Abstract
The accurate calculation of the real contact area between rough surfaces is a key issue in tribology. In this paper, based on the geometrical information of total contact area and the number of contact patches with respect to surface separation, a new method is proposed to determine the relation between real contact area and normal load. The contact of rough surfaces is treated as an accumulation of equivalent circular contacts with varying average contact radius. For a realistic range of separation, the proposed model predicts a linear relation between real contact area and load, and coincides well with direct finite element calculations. Moreover, this model is general and not confined to isotropic Gaussian surfaces.
Issue Section:
Contact Mechanics
References
1.
Müser
, M. H.
, Dapp
, W. B.
, Bugnicourt
, R.
, Sainsot
, P.
, Lesaffre
, N.
, Lubrecht
, T. A.
, Persson
, B. N.
, Harris
, K.
, Bennett
, A.
, Schulze
, K.
, and Rohde
, S.
, 2017
, “Meeting the Contact-Mechanics Challenge
,” Trib. Lett.
, 65
(4
), p. 118
. 10.1007/s11249-017-0900-22.
Vakis
, A. I.
, Yastrebov
, V. A.
, Scheibert
, J.
, Nicola
, L.
, Dini
, D.
, Minfray
, C.
, Almqvist
, A.
, Paggi
, M.
, Lee
, S.
, Limbert
, G.
, and Molinari
, J. F.
, 2018
, “Modeling and Simulation in Tribology Across Scales: an Overview
,” Tribol. Int.
, 125
, pp. 169
–199
. 10.1016/j.triboint.2018.02.0053.
Archard
, J. F.
, 1957
, “Elastic Deformation and the Laws of Friction
,” Proc. R. Soc. A
, 243
(1233
), pp. 190
–205
.4.
Greenwood
, J. A.
, and Williamson
, J. B. P.
, 1966
, “Contact of Nominally Flat Surfaces
,” Proc. R. Soc. A
, 295
(1442
), pp. 300
–319
.5.
Bush
, A. W.
, Gibson
, R. D.
, and Thomas
, T. R.
, 1975
, “The Elastic Contact of a Rough Surface
,” Wear
, 35
(1
), pp. 87
–111
. 10.1016/0043-1648(75)90145-36.
Nayak
, P. R.
, 1971
, “Random Process Model of Rough Surfaces
,” ASME J. Lubr. Tech.
, 93
(3
), pp. 398
–407
. 10.1115/1.34516087.
Greenwood
, J. A.
, 2006
, “A Simplified Elliptic Model of Rough Surface Contact
,” Wear
, 261
(2
), pp. 191
–200
. 10.1016/j.wear.2005.09.0318.
Majumdar
, A.
, and Bhushan
, B.
, 1991
, “Fractal Model of Elastic-Plastic Contact Between Rough Surfaces
,” ASME J. Tribol.
, 113
(1
), pp. 1
–11
. 10.1115/1.29205889.
Persson
, B. N. J.
, 2001
, “Theory of Rubber Friction and Contact Mechanics
,” J. Chem. Phys.
, 115
(8
), pp. 3840
–3861
. 10.1063/1.138862610.
Carbone
, G.
, and Bottiglione
, F.
, 2008
, “Asperity Contact Theories: Do They Predict Linearity Between Contact Area and Load
,” J. Mech. Phys. Solids
, 56
(8
), pp. 2555
–2572
. 10.1016/j.jmps.2008.03.01111.
Abbott
, E. J.
, and Firestone
, F. A.
, 1933
, “Specifying Surface Quality-A Method Based on Accurate Measurement and Comparison
,” J. Mech. Eng.
, 55
, pp. 569
–572
.12.
Greenwood
, J. A.
, 1967
, “The Area of Contact Between Rough Surfaces and Flats
,” ASME J. Lubr. Tech.
, 89
(1
), pp. 81
–87
. 10.1115/1.361690613.
Hill
, R.
, and Storåkers
, B. A.
, 1990
,” “Concise Treatment of Axisymmetric Indentation in Elasticity,” Elasticity: Mathematical Methods and Applications
, G.
Eason
, and R. W.
Ogden
, eds., Ellis Horwood
, Chichester, UK
, pp. 199
–210
.14.
Greenwood
, J. A.
, 2010
, “Contact Between an Axisymmetric Indenter and a Viscoelastic Half-Space
,” Int. J. Mech. Sci.
, 52
(6
), pp. 829
–835
. 10.1016/j.ijmecsci.2010.01.01015.
Barber
, J. R.
, 2003
, “Bounds on the Electrical Resistance Between Contacting Elastic Rough Bodies
,” Proc. R. Soc. A
, 459
(2029
), pp. 53
–66
. 10.1098/rspa.2002.103816.
Barber
, J. R.
, 2013
, “Incremental Stiffness and Electrical Contact Conductance in the Contact of Rough Finite Bodies
,” Phys. Rev. E
, 87
(1
), p. 013203
. 10.1103/PhysRevE.87.01320317.
Sneddon
, I. N.
, 1946
, “Boussinesq Problem for a Flat-Ended Cylinder
,” Proc. Cambr. Phil. Soc.
, 42
(1
), pp. 29
–39
. 10.1017/S030500410002270218.
Nayak
, P. R.
, 1973
, “Random Process Model of Rough Surfaces in Plastic Contact
,” Wear
, 26
(3
), pp. 305
–333
. 10.1016/0043-1648(73)90185-319.
Greenwood
, J. A.
, 2007
, “A Note on Nayak’s Third Paper
,” Wear
, 262
(1–2
), pp. 225
–227
. 10.1016/j.wear.2006.04.01120.
Kanafi
, M. M.
, 2020
, “Surface Generator: Artificial Randomly Rough Surfaces
,” https://www.mathworks.com/matlabcentral/fileexchange/60817-surface-generator-artificial-randomly-rough-surfaces, Accessed September 30, 2020.21.
Hyun
, S.
, Pei
, L.
, Molinari
, J. F.
, and Robbins
, M. O.
, 2004
, “Finite-Element Analysis of Contact Between Elastic Self-Affine Surfaces
,” Phys. Rev. E
, 70
(2
), p. 026117
. 10.1103/PhysRevE.70.026117Copyright © 2021 by ASME
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