optimization of the tool geometry in the deep drawing of aluminium

Journal of Materials Processing Technology 72 (1997) 363–370

Optimization of the tool geometry in the deep drawingof aluminium

M.M. Moshksar *, A. ZamanianDepartment of Materials Science and Engineering, School of Engineering, Shiraz Uni6ersity, Shiraz, Iran

Received 11 August 1996

Abstract

The ability to predict a successful deep-drawing operation is important when designing a deep-drawing schedule. This paperpresents the results of a series of cup-drawing tests carried out to study the deep drawing of commercial aluminium blanks. Thecritical die and punch shoulder radii, the limiting blank diameters and the limiting drawing ratios were recorded. Over the rangesof conditions investigated, the drawing process was found to be strongly sensitive to the die and punch-nose radii. Based on theexperimental data obtained, the maximum punch force for aluminium cup drawing is proposed. © 1997 Elsevier Science S.A.

Keywords: Deep drawing; Cup drawing; Die and punch profile

1. Introduction

Deep drawing is a process for shaping flat sheets intocup-shaped articles without fracture or excessive local-ized thinning. The design and control of a deep-draw-ing process depends not only on the workpiecematerial, but also on the condition at the tool-work-piece interface, the mechanics of plastic deformationand the equipment used. The equipment and toolingparameters that affect the success or failure of a deep-drawing operation are the punch and die radii, thepunch and die clearance, the press speed, the lubrica-tion and the type of restraint to metal flow.

Hrivnak and Sobotova [1] and Date and Padmanab-han [2] have investigated the effect of material variableson the sheet metal forming processes, these variablesbeing the grain size, sheet thickness, surface roughness,void nucleation and growth, strain-hardening andstrain-rate sensitivity of the sheet metals.

Yossifon and Tirosh [3] have carried out a compre-hensive experimental and analytical investigation on thebehavior of the sheet blank materials, the propertiesinvestigated including strain hardening and anisotropy,the effect of friction and changes in metal sheet thick-ness. To reduce the effect of friction, an improved

deep-drawing tooling was used by Thiruvarudchelvanand Loh [4]. Kawai et al. [5] have also considered therole of friction in a similar operation.

Different analytical and numerical-calculation meth-ods are used to study plastic deformation in deep-draw-ing processes [6]. A recent mathematical model toprescribe the effect of anisotropy and the final shapes ofdeep-drawn products was developed recently by Chunget al. [7,8]. Szacinski and Thomson [9] and Ameziune-Hassani and Neale [10] have analyzed the wrinklingphenomenon and Kapinski [11] has investigated theinfluence of punch velocity on the deformation of thematerial in deep-drawn shapes.

The die and punch profile radii are the most impor-tant parameters of the tools in deep-drawing processes,determining the load at which the bottom of the drawnshell is torn out. Therefore the drawing process ishighly promoted by choosing appropriate punch anddie radii [12]. In this work, the effect of the punch anddie profile radii on the drawing load and formability ofaluminium sheet metal is discussed.

2. Basic analysis

The nature of the stresses and strains in deep-draw-ing operations is complex. The initial elements of the* Corresponding author.

0924-0136/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved.

PII S 0 924 -0136 (97 )00196 -9

M.M. Moshksar, A. Zamanian / Journal of Materials Processing Technology 72 (1997) 363–370M.M. Moshksar, A. Zamanian / Journal of Materials Processing Technology 72 (1997) 363–370364

sheet metal on the flat part of the die flange arecompressed in the circumferential direction. Wheneverthe compressed elements reach the die profile, they areformed into a hollow conical section by bending undertension. The metal is subsequently unbent into a cylin-drical cup after passing over the die profile. Thereforean accurate expression for calculating the drawing loadmust take account of both the stresses acting on the flatpart of the flange and those on the die profile. Thesestresses are as follow.

(a) The pure radial drawing stress sr1 on the flangetowards the die cavity:

sr1=hY( lnr0

r(1)

in which:

Y( = Kon

1+n(2)

where Y( is the mean tensile yield stress of the blankmaterial, r0 and r are the peripheral and current radii ofthe blank and h is the coefficient of constrained, givenas 1.15\h\1.

(b) The frictional radial stress sf1 required to over-come the effect of friction at the die–blank and blank–blank holder interfaces [12]:

sf1=mFb

pR0t0

(3)

where m is the coefficient of friction, Fb is the blank-holder force and t0 is the initial thickness of the blank.It follows that at a point on the flange the total radialdrawing stress becomes (sr1+sf1).

(c) The bending stress that is required to producebending over the die profile [6]:

sb=t0 [Y( 2+ (sr1+sf1)2]

3Y( (2rd+ t0)(4)

where rd is the radius of curvature of the die profile.(d) The radial drawing stress sr2 on the die profile.

