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A Generalised Asperity-Based Friction Model

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Abstract

Despite considerable research effort, the use of physics-based modelling to predict frictional behaviour is still a debatable question in modern tribological research. This article presents a dry-friction model, based on physical phenomena such as adhesion, elastic–plastic contact and deformation. This contribution offers a means to simulate all kinds of frictional behaviour that is observed in experimental research. The contact of two bodies through their surfaces is transformed into the contact of a body that is provided with asperities and containing material and geometrical information of both of the mating surfaces, and a counter profile, holding solely geometrical information. The local adhesion between the asperity tips and the counter profile, together with the elastic–plastic behaviour of the asperities themselves, form the basis for this model. The simulation results show qualitatively good agreement with experimental study. Friction and contact phenomena such as normal creep, increasing static coefficient of friction with increasing dwell time, pre-sliding hysteresis with nonlocal memory, Stribeck and viscous effect, frictional lag, stick–slip and dynamical oscillations are revealed by this model. Furthermore, future improvement and refinement of the model is possible (and ongoing) so as to incorporate lubrication and asperity wear.

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Abbreviations

δ j :

Spring deformation of the j-th element

δn :

Normal interference depth

Δ j :

Maximum spring deformation of the j-th Maxwell-Slip element

ζ:

Main damping ratio

ζTi :

Tangential damping ratio of the i-th asperity

ζNi :

Normal damping ratio of the i-th asperity

λ:

Mean counter profile wavelength

μ:

Coefficient of friction

μs :

Static coefficient of friction

σNi , σTi :

Yielding force

τ:

Non-dimensional time

ωN :

Main eigenfrequency of the system

ωnTi :

Tangential eigenfrequency of the i-th asperity

ωnNi :

Normal eigenfrequency of the i-th asperity

ωnPi :

Eigenfrequency of counter profile of the i-th asperity

A :

Amplitude of the applied excitation

cT,i , cN,i :

Dimensional tangential and normal damping of the i-th asperity

C T :

Dimensional main tangential damping

C :

Damping matrix

dx T,i :

Horizontal asperity distribution

f t :

Frequency of the applied excitation

F fric :

Non-dimensional global friction force

F norm :

Non-dimensional global normal contact force

F n :

Local normal contact force

F adh,i :

Adhesion force of the i-th asperity

F :

Force vector

k el :

Elastic spring stiffness

k pl :

Plastic spring stiffness

k p,i :

Profile stiffness of the i-th asperity

kT,i , kN,i :

Dimensional tangential and normal stiffness of the i-th asperity

K T :

Dimensional main tangential stiffness

K :

Stiffness matrix

l i :

Dimensional asperity length

L i :

Non-dimensional asperity length

m i :

Dimensional mass of the i-th asperity

M :

Dimensional main mass

M :

Mass matrix

N :

Number of asperities

q :

State vector

t :

Dimensional time

x, y:

Dimensional position

x i , y i :

Dimensional asperity mass position of the i-th asperity

xm, ym:

Dimensional position of the free end of the main spring

xt, yt:

Dimensional main mass position

X, Y:

Non-dimensional position

.:

Dimensional time derivation

′:

Non-dimensional time derivation

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Acknowledgements

This research is supported by the Fund for Scientific Research—Flanders (F.W.O.) under Grant FWO4283. This research is conducted utilising high performance computational resources provided by the University of Leuven, http://ludit.kuleuven.be/hpc. The scientific responsibility is assumed by its authors.

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Authors and Affiliations

  1. Mechanical Engineering Department, Division PMA, Katholieke Universiteit Leuven, Celestijnenlaan 300B, 3001, Heverlee, Belgium

    Kris De Moerlooze, Farid Al-Bender & Hendrik Van Brussel

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  1. Kris De Moerlooze
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  2. Farid Al-Bender
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Correspondence to Kris De Moerlooze.

Appendix

Appendix

See Table 1.

Table 1 Overview of the used model parameters
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De Moerlooze, K., Al-Bender, F. & Van Brussel, H. A Generalised Asperity-Based Friction Model. Tribol Lett 40, 113–130 (2010). https://doi.org/10.1007/s11249-010-9645-x

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