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    Adaptive FEM simulation for prediction of variable blank holder force in conical cup drawing.pdf

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    Adaptive FEM simulation for prediction of variable blank holder force in conical cup drawing.pdf

    fax 1-614-292-u.edu T. Altan.2003 Elsevier Ltd. All rights reserved.closed-loop controlthe drawing pro-method introducedThey determinedor asymmetric parts, an elasticsimulation.Hardt et al. [7,8] implthe drawn part [2]. To further improve the formabilitywhen drawing complexation and a desired BHF is obtained in a single FEMBHF profile. When selected properly, this BHF pro-file can eliminate wrinkles and delay fracture in thedrawn part [1,2].Usually, in deep drawing, a constant BHF is appliedover the punch stroke. During the drawing process, thestate of stress in the deforming material changes signifi-cantly. Consequently, the process conditions thatreduce wrinkling and fracture also change. To take intoaccount these changes, it is reasonable that the BHFvariable BHF profiles can be predicted analytically [5].However, so far, most analytically predicted BHF pro-files have not correlated well with experimental obser-vations [4]. An efficient method for predicting variableBHF profiles is to use a closed-loop controlled FEMsimulation. In this method, the forming process issimulated, and a control strategy suggests appropriateBHF levels based on the part formability predicted atany given time step in the process simulation. Thus, the2003 Elsevier Ltd. All rights reserved.Keywords Adaptive simulation; Feedback control; FEM; Blank holder force; Sheet metal forming1. IntroductionIn deep drawing, the quality of the formed part isaffected by the amount of metal drawn into the die cav-ity. Excessive metal flow will cause wrinkles in the part,while insufficient metal flow will result in tears or splits.The blank holder plays a key role in regulating theor segmented blank holder can be used to obtain anon-uniform BHF over the part flange area. Thus, it ispossible to account for variations of the metal flowover different locations of the blank holder surface[2,3].A good variable BHF profile is usually determinedby conducting time-consuming FEM simulations orInternational Journal of Machine ToolsAdaptive FEM simulation for predictionforce in conicalZ.Q. Sheng, S. Jirathearanat,Engineering Research Center for Net Shape Manufacturing ERC/NSM,Received 20 April 2003; received in revised formAbstractFracture and wrinkling are two primary failure modes in deeperly selected variable blank holder force BHF profile, i.e. variationdraw deeper parts. In this study, an adaptive simulation strategyduring the simulation process. Thus, a BHF profile is predictedreduced. The proposed strategy has been applied successfullyanufacture 44 2004 487–494www.elsevier.com/locate/ijmatoolof variable blank holdercup drawingT. AltanC3The Ohio State University, Columbus, OH 43210, USASeptember 2003; accepted 5 November 2003of sheet metal parts. Previous studies showed that prop-of BHF with punch stroke, can eliminate these failures todeveloped to adjust the magnitude of the BHF continuouslya single process simulation run and the computation time isconical cup drawing operations. The predictions have beenprofiles that improve the drawability of a round cupand a rectangular pan. In his method, the punch load,analysis employing initial imperfections [13]; 2 antions cut by planes perpendicular to the formingFig. 2. Geometry of steel conical cup tooling used at ERC/NSM.D 1582 mm, D 889 mm, R 16 mm, R 20 mm, D flange wrinkle amplitude FAM in FEM simulation of a conical cup.488 Z.Q. Sheng et al. / International Journal of Machine Tools adaptive simulationflow chart. Note SAM sidewall wrinkle amplitude; FAM flange wrinkle amplitude;seeFig.3.analysis of the incremental second-order energy [14];and 3 a geometrical method, which directly measureswrinkle dimensions of the deformed mesh [4,9,15].Inthis study, the geometrical method is adopted. Theflange wrinkle amplitude FAM is measured from thegap distance between blank holder surface and dieaddendum surface Fig. 3. The sidewall wrinkle ampli-tude SAM is measured by considering part cross-sec-2. Defect detectionWrinkling and fracture are the major failure modesor defects encountered in deep drawn parts. The pro-posed adaptive simulation method attempts to elimin-ate fracture by applying the BHF at the minimum levelnecessary for suppressing the wrinkles. Thus, stretchingis minimized and fracture is postponed.2.1. Wrinkling detectionWrinkling is affected by many factors, such as pro-cess parameters, contact condition, mechanical proper-ties, and geometry of the blank. In FEM simulation,wrinkles can be predicted by [11] 1 a bifurcationanalysis of a perfect structure [12] or a non-bifurcationd p d p b248 mm.a BHF profile for a round cup drawing through aclosed-loop controlled simulation system. Cao andBoyce [9] applied a similar method to predict a variableBHF profile for conical cup