Skip to main content
SpringerLink
Log in

Tire–Road Contact Stiffness

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

Abstract

When a rubber block is squeezed against a nominal flat but rough surface, the rubber bottom surface will penetrate into the substrate roughness profile. The relation between penetration depth \(w\) (or the average interfacial separation \(\bar{u}\)) and the applied squeezing pressure \(p\) determines the (perpendicular) contact stiffness \(K=\hbox {d}p/\hbox {d}w=-\hbox {d}p/\hbox {d}\bar{u}\), which is important for many applications. We have measured the relation between \(p\) and \(\bar{u}\) for a rubber block squeezed against 28 different concrete and asphalt road surfaces. We find a linear relation between \({\mathrm{log}}p\) and \(\bar{u}\), in agreement with theory predictions. The measured stiffness values correlate rather well with the theory prediction.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. Contact mechanics for layered materials (in this case rubber slab and rigid (steel) plate) can also be studied within the same formalism as used in deriving Eq. (3)–(5), see [23–25]

  2. The filled rubber compound we use exhibits strain softening with an elastic modulus which decreases from \(\approx 12 \ {\mathrm{MPa}}\) to \(\approx 4 \ {\mathrm{MPa}}\) as the strain increases from 0.1 to 10 %. The rubber strain in the asperity contact regions is approximately independent of the nominal contact pressure and relative large so the large strain \(E\)-module is most relevant and we take \(E\approx 4 \ {\mathrm{MPa}}\). The effective modulus for the confined rubber disk is approximately given by the equation derived by Gent and Lindley (see Ref. [16]): \(E_{\mathrm{eff}} \approx E(1+2 S^2)\) where \(S=D/4d \approx 2.5\) (where \(D\approx 10 \, {\mathrm{cm}}\) is the diameter of the disk and \(d=1 \, {\mathrm{cm}}\) the thickness of the disk). Thus, we get \(E_{\mathrm{eff}} \approx 13.5 E \approx 54 \, {\mathrm{MPa}}\).

References

  1. Barber, J.R.: Bounds on the electrical resistance between contacting elastic rough bodies. Proc. R. Soc. Lond. Ser. A 459, 53 (2003)

    Article  Google Scholar 

  2. Persson, B.N.J., Lorenz, B., Volokitin, A.I.: Heat transfer between elastic solids with randomly rough surfaces. Eur. Phys. J. E 31, 3 (2010)

    Article  Google Scholar 

  3. Campana, C., Persson, B.N.J., Müser, M.H.: Transverse and normal interfacial stiffness of solids with randomly rough surfaces. J. Phys. Condens. Matter 23, 085001 (2011)

    Article  Google Scholar 

  4. The data analyzed in this paper were presented before in: Wang, D., Ueckermann, A., Schacht, A., Oeser, M., Steinauer, B.: Relationship between the tire penetration depth and the road surface texture: a theoretical model and the practical application. In: Proceeding of International Conference GeoHubei 2014. However, the power spectra used in this reference was not accurate, and the results and conclusions obtained in the paper cited above are not accurate

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

    Article  Google Scholar 

  6. 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 

  7. Lorenz, B., Persson, B.N.J.: Interfacial separation between elastic solids with randomly rough surfaces: comparison of experiment with theory. J. Phys. Condens. Matter 21, 015003 (2009)

    Article  Google Scholar 

  8. Lorenz, B., Carbone, G., Schulze, C.: Average separation between a rough surface and a rubber block: comparison between theories and experiments. Wear 268, 984 (2010)

    Article  Google Scholar 

  9. 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 

  10. Pastewka, L., Prodanov, N., Lorenz, B., Mser, M.H., Robbins, M.O., Persson, B.N.J.: Finite-size effect in the interfacial stiffness of rough elastic contacts. Phys. Rev. E 87, 062809 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Gäbel, G., Kröger, M.: Proceedings of the INTER-NOISE 2007, Istanbul (2007)

  13. Gäbel, G., Moldenhauer, P., Kröger, M.: Local effects between the tyre and the road. ATZ 0612008 110, 71 (2008)

    Google Scholar 

  14. Gäbel, G.: Beobachtung und Modellierung lokaler Phänomene im Reifen-Fahrbahn-Kontakt. PhD thesis, University of Hannover (2009)

  15. Dapp, W.B., Prodanov, N., Müser, M.H.: Systematic analysis of perssons contact mechanics theory of randomly rough elastic surfaces. J. Phys. Condens. Matter 26, 355002 (2014)

  16. Anderson, M.L., Mott, P.H., Roland, C.M.: The compression of bonded rubber disks. Rubber Chem. Technol. 77, 293 (2004)

    Article  Google Scholar 

  17. Lyashenko, I.A., Pastewka, L., Persson, B.N.J.: On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness. Tribol. Lett. 52, 223 (2013)

    Article  Google Scholar 

  18. Pohrt, R., Popov, V.L., Filippov, A.E.: Normal contact stiffness of elastic solids with fractal rough surfaces for one- and three-dimensional systems. Phys. Rev. E 86, 026710 (2012)

    Article  Google Scholar 

  19. Barber, J.R.: Incremental stiffness and electrical contact conductance in the contact of rough finite bodies. Phys. Rev. E 87, 013203 (2013)

    Article  Google Scholar 

  20. 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)

  21. Persson, B.N.J.: On the fractal dimension of rough surfaces. Tribol. Lett. 54, 99 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Carbone, G., Mangialardi, L.: Analysis of the adhesive contact of confined layers by using a Green’s function approach. J. Mech. Phys. Solids 56, 684 (2008)

  24. Carbone, G., Lorenz, B., Persson, B.N.J., Wohlers, A.: Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties. Eur. Phys. J. E 29, 275 (2009)

  25. Persson, B.N.J.: J. Phys.: Contact mechanics for layered materials with randomly rough surfaces. Condens. Matter 24, 095008 (2012)

Download references

Acknowledgments

The work underlying this report was commissioned by the Federal Ministry of Transport, Building and Housing under FE SV.0003/2009, by the Federal Ministry of Economics and Technology under 19 S 11002 and on behalf of the German Research Foundation. We thank Stephan Westermann (Goodyear, Luxenburg) and Boris Lorenz for comments on the manuscript.

Author information

Authors and Affiliations

  1. Institute of Road and Traffic Engineering, RWTH Aachen University, 52074, Aachen, Germany

    D. Wang, A. Ueckermann, A. Schacht, M. Oeser & B. Steinauer

  2. PGI, FZ-Jülich, 52425, Jülich, Germany

    B. N. J. Persson

Authors
  1. D. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Ueckermann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Schacht
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Oeser
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Steinauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. B. N. J. Persson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. N. J. Persson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, D., Ueckermann, A., Schacht, A. et al. Tire–Road Contact Stiffness. Tribol Lett 56, 397–402 (2014). https://doi.org/10.1007/s11249-014-0417-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11249-014-0417-x

Keyword

Search

Navigation