59

Design considerations for cushion form bearings in artificial hip joints ~

D Dowson, CBE, FRS, FEng, FIMechE, J Fisher, BSc, PhD, CEng, MIMechE, Z M Jin, BSc, PhD, D D Auger, BASc, MASc and B Jobbins, CEng, MIMechE Department of Mechanical Engineering, University of Leeds Lubrication mechanisms and contact mechanics have been analysed in a new generation of ‘cushionform’ bearings for artificial hip joints, which comprise low elastic modulus layers on the articulating surfaces. Comparisons have been made with ‘hard’ bearings used in existing prostheses and also with the natural hip joint. Lubricating film thicknesses are enhanced by larger contact areas and lower contact pressures. For aJixed contact area, simultaneous changes in layer thickness and radial clearance have been shown to have a small effect on elastohydrodynamic film thickness. Hard bearings designed with the same contact area as the cushion bearings produced a similarfilm thickness, but lubricantJilm thickness is not optimized in current designs. The main advantage of using a cushion bearing with low elastic modulus layers was found to be associated with microelastohydrodynamic lubrication. Careful selection of the elastic modulus is important in order to ensure that this lubrication regime was effective. Low elastic modulus layers may also produce local deformations, which enhance squeezefilm action. The elastic modulus of the material should not be lower than necessary to produce effective microelastohydrodynamic lubrication, as a further reduction in modulus only increases the strain distribution in the material. A lubricantfilm thickness of 0.3 pm has been predicted for a cushion hip prosthesis with a femoral head diameter of 32 mm and radius of contact zone of 16 mm, using a 2 mm thick layer with an elastic modulus of 20 MPa. 1 INTRODUCTION

Cushion form bearings comprising layers of low elastic modulus materials are being investigated in a number of centres for use in total replacement joints (1-3) and hemiarthroplasty (4). The low elastic modulus lining on the bearing surface of the prosthesis is used to promote a continuous film of lubricant between the articulating surfaces and hence reduce both friction and wear. The low elastic modulus layer may be considered to fulfil a similar function to that performed by cartilage in the natural joint. It has been shown previously that the natural joint can articulate with fluid film lubrication throughout most of the walking cycle (5, 6). Bearing surfaces currently used in prostheses consist of very hard materials (either metal or ceramic) which articulate on an ultrahigh molecular weight polyethylene (UHMWPE) surface. The elastic modulus of the UHMWPE (1.4 GPa) is approximately 100 times greater than the elastic modulus of the cartilage. These joints operate with either a boundary or mixed lubrication regime in the body (7, 8) and this results in both higher friction than the natural joint and the generation of wear debris from the UHMWPE component (9, 10). Both of these factors may contribute to loosening of the prosthetic components (10). Recent experimental studies of cushion form bearings (11) using low elastic modulus layers (Young modulus E = 5-20 MPa) have shown that under physiological loading conditions continuous fluid film lubrication can be achieved with lubricant viscosities as low as 0.002 Pas. The promotion of a continuous film of lubricant may be attributed to conventional elastohydrodynamic lubrication and squeeze film effects (1, 11), microelastohydrodynamic lubrication (5, 8, 12) and local deformation of the low elastic modulus layers. In the natural synovial joint, which is lined with layers of cartilage, other factors such as a high fluid viscosity associated with boosted lubrication (13) and The M S was received on 13 March 1991 and was accepted for publication on I2 June 1991.

H00891 @ IMechE 1991

surface films (14, 15) may also provide additional benefits. In the design of a cushion form bearing, the surface roughness of the bearing surfaces should be as smooth as possible and the thickness of the lubricating film generated should be as large as possible. The former is clearly controlled by manufacturing tolerances and processes, while the latter is determined by the contact mechanics and lubricating mechanisms, as well as the viscosity of the fluid, the velocity and loading regime. In cushion form bearings, pressure perturbations produced by microelastohydrodynamic lubrication can flatten surface asperities, effectively producing smoother surfaces and hence maintaining the integrity of thinner fluid films. The thickness of the fluid film and deformation of the surface asperities can be controlled by appropriate selection of the following design parameters: elastic modulus of the thin layer (E), thickness of the layer (4, radial clearance (c) or equivalent radius (RJ and the diameter of the femoral head (D). The two objectives of this study were, firstly, to examine the contact and lubrication mechanics of ‘hard‘ bearing surfaces currently used in hip prostheses and to compare them with the natural hip joints and cushion form bearings that have been proposed (1) and secondly, to investigate the effect of variations in the thickness and elastic modulus of the layer, the radial clearance and head diameter on the contact stresses and lubricating film thickness in a design analysis of cushion form bearings. Four parameters have been considered in the analysis: the minimum film thickness generated by elastohydrodynamic lubrication, the squeeze film thickness after one second, the maximum dry contact pressure and the elastic deformation of the surface asperities during microelastohydrodynamic lubrication. 2 THEORY

