Behaviour of Couple Stress Fluids in Porous Annular Squeeze Films

Vimala Ponnuswamy^1*, Sumathi Govindaraj²

¹Department of Mathematics, Anna University, Chennai-600025, Tamil Nadu, India.
²Department of Mathematics, Adhiparasakthi Engineering College, Melmaruvathur-603319, Tamil Nadu, India.

DOI: 10.4236/jamp.2014.26042                

Abstract

The laminar squeeze flow of an incompressible couple stress fluid between porous annular disks is studied using hydrodynamic lubrication theory. The modified Reynolds’ equation is derived using Stokes microcontinuum theory and is solved analytically. Analytical expressions for the squeeze film pressure and the load carrying capacity are obtained in terms of Fourier-Bessel series. Numerical results are obtained for the sinusoidal motion of the upper disk. The effect of couple stresses and that of porous facing on the squeeze film behaviour are analysed through the squeeze film pressure and the load carrying capacity. Further, the equation for the gap width between the disks is obtained from the inverse problem.

Keywords

Squeeze Films, Hydrodynamic Lubrication, Couple Stresses, Non-Newtonian Fluid

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Archibald, F.R. (1956) Load Capacity and Time Relations for Squeeze Films. Transactions of the ASME, 78, 29-35.
[2]	Jones, A.F. and Wilson, S.D.R. (1975) On the Failure of Lubrication Theory in Squeezing Flows. ASME Transactions Journal of Lubrication Technology, 97, 101-104. http://dx.doi.org/10.1115/1.3452513
[3]	Pinkus, O. and Sternlicht, B. (1961) Theory of Hydrodynamic Lubrication. Mc-Graw Hill Book Company Inc., New York.
[4]	Tichy, J.A. and Winer, W.O. (1970) Inertial Considerations in Parallel Circular Squeeze Film Bearings. ASME Transactions Journal of Lubrication Technology, 92, 588-592. http://dx.doi.org/10.1115/1.3451480
[5]	Stokes, V.K. (1966) Couple Stress in Fluids. Physics of Fluids, 9, 1709-1715. http://dx.doi.org/10.1063/1.1761925
[6]	Ramanaiah, G. and Sarkar, P. (1978) Squeeze Films and Thrust Bearings Lubricated by Fluids with Couple Stresses. Wear, 48, 309-316. http://dx.doi.org/10.1016/0043-1648(78)90229-6
[7]	Naduvinamani, N.B., Fathima, S.T. and Hiremath, P.S. (2003) Hydrodynamic Lubrication of Rough Slider Bearing with Couple Stress Fluids. Tribology International, 36, 949-959. http://dx.doi.org/10.1016/0043-1648(78)90229-6
[8]	Elsharkawy, A.A. and Guedouar, L.H. (2001) An Inverse Solution for Finite Journal Bearings Lubricated with Couple Stress Fluids. Tribology International, 34, 107-118. http://dx.doi.org/10.1016/S0301-679X(00)00145-6
[9]	Wu, H. (1970) Squeeze Film Behaviour for Porous Annular Disks. ASME Transactions Journal of Lubrication Technology, 92, 593-596. http://dx.doi.org/10.1115/1.3451481
[10]	Bhat, V. and Deheri, G.M. (1991) Squeeze Film Behaviour in Porous Annular Disks Lubricated with Magnetic Fluid. Wear, 151, 123-128. http://dx.doi.org/10.1016/0043-1648(91)90352-U
[11]	Cusano, C. (1972) Lubrication of Porous Journal Bearings. ASME Transactions Journal of Lubrication Technology, 94, 69-73. http://dx.doi.org/10.1115/1.3451638
[12]	Murti, P.R.K. (1974) Squeeze Film Behaviour in Porous Circular Disks. ASME Transactions Journal of Lubrication Tech-nology, 96, 206-209. http://dx.doi.org/10.1115/1.3451923
[13]	Naduvinamani, N.B., Hiremath, P.S. and Gurubasavaraj, G. (2001) Squeeze Film Lubrication of a Short Porous Journal Bearing with Couple Stress Fluids. Tribology Inter-national, 34, 739-747. http://dx.doi.org/10.1016/S0301-679X(01)00064-0
[14]	Naduvinamani, N.B. and Siddangouda, A. (2007) Combined Effects of Surface Roughness and Couple Stresses on Squeeze Film Lubrication between Porous Circular Stepped Plates. Proceedings of IMechE Part J: Journal of Engineering Tribology, 221, 525-534.
[15]	Naduvinamani, N.B. and Siddangouda, A. (2007) Effects of Surface Roughness on the Hydrodynamic Lubrication of Porous Step Slider Bearings. Tribology International, 40, 780-793. http://dx.doi.org/10.1016/j.triboint.2006.07.003
[16]	Bujurke, N.M. and Basti, D.P. (2008) Surface Roughness Effects on Squeeze Film Behaviour in Porous Circular Disks with Couple Stress Fluid. Transactions of Porous Media, 71, 185-197. http://dx.doi.org/10.1016/j.triboint.2006.07.003