Sheet Metal Forming 2.810 D. Cooper w “Sheet Metal Forming” Ch. 16 Kalpakjian w “Design for Sheetmetal Working”, Ch. 9 Boothroyd, Dewhurst and Knight Examples-sheet metal formed Sheet metal stamping/drawing – car industry • 90million cars and commercial vehicles produced worldwide in 2014 Female die Metal sheet Blank holder (ring) on cushion Compressible Male die (punch/post) cushion Stamping Auto body panels • 3 to 5 dies each • Prototype dies ~ $50,000 • Production dies ~ $0.75-1 • Forming dies • Trimming station • Flanging station Objectives By the end of today you should be able to… …describe different forming processes, when they might be used, and compare their production rates, costs and environmental impacts …calculate forming forces, predict part defects (tearing, wrinkling, dimensional inaccuracy), and propose solutions …explain current developments: opportunities and challenges LMP Shop Brake press Finger brake Technology – a brief review Forming Speed Material drawn into shape • Conventional drawing/stamping – expensive tooling, no net thinning, quick 20-1000pts/hr • Hydro-forming – cheap tooling, no net thinning, slow, high formability 7-13cycles/hr Material stretched into shape • Stretch forming – very cheap tooling, net thinning, slow, low formability 3-8pts/hr • Super-plastic forming – cheap tooling, net thinning, expensive sheet metal, slow, very high formability 0.3-4pts/hr Drawing – expensive tooling, no net thinning, quick Deep-drawing Shallow-drawing (stamping) Deep-drawing Blank holder helps prevent wrinkling and reduces springback Blank holder not necessary if blank diameter / blank thickness is less than 25-40. Smaller values for deeper forming. http://www.thomasnet.com/articles/custom-manufacturing-fabricating/wrinkling-during-deep-drawing Blank holder force: forming window Wrinkling Tearing Window for forming Depthof draw Blankholder force Deep Drawing of drinks cans Hosford and Duncan (can making): http:// www.chymist.com/ Aluminum %20can.pdf Hydro-forming – cheap tooling, no net thinning, slow(ish), high formability Low volume batches Hydro-forming – cheap tooling, no net thinning, slow(ish), high formability Low volume batches Hydro-forming – cheap tooling, no net thinning, slow, high formability Small flexforming tool made by additive manufacturing Stretch forming – very cheap tooling, net thinning, slow, low formability, sheet metal up to 15mx9m Loading Pre-stretching Wrapping Release * source: http://www.cyrilbath.com/sheet_process.html Low volume batches Stretch forming: Example parts Higher aspect ratio, deeper parts Super-plastic forming – cheap tooling, net thinning, slow, expensive sheet metal, very high formability Low volume batches, 0.5-0.75 melting temp Forming forces and part geometry Tensile test – the Stress-strain diagram UTS σy=Y Nominal strain True stress & strain εtr = ln(1+εen ) σ tr = σ en (1+εen ) True stress can be expressed σ =Y using a power law (Hollomon y € equation): n σ tr = Kεtr € Power-Law Expression (Hollomon equation) n σ tr = Kεtr Can be re-written: log(σ tr ) = nlog(εtr ) + log K log(σ tr ) € € € -3 -2 -1 0 log(εtr ) € Power-Law