Analysis of a free boundary problem in partial lubrication
Authors:
G. Bayada and M. Chambat
Journal:
Quart. Appl. Math. 40 (1983), 369-375
MSC:
Primary 76D99; Secondary 35J85, 76B10
DOI:
https://doi.org/10.1090/qam/693872
MathSciNet review:
693872
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Abstract: Hydrodynamic lubrication is concerned with a particular form of creeping flow between surfaces in relative motion where cavitation takes place. The determination of the free boundary of the cavitation area is then of fundamental importance for the computation of the characteristics of the mechanisms. Different conditions at the free boundary have been introduced. We study two of them and compare corresponding solutions with respect to film extent and pressure repartition.
G. Bayada, Inéquations variationnelles elliptiques, applications à la résolution de Reynolds, Thése, University of Lyon, 1972
- G. Capriz, Variational techniques for the analysis of a lubrication problem, Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975) Springer, Berlin, 1977, pp. 47–55. Lecture Notes in Math., Vol. 606. MR 0479025
Glowinski, Lions, Tremolieres, Analyse numérique des inéquations variationelles, Dunod, Paris, 1976
S. M. Rohde and G. T. McAllister, A variational formulation for a class of free boundary problems arising in hydrodynamic lubrication, Int. J. Eng. Sci. 13, 841–850 (1975)
- Garrett Birkhoff and Donald F. Hays, Free boundaries in partial lubrication, J. Math. and Phys. 42 (1963), 126–138. MR 153199
Dowson, Godet, Taylor, Cavitation and related phenomena in lubrication, I.M.E., London (1975)
- Cavitation in real liquids, Elsevier Publ. Co., Amsterdam-London-New York, 1964. MR 0171452
G. I. Taylor, Cavitation of a viscous fluid in narrow passages, Fluid Mech. 16, 595–619 (1963)
G. Lundholm, The circumferential groove journal bearing considering cavitation and dynamic stability, Acta Poly. Scand. Mech. Eng., Series 12, Stockolm (1964)
C. H. T. Pan and R. A. Ibrahim, Cavitation in a short bearing with pressurized lubricant supply, in A.S.M.E. ASLE lubrication conference, San Francisco (1980)
C. S. Cryer, The method of Christopherson for solving F.B.P.for infinite journal bearings by means of finite difference, Math. Computation 25, 435–443 (1971)
G. Bayada, Inéquations variationnelles elliptiques, applications à la résolution de Reynolds, Thése, University of Lyon, 1972
G. Capriz, Variational techniques for the analysis of a lubrication problem, in Mathematical aspects of finite-element methods, springes Lecture Notes in Mathematics 606, 47–55 (1977)
Glowinski, Lions, Tremolieres, Analyse numérique des inéquations variationelles, Dunod, Paris, 1976
S. M. Rohde and G. T. McAllister, A variational formulation for a class of free boundary problems arising in hydrodynamic lubrication, Int. J. Eng. Sci. 13, 841–850 (1975)
G. Birkhoff and D. Hays, Free boundaries in partial lubrication, Journal Math. Phys. 42, 126–138 (1965)
Dowson, Godet, Taylor, Cavitation and related phenomena in lubrication, I.M.E., London (1975)
R. Davies, Symposium on cavitation in real liquids, Elsevier, New York (1964)
G. I. Taylor, Cavitation of a viscous fluid in narrow passages, Fluid Mech. 16, 595–619 (1963)
G. Lundholm, The circumferential groove journal bearing considering cavitation and dynamic stability, Acta Poly. Scand. Mech. Eng., Series 12, Stockolm (1964)
C. H. T. Pan and R. A. Ibrahim, Cavitation in a short bearing with pressurized lubricant supply, in A.S.M.E. ASLE lubrication conference, San Francisco (1980)
C. S. Cryer, The method of Christopherson for solving F.B.P.for infinite journal bearings by means of finite difference, Math. Computation 25, 435–443 (1971)
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Article copyright:
© Copyright 1983
American Mathematical Society
