Fast Methods for Solving Rough Contact Problems: A Comparative Study

A realistic description of rough surfaces will generally involve very large arrays of surface height data, which makes the application of conventional numerical methods of contact mechanics to rough contact analyses impractical. Recently, two fast numerical techniques have been applied to rough contact problems: the multi-level multi-summation (MLMS) and the fast Fourier transform (FFT). In this work, the computational efficiency of the two methods is compared by applying them to an example concentrated contact problem. It is shown that to achieve a numerical accuracy comparable to that of MLMS, the grid on which FFT is performed needs to be extended far beyond the contact area, which results in a dramatic increase in the computation time. When such a high accuracy is unnecessary, FFT can be applied on a smaller grid. However, the computational speed of MLMS can also be increased in this case by modifying certain algorithm parameters. Numerical results demonstrate that MLMS is more advantageous than FFT for solving three-dimensional concentrated contact problems, both when the maximum possible accuracy is desired and when a moderate accuracy goal is specified.

[1]  Takahisa Kato,et al.  Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model , 1997 .

[2]  J. Williamson,et al.  On the plastic contact of rough surfaces , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  D. Whitehouse,et al.  The properties of random surfaces of significance in their contact , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  A. Brandt,et al.  Multilevel matrix multiplication and fast solution of integral equations , 1990 .

[5]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[6]  L. Keer,et al.  A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques , 1999 .

[7]  Richard Timothy Hunt,et al.  Asperity persistence and the real area of contact between rough surfaces , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  J. A. Greenwood.  The Area of Contact Between Rough Surfaces and Flats , 1967 .

[9]  Herbert S. Cheng,et al.  Computer Simulation of Elastic Rough Contacts , 1985 .

[10]  E. Ioannides,et al.  A Fast Solution of the Dry Contact Problem and the Associated Sub-Surface Stress Field, Using Multilevel Techniques , 1991 .

[11]  J. A. Greenwood.  Problems with Surface Roughness , 1992 .

[12]  P. Nayak,et al.  Random Process Model of Rough Surfaces , 1971 .

[13]  Ning Ren,et al.  Contact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method , 1993 .

[14]  B. Bhushan,et al.  Fractal Model of Elastic-Plastic Contact Between Rough Surfaces , 1991 .

[15]  Leon M Keer,et al.  An analysis of the effect of hard coatings on near-surface rolling contact fatigue initiation induced by surface roughness , 1997 .

[16]  J. Kalker.  Numerical calculation of the elastic field in a half-space , 1986 .

[17]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[18]  J. Kalker,et al.  A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems , 1972 .

[19]  Irina Goryacheva,et al.  Multiple contact model in the problems of tribomechanics , 1991 .

[20]  R. S. Sayles,et al.  A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces , 1986 .

[21]  A Sackfield,et al.  A note on the hertz contact problem: A correlation of standard formulae , 1983 .

[22]  A. Lubrecht,et al.  Numerical Analysis of the Influence of Waviness on the Film Thickness of a Circular EHL Contact , 1996 .

[23]  Bharat Bhushan,et al.  Elastic-plastic contact model for bifractal surfaces , 1992 .

[24]  D. Berthe,et al.  An elastic approach to rough contact with asperity interactions , 1987 .

[25]  C. Venner.  Multilevel solution of the EHL line and point contact problems , 1991 .

[26]  C. P. Hendriks,et al.  Accurate Real Area of Contact Measurements on Polyurethane , 1995 .

[27]  R. Sayles,et al.  Surface topography as a nonstationary random process , 1978, Nature.

[28]  S. D. Probert,et al.  Real Area of Contact between a Rough Surface and a Softer Optically Flat Surface , 1970 .

[29]  D. Berthe,et al.  Influence of Surface Waviness and Roughness on the Normal Pressure Distribution in the Hertzian Contact , 1987 .

[30]  Mpf Sutcliffe,et al.  Flattening of Random Rough Surfaces in Metal-Forming Processes , 1999 .

[31]  Magnus R. Hestenes,et al.  Conjugate Direction Methods in Optimization , 1980 .

[32]  H. A. Francis.  The accuracy of plane strain models for the elastic contact of three-dimensional rough surfaces , 1983 .

[33]  J. Greenwood,et al.  Contact of nominally flat surfaces , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[34]  Aizoh Kubo,et al.  Contact Stress Between Rollers With Surface Irregularity , 1981 .

[35]  P. Nayak,et al.  Random process model of rough surfaces in plastic contact , 1973 .