Research Article An Alternate Method to Springback ...downloads.hindawi.com/journals/tswj/2014/301271.pdfResearch Article An Alternate Method to Springback Compensation for Sheet Metal

Research ArticleAn Alternate Method to Springback Compensation forSheet Metal Forming

Waluyo Adi Siswanto1 Agus Dwi Anggono2 Badrul Omar3 and Kamaruzaman Jusoff4

1 Department of Engineering Mechanics Universiti Tun Hussein Onn Malaysia Parit Raja Batu Pahat 86400 Johor Malaysia2 Department of Mechanical Engineering Muhammadiyah University of Surakarta Pabelan Kartasura 57162 Indonesia3 Department of Materials Engineering and Design Universiti Tun Hussein Onn Malaysia Parit Raja 86400 Johor Malaysia4 Faculty of Forestry Universiti Putra Malaysia Serdang 43400 Selangor Malaysia

Correspondence should be addressed to Waluyo Adi Siswanto waluyouthmedumy

Received 20 February 2014 Revised 6 May 2014 Accepted 18 May 2014 Published 11 June 2014

Academic Editor Hailiang Yu

Copyright copy 2014 Waluyo Adi Siswanto et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The aim of this work is to improve the accuracy of cold stamping product by accommodating springback This is a numericalapproach to improve the accuracy of springback analysis and die compensation process combining the displacement adjustment(DA) method and the spring forward (SF) algorithm This alternate hybrid method (HM) is conducted by firstly employing DAmethod followed by the SF method instead of either DA or SF method individually The springback shape and the target part areused to optimize the die surfaces compensating springback The hybrid method (HM) algorithm has been coded in Fortran andtested in two- and three-dimensionalmodels By implementing theHM the springback error can be decreased and the dimensionaldeviation falls in the predefined tolerance range

1 Introduction

The Sheet metal forming (SMF) is one of forming processesperformed on metal sheets strips and coils Press workingis the term often applied to sheet metal operations becausethe machines used to perform these operations are pressmachines A part produced in a sheet metal operation isoften called a stamping product SMF process consists ofstamping forming bending stretching and trimming Theterms refer to various processes used to convert a sheet metalinto different shapes for a large variety of finished usefulproducts Since SMF process produces the same productsit has become one of the most important manufacturingprocesses in industry particularly in the automotive and steelindustries [1]

Every process of sheet metal forming or stamping processinvolves elastic forming and then followed by permanentplastic deformation Since the presence of elastic properties

of metals after the unloading phase the elastic springbackphenomenon always occurs resulting in an off-target formedshape Springback is dimensional deviation due to the elastic-ity of a metal sheet during unloading and following forming[2] Although it is impossible to eliminate the springbackphenomenon minimizing springback can be done by adopt-ing three approaches The first one is based on controllingthe blank holder force (BHF) The blank holding force isnot fixed but as a controlled variable the blank holdingforce is known as variable blank holder force (VBHF) sothat the springback can be minimized The second approachis by using a hot forming process and the third one is byoptimizing die surfaces (die compensation) to accommodatethe springback

TheVBHFwas initially proposed byLiu et al [3] to reducethe springback error of U-bend model of NUMISHEET101584093The VBHF was determined by calculating the value of lowblank holder force (BHFL) and high blank holder force

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 301271 13 pageshttpdxdoiorg1011552014301271

2 The Scientific World Journal

(BHFS) In the report [3] the VBHF approach successfullyreduced the springback error compared with that from con-stant blank holder force (CBHF) The application of VBHFhas been extended and published by researchers recently Liet al [4] investigated the subsection of VBHF in rectangularparts and then Kitayama et al [5] presented specifically theoptimization of VBHF to reduce the springback A precisionbinder force control during forming is required makingthis process sensitive to any variations in manufacturingconditions such as punch speed time control and friction

The study of springback reduction by the temperaturevalue of tool in hot forming has been investigated [6] Itis found that the cold punch combined with the hot diecan reduce the springback up to 20 when compared toconventional room temperature bending test in the sheetforming process of U-bend aluminum 1050 The experimen-tal investigations in hot forming process can be found inthe latest publications [7ndash9] Temperature in the springbackprediction is becoming a topic that could be improved in thefuture investigation [2]The springback value before and aftersplitting process is differentThis has been studied using split-ring tests for aluminum alloy [10]

The major advantage of the first strategy to minimizespringback is that it is not necessary to modify the toolingsurface However there are several implementation difficul-ties such as implementing the force control or force sensor inthe application ofVBHFbeing highly cost sensitive Similarlyin the hot forming process it requires additional equipmentto control the temperatures of the tools and the blank sheetso that the forming process becomes more complicated andexpensive

In the third method (die compensation) it requires manysteps of works on tooling design stage but its potential tocompensate springback completely is faster and cheaper evenfor complex model Die face adjustment to compensate thespringback was donemanually in the past by doing extensivemeasurements on the prototype or even production tools andrefining the tool surface geometry by hand polishing whichis time consuming [11] Wagoner et al [2] categorized thecurrent research of springback in five topics that is plasticconstitutive equations variable Youngrsquos modulus through-thickness integration of stress magnesium and advancedhigh strength steels (AHSS)

Finite element (FE) and numerical and process simula-tion have gained popularity in the stamping industry due toits speed and low cost and it has been proven to be effectiveand efficient in the prediction of form ability and springbackbehavior [12 13] The accuracy of springback simulationis not only related to springback analysis itself but alsostrongly dependent on the accuracy of forming processesAny calculation error obtained from every simulation stepof forming processes will be accumulated As a result theaccumulated error influence the accuracy of the springbackprediction analysis at the last step of the simulation Linget al [13] tried to reduce springback in L-bending by usingthe optimization of die radius clearance step height and stepdistance The results show a good reduction in springbackbut this method is applied and tested in the L-bending onlyThe U-bending model is analyzed by Slota et al [14] in

both numerical and experimental analysesThe experimentalanalysis is conducted by using specimens of steel DC06UHSS TRIP RAK 4070 and HSS H220PD in orientations0∘ 45∘ and 90∘ The results show that the simulations arein a good agreement with the experiments The springbackin sheet forming can be simulated accurately by using finiteelement method but the big problem is to apply the results toproduce stamped parts in accurate dimension

