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Hydromechanical deep drawing of cups with stepped geometries
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 2 ( 2 0 0 8 ) 246–254
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Hydromechanical deep drawing of cups with stepped geometries T. Khandeparkar ∗ , M. Liewald ¨ Umformtechnik, Holzgartenstraße 17, Universitat ¨ Stuttgart, 70174 Stuttgart, Germany Institut fur
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper deals with the hydromechanical deep drawing of metal cups with complex
Received 7 August 2006
stepped geometries. Two materials, a low-carbon steel (DC04) and stainless steel (DIN
Received in revised form
1.4301), have been researched. A die set with a maximum possible deep drawing ratio
28 July 2007
ˇ0,max = 3.0 for a punch diameter ∅ 100 mm has been designed and constructed. The die set
Accepted 22 August 2007
is designed to withstand fluid counter pressures up to 200 MPa. Pressure control is achieved using a micro-metering pressure control valve. The process is initially simulated using the FEM solver LS-DYNA. Experiments have been conducted with two punch geometries. The
Keywords:
punch geometries consist of cylindrical and conical wall segments. Complex positive and
Hydromechanical deep drawing
negative features are manufactured in the punch bottom face. The ability of transferring
Pressure
complex features from the punch onto the blank surface with high deep drawing ratios is
Geometry
investigated. Extended limiting deep drawing ratios of ˇ0,max = 3.0 for DC04 and ˇ0,max = 2.875
FEM
for DIN 1.4301 have been achieved. © 2007 Elsevier B.V. All rights reserved.
Cup
1.
Introduction
Hydromechanical deep drawing is defined as a manufacturing process in which a metal sheet or a hollow body is drawn over a die using an inelastic punch into a fluid pressure medium. The lower die set in a hydromechanical deep drawing process consists of a drawing ring mounted on a pressure chamber. The pressure chamber is filled with a hydraulic fluid. The blank is deformed by the mechanical pressing action of the punch into the pressure chamber. The punch penetration into the hydraulic medium generates a pressure increase due to fluid compression that is controlled using a pressure control valve. The blank being drawn is pressed firmly onto the punch due to pressure build-up. This increases friction between the punch and blank and hence higher forces as compared to that in conventional deep drawing can be transferred to the deformation zone. The metal undergoing hydromechanical deep drawing thus fractures at a much higher stress value than
∗
in the conventional case. This results in a higher deep drawing ratio per drawing stroke and hence higher depths of draw. Hydromechanical deep drawing is thus a cost-effective solution to manufacture metal cups with high drawing ratios in a single drawing stroke (Rolla, 1987). The hydraulic medium wraps the metal blank around the punch and hence it is possible to emboss complex contours from the punch on to the blank. Due to the fluid cushion developed by the hydraulic counter pressure, the blank does not contact the drawing die radius. The outer surface quality of a part formed by hydromechanical deep drawing is thus better than in conventional deep drawing. The wall thickness is also uniform over the depth of draw as a result of the increased friction between punch and blank wall. The counter pressure curve plays an important role aiming to achieve a good deep drawn part. A very high counter pressure at the beginning of the process leads to bulge formation and resulting fracture in the unsupported blank between
Corresponding author. Tel.: +49 71168583827; fax: +49 71168583839. E-mail address: [email protected] (T. Khandeparkar). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.08.072
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punch and blank holder. Low pressure, on the other hand, leads to blank fracture at the punch radius due to lower force transmission to the deforming region of the blank. There is a possibility of fluid leakage through the gap between the blank flange and drawing ring shoulder, resulting in poor counter pressure control. Several researchers have attempted to increase the limiting drawing ratio ˇ0,max of complex deep ¨ drawn components. Burk (1967) used a sealing ring between the blank flange and drawing ring shoulder to prevent fluid leakage. Bensmann (1979) developed a wave-shaped die shoulder profile to ensure fluid sealing. Spacek et al. (1982) proposed a wave-shaped drawing ring shoulder and blank holder of a synthetic material which also allows parts to be drawn ¨ without a flange. The flexforming process (Stromblad, 1970; Johannisson, 2001) developed by Avure Technologies, Sweden, uses a flexible rubber membrane to separate the pressurized fluid medium from the blank. Fluid forming pressures up to 100 MPa have been reported using this process. The radial fluid pressure assisted counter pressure deep drawing method developed by Nakamura and Nakagawa (1987) utilizes a fluid bypass from the counter pressure chamber to the drawing ring shoulder in order to push the blank flange radially inwards in the direction of the punch. The fluid pressure applied radially on the flange edge reduces the radial stress and prevents premature rupture, thus ensuring higher limiting drawing ratios. Tirosh et al. (2000) discussed a variation of the radial fluid pressure assisted counter pressure deep drawing process by heating the blank in the flange region with the aim of increasing the material strain rate sensitivity and thereby achieving an “unlimited drawing ratio”. The hydromechanical deep drawing process has been extensively researched to produce metal hollow bodies with complex geometries. Zhang et al. (2000a,b) investigated the feasibility of drawing aluminum parabolic geometries. The possibility of deep drawing tapered rectangular boxes was tried numerically and experimentally (Zhang et al., 2000a,b; Lang et al., 2005). Wu et al. (2004) studied the forming limits of metal cups with stepped geometries using a numerical approach. Wan et al. (2001) used a theoretical approach to determine the fracture criteria and the limiting drawing ratio (LDR) for conventional deep drawing of conical cups.
In the present work, the modified hydromechanical deep drawing method patented by Siegert and Ziegler (1998) is used. This method uses a controllable sealing mechanism between the blank and drawing ring shoulder. A bulge forms in the unsupported blank region between the punch and drawing die radius during the hydromechanical deep drawing of con¨ ical parts (Siegert and Losch, 1999). High counter pressures result in fracture due to bulge rupture. In the present die set (Aust, 2001), a closed support pressure chamber formed by the punch, blank holder and the unsupported upper blank face is pressurized with a support pressure pst , thus optimizing the bulge height. This reduces the possibility of blank rupture due to bulging.
2.
Theoretical analysis
The critical radial stress in a conventional deep drawing operation r,conv. occurs at the punch radius at which the material is strain-hardened due to bending and unbending (Lange, 1985). The total tensile stress at the punch radius is the sum of the forming stress, frictional stress due to the blank holder, stress addition due to bending and unbending of the blank and friction at the drawing ring radius (Panknin, 1961; Marciniak and Duncan, 1992). The radial stress for conventional deep drawing is written as r,conv. =
1.10 ln
D0 2FBH db + db db t0 D
e +
t0 0 2rd + t0
(1)
D0 and t0 are the initial diameter and thickness of the blank, db the base diameter of a conical punch and rd is the drawing die radius. stands for the frictional coefficient due to Coulomb at the blank flange/drawing ring shoulder and blank flange/blank holder interface, 0 the flow stress of the blank material and is the semi-cone angle subtended by the blank at the tangent to the punch radius as shown in Fig. 1a. The blank holder force FBH acts over the entire blank flange in contact with the blank holder, i.e. from the outer blank diameter D0 to the inner blank holder diameter dBHi . FBH =
2 (D − d2BHi )pBH 4 0
(2a)
Fig. 1 – Conventional deep drawing of a conical component (a) and hydromechanical deep drawing of a conical component using support pressure pst (b).
