2004)
[5] Schwartz, J., Effio, T., Liu, X. T., Le, Q. V., Mbaruku, A. L., Schneider-Muntau, H. J., Shen, T. M., Song, H. H., Trociewitz, U. P., Wang, X. R., and Weijers, H. W. High field superconducting solenoids via high temperature superconductors. IEEE Transactions on Applied Superconductivity, 18(2), 70-81 (2008)
[6] Ling, J. Y., Voccio, J., Kim, Y., Hahn, S., Bascunan, J., Park, D. K., and Iwasa, Y. Monofil-ament MgB2 wire for a whole-body MRI magnet: superconducting joints and test coils. IEEE Transactions on Applied Superconductivity, 23(3), 6200304 (2013)
[7] Amemiya, N. and Akachi, K. Magnetic field generated by shielding current in high T(c) supercon-ducting coils for NMR magnets. Superconductor Science and Technology, 21(9), 095001 (2008)
[8] Huguet, M. and the ITER International Team and Participant Teams. The ITER magnets: prepa-ration for full size construction based on the results of the model coil programme. Nuclear Fusion, 43(5), 352-357 (2003)
[9] Zhu, J. Y., Luo, W., Zhou, Y. H., and Zheng, X. J. Contact mechanical characteristics of Nb3Sn strands under transverse electromagnetic loads in the CICC cross-section. Superconductor Science and Technology, 25(12), 125011 (2012)
[10] Xia, J., Yong, H. D., and Zhou, Y. H. A structural mechanics model for the 2-D mechanical char-acteristics of ITER cable-in-conduit conductor cable under transverse loads. IEEE Transactions on Applied Superconductivity, 23(5), 8401209 (2013)
[11] Markiewicz, W. D., Larbalestier, D. C., Weijers, H. W., Voran, A. J., Pickard, K. W., Sheppard, W. R., Jaroszynski, J., Xu, A. X., Walsh, R. P., Lu, J., Gavrilin, A. V., and Noyes, P. D. Design of a superconducting 32 T magnet with REBCO high field coils. IEEE Transactions on Applied Superconductivity, 22(3), 4300704 (2012)
[12] Ravaud, R., Lemarquand, G., Lemarquand, V., and Depollier, C. Analytical calculation of the magnetic field created by permanent-magnet rings. IEEE Transactions on Magnetics, 44(8), 1982- 1989 (2008)
[13] Gou, X. F., Yang, Y., and Zheng, X. J. Analytic expression of magnetic field distribution of rectangular permanent magnets. Applied Mathematics and Mechanics (English Edition), 25(3), 297-306 (2004) DOI 10.1007/BF02437333
[14] Jiang, X. H. and Campbell, A. M. Numerical calculation of magnetic fields in melt processed YBCO magnets. IEEE Transactions on Applied Superconductivity, 7(2), 1213-1215 (1997)
[15] Babic, S. I. and Akyel, C. Magnetic force calculation between thin coaxial circular coils in air. IEEE Transactions on Magnetics, 44(4), 445-452 (2008)
[16] Robertson, W., Cazzolato, B., and Zander, A. A simplified force equation for coaxial cylindrical magnets and thin coils. IEEE Transactions on Magnetics, 47(8), 2045-2049 (2011)
[17] Kim, K. B., Levi, E., Zabar, Z., and Birenbaum, L. Restoring force between two noncoaxial circular coils. IEEE Transactions on Magnetics, 32(2), 478-484 (1996)
[18] Ren, Y. Magnetic force calculation between misaligned coils for a superconducting magnet. IEEE Transactions on Applied Superconductivity, 20(6), 2350-2353 (2010)
Outlines

/

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals