0
Contact Mechanics

The Effect of Determining Topography Parameters on Analyzing Elastic Contact Between Isotropic Rough Surfaces

[+] Author and Article Information
Gorakh Pawar

Department of Mechanical Engineering
University of Utah
Salt Lake City, UT 84112

Pawel Pawlus

Rzeszow University of Technology
Department of Manufacturing
Processes and Production Organisation
Rzeszow, Poland

Izhak Etsion

Department of Mechanical Engineering
Technion – Israel Institute of Technology
Haifa, Israel

Bart Raeymaekers

Department of Mechanical Engineering
University of Utah
Salt Lake City, UT 84112
e-mail: bart.raeymaekers@utah.edu

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received May 15, 2012; final manuscript received September 5, 2012; published online December 20, 2012. Assoc. Editor: Robert L. Jackson.

J. Tribol 135(1), 011401 (Dec 20, 2012) (10 pages) Paper No: TRIB-12-1078; doi: 10.1115/1.4007760 History: Received May 15, 2012; Revised September 05, 2012

The elastic contact between two computer generated isotropic rough surfaces is studied. First the surface topography parameters including the asperity density, mean summit radius, and standard deviation of asperity heights of the equivalent rough surface are determined using an 8-nearest neighbor summit identification scheme. Second, many cross sections of the equivalent rough surface are traced and their individual topography parameters are determined from their corresponding spectral moments. The topography parameters are also obtained from the average spectral moments of all cross sections. The asperity density is found to be the main difference between the summit identification scheme and the spectral moments method. The contact parameters such as the number of contacting asperities, real area of contact, and contact load for any given separation between the equivalent rough surface and a rigid flat are calculated by summing the contributions of all the contacting asperities using the summit identification model. These contact parameters are also obtained with the Greenwood-Williamson (GW) model using the topography parameters from each individual cross section and from the average spectral moments of all cross sections. Three different surfaces and three different sampling intervals were used to study how the method to determine topography parameters affects the resulting contact parameters. The contact parameters are found to vary significantly based on the method used to determine the topography parameters, and as a function of the autocorrelation length of the surface, as well as the sampling interval. Using a summit identification model or the GW model based on topography parameters obtained from a summit identification scheme is perhaps the most reliable approach.

