Abstract
The use of metamodelling techniques in process design has become indispensable to perform faster solutions reducing time to market. This approach allows the implementation of decision support tools which are easier to use than the conventional numerical simulations. In this paper, a robust metamodelling technique has been designed and its feasibility has been validated for the crucial problem of localised thinning in sheet metal forming process. The proposed methodology is based on the innovative integration between the Design of Experimental statistical method and the Kriging one. This approach, in fact, allows to analyse contemporary the continuous and categorical factors and, as a consequence, to define a single tool for changing process conditions (i.e., material and product shape). To test the reliability of the mathematical approach, the same was performed for the case study of Incremental Sheet Forming, a process strongly affected by the not homogeneous distribution of the thickness. Taking advantage of this strategy, a wide experimental investigation has been performed to build the base of knowledge of the problem both for the metamodelling design and for the validation of the decision support tool; moreover, the experimental data were utilized to set and validate a numerical model, which was subsequently used to enrich the dataset. The proposed metamodel, suitably modified according to each process peculiarities, can be generally adapted for sheet thickness prediction.
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References
Altmeyer G, Abed-Meraim F, Balan T (2009) Formability prediction of thin metal sheets using various localization criteria. Int J Mater Form 2:423–426
Decultot N, Velay V, Robert L, Bernhart G, Massoni E (2000) Behaviour modelling of aluminium alloy sheet for single point incremental forming. Int J Mater Form 1:1151–1154
Di Lorenzo R, Fratini L, Micari F (1999) Optimal blankholder force path in sheet metal forming processes: an AI based procedure. CIRP Ann 48(1):231–234
Gan W, Wagoner RH (2004) Die design method for sheet springback. Int J Mech Sci. doi:10.1016/j.ijmecsci.2004.06.006
Mole N, Cafuta G, Štok B (2014) A 3D forming tool optimisation method considering springback and thinning compensation. J Mater Process Technol. doi:10.1016/j.jmatprotec.2014.03.017
Zein H, El Sherbiny M, Abd-Rabou M, El shazly M (2014) Thinning and spring back prediction of sheet metal in the deep drawing process. Mater Des 53:797–808. doi:10.1016/j.matdes.2013.07.078
Marretta L, Ingarao G, Di Lorenzo R (2010) Design of sheet stamping operations to control springback and thinning: a multi-objective stochastic optimization approach. Int J Mech Sci. doi:10.1016/j.ijmecsci.2010.03.008
Di Lorenzo R, Ingarao G, Chinesta F (2010) Integration of gradient based and response surface methods to develop a cascade optimisation strategy for Y-shaped tube hydroforming process design. Adv Eng Softw. doi:10.1016/j.advengsoft.2009.06.010
Hu W, Enying L, Li GY, Zhong ZH (2008) Optimization of sheet metal forming processes by the use of space mapping based metamodeling method. Int J Adv Manuf Technol 39(7–8):642–655
Hu W, Yao LG, Hua ZZ (2008) Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J Mater Process Technol 197(1):77–88
Wang H, Li E, Li GY (2009) The least square support vector regression coupled with parallel sampling scheme metamodeling technique and application in sheet forming optimization. Mater Des 30(5):1468–1479
Naceur H, Guo YQ, Batoz JL, Knopf-Lenoir C (2001) Optimization of drawbead restraining forces and drawbead design in sheet metal forming process. Int J Mech Sci 43(10):2407–2434
Guo YQ, Batoz JL, Naceur H, Bouabdallah S, Mercier F, Barlet O (2000) Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach. Comput Struct 78(1):133–148
Filice L, Ambrogio G (2013) Optimised tool-path design to reduce thinning in incremental sheet forming process. Int J Mater Form 6:173–178
Arfa H, Bahloul R, BelHadjSalah H (2013) 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 6:483–510
Manco G, Filice L, Ambrogio G (2011) Analysis of the thickness distribution varying tool trajectory in single-point incremental forming. Proc Inst Mech Eng B 225(3):348–356
Chen X, Kai W, Feng Y (2013) Stochastic kriging with qualitative factors. Proc Winter Simul Conf: Simulation: Making Decisions in a Complex World. IEEE Press, 2013 p 790–801
Ankenman B, Nelson B, Staum J (2010) Stochastic Kriging for simulation metamodeling. Oper Res. doi:10.1287/opre.1090.0754
Hamdaoui M, Oujebbour FZ, Habbal A, Breitkopf P, Villon P (2014) Kriging surrogates for evolutionary multi-objective optimization of CPU intensive sheet metal forming applications. Int J Mater Form. doi:10.1007/s12289-014-1190-y
Qian P, Wu HZ, Wu CJ (2008) Gaussian process models for computer experiments with qualitative and quantitative factors. Technometrics. doi:10.1198/004017008000000262
Jaeckel P, Rebonato R (1999) The most general methodology for creating a valid correlation matrix for risk management and option pricing purposes. J Risk 2(2):17–28
Haktanir T (2008) Three-step N–R algorithm for the maximum-likelihood estimation of the general extreme values distribution parameters. Adv Eng Softw. doi:10.1016/j.advengsoft.2007.03.008
Kitazawa K, Nakajima A (1999) Cylindrical incremental drawing of sheet metals by CNC incremental forming process. Proc. 6th ICTP Conf. Nürnberg 1495–1500
Jeswiet J, Micari F, Hirt G, Bramley A, Duflou J, Allwood J (2005) Asymmetric single point incremental forming of sheet metal. CIRP Ann. doi:10.1016/S0007-8506(07)60021-3
Ambrogio G, De Napoli L, Filice L, Muzzupappa M (2007) Experimental evidences concerning geometrical accuracy after unclamping and trimming incrementally formed components. Key Eng Mater. doi:10.4028/www.scientific.net/KEM.344.535
Antognini AB, Zagoraiou M (2010) Exact optimal designs for computer experiments via Kriging metamodeling. J Stat Plan Infer. doi:10.1016/j.jspi.2010.03.027
Zhao Z, Zhang Y (2011) Design of ensemble neural network using entropy theory. Adv Eng Softw. doi:10.1016/j.advengsoft.2011.05.027
Couckuyt I, Forrester A, Gorissen D, De Turck F, Dhaene T (2012) Blind Kriging: implementation and performance analysis. Adv Eng Softw. doi:10.1016/j.advengsoft.2012.03.002
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Ambrogio, G., Ciancio, C., Filice, L. et al. Innovative metamodelling-based process design for manufacturing: an application to Incremental Sheet Forming. Int J Mater Form 10, 279–286 (2017). https://doi.org/10.1007/s12289-015-1276-1
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DOI: https://doi.org/10.1007/s12289-015-1276-1