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2020-08-11
Friction-Free Permanent Magnet Bearings for Rotating Shafts: a Comprehensive Review
By
Progress In Electromagnetics Research C, Vol. 104, 171-186, 2020
Abstract
This article presents a comprehensive review of modeling,analysis,and development of permanent magnet bearings (PMB) for rotating shafts. The different configurations of PMB are highlighted with relevant approaches to estimate their features. The progress in mathematical approaches adopted and optimization of the static and dynamic bearing characteristics in terms of accuracy are discussed in depth. Further, key developments on instability issues and their realization in combination with other bearings for rotors stability in low and high-speed applications are reviewed. Finally, concluding remarks on key aspects to be followed in the design and development of PMB are presented.
Citation
Siddappa Iranna Bekinal, and Mrityunjay Doddamani, "Friction-Free Permanent Magnet Bearings for Rotating Shafts: a Comprehensive Review," Progress In Electromagnetics Research C, Vol. 104, 171-186, 2020.
doi:10.2528/PIERC20060402
References

1. Schweitzer, G. and H. Maslen, Magnetic Bearings, Theory, Design and Application to Rotating Machinery, Springer, 2009.

2. Schweitzer, G., "Magnetic bearings-applications, concepts and theory," JSME International Journal Series III, Vol. 33, No. 1, 13-18, 1990.

3. Coombs, T., A. M. Campbell, R. Storey, and R. Weller, "Superconducting magnetic bearings for energy storage flywheels," IEEE Trans. on Applied Super Conductivity, Vol. 9, No. 2, 968-971, 1999.
doi:10.1109/77.783459

4. Mukoyama, S., K. Nakao, H. Sakamoto, et al. "Development of superconducting magnetic bearing for 300 kw flywheel energy storage system," IEEE Trans. on Applied Super Conductivity, Vol. 27, No. 4, 1-4, 2017.
doi:10.1109/TASC.2017.2652327

5. Amati, N., X. De Lepine, and A. Tonoli, "Modeling of electrodynamic bearings," ASME Journal of Vibration and Acoustics, Vol. 130, 061007(1–9), 2008.

6. Detoni, J. G., "Progress on electrodynamic passive magnetic bearings for rotor levitation," Proc. IMechE, Part C: J. Mechanical Engineering Science, Vol. 228, No. 10, 1829-1844, 2014.
doi:10.1177/0954406213511798

7. Detoni, J. G., F., Impinna, A. Tonoli, and N. Amati, "Unified modelling of passive homopolar and heteropolar electrodynamic bearings," Journal of Sound and Vibration, Vol. 331, No. 19, 4219-4232, 2012.
doi:10.1016/j.jsv.2012.04.036

8. Baermann, M., German patent application B, 30042 dated 1954 (German specification No. 1071891).

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

10. Jungmayr, G., E. Marth, M. Panholzer, W. Amrhein, F. Jeske, and M. Reisinger, "Design of a highly reliable fan with magnetic bearings," Proc. IMechE, Part I: J. Systems and Control Engineering, Vol. 230, 361-369, 2016.
doi:10.1177/0959651815602829

11. 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

12. Kriswanto and Jamari, "Radial forces analysis and rotational speed test of radial permanent magnetic bearing for horizontal wind turbine applications," 3rd International Conference on Advanced Materials and Science and Technology (ICAMST 2015), AIP Conference Proceedings, Semarang, Indonesia, 0200341(1–10), 2015.

13. Fang, J., C. Wang, and J. Tang, "Modelling and analysis of a novel conical magnetic bearing for verniergimballing magnetically suspended flywheel," Proc. IMechE, Part C: J. Mechanical Engineering Science, Vol. 228, 2416-2425, 2014.
doi:10.1177/0954406213517488

14. 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

15. 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

16. Le, Y., J. Fang, and J. Sun, "Design of a Halbach array permanent magnet damping system for high speed compressor with large thrust load," IEEE Trans. Magn., Vol. 51, No. 1, 1-9, 2015.

17. 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

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

19. 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

20. 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.

21. 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

22. 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

23. 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.

24. 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.