Whilst the material is subjected to plastic bending as itpassing over the die profile, it is also subjected to afurther radial drawing stress because of reduction in theradius of elements from r to the punch radius rp.

sr2=hY( lnrrp

(5)

(e) The frictional radial stress sf2 on the die profile:

sf2= (sr1+sf1+sb)�

exp�mp

2�

−1n

(6)

where m is the coefficient of friction at the blank-dieprofile interface.

(f) The unbending stress su. The exact analysis of theunbending stress is complex. To a first approximation,the unbending stress can be obtained as the bending

stress (Eq. (4)), provided that srt is substituted for(sr1+sf1), i.e.:

su=t0 (Y( 2+s2

rt)

3Y( (2rd+ t0)(7)

where:

srt=sr1+sf1+sb+sr2+sf2 (8)

Assuming that the various effects are additive, the totalwall stress in the drawn cup becomes:

sw=sr1+sf1+sb+sr2+sf2+su (9)

and the punch force Fp is given by:

Fp=2prpt0sw (10)

3. Experimental procedure

3.1. Materials and equipment

Commercially-pure aluminum sheet with a thicknessof 1.5 mm was used for the blank material: For thinnerblanks, accurate variation in thickness during drawingcould not be measured. The minimum blank diameterwas limited respect to the blank-holder size and thedimensions of the dies. Preliminary experiments showedthat blanks with diameters of less than 75 mm aredrawn without failure, therefore blank diameters of 78,82, 86 and 90 mm were found to be the most suitablediameters for studying the effect of tool parameters onfailure. Tensile test were performed to obtain the accu-rate properties and anisotropy behavior of the material.Annealing of the blanks and tensile specimens wascarried out for one hour at 450°C in vacuum.

The deep-drawing machine that was used in thisinvestigation was an inverted double-action automatichydraulic press with a maximum load capacity of 120kN, a blank-holder force of 40 kN, a punching strokeof 80 mm, a blank-holding stroke of 8 mm and avariable punch speed of up to 180 mm min−1. In thispress the punch is mounted on the lower shoe and thedie on the upper shoe of the machine. The punchingand blank-holding forces and the punch stroke could bemeasured separately by indicators that were providedon the machine.

3.2. Punches and dies

The geometry of the punch and die, especially theirprofile radii, are the major variables in deep-drawingprocesses. In order to investigate these effects, fivedifferent shoulder radii were designed for both thepunches and the dies. It has been shown [12] that for apunch shoulder radius (rp) that is less than twice thethickness of the blank (t0), the cups fail due to tearing,

M.M. Moshksar, A. Zamanian / Journal of Materials Processing Technology 72 (1997) 363–370M.M. Moshksar, A. Zamanian / Journal of Materials Processing Technology 72 (1997) 363–370 365

whilst for rp\10t0 stretching may be introduced. Inaddition, within the region 4t0BrpB10t0 the radiusdoes not significantly affect the limiting drawing ratio(LDR). Therefore, according to the thickness of theblank, the most suitable shoulder radii for the dies andpunches were found to be 4, 6, 8, 10 and 12 mm with aconstant punch stem diameter of 40 mm and a diecavity diameter of 44 mm.

Proper tool steel with appropriate mechanical prop-erties and hardening treatment was used for the materi-als of the punches and dies. The tools were ground toan appropriate surface finish and a final hardness of 64HRC.

3.3. Test procedure

A proper drawing speed is important for the bestresults: excessive speeds can cause wrinkling or fracturein the formed part and damage of the tools; whilstinsufficient speeds reduce the rate of production. In thisinvestigation a drawing speed of 144 mm min−1 wasfound to be the most suitable speed. The blank-holderforce was chosen to be the minimum force required toprevent wrinkling of the largest blank and was found tobe 1 kN. For convenience, the tests were divided intofour groups, in each group a blank diameter beingselected and the shoulder radii of the punches and dieswere changed, thus in each group 25 different tests wereinvestigated. An operation sequence was arranged forthe tests and the punch forces were measured simulta-neously as a function of the punch stroke. For thereliability of the data, each test was repeated two orthree times, average values being obtained.

