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Elastohydrodynamic lubrication analysis of hip implants with ultra

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Elastohydrodynamic lubrication analysis of hip
implants with ultra high molecular weight polyethylene
cups under transient conditions

D Jalali-Vahid1, Z M Jin2* and D Dowson3
1
 D epartment of M aterial Engineering, Sahand U niversity of Technology, Tabriz, Iran
2
 M edical Engineering, School of Engineering, D esign and Technology, U niversity of Bradford, West Yorkshire, U K
3
 ‘R yedale’, Adel, Leeds, U K


               Abstract: The transient variation of both the load and speed experienced during walking in an
               elastohydrodynamic lubrication (EH L) analysis for arti cial hip joints employing an ultra high
               molecular weight polyethylene (U H M WPE) acetabular cup against either a metallic or ceramic
               femoral head was considered in this study. A general numerical procedure to solve the transient EH L
               problem in spherical ball-in-socket coordinates, developed in a previous study by Jalali-Vahid and Jin
               in 2002, was applied under three speci c conditions experienced during typical gait cycles, including
               speed reversal, a sudden load increase and a sudden load decrease. The predicted minimum lm
               thickness was found to stay remarkably constant and similar to that prior to the change in either the
               load or the angular velocity, despite a large change in these operating conditions. This was attributed
               to the remarkably effective squeeze- lm action of preserving and maintaining the lubricating lm
               developed before the transient variation in either the load or speed. It is therefore possible to neglect
               the effect of these speci c transient variations of load and speed under physiological walking
               conditions considered in the present study on the predicted lm thickness in hip implants with
               U H M WPE cups.

               Keywords: transient elastohydrodynamic lubrication (EH L), arti cial hip joint replacement, speed
               reversal, squeeze lm


NOTATION                                                                 x , y, z          linear coordinates

c                   radial clearance ˆ R 2 ¡ R 1                         d                 elastic deformation of the U H M WPE
d                   cup wall thickness ˆ R 3 ¡ R 2                                         liner de ned in equation (3)
ex , ey , ez        eccentricities between the centres of the            ex , ey , ez      non-dimensional eccentricity ratios
                    femoral head and the acetabular socket                                 ˆ ex =c, ey =c, ez =c
E                   modulus of elasticity for U H M WPE                  Z                 viscosity of synovial uid
fx , fy , fz        calculated load components de ned in                 n                 Poisson’ s ratio
                    equation (4)                                         f, y              angular coordinates in the entraining and
h                   total lm thickness                                                     side-leakage directions respectively
p                   pressure                                             o                 angular velocity
R1                  femoral head radius
R2                  cup radius
R3                  outside radius of the cup
t                   time from the change of load or speed
w                                                                        1    INTRODUCTION
                    applied load in the y direction

                                                                         N atural synovial joints such as hips and knees are
T he M S was received on 4 M arch 2003 and was accepted after revision   remarkable bearings. These bearings are expected to
for publication on 3 A pril 2003.                                        function in the human body for a lifetime while
* Corresponding author: M edical Engineering, S chool of Engineering,
Design and T echnology, University of Bradford, Bradford, W est          transmitting large dynamic loads and yet accommodat-
Y orkshire BD7 1DP, UK.                                                  ing a wide range of movements. H owever, diseases such

C03903 # IM echE 2003                                                    Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science
768                                                 D JALALI-VAH ID, Z M JIN AN D D DOWSON


