Mathematical modeling of quantitative changes in hydrogen and oxide inclusions in aluminum alloy
Abstract
In this article, mathematical modeling of quantitative changes in hydrogen and oxide inclusions in aluminum alloys is justified, developed, and analytically implemented. Usually, the methods of linear algebra are mostly used; in particular, the solutions of systems of inhomogeneous algebraic equations are obtained based on the method of Gauss, Cramer, and inverse matrices using the Maple 13 software package. Quantitative changes in hydrogen and oxide inclusions in the alloy are determined by a change in the average dispersion of the loaded flux. The connectivity functions of the change of oxide aluminum in the alloy β (%) with an increase in temperature Т ( 0 С) during the loading of the charge into the liquid bath are obtained. The connectivity functions to determine the change quantity of hydrogen λ (cm 3 /100 g) in the alloy depending on the time t (minute) holding of the heated charge in the period of research is obtained. Based on functional dependencies, graphs of changes in the mainly desired parameters and numerical indexes in tabular form for engineering and applied calculations are constructed. In particular, graphs of the change quantity of hydrogen and oxide inclusions in the alloy with an increase of average dispersion of the flux d, graphs of change quantity of hydrogen with an increase in temperature during loading of the charge into the liquid bath, changes of the quantity of oxide aluminum in the alloy β (%) with an increase in temperature Т ( 0 С) , patterns of change quantity of hydrogen in the alloy λ (cm 3 /100 g) and quantity of oxide η (%) were plotted depending on the time of holding the heated charge in period research.