Deep Drawing Process Design: A Multi Objective Optimization Approach

In sheet metal forming most of the problems are multi objective problems, generally characterized by conflicting objectives. The definition of proper parameters aimed to prevent both wrinkles and fracture is a typical example of an optimization problem in sheet metal forming characterized by conflicting goals. What is more, nowadays, a great interest would be focused on the availability of a cluster of possible optimal solutions instead of a single one, particularly in an industrial environment. Thus, the design parameters calibration, accomplishing all the objectives, is difficult and sometimes unsuccessful. In order to overcome this drawback a multi-objectives optimization procedure based on Pareto optimal solution search techniques seems a very attractive approach to deal with sheet metal forming processes design. In this paper, an integration between numerical simulations, response surface methodology and Pareto optimal solution search techniques was applied in order to design a rectangular deep drawing process. In particular, the initial blank shape and the blank holder force history were optimized as design variables in order to accomplish two different objectives: reduce excessive thinning and avoid wrinkling occurrence. The steps of the optimization procedure include: 1) application of Central Composite Design (CCD) for the identification of the necessary data over the domain of variation of the design variables; 2) numerical simulations of the samples identified by CCD; 3) development of a response surface model to interpret the final objectives as functions of the design variables; 4) Pareto optimal solution analysis to reach the most performing design variables. The final aim is to develop a predictive tool able to identify a sort of process window for the analyzed process also minimizing the computational effort in particular with respect to mono-objective optimization techniques or traditional trial and error methods. Many possible technological scenarios were investigated by the implemented procedure and a set of reliable solutions, i.e. able to satisfy different design requirements, were obtained.