4. Results and discussion

4.1. Materials properties

The flow properties and plastic anisotropic behaviorof the materials are described by the Ludwik–Hollo-man expression, s=Kon, and the plastic strain ratio,R=ow/ot, where n is the work-hardening exponent, K isthe strength coefficient, and ow and ot are the width andthickness strains, respectively. Fig. 1 indicates the re-sults of the tensile tests on the aluminum sheet metalbefore and after annealing, comparison of the curvesshowing the effect of the annealing process on theas-received sheet metal. The mean anisotropy value wasdefined by:

R( =R0+2R45+R90

4(11)

R( values for the original and annealed sheet metalswere obtained as 0.49 and 1, respectively. The plasticstrain ratio, R( , is a parameter that measures the plastic

anisotropy and is related to the crystallographic orien-tation within the metals. It indicates the ability of thesheet metal to resist thinning (R\1) or ease of thinning(RB1) when subjected to forces in the plane of thesheet. For the unannealed blanks, the easy thinningcontributed to the forming of the cups and caused thecups to become completely unsymmetric, large earsbeing formed in the drawn cups. By annealing thematerial and increasing its R-value, the drawability wasincreased and the earing effect was eliminated, whichendorses that the R-value may be considered a measureof sheet metal drawability.

4.2. Die geometry

Table 1 and Figs. 2 and 3 show examples of theresults of the deep-drawing tests that were performedon two sets of the blanks, similar tables and figures alsobeing obtained for all other dies, punches and blanks.The essential results were generally the same, but thequantities and critical values were changed. It wasnecessary to define a critical nose radius for the dies,this radius being that above which the blanks will bedrawn successfully and below which tearing will occurin the cup wall. For example, all 78 mm blanks weredrawn successfully, so for these blanks the critical dieshoulder radius could not be identified, but for theblanks with diameters of 82 and 86 mm the critical dieshoulder radius were observed, as indicated in Table 2.These results show that for the sharper punches, dieswith greater nose radii must be used. None of the 90mm blanks were drawn successfully, which means thatthe critical die nose radius for these blanks is greaterthan 12 mm.

Fig. 1. Stress-strain curves of the sheet metal: (A) and (B) as-received;(C) and (D) annealed.


Table 1Deep-drawing results for 82 mm blanks, arranged for the effect of the die shoulder radius

Max. punch load (kN)Die nose radius (mm) Result of testsPunch stroke at max. load (mm)Punch nose radius (mm)

4 14.2 15 Tearing417.5 Tearing6 14.6

14.5 20.58 Tearing13.7 Success2310

24 Success12 13

15.5 Tearing6 4 14.514.7 18.56 Tearing

Tearing14.5 20.5814 2310 Success

Success12 2314

15.3 218 Tearing415.1 226 Tearing

Success2114.5814.2 25 Success1013.4 2412 Success

15.2 Success4 231023 Success6 14.5

Success2414.1813.5 2310 Success13 2312 Success

15.7 Success4 261215.4 24 Success6

Success2514.5826 Success10 14.226 Success12 13.5

Fig. 4 shows the effect of the die profile radiuson the maximum punch load, the figure indicatingthat for a constant punch nose radius the maximumload is decreased as the die shoulder radius is in-creased, being due to increase in process work by

plastic bending and unbending over the smaller dieprofile: This result is in agreement with the predic-tions of previous theories. Comparison of the maxi-mum punch load (Fp)max, with the die shoulder radiird, indicates that:

Fig. 2. Effect of the die profile radius on the punch load (Punchprofile radius=6 mm; blank diameter=78 mm).

Fig. 3. Effect of the die profile radius on the punch load (Punchprofile radius=6 mm; blank diameter=82 mm).


Table 2Critical die shoulder radius

Blank diameter Critical die nose radiusPunch nose ra-dius (mm) (mm)(mm)

82 4 86 88 6

10 Less than 4Less than 412

4 More than 1286More than 126

8 1010 812 6

Table 3Proportional its constants of maximum punch load

baBlank diameter (mm)

0.062 0.21×10−2780.06282 0.1×10−2

86 0.070 0.37×10−3

0.1×10−30.06890

nose radius the axial stress in the cup wall remains lessthan the tensile strength of the material and the draw-ing operation can progress. Table 1 and Fig. 3 showthat for the cases where the maximum punch loadsarises at larger punch strokes, the blanks are drawnsuccessfully. Therefore the amount of the punch strokecan also be a measure of the drawability of the sheetmetal in the deep-drawing operation.

On the other hand, for larger blank diameters, anincrease in the drawing force is observed, due to theenlargement of the die-blank and blank-holder-blankinterfaces. Therefore the success of the drawing opera-tion is also dependent on the blank diameter, when fora particular die geometry a limiting blank diameter canalso be defined. Fig. 5 shows the results, together withthe measured LDRs. As the figure shows, the limitingblank diameter and the LDR increase with increase inthe shoulder radius of the die.

