DOI: 10.1243/pime_proc_1970_185_069_02. The Contact of Two Nominally Flat Rough Surfaces

The Contact of Two Nominally Flat Rough Surfaces

10.1243/pime_proc_1970_185_069_02

Crossref journal-article

SAGE Publications

Proceedings of the Institution of Mechanical Engineers (179)

Abstract

Most models of surface contact consider the surface roughness to be on one of the contacting surfaces only. The authors give a general theory of contact between two rough plane surfaces. They show that the important results of the previous models are unaffected: in particular, the load and the area of contact remain almost proportional, independently of the detailed mechanical and geometrical properties of the asperities. Further, a single-rough-surface model can always be found which will predict the same laws as a given two-rough-surface model, although the required model may be unrealistic. It does not seem possible to deduce the asperity shape or deformation mode from the load-compliance curve.

Bibliography

Greenwood, J. A., & Tripp, J. H. (1970). The Contact of Two Nominally Flat Rough Surfaces. Proceedings of the Institution of Mechanical Engineers, 185(1), 625â633.

Authors 2

J. A. Greenwood (first)
J. H. Tripp (additional)

References 40 Referenced 1,241

{'volume-title': 'Electric contacts handbook', 'year': '1958', 'author': 'Holm R.', 'key': 'bibr1-PIME_PROC_1970_185_069_02'} / Electric contacts handbook by Holm R. (1958)
{'volume-title': 'Friction and lubrication of solids', 'year': '1954', 'author': 'Bowden F. P.', 'key': 'bibr2-PIME_PROC_1970_185_069_02'} / Friction and lubrication of solids by Bowden F. P. (1954)
{'volume-title': 'The hardness of metals', 'year': '1951', 'author': 'Tabor D.', 'key': 'bibr3-PIME_PROC_1970_185_069_02'} / The hardness of metals by Tabor D. (1951)
10.1098/rspa.1957.0214
10.1016/0043-1648(59)90159-0
{'key': 'bibr6-PIME_PROC_1970_185_069_02', 'first-page': '217', 'volume': '7', 'author': 'Holm R.', 'year': '1929', 'journal-title': 'Wiss. Veröff. Siemens-Werk'} / Wiss. Veröff. Siemens-Werk by Holm R. (1929)
10.1088/0508-3443/17/12/310
10.1080/05698196408972041
10.1098/rspa.1966.0242
10.1098/rspa.1970.0068
10.1088/0022-3727/3/3/306
{'volume-title': '‘Some fundamental problems in the measurement of surfaces’', 'year': '1963', 'author': 'Bickel E.', 'key': 'bibr12-PIME_PROC_1970_185_069_02'} / ‘Some fundamental problems in the measurement of surfaces’ by Bickel E. (1963)
{'key': 'bibr13-PIME_PROC_1970_185_069_02', 'first-page': '57', 'volume': '183', 'author': 'Østvik R.', 'year': '1968', 'journal-title': 'Proc. Instn mech. Engrs'} / Proc. Instn mech. Engrs by Østvik R. (1968)
{'volume-title': 'Surface Mechanics', 'year': '1969', 'author': 'Williamson J. B. P.', 'key': 'bibr14-PIME_PROC_1970_185_069_02'} / Surface Mechanics by Williamson J. B. P. (1969)
10.1063/1.1723395
10.1007/978-1-349-15340-4
10.1115/1.3616906
{'key': 'bibr18-PIME_PROC_1970_185_069_02', 'first-page': '1447', 'volume': '10', 'author': 'Zhuravlev V. A.', 'year': '1940', 'journal-title': 'Zh. tekh. Fiz.'} / Zh. tekh. Fiz. by Zhuravlev V. A. (1940)
10.7312/gumb92958
