sheet metal forming - técnico lisboa - autenticação · sheet metal forming processes are usually...

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Sheet Metal FormingIntroductionIn sheet metal forming, an initially simple blank is plastically deformed between tools (or dies) to obtain the desired configuration. Thus, a simple part geometry is transformed into a complex one, whereby the tools ‘store’ the desired geometry and impart pressure on the deforming material through the tool/material interface.

Sheet metal forming processes are characterized by high productivity, with average production rates reaching up to 5000 pieces / hour.

Parts are produced with little or no scrap and the final part geometry is generated in a very short time, usually in one or a few strokes of a press.

Stretch forming and deep drawing are among the most important sheet metal forming processes and products cover a wide range of industries, such as transportation (automotive, aerospace, and aeronautics), food, medical and home appliances, among others.

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Sheet Metal FormingIntroductionSheet metal forming parts can be very different and they are often classified into two different groups: cylindrical parts, rectangular parts and complex parts.

Cilindrical parts

Rectangular parts

Complex parts

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Sheet Metal FormingIntroduction - notationSchematic illustration of a sheet metal forming process with nomenclature.

Cunho (Punção)

Matriz

Peça

(Cerra-chapas)Encostador

Sistema de ejecção

Peça

Punch

Blankholder

Die

Part

Ejector

Part

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Sheet Metal FormingIntroduction - notationSheet metal forming processes are usually classified into two different groups: Stretch forming and deep drawing.

• Deep drawingThis process is performed in two sequential stages. In the initial stage the blank deforms in the bottom and in the corner of the punch leading to thickness reduction in these areas. In the final stage the flange moves into the die and builds up the cylindrical wall.

• Stretch FormingThis process is performed in a single stage corresponding to the initial stage of the deep-drawing process because the pressure of the blankholder and the beads avoid the flange from drawing into the die.The blank deforms by expansion and its thickness is reduced throughout the part.

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Sheet Metal FormingDeep drawing

Deep drawing is performed in one stage or, when the part to produce is very deep, in a sequence of several stages (multi-stage).

• Conventional deep drawing – in one stroke.

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• Redrawing - when the outer surface of the part remains (outer) after the second operation.

Cups of a depth greater than permitted are made by further forming after initial cupping.

• Reverse redrawing - when the outer surface of the part is "turned inside out" and becomes theinner surface.

(Conventional) Redrawing Reverse redrawing

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Schematic representation of reverse redrawing.

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Sheet Metal FormingStretch forming

Stretch forming is widely used in the production of complex parts such as those generally may found in the automotive industry. These parts are generally shallow and therefore its manufacturing is almost always done in one stage.

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Sheet Metal FormingStretch forming

Stretch forming is widely used in the production of complex parts such as those generally may found in the automotive industry. These parts are generally shallow and therefore its manufacturing is almost always done in one stage.

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Sheet Metal FormingDeep drawingThe production of beverage cans involves a sequence of deep drawing stages followed by ironing and doming, necking and seaming operations.

The ironing operation evolves wall thinning

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The production of beverage cans involves a sequence of deep drawing stages followed by ironing and doming, necking and seaming operations.

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Sheet Metal Forming

Presses Force(kN)

Velocity(m/s)

Stroke rate/min

Shut height

(m)

Mechanical efficiency

Hydraulic,Stamping 10-40000 0.5 20-130 0.1-1 0.5-0.7

Mechanic,Stamping 10-20000 1 10-180 0.1-0.8 0.3-0.7

Presses

Presses that are used in sheet metal forming can be classified as a function of their structure:

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Sheet Metal FormingMechanical presses

Apart from special-purpose equipment, most sheet metal forming processes make use of mechanically driven or hydraulic presses.

Small presses may only have one or two independently movable rams whereas larger presses may have two or three independently movable rams, one moving inside the other.

Mechanical presses (knucle joint) can operate at rates of up to 600 strokes per minute.

Knucle-jointConventional

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Sheet Metal FormingHydraulic presses

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Deep DrawingMechanics of deformation

Main stages of a cylindrical deep drawing operation :

• The punch moves until getting into contact with the blank• Stage 1 (stretching)• Stage 2 (deep drawing)• End

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1st Stage (Stretching):

• Starts when the punch gets into contact with the blank

• Elastic behaviour of the material of the blank located over the die and under the blankholder

• The overall area of the part is increased with the displacement of the punch and gives rise to

a conical shape in the region between the punch and die (clearance)(This geometry is only possible due to loss of thickness in the bottom and corner radius of the punch as a

result of the plastic deformation in those areas)

• Further displacement of the punch causes a build up of stress on the flange with forces

being transmitted throughout the conical area of the part being formed.

• The first stage ends when plastic deformation of the flange begins.

