Sensitivity Analysis of Wear on Metal-On-Metal Bearing Couples via Verification of Numeric and Analytic Methods

Abstract

Wear mechanism is important since it leads to revisions in Total Hip Replacement (THR) surgeries. Contact pressure plays an important role in wear mechanisms and needs to be investigated in detail to obtain more accurate wear predictions to understand the wear performance of the implant in the design stage. This study proposes a methodology for verification of contact pressure and pressure distribution via numeric and analytic methods to be used in wear calculations. Based on Hertz’s contact theory, the contact pressure and the contact area ae calculated in the analytical method. The results are compared to the numeric method’s results obtained from the finite element method. The linear and volumetric wear rates of bearing couples’ surfaces were estimated by Archard’s wear equation. The effect of design parameters on pressure such as head radius, cup thickness, material combination of bearing couples, coating film material, and film thickness are investigated in this study using the proposed methodology. The minimum error between the analytical and numerical results was 0.24% for 28 mm of head diameter, while the maximum error was 11.79 % for 48- mm of head diameter. The minimum contact pressure values were obtained from 48- mm of head radius at a half contact angle of 190 (degrees) in FEM and Hertz calculations, respectively. The maximum linear wear rate was calculated at 0.0026 mm/Mc at a 1- mm cup thickness, while minimum linear wear rate was 0.0022 mm/Mc at a 10- mm cup thickness in the numeric method. The maximum survival cycles of coating materials rate were 31847 cycles for the Stainless-steel coated cup with 500 μm of coating thickness, while the minimum cycles was 2359 cycles for the Ti64 coated cup surface with 100 μm of coating thickness. It is concluded that the most important design parameters are the cup thickness and the material combinations since they have a significant effect on the contact pressure and the contact area. This study provides a verification methodology for the parametric sensitivity analysis before experimental validations. The methodology utilized in this study could be utilized by designers while optimizing the design parameters to minimize the wear.

Keywords

• Hertz contact theory
• Archard’s wear law
• linear and volumetric wear rates
• finite element analysis
• parametric design of hip implants

References

1. 1. Merola M, Affatato S. Materials for hip prostheses: A review of wear and loading considerations. Materials. 2019;12(3).
2. 2. Charnley J, Cupic Z. The Nine and Ten Year Results of the Low-Friction Arthroplasty of the Hip. Clinical Orthopaedics and Related Research®. 1973;95.
3. 3. McKee GK, Watson-Farrar J. REPLACEMENT OF ARTHRITIC HIPS BY THE McKEE-FARRAR PROSTHESIS. The Journal of Bone and Joint Surgery British volume [Internet]. 1966 May 1;48-B(2):245–59. Available from: https://doi.org/10.1302/0301-620X.48B2.245
4. 4. Smith SL, Dowson D, Goldsmith AAJ. The lubrication of metal-on-metal total hip joints: A slide down the Stribeck curve. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology [Internet]. 2001 May 1;215(5):483–93. Available from: https://doi.org/10.1243/1350650011543718
5. 5. Learmonth ID, Gheduzzi S, Vail TP. Clinical experience with metal-on-metal total joint replacements: Indications and results. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine [Internet]. 2006 Feb 1;220(2):229–37. Available from: https://doi.org/10.1243/095441105X69123
6. 6. Fisher J, Bell J, Barbour PSM, Tipper JL, Mattews JB, Besong AA, et al. A novel method for the prediction of functional biological activity of polyethylene wear debris. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine [Internet]. 2001 Feb 1;215(2):127–32. Available from: https://doi.org/10.1243/0954411011533599
7. 7. National Joint Registry for England Wales Northern Ireland and the Isle of Man. 16th Annual Report 2019:National Joint Registry for England, Wales, Northern Ireland and the Isle of Man. NJR 16th Annual Report 2019 [Internet]. 2019;(December 2018):1–248. Available from: https://www.hqip.org.uk/wp-content/uploads/2018/11/NJR-15th-Annual-Report-2018.pdf
8. 8. Mak MM, Jin ZM. Analysis of contact mechanics in ceramic-on-ceramic hip joint replacements. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine [Internet]. 2002 Apr 1;216(4):231–6. Available from: https://doi.org/10.1243/09544110260138718

