0
Contact Mechanics

Numerical Method of Analyzing Contact Mechanics between a Sphere and a Flat Considering Lennard-Jones Surface Forces of Contacting Asperities and Noncontacting Rough Surfaces

[+] Author and Article Information
Kyosuke Ono

 Emeritus ProfessorTokyo Institute of Technology, Nanyodai-cho 2-27-4, Hachioji-shi, Tokyo, 192-0371, Japanono_kyosuke@nifty.com

J. Tribol 134(1), 011402 (Mar 06, 2012) (15 pages) doi:10.1115/1.4005643 History: Received April 03, 2010; Revised November 26, 2010; Published March 05, 2012; Online March 06, 2012

A new numerical method of analyzing adhesive contact mechanics between a sphere and a flat with sub-nanometer roughness is presented. In contrast to conventional theories, the elastic deformations of mean height surfaces and contacting asperities, and Lennard-Jones (LJ) surface forces of both the contacting asperities and noncontacting rough surfaces including valley areas are taken into account. Calculated contact characteristics of a 2-mm-radius glass slider contacting a magnetic disk with a relatively rough surface and a 30-mm-radius head slider contacting a currently available magnetic disk with lower roughness are shown in comparison with conventional adhesive contact theories. The present theory was found to give a larger adhesive force than the conventional theories and to converge to a smooth sphere-flat contact theory as the roughness height approaches zero.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Analytical model of adhesive contact between sphere and flat

Grahic Jump Location
Figure 2

Flowchart of iterative numerical calculation

Grahic Jump Location
Figure 3

LJ attractive pressures, Hertzian contact pressure, and external pressure for RHS, MHS and MCEB theories and effective area ratios as a function of normalized spacing in case A when mean surface deformation is ignored. (a) LJ attractive pressures PLJca , PLJm, PLJnca , and PLJncr and Hertzian contact pressure PH , (b) External pressure −Pex (= PH  − PLJca  − αr PLJncr (RHS theory), PH  − PLJca  − αm PLJm (MHS theory), and PH  − PLJca  − PLJnca (MCEB theory)). (c) Effective area ratios of αr for RHS theory and αm for MHS theory.

Grahic Jump Location
Figure 4

LJ attractive pressures, Hertzian contact pressure, and external pressure for RHS, MHS and MCEB theories and effective area ratios as a function of normalized spacing in case B when mean surface deformation is ignored. (a) LJ attractive pressures PLJca , PLJm , PLJnca , and PLJncr and Hertzian contact pressure PH ; (b) External pressure −Pex (= PH  − PLJca −αr PLJncr (RHS theory), PH  − PLJca  − αm PLJm (MHS theory), and PH  − PLJca  − PLJnca (MCEB theory)). (c) Effective area ratios of αr for RHS theory and αm for MHS theory.

Grahic Jump Location
Figure 5

Comparison of RHS, MHS and EMCEB theories for LJ force due to contacting asperities −FLJca , LJ force due to noncontacting surface −FLJncr (−FLJm or −FLJnca ), Hertzian contact force FH , and external force −Fex in case A. (a) RHS theory, (b) MHS theory and (c) EMCEB theory.

Grahic Jump Location
Figure 6

Contact characteristics by RHS theory for case A when d is changed from zm  + 5σa (= 2.8 nm) to zm  − 4σa (= −0.296 nm). (a) Deformation w versus radial position r, (b) Normalized spacing ha /σa versus r, (c) Effective area ratios ηa , ηr and ηH versus r, (d) FH , −Fex , −FLJca , and −FLJncr versus minimum spacing h0 .

Grahic Jump Location
Figure 7

Comparison of RHS, MHS and EMCEB theories for LJ force due to contacting asperities −FLJca , LJ force due to noncontacting surface −FLJncr (−FLJm or −FLJnca ), Hertzian contact force FH , and external force −Fex as a function of separation d in case B. (a) RHS theory, (b) MHS theory and (c) EMCEB theory.

Grahic Jump Location
Figure 8

Adhesive contact characteristics between 30-mm-radius sphere and flat by RHS theory for case B when d is changed from zm  + 9σa (= 2.25 nm) to zm  −  σa (= 0.25 nm). (a) Deformation w versus r, (b) ha /σa versus r, (c) αr PLJncr and PLJca versus r, (d) −Pex versus r, (e) ηa , ηr , ηH versus r, and (f) FH , −Fex , −FLJca and −FLJncr versus h0 .

Grahic Jump Location
Figure 9

Adhesive contact characteristics of a 30-nm-radius sphere contacting a magnetic disk for four different values of contact spacing σ. (a) LJ force between mean height surfaces FLJm versus spacing h0 , (b) −FLJm versus separation d, (c) Hertzian contact force FH versus d, and (e) external force −Fex versus d.

Grahic Jump Location
Figure 10

Numerically calculated adhesive contact characteristics of 1.24-μm-radius asperity in case A when contact spacing is assumed to be z0 . (a) Deformation w of the mean height surface of the flat, (b) attractive pressure, PLJm , between mean height surfaces and dotted line showing 10% of the maximum pressure, (c) ratio, Ri/t , of attractive force inside a circle with ref to the total attractive force, (d) spacing, hm , between mean height surfaces, (e) various forces, −FLJm , FH , −Fex , and FLJ* , versus separation d, and (f) contact radius rH versus external force −Fex , and those of DMT and JKR models.

Grahic Jump Location
Figure 11

Numerically calculated relationships between effective radius, ref , for adhesive force of contacting asperity and Hertzian contact radius, rH , in cases A and B and their fitted linear functions of form ref  = 2rH /3 + λ

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In