as osteoarthritis and rheumatoid arthritis and trauma                          joint replacements. F urthermore, it has been pointed out
sometimes require these natural bearings to be replaced                        that the average transient minimum lm thickness
by arti cial ones. Total joint replacement has been the                        predicted throughout one cycle is very close to that
most successful surgical treatment for hip joint diseases                      under quasi-static conditions based upon the average
in the last forty years. Currently, more than 800 000 hip                      angular velocity and load. D ue to the convergence
joint replacements are carried out worldwide every year.                       problem of the numerical method commonly experi-
The majority of current arti cial hip joints utilize a                         enced with EH L solutions, only a cyclic sinusoidal speed
material combination of ultra high molecular weight                            with a constant load and a cyclic sinusoidal load with a
polyethylene (U H M WPE) articulating against either a                         constant speed were considered. Although it is generally
metallic or ceramic component. These man-made                                  desirable to consider the complete cyclic nature of gait
bearings can sometimes last 20 years in the body                               cycles, the load in the swing phase is generally much
without failure. H owever, problems such as osteolysis                         smaller and less well de ned, and often considered to be
and loosening of the prosthesis have recently been                             less important compared with the stance phase load. In
identi ed as the main factor limiting the in vivo                              many studies, the load in the swing phase is not even
performance of implants, particularly with the increas-                        given. M ore recently, it has been demonstrated that in
ing use of these devices in younger patients with life                         vivo microseparation can occur between the femoral
expectancies after surgery in excess of 25 years.                              head and the acetabular cup during gait. Average
Osteolysis and loosening are usually caused by an                              separations in subjects with U H M WPE-on-metal hip
adverse tissue reaction to wear particles of U H M WPE                         prostheses have been shown to be 2 mm [14, 15]. This
[1–3].                                                                         microseparation occurs during the swing phase in the
   Tribological studies of arti cial hip joints with                           direction along the axis of the cup, and when a load is
U H WM PE acetabular cups play a major role in the                             applied in the stance phase, the femoral head contacts
long-term success of these implants. The wear particles,                       the superior rim of the cup because of the load vector
which can cause adverse biological reactions, are mainly                       imposed on the hip joint at this instant of the walking
generated at the articulating bearing surfa ces because of                     cycle. The implication of the microseparation on the
a mixed or boundary lubrication regime experienced in                          swing phase load is still debatable [16], but the
the majority of these hip implants [4, 5]. The generation                      magnitude of the swing phase load must be very small.
of wear particles can be greatly reduced by improving                          Although a small load generally favours the numerical
the wear resistance of the bearing materials. H owever, it                     solution to EH L problems, a sudden decrease in load
may also be possible to reduce the proportion of the                           after the stance phase may pose the problem of
total load carried by asperity contact by promoting uid                        numerical convergence. Similar problems could also be
  lm lubrication in these man-made bearings, since the                         encountered just before the stance phase when the load
two articulating surfaces are then partially separated. It                     is suddenly increased. F urthermore, the angular speed is
is therefore important to predict the magnitude of the                         reversed during the stance phase, which has not been
lubricating lm thickness in hip joint replacements in                          considered in the previous transient EH L analysis of hip
order to assess the lubrication regime and to improve                          implants [13]. Therefore, it is important to analyse the
the contribution of uid lm lubrication to the                                  lubricating lm thickness under these speci c transient
performance of these implants.                                                 periods during the gait cycle. The purpose of this study
   Quasi-static entraining motion has been considered in                       was to apply the general transient EH L methodology
a number of previous elastohydrodynamic lubrication                            developed in a previous study [13] to an example of hip
studies of arti cial hip joints with U H M WPE cups [5–7].                     implants with U H M WPE cups under three transient
In addition, a number of squeeze- lm lubrication                               periods during a typical gait cycle: (a) angular speed
analyses have also been carried out [8–11]. It is well                         reversal, (b) a sudden increase in load and (c) a sudden
known that neither the load nor the speed experienced in                       decrease in load.
hip joints are constant during walking cycles [12].
R ecently, a general numerical procedure to solve the
transient elastohydrodynamic lubrication (EH L) pro-
blem in spherical ball-in-socket coordinates has been                          2   LUBRICATION MODEL, GOVERNING
developed by Jalali-Vahid and Jin [13] and applied to an                           EQUATIONS AND NUMERICAL ANALYSIS
example of hip implants with U H M WPE cups under
transient cyclic variations of load and speed. The                             A simple ball-in-socket con guration was considered in
predicted minimum lm thickness was shown to stay                               this study for EH L analysis of arti cial hip joints with
remarkably constant, despite a large change in the                             U H M WPE cups, as shown in F ig. 1. The important
angular velocity and the load. This has been attributed                        parameters required for the EH L analysis are the radius
to the combined effect of entraining and squeeze- lm                           of the femoral head …R 1†, the radius of the acetabular
actions in generating, replenishing and maintaining load                       cup …R 2† or the radial clearance …c ˆ R 2 ¡ R 1 †, and the
support by means of a lubricating lm in arti cial hip                          thickness of the cup wall …d†, the elastic modulus …E†

Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science                                          C03903 # IMechE 2003
                 EHL AN ALYSIS OF H IP IM PLANTS WITH UH M WPE CUPS UNDER TR AN SIENT CON DITIONS                                      769


                                                               Case b: sudden increase in load, as shown in Fig. 2b. This
                                                                 sudden increase in load commences just before heel
                                                                 strike and is completed shortly afterwards. The load
                                                                 increases signi cantly from a small fraction of body-
                                                                 weight, while the speed remains relatively constant.
                                                                 F or this case, the load was assumed to increase
                                                                 linearly from 200 to 2100 N in 0.05 s, under a constant
                                                                 angular speed of 1 rad/s.
                                                               Case c: sudden decrease in load, as shown in Fig. 2c. The
                                                                 load decreases rapidly just before toe off. F or this
                                                                 case, the load was assumed to decrease from 2100 to
                                                                 200 N in 0.05 s. Although the speed reverses during
Fig. 1   A simple ball-in-socket model for the transient EHL     this stage of the walking cycle, a constant speed of
         analysis of hip joint replacements with U H M WPE       1 rad/s was assumed in the present analysis.
         cups
                                                                 The governing equation for the pressure generation
                                                               …p† for the present EH L problem is the R eynolds
and Poisson’s ratio …n† for the U H M WPE cup. A typical       equation in spherical coordinates (shown in F ig. 3), as
hip joint replacement was considered with the following        detailed below [13, 17]:
parameters:                                                                            ´              ´
                                                                        q           qp      q      qp
                                                                 sin y     h3 sin y      ‡      h3
(a)   femoral head radius …R 1† of 14 mm,                              qy           qy     qf      qf
(b)   cup radius …R 2† of 14.1 mm,                                                               ´
                                                                                       qh     qh
(c)   cup thickness …d† of 7 mm,                                    ˆ 6ZR 2 sin 2 y o
                                                                          2               ‡2                        …1†
                                                                                       qf     qt
(d)   elastic modulus …E† of 1 G Pa,
(e)   Poisson’s ratio …n) of 0.4.                              Other equations include the geometrical representation
                                                               of lm thickness …h†:
   The femoral head articulating with the U H M WPE
cup is usually metallic or ceramic. The modulus of these              ¡                                              ¢
                                                                 h ˆ c 1 ¡ ex sin y cos f ¡ ey sin y sin f ¡ ez cos y ‡ d
hard materials is at least two orders of magnitude
greater than that of U H M WPE and therefore the                                                                                      …2†
femoral head was assumed to be rigid. F urthermore,
                                                               where the elastic deformation of the U IH M WPE cup …d†
the lubricant present in arti cial hip implants, synovial
                                                               was calculated, based on a simple constrained column
  uid, was assumed to be N ewtonian and iso-viscous for
                                                               model:
the purpose of lubrication analysis in the present study
                                                                                    h                i
[5]. A relatively high viscosity of 0.01 Pa s was adopted
                                                                                 R 2 …R 3 =R 2 †3 ¡1
in order to facilitate convergence of numerical solutions        dˆ n                                       op     …3†
[13].                                                                E 1=…1 ¡ 2n† ‡ ‰2=…1 ‡ n†Š…R 3 =R 2 †3
   The load and speed experienced in hip joints during
walking are generally three-dimensional, but the main          F inally, the integration of the pressure distribution must
load component is in the vertical direction and the main       be balanced by the external load applied:
motion is exion and extension. Therefore, only the load                     …p …p
in the y direction …w† and the angular velocity around                    2
                                                                  fx ˆ R 2        p sin y cos f sin y dy df ˆ 0
the z axis …o† were considered. F igure 2 shows the
variation of both the vertical load and the angular speed                   …0 …0
                                                                             p p
( exion/extension) during one walking cycle [17]. Three           fy ˆ R 22       p sin y sin f sin y dy df ˆ w
                                                                             0 0
speci c transient periods during the walking cycles were                    …p …p
considered:                                                       fz ˆ R 22       p cos y sin y dy df ˆ 0
                                                                             0   0
Case a: speed reversal during the stance phase, as shown                                                                              …4†
  in Fig. 2a. This period occurs just after the heel strike.
  The load increases signi cantly and stays relatively           The following boundary conditions for the present
  constant, while the direction of the speed is reversed.      lubrication problem were adopted:
  The load was assumed to be 2100 N (three times
                                                               (a) zero pressure at the edge of the cup in the plane …x z†,
  bodyweight for a person with 70 kg mass). The
                                                               (b) cavitation on the outlet boundary.
  angular speed was assumed to decrease linearly from
  1.7 rad/s to zero in 0.12 s, and then to increase from 0     The speed reversal was considered in the present study
  to 1.7 rad/s in the opposite direction in 0.12 s.            by simply changing the inlet and the outlet boundaries.

