Mathematical model of the metal quality forecast

Introduction . The quality of massive metal products is influenced by many factors, which makes it difficult to assess them by non-destructive methods of control. Since the theory of fractals makes it possible to more adequately evaluate the structure of complex objects of different nature, then the possibility of applying this theory to a more adequate assessment of elements of the structure of the metal at the microstructural level is considered. Method. The mathematical modeling of the quality criteria of cast iron rolls on the basis of analysis of the fractal dimension of elements of their structure is applied. The calculation of the fractal dimension of the metal was carried out on the basis of the developed methodology. Practical meaning. The sensitivity of the mechanical properties of cast-iron rollers to the fractal dimension of the elements of their structure (perlite, carbides, graphite) was established. The greatest sensitivity of the strength indicators was fixed to the fractal dimension of carbides and graphite. This approach allowed to construct a mathematical model that allows to predict the mechanical properties of rolls with an error of 5-7% based on their dependence on the most sensitive indicators of the dimension of structural elements. Conclusions. It is shown that the quality criteria of cast-iron rolls can be described by a fractal model based on the analysis of elements of their structure.