A Reduced Order Model of the Thermal Profile of the Rolls for the Real-Time Control System

Effective real-time control systems require fast and accurate models. The thermal profile models of the rolls presented in this paper are proposed for a real-time control system for the design of the rolling schedule. The thermal profile of the roll defines the shape of the roll surface, its convexity, and, finally, the shape of the final product of the flat rolling, its convexity, and flatness. This paper presents accurate semi-analytical and finite element (FE) models, which serve to obtain an accurate solution of the joint thermal and mechanical problem, that is, heat transfer and thermal expansion. The results of the FE simulation are used for training the developed thermal model based on the neural network (NN) and for the creation of a dynamic reduced order model (ROM) of the roll surface profile. The pre-trained NN model gives accurate results and is faster than the FE model, but the model is not very useful for fast calculations in a real-time control system, mainly because the temperature distribution inside the rolls is not explicitly used in further calculations. In contrast, the ROM is fast and accurate and provides surface-shaped results that can be immediately used by other models of the real-time control system. The results of the simulation of the real process are also shown. Calculations of the roll campaign (more than 9 h) by the FEM model last several hours, while by the ROM less than 20 s.