volume | PIER Journals

Abstract

This paper represents the force calculation in a radial passive magnetic bearing using Monte Carlo technique with general division approach (s-MC). The expression of magnetic force is obtained using magnetic surface charge density method which incurs a multidimensional integration with complicated integrand. This integration is solved using Monte Carlo technique with 1-division (1-MC) and 2-division (2-MC) approaches with a MATLAB programming. Analysis using established methods such as finite element method (FEM), semi-analytical method, and adaptive Monte Carlo (AMC) method has been carried out to support the proposed technique. Laboratory experiment has been conducted to validate the proposed method. 2-MC gives better result than 1-MC. The computation time of the proposed method is compared with the quadrature method, FEM and AMC. It is observed that the proposed method invites less computational burden than those methods as the algorithm adaptively traverses the domain for promising parts of the domain only, and all the elementary regions are not considered with equal importance.

1. 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 Google Scholar

2. Fang, J., Y. Le, J. Sun, and K. Wang, "Analysis and design of passive magnetic bearing and damping system for high-speed compressor," IEEE Trans. Magn., Vol. 48, No. 6, 2528-2537, 2012.
doi:10.1109/TMAG.2012.2196443 Google Scholar

3. Wang, F., J.Wang, Z. Kong, and F. Zhang, "Radial and axial force calculation of BLDC motor with passive magnetic bearing," 4th International Power Electronics and Motion Control Conference, IPEMC 2004, Vol. 1, 290-293, Xi'an, China, Aug. 14–16, 2004. Google Scholar

4. Mukhopadhyay, S. C., T. Ohji, M. Iwahara, and A. Member, "Modeling and control of a new horizontal-shaft hybrid-type magnetic bearing," IEEE Trans. Ind. Electron., Vol. 47, No. 1, 100-108, 2000.
doi:10.1109/41.824131 Google Scholar

5. Tan, Q., W. Li, and B. Liu, "Investigations on a permanent magnetic hydrodynamic hybrid journal bearing," Tribol. Int., Vol. 35, No. 7, 443-448, 2002.
doi:10.1016/S0301-679X(02)00026-9 Google Scholar

6. 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 Google Scholar

7. Bekinal, S. I., A. R. Tumkur Ramakrishna, and S. Jana, "Analysis of axially magnetized permanent magnetic bearing characteristics," Progress In Electromagnetics Research B, Vol. 44, 327-343, 2012.
doi:10.2528/PIERB12080910 Google Scholar

8. Paden, B., N. Groom, and J. F. Antaki, "Design formulas for permanent-magnet bearings," ASME J. Mech. Des., Vol. 125, No. 3, 734-738, 2003.
doi:10.1115/1.1625402 Google Scholar

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 Google Scholar

10. 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. Google Scholar

11. Santra, T., D. Roy, and S. Yamada, "Calculation of force between two ring magnets using adaptive Monte Carlo technique with experimental verification," Progress In Electromagnetics Research M, Vol. 49, 181-193, 2016.
doi:10.2528/PIERM16052101 Google Scholar

12. Pennanen, T. and M. Koivu, "An adaptive importance sampling technique," Monte Carlo and Quasi-Monte Carlo Methods, 443-455, Springer, 2004. Google Scholar

13. Rakotoarison, H. L., J. P. Yonnet, and B. Delinchant, "Using coulombian approach for modelling scalar potential and magnetic field of a permanent magnet with radial polarization," IEEE Trans. Magn., Vol. 43, No. 4, 1261-1264, 2007.
doi:10.1109/TMAG.2007.892316 Google Scholar

14. Wangsness, R. K., Electromagnetic Fields, Wiley, 1979.

15. Parker, R. J., "Analytical methods for permanent magnet design," Electro-Technology, 1960. Google Scholar

16. 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 Google Scholar

17. Alrefaei, M. H. and H. M. Abdul-Rahman, "An adaptive Monte Carlo integration algorithm with general division approach," Math. Comput. Simul., 2007, doi:10.1016/j.matcom.2007.09.009. Google Scholar

Dr. Tapan Santra

Prof. Debabrata Roy

Dr. Amalendu Bikash Choudhury