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.

References

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
.
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