Abstract
The purpose of the work is to create a mathematical model of furnace thermal operation for control problems, on the basis of which a "virtual twin" of the homogenizing furnace can be implemented. Recently, the heating quality indicators of aluminum semi-finished products and products before further processing are becoming particularly relevant in the processes of aging or hardening also due to the introduction of the international quality standard ISO at metallurgical enterprises. At the same time, the existing control systems of heating furnace parameters mainly regulate the local heater by measuring the air temperature near it. The task of maintaining the desired heating volume of the entire furnace and the charge is quite difficult under this type of control and requires constant adjustment of the proportional-integral-differentiating regulators by an experienced employee. The energy intensity of aluminum processing is also high but not all enterprises are able to replace outdated furnaces. Then the resource-saving opportunities center around the improvement of control systems. In particular, the replacement of traditional response regulation with proactive regulation is a promising direction. Therefore, the development of mathematical models and software enabling to calculate and predict the temperatures of different areas of a furnace and heated materials depending on the change in heating conditions is a relevant task. Modeling and studies are carried out using ordinary differential equations and explicit difference schemes. The paper proposes a dynamic model of heat transfer in a homogenizing furnace and performs test calculations demonstrating the applicability of this model to the selection of heating modes and algorithms. The model can also be used as a basis for the development of a furnace digital twin. The presented models and calculation methods are applicable as developments of modern control systems and heating optimization of not only metal products but any materials.
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