Effect of Circular and Rectangular Drawbeads in Hemispherical Cup Forming: Finite Element Analysis and Experimental Validation G. Murali, M. Gopal & A. Rajadurai
Arabian Journal for Science and Engineering ISSN 1319-8025 Arab J Sci Eng DOI 10.1007/s13369-012-0276-4
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Author's personal copy Arab J Sci Eng DOI 10.1007/s13369-012-0276-4
R E S E A R C H A RT I C L E - M E C H A N I C A L E N G I N E E R I N G
G. Murali · M. Gopal · A. Rajadurai
Effect of Circular and Rectangular Drawbeads in Hemispherical Cup Forming: Finite Element Analysis and Experimental Validation
Received: 10 July 2010 / Accepted: 25 December 2010 © King Fahd University of Petroleum and Minerals 2012
Abstract Drawbeads are often applied in the deep drawing process to improve control of the material flow during the forming operation. Drawbeads restrain the sheet from flowing freely into die cavity. This paper deals with analysis of effect of draw bead geometry in sheet metal drawing process. Finite element analysis of drawing of circular blanks into axi-symmetric hemispherical cup was done. Circular and rectangular drawbeads were introduced into the Finite Element models and their influence in distribution of strain and thickness were investigated. DYNAFORM and LS-DYNA, a commercially available explicit FEA code were used to model and analyze the forming process respectively. These outcomes are compared with experimental results. The numerical results were found in good agreement with the experimental results. Plastic strain and Von-Mises stresses produced by rectangular drawbeads are higher when compared with the use of circular drawbead. Due to its geometry rectangular drawbead bends and unbends the sheet four times and restrains the material more than circular drawbead. Keywords Sheet metal forming · Drawbead · LS-DYNA · Plastic strain
G. Murali (B) · M. Gopal School of Mechanical Engineering, SRM University, Chennai 603203, India E-mail:
[email protected] A. Rajadurai Department of Production Technology, Madras Institute of Technology, Anna University, Chennai 600044, India
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Fig. 1 Location of drawbead on press tool
1 Introduction The sheetmetal forming process is used frequently in the automotive or packaging industry to manufacture products with sometimes complicated shapes and curvatures. In sheet metal forming, the rate of material flow into die cavity must be controlled so that a better quality is maintained and defects like wrinkling, tearing and galling are prevented. Generally the restraining force required to control the material flow is provided by either the blank holder or the drawbeads. The blank holder creates restraining force by friction between sheet and the tooling. When a high restraining force is required, higher binder pressure must be applied to increase the frictional resistance force, which may cause excessive wear in the tooling and galling in strip. In some cases the blank holder does not make contact with the entire blank, which implies that in practice the material flow can hardly be controlled by the blank holder. Hence a local mechanism is desired which restrains the material flow sufficiently at relatively low blank holder pressure [1,2]. The draw bead consists of a small groove on the die surface/binder surface matched by protrusion on the binder surface/die surface as shown in Fig. 1. After the binder closure, the sheet metal is drawn over the drawbead and is subjected to a bending and a subsequent unbending around the entry shoulder, bead and at the exit shoulder. These bending and unbending deformations together with the frictional force account for the draw bead restraining force. While drawbeads have been used to control the flow of sheet in to a die cavity for many years, there is little published work on them. These include study of steady state experiments conducted by Nine [3,4] who investigated stamping variables affecting the drawbead restraining force (DBRF) and proposed DBRF and bead exit pre-strain at the upper and