A study on optimal design of process parameters in single point incremental forming of sheet metal by combining Box–Behnken design of experiments, response surface methods and genetic algorithms

Incremental forming is a sheet metal forming process characterized by high flexibility; for this reason, it is suggested for rapid prototyping and customized products. On the other hand, this process is slower than traditional ones and requires in-depth studies to know the influence and the optimization of certain process parameters. In this paper, a complete optimization procedure starting from modeling and leading to the search of robust optimal process parameters is proposed. A numerical model of single point incremental forming of aluminum truncated cone geometries is developed by means of Finite Element simulation code ABAQUS and validated experimentally. One of the problems to be solved in the metal forming processes of thin sheets is the taking into account of the effects of technological process parameters so that the part takes the desired mechanical and geometrical characteristics. The control parameters for the study included wall inclination angle (α), tool size (D), material thickness (Thini), and vertical step size (In). A total of 27 numerical tests were conducted based on a 4-factor, 3-level Box–Behnken Design of Experiments approach along with FEA. An analysis of variance (ANOVA) test was carried out to obtain the relative importance of each single factor in terms of their main effects on the response variable. The main and interaction effects of the process parameters on sheet thinning rate and the punch forces were studied in more detail and presented in graphical form that helps in selecting quickly the process parameters to achieve the desired results. The main objective of this work is to examine and minimize the sheet thinning rate and the punch loads generated in this forming process. A first optimization procedure is based on the use of graphical response surfaces methodology (RSM). Quadratic mathematical models of the process were formulated correlating for the important controllable process parameters with the considered responses. The adequacies of the models were checked using analysis of variance technique. These analytical formulations allow the identification of the influential parameters of an optimization problem and the reduction of the number of evaluations of the objective functions. Taking the models as objective functions further optimization has been carried out using a genetic algorithm (GA) developed in order to compute the optimum solutions defined by the minimum values of sheet thinning and the punch loads and their corresponding combinations of optimum process parameters. For validation of its accuracy and generalization, the genetic algorithm was tested by using two analytical test functions as benchmarks of which global and local minima are known. It was demonstrated that the developed method can solve high nonlinear problems successfully. Finally, it is observed that the numerical results showed the suitability of the proposed approaches, and some comparative studies of the optimum solutions obtained by these algorithms developed in this work are shown here.

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