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2nd Stage (deep drawing):

• Material of the flange and located around the die corner gets into plastic deformation

• Material of the bottom and located around the punch corner unloads and goes into the elastic

regime(because that the amount of material that is necessary to pull into the die becomes increasingly less)

• The second stage ends when all the material goes into the die (in case, the part is to be

produced without a flange) and results in a cup with a cylindrical wall

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Nomenclature of the 1st and 2nd stages in a cylindrical deep drawing process:

AB - Bottom (base)BC - Corner of the punchCD - Conical evolving into a cylindrical wallDE - Corner of the dieEF - Flange

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Membrane analysis with thickness variation based on an infinitesimal volume element:

2

r

r

h

h+dh

d

+d

Eixo

de

Rev

oluç

ão ( Corte Axial )

d

( Planta )

r

r r

r1

dr

A

B

C

D

E

F

GH

0FFF tangencialradialthickness

Membrane analysis according to the slab method.The stresses r , z and are aligned along the principal directions of the infinitesimal volume element (local stress axis).

Axial cut

Axis

of r

evol

utio

n

(Plan)

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Deep Drawing

A

B

C

D

E

F

GH

Mechanics of deformation

Force equilibrium in the thickness direction:

d/2z

z

rr

r

sen

cos-

2dsen

d/2Pormenor

+d

d

d/2

d2

sen

sen2

d

0cos2

22

2 11

dhdrdhdrdrdr rz

0Fthickness

cos2 rr

drdrh 11

021

rrhrz

Detail

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Deep Drawing

A

B

C

D

E

F

GH

Mechanics of deformation

Force equilibrium in the radial (meridional) direction:

d/2z

z

rr

r

sen

cos-

2dsen

d/2Pormenor

+d

d

d/2

d2

sen

sen2

d

0 radialF

0sen2

2 11

hdrddrdr

hdrdrdrdhhddrrdr

drd

z

rr

r

sen1 drdr

hdrdr 1

0hsen

r

drdh

hrdrd zrr

Detail

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Deep DrawingMechanics of deformation (1st stage)

AB - Bottom (base)

Application of the equilibrium equation in the thickness direction:

021

rrhrz

21 rr

0021

zrz

rrh

This allows concluding that there is no contact between the bottom of the cup and the punch.

This result corroborates the observation that the clearance between the punch and die and the bending moment deviates the bottom of the cup from the punch.

As a result of this, the main action is located at the corner of the punch.

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Deep Drawing

0drdh

0hsen

r

drdh

hrdrd zrr

Yzr31

Mechanics of deformation (1st stage)

AB - Bottom (base)

Application of the equilibrium equation in the radial direction:

03 z

The blank located at the bottom of the cup is under plane stress loading conditions z = 0 and r = = Y.

Yrrr 0

rdrd

1r

Tresca

Tracção

e

k

e

j

e

e

Tracção

ivon Mises

r

Tension

Tension

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AB - Bottom (base)

Application of the Levy-Mises equations:

0z

The blank located at the bottom of the cup is subject to a strain loading path characterized by a balanced biaxial tension with loss of thickness.

Yr

rzz

zr

zrr

dd

dd

dd

212121

ez

e

er

dd

dd

dd

2121 A

B

CD

E FG H

I

CLE

11

1

-1/2

1/2-1

1

2

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Deep Drawing

021

rrhrz

Yzr31


BC - Corner of the punch

hrr 2,

This result allows concluding that the punch promotes a compressive stress against the blank, whose value is smaller than the radial stress because the punch corner radius rcc is generally greater than the thickness h of the sheet.

ccrz r

h

Application of the yield criterion:

ccrr 1

1r

cc

Yexpr

rh1

This result allows obtaining the radial stress that is associated with material expansion along the corner of the punch.

03 z


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Deep Drawing

cc

Yr

rh1




The material located at the corner of punch is also subject to a state of stress r = but with a compressive stress in the thickness direction z .

0hsen

r

drdh

hrdrd zrr

cc

Yexpr

rh1

0drdh

0

drd r

03 z

1r

0

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Deep Drawing

0

bendingrfrictionrexprrzr 0

senhr


BC - Corner of the punchApplication of the equilibrium equation in the radial direction (considering friction and bending):

This result shows that a larger stress r is applied at the punch corner because of the stress increment resulting from friction and bending by traction forces.

0hsen

r

drdh

hrdrd zrr

cc

Yexpr

rh1

0drdh

0

drd r

03 z

1r

0

dl

dr

Cunho

d

r C

C

B

z

z

r B

Punch

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0z

The blank located at the corner of the punch is under biaxial tension, thereby increasing radii and reducing thickness

0 r

rzz

zr

zrr

dd

dd

dd

212121

A

B

CD

E FG H

I

CLE

11

1

-1/2

-1

1

2

1/2

021

021

021

rzz

zr

zrr

dd

dd

dd

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Deep Drawing

021

rrhrz

1r



0 z

The conical area is subject to uniaxial tension because the radial stress is the only nonzero and positive stress.