In order to accommodate the springback and to opti-mize the die based on surface modification there aretwo methodologies available called displacement adjustment(DA) compensation and spring forward (SF) compensationThe concept of DAmethod [15] is to translate the nodes in thedirection opposite to the springback which is adopted fromthe real springback investigation whereas the SF method isbased on stress state during forming which is multipliedby negative factor and then loaded to the deformed shapeto realize the compensated surface [16] The compensationmethod based on calculated springback by implementing theDA method can be done in a computer program [17] Themodification of die surface for springback compensation canbe done faster There are many researchers who reported theimplementation of these two methods in various springbackaccommodation problems and are dealing with minimizingspringback errors [18ndash20]

One of the advantages of DA method is that it canconverge rapidly because of the algorithm being based onthe real springback measurements not virtual springbackcalculation whichmay develop instability during the numer-ical solution [15] Unfortunately the original DA method ismostly applicable to compensate surfaces in the direction ofthe punch travel The wall area of the dies therefore couldnot be compensated [21]

On the other hand the SF method could compensate diesurface in almost all directions because of the deformationbeing caused by the stresses of the deformed part in theopposite direction [22] In the original concept of springforward [16] only inverted bending stress will be used tocreate the spring forward shape The inverted membranestresses must be eliminated since they will contribute to theunstable buckling condition during the numerical calcula-tion Another disadvantage of SFmethod is that the approachis not based on the reality of physical occurrence but aninverted springbok The complexity of inverted bendingstress distribution in the deformed shape is very difficult toapply in an experiment even impossible [21] In order to solvethe problem finite element simulation analysis can be used toexplain the influence of residual stress in springback formingas done by Brabie et al [23] It shows that residual stressis influenced by the BHF and coefficient of friction in bothcylindrical and conical forming They analyze the residualstress during forming and after springback but do not explainhow tominimize the springback related to the residual stress

Force descriptor method (FDM) proposed by Karafillisand Boyce [22] is SF method based This method has twoparameter vectors the original part shape and the inter-nal forces The theoretical base of the FDM is that afterbeing formed to the original tooling shape the part wouldspringback to the original unloaded shape recovering from

The Scientific World Journal 3

Blank sheet

Form to target

(1)

(2)

1st compensated dies

Form to 1st compensated dies

(Force is recorded)

compensated dies

(Errorvalue = Δl )

Compare spring minus target

(Apply force to deformed part)

f f

Compare springback minus target

2nd

Figure 1 Illustration of compensation procedures in hybrid method

the internal force By spring forward the stress free originalshape with the reversed internal force a tooling shape closeto the original shape could be obtained Considering a simplebending case the internal force in the first iteration is lowerthan the final force which means that the FDM needed moreiterations Cheng et al [21] modified this approach in thefirst iteration by replacing the internal force with the internalforce obtained from the manual calculation to accelerate thecompensation

Wagoner et al [24] proposed the displacement adjust-ment method At first forming a flat sheet is deformed to theoriginal die shape After springback the shape is comparedwith its target to obtain the shape error In the next step theamount of shape error is added to the current die shape toobtain the new compensated shape During the next iterationa blank sheet is deformed to the new compensated shapeIf the shape error is not in the range of tolerance anotheriteration will be conducted Wagoner and coworkers claimedthis method is effective and converges more rapidly than theFDM

In the present research a new approach in accommodat-ing springback is themain objectiveThis research aims at thedevelopment of a compensation procedure that can performthe optimization process using the combination of fastconvergence displacement adjustment (DA) and the flexiblespring forward (SF)methods so that the combinationmethodwill be fast and applicable for all die surfaces The methodguides the die surface modification process to compensatefor springback following the displacement adjustment thenit continues to compensate the springback error in forwarddirection (spring forward) The new combined method isthen called hybrid method (HM) die compensation

2 Proposed Compensation Method

The hybrid method (HM) is a combination of DA and SFmethod The procedures of HM are illustrated in Figure 1

The basic process of the hybrid method can be explained as asimple forming process a flat metal sheet is bent downwardsbeyond its elastic region

The part is deformed into the initial reference geometryas indicated by 119862119894tool After the springback the formed shapedistorted to an error value Δ119871 as seen in Figure 1(1) Thereference target shape is then adjusted to Δ119910 = minusΔ119871 Thenew shape modification field 119862119894+1tool is adjusted directly fromthe reference product 119862119894tool producing the first compensateddie geometry 119862119894+1tool = 119862

119894

tool + Δ119910119894

This process is basically following the DA method Thenew die shape is then used for the next forming as seen inFigure 1(2)

If the springback after the unloading process falls outof tolerance at the first compensation then the part is bentdownwards to the new geometry by applying the invertedinternal force 119865119894internal calculated from residual stress (SFalgorithm) read as

119862119894+1

tool = 119862119894

tool + 119865119894

internal (1)

and then sprung forward to the new shape The deviationshould be lower than before and much closer to the referencegeometry If the error is still out of the acceptable tolerancethe compensation process is then continued to new iterationcycle by considering the deviation field (Δ119910119894+1) to create a newdie surface The shape deviation field is calculated betweenthe reference geometry to the last springback geometryThe resulting shape modification field needs to be appliedfollowing (1) to the last compensation geometry

The iteration process continues until the formed shapeafter the springback falls withn the allowable tolerance of thedesired shape by implementing an alternate hybrid algorithmof DA and SF The algorithms are coded in Fortran to dothe iteration processes The internal residual stresses of theformed shape are obtained from the fully formed simulationresults The internal bending stresses are then converted into


finite elemental forces as the input load to the HM springforward phase The forces are then applied to the finiteelements of the springback shape The result is compared tothe original shape to check the shape deviation error

To validate the accuracy of the developed hybrid algo-rithm for die compensation a compensated die surfacegenerated by hybrid method was tested in Autoform Thespringback was then simulated in this software and thencompared with the reference shape To use the die surfaceof HM in Autoform the finite elements of the die surfacesshould be modified to complete die parts that is binder andpunch For this purpose CATIA was selected to modify andcreate a surface for springback simulation in Autoform TheHM springback result is then compared with that from Aut-oform build-in springback compensation module The toolsurfaces are automatically adapted to the new compensatedgeometry On the compensation stage the sprung back shapeand the reference geometry are neededTheoverall procedureis shown in Figure 2