drawing and increased thefailure-free drawing depth of a conical cup over thatobtained with a constant BHF profile. In their method,major principal strains and amplitudes of wrinklesoccurring at the die radius were used as state variablesfor adjusting BHF. Thomas [4] also devised a closed-loop controlled FEM system to predict variable BHFdirection [15].Fig. 3. Determination of sidewall wrinkle amplitude SAM andtry to indicate probability of fracture [4]. Therefore, inthe present study, we also selected wall thinning as astrategy can be done by comparing the wrinkle tend-Xi, cal value and the cup wall is not being thinned.Tools 1IswSAMiC0SAMiC01SAMiC01; 2fracture criterion. This procedure is an approximatemethod because the critical maximum thinning is affec-ted by strain paths. Nevertheless, the thinning criterionis still useful and effective in estimating the occurrenceof fracture in most deep drawing operations.3. Control strategyThe control strategy proposed in this study tries tomaintain the wrinkle amplitude at an acceptable levelby automatically adjusting the BHF at each controltime step. It is well known that the tendency of flangewrinkles to occur is highest at the initial drawing stage[20]. Therefore see Fig. 4, the current control strategybegins with flange wrinkle control and later switches tosidewall wrinkle control. The switching of the controlBased on observations of both simulations andexperiments in conical cup drawing, the most serioussidewall wrinkle is usually located at 25 cup depthsee Fig. 3. Therefore, in this study, the largest SAMoccurring at this cup location is used to represent theseverity of the sidewall wrinkle. Based on literature[4,9], the critical wrinkle amplitudes for determiningthe existence of a flange wrinkle and a sidewall wrinkleare chosen to be at 5 and 20 of nominal sheetthickness, respectively. These critical wrinkle ampli-tudes, however, would be different for different partsdepending on the part functionality.2.2. Fracture detectionAn extensive literature review on this topic can befound in [4,15]. Generally, fracture can be predicted by1 strain based criteria, e.g. forming limit diagramsFLDs [16,17] and maximum part thinning [4]; 2stress based criteria, e.g. forming limit stress diagramsFLSDs [18]; and 3 ductile damage criteria, e.g. theCockroft and Latham criterion [19].Thinning in the part wall is commonly used in indus-Z.Q. Sheng et al. / International Journal of Machinewhere FAMiis the flange wrinkle amplitude at the ithstep, FAMiC01is the flange wrinkle amplitude at theiC01th step, SAMiis the sidewall wrinkle amplitude atthe ith step, and SAMiC01is the sidewall wrinkle ampli-tudes at the iC01th step.In the adaptive simulation, a PI mode feedback con-troller algorithm is applied to determine changes inBHF needed for keeping the wrinkle amplitude at thedesired value. The sampling period for the proposed PIcontroller is at every control time step i.e. 1000 simu-lation steps, around punch travel of 0.3 mm. The vari-ation of BHF is calculated using Eqs. 3 and 4Fig. 4. Flowchart of adaptive strategy at one control time step.BHFi1 BHFi b C3KpC3 DeijiC0l1Dejl 3andDei SAMiC0SAMcor FAMiC0FAMc4whereBHFiistheBHFforthecurrentithstep,BHFi1is the BHF for the next i1th step, FAMcis the criticalflange wrinkle amplitude 5 nominal sheet thickness,SAMcis the critical sidewall wrinkle amplitude 20nominal sheet thickness, Kpis the proportional gain, l isthe length of integral time, and b is the coefficient for thethinningcontrol.When Dei 0, and the thinning rate i.e. TmiC0TmiC01,change of maximum thinning during one control timestep is lower than a certain value i.e. 0.001, b 0;otherwise, b 1. The physical meaning of b 0 is thatthe BHF stays the same for the next control time steponly when the wrinkle amplitude is lower than the criti-formed are detected and treated as state variables inthe feedback control loop for calculating changes ofDue to symmetry, only one quarter of the toolingof Eq. 3 are determined by a sensitivity analysis onthe integration length lffor flange wrinkle and lswrinkle or Dei FAMiC0FAMcfor flange wrinkle,flange wrinkle control, K 2kNmm and l 5 con-490 Z.Q. Sheng et al. / International Journal of Machine Tools binder/blank,0.15; die/blank, 0.15From Eq. 3, it can be seen that once the detectedwrinkle amplitude value exceeds the critical value, theBHF is increased for eliminating this deviation, thussuppressing the wrinkles back to the critical amplitudevalue. If the detected wrinkle amplitude should becomeless than the critical value, the BHF may be decreasedor maintained the same, depending on the thinning ratei.e. b, to let the wrinkles grow back to the criticalamplitude value.4. ImplementationThe adaptive simulation method has been imple-mented. A controller subroutine was coded and inte-grated into PAM-STAMP explicit FEM code. Ateach control time step, the defects in the part beinga stable BHF profile is predicted through a few trialadaptive simulation runs. For sidewall wrinkle control,Kp 3kNmm and l 5 control time steps. For