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In this paper, a method to determine optimal adjustment trajectories for the loading and unloading phases of heavy plate levelers is proposed. Due to the high leveling forces, the elastic structure of the leveler is deformed. The available adjustment possibilities of the machine are typically used to actively compensate for the deflection of its work rolls. However, only a small subset of the available degrees of freedom of the leveler may be controlled under load. Therefore, the optimal adjustment is typically determined for the highest expected load and uniformly applied during the whole leveling process. As a consequence, the deflection is overcompensated during the loading and unloading phases of the plate and the head and tail ends of the plate might develop ski-ends. To avoid such an overcompensation, the adjustable degrees of freedom of the leveler can be used. Based on an accurate deflection model of the leveler, the loading and unloading phases of the plate are simulated and the input trajectories for the adjustable degrees of freedom of the leveler are optimized. The proposed approach is validated with simulations.

In this paper, a mathematical deflection model of a leveler for cold heavy plates is presented. The model calculates the work roll profile and the leveling forces for a given plate and adjustment of the leveler. The force-deflection relations of the machine model are combined with a nonlinear plate model and solved for the unknown displacements of the work rolls. The plate model is based on a leveling model found in literature. The analytical solution of this model ensures a short computation time. Therefore, the model is suitable for feedforward control and optimization. Finally, the model serves as a basis for calculating the optimal adjustment of the leveler subject to force constraints, which avoids overloading of the machine.