A Numerical Method for Analysis of Extended Rough Wavy Surfaces in Contact

[+] Author and Article Information
Yu. A. Karpenko, Adnan Akay

Carnegie Mellon University, Mechanical Engineering Department, Pittsburgh, PA 15213

J. Tribol 124(4), 668-679 (Sep 24, 2002) (12 pages) doi:10.1115/1.1467082 History: Received April 17, 2001; Revised September 27, 2001; Online September 24, 2002
Copyright © 2002 by ASME
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Bowden, F. P., and Tabor, D., 1950, The Friction and Lubrication of Solids, Clarendon Press, Oxford.
Kragelsky, I. V., Dobychin, M. N., and Kombalov, V. S., 1982, Friction and Wear Calculation Methods, Pergamon Press, New York.
Williamson,  J. B. P., 1967, “The Microtopography of Surfaces,” Properties and Metrology of Surfaces, Proc. Inst. Mech. Eng., 182, Part 3k, pp. 21–30.
Peklenik,  J., 1967, “New Developments in Surface Characterization and Measurement by Means of Random Process Analysis,” Proc. Inst. Mech. Eng., 182, Part 3k, pp. 108–126.
Whitehouse,  D. J., 1971, “Typology of Manufactured Surfaces,” Annals of the CIRP, XVIV, pp. 417–431.
Greenwood,  J. A., and Williamson,  J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, A295, pp. 300–319.
Johnson, K. L., 1987, Contact Mechanics, Cambridge University Press, Cambridge UK.
Whitehouse,  D. J., and Archard,  J. F., 1970, “The Properties of Random Surfaces of Significance in Their Contact,” Proc. R. Soc. London, Ser. A, A316, pp. 97–121.
Onions,  R. A., and Archard,  J. F., 1973, “The Contact of Surfaces Having a Random Surface Structure,” J. Appl. Phys., J. Phys. D, 6, pp. 289–304.
Hisakado,  T., 1974, “Effect of Surface Roughness on Contact Between Solid Surfaces,” Wear, 28, pp. 217–234.
Francis,  H. A., 1977, “Application of Spherical Indentation Mechanics to Reversible and Irreversible Contact Between Rough Surfaces,” Wear, 45, pp. 221–269.
Francis,  H. A., 1976, “Phenomenological Analysis of Plastic Spherical Indentation,” ASME J. Eng. Mater. Technol., 98, pp. 272–281.
Chang,  W. R., Etsion,  I., and Bogy,  D. B., 1987, “Elastic Plastic Model for the Contact of Rough Surfaces,” ASME J. Tribol., 109, pp. 257–263.
Westergaard,  H. M., 1939, “Bearing Pressures and Cracks,” ASME J. Appl. Mech., 6, pp. A49–A53.
Shtaerman, I. Y., 1949, “Contact Problem in the Theory of Elasticity,” Gostehizdat, Moscow,(In Russian).
Dundurs,  J., Tsai,  K. C., and Keer,  L. M., “Contact Between Elastic Bodies With Wavy Surfaces,” J. Elast., 3, pp. 109–115.
Johnson,  K. L., Greenwood,  J. A., and Higginson,  J. G., 1985, “The Contact of Elastic Regular Wavy Surfaces,” Int. J. Mech. Sci., 27(6), pp. 383–396.
Kragelsky,  I. V., and Demkin,  N. B., 1960, “Contact Areas of Rough Surfaces,” Wear, 3, pp. 170–187.
Greenwood,  J. A., and Tripp,  J. H., 1967, “The Elastic Contact of Rough Spheres,” ASME J. Appl. Mech., 34, pp. 153–159.
Back, N., Burdekin, M., and Cowley, A., 1973, “Review of the Research on Fixed and Sliding Joints,” Proc. 13th Internat. Machine Tool Design and Research Conference, eds. Tobias, S. A., and Koenigsberger, F., MacMillan, London, pp. 87–97.
Singh,  K. P., and Paul,  B., 1974, “Numerical Solution of Non-Hertzian Contact Problems,” ASME J. Appl. Mech., 96, pp. 484–490.
Webster,  M. N., and Sayles,  R. S., 1986, “A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces,” ASME J. Tribol., 108, pp. 314–320.