25. 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

26. Yang, H., R. Zhao, and S. Yang, "New analytical solution for the analysis and design of permanent magnet thrust bearings," Journal Zhejiang University. SC. A, Vol. 10, No. 8, 1199-1204, 2009.
doi:10.1631/jzus.A0820520

27. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "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

28. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "The three exact components of the magnetic field created by a radially magnetized tile permanent magnet," Progress In Electromagnetics Research, Vol. 88, 307-319, 2008.
doi:10.2528/PIER08112708

29. 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

30. Tan, Q., W. Li, and B. Liu, "Investigations on a permanent magnetic hydrodynamic journal bearing," Tribology International, Vol. 35, 443-448, 2002.
doi:10.1016/S0301-679X(02)00026-9

31. 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

32. 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

33. 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

34. 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

35. 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.

36. Jiang, W., et al., "Stiffness analysis of axially polarized radial permanent magnet bearings," Proceedings of Eighth International Symposium on Magnetic Bearings, 527-532, Mito, Japan, 2002.

37. 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

38. Bekinal, S. I., T. R. Anil, and S. Jana, "Analysis of radial magnetized permanent magnet bearing characteristics," Progress In Electromagnetics Research B, Vol. 47, 87-105, 2013.
doi:10.2528/PIERB12102005

39. 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

40. 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

41. Tian, L., A. Xun-Peng, and Y. 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

42. Marth, E., G. Jungmayr, and W. Amrhein, "A 2-D-based analytical method for calculating permanent magnetic ring bearings with arbitrary magnetisation and its application to optimal bearing design," IEEE Trans. Magn., Vol. 50, No. 5, 1-8, 2014.
doi:10.1109/TMAG.2013.2295550

43. 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

44. 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 Tribolog, Vol. 138, No. 3, 2016.

45. Zhang, L., "Design, analysis, and experiment of multi-ring permanent magnet bearings by means of equally distributed sequences based Monte Carlo method," Mathematical Problems in Engineering, 1-17, 2019.

46. Lijesh, K. P. and H. Hirani, "Development of analytical equations for design and optimization of axially polarised radial passive magnetic bearing," ASME Journal of Tribology, Vol. 137, 011103(1–9), 2015.

47. Lijesh, K. P., "Design methodology for monolithic layer radial passive magnetic bearing," Proc. IMechE, Part J: Journal of Engineering Tribology, Vol. 233, No. 6, 992-1000, 2019.

48. Moser, R., J. Sandtner, and H. Bleuler, "Optimization of repulsive passive magnetic bearings," IEEE Trans. Magn., Vol. 42, No. 8, 2038-2042, 2006.

49. 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.

50. 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.

51. 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.

52. 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.

53. 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.

54. 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.

55. Sodano, H. A., D. J. Inman, and W. K. Belvin, "Development of a new passive-active magnetic damper for vibration suppression," ASME Journal of Vibration and Acoustics, Vol. 128, 318-327, 2006.

56. Sodano, H. A. and D. J. Inman, "Modeling of a new active eddy current vibration control system," ASME Journal of Dynamic Systems, Measurement and Control, Vol. 130, 021009-1-11, 2008.

57. Filatov, A., L. Hawkins, V. Krishnan, et al. "Active axial electromagnetic damper," Proceedings of Eleventh International Symposium on Magnetic Bearings, Japan, Nara, 2000.

58. Tonoli, A., "Dynamic characteristics of eddy current dampers and couplers," Journal of Sound and Vibration, Vol. 301, 576-591, 2006.

59. Sodano, H. A., J. S. Bae, D. J. Inman, and W. K. Belvin, "Improved concept and model of eddy current damper," ASME Journal of Vibration and Acoustics, Vol. 128, No. 3, 031002(1–10), 2006.

60. Tonoli, A. and N. Amati, "Dynamic modelling and experimental validation of eddy current dampers and couplers," ASME Journal of Vibration and Acoustics, Vol. 130, No. 2, 021011(1–9), 2008.

61. Ribeiro, E. A., J. T. Pereira, and C. A. Bavastri, "Passive vibration control in rotor dynamics: optimization of composed support using viscoelastic materials," Journal of Sound and Vibration, Vol. 351, 43-56, 2015.

62. Tecza, J. A., Damping for passive magnetic bearings, Patent 5521448, USA, 1996.

63. Imlach, J., Passive magnetic support and damping system, Patent 6448679 B1, USA, 2002.

64. Detoni, J. G., Q. Cui, N. Amati, and A. Tonoli, "Modelling and evaluation of damping coefficient of eddy current dampers in rotordynamic applications," Journal of Sound and Vibration, Vol. 373, 52-65, 2016.

