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Hydromechanical deep-drawing of aluminum parabolic workpieces—experiments and numerical simulation
International Journal of Machine Tools & Manufacture 40 (2000) 1479–1492
Hydromechanical deep-drawing of aluminum parabolic workpieces—experiments and numerical simulation S.H. Zhang a
b
a,*
, L.H. Lang b, D.C. Kang b, J. Danckert c, K.B. Nielsen
c
NERC, Institute of Metal Research, Academia Sinica, 72 Wenhua Road, Shenyang 110015, People’s Republic of China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China c Department of Production, Aalborg University, Fibigerstraede 16, DK-9220 Aalborg, Denmark Received 24 May 1999; accepted 14 January 2000
Abstract Aluminum parabolic workpieces were formed with hydromechanical deep-drawing technology. The deep-drawing process was analyzed by using the explicit finite element method with various process parameters. Defects of wrinkling and rupture are predicted for some forming conditions, and the thickness distribution results are in good agreement with the experimental results. Thinning mainly takes place during the first third of the punch travel, while wrinkling mainly takes place during the final half-stage of the punch travel. The effects of chamber pressure and blank holding force on the deformation of the workpieces are discussed. The numerical results are compared with those obtained in the experiments. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Hydromechanical deep-drawing; Bulging; Chamber pressure; Aluminum parabolic work piece; Explicit finite element
1. Introduction Hydromechanical deep-drawing (HDD) technology has been widely used in forming complexshaped sheet metal parts [1–4]; parabolic workpieces are one of the typical workpieces formed with this process. The main advantage in using HDD technology to form parabolic workpieces is that they can be formed in one step, while six steps are typically necessary to form a parabolic
* Corresponding author. Tel.: +0086-24-2384-3531; fax: +0086-24-2389-1320. E-mail address: [email protected] (S.H. Zhang).
0890-6955/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 0 0 6 - 7
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workpiece using conventional deep-drawing technology. In addition, the dimensional accuracy of the products is remarkably improved when using HDD technology: surface quality is improved, the structure of the tooling system is simple and the number of tool components is reduced and thus the tooling costs are lowered significantly. However, body wrinkling and premature rupture often occur if the process parameters are not used properly. Process and tool design normally requires a lot of trial-and-error work. Numerical simulations have proven very useful in the design of tools and the process layout, which can help to find the optimal process parameters and to reduce the trial-and-error work. This paper is aimed at investigating the HDD process of parabolic workpieces experimentally and numerically. An explicit finite element code has been used to analyze the process. The numerical results are compared with the experimental results, and the deformation process of the workpieces is discussed. Wrinkling and local thinning of the workpieces under different forming conditions are predicted and the effects of the chamber pressure on deformation are analyzed. 2. Experimental Parabolic workpieces were formed by using HDD technology with different chamber pressures and blank holder forces. The parabolic punch consists of three parts: the punch head, the punch body and the punch base. The punch head is a spherical cap, and the punch body is a parabolic part, which connects the punch head and the cylindrical punch base. The punch head and the punch body determine the final shape of the workpiece, whose entire effective height is 108 mm. Five workpieces were formed under two different forming conditions (see Table 1). 1. Fixed gap method: spacers were used to fix the gap between the blank holder and the die surface (specimens A, B and C). The experimental system is shown in Fig. 1. In this case, four spacers were placed between the blank holder and the die surface to fix the gap between them, and the fluid can flow out of the flange when the chamber pressure is high enough. 2. Constant blank holder force method: no spacers were used and a constant blank holder force was used for every specimen (specimens D and E). When using the fixed gap method, the effects of the blank holder force are incorporated with the gap. The spacers are specially designed such that the gap between the blank holder and the Table 1 Forming conditions of the five specimensa Specimen
Forming conditions
A B C D E
Fixed gap method, BHPmax=7.0 MPa Fixed gap method, BHPmax=3.0 MPa Fixed gap method, BHPmax=20 MPa Constant blank holder force, BHP=1.0 MPa Constant blank holder force, BHP=0.7 MPa a
BHP, blank holder pressure.
