Lubricants and Lubrication / D. Dowson et al. (Editors) 0 1995 Elsevier Science B.V. All rights reserved.
Analysis of artificial hip joints as spherical bearings M. Kothari and J. F. Booker and D. L. Bartel School of Mechanical and Aerospace Engineering Cornell University, Ithaca, New York, USA 14853 Artificial hip joints commonly pair a metal ball and a plastic cup; however the problem of polyethylene wear debris has sparked renewed interest in metal-on-metal joints. For lubrication studies such joints can be modeled as spherical bearings. A finite element code has been developed to carry out modal elastohydrodynamic lubrication analysis of spherical bearings. An operating environment which accurately represents that seen in the human hip was determined. Lubricant film thicknesses were predicted and compared for different designs. The lubrication analysis indicates elastohydrodynamic lubrication analysis may be necessary. It also suggests that manufacturing tolerances may be important for the success or failure of the metal-on-metal hip replacements. 1. INTRODUCTION Human joints provide the basis of movement by allowing bones to articulate on one another. Joints allow a combination of stability and mobility, the proportions of which vary, depending on the position and function. Joint function may, however, be compromised by trauma, disease or abnormal usage. The result is pain and loss of mobility which can lead to permanent deformity around the affected joint. Treatments can range from the relief of pain using analgesics to joint arthroplasty. Arthroplasty implies the creation of a new joint by replacing one or both of the joint surfaces. Tribological characteristics of artificial joints can significantly affect the performance and life of a prosthesis. With the average age of prospective recipients of artificial hip prosthesis dropping, it is becoming necessary to improve present designs of the hip joint so that the average life of a prosthesis increases. The long term failure has been attributed, among other reasons, to the body’s reaction to wear debris [l-31. Thus improving the tribological characteristics of joint could increase the life of the prosthesis.
At present, the artificial hip joint commonly consists of a metal ball articulating with a polyethylene cup. Two different approaches are being studied to reduce polyethylene wear debris. The first one consists of the creation of a soft porous layer on the cup surface in an attempt to mimic the cartilage found in a natural hip joint [4-51.The second approach consists of getting rid of the plastic itself in favor of metal-on-metal articulation . This concept is not new; indeed, the McKeeFarrar metal-on-metal total hip prosthesis designed in the mid sixties was used extensively. The McKee-Farrar metal-on-metal hip prosthesis exhibited a high incidence of early failure due to loosening of the acetabular component. The short-term failure has been attributed to the high frictional torque generated as a result of equatorial seizure. Proper design and tolerancing of the ball and the cup could prevent such failures and could possibly lead to fhe generation of fluid film lubrication. It is essential to determine the longterm effects of the design and to determine the criteria that should be optimized to ensure the success of the design. Our present work utilizes a realistic load environment for the bearing. It extends the design space to include ellipsoidal cups.
94 Lubrication analysis is carried out and the predicted film properties are studied. Finally, different design criteria that can affect longterm functionality of metal-on-metal prostheses are discussed. 2. ANALYSIS
A finite element code was developed to carry out elastohydrodynamic lubrication analysis of spherical bearings following a modal approach developed previously ; it uses the Murty algorithm to determine cavitation regions. Triangular, linear finite elements were used to nodel the lubricant iilm. The analysis is formulated in 3-dimensional Cartesian coordinates, thereby avoiding singularities that arise with spheiical coordinates .Figure 1 is an exaggerated view of the resulting mesh showing the triangular finite elements and the faceted nature of the mesh. Figure 2 is a view of the actual mesh used for the studies.
Figure 1.Triangular finite elements Since analytical solutions for spherical bearings are generally unavailable (except in very specialized cases, such as polar axisymmetric squeeze), previously published numerical results were used to validate the present code [ 8 ] .
Figure 2 : Fluid film mesh Although the code is capable of EHL analysis, only rigid body modes were considered in this study, thus reducing the lubrication regime to one of hydrodynamic lubrira tim. 3. PROBLEM DESCRIPTION
Normally both the femoral head and the acetabular cup in an hip prosthesis are designed to be spherical in shape. For polyethylene acetabular cups, it has been shown that conforming spherical geometry of the ball-cup system gives the lowest contact stresses ; however, this result is not necessarily true for metal-on-metal hip joints. Previous studies conducted for cylindrical bearings with elliptical journal and sleeve suggest that the "optimum" hip joint design for lubrication performance is not spherical [ 101; moreover, experimental measurements show that the ball and cup often exhibit out-of roundness, and the degree of the out-ofroundness measured could be sufficient to have an effect on the lubrication process [ll]. In the present analysis, the cup is assumed to be ellipsoidal while the ball is perfectly spherical. The geometry of the ballcup system and the loading environment are defined below.
95 Table 1 Geometry Component
Semi-minor axis Semi-major axis
c = a -r
Figure 3 is a representation of the ballcup system. The inner surface of the cup is ellipsoidal. Table 1 lists the various parameters that define the bearing geometry.