The flow of simulations starts from input data of surfacedie tools consisting of die punch binder and reference sur-face The part after springback is compared to the referencegeometry for a deviation gap (error) checking If the error islarger than the allowable tolerance the die surface needs to becompensated The generation of compensating surface datais delivered by the software based on DA algorithm Anothersimulation is conducted with the new compensated surfaceuntil the error is within the tolerance [25]

In this presented research work the results of HM arecompared with those from the stand alone of DA and SFThecomparison results show some critical issues the maximumerror at every iteration cycle the number of iterations tocompensate the die surface and the total CPU time toconverge the compensated die surfaces

3 Numerical Simulation Results

The usage of the hybrid method (HM) algorithm to compen-sate springback by combining two methods of DA and SF ispresented in this section The results are compared againstthose from application software Autoform with springbackcompensation module

Two models representing two- and three-dimensionalproblems are used The two-dimensional (2D) springbackmodel is taken from the U-bending springback problemin NUMISHEET 1993 [26] while the three-dimensional(3D) springback problem is the S-rail benchmark model ofNUMISHEET 2008 [27]

31 Springback of 2D Model The U-bending problem con-sists of a set of punch holder die and blank sheet [26] Thethickness of the blank sheet is 08mm with the maximumpunch drawing 70mmat constant speed of 43msThe blankholder force varies between 1 5 10 15 20 and 25 kN Thesheet material is mild steel DC04 having a Youngrsquos modulus210GPa and Poissonrsquos ratio 03 An initial yield stress is1679MPa the reference stress value 119870 is equal to 550MPaand the work hardening exponent 119899 = 0223

Surface datadefine tolerance (ε)

Forming and springbacksimulation

Definition surface and compensation factor

Comparison springback part vs reference surface

Generate compensated surface

Export surfaces

Yes

No|Error| lt tolerance (120576)

Figure 2 Procedure of die compensation

Table 1 Properties of mesh refinement

AccuracyRadius

penetration(mm)

Maximumelement angle

(deg)

Maximumdisplacement angle

(deg)

Rough 032 45 32

Standard 022 30 22

Fine 016 225 16

The mesh quality in Autoform depends on the sets valueof parameters radius penetration maximum element angleand maximum displacement angle The mesh refinementvaries from rough standard and fine as shown in Table 1

The results of springback in various BHF are shownin Figure 3 The lowest springback deviation recorded infine mesh is 132mm under the highest BHF of 25 kN Thehigher the BHF the less the springback Kergen and Jodogne[28] have shown similar BHF trends against springbackin determining the minimum BHF for steels Hishida andWagoner [29] determined that a quality defect of productsformed by stamping processes such as fracture wrinkles andsurface distortion can be suppressed by the selection of theoptimum BHF values For the present 2D model here thelowest springback can be achieved by applying higher BHF

Investigation of the BHF effect continued with increasingthe value to reach the failure in forming simulation and tosee the thinning history The holding forces are extended to26 272 and 275 kN in terms of finding the optimum BHFFigure 3 and Table 2 show clearly that the high springbackdeviations (higher than 3mm) occur when the appliedholding forces are at 1 5 10 and 15 kN The risks of failurethinning and high strain arise under excessive holding forcesat 25 27 and 272 kN In the range from 25 to 275 kNthe simulations fail due to the high risk of splitting andfailure This can be seen from the forming limit diagramshown in Figure 4 as indicated in bright color The resultvariable maximum failure is defined as the ratio between the


0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Sprin

gbac

k (m

m)

BHF (kN)

Figure 3 Principal result of springback prediction

Table 2 BHF effect in springback thinning strain and failure

BHF(kN)

Springback(mm)

Thinning()

Plasticstrain Failure

1 727 002 007 0085 723 002 007 00710 475 004 008 01315 381 004 009 01920 198 006 012 02825 132 008 016 0426 131 008 020 04427 131 011 030 06272 131 014 040 07275 136 020 060 10

maximum major strain of an element and the major strainon the forming limit curve (FLC) for the same minor strainBased on the results the holding force in the range from 20to 24 kN is suggested as the optimum range of BHF that givesless springback without having a failure risk on the formedsheet

The adaptive refinement mesh type in Autoform affectsthe results of springback Figure 5 shows how element qualityaffects the springback in the selected holding force 20 kNThe fine meshing shows the closest springback to the exper-imental result [26] The highest springback however occursat the flange positionThe deviations of other positions of theworkpiece are closer to the experimental results

32 Compensation of 2D Model For the compensation test-ing the case BHF 20 kN is selected with the fine mesh qualityand the friction coefficient 03This coefficient value is for thegeneral lubricated condition in the forming process [11] Inthe sheet metal forming boundary lubrication is the most

widely encountered It is defined as a condition where thesolid surfaces are so close The reference and springbacknodes generated by Autoform are modified to the coordinate119909 119910 and 119911 under text format to suit the HM input formatThere are 601 common points being selected at the referenceand springback used for the calculation of error and nodestranslations

Forming simulation for the second cycle is conducted byusing new compensated surfaces whichwere generated undercompensation factor 10 The compensation types availablein Autoform direct fixed and rigid body are tried It canbe seen in Table 3 that springback results are higher thanthe initial springback error 198mm (see Table 2) for rigidbody types Figure 6 shows the comparison of springbackhistory results for all compensation typesThe fixed draft typeconverges into the smallest springback error 153mmafter thefifth iteration

In rigid body there are three adjustments to compensateautomatic automatic 119911-direction and manual The entirearea defined as a rigid body is compensated relative to theaverage vector From the result this is only effective fora number of iterations not more than two At the seconditeration the rigid body can reach the lowest springbackvalue 158mm and then deviates more on the next iterationsDirect compensation type is influenced by compensationfactors only The compensation factor is 10 in each iterationThis compensation makes translation in every direction(119909 119910 119911) become based on the reference of a springbackshape By using fixed draft type it allows the compensationof surface regions while maintaining their angle towardsworking direction This fixed type gives better result thanothers and the springback deviation is only 153mm

