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Tribology Letters

, 66:146 | Cite as

Theoretical and Finite Element Analysis of Static Friction Between Multi-Scale Rough Surfaces

  • Xianzhang WangEmail author
  • Yang Xu
  • Robert L. Jackson
Original Paper
  • 193 Downloads

Abstract

The current work considers the multi-scale nature of roughness in a new model that predicts the static friction coefficient. This work is based upon a previous rough surface contact model, which used stacked elastic–plastic 3-D sinusoids to model the asperities at multiple scales of roughness. A deterministic model of a three-dimensional deformable rough surface pressed against a rigid flat surface is also carried out using the finite element method (FEM). The accuracy of the deterministic FEM model is also considered. At the beginning of contact, which is surface-point contact, the asperities or peaks are isolated, sharp, and the contact areas consist of an inadequate number of elements and sources of error. In this range of contact, the results are not presented as real or accurate. As the normal load increases, the number of the contact elements become larger, and thus, the results become more accurate. That is, the deterministic FEM results are most accurate at high loads. Spectral interpolation is used to smooth the geometry in between the original measured nodes. The effects of normal load and plasticity index on static friction are then analyzed. The results predicted by the theoretical model are also compared to other existing rough surface friction contact models and the FEM results. They are in a good qualitative agreement, especially for higher loads and higher plasticity indices. The FEM model also has significant error, but it is more accurate at higher loads where the proposed multi-scale static friction model and FEM model are in better agreement.

Keywords

Contact mechanics Static friction Surface roughness analysis and models 

Abbreviations

Nomenclature

A

Area of contact

A0

Contact area under normal preload only

An

Nominal contact area of the surface

Ar

Real contact area

As

Contact area at sliding inception

C

Critical yield stress coefficient

E

Elastic modulus

E′

\({E \mathord{\left/ {\vphantom {E {\left( {1 - {v^2}} \right)}}} \right. \kern-0pt} {\left( {1 - {v^2}} \right)}}\)

f

Spatial frequency (reciprocal of wavelength)

F

Contact force for single asperity

Ff

Friction force

Fn

Normal preload

\(F_{n}^{*}\)

Dimensionless normal preload

Ft

Tangential load

L

Scan length

N

Number of nodes

\({N_e}\)

Number of elements

\({p^{\text{*}}}\)

Average pressure to cause complete contact (Elastic)

\(p_{{ep}}^{*}\)

Average pressure to cause complete contact (Elastic–plastic)

\(\bar {p}\)

Average pressure over the entire surface

\({S_y}\)

Yield strength

\({u_x}\)

Displacement in the x direction

Greek symbols

\(\lambda\)

Asperity wavelength

\(\Delta\)

Asperity amplitude

\({\Delta _c}\)

Critical asperity amplitude

\(\psi\)

Sinusoidal asperity parameter

\(\Psi\)

Plasticity index

\(\sigma\)

Standard derivation on the surface heights

\({\sigma _s}\)

Standard derivation on the asperity heights

\(\nu\)

Poisson’s ratio

\({\tau _c}\)

Critical interfacial shear strength

\({\omega _0}\)

Interference under normal preload

\({\omega _c}\)

Critical interference (full stick condition)

\({\omega _{cs}}\)

Critical interference (perfect slip condition)

\({\mu _s}\)

Static friction coefficient

\({\mu _s}\)

Static friction coefficient

Subscripts

c

Critical value at the onset of plastic deformation (full stick condition)

ave

Average value

max

Maximum value

ep

Elastic–plastic

JGH

From model by Johnson, Greenwood, and Higgson [1]

x

In the x direction

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentAuburn UniversityAuburnUSA

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