Analysis of lateral metal flow-induced flatness deviations of rolled steel strip: Mathematical modeling and simulation experiments

•A mathematical model of flatness defects accounting for lateral metal flow is proposed.•A 3D finite element model for the strip and work roll with variable roll contour was developed.•Rolling experiments in a hot rolling mill confirmed the accuracy of the simulation.•Influences of reduction rate and entry thickness of strip on flatness were investigated.•Coupling effect between crown ratio, lateral metal flow, and flatness was studied. Geometric dissimilarity between the thickness profile of the entry strip and the deformed roll gap is the main cause of flatness defects. However, the combination of the crown ratio and the lateral metal flow complicates the flatness defect mode, making it difficult to predict. A variety of rolled flatness defects may result, generally occurring as center waviness, edge waviness, M-mode waviness, and W-mode waviness. The effect of lateral metal flow on the flatness has rarely been considered or quantified in the traditional flatness model. To address this deficiency, an original mathematical model is proposed for computing the rolled flatness defects while accounting for lateral metal flow during the rolling process. The proposed analytical model was employed to compute the flatness deviations with and without lateral metal flow, and the flatness calculated results were compared with the numerical solutions provided by a three-dimensional finite element model. The influence of the lateral metal flow on the strip flatness distribution was clearly identified and explained. Finally, the effects of the reduction rate, entry thickness, and exit crown ratio on the flatness deviation and lateral metal flow are described and discussed.