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Research Papers: Contact Mechanics

# A New Three-Dimensional Numerical Model of Rough Contact: Influence of Mode of Surface Deformation on Real Area of Contact and Pressure Distribution

[+] Author and Article Information
A. Jourani

Laboratoire Roberval,
Centre de Recherches de Royallieu,
Université de Technologie de Compiègne,
CNRS UMR 6253, BP20259,
Compiegne 60205, France
e-mail: abdeljalil.jourani@utc.fr

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 25, 2014; final manuscript received August 10, 2014; published online September 5, 2014. Assoc. Editor: Mircea Teodorescu.

J. Tribol 137(1), 011401 (Sep 05, 2014) (11 pages) Paper No: TRIB-14-1045; doi: 10.1115/1.4028286 History: Received February 25, 2014; Revised August 10, 2014

## Abstract

Surface roughness causes contact to occur only at discrete spots called microcontacts. In the deterministic models real area of contact and pressure field are widely evaluated using Flamant and Boussinesq equations for two-dimensional (2D) and three-dimensional (3D), respectively. In this paper, a new 3D geometrical contact approach is developed. It models the roughness by cones and uses the concept of representative strain at each asperity. To discuss the validity of this model, a numerical solution is introduced by using the spectral method and another 3D geometrical approach which models the roughness by spheres. The real area of contact and the pressure field given by these approaches show that the conical model is almost insensitive to the degree of isotropy of the rough surfaces, which is not the case for the spherical model that is only valid for quasi-isotropic surfaces. The comparison between elastic and elastoplastic models reveals that for a surface with a low roughness, the elastic approach is sufficient to model the rough contact. However, for surfaces having a great roughness, the elastoplastic approach is more appropriate to determine the real area of contact and pressure distribution. The results of this study show also that the roughness scale modifies the real contact area and pressure distribution. The surfaces characterized by high frequencies are less resistant in contact and present the lowest real area of contact and the most important mean pressure.

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## Figures

Fig. 1

Spherical and conical indentation

Fig. 2

Presentation of the summits of the roughness by deformable indenters

Fig. 3

Conical geometry of an asperity i

Fig. 4

(a) Sanded surface; (b) localization of summits of sanded surface; and (c) pressure distribution

Fig. 5

Comparison between spectral method and matrix store method by using a sanded surface

Fig. 6

Topographies of surfaces: (a) unidirectional ground surface (Ra = 0.23 μm) and (b) sanded surface (Ra = 7.52 μm)

Fig. 7

Evolution of displacement as function of the normal load for a unidirectional ground surface by using the two geometrical models and spectral method

Fig. 8

Evolution of displacement as function of the normal load for sanded surface by using the two geometrical models and spectral method

Fig. 9

Indentation curves: (a) ground surface and (b) sanded surface [44]

Fig. 10

Contact area ratio Ar for the ground and sanded surface by using elastoplastic spherical and conical models

Fig. 11

Contact area ratio Ar as function of nominal contact pressure for the ground surface by using the spectral method and elastoplastic conical model

Fig. 12

Contact area ratio Ar as function of nominal contact pressure for the sanded surface by using the spectral method (elastic) and elastoplastic conical model

Fig. 13 (a)

Sanded surface (original surface); low-pass filtering of sanded surface: (b) λf = 20 mm−1; (c) λf = 10 mm−1; and (d) λf = 5 mm−1

Fig. 14

Mean pressure by using the sanded surface (original surface) and low-pass filtered surfaces with λf = 5, 10, 20 mm−1

Fig. 15

Contact area ratio Ar (%) by using the sanded surface (original surface) and low-pass filtered surfaces with λf = 5, 10, 20 mm−1

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