Simulation mathematical model of the rolling process on a continuous sheet mill

The process of continuous sheet rolling has been known for a long time, and seems to be comprehensively studied, but the economic situation is forcing enterprises to continuously improve it, and look for more and more new ways to improve product quality, while maintaining, and preferably increasing, productivity. And the existing methods and approaches are ineffective, because they contain a large number of assumptions and simplifications. On the other hand, modern plate-rolling machines are expensive and high-performance, which significantly increases the cost of errors in working with them. In this situation, it seems very promising to create digital twins, which would allow a more detailed study of the technological process, effectively train personnel, and exclude the adoption of inefficient or potentially dangerous technical solutions. This article solves the problem of creating a simulation mathematical model of the process of hot rolling of a sheet on a continuous mill. Based on the proven approaches, a kinematically possible velocity field in the billet metal is constructed, and the thermal problem is solved. The application of the power balance equation makes it possible to determine the critical angles in each of the stands, and, depending on the initial data, to determine either the interstand tensions for a given speed mode, or the roll revolutions in each stand for a given tension mode. When determining the power of the forces acting in the mill, the processes of hardening-softening of the sheet metal are taken into account. The data obtained as a result of numerical experiments are consistent with the known experimental dependencies, and qualitatively correctly reflect the physical essence of the processes occurring in the mill. The development of this model made it possible to lay the foundation for further construction of a digital twin of a continuous sheet rolling mill.