Research Papers: Contact Mechanics

Frictional Energy Dissipation in a Rough Hertzian Contact

[+] Author and Article Information
D. Dini1

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

D. A. Hills

Department of Engineering Science, University of Oxford, Parks Road, OX1 3PJ, Oxford, UK


Corresponding author.

J. Tribol 131(2), 021401 (Mar 03, 2009) (8 pages) doi:10.1115/1.3063697 History: Received March 19, 2007; Revised November 13, 2008; Published March 03, 2009

The interfacial contact pressure and shear traction distributions are found for a sphere pressed onto an elastically similar half-space whose surface is populated by a uniform array of spherical asperities, when the normal load is constant and an oscillatory shear, less than that needed to cause sliding, is imposed. Details of the load history suffered by asperities in an outer sliding annulus and an inner disk, where they experience partial slip, are found, together with the effects of the roughness on the overall tangential compliance and the frictional energy losses. It is shown that for the example combination of parameters chosen, under light shear loads, the rough contact absorbs less energy than a smooth one subject to the same loading history, but that for larger shearing forces the reverse is true.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

(a) Hertzian contact problem and (b) equivalent idealized rough contact

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Figure 2

“Isometric” asperity distribution

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Figure 3

Example problem: pressure distribution

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Figure 4

A discrete evolution of the stick region as a function of the tangential load Q. (a) Due to the discrete nature of the problem, the asperities centered on “rings” A–F (central asperity) will enter the slip annulus discontinuously while varying the tangential load Q monotonically from 0 to fP. (b) Example distribution for Q/fP=0.5: Here only six asperities belong to the slip annulus (schematically approximated by the dotted lines).

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Figure 5

Shear traction distribution for Q/fP=0.5: (a) overall and (b) localized (central asperity) three-dimensional distributions

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Figure 6

Normalized pressure and shear traction distribution for Q/fP=0.5 and y=0

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Figure 7

Dimensionless (a) shearing forces and (b) displacements at asperity level as a function of the dimensionless tangential load Q/fP

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Figure 8

Normalized displacements versus normalized shear force loops for Qmax/fP=0.5: (a) smooth equivalent contact and (b) asperities

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Figure 9

(a) Normalized frictional energy dissipated as a function of the macroscopic normalized shear force. Two examples of shear traction distributions corresponding to two loading conditions are also displayed as an inset to the figure. (b) Zoom-in of the plot in Fig. 9 at low levels of normalized tangential forces. Two examples of shear traction distributions corresponding to two loading conditions are also displayed as an inset to the figure.




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