{'key': 'bibr20-PIME_PROC_1970_185_069_02', 'first-page': '85', 'volume': '86', 'author': 'Peklenik J.', 'year': '1964', 'journal-title': 'Trans. Am. Soc. mech. Engrs'} / Trans. Am. Soc. mech. Engrs by Peklenik J. (1964)
10.1016/0020-7357(69)90013-4
El Refaie M. Auto-correlation analysis of a statistical model of surface profile. (To be published.).
{'key': 'bibr23-PIME_PROC_1970_185_069_02', 'first-page': '60', 'volume-title': 'Tribology Convention', 'author': 'Halling J.', 'year': '1971'} / Tribology Convention by Halling J. (1971)
{'volume-title': '‘A numerical solution for the problem of contact of a sphere and a rough surface’', 'author': 'El Refaie M.', 'key': 'bibr24-PIME_PROC_1970_185_069_02'} / ‘A numerical solution for the problem of contact of a sphere and a rough surface’ by El Refaie M.
Francis H. A. ‘ Predicting contact area using the algebraic sum of two surfaces.’ (To be published.).
{'volume-title': 'Topographic analysis of friction between a pair of rough surfaces', 'year': '1970', 'author': 'Gupta P. K.', 'key': 'bibr26-PIME_PROC_1970_185_069_02'} / Topographic analysis of friction between a pair of rough surfaces by Gupta P. K. (1970)
{'key': 'bibr27-PIME_PROC_1970_185_069_02', 'first-page': '569', 'volume': '55', 'author': 'Abbott E. j.', 'year': '1933', 'journal-title': 'Mech. Engng'} / Mech. Engng by Abbott E. j. (1933)
Rhines R. N. ‘Origins of quantitative metalography’, The Sorby Cent. Symp. on the History of Metallurgy 1965, 417 (Gordon and Breach Scientific Publications, New York, American Institute for Metallurgical Engineering).
Gradshteyn I. S., Rhyzhik I. M. Table of integrals series and products 1965, 284 (Academic Press Inc., New York).
{'author': 'Mikic B. B.', 'journal-title': 'J. Lubric. Technology, Trans. Am. Soc. mech. Engrs.', 'key': 'bibr30-PIME_PROC_1970_185_069_02'} / J. Lubric. Technology, Trans. Am. Soc. mech. Engrs. by Mikic B. B.
Mikic B., Roca R. ‘On elastic deformation of rough surfaces in contact’. (To be published.).
{'key': 'bibr32-PIME_PROC_1970_185_069_02', 'first-page': '81', 'volume': '90', 'author': 'Tsukizoe T.', 'year': '1968', 'journal-title': 'Trans. Am. Soc. mech. Engrs'} / Trans. Am. Soc. mech. Engrs by Tsukizoe T. (1968)
10.1016/0043-1648(70)90185-7
10.1299/jsme1958.1.329
{'key': 'bibr35-PIME_PROC_1970_185_069_02', 'first-page': '21', 'volume': '182', 'author': 'Williamson J. B. P.', 'year': '1967', 'journal-title': 'Proc. Instn mech. Engrs'} / Proc. Instn mech. Engrs by Williamson J. B. P. (1967)
{'volume-title': 'Random process model of rough surfaces', 'year': '1970', 'author': 'Nayak P. Ranganath', 'key': 'bibr36-PIME_PROC_1970_185_069_02'} / Random process model of rough surfaces by Nayak P. Ranganath (1970)
Archard J. F. Personal communication, 1970.
{'volume-title': 'Influence of dressing and performance of grinding wheels', 'year': '1970', 'author': 'Bhateja C. P.', 'key': 'bibr38-PIME_PROC_1970_185_069_02'} / Influence of dressing and performance of grinding wheels by Bhateja C. P. (1970)
10.1016/0022-5096(70)90029-3
Cramer H. Extreme value problems in stochastic processes. Unpublished proceedings of Oceanography Conference, Portugal, 1968.

