Numerical Analysis of Edge Deformation and Force via Continuous Function Curves in Vertical Rolling Process

Vertical rolling is usually arranged before horizontal rolling in continuous hot rolling to control the width precision and improve the process quality. Due to the complicated contact and deformation rule, it is significant to establish a method to accurately calculate rolling force and edge deformation. A continuous functions model is proposed to describe the edge deformation, and the velocity and strain rate fields are derived according to the properties of stream function. The adhesion of the contact interface is successfully considered in the analysis of friction. By using Mises yield criterion and Pavlov projection principle, the total power functional is obtained. The vertical rolling force and plastic deformation are calculated by the theory of energy minimization, and the result is well verified by specific examples. The effects of equipment parameters and slab size on rolling force, rolling power and edge deformation are analyzed. The proposed mathematical model successfully applies functional analysis to the engineering field, which is helpful for controlling slab shape and optimizing vertical rolling process.