Research Papers: Contact Mechanics

Numerical Simulation Method of Rough Surfaces Based on Random Switching System

[+] Author and Article Information
Tingjian Wang, Dezhi Zheng, Le Gu

School of Mechatronics Engineering,
Harbin Institute of Technology,
Harbin 150001, China

Liqin Wang

School of Mechatronics Engineering,
State Key Laboratory of Robotics and System,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: lqwanghit@hotmail.com

Xiaoli Zhao

School of Mechatronics Engineering,
State Key Laboratory of Robotics and System,
Harbin Institute of Technology,
Harbin 150001, China

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 20, 2014; final manuscript received January 14, 2015; published online February 11, 2015. Assoc. Editor: Sinan Muftu.

J. Tribol 137(2), 021403 (Apr 01, 2015) (9 pages) Paper No: TRIB-14-1261; doi: 10.1115/1.4029644 History: Received October 20, 2014; Revised January 14, 2015; Online February 11, 2015

In this paper, a numerical simulation method for generating rough surfaces with desired autocorrelation function (ACF) and statistical parameters, including root mean square (rms), skewness (Ssk), and kurtosis (Ku), is developed by combining the polar method, Johnson translation system, and random switching system. This method can be used to generate Gaussian, non-Gaussian, isotropic, and nonisotropic rough surfaces. The simulation results show the excellent performance of present method for producing surface with various desired statistical parameters and ACF. The advantage of present method is that the deviation of statistical parameters and ACF from the desired ones can be as small as required since it is controlled by iterative algorithms.

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Grahic Jump Location
Fig. 1

Typical profiles with varying skewness and kurtosis: (a) Ssk < 0, (b) Ssk > 0, (c) Ku < 3, and (d) Ku > 3

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Fig. 2

The overall algorithm flow chart of the surface simulation method

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Fig. 3

Perspective views of Gaussian rough surfaces: (a) surface 1 with rms = 1.0 μm, βx = 20.0 μm and βy = 20.0 μm, (b) surface 2 with rms = 1.0 μm, βx = 20.0 μm and βy = 80.0 μm

Grahic Jump Location
Fig. 4

ACFs of Gaussian rough surfaces with different autocorrelation lengths: (a) ACFs in x direction and (b) ACFs in y direction

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Fig. 5

Probability density function p(z) of heights distribution of Gaussian rough surfaces with different autocorrelation lengths

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Fig. 6

Perspective views of surfaces: (a) surface 3 with rms = 1.0 μm, Ssk = 0.0, Ku = 7.0, βx = 20.0 μm and βy = 20.0 μm, (b) surface 8 with rms = 1.0 μm, Ssk = −1.0, Ku = 7.0, βx = 20.0 μm and βy = 80.0 μm

Grahic Jump Location
Fig. 7

ACFs of non-Gaussian isotropic rough surfaces with βx = 20.0 μm and βy = 20.0 μm and various statistical parameters: (a) ACFs in x direction and (b) ACFs in y direction

Grahic Jump Location
Fig. 8

ACFs of non-Gaussian nonisotropic rough surfaces with βx = 20.0 μm and βy = 80.0 μm and various statistical parameters: (a) ACFs in x direction and (b) ACFs in y direction

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Fig. 9

Probability density function p(z) of heights distribution of non-Gaussian rough surfaces with various statistical parameters: (a) surfaces with βx = 20.0 μm and βy = 20.0 μm and (b) surfaces with βx = 20.0 μm and βy = 80.0 μm

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Fig. 10

(a) perspective view of real surface, (b) perspective view of modeled surface, (c) ACFs in x direction, and (d) ACFs in y direction

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Fig. 11

Probability density function p(z) of heights distribution for both the real engineering surface and its modeled surface




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