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where pBH is the blank holder pressure defined by Siebel.
3
pBH = 0.002· · ·0.003 (ˇ0 − 1) +
punch and thus increases the load carrying capacity of the blank. The fracture criterion is modified to FBr,hyd. .
0.5db u = 0 100t0
(2b) FBr,hyd. = db t0 u aR +
ˇ0 = D0 /db is defined as the drawing ratio. u is the ultimate tensile strength of a blank. Eq. (1) can be written in terms of the initial drawing ratio ˇ0 , the instantaneous drawing ratio ˇ = D/db and a geometry constant C = dBHi /db .
r,conv. =
d 1.1 ln ˇ0 + b 2t0
ˇ02 − C2
e
ˇ
t0 + 2rd + t0
0 (3)
During the drawing process, the thickness strain distribution and strain hardening vary throughout the flange and hence the flow stress is not constant. Also, the subtended semi-cone angle tends to the physical punch semi-cone angle ˛ with increasing draw depth. To account for such dynamic factors, an additional term qf is added to the relation for punch force. The maximum punch force that can be successfully transferred to the blank deformation zone Fp,max,conv. determines the limiting drawing ratio ˇ0,max for the deep drawn part. Fp,max,conv. = db t0 qf r,max,conv.
= db t0 qf
+
d 1.1 ln ˇ0 + b 2t0
t0 (2rd + t0 )
0 sin
ˇ02 − C2 ˇ
e
(4)
The punch force is thus a function of the drawing ratio ˇ0 , the punch base diameter db , friction coefficient , factor for strain hardening qf and the drawing die radius rd in addition to other factors. Fp,max,conv. = f (ˇ0 , db , rd , t0 , qf , , , pBH , 0 )
= db t0 u aR,mod.
aR,mod. = aR +
aR = e(n−ϕn )
ϕ + ϕ n t n n
hk cos ˛
d + h tan ˛ b k db t0 u
p,Bl pg > aR
(7b)
The unsupported blank in the drawing ring clearance is lifted by the fluid pressure during hydromechanical deep drawing process, thus forming a bulge in the direction opposite to the drawing direction. The blank thus moves over a fluid cushion and is not bent over the die radius as in the case of conventional deep drawing. Bending forces over the drawing die radius and frictional forces due to bending over the drawing die radius are thus absent in hydromechanical deep drawing. Excessive bulging however results in blank rupture at the transition line where the element stress state changes from compressive hoop stresses in the flange region to tensile stresses on the punch wall. This type of fracture can be prevented by the use of support pressure pst in the support pressure chamber formed by the punch, blank holder and the unsupported bulged region of the blank (Fig. 1b). The blank in hydromechanical deep drawing is pressed by the fluid pressure onto the punch surface and hence the subtended semi-cone angle decreases to nearly the physical semi-cone angle of the punch ˛. The critical radial stress r,max,hyd. occurs at hk on the punch wall where the blank loses contact with the punch.
r,max,hyd.
FBr,conv. = db t0 u aR
(7a)
Here, p,Bl is the frictional coefficient in the punch wall/blank contacting region, pg the fluid counter pressure acting on the blank and hk is the depth of draw at the contacting punch diameter. aR,mod. is a modified fracture factor for hydromechanical deep drawing of conical parts obtained by rearranging Eq. (7a).
(5)
The limiting condition for a successful deep drawing operation is given by the fracture strength of the material FBr,conv. .
hk (d + hk tan ˛)p,Bl pg cos ˛ b
d = 1.10 ln ˇ0 + 0 b 2t0 +
ˇ02 − C2
ˇ
(pg − pst )(dBHi − dk ) 2t0
(8a)
(6a) (6b)
The fracture factor aR after Doege is a function of the tangential true strain ϕt , the thickness true strain ϕn and the strain hardening exponent n. The value of aR for conventional deep drawing process ranges from 1.0 to 1.4. From Eqs. (5) and (6), the deep drawing operation is successful as long as Fp,max < FBr,conv. . It is hence possible to achieve only low drawing ratios ˇ0 for small values of the subtended semi-cone angle , i.e. for conical punches with a small punch semi-cone angle ˛. During hydromechanical deep drawing of conical parts, the fluid medium presses the blank on the punch wall, as shown in Fig. 1b. This increases friction between the blank wall and
dk = db + 2hk tan ˛
(8b)
Rearranging the terms, the maximum radial stress for hydromechanical deep drawing is written as r,max,hyd. = 1.10 ln ˇ0 + 0 +
db 2t0
ˇ02 − C2
ˇ
(pg − pst )(dBHi − db − 2hk tan ˛) 2t0
(9)
An optimized fluid counter pressure curve ensures an optimal bulge formation and higher values of depth of draw hk . The maximum punch force that can be successfully transferred to the deformation zone Fp,max,hyd. determines the limiting
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drawing ratio in hydromechanical deep drawing. Fp,max,hyd. = dk t0 qf r,max,hyd.
The strength coefficient K is then calculated from Eqs. (14), (16) and (17) (10a) K=
Fp,max,hyd. = (db + 2hk tan ˛)t0 qf 0
d 1.1 ln ˇ0 + b 2t0
×
+
ˇ02 − C2
ˇ
(pg − pst )(dBHi − db − 2hk tan ˛) 2t0 0
0 = u
Fp,max,hyd. = f (ˇ0 , dk , dBHi , t0 , qf , , ˛, pg , pst , pBH , 0 )
4.
(11)
Method to calculate the flow stress 0
The Swift instability criterion (Swift, 1952) at the point of necking in a tensile test n is written as dn dεn
(12)
This equation is substituted in the Hollomon plastic flow strain hardening relation: 0 = Kεn
(13)
where K is the material strength coefficient and n is the strain hardening exponent. At the point of necking, the plastic flow criterion is n = Kεnn =
dn dεn
e ε n
(19)
n
(10b)
The punch force in hydromechanical deep drawing is thus much higher than in conventional deep drawing. The higher fracture strength as seen in Eq. (7) allows higher forces to be transferred to the deformation zone, thus resulting in higher possible limiting drawing ratios ˇ0,max . The flow stress 0 can be calculated as discussed in the following section.
n =
(18)
The flow stress 0 is then written from Eqs. (13) and (18) as
The punch force is thus a function of the drawing ratio ˇ0 , the contacting diameter dk , friction coefficient , factor for strain hardening qf , counter pressure pg and other factors.