The model selected for analysis of the cusion form hip prosthesis consisted of a rigid ball (radius R,) rotating

0954-4119/91 $2.00 + .05 Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

Proc lnstn Mech Engrs Vol 205

D DOWSON, J FISHER. 2 M JIN, D D AUGER AND B JOBBINS

60

on a compliant layer (thickness 6) bonded to a rigid substrate. This model approximated the cushion bearing as shown in Fig. 1, where

and the elasticity equations. In the present study the lubricant was assumed to be isoviscous and incompressible (12). For the case of a semi-infinite solid the wellknown Hamrock and Dowson formula (18) was used to predict the film thickness between an equivalent elastic sphere and a rigid plane: 0.65

where

R , = radius of the femoral head (2R, = 0) R2 = radius of the cup (R, + c) c = radial clearance

RX

where the entraining velocity is

The effect of the curvature of the layer was neglected in this model. Linear elasticity theory was applied to predict the layer deformation and contact stresses (16, 17). For the hard prostheses, which do not use thin layers, Hertzian analysis was used to predict the contact characteristics, while the Reynolds equation was adopted to perform the lubrication analysis. 2.1 Contact mechanics

Contact analysis was performed to determine the contact area and stress distribution under maximum load. Methods for solving the full elasticity equations for thin layers have been presented previously (16, 17). For the hard prosthesis, a ball acting on a semi-infinite solid (Hertzian theory) was used (18): Radius of the contact zone or contact half-width

(22)

Maximum pressure po = 1

1 1-v:

E= - 2(,+-)

1-v2

-0.21

(3) (4)

E* where F is the maximum load, El and E 2 represent the elastic moduli of the ball and the cup respectively and E' is the effective elastic modulus of an equivalent elastic sphere near a plane. 2.2 Lubrication analysis 2.2.1 Elastohydrodynamic lubrication

Analysis of the thickness of the lubricating film (h) required simultaneous solution of both the Reynolds

u=-

u1

+ u2 2

where u1 and u2 are sliding velocities of the components, and q is the fluid viscosity. A full analysis of the elastohydrodynamic lubrication of thin layers of compliant bearing materials upon rigid substrates has been developed by Dowson and Yao (19). In this analysis, the plane strain column model simplification adopted earlier for line (cylindrical) contacts (12, 20) was adopted and applied to point (elliptical) conjunctions. The model was thus restricted to compliant materials having a Poisson ratio less than about 0.4, but within this limitation it was found that the minimum film thickness could be represented with good accuracy for circular contacts by the expression -0.19 d 0.37 k i n =1 . 3 7 [ E y . ~ ~ [ L ] (7) RX ER, ER," where d represents the thickness of the compliant layer. Articular cartilage and potential cushion bearing materials such as polyurethane exhibit the Poisson ratios closer to 0.5 than 0.4 and it is therefore necessary to apply equation (7) with care. The procedure adopted here was to evaluate an adjusted value of the effective modulus (E') and a Poisson ratio of 0.4 to yield a dry contact patch from the column model of identical size to that revealed by a full elasticity solution. The adjusted effective modulus used in the film thickness calculation with a Poisson ratio of 0.4 was between 1.5 and 7 times greater than the true effective modulus of the material depending on the a/d ratio for the contact. The film thickness was then evaluated for a constant entraining velocity (u) and maximum load (F) using equation (7), which was derived by Dowson and Yao (19),based on their numerical solutions.

