Shape prediction in continuous roll forming of sheet metal based on rigid rolls

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The continuous roll forming based on rigid rolls (CRFRR) is an innovative process for rapid fabrication of doubly curved surfaces of sheet metal. The curved parts with different shapes and sizes can be obtained by adjusting the generatrix radius of the two rigid rolls or controlling the rolling reduction. In this paper, the principle of CRFRR is introduced and the process that a 3D surface of sheet metal with positive or negative Gaussian curvature is formed using two rigid rolls is analyzed based on the distribution of exit velocity. The exit velocity of material after the sheet metal passes through the roll gap is decomposed into two portions: a linearly distributed velocity and a very small additional velocity. On the basis of exit velocity decomposition and shallow shell theory, an analytical method for predicting the shape of formed surface in CRFRR process is proposed for the first time. The primary part of curvature of the formed 3D surface in longitudinal direction is determined by the linear portion of exit velocity and that in transverse direction is determined by the generatrix radius of the two rigid rolls. The curvature change in the final shape of 3D surface is induced by the additional portion of exit velocity and it is solved from equilibrium equation of shallow shell. The final curvature of the formed surface is acquired through superimposing the primary curvature and the curvature change. Numerical simulations and forming experiments have been carried out on convex and saddle-shaped parts, and the results confirm the validity and accuracy of presented method.