3.
n
u en e n = = u n εn nn n
(14)
Tooling and die design
The die set was designed to withstand high hydraulic pressures. The counter pressure recipient was designed as a thick-walled pressure vessel for pressures up to 200 MPa with inner diameter ∅ 108 mm. High strength tool steel DIN 1.2344 hardened to HRC 54 was used for the same. A punch stem diameter ∅ 100 mm and drawing ring opening diameter Dd ∅ 104 mm were selected. A modular die set design was considered (Fig. 2) with interchangeable punch heads (Fig. 3) with different geometries threaded to the punch stem. A blank holder and sealing system were integrated in the drawing ring shoulder and were separately controlled by independent hydraulic circuits and pressure control valves. The counter pressure was controlled using a micro-metering high-pressure flow control valve. A safety disc was used in order to limit the highest pressure in the pressure chamber. The experiments were carried out in a 6000 kN hydraulic press. The counter pressure, blank holder pressure and punch displacement were recorded using pressure and displacement transducers, respectively. The data acquisition software LabVIEW was used for data collection and processing. A punch with a stepped conical geometry and a chamfered punch with positive and negative elliptical milled contours (Fig. 3) were used for the present work.
5.
Numerical simulation
The process was simulated using the explicit finite element solver LS-DYNA (Hallquist, 1999). The 3-parameter Barlat anisotropic material model was used to define the flow characteristics of the blank material. The material properties (Table 1) were obtained by a uniaxial tensile test. The blank was meshed as a Belytschko–Lin–Tsay shell element with five through-
Differentiating Eq. (14), we get dn = Knεn−1 n dεn
(15) Table 1 – Material data for DC04 and SS304 (DIN 1.4301) DC04
From Eqs. (13) through (15), εn = n
(16)
The strain hardening exponent n thus determines the ductility of the material. The flow stress at the point of necking n can thus be written in terms of the ultimate tensile strength u as n =
Fp,max Fp,max A0 = = u eεn = u en An A0 An
(17)
Initial blank thickness, t0 (mm) UTS, su (MPa) Yield strength, se (MPa) Young’s modulus, E (GPa) Strain hardening exponent, n Normal anisotropy, r00 Normal anisotropy, r45 Normal anisotropy, r90 Elongation to fracture, A80 (%)
0.80 297 138.7 173.27 0.23 2.158 2.16 2.988 44.31
SS304 (1.4301) 0.80 625.55 263.80 194.02 0.193 0.926 1.123 0.909 46.70
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Fig. 2 – Die set for the modified hydromechanical deep drawing with punch diameter ∅ 100 mm.
thickness integration points. The blank mesh was adaptively refined for elements bending by more than 5◦ with respect to the neighboring elements. The punch, die, blank holder and sealing were modeled as rigid tools. The blank holder and sealing were considered as force-controlled whereas the punch as motion-controlled. Friction between the blank and contacting drawing ring and blank holder surfaces was modeled using the Coulombs friction model. A lower friction coefficient ( = 0.08) was used at the flange contacting interfaces whereas a higher friction coefficient ( = 0.125) was considered at the punch/cup wall contact interface. The counter pressure was taken as a compressive stress in the normal direction applied on elements lying within a load mask curve (the sealing diameter). A pressure–displacement load curve was used to vary the fluid counter pressure along the punch stroke. The process simulation was carried out by using different counter pressure curves in order to optimize the drawn cup thickness (Liewald et al., 2006). It was found especially for the stepped conical punch geometry that low pressures in the beginning and high pres-
Fig. 3 – Punch geometry with cylindrical and conical sections (a) and punch geometry with chamfered face and elliptical contours (b).
sures later along the punch stroke result in an optimized blank thickness distribution and thus a sound part. The initial blank mesh size was chosen such that at least three elements lie on the drawing ring radius. The process was numerically accelerated using a punch velocity scaling factor of 500 (resulting in a numerical velocity of 2000 mm/s for an actual velocity of 4 mm/s) (Maker and Zhu, 2000).
6.
Results and discussion
The main objective of this study is to investigate the possibility of manufacturing deep drawn parts with high deep drawing ratios and complex features in a single deep drawing stroke. The punch contour has been designed to incorporate cylindrical and conical punch sections with large die clearances. A small physical semi-cone angle (Fig. 3a) is chosen to study the effect of fluid counter pressure on the drawing operation. The chamfered punch (Fig. 3b) is non-axisymmetric and contains complex positive and negative elliptical features. Hydromechanical deep drawing of complex parts requires optimization of the counter pressure curve (Siegert and Khandeparkar, 2002; Palumbo and Tricarico, 2003). The portion of the blank between the punch and the die is unsupported in the case of conical cup drawing. High counter pressure at the beginning would lead to premature rupture of the blank in the unsupported region. The counter pressure is therefore chosen to be low at the beginning of the process. This ensures contact between the blank and punch and an increase in the load transferring capability with increasing draw depth. The results of process simulation for the stepped conical and chamfered punch geometries are shown in Fig. 4. The transition between the cylindrical and conical portions of the stepped conical punch is found to be the critical zone. Also, the elliptical features in the chamfered punch head are critical zones with maximum material thinning, which can be attributed to loading in biaxial tension in the bulged halfellipsoid. The elliptical bulge fails by rupture at the pole along the major axis, which is confirmed by Yousif et al. (1970). The counter pressure curves and the drawn parts for the stepped
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251
Fig. 4 – Blank thickness distribution for hydromechanical deep drawing of stepped conical (a) and chamfered (b) punch geometries by FEM process simulation.
conical punch and chamfered punch are shown in Figs. 5 and 6. The stepped conical punch has been tested using two materials, viz. a low-carbon steel DC04 (limiting drawing ratio ˇ0,max = 3.0) and stainless steel DIN 1.4301 (ˇ0,max = 2.87). The maximum pressure achieved is dependent on the sealing pressure. The wrinkling tendency in the cup wall is suppressed to a great extent by the applied counter pressure. The fluid counter pressure needs to be relatively low in the conical portion due to the larger die clearance. Wrinkles formed in the conical region in the case of SS DIN 1.4301 (Fig. 5) due to the relatively low fluid pressures are difficult to remove at higher drawing depths with high counter pressures. Sealing difficulties prevent pres-
Fig. 6 – Counter pressure during hydromechanical deep drawing of metal sheets using a chamfered punch with elliptical features (DC04, ˇ0 = 2.8, t0 = 0.8 mm, lubricant: M100, 3 g/m2 ).
Fig. 5 – Counter pressure during hydromechanical deep drawing of metal sheets using a stepped conical punch (DC04, ˇ0 = 3.0, t0 = 0.8 mm, lubricant: M100, 3 g/m2 ; SS DIN 1.4301, ˇ0 = 2.87, t0 = 0.8 mm, lubricant: polyolefin surface protection tape and M100, 3 g/m2 ).
sures above 100 MPa to be realized. The limiting drawing ratio ˇ0,max = 2.8 for DC04 with a chamfered punch. Higher drawing ratios lead to premature rupture at high blank holding pressures or flange wrinkling and resulting rupture. However, higher pressures also lead to better transfer of small features from the punch to the blank surface. Hence, an optimum pressure curve is needed for the manufacture of a sound part (see Fig. 6). Figs. 7 and 8 show the cup thickness variation for cups with complex stepped geometries produced by hydromechanical deep drawing. The predictions of process numerical simulation are seen to be comparable to that of experi-
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Fig. 7 – Experimental and numerical cup thickness in different directions for a hydromechanical deep drawn cup with stepped conical punch geometry (db = 80 mm). Material: DC04 (D0 = 240 mm, t0 = 0.8 mm), draw depth: 130 mm, drawing ratio: ˇ0 = 3.0, maximum counter pressure: pg = 44 MPa.
