Skip to main content
SpringerLink
Log in

Simplified simulation of fretting wear using the method of dimensionality reduction

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

We study the problem of wear of a rotationally symmetric profile subjected to oscillations with small amplitude. Under these conditions, sliding occurs at the boundary of the contact area while the inner parts of the contact area may still stick. In a recent paper, Dimaki with colleagues proposed a numerically exact simulation procedure based on the method of dimensionality reduction (MDR). This drastically reduced the simulation time compared with conventional finite element simulations. The proposed simulation procedure requires carrying out the direct and the inverse MDR transformations in each time step. This is the main time consuming operation in the proposed method. However, solutions obtained with this method showed a remarkable simplicity of the development of wear profiles in the MDR space. In the present paper, we utilize these results to formulate an approximate model, in which the wear is simulated directly in the one-dimensional space without using integral transformations. This speeds up the simulations of wear by further several orders of magnitude.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ko, P.L., Experimental Studies of Tube Frettings in Steam Generators and Heat Exchangers, J. Press. Vessel Technol., 1979, vol. 101, pp. 125–133.

    Article  Google Scholar 

  2. Fisher, N.J., Chow, A.B., and Weckwerth, M.K., Experimental Fretting Wear Studies of Steam Generator Materials, J. Press. Vessel Technol., 1995, vol. 117, pp. 312–320.

    Article  Google Scholar 

  3. Lee, C.Y., Tian, L.S., Bae, J.W., and Chai, Y.S., Application of Influence Function Method on the Fretting Wear of Tube-to-Plate Contact, Tribol. Int., 2009, vol. 42, pp. 951957.

    Google Scholar 

  4. Collier, J.P., Mayor, M.B., Jensen, R.E., and Surphenant, V.A., Mechanisms of Failure of Modular Prostheses, Clin. Orthop. Relat. Res., 1992, vol. 285, pp. 129–139.

    Google Scholar 

  5. Antler, M., Survey of Contact Fretting in Electrical Connectors, Compon. Hybrids Manuf. Technol., 1985, vol. 8, pp. 87–104.

    Article  Google Scholar 

  6. Rajasekaran, R. and Nowell, D., Fretting Fatigue in Dovetail Blade Roots: Experiment and Analysis, Tribol. Int., 2006, vol. 39, pp. 1277–1285.

    Article  Google Scholar 

  7. Ciavarella, M. and Demelio, G., A Review of Analytical Aspects of Fretting Fatigue, with Extension to Damage Parameters, and Application to Dovetail Joints, Int. J. Solids Struct., 2001, vol. 38, pp. 1791–1811.

    MATH  Google Scholar 

  8. Reye, T., Zur Theorie der Zapfenreibung, Der Civilingenieur, 1860, vol. 4, pp. 235–255.

    Google Scholar 

  9. Khrushchov, M.M. and Babichev, M.A., Investigation of Wear of Metals, Moscow: AN SSSR, 1960.

    Google Scholar 

  10. Archard, J.F. and Hirst, W., The Wear of Metals under Unlubricated Conditions, Proc. R. Soc. Lond. A, 1956, vol. 236, pp. 397–410.

    Article  ADS  Google Scholar 

  11. Popov, V.L., Contact Mechanics and Friction. Physical Principles and Applications, Berlin: Springer, 2010.

    Book  MATH  Google Scholar 

  12. Lee, C.Y., Tian, L.S., Bae, J.W., and Chai, Y.S., Application of Influence Function Method on the Fretting Wear of Tube-to-Plate Contact, Tribol. Int., 2009, vol. 42, pp. 951957.

    Google Scholar 

  13. Popov, V.L., Method of Reduction of Dimensionality in Contact and Friction Mechanics: A Linkage between Micro and Macro Scales, Friction., 2013, vol. 1, no. 1, pp. 41–62.

    Article  Google Scholar 

  14. Dimaki, A.V., Dmitriev, A.I., Chai, Y.S., and Popov, V.L., Rapid Simulation Procedure for Fretting Wear on the Basis of the Method of Dimensionality Reduction, Int. J. Solids Struct., 2014 (in print).

    Google Scholar 

  15. Heß, M., Über die Abbildung ausgewählter dreidimensionaler Kontakte auf Systeme mit niedrigerer räumlicher Dimension, Göttingen: Cuvillier-Verlag, 2011.

    Google Scholar 

  16. Heß, M., On the Reduction Method of Dimensionality: The Exact Mapping of Axisymmetric Contact Problems with and without Adhesion, Phys. Mesomech., 2012, vol. 15, no. 5–6, pp. 264–269.

    Article  Google Scholar 

  17. Johnson, K.L., Contact Mechanics, Cambridge: Cambridge University Press, 1987.

    Google Scholar 

  18. Popov, V.L. and Heß, M., Methode der Dimensionsreduktion in Kontaktmechanik und Reibung, Berlin: Springer, 2013.

    Book  Google Scholar 

  19. Cattaneo, C., Sul contatto di due corpi elastici: distribuzione locale degli sforzi, Rend. dell’Accademia Naz. dei Lincei., 1938, vol. 27, pp. 342–348, 434–436, 474–478.

    Google Scholar 

  20. Mindlin, R.D., Compliance of Elastic Bodies in Contact, J. Appl. Mech., 1949, vol. 16, pp. 259–268.

    MATH  MathSciNet  Google Scholar 

  21. Jäger, J., Axi-symmetric Bodies of Equal Material in Contact under Torsion or Shift, Arch. Appl. Mech., 1995, vol. 65, pp. 478–487.

    Article  MATH  Google Scholar 

  22. Ciavarella, M. and Hills, D.A., Brief Note: Some Observations on the Oscillating Tangential Forces and Wear in General Plane Contacts, Eur. J. Mech. A. Solids, 1999, vol. 18, pp. 491–497.

    Article  ADS  MATH  Google Scholar 

  23. Popov, V.L., Analytic Solution for the Limiting Shape of Profiles due to Fretting Wear, Sci. Rep., 2014, vol. 4, p. 3749.

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Berlin, Berlin, D-10623, Germany

    Q. Li

  2. Donetsk Institute for Physics and Engineering, NASU, Donetsk, 83114, Ukraine

    A. E. Filippov & V. L. Popov

  3. Institute of Strength Physics and Materials Science, SB RAS, Tomsk, 634055, Russia

    A. V. Dimaki

  4. School of Mechanical Engineering, Yeungnam University, Gyongsan, 712-749, South Korea

    Y. S. Chai

  5. National Research Tomsk State University, Tomsk, 634050, Russia

    A. V. Dimaki & V. L. Popov

  6. National Research Tomsk Polytechnic University, Tomsk, 634050, Russia

    V. L. Popov

Authors
  1. Q. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. E. Filippov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Dimaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. S. Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. V. L. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. L. Popov.

Additional information

Original Text © Q. Li, A.E. Filippov, A.V. Dimaki, Y.S. Chai, V.L. Popov, 2014, published in Fizicheskaya Mezomekhanika, 2014, Vol. 17, No. 3, pp. 92–97.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Q., Filippov, A.E., Dimaki, A.V. et al. Simplified simulation of fretting wear using the method of dimensionality reduction. Phys Mesomech 17, 236–241 (2014). https://doi.org/10.1134/S1029959914030102

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959914030102

Keywords

Search

Navigation