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Effect of Wear on the Evolution of Contact Pressure at a Bimaterial Sliding Interface

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Abstract

The eigenfunction method pioneered by Galin (J Appl Math Mech 40: 981–986, 1976) is extended to provide a general solution to the transient evolution of contact pressure and wear of two sliding elastic half-planes, under the assumption that there is full contact and that the Archard–Reye wear law applies. The governing equations are first developed for sinusoidal profiles with exponential growth rates. The contact condition and the wear law lead to a characteristic equation for the growth rate and more general solutions are developed by superposition. The case of general initial profiles can then be written down as a Fourier integral. Decay rates increase with wavenumber, so fine-scale features are worn away early in the process. Qualitative features of the problem are governed by two dimensionless wear coefficients, which for many material combinations are small compared with unity. If one of the bodies does not wear and is non-plane, the system evolves to a non-trivial steady state in which the wearing body acquires a profile which migrates over its surface.

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References

  1. Dundurs, J., Comninou, M.: Shape of a worn slider. Wear 62, 419–424 (1980)

    Article  Google Scholar 

  2. Reichner, P.: Wear-induced profiles of brushes on eccentric rotors. Wear 78, 207–217 (1982)

    Article  Google Scholar 

  3. Reye, T., Zur, T.: Theorie der Zapfenreibung. J Der Civilingenieur 4, 235–255 (1860)

    Google Scholar 

  4. Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24, 981–988 (1953)

    Article  Google Scholar 

  5. Galin, L.A.: Contact problems of the theory of elasticity in the presence of wear. J. Appl. Math. Mech. 40, 981–986 (1976)

    Article  Google Scholar 

  6. Galin, L.A., Goryacheva, I.G.: Axi-symmetric contact problem of the theory of elasticity in the presence of wear. J. Appl. Math. Mech. 41(5), 826–831 (1977)

    Article  Google Scholar 

  7. Komogortsev, V.F.: Contact between a moving stamp and an elastic half-plane when there is wear. J. Appl. Math. Mech. 49, 243–246 (1985)

    Article  Google Scholar 

  8. Kovalenko, E.V.: Study of the axisymmetric contact problem of the wear of a pair consisting of an annular stamp and a rough half-space. J. Appl. Math. Mech. 49, 641–647 (1985)

    Article  Google Scholar 

  9. Argatov, I.I., Fadin, Y.A.: A macro-scale approximation for the running-in period. Tribol. Lett. 42, 311–317 (2011)

    Article  CAS  Google Scholar 

  10. Goryacheva, I.G.: Contact problem in the presence of wear for a piston ring inserted into a cylinder. J. Appl. Math. Mech. 44(2), 255–257 (1980)

    Article  Google Scholar 

  11. Liu, Y., Jang, Y.H., Barber, J.R.: Finite element implementation of an eigenfunction solution for the contact pressure variation due to wear. Wear 309, 134–138 (2014)

    Article  CAS  Google Scholar 

  12. Kato, K.: Friction and wear of passive metals and coatings. In: Tribocorrosion of Passive Metals and Coatings (pp. 65–99). Woodhead Publishing, Cambridge (2011)

  13. Di Puccio, F., Mattei, L.: A novel approach to the estimation and application of the wear coefficient of metal-on-metal hip implants. Tribol. Int. 83, 69–76 (2015)

    Article  Google Scholar 

  14. Mattei, L., Di Puccio, F., Joyce, T.J., Ciulli, E.: Numerical and experimental investigations for the evaluation of the wear coefficient of reverse total shoulder prostheses. J. Mech. Behav. Biomed. Mater. 55, 53–66 (2016)

    Article  Google Scholar 

  15. Bao, J.S., Zhu, Z.C., Tong, M.M., Yin, Y., Peng, Y.X.: Influence of braking pressure on tribological performance of non-asbestos brake shoe for mine hoister during emergency braking. Indus. Lubr. Tribol. 64(4), 230–236 (2012)

    Article  Google Scholar 

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Acknowledgements

MC and AP acknowledge the support by the Italian Ministry of Education, University and Research under the Programme “Department of Excellence” Legge 232/2016 (Grant No. CUP - D94I18000260001). A.P. is thankful to the DFG (German Research Foundation) for funding the project PA 3303/1-1. A.P. acknowledges support from ”PON Ricerca e Innovazione 2014-2020 -Azione I.2 - D.D. n. 407, 27/02/2018, bando AIM (Grant No. AIM1895471).

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Authors and Affiliations

  1. Department of Mechanics Mathematics and Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy

    M. Ciavarella & A. Papangelo

  2. Department of Mechanical Engineering, Hamburg University of Technology, Am Schwarzenberg-Campus 1, 21073, Hamburg, Germany

    M. Ciavarella & A. Papangelo

  3. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    J. R. Barber

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  1. M. Ciavarella
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  2. A. Papangelo
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  3. J. R. Barber
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Correspondence to A. Papangelo.

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Ciavarella, M., Papangelo, A. & Barber, J.R. Effect of Wear on the Evolution of Contact Pressure at a Bimaterial Sliding Interface. Tribol Lett 68, 27 (2020). https://doi.org/10.1007/s11249-020-1269-1

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