This paper presents a simple mathematical model to determine the force, stiffness and moment parameters in Permanent Magnet (PM) bearings made of radial magnetized ring magnets using Coulombian model and vector approach for five degrees of freedom. MATLAB codes are written to evaluate the bearing characteristics for three translational (x, y and z) and two angular (ξ and γ) degrees of freedom of the rotor magnet. The results of the mathematical model are compared with the results of Finite Element Analysis (FEA) using ANSYS and experiments for a PM bearing with one ring pair, thereby the presented mathematical model is validated. Furthermore, the PM bearing with three ring pairs with alternate radial polarizations are analysed by extending the presented mathematical model and also using ANSYS. Finally, the 5×5 stiffness matrix consisting of principal and cross coupled values is presented for the elementary structure as well as for the stacked structure with three ring pairs.
2. 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.
3. Guilherme, G. S., R. Andrade, and A. C. Ferreira, "Magnetic bearing sets for a flywheel system," IEEE Trans. on Applied Super Conductivity, Vol. 172, 2150-2153, 2007.
4. Jinji, S., R. Yuan, and F. Jiancheng, "Passive axial magnetic bearing with Halbach magnetized array in magnetically suspended control moment gyro application," Journal of Magnetism and Magnetic Materials, Vol. 323, No. 5, 2103-2107, 2011.
5. 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.
6. 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.
7. 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.
8. 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.
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.
10. Paden, B., N. Groom, and J. Antaki, "Design formulas for permanent-magnet bearings," ASME Trans., Vol. 125, 734-739, 2003.
11. 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.
12. 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.
13. Lang, M., "Fast calculation method for the forces and stiffnesses of permanent-magnet bearings," 8th International Symposium on Magnetic Bearing , 533-537, 2002.
14. Samanta, P. and H. Hirani, "Magnetic bearing configurations: Theoretical and experimental studies," IEEE Trans. Magn., Vol. 44, No. 2, 292-300, 2008.
15. 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.
16. 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.
17. 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.
18. 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, 161-168, 2011.
19. Ravaud, R. and G. Lemarquand, "Halbach structures for permanent magnets bearings," Progress In Electromagnetics Research M, Vol. 14, 263-277, 2010.
20. Earnshaw, S., "On the nature of the molecular forces which regulate the constitution of the luminiferous ether," Transactions of the Cambridge Philosophical Society, Vol. 7, 97-112, 1842.
21. Jiang, W., et al., "Forces and moments in axially polarized radial permanent magnet bearings," Proceedings of Eighth International Symposium on Magnetic Bearings, 521-526, 2002.
22. Jiang, W., et al., "Stiffness analysis of axially polarized radial permanent magnet bearings," Proceedings of Eighth International Symposium on Magnetic Bearings, 527-532, 2002.
23. 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.