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Abstract
We study the motion which results when a fluid film is squeezed between two parallel surfaces in relative motion. Particular attention is given to the special case where one surface is fixed and the other is impulsively accelerated from a state of rest to a state of sinusoidal oscillations in a direction normal to its plane. In addition to the presentation of analytic solutions which are based on the regular perturbation technique and on the linearised analysis of the resulting nonlinear partial differential equation, a numerical solution of the full nonlinear equation based on a finite-difference scheme is obtained. The effects of the sinusoidal motion on the velocity profiles and on the normal forces which the fluid exerts on the surfaces are investigated.
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References
- ABRAMOWITZ, M. and STEGUN, I.A. 1970. Handbook of mathematical functions. Dover Publications, INC., New York. p 224.
- FULLER, D.D.1956. Theory and practice of lubrication for Engineers. Wiley, New York, N. Y. 136-141.
- HAMZA, E.A. and MACDONALD, D.A.1981. A fluid film squeezed between two parallel plane surfaces. J. Fluid Mech., 109: 147-160.
- HUNT, J.B.1966. Pressure distribution in a plane fluid film subjected to normal sinusoidal excitation. Nature, Sept : 1137-1139.
- ISHIZAWA, S.A. 1966. The unsteady laminar flow between two parallel disks with arbitrarily varying gap width. Bull. of the JSME, 9: 533-550.
- JONES, A.F. and WILSON, S.D. R.1975. On the failure of lubrication theory in squeezing flows. Trans. ASME Series F, 97: 101-104.
- KUHN, K.C. and Y. ATES, C.C. 1964. Fluid inertia effect on the film Pressure between axially oscillating parallel circular plates. TRANS. ASME, 7: 299-303.
- KUZMA, D.C. 1967. Fluid inertia effects in squeeze films. Appl. Sc. Res, 18: 15-20.
- REYNOLDS, O.1874. On the theory of lubrication and its application to Mr. BeauchamI:Tower's experiments, including an experimental determination of the viscosity of olive. Phil. Trans. Roy. Soc., London, 177: 157-234.
- STEFAN, J. 1874. Versuche uber die scheinbare Adhesion. K.Akad Wissenschaften. Math-Naturwissenschaftliche Klasse, Wien. Sitzungsberichte, 69: 713.
- TERRILL, R.M. 1969. The flow between two parallel circular disks, one of which is subject to a normal oscillation. Asme Journal of Lubrication Technology, 91: 126-131.
- TICHY, J.A. and WINER, W.O. 1970. Inertial considerations in parallel circular squeeze film bearings. ASME Ser. F, J. Lubrication Technology, 92: 588-592.
- TICHY, J.A. and MODEST, M.F. 1978. Squeeze film flow between arbitrary two- dimensional surfaces subject to normal oscillations. Asme Journal of Lubrication Technology, 100: 316-322.
References
ABRAMOWITZ, M. and STEGUN, I.A. 1970. Handbook of mathematical functions. Dover Publications, INC., New York. p 224.
FULLER, D.D.1956. Theory and practice of lubrication for Engineers. Wiley, New York, N. Y. 136-141.
HAMZA, E.A. and MACDONALD, D.A.1981. A fluid film squeezed between two parallel plane surfaces. J. Fluid Mech., 109: 147-160.
HUNT, J.B.1966. Pressure distribution in a plane fluid film subjected to normal sinusoidal excitation. Nature, Sept : 1137-1139.
ISHIZAWA, S.A. 1966. The unsteady laminar flow between two parallel disks with arbitrarily varying gap width. Bull. of the JSME, 9: 533-550.
JONES, A.F. and WILSON, S.D. R.1975. On the failure of lubrication theory in squeezing flows. Trans. ASME Series F, 97: 101-104.
KUHN, K.C. and Y. ATES, C.C. 1964. Fluid inertia effect on the film Pressure between axially oscillating parallel circular plates. TRANS. ASME, 7: 299-303.
KUZMA, D.C. 1967. Fluid inertia effects in squeeze films. Appl. Sc. Res, 18: 15-20.
REYNOLDS, O.1874. On the theory of lubrication and its application to Mr. BeauchamI:Tower's experiments, including an experimental determination of the viscosity of olive. Phil. Trans. Roy. Soc., London, 177: 157-234.
STEFAN, J. 1874. Versuche uber die scheinbare Adhesion. K.Akad Wissenschaften. Math-Naturwissenschaftliche Klasse, Wien. Sitzungsberichte, 69: 713.
TERRILL, R.M. 1969. The flow between two parallel circular disks, one of which is subject to a normal oscillation. Asme Journal of Lubrication Technology, 91: 126-131.
TICHY, J.A. and WINER, W.O. 1970. Inertial considerations in parallel circular squeeze film bearings. ASME Ser. F, J. Lubrication Technology, 92: 588-592.
TICHY, J.A. and MODEST, M.F. 1978. Squeeze film flow between arbitrary two- dimensional surfaces subject to normal oscillations. Asme Journal of Lubrication Technology, 100: 316-322.