The random Gaussian surface model proposed by Nayak is important to many statistical summit-based microcontact models. A Gaussian distribution is usually assumed for the summit heights as many surfaces have a Gaussian distribution of surface heights. In this work, based on Nayak’s model, the skewness and kurtosis of the summit-height distribution are derived as a function of the bandwidth parameter α. The correctness of these two equations is verified using a numerical scheme that generates random Gaussian surfaces with various α values. Also, practical contact simulations are performed to demonstrate the significance of the proposed equations and also to show the error of using a Gaussian distribution versus a correct asymmetric distribution for the summit heights.
Issue Section:
Research Papers
1.
Coulomb, C. A., 1785, “The´orie des Machines Simples, en ayant regard au Frottement de leurs Parties, et a la Roideur dews Cordages,” Mem. Math. Phys., X, Paris, pp. 161–342.
2.
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
, pp. 97
–121
.3.
Nayak
, P. R.
, 1971
, “Random Process Model of Rough Surfaces
,” ASME J. Lubr. Technol.
, 93
(3
), pp. 398
–407
.4.
Russ, J. C., 1994, Fractal Surfaces, Plenum, New York.
5.
Greenwood
, J. A.
, and Williamson
, J. P. B.
, 1966
, “Contact of Nominally Flat Surfaces
,” Proc. R. Soc. London, Ser. A
, 295
, pp. 300
–319
.6.
Bush
, A. W.
, Gibson
, R. D.
, and Keogh
, G. P.
, 1976
, “The Limits of Elastic Deformation in the Contact of Rough Surfaces
,” Mech. Res. Commun.
, 3
, pp. 169
–174
.7.
McCool
, J. I.
, 1986
, “Comparison of Models for the Contact of Rough Surfaces
,” Wear
, 107
, pp. 37
–60
.8.
Chang
, W. R.
, Etsion
, I.
, and Bogy
, D. B.
, 1987
, “An Elastic-Plastic Model for the Contact of Rough Surfaces
,” ASME J. Tribol.
, 109
, pp. 257
–263
.9.
McCool
, J. I.
, 1987
, “Relating Profile Instrument Measurements to the Functional Performance of Rough Surfaces
,” ASME J. Tribol.
, 109
, pp. 264
–270
.10.
Longuet-Higgins
, M. S.
, 1957
, “The Statistical Analysis of a Random Moving Surfaces
,” Philos. Trans. R. Soc. London, Ser. A
, 249
, pp. 321
–387
.11.
Sayles
, R. S.
, and Thomas
, T. R.
, 1979
, “Measurement of the Statistical Microgeometry of Engineering Surfaces
,” ASME J. Lubr. Technol.
, 101
, pp. 409
–417
.12.
Greenwood, J. A., 1992, “Problem with Surface Roughness,” Fundamental of Friction: Macroscopic and Microscopic Processes, I. L. Singer and H. M. Pollock, eds., Kluwer, Boston, pp. 57–76.
13.
Yu
, N.
, and Polycarpou
, A. A.
, 2002
, “Contact of Rough Surfaces with Asymmetric Distribution of Asperity Heights
,” ASME J. Tribol.
, 124
, pp. 367
–376
.14.
Williamson, J. B. P., Pullen J., Hunt, R. T., 1969, “The Shape of Solid Surfaces,” Surface Mechanics, F. F. Ling, eds., ASME, New York, pp. 24–35.
15.
Williams, J. A., 1994, Engineering Tribology, Oxford, New York, pp. 47–55.
16.
Suh
, A. Y.
, and Polycarpou
, A. A.
, 2003
, “Adhesive and Pull-Off Forces for Polysilicon MEMS Surfaces Using the sub-Boundary Lubrication Model
,” ASME J. Tribol.
, 125
, pp. 193
–199
.17.
Ogilvy
, J. A.
, 1991
, “Numerical Simulation of Friction Between Contacting Rough Surfaces
,” J. Phys. D
, 24
, pp. 2098
–2109
.18.
Polycarpou, A. A., Boutaghou, Z. E., and Burbank, D. P., 2003, “Texture Structure for Optimizing Head Disk Interface,” U.S. Patent 6,611,400, August 26, 2003.
19.
Kogut
, L.
, and Etsion
, I.
, 2004
, “A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces
,” ASME J. Tribol.
, 126
, pp. 34
–40
.20.
Bhushan, B. 1999, Handbook of Micro/Nanotribology, CRC Press, New York, pp. 769–770, 822–823.
21.
Houston
, M. R.
, Maboudian
, R.
, and Howe
, R. T.
, 1997
, “Effect of Hydrogen Termination on the Work of Adhesion Between Rough Polycrystalline Silicon Surfaces
,” J. Appl. Phys.
, 81
, pp. 3474
–3483
.22.
Liu
, X.
, Chetwynd
, G.
, and Gardner
, J. W.
, 1998
, “Surface Characterization of Electro-Active Thin Polymeric Film Bearings
,” Int. J. Mach. Tools Manuf.
, 38
, pp. 669
–675
.23.
Yu
, N.
, Pergande
, S. R.
, and Polycarpou
, A. A.
, 2004
, “Static Friction Coefficient Model for Rough Surfaces With Asymmetric Distribution of Asperity Heights
,” ASME J. Tribol.
, 126
, pp. 626
–629
.Copyright © 2004
by ASME
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