Finite element analysis Finite element analysis of springback in L-of springback in L-

bending of sheet metalbending of sheet metal

Y.E. Ling H.P. Lee B.T. Y.E. Ling H.P. Lee B.T. CheokCheok

A Presentation A Presentation by:by:

Rose WielandRose Wieland

7 February 7 February 20072007

OverviewOverview

IntroductionIntroduction Set upSet up Effects of Die ClearanceEffects of Die Clearance Effects of Step SizeEffects of Step Size Conclusion/RecommendationsConclusion/Recommendations

IntroductionIntroduction

Increasing demand for tight Increasing demand for tight tolerancestolerances

Springback is biggest problem to Springback is biggest problem to tolerancestolerances

FEM models allow for effect of die FEM models allow for effect of die clearance, die radii, and step size clearance, die radii, and step size to be analyzedto be analyzed

Idea of how to minimize springbackIdea of how to minimize springback

ME ME 482482 -- Manufacturing SystemsManufacturing Systems

Bending model - springbackBending model - springback

e

Elastic Recovery

Springback is a measure of elastic recovery after plastic load released

SB = (A’ – Ab’)/ Ab’

To compensate:

• Overbending – increase punch angle and decrease punch radius

• Bottoming – plastically deform with additional punch pressure

Springback is a measure of elastic recovery after plastic load released

SB = (A’ – Ab’)/ Ab’

To compensate:

• Overbending – increase punch angle and decrease punch radius

• Bottoming – plastically deform with additional punch pressure

HistoryHistory

1958 – first mathematical model 1958 – first mathematical model for springback correctionsfor springback corrections

1991/1992 – FEM models used to 1991/1992 – FEM models used to analyze springbackanalyze springback

Never in the paper is the Never in the paper is the accuracy of FEM models versus accuracy of FEM models versus real experimental data discussed!real experimental data discussed!

FEM ModelFEM Model

Die, punch, and Die, punch, and pressure pad rigidpressure pad rigid

Workpiece is a Workpiece is a deformable meshdeformable mesh

Die step height, Die step height, step distance, die step distance, die clearance, and clearance, and die radii varieddie radii varied

Material used : Material used : AL2024-T3AL2024-T3

Effects of Die Effects of Die ClearanceClearance

Bend Leg analysisBend Leg analysis

Otherwise, bend leg remains strait

Bend leg curves between clearances of 1t and 0.8 t with maximum between 0.9 t and 0.95 t

Stress AnalysisStress Analysis

Effects of Die RadiusEffects of Die Radius

K = springback K = springback factorfactor

A = bend angle A = bend angle after springbackafter springback

AA11= bend angle = bend angle during bendingduring bending

1A

AK

Springback factor of Springback factor of 1 most desirable1 most desirable

Effects of Step Height Effects of Step Height and Distanceand Distance

Design Design RecommendationsRecommendations Die radius, clearance, and step Die radius, clearance, and step

height and distance all effect height and distance all effect springbackspringback

Die radius and clearance have Die radius and clearance have greatest effectgreatest effect

Effects are exclusive and additive Effects are exclusive and additive i.e.i.e.

die radius = 2.0t die clearance = 0.75t;step height = 0.2t step distance = 0t.springback reduction for die radius 2.0t and die clearance 0.75t is 1.37◦ springback reduction for using a step height of 0.2t and step distance 0t at that die radius and clearance is 1.08◦ The total springback reduction is 1.37◦ + 1.08◦ = 2.45◦(values from Table 2 and Table 3)

Beware bend leg Beware bend leg elongationelongation

Accounting for Accounting for ElongationElongation Radius most Radius most

important factor to important factor to elongationelongation

Bend leg elongation Bend leg elongation only happens at only happens at clearance less than clearance less than the thicknessthe thickness

Step height and step Step height and step distance do not alter distance do not alter bend allowances bend allowances significantlysignificantly

ConclusionConclusion

Established trends for effect of die Established trends for effect of die clearance, die radius, step height clearance, die radius, step height and distanceand distance