lower skins of sheet when a circular drawbead is employed in a binder holding process. Wang [5] proposed a mathematical model of the drawbead forces for calculating the force required to draw sheet metal past a drawbead of constant cross-section. Levy [6] had improved Wang and Nine’s study on drawbeads in 1983. A theoretical model based on virtual work principle was proposed by Chen and Tszeng [7] to calculate the restraining force produced by the drawbead located on a stamping die surface. Samuel [8] devised a numerical model to determine the pull force, shear force and bending moment required to form sheet metal subjected to plane strain. Yellup and Painter [9] predicted the restraining forces by the computer modeling of a shallow drawbead system. Keum et al. [10] have formulated an expert drawbead model which can replace the drawbead and its boundary conditions. A simple and very effective algorithm has been outlined and demonstrated for the optimal drawbead design problem for deep drawing cups without ears by Vahdat et al. [11]. The algorithm uses an iterative process to arrive at the optimum drawbead contour. Firat [12] derived an analytical model for the prediction of the drawing restraint force and thinning characteristics of automotive sheets with a square type drawbead element. An assessment of the model prediction showed the overall good performance of the proposed model at all bead penetration levels for conventional mild and high strength steel grades. In 2009, Firat et al. [13] proposed a finite element modeling to improve the accuracy of contact type drawbead element in panel forming analyses. For the study the authors considered round draw bead profile. An evaluation of thickness distribution computed with proposed technique showed an improved correlation with experiment results. Livatyali et al. [14] conducted an experiment to analyze drawing characteristics of a dual-phase steel through a round drawbead and suggested equivalent drawbead model for FE simulations. The work reported in this paper concentrates on numerical analysis of influence of a circular and rectangular drawbead location on the strain and thickness distribution over the formed cup. Numerical investigations are carried out using LS-DYNA to observe strain and thickness distribution. Experiments were conducted to validate the numerical findings. The results obtained were used to validate the numerical findings. 2 Numerical Modeling Numerical modeling of press tool and blank and pre-processing were done using DYNAFORM and finite element analysis was done using LS-DYNA. The punch and die were modeled using shell elements and have
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Table 1 Mechanical properties of AISI 1008 Material
Young’s modulus (GPa)
Mass density (kg/m3 )
Poisson’s ratio
Yield stress (MPa)
Cold rolled steel (AISI 1008)
210
7,800
0.28
280
Table 2 Parameters of drawbeads Drawbead type
Circular
Rectangular
Depth (mm) Width (mm) Entrance radius (mm) Groove radius (mm) Groove angle (◦ ) Entrance angle (◦ ) Groove width (mm)
3.5 6.5 1.5 1.5 55 55 0
3.5 6.5 1.5 1.5 55 55 1.5
Fig. 2 Profiles of circular and rectangular drawbeads
been assigned with RIGID MATERIAL MODEL [15] with surface mesh option. The diameter of punch was 100 mm and diameter of die was 102.2 mm with suitable entry radius. The blank of 174 mm diameter was assigned with TRANSVERSELY_ANISOTROPIC_ELASTIC-PLASTIC model [16] and shell element with uniform thickness of 1.02 mm. The material considered for this study was cold rolled steel (AISI 1008) and its properties are given in Table 1. 