Advertisement

Experimental Verification of Force and Stiffness Between Two Ring Magnets Calculated by Monte Carlo Integration Technique

  • T. SantraEmail author
  • D. Roy
  • A. B. Choudhury
  • S. Yamada
Original Contribution
  • 2 Downloads

Abstract

This paper presents the calculation and experimental verification of force and stiffness between two concentric ring-shaped rare earth magnets. This kind of magnet configuration is invariably used in magnetic bearing, micromass measurement system, turbomachineries and space applications. Estimation of magnetic force and stiffness is always important in any application of permanent magnet as it influences the stability and performance of the system. Some analytical methods are available which involve direct solution of elliptic integral, which made the calculation tedious, complex, time- and space consuming. In this work, a simple approach based on Monte Carlo integration technique is proposed to calculate the force and stiffness. Monte Carlo integration technique is preferred to calculate the multidimensional elliptic integrals due to simplicity of the method, less computational time and memory requirement. The result is compared with existing finite element method and verified with experimental result. The verification process indicates that there is a small deviation in result of the proposed method from experimentally obtained result, but taking into account simplicity, space and time requirement, this approach may be considered to be a useful alternative method to calculate force and stiffness of a magnetic system. The proposed method is one of the best examples of utilizing an old computational concept in modern complicated problem solution.

Keywords

Ring magnet Magnetic force Stiffness Monte Carlo integration Stability 

Notes

References

  1. 1.
    S.C. Mukhopadhyay, T. Ohji, M. Iwahara, S. Yamada, F. Matsumura, A new repulsive type magnetic bearing—modeling and control. IEEE Trans. Magn. 47(1), 100–108 (2000)Google Scholar
  2. 2.
    R. Ravaud, G. Lemarquand, Halbach structures for permanent magnets bearings. Prog. Electromagn. Res. 14, 263–277 (2010)CrossRefGoogle Scholar
  3. 3.
    A. Hussien et al., Application of the repulsive-type magnetic bearing for manufacturing micro-mass measurement balance equipment. IEEE Trans. Magn. 41(10), 3802–3804 (2005)CrossRefGoogle Scholar
  4. 4.
    H.Y. Chu, Y. Fan, C.S. Zhang, A novel design for the flywheel energy storage system, in Proceedings of the Eighth International Conference on Electrical Machines and Systems, Vol. 2 (2005), pp. 1583–1587Google Scholar
  5. 5.
    S. Earnshaw, On the nature of molecular forces which regulate the constitution of luminiferous ether. Trans. Camb. Philos. Soc. 7, 97–112 (1839)Google Scholar
  6. 6.
    G. Jungmayr, E. Marth, W. Amrhein, H.-J. Berroth, F. Jeske, Analytical stiffness calculation for permanent magnetic bearings with soft magnetic materials. IEEE Trans. Magn. 50(8), Article No. 8300108 (2014)Google Scholar
  7. 7.
    P. Samanta, H. Hirani, Magnetic bearing configurations: theoretical and experimental studies. IEEE Trans. Magn. 44(2), 292–300 (2008)CrossRefGoogle Scholar
  8. 8.
    J.P. Yonnet, Permanent magnetic bearings and couplings. IEEE Trans. Magn. 17(1), 1169–1173 (1981)CrossRefGoogle Scholar
  9. 9.
    J. Delamare, E. Rulliere, J.P. Yonnet, Classification and synthesis of permanent magnet bearing configurations. IEEE Trans. Magn. 31(6), 4190–4192 (1995)CrossRefGoogle Scholar
  10. 10.
    M. Lang, Fast calculation method for the forces and stiffness of permanent-magnet bearings, in 8th International Symposium on Magnetic Bearing (2002), pp. 533–537Google Scholar
  11. 11.
    W. Jiang, et al., Forces and moments in axially polarized radial permanent magnet bearings, in Proceedings of Eighth International Symposium on Magnetic Bearings (Mito, Japan, 2002), pp. 521–526Google Scholar
  12. 12.
    R. Ravaud, G. Lemarquand, V. Lemarquand, Force and stiffness of passive magnetic bearings using permanent magnets. Part 1: axial magnetization. IEEE Trans. Magn. 45(7), 2996–3002 (2009)CrossRefGoogle Scholar
  13. 13.
    S.I. Bekinal, T.R. Anil, S. Jana, Force, moment and stiffness characteristics of permanent magnet bearings, in Proceedings of National Symposium on Rotor Dynamics (Indian Institute of Technology, Madras, India, 2011), pp. 161–168Google Scholar
  14. 14.
    R. Ravaud, G. Lemarquand, Comparison of the Coulombian and Amperian current models for calculating the magnetic field produced by radially magnetized arc-shaped permanent magnets. Prog. Electromagn. Res. 95, 309–327 (2009)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2019

Authors and Affiliations

  • T. Santra
    • 1
    Email author
  • D. Roy
    • 1
  • A. B. Choudhury
    • 1
  • S. Yamada
    • 2
  1. 1.Electrical Engineering DepartmentIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia
  2. 2.Division of Biological Measurement and Application, Institute of Nature and Environmental Technology (K-INET)Kanazawa UniversityKanazawaJapan

Personalised recommendations