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Numerical design optimisation of drawbead position and experimental validation of cup drawing process
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
journal homepage: www.elsevier.com/locate/jmatprotec
Numerical design optimisation of drawbead position and experimental validation of cup drawing process N. Mohamed Sheriff ∗ , M. Mohamed Ismail Syed Ammal Engineering College, Ramanathapuram 623 502, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
In sheet metal forming processes, prediction and prevention of flange and side-wall wrin-
Received 6 May 2006
kling, tearing and galling are extremely important during the design of tooling. In this paper,
Received in revised form
finite element method was used to optimise the location of a rectangular drawbead and
25 October 2007
analyze the strain and thickness variation during the cup drawing process with rectan-
Accepted 4 December 2007
gular drawbead. Modeling was done with DYNAFORM and analysis was carried out using LS-DYNA, a commercially available explicit FEA code. In simulation, a hemispherical cup of diameter 100 mm was considered and simulation studies were carried out for all the
Keywords:
possible locations of the drawbead, and location which gave minimum value of major prin-
DYNAFORM
cipal strain is taken as the optimised one. Experiments were conducted using a die block of
Drawbead
102 mm diameter and punch of 100 mm diameter on AISI 1020 steel of thickness 1.02 mm
Optimum
(19 SWG). Rectangular drawbead of a specific height was made on the binder surface at the
Sheet metal forming
optimal location and corresponding groove was machined on the die block and the forming
Wrinkling
process was executed. Strain and thickness variations were measured for the cup drawing process. For experimental strain verification, circular grid method was used. Forming Limit Diagrams were used to determine the safe limit of the sheet metal operation. The results demonstrate excellent agreements between the numerical method and experiment. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Metallic sheet under the blank holder is drawn into the deformation zone by the punch during sheet metal forming process. As a result, compressive hoop stress and thus wrinkling are developed in the sheet metal under the holder (flange wrinkling) as well as those in the side-wall because wrinkling is a phenomenon of compressive instability (Wang and Cao, 2000). The rate of metal flow into die cavity must be controlled so that a better quality is maintained for the strip and defects of wrinkling and tearing are prevented. The restraining force required to control the sheet flow is provided by either the blank holder or the drawbeads or others (Samuel, 2004). Simulation of metal forming has been earlier done using DEFORM2 (Gadala and
∗
Corresponding author. Tel.: +91 4567 226930; fax: +91 4567 227740. E-mail address: [email protected] (N.M. Sheriff). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.12.017
Wang, 1999) which were two dimensional in nature. Influence of drawbead geometry on metal forming has been studied by Samuel (2002) using the circular drawbead with square female bead. The prediction of strip shape was studied by Yellup and Painter (1985) and the importance of restraining force was elaborated. This paper focuses on the numerical analyses about a rectangular drawbead position on the die surface and its effect on the strain and thinning distribution over the formed area. Experiments were conducted to validate the numerical observations. As the metal passes through the drawbead of specified geometry, it undergoes bending deformation in a short path followed by sliding. Numerical investigations were carried out to observe the details like strain distribution, tearing and
84
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
in steps of 1 mm. A uniform gap of 0.2 mm was maintained between blank, blank holder and die surface using the AUTOPOSITION option.
3.
Fig. 1 – Numerical model for punch, blank holder, blank and die.
galling on the drawn part as well the thinning phenomenon during the metal forming using the commercial explicit software code LSDYNA. Thinning and strain behaviour of the steel sheet were recorded in the post-processor of the DYNAFORM PC which is developed for the LSDYNA solver. Experiments were carried out on a hydraulic press to get the forming of cup. The results obtained from experiment were used to validate the numerical findings.
2.