2.1 Numerical Simulation In numerical simulation, contact is necessary between the sliding bodies for the metal forming process. In this study CONTACT_FORMING_ONE_WAY_SURFACE_TO_SURFACE title algorithm [15,16] was used for the contact between the punch, die, blank holder and blank. The blank was treated as master surface and others were treated as slave surfaces. The static coefficient of friction between the contacts were taken as 0.14. An artificial velocity of 5 m/s was given to the punch in Z direction downwards with stroke distance of 50 mm. The binder force was set as 8.5 tons towards negative Z direction. The flow of material on the drawbead during forming process is controlled by bending and normal load curve provided in DYNAFORM. Numerical simulations were carried out for the given conditions and results were obtained. The circular and rectangular drawbeads were modeled on the die surface with the dimensions given in Table 2. The profile of drawbeads given in DYNAFORM is shown in Fig. 2. A uniform gap of 0.2 mm was maintained between blank, blank holder and die surface using AUTOPOSITION command. 2.2 Optimization of Drawbead Location The location of the drawbeads on die surface is crucial to their effectiveness. They should be close to the area requiring restraint and perpendicular to the flow of material. The drawbead is positioned at various locations over the die surface from the center of the die cavity. Initially at a distance of 62 mm from the centre of die cavity a circular drawbead of width 6.5 mm and depth 3.5 mm was created and numerical simulation was carried out. Maximum value of Effective strain, Von-Mises stress, maximum and minimum thickness were
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Table 3 Optimization of drawbead location Location of the draw bead (mm)
Maximum effective strain
Maximum Von-Mises stress (Mpa)
Maximum thickness (mm)
Minimum thickness (mm)
62 63 64 65 66 67
0.2900 0.2960 0.2970 0.2840 0.3070 0.3068
757 735 725 720 760 764
1.0480 1.0500 1.0430 1.0500 1.0465 1.0460
0.7990 0.8110 0.7610 0.8080 0.7899 0.7899
Maximum Effective strain
0.307
Maximum Von-Mises stress (MPa)
0.31 0.3068
0.305 0.3 0.297
0.296
0.295 0.29
0.29 0.285
0.284
0.28 61
62
63
64
65
66
67
Draw bead location from die cavity centre (mm)
68
770 765 760
764 760
757
755 750 745 740 735
735
730 725
725 720
720
715 61
62
63
64
65
66
67
68
Draw bead location from die cavity centre (mm)
Fig. 3 Comparison of maximum effective strain and maximum Von-Mises stress at the optimized location of circular drawbead
identified. The same procedure was repeated by positioning drawbead at different locations from 62 to 67 mm in steps of 1 mm and the outcomes are presented in Table 3. All the outcomes are plotted against the drawbead position and shown in Fig. 3. It is observed from Fig. 3 that the maximum effective strain observed is 0.29 and it increases as the distance from die cavity increases due to the reason when the bead is closer to die cavity it acts like a locking bead and does not allow material freely. When it is far away the effect of draw bead is minimized since after leaving the drawbead the material comes under blank holder force for longer distance in turn under more frictional force. In between these two conditions, at 65 mm from die center the maximum effective strain reaches minimum value (0.284) and maximum Von-Mises stress reaches minimum value of 720 MPa. From the Table 3 at location 65 the value of maximum thickness 1.05 mm and minimum thickness 0.808 mm are observed. 2.3 Numerical Results Numerical simulations were conducted in three phases namely, hemispherical cup forming without drawbead, with circular and rectangular drawbeads at optimized location (65 mm from die centre) similar to the experiments, which were performed later. Post processor of LS-DYNA was utilized to obtain the thickness distribution, strain distribution, Von-Mises stress distribution on the formed cup and the observations are tabulated. The thickness of drawn cup was noted at locations in the direction starting from the centre of the cup to the flange as shown in Fig. 4. The numerical results of thickness variation for all three cases are shown in Fig. 5a–c. Minimum thickness of 0.869129 mm at element 2867, maximum thickness of 1.06396 mm at element 50 are observed when there is no drawbead used whereas when circular drawbead is used the minimum thickness observed is 0.742146 mm at element 5307 and the maximum thickness is 1.03982 mm at element 18. But the results of rectangular drawbead show the minimum thickness as 0.728804 mm at element 6043 which is the least and maximum thickness as 1.07602 mm at element 6063 which is the highest among the three cases considered. Numerical thickness values along the cup wall are measured from Fig. 5a–c using option available in LSPOST module and are tabulated in Table 4. 3 Experimental Work For the validation of finite element analysis, comparison with experimental finding is very important. Experimental setup was prepared and press tools were designed and manufactured in order to obtain appropriate
