New method for modeling plastic deformation in incremental sheet forming

This paper proposes a new fast method for determining plastic deformation of sheet metal. The method is applied to a flexible metal shaping process, incremental sheet forming (ISF), which is applicable to low volume manufacturing and rapid prototyping. Being able to predict the deformation of the sheet is a key requirement of a model predictive based control system to regulate the geometric accuracy of parts formed by the process. Existing models for ISF, which are predominantly based on finite element modeling, are slow since the model must be updated at every time step of the process. Other modeling approaches have combined plane-strain or shear deformation equations with approximate empirical relationships, but their accuracy is limited by the conditions under which these experimental relationships were obtained. Here, a fast executing model for the incremental forming process is proposed that is based on the numerical minimization of the plastic energy within the plate. The optimization can be formulated as a second order cone program (SOCP), which can be solved using efficient numerical methods.