0
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

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/A00.484±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/A00.528±0.011 to A/A00.431±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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bruggeman, D. A. G. , 1935, “ Berechnung Verschiedener Physikalischer Konstanten Von Heterogenen Substanzen,” Ann. Phys., 416(7), pp. 636–679. [CrossRef]
Greenwood, J. A. , and Williamson, J. B. P. , 1966, “ Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, 295(1442), pp. 300–319. [CrossRef]
Bush, A. W. , Gibson, R. D. , and Thomas, T. R. , 1975, “ The Elastic Contact of a Rough Surface,” Wear, 35(1), pp. 87–111. [CrossRef]
Greenwood, J. A. , 2006, “ A Simplified Elliptic Model of Rough Surface Contact,” Wear, 261(2), pp. 191–200. [CrossRef]
Hyun, S. , Pei, L. , Molinari, J. F. , and Robbins, M. O. , 2004, “ Finite-Element Analysis of Contact Between Elastic Self-Affine Surfaces,” Phys. Rev. E, 70(2 Pt. 2), p. 026117. [CrossRef]
Pei, L. , Hyun, S. , Molinari, J. F. , and Robbins, M. O. , 2005, “ Finite Element Modeling of Elasto-Plastic Contact Between Rough Surfaces,” J. Mech. Phys. Solids, 53(11), pp. 2385–2409. [CrossRef]
Yang, C. , Tartaglino, U. , and Persson, B. N. J. , 2006, “ A Multiscale Molecular Dynamics Approach to Contact Mechanics,” Eur. Phys. J. E, 19(1), pp. 47–58. [CrossRef]
Pohrt, R. , and Popov, V. L. , 2012, “ Normal Contact Stiffness of Elastic Solids With Fractal Rough Surfaces,” Phys. Rev. Lett., 86(2), p. 104301. [CrossRef]
Zhang, F. , Liu, J. , Ding, X. , and Yang, Z. , 2017, “ An Approach to Calculate Leak Channels and Leak Rates Between Metallic Sealing Surfaces,” ASME J. Tribol., 139(1), p. 011708. [CrossRef]
Persson, B. N. J. , and Yang, C. , 2008, “ Theory of the Leak-Rate of Seals,” J. Phys.: Condens. Matter, 20(31), p. 315011. [CrossRef]
Stauffer, D. , and Aharony, A. , 1991, An Introduction to Percolation Theory, 2nd ed., CRC Press, Boca Raton, FL.
Persson, B. N. J. , Prodanov, N. , Krick, B. A. , Rodriguez, N. , Mulakaluri, N. , Sawyer, W. G. , and Mangiagalli, P. , 2012, “ Elastic Contact Mechanics: Percolation of the Contact Area and Fluid Squeeze-Out,” Eur. Phys. J. E, 35(1), p. 5. [CrossRef]
Li, W. , and Chien, W. , 2004, “ Parameters for Roughness Pattern and Directionality,” Tribol. Lett., 17(3), pp. 547–551. [CrossRef]
Dapp, W. B. , Lücke, A. , Persson, B. N. J. , and Müser, M. H. , 2012, “ Self-Affine Elastic Contacts: Percolation and Leakage,” Phys. Rev. Lett., 108(24), p. 244301. [CrossRef] [PubMed]
Putignano, C. , Afferrante, L. , Carbone, G. , and Demelio, G. , 2013, “ A Multiscale Analysis of Elastic Contacts and Percolation Threshold for Numerically Generated and Real Rough Surfaces,” Tribol. Int., 64(3), pp. 148–154. [CrossRef]
Manesh, K. K. , Ramamoorthty, B. , and Singaperumal, M. , 2010, “ Numerical Generation of Anisotropic 3D Non-Gaussian Engineering Surfaces With Specified 3D Surface Roughness Parameters,” Wear, 268(11–12), pp. 1371–1379. [CrossRef]
Wang, Z. , Wang, W. , Hu, Y. , and Wang, H. , 2010, “ A Numerical Elastic-Plastic Contact Model for Rough Surfaces,” Tribol. Trans., 53(2), pp. 224–238. [CrossRef]
Patir, N. , 1978, “ A Numerical Procedure for Random Generation of Rough Surfaces,” Wear, 47(2), pp. 263–277. [CrossRef]
Barber, J. R. , 2010, Elasticity, 3rd ed., Springer, Dordrecht, The Netherlands.
Wang, W. , Hu, Y. , and Wang, H. , 2006, “ Numerical Solution of Dry Contact Problem Based on Fast Fourier Transform and Conjugate Gradient Method,” Chin. J. Mech. Eng., 42(7), p. 14. [CrossRef]
Barber, J. R. , 2013, “ Incremental Stiffness and Electrical Contact Conductance in the Contact of Rough Finite Bodies,” Phys. Rev. E, 87(1), p. 013203. [CrossRef]
Yastrebov, V. A. , Anciaux, G. , and Molinari, J. F. , 2015, “ From Infinitesimal to Full Contact Between Rough Surfaces: Evolution of the Contact Area,” Int. J. Solids. Struct., 52, pp. 83–102. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 1

Determining the percolation threshold

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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).

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In