Dates

Type	When
Created	17 years, 10 months ago (Oct. 1, 2007, 11:12 a.m.)
Deposited	11 months ago (Sept. 26, 2024, 7:44 p.m.)
Indexed	22 hours, 36 minutes ago (Aug. 30, 2025, 1:02 p.m.)
Issued	55 years, 2 months ago (June 1, 1970)
Published	55 years, 2 months ago (June 1, 1970)
Published Online	55 years, 2 months ago (June 1, 1970)
Published Print	55 years, 2 months ago (June 1, 1970)

Funders 0

None

BibTeX

@article{Greenwood_1970, title={The Contact of Two Nominally Flat Rough Surfaces}, volume={185}, ISSN={2058-1203}, url={http://dx.doi.org/10.1243/pime_proc_1970_185_069_02}, DOI={10.1243/pime_proc_1970_185_069_02}, number={1}, journal={Proceedings of the Institution of Mechanical Engineers}, publisher={SAGE Publications}, author={Greenwood, J. A. and Tripp, J. H.}, year={1970}, month=jun, pages={625–633} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        30
      ]
    ],
    "date-time": "2025-08-30T17:02:46Z",
    "timestamp": 1756573366065
  },
  "reference-count": 40,
  "publisher": "SAGE Publications",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1970,
            6,
            1
          ]
        ],
        "date-time": "1970-06-01T00:00:00Z",
        "timestamp": 13046400000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://journals.sagepub.com/page/policies/text-and-data-mining-license"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1970,
        6
      ]
    ]
  },
  "abstract": "<jats:p> Most models of surface contact consider the surface roughness to be on one of the contacting surfaces only. The authors give a general theory of contact between two rough plane surfaces. They show that the important results of the previous models are unaffected: in particular, the load and the area of contact remain almost proportional, independently of the detailed mechanical and geometrical properties of the asperities. Further, a single-rough-surface model can always be found which will predict the same laws as a given two-rough-surface model, although the required model may be unrealistic. It does not seem possible to deduce the asperity shape or deformation mode from the load-compliance curve. </jats:p>",
  "DOI": "10.1243/pime_proc_1970_185_069_02",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2007,
        10,
        1
      ]
    ],
    "date-time": "2007-10-01T15:12:07Z",
    "timestamp": 1191251527000
  },
  "page": "625-633",
  "source": "Crossref",
  "is-referenced-by-count": 1241,
  "title": "The Contact of Two Nominally Flat Rough Surfaces",
  "prefix": "10.1177",
  "volume": "185",
  "author": [
    {
      "given": "J. A.",
      "family": "Greenwood",
      "sequence": "first",
      "affiliation": [
        {
          "name": "The University of Cambridge, University Engineering Department, Trumpington Street, Cambridge, CB2 1PZ."
        }
      ]
    },
    {
      "given": "J. H.",
      "family": "Tripp",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Physics, University of Connecticut"
        }
      ]
    }
  ],
  "member": "179",
  "published-online": {
    "date-parts": [
      [
        1970,
        6,
        1
      ]
    ]
  },
  "reference": [
    {
      "volume-title": "Electric contacts handbook",
      "year": "1958",
      "author": "Holm R.",
      "key": "bibr1-PIME_PROC_1970_185_069_02"
    },
    {
      "volume-title": "Friction and lubrication of solids",
      "year": "1954",
      "author": "Bowden F. P.",
      "key": "bibr2-PIME_PROC_1970_185_069_02"
    },
    {
      "volume-title": "The hardness of metals",
      "year": "1951",
      "author": "Tabor D.",
      "key": "bibr3-PIME_PROC_1970_185_069_02"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr4-PIME_PROC_1970_185_069_02",
      "DOI": "10.1098/rspa.1957.0214"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr5-PIME_PROC_1970_185_069_02",
      "DOI": "10.1016/0043-1648(59)90159-0"
    },
    {
      "key": "bibr6-PIME_PROC_1970_185_069_02",
      "first-page": "217",
      "volume": "7",
      "author": "Holm R.",
      "year": "1929",
      "journal-title": "Wiss. Ver\u00f6ff. Siemens-Werk"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr7-PIME_PROC_1970_185_069_02",
      "DOI": "10.1088/0508-3443/17/12/310"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr8-PIME_PROC_1970_185_069_02",
      "DOI": "10.1080/05698196408972041"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr9-PIME_PROC_1970_185_069_02",
      "DOI": "10.1098/rspa.1966.0242"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr10-PIME_PROC_1970_185_069_02",
      "DOI": "10.1098/rspa.1970.0068"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr11-PIME_PROC_1970_185_069_02",
      "DOI": "10.1088/0022-3727/3/3/306"
    },
    {
      "volume-title": "\u2018Some fundamental problems in the measurement of surfaces\u2019",
      "year": "1963",
      "author": "Bickel E.",
      "key": "bibr12-PIME_PROC_1970_185_069_02"
    },
    {
      "key": "bibr13-PIME_PROC_1970_185_069_02",
      "first-page": "57",
      "volume": "183",
      "author": "\u00d8stvik R.",
      "year": "1968",
      "journal-title": "Proc. Instn mech. Engrs"
    },
    {
      "volume-title": "Surface Mechanics",
      "year": "1969",
      "author": "Williamson J. B. P.",
      "key": "bibr14-PIME_PROC_1970_185_069_02"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr15-PIME_PROC_1970_185_069_02",
      "DOI": "10.1063/1.1723395"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr16-PIME_PROC_1970_185_069_02",
      "DOI": "10.1007/978-1-349-15340-4"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr17-PIME_PROC_1970_185_069_02",
