Editorial Type:
Article Category: Research Article
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Online Publication Date: 02 May 2019

Comparison of Analytical Model for Contact Mechanics Parameters with Numerical Analysis and Experimental Results

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Page Range: 168 – 187
DOI: 10.2346/tire.19.180198
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ABSTRACT

Being able to estimate tire/rubber friction is very important to tire engineers, materials developers, and pavement engineers. This is because of the need for estimating forces generated at the contact, optimizing tire and vehicle performance, and estimating tire wear. Efficient models for contact area and interfacial separation are key for accurate prediction of friction coefficient. Based on the contact mechanics and surface roughness, various models were developed that can predict real area of contact and penetration depth/interfacial separation. In the present work, we intend to compare the analytical contact mechanics models using experimental results and numerical analysis. Nano-indentation experiments are performed on the rubber compound to obtain penetration depth data. A finite element model of a rubber block in contact with a rough surface was developed and validated using the nano-indentation experimental data. Results for different operating conditions obtained from the developed finite element model are compared with analytical model results, and further model improvements are discussed.

Keywords: friction; Hertzian contact mechanics; penetration depth; nano-indentation; finite element; sliding contact
FIG. 1 —
FIG. 1 —

Hertz contact of plane surface with spherical asperity.

FIG. 2 —
FIG. 2 —

(A) Identical asperities; (B) spherical asperities with height distribution.

FIG. 3 —
FIG. 3 —

Deformation at the contact interface representing the mean surface profile < z > and mean separation distance d.

FIG. 4 —
FIG. 4 —

Raw material modulus data used for obtaining the Prony series.

FIG. 5 —
FIG. 5 —

Mean square error (MSE) for both real and imaginary components.

FIG. 6 —
FIG. 6 —

Final results after fitting using the Prony equation.

FIG. 7 —
FIG. 7 —

Nano-indentation simulation model.

FIG. 8 —
FIG. 8 —

Rubber block sliding on a rigid surface.

FIG. 9 —
FIG. 9 —

Comparison of rubber block with sharp edges (top) vs rounded edged (bottom).

FIG. 10 —
FIG. 10 —

Nano-indentation equipment.

FIG. 11 —
FIG. 11 —

Creep test of Compound A sample with a maximum load of 2 mN.

FIG. 12 —
FIG. 12 —

Repeatability of loading step up to 2 mN at eight different spots in the rubber sample.

FIG. 13 —
FIG. 13 —

Indentation depth vs load for nine different loads from 0.5 to 2 mN.

FIG. 14 —
FIG. 14 —

(A) Maximum load vs penetration depth; (B) contact area at maximum load.

FIG. 15 —
FIG. 15 —

(A) DMA master curve data for Compound A; (B) surface profile for 120-grit surface.

FIG. 16 —
FIG. 16 —

Axisymmetric indentation simulation of a spherical sphere on a flat rubber sample.

FIG. 17 —
FIG. 17 —

Comparison of analytical (Hertz theory), numerical analysis using finite elements and experimental testing.

FIG. 18 —
FIG. 18 —

(A) Surface profile in ABAQUS; (B) model of the rubber block sliding on a rough substrate.

FIG. 19 —
FIG. 19 —

Deformation of the contact interface under different loading conditions.

FIG. 20 —
FIG. 20 —

Comparison of separation distance using (left) numerical analysis and (right) analytical model.

FIG. 21 —
FIG. 21 —

Greenwood Williamson's function.

Contributor Notes

1 Corresponding author. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, 100 B Randolph Hall, 460 Old Turner Street, Blacksburg, Virginia 24060, USA. Email: sunish90@vt.edu
2 Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, 100 B Randolph Hall, 460 Old Turner Street, Blacksburg, Virginia 24060, USA. Email: anouri@vt.edu
3 Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, 100 C Randolph Hall, 460 Old Turner Street, Blacksburg, Virginia 24060, USA
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