IDFT numerical simulation method for Gaussian rough surface with relatively large correlation length

Abstract

A numerical simulation method based on inverse discrete Fourier transform(IDFT)is presented for generating Gaussian rough surface with a desired autocorrelation function(ACF). The probability density function of the height distribution of the generated Gaussian surface and the root-mean-square height of the rough surface are also considered. It is found that the height distribution of the generated surface follows the Gaussian distribution, the deviation of the root-mean-square height of the modeled rough surface from the desired value is smaller than that of Patir’s method, and the autocorrelation function of the modeled surface is also in good agreement with the desired autocorrelation function. Compared with Patir’s method, the modeled surface generated by the IDFT method is in better agreement with the desired autocorrelation function, especially when the correlation length is relatively large.

Keywords

numerical simulation / Gaussian rough surface / autocorrelation function / root-mean-square height / IDFT

References

[1] Bucher F. Considering real and synthetic microroughness in 2D and 3D metal contacts [J]. Tribology International, 2006, 39(5): 387-400.

[2] Polonsky I A, Keer L M. A numerical method for solving rough contact problems based on the multi-level multisummation and conjugate gradient techniques [J]. Wear, 1999, 231(2): 206-219.

[3] Ning R, Dong Z, Wayne C W, et al. A threedimensional deterministic model for rough surface linecontact EHL problems [J]. Journal of Tribology, 2009, 131(1): 1-9.

[4] Krantz T L. The Influence of Roughness on Gear Surface Fatigue[R], 2005.

[5] Patir N. A numerical procedure for random generation of rough surfaces [J]. Wear, 1978, 47(2): 263-277.

[6] Bakolas V. Numerical generation of arbitrarily oriented non-Gaussian three-dimensional rough surfaces [J]. Wear, 2003, 254(5–6): 546-554.

[7] Manesh K K, Ramamoorthy B, Singaperumal M. Numerical generation of anisotropic 3D non-Gaussian engineering surfaces with specified 3D surface roughness parameters [J]. Wear, 2010, 268(11–12): 1371-1379.

[8] Watson W, Spedding T A. The time series modeling of non-Gaussian engineering processes [J]. Wear, 1982, 83(2): 215-231.

[9] Whitehouse D J. The generation of two-dimensional random surfaces having a specified function [J]. CIRP Annals-Manufacturing Technology, 1983, 32(1): 495-498.

[10] Gu X J, Huang Y Y. The modeling and simulation of a rough surface [J]. Wear, 1990, 137(2): 275-285.

[11] Newland D E. An Introduction to Random Vibration and Spectral Analysis [M], 1984, 2nd ed London, UK: Longman.

[12] Hu Y Z, Tonder K. Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis [J]. International Journal of Machine Tools and Manufacture, 1992, 32(1): 83-90.

[13] Wu J J. Simulation of rough surfaces with FFT [J]. Tribology International, 2000, 33(1): 47-58.

[14] Majumdar A, Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of rough surfaces [J]. Journal of Tribology, 1990, 112(2): 205-216.

[15] Ganti S, Bhushan B. Generalized fractal analysis and its applications to engineering surfaces [J]. Wear, 1995, 180(1–2): 17-34.

[16] Chen H, Hu Y, Wang H, et al. Simulation and characterization of fractal rough surfaces [J]. Chinese Journal of Mechanical Engineering, 2006, 42(9): 219-223.

[17] Liang X, Lin B, Han X, et al. Fractal analysis of engineering ceramics ground surface [J]. Applied Surface Science, 2012, 258(17): 6406-6415.

[18] Bhushan B. Introduction to Tribology [M], 2002, New York, USA: John Wiley and Sons.

[19] Wen S Z, Huang P. Interface Science and Technology [M], 2001, Beijing, China: Tsinghua University Press.

[20] Gadelmawla E S, Koura M M, Maksoud T M A. Roughness parameters [J]. Journal of Materials Processing Technology, 2002, 123(1): 133-145.

[21] Peklenik J. New developments in surface characterization and measurements by means of random process analysis [C]. Proceedings of the Institution of Mechanical Engineers. London, UK, 1967, 182: 108-126.

[22] Whitehouse Archard J F. The properties of random surfaces of significance in their contact [J]. Proceedings of the Royal Society of London, Series A(Mathematical and Physical Sciences), 1970, 316(1524): 97-121.

[23] Allen B S, Kurt B. Discrete Fourier Analysis and Wavelets [M], 2009, New York, USA: John Wiley and Sons.

[24] Shewchuk J R. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain[M], 1994, Pittsburgh, PA, USA: Carnegie Mellon University.