The sectional view of compensated die and spring-back position can be seen in Figure 7 At the first itera-tion the springback position falls below the reference part(Figure 7(a)) whereas the fifth iteration the unloaded partstays at the top of reference surface (Figure 7(b))

Since the compensation algorithm in Autoform adoptsthe DAmethod which considers punch-axis direction there-fore the shape distortion in the sidewall is still significant asis clearly seen in Figure 8

The springback comparison between HM and Autoformfor 2D model is shown in Figure 9 It can be seen clearly thatHM performs better than Autoform At the first iterationthe springback can be decreased significantly to 126mmTheerror continues to decrease in the second and third iterationsbut then it fluctuates in the fourth iteration showing a highervalue than the previous one The springback reduction trendcontinues to the last (fifth) iteration The second and thirditeration results are getting higher due to the application ofSF method In the first iteration it gives a higher residualstress than that from the third iteration that will be used inthe SFmethod in the second and fourth iterationsThereforethe high residual stress has delivered high compensationvalue too as shown at the second iteration for 117mmand 097mm at the fourth iteration The proposed alternatehybrid method of DA and SF has successfully decreasedthe springback deviation to 067mm (reducing 66 from


Splits

Risk of Splits

Compressing

Safe

Thicking

Splits Risk of Splits

Compressing

Safe

Thickingminus05 minus04 minus03 minus02 minus01 00 01 02 03

Minor strain (true strain)

08

07

06

05

04

03

02

01

00

Maj

or st

rain

(tru

e str

ain)

Figure 4 Forming limit diagram under BHF of 275 kN

xxxx

x

x

Target

x

x

Target shape

minus10 0 10 20 30 40 50 60 70

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

X along projection

ExperimentFine

StandardRough

Figure 5 The influence of mesh refinement BHF 20 kN

the initial error) while Autoform decreased the springbackto 149mm (reducing 25 from the initial error)

The alternate HM method also improves the accuracy ofthe formed product in the sidewall The maximum deviation

0

05

1

15

2

25

0 1 2 3 4 5 6

Sprin

gbac

k (m

m)

Iteration

Rigid bodyDirectFixed draft

Figure 6 Springback error in every cycle of compensation

after the fifth iteration is 0935mm which is lower than thatfrom Autoform result 1533mm

33 Springback of 3D Model The benchmark of NUMISH-EET2008 has included an additional problemwhich is relatedto springback In this analysis the accuracy of springbackprediction is presented for three different models that is


XXX

X

X

X

XX

Compensated dieSpringback shapeX

minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

(a) Result from the first iteration


X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107

(b) Result from the fifth iteration


Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration

Figure 8 Highest deviation in the sidewall area

Table 3 Springback error after the fifth compensation BHF 20 kN

Type Compensation factor Working direction SpringbackDirect 10 119909 119910 119911 171Fixed draft 10 119911 153Rigid body 10 119911 235

without draw beads smooth draw beads and locking drawbeads

The material HX260LAD type of microalloyed steelgrades with high yield strength for cold forming has beenselected as the blank sheetmaterialThe summary ofmechan-ical properties of the material is shown in Table 4

Variations of BHF 90 120 and 150 kN are applied on theblank holder parallel to punch direction The comparisonresults use several reference sections of A B C and D [27]

The difference of draw bead design in the part geom-etry has a significant effect on springback The springbackdeviation in every section does not show consistent trendwhen different BHFs are appliedThe inconsistent springback


0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM

AutoformHybrid method

U-bend autoform

Figure 9 Compensation of U-bending results

Table 4 Summary of mechanical properties HX260LAD

Orient Thickness(mm)

Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981

results are presented in Figures 10(a) 10(b) and 10(c) In thelock beadmodel the increase of BHF from 90 to 120 kN giveshigher springback of 206mm and 215mm in sections Band D and lower springback in sections A and C of 212mmand 195mm respectively When the BHF is applied higherat 150 kN the springback decreased in sections B and C to192mm and 195mm respectively All of these deviationsshow that the S-rail is in a twisting mode In a square cupmodel where twisting does not occur Demirci et al [30]showed the trend of higher BHF to reduce the springbackerror In this result the experimental validation with drawbeads is not directly performedThe springback experimentalvalidation however has been conducted in different spring-back benchmark problems [26 27] and found that Autoformcan predict springback in the range of experimental results

By looking at the average springback in all sections(Figure 10(d)) the trend of springback in different holding

forces can be seen Both smooth and locked beads showthat increasing the holding force can reduce the springbackdeviation Under the smooth beads the springback decreasesfrom 197mm to 187mm when the holder force increasedfrom 90 kN to 150 kN A similar trend is shown for lockedbeads It decreases the springback from 21mm to 205mmWhen the drawing process does not use any beads thetendency of the springback error to the increasing holdingforce cannot be predicted but fluctuated

In terms of the meshing variation the recorded meanspringback error in standard mesh type (33147 elements) is187mm the fined mesh 178mm (56054 elements) and theroughmesh 192mm (17758 elements)Themesh density andthe computer CPU (Central Processing Unit) time in Inteli5 processor are shown in Figures 11(a) and 11(b) The totalCPU time to finish the simulation for finemesh type is 26786minutes the standard mesh needs 12136 minutes and therough type only needs 511 minutes

The increment number of fines standard and rough typesare 36 33 and 29 increments at the end of the simulation

The optimum result can be achieved with the com-bination parameters of holder force 150 kN with smoothdraw beads in standard mesh type The forming limitdiagram (FLD) using thementioned combination is shown inFigure 12 The figure shows that there is no risk of splits andexcess thinning when the blank sheet has been fully formed

34 Compensation of 3D Model For die compensation theS-rail model material HX260LAD BHF 150 kN with smoothbeads in standard mesh type is selected The mean spring-back result of this case is 187mm as depicted in Figure 13(a)The reference and springback model of S-rail is convertedas point clouds to be used as the input file of HM Thefirst iteration is conducted by translating the springbacknodes following the DA method and then to the inverse ofspringback (SF algorithm) to get the first compensated die asshown in Figure 13(b)

