Optimization of Forging Preforms by Using Pseudo Inverse Approach
In the cold forging process, an initial billet is plastically deformed under a powerful tool pressure. This process changes not only the shape but also the metal’s properties such as the strength, ductility and toughness. Forged parts are often used for high performance and reliability applications. A new simplified approach called Pseudo Inverse Approach (PIA) has been proposed for the axisymmetric cold forging modeling. This approach exploits at maximum the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without classical contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, which leads to a very fast and robust plastic integration procedure. Numerical tests have shown that the Pseudo Inverse Approach is very fast compared to the incremental approach. In this paper, the PIA will be used in an optimization loop for the preliminary preform design in multi-stage forging processes.
The optimization problem is to minimize the effective strain variation in the final part and the maximum forging force during the forging process. The optimization was performed in modeFrontier by using the NSGA-II algorithm, as it appears to be one of the most efficient algorithms for identifying the optimal Pareto set with a great variety of solutions. Since the multi-objective optimization process requires a large number of forging simulations and cab be very time-consuming, a Kriging method response surface has been trained by using much less simulation results. The selection of DOE points has had an important influence on the accuracy and the cost of the meta-model. The numerical results of the optimization method using the PIA are compared to those using the classical incremental approaches to show the efficiency and limitations of the PIA. The distributions of the equivalent plastic strain and equivalent stress of the optimal solution obtained by the PIA have been validated in ABAQUS®/Explicit and were very close to those obtained by the latter.