ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING Vol. VI 2006 No. 1 Optimisation of a stamping process by a design of experiment linked to a modal analysis of geometric defects Y. LEDOUX, S. SAMPER, H. FAVRELIÈRE, F. FORMOSA, E. PAIREL, R. ARRIEUX Laboratory of Applied Mechanics, University of Savoy, BP 806, 74016 ANNECY Cedex, France The aim of this work was to present a method that gives an optimized set of values for the process pa- rameters in order to obtain stamped parts with the fewest defects. The springback, influenced by process parameters, is one of the sources of defects. The process is simulated by the finite element method. A de- sign of experiments is used to compute the mathematical model and to minimize the trials number. The defects are characterized by a set of modal shapes. A defect criterion is calculated from this decomposi- tion. Then an optimisation is made by minimizing of this criterion in order to obtain the best process pa- rameters. An example is shown in order to explain the method. Keywords: design of experiments, modal shapes, stamping, springback 1. Introduction In sheet metal forming, the springback is often the most serious defect observed. This problem encourages engineers to make several prototypes by using a “trial and errors” method. Several tool parameters influence the springback defect. Three differ- ent types of process parameters are identified, i.e., the tool dimensions, the process conditions (lubricant, stamping speed, etc.) and the blank initial geometry. The aim was to build a mathematical model representing the process in order to make an optimisation that will give the values of the process parameters to obtain the part required. A Design of Experiment (DOE) [1–2] is made in order to obtain the mathematical model and to minimise the number of experiments. This model links the geometrical defects of the part to the process parameters. In a previous work [3], this method has been presented and applied to the other (2D) example without taking into account form defects. A series of experiments is carried out using the finite element method. The part suffers from geometrical defects which must be characterized and then minimized. These are size defects, position defects and form defects. We propose a new method in which all these defects are intrinsically included and defined in this modal basis. The part defects are projected in this modal basis and allow the calcula- tion of each mode contribution. By using a mathematical model of the DOE, the process parameters are optimised to obtain the values of the three kinds of process parameters that minimize the geo- metrical defects of the stamped part. A 3D example is presented in order to show different steps of the method.