For convergence control a tolerance error 1mm is usedAfter the fifth cycle the mean springback can be decreased aslow as 083mm and the iteration process terminated (error lt1mm) Figure 14 shows the compensated die surface and thespringback after fifth iteration

To use the die surface of HM results in Autoformthe elements must be modified to form the die surfacecomponents that is binder and punch CATIA is used tomodify and to create surface for springback simulation inAutoform After springback simulation theHM result is thencompared with the springback from Autoform

Figure 15 shows the springback compensation history ofthe alternate HM method compared with Autoform Thefirst iteration of HM has decreased the springback error to113mm(39 reduction from initial value)With the alternateDA and SF after the fifth iteration the springback deviationcan be reduced by 55 from the initial error value from187mm to 083mm while Autoform can only reduce to123mm or 34 reduction


19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)

(b) Smooth bead model

0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)

(c) Without bead model

185

19

195

2

205

21

215

0 50 100 150 200

LockbeadSmoothbeadNobead

BHF (kN)

Sprin

gbac

k (m

m)

(d) Springback mean value

Figure 10 Springback error in sections A B C and D

The fluctuation of HM shown in Figure 15 is due to theswitching method from DA to SF in the first time In thenext iteration cycle the shape is in a stable condition and canconverge to reduce the springback deviation

4 Discussion

In die compensation the die surface results rely on spring-back analysis and the deflection history of elements under thebending and unbending processes

Deformation theory could be used in prediction insteadof flow theory Accurate data and parameters will requiremore complicated optimization to accommodate deforma-tion history Therefore the springback analysis accuracy wasinfluenced by many factors

Theuse of appropriatematerialmodel in springback anal-ysis is one factor to improve the accuracy because the correctmaterial can provide an accurate stress state at the end ofthe forming stage It is useful if the material model is basedon the initial yielding and hardening parameters obtainedfrom the average of multiple experiments The accuracy ofspringback prediction is also influenced by the coefficient offriction between the blank sheet and the die surfaces

The use of combination between optimum blank holderforce and draw beads will reduce the springback deviationFor complicated three-dimensional model where the spring-back is not as simple as bending problem but involvingtwisting mode finding the optimum drawing parameters isnot straight forward but a simulation series is required to findthe best configuration for a minimum springback


0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0

(a) Element mesh increment

Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01

0minus03 minus01minus02 0 01 02 03 04


Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking

Figure 12 Forming limit diagram of the BHF 150 kN

Springback distortion also depends on the bendingmoment which in turn depends on the stress distributionthrough sheet thickness Shell elements require numericalintegration of stress and strain distribution The largest ofintegration points will improve the accuracy but conse-quently is more time consuming

In these works the HM has been coded in Fortranmainly to enable the alternate methods of DA and SFThe displacement adjustment (DA) strategy is intended to

generate compensated nodes by translating the nodes in theopposite direction to the springback The magnitude of thevector translations calculated from the origin and springbackposition are distributed in all directions Δ119910 Δ119909 and Δ119911corresponding to the axes of 119909 119910 and 119911

The strategy to speed up the springback reduction is byusing a large compensation factor to the translation vectorswhich later copied to the die surfaces This reduces thespringback error significantly in the first cycle (see Figure 15)


After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface

(a) Springback from original die

After springbackTarget surface1st compensated surface

xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection

(b) Compensation from the first springback

Figure 13 Springback and compensation

xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

After springbackCompensated surfacex

Figure 14 HM die compensation after five cycles

In the subsequent process the applied load force in springforward algorithm is obtained from the internal stress at fullyloaded phase The stresses are converted to inverted loadforces

5 Conclusion

In this research two different methods displacement adjust-ment (DA) and spring forward (SF) are joined in alternatemanner to compensate the die tools to minimize springbackerror called hybrid method (HM) When it is used in onealgorithm there are advantages to converge faster and abili-ties to compensate in all sides A new approach in springbackaccommodation using the alternate hybrid method (HM)has been tested in two- and three-dimensional springbackproblem models The results show that in two-dimensionalmodels it can reduce the springback up to 66 in afterfive iteration cycles and in three-dimensional 55 In thecomparison result with Autoform the HM method showsbetter performance while the Autoform can reduce 22 and35 only for two- and three-dimensional models The HM isan alternate method to reduce springback error based on dietool compensationThis is applicable for sheet metal formingon stamping process having lower and upper dies

The implication of this research is that the approach ofaccommodating springback can be further extended to theimplementation of HM in user friendly application softwareIn this work the proposed HM approach works on finiteelement nodes and uses an external CAD program to modifythem to point clouds before redrawing them as the die partsIn the future study an automatic implementation of HMshould be ported in a finite element forming simulationprogram so that the implementation will be easier and userfriendly


0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

Hybrid method S-rail

Hybrid methodAutoform

Figure 15 Comparisons betweenAutoform andHMcompensation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the Universiti Tun HusseinOnn Malaysia (UTHM) This research work has been sup-ported by a Fundamental Research Grant Scheme (FRGS)Vot no 0748

References

[1] M P Groover Fundamentals of Modern Manufacturing Mate-rials Processes and Systems JohnWiley amp Sons New York NYUSA 2007

[2] R H Wagoner H Lim and M-G Lee ldquoAdvanced issues inspringbackrdquo International Journal of Plasticity vol 45 pp 3ndash202013

[3] G Liu Z Lin W Xu and Y Bao ldquoVariable blankholder forcein U-shaped part forming for eliminating springback errorrdquoJournal of Materials Processing Technology vol 120 no 1ndash3 pp259ndash264 2002

[4] J Q Li S F Jiang H P Wu W Zhu and C D Lu ldquoStudyon subsection variable blank holder force in deep drawingof rectangular partsrdquo Materials Research Innovations vol 15supplement 1 pp S230ndashS233 2011

[5] S Kitayama S Huang and K Yamazaki ldquoOptimization of vari-able blank holder force trajectory for springback reduction viasequential approximate optimization with radial basis function

networkrdquo Structural andMultidisciplinary Optimization vol 47no 2 pp 289ndash300 2013