C03903 # IM echE 2003                                          Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science
770                                                 D JALALI-VAH ID, Z M JIN AN D D DOWSON




             Fig. 2    Transient variation of the load and speed for simulating (a) speed reversal during the stance phase
                       (case a), (b) a sudden load increase before the heel strike (case b) and (c) a sudden load decrease after
                       the toe off (case c)



Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science                                         C03903 # IMechE 2003
                 EHL AN ALYSIS OF H IP IM PLANTS WITH UH M WPE CUPS UNDER TR AN SIENT CON DITIONS                                     771


                                                                 F igure 6a shows the minimum and central lm
                                                              thicknesses as a function of time after the load is
                                                              decreased from 2100 to 200 N (case c). The lm pro le
                                                              and the pressure distribution are shown in F igs 6b and c
                                                              respectively at various instants during the load change.
                                                              The lm pro les after the load is kept constant at 200 N
                                                              for a further 0.5 s are shown in F ig. 6d.



                                                              4   DISCUS SION

                                                              It can be seen from F ig. 4a that both the central and the
                                                              minimum        lm thicknesses decrease as the speed
                                                              decreases, up to the instant when the direction of
      Fig. 3   De nition of spherical coordinates …f, y†      motion is reversed …t ˆ 0.12 s†. H owever, the reduction
                                                              in the lm thickness is both gentle and small. N either the
                                                              central nor the minimum lm thickness fall to zero at the
The effect of cavitation on the location of the inlet         instant of speed reversal when the speed is reduced to
boundary and ow continuity during speed reversal              zero due to squeeze- lm action. After the speed reversal,
were not considered in the present analyses. The effect       the minimum lm thickness quickly increases by a small
of these assumptions on the predicted lubricant lm            amount and stays relatively constant, while the central
thickness has been shown to be negligible in an EH L            lm thickness continues to decrease at a very slow rate.
analysis considering speed reversal, particularly under       F or example, at the end of the simulation period of
heavily loaded conditions [18].                               0.72 s from the start of the speed change, the central lm
   The nite difference method was employed to solve           thickness is decreased by only 12 per cent, while the
the governing equations (1) to (4), subject to the load       minimum lm thickness is almost identical to that
and speed variations shown in F igs 2a, b and c. The          established before the speed change. The detailed
details of the numerical method have been given               changes of the lm thickness at different time instants
elsewhere [13]. The number of mesh grids used in the          are shown in F ig. 4b. It is evident that the effect of speed
present study was between 4806480 and 9616961. The            reversal upon the lm pro les is most pronounced in the
time step was chosen between 0.05/300 and 0.24/300 s.         inlet region, both before and after the speed reversal.
