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| Technology - Wrinkle Free Products Using Deep Drawing Process |
Anupam Agrawal, N. V. Reddy, and P.M. Dixit
09/18/2006
DETERMINATION OF OPTIMUM PROCESS PARAMETERS FOR WRINKLE FREE PRODUCTS IN DEEP DRAWING PROCESS Figure 1. Cup geometry Figure 3. Minimum Blank holding Pressure required to suppress wrinkles
ABSTRACT
In the present work, an attempt is made to predict the minimum blank holding pressure required to avoid wrinkling in the flange region during axisymmetric deep drawing process. Thickness variation during the drawing is estimated using an upper bound analysis. The minimum blank holding pressure required to avoid wrinkling at each punch increment is obtained by equating the energy responsible for wrinkling to that which suppresses the wrinkles. The predictions of the developed model are validated with the published numerical and experimental results and are found to be in good agreement.
1 INTRODUCTION
Deep drawing process design involves, among the other things, determination of minimum blank holding pressure that is required to avoid wrinkles during the process. There have been many attempts to obtain the minimum blank holding pressure that prevents wrinkling. Senior [1956] and Yu and Johnson [1982] studied the effect of blank holder pressure on the buckling behavior of the flange. The literature survey shows that various approaches used for finding the appropriate blank holding pressure have made assumptions that the sheet thickness does not change or the material is isotropic and non-hardening. These assumptions are relaxed in the present work which addresses the problem of predicting the minimum blank holding pressure required to avoid wrinkling in the flange region during axisymmetric deep drawing process.
2 FORMULATION
2.1 Analysis for Thickness Variation
The total deformation region is divided into different zones as shown in figure 1. Analysis of each zone is carried out by proposing a kinematically admissible velocity field. Thickness and velocity distribution in each zone is found out. Using appropriate boundary condition, the expression for thickness variation at any section within the flange is obtained.
2.2 Wrinkling Analysis
For the prediction of number of wrinkles and blank holding pressure necessary to avoid wrinkling, first a suitable waveform is assumed based on geometrical and process conditions. Equating the two opposing energies values gives the critical condition for onset of wrinkling. The factor responsible for wrinkling is the energy due to compressive hoop stress. The bending energy, and the restraining energy provided by the blank holder are the factors resisting the compressive instability (occurrence of wrinkling) of the flange. The condition for onset of wrinkling can be written as,
Hoop stress energy = Bending energy + Restraining blank holder energy (1)
Boundary condition for the wrinkled flange is taken as; wave amplitude is zero at the die entrance and has a maximum value at the free end. Substitution of all energy terms in equation 1 and rearranging, one gets a function for blank holding force in terms of number of wrinkles N. Differentiating this function w.r.t. N, one can obtain the minimum blank holding pressure required to suppress these wrinkles.
3 RESULTS and DISCUSSION
To validate the predictions of the present methodology its results are compared with published theoretical and experimental results (figure 2, 3). The predictions of the present model are in very good agreement with the experimental results; this can be attributed to the fact that present analysis considers the variation in thickness as well as the effect of anisotropy and strain hardening. 
It has been observed that number of wrinkles increases and the minimum blank holding pressure required decreases with normal anisotropy. And number of wrinkles decreases and minimum blank holding pressure required increases with initial sheet thickness. The thickening of the flange increases with decrease in normal anisotropy, hence the energy required to further bend the sheet for the given number of wrinkles increases. To avoid the further bending, pressure required to suppress wrinkles increases.
4 CONCLUSIONS
A model based on energy equilibrium method is proposed to predict the minimum blank holding force required to prevent wrinkling. The predictions of the present model are in very good agreement with the experimental results.
REFERENCES
B.W. Senior, J. Mech. Phys. Solids, Vol.4 (1956), 235-246
T.X. Yu and W. Johnson, Int. J. Mech. Sci., Vol.24, No.3 (1982), 175-188
N. Kawai, Bulletins of JSME, Vol.4-13 (1961), 169-192
R. Hill, The Math. Th. Plast., Oxford University Press, London, (1964), 317–340
Contact email: anupamag@iitk.ac.in (Anupam) )
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