Deep drawing is one of the most common sheet metal forming processes. It is largely used for mass production of parts in various shapes in automobile, packaging, and household appliance industries. During this process, the stamped part is susceptible to the process failures, especially springback if the process parameters are not correctly selected. The objective of this article is to propose a complete and an efficient optimization approach, starting from modeling and ending with identification of optimal process parameters. Our approach is based on the combination of finite element simulation, design of experiments (DOE), artificial neural network (ANN), and particle swarm optimization (PSO). Based on the comparison of simulation results with experimental results, a finite element model (FEM), which can replace the real deep drawing and predict the springback accurately, has been developed. In this article, process parameters are optimized according to their degree of importance. For this reason, the analysis of variance (ANOVA) method was used to assess the degree of importance of each of the process parameters on springback. An artificial neural network (ANN) model was developed, as a predictor, to relate critical process parameters to springback. Particle swarm optimization (PSO) is then implemented to identify the optimal values of the process parameters. The results indicate an important minimization of springback could be achieved with the use of FEM-ANN-PSO strategy. This approach can, therefore, be used for the optimization of process failures of highly non-linear mechanical systems.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Ablat MA, Qattawi A (2017) Numerical simulation of sheet metal forming: a review. Int J Adv Manuf Technol 89(1):1235–1250
Ambrogio G, Ciancio C, Filice L, Gagliardi F (2017) Innovative metamodelling-based process design for manufacturing: an application to incremental sheet forming. Int J Mater Form 10(3):279–286
Atul S, Takalkar, Babu MCL (2019) A review on effect of thinning, wrinkling and spring-back on deep drawing process. Proc Inst Mech Eng B J Eng Manuf 233(4):1011–1036
Bonte MHA, van den Boogaard AH, Huétink J (2008) An optimisation strategy for industrial metal forming processes. Struct Multidiscip Optim 35(6):571–586
Chatti S, Hermi N (2011) The effect of non-linear recovery on springback prediction. Comput Struct 89(13):1367–1377
Colgan M, Monaghan J (2003) Deep drawing process: analysis and experiment. J Mater Process Technol 132(1):35–41
Dilmec M, Arap M (2016) Effect of geometrical and process parameters on coefficient of friction in deep drawing process at the flange and the radius regions. Int J Adv Manuf Technol 86(1):747–759
Gašper Gantar, and Karl Kuzman. 2002 Sensitivity and stability evaluation of the deep drawing process. Journal of materials processing technology, 9 September 2002, 125–126 edition
Haftka RT, Villanueva D, Chaudhuri A (2016) Parallel surrogate-assisted global optimization with expensive functions – a survey. Struct Multidiscip Optim 54(1):3–13
Jamli MR, Ariffin AK, Wahab DA (2015) Incorporating feedforward neural network within finite element analysis for L-bending springback prediction. Expert Syst Appl 42(5):2604–2614
Kahhal P, Brooghani SYA, Azodi HD (2013) Multi-objective optimization of sheet metal forming die using genetic algorithm coupled with RSM and FEA. J Fail Anal Prev 13(6):771–778
Kardan M, Parvizi A, Askari A (2018) Influence of process parameters on residual stresses in deep-drawing process with FEM and experimental evaluations. J Braz Soc Mech Sci Eng 40(3):157
Kennedy J, Eberhart R (1995) Particle swarm optimization. Proceed ICNN’95 - Int Conf Neural Networks 4:1942–1948
Kenneth Alan De Jong. 1975. An analysis of the behavior of a class of genetic adaptive systems. Doctoral Dissertation, University of Michigan
Manoochehri M, Kolahan F (2014) Integration of artificial neural network and simulated annealing algorithm to optimize deep drawing process. Int J Adv Manuf Technol 73(1):241–249
Meinders T, Burchitz IA, Bonte MHA, Lingbeek RA (2008) Numerical product design: Springback prediction, compensation and optimization. Int J Mach Tools Manuf, Adv Sheet Metal Forming Appl 48(5):499–514
