The Multifractal Analysis of Periodic Surface Relief of Parts After Face Milling

The multifractal (MF) analysis was applied to prove the existence of self-similarity and fractal symmetry of special microforms formed on the surface of structural carbon steel C35 and aluminum alloy AA2024 after their face milling. The micro images of surface specimens previously milled at various cutting conditions were used as the input information to implement this approach to describe the state of surfaces. The paper calculates generalized statistical sums for the area and volumes of spatial microforms to prove the presence of linear dependences between their values and sizes of elementary particles in the method of coarse partitions. This result was used as a proof of the presence of fractal symmetry among the indicated surface parameters for the case of a periodic spatial relief formation on the surface as an outcome of cyclic action of face mill blade. The MF spectra and their basic parameters are calculated for the surfaces of samples formed under different cutting conditions. The correspondence of the characteristic functions of the performed MF analysis to their canonical forms was discussed. This is considered as a proof that the indicated geometric surface parameters of the material, even after machining, form a system with self-similarity and fractal symmetry properties. The quantitative relationships between the MF spectrum parameters of surface area and volumes of microforms formed with face milling and cutting conditions were discussed.