Lai,  W. T., and Cheng,  H. S., 1985, “Computer Simulation of Elastic Rough Contacts,” ASLE Trans., 28(2), pp. 172–180.
Lee,  S. C., and Ren,  N., 1996, “Behavior of Elastic-Plastic Rough Surface Contacts as Affected by Surface Topography, Load, and Material Hardness,” Tribol. Trans., 39(1), pp. 67–74.
Tian,  X., and Bhushan,  B., 1996, “A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle,” ASME J. Tribol., 118, pp. 33–42.
Akai, T. J., 1994, Applied Numerical Methods for Engineers, John Wiley & Sons, Inc., New York.
Ren,  N., and Lee,  S. C., 1993, “Contact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method,” ASME J. Tribol., 115, pp. 597–601.
Cooley,  J. W., and Tukey,  J. W., 1965, “An Algorithm for the Machine Calculation of Complex Fourier Series,” Math. Comput., 19, pp. 297–301.
Ju,  Y., and Farris,  T. N., 1996, “Spectral Analysis of Two-Dimensional Contact Problems,” ASME J. Tribol., 118, pp. 320–328.
Polonsky,  I. A., and Keer,  L. M., 2000, “Fast Methods for Solving Rough Contact Problems: A Comparative Study,” ASME J. Tribol., 122, pp. 36–41.
Jiang,  X., Hua,  D. Y., Cheng,  H. S., Ai,  X., and Lee,  Si C., 1999, “A Mixed Elastohydrodynamic Lubrication Model With Asperity Contact,” ASME J. Tribol., 121, pp. 481–491.
Noor,  A. K., Kamel,  H. A., and Fulton,  R. E., 1978, “Substructuring Techniques—Status and Projections,” Comput. Struct., 8, pp. 621–632.
Kondo,  M., and Sinclair,  G. B., 1985, “A Simple Substructuring Procedure for Finite Element Analysis of Stress Concentrations,” Commun. Appl. Numer. Methods, 1, pp. 215–218.
Ernst, H., and Merchant, M. E., 1940, “Surface Friction of Clean Metals—a Basic Factor in the Metal Cutting Process,” Proc. Special Summer Conf. on Friction and Surface Finish, Massachusetts Inst. Technology, Cambridge, MA, pp. 76–101.
Love,  A. E. H., 1929, “Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary,” Philos. Trans. R. Soc. London, Ser. A, A228, pp. 377–420.
Polonsky,  I. A., and Keer,  L. M., 2000, “A Fast and Accurate Method for Numerical Analysis of Elastic Layered Contacts,” ASME J. Tribol., 122, pp. 30–35.
Ai,  X., and Sawamiphakdi,  K., 1999, “Solving Elastic Contact Between Rough Surfaces as an Unconstrained Strain Energy Minimization by Using CGM and FFT Techniques,” ASME J. Tribol., 121, pp. 481–491.
Kragelsky, I. V., 1965, Friction and Wear, Butterworths, WA.
Woo,  K. L., and Thomas,  T. R., 1980, “Contact of Rough Surfaces: A Review of Experimental Work,” Wear, 58, pp. 331–340.
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.
Forsythe, G. E., Malcolm, M. A., and Moler, C. B., 1977, Computer Methods for Mathematical Computations, Prentice Hall, Englewood Cliffs, NJ.
Ogilvy,  J. A., 1991, “Numerical Simulations of Friction between Contacting Rough Surfaces,” J. Appl. Phys., J. Phys. D, 24, pp. 2098–2109.
Bhushan, B., 1990, Tribology and Mechanics of Magnetic Storage Devices, Springer-Verlag, NY.
Nuri,  K. A., and Halling,  J., 1975, “The Normal Approach between Rough Flat Surfaces in Contact,” Wear, 32, pp. 81–93.
Tworzydlo,  W. W., Cecot,  W., Oden,  J. T., and Yew,  C. H., 1998, “Computational Micro- and Macroscopic Models of Contact and Friction: Formulation, Approach and Applications,” Wear, 220, pp. 113–140.


