This paper represents a new simple technique to calculate force between two ring magnets using adaptive Monte Carlo integration technique. Elementary magnetic force is calculated by discretizing the pole faces of the passive magnets into tiny surfaces. To obtain the resultant force this elementary force equation is integrated over the dimensions of the ring magnets, which incur a multidimensional integration with complicated integral function. This multidimensional integration is solved using adaptive Monte Carlo technique considering singularity treatment and importance sampling. This method is advantageous over existing analytical or quasi analytical methods regarding singularity treatment and computational burden. It is more flexible, especially for using in digital computer. The result of the proposed technique is verified with finite element method and also validated by laboratory experiment. It is observed that the proposed result matches very well with the practical test result, particularly if self demagnetization is considered. So taking into account of simplicity, less computational burden and usefulness, the proposed method may be an alternative choice for magnetic force calculation.
1. Chu, H. Y., Y. Fan, and C. S. Zhang, "A novel design for the flywheel energy storage system," Proceedings of the Eighth International Conference on Electrical Machines and Systems, Vol. 2, 1583-1587, 2005. doi:10.1109/ICEMS.2005.202817
2. Ohji, T., et al., "Conveyance test by oscillation and rotation to a permanent magnet repulsive-type conveyor," IEEE Trans. Magn., Vol. 40, No. 4, 3057-3059, 2004. doi:10.1109/TMAG.2004.832263
3. Hussein, 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
4. Yonnet, J. P., "Passive magnetic bearings with permanent magnets," IEEE Trans. Magn., Vol. 14, No. 5, 803-805, 1978. doi:10.1109/TMAG.1978.1060019
5. Lang, M., "Fast calculation method for the forces and stiffness of permanent-magnet bearings," 8th International Symposium on Magnetic Bearing, 533-537, 2002.
6. Jiang, W., et al., "Forces and moments in axially polarized radial permanent magnet bearings," Proceedings of Eighth International Symposium on Magnetic Bearings, 521-526, Mito, Japan, 2002.
7. 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.
8. 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.2009.2016088
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. Bekinal, S. I., A. R. Tumkur Ramakrishna, and S. Jana, "Analysis of axially magnetized permanent magnetic bearing characteristics," Progress In Electromagnetic Research B, Vol. 44, 327-343, 2012. doi:10.2528/PIERB12080910
11. Lijesh, K. P. and H. Hirani, "Development of analytical equations for design and optimization of axially polarized radial passive magnetic bearing," Journal of Tribology, Vol. 137, 011103-9, 2015.
12. Mishra, M. and N. Gupta, "Monte Carlo integration technique for the analysis of electromagnetic scattering from conducting surfaces," Progress In Electromagnetics Research, Vol. 79, 91-106, 2008. doi:10.2528/PIER07092005
13. Pennanen, T. and M. Koivu, "An adaptive importance sampling technique," Monte Carlo and Quasi-Monte Carlo Methods, 443-455, Springer, 2004.
14. Alrefaei, M. H. and H. M. Abdul-Rahman, "An adaptive Monte Carlo integration algorithm with general division approach," Math. Comput. Simul..
15. Jourdain, B., "Adaptive variance reduction techniques in finance," Radon Series Comp. Appl. Math., Vol. 8, 1-18, De Gruyter, 2009.
16. Parker, R. J., "Analytical methods for permanent magnet design," Electro-Technology, 1960.