Miranda SS, Barbosa MR, Santos AD, Pacheco JB, Amaral RL (2018) Forming and Springback prediction in press brake air bending combining finite element analysis and neural networks. J Strain Anal Eng Design 53(8):584–601
Naceur H, Guo YQ, Ben-Elechi S (2006) Response surface methodology for design of sheet forming parameters to control springback effects. Comput Struct 84(26):1651–1663
Narayanasamy R, Padmanabhan P (2012) Comparison of regression and artificial neural network model for the prediction of Springback during air bending process of interstitial free steel sheet. J Intell Manuf 23(3):357–364
NUMISHEET’93 (1993) Proceedings of the second international conference of numerical simulation of 3-D sheet metal forming processes, Isehara
Oujebbour F-Z, Habbal A, Ellaia R (2015) Optimization of stamping process parameters to predict and reduce springback and failure criterion. Struct Multidiscip Optim 51(2):495–514
Padmanabhan R, Oliveira MC, Alves JL, Menezes LF (2007) Influence of process parameters on the deep drawing of stainless steel. Finite Elem Anal Des
Papeleux L, Ponthot J-P (2002) Finite element simulation of Springback in sheet metal forming. J Mater Process Technol 125–126:785–791
Park H-S, Anh T-V (2013) Development of two-phase neural network-genetic algorithm hybrid model in modeling damage evolution in roll forming of aluminum sheet. Int J Mater Form 6(4):423–436
Park J-W, Kang B-S (2019) Comparison between regression and artificial neural network for prediction model of flexibly reconfigurable roll forming process. Int J Adv Manuf Technol 101(9):3081–3091
Raju S, Ganesan G, Karthikeyan R (2010) Influence of variables in deep drawing of AA 6061 sheet. Trans Nonferrous Metals Soc China 20(10):1856–1862
Reddy ACS, Rajesham S, Reddy PR, Kumar TP, Goverdhan J (2015) An experimental study on effect of process parameters in deep drawing using Taguchi technique. Int J Eng Sci Technol 7(1):21–32
Rodney H, Egon O (1948) A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London. Series A Math Phys Sci 193(1033):281–297
Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61(January):85–117
Sener B, Kurtaran H (2016) Optimization of process parameters for rectangular cup deep drawing by the Taguchi method and genetic algorithm. Mater Testing 58(3):238–245
Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1(1):1–18
Taguchi G, Konish S (1987) 1987 Taguchi method. Orthogonal Arrays and Linear Graphs, Tools for Quality Engineering. American Supplier Institute
Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–380
Wang H, Ye F, Chen L, Li E (2017) Sheet metal forming optimization by using surrogate modeling techniques. Chin J Mech Eng 30(1):22–36
Wenfeng Zhang, and Rajiv Shivpuri. 2009 Probabilistic design of aluminum sheet drawing for reduced risk of wrinkling and fracture. reliability engineering & system safety, 94 edition
Wiebenga JH, van den Boogaard AH, Klaseboer G (2012) Sequential robust optimization of a V-bending process using numerical simulations. Struct Multidiscip Optim 46(1):137–153
Xie Y, Tang W, Zhang F, Pan BB, Yue Y, Feng M (2019) Optimization of variable blank holder force based on a sharing niching RBF neural network and an improved NSGA-II algorithm. Int J Precis Eng Manuf 20(2):285–299
Conflict of interest
The authors declare that they have no conflict of interest.
Replication of results
The authors state that they have the willing to share the computer codes as well as numerical data used to draw figures and FE input, although all necessary details are included in the paper and solution files can be obtained by contacting the corresponding author.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Responsible Editor: Axel Schumacher
About this article
Cite this article
El Mrabti, I., Touache, A., El Hakimi, A. et al. Springback optimization of deep drawing process based on FEM-ANN-PSO strategy. Struct Multidisc Optim (2021). https://doi.org/10.1007/s00158-021-02861-y
- Deep drawing
- Numerical simulation
- Design of experiments
- Artificial neural network (ANN)