Multi-roll levelling method for longitudinal waves in metal sheet based on a coupled curvature integration model

Longitudinal waves are the main flatness defects of metal sheets. This defect is typically eliminated by repeated elastoplastic bending via a multi-roll leveller to make the residual curvature of the sheet as small as possible. Therefore, an effective mathematical model is important for the leveller design and levelling parameter adjustment. In this paper, based on the basic principle of multi-roll levelling for the longitudinal wave of a metal sheet, a geometric model of multi-roll levelling was established via the curvature integration method; a bending-moment curvature model was also established to account for the residual curvature of reverse bending and the difference between the elastic section and the elastoplastic section. A coupled curvature integration model was constructed by combining the two models to systematically describe the multi-roll levelling process, and the variation of the curvature, surface profile curve and plastic deformation rate of the sheet during levelling were discussed; the influence of the intermesh of the work rolls on the levelling effect of the longitudinal wave was analysed. The results show that there are infinite intermesh combinations of the first work roll and the last work roll that make the residual curvature of the sheet close to zero after levelling. The results also show that the residual curvature is much more sensitive to the variation of the first work roll than to the variation of the last work roll.