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Variation in Fractal Properties and Non-Gaussian Distributions of Microcontact Between Elastic-Plastic Rough Surfaces With Mean Surface Separation

[+] Author and Article Information
Jung Ching Chung

Department of Mechanical Engineering, National Cheng Kung University, Tainan City, 70101, Taiwan

Jen Fin Lin

Department of Mechanical Engineering, National Cheng Kung University, Tainan City, 70101, Taiwanjflin@mail.ncku.edu.tw

J. Appl. Mech 73(1), 143-152 (May 12, 2005) (10 pages) doi:10.1115/1.2061967 History: Received June 16, 2004; Revised May 12, 2005

The fractal parameters (fractal dimension and topothesy), describing the contact behavior of rough surface, were considered as constant in the earlier models. However, their results are often significantly different from the experimental results. In the present study, these two roughness parameters have been derived analytically as a function of the mean separation first, then they are found with the aid of the experimental results. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variation of topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained from the experimental results of the number of contact spots and the power spectrum function at different mean separations. The probability density function of asperity heights, achieved at a different mean separation, was obtained from experimental results as a non-Gaussian distribution; it is expressed as a function of the skewness and the kurtosis. The relationship between skewness and mean separation can be established through the fitting of experimental results by this non-Gaussian distribution. For a sufficiently small mean separation, either the total load or the real contact area predicted by variable fractal parameters, as well as non-Gaussian distribution, is greater than that predicted by constant fractal parameters, as well as Gaussian distribution. The difference between these two models is significantly enhanced as the mean separation becomes small.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

The schematic diagram of two contact surface with deformation

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Figure 2

The experimental results of N(a′)∕Aa shown in the study of Othmani and Kaminsky (23) as a function of the contact spot area a′. The solid curves are applied to fit the experimental data by adjusting the slope value.

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Figure 3

The fractal dimensions varying with the dimensionless mean separation. These data of D are obtained from the slope values of the four curves shown in Fig. 2.

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Figure 4

Determination of the region satisfying Eq. 25. The tribological behavior in the present study is analyzed according to curve 2(a)-curve 2(c).

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Figure 5

Probability density functions of asperity heights (23)

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Figure 6

Variations of the skewness parameter with the dimensionless mean separation. These skewness data are obtained from the fittings shown in Fig. 5.

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Figure 7

Variations of the skewness parameter with the fractal dimension. They are established using Figs.  36.

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Figure 8

Variations of the dimensionless mean separation with the dimensionless total load. They are presented to compare the evaluations based on variable G and D as well as non-Gaussian g(z¯), with the evaluations based on constant G and D as well as Gaussian g(z¯).

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Figure 9

Variations of the dimensionless real contact area with the dimensionless total load. They are presented to compare the evaluations based on the two different models described in Fig. 8.

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Figure 10

Variations of N(a′)∕Aa with the dimensionless mean separation. They are presented to compare the evaluations based on the two different models described in Fig. 8.

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