FIGURES IN THIS ARTICLE
<>
© 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Greenwood, J. A., and Williamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. A. Math. Phys., 295, pp. 300–319. [CrossRef]
Greenwood, J. A., and Tripp, J. H., 1967, “The Elastic Contact of Rough Spheres,” J. Appl. Mech., 34(1), pp. 153–159. [CrossRef]
Greenwood, J. A., and Tripp, J. H., 1970, “The Contact of Two Nominally Flat Surfaces,” Proc. Int. Mech. Eng., 185, pp. 625–634. [CrossRef]
Bush, A. W., Gibson, R. D., and Thomas, T. R., 1975, “The Elastic Contact of Rough Surface,” Wear, 35(1), pp. 87–111. [CrossRef]
O'Callaghan, M., and Cameron, M., 1976, “Static Contact Under Load Between Nominally Flat Surfaces in Which Deformation Is Purely Elastic,” Wear, 36(1), pp. 79–97. [CrossRef]
Greenwood, J. A., 2006, “A Simplified Elliptical Model for Rough Surface Contact,” Wear, 261(2), pp. 191–200. [CrossRef]
Carbone, G., and Bottiglione, F., 2008, “Asperity Contact Theories: Do They Predict Linearity Between Contact Area and Load?” J. Mech. Phys. Solids, 56(8), pp. 2555–2572. [CrossRef]
Paggi, M., and Ciavarella, M., 2010, “The Coefficient of Proportionality κ Between Real Contact Area and Load, With New Asperity Models,” Wear, 268, pp. 1020–1029. [CrossRef]
Carbone, G., and Bottiglione, F., 2011, “Contact Mechanics of Rough Surfaces: A Comparison Between Theories,” Meccanica, 46(3), pp. 557–565. [CrossRef]
Majumbdar, A., and Bhushan, B., 1991, “Fractal Model of Elastic–Plastic Contact Between Rough Surfaces,” ASME J. Tribol., 113, pp. 1–11. [CrossRef]
Persson, B. N. J., 2001, “Theory of Rubber Friction and Contact Mechanics,” J. Chem. Phys., 115, 3840–3861. [CrossRef]
McCool, J. I., 1986, “Comparison of Models for the Contact of Rough Surfaces,” Wear, 107(1), pp. 37–60. [CrossRef]
McCool, J. I., 1986, “Predicting Microcontact in Ceramics Via a Microcontact Model,” ASME J. Tribol., 108(3), pp. 380–386. [CrossRef]
McCool, J. I., 1987, “Relating Profile Instrument Measurements to the Functional Performance of Rough Surfaces,” ASME J. Tribol., 109(2), pp. 264–270. [CrossRef]
Zhao, Y., and Chang, L., 2001, “A Model of Asperity Interactions in Elastic-Plastic Contact of Rough Surfaces,” ASME J., 123(4), pp. 57–64. [CrossRef]
Lee, C. H., and Polycarpou, A., 2007, “Static Friction Experiments and Verification of an Improved Elastic-Plastic Model Including Roughness Effects,” ASME J. Tribol., 129(4), pp. 754–760. [CrossRef]
Akbarzadeh, S., and Khonsari, M., 2008, “Performance of Spur Gears Considering Surface Roughness and Shear Thinning Lubricant,” ASME J. Tribol., 130(2), p. 021503. [CrossRef]
Uchidate, M., Iwabuchi, A., Kikuchi, K., and Shimizu, T., 2009, “Research on the Validity of Using Nayak's Theory for Summit Parameters of Discrete Isotropic Gaussian Surfaces,” J. Adv. Mech. Des. Syst. Manuf., 3(2), pp. 125–135. [CrossRef]
Wilson, W. E., Angadi, S. V., and Jackson, R. L., 2010, “Surface Separation and Contact Resistance Considering Sinusoidal Elastic–Plastic Multi-Scale Rough Surface Contact,” Wear, 268(1–2), pp. 190–201. [CrossRef]
Lee, C. H., Eriten, M., and Polycarpou, A., 2010, “Application of Elastic-Plastic Static Friction Models to Rough Surfaces With Asymmetric Asperity Distribution,” ASME J. Tribol., 132(3), p. 031602. [CrossRef]
Dickey, R. D. I., Jackson, R., and Flowers, G., 2011, “Measurements of the Static Friction Coefficient Between Tin Surfaces and Comparison to a Theoretical Model,” ASME J. Tribol., 133(3), p. 031408. [CrossRef]
Kogut, L., and Jackson, R., 2006, “A Comparison of Contact Modeling Utilizing Statistical and Fractal Approaches,” ASME J. Tribol., 128(1), pp. 213–217. [CrossRef]
Etsion, I., and Amit, M., 1993, “The Effect of Small Normal Loads on the Static Friction Coefficient for Very Smooth Surfaces,” ASME J. Tribol., 115(3), pp. 406–410. [CrossRef]
Raeymaekers, B., Etsion, I., and Talke, F. E., 2007, “Enhancing Tribological Performance of the Magnetic Tape/Guide Interface by Laser Surface Texturing,” Tribol. Lett., 27(1), pp. 89–95. [CrossRef]
