Optimization of a Classical Stamping Progression by Modal Correction of Anisotropy Ears

This work is a development from the Inetforsmep European project. We proposed to realize a global optimization of a deep drawing industrial progression (made of several stages) for a cup manufacture. The objectives of the process were the thickness decrease and the geometrical parameters (especially the height). This paper improves on this previous work in the aim of mastering the contour error. From the optimal configuration, we expect to cut down the amount of the needed material and the number of forming operations. Our action is focused on the appearance of unexpected undulations (ears) located on the rim of the cups during forming due to a nonuniform crystallographic texture. Those undulations can cause a significant amount of scraps, productivity loss, and cost during manufacture. In this paper, this phenomenon causes the use of four forming operations for the cup manufacture. The aim is to cut down from four to two forming stages by defining an optimal blank (size and shape). The advantage is to reduce the cost of the tool manufacturing and to minimize the needed material (by suppressing the part flange). The chosen approach consists in defining a particular description of the ears’ part by modal decomposition and then simulating several blank shapes and sizes generated by discrete cosine transformation (DCT). The use of a numerical simulation for the forming operation and the design of an experiment technique allow mathematical links between the ears’ formation and the DCT coefficients. An optimization is then possible by using mathematical links. This original approach leads the ears’ amplitude to be reduced by a factor of 10, with only 15 numerical experiments. Moreover, we have limited the number of forming stages from 4 to 2 with a minimal material use.