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Fig. 1. Schematic illustration of the hydromechanical deep-drawing system and formed parabolic workpieces.
die surface could be regarded unchanged during the process under a certain amount of blank holder force; then the chamber pressure is easy to determine. In experiments the gap value can be measured. In this case, the main process parameter is the chamber pressure curve, which can determine the feasibility of the process. This method has proven to be feasible. Wrinkling and rupture are the two main failure modes in the HDD process of parabolic workpieces. The experiments showed that too high a chamber pressure or too fast growing of the chamber pressure could
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lead to premature rupture; too high blank holder force or too small spacer height could also lead to rupture. Insufficient chamber pressure and lower blank holder force (or higher spacer height) could lead to body wrinkling. Therefore, the proper chamber pressure curves and proper blank holder forces (or spacer height) were very important in carrying out the forming process successfully. Experimental specimens A, B and C were formed with the fixed gap method. Specimen A was formed successfully with the proper chamber pressure curve and a blank holding force of 7.0 MPa, while specimen B was severely wrinkled with a lower chamber pressure curve and a blank holding force of 3.0 MPa. Specimen C was torn because of its fast growing chamber pressure and high blank holder force of 20 MPa, which reduced the gap remarkably. When the constant blank holder force method was used, the chamber pressure is generated by the penetration of the punch only, the chamber pressure curves are to some extent determined by the blank holder forces; specimens D and E were formed with different blank holder forces. Specimen D used the blank holder force of 1.0 MPa, which led to a suitable chamber pressure curve and the formed workpiece was good; specimen E used a lower blank holder force of 0.7 MPa which led to a lower chamber pressure curve, and the workpiece wrinkled severely. The experimental material was pure aluminum L2 (Chinese grade, similar to A1100). The mechanical parameters of the materials and the process parameters are shown in Table 2. The experiments were carried out on a 200-ton hydraulic press. Lubricants were used between the die and the blank, and between the blank and the blank holder. The experimental system was controlled and measured with a personal computer system and the maximum chamber pressure was preset with a relief valve. The actual chamber pressure at the chamber center was measured in the experiments; the chamber pressure as a function of
Table 2 Main material parameters and process parameters of the experiments Material
L2
Blank diameter D0 (mm) Thickness (mm) Poisson ratio Young’s modulus E (MPa) Density (g/cm3) Yield stress (MPa) Hardening modulus Et (MPa) Punch diameter Dp (mm) Diameter of die opening (mm) Die profile radius (mm) Punch speed (mm/s) Friction coefficient (blank and die) Friction coefficient (blank and punch) Friction coefficient (blank and binder) Friction coefficient (blank edge and die) Gap between binder and die (mm) Anisotropy R
210 0.9 0.33 71 000 2.7 100 690 118.0 122.16 8 8 0.05 0.20 0.06 0.08 1.0 0.70
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the punch travel is shown in Fig. 2. The thickness distributions of the cups after forming were also measured. 3. Finite element simulations Some researchers have investigated the HDD process of cylindrical cups and complex-shaped parts with the finite element method (FEM) [5–9]. Results published about using the FEM indicate that further efforts are still necessary to get satisfactory results for this process, especially for the prediction of the thinning distribution for the upper part of the cup. We have carried out FE simulations of the HDD process of parabolic workpieces using the explicit finite element code DYNA3D. Detailed descriptions about the code and its application in simulating sheet metalforming operations can be found in [10–12]. The FE models are shown in Fig. 3. Only a quarter of the blank and the tool components were simulated because of symmetry. The Belytschko–Tsay thin-shell elements were used for the blank, the tool components were treated as rigid bodies. Thin-shell elements were also used for the tool components and only the surfaces which could get in contact with the blanks were considered. The blank model contained 2136 nodes and 1913 four-noded thin-shell quadrilateral elements; the tools contained 4516 nodes and 4140 elements. The following constitutive material models have been tried: the von Mises isotropic material model, Hill’s transversely anisotropic model (Hill 1948 model) and Barlat–Lian’s three-parameter model. Both Hollomon’s hardening model and the bilinear hardening model have been investigated for these models. The best results were obtained using the bilinear hardening model.
Fig. 2. Measured chamber pressure curves.
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Fig. 3. The exploded view of the FEM models (one-quarter geometry).
Compared to the experimental results the best results were obtained using Hill’s transversely anisotropic model. In [13] it is suggested that Barlat–Lian’s model is better suited to model the forming of aluminum than the two other models; however, FE simulations using this model showed more wrinkling than experimental observations and results obtained using this model are not discussed in this paper. Contact assuming Coulomb friction between the blank and the punch, between the blank and the die surface, and between the blank and the blank holder was modeled. Friction between the blank and the die surface was very low (friction coefficient 0.05 or lower) due to the fluid pressure. Higher friction (friction coefficient 0.08) was assumed between the blank edge (about 10 mm in radial direction) and the die surface, where the contacting condition was highly changed due to the severe thickening and lower fluid pressure. The friction coefficient between the blank and the punch was assumed to be 0.20; between the blank and the blank holder the friction was assumed to be much lower than that between the blank and the punch because of the lubricant used between the blank and the blank holder. Symmetrical boundary conditions were specified on the appropriate edges of the blank. The liquid was not modeled; instead a uniform distribution pressure within the die opening was used to apply the fluid pressure directly on the blank, while the fluid pressure was assumed to be linearly lowered in the radial direction under the blank flange, until it was zero at the edge of the blank. The pressure distribution was assumed to vary with the punch travel along the flange area. This distribution rule has been verified in [5].
