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.