Sheet Metal Forming2.810 Fall 2006Professor Tim GutowskiMinoan gold pendant of bees encircling the Sun, showing the use of granulation, from a tomb at Mallia, 17th century BC. In the Archaeological Museum, Iráklion, Crete.Historical Note;Sheet metal stamping was developed as a mass production technology for the production of bicycles around the 1890’s. This technology played an important role in making the system of interchangeable parts economical (perhaps for the first time).Steps in making Hub Steps in Sprocket makingStress Strain diagram – materials selectionBasic Sheet Forming Processes(from http://www.menet.umn.edu/~klamecki/Forming/mainforming.html)ShearingBendingDrawingShear and corner pressBrake pressFinger pressShearing Operation Force RequirementDieSheetPunchTDPart or slugF = 0.7 T L (UTS)T = Sheet ThicknessL = Total length ShearedUTS = Ultimate Tensile Strength of materialYield CriteriaστYY/2TrescaMisesτmax= (2/3)1/2Yτmax= (1/2) YSchematic of a Blanked EdgeBending Force RequirementPunchWorkpieceTDieWForceT = Sheet ThicknessW = Width of Die Opening L = Total length of bend(into the page)UTS = Ultimate Tensile Strength of materialEngineering Strain during Bending: e = 1/((2R/T) + 1)R = Bend radiusMinimum Bend radius: R = T ((50/r) – 1)r = tensile area reductionin percent)(2UTSWLTF =Stress distribution through thethickness of the partσ σyYY-Yσh-YYElastic Elastic-plastic Fully plasticSpringback•Over-bend•Bottom•StretchtensioncompressionPure BendingBending & StretchingStretch FormingLoading Pre-stretchingWrapping Release* source: http://www.cyrilbath.com/sheet_process.htmlStretch FormingStretch formingStretch Forming Force RequirementF = (YS+ UTS)/2 * AF = stretch forming force (lbs)YS= material yield strength (psi)UTS = ultimate tensile strength of the material (psi)A = Cross-sectional area of the workpiece (in2)• Example of Force CalculationCalculate the force required to stretch form a wing span having a cross-sectional area of .50X120” made from 2219 aluminum alloy having a yield strength of 36,000 psi and a UTS of 52,000 psi:F = 88000/2 * 60 = 2,640,000 lbs = 1320 tonsCalculate the force required to shear a 10” diameter, 1/8” thick blank from mild steel with a UTS of 45,000 psi:F = 0.7 (.125)(π)(10) 45,000 = 62 tonsAuto body panels 10 - 11 panels•3 to 5 dies each• ~$0.5M each• ~$20M investmentTooling for Automotive StampingMachinesMaterial SelectionMaterial selection is critical in both product and process design.Formability is the central material property.This property must be balanced with other product and process considerations such as strength, weight, cost, and corrosion resistance.Auto vs. Aerospace ExampleAuto Body Panel Airplane Body PanelProgressive stamping stretch forming1010 Steel, cold-rolled 2024 Aluminum, T3 temper.04” sheet, custom order .08” sheet, oversizeDouble-sided Zinc clad mechanically polishedCost ~ $.35-.45/lb Cost ~ $4.0/lbUTS ~ 300 MPa UTS ~ 470 MPaYS ~ 185 MPa YS ~ 325 MPaElongation ~ 42% Elongation ~ 20%n = .26 n = .16Comparison of representative Parts: Aero and AutoAuto AeroPart Description Body Panel Body Panel54"X54" 54"X54"Forming Process Progressive Stamping Stretch FormingMATERIALMaterial1010 Steel, cold-rolled, .04" sheet, custom order double-sided Zinc clad2024 Aluminum, T3 temper, .08" sheet, oversize mechanically polishedScrap 40% 20%Material Cost $0.45/lb $4.00/lbPer part $15.75 $105.00LABORSet-up Time 1.5hr 1.0hrParts/Run 2,000 30Cycle Time 0.25 min 2.5 minTotal Labor 0.30 min 4.5 minLabor Rate** $20.00/hr $20.00/hrStretch-Form Labor Cost $0.10 $1.50FIXEDEquipment $5,000,000 $1,000,000Tools/Dies $900,000 $45,000(200 manhours labor)TOTAL TRANSFER COST $25 $265Parts ReceivedMylar Protection Applied‘Burr’ Edges in tensionStretch FormingIndex to Block‘Burr’ Edges and InspectHand TrimChemical MillingAerospace Stretch Forming Body Panel ProcessClad and Prime SurfacesProcess Flow for Automobile Door Stamping OperationRaw materialBlank material starting dimensionsDrawing PierceFlangeRestrikeDesign: Stretch Forming vs. Stamping• Stretch Forming Advantages over Stamping– Tighter tolerances are possible: as tight as .0005 inches on large aircraft parts– Little problem with either wrinkling or spring back– Large, gently contoured parts from thin sheets• Stretch forming Disadvantages over Stamping– Complex or sharply cornered shapes are difficult or impossible to form– Material removal – blanking, punching, or trimming – requires secondary operations– Requires special preparation of the free edges prior to formingSpringbackElastic Springback AnalysisLxyhb1. Assume plane sections remain plane:εy= - y/ρ (1)2. Assume elastic-plastic behavior for materialMρ = 1/KMyσεEεyσYσ= E ε ε <ε ?σ= σYε >εM1/ρEI1/ρYMYLoadingEIUnloading1/R01/R13. We want to construct the following Bending Moment “M” vs. curvature “1/ρ” curveSpringback is measured as 1/R0– 1/R1(2)Permanent set is 1/R14. Stress distribution through the thickness of the beamσ σyYY-Yσh-YYElastic Elastic-plastic Fully plastic5. M = ∫Aσ y dAElastic regionAt the onset of plastic behaviorσ = - y/ρ E = - h/2ρ E = -Y (4) σYThis occurs at 1/ρ = 2Y / hE = 1/ρY(5)dσydAbhdySubstitution into eqn (3) gives us the moment at on-set of yield, MYMY= - EI/ρY= EI 2Y / hE = 2IY/h (6)After this point, the M vs 1/r curve starts to “bend over.” Note from M=0 to M=MYthe curve is linear.ρρσEIdAyEydAM −=−==∫ ∫2(3)In the elastic – plastic regionσyYYYbyyhYbybyYyYbYbydyyyYbydyybdyMYYyYhyhyyYYYYY222032/22/032)4( 3222 22+−=+=+==∫ ∫ ∫σ−=222/3114 hyYbhMYNote at yY=h/2, you get on-set at yield, M = MYAnd at yY=0, you get fully plastic moment, M = 3/2 MY(7)To write this in terms of M vs 1/ρ rather than M vs yY, note that the yield curvature (1/ρ)Ycan be written as (see eqn (1))2/1hYYερ= (8)Where εYis the strain at yield. Also since the strain at yYis -εY, we can writeYYyερ=1(9)Combining (8) and (9) givesρρ1)1(2/YYhy=(10)Substitution into (7) gives the result we seek:−=21)1(31123ρρYYMM(11)M1/ρEI1/ρYMYLoadingEIUnloading1/R01/R1Eqn(11)Elastic unloading curve−=111)1( RMMYYρρ(12)Now, eqn’s (12) and (13) intersect at 1/ρ = 1/R0Hence,−=−20101)1(3112311)1( RMRRMYYYYρρRewriting
View Full Document
Unlocking...