An extension of the flower pattern diagram for roll forming

The initial process design of a roll forming system is often based on the traditional ‘flower pattern diagram’. In this diagram, the cross sections of the strip at each roll stand are superimposed on a single plane; the diagram is a 2D representation of the 3D process. In the present work, the flower pattern is extended into three dimensions. To demonstrate the method, the forming path or trajectory of a point at the edge of the strip during forming a V-section is considered. The forming path is a surface curve that lies on a cylindrical surface having its axis along the machine axis. This surface is unwrapped to give its plane development and important features of the forming process can be determined and are readily interpreted from this plane curve. It is shown that at any stage in the process, the axial strain and the curvature of the sheet adjacent to the point are dependent on the slope of the trajectory in this plane projection. This new diagram, which apparently has not been used previously, provides a useful initial method of examining the roll forming process and optimising the flower pattern. The model is purely geometric, as is the original flower pattern approach, and does not include the effect of material behaviour. The concept is applied to several cases available in the literature. It shows that the lowest level of shape defect in the part is achieved when the trajectory of the strip edge follows the shortest line length between the start and finish of forming, leading to the least longitudinal strain introduced in the flange. This trend is in agreement with previous experimental observations, suggesting that the analytical model proposed may be applied for early process design and optimisation before time-consuming numerical analysis is performed.