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Time scaling was used to get a reasonable CPU time, the scaling factor was taken as 500, i.e. the artificial punch speed was 4.0 m/s (the actual punch speed was 8 mm/s). In such a case, the calculation time was about 20 to 30 h on a Silicon Graphics workstation. A higher time scaling factor was used when prerunning the process. When good results had been obtained, the time scaling factor was set to 500 and recalculation was made to obtain more accurate results. A high scaling factor may sometimes result in false results, especially false wrinkling, or it may give a good result while in low scaling factor situation fracture may take place. Therefore, high scaling factors can only be used in prerunning, and the scaling factor should be as low as possible in normal calculation to limit dynamic effects. The scaling factor is suggested to be lower than 600, best lower than 500 for the present simulations. However, time scaling is strongly related to the actual process and geometry. It needs much experience to find a proper time scaling factor for a specific process.
4. Results and discussion In the HDD process of the parabolic workpieces, chamber pressure plays quite an important role in the deformation of the blank. A large area of the blank between the punch and the die surface is unsupported. The central area of the blank was first forced to get in contact with the punch head due to the chamber pressure, while the unsupported area bulges with remarkable height; the bulging (or the reverse bulging) even continues when the punch has descended downwards for a distance. The simulations were carried out with two different forming conditions according to the experiments. (a) The fixed-gap method was used for specimens A, B and C, and spacers were used to get a fixed gap between the blank holder and the die surface. (b) The constant blank holder force method was used for specimens D and E, the blank holder force was kept constant during the forming process, and no spacers were used. 4.1. Process with a fixed gap between the blank holder and the die In these experiments, blank holder forces were required to be higher to maintain the gap caused by the spacers. The maximum chamber pressure was set at 15.0 MPa for specimen A, the chamber pressure reached 15 MPa at the punch travel of 50 mm, while for specimen B, the blank holder force was lower, and the chamber pressure did not reach 15 MPa. For specimen C, the blank holder force was too high, the chamber pressure grew very fast and the workpiece was ruptured during drawing. The specimens A, B and C were simulated with different chamber pressure curves. Specimen A had the optimum chamber pressure curve and the blank was drawn into a parabolic shape with only slight wrinkling occurring on the edge of the upper wall during the final stage. This is in agreement with the experiment. Fig. 4 shows the deformation process of workpiece A. It shows that the chamber pressure causes reverse bulging on the unsupported area (Fig. 4a and b), and no wrinkling occurs in this situation. In Fig. 4c, the chamber pressure is insufficient to cause reverse bulging and wrinkling begins in the unsupported areas. The numerical results are in good
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Fig. 4. The deformation process of parabolic workpiece A (PT=punch travel).
agreement with the experiment, although the predicted wrinkles are slightly larger than those observed in the experiments. When the chamber pressure is insufficient, wrinkling occurs in the unsupported areas at the early deformation stage. Fig. 5 shows the deformation of workpiece B with a lower chamber pressure. It can be seen in Fig. 5 that when the punch travel is about 55 mm, wrinkling begins in the unsupported areas of the workpiece. This is in agreement with experiment. The wrinkling increases with the increase of the punch travel and cannot be removed. Figs. 4 and 5 show that the chamber pressure should be high enough to avoid wrinkling in the unsupported areas, i.e. a reverse bulging deformation on the unsupported areas is necessary to
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Fig. 5. The wrinkling process of shell B (PT=punch travel).
keep these areas free from wrinkling. Wrinkling will occur when the chamber pressure is not high enough to maintain the reverse bulging. This can be seen in Figs 4c and 5b. When the blank holder force is very high and the chamber pressure is not high enough, wrinkling may not take place while local thinning usually takes place and the workpiece undergoes tearing. When the chamber pressure is too high or grows too fast, the workpiece may fracture at the early stage of forming. The FE results of specimen C show that local thinning occurs during forming. Fig. 6 shows the predicted profile of the workpiece with local thinning. Fig. 7 shows the thinning distribution in comparison with the experimental results. The FEM results are in good agreement with the experimental results in the punch head area. The thinnest
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Fig. 6. Local thinning of shell C.
