Sensitivity based optimization of sheet metal forming tools

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 are used. Some energy measures of deforming sheet metal treated as a cost functional and its gradients with respect to the tool (punch) shape parameters is evaluated. Tool shape optimization based on “exact” sensitivity results is performed. Calculated sensitivities with respect to the tool shape parameters are the input for each iteration of the optimization algorithm (treated here as a “black box”) from which new values of the design variables are obtained until the cost functional is minimized, yielding the optimal shape for the considered functional. As an example the axisymmetrical part of the compressor cover produced in one of sheet stamping factories is considered. It was impossible to produce it without shape modifications. Energy consumption measure is minimized here but other objective functions can easily be included in the algorithm.