Skip to main content
Log in

Interaction of several bodies as applied to solving tribo-fatigue problems

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Mechanical systems that work in conditions of both mechanical fatigue and contact with friction are studied by tribo-fatigue. Such systems (wheel/rail, gearings, pipe-viscous fluid flow) are of significant practical importance. They require a special statement of the problem for contact interaction of several bodies with the account of the set of non-contact boundary conditions. Equations for determining the three-dimensional stress-strain state for a multi-component system of solids are constructed and analyzed. Their solution using the boundary element method is considered. The example of calculation of contact pressure change under the influence of non-contact loading in a roller/shaft tribo-fatigue system is given.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sosnovskiy L.A.: Tribo-fatigue: Wear-fatigue Damage and Its Prediction (Foundations of engineering mechanics). Springer, Berlin (2005)

    Google Scholar 

  2. Zhuravkov, M.A., Sosnovskiy, L.A., Sherbakov, S.S.: Mathematical modeling in tribo-fatigue. In: Proceedings of the X Belarusian Mathematical Conference. Minsk, Belarus, pp. 120–121 (2008) (in Russian)

  3. Zhuravkov, M.A.: Fundamental and applied problems of tribo-fatigue. In: Proceedings of the VI International Symposium on Tribo-Fatigue (ISTF 2010). Minsk, Belarus, vol. 1, pp. 87–96 (2010) (in Russian)

  4. Vityaz, P.A., Sosnovskiy, L.A., Sherbakov, S.S.: New approaches in mechanics of deformable systems. In: Proceedings of NAS Belarus, vol. 53, pp. 102–110 (2009) (in Russian)

  5. Sosnovskiy L.A., Sherbakov S.S.: Mechanothermodynamical system and its behavior. Continuum Mech. Thermodyn. 24, 239–256 (2012)

    Article  Google Scholar 

  6. Sosnovskiy L.A., Sherbakov S.S.: Vibro-impact in rolling contact. J. Sound Vib. 308, 489–503 (2007)

    Article  Google Scholar 

  7. Schiehlen W.: Computational dynamics: theory and applications of multibody systems. Eur. J. Mech. A/Solids 25, 566–594 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Strömberg N.: An implicit method for frictional contact, impact and rolling. Eur. J. Mech. A/Solids 24, 1016–1029 (2005)

    Article  MATH  Google Scholar 

  9. Hart R., Cundall P.A., Lemos J.: Formulation of three-dimensional discrete element model. Part II, Mechanical calculation for motion and interaction of a system composed of many polyhedral blocks. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25, 117–125 (1988)

    Google Scholar 

  10. Aigner L.G., Gerstmayr J., Pechstein A.S.: A two-dimensional homogenized model for a pile of thin elastic sheets with frictional contact. Acta Mechanica 218, 31–43 (2011)

    Article  MATH  Google Scholar 

  11. Barbosa R.E., Ghaboussi J.: Discrete finite element method for multiple deformable bodies. Finite Elem. Anal. Des. 7, 145–158 (1990)

    Article  Google Scholar 

  12. Cundall, P.A. (1987) Distinct element models of rock and soil structure. In: Brown, E.T. (ed.) Analytical and Computational Methods in Engineering Rock Mechanics. George Allen & Unwin, London, pp. 129–163

  13. Cundall P.A., Hart R.D.: Numerical modeling of discontinua. Eng. Comput. 9, 101–113 (1992)

    Article  Google Scholar 

  14. Zhang C.H., Pekau O.A., Jin F., Wang G.L.: Application of discrete element method in dynamic analysis of high rock slopes and blocky structures. Soil Dyn. Earthq. Eng. 16, 385–394 (1997)

    Article  Google Scholar 

  15. Feng J., Zhang C., Hu W., Wang J.: 3D mode discrete element method: elastic model. Int. J. Rock Mech. Min. Sci. 48, 59–66 (2011)

    Article  Google Scholar 

  16. Fabrikant V.I.: Frictionless elastic contact problem for a curved rigid punch of arbitrary shape. Acta Mechanica 67, 1–25 (1987)