0r

Application of the equilibrium equation in the radial direction :

The conical area ensures the transmission of the stresses from the punch corner radius to the upper regions of the blank (die corner radius and flange).This result allows concluding that the material located in the conical area remains always in the elastic regime (in the limit ( r )C = y then ( r )D < y ) .

0hsen

r

drdh

hrdrd zrr 0

rdr

d rr CrD

CDr r

r

Punch

CD - Conical wall

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CD - Conical wall

Application of the Hooke law (elasticity):

0 r

The conical area is under uniaxial tension with very low values of strain.

0 z

rz

rr

E

E

01 A

B

CD

E FG H

I

CLE

11

1

-1/2

-1

1

2

1/2

rzz

zr

zrr

E

E

E

1

1

1

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Deep DrawingMechanics of deformation (2nd stage)

EF – Flange

Application of the equilibrium equation in the thickness direction :

021

rrhrz

21 rr

0021

zrz

rrh

This result is consistent with the absence of blankholder.

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Deep Drawing

0drdh

0drdh

hsenhrdrd rzrr

Yr31

Mechanics of deformation (2nd stage)

EF – Flange (without blankholder)

Application of the equilibrium equation in the radial direction :

02z

This result shows that the flange area is subjected to a plane stress state z = 0, characteristic from the second quadrant of the principal stresses space.

01r

Tresca

Tracção

e

r

p=0k

e

j

e

e

Tracção

i

von Mises

03

Crln0rdr

dYr

Yr

Traction

Traction

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Application of the equilibrium equation in the radial direction (continuation):

This result allows us to define the ratio rE/rF = 0.37 as the minimum theoretical relationship below which can not be perform a stamping operation.

0 FrFrr

Crln0rdr

dYr

Yr

1rrln)(0

rrln F

YYrzF

Yr

Fr / r

r

0

e

e

10.80.60.40.200.37 z

FE

F1

EYE

FYEr

r37.0r

rerrrln

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This result shows that:• the strain increment in the tangential direction is negative• the strain increment in the radial direction is positive • the strain increment in the thickness can be either positive or negative depending on the relative values between the tangential and radial stress.

rzz

zr

zrr

dd

dd

dd

212121

A

B

CD

E FG H

I

CLE

11

1

-1/2

-1

1

2

1/2

rz

rr

r

dd

dd

dd

21

021

021

02 z

01 r

03

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This result allows concluding that the final thickness in the outer region of the flange can increase by 30 ~ 40% in case the ratio rFt0/rFt is within the range of 0.5 ~ 0.6.

Wrinkling is a plastic instability phenomenon that takes place at the outer region of the flange due to the high values of tangential compressive stresses.

rz

rr

r

dd

dd

dd

21

021

021

Frr

r

E

F

zr d2d2d

21

00

00

ln21ln

tF

tFt

tF

tFz

tF

tF

rr

hhrr

rr

2

3

EF

crit rrhEP

(uniaxial tensile stress state)

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EF – Flange (with blankholder)

Application of the equilibrium equation in the radial direction:

Blankholders are responsible for lowering the ideal limiting drawing ratio because the radial stress at F causes the radial stress to reach the yield stress for higher values of the ratio r / rF .

Friction at the contact interface with the blankholder and die leads to the same conclusion and justifies the reason why these regions must be well lubricated.

Crln0rdr

dYr

Yr

Frr

hr

Fhr

F

F

enc

F

encFr

22

FrF

YYr

zFrF

Yr

1rrln)(

0,rrln

Fr / r

r

0.370

e

e

0.80.60.40.20z

r

Sem encostador

Com encostador

r F

Fr

1

Without blankholder

With blankholder

37

Deep Drawing

frictionr


DE – Corner of the die

a) Plastic deformation leads to reduction in the perimeter

b) There is instantaneous bending and unbending

c) There is friction between the material and the surface of the die

Using a methodology similar to that previously used for the flange it can be concluded that:

ErE

DYretr r

rlnD

frictionrDrErretrDr

DrEr ,

This result allows concluding that the material located at the corner of the die behaves similarly to that located at the flange.

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021

rrhrz


CD – Cylindrical wall

Application of the equilibrium equation in the thickness direction :

1r 0 z

This result shows that the cylindrical wall is subject to a state of uniaxial tensile stress, where the radial stress is the only stress that is nonzero and positive.

0r

Because the radial stress at point D is always lower than the yield stress of the material, ( r )D < Y it can be concluded that the cylindrical wall (like the conical wall) is in the elastic regime.

Thickness variation in this region is negligible.

