Abstract
The deforming zone in the die determined by the cross-sectional shape of the final product plays a key role in the extrusion process affecting the extrusion pressure and product quality. Therefore, prediction of the optimal profile of the deforming region is the main objective for an effective extrusion process. In this study, using the analogy between the conventional plasticity theorem and electrostatics, the notion of equi-potential lines (EPLs) was applied to accurate representation and 3D design of the deforming region in the extrusion process of a complex section. To implement the analogy in the extrusion, the initial and final shapes were considered, and two different potentials were assigned between the inlet and outlet surfaces. Then, the EPLs were drawn that show the minimum work path between the entry and exit sections. The drawn EPLs were connected to build up a 3D-profile for the deforming region in the extrusion process. In addition, the EPLs were used in accurate representation of the deforming region using high-order polynomial curves. The effectiveness of the proposed method was examined using a complex section (U-shaped) from the literature. Then, the extrusion pressure for different profiles in the deforming region was analyzed numerically and experimentally. Moreover, the obtained polynomial curves were used in the upper bound (UB) solution for prediction of the extrusion pressure. There were reasonable agreements between the analytical, numerical, and experimental results. An acceptable reduction in the extrusion pressure for 3D modelling of the deforming region with the EPLs was reported. It was shown that the EPLs could be used for accurate representation of the deforming region in the extrusion of complex sections.
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References
Juneja BI, Prakash R (1975) An analysis for drawing and extrusion of polygonal sections. Int J Mach Tools Des Res 15:1–13
Yang DY, Lee CH (1978) Analysis of three dimensional extrusion sections through curved dies by conformal transformation. Int J Mech Sci 20:541–552
Ulysse P (1999) Optimal extrusion die design to achieve flow balance. Int J Mach Tools Manuf 39:1047–1064
Ulysse P (2002) Optimal extrusion die design to achieve flow balance using FE and optimization methods. Int J Mech Sci 44:319–341
Chen H, Zhao G, Zhang C et al (2011) Numerical simulation of extrusion process and die structure optimization for a complex aluminium multi-cavity wallboard of high-speed train. J Mater Manuf Process 26:1530–1538
Chung JS, Hwang SM (1997) Application of a genetic algorithm to the optimal design of the die shape in extrusion. J Mater Process Technol 72:69–77
Gordona WA, Van Tyne CJ, Moon YH (2007) Overview of adaptable die design for extrusions. J Mater Process Technol 187–188:662–667
Wu C-Y, Hsu Y-C (2002) Optimal shape design of an extrusion die using polynomial networks and genetic algorithm. Int J Adv Manuf Technol 19:79–87
Yeo HT, Hur KD (2001) Analysis and design of the prestressed cold extrusion die. Int J Adv Manuf Technol 20:128–137
Mu Y, Zhao G, Wu X, Zhang C (2010) An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II. Int J Adv Manuf Technol 50:517–532
Zhang C, Zhao G, Chen H, Guan Y, Li H (2012) Optimization of an aluminum profile extrusion process based on Taguchi’s method with S/N analysis. Int J Adv Manuf Technol 60:589–599
Zhao G, Chen H, Zhang C, Guan Y (2013) Multi objective optimization design of porthole extrusion die using Pareto-based genetic algorithm. Int J Adv Manuf Technol 69:1547–1566
Lee SR, Lee YK, Park CH, Yang DY (2002) A new method of preform design in hot forging by using electric field theory. Int J Mech Sci 44:773–792
Xiaona W, Fuguo L (2009) A quasi-equi potential field simulation for preform design of P/M superalloy disk. Chin J Aeronaut 22:81–86
Tabatabaei SA, Faraji G, Mashadi MM et al (2013) Preform shape design in tube hydroforming process using equi-Potential line method. Mater Manuf Process 28(3):260–264
Tabatabaei SA, Shariat Panahi M, Mosavi Mashadi M et al (2013) Optimum design of preform geometry and forming pressure in tube hydroforming using the equi-potential lines method. Int J Adv Manuf Technol 69:2787–2792
Tabatabaei SA, Abrinia K, Besharati Givi MK et al (2013) Application of the equi-potential lines method in upper bound estimation of the extrusion pressure. Mater Manuf Process 28(3):271–275
Tabatabaei SA, Abrinia K, Besharati Givi MK (2014) Application of equi-potential lines method for accurate definition of the deforming zone in the upper-bound analysis of forward extrusion problems. Int J Adv Manuf Technol 72:1039–1050
Cai J, Li F, Liu T (2001) A new approach of preform design based on 3D electrostatic field simulation and geometric transformation. Int J Adv Manuf Technol 56:579–588
Yu, H-S (2006) General elastic–plastic theorems. In: Gao DY, Ogden RW (eds) Plasticity and geotechnics. Springer, US, pp 40–68
Abrinia K, Ghorbani M (2012) Theoretical and experimental analyses for the forward extrusion of non symmetric sections. Mater Manuf Process 27:420–429
Johnson W, Mellor PB (1983) Engineering plasticity. Ellis Horwood Ltd, UK
Abrinia K, Fazlirad A (2009) Three-dimensional analysis of shape rolling using a generalized upper bound approach. J Mater Process Technol 209:3264–3277
Ponalagusamy R, Narayanasamy R, Srinivasan P (2005) Design and development of streamlined extrusion dies a Bezier curve approach. J Mater Process Technol 161:375–380
Narayanasamy R, Srinivasan P, Venkatesan R (2003) Computer aided design and manufacture of streamlined extrusion dies. J Mater Process Technol 138:262–264
Narayanasamy R, Ponalagusamy R, Venkatesan R, Srinivasan P (2006) An upper bound solution to extrusion of circular billet to circular shape through cosine dies. Mater Des 27:411–415
Celik KF, Chitkara NR (2002) Extrusion of non-symmetric U- and I-shaped sections, through ruled-surface dies: numerical simulations and some experiments. Int J Mech Sci 44:217–246
Chitkara NR, Celik KF (2001) Extrusion of non-symmetric T-shaped sections, an analysis and some experiments. Int J Mech Sci 43:2961–2987
Abrinia K, Davarzani H (2012) A universal formulation for the extrusion of sections with no axis of symmetry. J Mater Process Technol 212:1355–1366
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Tabatabaei, S.A., Besharati Givi, M.K., Abrinia, K. et al. 3D profile modelling and accurate representation of the deforming region in the extrusion process of complex sections using equi-potential lines method. Int J Adv Manuf Technol 80, 209–219 (2015). https://doi.org/10.1007/s00170-015-6976-7
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DOI: https://doi.org/10.1007/s00170-015-6976-7