A general numerical methodology was developed in the present study to analyse the elastohydrodynamic lubrication problem of a compliant layered socket against a rigid ball under steady state rotation representing flexion and extension during walking, with particular reference to artificial hip joint replacements. The general numerical methodology consisted of using the Newton-Raphson method to solve the Reynolds equation, simultaneously with the full elasticity equation using the finite element method in combination with the fast Fourier transform technique. Two specific types of acetabular cup were considered, one with ultra-high molecular weight polyethylene used in current total hip joint replacements, and one with polyurethane proposed for compliant layered ‘cushion form bearings’ for future developments. The film thickness and the pressure distribution for both cups were obtained under a wide range of operating conditions. The predicted central or average film thicknesses within the contact conjunction were compared with those estimated from various simplified theories available in the literature. A simple analytical methodology was consequently established to estimate the lubricating film thickness in a compliant layered socket, based on the corresponding ball-on-plane model and the consideration of the curvature effect.
BenjaminM. K.CastelliV.A theoretical investigation of compliant surface journal bearingsTrans. ASME, J. Lubric. Technol., 1971, 93 (1), 191–201.
2.
DowsonD.JinZ. M.Micro-elastohydrodynamic lubrication of synovial jointsEngng Medicine, 1986, 15, 63–65.
3.
AugerD. D.DowsonD.FisherJ.JinZ. M.Friction and lubrication in cushion form bearings for artificial hip jointsProc. Instn Mech. Engrs, Part H: J. Engineering in Medicine, 1993, 207 (H1), 25–33.
4.
SmithS. L.AshH. E.UnsworthA.A tribological study of UHMWPE acetabular cups and polyurethane compliant layer acetabular cupsJ. Biomed. Mater. Res., 2000, 53 (6), 710–716.
5.
JenningsL. M.FisherJ.A biomechanical and tribological investigation of a novel compliant all polyurethane acetabular resurfacing system. In Proceedings of the International Conference: Engineers and Surgeons Joined at the Hip, 2002, paper C601/032/2002 (PE Publishing, London).
6.
CookeA. V.DowsonD.WrightV.The rheology of synovial fluid and some potential synthetic lubricants for degenerate synovial jointsEngng Medicine, 1978, 7, 66–72.
7.
JinZ. M.Elastohydrodynamic lubrication of a circular point contact for a compliant layered surface bonded to a rigid substrate. Part 2: Numerical resultsProc. Instn Mech. Engrs, Part J: J. Engineering Tribology, 2000, 214 (J3), 281–289.
8.
Jalali-VahidD.JagatiaM.JinZ. M.DowsonD.Prediction of lubricating film thickness in a ball-in-socket model with a soft lining representing human natural and artificial hip jointsProc. Instn Mech. Engrs, Part J: Journal of Engineering Tribology, 2001, 215 (J4), 363–372.
9.
DowsonD.YaoJ. Q.Elastohydrodynamic lubrication of soft-layered solids at elliptical contacts. Part II: Film thickness analysisProc. Instn Mech. Engrs, Part J: J. Engineering Tribology, 1994, 208 (J1), 43–52.
10.
JinZ. M.JagatiaM.Jalali-VahidD.Prediction of lubricating film thickness in UHMWPE hip joint replacements In Friction, Lubrication and Wear of Artificial Joints (Ed. HutchingsI.), 2002, pp. 75–87 (Professional Engineering Publishing Limited, Bury St Edmunds and London).
11.
JinZ. M.DowsonD.FisherJ.Stress analysis of cushion form bearings for total hip replacementsProc. Instn Mech. Engrs, Part H: J. Engineering in Medicine, 1991, 205 (H4), 219–226.
12.
JinZ. M.DowsonD.FisherJ.Effect of porosity of articular cartilage on lubrication of a normal human hip jointProc. Instn Mech. Engrs, Part H: J. Engineering in Medicine, 1992, 206 (H3), 117–124.
13.
UnsworthA.PearcyM. J.WhiteE. F.T.WhiteG.Soft layer lubrication of artificial hip joints In Fifty Years On, Proceedings of an International Conference, 1987, pp. 715–724 (Mechanical Engineering Publications Limited, London).