[6] Y H Moon S S Kang J R Cho and T G Kim ldquoEffect of tooltemperature on the reduction of the springback of aluminumsheetsrdquo Journal of Materials Processing Technology vol 132 no1ndash3 pp 365ndash368 2003

[7] R Barea G Conejero N Candela and M Carsı ldquoHot formingof a new steel used in stamping dies and toolingrdquo InternationalJournal of Materials Research vol 104 no 3 pp 281ndash285 2013

[8] X Fan Z He S Yuan and K Zheng ldquoExperimental investi-gation on hot forming-quenching integrated process of 6A02aluminum alloy sheetrdquoMaterials Science and Engineering A vol573 pp 154ndash160 2013

[9] S Hoja H Klumper-Westkamp F Hofmann and H-W ZochldquoPlasmanitriding of tool steels for hotmassive formingrdquo Journalof Heat Treatment and Materials vol 68 no 1 pp 3ndash12 2013

[10] H Laurent R Greze M C Oliveira L F Menezes P YManach and J L Alves ldquoNumerical study of springbackusing the split-ring test for an AA5754 aluminum alloyrdquo FiniteElements in Analysis andDesign vol 46 no 9 pp 751ndash759 2010

[11] H Tschaetsch Metal Forming Practise ProcessesmdashMachinesmdashTools Springer New York NY USA 2005

[12] M Kadkhodayan and I Zafarparandeh ldquoOn the relation ofequivalent plastic strain and springback in sheet draw bendingrdquoInternational Journal of Material Forming vol 1 no 1 pp 141ndash144 2008

[13] Y E Ling H P Lee and B T Cheok ldquoFinite element analysisof springback in L-bending of sheet metalrdquo Journal of MaterialsProcessing Technology vol 168 no 2 pp 296ndash302 2005

[14] J Slota M Jurcisin and M Dvorak ldquoExperimental andnumerical analysis of springback prediction in U-bendingsof anisotropic sheet metalsrdquo Zeszyty Naukowe PolitechnikiRzeszowskiej Mechanika vol 85 no 4ndash13 pp 525ndash533 2013

[15] W Gan and R H Wagoner ldquoDie design method for sheetspringbackrdquo International Journal of Mechanical Sciences vol46 no 7 pp 1097ndash1113 2004

[16] A P Karafillis and M C Boyce ldquoTooling design in sheet metalforming using springback calculationsrdquo International Journal ofMechanical Sciences vol 34 no 2 pp 113ndash131 1992

[17] Autoform Autoform Plus R2 Documentation Autoform Neer-ach Switzerland 2010

[18] W A Siswanto and B Omar ldquoDie surface design optimizationaccommodating springback assisted by an automatic surfacegeneratorrdquo International Journal of Material Forming vol 2 no1 supplement pp 797ndash800 2009

[19] X Li X Zhan X Liu and B Deng ldquoDie surface compensationbased on the springbackrdquo Journal of Theoretical and AppliedInformation Technology vol 45 no 2 pp 675ndash680 2012

[20] X-A Yang and F Ruan ldquoCompensation direction for die-faceadjustment based on springback compensationrdquo Journal of JilinUniversity (Engineering and Technology Edition) vol 42 no 1pp 103ndash108 2012

[21] H S Cheng J Cao and Z C Xia ldquoAn accelerated springbackcompensation methodrdquo International Journal of MechanicalSciences vol 49 no 3 pp 267ndash279 2007

[22] A P Karafillis and M C Boyce ldquoTooling and binder design forsheet metal forming processes compensating springback errorrdquoInternational Journal ofMachine Tools andManufacture vol 36no 4 pp 503ndash526 1996


[23] G Brabie B Chirita N Nanu and V Ciubotariu ldquoAnalysis ofspringback and residual stresses generated by cold plastic form-ing in drawn round parts made from steel sheetsrdquo MetalurgiaInternational vol 14 no 12 pp 21ndash27 2009

[24] R H Wagoner W Gan K Mao S Prise and F RasoulildquoDesign of sheet forming dies for springback compensationrdquoin Proceedings of the 6th International ESAFORM Conference2003

[25] L Wei and Y Yuying ldquoMulti-objective optimization of sheetmetal forming process using pareto-based genetic algorithmrdquoJournal of Materials Processing Technology vol 208 no 1ndash3 pp499ndash506 2008

[26] K B Nielsen and N Bronnberg ldquoSimulation of the 2D drawbending process numisheet benchmarkrdquo in Proceedings of the2nd International Conference (NUMISHEET 93) NumisheetTokyo Japan August-September 1993

[27] K Roll K Wiegand and P Hora ldquoBenchmark 2mdashInfluenceof drawbeads on the springback behaviourrdquo in Proceeding ofthe 7th International Conference and Workshop on NumericalSimulation of 3d Sheet Metal Forming Processes InterlakenSwitzerland September 2008

[28] R Kergen and P Jodogne ldquoComputerized control of the blankholder pressure on deep drawing pressesrdquo Technical Paper920433 Society of Automotive Engineers 1992

[29] Y Hishida and R H Wagoner ldquoExperimental analysis of blankholding force control in sheet formingrdquo Technical Paper 930285Society of Automotive Engineers 1993

[30] H I Demirci C Esner andM Yasar ldquoEffect of the blank holderforce on drawing of aluminum alloy square cup theoreticaland experimental investigationrdquo Journal of Materials ProcessingTechnology vol 206 no 1ndash3 pp 152ndash160 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



(BHFS) In the report [3] the VBHF approach successfullyreduced the springback error compared with that from con-stant blank holder force (CBHF) The application of VBHFhas been extended and published by researchers recently Liet al [4] investigated the subsection of VBHF in rectangularparts and then Kitayama et al [5] presented specifically theoptimization of VBHF to reduce the springback A precisionbinder force control during forming is required makingthis process sensitive to any variations in manufacturingconditions such as punch speed time control and friction

