A Physical Based Method to Predict Spread and Shape during Flat Rolling for Real‐Time Application

Abstract

A physical based method is developed that gives real‐time solutions for the transverse variations, across the strip width, for the strip stresses and strains during rolling. From this the strip spread and downstream shape defect are predicted for a given variation in the thickness reduction across the width. The method implicitly couples the downstream residual stresses of the strip under tension, due to non‐uniform strip elongations or shape, to the stress field within the roll gap. The case of a parabolic variation in thickness reduction across the strip width is investigated with the sensitivity of shape defect with the non‐uniform reduction predicted, for various strip thicknesses and widths. These results are shown to be consistent with previously published experimental results. The model is therefore useful in predicting the limits of thickness profile change during rolling before shape defects are formed. Furthermore, being an analytical method the prediction of spread and shape defects can be made in real‐time with a minimum of computational cost. The spread model is then coupled to a roll stack deflection model so that the non‐uniform thickness reduction is also calculated for a set of rolling conditions. The full model solution is calculated within several seconds on a PC, making it possible for real‐time application.