0
Research Papers: Applications

Generalized Three-Dimensional Mathematical Models for Force and Stiffness in Axially, Radially, and Perpendicularly Magnetized Passive Magnetic Bearings With “n” Number of Ring Pairs

[+] Author and Article Information
Siddappa I. Bekinal

Bearings Laboratory,
Department of Mechanical Engineering,
KLS Gogte Institute of Technology,
Belagavi 590008, Karnataka, India
e-mail: sibekinal@git.edu

Soumendu Jana

Bearings and Rotor Dynamics Laboratory,
Propulsion Division,
National Aerospace Laboratories,
Bengaluru 560017, Karnataka, India
e-mail: sjana@nal.res.in

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 15, 2015; final manuscript received January 7, 2016; published online May 6, 2016. Assoc. Editor: Daejong Kim.

J. Tribol 138(3), 031105 (May 06, 2016) (9 pages) Paper No: TRIB-15-1298; doi: 10.1115/1.4032668 History: Received August 15, 2015; Revised January 07, 2016

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Yonnet, J. P. , 1978, “ Passive Magnetic Bearings With Permanent Magnets,” IEEE Trans. Magn., 14(5), pp. 803–805. [CrossRef]
Yonnet, J. P. , 1981, “ Permanent Magnetic Bearings and Couplings,” IEEE Trans. Magn., 17(1), pp. 1169–1173. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Paden, B. , Groom, N. , and Antaki, J. , 2003, “ Design Formulas for Permanent-Magnet Bearings,” ASME J. Mech. Des., 125(4), pp. 734–739. [CrossRef]
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.
Samanta, P. , and Hirani, H. , 2008, “ Magnetic Bearing Configurations: Theoretical and Experimental Studies,” IEEE Trans. Magn., 44(2), pp. 292–300. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Wangsness, R. K. , 1979, Electromagnetic Fields, Wiley, New York.

Figures

Grahic Jump Location
Fig. 1

PMB configurations with (a) n axially polarized ring pairs, (b) n radially polarized ring pairs, and (c) n perpendicularly polarized ring pairs

Grahic Jump Location
Fig. 2

The pth ring pair of PMB with axially polarized ring pairs with elements on polarized surfaces

Grahic Jump Location
Fig. 3

The pth ring pair of PMB with radially polarized ring pairs with elements on polarized surfaces

Grahic Jump Location
Fig. 4

The pth ring pair of PMB with perpendicularly polarized ring pairs with elements on polarized surfaces

Grahic Jump Location
Fig. 5

Comparison of results of an axial force by 3D mathematical model and 3D FEA for five ring pairs: (a) configuration I, (b) configuration II, (c) configuration III, and (d) maximum axial force generated in configuration II in ansys

Grahic Jump Location
Fig. 6

The axial force generated by the outer rings on the inner rings for different axial positions of the rotor in the configuration I: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

Grahic Jump Location
Fig. 7

The axial stiffness of configuration I for different axial positions of the rotor: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

Grahic Jump Location
Fig. 8

The axial force generated by the outer rings on the inner rings for different axial positions of the rotor in configuration II: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

Grahic Jump Location
Fig. 9

The axial stiffness of configuration II for different axial positions of the rotor: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

Grahic Jump Location
Fig. 10

The axial force generated by the outer rings on the inner rings for different axial positions of the rotor in configuration III: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

Grahic Jump Location
Fig. 11

The axial stiffness of configuration III for different axial positions of the rotor: (a) PMB with 1–5 ring pairs and (b) PMB with 6–10 ring pairs

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In