Effective real-time control systems require fast and accurate models. The roll bending models presented in this paper are proposed for a real-time control system for the design of the rolling schedule. The roll bending, with other factors, defines the shape of the roll surface, its convexity, and finally the shape of the final product of the flat rolling, its convexity, and its flatness. This paper presents accurate finite element (FE) models for a four-high mill. The models serve to obtain accurate solutions to the problem of roll bending, taking into account the rolling force, width of the rolling sheet (strip), initial shape of the roll surface, and the anti-bending force. The results of the FE simulation are used to train three models developed on the basis of the neural network (NN) for the solution of one direct and two inverse tasks. The pre-trained NN model gives accurate results and is faster than the FE model (FEM). The calculation time on a personal computer for one case of 3D FEM is 1 to 2 min, for 2D FEM it is 1 s, and for NN it is less than 1 ms. The results can be immediately used by other models of the real-time control system. A novelty of the research presented in the paper is the creation of complex applications of the FE method and an NN as a reduced-order model (ROM) for prediction of roll bending and calculation of sheet (strip) convexity, rolling, and anti-bending forces to obtain the required convexity.
Dmytro Svyetlichnyy (Tue,) studied this question.