Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Tribology Letters
Published in: Tribology Letters 1/2015

01-04-2015 | Original Paper

Contact Mechanics for Randomly Rough Surfaces: On the Validity of the Method of Reduction of Dimensionality

Author: Bo N. J. Persson

Published in: Tribology Letters | Issue 1/2015

Log in

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

search-config
loading …

Abstract

Recently, a 1D mapping procedure has been applied to many contact mechanics problems between randomly rough surfaces. I present a simple “back-of-the-envelope” argument to show that this theory fails qualitatively, in particular when surface roughness occurs on many length scales.
previous article Wear and Friction-Induced Vibration of Brake Friction Materials with Different Weight Average Molar Mass Phenolic Resins
next article In Situ Fabrication of Low-Friction Sandwich Sheets Through Functionalized Graphene Crosslinked by Ionic Liquids

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!

inform now

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!

inform now
Footnotes
1
In the contact mechanics theory of Popov et al., the roughness of the 1D substrate has a power spectrum related to that of the original 2D surface via the equation: \(C_\mathrm{1D} (q) = \pi q C_\mathrm{2D}(q)\). This definition of \(C_\mathrm{1D}\) result in a 1D line profile having the same mean-square (ms) roughness as the original 2D surface (with the power spectrum \(C_\mathrm{2D}\)). Using standard methods, a randomly rough line profile was generated using \(C_\mathrm{1D} (q)\). This line profile will have nearly the same statistical properties as a line scan from the original 2D surface with the power spectrum \(C_\mathrm{2D}\).
 
