This paper comprises a report on recent developments in the application of the finite element method in the analysis of elastohydrodynamic lubrication (e.h.l.) problems. The basic formulation is effected, using the Galerkin approach and the domain under investigation is discretized using isoparametric elements. The techniques used to locate the inlet and outlet boundaries and those employed during successive iterations are illustrated by application to particular examples.
Get full access to this article
View all access options for this article.
References
1.
TurnerM. J.CloughR. W.MartinH. C.ToppL. J. ‘Stiffness and deflection analysis of complex structures’, J. Aeronaut. Sci.195623 (No. 9), 805.
2.
ZienkiewiczO. C.CheungY. K. ‘Finite elements in the solution of field problems’, Engineer, Lond.1965220, 507.
3.
VisserW. ‘A finite element method for the determination of non-stationary temperature distribution and thermal deformations’, Proc. Conf. Matrix Meth. struct. Mech. 1965 (Wright–Patterson Air Force Base, Ohio).
4.
WeberC. ‘Zur hydrodynamischen Schmiertheorie des Zapfenlagers’, Z. angew. Math. Mech.195030, 112.
5.
TipeiN.Theory of lubrication1962, 168 (Stanford University Press, Stanford, California).
6.
HaysD. F. ‘A variational approach to lubrication problems and the solution of the finite journal bearing’, J. bas. Engng, Trans. Am. Soc. mech. Engrs195981 (No. 1), 13.
7.
TaoL. N. ‘On the variational principle and Lagrange equations in studies of gas dynamic lubrication’, J. appl. Mech., Trans. Am. Soc. mech. Engrs196486 (Series E), 43.
8.
ReddiM. M. ‘Finite element solution of the incompressible lubrication problem’, J. Lubric. Technol., Trans. Am. Soc. mech. Engrs196991 (Series F), 524.
9.
ArgyrisJ. H.ScharpeD. W. ‘The incompressible lubrication problem’, Jl R. aeronaut. Soc.196973, 1044.
10.
ReddiM. M.ChuT. Y. ‘Finite element solution of the steady-state compressible lubrication problem’, J. Lubric. Technol., Trans. Am. Soc. mech. Engrs196991 (Series F), 495.
11.
ArchardG. D.GairF. C.HirstW. ‘The elastohydrodynamic lubrication of rollers’, Proc. R. Soc.1961A262, 51.
12.
ErgatoudisJ. G.Isoparametric finite elements in two and three dimensional stress analysis Ph. D. Thesis, University of Wales, Swansea.
13.
MartinH. M. ‘Lubrication of gear teeth’, Engineering, Lond.1916102, 199.
14.
CameronA.The principles of lubrication1966 (Longmans, Green & Co., Harlow).
15.
DowsonD.HigginsonG. R.Elastohydrodynamic lubrication: the fundamentals of roller and gear lubrication1966 (Pergamon Press, Oxford).
16.
OsterleJ. F.StephensonR. R. ‘A direct solution of the elastohydrodynamic lubrication problem’, Trans. Am. Soc. lubric. Engrs19625 (No. 2), 365.
17.
SternlichtB.LewisP.FlynnP. ‘Theory of lubrication and failure of rolling contacts’, J. bas. Engng, Trans. Am. Soc. mech. Engrs196183 (Series D), 213.
18.
DowsonD.WhitakerA. V. ‘A numerical procedure for the solution of the elastohydrodynamic problem of rolling and sliding contacts lubricated by a Newtonian fluid’, Symp. Elastohydr. Lubric, Proc. Instn mech. Engrs1965–66180 (Pt 3B), 57.
19.
ChengH. S.SternlichtB. ‘A numerical solution for the pressure, temperature and film thickness between two infinitely long, lubricated rolling and sliding cylinders, under heavy loads’, Proc. Int. Lubric. Conf. 1965 (American Society of Mechanical Engineers, New York).
20.
HerrebrughK. ‘Solving the incompressible and isothermal problem in elastohydrodynamic lubrication through an integral equation’, Trans. Am. Soc. mech. Engrs196890 (Series F), 262.
21.
CrandallS.Engineering analysis1956 (McGraw-Hill Book Co. Inc., New York and London).
22.
SzaboP. A.LeeG. C. ‘Derivation of the stiffness matrix for plates by Galerkin method’, Int. J. Num. Meth. Engng19691, 301.
23.
ZienkiewiczO. C.CheungY. K.The finite element method in structural and continuum mechanics1967 (McGraw-Hill Inc., New York and London).
24.
ErgatoudisJ. G.IronsB. M.ZienkiewiczO. C. ‘Curved isoparametric, quadrilateral elements for finite element analysis’, Int. J. Solids Structures19684, 31.
25.
ErgatoudisJ. G.IronsB. M.ZienkiewiczO. C. ‘Three-dimensional analysis of dams and their foundations’, Proc. Symp. Arch Dams1968 (Institution of Civil Engineers, London).
26.
IronsB. M. ‘Numerical integration applied to finite element methods’, Conf. Use Dig. Comp. Struct. Engng. 1967 (University of Newcastle upon Tyne).
