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Research Papers: Biotribology

Nonsphericity of Bearing Geometry and Lubrication in Hip Joint Implants

[+] Author and Article Information
F. C. Wang1

School of Mechanical Engineering, Wuhan University of Science and Technology, Wuhan 430081, Chinaf.c.wang@wust.edu.cn

S. X. Zhao

School of Mechanical Engineering, Wuhan University of Science and Technology, Wuhan 430081, China

A. Félix Quiñonez

IJsselstein, 3401 LL, The Netherlands

H. Xu, X. S. Mei

School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Z. M. Jin

School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK

1

Corresponding author.

J. Tribol 131(3), 031201 (May 26, 2009) (11 pages) doi:10.1115/1.3118782 History: Received March 02, 2007; Revised March 12, 2009; Published May 26, 2009

A general elastohydrodynamic lubrication model was developed to consider the nonsphericity of the bearing geometry in hip joint implants, both under the steady and transient conditions. The articulation between the femoral head and the acetabular cup was represented by a nominal ball-in-socket configuration. The nonsphericity was introduced on the acetabular cup and femoral head bearing surfaces in the form of an ellipsoidal surface represented by variations of the radii of curvature given by the three semi-axis lengths of the ellipsoid with regard to a nominal spherical surface. An appropriate spherical coordinate system and solution domain discretization were used to facilitate the numerical simulations. Both the equivalent discrete spherical convolution model and the corresponding spherical fast Fourier transform technique were used to evaluate the elastic deformation of either the spherical or nonspherical bearing surfaces. A fixed-tracked method was also developed to simulate the complex morphology introduced by moving the interface of the nonspherical bearing surfaces. The general methodology for the nonspherical bearing was first applied to investigate the steady-state elastohydrodynamic lubrication of an ellipsoidal cup articulating against a spherical head in a typical metal-on-metal hip joint implant. Subsequently, the problem of an ellipsoidal head articulating against a spherical cup was considered under the transient conditions. The significance of nonsphericity of bearing geometry in hip joint implants due to manufacturing, designing, and wear was discussed. The results obtained showed that the effect of a nonspherical bearing surface geometry on elastohydrodynamic lubrication was dependent on the orientation, the magnitude, and the deviation direction of the nonsphericity. A well-controlled nonsphericity was seen to be beneficial for improving the lubrication.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A basic ball-in-socket configuration for a hip joint implant with the cup positioned horizontally under a vertical load with a flexion-extension motion around the x-axis

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Figure 2

Spherical coordinates with the z-axis passing through the poles and three semi-axis lengths of an ellipsoidal bearing surface

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Figure 3

Schematic diagram for nonspherical geometry and mesh-grids with the z-axis passing through the poles of the spherical coordinates: (a) with the variations of semi-axes δa and δb along x and y; (b) with the variations of semi-axes δa and δc along x and z

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Figure 4

The variations of the predicted minimum film thickness versus the nonsphericity of cup with an ellipsoidal bearing surface δ from −6 μm to +6 μm in different orientations

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Figure 5

The variations of the predicted central film thickness versus the nonsphericity of cup with an ellipsoidal bearing surface δ from −6 μm to +6 μm in different orientations

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Figure 6

The variations of the predicted maximum film pressure versus the nonsphericity of cup with an ellipsoidal bearing surface δ from −6 μm to +6 μm in different orientations

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Figure 7

Comparison of cross-sectional film thickness profiles through the center of cup with different nonsphericities δa along the x-axis: (a) in φ direction and (b) in θ direction

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Figure 8

Comparison of cross-sectional film thickness profiles through the center of cup with different nonsphericities δb along the y-axis: (a) in φ direction and (b) in θ direction

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Figure 9

Comparison of cross-sectional film thickness profiles through the center of cup with different nonsphericities δc along the z-axis: (a) in φ direction and (b) in θ direction

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Figure 10

Comparison of cross-sectional film pressure profiles through the center of cup with different nonsphericities δa along the x-axis: (a) in φ direction and (b) in θ direction

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Figure 11

Comparison of cross-sectional film pressure profiles through the center of cup with the different nonsphericities δb along y-axis: (a) in φ direction and (b) in θ direction

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Figure 12

Comparison of cross-sectional film pressure profiles through the center of cup with different nonsphericities δc along the x -axis: (a) in φ direction and (b) in θ direction

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Figure 13

Results for an ellipsoidal head bearing surface with δb=−6 μm articulating against a spherical cup under transient conditions with the motion period of T=0.75 s: (a) minimum film thickness, (b) central film thickness, and (c) maximum film pressure

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Figure 14

Results for an ellipsoidal head bearing surface with δb=+6 μm articulating against a spherical bearing surface for cup under transient conditions with the motion period of T=0.75 s: (a) minimum film thickness, (b) central film thickness, and (c) maximum film pressure

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