Research Papers: Applications

Development of Analytical Equations for Design and Optimization of Axially Polarized Radial Passive Magnetic Bearing

[+] Author and Article Information
K. P. Lijesh

Department of Mechanical Engineering
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: lijesh_mech@yahoo.co.in

Harish Hirani

Associate Professor
Department of Mechanical Engineering
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: hirani@mech.iitd.ac.in

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 1, 2014; final manuscript received August 25, 2014; published online October 6, 2014. Assoc. Editor: Bugra Ertas.

J. Tribol 137(1), 011103 (Oct 06, 2014) (9 pages) Paper No: TRIB-14-1100; doi: 10.1115/1.4028488 History: Received May 01, 2014; Revised August 25, 2014

In the present research work, analytical equations have been developed for design and optimization of radial axial polarized passive magnetic bearing (PMB) with single layer for facilitating easy and quick solution, obviating the need of costly software. Seven design variables: eccentricity, rotor width, stator width, rotor length, stator length, clearance, and mean radius were identified as the main factors affecting the design and were thus considered in the development of analytical equations. The results obtained from the developed analytical equations have been validated with the published results. The optimization of the bearing design, with minimization of magnet volume as the objective function, was carried out to demonstrate the accuracy and usefulness of the developed equations.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Yonnet, J. P., 1981, “Permanent Magnet Bearings and Couplings,” IEEE Trans. Magn., 15(1), pp. 1169–1173. [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]
Moser, R., Sandtner, J., and Bleuler, H., 2006, “Optimization of Repulsive Passive Magnetic Bearings,” IEEE Trans. Magn., 42(8), pp. 2038–2042. [CrossRef]
Mukhopadhyay, S. C., Ohji, T., Iwahara, M., and Member, A., 2000, “Modeling and Control of a New Horizontal-Shaft Hybrid-Type Magnetic Bearing,” IEEE Trans. Ind. Electron., 47(1), pp. 100–108. [CrossRef]
Tan, Q., Li, W., and Liu, B., 2002, “Investigations on a Permanent Magnetic–Hydrodynamic Hybrid Journal Bearing,” Tribol. Int., 35(7), pp. 443–448. [CrossRef]
Akoun, G., and Yonnet, J. P., 1984, “3D Analytical Calculation of the Forces Exerted Between Two Cuboidal Magnets,” IEEE Trans. Magn., 20(5), pp. 1962–1964. [CrossRef]
Samanta, P., and Hirani, H., 2007, “A Simplified Optimization Approach for Permanent Magnetic Journal Bearing,” Indian J. Tribol., 2(2), pp. 23–34.
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]
Yonnet, J. P., Hemmerlin, S., Rulliere, E., and Lemarquand, G., 1993, “Analytical Calculation of Permanent Magnet Couplings,” IEEE Trans. Magn., 29(6), pp. 2932–2934. [CrossRef]
Yonnet, J. P., Lemarquand, G., Hemmerlin, S., and Olivier-Rulliere, E., 1991, “Stacked Structures of Passive Magnetic Bearings,” J. Appl. Phys., 70(10), p. 6633. [CrossRef]
Paden, B., Groom, N., and Antaki, J. F., 2003, “Design Formulas for Permanent-Magnet Bearings,” ASME J. Mech. Des., 125(4), pp. 734–738. [CrossRef]
Muzakkir, S. M., Lijesh, K. P., and Hirani, H., 2014, “Tribological Failure Analysis of a Heavily-Loaded Slow Speed Hybrid Journal Bearing,” Eng. Failure Anal., 40, pp. 97–113. [CrossRef]
Fengxiang, W., Jiqiang, W., Zhiguo, K., and Fengge, Z., 2004, “Radial and Axial Force Calculation of BLDC Motor With Passive Magnetic Bearing,” 4th International Power Electronics and Motion Control Conference, IPEMC 2004, Xi'an, China, Aug. 14–16, Vol. 1, pp. 290–293.
Hirani, H., and Samanta, P., 2007, “Hybrid (hydrodynamic + permanent magnetic) Journal Bearings,” Proc. Inst. Mech. Eng. Part J., 221(8), pp. 881–891. [CrossRef]
Sung, H. P., 1996, Robust Design and Analysis for Quality Engineering, Chapman and Hall, London, UK, pp. 46–59.
Levenberg, K., 1944, “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Q. Appl. Math., 2(2), pp. 164–168.


Grahic Jump Location
Fig. 1

Radial Magnetic bearing: (a) front view and (b) section side view

Grahic Jump Location
Fig. 2

Percentage mean square values: (a) force and (b) stiffness

Grahic Jump Location
Fig. 3

Comparison of numerical and analytical equations for ɛ: (a) β = C(1−ɛ) and (b) β = C(1 − 0.2ɛ2)

Grahic Jump Location
Fig. 4

Comparison of numerical and analytical methods for Rm: (a) mean value and (b) lowest value

Grahic Jump Location
Fig. 5

Comparison of numerical and analytical equation for α: (a) comparison for α and (b) comparison for 0.9 T'0.4 (1−0.0111T'-5.4)

Grahic Jump Location
Fig. 6

Comparison of numerical and proposed equations for b: (a) Numerical equation (3) and (b) analytical equation (9b)

Grahic Jump Location
Fig. 7

Force versus L for dimensions provided in Ref. [5]

Grahic Jump Location
Fig. 8

Force versus L for dimensions provided in Ref. [12]

Grahic Jump Location
Fig. 9

Force versus L for bearing described in Ref. [15]



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