Slides accompanying 2.008x* video module on Sheet Metal Forming, Prof. David Hardt, MIT, 2016.
*Fundamentals of Manufacturing Processes on edX: https://www.edx.org/course/fundamentals-manufacturing-processes-mitx-2-008x
2. Manufacturing
Key Topics
• Products and Processes
• The Process Taxonomy
• Demonstrations
– Pure Bending
– Adding Stretch
• Processes and Mechanics
• Comparison Criteria
– Rate
– Quality
– Flexibility
– Cost
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3. Manufacturing
Process Taxonomy
• Shape Change Mechanism?
– Removal (2-D)
• Mechanical Shear
• Water Jet (Fluid Shear)
• Thermal Ablation or Melting
– Plastic Deformation (2 and 3-D)
• Simple Bending (Along a Line)
• Bending + Stretching
• 3D Draw-Forming
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4. Manufacturing
The “Big Four”
• Rate
– What Limits This?
• Quality
– What Causes Dimensions/Shape/Properties to
Vary from Specifications?
• Cost
– Material/Machine/Labor
• Flexibility
– Ease of Product Changeover
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5. Manufacturing
Amada CNC Automated Shear Punch
• Removal (Cutting)
• What Determines
the Part
Geometry?
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Amada
CNC Punch Press
9. Manufacturing
Combined Die Cutting and Bending
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• “Progressive” Dies
• Strip of Sheet Sequences Through a
“Progression” of Cutting and Bending Tools
http://stampingworld.com/stripjoint/highspeedstamping/10
Electrical Connectors
10. Manufacturing
Making Airplane Skins: Large Smooth
Panels with Compound Curvature:
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From Cyril Bath Co.
Why do we need the Stretch?
What Determines the Part Geometry?
Stretch Forming Process
11. Manufacturing
3D Sheet Stamping for Car Bodies
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Simultaneous Deformation over the Area of the Part
What Determines the Part Geometry?
12. Manufacturing
Process Mechanics
• Removal
– Serial Shear (Shearing)
– Parallel Shear (Punching)
• Planar Deformation
– Focus on Simple Bending but with Plasticity
• Elastic Springback
– Effect of Adding Stretch
• Reduction of Springback
• Potential for Tensile Failure
• General 3D Deformation
– Bending, Tension and Compression
• Buckling!
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13. Manufacturing
Processes and Mechanics
• Cutting
– Similar to Machining
– Large Shear at Tool - Material interface
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Looks just like
machining at the
interface
17. Manufacturing
Simple Bending Mechanics:
• Tool Shape (Rtool) determines the shape
under load
• Can Model as Pure Moment Beam Bending
• Elastic Springback determines the final shape
• What determines the Springback?
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18. Manufacturing
h
b
M
r = 1/K
y
e=K y
M
K = curvature of the tooling
h = thickness of the sheet
e(y) = through thickness strain
What is M(K)
(or K(M)) ?
Simple Bending Model
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19. Manufacturing
Moment – Curvature for Bending
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• Relates the Shape to the Applied Moment
• Is the Bending Equivalent to Force-
Displacement or Stress-Strain
• Will look similar:
K
M
26. Manufacturing
h
b
M
r = 1/K
y
e=K y
M
ε(y) = Ky
σ = f (ε)
M = σ (y)ybdy
−h/2
h/2
∫
dA
moment arm
Given K,
M = ?
Analysis: Simple Beam
Theory
ds
y
dA
b
h
dy
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From 2.001 Elastic Beam Bending
(stress-strain curve)
28. Manufacturing
K
h
2
= εmax < εY
If the die curvature K is such that:
Then only elastic deformation will
take place and:
M = σ(y)ybdy−h/ 2
h / 2
∫ = EKy
2
bdy−h/ 2
h / 2
∫
= loaded curvature bending
stiffness
= KE
bh3
12
= KEI
Moment - Curvature
Relationship M(K)
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(All strains are below yield)
29. Manufacturing
Moment - Curvature
Relationship
As K increases, eventually:
K
h
2
> εY ∴yielding occurs
But for all e> e Y, s= s Y (i.e. constant stress)
From M = Melastic + M Plastic
M =
3
2
My 1− 1
3
Ky
K
"
#
$
%
&
'
2
"
#
$
%
&
'
KY =εY /(h / 2)
MY = EI KY
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We can get
37. Manufacturing
Final Shape: Springback
ΔK =
Mmax
EI
∴Kpart = Ktool − ΔK
K = shape of tool
E= material modulus
I =
1
12
bh3
cubic dependence on thickness
Mmax = ?
Mmax = Φ (KY, EI)
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M
K
EI
KY
MY
3/2 MY
EI
KtoolKpart
DK
Mmax
38. Manufacturing
Effect of Material Variations:
Increase in Yield Stress
M
K
EI
KY
MY
Ktool
DK
Kpart
MY
DK
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39. Manufacturing
Other Possible Variations
• Yield Stress (+ 10%reported)
– Chemistry, working history
• Thickness
– Rolling mill quality
– Design vs. manufacturing specs
• Tooling Errors
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40. Manufacturing
Conclusions for
Simple Bending
• High Degree of Springback
• Strong Material Dependence
• Yield Strength
• Strain Hardening
• Thickness
• Low Forming Forces
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41. Manufacturing
More Precision?
• Bend + Stretch
– Reduction in Springback
• Higher Accuracy
– Increase in Forces
– Increase in strain: more failure
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43. Manufacturing
Effect of Tensile Strain with Bending
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M M
F F
ε(y)
Pure Bending Moment “M”
Added Tensile Force “F”
Bending Strains are Biased toward Tensile
!
46. Manufacturing
Processes and Mechanics
• Deep Drawing (3D Bend + Stretch)
– Extreme Deformation
– Large Compressive Strains
• Buckling Failure possible
– Large Forces
– Critical Flow Control
• Sheet Formability
– Balance of Biaxial Strains (++ and +-)
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47. Manufacturing
The Big Four
• Rate Limits
– Deformation Speed (Usually “Fast”)
– Parallel Processes – Large Areas “Fast”
• Quality
– Springback
– Strong Material Property Dependence
• Cost
– High Volumes – Material Dominates, but Low
Waste in General
– Low Volumes – Tooling and Machine Dominates
• Flexibility
– Serial Processes – Trajectory Easily Changed
– Parallel Processes – Low – Complex and Costly
Tooling
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48. Manufacturing
Process Comparisons
• Rate
• Quality
• Cost
• Flexibility
Sheet Forming Machining
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High
High
High
Low
Moderate
Low
Low
Moderate-High
