Journal of Materials Processing Technology 187188 (2007) 8993

A study on the springback in the shee-Tasity, Ansu, I

Abstract

The flang nk ussupporter. T cernsnot parallel affec

This study etal fllike the punc rce (B

The sprin t usinwhat the ma nentbeen reveale fact hwith the dev

The Tagu f thesection para ts shfactor of the 2006 Else

Keywords: Flange drawing; Springback; Taguchi method

1. Introdu

The flanfrom the shoptionally wis firmly grmoves dowkeep the flaobtain a flathe formedof angle ofsentative inthe blank bredistributi

Variousspringbackprocess facthe flange d

CorresponE-mail ad

0924-0136/$doi:10.1016/jction

ge drawing process is used widely to make flangeseet metal blank using the die, punch and blank holder

ith the supporter. As shown in Fig. 1, while the blankipped with the blank holder and the die, the punchn to make flange. The supporter could be used tonge section as flat as possible during the process to

nge with higher flatness. When the die set is removedblank experiences springback to result in the changethe flange section, which is considered as a repre-dicator showing the effect of the residual stress inecause springback phenomenon occurs due to the

on of internal stress of the blank.process factors of the flange drawing can affect the. It is very important to find out the most influencingtor on springback to design a successful die set forrawing.

ding author. Tel.: +82 41 530 1356; fax: +82 41 530 1550.dress: swlee@sch.ac.kr (S.-W. Lee).

In this work, several process factors have been first cho-sen by carrying out some finite element analyses with relatedexperiments. Secondly, these factors have been assessed com-prehensively by the Taguchi method.

2. Finite element modeling

Fig. 2 shows a finite element model for the flange draw-ing process. The commercial code LS-DYNA3D was used forthe simulation. It is assumed that the blank is under the planestrain condition because of relatively very large width com-pared with the thickness of the blank. The blank was modeledwith Belytschko-Tsay shell elements while the die set was mod-eled with rigid elements. Seven integration points are allocatedalong the thickness direction of the blank to take up bendingdeformation effectively. The blank-holding-force (BHF) and thesupporting-force (SF) are applied to the model in the form ofconcentrated forces on nodes. Three types of corner radii, 3,6 and 9 mm, are used to describe the die corner (DR) and thepunch corner (PR) for the purpose of comparison. The num-ber of elements used to depict the corner radii was determinedfrom the guidelines of Ref. [1]. The material for the blank is

see front matter 2006 Elsevier B.V. All rights reserved..jmatprotec.2006.11.079Sang-Wook Lee a,, Yoona Department of Mechanical Engineering, Soonchunhyang Univer

b Kyungshin Industrial Co. Ltd., 994-13 Dongchun 2, Yeo

e drawing process is used to make flanges from the sheet metal blahis process is being applied in many sheet metal industries. One of conwith the original blank due to the springback occurrence, which could

has focused on the evaluation of springback occurring in the sheet mh corner radius (PR) and die corner radius (DR), the blank-holding-fo

gback phenomenon in the flange drawing process has been studied firsin causes of springback are. The distribution pattern of local x-compod to be very important in predicting the final shape of the flange. Thiseloped test dies.chi table L18 has been used to determine which of the process factors ollel with the original blank in spite of springback occurrence. The resulprocess.vier B.V. All rights reserved.t metal flange drawinge Kim bsan, Chungnam 336-745, South Koreancheon 406-130, South Korea

ing the die, punch and blank holder optionally with theof this process is that the flanged section formed is mostlyt the quality of the formed part.ange drawing process by controlling some process factorsHF), the supporting-force (SF), the lubrication and so on.g the finite element method (FEM) in order to understandof stress along the longitudinal direction of the blank hasas been backed up by the experimental results carried out

flange drawing is the most influencing to make the flangedow that the punch corner radius (PR) is the most important

90 S.-W. Lee, Y.-T. Kim / Journal of Materials Processing Technology 187188 (2007) 8993

Fig. 1. A schematic drawing showing the configuration of the flange drawingprocess.

Fig.

SUS316L.and the pro

An expeelement of[2]. A lighthe blank sinto the die

Fig. 3. Illustrative drawing of the expected path of the local x-component ofstress of the blank element during the forming stage.

stress on its upper surface rises up to the point C during bending.Unbending follows just after the bending mode finishes at about

fwaylocal

ave

die cstre

ific pmenmen

Table 1Process param

Process param

Max. Punch s

Punch velocit

Blank-holding

Initial blank sInitial blank t

Material: SUSYoungs mPoissons rLankford vYield stressStressstrathe halof thestress wat the

Thea specthe elethe ele2. Finite element model for the flange drawing process.

