Optimal blank shape prediction considering sheet thickness variation for multistage deep drawing

Deep drawing is one of the very old and widely practiced processes in the sheet metal industries for producing beverage cans and automobile components. Many of the deep drawn components need multiple draws to achieve the required dimensions, because often it is not possible to obtain the desired reduction in the first draw. Among several defects that occur during the process, earing is one of the prominent and common defect. In the present work, analysis has been carried out by dividing the total deformation region into several zones. Analysis of each zone is carried out by proposing kinematically admissible velocity field, i.e. the velocity field satisfying the condition of normal velocity continuity and volume constancy. The input material (already drawn cup) for redrawing is pre-strained from the previous stage drawing operation and this has been considered while carrying out the analysis. Thickness and punch load predictions are validated by comparing them with the published results and are found to be in good agreement. The optimal blank shape, that will result in earing free cup after the final drawing operation, has been determined. For the prediction of optimal blank shape for multistage deep drawing, addition-subtraction scheme has been developed and successfully implemented; the modification of the initial blank is done after each stage of drawing. The optimal blank shape obtained has been tested, using simulation, to draw the cup and it yields the final cup height with percentage earing less than 1%. However, in a few cases, three or four iterations for the modification of blank may be required, to bring the percentage earing within the specified limit