Numerical modeling of forming tools
DYNAFORM was used as simulation tool for the numerical analysis. Numerical model for punch, die, blank and blank holder are shown in Fig. 1. The punch and die were modeled using shell elements with surface mesh option. They have been assigned RIGID MATERIAL MODEL (DYNAFORM, 2001). The diameter of the punch is 100 mm. The outer diameter of the die is 250 mm and inner diameter is 102.2 with entry radius is 4 mm. Thickness of the die block is 50 mm. BELYTSCHKO TSAY type element was selected for the blank which has a diameter of 174 and 1.02 mm thickness. The blank was assigned TRANSVERSELY ANISOTROPIC ELASTIC PLASTIC MODEL (LS-DYNA, 2001) and it was made up of AISI 1020 steel for which the properties are given in Table 1. The trimmed portion of the blank was obtained using “blank trim” option in the four line mesh. The rectangular drawbead was modeled on the die surface with height of 3.5 mm and width of 6.5 mm and was positioned at a distance of 62–68 mm from the center of the die block
Table 1 – Mechanical properties of material Material Young’s modulus (GPa) Mass density (kg/m3 ) Poisson’s ratio Yield stress (MPa) Anisotropic parameter
AISI 1020 steel 207 7830 0.28 230 1
Numerical simulation
In numerical simulation, contact is necessary between the sliding bodies for the metal forming process. In this model CONTACT FORMING ONE WAY SURFACE TO SURFACE title algorithm (DYNAFORM, 2001; LS-DYNA, 2001) was used for the contact between punch, die, blank holder and blank. The blank was treated as a master surface and others were treated as slave surfaces. The static co-efficient of friction between the contact was taken as 0.14. A velocity of 10 mm/s was given to the punch in the negative (downwards) z-direction with stroke distance of 40 mm. Binder force was set as 8.5 T (Donaldson, 2001) towards negative z-direction. The flow of sheet metal blank on the drawbead during the forming operation is controlled by the bending and normal load curve definition in numerical simulation. Numerical simulations were carried out for the given punch velocity on the steel blank with thickness 1.02 mm in the mode of ADAPTIVE MESH option. Various simulations were carried out and results are obtained.
3.1.
Optimization of drawbead position
Initially at a distance of 62 mm from the center of the die surface a rectangular drawbead was created with height 3.5 mm, width 6.5 mm and entry radius 1.5 mm. Then the numerical simulation was carried out at this position and major principal strain on the blank was obtained. Same procedure was pursued to analyze drawbead at positions from 62 to 68 mm. The major principal strain values were obtained for each position and are given in Table 2. The major principal strain values were plotted based on the drawbead position and shown in Fig. 2. It is observed that the drawbead at 65 mm from die center has the minimum major principal strain value and hence this position is the optimum distance for the drawbead from the centre of the die.
3.2.
Numerical results
Numerical simulations were carried out for the conditions similar to the experiments which were performed later and
Table 2 – Major principal strain at various drawbead locations Drawbead position from die center (mm) 62 63 64 65 66 67 68
Major principal strain 0.4211 0.4397 0.4275 0.3594 0.4117 0.4114 0.4054
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
Fig. 2 – Optimised position of drawbead.
Table 3 – Numerical values—cup thickness, major and minor strain for drawbead at optimised position Location
Cup thickness
Strain Major strain in %
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.771 0.765 0.755 0.750 0.747 0.746 0.749 0.760 0.802 0.835 0.871 0.955 0.989 0.999 1.010 1.025
20.18 18.34 18.87 20.70 22.40 25.39 25.56 29.02 27.62 22.61 13.43 15.81 9.49 11.93 6.42 1.24
Minor strain in % 18.08 17.62 17.33 17.84 18.00 16.73 14.92 11.62 7.98 3.68 −0.59 0 −4.07 −0.92 −2.76 −3.20
deformation pattern, thickness distribution and strain plot were obtained. The CIRCULAR GRID ANALYSIS (CGA) facility available in the DYNAFORM Post GL software has been utilized to get the strain distribution on the formed blank during the numerical analysis. The major principal strain and thickness variation at different position of drawbead were obtained and shown in Figs. 3(a–g) and 4(a–g). The thickness of the drawn cup was noted in the postprocessor of the DYNAFORM and the measurement was carried out in the direction starting from the centre of the cup and moving outwardly towards the edge. Totally sixteen points were fixed and the readings are noted at these locations. Strain and thickness values were obtained from the numerical analysis for the drawbead and are given in Table 3.
4.
Experiments
The experiments were carried out using the single action hydraulic press with capacity of 100 T. The arrangement of the tool and die for the experiment is shown in Fig. 5.
