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Sheet Metal Forming
2.810 Fall 2008
Professor Tim Gutowski
Minoan gold pendant of bees encircling the Sun, showing theuse of granulation, from a tomb at Mallia, 17th century BC. In
the Archaeological Museum, Irklion, Crete.
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Readings1. Sheet Metal Forming Ch. 16 Kalpakjian
2. Design for Sheetmetal Working, Ch. 9Boothroyd, Dewhurst and Knight
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Historical Note;
Sheet metal stamping was developed as a mass
production technology for the production of bicyclesaround the 1890s. This technology played animportant role in making the system of interchangeableparts economical (perhaps for the first time).
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Steps in making Hub Steps in Sprocket making
Ref Hounshell
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Stress Strain diagram materialsselection
E
y
Y
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Basic Sheet Forming Processes(from http://www.menet.umn.edu/~klamecki/Forming/mainforming.html)
Shearing
Bending
Drawing
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Shear and corner press
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Brake press
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Finger press
LMP Shop Video
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Shearing Operation ForceRequirement
Die
SheetPunch TD
Part or slug
F = 0.7 T L (UTS)
T = Sheet ThicknessL = Total length ShearedUTS = Ultimate Tensile Strength of material
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Yield Criteria
Y
Y/2
Tresca Mises
max = (2/3)1/2Y = 0.82Y max = (1/2) Y
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Schematic of a Blanked Edge
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bending strain
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Stress distribution through thethickness of the part
yY
Y
-Y
Y
Elastic Elastic-plastic
Resulting Moment, M = 2Y (b h/2) h/4 = Ybh2/4
h
-Y
Fully plastic
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Balance external and internal moments
h
-Y
Fully plastic
F
F/2 F/2
Ybh2/4 = FL/4
F = bh2Y/L
L
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Bending Force Requirement
PunchWorkpiece T
Die
W
Force
T = Sheet ThicknessW = Width of Die OpeningL = Total length of bend
(into the page)UTS = Ultimate TensileStrength of material
)(2
UTSW
LTF=
Show Bending Video
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Bending Moment Curvature
M
1/
EI
1/Y
MY
Loading
EI Unloading
1/R01/R1
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Springback
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Elastic Springback Analysis
L
x
y
h
b
1. Assume plane sections remain plane:y = - y/ (1)
2. Assume elastic-plastic behavior for material
M
= 1/K
My
E
y
Y = E
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M
1/
EI
1/Y
MY
Loading
EI Unloading
1/R01/R1
3. We want to construct the followingBending Moment M vs. curvature 1/ curve
Springback is measured as 1/R0 1/R1 (2)Permanent set is
1/R1
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4. Stress distribution through the thickness of the beam
yY
Y
-Y
h
-Y
Y
Elastic Elastic-plastic Fully plastic
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5. M = A y dA
Elastic region
At the onset of plastic behavior= - y/E = - h/2E = -Y (4)
Y
This occurs at1/= 2Y / hE = 1/Y (5)
d
y
dAb
hdy
Substitution into eqn (3) gives us the moment at on-set of
yield, MYMY= - EI/Y= 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.
EIdAyEydAM ===
2
(3)
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In the elastic plastic region yY
Y
Ybyyh
Yb
yb
y
YyYb
Ybydy
y
yYbydyybdyM
YY
y
Y
h
y
h
y
y
Y
Y
Y
Y
Y
222
0
32/
2
2/
0
3
2)
4(
32
22
22
+=
+=
+==
=
22
2/3
1
14 h
y
Y
bh
MY
Note atyY=h/2, you get on-set at yield, M = MYAnd atyY=0, you get fully plastic moment, M = 3/2 MY
(7)
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To write this in terms ofMvs 1/ rather than M vsyY, notethat the yield curvature (1/)
Y
can be written as (see eqn (1))
2/
1
h
Y
Y
= (8)
Where Y is the strain at yield. Also since the strain atyYis -Y, we can write
Y
Y
y
=1
(9)
Combining (8) and (9) gives
1
)1(
2/
YY
h
y= (10)
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Substitution into (7) gives the result we seek:
=
2
1)1(
311
23
Y
YMM (11)
M
1/
EI
1/Y
MY
Loading
EI Unloading
1/R01/R1
Eqn(11)
Elastic unloading curve
= 1
11
)1( R
M
M Y
Y
(12)
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Now, eqns (12) and (13) intersect at 1/= 1/R0
Hence,
=
2
010 1
)1(
3
11
2
311
)1( RM
RR
M YY
Y
Y
Rewriting and using 1/= 2Y / hE, we get
3
2
0
1043
11
=
hEY
RhE
Y
RR (13)
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tension
compression
Pure Bending
Bending & Stretching
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Stretch Forming
Loading Pre-stretching
Wrapping Release
* source: http://www.cyrilbath.com/sheet_process.html
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Stretch forming
F = (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)
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Auto body panels
10 - 11 panels3 to 5 dies each
~$0.5M each ~$20M investment
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Tooling for Automotive Stamping
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Forming Limit Diagram
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Material 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 processconsiderations such as strength, weight, cost, and corrosionresistance.
