Abstract
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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References
Hagan E, Jeswiet J (2003) A review of conventional and modern single point sheet metal forming methods. Proc IME B J Eng Manufact 217:213–225
Jeswiet J, Micari F, Hirt G, Bramley A, Duflou JR, Allwood J (2005) Asymmetric single point incremental forming of sheet metal (SheMet). Ann CIRP–Manuf Technol 54(2):623–649
Jeswiet J (2005) Asymmetric incremental sheet forming. Proceedings of the Eleventh International Conference on Sheet Metal (SheMet), Erlangen–Nuremberg, Germany, pp 35–58
Bahloul R, Arfa H, Bel Hadj Salah H (2011) Process analysis based on experimental tests and numerical modelling of single point incremental forming of sheet metal: effect of the principal process parameters. Proceedings of the XI International Conference on Computational Plasticity (COMPLAS), Barcelona, Spain
Ben Hmida R, Thibaud S, Gilbin A, Richard F (2013) Influence of the initial grain size in single point incremental forming process for thin sheets metal and microparts: experimental investigations. J Mater Des 45:155–165
Martins PAF, Bay N, Skjoedt M, Silva MB (2008) Theory of single point incremental forming. Ann CIRP–Manuf Technol 57:247–252
Jackson K, Allwood J (2009) The mechanics of incremental sheet forming. J Mater Process Technol 209:1158–1174
Hussain G, Gao L, Hayat N, Ziran X (2009) A new formability indicator in single point incremental forming. J Mater Process Technol 209:4237–4242
Bambach M, Ames J, Azaouzi M, Campagne L, Hirt G, Batoz JL (2005) New forming strategies for single point incremental sheet forming: experimental evaluation and numerical simulation. Proceedings of the eighth International Conference on Material Forming (ESAFORM), pp 671–674
Arfa H, Bahloul R, BelHadjSalah H (2012) Finite element modelling and experimental investigation of single point incremental forming process of aluminum sheets: influence of process parameters on punch force monitoring and on mechanical and geometrical quality of parts. Int J Mater Form. doi:10.1007/s12289-012-1101-z
Duflou JR, Tunçkol Y, Szekeres A, Vanherck P (2007) Experimental study on force measurements for single point incremental forming. J Mater Process Technol 189:65–72
Ambrogio G, Filice L, Micari F (2006) A force measuring based strategy for failure prevention in incremental forming. J Mater Process Technol 177:413–416
Ham M, Jeswiet J (2007) Single point incremental forming limits using a Box-Behnken design of experiment. Key Eng Mater 344:629–636
Ham M, Jeswiet J (2007) Forming limit curves in single point incremental forming. Ann CIRP 56:277–280
Arfa H, Bahloul R, BelHadjSalah H (2009) Simulation numérique du formage incrémental. 19ème Congrès Français de Mécanique (CFM’2009), Marseille
Dejardin S, Thibaud S, Gelin JC, Michel G (2010) Experimental investigations and numerical analysis for improving knowledge of incremental sheet forming process for sheet metal parts. J Mater Process Technol 210:363–369
Thibaud S, Ben Hmida R, Richard F, Malécot P (2012) A fully parametric toolbox for the simulation of single point incremental sheet forming process: numerical feasibility and experimental validation. Simul Model Pract Theory 29:32–43
Bouffioux C, Lequesne C, Vanhove H, Duflou JR, Pouteau P, Duchêne L, Habraken AM (2011) Experimental and numerical study of an AlMgSc sheet formed by an incremental process. J Mater Process Technol 211:1684–1693
Bouffioux C, Henrard C, Eyckens P, Aerens R, Van Bael A, Sol H, Duflou JR, Habraken AM (2008) Comparison of the tests chosen for material parameter identification to predict single point incremental forming forces. Proceedings of IDDRG Conference, Olofström, Sweden, pp 133–144
Bouffioux C, Pouteau P, Duchêne L, Vanhove H, Duflou JR, Habraken AM (2010) Material data identification to model the single point incremental forming process. Int J Mater Form 3(Suppl 1):979–982. doi:10.1007/s12289-010-0933-7
Lequesne C, Henrard C, Bouffioux C, Duflou JR, Habraken AM (2008) Adaptive remeshing for incremental forming simulation. Proceedings of Numisheet Conference, Interlaken, Switzerland, pp 399–403
Henrard C, Bouffioux C, Duchene L, Duflou JR (2007) Validation of a new finite element for incremental forming simulation using a dynamic explicit approach. Key Eng Mater 344:495–502
Henrard C, Bouffioux C, Eyckens P, Sol H, Duflou JR, Van Houtte P, Van Bael A, Duchene L, Habraken AM (2011) Forming forces in single incremental forming: prediction by finite element simulations, validation and sensitivity. Comput Mech 47:573–590
