Reconstruction of three-dimensional turned shaft surfaces with fractal functions

A method for the reconstruction of turned shaft surfaces with a (fractal) Weierstrass-Mandelbrot-function (WMF) is presented. The WMF is modified to allow to freely choose a phase-shift for every frequency. The reconstruction is based on distinct profiles in axial and tangential direction and the statistical distribution of low-wavelength portions of the surface is taken into account by adding t-distributed random deviations to the surface. The work is validated by reconstructing measured shaft surfaces with different manufacturing parameters, which shows good accuracy for periodic surfaces. This method allows for a characterization of surfaces with a limited number of parameters and can be used to store the characteristics of measured surfaces with a reduced amount of data compared to a point-cloud surface. (C) 2015 Elsevier Ltd. All rights reserved.