A Coupling Model of Vertical Rolling Process Based on Upper Bound Method and Elastic Theory

Abstract

Abstract Vertical rolling is an important plastic forming process of metal. The establishment of accurate mechanical model is essential for parameter presetting and online control of the process. A prediction model of vertical rolling force with consideration of mechanism displacement is proposed. Using Γ function and parabolic function to describe edge deformation, the corresponding 3D velocity field, strain rate field and total power functional are derived. On this basis, an energy model for calculating rolling force and edge deformation is established. Simultaneously, an analysis method of mechanism displacement 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 repeated iteration. The study of bearing structure is carried out, of which the results show that the fluctuation of rolling force caused by bearing azimuth can be ignored. The accuracy of the presented model is verified by comparison with other models and factory measurements. Subsequently, the influences of main rolling parameters on rolling process are analyzed and a series of results are obtained. The influence of width reduction rate and slab thickness on edge deformation and rolling force is greater than that of vertical roller radius and slab width. The compensation value of rolling force has a similar change trend to the compensation value of displacement. In the rolling position, the axis displacement is much greater than deflection. The proportion of axis displacement in total radial displacement rises at first and then falls with the increase of width reduction rate and slab thickness. The proposed model could provide some references for the optimization of vertical rolling process and the improvement of slab quality and yield ratio.