The study of springback reduction by the temperaturevalue of tool in hot forming has been investigated [6] Itis found that the cold punch combined with the hot diecan reduce the springback up to 20 when compared toconventional room temperature bending test in the sheetforming process of U-bend aluminum 1050 The experimen-tal investigations in hot forming process can be found inthe latest publications [7ndash9] Temperature in the springbackprediction is becoming a topic that could be improved in thefuture investigation [2]The springback value before and aftersplitting process is differentThis has been studied using split-ring tests for aluminum alloy [10]

The major advantage of the first strategy to minimizespringback is that it is not necessary to modify the toolingsurface However there are several implementation difficul-ties such as implementing the force control or force sensor inthe application ofVBHFbeing highly cost sensitive Similarlyin the hot forming process it requires additional equipmentto control the temperatures of the tools and the blank sheetso that the forming process becomes more complicated andexpensive

In the third method (die compensation) it requires manysteps of works on tooling design stage but its potential tocompensate springback completely is faster and cheaper evenfor complex model Die face adjustment to compensate thespringback was donemanually in the past by doing extensivemeasurements on the prototype or even production tools andrefining the tool surface geometry by hand polishing whichis time consuming [11] Wagoner et al [2] categorized thecurrent research of springback in five topics that is plasticconstitutive equations variable Youngrsquos modulus through-thickness integration of stress magnesium and advancedhigh strength steels (AHSS)

Finite element (FE) and numerical and process simula-tion have gained popularity in the stamping industry due toits speed and low cost and it has been proven to be effectiveand efficient in the prediction of form ability and springbackbehavior [12 13] The accuracy of springback simulationis not only related to springback analysis itself but alsostrongly dependent on the accuracy of forming processesAny calculation error obtained from every simulation stepof forming processes will be accumulated As a result theaccumulated error influence the accuracy of the springbackprediction analysis at the last step of the simulation Linget al [13] tried to reduce springback in L-bending by usingthe optimization of die radius clearance step height and stepdistance The results show a good reduction in springbackbut this method is applied and tested in the L-bending onlyThe U-bending model is analyzed by Slota et al [14] in

both numerical and experimental analysesThe experimentalanalysis is conducted by using specimens of steel DC06UHSS TRIP RAK 4070 and HSS H220PD in orientations0∘ 45∘ and 90∘ The results show that the simulations arein a good agreement with the experiments The springbackin sheet forming can be simulated accurately by using finiteelement method but the big problem is to apply the results toproduce stamped parts in accurate dimension

In order to accommodate the springback and to opti-mize the die based on surface modification there aretwo methodologies available called displacement adjustment(DA) compensation and spring forward (SF) compensationThe concept of DAmethod [15] is to translate the nodes in thedirection opposite to the springback which is adopted fromthe real springback investigation whereas the SF method isbased on stress state during forming which is multipliedby negative factor and then loaded to the deformed shapeto realize the compensated surface [16] The compensationmethod based on calculated springback by implementing theDA method can be done in a computer program [17] Themodification of die surface for springback compensation canbe done faster There are many researchers who reported theimplementation of these two methods in various springbackaccommodation problems and are dealing with minimizingspringback errors [18ndash20]

One of the advantages of DA method is that it canconverge rapidly because of the algorithm being based onthe real springback measurements not virtual springbackcalculation whichmay develop instability during the numer-ical solution [15] Unfortunately the original DA method ismostly applicable to compensate surfaces in the direction ofthe punch travel The wall area of the dies therefore couldnot be compensated [21]

On the other hand the SF method could compensate diesurface in almost all directions because of the deformationbeing caused by the stresses of the deformed part in theopposite direction [22] In the original concept of springforward [16] only inverted bending stress will be used tocreate the spring forward shape The inverted membranestresses must be eliminated since they will contribute to theunstable buckling condition during the numerical calcula-tion Another disadvantage of SFmethod is that the approachis not based on the reality of physical occurrence but aninverted springbok The complexity of inverted bendingstress distribution in the deformed shape is very difficult toapply in an experiment even impossible [21] In order to solvethe problem finite element simulation analysis can be used toexplain the influence of residual stress in springback formingas done by Brabie et al [23] It shows that residual stressis influenced by the BHF and coefficient of friction in bothcylindrical and conical forming They analyze the residualstress during forming and after springback but do not explainhow tominimize the springback related to the residual stress

Force descriptor method (FDM) proposed by Karafillisand Boyce [22] is SF method based This method has twoparameter vectors the original part shape and the inter-nal forces The theoretical base of the FDM is that afterbeing formed to the original tooling shape the part wouldspringback to the original unloaded shape recovering from


Blank sheet

Form to target

(1)

(2)



(Force is recorded)

compensated dies

(Errorvalue = Δl )



f f


2nd









119894

tool + Δ119910119894



119862119894+1

tool = 119862119894

tool + 119865119894

internal (1)

















Export surfaces

Yes




AccuracyRadius

penetration(mm)


(deg)


(deg)

Rough 032 45 32

Standard 022 30 22

Fine 016 225 16





0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Sprin

gbac

k (m

m)

BHF (kN)



BHF(kN)

Springback(mm)

Thinning()


1 727 002 007 0085 723 002 007 00710 475 004 008 01315 381 004 009 01920 198 006 012 02825 132 008 016 0426 131 008 020 04427 131 011 030 06272 131 014 040 07275 136 020 060 10











Splits

Risk of Splits

Compressing

Safe

Thicking


Compressing

Safe



08

07

06

05

04

03

02

01

00

Maj

or st

rain

(tru

e str

ain)


xxxx

x

x

Target

x

x

Target shape

minus10 0 10 20 30 40 50 60 70

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

X along projection

ExperimentFine

StandardRough




0

05

1

15

2

25

0 1 2 3 4 5 6

Sprin

gbac

k (m

m)

Iteration






XXX

X

X

X

XX


minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107



X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107



Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration









0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Blank sheet

Form to target

(1)

(2)



(Force is recorded)

compensated dies

(Errorvalue = Δl )



f f


2nd









119894

tool + Δ119910119894



119862119894+1

tool = 119862119894

tool + 119865119894

internal (1)

















Export surfaces

Yes




AccuracyRadius

penetration(mm)


(deg)


(deg)

Rough 032 45 32

Standard 022 30 22

Fine 016 225 16





0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Sprin

gbac

k (m

m)

