This work deals with generalized three-dimensional (3D) mathematical model to estimate the force and stiffness in axially, radially, and perpendicularly polarized passive magnetic bearings with “n” number of permanent magnet (PM) ring pairs. Coulombian model and vector approach are used to derive generalized equations for force and stiffness. Bearing characteristics (in three possible standard configurations) of permanent magnet bearings (PMBs) are evaluated using matlab codes. Further, results of the model are validated with finite element analysis (FEA) results for five ring pairs. Developed matlab codes are further utilized to determine only the axial force and axial stiffness in three stacked PMB configurations by varying the number of rings. Finally, the correlation between the bearing characteristics (PMB with only one and multiple ring pairs) is proposed and discussed in detail. The proposed mathematical model might be useful for the selection of suitable configuration of PMB as well as its optimization for geometrical parameters for high-speed applications.
Issue Section:
Applications
Topics:
Magnetic bearings,
Rotors,
Stiffness,
Finite element analysis,
Bearings,
Magnets,
Stators,
Matlab
References
1.
Ohji
, T.
, Ichiyama
, S.
, Amei
, K.
, Sakui
, M.
, and Yamada
, S.
, 2004
, “Conveyance Test by Oscillation and Rotation to a Permanent Magnet Repulsive-Type Conveyor
,” IEEE Trans. Magn.
, 40
(4
), pp. 3057
–3059
.2.
Sotelo
, G. G.
, Andrade
, R.
, and Ferreira
, A. C.
, 2007
, “Magnetic Bearing Sets for a Flywheel System
,” IEEE Trans. Appl. Supercond.
, 17
(2
), pp. 2150
–2153
.3.
Fang
, J.
, Le
, Y.
, Sun
, J.
, and Wang
, K.
, 2012
, “Analysis and Design of Passive Magnetic Bearing and Damping System for High-Speed Compressor
,” IEEE Trans. Magn.
, 48
(9
), pp. 2528
–2537
.4.
Bekinal
, S. I.
, Anil
, T. R.
, Kulkarni
, S. S.
, and Jana
, S.
, 2014
, “Hybrid Permanent Magnet and Foil Bearing System for Complete Passive Levitation of Rotor
,” 10th International Conference on Vibration Engineering and Technology of Machinery
(VETOMAC X 2014
), Manchester, UK, Sept. 9–11, pp. 939
–949
.5.
Yonnet
, J. P.
, 1978
, “Passive Magnetic Bearings With Permanent Magnets
,” IEEE Trans. Magn.
, 14
(5
), pp. 803
–805
.6.
Yonnet
, J. P.
, 1981
, “Permanent Magnetic Bearings and Couplings
,” IEEE Trans. Magn.
, 17
(1
), pp. 1169
–1173
.7.
Delamare
, J.
, Rulliere
, E.
, and Yonnet
, J. P.
, 1995
, “Classification and Synthesis of Permanent Magnet Bearing Configurations
,” IEEE Trans. Magn.
, 31
(6
), pp. 4190
–4192
.8.
Yonnet
, J. P.
, Lemarquand
, G.
, Hemmerlin
, S.
, and Rulliere
, E. O.
, 1991
, “Stacked Structures of Passive Magnetic Bearings
,” J. Appl. Phys.
, 70
(10
), pp. 6633
–6635
.9.
Paden
, B.
, Groom
, N.
, and Antaki
, J.
, 2003
, “Design Formulas for Permanent-Magnet Bearings
,” ASME J. Mech. Des.
, 125
(4
), pp. 734
–739
.10.
Lijesh
, K. P.
, and Hirani
, H.
, 2015
, “Development of Analytical Equations for Design and Optimization of Axially Polarized Radial Passive Magnetic Bearing
,” ASME J. Tribol.
, 137
(1
), pp. 1
–9
.11.
Samanta
, P.
, and Hirani
, H.
, 2008
, “Magnetic Bearing Configurations: Theoretical and Experimental Studies
,” IEEE Trans. Magn.