\

/n

I

/

Fig. 1 Sphere on a plane model used for the analysis of a cushion hip joint @ IMechE 1991

Part H : Journal of Engineering in Medicine Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

DESIGN CONSIDERATIONS FOR CUSHION FORM BEARINGS IN ARTIFICIAL HIP JOINTS

the elastic deformation of the asperities (6) was given by

2.2.2 Squeeze film lubrication

Squeeze film action also contributes to the enhancement of the lubricating film thickness in both natural and artificial joints (6, 11). The solution of the squeeze film problem under dynamic loading conditions is complex and requires an excessive amount of computing time. An approximate solution for a rigid sphere on an elastic solid was presented by Higginson (21). The squeeze film time is given by

(10)

where p, is the pressure perturbation and I is the wavelength of the sinusoidal surface. It is clear from equation (10) that for a given pressure perturbation (determined by surface roughness and film thickness) the deformation is inversely proportional to the elastic modulus and directly proportional to the wavelength of the surface roughness. 3 MATERIALS AND METHODS

where

3.1 Analysis of existing joints

t = squeeze film time

h, = starting film thickness h, = squeeze film thickness at time t When the starting film thickness was large, the squeeze time is t=-

61

3nqa4 4Fh:

(9)

Four prosthetic hip joints were compared to a natural hip joint. The McKee-Farrar (metal on metal), the Muller (32 mm femoral head) and the Charnley (22 mm femoral head) (both metal on UHMWPE) were studied. In addition a cushion form prosthesis of the design proposed by Unsworth (1, 11) was analysed. Details of the prosthesis considered are given in Table 1. A maximum load of 2.5 kN (22) and lubricant viscosity of 0.001 Pa s were used in the analysis. Analysis was performed for an entraining velocity (u) of 0.075 m/s.

2.2.3 Microelastohydrodynamic lubricution This mechanism has already been shown to be important in natural joints (5, 12) when the mean thickness of the fluid film is similar to the size of the asperities. Pressure perturbations were produced in the fluid films due to flow of the lubricating fluid over the surface asperities. In the case of low elastic modulus materials, the pressure perturbations cause deformation or substantial flattening of the surface asperities, so helping to maintain a continuous film of lubricant. The efficiency of microelastohydrodynamic action is primarily dependent upon two factors: (a) the size of the pressure perturbation generated and (b) the ease of deformation of the asperities. The former is influenced by the film thickness and the characteristics of the surface roughness, and in general the larger the surface roughness and/or smaller the film thickness, the larger the pressure perturbations. In practice the pressure perturbations must be limited by the normal contact pressure but it can readily be shown that they are normally a tiny fraction of the ‘dry’ contact pressures for compliant materials (5). For a surface roughness modelled as a sinusoidal form,

3.2 Analysis of the design parameters in cushion form bearings

In the design of a cushion form hip prosthesis four parameters were considered in order to alter the contact and lubrication conditions. These were the femoral head layer thickness (4, elastic modulus (E) and diameter (D), equivalent radius ( R J , which is derived from the radial clearance (c) and head diameter. In this analysis the head diameter was fixed at 32 mm, the maximum size currently used. This dimension was constrained by the overall size of the natural acetabular cup. Polyurethane was selected as the material for investigation and a range of elastic moduli from 5 to 100 MPa was studied. A Poisson ratio of 0.499 was used with layer thickness of 1-3 mm. For practical reasons the minimum radial clearance was restricted to 0.05 mm, and a maximum value of 1 mm was used in the analysis. This gave a range in equivalent radii of 0.27-5.0 m. The radius of the contact zone or contact half-width (a) was also constrained within the dimensions of the cup, with a maximum value of 16 mm applied to the analysis. At

Table 1 SDecification of the existine ioints analvsed Natural synovial joint

McKee-Farrar

Muller

Charnley

Cushion bearing

Material combination

Cartilage Cartilage

CMr-Mo Cdr-Mo

UHMWPE Cdr-Mo

UHMWPE 316L

Polyurethane Metal

R , (mm)

