Trans. Nonferrous Met. Soc. China 22(2012) s207−s213 Optimization of cold forging perform tools using Pseudo Inverse Approach Ali HALOUANI, Yu-ming LI, ABBES Boussad, Ying-qiao GUO GRESPI/MPSE, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2, France Received 28 August 2012; accepted 25 October 2012 Abstract: A new fast method called “Pseudo Inverse Approach” (PIA) for the multi-stage axi-symmetrical cold forging modelling is presented. The approach is based on 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 contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, leading to a very efficient and robust plastic integration procedure. Numerical tests show that the Pseudo Inverse Approach is very fast compared with the incremental approach. The PIA is used in an optimization procedure for the preliminary preform tool design in multi-stage cold forging processes. This optimization problem aims to minimize the equivalent plastic strain and the punch force during the forging process. The preform tool shapes are represented by B-Spline curves. The vertical positions of the control points of B-Spline are taken as design variables. The evolution of the objective functions shows the importance of the tool preform shape optimization for the forging quality and energy saving. The forging results obtained by using the PIA are compared with those obtained by the classical incremental approaches to show the efficiency and accuracy of the PIA. Key words: cold forging process; Pseudo Inverse Approach; preform design; B-Spline; shape optimization; Pareto front 1 Introduction Forged parts are often used for high performance and reliability applications. In a cold forging process, the initial billet is plastically deformed under a powerful tool pressure. Two or more forging stages may be required to make a complicated forging product. The achievement of high-quality products by forging process largely depends on the preform tool design. In industry, the preform design for a forging process involves expensive trials-corrections on forging tools. The actual tendency is to use the numerical simulation and optimization in order to obtain the process information and optimal forging parameters. The classical incremental methods are widely used for the forging simulation and optimization [1−5]. Very advanced works have been done by FOURMENT et al [6,7] from CEMEF in France. The corresponding software FORGE® is largely used in the forging industry. The incremental methods give good results, but they are very time consuming. The considerable calculation cost makes their application difficult to industrial optimization problems. In this context, it will be very useful to develop a fast and robust forging solver for the preform design and optimization. A new simplified approach called Pseudo Inverse Approach (PIA) has been proposed for the axi-symmetric cold forging modelling [8,9]. This approach exploits at maximum the knowledge of the final part shape. Some intermediate configurations are introduced to take into account the deformation history. A free surface method is developed to make these configurations not only kinematically but also mechanically admissible. A new algorithm of plastic integration called Direct Scalar Algorithm (DSA) [10,11] has been proposed in the PIA, which is very efficient and robust compared to the classical Return Mapping Algorithm (RMA), especially for very large strain increments. The main objective of this work is to simulate and optimize a two-stage metal forging process using an optimization procedure combined with the PIA in order to obtain an optimal preform tool shape. The optimization target is to minimize the equivalent plastic strain variation in the final part and the punch force during the forming process. In the optimization loop, the design variables are modified to improve the objective functions, leading to an optimum tool shape. A surrogate Corresponding author: LI Yu-ming; Tel/Fax: +33-326918701; E-mail: yuming.li@univ-reims.fr DOI: 10.1016/S1003-6326(12)61710-5