    Article  MATH  Google Scholar 

  17. Cao D.Q., Liu D., Wang C.: Three-dimensional nonlinear dynamics of slender structures: cosserat rod element approach. Int. J. Solids Struct. 43, 760–783 (2005)

    Article  Google Scholar 

  18. Willis J.R.: Exact effective relations for dynamics of a laminated body. Mech. Mater. 41, 385–393 (2009)

    Article  Google Scholar 

  19. Martin D., Aliabadi M.H.: Boundary element analysis of two-dimensional elastoplastic contact problems. Eng. Anal. Boundary Elem. 21, 349–360 (1998)

    Article  MATH  Google Scholar 

  20. Rodríguez-Tembleque L., Abascal R., Aliabadi M.H.: A boundary element formulation for wear modeling on 3D contact and rolling-contact problems. Int. J. Solids Struct. 47, 2600–2612 (2010)

    Article  MATH  Google Scholar 

  21. Rodríguez-Tembleque L., Abascal R.: A 3D FEM–BEM rolling contact formulation for unstructured meshes. Int. J. Solids Struct. 47, 330–353 (2010)

    Article  MATH  Google Scholar 

  22. Johnson K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  23. González J.A., Abascal R.: Efficient stress evaluation of stationary viscoelastic rolling contact problems using the boundary element method: application to viscoelastic coatings. Eng. Anal. Boundary Elem. 30, 426–434 (2006)

    Article  MATH  Google Scholar 

  24. Segonda D., Tafreshi A.: Stress analysis of three-dimensional contact problems using the boundary element method. Eng. Anal. Boundary Elem. 22, 199–214 (1998)

    Article  Google Scholar 

  25. Banerjee P.K., Butterfield R.: Boundary Element Methods in Engineering Science. McGraw-Hill, New York (1981)

    MATH  Google Scholar 

  26. Zhuravkov, M.A., Martynenko, M.D.: Theoretical fundamentals of deformation mechanics of block-laminated massif of salt rocks. BSU Press, Minsk (1995) (in Russian)

  27. Sherbakov, S.S.: Interaction of continua. In: Proceedings of the VI International Symposium on Tribo-Fatigue (ISTF 2010), vol. 2. Minsk, Belarus, pp. 439–446 (in Russian)

  28. Sherbakov, S.S.: Generalized tribo-fatigue problem. Mech. Mach. Mech. Mater. 1, 83–87 (2011) (in Russian)

    Google Scholar 

  29. Mase G.: Theory and Problems of Continuum Mechanics. McGraw-Hill, New York (1970)

    Google Scholar 

  30. Zhuravkov, M.A.: Mathematical Modeling of Deformable Processes in Solid Deformable Media (by the Example Of Mechanics Of Rocks And Massifs): Course Of Lectures. BSU Press, Minsk (2002) (in Russian)

  31. Zhuravkov, M.A., Martynenko, M.D.: Singular Solutions and Integral Equations in Mechanics of Deformable Media. BSU Press, Minsk (1999) (in Russian)

  32. Zhuravkov, M.A.: Fundamental Solutions of the Elasticity Theory and Some of Their Applications in Geomechanics of Soils and Bases. BSU Press, Minsk (2008) (in Russian)

  33. Sosnovskii L.A., Komissarov V.V., Shcherbakov S.S.: A method of experimental study of friction in a active system. J. Frict. Wear 33, 136–145 (2012)

    Article  Google Scholar 

  34. Sosnovskii L.A., Komissarov V.V., Shcherbakov S.S.: Comparative experimental study of friction parameters in a tribopair and a force system. J. Frict. Wear 33, 258–264 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. S. Sherbakov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sherbakov, S.S., Zhuravkov, M.A. Interaction of several bodies as applied to solving tribo-fatigue problems. Acta Mech 224, 1541–1553 (2013). https://doi.org/10.1007/s00707-013-0822-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-0822-5

Keywords

Navigation