theinitthe magnitudes of the controlpconstants are varied until45andls 64 control time steps, respectively. Then,at Kfp init 36kNmm, Ksp init 183kNmm, lfinit17.2 kN, the initial control constants are determineding two simulations with constant BHFs of 18 andin one simulation with a constant BHF. By conduct-fied wrinkle and fracture criteria. Compared with thecup formed with the optimal constant BHF, this repre-Fig. 8. Al alloy cup geometry [9].Z.Q. Sheng et al. / International Journal of Machine Tools binder/blank,0.15; die/blank, 0.15Fig. 10. The experimental BHFTable 2AKDQ steel experiments.Z.Q. Sheng et al. / International Journal of Machine Tools Manufacture 44 2004 487–494 493Fig. 12. Comparison of thinning distribution in AKDQ steel conicalcups formed with the optimum constant BHF.cups. This BHF profile can improve the formability ofthe conical cup drawing process, i.e. increasing a thethis support.56 1964 25–48.[17] G.M. Goodwin, Application of strain analysis to sheet metalformingproblemsinthepressshop,SAEPaperNo.680093,1968.[18] R. Arrieux, Determination and use of the forming limit stressdiagrams in sheet metal forming, Journal of Materials Proces-sing Technology 53 1995 47–56.The authors would also like to thank the ESI groupfor providing PAM-STAMP 2000 and the subroutinedevelopment library.References[1] M. Ahmetoglu, T. Altan, Deep drawing of round cups usingvariable blank holder force BHF, Report No. ERC/NSM-S-92-50, Engineering Research Center for Net Shape Manufactur-ing, Ohio State University, 1992.[2] E.J. Obermeyer, S.A. Majlessi, A review of recent advances inthe application of blank holder force towards improving theforming limits of sheet metal parts, Journal of Materials Proces-sing Technology 75 1998 222–234.[3] K. Siegert, E. Dannenmann, A. Galeiko, Closed-loop controlsystem for blank holder forces in deep drawing, Annals of theCIRP 44 1 1995 251–254.[4] W. Thomas, Product tool and process design methodology fordeep drawing and stamping of sheet metal parts, Ph.D. Disser-tation, Ohio State University, 1999.[5] E. Siebel, H. Beisswanger, Deep Drawing, Carl Hanser, Munich,1955.[6] H.B. Sim, M.C. Boyce, Finite element analyses of real-time stab-ility control in sheet forming processes, ASME Journal of Engin-eering Materials and Technology 114 1992 180–188.[7] D.E. Hardt, M.C. Boyce, R.P. Fenn, Real-time control of binderforce during stamping, Proceedings of the 16th Biennial Con-gress of the IDDRGInternational Deep Drawing ResearchGroup, 1990, pp. 17–27.[8] D.E. Hardt, R.C. Fenn, Real-time control of sheet stability dur-ing forming, ASME Journal of Engineering for Industry 1151993 299–308.[9] J. Cao, M.C. Boyce, Design and control of forming parametersusing finite element analysis, Computational Material Modeling,ASME 42/PVP–vol. 294 1994 265–285.[10] J. Cao, P. Jalkh, M.C. Boyce, D.E. Hardt, Improvement offorming height and stability of aluminum parts using active bin-der control, IDDRG’94, 1994, pp. 1–13.[11] M. Strano, S. Jirathearanat, T. Altan, Adaptive simulation con-cept for tube hydroforming, Proceedings of Innovations in TubeHydroforming Technology, Troy, June, 2000.[12] J.B. Kim, et al., Investigation into wrinkling behavior in theelliptical cup deep drawing process by finite element analysisusing bifurcation theory, Journal of Materials Processing Tech-nology 111 2001 170–174.[13] J. Cao, M.C. Boyce, A predictive tool for delaying wrinklingand tearing failures in sheet metal forming, Journal of Engineer-ing Materials and Technology, Transactions of the ASME 119Oct 1997 354–365.[14] P. Nordlund, Prediction of wrinkle tendencies in explicit sheetmetal-forming simulations, International Journal for NumericalMethods in Engineering 40 1997 127–143.[15] Z.Q. Sheng, J.B. Yang, S. Jirathearanat, T. Altan, Drawing ofconical cupsprevention of wrinkling and fracture by control-ling blank holder force, ERC Report /ERC/NSM-01-R-47-A,Engineering Research Center for Net Shape Manufacturing,Ohio State University, 2001.[16] S.P. Keeler, W.A. Backofen, Plastic instability and fracture insheet stretched over rigid punches, ASM Transactions Quarterlyfailure-free drawing depth, and b the uniformity ofthe wall thinning distribution.The proposed method can be further improved todetermine nearly optimum BHF profiles for drawingmore complex parts, such as rectangular pan or non-symmetric automotive stampings. This will be investi-gated in the future.AcknowledgementsThis work was funded by USAMP-AMD 301 andthe ERC/NSM. The authors gratefully acknowledge6. ConclusionsFrom this study, it can be concluded that the pro-posed adaptive simulation method can predict an‘‘optimum’’ variable BHF profile for drawing conicalFig. 13. Comparison of thinning distribution in AKDQ steel conicalcups formed with the optimum variable BHF profile.[19] M.G. Cockcroft, D.J. Latham, Ductility and workability ofmetals, Jounal of the Institute of Metals 96 1968 33–39.[20] C.T. Wang, G. Kinzel, T. Altan, Wrinkling criterion for ananisotropy shell wit

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