volume | PIER Journals

Abstract

This article presents the design and optimization of multi-ring permanent magnet thrust bearing (PMTB) with an axial air gap between successive axial stacks. Larger air gap due to the inclusion of conductive materials needs to be critically analysed in permanent magnet bearings with eddy current damper. High conductivity materials can be filled in an axial air gap instead of a radial air gap to increase the required amount of damping. Three-dimensional (3D) mathematical model for load-carrying capacity for the said configuration is presented using the Coulombain model. The significance of an axial air gap between successive ring pairs in the configuration concerning maximization in the bearing characteristics is presented. Variables such as the number of axial stacks, an axial air gap between the successive rings, an inside radius of rotor ring magnets, and an inside radius of stator ring magnets are optimized at different air gap values for maximizing the load-carrying capacity and stiffness. A significant increase in the values of bearing characteristics is observed in the optimized configuration as compared to bearing with a single permanent magnet ring pair. Optimized PMTB with comparable load carrying capacity and stiffness values can be used to replace conventional bearings used in high-speed applications to improve system efficiency.

1. Backers, F. T., "A magnetic journal bearing," Philips Tech. Rev., Vol. 22, 232-238, 1960-61.

2. 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

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

4. Schweitzer, G., "Magnetic bearings-applications, concepts and theory," JSME International Journal, Series III, Vol. 3, 13-18, 1990.

5. 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. 9, 2528-2537, 2012.
doi:10.1109/TMAG.2012.2196443

6. Morales, W., R. Fusaro, and A. Kascak, "Permanent magnetic bearing for spacecraft applications," Tribology Transactions, Vol. 46, No. 3, 460-464, 2003.
doi:10.1080/10402000308982651

7. Bekinal, S. I., S. Jana, and S. S. Kulkarni, "A hybrid (permanent magnet and foil) bearing set for complete passive levitation of high-speed rotors," Proc. IMechE, Part C: J. Mechanical Engineering Science, Vol. 231, 3679-3689, 2017.
doi:10.1177/0954406216652647

8. Sotelo, G. G., 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

9. Marinescu, M. and N. Marinescu, "A new improved method of for computation of radial stiffness of permanent magnet bearings," IEEE Trans. Magn., Vol. 30, 3491-3494, 1994.
doi:10.1109/20.312691

10. 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

11. Lang, M., "Fast calculation method for the forces and stiffness of permanent-magnet bearings," Proceedings of Eighth International Symposium on Magnetic Bearings, 533-537, Mito, Japan, 2002.

12. Jiang, S., Y. Liang, and H. Wang, "A simplified method of calculating axial force for a permanent magnetic bearing," Proc. IMechE, Part C: J. Mechanical Engineering Science, Vol. 224, 703-708, 2009.

13. 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

14. 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

15. 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

16. 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.
doi:10.2528/PIERB12080910

17. Bekinal, S. I., T. R. Anil, and S. Jana, "Analysis of radial magnetized permanent magnet bearing characteristics for five degrees of freedom," Progress In Electromagnetics Research B, Vol. 52, 307-326, 2013.
doi:10.2528/PIERB13032102

18. Bekinal, S. I., T. R. Anil, S. Jana, S. S. Kulkarni, A. Sawant, N. Patil, and S. Dhond, "Permanent magnet thrust bearing: Theoretical and experimental results," Progress In Electromagnetics Research B, Vol. 56, 269-287, 2013.
doi:10.2528/PIERB13101602

19. Yonnet, J. P., G. Lemarquand, S. Hemmerlin, and E. Olivier-Rulliere, "Stacked structures of passive magnetic bearings," Journal Applied Physics, Vol. 70, 6633-6635, 1991.
doi:10.1063/1.349857

20. 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

21. Tian, L.-L., X.-P. Ai, and Y.-Q. Tian, "Analytical model of magnetic force for axial stack permanent-magnet bearings," IEEE Trans. Magn., Vol. 48, No. 10, 2592-2599, 2012.
doi:10.1109/TMAG.2012.2197635

22. Bekinal, S. I. and S. Jana, "Generalized three-dimensional mathematical models for force and stiffness in axially, radially, and perpendicularly magnetized passive magnetic bearings with `n' number of ring pairs," ASME Journal of Tribology, Vol. 138, No. 3, 031105(1-9), 2016.
doi:10.1115/1.4032668

23. Moser, R., J. Sandtner, and H. Bleuler, "Optimization of repulsive passive magnetic bearings," IEEE Trans. Magn., Vol. 42, No. 8, 2038-2042, 2006.
doi:10.1109/TMAG.2005.861160

24. Lijesh, K. P., M. R. Doddamani, and S. I. Bekinal, "A pragmatic optimization of axial stack-radial passive magnetic bearings," ASME Journal of Tribology, Vol. 140, 021901(1-9), 2018.

25. Bekinal, S. I., M. R. Doddamani, and N. D. Dravid, "Utilization of low computational cost two dimensional analytical equations in optimization of multi rings permanent magnet thrust bearings," Progress In Electromagnetics Research M, Vol. 62, 51-63, 2017.
doi:10.2528/PIERM17072007

26. Beneden, M. V., V. Kluyskens, and B. Dehez, "Optimal sizing and comparison of permanent magnet thrust bearings," IEEE Trans. Magn., Vol. 53, No. 2, 2017.

27. Bekinal, S. I., M. R. Doddamani, and S. Jana, "Optimization of axially magnetised stack structured permanent magnet thrust bearing using three dimensional mathematical model," ASME Journal of Tribology, Vol. 139, No. 3, 031101(1-9), 2017.
doi:10.1115/1.4034533

28. Bekinal, S. I., M. R. Doddamani, B. V. Mohan, and S. Jana, "Generalized optimization procedure for rotational magnetized direction permanent magnet thrust bearing configuration," Proc. IMechE, Part C: J. Mechanical Engineering Science, Vol. 233, 2563-2573, 2019.
doi:10.1177/0954406218786976

29. Lijesh, K. P., M. R. Doddamani, S. I. Bekinal, and S. M. Muzakkir, "Multi-objective optimization of stacked radial passive magnetic bearing," Proc. IMechE Part J: J. Engineering Tribology, Vol. 232, 1140-1159, 2018.
doi:10.1177/1350650117733374

30. Filatov, A., L. Hawkins, V. Krishnan, and B. Lam, "Active axial electromagnetic damper," Proceedings of Eleventh International Symposium on Magnetic Bearings, 2000.

31. Cheah, S. K. and H. A. Sodano, "Novel eddy current damping mechanism for passive magnetic bearings," Journal of Vibration and Control, Vol. 14, No. 11, 1749-1766, 2008.
doi:10.1177/1077546308091219

32. Yoo, S. Y., W. Kim, S. Kim, W. Lee, Y. Bae, and M. Noh, "Optimal design of non-contact thrust bearing using permanent magnet rings," Int. Journal of Precision Engg. and Manufacturing, Vol. 12, No. 6, 1009-1014, 2011.
doi:10.1007/s12541-011-0134-4

33. Safaeian, R. and H. Heydari, "Comprehensive comparison of different structures of passive permanent magnet bearings," IET Electric Power Appl., Vol. 12, 179-187, 2017.

Dr. Siddappa Iranna Bekinal

Dr. Mrityunjay Doddamani