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Research Papers: Contact Mechanics

# Topography Analysis of Random Anisotropic Gaussian Rough Surfaces

[+] Author and Article Information
Deepak K. Prajapati

Department of Mechanical Engineering,
Indian Institute of Technology,
Patna 801103, India
e-mail: deepak.pme14@iitp.ac.in

Mayank Tiwari

Department of Mechanical Engineering,
Indian Institute of Technology,
Patna 801103, India
e-mail: mayankt@iitp.ac.in

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 4, 2016; final manuscript received September 26, 2016; published online April 4, 2017. Assoc. Editor: James R. Barber.

J. Tribol 139(4), 041402 (Apr 04, 2017) (9 pages) Paper No: TRIB-16-1209; doi: 10.1115/1.4034960 History: Received July 04, 2016; Revised September 26, 2016

## Abstract

Engineered surfaces (ground and similarly structured rough surfaces) show anisotropic characteristics and their topography parameters are direction dependent. Statistical characterization of these surfaces is still complex because of directional nature of surfaces. In this technical brief, an attempt is made to simulate anisotropic surfaces through use of topography parameters (three-dimensional (3D) surface parameters). First, 3D anisotropic random Gaussian rough surface is generated numerically with fast Fourier transform (FFT). Numerically generated anisotropic random Gaussian rough surface shows statistical properties (texture direction, texture ratio) similar to ground and similarly directional anisotropic rough surfaces. For numerically generated anisotropic Gaussian rough surface, important 3D roughness parameters are determined. Sayles and Thomas' (1976, “Thermal Conductance of Rough Elastic Contact,” Appl. Energy, 2(4), pp. 249–267.) theoretical model for directional anisotropic rough surface is adopted here for calculating the summit parameters, i.e., equivalent bandwidth parameter, mean summit curvature, skewness of summit height, standard deviation of summit height, and equivalent spectral moments. This work demonstrates the variation of spectral moments in both across and parallel to the lay directions with pattern ratio ($γ=βx/βy$). Correlation length (βx) is fixed $10μm$ and correlation length (βy) is varied from 100 to 10 $μm$. Variation of summit parameters with pattern ratio is also discussed in detail. Results shows that mean summit curvature and skewness of summit heights increase with increase in pattern ratio, whereas standard deviation of summit heights and equivalent bandwidth parameter (αe) decreases with pattern ratio. A significant difference is found in “Abbott-Firestone” parameters when calculated in both perpendicular and parallel to lay directions. Effect of these parameters on wear process is discussed in brief.

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## Figures

Fig. 5

Contour plot of areal autocorrelation function at βx=10μm,βy=10μm

Fig. 4

Comparison of autocorrelation function in y direction (βy = 50 μm)

Fig. 3

Comparison of autocorrelation function in x direction (βx = 10 μm)

Fig. 2

Isometric view of anisotropic Gaussian rough surface

Fig. 1

Surface map of numerically generated anisotropic Gaussian rough surface at βx=10μm,βy=50μm

Fig. 6

Surface map for numerically generated directionally anisotropic Gaussian rough surface, 1280 × 1280 sampling points (βx=50μm,βy=20μm)

Fig. 15

Bearing area curve along x direction (across the lay direction) at βx=10μm,βy=100μm

Fig. 11

Variation of skewness of summit heights (σsk) with pattern ratio (γ)

Fig. 12

Variation of equivalent bandwidth parameter (αe) of summit heights with pattern ratio (γ)

Fig. 13

Variation of mean summit curvature (κm) of summit heights with pattern ratio (γ)

Fig. 14

Variation of standard deviation of summit heights (σs) with pattern ratio (γ)

Fig. 7

Variation of second-order spectral moments m20 (along x direction), m02 (along y direction) with pattern ratio (γ)

Fig. 8

Roughness profile in x direction for correlation length, βx = 10 μm

Fig. 9

Variation of roughness profile in y direction for correlation lengths, βy = 10 μm, 20 μm, and 50 μm

Fig. 10

Variation of fourth-order spectral moments m40 (along x direction), m04 (along y direction) with pattern ratio (γ)

Fig. 16

Bearing area curve along y direction (parallel to the lay direction) at βx=10μm,βy=100μm

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