Roughness characteristic length scales of belt finished surface

Surface integrity, dynamic properties and mechanical characteristics of belt finished surfaces strongly depend on the achieved surface roughness produced by the abrasion process. A new approach based on the scaling analysis of the roughness characterization is introduced on a surface obtained by a set of roughness process parameters. Experimental results show that range roughness amplitude depends on the scan size and that roughness amplitude follows two stages. Stage I presents a linear power-law roughness distribution—a linear relation. Stage II presents a non-linear power-law roughness distribution. The latter is divided into two sub-stages: the first sub-stage (sub-stage II.a) characterizes the fractal behaviour of the surface until a critical length where the second sub-stage (sub-stage II.b) starts and characterize roughness by extreme values statistics. Fractal parameters, extreme values estimators and transition scale threshold between stages II.a and II.b are shown to be related to the abrasion process. As a result, an original probabilistic model based on the generalized lambda distribution is proposed to estimate the extreme range amplitude roughness values in stage II, depending on the observation scale. Finally, the maximal roughness amplitude PDF is estimated, at a scale higher than the scanning length with the aid of a bootstrap protocol coupled with a Monte-Carlo simulation.