volume | PIER Journals

Abstract

With an increase in the number of high speed applications, researchers have been concentrating on permanent magnet bearings due to their suitability. This paper presents a mathematical model of a permanent magnet bearing made of ring magnets with radial polarizations. Coulombian model and vector approach are used to estimate the force, moment and stiffness. A MATLAB code is developed for evaluating the envisaged parameters for three degrees (translational) of freedom of the rotor. The proposed model is validated with the available literature. Comparison of force and stiffness results of the presented model with that reported in the literature and also with the results of 3D finite element analysis shows good agreement. Then, it is extended to analyse stacked ring magnets with alternate radial polarizations. Finally, the cross coupled stiffness values in addition to the principal stiffness values are presented for the elementary structure and also for stacked structure with three ring permanent magnets with alternate radial polarizations.

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

2. Yonnet, J. P., "Permanent magnetic bearings and couplings," IEEE Trans. Magn., Vol. 17, No. 1, 1169-1173, 1981.
doi:10.1109/TMAG.1981.1061166

3. Delamare, J., E. Rulliere, and J. P. Yonnet, "Classification and synthesis of permanent magnet bearing configurations," IEEE Trans. Magn., Vol. 31, No. 6, 4190-4192, 1995.
doi:10.1109/20.489922

4. 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.

5. Guilherme, G. S., R. Andrade, and A. C. Ferreira, "Magnetic bearing sets for a flywheel system," IEEE Trans. on Applied Super Conductivity, Vol. 17, No. 2, 2150-2153, 2007.
doi:10.1109/TASC.2007.899268

6. Hussien, 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

7. 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

8. Yonnet, J. P., et al. "Stacked structures of passive magnetic bearings," J. Appl. Phys., Vol. 70, No. 10, 6633-6635, 1991.
doi:10.1063/1.349857

9. Ravaud, R., G. Lemarquand, and R. Lemarquand, "Analytical calculation of the magnetic field created by permanent magnet rings," IEEE Trans. Magn., Vol. 44, No. 8, 1982-1989, 2008.
doi:10.1109/TMAG.2008.923096

10. 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.
doi:10.2528/PIER09042105

11. 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

12. Babic, S. I. and C. Akyel, "Improvement in the analytical calculation of the magnetic field produced by permanent magnet rings ," Progress In Electromagnetics Research C, Vol. 5, 71-82, 2008.

13. Selvaggi, J. P., et al. "Calculating the external magnetic field from permanent magnets in permanent-magnet motors --- An alternative method," IEEE Trans. Magn., Vol. 40, No. 5, 3278-3285, 2004.
doi:10.1109/TMAG.2004.831653

14. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Magnetic field created by tile permanent magnets," IEEE Trans. Magn., Vol. 45, No. 7, 2920-2926, 2009.
doi:10.1109/TMAG.2009.2014752

15. Azukizawa, T., S. Yamamoto, and N. Matsuo, "Feasibility study of a passive magnetic bearing using the ring shaped permanent magnets ," IEEE Trans. Magn., Vol. 44, No. 11, 4277-4280, 2008.
doi:10.1109/TMAG.2008.2001490

16. Paden, B., N. Groom, and J. Antaki, "Design formulas for permanent-magnet bearings," ASME Trans., Vol. 125, 734-739, 2003.
doi:10.1115/1.1625402

17. Chen, C., et al. "A magnetic suspension theory and its application to the heart quest ventricular assist device ," Artificial Organs, Vol. 26, No. 11, 947-951, 2002.
doi:10.1046/j.1525-1594.2002.07125.x

18. Yoo, S., et al. "Optimal design of non-contact thrust bearing using permanent magnet rings," International Journal of Precision Engineering and Manufacturing, Vol. 12, No. 6, 1009-1014, 2011.
doi:10.1007/s12541-011-0134-4

19. Samanta, P. and H. Hirani, "Magnetic bearing configurations: Theoretical and experimental studies," IEEE Trans. Magn., Vol. 44, No. 2, 292-300, 2008.
doi:10.1109/TMAG.2007.912854

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

21. 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

22. 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:10.1109/TMAG.2009.2025315

23. Bekinal, S. I., T. R. Anil, and S. Jana, "Force, moment and stiffness characteristics of permanent magnet bearings," Proceedings of National Symposium on Rotor Dynamics, Indian Institute of Technology, Madras, India, 161-168, 2011.

24. Bekinal, S. I., T. R. Anil, and S. Jana, "Analysis of axially magnetized permanent magnet bearing characteristics," Progress In Electromagnetics Research B, Vol. 44, 327-343, 2012.

25. Ravaud, R. and G. Lemarquand, "Halbach structures for permanent magnets bearings," Progress In Electromagnetics Research M, Vol. 14, 263-277, 2010.
doi:10.2528/PIERM10100401

26. Mukhopadhaya, S. C., et al. "Fabrication of a repulsive-type magnetic bearing using a novel arrangement of permanent magnets for vertical-rotor suspension ," IEEE Trans. Magn., Vol. 39, No. 5, 3220-3222, 2003.
doi:10.1109/TMAG.2003.816727

Dr. Siddappa Iranna Bekinal

Dr. Anil Tumkur Ramakrishna

Dr. Soumendu Jana