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The one-dimensional gas-lubricated slider bearing

Published online by Cambridge University Press:  17 February 2009

J. J. Shepherd
J. J. Shepherd
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic InstituteTroy, New York 12181, U.S.A.
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Abstract

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Under the appropriate physical hypotheses, the problem of determining the pressure distribution in a gas-filled slider bearing becomes a singular perturbation problem as Λ, the bearing number, tends to infinity. This paper extends the results of an earlier one by the author to consider the case where the film profile has jump discontinuities in slope at points interior to the bearing. Application of the methods of general singular perturbation theory establishes the appropriate existence-uniqueness results for this problem, and a means is devised by which uniformly valid asymptotic approximations to the pressure distribution may be obtained for large values of Λ.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 1 , July 1980 , pp. 75 - 97
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Prima, R. C. Di, “Asymptotic methods for an infinitely long slider squeeze-film bearing”, Trans. ASME J. Lub. Tech. 90 (1968), 173–183.Google Scholar
[2]Prima, R. C. Di, “Higher order approximations in the asymptotic solution of the Reynolds equation for slider bearings at high bearing numbers”, Trans. ASME J. Lub. Tech. 91 (1969), 45–51.Google Scholar
[3]Habets, P., “A singular boundary value problem in gas lubrication theory”, Seminaire de Mathématique appliquée et mécanique, Institut de Mathematique Pure et Appliquée, Université Catholique du Louvain 119 (1978).Google Scholar
[4]Liusternik, L. and Sobolev, V., Elements of functional analysis (Hindu Publishing Corp., Delhi, 1974).Google Scholar
[5]Rosenblat, S., “Asymptotically equivalent singular perturbation problems”, Studies in Appl. Math. 55 (1976), 249–80.CrossRefGoogle Scholar
[6]Schmitt, J. A. and Prima, R. C. Di, “Asymptotic methods for an infinite slider bearing with a discontinuity in film slope”, Trans. ASME J. Lub. Tech. 98 (1976), 446–452.CrossRefGoogle Scholar
[7]Sereny, A. and Castelli, V., “Perturbation solution of the 1-D Reynolds equation with slip boundary conditions”, Trans. ASME J. Lub. Tech. 100 (1978), 70–73.CrossRefGoogle Scholar
[8]Shepherd, J. J., “On the asymptotic solution of the Reynolds equation”, SIAM J. Appl. Math. 34 (1978), 774–791.CrossRefGoogle Scholar
[9]Steinmetz, W. J., “On a nonlinear singular perturbation boundary value problem in gas lubrication theory”, SIAM J. Appl. Math. 26 (1974), 816–827.CrossRefGoogle Scholar