sheet metal forming (mit 2.008x lecture slides)
TRANSCRIPT
2.008x
Sheet Metal FormingMIT 2.008x
Prof. David E. Hardt
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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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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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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Manufacturing
Amada CNC Automated Shear Punch
• Removal (Cutting)
• What Determines
the Part
Geometry?
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Amada
CNC Punch Press
Manufacturing
Processes
• Removal (Cutting)
– Serial Thermal Energy
• What Determines the
Part Geometry?
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CNC Laser
Cutter
Manufacturing
Simple Bending
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• Plastic Deformation Via Bending Stresses
Manufacturing
Processes: Bending
• Local High Bending Stress
• Plastic Deformation
• What Determines the Part Geometry?
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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
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
Manufacturing
3D Sheet Stamping for Car Bodies
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Simultaneous Deformation over the Area of the Part
What Determines the Part Geometry?
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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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
Manufacturing
Processes and Mechanics
• Simple Bending
– Bending Only
– Low Forces
– Large Springback
• Low accuracy
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Manufacturing
M M
ε
σ
Brake Bending of Sheet
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• Simple Process
• Complex Mechanics
• Variable Moments
• Variable Curvature
• Combined Elastic-
Plastic Zones
Manufacturing
Simple Model : Pure Moment Bending
Constant Radius Tool
Springback
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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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Manufacturing
h
b
M
r = 1/K
ye=K y
M
K = curvature of the toolingh = thickness of the sheete(y) = through thickness strain
What is M(K) (or K(M)) ?
Simple Bending Model
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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
Manufacturing
Stress and Strain in Bending
K
M
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Manufacturing
Stress and Strain in Bending
K
M
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Manufacturing
Stress and Strain in Bending
K
M
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In Elastic Range
Stress is
Proportional to Strain
Manufacturing
Stress and Strain in Bending
K
M
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NB: Yield exceeded
Manufacturing
Stress and Strain in Bending
K
M
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NB: Yield exceeded
Manufacturing
Stress and Strain in Bending
K
M
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NB: Yield exceeded
Manufacturing
h
b
M
r = 1/K
ye=K y
M
ε(y)= Kyσ = f (ε)
M = σ (y)ybdy−h/2h/2∫
dAmoment arm
Given K,
M = ?
Analysis: Simple Beam
Theory
dsy
dAb
hdy
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From 2.001 Elastic Beam Bending
(stress-strain curve)
Manufacturing
s
e
E
eY
sY
Idealized Material Model:
Elastic Perfectly Plastic
s= E e e <eY
s= sY e >eY
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Manufacturing
K h2= 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
∫ = EKy2bdy−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)
Manufacturing
Moment - Curvature
Relationship
As K increases, eventually:
K h2> εY ∴yielding occurs
But for all e> e Y, s= s Y (i.e. constant stress)
From M = Melastic + M Plastic
M =32My 1− 1
3Ky
K" # $
% & ' 2"
# $
%
& '
KY = εY / (h / 2)MY = EI KY
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We can get
Manufacturing
The Resulting M-K Curve
M
K
EI
KY
MY
3/2 MY
Loading
EIUnloading
KtoolKpart
DK
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Mmax
Manufacturing
Stress and Strain in Bending
K
M
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Manufacturing
Stress and Strain in Bending
K
M
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Manufacturing
Stress and Strain in Bending
K
M
10/12/16 2.008 Fall 2016
Manufacturing
Stress and Strain in Bending
K
M
10/12/16 2.008 Fall 2016
Manufacturing
Stress and Strain in Bending
K
M
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Manufacturing
Stress and Strain in Bending
K
M
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Manufacturing
Final Shape: Springback
ΔK =Mmax
EI∴Kpart = Ktool − ΔK
K = shape of tool
E= material modulus
I = 112bh3 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
Manufacturing
Effect of Material Variations:
Increase in Yield Stress
M
K
EI
KY
MY
Ktool
DK
Kpart
MY�
DK
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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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Manufacturing
Conclusions for
Simple Bending
• High Degree of Springback
• Strong Material Dependence
• Yield Strength
• Strain Hardening
• Thickness
• Low Forming Forces
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Manufacturing
More Precision?
• Bend + Stretch
– Reduction in Springback
• Higher Accuracy
– Increase in Forces
– Increase in strain: more failure
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Manufacturing
Adding Stretch to Pure Bending
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F F
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
!
Manufacturing
Effect on Stresses?
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M M
σ(y)
F F
Stresses Are Likewise Biased Toward Tensile
Manufacturing
Effect on Springback?
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M M
F F
ε(y)
ε(h/2) = εY
M M
F F
σY
Uniform Stress:
No Springback
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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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
Tooling10/12/16 2.008 Fall 2016
Manufacturing
Process Comparisons
• Rate
• Quality
• Cost
• Flexibility
Sheet Forming Machining
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High
High
High
Low
Moderate
Low
Low
Moderate-High