The RAM speed of the press is 10 mm/s in pressing and 135 mm/s in return stroke. The size of the table and RAM plate is 800 mm × 800 mm. The RAM plate had the maximum stroke distance of 150 mm. The maximum working pressure of the press was 163 kg/cm2 with motor capacity of 20 HP. To make a hemispherical cup of 100 mm diameter and 40 mm height from a flat sheet of 1.02 mm thickness, the requisite elements like punch, die, blankholder, and fixture devices were designed and fabricated to suit the press specification. The drawing force required to convert the blank of diameter 174 mm with thickness of 1.02 mm into a hemispherical shape of cup is 8.5 T (Donaldson, 2001). Additional force of 20–40% has been added to take into account the drastic change in the shape. As the press had the capacity of 100 t, it was selected for the experimental studies. The punch was made from high carbon high chromium steel and was given a radius of 50 mm. The die block was made from oil hardening steel. The outer and inner diameter of the die block was taken as 250 and 102.2 mm, respectively, and the entry radius of 4 mm to the block was provided. Thickness of the die block was taken sufficiently higher (40 mm) to facilitate machining of the drawbead. The rectangular drawbead was made on the top surface of the die as shown in Fig. 6. The geometrical details of the rectangular drawbead are shown in Fig. 7. To analyse the strain pattern obtained from the forming operation, a circular grid method was employed. Arrays of contacting circles with diameter of 5 mm were printed on the steel blank by using screen printing method. Then the blank was etched by electro-chemical etching process (shown in Fig. 8). After deformation, the circles were deformed into ellipse. The direction of the strain is indicated by the major and minor axis of the ellipse. The etched blank before forming is shown in Fig. 9. The required circular geometry was cut from a rectangular sheet.
Table 4 – Experimental values—cup thickness, major and minor strain for drawbead at optimised position Location
Cup thickness
Strain Major strain in %
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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 1.049
25.00 24.00 21.60 25.00 25.00 26.66 31.66 36.66 35.00 30.00 26.66 25.00 18.33 20.00 25.00 18.33
Minor strain in % 20.00 18.33 20.00 16.66 16.66 20.00 15.00 13.33 10.00 8.33 5.00 3.33 −1.66 −1.67 −6.67 −8.33
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Fig. 3 – Major principal strain: (a) bead positioned 62 mm from die center; (b) bead positioned 63 mm from die center; (c) bead positioned 64 mm from die center; (d) bead positioned 66 mm from die center; (e) bead positioned 67 mm from die center; (f) bead positioned 68 mm from die center; (g) bead positioned 65 mm from die center.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
87
Fig. 4 – Cup thickness variation: (a) bead positioned 62 mm from die center; (b) bead positioned 63 mm from die center; (c) bead positioned 64 mm from die center; (d) bead positioned 66 mm from die center; (e) bead positioned 67 mm from die center; (f) bead positioned 68 mm from die center; (g) bead positioned 65 mm from die center.
88
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
Fig. 8 – Blank preparation—electro chemical etching process.
Fig. 5 – Experimental set-up with punch and die.
Fig. 6 – Schematic of drawbead on the die. Fig. 9 – Etched blank. Numbers of experiments were carried out in the set up, in the presence of drawbead. Displacement of specific points on the fixed locations of formed cup was measured using a dial gauge attached fixture which is shown in Fig. 10(b). The dial gauge pointer is set at zero position, when the dial gauge stem edge and fixture stem edge are touching with each other. The cup was placed between both edges, the dial gauge pointer indicate the direct reading of cup thickness. Before taking the readings, the cup was marked 16 locations of equal division of 5 mm gap along three directions on the cup surface. The deformation readings were taken along three directions and average values were used for analysis. The strain values were recorded using Mylar tapes and the thickness and strain values were given in Table 4. In
Fig. 7 – Geometrical details of the drawbead.
order to measure the displacement of same points on the profile before and after forming operation, Coordinate measuring machine (Make MTAB, model 112-202) was employed and readings observed were compared and shown in Table 5. It is observed that the deviation is in line with the numerical predictions.
5.
Comparison of results
The formed hemispherical cup from the experiment is compared with the numerical prediction obtained from LS-DYNA. The grid pattern obtained from numerical simulation is shown in Fig. 11 and the etched pattern obtained from experiment is shown in Fig. 12. The outcome of the experimental geometry is in good agreement with the numerical prediction. The details of the thickness measured at 16 locations are given in Table 5 for experiment and numerical studies. The original thickness of 1.02 mm had varied because of cup drawing process from 0.74 to 1.05 mm in experimental specimens. The increase in thickness is observed in the flange area and the maximum reduction of thickness is observed at the centre of the punch. During numerical simulations, the predicted
89
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
Table 5 – Comparison of displacement at different places—experimental and numerical values Location
Blank thickness (mm) Before forming
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1.021 1.018 1.018 1.016 1.019 1.020 1.015 1.010 0.997 0.989 0.952 1.016 1.020 1.018 1.020 1.019
Displacement (%)
After forming Numerical
Experimental
0.771 0.765 0.755 0.750 0.747 0.746 0.749 0.760 0.802 0.835 0.871 0.955 0.989 0.999 1.010 1.025
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 1.049
Numerical
Experimental
24.486 24.853 25.835 26.181 26.693 26.863 26.207 24.752 19.559 15.571 8.508 6.004 3.039 1.866 0.980 −0.589
23.604 24.067 25.442 26.181 25.908 27.157 23.153 21.287 20.060 15.369 6.197 14.173 12.549 1.768 −3.235 −2.944
variation of thickness is between 0.74 and 1.03 mm, which is in close agreement with experimental results. The thickness variation graph was plotted for numerical and experimental values are shown in Fig. 13. It is found that the experiment as well as numerical findings, the percentage of error in cup thickness variation is less than 11%. The obtained major and minor strain values for both simulation and experimental work are given in Tables 3 and 4 respectively. It results a good correlation between the experimental and numerical results (Table 6).