, 44
(2
), pp. 292
–300
.12.
Ravaud
, R.
, Lemarquand
, G.
, and Lemarquand
, V.
, 2009
, “Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets—Part 1: Axial Magnetization
,” IEEE Trans. Magn.
, 45
(7
), pp. 2996
–3002
.13.
Ravaud
, R.
, Lemarquand
, G.
, and Lemarquand
, V.
, 2009
, “Force and Stiffness of Passive Magnetic Bearings Using Permanent Magnets—Part 2: Radial Magnetization
,” IEEE Trans. Magn.
, 45
(9
), pp. 3334
–3342
.14.
Bekinal
, S. I.
, Anil
, T. R.
, and Jana
, S.
, 2014
, “Analysis of the Magnetic Field Created by the Permanent Magnet Rings in Permanent Magnet Bearings
,” Int. J. Appl. Electromagn. Mech.
, 46
(1
), pp. 255
–269
.15.
Bekinal
, S. I.
, Anil
, T. R.
, and Jana
, S.
, 2012
, “Analysis of Axially Magnetized Permanent Magnet Bearing Characteristics
,” Prog. Electromagn. Res. B
, 44
, pp. 327
–343
.16.
Bekinal
, S. I.
, Anil
, T. R.
, and Jana
, S.
, 2013
, “Analysis of Radial Magnetized Permanent Magnet Bearing Characteristics for Five Degrees of Freedom
,” Prog. Electromagn. Res. B
, 52
, pp. 307
–326
.17.
Bekinal
, S. I.
, Anil
, T. R.
, Jana
, S.
, Kulkarni
, S. S.
, Sawant
, A.
, Patil
, N.
, and Dhond
, S.
, 2013
, “Permanent Magnet Thrust Bearing: Theoretical and Experimental Results
,” Prog. Electromagn. Res. B
, 56
, pp. 269
–287
.18.
Tian
, L.
, Xun-Peng
, A.
, and Tian
, Y.
, 2012
, “Analytical Model of Magnetic Force for Axial Stack Permanent-Magnet Bearings
,” IEEE Trans. Magn.
, 48
(10
), pp. 2592
–2599
.19.
Marth
, E.
, Jungmayr
, G.
, and Amrhein
, W.
, 2014
, “A 2-D-Based Analytical Method for Calculating Permanent Magnetic Ring Bearings With Arbitrary Magnetization and Its Application to Optimal Bearing Design
,” IEEE Trans. Magn.
, 50
(5
), pp. 1
–8
.20.
Ravaud
, R.
, Lemarquand
, G.
, Lemarquand
, V.
, and Depollier
, C.
, 2008
, “Analytical Calculation of the Magnetic Field Created by Permanent-Magnet Rings
,” IEEE Trans. Magn.
, 44
(8
), pp. 1982
–1989
.21.
Ravaud
, R.
, Lemarquand
, G.
, Lemarquand
, V.
, and Depollier
, C.
, 2008
, “The Three Exact Components of the Magnetic Field Created by a Radially Magnetized Tile Permanent Magnet
,” Prog. Electromagn. Res., PIER
, 88
, pp. 307
–319
.22.
Ravaud
, R.
, Lemarquand
, G.
, Lemarquand
, V.
, and Depollier
, C.
, 2009
, “Discussion About the Analytical Calculation of the Magnetic Field Created by Permanent Magnets
,” Prog. Electromagn. Res. B
, 11
, pp. 281
–297
.23.
Akoun
, G.
, and Yonnet
, J. P.
, 1982
, “3D Analytical Calculation of the Forces Exerted Between Two Cuboid Magnets
,” IEEE Trans. Magn.
, 20
(5
), pp. 1962
–1964
.24.
Wangsness
, R. K.
, 1979
, Electromagnetic Fields
, Wiley
, New York
.Copyright © 2016 by ASME
You do not currently have access to this content.
