2. Methodology and approach
In deep drawing the process window is limited by the
occurrence of wrinkles and bottom cracks. Elimination of
lubrication increases the friction forces, and thus the deep drawing
force will be increased. As a result a bottom crack becomes more
probable. Therefore, it is necessary to decrease the acting friction
force, especially in the flange area, to ensure a large process
window. In order to decrease the amount of friction force for a
given friction coefficient, the integral of the contact pressure over
the contact area has to be reduced. To achieve that, macro
structured deep drawing tools are developed, that have only line
contact with the sheet metal, see Fig. 1(a). As a result of this
measure, the risk of wrinkling in the unsupported sheet metal areas is increased, because the usually utilised blankholder force is
not applicable. By increasing the geometrical moment of inertia of
the sheet, this effect is avoided. For the developed process, this is
achieved by immersing the blankholder slightly into the drawing
die inducing an alternating bending mechanism. This creates a
wave structure in the flange with the desired increased geometrical
moment of inertia. Contrary to draw beads, which are primary
used to control the material flow, macro structured deep drawing
tools are designed to reduce the friction force due to a minimal
contact area and to increase the resistance against wrinkling.
Consequently, by using a macro structured deep drawing tool, four
positive and stabilising effects are achieved:
reduction of the contact area up to 80%,
increasing the resistance of the sheet against wrinkling,
reduction of the blankholder force of up to 90%,
and possible material flow control by the amount of immersion.
The given risk of high tool wear is reduced due to the low
contact pressure in macro structured tools. Furthermore, Kunze
et al. showed in [4] that for industrial applications, the wear
resistance can be improved up to 90% by a combination of ta-C
coating and a laser patterning (DLIP). Additionally, this coating
results in a 15% lower friction. Fig. 1 schematically illustrates the
macro structured tools with important geometrical parameters.
The wavelength l and immersion depth d are two process
parameters which determine the geometry of bending and are
used as setting parameters in order to ensure a stable process for the deep drawing with macro structured tools. The resulting
bending radius rb and angle of bending u affect the tendency for
wrinkling as well as the risk of material crack. In order to
determine the critical values of these parameters, the resultant
forming energy will be considered.
In general, smaller immersion depth and higher wavelength
result in larger bending radii that decrease the buckling stiffness of
the sheet. Therefore, the risk of wrinkling in the flange area
increases. Oppositely, higher immersion depth and smaller
wavelength lead to higher bending radii as well as higher total
forming energy, which favours bottom cracks.
Therefore, a stable process needs an intermediate level of the
bending radius in the macro structured tool resulting from a suitable
choice of the two contradicting parameters wavelength l and
immersion depth d. For a time efficient handling of this conflicting
correlation, the following analytical model is developed.