65. 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.

66. Safaeian, R. and H. Heydari, "Comprehensive comparison of different structures of passive permanent magnet bearings," IET Electric Power Applications, Vol. 12, No. 2, 179-187, 2017.

67. Safaeian, R. and H. Heydari, "Optimal design of a compact passive magnetic bearing based on dynamic modelling," IET Electric Power Applications, Vol. 13, No. 6, 720-729, 2019.

68. Marth, E., G. Jungmayr, and W. Amrhein, "Fundamental considerations on introducing damping to passively magnetically stabilized rotor systems," Advances in Mechanical Engineering, Vol. 8, No. 12, 1-9, 2016.

69. D’Angola, A., G. Carbone, L. Mangialardi, and C. Serioa, "Non-linear oscillations in a passive magnetic suspension," International Journal of Non-Linear Mechanics, Vol. 41, 1039-1049, 2006.

70. Sugai, T., T. Inoue, and V. Ishida, "Nonlinear theoretical analysis of contacting forward whirling vibration of a rotating shaft supported by a repulsive magnetic bearing," Journal of Sound and Vibration, Vol. 332, 2735-2749, 2013.

71. Lijesh, K. P. and H. Hirani, "Magnetic bearing using RMD configuration," ASME Journal of Tribology, Vol. 137, No. 4, 42201, 2015.

72. Passenbrunner, J., G. Jungmayr, and W. Amrhein, "Design and analysis of a 1d actively stabilized system with viscoelastic damping support," Actuators, Vol. 8, No. 33, 2-18, 2019.

73. 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.

74. McLachlan, N. W., Theory and Application of Mathieu Functions, Claredon Oxford, 1947.

75. Bassani, R., "A stability space of a magneto-mechanical bearing," ASME, J. Dyn. Sys. Meas. Control, Vol. 129, No. 2, 178-181, 2007.

76. Bassani, R., "Stability of permanent magnets bearings under parametric excitations," Tribology Trans., Vol. 48, 457-463, 2005.

77. Bassani, R., "Dynamic stability of passive magnetic bearings," Nonlinear Dynamics, Vol. 50, 161-168, 2007.

78. Takeshi, M. and A. Mitsunori, "Repulsive magnetic bearing using a piezoelectric actuator for stabilization," JSME Int. Journal C: Mechanical Systems Machine Elements and Manufacturing, Vol. 46, 378-384, 2003.

79. Bassani, R., "Magnetoelastic stability of magnetic axial bearings," Tribology Letters, Vol. 49, 397-401, 2013.

80. Delamare, J., J. P. Yonnet, and E. Rulliere, "A compact magnetic suspension with only one axis control," IEEE Trans. Magn., Vol. 30, No. 6, 4746-4748, 1994.

81. Siebert, M., B. Ebihara, and R. Jansen, "A passive magnetic bearing flywheel," NASA/TM — 2002-211159, 2002.

82. Qian, K. X., P. Zeng, W. M. Ru, and H. Y. Yuan, "New concepts and new design of permanent maglev rotary artificial heart blood pumps," Medical Engineering & Physics, Vol. 28, No. 4, 383-388, 2006.

83. Mukhopadhyay, S. C., et al., "Design, analysis and control of a new repulsive type magnetic bearing," IEE Proc. on Electrical Power Applications, Vol. 146, No. 1, 33-40, 1999.

84. Mukhopadhyay, S. C., et al., "Modeling and control of a new horizontal shaft hybrid type magnetic bearing," IEEE Trans. Ind. Electronics, Vol. 47, No. 1, 100-108, 2000.

85. 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, 3220-3222, 2003.

86. 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.

87. Falkowski, K. and M. Henzel, "High efficiency radial passive magnetic bearing," Solid State Phenomena, Vol. 164, 360-365, 2010.

88. Lijesh, K. P. and H. Hirani, "Modelling and development of rmd configuration magnetic bearing," Tribology in Industry, Vol. 37, 225-235, 2015.

89. 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.

90. Lijesh, K. P. and H. Hirani, "Design and development of permanent magneto-hydrodynamic hybrid journal bearing," ASME Journal of Tribology, Vol. 139, No. 4, 044501(1–9), 2017.