Skip to main content
Top
Published in: Tribology Letters 1/2014

01-07-2014 | Original Paper

Rolling Friction: Comparison of Analytical Theory with Exact Numerical Results

Authors: Michele Scaraggi, Bo N. J. Persson

Published in: Tribology Letters | Issue 1/2014

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We study the contact mechanics of a smooth hard cylinder rolling on a flat surface of a linear viscoelastic solid. Using the measured viscoelastic modulus of unfilled and filled (with carbon black) nitrile rubber, we compare numerically exact results for the rolling friction with the prediction of a simple analytical theory. For the unfilled rubber, the two theories agree perfectly while some small difference exists for the filled rubber. The rolling friction coefficient depends nonlinearly on the normal load and the rolling velocity.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Footnotes
1
It can be easily shown that the discrete formulation of the viscoelastic line contact kernel presents an analytical formulation as it occurs for the elastic case. This largely simplifies the viscoelastic integration.
 
Literature
1.
go back to reference Persson, B.: Sliding Friction: Physical Principles and Applications, 2nd edn. Springer, Heidelberg (2000)CrossRef Persson, B.: Sliding Friction: Physical Principles and Applications, 2nd edn. Springer, Heidelberg (2000)CrossRef
2.
go back to reference Grosch, K.: The relation between the friction and visco-elastic properties of rubber. Proc. R. Soc. Lond. A Mat. 274, 21–39 (1963)CrossRef Grosch, K.: The relation between the friction and visco-elastic properties of rubber. Proc. R. Soc. Lond. A Mat. 274, 21–39 (1963)CrossRef
3.
go back to reference Persson, B.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 22, 325107 (2010) Persson, B.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 22, 325107 (2010)
4.
go back to reference Persson, B.: Rubber friction: role of the flash temperature. J. Phys.: Condens. Matter 18, 7789–7823 (2006) Persson, B.: Rubber friction: role of the flash temperature. J. Phys.: Condens. Matter 18, 7789–7823 (2006)
5.
go back to reference Persson, B., Albohr, O., Tartaglino, U., Volokitin, A., Tosatti, E.: On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J. Phys.: Condens. Matter 17, R1–R62 (2005) Persson, B., Albohr, O., Tartaglino, U., Volokitin, A., Tosatti, E.: On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J. Phys.: Condens. Matter 17, R1–R62 (2005)
6.
go back to reference Heinrich, G., Klüppel, M., Vilgis, T.: Evaluation of self-affine surfaces and their implication for frictional dynamics as illustrated with a Rouse material. Comput Theory Polym S 10, 53–61 (2000)CrossRef Heinrich, G., Klüppel, M., Vilgis, T.: Evaluation of self-affine surfaces and their implication for frictional dynamics as illustrated with a Rouse material. Comput Theory Polym S 10, 53–61 (2000)CrossRef
7.
go back to reference Heinrich, G., Klüppel, M.: Rubber friction, tread deformation and tire traction. Wear 265, 1052–1060 (2008)CrossRef Heinrich, G., Klüppel, M.: Rubber friction, tread deformation and tire traction. Wear 265, 1052–1060 (2008)CrossRef
8.
go back to reference Persson, B., Volokitin, A.: Rubber friction on smooth surfaces. Eur. Phys. J. E 21, 69–80 (2006)CrossRef Persson, B., Volokitin, A.: Rubber friction on smooth surfaces. Eur. Phys. J. E 21, 69–80 (2006)CrossRef
9.
go back to reference Carbone, G., Lorenz, B., Persson, B., Wohlers, A.: Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties. Eur. Phys. J. E 29, 275–284 (2009)CrossRef Carbone, G., Lorenz, B., Persson, B., Wohlers, A.: Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties. Eur. Phys. J. E 29, 275–284 (2009)CrossRef