Literature
1.
Popov, V.L., Heß, M.: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin (2014)
2.
Sneddon, I.N.: The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965)CrossRef
3.
Li, Q., Dimaki, A., Popov, M., Psakhie, S.G., Popov, V.L.: Kinetics of the coefficient of friction of elastomers. Sci. Rep. 4, 5795 (2014)
4.
Popov, V.L., Voll, L., Li, Q., Chai, Y.S., Popov, M.: Generalized law of friction between elastomers and differently shaped rough bodies. Sci. Rep. 4, 3750 (2014)
5.
Pohrt, R., Popov, V.L.: Contact stiffness of randomly rough surfaces. Sci. Rep. 3, 3293 (2013)CrossRef
6.
Paggi, M., Pohrt, R., Popov, V.L.: Partial-slip frictional response of rough surfaces. Sci. Rep. 4, 5178 (2014)
7.
Geike, T., Popov, V.L.: Mapping of three-dimensional contact problems into one dimension. Phys. Rev. E 76, 036710 (2007)CrossRef
8.
Pohrt, R., Popov, V.L.: Normal contact stiffness of elastic solids with fractal rough surfaces. Phys. Rev. Lett. 108, 104301 (2012)CrossRef
9.
Pohrt, R., Popov, V.L., Filippov, A.: Normal contact stiffness of elastic solids with fractal rough surfaces for one- and three-dimensional systems. Phys. Rev. E 86, 026710 (2012)CrossRef
10.
Popov, V.L., Filippov, A.E.: Force of friction between fractal rough surface and elastomer. Tech. Phys. Lett. 36, 525 (2010)CrossRef
11.
Popov, V.L.: Contact Mechanics and Friction, Physical Principles and Applications. Springer, Berlin (2010). (See Chapter 19)
12.
13.
Popov, V.L., Filippov, A.E.: Applicability of a reduced model to description of real contacts between rough surfaces with different Hirsch indices. Tech. Phys. Lett. 34, 722 (2008)CrossRef
14.
Birthe, G., Pohrt, R., Teidelt, E., et al.: Maximum micro-slip in tangential contact of randomly rough self-affine surfaces. Wear 309, 256 (2014)CrossRef
15.
Popov, V.L.: Method of dimensionality reduction in contact mechanics and tribology. Heterogeneous media. Phys. Mesomech. 17, 50 (2014)CrossRef
16.
Li, Q., Popov, M., Dimaki, A., et al.: Friction between a viscoelastic body and a rigid surface with random self-affine roughness. Phys. Rev. Lett. 111, 034301 (2013)CrossRef
17.
Psakhie, S.G., Popov, V.L.: Mesoscopic nature of friction and numerical simulation methods in tribology. Phys. Mesomech. 15, 251 (2012)CrossRef
18.
Dimaki, A.V., Popov, V.L.: The method of reduction of dimensionality and its application to simulation of elastomer friction under complex dynamic loads. Phys. Mesomech. 15, 319 (2012)CrossRef
19.
Pohrt, R., Popov, V.L.: Investigation of the dry normal contact between fractal rough surfaces using the reduction method, comparison to 3D simulations. Phys. Mesomech. 15, 275 (2012)CrossRef
20.
Popov, V.L., Filippov, A.E.: Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: a simulation with the method of reduction of dimensionality. Phys. Mesomech. 15, 324 (2012)CrossRef
21.
Nguyen, H.X., Teidelt, E., Popov, V.L., et al.: Dynamic tangential contact of rough surfaces in stick-slip microdrives: modeling and validation using the method of dimensionality Reduction. Phys. Mesomech. 17(4), 304–310 (2014)CrossRef
22.
Grzemba, B., Pohrt, R., Teidelt, E., et al.: Maximum micro-slip in tangential contact of randomly rough self-affine surfaces. Wear 309, 256 (2014)CrossRef
23.
Popov, V.L.: Basic ideas and applications of the method of reduction of dimensionality in contact mechanics. Phys. Mesomech. 15(5–6), 254–263 (2012)CrossRef
24.
Teidelt, E., Willert, E., Filippov, A.E., et al.: Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality. Phys. Mesomech. 15, 287 (2012)CrossRef
25.
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(3), 223–229 (2013)CrossRef
26.
Lyashenko, I.A., Pastewka, L., Persson, B.N.J.: Comment on friction between a viscoelastic body and a rigid surface with random self-affine roughness. Phys. Rev. Lett. 111, 189401 (2013)CrossRef
27.
Pastewka, L., Prodanov, N., Lorenz, B., Müser, M.H., Robbins, M.O., Persson, B.N.J.: Finite-size effects in the interfacial stiffness of rough elastic contacts. Phys. Rev. E 87, 062809 (2013). See also arXiv:​1210.​4255v1 and arXiv:​1210.​4635v1
28.
Scaraggi, M., Putignano, C., Carbone, G.: Elastic contact of rough surfaces: a simple criterion to make 2D isotropic roughness equivalent to 1D one. Wear 297, 811 (2013)CrossRef
29.
Persson, B.N.J.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115, 3840 (2001)CrossRef
30.
Klüppel, M., Heinrich, G.: Rubber friction on self-affine road tracks. Rubber Chem. Technol. 73, 578 (2000)CrossRef
31.
Westergaard, H.M.: Bearing pressures and cracks. Trans. ASME J. Appl. Mech. 6, 49 (1939)
32.
Persson, B.N.J.: On the fractal dimension of rough surfaces. Tribol. Lett. 54, 99 (2014)CrossRef
Metadata
Title
Contact Mechanics for Randomly Rough Surfaces: On the Validity of the Method of Reduction of Dimensionality
Author
Bo N. J. Persson
Publication date
01-04-2015
Publisher
Springer US
Published in
Tribology Letters / Issue 1/2015
Print ISSN: 1023-8883
Electronic ISSN: 1573-2711
DOI
https://doi.org/10.1007/s11249-015-0498-1

Other articles of this Issue 1/2015

Tribology Letters 1/2015 Go to the issue

Original Paper

In Situ Fabrication of Low-Friction Sandwich Sheets Through Functionalized Graphene Crosslinked by Ionic Liquids

Original Paper

Self-Healing of Abrasion Damage in Epoxy Resin–Ionic Liquid Nanocomposites

Original Paper

Cavitation Bubble Measurement in Tribological Contacts Using Digital Holographic Microscopy

Original Paper

The Stability of the Coefficient of Friction and Wear Behavior of C/C–SiC

Original Paper

Efficient Solution to the Cavitation Problem in Hydrodynamic Lubrication

Response to the Commentary

Reply to the Comment by Scott Bair, Philippe Vergne, Punit Kumar, Gerhard Poll, Ivan Krupka, Martin Hartl, Wassim Habchi, Roland Larson on “History, Origins and Prediction of Elastohydrodynamic Friction” by Spikes and Jie in Tribology Letters

Premium Partners

    Image Credits