New Iteration based Algorithm for Shape Optimization of Internal and External Boundaries of the Initial Blank in the Deep Drawing Process

Journal of Advanced Materials and Processing

دوره 8، شماره 3، آذر 2020، صفحه 35-52   

نوع مقاله: Research Paper

نویسندگان

Hamidreza Gharehchahi؛ Mohammad Javad Kazemzadeh-Parsi^* ؛ Ahmad Afsari؛ Mehrdad Mohammadi

Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

چکیده

In the deep drawing process, the optimal design of the initial blank shape has many advantages such as reducing the cost of production and waste and improving the quality of the process and thickness distribution.  The deep drawing process is highly nonlinear due to the large deformation, plastic deformation of the material and the contact phenomenon.  Therefore, the general solution to such problems is to use iterative methods based on numerical simulation.  The present study implements a similar approach and presents a new algorithm to make geometrical corrections to the external boundaries of a blank, as well as its internal boundaries, in several iterations.  A computer program was developed to automatically run these iterations to study the features of the proposed algorithm.  Next, an example problem was solved, and the results are compared with other studies.  The results showed that the proposed algorithm is sufficiently robust against the initial guesses for the blank, which is an advantage of the present algorithm over those from other algorithms.  Because in other algorithms presented in the articles, if the appropriate initial guess is not selected, the algorithm will not converge to the answer.  The proposed algorithm also has a higher convergence speed in achieving optimal blank.

کلیدواژه‌ها

Deep drawing؛ Shape optimization؛ Blank optimization؛ Finite element method

مراجع

[1] V.V. Hazek, K. Lange, “Use of the slip-line method in deep drawing of large irregular shaped components”, in: Proceedings of the 7th North American Metalwork Research Conference, SME, 1979, pp. 65–71.

[2] K. Lange, H. Gloeckl, “Computer aided design of blanks for deep drawn irregular shaped components”, in: Proceedings of the 11th North American Manufacturing Research Conference, SME, 1983, pp. 243–251.

[3] R. Sowerby, N. Chandrasekharan, X. Chen, M. Rooks, P. Correa, “the development of computer aids for sheet metal stampings”, in: S.K. Ghosh, A. Niku-Lari (Eds.), CAD/CAM and FEM in Metal working, 3rd International Conference on SAS, Pergamon Press, 1988, p.187.

[4] M. Karima, “Blank development and tooling design for drawn parts using a modified slip line field based approach”, J. Eng. Ind. Trans. ASME 111, 1989, pp 345–350. https://doi.org/10.1115/1.3188770.

[5] J.H. Vogel, D. Lee, “An analytical method for deep drawing process design”, Int. J. Mech. Sci. 32 (11), 1990, pp 891-907. https://doi.org/10.1016/0020-7403(90)90062-N.

[6] X. Chen, R. Sowerby, “The development of ideal blank shapes by the method of plane stress characteristics”, Int. J. Mech. Sci. 2, 1992, pp.159-166. https://doi.org/10.1016/0020-7403(92)90080-Z.

[7] X. Chen, R. Sowerby, “Blank development and the prediction of earing in cup drawing”, Int. J. Mech. Sci.  38, 1996, pp. 509–516. https://doi.org/10.1016/0020-7403(95)00068-2.

[8] T. Kuwabara, W.H. Si, “PC-based blank design system for deep drawing irregularly shaped prismatic shells with arbitrarily shape flange”, J. Mater. Process Technol. 63, 1997, pp. 89–94. https://doi.org/10.1016/S0924-0136(96)02605-2.

[9] M.H. Parsa, P.H. Matin, M.M. Mashhadi, “Improvement of initial blank shape for intricate products using slip line field”, J. Mater. Process. Technol. 145, 2004, pp. 21–26. https://doi.org/10.1016/S0924-0136(03)00858-6.

[10] N. Kim, S. Kobayashi, “Blank design in rectangular cup drawing by an approximate method”, Int. J. Mach. Tool. Des. Res. 26, 1986, pp. 125–135. https://doi.org/10.1016/0020-7357(86)90213-1.

[11] Sowerby, R., Duncan, J. L. and Chu, E., “The modeling of sheet metal stampings”, Int. J. Mech. Sci., 28, 1986, pp. 415-430. https://doi.org/10.1016/0020-7403(86)90062-7.

