Using an Airy Function to Predict Stresses in Wound Metal Strip Having Asymmetric Thickness Profile

This work analyzes the evolution of stresses during the rewinding of flat-rolled steels having asymmetric strip thickness profile (or wedge). When monitoring the stress distribution across the width of the sheet, control systems with strip flatness meters are unable to distinguish between “rolled-in” stresses and the stresses caused by winding. To avoid strip flatness defects, an efficient and accurate method was developed to separate the winding stress contribution from the overall stresses that are measured indirectly by a flatness control system. Commercial finite element software was first applied to determine in-plane evolution of stresses in a strip containing 2.4% wedge for various numbers of mandrel wraps during re-winding. The finite element analysis enabled a trend study that provided insight as to how the in-plane stresses in the rolled sheet evolve during the winding process. Coefficients of a 4^th order polynomial Airy Stress Function were then obtained to predict the stresses according to the mandrel wrap number and planar spatial position on the strip. With this approach, only a single function is needed to predict the entire in-plane stress field. This paper illustrates development of the Airy Stress function as characteristics of the in-plane stresses during winding of strip with asymmetric thickness profile.