Fig. 11 – Numerical-cup formed with drawbead using CGA pattern.
Fig. 10 – (a) Displacement measurement of the drawn cup using Dial gauge setup, (b). Measurement of deformation at various points along the profile using coordinate measuring machine (CMM).
Fig. 12 – Experimental-cup formed with drawbead using circular grid method.
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
Forming limit diagram (FLD) is a good representation of the stretchability of the sheet metal being drawn. Since anisotropic material is taken for analysis, Hollomon power law hardening parameters such as hardening exponent (n), anisotropic parameter (r) are taken as 0.23 and 1.73, respectively. The forming limit diagram obtained using the maximum principal strain values from numerical analyses is shown in Fig. 14. It is notices that the crack zone is not predicted and even the risk of crack zone is less than 3% of the total area of the blank. From experiments also it is confirmed that among thirty specimens made, none of the specimen had shown the initiation of crack at the formed zone. It is also observed that the experimental as well as numerical values fall in the safe region of the forming limit diagram.
Fig. 13 – Variation of thickness—numerical and experimental.
6. Table 6 – Percentage of error on thickness values (experimental vs. numerical) drawbead at optimised position Location
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Cup thickness in mm (with drawbead) Experimental
Numerical
Difference
% of error
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 1.049
0.771 0.765 0.755 0.750 0.747 0.746 0.749 0.760 0.802 0.835 0.871 0.955 0.989 0.999 1.010 1.025
0.009 0.008 0.004 0 0.008 0.003 0.031 0.035 0.005 0.002 0.022 0.083 0.097 0.001 0.043 0.024
1.154 1.035 0.527 0 1.059 0.404 3.974 4.403 0.627 0.239 2.464 9.518 10.874 0.100 4.084 2.288
Conclusions
The location of the rectangular drawbead has been optimised numerically by carrying out requisite analysis using DYNAFORM software. The forming parameters like thinning, strain distribution and wrinkle pattern on the surface of the drawn part were numerically simulated. Experiments were carried out to get the parameters for the drawbead located at optimum distance from the die centre. The parameters such as thinning and strain values were measured using circular grid pattern method and these details were used to validate the numerical findings. It is observed that the numerical results on thinning phenomenon are very close to the experimental observation. The strain values observed during experiments compare well with the numerical values. The forming limit curves which is one of the method in examining the failure potential and a good representation of material’s stretchability is made used to verify the safe limit for the cup drawing process. Thus the numerical procedure could be used to enhance the effectiveness of the metal forming procedure to reduce the developmental lead time to a minimum.
Fig. 14 – Forming limit diagram obtained using numerical simulation.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
references
Donaldson, 1976. Tool Design. Tata McGraw Hill Publication, New Delhi. DYNAFORM, 2001. Application Manual and Theoretical Manual LSTC. Gadala, M.S., Wang, J., 1999. Simulation of metal forming processes with finite element methods. Int. J. Numer. Methods Eng. 44, 1397–1428. LS-DYNA, 2001. User Manual and Theoretical Manual, LSTC.