BHF (kN)



BHF(kN)

Springback(mm)

Thinning()


1 727 002 007 0085 723 002 007 00710 475 004 008 01315 381 004 009 01920 198 006 012 02825 132 008 016 0426 131 008 020 04427 131 011 030 06272 131 014 040 07275 136 020 060 10











Splits

Risk of Splits

Compressing

Safe

Thicking


Compressing

Safe



08

07

06

05

04

03

02

01

00

Maj

or st

rain

(tru

e str

ain)


xxxx

x

x

Target

x

x

Target shape

minus10 0 10 20 30 40 50 60 70

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

X along projection

ExperimentFine

StandardRough




0

05

1

15

2

25

0 1 2 3 4 5 6

Sprin

gbac

k (m

m)

Iteration






XXX

X

X

X

XX


minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107



X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107



Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration









0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























Export surfaces

Yes




AccuracyRadius

penetration(mm)


(deg)


(deg)

Rough 032 45 32

Standard 022 30 22

Fine 016 225 16





0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Sprin

gbac

k (m

m)

BHF (kN)



BHF(kN)

Springback(mm)

Thinning()


1 727 002 007 0085 723 002 007 00710 475 004 008 01315 381 004 009 01920 198 006 012 02825 132 008 016 0426 131 008 020 04427 131 011 030 06272 131 014 040 07275 136 020 060 10











Splits

Risk of Splits

Compressing

Safe

Thicking


Compressing

Safe



08

07

06

05

04

03

02

01

00

Maj

or st

rain

(tru

e str

ain)


xxxx

x

x

Target

x

x

Target shape

minus10 0 10 20 30 40 50 60 70

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

X along projection

ExperimentFine

StandardRough




0

05

1

15

2

25

0 1 2 3 4 5 6

Sprin

gbac

k (m

m)

Iteration






XXX

X

X

X

XX


minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107



X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107



Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration









0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30

Sprin

gbac

k (m

m)

BHF (kN)



BHF(kN)

Springback(mm)

Thinning()


1 727 002 007 0085 723 002 007 00710 475 004 008 01315 381 004 009 01920 198 006 012 02825 132 008 016 0426 131 008 020 04427 131 011 030 06272 131 014 040 07275 136 020 060 10











Splits

Risk of Splits

Compressing

Safe

Thicking


Compressing

Safe



08

07

06

05

04

03

02

01

00

Maj

or st

rain

(tru

e str

ain)


xxxx

x

x

Target

x

x

Target shape

minus10 0 10 20 30 40 50 60 70

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

X along projection

ExperimentFine

StandardRough




0

05

1

15

2

25

0 1 2 3 4 5 6

Sprin

gbac

k (m

m)

Iteration






XXX

X

X

X

XX


minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107



X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107



Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration









0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Splits

Risk of Splits

Compressing

Safe

Thicking


Compressing

Safe



08

07

06

05

04

03

02

01

00

Maj

or st

rain

(tru

e str

ain)


xxxx

x

x

Target

x

x

Target shape

minus10 0 10 20 30 40 50 60 70

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107

X along projection

ExperimentFine

StandardRough




0

05

1

15

2

25

0 1 2 3 4 5 6

Sprin

gbac

k (m

m)

Iteration






XXX

X

X

X

XX


minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107



X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107



Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration









0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










XXX

X

X

X

XX


minus10 0 10 20 30 40 50 60 70

X along projection

Hei

ght(times1000)

minus099

minus1

minus101

minus102

minus103

minus104

minus105

minus106

minus107



X X

X

X

X

X

X X X

minus10 0 10 20 30 40 50 60 70 80

X along projectionH

eigh

t(times1000)

minus099

minus101

minus1

minus102

minus103

minus104

minus105

minus106

minus107



Maximum 1497372

1497372

146

(a) 1st iteration

Maximum 1533426

101

0443

1533426

146

06780264

(b) 5th iteration









0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

05

1

15

2

25

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration

-HM


U-bend autoform




Yield stress(MPa)

UTS(MPa)

Uniformelongation

119903-value

L 100 3943 4637 164 0581T 100 4277 4660 175 1013D 100 3953 4470 170 1166

Mean 100 4058 4589 169 0981












19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










19

195

2

205

21

215

22

225

23

0 50 100 150 200

Sprin

gbac

k (m

m)

BHF (kN)

Sec ASec B

Sec CSec D

(a) Lock bead model

0

05

1

15

2

25

0 50 100 150 200

Sec ASec B

Sec CSec D

Sprin

gbac

k (m

m)

BHF (kN)


0 50 100 150 200BHF (kN)

Sec ASec B

Sec CSec D

0

05

1

15

2

25

Sprin

gbac

k (m

m)


185

19

195

2

205

21

215

0 50 100 150 200


BHF (kN)

Sprin

gbac

k (m

m)




4 Discussion






0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 35 40

Increment

Fine mesh

Standard mesh

Rough mesh

Elem

ents

(times1000

)60

50

40

30

20

10

0


Fine mesh

Standard mesh

Rough mesh

0 5 10 15 20 25 30 35 40

Increment

30

25

20

15

10

5

0CP

U ti

me (

min

)

(b) CPU time


Splits

Compressing

Safe

Thicking

Risk of splits

06

05

04

03

02

01



Maj

or st

rain

(tru

e str

ain)


Compressing

Safe

Thicking







After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










After springback

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

minus5 0

0

5

5

10 15 20 25 30 35 40

X along projection

Target surface



xxx

x

x

x

x

x

xxxx

x

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght

0

5

minus5 0 5 10 15 20 25 30 35 40

X along projection



xxx

x

x

x

x

x

x

xxxx

minus5 0 5 10 15 20 25 30 35 40

X along projection

minus5

0

5

minus10

minus15

minus20

minus25

minus30

minus35

minus40

Hei

ght




5 Conclusion




0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

12

14

16

18

2

0 1 2 3 4 5

Sprin

gbac

k (m

m)

Iteration






Acknowledgments


References



































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article An Alternate Method to Springback ...downloads.hindawi.com/journals/tswj/2014/301271.pdfResearch Article An Alternate Method to Springback Compensation for Sheet Metal