Fig. 7. Thickness variations of specimen A.
position is located at the position where the parabolic profile joins the spherical punch head. The difference between the FE results and the experimental results is greater around the upper wall of the workpiece. The FEM results showed another special thinning position, which was on the upper wall of the workpiece. This indicates that local thinning may happen on the wall or the
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die profile if the blank holder force or the chamber pressure is too high, which seldom happens in conventional deep drawing. Another proposal to avoid wrinkling is to increase the blank thickness. Additional FE simulation shows that shell A does not show any wrinkling when the blank thickness is increased to 1.0 mm, and shell B shows much less wrinkling. Fig. 8 shows the thickness variations on workpiece A at different punch travel positions. There is a critical position (approximately a circle with radius 85 mm) on the blank flange; within this portion (the portion within the circle) thinning takes place from the very beginning, while outside this circle thickening takes place during the early stage of the deformation. Some thinning also takes place immediately outside the circle at the final drawing stage when the edge of the flange was severely thickened. The blank was severely thinned around this circle, which may develop into a local neck when the forming conditions are not suitable. Regarding the thinning within the circle, it was seen that thinning takes place from the punch head and spreads to the flange with the increase in the punch travel. The thinning within the 60-mm radius stops when the punch has traveled 41 mm. That is, the friction between the punch and the blank prevents further thinning in the contacting areas and the maximum thinning is achieved during the first third of the drawing stage, and no severe thickening takes place on the outer flange portion during this stage. When the punch travel is greater than 41 mm, thinning gradually spread to the area near to the critical position, and remarkable thickening happened on the outer flange area, especially during the final drawing stage. The critical position can also be found in the experimental results (see Fig. 7).
Fig. 8. Thickness variations of specimen A at different punch travel (PT, in mm).
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4.2. Process with constant blank holder force For the process with constant blank holder force (the spacers were removed), the experimental results showed that it is more difficult to determine the working ranges of suitable blank holder forces and suitable chamber pressure curves than in the fixed gap method. The blank holder force required is much lower, the chamber pressure curves and the body wrinkling and local thinning are very sensitive to the blank holder force. Some specimens were formed successfully with this method and some wrinkled severely. The deformation procedure of the workpieces was almost the same as in the fixed gap method. When carrying out FE simulations the main difference using the constant blank holder force method in the calculation is that the actual blank holder force was applied upon the blank holder, unlike in the fixed gap method where the blank holder force was incorporated in the fixed gap. Simulations were carried out for specimens D and E where a constant blank holder force was used in the process. Without spacers, the chamber pressure depends to a greater extent on the blank holder forces. Fig. 9 shows the deformed profiles of specimens D and E. Severe wrinkling can be seen in specimen E, similar to the wrinkling of specimen B in Fig. 5. 5. Conclusions Aluminum parabolic workpieces have been formed with the HDD process by the fixed gap method and the constant blank holder force method. The explicit finite element method successfully simulated the HDD processes of the parabolic workpieces. Defects of wrinkling and rupture have been predicted for some forming conditions, the thickness distribution results are in good agreement with the experimental results. Thinning mainly takes place during the first third of the punch travel in a drawing process, while wrinkling mainly happened during the final half-stage
Fig. 9. Deformed profiles of specimens (a) D and (b) E.
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of the punch travel. The chamber pressure should be high enough to maintain the reverse bulging deformation of the unsupported areas to avoid wrinkling of the workpieces. Higher blank thickness can reduce wrinkling. A critical circle on the flange exists, which has more thinning and may develop into a local neck if the forming conditions are not suitable.
Acknowledgements This work was performed under the Danish Materials Development Program financed by the Danish Agency for Development of Trade and Industry, the Danish Natural Science Foundation and the Danish Technical Research Council. The work was also supported by the Natural Science Foundation of China. The authors express their appreciation to M.R. Jensen for fruitful discussions and his valuable suggestions.
References [1] B. Larsen, Hydromechanic forming of sheet metal, Sheet Metal Industries February (1977) 162–166. [2] H. Amino, K. Nakamura, T. Nakagawa, Counter-pressure deep drawing and its application in the forming of automobile parts, Journal of Materials Processing Technology 23 (1990) 243–265. [3] T. Nakagawa, K. Nakamura, H. Amino, Various applications of hydraulic counter pressure deep drawing, Journal of Materials Processing Technology 71 (1997) 160–167. [4] S.H. Zhang, J. Danckert, Development of hydromechanical deep drawing, Journal of Materials Processing Technology 83 (1998) 14–25. [5] D.Y. Yang, H.G. Kim, H.S. Lee, K.W. Kim, Analysis of the axi-symmetrical deep-drawing process by using the finite element method, Trans. KSME 16 (5) (1992) 873–882. [6] J.C. Gelin, P. Delassus, Modeling and simulation of the aqua-draw deep drawing process, Annals of the CIRP 42 (1993) 305–308. [7] D.Y. Yang, J.B. Kim, D.W. Lee, Investigation into manufacturing of very long cups by hydro-mechanical deep drawing and ironing with controlled radial pressure, Annals of the CIRP 44 (1995) 255–258. [8] Y. Qin, R. Balendra, FE simulation of hydromechanical