Grahic Jump Location
Sample profile of a machined surface: (a) profile, (b) roughness, and (c) waviness, where dashed lines show the positions of the corresponding mean surfaces, hw≈O(μm), and λw≈O(mm)
Grahic Jump Location
Schematic of (a) two three-dimensional extended surfaces in contact and (b) corresponding contact areas, where Ac and ar denote contour areas of contact and true contacts, respectively
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Diagram of the extended surfaces denoted by 1 and 2: (a) before contact and (b) after deformation. The positions of their mean surfaces before and after deformation are shown with dashed lines.
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Schematic description of asperities in contact (a) and the corresponding contact force distribution (b). Dotted lines represent the undeformed shapes of the asperities. Solid lines represent their deformed slopes. The positions of the matching surface points before the contact and after the deformation are denoted with 1 and 2, and 1* and 2* , respectively, where δ−h(x,y) describes their contact approach.
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Flow chart of the computer program that calculates iteratively contact parameters between two extended surfaces using the three-stage loop to solve for self-consistent displacement and pressure distributions
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Substructuring of the contact domain between nominally flat surface and wavy and rough surface based on the K-D notion of surface contacts 18: the distribution of contour areas of contact over the nominal contact area of size 1024 mm2 (a), the distribution of asperity contacts inside a contour area of contact (b), and an asperity contact (c). The external normal load P is equal to 300 N. The asperities of the equivalent rough surface have the standard deviation σe=0.43 μm. The surface waviness has wavelength λw(c)=11 mm and wave amplitude hw(c)=6 μm. The sizes of traction elements used for the computations are as follows: dx(1)=dy(1)=62.5 μm,dx(2)=dy(2)=6.25 μm, and dx(3)=dy(3)=0.2 μm.
Grahic Jump Location
Predicted variation of true contact area between two extended surfaces (A0=1024 mm2 and E=83 GPa) with external load. Solid lines represent the results from the present method, where symbols ○ and □ mark the results for the first set (where surfaces have λw(s)=17 mm,hw(s)=8 μm, and σ(s)=0.35 μm and λw(c)=11 mm,hw(c)=6 μm, and σ(c)=0.25 μm) and the second set (where surfaces have σ(s)=0.35 μm and λw(c)=11 mm,hw(c)=6 μm, and σ(c)=0.25 μm) of surface topographies, respectively. Dotted line—the variation of true contact area given by the contact model presented in 17; dashed line—the G-W model 6, and dashed dotted line—the model by Bowden and Tabor 1.
Grahic Jump Location
Variation of contact parameters between extended surfaces (A0=1024 mm2 and E=83 GPa) with load predicted by the present method for two sets of surface topographies: (a) number of asperity contacts, Γ, where Γ=∑jkmj; (b) mean contact area per asperity contact normalized with respect to the mean area of the asperity base, πRe2, where Re=0.99 mm; (c) mean contact pressure normalized with respect to the hardness of the softer solid (Hs=800 MPa), and (D) mean distance between asperity contacts normalized with respect to the correlation radius ρ (ρ=45 μm). The results for the first set of topographies (where surfaces have λw(s)=17 mm,hw(s)=8 μm, and σ(s)=0.35 μm and λw(c)=11 mm,hw(c)=6 μm, and σ(c)=0.25 μm) are marked with ○’s while the corresponding results for the second set (where surfaces have σ(s)=0.35 μm and λw(c)=11 mm,hw(c)=6 μm, and σ(c)=0.25 μm) are marked with □’s. The dashed lines show the corresponding results from the G-W model 6, for comparison.
Grahic Jump Location
Contact approach between two extended surfaces (E=83 GPa) versus external load, where symbols ○ and □ mark the results for the first set (where surfaces have λw(s)=17 mm, hw(s)=8 μm, and σ(s)=0.35 μm and λw(c)=11 mm, hw(c)=6 μm, and σ(c)=0.25 μm) and the second set (where surfaces have σ(s)=0.35 μm and λw(c)=11 mm, hw(c)=6 μm, and σ(c)=0.25 μm) of surface topographies, respectively.



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