A coupling model of vertical rolling process based on upper bound method and elastic theory

A mathematical model of vertical rolling process with the consideration of mechanism displacement is proposed. Using Γ function and parabola function to describe edge deformation, the corresponding 3D velocity field, strain rate field and total power functional are derived. Simultaneously, an analysis method of mechanism deformation is proposed. The deflection of vertical roller and the radial displacement of support bearings are calculated by applying superposition principle and Palmgren’s modified formula respectively. The coupling calculation of slab deformation and mechanism displacement is realized through minimizing the total functional and repeated iteration. The accuracy of the presented model is verified by comparison with other models and factory measurements. Subsequently, the influences of main rolling parameters on edge deformation, rolling force and mechanism displacement are analyzed. The proposed model could provide some references for the optimization of vertical rolling process and the improvement of slab quality and yield ratio.