Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Effect of Magnetic Field and Non-Uniform Surface on Squeeze Film Lubrication

Journal of Applied Nonlinear Dynamics 9(2) (2020) 223--230 | DOI:10.5890/JAND.2020.06.005

P. Muthu, V. Pujitha

Department of Mathematics, National Institute of Technology, Warangal-506004. Telangana, India

Download Full Text PDF



In the present paper, the combined effect of magnetic field and nonuniform shape of the surface on squeeze film characteristics is investigated. The non-uniform squeeze film thickness is calculated using Lagrange interpolation technique. Numerical integration procedure is used to obtain the solution for pressure, load carrying capacity. The effects of field parameters on squeeze film characteristics are discussed and are presented graphically. It is observed that externally applied magnetic field and non-uniform shape of the bearing surface enhance the squeeze film lubrication.


  1. [1]  Dowson, D. and Wright, Y. (1973), Bio-Tribology, in The rheology of lubricants, editors T. C. Davenport, Applied Science: England, 81-88.
  2. [2]  Chandra, P. (1975), Mathematical Model for Synovial Joints - A Lubrication Biomechanical Study, PhD Thesis, IIT Kanpur.
  3. [3]  MacConaill, M.A. (1932), The function of intra-articular fibro-cartilage with special reference to the knee and inferior redioular joints, J. Anatomy, 66, 210-227.
  4. [4]  Walker, P.S., Dowson, D., Longfield, M.D. and Wright, V. (1968), Boosted lubrication in synovial joints by entrapment and enrichment, Ann. Rheum. Dis, 27, 512-522.
  5. [5]  Lewis, P.R. and MacCutchen, C.W. (1959), Mechanism of animal joints, Nature, 184, 1284-1285.
  6. [6]  MacCutchen, C.W. (1962), The frictional properties of animal joints, Wear, 5, 1-17.
  7. [7]  MacCutchen, C.W. (1967), Physiological lubrication, Proc. Inst. Mech. Eng, 181(3J), 55-62.
  8. [8]  Dowson, D. (1967), Modes of lubrication in human joints, Proc. Inst. Mech. Eng, 181(3J), 45-54.
  9. [9]  Torzilli, P.A. and Mow, V.C. (1976), On the fundamental fluid transport mechanisms through normal and pathological articular cartilage durong functon-II - The analysis, solution and conclusions, J. Biomechanics, 9, 587-606.
  10. [10]  Collins, R. (1982), A model of lubricant gelling in synovial joints, J. Applied Mathematics and Physics, 33, 93-123.
  11. [11]  Sinha, P., Singh, C., and Prasad, K.R. (1982), Lubrication of human joints - A microcontinuum approach, Wear, 80, 159-181.
  12. [12]  Tandon, P.N., Bong, N.H., and Kushwaha, K. (1994), A new model for synovial joint lubrication, Int. J. Bio-Medical Computing, 35, 125-140.
  13. [13]  Bujurke, N.M., Jagadeeswar, M., and Hiremath, P.S. (1987), Analysis of normal stress effects in a squeeze film porous bearing, Wear, 116, 237-248.
  14. [14]  Bujurke, N.M. and Kudenatti, R.B. (2006), Surface roughness effects on squeeze film poroelastic bearings, Applied Mathematics and Computation, 174, 1181-1195.
  15. [15]  Ahmad, N. and Singh, J.P. (2007), A model for couple-stress fluid film mechanism with reference to human joints, Proc. Inst. Mech. Engg, Part J : Journal of Engg. Tribology, 221, 755-759.
  16. [16]  Lin, J.R. (2003), Magneto-hydrodynamic squeeze film characteristics for finite rectangular plates, Industrial Lubrication and Tribology, 55(2), 84-89.
  17. [17]  Bujurke, N.M., Naduvinamani, N.B., and Basti, D.P. (2011), Effect of surface roughness on magnetohydrodynamic squeeze film characteristics between finite rectangular plates, Tribology International, 44, 916-921.
  18. [18]  Fathima, S.A.N., Biradar, T., Fathima, S.T., and Hanumagowda, B.N. (2016) Study of effect of porosity in the presence of applied magnetic field on a cosine form convex curved plate model, Int. J. Mathematical Archive, 7(9), 162-171.
  19. [19]  Tandon, P.N. and Chaurasia, A. (1991), Application of magnetic fields to synovial joints, Computers Math. Applic, 22(12), 33-45.
  20. [20]  Wierzcholski, K. and Miszczak, A. (2017), Magneto-therapy of human joint cartilage, Acta of bioengineering and biomechanics, 19(1), 115-124.
  21. [21]  Pinkus, O. and Sternlicht, B. (1961), Theory of hydrodynamic lubrication, McGraw-Hill: New York
  22. [22]  Prakash, J. and Vij, S.K. (1973), Load capacity and time-height relations for squeeze films between porous plates, Wear, 24, 309-322.
  23. [23]  Gerald, C.F. and Wheatley, P.O. (1984), Applied numerical analysis, Addison-Wesley.
  24. [24]  Atkinson, K. (1978), Numerical analysis, John Wiley: Singapore.