Development of mathematical models of changes in emulsion concentration and the content of mechanical impurities in technological fluids using the MATLAB package for experimental data processing

The article presents the results of the study of the processes of modeling changes in the concentration of emulsions and the content of mechanical impurities in technological fluids used in cold rolling conditions. The main goal of the work is to develop mathematical models to describe the relationships between the concentration of emulsions and mechanical impurities, as well as to estimate the rate of their changes over time, which will allow to increase the efficiency of technological process control and ensure stable product quality. The study is based on the analysis of experimental data obtained for different types of emulsols, such as «LUBRO DL ZPS», «ROLLUB 988-AR», «OPTIMAL-PRO» and «TRENOIL S 740», on the reversible state 1680 and the continuous four-cell state "Tandem" under the conditions of PJSC «Zaporizhstal». The models were built with high-precision linear, quadratic and exponential approximation, and their accuracy was assessed based on the coefficient of determination. To automate data processing, the MATLAB software environment was used, which provided convenience in working with large data sets, the ability to visualize them and build approximation models. As a result of processing the experimental data, optimal mathematical models of the dependence of the concentration of emulsions on time and the concentration of mechanical impurities on time were obtained, and the rate of change of these parameters was also calculated. Analysis of the relationship between the concentration of emulsions and mechanical impurities revealed extremum points, in particular the maximum concentration of mechanical impurities and critical concentration values, which are key to ensuring the efficiency of lubrication processes. The results obtained allow not only to better understand the patterns of accumulation of mechanical impurities in technological fluids, but also to offer tools for optimizing technological processes in industrial conditions. The proposed approaches can be integrated into existing control systems to ensure the stability of technological operations