The relation between fractal signature and topography parameters: a numerical and experimental study

Abstract

Surfaces generated by various finishing techniques are inherently rough and manifest different characteristics at multiple scales. Due to the multiscale nature of rough surfaces, roughness parameters are different when calculated at different scales. In this work, self-affine surfaces are numerically generated and characterized using fractal, spectral, and statistical methodologies. Two new closed-form expressions are proposed to determine the mean summit radius and standard deviation of summit height. The atomic force microscope (AFM) is utilized to measure the polished surfaces. It is found that the fractal dimension of smooth surface is in the range of 2.15 ± 0.15. The effect of roll-off vector on roughness parameters is also discussed. Wear experiments are performed on pin-on-disc tribometer to see the evolution of fractal signature (H) with sliding time. It is shown numerically and verified experimentally that root mean square roughness decreases with increase in the fractal signature. This work is a part of understanding the fractal nature of surfaces, which can be further utilized to see the evolution of surface topography during the wear and rolling contact fatigue process. Furthermore, this work will be useful to analyze the surfaces produced by machining process like grinding, friction between the elastomer and self-affine fractal surfaces, in which wave vectors and topography parameters play significant role in controlling of friction.