Sheet metal stamping was developed in the 1890s for mass production of bicycles, playing an important role in making interchangeable parts economical. Basic sheet forming processes include shearing, bending, drawing, and involve tools like shear presses, brake presses, and finger presses. Material selection is critical, balancing formability with strength, weight, cost, and corrosion resistance. Stretch forming allows tighter tolerances than stamping but is difficult for complex shapes. New developments include tailored blanks, binder force control, and quick die exchange. Alternative auto body materials offer cost and environmental benefits compared to steel.
1. Sheet Metal Forming
2.810 Fall 2002
Professor Tim Gutowski
Minoan 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.
2. 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).
12. Bending Force Requirement
Punch
Workpiece T
Die
L
Force
T = Sheet Thickness
W = Total Width Sheared
(into the page)
L =Span length
UTS = Ultimate Tensile
Strength of material
Engineering Strain during Bending: e = 1/((2R/T) + 1)
R = Bend radius
Minimum Bend radius: R = T ((50/r) – 1)
r = tensile area reduction
in percent
)(
2
UTS
L
WT
F =
13. Stress distribution through the
thickness of the part
σ σ yY
Y
-Y
σ h
-Y
Y
Elastic Elastic-plastic Fully plastic
19. Stretch Forming Force
Requirement
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
)
• Example of Force Calculation
Calculate 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 tons
Calculate 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 tons
20. Auto body panels
10 - 11 panels
•3 to 5 dies each
• ~$0.5M each
• ~$20M investment
23. Material Selection
Material 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 Example
Auto Body Panel Airplane Body Panel
Progressive stamping stretch forming
1010 Steel, cold-rolled 2024 Aluminum, T3 temper
.04” sheet, custom order .08” sheet, oversize
Double-sided Zinc clad mechanically polished
Cost ~ $.35-.45/lb Cost ~ $4.0/lb
UTS ~ 300 MPa UTS ~ 470 MPa
YS ~ 185 MPa YS ~ 325 MPa
Elongation ~ 42% Elongation ~ 20%
n = .26 n = .16
24. Comparison of representative
Parts: Aero and Auto
Auto Aero
Part Description Body Panel Body Panel
54"X54" 54"X54"
Forming Process Progressive Stamping Stretch Forming
MATERIAL
Material
1010 Steel, cold-rolled,
.04" sheet, custom order
double-sided Zinc clad
2024 Aluminum, T3
temper, .08" sheet,
oversize mechanically
polished
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 30
Cycle Time 0.25 min 2.5 min
Total Labor 0.30 min 4.5 min
Labor 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
25. Parts
Received
Mylar Protection
Applied
‘Burr’ Edges
in tension
Stretch
Forming
Index to
Block
‘Burr’ Edges
and Inspect
Hand
Trim
Chemica
l Milling
Aerospace Stretch Forming Body Panel Process
Clad and
Prime
Surfaces
Process Flow for Automobile Door Stamping Operation
Raw
material
Blank material
starting dimensions
Drawing Pierce
FlangeRestrike
26. Design: 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 forming
28. Elastic Springback Analysis
L
x
y
h
b
1. Assume plane sections remain plane:
εy = - y/ρ (1)
2. Assume elastic-plastic behavior for material
M
ρ = 1/K
M
y
σ
ε
E
εy
σY
σ= E ε ε <ε
σ= σY ε >ε
30. 4. Stress distribution through the thickness of the beam
σ σ yY
Y
-Y
σ h
-Y
Y
Elastic Elastic-plastic Fully plastic
31. 5. M = ∫A σ y dA
Elastic region
At the onset of plastic behavior
σ = - y/ρ E = - h/2ρ E = -Y (4) σ
Y
This occurs at
1/ρ = 2Y / hE = 1/ρY (5)
dσ
y
dA
b
h
dy
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.
ρρ
σ
EI
dA
y
EydAM −=−== ∫ ∫
2
(3)
32. In the elastic – plastic region
σ yY
Y
Ybyy
h
Yb
y
b
y
Yy
Yb
Ybydy
y
y
YbydyybdyM
YY
y
Y
h
y
h
y
y
Y
Y
Y
Y
Y
22
2
0
32/2
2/
0
3
2
)
4
(
3
2
2
2
22
+−=
+=
+== ∫ ∫ ∫σ
−=
22
2/3
1
1
4 h
y
Y
bh
M Y
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
(7)
33. 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))
2/
1
h
Y
Y
ε
ρ
= (8)
Where εY is the strain at yield. Also since the strain at yY is
-εY, we can write
Y
Y
y
ε
ρ
=
1
(9)
Combining (8) and (9) gives
ρ
ρ
1
)1(
2/
YY
h
y
= (10)
34. Substitution into (7) gives the result we seek:
−=
2
1
)1(
3
1
1
2
3
ρ
ρ Y
YMM (11)
M
1/ρ
EI
1/ρY
MY
Loading
EI Unloading
1/R01/R1
Eqn(11)
Elastic unloading curve
−=
1
11
)1( R
M
M
Y
Y
ρρ
(12)
35. Now, eqn’s (12) and (13) intersect at 1/ρ = 1/R0
Hence,
−=
−
2
010 1
)1(
3
1
1
2
311
)1( R
M
RR
M Y
Y
Y
Y ρ
ρ
Rewriting and using 1/ρ = 2Y / hE, we get
3
2
0
10
43
11
−=
−
hE
Y
R
hE
Y
RR
(13)
51. Summary
Note on Historical Development
Materials and Basic Mechanics
Aerospace and Automotive Forming
New Developments
Environmental Issues
Solidworks and Metal Forming your Chassis
52. Readings
1. “Sheet Metal Forming” Ch. 16 Kalpakjian (3rd
ed.)
2. “Economic Criteria for Sensible Selection of Body
Panel Materials” John Busch and Jeff Dieffenbach
3. Handout from Shigeo Shingo, The SMED System
4. “Steps to Building a Sheet Metal Chassis for your
2.810 Car Using Solidworks”, by Eddy Reif
5. “Design for Sheetmetal Working”, Ch. 9 Boothroyd,
Dewhurst and Knight
Notas do Editor
Max and RMS error results
Nearly identical results were found for spherical and saddle shaped parts