91
Samuel, M., 2002. Influence of Drawbead geometry on sheet metal forming. J. Mater. Process. Technol. 122, 94–103. Samuel, M., 2004. Numerical and experimental investigations of forming limit diagrams in metal sheets. J. Mater. Process. Technol., 424–431. Wang, X, Cao, J., 2000. On the prediction of side-wall wrinkling in sheet metal forming processes. Int. J. Mech. Sci. 42, 2369– 2394. Yellup, J.M., Painter, 1985. The prediction of strip shape and restraining force for shallow drawbead. J. Appl. Met. Work 4, 30–38.
journal homepage: www.elsevier.com/locate/jmatprotec
Numerical design optimisation of drawbead position and experimental validation of cup drawing process N. Mohamed Sheriff ∗ , M. Mohamed Ismail Syed Ammal Engineering College, Ramanathapuram 623 502, India
a r t i c l e
i n f o
a b s t r a c t
Article history:
In sheet metal forming processes, prediction and prevention of flange and side-wall wrin-
Received 6 May 2006
kling, tearing and galling are extremely important during the design of tooling. In this paper,
Received in revised form
finite element method was used to optimise the location of a rectangular drawbead and
25 October 2007
analyze the strain and thickness variation during the cup drawing process with rectan-
Accepted 4 December 2007
gular drawbead. Modeling was done with DYNAFORM and analysis was carried out using LS-DYNA, a commercially available explicit FEA code. In simulation, a hemispherical cup of diameter 100 mm was considered and simulation studies were carried out for all the
Keywords:
possible locations of the drawbead, and location which gave minimum value of major prin-
DYNAFORM
cipal strain is taken as the optimised one. Experiments were conducted using a die block of
Drawbead
102 mm diameter and punch of 100 mm diameter on AISI 1020 steel of thickness 1.02 mm
Optimum
(19 SWG). Rectangular drawbead of a specific height was made on the binder surface at the
Sheet metal forming
optimal location and corresponding groove was machined on the die block and the forming
Wrinkling
process was executed. Strain and thickness variations were measured for the cup drawing process. For experimental strain verification, circular grid method was used. Forming Limit Diagrams were used to determine the safe limit of the sheet metal operation. The results demonstrate excellent agreements between the numerical method and experiment. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Metallic sheet under the blank holder is drawn into the deformation zone by the punch during sheet metal forming process. As a result, compressive hoop stress and thus wrinkling are developed in the sheet metal under the holder (flange wrinkling) as well as those in the side-wall because wrinkling is a phenomenon of compressive instability (Wang and Cao, 2000). The rate of metal flow into die cavity must be controlled so that a better quality is maintained for the strip and defects of wrinkling and tearing are prevented. The restraining force required to control the sheet flow is provided by either the blank holder or the drawbeads or others (Samuel, 2004). Simulation of metal forming has been earlier done using DEFORM2 (Gadala and
∗
Corresponding author. Tel.: +91 4567 226930; fax: +91 4567 227740. E-mail address: [email protected] (N.M. Sheriff). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.12.017
Wang, 1999) which were two dimensional in nature. Influence of drawbead geometry on metal forming has been studied by Samuel (2002) using the circular drawbead with square female bead. The prediction of strip shape was studied by Yellup and Painter (1985) and the importance of restraining force was elaborated. This paper focuses on the numerical analyses about a rectangular drawbead position on the die surface and its effect on the strain and thinning distribution over the formed area. Experiments were conducted to validate the numerical observations. As the metal passes through the drawbead of specified geometry, it undergoes bending deformation in a short path followed by sliding. Numerical investigations were carried out to observe the details like strain distribution, tearing and
84
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
in steps of 1 mm. A uniform gap of 0.2 mm was maintained between blank, blank holder and die surface using the AUTOPOSITION option.
3.
Fig. 1 – Numerical model for punch, blank holder, blank and die.
galling on the drawn part as well the thinning phenomenon during the metal forming using the commercial explicit software code LSDYNA. Thinning and strain behaviour of the steel sheet were recorded in the post-processor of the DYNAFORM PC which is developed for the LSDYNA solver. Experiments were carried out on a hydraulic press to get the forming of cup. The results obtained from experiment were used to validate the numerical findings.
2.
