A NUMERICAL PROCEDURE TO GENERATE
NONGAUSSIAN ROUGH SURFACES
Ana
URZICĂ
sf_ana8107@yahoo.com
Spiridon CREŢU
spcretu@mail.tuiasi.ro
Department of
Machine Design, Technical University of Iaşi, ROMANIA
Abstract.
The paper presents an algorithm for computer
simulation of nonGaussian surfaces. By using a random number
generator, a input matrix is formed as a first representation of a
Gaussian roughness with zero mean, and unit standard deviation. The
autocorrelation function was assumed to have an exponential form. To
fulfill this requirement, in the first step, the matrix containing
the roughness heights was obtained by a linear transformation of the
input matrix. In the second step the skewness and kurtosis of the
input sequence have been established for the desired skewness and
kurtosis of an output sequence. Finally the nonGaussian random
series have been generated by using the Johnson translator system.
The numerical results pointed out that the developed algorithm can
be further used to simulate manufacturing processes that produce
real surfaces which may present a nonGaussian distribution, as well
as the abrasive wear and running in phenomena.
Keywords:
roughness, autocorrelation, skewness, kurtosis
References

Bakolas V.,
2003, “Numerical Generation of Arbitrarily Oriented NonGaussian
ThreeDimensional Rough Surfaces”. Wear, 254, pp.
546554.

Bushan B.,
Kim T.W. and Cho Y.J., 2006, „The Contact Behavior of
Elastic/Plastic nonGaussian rough surfaces”. Tribology
Letters, 22, pp. 112.

Creţu
S. Sp., 2006, „Random Simulation of
Gaussian Rough Surfaces. Part 1 Theoretical Formulations.”,
Bul. IPI, LII (LVI), 12, pp. 117.

Creţu S. Sp.,
2006, “The Influence of the Correlation Length on Pressure
Distribution and Stresses State in ElasticPlastic Rough
Contacts”, IJTC2006, paper 12339, San Antonio, TX, USA.

Elderton W.P. and
Johnson N.L., 1969, „System of Frequency Curves.”
Cambridge University Press, London.

Greenwood J.A.,
Wu J.J., 2001, „Surface Roughness and Contact: An Apology.”
Meccanica, 36, pp. 617630.

Hill I.D., Hill
R., Holder R. L., 1976, „Fitting Johnson’s Curves by
Moments.” Applied Statistics, 25, pp. 180189.

Hu Y.Z. and
Tonder K., 1992, „Simulation of 3D Random Rough Surface by
2D Digital Filter and Fourier Analysis.”, Int. J. Mach.
Tools Manufact, Vol. 32, pp. 8390.

McCool J., 1986,
„Comparison Models for the Contact of Rough Surfaces.”, WEAR,
107, pp. 3760.

Patir N., 1978, „A
Numerical Procedure for Random Generation of Rough Surfaces.”,
Wear, 263277.

RobbeValloire F.,
2001, „Statistical Analysis of Asperities on a Rough Surface.”,
Wear, 249, pp. 401408.

Watson W.
and Spedding T.A., 1982, „The Time Series Modelling of
NonGaussian Engineering Processes.”, Wear, 83, pp.
215231.
