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Research Papers: Contact Mechanics

# A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems

[+] Author and Article Information
Raynald Guilbault

Department of Mechanical Engineering, Ecole de Technologie Superieure, 1100 rue Notre-Dame Ouest, Montreal, QC, H3C 1K3, Canada e-mail: raynald.guilbault@etsmtl.ca

J. Tribol 133(3), 031402 (Jul 01, 2011) (10 pages) doi:10.1115/1.4003766 History: Received September 21, 2010; Revised February 28, 2011; Published July 01, 2011; Online July 01, 2011

## Abstract

Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of which are based on the Boussinesq–Cerruti solution. This paper presents a new approach, which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without engendering any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor $(ψ)$, which accounts for the normal load. The expression $ψ$ is derived from the Hetényi correction process, and the resulting displacements show an enhanced correspondence with validation finite element method models; with an imposed fluctuating pressure, the maximum edge displacement error was −21.90% for a shear load correction (Poisson coefficient $ν=0.3$), and introducing the $ψ$ factor reduced the deviation to −9.55%, while for $ν$ of 0.15, the maximum error was −11.30%, which was reduced to $+0.60%$ with the $ψ$ factor. This study introduces the factor $ψ$ in a 3D elastic contact algorithm. The resulting calculation scheme is then able to simulate any point or line contact problems. Compared with coincident ends and sharp edge contact validation values, the model shows high conformity levels.

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## Figures

Figure 1

Experimental contact area (reproduced from Ref. [7])

Figure 2

Half-space free surface internal stresses

Figure 3

Pressure cells and mirror correction

Figure 4

Half-plane with concentrated forces

Figure 5

Quarter-plane states

Figure 6

Quarter-plane conditions

Figure 7

Test form

Figure 8

Edge displacement (ν=0.15)

Figure 9

Edge displacement (ν=0.30)

Figure 10

Edge displacement (ν=0.45)

Figure 11

Maximum error curve along edges

Figure 12

FEM model for coincident cylinder ends

Figure 13

Transversal pressure distributions for coincident end

Figure 14

3D OCCM pressure distribution

Figure 15

Pressure distributions along the z-axis

Figure 16

Normalized pressure distributions along the z-axis

Figure 17

Contact cell number influence

Figure 18

Contact cell number influence—error curves

Figure 19

Experiment—contact area (rubber sheet-aluminum cylinder)

Figure 20

OCCM—calculated pressure distribution

Figure 21

Experiment—measured and calculated contact areas

Figure 22

Experiment—experimental and calculated normalized contact widths

Figure 23

Rubber cylinder—aluminum plate—calculated pressure distribution

Figure 24

Rubber cylinder—aluminum plate—calculated contact area

Figure 25

Rubber cylinder—aluminum plate—calculated normalized contact width

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