sheet metal forming (mit 2.008x lecture slides)

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

10/12/16 2.008 Fall 2016

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

2.008 Fall 201610/12/16

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

2.008 Fall 201610/12/16

Manufacturing

Amada CNC Automated Shear Punch

• Removal (Cutting)

• What Determines

the Part

Geometry?

2.008 Fall 201610/12/16

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:

2.008 Fall 201610/12/16

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!

2.008 Fall 201610/12/16

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


• 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

10/12/16 2.008 Fall 2016

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?

10/12/16 2.008 Fall 2016

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

2.008 Fall 201610/12/16

• 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


K

M

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In Elastic Range

Stress is

Proportional to Strain

Manufacturing


K

M

10/12/16 2.008 Fall 2016

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

10/12/16 2.008 Fall 2016

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

10/12/16 2.008 Fall 2016

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


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)

10/12/16 2.008 Fall 2016

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

10/12/16 2.008 Fall 2016

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

2.008 Fall 201610/12/16

M M

F F

ε(y)

Pure Bending Moment “M”

Added Tensile Force “F”

Bending Strains are Biased toward Tensile

!

Manufacturing

Effect on Stresses?

2.008 Fall 201610/12/16

M M

σ(y)

F F

Stresses Are Likewise Biased Toward Tensile

Manufacturing

Effect on Springback?

2.008 Fall 201610/12/16

M M

F F

ε(y)

ε(h/2) = εY

M M

F F

σY

Uniform Stress:

No Springback

Manufacturing


• 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 +-)

10/12/16 2.008 Fall 2016

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

10/12/16 2.008 Fall 2016

High

High

High

Low

Moderate

Low

Low

Moderate-High

sheet metal forming (mit 2.008x lecture slides)

Engineering