stretch forming with reconfigurable

8/13/2019 Stretch Forming With Reconfigurable

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Sheet Metal Forming

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.

.

T. Gutowski

Sheet Metal Forming Ch. 16 KalpakjianDesign for Sheetmetal Working,

Ch. 9 Boothroyd, 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 an importantrole in making the system of interchangeable parts

.


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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

SheetPunch TD

D e Part or s ug

F = 0.7 T L (UTS)

T = Sheet ThicknessL = Total length ShearedUTS = Ultimate Tensile Strength of material


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Yield Criteria

Y/2

Y

Tresca Mises

max = (2/3)1/2Y = 0.82Y max= (1/2) Y


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For a general state of stress useeffective stress

Yielding occurs when effective = Y

Material taken from Metal Forming, by Hosford and Caddell


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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

h

-Y

Elastic Elastic-plastic

Resulting Moment, M = 2Y (b h/2) h/4 = Ybh2/4

-Y

Fully plastic


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Balance external and internal moments

h

F

-

Fully plastic F/2 F/2

Ybh2/4 = FL/4

F = bh2Y/L


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Bending Force Requirement

PunchWorkpiece T

Force

T = Sheet ThicknessW = Width of Die OpeningL = Total len th of bend

)(2

UTSW

LTF =

Die

W

(into the page)UTS = Ultimate TensileStrength of material

Show Bending Video


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Bending Moment Curvature

MLoading

1/

EI

1/Y

Y

EI Unloading

1/R01/R1


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Springback


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Elastic Springback Analysis

L

x

y

h

b

= 1/K

1. Assume plane sections remain plane:y = - y/ (1)

2. Assume elastic-plastic behavior for material

MMy

E

y

Y = E


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MMY

Loading

3. We want to construct the followingBending Moment M vs. curvature 1/ curve

1/

EI

1/Y

EI Unloading

1/R01/R1

Springback is measured as 1/R0 1/R1 (2)Permanent set is 1/R

1


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4. Stress distribution through the thickness of the beam

yY

Y

h

Y

-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

d

y

dAb

hdy

EIdAyEydAM ===

2

(3)

- - -

This occurs at1/= 2Y / hE = 1/Y (5)

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.


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In the elastic plastic region yY

Y

yb

y

YyYb

Ybydy

y

yYbydyybdyM

yh

h

y

y

Y

Y

Y

Y

32/

2

2/

0

32

22

22

+=

+==

Ybyyh

Yb YY

Y

222

3

2)

4( +=

=

22

2/3

1

14 h

y

Y

bh

M Y

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 ofM vs 1/ rather thanM 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(

3

112

3

YYMM (11)

M

1/

EI

1/Y

MY

Loading

EI Unloading

1/R01/R1

Elastic unloading curve

=

1

11

)1( R

M

M Y

Y

(12)


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Now, eqns (11) and (12) intersect at 1/= 1/R0

Hence,

=

2

1

)1(

3

11

2

311

1 RM

RR

M YY

Y

Rewriting and using 1/= 2Y / hE, we get

3

2

0

1043

11

=

hE

Y

RhE

Y

RR (13)


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tension

compression

Pure Bending

Bending & Stretching


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Stretch Forming

Loadin Pre-stretchin

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

Video


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Forming Limit Diagram


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For a general state of stress

=Kn


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Note on strain


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Steel can production at Toyo Seikan

See Appendix D; http://itri.loyola.edu/ebm/


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DWI TULC steel can w/ tin

limits recycling ironing process

requires lubricants &

tin free steel

dry forming with 20uml r h

coolant waste water painting process

requires coating and

baking VOCs andCO2

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

Al/Mg alloy

secon ary a um numrequires 95% lessenergy than primaryaluminum

Can recycling limitedby Mg alloy


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duction

Process

Mining

4 MJ/kg Al

Bayer Process

30.4 MJ/kg

A

luminumP

r

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

Energy to make

Shredded De-

lacquer

Melt

4+30.4+245.3+20.3=

= 300MJ/kg

Recycling avoids the

first three steps

Screen

&

Blend

RollPour


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Recycling Aluminum CansShredded

De-lacquer

Melt

Separate

forLead

Screen

&

Blend

RollPour

Separatefor Mg


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Recycling rates over time


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Related developments Springback in Carbon nanotubes

Tailored blanks Binder force control

Segmented dies Alternative materials; cost issues


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Carbon SWNT

Unzipping Carbon Nanotubes Can Make Graphene RibbonsTeams at Rice and Stanford announce

Nature 2009


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International Journal of Applied Mechanics


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Coordinate system

Large strain behavior of


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Large strain behavior of

anisotropic sheet


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Tailored Blanks


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-

SHAPEMEASUREMENT

SHAPECONTROLLER

WORKPIECE

desired

shape + shape

error

finished

partDISCRETE DIE

SURFACE

The Shape Control Concept

DISCRETE DIE

FORMING PRESS

CONTROLLER

TRACING CMM

Part Error

Die Shape

Change

NewPart

Shape


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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 Press Motion

Programmable

Tool

Passive

Tool

Cylindrical Part Error


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Cylindrical Part Error

Reduction

40

50

60

1

1.2

1.4

1.6

[x0.0

01in.]

MAX

RMS

SHAPEERROR

001in.]

0

10

20

P1 P2 P3 P4

PART CYCLE

0

0.2

0.4

0.6

.

RMSE

rro

SSYYSSTTEEMM EERRRROORR TTHHRREESSHHOOLLDD

MAXIM

AL

[x0


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Large Scale Tool

6 feet

Stretch Forming with Reconfigurable


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Tool @ Northrop Grumman

Alternative materials for auto


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Alternative materials for auto

body panels

Comparison


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Co pa so

Steel Vs SMC $0.35/lb

0.03 thick

7.6 lb

40% scrap

$4.25 matl cost

400/hr

$0.65/lb

.0.12 thick

7.0 lb

6% scrap

$4.84 matl cost

40/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

$12.50/hr (non-Union)

$0.63 labor cost $1,200,000 eqipment

$250,000 tools

$7.75 unit cost at 100,000 units

These costs are now dated but the relative result is instructive

Ref John Busch

Cost comparison between sheet


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p

steel and plastics and composites forautomotive panels ref John Busch

stretch forming with reconfigurable

Documents