F urthermore, numerical solutions to the lm pro le and        Before the speed reversal …t < 0.12 s†, the inlet region is
the pressure distribution were computed only for the          on the left of the contact in F ig. 4b and the convergent
speci c transient periods of 0.72 s for case (a) and 0.55 s     lm pro les can be seen from left (inlet) to right (outlet).
for both cases (b) and (c).                                   After the speed reversal …t > 0.12 s†, the inlet region
                                                              moves to the right of the contact. It is interesting to note
                                                              that the lm thicknesses begin to increase on the right of
                                                              the conjunction (inlet), while the lm thicknesses on the
3   RESULTS                                                   left (outlet) decrease. H owever, both the central and the
                                                              minimum lm thicknesses stay relatively constant, as
The predicted minimum and central lm thicknesses as a         shown in F ig. 4a. It should be pointed out that at 0.72 s,
function of time after the rapid speed change at constant     the lubricating lm thickness is convergent between
load (case a) are shown in F ig. 4a. The corresponding        f ˆ 1358 and 1228 and divergent from f ˆ 1228 to 458
  lm shape and thickness and pressure distributions           within the contact conjunction. D espite relatively large
along the centre-line in the entraining direction …f† are     changes of the lm pro les, the change in the pressure
shown in F igs 4b and c respectively for different time       distribution is negligible due to the assumption of a
instants.                                                     constant load (F ig. 4c).
   The time history of the predicted central and                 The effect of a sudden load increase from 200 to
minimum lm thicknesses when the load is increased             2100 N on the predicted minimum and central lm
from 200 to 2100 N in 0.05 s, and then kept constant for      thicknesses is quite small, as shown in F ig. 5a. A slight
another 0.5 s (case b), is shown in F ig. 5a. The changes     increase in both the minimum and the central lm
in lm shape and thickness and pressure distributions at       thicknesses around t ˆ 0.05 s is probably due to the large
different time instants during the ramp period of 0.05 s      squeeze- lm velocity at the outlet region. This becomes
are shown in F igs 5b and c. F igure 5d shows how the         more evident when the lm pro les at different time
  lm shape and thickness changes during and after the         instants shown in F ig. 5b are considered. It is clear that
load increase from 200 to 2100 N .                            the load increase leads to an increase in the width of the

C03903 # IM echE 2003                                         Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science
772                                                 D JALALI-VAH ID, Z M JIN AN D D DOWSON




             Fig. 4    (a) Prediction of the central and minimum lm thicknesses as a function of time from the speed change
                       (case a); (b) lm pro les at different instants after the speed change (case a); (c) pressure distributions
                       at different instants after the speed change (case a)

Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science                                          C03903 # IMechE 2003
                 EHL AN ALYSIS OF H IP IM PLANTS WITH UH M WPE CUPS UNDER TR AN SIENT CON DITIONS                                  773




                                                                           Fig. 5    (continued over)

C03903 # IM echE 2003                                      Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science
774                                                 D JALALI-VAH ID, Z M JIN AN D D DOWSON