23 0.5415

16 0.5 0.528 -

16 0.25 1.04

11 0.125 0.979

-

-

16 0.25 1.04 2

2.1 x 105 2.1 x 105 0.310.3

1.4 x 103 2.1 1 0 5 0.410.3

1.4 x 103 2.0 x 105 0.410.3

(mm) R, (m)

c

d (mm) E (MPa) V

1

2 16 16 0.510.35

Current joint replacement

@ IMechE 1991

20 105 0.510.3 Proc Instn Mech Engrs Vol 205

Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

D DOWSON, J FISHER, Z M JIN, D D AUGER AND B JOBBINS

62

higher values the model applied to a sphere on a plane becomes less accurate. In addition, practical constraints of edge effects, which may restrict the convergent entry zone that is necessary for elastohydrodynamic lubrication, may become significant. Initially the effect of varying a single parameter was studied. In the second part of the analysis the contact half-width was fixed by adjusting two of the parameters under investigation (E, R, or d) simultaneously. 4 RESULTS

4.1 Analysis of existing prostheses

Table 2 shows the results of the analysis of existing prostheses for the contact half-width (a),minimum film thickness (hmi,,), maximum contact pressure (po) and squeeze film thickness (h,) at one second. The analysis showed a larger film thickness and increased contact half-width in the natural joint and cushion form bearing compared to the relatively hard bearings currently used. However, it is important to note that the film thicknesses (hminand h,) were primarily dependent on contact half-width. If the contact half-width of the Muller prosthesis was increased to 15 mm, by reducing the radial clearance to 0.08 111111, the minimum film thickness (hmin) would increase to 0.17 pm and the squeeze film thickness (h,) increased to 0.22 pm. This was close to the value for the bearings with the low elastic modulus layer. However, the low elastic modulus material of the cushion form bearing provided better conditions for microelastohydrodynamic lubrication than the UHMWPE cup. Equation (10) shows that the deformation of the asperities was inversely proportional to the elastic modulus of the materials. For a pressure perturbation of 1 MPa and assuming a sinusoidal surface form of wavelength 20 pm, the deformation of the asperities was 0.25 pm in the cushion bearing with E of 20 MPa and 0.034 pm in the UHMWPE cup. For a lubricating film thickness of 0.22 jim, the deformation of the asperities would be insignificant in the UHMWPE cup, but would play an important role in reducing the effective surface roughness and maintaining the fluid film in the cushion bearing.

4.2 Analysis of cushion form bearings The variation of contact half-width with radial clearance, elastic modulus and layer thickness predicted by

the full elasticity solution is shown in Fig. 2a and b. Normal contact stresses reduced as the area of contact increased (as E decreased, d increased or c decreased). However, when the contact width was fixed by simultaneously altering two of the parameters, only small changes in the stress distribution were found. Figure 3 shows the normal stress distribution for contact halfwidths of 8 and 16 mm and layer thicknesses of 1-3 mm. For each layer thickness the radial clearance (c) was adjusted to maintain a constant contact width, for material with an elastic modulus of 20 MPa. Similar curves were found when the layer thickness was reduced and the contact half-width was fixed by reducing the modulus. Simultaneous changes in E and R, at a fixed contact width did not alter the pressure distribution (17). For any particular contact width, peak normal stresses increased by a small amount for a reduced layer thickness. The minimum film thickness (hmin) derived from elastohydrodynamic theory was plotted against radial clearance (c) in Fig. 4a for materials with different elastic modulus and in Fig. 4b for different layer thickness (d). The film thickness increased with reduced radial clearance and elastic modulus and increased layer thickness. In each case film thickness increased as the contact area increased (compare Figs 4 and 1). Figure 5a and b shows similar characteristics for the squeeze film thickness at one second with an increase in film thickness with reduced radial clearance, reduced elastic modulus and increased layer thickness. As predicted by equation (9), squeeze film thickness is directly proportional to the contact half-width ( u ) ~It. is clear from Figs 2, 4 and 5 and equation (9) that the contact width is the predominant factor controlling the film thickness generated by elastohydrodynamic and squeeze film lubrication. A particular contact width can be achieved by appropriate selection of the variables E, d and c. Figures 6 and 7 show the film thickness calculated from equations (6) and (9) as a function of contact half-width. The relationship for squeeze film thickness is independent of the choice of the combinations of variables E , d and c. However, this is not the case for the elastohydrodynamic film thickness (Fig. 7), where at any contact halfwidth the film thickness is slightly higher when the modulus is higher or the layer thickness is smaller. This corresponds to a reduced radial clearance in each case. The variation in film thickness associated with the selection of the parameters at each specified contact width is

