Computer-aided engineering for sheet metal forming: definition of a springback quality function

Computer-aided engineering methods are extensively applied to sheet metal forming integrated design. The adoption of a new class of materials, the advanced high strength steels, has increased the occurrence of springback, and consequently the request for tools oriented to springback reduction and optimization. This paper presents an approximated formulation to compute the springback field after stamping through the finite element analysis of the process. This can be found assuming that the residual field of nodal forces after stamping produces a springback shape referable to a linear combination of n modes of vibration of the nominal shape of the component. The aim of this formulation is not that of substituting the finite element analysis of the springback but rather to make use of the coefficients of the linear combination, so to define a global quality function for springback. In this way, Robust Design methods or other current optimization procedures to improve the stamping process as for structural defects (such wrinkling, necking and flatness) can be applied also for the reduction of springback. The meaning of these coefficients will be shown through three test cases and the consistency of the formulation will be discussed according to the number of modes of vibration included in the computation.