             Fig. 5    (a) Prediction of the central and minimum lm thicknesses as a function of time from the load increase
                       from 200 to 2100 N (case b); (b) lm pro les at different instants during the load increase from 200 to
                       2100 N (case b); (c) pressure distributions at different instants during the load increase from 200 to
                       2100 N (case b); (d) lm pro les at different instants after the load increase from 200 to 2100 N (case b)



contact conjunction and a large decrease in the lm                             2100 N prior to the load change but still considerably
thicknesses in both the inlet and the outlet regions.                          smaller than the steady state prediction of 0.267 mm at a
H owever, the lm thickness in the central part of the                          load of 200 N , as shown in F ig. 6d. The maximum
contact region between f ˆ 648 and 1148, mainly                                pressure decreases rapidly, from 29 to 8 M Pa as shown
corresponding to the contact region of 200 N , stays                           in F ig. 6c, as the load is decreased from 2100 to 200 N .
remarkably constant, due to the squeeze- lm action.                               It has been pointed out that it is important to estimate
Consequently, this leads to almost constant minimum                            the lubricating lm thickness under general transient
and central lm thicknesses, as shown in F ig. 5a. It is                        conditions. It has been shown previously that under
also interesting to note that even after 0.55 s (or 0.50 s                     cyclic variations of both the load and speed, the use of a
after the maximum load of 2100 N has been achieved),                           steady state formula based on the average load, speed
the transient lm thickness predicted in the present                            and viscosity gives a good estimate of the transient lm
study does not resemble that under the steady state                            thickness. It is clear from the present study that under
condition shown in F ig. 5d. The minimum lm thickness                          physiological walking conditions imposing a relatively
predicted at 0.55 s was 0.254 mm, as compared with                             short cycle of time, the effect of speed reversal has a
0.267 mm at the onset of the load change and 0.180 mm at                       negligible effect upon the predicted lm thickness. This
a steady state load of 2100 N . This once again implies                        is also true when either a sudden load increase or a
the importance of the squeeze- lm action in preserving                         sudden load decrease occurs. D ue to the powerful
the lubricating lm thickness developed under low load.                         squeeze- lm action, the lubricant lm developed prior to
Although the pressure builds up rapidly in both the inlet                      the transient condition stays relatively unchanged for
and the outlet regions as the load increases, the                              quite a long time of 0.5 s, when either the load is
magnitude, located within the centre of the contact, is                        increased or decreased or the direction of motion is
largely determined by the load imposed as shown in                             reversed. These observations are consistent with the
F ig. 5c.                                                                      persistence of a relatively constant lubricant lm
   The effect of a sudden load decrease on the predicted                       thickness during walking cycles reported from previous
minimum and central lm thicknesses is shown in                                 theoretical studies of both synovial joints and their
F ig. 6a. U nder transient conditions, a decrease in load                      replacements by D owson and Jin [19], Jin et al. [20],
actually results in a decrease in the predicted minimum                        Chan et al. [21] and Jalali-Vahid and Jin [13]. It is
and the central lm thicknesses, throughout two thirds                          reassuring that the major load increase experienced in
of the duration of the load change. After that, both the                       the stance phase has a very small effect on the predicted
central and minimum lm thicknesses begin to increase,                          transient lm thickness and the load decrease in the
as also shown in F ig. 6b. H owever, at the end of the                         swing phase considered in the present study is also
simulation (0.55 s) after the load has remained constant                       unlikely to lead to a large increase in the lubricating lm.
at 200 N for 0.5 s, the predicted minimum lm thickness                            It should be pointed out that the main purpose of the
was 0.167 mm, similar to that of 0.180 mm at a load of                         present study was to assess the effect on uid lm

Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science                                          C03903 # IMechE 2003
                 EHL AN ALYSIS OF H IP IM PLANTS WITH UH M WPE CUPS UNDER TR AN SIENT CON DITIONS                                  775




                                                                    Fig. 6    (continued over)

C03903 # IM echE 2003                                      Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science
776                                                 D JALALI-VAH ID, Z M JIN AN D D DOWSON




