Vol. 13

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2009-03-11

Mechanical Properties of a Ferrofluid Seal: Three-Dimensional Analytical Study Based on the Coulombian Model

By Romain Ravaud and Guy Lemarquand
Progress In Electromagnetics Research B, Vol. 13, 385-407, 2009
doi:10.2528/PIERB09020601

Abstract

This paper presents a general method for studying the mechanical properties of a ferrofluid seal by using a three-dimensional analytical approach based on the coulombian model of a magnet. The fundamental Maxwell's equations lead us to define the concept of magnetic energy of the ferrofluid seal by using only the threedimensional equations of the magnetic field created by ring permanent magnets radially magnetized. Our study corresponds to the specific case when the ferrofluid is submitted to a very high magnetic field. Under these conditions, we assume that the mechanical properties of the ferrofluid depend only on the magnetic field created by the permanent magnets. Throughout this paper, the remanence polarization J of the magnets used is higher than 1T. The magnetic field we use in order to align the magnetic particles is very intense, greater than 400 kA/m. Consequently, the magnetic particles are assumed to be saturated and the magnetic field they create can be omitted. In this paper, a cylindrical structure consisting of two outer ring permanent magnets radially magnetized and an inner nonmagnetic cylinder is considered. In addition, a ferrofluid seal is placed between them. The calculation of the magnetic pressure of the ferrofluid seal has been analytically established in three dimensions in order to determine its shape. Moreover, the geometrical evolution of the ferrofluid seal shape is presented when the inner non-magnetic cylinder crushes the ferrofluid seal. The radial stiffness of the ferrofluid seal is determined in three dimensions when the inner cylinder is decentered. Furthermore, a way of obtaining the ferrofluid seal static capacity is discussed.

Citation


Romain Ravaud and Guy Lemarquand, "Mechanical Properties of a Ferrofluid Seal: Three-Dimensional Analytical Study Based on the Coulombian Model," Progress In Electromagnetics Research B, Vol. 13, 385-407, 2009.
doi:10.2528/PIERB09020601
http://www.jpier.org/PIERB/pier.php?paper=09020601

References


    1. Rosensweig, R. E., Y. Hirota, S. Tsuda, and K. Raj, "Study of audio speakers containing ferrofluid," J. Phys.: Condens. Matter, Vol. 20, 2008.
    doi:10.1088/0953-8984/20/20/204147

    2. Rosensweig, R. E., "Ferrohydrodynamics," Dover, 1997.

    3. Raj, K., V. Moskowitz, and R. Casciari, "Advances in ferrofluid in ferrofluid technology," Journal of Magnetism and Magnetic Materials, Vol. 149, 174-180, 1995.
    doi:10.1016/0304-8853(95)00365-7

    4. Babic, S. and C. Akyel, "Improvement in the analytical calculation of the magnetic field produced by permanent magnet rings," Progress In Electromagnetics Research C, Vol. 5, 71-82, 2008.

    5. Babic, S. and C. Akyel, "An improvement in the calculation of the magnetic field for an arbitrary geometry coil with rectangular cross section," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 18, 493-504, November 2005.
    doi:10.1002/jnm.594

    6. Babic, S., C. Akyel, and M. M. Gavrilovic, "Calculation improvement of 3D linear magnetostatic field based on fictitious magnetic surface charge," IEEE Trans. Magn, Vol. 36, No. 5, 3125-3127, 2000.
    doi:10.1109/20.908707

    7. Babic, S., C. Akyel, S. Salon, and S. Kincic, "New expressions for calculating the magnetic field created by radial current in massive disks," IEEE Trans. Magn., Vol. 38, No. 2, 497-500, 2002.
    doi:10.1109/20.996131

    8. Babic, S., C. Akyel, and S. Salon, "New procedures for calculating the mutual inductance of the system: Filamentary circular coilmassive circular solenoid," IEEE Trans. Magn., Vol. 39, No. 3, 1131-1134, 2003.
    doi:10.1109/TMAG.2003.810550

    9. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Analytical calculation of the magnetic field created by permanent-magnet rings," IEEE Trans. Magn., Vol. 44, No. 8, 1982-1989, 2008.
    doi:10.1109/TMAG.2008.923096

    10. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Discussion about the analytical calculation of the magnetic field created by permanent magnets," Progress In Electromagnetics Research B, Vol. 11, 281-297, 2009.
    doi:10.2528/PIERB08112102

    11. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "The three exact components of the magnetic field created by a radially magnetized tile permanent magnet," Progress In Electromagnetics Research, PIER 88, 307-319, 2008.

    12. Selvaggi, J. P., S. Salon, O. M. Kwon, and M. V. K. Chari, "Calculating the external magnetic field from permanent magnets in permanent-magnet motors --- An alternative method," IEEE Trans. Magn., Vol. 40, No. 5, 3278-3285, 2004.
    doi:10.1109/TMAG.2004.831653

    13. Choi, H. S., Y. S. Kim, K. T. Kim, and I. H. Park, "Simulation of hydrostatical equilibrium of ferrofluid subject to magneto-static field," IEEE Trans. Magn., Vol. 44, No. 6, 818-821, 2008.
    doi:10.1109/TMAG.2007.915962

    14. Shah, R. C. and M. Bhat, "Ferrofluid squeeze film in a long bearing," Tribology International, Vol. 37, 441-446, 2004.
    doi:10.1016/j.triboint.2003.10.007

