Fractals, engineering surfaces and tribology

Abstract Fractal geometry, which is based on modern mathematics and which admits fractional dimensions, is introduced in this paper. Examples of fractional dimensions are 2.2618 and 2.4950; these are, of course, inadmissible in Euclidean geometry. Engineering surfaces, viewed from a wide spectrum of scales which range from micro to macro extents, are then discussed as a vital part of tribology. Based on results of recent research including experimental findings, it is concluded that fractal geometry forms an attractive adjunct to Euclidean geometry in the modeling of engineering surfaces. In other terms, a judicious use of a dual-scale description of surfaces would be most powerful in attacking problems in such areas of tribology as boundary lubrication.

[1]  D. Dowson.  History of Tribology , 1979 .

[2]  B. Mandelbrot,et al.  Fractals: Form, Chance and Dimension , 1978 .

[3]  D. Farin,et al.  Chemistry in noninteger dimensions between two and three. II: Fractal surfaces of adsorbents , 1983 .

[4]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[5]  Bale,et al.  Integrated fractal analysis of silica: Adsorption, electronic energy transfer, and small-angle x-ray scattering. , 1986, Physical review letters.

[6]  F. F. Ling.  Scaling law for contoured length of engineering surfaces , 1987 .

[7]  J. Archard,et al.  Elastic Deformation and the Contact of Surfaces , 1953, Nature.

[8]  On Fractal Dimension of Engineering Surfaces , 1988 .

[9]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[10]  Peter Pfeifer,et al.  Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces , 1983 .

[11]  D. Avnir.  Fractal Aspects of Surface Science - An Interim Report , 1986 .

[12]  F. F. Ling,et al.  On weeping lubrication theory , 1969 .

[13]  On Model Studies of Metallic Surface Asperities , 1959 .

[14]  W M Lai,et al.  Fluid transport and mechanical properties of articular cartilage: a review. , 1984, Journal of biomechanics.

[15]  F. F. Ling.  On Temperature Transients at Sliding Interface , 1969 .

[16]  A. Sarkar.  Friction and wear , 1980 .

[17]  Joseph Naor,et al.  Multiple Resolution Texture Analysis and Classification , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Shmuel Peleg,et al.  Applications and limitations of boundary-line fractal analysis of irregular surfaces: proteins, aggregates, and porous materials , 1985 .

[19]  Peter Pfeifer,et al.  Surface geometric irregularity of particulate materials: the fractal approach , 1985 .