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.

References

1.
Menezes
,
P. L.
,
Kishore
,
Kailas
,
S. V.
, and
Lovell
,
M. R.
,
2011
, “
Role of Surface Texture, Roughness, and Hardness on Friction During Unidirectional Sliding
,”
Tribol. Lett.
,
41
(
1
), pp.
1
15
.10.1007/s11249-010-9676-3
2.
Kubiak
,
K. J.
,
Liskiewicz
,
T. W.
, and
Mathia
,
T. G.
,
2011
, “
Surface Morphology in Engineering Applications: Influence of Roughness on Sliding and Wear in Dry Fretting
,”
Tribol. Int.
,
44
(
11
), pp.
1427
1432
.10.1016/j.triboint.2011.04.020
3.
Sokoloff
,
J. B.
,
2012
, “
Surface Roughness and Dry Friction
,”
Phys. Rev. E
,
85
(
2
), p.
027102
.10.1103/PhysRevE.85.027102
4.
Polonsky
,
I. A.
, and
Keer
,
L. M.
,
1999
, “
A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques
,”
Wear
,
231
(
2
), pp.
206
219
.10.1016/S0043-1648(99)00113-1
5.
Zhang
,
S. G.
,
Wang
,
W. Z.
, and
Zhao
,
Z. Q.
,
2014
, “
The Effect of Surface Roughness Characteristics on the Elastic–Plastic Contact Performance
,”
Tribol. Int.
,
79
, pp.
59
73
.10.1016/j.triboint.2014.05.016
6.
Zhu
,
D.
, and
Wang
,
Q. J.
,
2013
, “
Effect of Roughness Orientation on the Elastohydrodynamic Lubrication Film Thickness
,”
ASME J. Tribol.
,
135
(
3
), p.
031501
.10.1115/1.4023250
7.
Pawar
,
G.
,
Pawlus
,
P.
,
Etsion
,
I.
, and
Raeymaekers
,
B.
,
2012
, “
The Effect of Determining Topography Parameters on Analyzing Elastic Contact Between Isotropic Rough Surfaces
,”
ASME J. Tribol.
,
135
(
1
), p.
011401
.10.1115/1.4007760
8.
Yan
,
X. L.
,
Wang
,
X. L.
, and
Zhang
,
Y. Y.
,
2014
, “
Influence of Roughness Parameters Skewness and Kurtosis on Fatigue Life Under Mixed Elastohydrodynamic Lubrication Point Contacts
,”
ASME J. Tribol.
,
136
(
3
), p.
031503
.10.1115/1.4027480
9.
Patir
,
N.
,
1978
, “
A Numerical Procedure for Random Generation of Rough Surfaces
,”
Wear
,
47
(
2
), pp.
263
277
.10.1016/0043-1648(78)90157-6
10.
Bakolas
,
V.
,
2003
, “
Numerical Generation of Arbitrarily Oriented Non-Gaussian Three-Dimensional Rough Surfaces
,”
Wear
,
254
(
5–6
), pp.
546
554
.10.1016/S0043-1648(03)00133-9
11.
Manesh
,
K. K.
,
Ramamoorthy
,
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
.10.1016/j.wear.2010.02.005
12.
Shewchuk
,
J. R.
,
1994
, “
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
,” http://www.cs.cmu.edu/-quakepapers/painless-conjugate-gradient.ps.
13.
Watson
,
W.
, and
Spedding
,
T. A.
,
1982
, “
The Time Series Modelling of Non-Gaussian Engineering Processes
,”
Wear
,
83
(
2
), pp.
215
231
.10.1016/0043-1648(82)90178-8
14.
Whitehouse
,
D. J.
,
1983
, “
The Generation of Two Dimensional Random Surfaces Having a Specified Function
,”
CIRP Ann. Manuf. Technol.
,
32
(
1
), pp.
495
498
.10.1016/S0007-8506(07)63447-7
15.
Gu
,
X. J.
, and
Huang
,
Y. Y.
,
1990
, “
The Modeling and Simulation of a Rough-Surface
,”
Wear
,
137
(
2
), pp.
275
285
.10.1016/0043-1648(90)90140-6
16.
Newland
,
D. E.
,
1984
,
An Introduction to Random Vibration and Spectral Analysis
, 2nd ed.,
Longman
,
London
.
17.
Hu
,
Y. Z.
, and
Tonder
,
K.
,
1992
, “
Simulation of 3-D Random Rough-Surface by 2-D Digital-Filter and Fourier-Analysis
,”
Int. J. Mach. Tools Manuf.
,
32
(
1–2
), pp.
83
90
.10.1016/0890-6955(92)90064-N
18.
Wu
,
J. J.
,
2000
, “
Simulation of Rough Surfaces With FFT
,”
Tribol. Int.
,
33
(
1
), pp.
47
58
.10.1016/S0301-679X(00)00016-5
19.
Wu
,
J. J.
,
2004
, “
Simulation of Non-Gaussian Surfaces With FFT
,”
Tribol. Int.
,
37
(
4
), pp.
339
346
.10.1016/j.triboint.2003.11.005
20.
Reizer
,
R.
,
2011
, “
Simulation of 3D Gaussian Surface Topography
,”
Wear
,
271
(
3–4
), pp.