[12] Blount, G. N. and Fischer, B. V., “Computerized blank shape prediction for sheet metal components having doubly-curved surfaces”, Int. J. Prod. Res., 33, 1995, pp. 993-1005. https://doi.org/10.1080/00207549508930190.

[13] A.M. Zaky, A.B. Nassr, M.G. El-Sebaie, “Optimum blank shape of cylindrical cups in deep drawing of anisotropic sheet metal”, J. Mater. Proc. Technol. 76, 1998, pp. 203–211. https://doi.org/10.1016/S0924-0136(97)00349-X.

[14] K. Chung, O. Richmond, “Ideal forming II. Sheet forming with optimum deformation”, Int. J. Mech. Sci. 34, 1992, pp. 617–633. https://doi.org/10.1016/0020-7403(92)90059-P.

[15] Iseki, H. and Sowerby, R., “Determination of the optimal blank shape when deep drawing non axisymmetric cups using a finite element method”, Jap. Soc. Mech. Engrs Int., A, 38, 1995, pp. 473-479. https://doi.org/10.1299/jsmea1993.38.4_473.

[16] Barlat, O., Batoz, J. L., Guo, Y. Q., Mercier, F., Naceur, H. and Knopf-Lenoir, C., “Optimum blank design of blank contours using the inverse approach and a mathematical programming technique”, In Proceedings of Numisheet, 96, 1996, pp. 178-185.

[17] Lee, C. H. and Huh, H., “Blank design and strain prediction of automobile stamping parts by an inverse finite element approach”, J. Mater. Proc. Technol., 63, 1997, pp. 645-650. https://doi.org/10.1016/S0924-0136(96)02700-8.

[18] Y.Q. Guo, J.L. Batoz, H. Naceur, S. Bouabdallah, F. Mercier, O. Barlet, “Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach”, Comput. Struct. 78, 2000, pp. 133–148. https://doi.org/10.1016/S0045-7949(00)00095-X.

[19] T.W. Ku, H.J. Lim, H.H. Choi, S.M. Hwang, B.S. King, “Implementation of backward tracing scheme of the FEM to blank design in sheet metal forming”, J. Mater. Proc. Technol. 111, 2001, pp. 90–97. https://doi.org/10.1016/S0924-0136(01)00518-0.

[20] H. Naceur, Y.Q. Guo, J.L. Batoz, “Blank optimization in sheet metal forming using an evolutionary algorithm”, J. Mater. Proc. Technol. 151, 2004, pp. 183–191. https://doi.org/10.1016/j.jmatprotec.2004.04.036.

[21] Z.Y. Cai, M.Z. Li, H.M. Zhang, “A simplified algorithm for planar development of 3D surface and its application in the blank design of sheet metal forming”, Finite Elem. Anal. Des. 43, 2007, pp. 301–310. https://doi.org/10.1016/j.finel.2006.10.005.

[22] M.H. Parsa, P. Pournia, “Optimization of initial blank shape predicted based on inverse finite element method”, Finite Elem. Anal. Des. 43, 2007, pp. 218–233. https://doi.org/10.1016/j.finel.2006.09.005.

[23] R. Azizi, A. Assempour, “Applications of linear inverse finite element method in prediction of the optimum blank in sheet metal forming”, Mater. Des. 29, 2008, pp. 1965–1972. https://doi.org/10.1016/j.matdes.2008.04.015.

[24] R. Azizi, “Different implementations of inverse finite element method in sheet metal forming, Mater”, Des. 30, 2009, pp. 2975–2980. https://doi.org/10.1016/j.matdes.2008.12.022.

[25] C.H. Toh, S. Kobayashi, “Deformation analysis and blank design in square cup drawing”, Int. J. Mach. Tool Des. Res. 25, 1985, pp. 15–32. https://doi.org/10.1016/0020-7357(85)90054-X.

[26] K. Chung, F. Barlat, J.C. Brem, D.J. Lege, O. Richmond, “Blank shape design for a planar anisotropic sheet based on ideal forming design theory and FEM analysis”, Int. J. Mech. Sci. 39, 1997, pp. 105–120. https://doi.org/10.1016/0020-7403(96)00007-0.