             Fig. 6    (a) Prediction of the central and minimum lm thicknesses as a function of time from the load
                       decrease from 2100 to 200 N (case c); (b) lm pro les at different instants during the load decrease
                       from 2100 to 200 N (case c); (c) pressure distribution at different instants during the load decrease
                       from 2100 to 200 N (case c); (d) lm pro les at different instants after the load decrease from 2100 to
                       200 N (case c)




lubrication of the transient variation of the load and                         average load, viscosity and average speed under the
speed experienced in hip joints during walking for a                           cyclic conditions considered in the present study.
typical hip joint replacement with an U H M WPE cup. It
is generally known that the lubricating lm thickness
developed in these hip implants is not suf ciently large                       REFERENCES
to separate completely the two bearing surfaces [5]. The
assumption of full uid lm lubrication is not valid for                         1 Willert, H. G. and Semlitsch, M. R eaction of the articular
these hip implants and the mode of lubrication is                                capsule to wear products of arti cial joint prostheses.
therefore boundary or mixed. H owever, the general                               J. Biomed. M ater. R es., 1977, 11, 157–164.
  ndings from this transient elastohydrodynamic lubri-                         2 Amstutz, H. C., Campell, P., Kossovsky, N. and Clark, I. C.
cation analysis for hip joint replacements with                                  M echanism and clinical signi cance of wear debris-induced
U H M WPE cups may be equally applicable to other                                osteolysis. Clin. Orthop. R elated R es., 1991, 276, 7–17.
forms of hip prostheses such as metal-on-metal material                        3 Ingham, E. and Fisher, J. Biological reactions to wear
combinations [22].                                                               debris in total joint replacement. Proc. Instn M ech. Engrs,
                                                                                 Part H : J. Engineering in M edicine, 2000, 214(H 1), 21–37.
                                                                               4 Unsworth, A., Dowson, D. and Wright, V. The frictional
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                                                                                 joints. T rans. A S M E, J. L ubric. T echnol., 1975, 97(3), 377–
                                                                                 382.
5     CONCLUSIO NS
                                                                               5 Jin, Z. M., Dowson, D. and Fisher, J. Analysis of uid lm
                                                                                 lubrication in arti cial hip joint replacements with surfaces
The effect of transient loads and speed reversals                                of high elastic modulus. Proc. Instn M ech. Engrs, Part H :
experienced during the walking cycles on the EH L of a                           J. Engineering in M edicine, 1997, 211(H 3), 247–256.
typical hip implant with an U H M WPE cup has been                             6 Jalali-Vahid, D., Jagatia, M., Jin, Z. M. and Dowson, D.
analysed in this study. Three speci c transient condi-                           Elastohydrodynamic lubrication analysis of U H M WPE
tions were investigated, speed reversal during the stance                        hip joint replacements. In Thinning Films and T ribological
phase, a sudden increase in load just before heel strike                         Interfaces, Proceedings of 26th Leeds–Lyon Symposium on
                                                                                 T ribology, 2000, pp. 329–339.
and a sudden decrease in load before toe off. It has been
                                                                               7 Jalali-Vahid, D., Jagatia, M., Jin, Z. M. and Dowson, D.
shown that under physiological walking conditions, the                           Prediction of lubrication lm thickness in U H M WPE hip
change in the predicted lubricating lm thickness within                          joint replacements. J. Biomechanics, 2001, 34, 261–266.
the conjunction is quite negligible. This results from the                     8 Sasada, T. and Mabuchi, K. Elastohydrodynamic lubrica-
powerful squeeze- lm action, and therefore the steady                            tion of total hip prosthesis. In Proceedings of the JSLE
state lm thickness formula can be used effectively to                            International Tribology Conference, Tokyo, Japan, 8–10
estimate the transient lm thickness based on the                                 July 1985.

Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science                                               C03903 # IMechE 2003
                 EHL AN ALYSIS OF H IP IM PLANTS WITH UH M WPE CUPS UNDER TR AN SIENT CON DITIONS                                         777


 9 Mabuchi, K. and Sasada, T. N umerical analysis of              17 Jin, Z. M. and Dowson, D. A full numerical analysis of
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C03903 # IM echE 2003                                             Proc. Instn M ech. Engrs Vol. 217 Part C: J. M echanical Engineering Science

				
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