ORIGINAL ARTICLE Integration of artificial neural network and simulated annealing algorithm to optimize deep drawing process Mohsen Manoochehri & Farhad Kolahan Received: 5 December 2012 /Accepted: 14 March 2014 /Published online: 13 April 2014 # Springer-Verlag London 2014 Abstract Deep drawing is characterized by very complicated deformation affected by the process parameter values includ- ing die geometry, blank holder force, material properties, and frictional conditions. The aim of this study is to model and optimize the deep drawing process for stainless steel 304 (SUS304). To achieve the purpose, die radius, punch radius, blank holder force, and frictional conditions are designated as input parameters. Thinning, as one of the major failure modes in deep drawn parts, is considered as the process output parameter. Based on the results of finite element (FE) analysis, an artificial neural network (ANN) has been developed, as a predictor, to relate important process parameters to process output characteristics. The proposed feed forward back prop- agation ANN is trained and tested with pairs of input/output data obtained from FE analysis. To verify the FE model, the results obtained from the FE model were compared with those of several experimental tests. Afterward, the ANN is integrat- ed into a simulated annealing algorithm to optimize the pro- cess parameters. Optimization results indicate that by selecting the proper process parameter settings, uniform wall thickness with minimum thinning can be achieved. Keywords Deep drawing . Finite element analysis . Optimization . Artificial neural networks Nomenclature BHF Blank holder force FE Finite element σy Yield stress σUTS Ultimate stress FLDs Forming limit diagrams FLSDs Forming limit stress diagrams DOE Design of experiment ANN Artificial neural network R p Punch radius R d Die radius μ 1 Friction coefficient between punch and blank μ 2 Friction coefficient between die and blank N Number of possible design L Number of factors STH m Minimum section thickness BPN Back propagation network FEM Finite element method MSE Mean square error SA Simulated annealing algorithm P r Probability number ΔC Difference between the present and the new objective function value T k Temperature in k-th iteration 1 Introduction Sheet metal forming is a widely used manufacturing process for mass production due to its high speed and low cost. Deep drawing is one of the most common sheet metal forming processes which is widely used for mass production of cup- shaped parts in automobile, petrochemical, and packaging industries [1–4]. Cup drawing is also used as a basic test for sheet metal formability. Figure 1 shows deep drawing tools and the states of forming parts. In this figure, D o , D p , c, R p , and T are the diameter of initial blank, diameter of punch, clear- ance between punch and die, punch radius, and thickness of blank, respectively. M. Manoochehri (*) : F. Kolahan Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran e-mail: manoochehrimohsen@yahoo.com F. Kolahan e-mail: kolahan@um.ac.ir Int J Adv Manuf Technol (2014) 73:241–249 DOI 10.1007/s00170-014-5788-5