Expression (Hollomon equation) n σ tr = Kεtr Can be re-written: log(σ tr ) = nlog(εtr ) + log K log(σ tr ) € k n € € -3 -2 -1 0 log(εtr ) € Tensile instability - necking Useful assumptions σ Only interested in plastic effects: Perfectly plastic material Y or At Y, material defoms (‘flows’) UTS in compression and fails in tension ε σ Y or Interested in elastic and plastic effects: UTS Elastic-perfectly plastic material E ε 3D Problems n In 1-D, σ = K ε assuming perfectly plastic, yielding at: σ = Y n In 3-D, σ eff = K ε eff assuming perfectly plastic, yielding at: σ eff = Y € € € € 3D Yield Criteria Tresca: Yielding occurs at a maximum shear Von Mises: Yielding at maximum stress distortion strain energy Effective stress (in principal directions): Effective stress (in principal directions): % 2 2( σ eff = [σ i − σ j ]max, 1 (σ 2 − σ 3) + (σ 3 − σ1) i≠ j σ = ×' * eff 2 2 &'+ (σ1 − σ 2) )* Yield criterion: Yield criterion: σ = Y σ = Y € eff eff Y Y = 3k τ = k = € max 2 Effective strain: Effective strain: 2 # & 2 2 2 ε = ε εeff = % ( × (ε1 + ε2 + ε3 ) eff ( i )max € $ 3' € € € Shearing Sheet T Punch D Die Part or slug F = 0.7 T L (UTS) T = Sheet Thickness L = Total length Sheared UTS = Ultimate Tensile Strength of material Shear press - LMP Shop Side Note: For a general state of stress use “effective stress” Yielding occurs when σeffective = Y Material taken from Metal Forming, by Hosford and Caddell Origin of effective strain σ = Kε n Material taken from Metal Forming, by Hosford and Caddell 3D Yield Effective stress σ1 € Tresca predicts ‘flow’ for lower stresses than σ2 von Mises σ3 = 0 € € Forming Limit Diagrams ε1=n=necking Tensile test ε1=-2ε2 Pure Shear ε1=-ε2 Stretch forming: Forming force F = (YS + UTS)/2 * A F = 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) Forces needed to bend sheet metal Bending Stress distribution through the thickness of the part Y Y y s s Y s h -Y -Y Elastic Elastic-plastic Fully plastic Fully Plastic Moment, M = Y (b h/2) h/2 = Ybh2/4 Balance external and internal moments F σ h L -Y F/2 F/2 Fully plastic σ σY 2 Ybh /4 = FL/4 = Mmax E F = bh2Y/L εy ε Bending Force Requirement LT 2 Force F = (UTS) W Punch Workpiece T T = Sheet Thickness W = Width of Die Opening L = Total length of bend Die (into the page) UTS = Ultimate Tensile Strength of material W Note: the notation used in the text (L, W) differs from that used in the previous development (b, L). LMP Shop Brake press Finger brake What shape have we created? Steel versus aluminum… Strength (σy) versus Stiffness (E) Mild steel (30E6psi) Mild steel (33,000psi) & Al. 5052H32 (33,000psi) Al. 5052H32 (10.6E6psi) Steel versus aluminum… Strength (σy) versus Stiffness (E) Mild steel (30E6psi) Low spring back Mild steel (33,000psi) & Al. 5052 Al. 5052H32 (33,000psi) H32 (10.6E6psi) High spring back Steel versus aluminum… Strength (σy) versus Stiffness (E) Al. 2024T3 (50,000psi) Mild steel (30E6psi) Low spring back Mild steel (33,000psi) & Al. 2024 & 5052 Al. 5052H32 (33,000psi) T3 H32 (10.6E6psi) High spring back Steel versus aluminum… Strength (σy) versus Stiffness (E) Al. 2024T3 (50,000psi) High spring