Malhotra R, Huang Y, Xue L, Cao J, Belytschko T (2010) An investigation on the accuracy of numerical simulations for single point incremental forming with continuum elements. Proceedings of the tenth International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM), Pohang, Korea, 1252: 221–227
Bambach M, Cannamela M, Azaouzi M, Hirt G, Batoz JL (2006) Computer-aided tool path optimization for single point incremental sheet forming. Adv Meth Mater Form:234–250
Attanasio A, Ceretti E, Giardini C, Mazzoni L (2008) Asymmetric two points incremental forming: improving surface quality and geometric accuracy by tool path optimization. Mater Process Technol 197:59–67
Matthieu R, Hascoet JY, Hamann JC, Plenel Y (2009) Tool path programming optimization for incremental sheet forming applications. J Comput Aided Des 41:877–885
Ham M, Jeswiet J (2006) Single point incremental forming and the forming criteria for AA3003. Ann CIRP–Manuf Technol 55(1):241–244
Bahloul R (2011) Optimisation of process parameters in flanging operation in order to minimise stresses and Lemaitre’s damage. J Mater Des 32:108–120
Wang H, Li GY, Zhong ZH (2008) Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J Mater Process Technol 197:77–88
Azaouzi M, Lebaal N (2012) Tool path optimization for single point incremental sheet forming using response surface method. Simul Model Pract Theory 24:49–58
Attanasio A, Ceretti E, Giardini C (2006) Optimization of tool path in two points incremental forming. J Mater Process Technol 177:409–412
Sun G, Li G, Gong Z, Cui X, Yang X, Li Q (2010) Multiobjective robust optimization method for drawbead design in sheet metal forming. J Mater Des 31:1917–1929
Filice L, Ambrogio G, Micari F (2006) On-line control of single point incremental forming operations through punch force monitoring. Ann CIRP–Manuf Technol 55(1):245–248
Ahari H, Khajepour A, Bedi S, Melek WW (2011) A genetic algorithm for optimization of laminated dies manufacturing. J Comput Aided Des 43:730–737
Bahloul R, Ben Ayed L, Potiron A, Batoz JL (2010) Comparison between three optimization methods for the minimization of maximum bending load and springback in wiping die bending obtained by an experimental approach. Int J Adv Manuf Technol 48:1185–1203
Liu W, Liu Q, Ruana F, Liang Z, Qiu H (2007) Springback prediction for sheet metal forming based on GA-ANN technology. J Mater Process Technol 187(188):227–231
Wei L, Yuying Y (2008) Multi-objective optimization of sheet metal forming process using Pareto-based genetic algorithm. J Mater Process Technol 208:499–506
Khoei AR, Keshavarz S, Biabanaki SOR (2010) Optimal design of powder compaction processes via genetic algorithm technique. Finite Elem Anal Des 46:843–861
Ledoux Y, Sébastian P, Samper S (2010) Optimization method for stamping tools under reliability constraints using genetic algorithms and finite element simulations. J Mater Process Technol 210:474–486
Aguir H, BelHadjSalah H, Hambli R (2011) Parameter identification of an elasto-plastic behaviour using artificial neural networks-genetic algorithm method. J Mater Des 32:48–53
Yin F, Mao H, Hua L (2011) A hybrid of back propagation neural network and genetic algorithm for optimization of injection molding process parameters. J Mater Des 32:3457–3464
Fu Z, Mo J, Chen L, Chen W (2010) Using genetic algorithm-back propagation neural network prediction and finite-element model simulation to optimize the process of multiple-step incremental air-bending forming of sheet metal. J Mater Des 31:267–277
Van Bael A, Eyckens P, He S, Bouffioux C, Henrard C, Habraken AM, Duflou JR, Van Houtte P (2007) Forming limit predictions for single-point incremental sheet metal forming. Proceedings of the tenth International Conference on Material Forming (ESAFORM), Zaragoza, Spain
Bahloul R, Arfa H, BelHadjSalah H (2013) Application of response surface analysis and genetic algorithm for the optimization of single point incremental forming process. Key Eng Mater 554(557):1265–1272. doi:10.4028/www.scientific.net/KEM.554-557.1265
MATLAB User’s guide, version 7.5.0.342 (R2007 b), (The MathWorks, Inc.)
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Bahloul, R., Arfa, H. & BelHadjSalah, H. 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. Int J Adv Manuf Technol 74, 163–185 (2014). https://doi.org/10.1007/s00170-014-5975-4
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DOI: https://doi.org/10.1007/s00170-014-5975-4