Model of assessment of the hardness of the iron rollers СПХН-43 and СШХНФ-47

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Relevance of the article. The quality criteria of massive metal products is affected by many technological parameters. Changing some of these parameters can lead to a significant change in the quality of the target product. Therefore, various types of models are widely used in materials science to simulate individual processes or predict individual criteria. An analysis of literary sources indicates the prospects of using fractal geometry to model the structure and properties of various materials. It is proposed to apply multifractal analysis to assess the structure of cast-iron rolls. Materials and methods. The influence of the structure of cast irons on their hardness was investigated. The microstructure of cast iron was investigated using quantitative methods of metallography (ГОСТ 3443) and multifractal analysis. The calculation of the spectrum of statistical dimensions of the cast iron microstructure was carried out according to the Renyi formula. The hardness indices of the roll-forming rolls СПХН-43 (520 ´ 1 000 mm) and СШХНФ-47 (680 ´ 1 000 mm) were determined at three points evenly spaced along the length of the roll barrel. Results and its discussion. The influence of the spectrum of statistical dimensions D 0 , D 1 , D 2 , D -100 and D 100 of carbides, lamellar and spherical graphite on the hardness indices of cast iron rolls is studied. It was found that the pair correlation coefficients in the prediction of hardness according to the traditional characteristics of the structure (length, diameter, area) are R 2 = 0,73...0,87. The correlation coefficients in the prediction of hardness by multifractal characteristics for rolls СПХН-43 are 0,78...0,88. For rolls СШХНФ-47, the correlation coefficients are 0,81...0,93. The obtained results confirm the effectiveness of using multifractal analysis in assessing the quality criteria of cast-iron rolls. Scientific novelty. The influence of multifractal dimensions of graphite and carbides on the hardness of cast iron rolls СПХН-43 and СШХНФ-47 is established. The sensitivity of the СПХН-43 roll hardness indices to the information and correlation dimensions of carbides, as well as to the fractal and statistical D -100 dimensions of plate graphite, was revealed. The sensitivity of hardness indices to the fractal and statistical D 100 dimensions of carbides and to the fractal and correlation dimensions of spherical graphite was established for the СШХНФ-47 rolls. Conclusions. Based on the results obtained, an approach has been developed to assess the hardness indices of rolls СПХН-43 and СШХНФ-47, which includes: 1) Determination of the spectrum of statistical dimensions of structural elements of cast irons. 2) Determination of sensitivity coefficients of hardness indicators to the spectrum of dimensions of structural elements. 3) Construction of a mathematical model for forecasting roll hardness. The approach considered can be interpreted as an alternative method for assessing the quality criteria of cast irons based on an analysis of their structure.