Contact Mechanics

The Influence of Surface Topography on Energy Dissipation and Compliance in Tangentially Loaded Elastic Contacts

[+] Author and Article Information
Simon Medina, Andrew V. Olver

Department of Mechanical Engineering,  Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK

Daniele Dini1

Department of Mechanical Engineering,  Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UKd.dini@imperial.ac.uk

Note that where h > 0 and p = 0, there is no such error, and these areas are neglected in this calculation.

It should be noted here that the assumption of a constant coefficient of friction at the contact interface has been made. Although a varying coefficient of friction at the contact interface could have been introduced based on the evolution of the frictional interface in the presence of oscillating load and partial slip [49], this is avoided here to keep the focus on the influence that surface topography has on normal and tangential stiffness. It would have also been possible to extend the treatment to replace the constant Coulomb-type friction law with yield inception-type descriptions (see, e.g., Ref. [36] and the comparison between different models performed in Ref. [32]). However, this would have required a rather more complex approach to implement plasticity in our deterministic description of the rough surfaces under investigation, rendering, therefore, impossible to concentrate on the effect of non-Gaussian roughnesses on the contact behavior. These developments will be discussed and presented in future contributions. The use of the elastic framework and a constant coefficient of friction is also motivated by the experimental evidence obtained by the authors and co-workers during the collaborative project supporting the research presented in this contribution [15].

Note that the same nomenclature used in Ref. [12] is adopted here.


Corresponding author.

J. Tribol 134(1), 011401 (Feb 24, 2012) (12 pages) doi:10.1115/1.4005641 History: Received July 16, 2010; Revised November 08, 2011; Published February 10, 2012; Online February 24, 2012

The influence of non-Gaussian surface roughness on elastic contacts loaded in both normal and tangential directions has been investigated. A numerical solution method based on the multilevel scheme and incorporating the theorem of Ciavarella/Jaeger has been implemented, which allows fast calculation of partial slip loading conditions, including the energy dissipation for a fully reversed tangential loading cycle. The effect of varying roughness rms, skewness, kurtosis, and correlation lengths on contact areas, stiffness values, and energy dissipation is presented, and the significance of these parameters and of the loading method are discussed. It was found that the energy dissipation can be greatly increased by greater surface roughness. Maps showing how the energy dissipation is distributed within the contact are presented, which provide some explanation for this observation and the scatter that may occur for surfaces of nominally similar roughness. The suitability of these parameters for predicting the contact behavior of rough surfaces is also considered.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Multilevel solution schematic

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Figure 2

(a) Tangential displacements within contact, (b) frictional hysteresis loop for surface, and (c) frictional hysteresis loop for node

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Figure 3

Comparison of pressure distribution on regular asperities rough surfaces for validation. (a) 3D plot of the pressure distribution and contour plot of the mismatch between the analytical solution derived in Ref. [12] and the numerical solution obtained using the methodology implemented by the authors, and (b) pressure distribution and mismatch for the case in (a) and at y = 0.

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Figure 4

Solution of (a) contact pressures, (b) tangential tractions, (c) slip, and (d) energy dissipation for a surface with scaled Rq and QP = 0.8. The left hand side shows RMS Rq0  = 0.0064, and the right hand side shows RMS Rq0  = 0.0512.

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Figure 5

Effect of Rq on (a) contact area, (b) contact regions, (c) normal stiffness, (d) tangential stiffness, and (e) energy dissipation for smooth and rough surfaces for QP = 0.8 (all rough surfaces have a kurtosis of 3.0)

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Figure 7

Example contour plots showing the effect of correlation length on pressure (left hand side) and energy dissipation (right hand side). RMS Rq0  = 0.091, QP = 0.8, and correlation lengths: (a) CL0  = 4.56, (b) CL0  = 7.29, (c) CL0  = 13.67, and (d) CL0  = 22.79.

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Figure 8

Effect of correlation length on (a) contact area, (b) contact regions, (c) normal stiffness, (d) tangential stiffness, and (e) energy dissipation. RMS Rq0  = 0.091, and QP = 0.8

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Figure 9

Comparisons of results in terms of (a) tangential stiffness and (b) energy dissipation for different generated surfaces characterised by RMS Rq /δ0  = 0.091 and QP = 0.8. Each marker indicates a new generated surface, which has been transformed to the same Rq , RSk , and RKu .

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Figure 10

Comparison of (a) load controlled and (b) displacement controlled friction loops for a coefficient of friction μ = 0.5. Surfaces Rough A and Rough B refer to two surfaces characterized by scaled RMSs Rq0  = 0.091 and Rq0  = 0.365, respectively.



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