Auto vs. Aerospace Example
Auto Body Panel Airplane Body Panel
Progressive stamping stretch forming1010 Steel, cold-rolled 2024 Aluminum, T3 temper.04 sheet, custom order .08 sheet, oversize
Double-sided Zinc clad mechanically polishedCost ~ $.35-.45/lb Cost ~ $4.0/lbUTS ~ 300 MPa UTS ~ 470 MPa
YS ~ 185 MPa YS ~ 325 MPaElongation ~ 42% Elongation ~ 20%
n = .26 n = .16
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Comparison of representative
Parts: Aero and AutoAuto Aero
Part Description Body Panel Body Panel
54"X54" 54"X54"
Forming Process Progressive Stamping Stretch FormingMATERIAL
Material
1010 Steel, cold-rolled,
.04" sheet, custom orderdouble-sided Zinc clad
2024 Aluminum, T3
temper, .08" sheet,
oversize mechanicallypolished
Scrap 40% 20%
Material Cost $0.45/lb $4.00/lb
Per part $15.75 $105.00
LABOR
Set-up Time 1.5hr 1.0hr
Parts/Run 2,000 30Cycle Time 0.25 min 2.5 min
Total Labor 0.30 min 4.5 minLabor Rate** $20.00/hr $20.00/hr
Stretch-Form Labor Cost $0.10 $1.50
FIXED
Equipment $5,000,000 $1,000,000
Tools/Dies $900,000 $45,000
(200 manhours labor)TOTAL TRANSFER COST $25 $265
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Steel can production at Toyo Seikan
See Appendix D; http://itri.loyola.edu/ebm/
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DWI Comparison TULC steel can w/ tin
limits recycling ironing process
requires lubricants &
coolant waste water painting process
requires coating and
baking VOCs andCO2
tin free steel
dry forming with 20umpolyester sheet
printing processreduces VOCs and
CO2
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reduced waste water & CO2
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Recycling Aluminum Cans ~50% of aluminum
cans are recycled 40% recycled contentin new cans
secondary aluminumrequires 95% lessenergy than primaryaluminum
Can recycling limitedby Mg alloy
Al/Mg alloy
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AluminumP
roduction
Process
Mining
4 MJ/kg Al
Bayer Process
30.4 MJ/kg
Rolling20.3 MJ/kg
Hall-Heroult
Process
245.3MJ/kg
Illustration from;IAI web pageData from; Alcoa; Martchek, Fisher & KlockoSAE paper 982177, 1998
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Recycling Aluminum Cans
50% of aluminumcans are recycled
40% recycled contentin new cans
95% less energy than
primary aluminum
Shredded
Screen
De-
lacquer
Melt
&
Blend
RollPour
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Recycling Aluminum Cans
50% of aluminumcans are recycled
40% recycled contentin new cans
95% less energy than
primary aluminum
Shredded
Screen
De-
lacquer
Melt
&
Blend
RollPour
Separate
for
Lead
Separate
for Mg
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New developments Tailored blanks
Binder force control Segmented dies
Alternative materials; cost issues
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-
SHAPEMEASUREMENT
SHAPECONTROLLER
WORKPIECE
desiredshape +
shapeerror
finishedpart
DISCRETE DIESURFACE
DISCRETE DIE
FORMING PRESS
CONTROLLER
TRACING CMM
Part Error
Die Shape
Change
New
Part
Shape
The Shape Control Concept
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Conventional Tooling
Tool
Pallet
Parking Lot
60 Ton Matched Discrete Die
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60 Ton Matched Discrete Die
Press(Robinson et al, 1987)
Tool Setup
Actuators
Programmable
Tool
Passive
Tool
Press Motion
Cylindrical Part Error
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Cylindrical Part Error
Reduction
0
10
20
30
40
50
60
P1 P2 P3 P4
PART CYCLE
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
RMSE
rror[x0.0
01in.]
MAX
RMS
SSYYSSTTEEMM EERRRROORR TTHHRREESSHHOOLLDD
MAXIM
ALSHAPEERR
OR
[x0.0
01in.]
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Large Scale Tool
6 feet
Stretch Forming with Reconfigurable
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Stretch Forming with Reconfigurable
Tool @ Northrop Grumman
Alternative materials for auto
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Alternative materials for auto
body panels
Comparison
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Comparison
Steel Vs SMC $0.35/lb
0.03 thick
7.6 lb 40% scrap
$4.25 matl cost
400/hr
5 workers
$18.90/hr (Union) $0.24 labor cost
$5,000,000 equipment
$900,000 tools
$7.71 unit cost at 100,000 units
$0.65/lb
.0.12 thick
7.0 lb 6% scrap
$4.84 matl cost
40/hr
$12.50/hr (non-Union)
$0.63 labor cost $1,200,000 eqipment
$250,000 tools
$7.75 unit cost at 100,000 units
Ref John Busch
Cost comparison between sheet
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Cost comparison between sheet
steel and plastics and composites forautomotive panels ref John Busch
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See websiteSteps to Building a Sheet Metal Chassis for your 2.810 Car Using
Solidworks, by Eddy Reif
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