Abstract
In the optimal control of billet heating in pass-through heating furnaces of rolling mills, the variable productivity of the mill in combination with the inertial properties of heating zones is a factor that greatly complicates the realization of optimal modes. The subsystem of predicting the temperature state of the furnace depending on the current productivity of the mill and taking into account the heat transfer between the heating zones will increase the efficiency of the optimal control system in transient modes of furnace operation. The work provides the results of the work analysis on the development of external heat exchange mathematical models in pass-through heating furnaces of rolling mills. Two main directions of external heat transfer mathematical models research are defined. The first group of researches includes the development of heat transfer models in which the heat transfer process is described by a system of analytical or numerical equations based on the physical laws of heat transfer taking into account the hydrodynamics of flue gas movement. The second group of research includes the development of empirical mathematical models based on the parameters of the observed process, and describing the correlation between these parameters. Research on the empirical mathematical model development of a pass-through heating furnace taking into account the dynamic characteristics of the process has been carried out. As a result of the research, a mathematical model is obtained, which determines the relationship between the fuel consumption distributed over the furnace zones and the temperature of the working space in these zones. The mathematical model takes into account the mutual influence of neighboring zones, furnace productivity on heating the workpieces, as well as the dynamic characteristics of the zones. As initial data for finding the coefficients of the equations were taken statistical data of wide strip hot rolling mill heating furnace operation. The coefficients of the mathematical model equations were determined by the search method, using the method of deformable polyhedron.
Keywords
heating furnace, metal pressure treatment, empirical model, deformable polyhedron method, the Nelder-Mead method, billet heating before rolling
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