Table 2 Analysis of existing prostheses Natural synovial joint

Material combination E (MPa) a (mm) h,i" elm) Pmax (MPa) h, arm)

Cartilage Cartilage 16 16 15.5 0.27 7.85 0.23

Hard prostheses current joint replacement McKee-Farrar

Muller

Charnley

Cushion bearing

C-Cr-Mo Cdr-Mo

UHMWPE Cdr-Mo

UHMWPE 316L

Polyurethane Metal

1.4 103 2.1 x 105 10.56 0.075 10.70

1.4 x 103

20 -

2.0 x 105 10.35 0.072

105 15.0 0.26 8.2 0.22

2.1 2.1

lo5 105 2.05

0.007 284.04 0.004

0.111

11.14 0.10

@ IMechE 1991

Part H: Journal of Engineering in Medicine Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

DESIGN CONSIDERATIONS FOR CUSHION FORM BEARINGS IN ARTIFICIAL HIP JOINTS

63

[ 4

4

t E = 5MPa V E = 10MPa E = 20MPa x E = 50MPa 0 E = 100 MPa

A

+

00

0.5

I .o Radial clearance mm

(a) For different elastic rnodulii (layer thickness 2 mm, load 2.5kN)

A d = 1.0mm V d = 1.5 mm d = 2.0 mm x d=2.5mm 0 d = 3.0mm

+

0

0

0.5 Radial clearance mm

(b) For different layer thickness (elastic modulus 20 MPa, load 2.5 kN)

Fig. 2 Contact half-widths plotted against radial clearances

a much smaller effect compared to the variation found with contact half-width. It is clear from equation (10) that the deformation of the asperities during microelastohydrodynamic lubrication is primarily dependent on the modulus of the material and the wavelength of the asperities. Reduction of the elastic modulus increases the deformation of the asperities, producing a smoother surface. However, it was only necessary to select a sufficiently low modulus to produce flattening of the asperities, as further reduction in the modulus produced no additional benefit. Figure 8 shows an example of asperity deforma-

tion as a function of modulus for a pressure perturbation of 1 MPa for a sinusoidal surface with a wavelength of 20,um. For a given surface roughness and film thickness the appropriate elastic modulus can be selected for the graph to ensure maximum benefit from microelastohydrodynamic lubrication. For surface roughness with larger wavelengths, greater degrees of flattening can be achieved. 5 DISCUSSION

The concept of cushion form bearings has been introduced in an attempt to design artificial joints in which Proc lnstn Mech Engrs V O 205 ~

@ IMechE 1991 Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

D DOWSON, J FISHER, Z M JIN, D D AUGER AND B JOBBINS

64

1

2

3

///

0

- 6 - 4 - 2

-8

2

4

6

8

r

mm (a) Of 8 mm width

-1s

-10 r

mm (b) Of 16 mrn width

Fig. 3

Normal surface stress distributions for contact halfwidths (nominal load 2.5 kN, E = 20 MPa) for vari-

able layer thicknesses the articulating surfaces are separated by a continuous film of lubricant. This has the advantage of reducing both friction and the generation of wear particles. This analysis was undertaken to investigate the effect of prosthesis geometry (D,d and c) and material modulus ( E ) on the contact mechanics and lubricating film thickness generated by elastohydrodynamic and squeeze film lubrication. Elastohydrodynamic film thickness was calculated for maximum load and maximum velocity conditions which occur at one point in the cycle. The squeeze film analysis used assumes that there was a large film thickness between the bearing surfaces when the maximum load was applied, but this was not a restrictive assumption. In the walking cycle the force across the joints in the lower limb drops to a very low level during the swing phase and the direction of the force vector moves considerably during the cycle. It is therefore not unreasonable to assume a large starting film thickness for the squeeze action just prior to heel strike (23).The film thickness generated should be at least three times the r.m.s. surface roughness of the asperities on the surface to ensure a continuous film of lubricant. Microelastohydrodynamic lubrication (5), which has a significant effect in protecting the surfaces of lower modulus materials, can also help to maintain the fluid film by effectively flattening the surface asperities.