10.
go back to reference Persson, B.: On the theory of rubber friction. Surf. Sci. 401, 445–454 (1998)CrossRef Persson, B.: On the theory of rubber friction. Surf. Sci. 401, 445–454 (1998)CrossRef
11.
go back to reference Le Gal, A., Yang, X., Klüppel, M.: Evaluation of sliding friction and contact mechanics of elastomers based on dynamic-mechanical analysis. J. Chem. Phys. 123, 014704 (2005) Le Gal, A., Yang, X., Klüppel, M.: Evaluation of sliding friction and contact mechanics of elastomers based on dynamic-mechanical analysis. J. Chem. Phys. 123, 014704 (2005)
12.
go back to reference Persson, B.: Theory of powdery rubber wear. J. Phys.: Condens. Matter 21, 485001 (2009) Persson, B.: Theory of powdery rubber wear. J. Phys.: Condens. Matter 21, 485001 (2009)
13.
go back to reference Mofidi, M., Prakash, B., Persson, B., Albohr, O.: Rubber friction on (apparently) smooth lubricated surfaces. J. Phys. Condens. Mat. 20, 085223 (2008) Mofidi, M., Prakash, B., Persson, B., Albohr, O.: Rubber friction on (apparently) smooth lubricated surfaces. J. Phys. Condens. Mat. 20, 085223 (2008)
14.
go back to reference Persson, B., Albohr, O., Creton, C., Peveri, V.: Contact area between a viscoelastic solid and a hard, randomly rough, substrate. J. Chem. Phys. 120, 8779–8793 (2004)CrossRef Persson, B., Albohr, O., Creton, C., Peveri, V.: Contact area between a viscoelastic solid and a hard, randomly rough, substrate. J. Chem. Phys. 120, 8779–8793 (2004)CrossRef
15.
go back to reference Greenwood, J., Johnson, K., Choi, S.-H., Chaudhury, M.: Investigation of adhesion hysteresis between rubber and glass using a pendulum. J. Phys. D: Appl. Phys. 42, 035301 (2009)CrossRef Greenwood, J., Johnson, K., Choi, S.-H., Chaudhury, M.: Investigation of adhesion hysteresis between rubber and glass using a pendulum. J. Phys. D: Appl. Phys. 42, 035301 (2009)CrossRef
16.
go back to reference She, H., Malotky, D., Chaudhury, M.: Estimation of Adhesion Hysteresis at Polymer/Oxide Interfaces Using Rolling Contact Mechanics. Langmuir 14, 3090–3100 (1998)CrossRef She, H., Malotky, D., Chaudhury, M.: Estimation of Adhesion Hysteresis at Polymer/Oxide Interfaces Using Rolling Contact Mechanics. Langmuir 14, 3090–3100 (1998)CrossRef
17.
go back to reference Greenwood, J., Tabor, D.: The friction of hard sliders on lubricated rubber: the importance of deformation losses. J. Phys. Soc. 71, 989 (1958)CrossRef Greenwood, J., Tabor, D.: The friction of hard sliders on lubricated rubber: the importance of deformation losses. J. Phys. Soc. 71, 989 (1958)CrossRef
18.
go back to reference Greenwood, J.A., Minshall, H., Tabor, D.: Hysteresis losses in rolling and sliding friction. Proc R. Soc. Lond. A Mat. 259, 480–507 (1961)CrossRef Greenwood, J.A., Minshall, H., Tabor, D.: Hysteresis losses in rolling and sliding friction. Proc R. Soc. Lond. A Mat. 259, 480–507 (1961)CrossRef
19.
go back to reference Tabor, D.: The rolling and skidding of automobile tyres. Phys. Rev. Spec. Top-Ph 29, 301 (1994) Tabor, D.: The rolling and skidding of automobile tyres. Phys. Rev. Spec. Top-Ph 29, 301 (1994)
20.
go back to reference Felhos, D., Xu, D., Schlarb, A., Vradi, K., Goda, T.: Viscoelastic characterization of an EPDM rubber and finite element simulation of its dry rolling friction. Express Polym. Lett. 2, 157–164 (2008)CrossRef Felhos, D., Xu, D., Schlarb, A., Vradi, K., Goda, T.: Viscoelastic characterization of an EPDM rubber and finite element simulation of its dry rolling friction. Express Polym. Lett. 2, 157–164 (2008)CrossRef