Need for research with other Need for research with other materialsmaterials– This research took 1000+ hoursThis research took 1000+ hours– Perhaps small samples of other Perhaps small samples of other

materials could be tested to show materials could be tested to show trendstrends

ReferencesReferences

[1] A.G. Gardiner, The spring back of metals, Trans. ASME, J. Appl.Mech. 79 (1957) 1–9. [2] W. Johnson, T.X. Yu, Springback after the biaxial elastic-plastic pure bending of a rectangular plate – I, Int. J. Mech. Sci. 23 (10)

(1981)619–630. [3] W. Johnson, T.X. Yu, On the range of applicability of results forthe springback of an elastic/perfectly plastic rectangular plate

aftersubjecting it to biaxial pure bending – II, Int. J. Mech. Sci. 23 (10)(1981) 631–637. [4] R.A. Ayres, SHAPESET: a process to reduce sidewall curl springbackin high-strength steel rails, J. Appl. Metalworking 3 (2)

(1984)127–172. [5] C. Wang, G. Kinzel, T. Altan, Mathematical modeling of planestrainbending of sheet and plate, J. Mater. Proc. Tech. 39 (3/4)(1993)

279–304. [6] Y.K.D.V. Prasad, S. Somasundaram, Mathematical model for bendallowance calculation in automated sheet-metal bending, J. Mater. Proc. Tech. 39 (3/4) (1993) 337–356.[7] D.K. Leu, A simplified approach for evaluating bendability andspringback in plastic bending of

anisotropic sheet metals, J. Mater.Proc. Tech. 66 (1997) 9–17. [8] J.C. Nagtegaal, L.M. Taylor, Comparison of implicit and explicitfinite element methods for analysis of sheet forming problems

FESimulationof 3-D Sheet Metal Forming Processes in AutomotiveIndustry, 894, VDI, Berichte, 1991, pp. 705–725. [9] A.P. Karafillis, M.C. Boyce, Tooling design in sheet metal formingusing springback calculations, J. Mech. Sci. 34 (1992) 113–131. [10] H.B. Sim, M.C. Boyce, Finite element analyses of real time stabilitycontrol in sheet metal forming processes, ASME J. Eng.

Mater.Technol. 114 (1992) 80–188. [11] M.J. Finn, P.C. Galbraith, L. Wu, J.O. Hallquist, L. Lum, T.L. Lin,Use of a Coupled Explicit–Implicit Solver for Calculating SpringBack in

Automotive Body Panels, Livermore Software TechnologyCorporation, Livermore, CA, 1992. [12] L. Wu, C. Du amd, L. Zhang, Iterative FEM Die surface designto compensate for springback in sheetmetal stampings, in:Proceedings

of NUMIFORM ’95, Ithaca, NY, 1995, pp. 637–641.[13] A.P. Karafillis, M.C. Boyce, Tooling and binder design for sheetmetal forming processes compensating springback error, Int. J. Mach.Tools Manuf. 36 (4) (1996) 503–526.

[14] M. Sunseri, J. Cao, A.P. Karafillis, M.C. Boyce, Accommodation ofspringback error in channel forming using active binder force control:numerical simulations and experiments, ASME J. Eng. Mater.Technol. 118 (1996) 426–434.

[15] Y. Ming, K. Manabe, H. Nishimura, Development of an intelligenttool system for flexible L-bending process of metal sheets, SmartMater. Struct. 7 (4) (1998) 530–536.

[16] I.N. Chou, C. Hung, Finite element analysis and optimization onspringback reduction, Int. J. Mach. Tools Manuf. 39 (3) (1999)517–536.

[17] M. Samuel, Experimental and numerical prediction of springbackand side wall curl in U-bending of anisotropic sheet metals, J. Mater.Proc. Tech 105 (3) (2000) 382–393.

[18] N. Narkeeran, M. Lovell, Predicting springback in sheet metal forming:an explicit to implicit sequential solution procedure, Finite Elements,Anal. Des. 33 (1) (1999) 29–42.

[19] Baumeister, Avallone, Mark’s Standard Handbook For MechanicalEngineers, 8th ed., McGraw-Hill, 1979. [20] G. Sachs, Principles and Methods of Sheet Metal Fabricating, 2nded., Reinhold Publishing Corporation, New York, 1966.