The analysis carried out on existing clinical ‘hard’ bearings and cushion bearings, which have been proposed by other workers (l), showed that there were some benefits in using cushion bearings. The film thicknesses predicted due to elastohydrodynamic and squeeze film action in cushion bearings are similar to those predicted for the natural synovial hip joint for a similar fluid viscosity. Both of these yield much larger films than existing hard bearings. It is clear from Table 2 that the film thicknesses generated are primarily dependent on the contact areas that can be achieved. The lower contact half-widths in the Charnley and Muller prostheses are associated with lower predicted film thicknesses. If the Muller prosthesis were redesigned and had a smaller radial clearance (0.08 mm) to give a larger contact half-width (15 mm), the predicted film thickness would be similar to that of the cushion bearing. This might indicate that provided the geometry and/or contact areas were identical, there would be little benefit in using a lower modulus material. However, the lower elastic modulus layer in the cushion bearing has four distinct advantages. Firstly, microelastohydrodynamic effects and flattening of asperities will be much greater in low elastic modulus materials than in UHMWPE. Secondly, the ease with which dimples are formed in the soft layer, which was not taken into account in the application of the squeeze film equation, may help to trap lubricant and further increase the squeeze film times. Thirdly, the soft layer can deform to accommodate ‘out of roundness’ of components which might otherwise produce high localized pressures in harder bearing surfaces. Finally, the contact stress distribution in a cushion bearing is markedly different to that in a hard bearing which may be approximated as a Hertzian contact. In the UHMWPE cup of a hard bearing, the maximum shear stresses occur just below the articulating surface in the centre of the contact (24). This may be an important factor in fatigue failure and excessive wear of the surface of the UHMWPE component. This stress distribution is modified in the cushion form bearing, with reduced shear stress in the centre of the contact (17). The cushion bearing proposed goes some way to reproducing the lubrication mechanisms found in the natural synovial joint. Other lubrication mechanisms which are deemed to be important in the natural joint, such as boosted lubrication (13) and a higher fluid viscosity (14) are less likely to benefit a cushion bearing manufactured with non-porous polyurethane. The design analysis carried out on the geometrical factors and material properties in cushion bearings showed that the film thickness generated could be optimized by maximizing the area of the contact. The contact area should be optimized within the constraint of the cup by appropriate selection of E, d and c. The film thickness is not particularly sensitive to changes in geometry at any fixed contact width. A contact width of 16 mm for a 32 mm diameter head allowed a substantial convergent entry zone to be maintained at the edge of the contact. This is essential for satisfactory fluid-film lubrication. The lubrication analysis considered a constant velocity and did not take into account reversals of velocity. There is some concern that this effect may become important when the stroke length is of similar proportions to the contact zone. This may suggest that 0 IMechE 1991

Part H : Journal of Engineering in Medicine Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

65

DESIGN CONSIDERATIONS FOR CUSHION FORM BEARINGS IN ARTIFICIAL HIP JOINTS

0.6

-

0.5 -

A

5MPa

v E=

10MPa E = 20MPa x E = 50MPa E = 100 MPa

+

-

0.4

E=

5 0.3 0.2 -

-

0.1

0 0

0.6

0.5

1

t

I

t

I

1

t

1

I

I

1 .o

0.5

fa

A d = I.Omm vd=1.5mm d = 2 . 0 mm x d = 2.5mm d = 3.0mrn

+

I&

0.31

0.4

0.2

0

1

I

1

I

I

I

I

I

I

0.5

0

1

1 .o

Radial clearance rnm

(b) For different layer thicknesses (elastic modulus 2 0 MPa)

Fig. 4 Minimum film thicknesses plotted against radial clearances

the benefits of using very large contact areas to achieve maximum film thickness may not be fully realized in practice. Current experimental work should enable the importance of stroke length to be understood. The elastic modulus of the compliant layer should be low enough to produce effective microelastohydrodynamic lubrication and flattening of asperities. However, there is little benefit to be achieved by further reduction in the elastic modulus (Fig. 7). Consideration of the contact mechanics also showed that it was important not to use a material with a very

low elastic modulus. Both the normal and shear stress distributions are primarily dependent on contact area (17). Reduction in elastic modulus would produce an increase in strain and an increased likelihood of fatigue failure. The results of this lubrication analysis were consistent with the initial experimental findings of Unsworth (l), who suggested that there was an optimal combination of layer thickness and elastic modulus for the lubrication of cushion bearings. Table 3 gives the specification of a design configuration for a cushion bearing with a Proc Instn Mech Engrs Vol 205