21.
go back to reference Hunter, S.: The rolling contact of a rigid cylinder With a viscoelastic half space. J. Appl. Mech. 28, 611–617 (1961)CrossRef Hunter, S.: The rolling contact of a rigid cylinder With a viscoelastic half space. J. Appl. Mech. 28, 611–617 (1961)CrossRef
22.
go back to reference Goryacheva, I.G.: Contact problem of rolling of a viscoelastic cylinder on a base of the same material. J. Appl. Math. Mech. 37 877–885 (1973) Goryacheva, I.G.: Contact problem of rolling of a viscoelastic cylinder on a base of the same material. J. Appl. Math. Mech. 37 877–885 (1973)
23.
go back to reference Panek, C., Kalker, J.: Three-dimensional contact of a rigid roller traversing a viscoelastic half space. IMA. J. Appl. Math. 26, 299–313 (1980)CrossRef Panek, C., Kalker, J.: Three-dimensional contact of a rigid roller traversing a viscoelastic half space. IMA. J. Appl. Math. 26, 299–313 (1980)CrossRef
24.
go back to reference Vollebregt, E.: User guide for CONTACT, Vollebregt and Kalker’s rolling and sliding contact model. Techical report TR09-03, version 13.1 (2013) Vollebregt, E.: User guide for CONTACT, Vollebregt and Kalker’s rolling and sliding contact model. Techical report TR09-03, version 13.1 (2013)
25.
go back to reference Persson, B.: Rolling friction for hard cylinder and sphere on viscoelastic solid. Eur. Phys. J. E 33, 327–333 (2010)CrossRef Persson, B.: Rolling friction for hard cylinder and sphere on viscoelastic solid. Eur. Phys. J. E 33, 327–333 (2010)CrossRef
26.
go back to reference Carbone, G., Putignano, C.: A novel methodology to predict sliding and rolling friction of viscoelastic materials: theory and experiments. J. Mech. Phys. Solids 61, 1822–1834 (2013)CrossRef Carbone, G., Putignano, C.: A novel methodology to predict sliding and rolling friction of viscoelastic materials: theory and experiments. J. Mech. Phys. Solids 61, 1822–1834 (2013)CrossRef
27.
go back to reference Persson, B.: Contact mechanics for layered materials with randomly rough surfaces. J. Phys. Condens. Mat. 24, 095008 (2012) Persson, B.: Contact mechanics for layered materials with randomly rough surfaces. J. Phys. Condens. Mat. 24, 095008 (2012)
28.
go back to reference Scaraggi, M., Persson, B.: Theory of viscoelastic lubrication. Tribol Int 72, 118–130 (2014)CrossRef Scaraggi, M., Persson, B.: Theory of viscoelastic lubrication. Tribol Int 72, 118–130 (2014)CrossRef
29.
go back to reference Yang, C. Persson, B.: Contact mechanics: contact area and interfacial separation from small contact to full contact. J. Phys. Condens. Mat. 20, 215214 (2008) Yang, C. Persson, B.: Contact mechanics: contact area and interfacial separation from small contact to full contact. J. Phys. Condens. Mat. 20, 215214 (2008)
30.
go back to reference Lorenz, B., Pyckhout-Hintzen, W., Persson, B.: Master curve of viscoelastic solid: using causality to determine the optimal shifting procedure, and to test the accuracy of measured data. Polymer 55, 565–571 (2014)CrossRef Lorenz, B., Pyckhout-Hintzen, W., Persson, B.: Master curve of viscoelastic solid: using causality to determine the optimal shifting procedure, and to test the accuracy of measured data. Polymer 55, 565–571 (2014)CrossRef
Metadata
Title
Rolling Friction: Comparison of Analytical Theory with Exact Numerical Results
Authors
Michele Scaraggi
Bo N. J. Persson
Publication date
01-07-2014
Publisher
Springer US
Published in
Tribology Letters / Issue 1/2014
Print ISSN: 1023-8883
Electronic ISSN: 1573-2711
DOI
https://doi.org/10.1007/s11249-014-0327-y

Other articles of this Issue 1/2014

Tribology Letters 1/2014 Go to the issue

Premium Partners