back Mild steel (30E6psi) Low spring back Mild steel (33,000psi) & Al. 5052H32 (33,000psi) Al. 2024T3 & 5052H32 Low spring back (10.6E6psi) High spring back σ Ti € Mild steel Al EC ε €€ σ Ti € Mild steel Al EC ε εˆ €€ € σ Ti € Mild steel Al EC ε εˆ €€ € σ Ti € Mild steel Al EC ε εˆ €€ € Springback note R in the figure below is mislabeled, should go to the centerline of the sheet Elastic Springback Analysis y x h L b r = 1/K M M y 1. Assume plane sections remain plane: ey = - y/r (1) 2. Assume elastic-plastic behavior for material s sY σ = E e e <e ψ E σ= σY e >e ey e Bending Moment – Curvature M Loading MY EI EI Unloading 1/rY 1/R1 1/R0 1/r 3. We want to construct the following Bending Moment “M” vs. curvature “1/ρ” curve M Loading M M Y & 1 1 # Y M = $ − ! (1 ρ)Y % ρ R1 " EI EI Unloading 1/ρY 1/R1 1/R0 1/ρ Springback is measured as 1/R0 – 1/R1 (2) Permanent set is 1/R1 4. Stress distribution through the thickness of the beam Y Y y σ σ Y σ h -Y -Y Elastic Elastic-plastic Fully plastic dσ dA b y 5. M = ∫ σ y dA dy A h Elastic region y 2 EI M = σydA = −E dA = − (3) ∫ ∫ ρ ρ Y At the onset of plastic behavior σ = - y/ρ E = - h/2ρ E = -Y (4) σ This occurs at 1/ρ = 2Y / hE = 1/ρY (5) Substitution into eqn (3) gives us the moment at on-set of yield, MY MY = - 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=MY the curve is linear. Y In the elastic – plastic region y σ Y y h/ 2 Y y M = σybdy = 2 Ybydy + 2 Ybydy ∫ ∫yY ∫ 0 yY h/ 2 y y 2 Y y3 Y = 2Yb + 2 b 2 yY 3 yY 0 h2 2 = Yb( − y 2 ) + y 2Yb 4 Y 3 Y 2 bh2 & 1 , y ) # M = Y $1− * Y ' ! (7) 4 %$ 3 + h / 2 ( "! Note at yY=h/2, you get on-set at yield, M = MY And at yY=0, you get fully plastic moment, M = 3/2 MY To write this in terms of M vs 1/ρ rather than M vs yY, note that the yield curvature (1/ρ)Y can be written as (see eqn (1)) 1 ε = Y (8) ρY h / 2 Where εY is the strain at yield. Also since the strain at yY is -εY, we can write 1 ε = Y (9) ρ yY Combining (8) and (9) gives y (1 ρ) Y = Y (10) h / 2 1 ρ Substitution into (7) gives the result we seek: 2 3 & 1 , (1 ρ) ) # M = M $1− * Y ' ! (11) 2 Y 3 * 1 ρ ' %$ + ( "! Eqn(11) M Loading MY EI EI Unloading 1/ρY 1/R1 1/R0 1/ρ M Y & 1 1 # M = $ − ! (12) Elastic unloading curve (1 ρ)Y % ρ R1 " Now, eqn’s (11) and (12) intersect at 1/ρ = 1/R0 Hence, & 2 # M Y & 1 1 # 3 1 , (1 ρ)Y ) $ − ! = M Y $1− * ' ! (1 ρ) R R 2 3 * 1 R ' Y % 0 1 " %$ + 0 ( "! Rewriting and using (1/ρ)Y = 2Y / hE (from a few slides back), we get 3 - 1 1 * Y 2 & Y # + − ( = 3 − 4R0 $ ! (13) , R0 R1 ) hE % hE " R0=R1 Methods to reduce springback • Smaller Y/E • Larger thickness • Over-bending • Stretch forming • “coining” or bottoming the punch Y Pure Bending tension σ h compression -Y Fully plastic Y σ h Y Fully plastic Bending & Stretching Stretch forming: can we achieve a strain of 0.035 at A? R=8m, θ=0.25 A R’=0.1m, , θ=1.25 Sheet thickness 1mm, B Punch µ=0.1 C Material: Grips σ=520ε0.18MPa Can we achieve a strain of 0.035 at A? Sheet thickness 1mm, µ=0.1 Material: σ=520ε0.18MPa R=8m, θ=0.25 A R’=0.1m, , θ=1.25 0.18 B FA = 0.001*520*(0.035) =284kN/m Punch F =F *exp(0.1*0.25)=292kN/m B A C FC=FB*exp(0.1*1.05)=323kN/m Grips Max