539
543
.10.1016/j.wear.2010.04.009
21.
Ganti
,
S.
, and
Bhushan
,
B.
,
1995
, “
Generalized Fractal Analysis and Its Applications to Engineering Surfaces
,”
Wear
,
180
(
1–2
), pp.
17
34
.10.1016/0043-1648(94)06545-4
22.
Chen
,
H.
,
Hu
,
Y. Z.
,
Wang
,
H.
, and
Wang
,
W. Z.
,
2006
, “
Simulation and Characterization of the Fractal Characteristics of Rough Surface
,”
Chin. J. Mech. Eng.
,
42
, pp.
219
223
(in Chinese).
23.
Lu
,
Y.
, and
Liu
,
Z.
,
2013
, “
Coupled Effects of Fractal Roughness and Self-Lubricating Composite Porosity on Lubrication and Wear
,”
Tribol. Trans.
,
56
(
4
), pp.
581
591
.10.1080/10402004.2012.711437
24.
Liang
,
X. H.
,
Lin
,
B.
,
Han
,
X. S.
, and
Chen
,
S. G.
,
2012
, “
Fractal Analysis of Engineering Ceramics Ground Surface
,”
Appl. Surf. Sci.
,
258
(
17
), pp.
6406
6415
.10.1016/j.apsusc.2012.03.050
25.
Grzemba
,
B.
,
Pohrt
,
R.
,
Teidelt
,
E.
, and
Popov
,
V. L.
,
2014
, “
Maximum Micro-Slip in Tangential Contact of Randomly Rough Self-Affine Surfaces
,”
Wear
,
309
(
1–2
), pp.
256
258
.10.1016/j.wear.2013.11.050
26.
Marsaglia
,
G.
, and
Bray
,
T. A.
,
1964
, “
A Convenient Method for Generating Normal Variables
,”
SIAM Rev.
,
6
(
3
), pp.
260
264
.10.1137/1006063
27.
Johnson
,
N. L.
,
1949
, “
Systems of Frequency Curves Generated by Methods of Translation
,”
Biometrika
,
36
(
1–2
), pp.
149
176
.10.1093/biomet/36.1-2.149
28.
Hill
,
I. D.
,
Hill
,
R.
, and
Holder
,
R. L.
,
1976
, “
Fitting Johnson Curves by Moments
,”
Appl. Stat.
,
25
(
2
), pp.
180
189
.10.2307/2346692
29.
Gadelmawla
,
E. S.
,
Koura
,
M. M.
,
Maksoud
,
T. M. A.
,
Elewa
,
I. M.
, and
Soliman
,
H. H.
,
2002
, “
Roughness Parameters
,”
J. Mater. Process. Technol.
,
123
(
1
), pp.
133
145
.10.1016/S0924-0136(02)00060-2
30.
Whitehouse
,
D. J.
,
1994
,
Handbook of Surface Metrology
,
Institute of Physics
,
Bristol
.
31.
Peklenik
,
J.
,
1967
, “
New Developments in Surface Characterization and Measurements by Means of Random Process Analysis
,”
Proc. Inst. Mech. Eng.
,
182
(
311
), pp.
108
126
.10.1243/PIME_CONF_1967_182_309_02
32.
Whitehouse
,
D. J.
, and
Archard
,
J. F.
,
1970
, “
The Properties of Random Surface of Significance in Their Contact
,”
Proc. R. Soc. London, Ser. A
,
316
(
1524
), pp.
97
121
.10.1098/rspa.1970.0068
33.
Box
,
G. E. P.
, and
Muller
,
M. E.
,
1958
, “
A Note on the Generation of Random Normal Deviates
,”
Ann. Math. Stat.
,
29
(
2
), pp.
610
611
.10.1214/aoms/1177706645
34.
Kundu
,
D.
, and
Gupta
,
R. D.
,
2007
, “
A Convenient Way of Generating Gamma Random Variables Using Generalized Exponential Distribution
,”
Comput. Stat. Data Anal.
,
51
(
6
), pp.
2796
2802
.10.1016/j.csda.2006.09.037
35.
Thomas
,
D. B.
,
Luk
,
W.
,
Leong
,
P. H. W.
, and
Villasenor
,
J. D.
,
2007
, “
Gaussian Random Number Generators
,”
ACM Comput. Surv.
,
39
(
4
), p. 11.10.1145/1287620.1287622
36.
Zhang
,
R.
, and
Leemis
,
L. M.
,
2012
, “
Rectangles Algorithm for Generating Normal Variates
,”
Nav. Res. Logist.
,
59
(
1
), pp.
52
57
.10.1002/nav.21474
37.
Lehmer
,
D. H.
,
1949
, “
Mathematical Methods in Large-Scale Computing Units
,”
Proceedings of the 2nd Symposium on Large-Scale Digital Calculating Machinery
, Harvard University Press, Cambridge, MA, pp.
141
146
.
38.
Lecuyer
,
P.
,
1988
, “
Efficient and Portable Combined Random Number Generators
,”
Commun. ACM
,
31
(
6
), pp.
742
749
.10.1145/62959.62969
39.
Abramowitz
,
M.
, and
Stegun
,
I.
,
1972
,
Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables
,
Dover Publications
,
New York
.
You do not currently have access to this content.