@ IMechE 1991 Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

66

-

0.6

E = 5MPa V E = 10MPa E = 20 MPa X E = 50MPa A

-

0.5

+

0.4 5

0.3

-

0.2

-

0 E = 100MPa

0.1 -

0

I

I

1

1

I

I

1

1

I

1

1.O

0.5

0

Radial clearance mm

(a) For different elastic moduli (layer thickness 2 mm) 0.6

h 0

1

A d = I.Omm

V d d x d d

+

I

I

I

1

1

= 1.5mm

2.0mm 2.5 mm = 3.0 mm = =

I

I

I

I

I .o

0.5

0

Radial clearance mm

(b) For different layer thicknesses

Fig. 5 Squeeze film thicknesses at one second plotted against radial clearances

large contact width, high predicted film thickness and low contact stresses, and effective microelastohydrodynamic lubrication. A number of different designs of cushion joints based upon this analysis are Table 3 Specification of a cushion bearing with a large contact area ~

Diameter of femoral head Elastic modulus Layer thickness Equivalent radius Contact half-width

D E

d R, a

32 mm 20 M P a 1-2 mm 1.5-1 m 16 mm

currently being investigated in joint simulators and their performance will be reported in subsequent papers. Preliminary results with both the hip and knee prostheses indicate improved lubrication with cushion bearings. 6 CONCLUSIONS

1. Hip joint replacements based upon the cushion bearing concept enjoy vastly improved lubrication characteristics compared with existing forms of implants.

Part H : Journal of Engineering in Medicine

@ IMechE 1991 Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

DESIGN CONSIDERATIONS FOR CUSHION FORM BEARINGS IN ARTIFICIAL HIP JOINTS

0’5

67

2. Selection of a low elastic modulus material in which the surface asperities will deform and microelastohydrodynamic lubrication will occur is an important factor in the performance of such implants. 3. The approximate elastohydrodynamic lubrication analysis adopted in this study indicates that larger fluid film thicknesses will be achieved with larger contact areas. Practical limitations of this have still to be determined. 4. The elastic modulus of the material used should not be lower than necessary to produce effective microelastohydrodynamic lubrication, as a further reduction in modulus will produce increased shear strains.

F

L--

v) 0-

n

8/

00

1 .o

0.5

Contact half-width/femoralhead radius

Fig. 6

Squeeze film thickness at one second as a function of contact half-width/femoral head radius (femoral head radius = 16 mm, load = 2.5 kN)

0.5

REFERENCES

-

E=

5 MPa. d = 3 rnrn

0.3 -

E,

0.2 0.1 -

Fig. 7

This work was supported by the Science and Engineering Research Council and the Arthritis and Rheumatism Council.

-

+ E = 100 MPa, d = I mm 0.4

ACKNOWLEDGEMENTS

I 1

Minimum film thickness plotted against contact halfwidth/femoral head radius (femoral head radius = 16 mm, load = 2.5 kN)