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14 15 13 12 11 10 9 8
1 2
3
4
5
6
7
Fig. 4 Thickness measurement locations on cup surface
Fig. 5 Thickness distribution (numerical). a Without drawbead. b With circular drawbead. c With rectangular drawbead Table 4 Comparison of thickness distribution (with circular and rectangular drawbeads placed at 65 mm from die centre)— numerical and experimental values Locations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Thickness (mm) Without drawbead Numerical Experiment
Circular drawbead Numerical Experiment
Rectangular drawbead Numerical Experiment
0.88011 0.87725 0.87133 0.87045 0.87230 0.87718 0.88368 0.90934 0.92991 0.95383 0.97298 0.98816 0.99500 1.04165 1.05276
0.77136 0.76495 0.75456 0.75001 0.74704 0.74606 0.74565 0.76048 0.77674 0.80234 0.83532 0.87119 0.98952 1.00900 1.02546
0.7534 0.7515 0.7457 0.7413 0.7385 0.7380 0.7381 0.7422 0.7514 0.7693 0.7931 0.8236 0.9085 1.0476 1.0575
0.810 0.810 0.801 0.786 0.787 0.802 0.820 0.825 0.835 0.853 0.886 0.866 0.895 0.935 1.030
0.785 0.793 0.780 0.777 0.764 0.780 0.840 0.853 0.832 0.854 0.863 0.882 0.901 1.028 1.031
0.780 0.773 0.759 0.750 0.755 0.743 0.780 0.795 0.797 0.837 0.893 0.872 0.892 1.000 1.053
experimental results. For drawing a hemispherical cup of 100 mm diameter and 50 mm height from the flat sheet blank of 1.02 mm thickness, the press tool was designed using standard press tool design procedure [17,18]. Diameter of blank was computed as 174 mm. Punch was manufactured from high carbon high chromium steel stock. Die block was made from oil hardened steel. The inner diameter of die was taken as 102.2 mm including clearance and outer diameter was taken as 250 mm to accommodate the blank. Thickness of die block was taken as 50 mm to facilitate machining of drawbeads. Based on the punch force the 100 ton hydraulic press with die cushion rod was selected. The ram speed of 10 mm/s and maximum stroke distance of 50 mm were selected for the experiment. The complete die set, which comprises of die, punch and binder, was mounted on the hydraulic press with the help of suitable fixture as shown in Fig. 6. Few numbers of hemispherical cups were formed without the presence of drawbead. The thickness distribution of formed cup were measured at selective locations as shown in Fig. 4 using dial gauge. At optimized location circular drawbead of height 3.5 mm was machined on die surface (Fig. 7) and a contra bead called the female bead was machined on the blankholder. Cups were formed (Fig. 8) and thickness measurements were taken for comparison. The same procedure was repeated with rectangular draw bead of height 3.5 mm and experiments were conducted.
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Fig. 6 Experimental setup
Fig. 7 Die with circular drawbead
Fig. 8 Formed cups without and with circular drawbead
4 Results and Discussion To obtain the effect of drawbeads in sheet metal forming few cups were drawn without the presence of drawbeads and thickness and strain were measured. Circular and rectangular drawbeads were introduced at optimized locations at die blank holder interface and experiments were repeated.
4.1 Thickness Distribution The details of the thickness measured at 15 locations are given in Table 4 for experimental and numerical studies conducted with drawbead located at 65 mm from die centre. The thickness of the cup had varied from 0.786 to 1.03 mm in the experimental specimens, whereas in numerical simulations the variation is from 0.87 to 1.05 mm. The thickness comparison graph is shown in Fig. 9.
