Minimization of the energy in metal forming process of the cylindric shape tool through punch shape changes

Włodzimierz Sosnowski; Izabela Marczewska

Włodzimierz Sosnowski Institute of Fundamental Technological Research, Polish Academy of Sciences
Izabela Marczewska Institute of Fundamental Technological Research, Polish Academy of Sciences

Abstract

In this paper the sensitivity based optimization problem is considered. The shape of the first of two contacting bodies is optimized on the basis of sensitivities calculated for the second body i.e. workpiece. The finite element simulation of sheet metal forming process and direct differentiation method of sensitivity analysis is used. Some energy measure of deforming sheet metal is chosen as a cost functional. Its gradients with respect to the tool (punch) shape parameters are evaluated. Tool shape optimization based on 'exact' sensitivity results is performed. Calculated sensitivities with respect to the tool shape parameters are the input for the optimization algorithm. The cost functional is minimized, yielding the optimal shape of the tool. The theory is illustrated by numerical example. Shape optimization of the compressor cover produced in one of sheet stamping factories is performed.

Keywords

sheet metal forming, sensitivity, optimization, tools design,

References

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