[27] S.H. Park, J.W. Yoon, D.Y. Yang, Y.H. Kim, “Optimum blank design in sheet metal forming by the deformation path iteration method”, Int. J. Mech. Sci. 41, 1999, pp. 1217–1232. https://doi.org/10.1016/S0020-7403(98)00084-8.

[28] V. Pegada, Y. Chun, S. Santhanam, “an algorithm for determining the optimal blank shape for the deep drawing of aluminum cups”, J. Mater. Proc. Technol. 125–126, 2002, pp. 743–750. https://doi.org/10.1016/S0924-0136(02)00382-5.

 [29] H. Shim, K. Son, “Optimal blank shape design by the iterative sensitivity method”, Proc. IMECHE Part B J. Eng. Manuf., 216, 2002, pp. 867–878. https://doi.org/10.1243/095440502320192996.

 [30] K.C. Son, H.B. Shim, “Optimal blank shape design using the initial velocity of boundary nodes”, J. Mater. Process. Technol. 134, 2003, pp. 92–98.

[31] A. Vafaeesefat, “Optimum blank shape design in sheet metal forming by boundary projection method”, Int. J. Mater. Form. 1, 2008, pp. 189–192. https://doi.org/10.1007/s12289-008-0023-2.

[32] M. Azaouzi, H. Naceur, A. Delame´ziere, J.L. Batoz, S. Belouettar, “a heuristic optimization algorithm for the blank shape design of high precision metallic parts obtained by a particular stamping process”, Finite Elem. Anal. Des. 44, 2008, pp. 842–850. https://doi.org/10.1016/j.finel.2008.06.008.

[33] W. Hammami, R. Padmanabhan, M.C. Oliveira, H. BelHadjSalah, J.L. Alves, L.F. Menezes, “A deformation based blank design method for formed parts”, Int. J. Mech. Mater. Des. 5, 2009, pp. 303–314.  https://doi.org/10.1007/s10999-009-9103-9.

[34] R. Padmanabhan, M.C. Oliveira, A.J. Baptista, J.L. Alves, L.F. Menezes, “Numerical study on the influence of initial anisotropy on optimal blank shape”, Finite Elem. Anal. Des. 45, 2009, pp. 71-80. https://doi.org/10.1016/j.finel.2008.07.012.

[35] A. Fazli, B. Arezoo, “A comparison of numerical iteration based algorithms in blank optimization”, Finite Elem. Anal. Des., 50, 2012, pp. 207-216. https://doi.org/10.1016/j.finel.2011.09.011.

[36] M.J. Kazemzadeh-Parsi, “Numerical flow simulation in gated hydraulic structures using smoothed fixed grid finite element method”, Applied Mathematics and Computation, Vol. 246, 2014, pp. 447-459.

[37] M.J. Kazemzadeh-Parsi and F. Daneshmand, “Inverse geometry heat conduction analysis of functionally graded materials using smoothed fixed grid finite element method”, Inverse problems in Science and Engineering, Vol. 21, No. 2, 2013, pp. 235-250.

[38] Liu T. Itoh, “Numerical Techniques for Microwave and Millimeter and Millimeter-Wave Passive Structures”, Second Edition, New York: Wiley, 1989, pp. 305-320,

 

[39]. W. Zhanga, J. Gaob, J. Caob, “Blank geometry design for carbon fiber reinforced plastic (CFRP) preforming using finite element analysis (FEA)”, Procedia Manufacturing 48, 2020, pp. 197–203.  https://doi.org/10.1016/j.promfg.2020.05.038

[40]. S. Yaghoubi, F. Fereshteh-Saniee, “Optimization of the geometrical parameters for elevated temperature hydro-mechanical deep drawing process of 2024 aluminum alloy”, Proc IMechE Part E: J Process Mechanical Engineering, 0(0), 2020, pp. 1–11.  https://doi.org/10.1177/0954408920949364

[41]. M. Ghasemabadian, M. Kadkhodayan, W. Altenhof, “Experimental, numerical, and multi-objective optimization investigations on the energy absorption features of single- and bi-layer deep-drawn cups”, Proc IMechE Part L: J Materials: Design and Applications, 0(0), 2020, pp. 1–22. https://doi.org/10.1177/1464420720972431