Multiscale characterization of computational rough surfaces and their wear using self-affine principal profiles

Abstract

► A hybrid surface characterization method is proposed. ► It is based on principal component analysis with fractal principal profiles. ► A small number of principal profiles are enough for characterizing a surface. ► Fractal definition of profiles allows not to loss multiscale information. ► The method can be also used for characterization and modelling of worn surfaces. A methodology is introduced where principal component analysis (PCA) and fractal profile description are combined for characterizing and modelling computational rough surfaces for their use in computer-aided-engineering (CAE) processes. The main idea is to extract principal profiles (PPs) from digital surfaces acquired using confocal microscopy and to model the projection of the original surface onto these PPs by means of Weierstrass–Mandelbrot series; thus, the method is called self-affine principal profile (SAPP) analysis. These PPs are the eigenvectors of the covariance matrix of the digital surface. Profiles modelled in this way preserve information about all scales due to the scale-invariant nature of self-affine profiles. PPs are selected to be those containing the greater amount of information about the surface in terms of spatial variance. It is shown that just the first few PPs are enough to approximately reproduce a given surface and that this approximation can be measured. The methodology is applied to build families of surfaces with specific fractal dimensions and to characterize surface evolution due to wear. The quality of surfaces obtained is quantified in terms of mesh resolution, number of PPs used for modelling the surface and number of terms in the Weierstrass–Mandelbrot series, which are all relevant parameters for building meshes for CAE.