14.
DowsonD.FisherJ.JinZ. M.AugerD. D.JobbinsB.Design consideration of cushion form bearings in artificial hip jointsProc. Instn Mech. Engrs, Part D: J. Engineering in Medicine, 1991, 205 (H2), 59–68.
15.
JinZ. M.MedleyJ. B.DowsonD.Fluid film lubrication in artificial hip joints inTribological research and design for engineering systems (Edited by DowsonD.), 2003, pp. 237–256 (Elsevier, Amsterdam).
16.
Jalali-VahidD.JinZ. M.Transient elastohydrodynamic lubrication analysis of UHMWPE hip joint replacementsProc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 2002, 216 (C4), 409–420.
17.
JinZ. M.DowsonD.FisherJ.Fluid film lubrication in natural hip joints In Thin Films in Tribology, Proceedings of the 19th Leeds-Lyon Symposium on Tribology, Tribology Series, Vol. 25 (Eds DowsonD.TaylorC. M.GodetM.), 1993, pp. 545–555 (Elsevier, Amsterdam).
18.
ChanF. W.MedleyJ. B.BobynJ. D.KrygierJ. J.`Numerical analysis of time-varying fluid film thickness in metal-on-metal hip implants in simulator tests’ In Alternative Bearing Surfaces in Total Joint Replacement, ASTM STP 1346 (Eds JacobsJ. J.CraigT. L.), 1998, pp. 111–128 (American Society for Testing and Materials, Philadelphia, Pennsylvania).
19.
RoterG. E.MedleyJ. B.BobynJ. D.KrygierJ. J.ChanF. W.Intermittent motion: a novel simulator protocol for the wear of metal-metal hip implants. 28th Leeds-Lyon Symposium on Tribology, Vol. 40, 2002, pp. 367–376 (Elsevier, Amsterdam).
20.
SaarriH.SantavirtaS.NordstromD.PaavolainenP.KonttinenY. T.Hyaluronate in total hip replacementJ. Rheumatol., 1993, 20 (1), 87–90.
21.
DelecrinJ.OkaM.TakahashiS.YamamuroT.NakamuraT.Changes in joint fluid after total arthroplastyClin. Orthop. Related Res., 1994, 307, 240–249.
22.
YaoJ. Q.LaurentM. P.JohnsonT. S.BlanchardC. R.CrowinshieldR. D.The influence of lubricant and material on polymer/CoCr sliding frictionWear, 2003, 255, 780–784.
23.
PiotrowskiG.Persistence of non-Newtonian squeeze in joints. In Proceedings of the Second Mid-Atlantic Biofluid Mechanics Conference (Ed. SchneckD. J.), 1980, pp. 125–145 (Plenum, New York).
24.
WangF. C.JinZ. M.Prediction of elastic deformation of acetabular cup and femoral head for lubrication analysis of artificial hip jointsProc. Instn Mech. Engrs, Part J: J. Engineering Tribology, 2004 (in press).
25.
JagatiaM.JinZ. M.Elastohydrodynamic lubrication of metal-on-metal hip prosthesis under steady-state entraining motionProc. Instn Mech. Engrs, J. Engineering in Medicine, 2001, 215 (H6), 531–541.
26.
WangD.Elastohydrodynamic lubrication of point contacts for layers of soft solids and for `monolithic’ hard materials in the transient bouncing ball problem. PhD thesis, University of Leeds, 1994.
27.
Jalali-VahidD.JagatiaM.JinZ. M.DowsonD.Prediction of lubrication film thickness in UHMWPE hip joint replacementsJ. Biomechanics, 2001, 34, 261–266.
28.
JinZ. M.HengS. M.NgH. W.AugerD. D.An axisymmetric contact model of ultra high molecular weight polyethylene cups against metallic femoral heads for artificial hip joint replacementsProc. Instn Mech. Engrs, Part H: J. Engineering in Medicine, 1999, 213 (H4), 317–327.
29.
BergmannG.DeuretzbacherG.HellerM.GraichenF.RohlmannA.StraussJ.DudaG. N.Hip contact forces and gait patterns from routine activitiesJ. Biomechanics, 2001, 34 (7), 859–871.
