Skip to main content
Log in

Time-Dependent Fluid Squeeze-Out Between Soft Elastic Solids with Randomly Rough Surfaces

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

We study the time dependency of the interfacial separation and of the area of real contact between a soft elastic cylinder and a rigid solid with a randomly rough surface, squeezed with normal approach in a fluid. This problem is relevant for biological, as well as for bio-medical, seals and tires applications. An ad-hoc numerical scheme is developed to solve the transient mixed-EHD homogenized lubrication problem. We show that, for the soft contact case, the transition from the EHD to the boundary regime can be much more efficiently studied within a simplified (Grubin-like) problem formulation then with the full numerical scheme. This is not only of great conceptional importance, but also of practical importance as the latter calculation is much simpler and faster than the full scheme calculation.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Bowden, F.P., Tabor, D.: Friction and Lubrication of Solids. Wiley, New York (1956)

    Google Scholar 

  2. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1966)

    Google Scholar 

  3. Persson, B.N.J.: Sliding Friction: Physical Principles and Applications. 2nd edn. Springer, Heidelberg (2000)

    Google Scholar 

  4. Israelachvili, J.N.: Intermolecular and Surface Forces. Academic Press, London (1995)

    Google Scholar 

  5. Persson, B.N.J., Albohr, O., Tartaglino, U., Volokitin, A.I., Tosatti, E.: On the nature of surface roughness with application to contact mechanics sealing rubber friction and adhesion. J. Phys. Condens. Matter 17, R1 (2005)

    Article  CAS  Google Scholar 

  6. Persson, B.N.J., Yang, C.: Theory of the leak-rate of seals. J. Phys. Condens. Matt. 20, 315011 (2008)

    Article  Google Scholar 

  7. Persson, B.N.J.: Capillary adhesion between elastic solids with randomly rough surfaces. J. Phys. Condens. Matt. 20, 315007 (2008)

    Article  Google Scholar 

  8. Putignano, C., Afferrante, L., Carbone, G., Demelio, G.: The influence of the statistical properties of self-affine surfaces in elastic contacts: a numerical investigation. J. Mech. Phys. Solids 60, 973–982 (2012)

    Article  Google Scholar 

  9. Akarapu, S., Sharp, T., Robbins, M.O.: Stiffness of contacts between rough surfaces. Phys. Rev. Lett. 106, 204301 (2011)

    Article  Google Scholar 

  10. Almqvist, A., Campana, C., Prodanov, N., Persson, B.N.J.: Interfacial separation between elastic solids with randomly rough surfaces: comparison between theory and numerical techniques. J. Mech. Phys. Solids. 59, 2355 (2011)

    Article  Google Scholar 

  11. Persson, B.N.J.: Relation between interfacial separation and load: a general theory of contact mechanics. Phys. Rev. Lett. 99, 125502 (2007)

    Article  CAS  Google Scholar 

  12. Persson, B.N.J.: Contact mechanics for randomly rough surfaces. Surf. Sci. Rep. 61, 201–227 (2006)

    Article  CAS  Google Scholar 

  13. Hyun, S., Pei, L., Molinari, J.F., Robbins, M.O.: Finite-element analysis of contact between elastic self-affine surfaces. Phys. Rev. E 70, 026117 (2004)

    Article  CAS  Google Scholar 

  14. Campana, C., Müser, M.H.: Contact mechanics of real vs. randomly rough surfaces: a Green’s function molecular dynamics study. EPL 77, 38005 (2007)

    Article  Google Scholar 

  15. Persson, B.N.J: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115, 3840 (2001)

    Article  CAS  Google Scholar 

  16. Carbone, G., Scaraggi, M., Tartaglino, U.: Adhesive contact of rough surfaces: comparison between numerical calculations and analytical theories. Eur. Phys. J. E 30, 65 (2009)

    Article  CAS  Google Scholar 

  17. Scaraggi, M., Carbone, G., Persson, B.N.J., Dini, D.: Lubrication in soft rough contacts: a novel homogenized approach. Part I—Theory. Soft Matter 7, 10395–10406 (2011)

    Article  CAS  Google Scholar 

  18. Scaraggi, M., Carbone, B.N.J., Dini, D.: Lubrication in soft rough contacts: a novel homogenized approach. Part II—Discussion. Soft Matter 7, 10407–10416 (2011)