      "DOI": "10.1115/1.3616906"
    },
    {
      "key": "bibr18-PIME_PROC_1970_185_069_02",
      "first-page": "1447",
      "volume": "10",
      "author": "Zhuravlev V. A.",
      "year": "1940",
      "journal-title": "Zh. tekh. Fiz."
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr19-PIME_PROC_1970_185_069_02",
      "DOI": "10.7312/gumb92958"
    },
    {
      "key": "bibr20-PIME_PROC_1970_185_069_02",
      "first-page": "85",
      "volume": "86",
      "author": "Peklenik J.",
      "year": "1964",
      "journal-title": "Trans. Am. Soc. mech. Engrs"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr21-PIME_PROC_1970_185_069_02",
      "DOI": "10.1016/0020-7357(69)90013-4"
    },
    {
      "unstructured": "El Refaie M. Auto-correlation analysis of a statistical model of surface profile. (To be published.).",
      "key": "bibr22-PIME_PROC_1970_185_069_02"
    },
    {
      "key": "bibr23-PIME_PROC_1970_185_069_02",
      "first-page": "60",
      "volume-title": "Tribology Convention",
      "author": "Halling J.",
      "year": "1971"
    },
    {
      "volume-title": "\u2018A numerical solution for the problem of contact of a sphere and a rough surface\u2019",
      "author": "El Refaie M.",
      "key": "bibr24-PIME_PROC_1970_185_069_02"
    },
    {
      "unstructured": "Francis H. A. \u2018 Predicting contact area using the algebraic sum of two surfaces.\u2019 (To be published.).",
      "key": "bibr25-PIME_PROC_1970_185_069_02"
    },
    {
      "volume-title": "Topographic analysis of friction between a pair of rough surfaces",
      "year": "1970",
      "author": "Gupta P. K.",
      "key": "bibr26-PIME_PROC_1970_185_069_02"
    },
    {
      "key": "bibr27-PIME_PROC_1970_185_069_02",
      "first-page": "569",
      "volume": "55",
      "author": "Abbott E. j.",
      "year": "1933",
      "journal-title": "Mech. Engng"
    },
    {
      "unstructured": "Rhines R. N. \u2018Origins of quantitative metalography\u2019, The Sorby Cent. Symp. on the History of Metallurgy 1965, 417 (Gordon and Breach Scientific Publications, New York, American Institute for Metallurgical Engineering).",
      "key": "bibr28-PIME_PROC_1970_185_069_02"
    },
    {
      "unstructured": "Gradshteyn I. S., Rhyzhik I. M. Table of integrals series and products 1965, 284 (Academic Press Inc., New York).",
      "key": "bibr29-PIME_PROC_1970_185_069_02"
    },
    {
      "author": "Mikic B. B.",
      "journal-title": "J. Lubric. Technology, Trans. Am. Soc. mech. Engrs.",
      "key": "bibr30-PIME_PROC_1970_185_069_02"
    },
    {
      "unstructured": "Mikic B., Roca R. \u2018On elastic deformation of rough surfaces in contact\u2019. (To be published.).",
      "key": "bibr31-PIME_PROC_1970_185_069_02"
    },
    {
      "key": "bibr32-PIME_PROC_1970_185_069_02",
      "first-page": "81",
      "volume": "90",
      "author": "Tsukizoe T.",
      "year": "1968",
      "journal-title": "Trans. Am. Soc. mech. Engrs"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr33-PIME_PROC_1970_185_069_02",
      "DOI": "10.1016/0043-1648(70)90185-7"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr34-PIME_PROC_1970_185_069_02",
      "DOI": "10.1299/jsme1958.1.329"
    },
    {
      "key": "bibr35-PIME_PROC_1970_185_069_02",
      "first-page": "21",
      "volume": "182",
      "author": "Williamson J. B. P.",
      "year": "1967",
      "journal-title": "Proc. Instn mech. Engrs"
    },
    {
      "volume-title": "Random process model of rough surfaces",
      "year": "1970",
      "author": "Nayak P. Ranganath",
      "key": "bibr36-PIME_PROC_1970_185_069_02"
    },
    {
      "unstructured": "Archard J. F. Personal communication, 1970.",
      "key": "bibr37-PIME_PROC_1970_185_069_02"
    },
    {
      "volume-title": "Influence of dressing and performance of grinding wheels",
      "year": "1970",
      "author": "Bhateja C. P.",
      "key": "bibr38-PIME_PROC_1970_185_069_02"
    },
    {
      "doi-asserted-by": "publisher",
      "key": "bibr39-PIME_PROC_1970_185_069_02",
      "DOI": "10.1016/0022-5096(70)90029-3"
    },
    {
      "unstructured": "Cramer H. Extreme value problems in stochastic processes. Unpublished proceedings of Oceanography Conference, Portugal, 1968.",
      "key": "bibr40-PIME_PROC_1970_185_069_02"
    }
  ],
  "container-title": "Proceedings of the Institution of Mechanical Engineers",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://journals.sagepub.com/doi/pdf/10.1243/PIME_PROC_1970_185_069_02",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://journals.sagepub.com/doi/pdf/10.1243/PIME_PROC_1970_185_069_02",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        9,
        26
      ]
    ],
    "date-time": "2024-09-26T23:44:57Z",
    "timestamp": 1727394297000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://journals.sagepub.com/doi/10.1243/PIME_PROC_1970_185_069_02"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1970,
        6
      ]
    ]
  },
  "references-count": 40,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          1970,
          6
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1243/PIME_PROC_1970_185_069_02"
  ],
  "URL": "http://dx.doi.org/10.1243/PIME_PROC_1970_185_069_02",
  "relation": {},
  "ISSN": [
    "0020-3483",
    "2058-1203"
  ],
  "subject": [],
  "container-title-short": "Proceedings of the Institution of Mechanical Engineers",
  "published": {
    "date-parts": [
      [
        1970,
        6
      ]
    ]
  }
}