mental test results. The deviation of numerical predictions from the experimentally obtained results can be attributed to experimental factors such as die set and machine elastic deformations, changes in tribological properties during the drawing operation, fluid compressibility and variable punch velocity, which are unaccounted for in numerical process simulation. It is seen that high counter pressures help in reducing material thinning. The fluid counter pressure allows larger magnitudes of tensile longitudinal strains and compressive hoop strains in the drawn part wall. This results in lower strains in the thickness direction and results in a more uniform part wall thickness distribution. This phenomenon can be explained by the use of a forming limit diagram (FLD). The forming limit diagram shows the onset of plastic necking for various loading conditions. An increase in compressive hoop stress requires a corresponding increase in longitudinal strain in order to induce plastic necking. The FLD is normally determined exper-
Fig. 8 – Experimental and numerical cup thickness in different directions for a hydromechanical deep drawn cup with chamfered punch geometry. Material: DC04 (D0 = 280 mm, t0 = 0.8 mm), draw depth: 170 mm, drawing ratio: ˇ0 = 2.8, maximum counter pressure: pg = 50 MPa.
imentally by using the Nakazima test, Swift cupping test, Marziniak test and hydraulic bulging, which emulate different loading conditions in the specimen (Banabic et al., 2000). An alternative method is to use the semi-empirical method due to Keeler and Marziniak-Kuczynski, wherein the curve traverse is determined as a function of the sheet thickness and the strain hardening exponent. A safety limit curve is generated by offsetting the FLD in order to account for unaccounted parameters such as sheet charge material property fluctuations. The numerically predicted part wall strain distribution is shown in Fig. 9a. The FLD is drawn semi-empirically by considering the sheet thickness and strain hardening exponent. The strains are seen to lie below the safety limit of 20%. It is seen that high true strains in the range of 1.0 are predicted in hydromechanical deep drawing. The part wall in-plane strains are determined by using the circular grid method. Here, a grid of circles with a known diameter is etched on to the sheet prior to forming. The circles are transformed into ellipses due to material forming. The lengths of the semi-axes are compared to the circle diameter in order to determine the part wall
Fig. 9 – Cup wall strain distribution by FEM process simulation (a) and by experimental analysis (b) for the chamfered punch. Material: DC04 (D0 = 280 mm, t0 = 0.8 mm), maximum counter pressure: pg = 50 MPa. The true strains are much higher than in conventional deep drawing.
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strains. Fig. 9b shows the part wall strains for an experimental deep drawn cup. The high strains confirm the predictions of numerical process simulation. Higher compressive hoop strains and lower normal strains in hydromechanical deep drawing also lead to a lower decrease in normal anisotropy during the forming operation. The geometrical accuracy is found to be higher as a result of the blank being pressed on to the punch wall due to the fluid counter pressure. The blank is drawn over a fluid cushion and does not contact the drawing ring radius. Hence, the final part surface quality is better as compared to a similar part produced by using conventional deep drawing.
7.
Conclusions
Hydromechanical deep drawing of stepped geometries is proven to be feasible. The advantages of hydromechanical deep drawing such as increased deep drawing ratio, transfer of complex contours from punch to the blank surface, reduction of drawing stages and better part quality have been successfully investigated. The successful manufacture of metal cups with complex stepped contours is found to require good control over the counter pressure curve. The optimum counter pressure curve is realized using numerical techniques. The die set is then designed based on the numerical results. Pressure sealing in the blank flange region helps to produce a reliable and repeatable counter pressure curve. It is to be noted that high pressures at the beginning of the drawing process are counterproductive. The counter pressure should be selected so that the blank is wrapped around the punch profile with the least bulge formation in the unsupported zone. The process has applications in the production of complex geometries such as automotive headlight reflectors, exhaust couplings, fenders, etc.
Acknowledgements This work has been carried out under the Wirkmedienbasierte Fertigungstechniken zur Blechumformung (sheet metal forming with pressure medium) program (SPP 1098) of the Deutsche Forschungsgemeinschaft (DFG). The authors are grateful towards financial support for this work.
references
Aust, M., 2001. Modified hydromechanical deep drawing. In: Siegert, K. (Ed.), Proceedings of the International Conference on Hydroforming of Tubes, Extrusions and Sheets, vol. 2. MAT-INFO Werkstoff-Informations-Gesellschaft, Frankfurt, pp. 215–234. ¨ Banabic, D., Bunge, H.-J., Pohlandt, K., Tekkaya, A.E., 2000. Formability of Metallic Materials. Springer, ISBN 3-540-67906-5. Bensmann, G., 1979. Offenlegungsschrift DE 2802601, Int. Cl.2 B21 D 26/02, Fried. Krupp GmbH, Essen, Werkzeug zum hydromechanischen Tiefziehen (in German). ¨ Burk, E., 1967. Hydromechanical drawing. Sheet Met. Ind., 182–188.