9. 9. Cilingir AC. Finite element analysis of the contact mechanics of ceramic-on-ceramic hip resurfacing prostheses. Journal of Bionic Engineering [Internet]. 2010;7(3):244–53. Available from: http://dx.doi.org/10.1016/S1672-6529(10)60247-8
10. 10. Chethan KN, Shyamasunder Bhat N, Zuber M, Satish Shenoy B. Finite element analysis of hip implant with varying in taper neck lengths under static loading conditions. Computer Methods and Programs in Biomedicine [Internet]. 2021;208:106273. Available from: https://doi.org/10.1016/j.cmpb.2021.106273
11. 11. K N C, Ogulcan G, Bhat N S, Zuber M, Shenoy B S. Wear estimation of trapezoidal and circular shaped hip implants along with varying taper trunnion radiuses using finite element method. Computer Methods and Programs in Biomedicine [Internet]. 2020;196:105597. Available from: https://doi.org/10.1016/j.cmpb.2020.105597
12. 12. Pandiyarajan R, Starvin MS, Ganesh KC. Contact Stress Distribution of Large Diameter Ball Bearing Using Hertzian Elliptical Contact Theory. Procedia Engineering [Internet]. 2012;38:264–9. Available from: https://www.sciencedirect.com/science/article/pii/S1877705812019479
13. 13. Wang QJ, Zhu D. Hertz Theory: Contact of Spherical Surfaces BT - Encyclopedia of Tribology. In: Wang QJ, Chung Y-W, editors. Boston, MA: Springer US; 2013. p. 1654–62. Available from: https://doi.org/10.1007/978-0-387-92897-5_492
14. 14. Mihçin Ş, Ciklacandir S. TOWARDS INTEGRATION OF THE FINITE ELEMENT MODELING TECHNIQUE INTO BIOMEDICAL ENGINEERING EDUCATION. Biomedical Engineering: Applications, Basis and Communications [Internet]. 2021 Nov 3;2150054. Available from: https://doi.org/10.4015/S101623722150054X
15. 15. Göktaş H, Subaşi E, Uzkut M, Kara M, Biçici H, Shirazi H, et al. Optimization of Hip Implant Designs Based on Its Mechanical Behaviour BT - Biomechanics in Medicine, Sport and Biology. In: Hadamus A, Piszczatowski S, Syczewska M, Błażkiewicz M, editors. Cham: Springer International Publishing; 2022. p. 37–43.
16. 16. Celik E, Alemdar F, Bati M, Dasdemir MF, Buyukbayraktar OA, Chethan KN, et al. Mechanical Investigation for the Use of Polylactic Acid in Total Hip Arthroplasty Using FEM Analysis BT - Biomechanics in Medicine, Sport and Biology. In: Hadamus A, Piszczatowski S, Syczewska M, Błażkiewicz M, editors. Cham: Springer International Publishing; 2022. p. 17–23.
17. 17. Mihcin S, Sahin AM, Yilmaz M, Alpkaya AT, Tuna M, Akdeniz S, et al. Database covering the prayer movements which were not available previously. Scientific Data [Internet]. 2023;10(1):276. Available from: https://doi.org/10.1038/s41597-023-02196-x
18. 18. Hertz H. Ueber die Berührung fester elastischer Körper. Ueber die Berührung fester elastischer Körper [Internet]. 1882; Available from: https://www.degruyter.com/document/doi/10.1515/crll.1882.92.156/html
19. 19. Alpkaya AT, Mihcin S. Dynamic computational wear model of PEEK-on-XLPE bearing couple in total hip replacements. Medical Engineering & Physics [Internet]. 2023;104006. Available from: https://www.sciencedirect.com/science/article/pii/S1350453323000619
20. 20. Alpkaya AT, Mihçin Ş. The Computational Approach to Predicting Wear: Comparison of Wear Performance of CFR-PEEK and XLPE Liners in Total Hip Replacement. Tribology Transactions [Internet]. 2023;66(1):59–72. Available from: https://doi.org/10.1080/10402004.2022.2140727
21. 21. Alpkaya AT, Yılmaz M, Şahin AM, Mihçin DŞ. Investigation of stair ascending and descending activities on the lifespan of hip implants. Medical Engineering and Physics. 2024;126.
22. 22. Archard JF, Hirst W, Allibone TE. The wear of metals under unlubricated conditions. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences [Internet]. 1956 Aug 2;236(1206):397–410. Available from: https://doi.org/10.1098/rspa.1956.0144
23. 23. Varady PA, Glitsch U, Augat P. Loads in the hip joint during physically demanding occupational tasks: A motion analysis study. Journal of Biomechanics [Internet]. 2015;48(12):3227–33. Available from: http://dx.doi.org/10.1016/j.jbiomech.2015.06.034
24. 24. Bergmann G, Graichen F, Rohlmann A. Hip joint loading during walking and running, measured in two patients. Journal of Biomechanics. 1993;26(8):969–90.
25. 25. Bergmann G, Bergmann G, Deuretzabacher G, Deuretzabacher G, Heller M, Heller M, et al. Hip forces and gait patterns from rountine activities. Journal of Biomechanics. 2001;34:859–71.
26. 26. Uddin MS, Zhang LC. Predicting the wear of hard-on-hard hip joint prostheses. Wear [Internet]. 2013;301(1– 2):192–200. Available from: http://dx.doi.org/10.1016/j.wear.2013.01.009
27. 27. Nithyaprakash R, Shankar S, Uddin MS. Computational wear assessment of hard on hard hip implants subject to physically demanding tasks. Medical and Biological Engineering and Computing. 2018;56(5):899– 910.