Table 1 shows the material properties of SUS316Lcess parameters used in the simulation.cted path of the local x-component of stress for anthe blank during the forming stage is shown in Fig. 3t-stretching mode occurs at the interval of A to B astarts to deform. When the element of the blank enters

corner zone, bending deformation takes place. The

Fig. 3. Thuconsidereddepends on

3. Represe

3.1. Case

A schemfiguration a

eters and material properties used in the finite element simulation

eters

troke

y

-force and supporting-force per unit width

izehickness

316Lodulus (E)atio ()alue (R)(y)

in curvepoint along the die corner to cause the sign reversalstress (from C to D). The stress relaxation caused bys coming out from the bending and unbending eventsorner takes place at the interval of D to E [3].ss distribution over the entire elements of the blank atrocess time can be obtained from the information ofts position in the die set since the local stresses of allts in the blank move along the stress path as shown ins, the stress distribution just after the forming stage isthe most important because the shape by springbackly on the internal stress state.

ntative cases of springback

1: PR = DR and BHF = SF

atic drawing showing the expected deformed con-nd the sign of stress at the outer surface of the blankValue/condition

30 mm

1000 mm/s (in analysis)0.25 mm/s (in experiment)50 N (total: 1.75 kN)100 N (total: 3.5 kN)200 N (total: 7.0 kN)35.0 mm 173 mm0.6 mm

185.232 GPa0.31.81230.157 MPa = K(o + p)n: o = 0.022638, K = 1257.614 MPa, n = 0.4483

S.-W. Lee, Y.-T. Kim / Journal of Materials Processing Technology 187188 (2007) 8993 91

Fig. 4. A schethe signs of swhen PR = DR

Fig. 5. The dments of the b

is represenequals to Sexpected todition. The(upper or lo

A compAs expecteis point-sythe stress dthat the regforming staand vice veof stress of

Fig. 6. The dthe experimen

schematic diagram showing the expected deformed configuration ands of stress at the outer surface of the blank just after the forming stage

< DR and BHF = SF.

rredbackted sat ofblan

ngbato b

ase 2matic diagram showing the expected deformed configuration andtress at the outer surface of the blank just after the forming stage

and BHF = SF.

Fig. 7. Athe signwhen PR

be infespringcompuwith thof theof sprichange

3.2. Cistribution of the local x-component of stress over the entire ele-lank before and after springback when PR = DR and BHF = SF.

ted in Fig. 4 in which PR equals to DR and BHFF. The amount of draw-in at both ends of the blank isbe the same because of the balanced boundary con-expected sign of the local stress at the outer surfacewer surface) of the blank is deduced from Fig. 3.uted result of stress distribution is shown in Fig. 5.d from Fig. 4, the left half side of stress distributionmmetric against the right one. The sign reversal ofuring the springback stage can be seen. This meansions having the positive sign of stress just after thege tend to bend inward during the springback stagersa. Therefore, with the information about the signthe outer surface in hand, springback shape could

eformed shape before and after springback by computation withtal result when PR = DR and BHF = SF.

Fig. 7 shtion when DSF being ecorner radiside becaucorner radition occursFig. 8. Notis wider wlocal stressresult aftermental resuthe doubleas shown inhaving the

Fig. 8. The dments of the b. Fig. 6 shows the deformed shape before and afterby computation with the experimental result. Thehape of after springback is seen very well coincidentthe experiment. It is notable that the two flat sectionsk keep almost parallel with each other regardlessck, meanwhile the wall region undergoes geometricecome z-shaped configuration due to springback.

: PR = DR and BHF = SF

ows a schematic drawing of the expected configura-R is greater than PR under the condition of BHF and

qual. The amount of draw-in at the side with a largerus is expected to be much more than that at the otherse the material flow tends to be much easier as theus becomes larger. Therefore, most of the deforma-at the side with the larger corner radius as shown in

ice that the unbending and relaxation region in Fig. 8hen compared with Fig. 5. The sign reversal of theduring springback can be also seen. The computedspringback is seen well coincident with the experi-lt as represented in Fig. 9. It is noticeable that whendotted line is drawn extending the flat flange sectionFig. 9, the springback occurs actually at the left sidelarger corner radius.

istribution of the local x-component of stress over the entire ele-lank before and after springback when PR < DR and BHF = SF.

92 S.-W. Lee, Y.-T. Kim / Journal of Materials Processing Technology 187188 (2007) 8993

Fig. 9. The dthe experimen

Fig. 10. A schthe signs of swhen PR = DR

Fig. 11. Theelements of th

3.3. Case

A schemBHF is grethe amountthan that athe formindraw-in, wat the side

4. Estimamethod

The amdefined as

The deformed shape before and after springback by computation withrimen

. This thonalmendeformed shape before and after springback by computation withtal result when PR < DR and BHF = SF.

Fig. 12.the expe

Fig. 13factororthogrecom

[4].ematic diagram showing the expected deformed configuration andtress at the outer surface of the blank just after the forming stage

and BHF > SF.

distribution of the local x-component of stress over the entiree blank before and after springback when PR = DR and BHF > SF.

3: PR = DR and BHF = SF

atic diagram for the case when PR equals to DR butater than SF is shown in Fig. 10. It is expected thatof draw-in at the side with a smaller force is larger

t the other side. Thus, most of the deformation byg operation is concentrated on the side of the largerhich is presented in Fig. 11. Springback also occursof large draw-in as shown in Fig. 12.

tion of the process factors using Taguchi

ount of springback in the flange drawing process isthe angle between the two flat sections shown in

Based ofollowing fi

Lubrication (LGreas

Punch corner3 mm

Die corner rad3 mm

Blank-holding50 N

Supporting-fo50 N

Table 2back angle(ANOVA)the effectsof ANOVAhave contriThe F-testexplainingThis meansare selected

The ordlows: PR >

Only PRof 0.1. It islutely domnegligible.