Deep Drawing

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Evolution of the radial and tangential stresses along a cross section of the cup

During the first stage of deep drawing the material located at the bottom of the cup and at the punch corner undergoes plastic deformation and the radial stress at point D of the conical wall, which remains elastic, will progressively increase with the movement of the punch. Once this stress reaches the required value for the material located at the die corner and flange to start plastic deformation, the remaining material unloads and ceases deforming.

The critical value for the transition between the two modes of deformation is (σr )D , and depends on the geometry of the blank, friction (lubrication), blankholder pressure and die corner radii.

Cunho

Matriz

Encostador

atrr D

r E

FE

D

D

r D

rF

Fr

r

0 0.2 0.4 0.6 0.8 1

e

e

0r / rF

r

Punch

Blankholder

Die

fr

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The thinning at the bottom of the cup mainly occurs during the 1st stage of the deep drawing operation.

Material located at the punch corner deforms under high radial stresses than that located at the bottom as a result of the increase in stress due to friction and instantaneous bending. This leads to greater thinning and necking at point C, which will be increasing until the stress at point D triggers plastic deformation and the 2nd stage of deep drawing.

From point D to the outer flange – point F – there is an increase of the thickness up to values above the initial sheet thickness.

B

C

D

E

F

A

di/D0

F

E

DC

BA

h/h

The stress and strain analysis that was previously performed to indicates that the thickness of the cup does not remain constant during deep drawing.

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Deep DrawingLimiting drawing ratio LDR

The drawing ratio m is the ratio between the diameter of the cup d and the diameter of the blank D0.

MDdm0

Material 1st StageM1

Following stagesM2

Theorectical value 0.37 0.37

Drawing steel 0.60 – 0.65 0.80

Deep Drawing steel 0.55 – 0.60 0.75 – 0.80

Car bodywork steel 0.52 – 0.58 0.75 – 0.80

Stainless steel 0.50 – 0.55 0.80 – 0.85

Copper 0.55 – 0.60 0.85

Brass 0.50 – 0.55 0.75 – 0.80

Alumium 0.53 – 0.60 0.80

The limiting drawing ratio value M is determined by means of experimental tests that make use of normalized operating parameters and allows determining the minimum diameter dmin a blank that can be drawn for a blank of diameter D0

When m is lower than M there is need to perform multi-stage deep drawing operations (redrawing).

d1

d2

d3

D0

42

Cunho

Matriz

Encostador

atrr D

r E

FE

D

D

r D

rF

Fr

r

0 0.2 0.4 0.6 0.8 1

e

e

0r / rF

r

C

Deep Drawing

CrD

CDr r

r

Limiting drawing ratio LDRWhen the limiting drawing ratio M is exceeded, the radial stress of the material located at the punch corner (point C, (σr )D ) becomes very high and cracking takes place after localized necking.

All this occurs before starting the 2nd stage of deep drawing.

Punch

Punch

Blankholder

Die

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Deep DrawingForming Limit Curve (FLC)

The forming limit curve defines the strain pairs at the onset of plastic instability (necking).

A

B

CD

E FG H

I

CLE

11

1

-1/2

1/2-1

1

2

DeformaçãoTracção uniaxial

pressão

Expansão biaxial

CLE

l

R

pressão

plana

1

2

Biaxial expansion

Plane strain

Tensile Test

44

Deep DrawingForce and energy - cylindrical deep drawing

The force is calculated from the radial stresses in the material located at the die corner (point C)

sen2 hrF CCr

º90

mc rr

RDr

fRmmax QhrF 2

ri/r0 0.55 0.575 0.6 0.625 0.65 0.675 0.7 0.725 0.75 0.775 0.8

Qf 1 0.93 0.86 0.79 0.72 0.66 0.6 0.55 0.5 0.45 0.4

Qw 0.65 to 0.77

wtest QlFW max

Punch

Die

Force

Displacement

45

Deep Drawing

tef Chh 0

Initial blank - cylindrical deep drawing

Thickness variation along the cross section is negative and positive (as a function of the location under analysis) and, therefore, calculations will be performed with an average thickness h equal to that of the initial blank.

0VVf 0AAf

P

Q

l rG

lrA G 2

In practice, the initial blank can be determined from the equivalence between the areas of the original and deformed blanks.

The area can be calculated by the Pappus-Guldin theorem.

46

Deep DrawingInitial blank

47

Sheet Metal Forming

Incremental Sheet Metal Forming (Chapter 21 of the book)

Variants

48

Sheet Metal FormingSelf-study

Solve the proposed exercises 22.2, 22.4, 22.10, 22.11 and 22.12

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Sheet Metal FormingOther processes

Bending (Chapter 18 of the book)

50


Roll bending (Chapter 19 of the book)

51


Roll Forming (Chapter 20 of the book)

52


Spinning (Chapter 21 of the book)

sheet metal forming - técnico lisboa - autenticação · sheet metal forming processes are usually...

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