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.

中文翻译：

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基于刚性辊的金属板材连续滚压成形形状预测


基于刚性辊的连续辊轧成型（CRFRR）是一种快速制造金属板材双曲面的创新工艺。通过调节两刚性辊的母线半径或控制压下量，可以获得不同形状和尺寸的弯曲零件。本文介绍了CRFRR的原理，并根据出口速度分布分析了利用两个刚性辊形成具有正高斯曲率或负高斯曲率的金属板材3D表面的过程。板材通过辊缝后材料的出口速度分解为两部分：线性分布的速度和很小的附加速度。基于出口速度分解和浅壳理论，首次提出了一种预测CRFRR过程成形表面形状的解析方法。所形成的3D表面在纵向上的曲率的主要部分由出口速度的线性部分确定，而在横向上的曲率的主要部分由两个刚性辊的母线半径确定。 3D 表面最终形状的曲率变化是由出口速度的附加部分引起的，并通过浅壳的平衡方程求解。通过主曲率和曲率变化的叠加得到成形曲面的最终曲率。对凸形和马鞍形零件进行了数值模拟和成形实验，结果验证了该方法的有效性和准确性。