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Research Papers: Other (Seals, Manufacturing)

# The Effect of Anisotropy on the Percolation Threshold of Sealing Surfaces

[+] Author and Article Information
Zhimeng Yang

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District, Beijing 100081, China
e-mail: bitzhimengyang@gmail.com

Jianhua Liu

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District, Beijing 100081, China
e-mail: jeffliu@bit.edu.cn

Xiaoyu Ding

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District, Beijing 100081, China
e-mail: xiaoyu.ding@bit.edu.cn

Feikai Zhang

School of Mechanical Engineering,
Beijing Institute of Technology,
5 South Zhongguancun Street,
Haidian District, Beijing 100081, China
e-mail: zhangfkbit@163.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 14, 2018; final manuscript received September 25, 2018; published online November 1, 2018. Assoc. Editor: Noel Brunetiere.

J. Tribol 141(2), 022203 (Nov 01, 2018) (8 pages) Paper No: TRIB-18-1112; doi: 10.1115/1.4041616 History: Received March 14, 2018; Revised September 25, 2018

## Abstract

The percolation threshold strongly affects sealing performance. This paper investigates the relationship between the percolation threshold and the rough surface anisotropy, which is represented by the Peklenik number, $γ$. A series of anisotropic rough surfaces were generated and the conjugate gradient-fast Fourier transform (CG-FFT) method was used to determine the percolation threshold. The percolation threshold was found to be $A/A0≈0.484±0.009$ (averaged over 45 surfaces) was established for an isotropic rough surface ($γ=1$). Furthermore, it was also found that the percolation threshold decreased from $A/A0≈0.528±0.011$ to $A/A0≈0.431±0.008$ as $1/γ$ increased from 0.6 to 2. Our results differ from the theoretical result of Persson et al., where $A/A0=γ/(1+γ)$. Comparing our calculated results with the theoretical results established the presence of an intersection value of $1/γ$ that was related to the effect of elastic deformation on the percolation threshold. When $1/γ$ was smaller than the intersection value, our calculated results were lower than the theoretical ones; and when $1/γ$ was greater than the intersection value, our calculated results were higher than the theoretical ones.

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## References

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## Figures

Fig. 1

Determining the percolation threshold

Fig. 2

Contact status of a rough surface transformed into a search matrix: (a) contact status of a rough surface and (b) search matrix S of the contact status

Fig. 3

Numerically generated Gaussian rough surfaces: (a) 128 × 128 heights, (b) 256 × 256 heights, and (c) 512 × 512 heights

Fig. 4

Comparison of the autocorrelation functions in the x and y directions. The solid linerepresents the input autocorrelation functions and the dots denote the generated autocorrelation functions. (a) Autocorrelation function in the x direction of the rough surface with 128 × 128 heights, (b) autocorrelation function in the y direction of the rough surface with 128 × 128 heights, (c) autocorrelation function in the x direction of the rough surface with256 × 256 heights, (d) autocorrelation function in the y direction of the rough surface with 256 × 256 heights, (e) autocorrelation function in the x direction of the rough surface with512 × 512 heights, and (f) autocorrelation function in the y direction of the rough surface with 512 × 512 heights.

Fig. 5

Contact status of an isotropic rough surface (γ=1). The contact area percolates at A/A0 ≈ 0.47. (a) A/A0 ≈ 0.21, (b) A/A0 ≈ 0.36, (c) A/A0 ≈ 0.47, and (d) A/A0 ≈ 0.56.

Fig. 6

Percolation area of an isotropic rough surface as a function of autocorrelation length. The dots represent the average values of each group; the bars represent the standard deviation.

Fig. 7

The power spectrum of the isotopic rough surfaces with different autocorrelation lengths: (a) the power spectrum of the isotropic rough surface with autocorrelation length 20 μm, (b) the power spectrum of the isotropic rough surface with autocorrelation length 40 μm, and (c) the power spectrum of the isotropic rough surface with autocorrelation length 60 μm

Fig. 8

Contact status for an anisotropic rough surface (1/γ=2). The contact area percolates at A/A0 ≈ 0.41. (a) A/A0 ≈ 0.19, (b) A/A0 ≈ 0.35, (c) A/A0 ≈ 0.41, and (d) A/A0 ≈ 0.61.

Fig. 9

Percolation area as a function of anisotropy, γ, compared with the theoretical results according to Eq. (1). The red dots represent the average values of each group and the blue bars represent the standard deviation. The solid curve is that predicted by Eq. (1).

## Errata

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