Understanding the friction laws of Amontons and Coulomb by evaluating the real contact area

Kalin, Mitjan (author), Jan, Petra (author)

Friction is a complex phenomenon that depends on many parameters. Despite this, we still rely on and describe friction in the vast majority of cases with a single value, namely, the coefficient of friction (µ), as first proposed by Amontons in 1699. Later, Coulomb introduced a two-parameter description by separating the adhesive and load-dependent terms. However, experimental evidence that determines under what conditions either of the two historical models is more appropriate has not been investigated in detail. In particular, to take full advantage and achieve better accuracy with the two-parameter equation, the real contact area must be well characterized to determine the constant adhesive component sufficiently and accurately. In this study, we performed sliding experiments and measured friction, but at the same time, we also measured the real contact area with sub-micron lateral resolution, which allowed us to design a two-parameter (Coulomb-type) friction equation. We compared these results with the historical friction models of Amontons and Coulomb to better understand the actual differences between them and how this corresponds to the linearity between the friction force and the normal force, which is a key assumption in the more common and simpler Amontons relation. A strong scaling effect of roughness was observed, as well as the related nonlinearity between the normal load, friction, and real contact area. Under high loads and roughnesses, the one- or two-parameter friction descriptive models differed from experiments by only a few percent, and the variation among them was small in the same range. However, for very low roughnesses and loads (close to the nanoscale region), the two-parameter Coulomb model was required for any relevant friction prediction due to the strong adhesive contribution, while the one-parameter description was not appropriate.

• Language: English
• Keywords: real contact area, friction, sliding, Amontons, Coulomb
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 14 str.
• Numbering: Vol. 13, iss. 1, art. 9440986
• PID: 20.500.12556/RUL-166909
• UDC: 531.4
• ISSN on article: 2223-7690
• DOI: 10.26599/FRICT.2025.9440986
• COBISS.SI-ID: 218328835
• Publication date in RUL: 30.01.2025

Record is a part of a journal

• Title: Friction
• Shortened title: Frict.
• Publisher: Tsinghua University Press
• ISSN: 2223-7690
• COBISS.SI-ID: 525351449

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: pravo kontaktno območje, trenje, drsenje