drawing of components with concave local features, in: Proceedings of the 4th International Conference on Sheet Metal, Enschede, The Netherlands, 1–3 April, vol. 2, 1996, pp. 205–214. [9] J. An, A.H. Soni, Three dimensional computer simulation of a sheet metal hydroforming process, in: Advanced Technology of Plasticity, Proceedings of the 5th International Conference on Technology of Plasticity, Columbus, Ohio, USA, 7–10 October, 1996, pp. 827–830. [10] P.C. Galbraith, M.J. Finn, S.R. MocEwen, A.R. Carr, K.M. Gatenby, T.L. Lin, G.A. Clifford, J.O. Hallquist, D. Stillman, Evaluation of an LS-DYNA3D model for deep-drawing of aluminum sheet, in: VDI BERICHE 894, FE-simulation of 3-D Sheet Metal Forming Process in Automotive Industry. International Conference with Workshop, 14–16 May, Zurich, Switzerland, 1991, pp. 441–465. [11] K. Mattiasson, L. Bernspang, A. Honecker, E. Schedin, T. Hammam, A. Melander, On the use of explicit time integration in finite element simulation of industrial sheet metal forming processes, in: VDI BERICHE 894, FEsimulation of 3-D Sheet Metal Forming Process in Automotive Industry. International Conference with Workshop, 14–16 May, Zurich, Switzerland, 1991, pp. 479–497. [12] R.G. Whirley, B.E. Englmann, R.W. Logan, Some aspects of sheet forming simulation using explicit finite element techniques, in: Numerical Methods for Simulation of Industrial Metal Forming Processes, ASME, CED-vol. 5/AMD vol. 156, 1992, pp. 77–83. [13] K.N. Shah, R.E. Dick, Evaluation of various yield criteria in LS-DYNA3D for sheet forming application for
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Hydromechanical deep-drawing of aluminum parabolic workpieces—experiments and numerical simulation S.H. Zhang a
b
a,*
, L.H. Lang b, D.C. Kang b, J. Danckert c, K.B. Nielsen
c
NERC, Institute of Metal Research, Academia Sinica, 72 Wenhua Road, Shenyang 110015, People’s Republic of China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China c Department of Production, Aalborg University, Fibigerstraede 16, DK-9220 Aalborg, Denmark Received 24 May 1999; accepted 14 January 2000
Abstract Aluminum parabolic workpieces were formed with hydromechanical deep-drawing technology. The deep-drawing process was analyzed by using the explicit finite element method with various process parameters. Defects of wrinkling and rupture are predicted for some forming conditions, and the thickness distribution results are in good agreement with the experimental results. Thinning mainly takes place during the first third of the punch travel, while wrinkling mainly takes place during the final half-stage of the punch travel. The effects of chamber pressure and blank holding force on the deformation of the workpieces are discussed. The numerical results are compared with those obtained in the experiments. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Hydromechanical deep-drawing; Bulging; Chamber pressure; Aluminum parabolic work piece; Explicit finite element
1. Introduction Hydromechanical deep-drawing (HDD) technology has been widely used in forming complexshaped sheet metal parts [1–4]; parabolic workpieces are one of the typical workpieces formed with this process. The main advantage in using HDD technology to form parabolic workpieces is that they can be formed in one step, while six steps are typically necessary to form a parabolic
* Corresponding author. Tel.: +0086-24-2384-3531; fax: +0086-24-2389-1320. E-mail address: [email protected] (S.H. Zhang).
0890-6955/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 0 0 6 - 7
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workpiece using conventional deep-drawing technology. In addition, the dimensional accuracy of the products is remarkably improved when using HDD technology: surface quality is improved, the structure of the tooling system is simple and the number of tool components is reduced and thus the tooling costs are lowered significantly. However, body wrinkling and premature rupture often occur if the process parameters are not used properly. Process and tool design normally requires a lot of trial-and-error work. Numerical simulations have proven very useful in the design of tools and the process layout, which can help to find the optimal process parameters and to reduce the trial-and-error work. This paper is aimed at investigating the HDD process of parabolic workpieces experimentally and numerically. An explicit finite element code has been used to analyze the process. The numerical results are compared with the experimental results, and the deformation process of the workpieces is discussed. Wrinkling and local thinning of the workpieces under different forming conditions are predicted and the effects of the chamber pressure on deformation are analyzed. 2. Experimental Parabolic workpieces were formed by using HDD technology with different chamber pressures and blank holder forces. The parabolic punch consists of three parts: the punch head, the punch body and the punch base. The punch head is a spherical cap, and the punch body is a parabolic part, which connects the punch head and the cylindrical punch base. The punch head and the punch body determine the final shape of the workpiece, whose entire effective height is 108 mm. Five workpieces were formed under two different forming conditions (see Table 1). 1. Fixed gap method: spacers were used to fix the gap between the blank holder and the die surface (specimens A, B and C). The experimental system is shown in Fig. 1. In this case, four spacers were placed between the blank holder and the die surface to fix the gap between them, and the fluid can flow out of the flange when the chamber pressure is high enough. 2. Constant blank holder force method: no spacers were used and a constant blank holder force was used for every specimen (specimens D and E). When using the fixed gap method, the effects of the blank holder force are incorporated with the gap. The spacers are specially designed such that the gap between the blank holder and the Table 1 Forming conditions of the five specimensa Specimen
Forming conditions
A B C D E
Fixed gap method, BHPmax=7.0 MPa Fixed gap method, BHPmax=3.0 MPa Fixed gap method, BHPmax=20 MPa Constant blank holder force, BHP=1.0 MPa Constant blank holder force, BHP=0.7 MPa a
BHP, blank holder pressure.