5r

1 Unsworth, A., Pearcy, M. J., White, E. F. T. and White, G. Frictional properties of artificial hip joints. Enyny in Medicine, 1988, 17, 101-104. 2 Auger, D. D., Medley, J. B., Fisher, J. and Dowson, D. A preliminary investigation of cushion form bearings in artificial joints. In Mechanics of coatings (Eds D. Dowson, C. M. Taylor and M. Godet), 1990, pp. 264269 (Elsevier, Amsterdam). 3 Oka, M., Noguchi, T., Kumar, P., Ikeuchi, K., Yamamuro, T., Hyon, S. H. and Ikado, Y. Development of an artificial articular cartilage. Clin. Muter., 1990, 6, 361-381. 4 Medley, J. B., Pilliar, R. M., Wong, E. W. and Shang, A. B. Hydrophyllic polyurethane elastomers for hemiarthroplasty. Enyny in Medicine, 1980,9, 59-68. 5 Dowson, D. and Jin, Z. M. Micro elastohydrodynamic action in the lubrication of synovial joints. Engny in Medicine, 1986, 15, 63-65. 6 Higginson, G. R. Elastohydrodynamic lubrication in human joints. Enyny in Medicine, 1978,7, 35-41. 7 Unsworth, A. The effects of lubrication in hip joint prostheses. Phys. Med. Biol., 1978,23, 253-268. 8 Dowson, D. Are our joint replacement materials adequate? Proc. Instn Mech. Engrs, l989,203H, 1-5. 9 Atkinson, J. R., Dowson, D., Issac, G. H. and Wrohlewski, B. M. Laboratory wear tests and clinical observations of the penetration of femoral heads into acetabular cups in total hip joints. Wear, 1985,104,217-224. 10 Clarke, I. C. Wear of artificial joint materials IV. Engny in Medicine, 1981, 10, 189-198. 11 Unsworth, A., Pearcy, M. J., White, E. F. T. and White, G. Soft layer lubrication of artificial hip joints. Friction lubrication and wear fifty years on. Proc. Instn Mech. Engrs, 1987,20lH, 715-724. 12 Dowson, D. and Jin, Z. M. An analysis of micro elastohydrodynamic lubrication on synovial joints considering cyclic loading and enhancing velocities. In Fluid film lubrication (Ed. D. Dowson), 1987, pp. 375-386 (Elsevier, Amsterdam). 13 Walker, P. S., Dowson, D., Longfield, M. D. and Wright, V. Boosted lubrication in synovial joints by fluid entrapment and enrichment. Ann. Rheum. Dis., 1968,27,512-516. 14 Unsworth, A., Dowson, D. and Wright, V. Some new evidence of human joint lubrication. Ann. Rheum. Dis., 1975,34,277-285. 15 Dowson, D. Biomechanics of natural and replacement synovial joints. In Biomechanics of diarthrodial joints (Eds V. C . Mow and S. L. Y.Woo), 1990, pp. 303-345 (Springer Verlag, New York). 16 O’Carrol, S., Jin, Z. M., Dowson, D., Fisher, J. and Jobbins, B. Determination of contact area in cushion form bearings for artificial hip joints. J . Engny Medicine, l990,204H, 217-223. 17 Dowson, D., Fisher, J., Johbins, B., O’Carrol, S. and Jin, Z. M. Contact mechanics of low elastic modulus layers in cushion form bearings for artificial hip joints. Proceedings of 7th Meeting of the European Society of Biomechanics, Aarhus, 1990, paper C.19.

P

00

10

100

Elastic deformation vm

Fig. 8 Asperity deformation as a function of elastic modulus for a wavelength of 20 pm and pressure perturbation of 1 MPa @

Proc lnstn Mech Engrs Vol 205

IMechE 1991 Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

68

D DOWSON, J FISHER, 2 M JIN, D D AUGER AND B JOBBINS

18 Hsmrock, B. J. and Dowson, D. Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. J . Lubric. Technol., 1978, 100,236245. 19 Dowson, D. and Yno, J. Q. A study of the deformation and lubrication of synovial joints. Proc. Instn Mech. Engrs, Part H, 1991 (to be published) . 20 Medley, J. B., Dowson, D. and Wright, V. Transient elastohydrodynamic lubrication models for the human ankle joint. Engng Medicine, 1984, 13, 127-151. 21 Higginson, G. R. Squeeze films between compliant solids. Wear, 1978,46,387-395.

22 Morrison, J. B. and Proctor, P. Loading of orthopaedic implants. In Progress in bioengineering (Ed. J. P. Paul), 1989, pp. 96103 (Adam Hilger, Bristol). 23 Gore, T. A., Higginson, G. R. and Kornberg, R. E. Some evidence of squeeze film lubrication in hip prostheses. Engng in Medicine, 1981,10,89-95. 24 Johnson, K. L. Contacf mechanics, 1985, pp. 8 4 1 1 0 (Cambridge University Press).

Part H : Journal of Engineering in Medicine

@ IMechE 1991 Downloaded from pih.sagepub.com at UNIV CALIFORNIA SANTA BARBARA on August 27, 2015

Design considerations for cushion form bearings in artificial hip joints.

Lubrication mechanisms and contact mechanics have been analysed in a new generation of 'cushion form' bearings for artificial hip joints, which compri...
785KB Sizes 0 Downloads 0 Views