A NUMERICAL PROCEDURE TO GENERATE NON-GAUSSIAN 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 non-Gaussian 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 non-Gaussian 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 non-Gaussian distribution, as well as the abrasive wear and running in phenomena.
 

Keywords: roughness, autocorrelation, skewness, kurtosis

References

1. Bakolas V., 2003, “Numerical Generation of Arbitrarily Oriented Non-Gaussian Three-Dimensional Rough Surfaces”. Wear, 254, pp. 546-554.

2. Bushan B., Kim T.W. and Cho Y.J., 2006, „The Contact Behavior of Elastic/Plastic non-Gaussian rough surfaces”. Tribology Letters, 22, pp. 1-12.

3. Creţu S. Sp., 2006, „Random Simulation of Gaussian Rough Surfaces. Part 1- Theoretical Formulations.”, Bul. IPI, LII (LVI), 1-2, pp. 1-17.

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

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

6. Greenwood J.A., Wu J.J., 2001, „Surface Roughness and Contact: An Apology.” Meccanica, 36, pp. 617-630.

7. Hill I.D., Hill R., Holder R. L., 1976, „Fitting Johnson’s Curves by Moments.” Applied Statistics, 25, pp. 180-189.

8. 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 Manufact, Vol. 32, pp. 83-90.

9. McCool J., 1986, „Comparison Models for the Contact of Rough Surfaces.”, WEAR, 107, pp. 37-60.

10. Patir N., 1978, „A Numerical Procedure for Random Generation of Rough Surfaces.”, Wear, 263-277.

11. Robbe-Valloire F., 2001, „Statistical Analysis  of Asperities on a Rough Surface.”, Wear, 249, pp. 401-408.

12. Watson W. and Spedding T.A., 1982, „The Time Series Modelling of Non-Gaussian Engineering Processes.”, Wear, 83, pp. 215-231.