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Fig. 1. Schematic illustration of the hydromechanical deep-drawing system and formed parabolic workpieces.
die surface could be regarded unchanged during the process under a certain amount of blank holder force; then the chamber pressure is easy to determine. In experiments the gap value can be measured. In this case, the main process parameter is the chamber pressure curve, which can determine the feasibility of the process. This method has proven to be feasible. Wrinkling and rupture are the two main failure modes in the HDD process of parabolic workpieces. The experiments showed that too high a chamber pressure or too fast growing of the chamber pressure could
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lead to premature rupture; too high blank holder force or too small spacer height could also lead to rupture. Insufficient chamber pressure and lower blank holder force (or higher spacer height) could lead to body wrinkling. Therefore, the proper chamber pressure curves and proper blank holder forces (or spacer height) were very important in carrying out the forming process successfully. Experimental specimens A, B and C were formed with the fixed gap method. Specimen A was formed successfully with the proper chamber pressure curve and a blank holding force of 7.0 MPa, while specimen B was severely wrinkled with a lower chamber pressure curve and a blank holding force of 3.0 MPa. Specimen C was torn because of its fast growing chamber pressure and high blank holder force of 20 MPa, which reduced the gap remarkably. When the constant blank holder force method was used, the chamber pressure is generated by the penetration of the punch only, the chamber pressure curves are to some extent determined by the blank holder forces; specimens D and E were formed with different blank holder forces. Specimen D used the blank holder force of 1.0 MPa, which led to a suitable chamber pressure curve and the formed workpiece was good; specimen E used a lower blank holder force of 0.7 MPa which led to a lower chamber pressure curve, and the workpiece wrinkled severely. The experimental material was pure aluminum L2 (Chinese grade, similar to A1100). The mechanical parameters of the materials and the process parameters are shown in Table 2. The experiments were carried out on a 200-ton hydraulic press. Lubricants were used between the die and the blank, and between the blank and the blank holder. The experimental system was controlled and measured with a personal computer system and the maximum chamber pressure was preset with a relief valve. The actual chamber pressure at the chamber center was measured in the experiments; the chamber pressure as a function of
Table 2 Main material parameters and process parameters of the experiments Material
L2
Blank diameter D0 (mm) Thickness (mm) Poisson ratio Young’s modulus E (MPa) Density (g/cm3) Yield stress (MPa) Hardening modulus Et (MPa) Punch diameter Dp (mm) Diameter of die opening (mm) Die profile radius (mm) Punch speed (mm/s) Friction coefficient (blank and die) Friction coefficient (blank and punch) Friction coefficient (blank and binder) Friction coefficient (blank edge and die) Gap between binder and die (mm) Anisotropy R
210 0.9 0.33 71 000 2.7 100 690 118.0 122.16 8 8 0.05 0.20 0.06 0.08 1.0 0.70
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the punch travel is shown in Fig. 2. The thickness distributions of the cups after forming were also measured. 3. Finite element simulations Some researchers have investigated the HDD process of cylindrical cups and complex-shaped parts with the finite element method (FEM) [5–9]. Results published about using the FEM indicate that further efforts are still necessary to get satisfactory results for this process, especially for the prediction of the thinning distribution for the upper part of the cup. We have carried out FE simulations of the HDD process of parabolic workpieces using the explicit finite element code DYNA3D. Detailed descriptions about the code and its application in simulating sheet metalforming operations can be found in [10–12]. The FE models are shown in Fig. 3. Only a quarter of the blank and the tool components were simulated because of symmetry. The Belytschko–Tsay thin-shell elements were used for the blank, the tool components were treated as rigid bodies. Thin-shell elements were also used for the tool components and only the surfaces which could get in contact with the blanks were considered. The blank model contained 2136 nodes and 1913 four-noded thin-shell quadrilateral elements; the tools contained 4516 nodes and 4140 elements. The following constitutive material models have been tried: the von Mises isotropic material model, Hill’s transversely anisotropic model (Hill 1948 model) and Barlat–Lian’s three-parameter model. Both Hollomon’s hardening model and the bilinear hardening model have been investigated for these models. The best results were obtained using the bilinear hardening model.