Numerical modeling of forming tools
DYNAFORM was used as simulation tool for the numerical analysis. Numerical model for punch, die, blank and blank holder are shown in Fig. 1. The punch and die were modeled using shell elements with surface mesh option. They have been assigned RIGID MATERIAL MODEL (DYNAFORM, 2001). The diameter of the punch is 100 mm. The outer diameter of the die is 250 mm and inner diameter is 102.2 with entry radius is 4 mm. Thickness of the die block is 50 mm. BELYTSCHKO TSAY type element was selected for the blank which has a diameter of 174 and 1.02 mm thickness. The blank was assigned TRANSVERSELY ANISOTROPIC ELASTIC PLASTIC MODEL (LS-DYNA, 2001) and it was made up of AISI 1020 steel for which the properties are given in Table 1. The trimmed portion of the blank was obtained using “blank trim” option in the four line mesh. The rectangular drawbead was modeled on the die surface with height of 3.5 mm and width of 6.5 mm and was positioned at a distance of 62–68 mm from the center of the die block
Table 1 – Mechanical properties of material Material Young’s modulus (GPa) Mass density (kg/m3 ) Poisson’s ratio Yield stress (MPa) Anisotropic parameter
AISI 1020 steel 207 7830 0.28 230 1
Numerical simulation
In numerical simulation, contact is necessary between the sliding bodies for the metal forming process. In this model CONTACT FORMING ONE WAY SURFACE TO SURFACE title algorithm (DYNAFORM, 2001; LS-DYNA, 2001) was used for the contact between punch, die, blank holder and blank. The blank was treated as a master surface and others were treated as slave surfaces. The static co-efficient of friction between the contact was taken as 0.14. A velocity of 10 mm/s was given to the punch in the negative (downwards) z-direction with stroke distance of 40 mm. Binder force was set as 8.5 T (Donaldson, 2001) towards negative z-direction. The flow of sheet metal blank on the drawbead during the forming operation is controlled by the bending and normal load curve definition in numerical simulation. Numerical simulations were carried out for the given punch velocity on the steel blank with thickness 1.02 mm in the mode of ADAPTIVE MESH option. Various simulations were carried out and results are obtained.
3.1.
Optimization of drawbead position
Initially at a distance of 62 mm from the center of the die surface a rectangular drawbead was created with height 3.5 mm, width 6.5 mm and entry radius 1.5 mm. Then the numerical simulation was carried out at this position and major principal strain on the blank was obtained. Same procedure was pursued to analyze drawbead at positions from 62 to 68 mm. The major principal strain values were obtained for each position and are given in Table 2. The major principal strain values were plotted based on the drawbead position and shown in Fig. 2. It is observed that the drawbead at 65 mm from die center has the minimum major principal strain value and hence this position is the optimum distance for the drawbead from the centre of the die.
3.2.
Numerical results
Numerical simulations were carried out for the conditions similar to the experiments which were performed later and
Table 2 – Major principal strain at various drawbead locations Drawbead position from die center (mm) 62 63 64 65 66 67 68
Major principal strain 0.4211 0.4397 0.4275 0.3594 0.4117 0.4114 0.4054
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 83–91
Fig. 2 – Optimised position of drawbead.
Table 3 – Numerical values—cup thickness, major and minor strain for drawbead at optimised position Location
Cup thickness
Strain Major strain in %
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.771 0.765 0.755 0.750 0.747 0.746 0.749 0.760 0.802 0.835 0.871 0.955 0.989 0.999 1.010 1.025
20.18 18.34 18.87 20.70 22.40 25.39 25.56 29.02 27.62 22.61 13.43 15.81 9.49 11.93 6.42 1.24
Minor strain in % 18.08 17.62 17.33 17.84 18.00 16.73 14.92 11.62 7.98 3.68 −0.59 0 −4.07 −0.92 −2.76 −3.20
deformation pattern, thickness distribution and strain plot were obtained. The CIRCULAR GRID ANALYSIS (CGA) facility available in the DYNAFORM Post GL software has been utilized to get the strain distribution on the formed blank during the numerical analysis. The major principal strain and thickness variation at different position of drawbead were obtained and shown in Figs. 3(a–g) and 4(a–g). The thickness of the drawn cup was noted in the postprocessor of the DYNAFORM and the measurement was carried out in the direction starting from the centre of the cup and moving outwardly towards the edge. Totally sixteen points were fixed and the readings are noted at these locations. Strain and thickness values were obtained from the numerical analysis for the drawbead and are given in Table 3.
4.
Experiments
The experiments were carried out using the single action hydraulic press with capacity of 100 T. The arrangement of the tool and die for the experiment is shown in Fig. 5.