Newtonian ; however for the range of shear rates seen in the hip joint, it can be assumed to have a constant viscosity. The viscosity also varies depending on the disease affecting the patient . Therefore, for the design of the nrosthesis, ihe lubrication analysis should encompass a range of synovial fluid properties 3.3. Duty Cycle
Figure 3. Geometrical parameters 3.2.Material Properties Synovial fluid acts a lubricant in the hip joint. The reported values of viscosity of SYnovial fluid vary widely) ranging from 0.l Pa-s to 1Pa-s . SynOVial Fluid is non-
The joint can experience a variety of operating conditions depending on the motion of the body. Walking is one of the predominant motion patterns that the joint experiences. A person typically takes over a million steps a year. Walking is currently used as one of the critical motions for the design of hip implants. This is especially true while considering longterm effects such as wear debris generation, where it predominates over other forms of motion The load and angular velocity histories of the ball Li the cup in the human body are difficult to determine; they vary from individual to individual and change with the position of implant in the human body. The
96 load and time histories are obtained from gait studies . The force and angular velocity vectors are expressed to the cup coordinate frame which is shown in Figure 4. The cup coordinate frame is determined by positioning the cup as per recommended surgical practice .The force and the angular velocity histories are shown in Figure 5.
Figure 4. Cup coordinate system
Figure 5. Load cycle
The results are for a bearing with a ball radius of 20 mm and a viscosity of 1 Pa-sec. Figure 7 shows the variation of minimum film thickness with time for a design with a hemispherical cup ( E = 1.0 ). The solution becomes essentially periodic in roughly seven load cycles. Figure 8 shows the variation of minimum film thickness with time for a design with an ellipsoidal cup (E = 1.6 ). Figure 9 shows how the variation of cyclical minimum film thickness with radial clearance with different cup designs.
Figure 6 . Angular velocity cycle
Figure 7. Variation of minimum film thickness with time ( E = 1.0)
Fig 9. Cyclical Minimum Film Thickness Vs Equatorial Clearance 5. DISCUSSION
Figure 7 and Figure 8 show that the minimum film thickness is of the order of 10 micrometers. Figure 9 shows that small clearances are required in order to maintain a fluid film. In addition, small changes in out of roundness of the cup have large effects on the predicted fluid film properties. The film thicknesses are of the order of the magnitude of elastic deformation of the cup surface. This suggests that there is a need to carry out elastohydrodynamic lubrication analysis.
! ? 0
0 ._ 5
c l l
Figure 8. Variation of minimum film thickness with time ( E = 1.6)
The effects of out-of roundness can be quite significant. Figure 8 shows that the minimum film thickness can be increased over that obtained using a spherical bearing. Thus, non-spherical geometry open up an large set of design possibilities. It is critical to identify the mechanics influencing the long-term success of a metalon-metal prosthesis. The causes for long-term
98 failure of previous metal-on-metal implants have not yet been established. Two parameters that could directly be linked to failure are: Maximum pressure generated during the gait cycle Wear generated during the gait cycle Metallic debris is toxic, and it is known that it can cause a reaction which could lead to the loosening of the prosthesis. Minimization of wear debris generation could be important for long-term success. A wear model will have to be determined which will link the contact stress with debris generation. In particular, maximum contact stress is linked to wear generation. Higher contact stresses give rise to higher wear rates in bearings. Therefore, trying to minimize the maximum pressure generated may result in minimal wear debris generation. It is important to realize that lubrication analysis may only be the first step in this design process. Analyses of retrieved implants seem to indicate that loosening of the cups, and hence failure of the prosthesis, oflen occurs because of failure of the bond between the bone cement and the bone. Solid finite element analysis of the bone-prosthesis system may be required with surface loading conditions determined by the lubrication analysis. ACKNOWLEDGEMENT This work was supported by the Hospital for Special Surgery, New York, NY, USA. REFERENCES 1. J. M. Mirra, R. A. Marder, and I-:. A. Amstutz, Clinical Orthopaedics 170:175, 1982 2. B. M. Wroblewski, J. Bone Joint Surg. 618:498,1979 3. A. Pizzoferrato, Biomater. Med. Devices Artif. Organs 7257, 1979
4. L. Caravia, D. Dowson, P. H. Corkhill and B. J. Tighe, Proc. 20th Leeds-Lyon Symposium on Tribology, 'Thin Films in Lubrication', Elsevier, Amsterdam, 1993, 529 5. J. M. Blarney, Proc. 20th Leeds-Lyon Symposium on Tribology, 'Thin Films in Lubrication', Elsevier, Amsterdam, 1993, 535 6 G. McKee, Total Hip Replacement, Publishing, 1971,47 7. K. P. Oh and P. K. Goenka, ASMEJournalof Tribology, 107389,1985 8. P. K. Goenka, ASME, Journal of Lubrication Technology, 104:478,1982 9. D. L. Bartel, V. L. Bicknell and T. M. Wright, J. of Bone and Jnt. Surg. 68A:1041, 1986 10. P. K. Goenka, PhD. dissertation, Cornell University, 1982 11. M. Kothari, Unpubished retrieval analysis study 12. P. S. Walker, " Human joints and their artificial replacements ",Thomas, 1977 13. J. P. Paul, PhD. dissertation, University of Glasgow, 1967