Surface topography as a nonstationary random process

Sliding susceptibility of a rough cylinder on a rough inclined perturbed surface

“…A great deal of experimental data [19,20,21,22] corroborate a robust scaling relation for w(L) along an impressive interval of variability of eight decades in L, from typically 10 −6 m to 10 2 m:…”

“…We conjecture that the origin of the tendency of χ(L) for interacting rough surfaces to display power laws in L in several physical situations as exemplified in Figs. 2 to 5 is connected with the frequently observed fractal nonstationary behavior of the roughness of surfaces [1,15,19]; by this we understand that a sample of finite length L taken from a real surface will never, however long, completely represents its properties. If the height h(x) of a surface as a function of the position along a particular cut, x, is measured, the associated roughness can be defined by the width w = h(x) 2 − h(x) 2 1/2 , where h(…”

A Study on the Gray Value Distribution Contour Curve Extraction Based on the Image of the Fracture Surface of the Material and Its Fractal Dimension

“…Early in 1978, Sayles [7] believed that the surface morphology was unstable stochastic processes, the traditional some statistical parameters could not characterize the random behavior and detailed features of the fracture morphology comprehensively. As the fractal geometry came into being, in 1984, Mandelbrot [8] first proposed to characterizing the morphology characteristic of fracture surface of metal quantitatively by the fractal dimension; from then on, the fractal geometry was used to characterize the characterize the morphology characteristic of fracture surface of materials widely.…”

Special features in the application of fractal analysis for examining the surface microrelief formed at face milling

“…The existence of quantitative information of this kind will subsequently make it possible to optimize conditions for the machining of parts and to provide for the required level of parameters of surface microrelief. That is why present work should be considered as further development and practical application of approaches and results [1][2][3][4][5][6][7].…”

“…Given this, it becomes clear why significant attention is paid to studying the microrelief of the surface of samples both theoretically and practically. Among the theoretical directions in the studies of the surface microrelief state, of special interest are the series of articles that deal with the application of sufficiently new, nontrivial mathematical methods for analysis of the surface relief state [1][2][3][4][5][6][7]. They include papers on the application of fractal representations to the description of the self-similar states, which are formed either naturally, for example, due to the reflection by the surface of crystallographic properties of the volume of material of the base layer [8,9], or due to the periodic action on the surface of machnining tool [10,11].…”