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14 15
without drawbead circular drawbead rectangular drawbead
13 12 11 10
1.1
9 8
Thickness (mm)
6
1
4
3
1 2
7
5
0.9 0.8 0.7 0.6 1
2
3
4
5
6
7 8 9 Locations
10
11
12
13
14
15
14
15
Fig. 9 Comparison of thickness distribution (numerical)
Without drawbead
1.1 14 15
circular drawbead
13 12 11
Thickness (mm)
1
rectangular drawbead
10 9 8 6 1 2
0.9
3
4
7
5
0.8 0.7 0.6 1
2
3
4
5
6
7
8
9
10
11
12
13
Locations
Fig. 10 Comparison of thickness distribution (experimental) Circular drawbead
Rectangular drawbead Numerical Experimental
1.1 1 0.9 0.8 0.7 0.6 1
2
3
4
5
6
7
8
9
Locations
10 11 12 13 14 15
Thickness (mm)
Thickness (mm)
Numerical
Experimental
1.1 1 0.9 0.8 0.7 0.6 0
2
4
6
8
10
12
14
16
Locations
Fig. 11 Comparison of numerical and experimental thickness. a With circular drawbead. b With rectangular drawbead
Due to compressive strain the flange portion has the maximum thickness, which is even thicker than original sheet thickness. From Table 4 it is observed that there is a deviation of about only 10 % between experimental and numerical findings which shows good agreement between them. Introduction of drawbead reduces the thickness in the side and bottom portion of the cup but there is no considerable change in the flange area. From Figs. 9 and 10 the thickness reduction caused by rectangular drawbead is more compared to circular drawbead due to the reason that blank is bent and unbent four times over rectangular bead instead of three times over circular bead. Since the rectangular drawbead controls more material, the flange portion is thicker than other two cases. This is visible at the right end of the curve (locations 13 to 14) in Figs. 9 and 10. Figure 11a, b shows a comparison between the experimental and numerical results for thickness distribution along the cup wall for the cases of circular and rectangular beads. In both figures, it can be seen that the results obtained from the numerical model agree with those obtained from the experimental tests with less than 5 % discrepancy except at few locations (locations 7–10 in the case of circular drawbead and locations 7–12 in the case of rectangular drawbead) where the deviations are close to 10 %.
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Fig. 12 Plastic strain distribution (numerical). a Without drawbead. b With circular drawbead. c With rectangular drawbead Table 5 Comparison of plastic strain (numerical) Locations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Plastic strain Without drawbead
With circular drawbead
With rectangular drawbead
0.1971 0.1901 0.1910 0.1895 0.2101 0.2574 0.3063 0.3545 0.4013 0.4324 0.4354 0.4071 0.3452 0.2680 0.2146
0.3465 0.3498 0.3511 0.3509 0.3563 0.3436 0.3177 0.3601 0.3945 0.4047 0.3775 0.3010 0.2230 0.1815 0.1638
0.3681 0.3767 0.3675 0.3663 0.3437 0.3269 0.3005 0.3265 0.4083 0.4072 0.3476 0.2019 0.1155 0.0960 0.0800 without drawbead circular drawbead rectangular drawbead
Plastic strain
0.5 0.4 0.3 0.2 0.1 0 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Locations on cup surface
Fig. 13 Comparison of plastic strain distribution (numerical)
4.2 Plastic Strain Distribution The numerical simulation of distribution of plastic strain during cup formation with and without drawbeads are shown in Fig. 12. The plastic strain values are measured from Fig. 12 and tabulated in Table 5. The same values are plotted in a graphical form for better comparison in Fig. 13. The strain distribution patterns obtained during cup formation without the presence of drawbead shows that the strain distribution is constant over cup wall region whereas in the neck region the strain value increases and near flange region it comes down. The pattern of distribution of strain in cases with drawbead differs on three accounts. Firstly the presence of high strain in the apex region of the hemisphere (locations 1–5). Secondly, a marginal reduction in strain in the shoulder region of the hemisphere (locations 6–8) and thirdly reduced strain in the flange region (locations 12–15). At flange region, the strain induced due to rectangular drawbead is lower than strain induced when circular drawbead is used. This is due to the fact that the geometry of rectangular bead involves relatively sharp corners resulting in concentrated contact area over an even smaller region than