Fig. 2. Measured chamber pressure curves.
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Fig. 3. The exploded view of the FEM models (one-quarter geometry).
Compared to the experimental results the best results were obtained using Hill’s transversely anisotropic model. In [13] it is suggested that Barlat–Lian’s model is better suited to model the forming of aluminum than the two other models; however, FE simulations using this model showed more wrinkling than experimental observations and results obtained using this model are not discussed in this paper. Contact assuming Coulomb friction between the blank and the punch, between the blank and the die surface, and between the blank and the blank holder was modeled. Friction between the blank and the die surface was very low (friction coefficient 0.05 or lower) due to the fluid pressure. Higher friction (friction coefficient 0.08) was assumed between the blank edge (about 10 mm in radial direction) and the die surface, where the contacting condition was highly changed due to the severe thickening and lower fluid pressure. The friction coefficient between the blank and the punch was assumed to be 0.20; between the blank and the blank holder the friction was assumed to be much lower than that between the blank and the punch because of the lubricant used between the blank and the blank holder. Symmetrical boundary conditions were specified on the appropriate edges of the blank. The liquid was not modeled; instead a uniform distribution pressure within the die opening was used to apply the fluid pressure directly on the blank, while the fluid pressure was assumed to be linearly lowered in the radial direction under the blank flange, until it was zero at the edge of the blank. The pressure distribution was assumed to vary with the punch travel along the flange area. This distribution rule has been verified in [5].
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Time scaling was used to get a reasonable CPU time, the scaling factor was taken as 500, i.e. the artificial punch speed was 4.0 m/s (the actual punch speed was 8 mm/s). In such a case, the calculation time was about 20 to 30 h on a Silicon Graphics workstation. A higher time scaling factor was used when prerunning the process. When good results had been obtained, the time scaling factor was set to 500 and recalculation was made to obtain more accurate results. A high scaling factor may sometimes result in false results, especially false wrinkling, or it may give a good result while in low scaling factor situation fracture may take place. Therefore, high scaling factors can only be used in prerunning, and the scaling factor should be as low as possible in normal calculation to limit dynamic effects. The scaling factor is suggested to be lower than 600, best lower than 500 for the present simulations. However, time scaling is strongly related to the actual process and geometry. It needs much experience to find a proper time scaling factor for a specific process.
4. Results and discussion In the HDD process of the parabolic workpieces, chamber pressure plays quite an important role in the deformation of the blank. A large area of the blank between the punch and the die surface is unsupported. The central area of the blank was first forced to get in contact with the punch head due to the chamber pressure, while the unsupported area bulges with remarkable height; the bulging (or the reverse bulging) even continues when the punch has descended downwards for a distance. The simulations were carried out with two different forming conditions according to the experiments. (a) The fixed-gap method was used for specimens A, B and C, and spacers were used to get a fixed gap between the blank holder and the die surface. (b) The constant blank holder force method was used for specimens D and E, the blank holder force was kept constant during the forming process, and no spacers were used. 4.1. Process with a fixed gap between the blank holder and the die In these experiments, blank holder forces were required to be higher to maintain the gap caused by the spacers. The maximum chamber pressure was set at 15.0 MPa for specimen A, the chamber pressure reached 15 MPa at the punch travel of 50 mm, while for specimen B, the blank holder force was lower, and the chamber pressure did not reach 15 MPa. For specimen C, the blank holder force was too high, the chamber pressure grew very fast and the workpiece was ruptured during drawing. The specimens A, B and C were simulated with different chamber pressure curves. Specimen A had the optimum chamber pressure curve and the blank was drawn into a parabolic shape with only slight wrinkling occurring on the edge of the upper wall during the final stage. This is in agreement with the experiment. Fig. 4 shows the deformation process of workpiece A. It shows that the chamber pressure causes reverse bulging on the unsupported area (Fig. 4a and b), and no wrinkling occurs in this situation. In Fig. 4c, the chamber pressure is insufficient to cause reverse bulging and wrinkling begins in the unsupported areas. The numerical results are in good
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Fig. 4. The deformation process of parabolic workpiece A (PT=punch travel).
agreement with the experiment, although the predicted wrinkles are slightly larger than those observed in the experiments. When the chamber pressure is insufficient, wrinkling occurs in the unsupported areas at the early deformation stage. Fig. 5 shows the deformation of workpiece B with a lower chamber pressure. It can be seen in Fig. 5 that when the punch travel is about 55 mm, wrinkling begins in the unsupported areas of the workpiece. This is in agreement with experiment. The wrinkling increases with the increase of the punch travel and cannot be removed. Figs. 4 and 5 show that the chamber pressure should be high enough to avoid wrinkling in the unsupported areas, i.e. a reverse bulging deformation on the unsupported areas is necessary to
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Fig. 5. The wrinkling process of shell B (PT=punch travel).
