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 blank holder 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, Kunzeet 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.