    15. Bajkowski, J., J. Nachman, M. Shillor, and M. Sofonea, "A model for a magnetorheological damper," Mathematical and computer modelling, Vol. 48, 56-68, 2008.
    doi:10.1016/j.mcm.2007.08.014

    16. Park, G. S. and K. Seo, "New design of the magnetic fluid linear pump to reduce the discontinuities of the pumping forces," IEEE Trans. Magn., Vol. 40, 916-919, 2004.
    doi:10.1109/TMAG.2004.824718

    17. Lemarquand, G., "Ironless loudspeakers," IEEE Trans. Magn., Vol. 43, No. 8, 3371-3374, 2007.
    doi:10.1109/TMAG.2007.897739

    18. Ravaud, R., G. Lemarquand, V. Lemarquand, and C. Depollier, "Ironless loudspeakers with ferrofluid seals," Archives of Acoustics, Vol. 33, No. 4, 3-10, 2008.

    19. Berkouk, M., V. Lemarquand, and G. Lemarquand, "Analytical calculation of ironless loudspeaker motors," IEEE Trans. Magn., Vol. 37, No. 2, 1011-1014, 2001.
    doi:10.1109/20.917185

    20. Tarapov, I., "Movement of a magnetizable fluid in lubricating layer of a cylindrical bearing," Magnetohydrodynamics, Vol. 8, No. 4, 444-448, 1972.

    21. Walker, J. and J. Backmaster, "Ferrohydrodynamics thrust bearings," Int. J. Eng. Sci., Vol. 17, 1171-1182, 1979.
    doi:10.1016/0020-7225(79)90100-9

    22. Tiperi, N., "Overall characteristics of bearings lubricated ferrofluids," ASME J. Lubr. Technol., Vol. 105, 466-475, 1983.

    23. Raikher, Y. L., V. I. Stepanov, J. C. Bacri, and R. Perzynski, "Orientational dynamics in magnetic fluids under strong coupling of external and internal relaxations," Journal of Magnetism and Magnetic Materials, Vol. 289, 222-225, 2005.
    doi:10.1016/j.jmmm.2004.11.064

    24. Miyake, S. and S. Takahashi, "Sliding bearing lubricated with ferromagnetic fluid," ASLE Trans., Vol. 28, 461-466, 1985.

    25. Chang, H., C. Chi, and P. Zhao, "A theoretical and experimental study of ferrofluid lubricated four-pocket journal bearing," Journal of Magnetism and Magnetic Materials, Vol. 65, 372-374, 1987.
    doi:10.1016/0304-8853(87)90074-6

    26. Zhang, Y., "Static characteristics of magnetized journal bearing lubricated with ferrofluids," ASME J. Tribol., Vol. 113, 533-538, 1991.
    doi:10.1115/1.2920656

    27. Osman, T., G. Nada, and Z. Safar, "Static and dynamic characteristics of magnetized journal bearings lubricated with ferrofluid," Tribology International, Vol. 34, 369-380, 2001.
    doi:10.1016/S0301-679X(01)00017-2

    28. Shah, R. C. and M. Bhat, "Anisotropic permeable porous facing abd slip velocity squeeze film in axially undefined journal bearing with ferrofluid lubricant," Journal of Magnetism and Magnetic Materials, Vol. 279, 224-230, 2004.
    doi:10.1016/j.jmmm.2004.01.082

    29. Cunha, F. and H. Couto, "A new boundary integral formulation to describe three-dimensional motions of interfaces between magnetic fluids," Applied Mathematics and Computation, Vol. 199, 70-83, 2008.
    doi:10.1016/j.amc.2007.09.035

    30. Chen, S., Q. Zhang, H. Chong, T. Komatsu, and C. Kang, "Some design and prototyping issues on a 20 krpm hdd spindle motor with a ferro-fluid bearing system," IEEE Trans. Magn., Vol. 37, No. 2, 805-809, 2001.
    doi:10.1109/20.917620

    31. Zhang, Q., S. Chen, S. Winoto, and E. Ong, "Design of high-speed magnetic fluid bearing spindle motor," IEEE Trans. Magn., Vol. 37, No. 4, 2647-2650, 2001.
    doi:10.1109/20.951262

    32. Miwa, M., H. Harita, T. Nishigami, R. Kaneko, and H. Unozawa, "Frequency characteristics of stiffness and damping effect of a ferrofluid bearing," Tribology Letter, Vol. 15, No. 2, 97-105, 2003.
    doi:10.1023/A:1024448930757

    33. Ochonski, W., "The attraction of ferrofluid bearings," Mach. Des., Vol. 77, No. 21, 96-102, 2005.

    34. Meng, Z. and Z. Jibin, "An analysis on the magnetic fluid seal capacity," Journal of Magnetism and Magnetic Materials, Vol. 303, e428-e431, 2006.
    doi:10.1016/j.jmmm.2006.01.060

    35. Matthies, G. and U. Tobiska, "Numerical simulation of normal-field instability in the static and dynamic case," Journal of Magnetism and Magnetic Materials, Vol. 289, 436-439, 2005.

    36. Ivanov, A., S. Kantorovich, V. Mendelev, and E. Pyanzina, "Ferrofluid aggregation in chains under the influence of a magnetic field," Journal of Magnetism and Magnetic Materials, Vol. 300, e206-e209, 2006.
    doi:10.1016/j.jmmm.2005.10.081

    37. Kuzhir, P., "Free boundary of lubricant film in ferrofluid journal bearings," Tribology International, Vol. 41, 256-268, 2008.
    doi:10.1016/j.triboint.2007.07.006