The RAM speed of the press is 10 mm/s in pressing and 135 mm/s in return stroke. The size of the table and RAM plate is 800 mm × 800 mm. The RAM plate had the maximum stroke distance of 150 mm. The maximum working pressure of the press was 163 kg/cm2 with motor capacity of 20 HP. To make a hemispherical cup of 100 mm diameter and 40 mm height from a flat sheet of 1.02 mm thickness, the requisite elements like punch, die, blankholder, and fixture devices were designed and fabricated to suit the press specification. The drawing force required to convert the blank of diameter 174 mm with thickness of 1.02 mm into a hemispherical shape of cup is 8.5 T (Donaldson, 2001). Additional force of 20–40% has been added to take into account the drastic change in the shape. As the press had the capacity of 100 t, it was selected for the experimental studies. The punch was made from high carbon high chromium steel and was given a radius of 50 mm. The die block was made from oil hardening steel. The outer and inner diameter of the die block was taken as 250 and 102.2 mm, respectively, and the entry radius of 4 mm to the block was provided. Thickness of the die block was taken sufficiently higher (40 mm) to facilitate machining of the drawbead. The rectangular drawbead was made on the top surface of the die as shown in Fig. 6. The geometrical details of the rectangular drawbead are shown in Fig. 7. To analyse the strain pattern obtained from the forming operation, a circular grid method was employed. Arrays of contacting circles with diameter of 5 mm were printed on the steel blank by using screen printing method. Then the blank was etched by electro-chemical etching process (shown in Fig. 8). After deformation, the circles were deformed into ellipse. The direction of the strain is indicated by the major and minor axis of the ellipse. The etched blank before forming is shown in Fig. 9. The required circular geometry was cut from a rectangular sheet.
Table 4 – Experimental values—cup thickness, major and minor strain for drawbead at optimised position Location
Cup thickness
Strain Major strain in %
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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 1.049
25.00 24.00 21.60 25.00 25.00 26.66 31.66 36.66 35.00 30.00 26.66 25.00 18.33 20.00 25.00 18.33
Minor strain in % 20.00 18.33 20.00 16.66 16.66 20.00 15.00 13.33 10.00 8.33 5.00 3.33 −1.66 −1.67 −6.67 −8.33
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Fig. 3 – Major principal strain: (a) bead positioned 62 mm from die center; (b) bead positioned 63 mm from die center; (c) bead positioned 64 mm from die center; (d) bead positioned 66 mm from die center; (e) bead positioned 67 mm from die center; (f) bead positioned 68 mm from die center; (g) bead positioned 65 mm from die center.
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Fig. 4 – Cup thickness variation: (a) bead positioned 62 mm from die center; (b) bead positioned 63 mm from die center; (c) bead positioned 64 mm from die center; (d) bead positioned 66 mm from die center; (e) bead positioned 67 mm from die center; (f) bead positioned 68 mm from die center; (g) bead positioned 65 mm from die center.
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Fig. 8 – Blank preparation—electro chemical etching process.
Fig. 5 – Experimental set-up with punch and die.
Fig. 6 – Schematic of drawbead on the die. Fig. 9 – Etched blank. Numbers of experiments were carried out in the set up, in the presence of drawbead. Displacement of specific points on the fixed locations of formed cup was measured using a dial gauge attached fixture which is shown in Fig. 10(b). The dial gauge pointer is set at zero position, when the dial gauge stem edge and fixture stem edge are touching with each other. The cup was placed between both edges, the dial gauge pointer indicate the direct reading of cup thickness. Before taking the readings, the cup was marked 16 locations of equal division of 5 mm gap along three directions on the cup surface. The deformation readings were taken along three directions and average values were used for analysis. The strain values were recorded using Mylar tapes and the thickness and strain values were given in Table 4. In
Fig. 7 – Geometrical details of the drawbead.
order to measure the displacement of same points on the profile before and after forming operation, Coordinate measuring machine (Make MTAB, model 112-202) was employed and readings observed were compared and shown in Table 5. It is observed that the deviation is in line with the numerical predictions.
5.
Comparison of results
The formed hemispherical cup from the experiment is compared with the numerical prediction obtained from LS-DYNA. The grid pattern obtained from numerical simulation is shown in Fig. 11 and the etched pattern obtained from experiment is shown in Fig. 12. The outcome of the experimental geometry is in good agreement with the numerical prediction. The details of the thickness measured at 16 locations are given in Table 5 for experiment and numerical studies. The original thickness of 1.02 mm had varied because of cup drawing process from 0.74 to 1.05 mm in experimental specimens. The increase in thickness is observed in the flange area and the maximum reduction of thickness is observed at the centre of the punch. During numerical simulations, the predicted
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Table 5 – Comparison of displacement at different places—experimental and numerical values Location
Blank thickness (mm) Before forming
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1.021 1.018 1.018 1.016 1.019 1.020 1.015 1.010 0.997 0.989 0.952 1.016 1.020 1.018 1.020 1.019
Displacement (%)
After forming Numerical
Experimental
0.771 0.765 0.755 0.750 0.747 0.746 0.749 0.760 0.802 0.835 0.871 0.955 0.989 0.999 1.010 1.025
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 1.049
Numerical
Experimental
24.486 24.853 25.835 26.181 26.693 26.863 26.207 24.752 19.559 15.571 8.508 6.004 3.039 1.866 0.980 −0.589
23.604 24.067 25.442 26.181 25.908 27.157 23.153 21.287 20.060 15.369 6.197 14.173 12.549 1.768 −3.235 −2.944
variation of thickness is between 0.74 and 1.03 mm, which is in close agreement with experimental results. The thickness variation graph was plotted for numerical and experimental values are shown in Fig. 13. It is found that the experiment as well as numerical findings, the percentage of error in cup thickness variation is less than 11%. The obtained major and minor strain values for both simulation and experimental work are given in Tables 3 and 4 respectively. It results a good correlation between the experimental and numerical results (Table 6).