    Article  CAS  Google Scholar 

  19. Persson, B.N.J., Scaraggi, M.: Lubricated sliding dynamics: flow factors and Stribeck curve. Eur. Phys. J. E 34, 113 (2011)

    Article  CAS  Google Scholar 

  20. Carbone, G., Scaraggi, M., Soria, L.: The lubrication regime at pin-pulley interface in chain CVTs. ASME J. Mech. Des. 131(1), 011003 (2009)

    Article  Google Scholar 

  21. Carbone, G., Scaraggi, M., Mangialardi, L.: EHL squeeze at pinpulley interface in CVTs: influence of lubricant rheology. Tribol. Int. 42(6), 862–868 (2009)

    Article  CAS  Google Scholar 

  22. Scaraggi, M., Carbone, G.: Transition from elastohydrodynamic to mixed lubrication in highly loaded squeeze contacts. J. Mech. Phys. Solids 58(9), 1361–1373 (2010)

    Article  CAS  Google Scholar 

  23. Scaraggi, M., De Novellis, L., Carbone, G.: EHL-squeeze in high loaded contacts: the case of chain CVT transmissions. Strojniski vestnik: J. Mech. Eng. 56(4), 245–252 (2010)

    Google Scholar 

  24. Persson, B.N.J., Scaraggi, M.: On the transition from boundary lubrication to hydrodynamic lubrication in soft contacts. J. Phys. Condens. Matter 21, 185002 (2009)

    Article  CAS  Google Scholar 

  25. Lorenz, B., Persson, B.N.J.: Time-dependent fluid squeeze-out between solids with rough surfaces. Eur. Phys. J. E 32, 281 (2010)

    Article  CAS  Google Scholar 

  26. Persson, B.N.J., Prodanov, N., Krick, B.A., Rodriguez, N., Mulakaluri, N., Sawyer, W.G., Mangiagalli, P.: Elastic contact mechanics: percolation of the contact area and fluid squeeze-out. Eur. Phys. J. E 35, 5 (2012)

    Article  CAS  Google Scholar 

  27. Patir, N., Cheng, H.S.: An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. J. Lubr. Technol. Trans. ASME 100, 12–17 (1978)

    Article  Google Scholar 

  28. Patir, N., Cheng, H.S.: Application of average flow model to lubrication between rough sliding surfaces. J. Lubr. Technol. Trans. ASME 101, 220–230 (1979)

    Article  Google Scholar 

  29. Persson, B.N.J.: Fluid dynamics at the interface between contacting elastic solids with randomly rough surfaces. J. Phys. Condens. Matter 22, 265004 (2010)

    Article  CAS  Google Scholar 

  30. Hamrock, B.J.: Fundamentals of Fluid Film Lubrication. McGraw-Hill Companies, New York (1994)

    Google Scholar 

  31. Sivebaek, I.M., Samoilov, V.N., Persson, B.N.J.: Effective viscosity of confined hydrocarbons. Phys. Rev. Lett. 108, 036102 (2012)

    Article  CAS  Google Scholar 

  32. Yang, C., Persson, B.N.J.: Contact mechanics: contact area and interfacial separation from small contact to full contact. J. Phys. Condens. Matter 20, 215214 (2008)

    Article  Google Scholar 

  33. Lorenz, B., Persson, B.N.J.: Leak rate of seals: effective-medium theory and comparison with experiment. Eur. Phys. J. E 31, 159 (2010)

    Article  CAS  Google Scholar 

  34. G. Carbone, private communication.

  35. Sahlin, F., PhD thesis, Lulea University of Technology (2008), see in particular Appendix F

  36. Dapp, W.B., Lücke, A., Persson, B.N.J., Müser, M.H.: Self-affine elastic contacts: percolation and leakage. Phys. Rev. Lett, 108, 244301 (2012)

    Google Scholar 

  37. Persson, B.N.J., Tartaglino, U., Albohr, O., Tosatti, E.: Sealing is at the origin of rubber slipping on wet roads. Nat. Mater. 3, 882 (2004)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. N. J. Persson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scaraggi, M., Persson, B.N.J. Time-Dependent Fluid Squeeze-Out Between Soft Elastic Solids with Randomly Rough Surfaces. Tribol Lett 47, 409–416 (2012). https://doi.org/10.1007/s11249-012-9996-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11249-012-9996-6

Keywords

Navigation