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the circular drawbead, where semi-circular cross-section contains more uniform area [8]. Moreover, the sheet undergoes two additional bends due to the geometry of the rectangular drawbead [1]. Hence, the material flow is controlled at the bead location, where the flange thickness increases and the effective strain decreases due to compressive stress. 5 Conclusion Two drawbead profiles (circular and rectangular) have been used to identify the thickness and strain distribution pattern in hemispherical cup forming using finite element analysis and experiment. For the purpose DYNAFORM and LS-DYNA have been used. The FEA outcome have good agreement with experimental outcomes. Based on the study the following observations are made: 1. Drawbead locations are crucial to their effectiveness. If the drawbead is too far from the punch opening line, then the drawbead is unable to supply sufficient restraining force to control the material. Whereas if the drawbead is too close to the punch opening line then the material is pulled over the bead easily. The simulation allows trying different locations for optimization. The drawbead located at 65 mm from centre of die cavity has been considered as an optimized location for further studies. 2. The reduction in thickness of the wall indicates that the presence of drawbead offer high restraining force or resistance to the flow of material. 3. On comparison circular drawbeads are preferred since the thickness reduction is lesser than when rectangular drawbeads are used. 4. Flange area thickening is more in the case of rectangular drawbead which is not desirable since the flange portion is generally trimmed off as a waste. References 1. Carleer, B.D.; Vreede, P.T.; Drent, P.; Louwes, M.F.M.; Huetink, J.: Modelling drawbeads with finite elements and verification. J. Mater. Process. Technol. 45, 63–68 (1994) 2. Meinders, T.; Carleer, B.D.; Geijselaers, H.J.M.; Huetink, J.: The implementation of an equivalent drawbead model in a finite-element code for sheet metal forming. J. Mater. Process. Technol. 83, 234–244 (1998) 3. Nine, H.D.: New drawbead concepts for sheetmetal forming. J. Appl. Metal Work. 2(3), 185–192 (1982) 4. Nine, H.D.: The applicability of Coulomb’s friction law to drawbeads in sheetmetal forming. J. Appl. Metal Work. 2(3), 200–210 (1982) 5. Wang, N.M.: A mathematical model of drawbead forces in sheetmetal forming. J. Appl. Metal Work. 2(3), 193–199 (1982) 6. Levy, B.S.: Development of predictive model for drawbead restraining force utilizing work of Nine and Wang. J. Appl. Metal Work. 3(1), 38–44 (1983) 7. Chen, F.; Tszeng, P.: An analysis of drawbead restraining force in stamping process. Int. J. Mach. Tools Manuf. 38, 827–842 (1998) 8. Samuel, M.: Influence of drawbead geometry on sheetmetal forming. J. Mater. Process. Technol. 122, 94–103 (2002) 9. Yellup, J.M.; Painter, M.J.: The prediction of strip shape and restraining force for shallow drawbead systems. J. Appl. Metal Work. 4(1), 30–38 (1985) 10. Keum, Y.T.; Ghoo, B.Y.; Kim, J.H.: Application of an expert drawbead model to the finite element simulation of sheet forming process. J. Mater. Process. Technol. 111, 155–158 (2001) 11. Vahdat, V.; Santhanam, S.; Chun, Y.W.: A Numerical investigation on the use of drawbeads to minimize ear formation in deep drawing. J. Mater. Process. Technol. 176, 70–76 (2006) 12. Firat, M.: An analysis of sheet drawing characteristics with drawbead elements. Comput. Mater. Sci. 41(3), 266–274 (2008) 13. Firat, M.; Livatyali, H.; Cicek, O.; Onhon, F.: Improving the accuracy of contact type drawbead elements in panel stamping analysis. Mater. Des. 30, 4003–4011 (2009) 14. Livatyali, H.; Firat, M.; Gurler, B.; Ozsoy, M.: An experimental analysis of drawing characteristics of a dual-phase steel through a round drawbead. Mater. Des. 31, 1639–1643 (2010) 15. DYNAFORM-Application Manual (2001) LSTC 16. Hallquist, J.O.: LS-DYNA-Theoretical Manual. (2001) LSTC 17. Donaldson, C.; LeCain, G.H.; Goold, V.C.: Tool Design. Tata McGraw-Hill, New Delhi (1976) 18. ASM Metals Handbook: Metalworking: Sheet Forming. 14B, pp. 191–336
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