Editorial Type:
Article Category: Research Article
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Online Publication Date: 07 May 2025

Determination of Penetration Depth and Excited Volume of Rubber in Klüppel Friction Theory from Friction Law

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Page Range: 14 – 31
DOI: 10.2346/507469
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ABSTRACT

This article aims to determine the excited volume and penetration depth in the theoretical friction model of rubber sliding on a corundum surface. The theoretical procedure of the Klüppel friction theory was implemented using the power spectral density of the corundum surface and viscoelastic model for rubber. The power spectral density was obtained with a power-law mode using the height difference correlation function parameters calculated from a surface measurement taken with a profilometer. Viscoelastic model parameters for the rubber were derived from a dynamic mechanical analyzer. Empirical law for friction coefficient obtained from the side force experiments and simulations of a laboratory abrasion tester (LAT 100) were used in this work. The friction coefficient from the theoretical procedure was matched with the empirical friction coefficient to estimate the penetration depth and excited volume of rubber. The correlation between the theoretical and empirical model was satisfactory. Estimating the penetration depth and excited volume of sliding rubber provides an insight into the contact conditions near surface asperities and the volume of rubber contributing to energy dissipation during the frictional process.

Keywords: friction; rubber; penetration depth; theoretical; fractals; viscoelastic
FIG. 1
FIG. 1

Flowchart for calculating penetration depth and excited volume of rubber.

FIG. 2
FIG. 2

Methodology for obtaining empirical friction law from LAT 100.

FIG. 3
FIG. 3

Empirical friction law for (a) compound A and (b) compound B.

FIG. 4
FIG. 4

Measured corundum surface profile.

FIG. 5
FIG. 5

HDCF for corundum surface.

FIG. 6
FIG. 6

Master curve of the complex modulus for (a) compound A and (b) compound B.

FIG. 7
FIG. 7

Smallest asperity length for (a) compound A and (b) compound B.

FIG. 8
FIG. 8

Ratio of actual contact area to nominal contact area for (a) compound A and (b) compound B.

FIG. 9
FIG. 9

Mean penetration depth.

FIG. 10
FIG. 10

Free parameter b for (a) compound A and (b) compound B.

FIG. 11
FIG. 11

Hysteresis friction coefficient for (a) compound A and (b) compound B.

FIG. 12
FIG. 12

Adhesive friction coefficient for (a) compound A and (b) compound B.

FIG. 13
FIG. 13

Comparison between theoretical friction coefficient and empirical friction coefficient values for (a) compound A and (b) compound B.

Contributor Notes

3Corresponding author. Email: rkkumar@iitm.ac.in
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