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Acta Mechanica

, Volume 230, Issue 6, pp 2295–2307 | Cite as

Effective wear coefficient and wearing-in period for a functionally graded wear-resisting punch

  • Ivan I. Argatov
  • Young S. ChaiEmail author
Note
  • 39 Downloads

Abstract

A two-dimensional wear contact problem for an elastic layer and a wear-resisting punch is considered. The contact area and the contact load are assumed to be fixed, whereas the punch’s shape changes according to Archard’s law of wear with variable wear coefficient. By neglecting the effect of tangential tractions, the problem of determining the normal contact pressure is reduced to a two-dimensional integral equation containing a Fredholm coordinate operator and a Volterra time operator. By the method of separation of variables, the transient contact pressure distribution has been constructed in terms of the solutions of some eigenvalue problem. A special attention is paid to quantities of practical interest, such as the wearing-in period and the transient effective wear coefficient.

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Notes

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Conflict of interest

The authors of the article declare not to have conflict of interest that may interfere in the impartiality of the scientific work.

References

  1. 1.
    Feppon, F., Sidebottom, M.A., Michailidis, G., Krick, B.A., Vermaak, N.: Efficient steady-state computation for wear of multimaterial composites. J. Tribol. 138, 031602 (2016)CrossRefGoogle Scholar
  2. 2.
    Li, Q., Forsbach, F., Schuster, M., Pielsticker, D., Popov, V.L.: Wear analysis of a heterogeneous annular cylinder. Lubricants 6, 28 (2018)CrossRefGoogle Scholar
  3. 3.
    Rodríguez-Tembleque, L., Aliabadi, M.H.: Numerical simulation of fretting wear in fiber-reinforced composite materials. Eng. Fract. Mech. 168, 13–27 (2016)CrossRefGoogle Scholar
  4. 4.
    Lee, G.Y., Dharan, C.K.H., Ritchie, R.O.: A physically-based abrasive wear model for composite materials. Wear 252, 322–331 (2002)CrossRefGoogle Scholar
  5. 5.
    Song, X., Huang, J., Leu, S.W., Zhou, K.: Wear characteristics of medical hearing-aid components and friction reduction mechanisms. J. Tribol. 139, 034504 (2017)CrossRefGoogle Scholar
  6. 6.
    Galin, L.: Contact problems of the theory of elasticity in the presence of wear. J. Appl. Math. Mech. 40, 931–936 (1976)CrossRefzbMATHGoogle Scholar
  7. 7.
    Aleksandrov, V.M., Galin, L., Piriev, N.P.: A plane contact problem for an elastic layer of considerable thickness in the presence of wear. Mekh Tverd Tela 4, 60–67 (1978). (in Russian)Google Scholar
  8. 8.
    Galin, L., Goryacheva, I.G.: Axisymmetric contact problem of the theory of elasticity in the presence of wear. J. Appl. Math. Mech. 41, 826–831 (1977)CrossRefzbMATHGoogle Scholar
  9. 9.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Popov, V.L., Heß, M.: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin (2015)CrossRefzbMATHGoogle Scholar
  12. 12.
    Goryacheva, I.: Contact Mechanics in Tribology. Kluwer Academic Publishers, Dordrecht (1998)CrossRefzbMATHGoogle Scholar
  13. 13.
    Argatov, I.I., Fadin, Y.A.: Calculation of tribological characteristics of composite materials. J. Frict. Wear 28, 182–186 (2007)CrossRefGoogle Scholar
  14. 14.
    Axén, N., Jacobson, S.: A model for the abrasive wear resistance of multiphase materials. Wear 174, 187–199 (1994)CrossRefGoogle Scholar
  15. 15.
    Khruschov, M.M.: Principles of abrasive wear. Wear 28, 69–88 (1974)CrossRefGoogle Scholar
  16. 16.
    Garrison, W.M.: Khruschov’s rule and the abrasive wear resistance of multiphase solids. Wear 82, 213–220 (1982)CrossRefGoogle Scholar
  17. 17.
    Yen, B.K., Dharan, C.K.H.: A model for the abrasive wear of fiber-reinforced polymer composites. Wear 195, 123–127 (1996)CrossRefGoogle Scholar
  18. 18.
    Argatov, I.I.: Solution of the plane Hertz problem. J. Appl. Mech. Tech. Phys. 42, 1064–1072 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Chai, Y.S., Lee, C.Y., Bae, J.W., Lee, S.Y., Hwang, J.K.: Finite element analysis of fretting wear problems in consideration of frictional contact. Key Eng. Mater. 297–300, 1406–1411 (2005)CrossRefGoogle Scholar
  20. 20.
    Lee, C.Y., Tian, L.S., Bae, J.W., Chai, Y.S.: Application of influence function method on the fretting wear of tube-to-plate contact. Tribol. Int. 42, 951–957 (2009)CrossRefGoogle Scholar
  21. 21.
    Feppon, F., Michailidis, G., Sidebottom, M.A., Allaire, G., Krick, B.A., Vermaak, N.: Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints. Struct. Multidiscipl. Optim. 55, 547–568 (2017)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Smirnov, V.I.: Course of Higher Mathematics. Integral Equations and Partial Differential Equations, vol. 4. Pergamon Press, Oxford (1964)zbMATHGoogle Scholar
  23. 23.
    Argatov, I.I., Fadin, Y.A.: A macro-scale approximation for the running-in period. Tribol. Lett. 42, 311–317 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für MechanikTechnische Universität BerlinBerlinGermany
  2. 2.School of Mechanical EngineeringYeungnam UniversityGyeongsanSouth Korea

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