  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.
