This paper reports on the use of the Newton successive overrelaxation method to solve problems of elastohydrodynamic lubrication of soft-layered solids at elliptical contacts. Solutions have been obtained for a range of load, speed, elastic layer thickness and conjunction ellipticity, enabling the film thickness to be determined. The empirical formula thus derived is used to estimate the effective film thickness in the major load-carrying synovial joints in the body.
Get full access to this article
View all access options for this article.
References
1.
DowsonD.HigginsonG. R.Elasto-hydrodynamic lubrication. The fundamentals of roller gear lubrication, 1966 (and SI edition 1977) (Pergamon Press, Oxford).
2.
HamrockB. J.DowsonD.Ball bearing lubrication; the elastohydrodynamics of elliptical contacts, 1981, John Wiley, New York).
JacobsonB. O.Rheology and elastohydrodynamic lubrication, 1991, Elsevier, Amsterdam).
5.
DowsonD.JinZ. M.Micro-elastohydrodynamic lubrication of synovial joints. Proc. Instn Mech. Engrs, Part H, 1986, 15(H2), 63–65.
6.
DowsonD.JinZ. M.Micro-elastohydrodynamic lubrication of low elastic modulus solids on rigid substrates. J. Phys. D: Appl. Phys., Frontiers of Tribology, 1992, 25(1A), 133–140.
7.
DowsonD.YaoJ. Q.A full solution to the problem of film thickness prediction in natural synovial joints. Proceedings of the Sixteenth Leeds-Lyon Symposium on Tribology, mechanics of coatings, 1990, paper iv(i), pp. 91–102 (Elsevier, Amsterdam).
8.
YaoJ. Q.DowsonD.Elastohydrodynamic lubrication of soft-layered solids at elliptical contacts. Part 1: Elasticity analysis. Proc. Instn Mech. Engrs, Part J, 1994, 208(J1), 31–41.
9.
DowsonD.FisherJ.JinZ. M.AugerD. D.JobbinsB.Design considerations for cushion form bearings in artificial hip joints. Proc. Instn Mech. Engrs, Part H, 1991, 205(H1), 59–68.
10.
BlokH.Review of data on elastohydrodynamic lubrication, 1959 (Technische Hogeschol, Laboratorium voor Werktuigonderdelen, Delft).
11.
ArchardJ. F.Non-dimensional parameters in isothermal theories of elastohydrodynamic lubrication. J. Mech. Engng Sci., 1968, 10(2), 165–167.
12.
GreenwoodJ. A.Presentation of elastohydrodynamic film-thickness results. J. Mech. Engng Sci., 1969, 11(2), 128–132.
13.
JohnsonK. L.Regimes of elastohydrodynamic lubrication. J. Mech. Engng Sci., 1970, 12(1), 9–16.
14.
KapitzaP. L.The hydrodynamic theory of lubrication in the presence of rolling. Zh. Tekh. Fiz., 1955, 25(4), 747–762.
15.
HamrockB. J.DowsonD.Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. Part I—fully flooded conjunction. Trans. ASME, J. Lubric. Technol., 1978, 100(2), 236–245.
16.
MedleyJ. B.DowsonD.WrightV.Transient elastohydrodynamic lubrication models for the human ankle joint. Engng in Medicine, 1984, 13(3), 137–151.
17.
DowsonD.JinZ. M.An analysis of microelasto-hydrodynamic lubrication in synovial joints considering cyclic loading and entraining velocities. Proceedings of the Thirteenth Leeds-Lyon Symposium on Tribology, 1987, pp. 375–386 (Elsevier, Amsterdam).
18.
DowsonD.The lubrication of synovial joints. Proceedings of the Ninth Canadian Congress on Applied mechanics, 1983, pp. 25–31.
19.
HookeC. J.O'DonoghueJ. PThe elastohydrodynamic lubrication of soft highly deformed contacts. J. Mech. Engng Sci., 1972, 14(1), 34–48.
20.
HookeC. J.A note on the elastohydrodynamic lubrication of soft contacts. Proc. Instn Mech. Engrs, Part C., 1986, 200(C3), 189–194.
21.
HookeC. J.The calculation of film thicknesses in soft, highly deformed contacts under dynamic conditions. Proc. Instn Mech. Engrs, Part C., 1987, 201(C3), 171–179.