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Hallquist, J.O., 1999. LS-DYNA Keyword User’s Manual, version 950. Livermore Software Technology Corporation, USA. Johannisson, T., 2001. Low volume production of sheet metal parts. In: Siegert, K. (Ed.), Proceedings of the International Conference on Hydroforming of Tubes, Extrusions and Sheets, vol. 2. MAT-INFO Werkstoff-Informations-Gesellschaft, Frankfurt, pp. 159–179. Lang, L., Danckert, J., Nielsen, K.B., Zhou, X., 2005. Investigation into the forming of a complex cup locally constrained by a round die based on an innovative hydromechanical deep drawing method. J. Mater. Process. Technol. 167, 191–200. Lange, K. (Ed.), 1985. Handbook of Metal Forming. McGraw-Hill Book Company, New York, 1172 pp. Liewald, M., Khandeparkar, T., Gehle, A., 2006. CAE process chain in hydromechanical deep drawing. In: Proceedings of the Conference Simulation in Metal Forming. ISD, Stuttgart, Germany. Maker, B.M., Zhu, X., 2000. Input Parameters for Metal Forming Simulation Using LS-DYNA. Livermore Software Technology Corporation, USA. Marciniak, Z., Duncan, J.L., 1992. The Mechanics of Sheet Metal Forming. Edward Arnold, 168 pp. Nakamura, K., Nakagawa, T., 1987. Sheet metal forming with hydraulic counter pressure in Japan. Ann. CIRP 36/1, 191–194. Palumbo, G., Tricarico, L., 2003. Effects of pressure growth law on sheet metal hydroforming. In: Proceedings of the Sixth Esaform Conference on Material Forming, Salerno, Italy. Panknin, W., 1961. Die Grundlagen des Tiefziehens im Anschlag ¨ ¨ unter besonderer Berucksichtigung der Tiefziehprufung. ¨ Bander Bleche Rohre 2/4, 5, 6, 133–143, 201–211, 264–271 (in German). Rolla, R., 1987. Hydromechanisches Tiefziehen—wirtschaftlich ¨ auch bei schwierigen Werkstuckformen. Werkstatt und Betrieb 120/5, 359–363 (in German). Siegert, K., Khandeparkar, T., 2002. Zwischenbericht zum Forschungsvorhaben Si 403/26-2, Tiefziehen von ¨ Blechformteilen bei extremen hydraulischen Gegendrucken. In: Proceedings of the Second Colloquium of the DFG Program SPP 1098, December, 2002, pp. 101–108 (in German). ¨ Siegert, K., Losch, B., 1999. Sheet metal hydroforming. In: Siegert, K. (Ed.), Proceedings of the International Conference on Hydroforming of Tubes, Extrusions and Sheets, vol. 1. MAT-INFO Werkstoff-Informations-Gesellschaft, Frankfurt, pp. 221–247. Siegert, K., Ziegler, M., 1998. Patent DE 19724767 A1 (Int. Cl.: B21 D 22/22), Verfahren zum hydromechanischen Tiefziehen und ¨ zugehorige Einrichtung (in German), Forschungsgesellschaft Umformtechnik mbH, Germany. Spacek, J., Smrcek, V.B., Kasik, J., 1982. Offenlegungsschrift DE ´ 3151382A1, Int. Cl.3 B21 D 26/02, Tovarny strojirenske´ techniky ¨ hydromechanisches Tiefziehen, koncern, Praha, Werkzeug fur insbesondere von Ziehteilen ohne Flansch (in German). ¨ Stromblad, I., 1970. Fluid forming of sheet steel in the Quintus press. Sheet Met. Ind. 47, 41–54. Swift, H.W., 1952. Plastic instability under plane stress. J. Mech. Phys. Solids 1, 1–18. Tirosh, J., Shirizly, A., Ben-David, B., Stange, S., 2000. Hydro-rim deep drawing processes of hardening and rate-sensitive materials. Int. J. Mech. Sci. 42, 1049–1067. Wan, M., Yang, Y., Li, S.B., 2001. Determination of fracture criteria during the deep drawing of conical cups. J. Mater. Process. Technol. 114, 109–113. Wu, J., Balendra, R., Qin, Y., 2004. A study on the forming limits of the hydromechanical deep drawing of components with stepped geometries. J. Mater. Process. Technol. 145, 242– 246. Yousif, M.I., Duncan, J.L., Johnson, W., 1970. Plastic deformation and failure of thin elliptical diaphragms. Int. J. Mech. Sci. 12, 959–972.
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Zhang, S.H., Lang, L.H., Kang, D.C., Danckert, J., Nielsen, K.B., 2000a. Hydromechanical deep drawing of aluminum parabolic workpiece-experiments and numerical simulation. Int. J. Mach. Tool Manuf. 40, 1479–1492.
Zhang, S.H., Nielsen, K.B., Danckert, J., Kang, D.C., Lang, L.H., 2000b. Finite element analysis of the hydromechanical deep-drawing process of tapered rectangular boxes. J. Mater. Process. Technol. 102, 1–8.
journal homepage: www.elsevier.com/locate/jmatprotec
Hydromechanical deep drawing of cups with stepped geometries T. Khandeparkar ∗ , M. Liewald ¨ Umformtechnik, Holzgartenstraße 17, Universitat ¨ Stuttgart, 70174 Stuttgart, Germany Institut fur
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper deals with the hydromechanical deep drawing of metal cups with complex
Received 7 August 2006
stepped geometries. Two materials, a low-carbon steel (DC04) and stainless steel (DIN
Received in revised form
1.4301), have been researched. A die set with a maximum possible deep drawing ratio
28 July 2007
ˇ0,max = 3.0 for a punch diameter ∅ 100 mm has been designed and constructed. The die set
Accepted 22 August 2007
is designed to withstand fluid counter pressures up to 200 MPa. Pressure control is achieved using a micro-metering pressure control valve. The process is initially simulated using the FEM solver LS-DYNA. Experiments have been conducted with two punch geometries. The
Keywords:
punch geometries consist of cylindrical and conical wall segments. Complex positive and
Hydromechanical deep drawing
negative features are manufactured in the punch bottom face. The ability of transferring
Pressure
complex features from the punch onto the blank surface with high deep drawing ratios is
Geometry
investigated. Extended limiting deep drawing ratios of ˇ0,max = 3.0 for DC04 and ˇ0,max = 2.875
FEM
for DIN 1.4301 have been achieved. © 2007 Elsevier B.V. All rights reserved.
Cup
1.
Introduction
Hydromechanical deep drawing is defined as a manufacturing process in which a metal sheet or a hollow body is drawn over a die using an inelastic punch into a fluid pressure medium. The lower die set in a hydromechanical deep drawing process consists of a drawing ring mounted on a pressure chamber. The pressure chamber is filled with a hydraulic fluid. The blank is deformed by the mechanical pressing action of the punch into the pressure chamber. The punch penetration into the hydraulic medium generates a pressure increase due to fluid compression that is controlled using a pressure control valve. The blank being drawn is pressed firmly onto the punch due to pressure build-up. This increases friction between the punch and blank and hence higher forces as compared to that in conventional deep drawing can be transferred to the deformation zone. The metal undergoing hydromechanical deep drawing thus fractures at a much higher stress value than
∗
in the conventional case. This results in a higher deep drawing ratio per drawing stroke and hence higher depths of draw. Hydromechanical deep drawing is thus a cost-effective solution to manufacture metal cups with high drawing ratios in a single drawing stroke (Rolla, 1987). The hydraulic medium wraps the metal blank around the punch and hence it is possible to emboss complex contours from the punch on to the blank. Due to the fluid cushion developed by the hydraulic counter pressure, the blank does not contact the drawing die radius. The outer surface quality of a part formed by hydromechanical deep drawing is thus better than in conventional deep drawing. The wall thickness is also uniform over the depth of draw as a result of the increased friction between punch and blank wall. The counter pressure curve plays an important role aiming to achieve a good deep drawn part. A very high counter pressure at the beginning of the process leads to bulge formation and resulting fracture in the unsupported blank between
Corresponding author. Tel.: +49 71168583827; fax: +49 71168583839. E-mail address: [email protected] (T. Khandeparkar). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.08.072
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punch and blank holder. Low pressure, on the other hand, leads to blank fracture at the punch radius due to lower force transmission to the deforming region of the blank. There is a possibility of fluid leakage through the gap between the blank flange and drawing ring shoulder, resulting in poor counter pressure control. Several researchers have attempted to increase the limiting drawing ratio ˇ0,max of complex deep ¨ drawn components. Burk (1967) used a sealing ring between the blank flange and drawing ring shoulder to prevent fluid leakage. Bensmann (1979) developed a wave-shaped die shoulder profile to ensure fluid sealing. Spacek et al. (1982) proposed a wave-shaped drawing ring shoulder and blank holder of a synthetic material which also allows parts to be drawn ¨ without a flange. The flexforming process (Stromblad, 1970; Johannisson, 2001) developed by Avure Technologies, Sweden, uses a flexible rubber membrane to separate the pressurized fluid medium from the blank. Fluid forming pressures up to 100 MPa have been reported using this process. The radial fluid pressure assisted counter pressure deep drawing method developed by Nakamura and Nakagawa (1987) utilizes a fluid bypass from the counter pressure chamber to the drawing ring shoulder in order to push the blank flange radially inwards in the direction of the punch. The fluid pressure applied radially on the flange edge reduces the radial stress and prevents premature rupture, thus ensuring higher limiting drawing ratios. Tirosh et al. (2000) discussed a variation of the radial fluid pressure assisted counter pressure deep drawing process by heating the blank in the flange region with the aim of increasing the material strain rate sensitivity and thereby achieving an “unlimited drawing ratio”. The hydromechanical deep drawing process has been extensively researched to produce metal hollow bodies with complex geometries. Zhang et al. (2000a,b) investigated the feasibility of drawing aluminum parabolic geometries. The possibility of deep drawing tapered rectangular boxes was tried numerically and experimentally (Zhang et al., 2000a,b; Lang et al., 2005). Wu et al. (2004) studied the forming limits of metal cups with stepped geometries using a numerical approach. Wan et al. (2001) used a theoretical approach to determine the fracture criteria and the limiting drawing ratio (LDR) for conventional deep drawing of conical cups.