28. 28. Strickland MA, Dressler MR, Taylor M. Predicting implant UHMWPE wear in-silico: A robust, adaptable computational-numerical framework for future theoretical models. Wear [Internet]. 2012;274–275:100–8. Available from: http://dx.doi.org/10.1016/j.wear.2011.08.020
29. 29. Ming Song ST, Ashkanfar A, English R, Rothwell G. Computational method for bearing surface wear prediction in total hip replacements. Journal of the Mechanical Behavior of Biomedical Materials. 2021 Jul 1;119.
30. 30. Ruggiero A, Sicilia A. Lubrication modeling and wear calculation in artificial hip joint during the gait. Tribology International [Internet]. 2020;142(September 2019):105993. Available from: https://doi.org/10.1016/j.triboint.2019.105993
31. 31. Bhatt H, Goswami T. Implant wear mechanisms - Basic approach. Biomedical Materials. 2008;3(4).
32. 32. Güden M, Alpkaya AT, Hamat BA, Hızlı B, Taşdemirci A, Tanrıkulu AA, et al. The quasi-static crush response of electron-beam-melt Ti6Al4V body-centred-cubic lattices: The effect of the number of cells, strut diameter and face sheet. Strain. 2022;58(3):1–20.
33. 33. Yang X, Hutchinson CR. Corrosion-wear of β-Ti alloy TMZF (Ti-12Mo-6Zr-2Fe) in simulated body fluid. Acta Biomaterialia [Internet]. 2016;42:429–39. Available from: http://dx.doi.org/10.1016/j.actbio.2016.07.008
34. 34. Chen Y, Wu JM, Nie X, Yu S. Study on failure mechanisms of DLC coated Ti6Al4V and CoCr under cyclic high combined contact stress. Journal of Alloys and Compounds [Internet]. 2016;688:964–73. Available from: http://dx.doi.org/10.1016/j.jallcom.2016.07.254
35. 35. Zhang T, Harrison NM, McDonnell PF, McHugh PE, Leen SB. A finite element methodology for wear-fatigue analysis for modular hip implants. Tribology International [Internet]. 2013;65:113–27. Available from: http://dx.doi.org/10.1016/j.triboint.2013.02.016
36. 36. Heuberger R, Stöck C, Sahin J, Eschbach L. PEEK as a replacement for CoCrMo in knee prostheses: Pin-on- disc wear test of PEEK-on-polyethylene articulations. Biotribology. 2021 Sep 1;27.
37. 37. Scholes SC, Unsworth A. Wear studies on the likely performance of CFR-PEEK/CoCrMo for use as artificial joint bearing materials. Journal of Materials Science: Materials in Medicine. 2009 Jan;20(1):163–70.
38. 38. Askari E, Andersen MS. A closed-form formulation for the conformal articulation of metal-on-polyethylene hip prostheses: Contact mechanics and sliding distance. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine [Internet]. 2018 Nov 16;232(12):1196–208. Available from: https://doi.org/10.1177/0954411918810044
39. 39. Meng Q, Liu F, Fisher J, Jin Z. Contact mechanics and lubrication analyses of ceramic-on-metal total hip replacements. Tribology International [Internet]. 2013;63:51–60. Available from: http://dx.doi.org/10.1016/j.triboint.2012.02.012
40. 40. Baxter JW, Bumby JR, Johnson KL. One Hundred Years of Hertz Contact. Proceedings of the Institution of Mechanical Engineers [Internet]. 1982 Jun 1;196(1):363–78. Available from: https://doi.org/10.1243/PIME_PROC_1982_196_039_02
41. 41. Li G, Peng Y, Zhou C, Jin Z, Bedair H. The effect of structural parameters of total hip arthroplasty on polyethylene liner wear behavior: A theoretical model analysis. Journal of Orthopaedic Research. 2020;38(7):1587–95.
42. 42. Tarasevicius S, Robertsson O, Kesteris U, Kalesinskas RJ, Wingstrand H. Effect of femoral head size on polyethylene wear and synovitis after total hip arthroplasty: A sonographic and radiographic study of 39 patients. Acta Orthopaedica. 2008;79(4):489–93.
43. 43. Masaoka T, Clarke IC, Yamamoto K, Tamura J, Williams PA, Good VD, et al. Validation of volumetric and linear wear-measurement in UHMWPE cups - A hip simulator analysis. Wear. 2003;254(5–6):391–8.
44. 44. Fisher J. Bioengineering reasons for the failure of metal-on-metal hip prostheses. The Journal of Bone and Joint Surgery British volume. 2011;93-B(8):1001–4.
45. 45. Medley JB, Chan FW, Krygier JJ, Bobyn D. Comparison of alloys and designs in a hip simulator study of metal on metal implants. Clinical Orthopaedics and Related Research. 1996;329(SUPPL.):148–59.
46. 46. Reinisch G, Judmann KP, Lhotka C, Lintner F, Zweymüller KA. Retrieval study of uncemented metal-metal hip prostheses revised for early loosening. Biomaterials. 2003;24(6):1081–91.
47. 47. Guu YY, Lin JF, Ai CF. The tribological characteristics of titanium nitride coatings part i. Coating thickness effects. Wear. 1996;194(1–2):12–21.
48. 48. Lin J, Sproul WD, Moore JJ, Lee S, Myers S. High rate deposition of thick CrN and Cr2N coatings using modulated pulse power (MPP) magnetron sputtering. Surface and Coatings Technology [Internet]. 2011;205(10):3226–34. Available from: http://dx.doi.org/10.1016/j.surfcoat.2010.11.039