On instabilities of force and grain size predictions in the simulation of multi-pass hot rolling processes

Abstract

In multi-pass rolling processes such as plate rolling, accurate predictions of roll force and torque over all roll passes are desired, so that the pre-calculated roll pass schedule can be put into practice without exceeding the limits of the roll stand. In this context, the grain size has two roles; the final grain size determines the product properties, and the evolution of grain size influences the force predictions. Since the grain size predicted after each roll pass enters the recrystallization kinetics and grain size evolution equations of the subsequent pass, a feed-back loop for the grain size calculation is created, which may become unstable so that the computed roll force and grain size become very sensitive to small variations in the input parameters. Although models for the evolution of grain size in multi-stage hot rolling have been applied in the industry for decades, their mathematical stability has not been given much attention, which poses difficulties for force and grain size predictions in cases subject to partial recrystallization. In this paper, the stability of a common semi-empirical model for static recrystallization and grain growth is investigated. The conditions under which instabilities occur are analyzed both for an industrial plate rolling pass schedule and for idealized load cycles. It is shown that complete recrystallization between roll passes leads to a stable grain size evolution, and that some states of partial recrystallization are unstable and hence problematic for force and grain size predictions. Instabilities in force and grain size predictions of an industrial pass schedules are analyzed by computing sensitivities using automatic differentiation of the model, showing that large amplification factors may occur if the states of partial recrystallization are treated by average strains and grain sizes. The instabilities are an inherent property of the closed-form equations for microstructure evolution for some states of partial recrystallization. However, the side effects of the instabilities can be reduced if the microstructure is not represented by average values of grain size and accumulated strain but by substructures generated by partial recrystallization. This way, the accuracy of roll force predictions can be considerably improved.