In the present work, the modified hydromechanical deep drawing method patented by Siegert and Ziegler (1998) is used. This method uses a controllable sealing mechanism between the blank and drawing ring shoulder. A bulge forms in the unsupported blank region between the punch and drawing die radius during the hydromechanical deep drawing of con¨ ical parts (Siegert and Losch, 1999). High counter pressures result in fracture due to bulge rupture. In the present die set (Aust, 2001), a closed support pressure chamber formed by the punch, blank holder and the unsupported upper blank face is pressurized with a support pressure pst , thus optimizing the bulge height. This reduces the possibility of blank rupture due to bulging.
2.
Theoretical analysis
The critical radial stress in a conventional deep drawing operation r,conv. occurs at the punch radius at which the material is strain-hardened due to bending and unbending (Lange, 1985). The total tensile stress at the punch radius is the sum of the forming stress, frictional stress due to the blank holder, stress addition due to bending and unbending of the blank and friction at the drawing ring radius (Panknin, 1961; Marciniak and Duncan, 1992). The radial stress for conventional deep drawing is written as r,conv. =
1.10 ln
D0 2FBH db + db db t0 D
e +
t0 0 2rd + t0
(1)
D0 and t0 are the initial diameter and thickness of the blank, db the base diameter of a conical punch and rd is the drawing die radius. stands for the frictional coefficient due to Coulomb at the blank flange/drawing ring shoulder and blank flange/blank holder interface, 0 the flow stress of the blank material and is the semi-cone angle subtended by the blank at the tangent to the punch radius as shown in Fig. 1a. The blank holder force FBH acts over the entire blank flange in contact with the blank holder, i.e. from the outer blank diameter D0 to the inner blank holder diameter dBHi . FBH =
2 (D − d2BHi )pBH 4 0
(2a)
Fig. 1 – Conventional deep drawing of a conical component (a) and hydromechanical deep drawing of a conical component using support pressure pst (b).
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where pBH is the blank holder pressure defined by Siebel.
3
pBH = 0.002· · ·0.003 (ˇ0 − 1) +
punch and thus increases the load carrying capacity of the blank. The fracture criterion is modified to FBr,hyd. .
0.5db u = 0 100t0
(2b) FBr,hyd. = db t0 u aR +
ˇ0 = D0 /db is defined as the drawing ratio. u is the ultimate tensile strength of a blank. Eq. (1) can be written in terms of the initial drawing ratio ˇ0 , the instantaneous drawing ratio ˇ = D/db and a geometry constant C = dBHi /db .
r,conv. =
d 1.1 ln ˇ0 + b 2t0
ˇ02 − C2
e
ˇ
t0 + 2rd + t0
0 (3)
During the drawing process, the thickness strain distribution and strain hardening vary throughout the flange and hence the flow stress is not constant. Also, the subtended semi-cone angle tends to the physical punch semi-cone angle ˛ with increasing draw depth. To account for such dynamic factors, an additional term qf is added to the relation for punch force. The maximum punch force that can be successfully transferred to the blank deformation zone Fp,max,conv. determines the limiting drawing ratio ˇ0,max for the deep drawn part. Fp,max,conv. = db t0 qf r,max,conv.
= db t0 qf
+
d 1.1 ln ˇ0 + b 2t0
t0 (2rd + t0 )
0 sin
ˇ02 − C2 ˇ
e
(4)
The punch force is thus a function of the drawing ratio ˇ0 , the punch base diameter db , friction coefficient , factor for strain hardening qf and the drawing die radius rd in addition to other factors. Fp,max,conv. = f (ˇ0 , db , rd , t0 , qf , , , pBH , 0 )
= db t0 u aR,mod.
aR,mod. = aR +
aR = e(n−ϕn )
ϕ + ϕ n t n n
hk cos ˛
d + h tan ˛ b k db t0 u
p,Bl pg > aR
(7b)
The unsupported blank in the drawing ring clearance is lifted by the fluid pressure during hydromechanical deep drawing process, thus forming a bulge in the direction opposite to the drawing direction. The blank thus moves over a fluid cushion and is not bent over the die radius as in the case of conventional deep drawing. Bending forces over the drawing die radius and frictional forces due to bending over the drawing die radius are thus absent in hydromechanical deep drawing. Excessive bulging however results in blank rupture at the transition line where the element stress state changes from compressive hoop stresses in the flange region to tensile stresses on the punch wall. This type of fracture can be prevented by the use of support pressure pst in the support pressure chamber formed by the punch, blank holder and the unsupported bulged region of the blank (Fig. 1b). The blank in hydromechanical deep drawing is pressed by the fluid pressure onto the punch surface and hence the subtended semi-cone angle decreases to nearly the physical semi-cone angle of the punch ˛. The critical radial stress r,max,hyd. occurs at hk on the punch wall where the blank loses contact with the punch.
r,max,hyd.
FBr,conv. = db t0 u aR
(7a)
Here, p,Bl is the frictional coefficient in the punch wall/blank contacting region, pg the fluid counter pressure acting on the blank and hk is the depth of draw at the contacting punch diameter. aR,mod. is a modified fracture factor for hydromechanical deep drawing of conical parts obtained by rearranging Eq. (7a).
