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Research Papers: Contact Mechanics

# A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness

[+] Author and Article Information
W. Wayne Chen, Q. Jane Wang

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

J. Tribol 131(2), 021402 (Mar 03, 2009) (8 pages) doi:10.1115/1.3063814 History: Received February 15, 2008; Revised November 04, 2008; Published March 03, 2009

## Abstract

The relative motion between two surfaces under a normal load is impeded by friction. Interfacial junctions are formed between surfaces of asperities, and sliding inception occurs when shear tractions in the entire contact area reach the shear strength of the weaker material and junctions are about to be separated. Such a process is known as a static friction mechanism. The numerical contact model of dissimilar materials developed by the authors is extended to evaluate the maximum tangential force (in terms of the static friction coefficient) that can be sustained by a rough surface contact. This model is based on the Boussinesq–Cerruti integral equations, which relate surface tractions to displacements. The materials are assumed to respond elastic perfectly plastically for simplicity, and the localized hardness and shear strength are set as the upper limits of contact pressure and shear traction, respectively. Comparisons of the numerical analysis results with published experimental data provide a validation of this model. Static friction coefficients are predicted for various material pairs in contact first, and then the behaviors of static friction involving rough surfaces are extensively investigated.

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## Figures

Figure 1

Contact problem shown in the x-z plane, where δx and δz are the rigid-body approaches, ux and uz are the normal elastic displacement, and h is the surface gap

Figure 2

Real contact area between a copper sphere and a smooth steel half-space under the normal load of P=6Pc. (The solid line is the contact area boundary with the normal load alone, and the dashed line is the contact area boundary at the gross sliding inception; the arrow indicates the direction of the tangential force application on the half-space.)

Figure 3

Real contact area between a copper sphere and a rough steel half-space (Rq=0.06 μm) under the normal load of P=6Pc (a) with the normal load alone and (b) at the gross sliding inception. (The gray area is in contact, and the arrow indicates the direction of the tangential force application on the half-space.)

Figure 4

Identification of the sliding inception moment for the contacts of a copper sphere and a steel half-space under the normal load of P=6Pc

Figure 5

Contact area variations with the increasing tangential force for the contacts of a copper sphere and a steel half-space under the normal load of P=6Pc. (Ac0 is the initial contact area under the normal load alone.)

Figure 6

Model validations through a comparison with the experimental results in Ref. 7: (a) the static friction coefficient versus dimensionless normal load for copper on sapphire and (b) maximum tangential force (static friction force) versus dimensionless normal load for copper on sapphire and copper on steel

Figure 7

Effect of discretization resolution on the static friction coefficient predicted for the contact involving a rough surface (copper ball on sapphire half-space)

Figure 8

Comparison of static friction coefficient variations as a function of the dimensionless normal load for the contacts of the copper ball on the rough half-space of different materials

Figure 9

Effects of surface rms roughness, Rq, on static friction coefficient for the copper ball on the sapphire half-space

## Errata

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