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Research Papers: Contact Mechanics

On the Significance of Asperity Models Predictions of Rough Contact With Respect to Recent Alternative Theories

[+] Author and Article Information
M. Ciavarella

Politecnico di BARI,
Viale Gentile 182,
Bari 70125, Italy
e-mail: mciava@poliba.it

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 24, 2016; final manuscript received June 20, 2016; published online October 27, 2016. Assoc. Editor: James R. Barber.

J. Tribol 139(2), 021402 (Oct 27, 2016) (4 pages) Paper No: TRIB-16-1063; doi: 10.1115/1.4034245 History: Received February 24, 2016; Revised June 20, 2016

Recently, it has been shown that while asperity models show correctly qualitative features of rough contact problems (linearity in area–load, negative exponential dependence of load on separation which means also linearity of stiffness with load), the exact value of the coefficients are not precise for the idealized case of Gaussian distribution of heights. This is due to the intrinsic simplifications, neglecting asperity coalescence, and interaction effects. However, the issue of Gaussianity has not been proved or experimentally verified in many cases, and here, we show that, for example, assuming a Weibull distribution of asperity heights, the area–load linear coefficient is not much affected, while the relationships load–separation and, therefore, also stiffness–load do change largely, particularly when considering bounded distributions of asperity heights. It is suggested that Gaussianity of surfaces should be further tested in the experiments, before applying the most sophisticated rough contact models based on the Gaussian assumption.

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Figures

Grahic Jump Location
Fig. 1

The PDF of the asperity height distributions used in the paper: Weibull with a = 1, 2, 3 and Gauss. Contact is approached either from the right, more usual unbounded side, or from the left, bounded side.

Grahic Jump Location
Fig. 2

Area–load (a), and load–separation (b), for the approach on the tail side of the Weibull tail. Notice that the separation is positive here as in standard asperity models.

Grahic Jump Location
Fig. 3

Area–load (a), and load–separation (b), for the approach on the bounded side of the Weibull tail. Notice that the separation is negative in this case as zero corresponds to just zero contact.

Grahic Jump Location
Fig. 4

Stiffness–load ratio, for the standard approach on the tail side of the Weibull (a), or on the bounded side (b)

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