(5)
The limiting condition for a successful deep drawing operation is given by the fracture strength of the material FBr,conv. .
hk (d + hk tan ˛)p,Bl pg cos ˛ b
d = 1.10 ln ˇ0 + 0 b 2t0 +
ˇ02 − C2
ˇ
(pg − pst )(dBHi − dk ) 2t0
(8a)
(6a) (6b)
The fracture factor aR after Doege is a function of the tangential true strain ϕt , the thickness true strain ϕn and the strain hardening exponent n. The value of aR for conventional deep drawing process ranges from 1.0 to 1.4. From Eqs. (5) and (6), the deep drawing operation is successful as long as Fp,max < FBr,conv. . It is hence possible to achieve only low drawing ratios ˇ0 for small values of the subtended semi-cone angle , i.e. for conical punches with a small punch semi-cone angle ˛. During hydromechanical deep drawing of conical parts, the fluid medium presses the blank on the punch wall, as shown in Fig. 1b. This increases friction between the blank wall and
dk = db + 2hk tan ˛
(8b)
Rearranging the terms, the maximum radial stress for hydromechanical deep drawing is written as r,max,hyd. = 1.10 ln ˇ0 + 0 +
db 2t0
ˇ02 − C2
ˇ
(pg − pst )(dBHi − db − 2hk tan ˛) 2t0
(9)
An optimized fluid counter pressure curve ensures an optimal bulge formation and higher values of depth of draw hk . The maximum punch force that can be successfully transferred to the deformation zone Fp,max,hyd. determines the limiting
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drawing ratio in hydromechanical deep drawing. Fp,max,hyd. = dk t0 qf r,max,hyd.
The strength coefficient K is then calculated from Eqs. (14), (16) and (17) (10a) K=
Fp,max,hyd. = (db + 2hk tan ˛)t0 qf 0
d 1.1 ln ˇ0 + b 2t0
×
+
ˇ02 − C2
ˇ
(pg − pst )(dBHi − db − 2hk tan ˛) 2t0 0
0 = u
Fp,max,hyd. = f (ˇ0 , dk , dBHi , t0 , qf , , ˛, pg , pst , pBH , 0 )
4.
(11)
Method to calculate the flow stress 0
The Swift instability criterion (Swift, 1952) at the point of necking in a tensile test n is written as dn dεn
(12)
This equation is substituted in the Hollomon plastic flow strain hardening relation: 0 = Kεn
(13)
where K is the material strength coefficient and n is the strain hardening exponent. At the point of necking, the plastic flow criterion is n = Kεnn =
dn dεn
e ε n
(19)
n
(10b)
The punch force in hydromechanical deep drawing is thus much higher than in conventional deep drawing. The higher fracture strength as seen in Eq. (7) allows higher forces to be transferred to the deformation zone, thus resulting in higher possible limiting drawing ratios ˇ0,max . The flow stress 0 can be calculated as discussed in the following section.
n =
(18)
The flow stress 0 is then written from Eqs. (13) and (18) as
The punch force is thus a function of the drawing ratio ˇ0 , the contacting diameter dk , friction coefficient , factor for strain hardening qf , counter pressure pg and other factors.
3.
n
u en e n = = u n εn nn n
(14)
Tooling and die design
The die set was designed to withstand high hydraulic pressures. The counter pressure recipient was designed as a thick-walled pressure vessel for pressures up to 200 MPa with inner diameter ∅ 108 mm. High strength tool steel DIN 1.2344 hardened to HRC 54 was used for the same. A punch stem diameter ∅ 100 mm and drawing ring opening diameter Dd ∅ 104 mm were selected. A modular die set design was considered (Fig. 2) with interchangeable punch heads (Fig. 3) with different geometries threaded to the punch stem. A blank holder and sealing system were integrated in the drawing ring shoulder and were separately controlled by independent hydraulic circuits and pressure control valves. The counter pressure was controlled using a micro-metering high-pressure flow control valve. A safety disc was used in order to limit the highest pressure in the pressure chamber. The experiments were carried out in a 6000 kN hydraulic press. The counter pressure, blank holder pressure and punch displacement were recorded using pressure and displacement transducers, respectively. The data acquisition software LabVIEW was used for data collection and processing. A punch with a stepped conical geometry and a chamfered punch with positive and negative elliptical milled contours (Fig. 3) were used for the present work.
5.
Numerical simulation
The process was simulated using the explicit finite element solver LS-DYNA (Hallquist, 1999). The 3-parameter Barlat anisotropic material model was used to define the flow characteristics of the blank material. The material properties (Table 1) were obtained by a uniaxial tensile test. The blank was meshed as a Belytschko–Lin–Tsay shell element with five through-
Differentiating Eq. (14), we get dn = Knεn−1 n dεn
(15) Table 1 – Material data for DC04 and SS304 (DIN 1.4301) DC04
From Eqs. (13) through (15), εn = n
(16)
The strain hardening exponent n thus determines the ductility of the material. The flow stress at the point of necking n can thus be written in terms of the ultimate tensile strength u as n =
Fp,max Fp,max A0 = = u eεn = u en An A0 An
(17)
Initial blank thickness, t0 (mm) UTS, su (MPa) Yield strength, se (MPa) Young’s modulus, E (GPa) Strain hardening exponent, n Normal anisotropy, r00 Normal anisotropy, r45 Normal anisotropy, r90 Elongation to fracture, A80 (%)
0.80 297 138.7 173.27 0.23 2.158 2.16 2.988 44.31
SS304 (1.4301) 0.80 625.55 263.80 194.02 0.193 0.926 1.123 0.909 46.70
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Fig. 2 – Die set for the modified hydromechanical deep drawing with punch diameter ∅ 100 mm.
thickness integration points. The blank mesh was adaptively refined for elements bending by more than 5◦ with respect to the neighboring elements. The punch, die, blank holder and sealing were modeled as rigid tools. The blank holder and sealing were considered as force-controlled whereas the punch as motion-controlled. Friction between the blank and contacting drawing ring and blank holder surfaces was modeled using the Coulombs friction model. A lower friction coefficient ( = 0.08) was used at the flange contacting interfaces whereas a higher friction coefficient ( = 0.125) was considered at the punch/cup wall contact interface. The counter pressure was taken as a compressive stress in the normal direction applied on elements lying within a load mask curve (the sealing diameter). A pressure–displacement load curve was used to vary the fluid counter pressure along the punch stroke. The process simulation was carried out by using different counter pressure curves in order to optimize the drawn cup thickness (Liewald et al., 2006). It was found especially for the stepped conical punch geometry that low pressures in the beginning and high pres-
Fig. 3 – Punch geometry with cylindrical and conical sections (a) and punch geometry with chamfered face and elliptical contours (b).
sures later along the punch stroke result in an optimized blank thickness distribution and thus a sound part. The initial blank mesh size was chosen such that at least three elements lie on the drawing ring radius. The process was numerically accelerated using a punch velocity scaling factor of 500 (resulting in a numerical velocity of 2000 mm/s for an actual velocity of 4 mm/s) (Maker and Zhu, 2000).
6.