keep these areas free from wrinkling. Wrinkling will occur when the chamber pressure is not high enough to maintain the reverse bulging. This can be seen in Figs 4c and 5b. When the blank holder force is very high and the chamber pressure is not high enough, wrinkling may not take place while local thinning usually takes place and the workpiece undergoes tearing. When the chamber pressure is too high or grows too fast, the workpiece may fracture at the early stage of forming. The FE results of specimen C show that local thinning occurs during forming. Fig. 6 shows the predicted profile of the workpiece with local thinning. Fig. 7 shows the thinning distribution in comparison with the experimental results. The FEM results are in good agreement with the experimental results in the punch head area. The thinnest
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Fig. 6. Local thinning of shell C.
Fig. 7. Thickness variations of specimen A.
position is located at the position where the parabolic profile joins the spherical punch head. The difference between the FE results and the experimental results is greater around the upper wall of the workpiece. The FEM results showed another special thinning position, which was on the upper wall of the workpiece. This indicates that local thinning may happen on the wall or the
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die profile if the blank holder force or the chamber pressure is too high, which seldom happens in conventional deep drawing. Another proposal to avoid wrinkling is to increase the blank thickness. Additional FE simulation shows that shell A does not show any wrinkling when the blank thickness is increased to 1.0 mm, and shell B shows much less wrinkling. Fig. 8 shows the thickness variations on workpiece A at different punch travel positions. There is a critical position (approximately a circle with radius 85 mm) on the blank flange; within this portion (the portion within the circle) thinning takes place from the very beginning, while outside this circle thickening takes place during the early stage of the deformation. Some thinning also takes place immediately outside the circle at the final drawing stage when the edge of the flange was severely thickened. The blank was severely thinned around this circle, which may develop into a local neck when the forming conditions are not suitable. Regarding the thinning within the circle, it was seen that thinning takes place from the punch head and spreads to the flange with the increase in the punch travel. The thinning within the 60-mm radius stops when the punch has traveled 41 mm. That is, the friction between the punch and the blank prevents further thinning in the contacting areas and the maximum thinning is achieved during the first third of the drawing stage, and no severe thickening takes place on the outer flange portion during this stage. When the punch travel is greater than 41 mm, thinning gradually spread to the area near to the critical position, and remarkable thickening happened on the outer flange area, especially during the final drawing stage. The critical position can also be found in the experimental results (see Fig. 7).
Fig. 8. Thickness variations of specimen A at different punch travel (PT, in mm).
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4.2. Process with constant blank holder force For the process with constant blank holder force (the spacers were removed), the experimental results showed that it is more difficult to determine the working ranges of suitable blank holder forces and suitable chamber pressure curves than in the fixed gap method. The blank holder force required is much lower, the chamber pressure curves and the body wrinkling and local thinning are very sensitive to the blank holder force. Some specimens were formed successfully with this method and some wrinkled severely. The deformation procedure of the workpieces was almost the same as in the fixed gap method. When carrying out FE simulations the main difference using the constant blank holder force method in the calculation is that the actual blank holder force was applied upon the blank holder, unlike in the fixed gap method where the blank holder force was incorporated in the fixed gap. Simulations were carried out for specimens D and E where a constant blank holder force was used in the process. Without spacers, the chamber pressure depends to a greater extent on the blank holder forces. Fig. 9 shows the deformed profiles of specimens D and E. Severe wrinkling can be seen in specimen E, similar to the wrinkling of specimen B in Fig. 5. 5. Conclusions Aluminum parabolic workpieces have been formed with the HDD process by the fixed gap method and the constant blank holder force method. The explicit finite element method successfully simulated the HDD processes of the parabolic workpieces. Defects of wrinkling and rupture have been predicted for some forming conditions, the thickness distribution results are in good agreement with the experimental results. Thinning mainly takes place during the first third of the punch travel in a drawing process, while wrinkling mainly happened during the final half-stage
Fig. 9. Deformed profiles of specimens (a) D and (b) E.
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of the punch travel. The chamber pressure should be high enough to maintain the reverse bulging deformation of the unsupported areas to avoid wrinkling of the workpieces. Higher blank thickness can reduce wrinkling. A critical circle on the flange exists, which has more thinning and may develop into a local neck if the forming conditions are not suitable.
Acknowledgements This work was performed under the Danish Materials Development Program financed by the Danish Agency for Development of Trade and Industry, the Danish Natural Science Foundation and the Danish Technical Research Council. The work was also supported by the Natural Science Foundation of China. The authors express their appreciation to M.R. Jensen for fruitful discussions and his valuable suggestions.
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