4.3. Punch geometry

In order to investigate the effect of the punch shoul-der radius on the deep-drawing process, a set of tablesand figures that indicate the role of the punch shoulderradius were prepared also, Table 4 and Figs. 6 and 7

(Fp)max:1rd

(12)

or:

(Fp)max=1

a+brd

(kN) (13)

where a and b are constants that depend on the diame-ter of the blank, The results are illustrated in Table 3.

Consequently, for any blank diameter, the averageform of the maximum punch load is approximated as:

(Fp)max=103

65+0.9rd

(kN) (14)

Increasing of the bending and unbending stresses dueto the decreasing of the die shoulder radii causes theaxial stress of the cup wall to increase and exceed thetensile strength of the sheet material and thereforefracture occurs in the cup wall, whereas for greater die

Fig. 4. Effect of the die profile radius on the maximum punch load(Punch profile radius=10 mm).

Fig. 5. Effect of the die profile radius on the limiting blank diameterand LDR.


Table 4Deep-drawing results on 78 mm blanks, arranged for the effect of the punch shoulder radius

Punch nose radius (mm) Punch stroke at max. load (mm)Max. punch load (kN)Die nose radius (mm)

17144 46 14 178 14.6 19

14 2110221412

13.5 176 46 13.4 17

198 13.310 13.7 22

2213.512

4 12.6 1986 12.8 19

21138211310

12 12.4 21

4 1710 1212.1 186

2112.1810 12 2212 11.8 22

4 2112 11.311.4 196

8 11.7 2211.6 2310

12 11.3 22

illustrating some examples of the results. As the tableand figures show, for a constant die nose radius themaximum punch loads do not change with change inthe punch nose radii. Indeed, the function of the punchnose radius is mainly to transmit the punch load to the

side walls of the cup. As was shown earlier, the punchload is proportional to the bending and unbendingstresses, the frictional stresses and the tensile strength ofthe sheet metals. In other words, the punch shoulderradius itself does not alter the punch load and its

Fig. 6. Effect of the punch profile radius on the punch load (Dieprofile radius=8 mm; blank diameter=82 mm).

Fig. 7. Effect of the punch profile radius on the punch load (Dieprofile radius=12 mm; blank diameter=90 mm).


Fig. 8. Effect of the die profile radius on the rupture force (Blankdiameter=90 mm).

is inversely proportional to the die nose radius, its valuefollowing the equation 103/(a+brd), where a and b areparameters that depend on the blank diameter, theirvalues being found. The limiting blanks diameter wereexamined, the LDRs being found to be within the range1.95–2.15. The punch shoulder radius did not con-tribute to the maximum punch load, its function beingto transmit the punch load to the cup walls. Therupture force and therefore the punch stroke anddrawability increased with increasing of the punch noseradius.

6. Nomenclature

a, b constantsFp punch forceK coefficient of strengthrp punch radius

blank thicknesst0

rd die profile radiuso effective strain

coefficient of frictionm

sb bending stresssu unbending stress

wall drawing stresssw

Fb blank holder forcework-hardening exponentnplastic strain ratioRperipheral and current radius of the blankr0, rpunch profile radiusrp

width and thickness strainsow, ot

h coefficient of constrainedsf1 frictional stress on the die flange

frictional stress on the die profilesf2

sr1 radial drawing stress on the die flangesr2 radial drawing stress on the die profile

Acknowledgements

Financial support by the Office of Research Councilof Shiraz University through grant number 69-EN-606-324 is appreciated.

References

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maximum value, but has an effect on the manner of thetransmission of the load. As Figs. 6 and 7 show, thegreater the punch radius, the more gradual is the rise ofthe punch load and the further that the punch travels,but the maximum punch load is almost unaffected.

Fig. 8 compares the rupture forces for differentpunch radii, from which it is observed that for aconstant punch nose radius the rupture forces are inde-pendent of the die shoulder radius, but are increased byincreasing the punch nose radius. In other words, byusing a greater punch nose radius, rupture occurs at agreater force and therefore a longer punch stroke takesplace, which means that drawability can be increasedby using a greater punch shoulder radius.

The failure sites were usually at the bottom of thecup walls close to the cup shoulder. The yield stress ofthe material in this area is low, because it has beenwork hardened the least in the drawing process. Toimprove the drawability, this failure site must be movedupwards into the material that has been strengthenedby more prior work hardening. Choosing a greaterpunch nose radius causes the failure site to move up-wards and therefore increases the drawability.

5. Conclusions

The cup drawing of commercial aluminum blanksusing a laboratory deep-drawing machine with 120 kNload capacity has been examined. The stress-straincurves and anisotropic behavior of the blanks materialwere determined. Within the range of blank diametersinvestigated the critical shoulder radii of the dies weredetermined. It is found that the maximum punch load


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optimization of the tool geometry in the deep drawing of aluminium

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