The aveshown in Fis the large

Fig. 13. Defintal result when PR = DR and BHF > SF.

e Taguchi method is used to estimate which processe most influencing one on the springback angle. Thearray L18 is chosen for use since it is one of the mosted table to investigate the main effects of the factors

n the results mentioned in the previous section, theve process factors and their levels are selected.

ub)e noneradius (PR)

6 mm 9 mmius (DR)

6 mm 9 mm-force per unit width (BHF)

100 N 200 Nrce per unit width (SF)

100 N 200 N

represents the computational results of spring-of all the eighteen cases. The analysis of variance

of is carried out in order to measure the degree ofof the factors on springback quantitatively. The result

is represented in Table 3. The model is shown tobution explaining about 80 % of the total variation.on the model shows that the model is significant forthe springback result at the significance level of 0.1.that the five factors, the components of the model,well.

er of strong factors influencing springback is as fol-DR > BHF > SF > Luband DR are the factors within the significance levelnoticeable that the effect of the PR factor is abso-

inant whereas the effect by lubrication is considered

rage response curves for the five process factors areig. 14. It is again confirmed that the variation by PR

st among the five factors.

ition of the springback angle in the flange drawing process.

S.-W. Lee, Y.-T. Kim / Journal of Materials Processing Technology 187188 (2007) 8993 93

Table 2Experimental layout of Taguchi table L18 and the obtained data

Case Lub PR (mm) DR (mm) BHF (N) SF (N) (deg)1 Grease 3 3 50 50 0.482 100 100 11.463456789

101112131415161718

Table 3Result of anal

Source of var

ModelLubPRDRBHFSF

ErrorTotal

Fig. 14. Avering.

5. Conclu

From thprocess facing conclus

(i) It haswherestrongGrease 3 6Grease 3 9Grease 6 3Grease 6 6Grease 6 9Grease 9 3Grease 9 6Grease 9 9None 3 3None 3 6None 3 9

None 6 3None 6 6None 6 9None 9 3None 9 6None 9 9

ysis of variance (ANOVA)iation Sum of squares DOF

362.347 (78.36%) 92.793 (0.60%) 1

239.598 (51.82%) 285.886 (18.57%) 223.126 (5.00%) 210.945 (2.37%) 2

100.085 (21.64%) 8462.433 (100%) 17

age response curves of the five process factors of the flange draw-

sions

e computational and experimental results with thetor estimation using the Taguchi method, the follow-ions can be drawn:

been shown that the information about the placespringback will occur inward or outward and how

ly it will happen can be obtained from the distribu-

tion oformin

(ii) Springthe amcorner

is, the(iii) The o

been sturned

Reference

[1] S.W. Lee,springbacJ. Mater. P

[2] S.W. Lee,cations toDaejeon,

[3] K. Mattiaspringbacceedings opp. 1151

[4] G. TaguchMichigan200 200 8.6550 100 10.02

100 200 16.76200 50 17.39100 50 11.51200 100 12.05

50 200 12.38200 200 0.46

50 50 12.00100 100 7.17100 200 20.09200 50 16.46

50 100 12.13200 100 10.75

50 200 16.68100 50 12.05

Mean square F0 Pr > F0

40.261 3.218 0.0572.793 0.223 0.649

119.799 9.576 0.008

42.943 3.433 0.08411.563 0.924 0.435

5.472 0.437 0.660

12.511

f the local x-component of stress just after the flangeg operation.back tends to occur more strongly on the side whereount of draw-in is large. Therefore, the larger theradius of die set and the smaller the clamping forcemore strongly the springback takes place.rder of strong factors influencing springback hashown as PR > DR > BHF > SF > Lub. Particularly PRout to be the most dominant factor among them.

s

D.Y. Yang, An assessment of numerical parameters influencingk in explicit finite element analysis of sheet metal forming process,rocess. Technol. 8081 (1998) 6067.Elastoplastic Explicit Finite Element Formulation and its Appli-Sheet Metal Working with Springback, Ph. D. Thesis, KAIST,

Korea, 1998.sson, P. Thilderkvist, A. Strange, A. Samuelsson, Simulation ofk in sheet metal forming, in: S. Shen, P.R. Dawson (Eds.), Pro-f NUMIFORM95, Balkema, Rotterdam, The Netherlands, 1995,24.i, S. Konishi, Orthogonal Arrays and Linear Graphs, ASI Press,

, 1987.

A study on the springback in the sheet metal flange drawingIntroductionFinite element modelingRepresentative cases of springbackCase 1: PR=DR and BHF=SFCase 2: PRDR and BHF=SFCase 3: PR=DR and BHFSF

Estimation of the process factors using Taguchi methodConclusionsReferences