An analytical approach for modelling asymmetrical hot rolling of heavy plates

During the hot rolling process of heavy plates, asymmetries in the roll gap due to different circumferential velocities, different work roll radii or vertical temperature gradients lead to a bending of the outgoing material. This so-called ski-effect brings along a degradation of the plate quality with respect to the flatness properties and may lead to problems in the further processing steps. Thus, it is aimed at designing a strategy to minimize the ski or even better to avoid the occurrence of the ski-effect. This work is devoted to the development of a mathematical model that can be used for online execution in process control as a basis of a ski control concept. Although most models in the literature are based on numerical methods (e.g. finite elements), we will present a semi-analytical approach utilizing the upper bound theorem for ideal rigid-plastic materials. Starting from a detailed model, simplifications are made to decrease the execution time. The results thus obtained are compared both with numerical data from finite element simulations and measurement data taken in a rolling mill by CCD-camera measurements.