Jackson, R. L., and Green, I., 2011, “On the Modeling of Elastic Contact Between Rough Surfaces,” Tribol. T., 54, pp. 300–314. [CrossRef]
Greenwood, J. A., 1984, “A Unified Theory of Surface Roughness,” Proc. R. Soc. A. Math. Phys., 393, pp. 133–157. [CrossRef]
Tomanik, E., Chacon, H., and Teixeira, G., 2003, “A Simple Numerical Procedure to Calculate the Input Data of Greenwood-Williamson Model of Asperity Contact for Actual Engineering Surfaces,” Tribol. S., 41, pp. 205–215. [CrossRef]
Yu, N., and Polycarpou, A., 2004, “Extracting Summit Roughness Parameters From Random Gaussian Surfaces Accounting for Asymmetry of the Summit Heights,” ASME J. Tribol., 126(4), pp. 761–766. [CrossRef]
Pawlus, P., 2007, “Digitisation of Surface Topography Measurement Results,” Measurement, 40(6), pp. 672–686. [CrossRef]
Suh, A., Polycarpou, A., and Conry, T., 2003, “Detailed Surface Roughness Characterization of Engineering Surfaces Undergoing Tribological Testing Leading to Scuffing,” Wear, 255(1–6), pp. 556–568. [CrossRef]
Li, M., Phillips, M. J., and Whitehouse, D. J., 1989, “Extension of Two-Dimensional Sampling Theory,” J. Phys. A. Math. Gen., 22, pp. 5053–5063. [CrossRef]
Poon, C. Y., and Bhushan, B., 1995, “Comparison of Surface Roughness Measurements by Stylus Profiler, AFM and Non-Contact Optical Profiler,” Wear, 190(1), pp. 76–88. [CrossRef]
Sayles, R. S., and Thomas, T. R., 1979, “Measurements of the Statistical Properties of Engineering Surfaces,” J. Lubr. Technol., 101, pp. 409–417. [CrossRef]
Wu, J. J., 2000, “Simulation of Rough Surfaces With FFT,” Tribol. Int., 33(1), pp. 47–58. [CrossRef]
ISO 25178 draft standard, “Geometrical Product Specifications—Surface Texture: Areal, Part 2: Terms, Definitions and Surface Texture Parameters.
Blunt, L., and Jiang, X., 2003, “Numerical Parameters for Characterization of Topography,” Advanced Techniques for Assessment Surface Topography, L.Blunt and X.Jiang, Eds., Kogan Page Science, London and Sterling, pp. 17–41.
Kogut, L., and Etsion, I., 2003, “A Finite Element Based Elastic Plastic Model for the Contact of Rough Surfaces,” Tribol. T., 46(3), pp. 383–390. [CrossRef]
Whitehouse, D. J., and Archard, J. F., 1970, “The Properties of Random Surfaces of Significance in Their Contact,” Proc. R. Soc. A. Math. Phys., 316, pp. 97–121. [CrossRef]
Chang, W. R., Etsion, I., and Bogy, D. B., 1987, “An Elastic-Plastic Model for the Contact of Rough Surfaces,” ASME J. Tribol., 109(2), pp. 257–263. [CrossRef]
Patir, N., and Cheng, H. S., 1978, “An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication,” J. Lubr. Technol., 100, pp. 12–17. [CrossRef]
Pawlus, P., and Zelasko, W., 2012, “The Importance of Sampling Interval for Rough Contact Mechanics,” Wear, 276–277, pp. 121–129. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

256 by 256 point sections of the 512 by 512 point rough surfaces, (a) surface 1, (b) surface 2, and (c) surface 3

Grahic Jump Location
Fig. 2

Equivalent rough surface and rigid flat

Grahic Jump Location
Fig. 3

(a) Number of contacting asperities and (b) percent error of the number of contacting asperities versus nondimensional separation based on surface heights

Grahic Jump Location
Fig. 4

(a) Nondimensional real area of contact and (b) percent error of real area of contact versus nondimensional separation based on surface heights

Grahic Jump Location
Fig. 5

(a) Nondimensional separation based on surface heights and (b) percent error of the nondimensional separation based on surface heights versus nondimensional normal load

Grahic Jump Location
Fig. 6

(a) Nondimensional real area of contact and (b) percent error of the real area of contact versus nondimensional normal load

Grahic Jump Location
Fig. 7

(a) Nondimensional real area of contact and (b) nondimensional separation based on surface heights versus nondimensional normal load

Grahic Jump Location
Fig. 8

Nondimensional separation based on surface heights versus nondimensional normal load for (a) surface 1, (b) surface 2, and (c) surface 3

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In