This article deals with the generalized procedure of designing and optimizing multi-ring radial and thrust permanent magnet bearings (PMBs) with an axial air gap for maximum force and stiffness per volume of the magnet. Initially, the procedure of determining optimized design variables in both the configurations is presented using the MATLAB codes written for solving the three dimensional (3D) equations of force and stiffness in PMB having `n' number of rings on the stator and rotor. The maximized results of the forces in both radial and thrust multi-ring PMBs are validated with the values obtained using finite element analysis (FEA). Then, the correlation between the optimized parameters and the air gap is obtained, and curve fit equations for the same are proposed in terms of stator outer diameter. Further, curve fit equations establishing the relationship between the maximized bearing features, and the aspect ratio (L/D4) of the bearing are expressed for different values of air gap in both the radial and thrust bearings. Finally, the generalized method of designing and optimizing the multi-ring PMB is demonstrated with a specific application. A designer can use the presented curve fit equations for optimizing design variables and calculating maximized bearing features in multi-ring radial and thrust PMBs easily just by knowing the bearing features for a single ring pair.
2. Backers, F. T., "A magnetic journal bearing," Philips Tech. Rev., Vol. 22, 232-238, Jan. 6, 1960.
3. Yonnet, J. P., "Passive magnetic bearings with permanent magnets," IEEE Trans. Magn., Vol. 14, No. 5, 803-805, 1978.
4. Yonnet, J. P., "Permanent magnetic bearings and couplings," IEEE Trans. Magn., Vol. 17, No. 1, 1169-1173, 1981.
5. 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.
6. Kriswanto, J., "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, Semaran, 0200341(1-10), 2015.
7. 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.
8. 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.
9. 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.
10. 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.
11. Bekinal, S. I. and M. Doddamani, "Friction-free permanent magnet bearings for rotating shafts: A comprehensive review," Progress In Electromagnetics Research C, Vol. 104, 171-186, 2020.
12. Paden, B., N. Groom, and J. Antaki, "Design formulas for permanent-magnet bearings," ASME Trans., Vol. 125, 734-739, 2003.
13. Tan, Q., W. Li, and B. Liu, "Investigations on a permanent magnetic hydrodynamic journal bearing," Tribology International, Vol. 35, 443-448, 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. 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.
16. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Halbach structures for permanent magnets bearings," Progress In Electromagnetics Research M, Vol. 14, 263-277, 2010.
17. Bekinal, S. I., A. R. Tumkur Ramakrishna, 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.
18. 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.
19. 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.
20. Moser, R., J. Sandtner, and H. Bleuler, "Optimization of repulsive passive magnetic bearings," IEEE Trans. Magn., Vol. 42, No. 8, 2038-2042, 2006.
21. 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.
22. 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.
23. Van Beneden, M., V. Kluyskens, and B. Dehez, "Optimal sizing and comparison of permanent magnet thrust bearings,", Vol. 53, No. 2, 1-10, 2017.
24. 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.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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.
30. Safaeian, R. and H. Heydari, "Comprehensive comparison of different structures of passive permanent magnet bearings," IET Electric Power Appl., Vol. 12, 179-187, 2017.
31. Bekinal, S. I. and M. Doddamani, "Improvement in the design calculations of multi ring permanent magnet thrust bearing," Progress In Electromagnetics Research M, Vol. 94, 83-93, 2020.