Results and discussion
The main objective of this study is to investigate the possibility of manufacturing deep drawn parts with high deep drawing ratios and complex features in a single deep drawing stroke. The punch contour has been designed to incorporate cylindrical and conical punch sections with large die clearances. A small physical semi-cone angle (Fig. 3a) is chosen to study the effect of fluid counter pressure on the drawing operation. The chamfered punch (Fig. 3b) is non-axisymmetric and contains complex positive and negative elliptical features. Hydromechanical deep drawing of complex parts requires optimization of the counter pressure curve (Siegert and Khandeparkar, 2002; Palumbo and Tricarico, 2003). The portion of the blank between the punch and the die is unsupported in the case of conical cup drawing. High counter pressure at the beginning would lead to premature rupture of the blank in the unsupported region. The counter pressure is therefore chosen to be low at the beginning of the process. This ensures contact between the blank and punch and an increase in the load transferring capability with increasing draw depth. The results of process simulation for the stepped conical and chamfered punch geometries are shown in Fig. 4. The transition between the cylindrical and conical portions of the stepped conical punch is found to be the critical zone. Also, the elliptical features in the chamfered punch head are critical zones with maximum material thinning, which can be attributed to loading in biaxial tension in the bulged halfellipsoid. The elliptical bulge fails by rupture at the pole along the major axis, which is confirmed by Yousif et al. (1970). The counter pressure curves and the drawn parts for the stepped
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 2 ( 2 0 0 8 ) 246–254
251
Fig. 4 – Blank thickness distribution for hydromechanical deep drawing of stepped conical (a) and chamfered (b) punch geometries by FEM process simulation.
conical punch and chamfered punch are shown in Figs. 5 and 6. The stepped conical punch has been tested using two materials, viz. a low-carbon steel DC04 (limiting drawing ratio ˇ0,max = 3.0) and stainless steel DIN 1.4301 (ˇ0,max = 2.87). The maximum pressure achieved is dependent on the sealing pressure. The wrinkling tendency in the cup wall is suppressed to a great extent by the applied counter pressure. The fluid counter pressure needs to be relatively low in the conical portion due to the larger die clearance. Wrinkles formed in the conical region in the case of SS DIN 1.4301 (Fig. 5) due to the relatively low fluid pressures are difficult to remove at higher drawing depths with high counter pressures. Sealing difficulties prevent pres-
Fig. 6 – Counter pressure during hydromechanical deep drawing of metal sheets using a chamfered punch with elliptical features (DC04, ˇ0 = 2.8, t0 = 0.8 mm, lubricant: M100, 3 g/m2 ).
Fig. 5 – Counter pressure during hydromechanical deep drawing of metal sheets using a stepped conical punch (DC04, ˇ0 = 3.0, t0 = 0.8 mm, lubricant: M100, 3 g/m2 ; SS DIN 1.4301, ˇ0 = 2.87, t0 = 0.8 mm, lubricant: polyolefin surface protection tape and M100, 3 g/m2 ).
sures above 100 MPa to be realized. The limiting drawing ratio ˇ0,max = 2.8 for DC04 with a chamfered punch. Higher drawing ratios lead to premature rupture at high blank holding pressures or flange wrinkling and resulting rupture. However, higher pressures also lead to better transfer of small features from the punch to the blank surface. Hence, an optimum pressure curve is needed for the manufacture of a sound part (see Fig. 6). Figs. 7 and 8 show the cup thickness variation for cups with complex stepped geometries produced by hydromechanical deep drawing. The predictions of process numerical simulation are seen to be comparable to that of experi-
252
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Fig. 7 – Experimental and numerical cup thickness in different directions for a hydromechanical deep drawn cup with stepped conical punch geometry (db = 80 mm). Material: DC04 (D0 = 240 mm, t0 = 0.8 mm), draw depth: 130 mm, drawing ratio: ˇ0 = 3.0, maximum counter pressure: pg = 44 MPa.
mental test results. The deviation of numerical predictions from the experimentally obtained results can be attributed to experimental factors such as die set and machine elastic deformations, changes in tribological properties during the drawing operation, fluid compressibility and variable punch velocity, which are unaccounted for in numerical process simulation. It is seen that high counter pressures help in reducing material thinning. The fluid counter pressure allows larger magnitudes of tensile longitudinal strains and compressive hoop strains in the drawn part wall. This results in lower strains in the thickness direction and results in a more uniform part wall thickness distribution. This phenomenon can be explained by the use of a forming limit diagram (FLD). The forming limit diagram shows the onset of plastic necking for various loading conditions. An increase in compressive hoop stress requires a corresponding increase in longitudinal strain in order to induce plastic necking. The FLD is normally determined exper-
Fig. 8 – Experimental and numerical cup thickness in different directions for a hydromechanical deep drawn cup with chamfered punch geometry. Material: DC04 (D0 = 280 mm, t0 = 0.8 mm), draw depth: 170 mm, drawing ratio: ˇ0 = 2.8, maximum counter pressure: pg = 50 MPa.
imentally by using the Nakazima test, Swift cupping test, Marziniak test and hydraulic bulging, which emulate different loading conditions in the specimen (Banabic et al., 2000). An alternative method is to use the semi-empirical method due to Keeler and Marziniak-Kuczynski, wherein the curve traverse is determined as a function of the sheet thickness and the strain hardening exponent. A safety limit curve is generated by offsetting the FLD in order to account for unaccounted parameters such as sheet charge material property fluctuations. The numerically predicted part wall strain distribution is shown in Fig. 9a. The FLD is drawn semi-empirically by considering the sheet thickness and strain hardening exponent. The strains are seen to lie below the safety limit of 20%. It is seen that high true strains in the range of 1.0 are predicted in hydromechanical deep drawing. The part wall in-plane strains are determined by using the circular grid method. Here, a grid of circles with a known diameter is etched on to the sheet prior to forming. The circles are transformed into ellipses due to material forming. The lengths of the semi-axes are compared to the circle diameter in order to determine the part wall
Fig. 9 – Cup wall strain distribution by FEM process simulation (a) and by experimental analysis (b) for the chamfered punch. Material: DC04 (D0 = 280 mm, t0 = 0.8 mm), maximum counter pressure: pg = 50 MPa. The true strains are much higher than in conventional deep drawing.
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strains. Fig. 9b shows the part wall strains for an experimental deep drawn cup. The high strains confirm the predictions of numerical process simulation. Higher compressive hoop strains and lower normal strains in hydromechanical deep drawing also lead to a lower decrease in normal anisotropy during the forming operation. The geometrical accuracy is found to be higher as a result of the blank being pressed on to the punch wall due to the fluid counter pressure. The blank is drawn over a fluid cushion and does not contact the drawing ring radius. Hence, the final part surface quality is better as compared to a similar part produced by using conventional deep drawing.
7.
Conclusions
Hydromechanical deep drawing of stepped geometries is proven to be feasible. The advantages of hydromechanical deep drawing such as increased deep drawing ratio, transfer of complex contours from punch to the blank surface, reduction of drawing stages and better part quality have been successfully investigated. The successful manufacture of metal cups with complex stepped contours is found to require good control over the counter pressure curve. The optimum counter pressure curve is realized using numerical techniques. The die set is then designed based on the numerical results. Pressure sealing in the blank flange region helps to produce a reliable and repeatable counter pressure curve. It is to be noted that high pressures at the beginning of the drawing process are counterproductive. The counter pressure should be selected so that the blank is wrapped around the punch profile with the least bulge formation in the unsupported zone. The process has applications in the production of complex geometries such as automotive headlight reflectors, exhaust couplings, fenders, etc.
Acknowledgements This work has been carried out under the Wirkmedienbasierte Fertigungstechniken zur Blechumformung (sheet metal forming with pressure medium) program (SPP 1098) of the Deutsche Forschungsgemeinschaft (DFG). The authors are grateful towards financial support for this work.
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