Fig. 11 – Numerical-cup formed with drawbead using CGA pattern.
Fig. 10 – (a) Displacement measurement of the drawn cup using Dial gauge setup, (b). Measurement of deformation at various points along the profile using coordinate measuring machine (CMM).
Fig. 12 – Experimental-cup formed with drawbead using circular grid method.
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Forming limit diagram (FLD) is a good representation of the stretchability of the sheet metal being drawn. Since anisotropic material is taken for analysis, Hollomon power law hardening parameters such as hardening exponent (n), anisotropic parameter (r) are taken as 0.23 and 1.73, respectively. The forming limit diagram obtained using the maximum principal strain values from numerical analyses is shown in Fig. 14. It is notices that the crack zone is not predicted and even the risk of crack zone is less than 3% of the total area of the blank. From experiments also it is confirmed that among thirty specimens made, none of the specimen had shown the initiation of crack at the formed zone. It is also observed that the experimental as well as numerical values fall in the safe region of the forming limit diagram.
Fig. 13 – Variation of thickness—numerical and experimental.
6. Table 6 – Percentage of error on thickness values (experimental vs. numerical) drawbead at optimised position Location
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Cup thickness in mm (with drawbead) Experimental
Numerical
Difference
% of error
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 1.049
0.771 0.765 0.755 0.750 0.747 0.746 0.749 0.760 0.802 0.835 0.871 0.955 0.989 0.999 1.010 1.025
0.009 0.008 0.004 0 0.008 0.003 0.031 0.035 0.005 0.002 0.022 0.083 0.097 0.001 0.043 0.024
1.154 1.035 0.527 0 1.059 0.404 3.974 4.403 0.627 0.239 2.464 9.518 10.874 0.100 4.084 2.288
Conclusions
The location of the rectangular drawbead has been optimised numerically by carrying out requisite analysis using DYNAFORM software. The forming parameters like thinning, strain distribution and wrinkle pattern on the surface of the drawn part were numerically simulated. Experiments were carried out to get the parameters for the drawbead located at optimum distance from the die centre. The parameters such as thinning and strain values were measured using circular grid pattern method and these details were used to validate the numerical findings. It is observed that the numerical results on thinning phenomenon are very close to the experimental observation. The strain values observed during experiments compare well with the numerical values. The forming limit curves which is one of the method in examining the failure potential and a good representation of material’s stretchability is made used to verify the safe limit for the cup drawing process. Thus the numerical procedure could be used to enhance the effectiveness of the metal forming procedure to reduce the developmental lead time to a minimum.
Fig. 14 – Forming limit diagram obtained using numerical simulation.
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references
Donaldson, 1976. Tool Design. Tata McGraw Hill Publication, New Delhi. DYNAFORM, 2001. Application Manual and Theoretical Manual LSTC. Gadala, M.S., Wang, J., 1999. Simulation of metal forming processes with finite element methods. Int. J. Numer. Methods Eng. 44, 1397–1428. LS-DYNA, 2001. User Manual and Theoretical Manual, LSTC.
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Samuel, M., 2002. Influence of Drawbead geometry on sheet metal forming. J. Mater. Process. Technol. 122, 94–103. Samuel, M., 2004. Numerical and experimental investigations of forming limit diagrams in metal sheets. J. Mater. Process. Technol., 424–431. Wang, X, Cao, J., 2000. On the prediction of side-wall wrinkling in sheet metal forming processes. Int. J. Mech. Sci. 42, 2369– 2394. Yellup, J.M., Painter, 1985. The prediction of strip shape and restraining force for shallow drawbead. J. Appl. Met. Work 4, 30–38.