Rolling versus other processes: a brief analysismetallurgie2012.sciencesconf.org/conference/metallurgie2012/pages/... · Rolling versus other processes: a brief analysis. ... for

Action Nationale de Formation – Métallurgie Fondamentale Aussois, 25 Octobre 2012

1/42

Rollingversus otherprocesses:

a brief analysis


2/42

Flat Products:free forging Long Products : extrusion

What are the advantages of rolling processes?

L = 5 m

l = 2 m0 = 100 MPa

F = 109 N = 100 000 T !!

0.. LlF

hRLcontact .Lcontact = 120 mm si R = 500 mm

h 100 70 mml = 2 m0 = 100 MPa

F = 2 400 T

FBillet Extruded part

Container

Die

FBillet Extruded part

Container

Die

0.. LlF 00

0 .. fS

SLnSF

100 70

F > 56 T 2 passes are necessary : 100 110x60

60x110 70 77 T 49 T

On a few alternatives

Rolling deforms a small amount of metal at a time moderate forces


3/42

Incremental processes obtain the same result : rolling vs cogging / hammering

Flat Products : very small productivity.But it was the only process to form flat plates(« lames ») for minting e.g. until Leonardo invented the rolling millby the end of the XVIth century

Example: « Elongation » of Zr, Ti bars(not far from here, in Ugine !)

Long Products : still intensively used


4/42

On strain, stress and temperature

heterogeneity


5/42

Deformation is most of the time heterogeneousDepending on geometrical ratios

Initial height 72 mm, Initial Radius 22 mm.

Reduction 50%

Initial height 12 mm, Initial Radius 22 mm.

Reduction 50%

If H/D is « large » :

• strain and strain rate are very heterogeneous

• strain unavoidably includes a notable shear component

H/D 0.27 0.10

D

H

H/D 1.64 0.58

Compression of cylinders


6/42

Stresses are heterogeneousDepending on friction

b) High friction (µ = 0.2)

a) Low friction (µ=0.02)

Compression of a thin parallelepiped

Normal stress Hydrostatic pressure

n = 80 MPa

n = 1750 MPa

ph = 80 MPa

ph = 1750 MPa


7/42

Friction is the major source of stress heterogeneity –and often of the major part of the stress

zz

zz

zz

s

s

s

s

hV

hV

hV

00

0210

0021

00

02

0

002

003

1,

2

32

23

23

zzzz

jiij sss

• stress deviator is homogeneous – as is strain rate tensor

• stress heterogeneity is concentrated in ph, and is due to friction

ham

hamLn

zz .45.01.3.3

)21(21


8/42

t

cc dnnMaxC0

.0,..

Stress heterogeneity / crack formation and opening

Large tensile stresses are often presentat both ends of the bite

An experimental studyby physical simulation (plasticine)

Cutting of transverse cracks and observation of their behaviour

Oriented Latham & Cockroft damage criterionC

rack

wid

th/ d

amag

e cr

iterio

nco

rrel

atio

n


9/42

Heat Transfer and temperature field

),,(. 2

2

2

2

2

2

zyxWzT

yT

xTk

dtdTC pl

),,(.... 2

2

2

2

2

2

zyxWzT

yT

xTk

zTV

yTV

xTV

tTC plzyx

CTzyxW

dtdTC pl

..),,(. 0

0

.0plW

gfr VW .

44. TTST

TTH conv .

Adiabatic approximation (centre)

5 – 10°C per pass in hot rolling, up to 100°C per pass in cold rolling

Heat Transfer Equation

Surface

core

consequences on microstructures


10/42

On cold rollingprocesses


11/42

Cold rolling mill : reversible ou multistand ?

Paper coilsCoiler

Workrolls (WR) Coiler

Paper coils

Roller levelling

Pay-off reel

Paper coil

Paper coilsCoiler


Paper coils

Roller levelling

Pay-off reel

Paper coil

Flyingshear

coilers

Flyingshear

coilersTandem mill with 5 4-high stands

Cluster mill (Sendzimir) for stainless steel rolling

Small work rolls lower forces: excellent for hard, thin stripBut work rolls must be strongly supported in both x and z directions complex roll set

Large productivity due to high speed (up to 50 m/s !) – complexity due to stand interactions (tension regulation, chatter…)


12/42

« skin pass » (temper rolling)

A rolling operation, 0.5 to 2.5% in reduction carbon steels, Cu alloys.3 goals:

- Improve flatness

Tension levelling Roller levelling

A small elongation compensatesfor heterogeneous « metal fibres » length,

A small plastic deformation, if homogeneous,eliminates residual stresses

(with the help of a leveller)


13/42

Electron Beam Texturing (EBT): periodic, deterministic roughness

Electro-Discharge Texturing (EDT) Random roughness

- Give adequate surface texture (roughness) to ensure easier deep drawing



- Improve flatness (with the help of a leveller)


14/42

- Go over the « tension hook », avoidinig Lüders bands.

Elongation by propagation ofLüders bands

Stre

ss

Strain

Network of linesduring deep drawing

Croos the dangerous area by a rolling process, with imposedthickness, solves the problem


- Give adequate surface texture (roughness) to ensure easier deep drawing


- Improve flatness (with the help of a leveller)


15/42

Some elementsof mechanical

analysis


16/42

n

n

Rh

tan

0 = 100 MPaR = 500 mm. V = 2 m/s. h = w = 400 mm25% reduction h = 100 mm :

Lcontact 220 mmF 8.8 106 N = 880 T. P 107 W = 13000 HP.Torque = P/ 2,5 106 N.m

µ > 0.45

High friction is necessary no lubrication* ! Only moderate reductions are possible at this stage a number of passes

* But for Al hot rolling, lubrication is necessary to avoid welding of slab on rolls!

Example of entrainment condition (linked with friction)

Steel ingot hot rolling

entrainment condition


17/42

Neutral point and forward slip

Under normal, stable conditions, the strip exit velocity is slightly largerthan the roll velocity, whereasthe entry velocity is smaller.

By continuity, Vstrip – Vroll = 0 on a certain surface inside the bite. This defines the « neutral point », or « neutral plane », « neutral line »…

is the forward slipR

RVS outf

R

Vout > RVin < R

V N=

R

Friction changes direction (sign) at the neutral point:an essential feature of the mechanics of rolling processes


18/42

The neutral line may be measured using embedded force transducers

• The direction change of the stress vector is clear

• The transverse component is evidenced, it opposes spread

Transverse direction


19/42

A simple, but seminal 1D modelSlab method, small angle

tgµµtg

dxhd xx

.1 )

32 - ( -2)( 0

xx

Equilibium equation:

• y- and z-independentstress and strain

• (x,y,z) = principal axes

Arctg-.Arctg 2µ exp.)1()( 22211

hRhRhRTh

hzz

2222

..Arctg 2µ exp.)1()( hRhRTh

hzz

Solution

32 ,/ - /0'0

'0zzzz

2

22

1

11'

0

22'

0

11 ,,,

hFt

hFttTtT

2

1

1

22

2

2

11.Ln.

Rh

41.Arctg

21.tan

Rh

TT

hh

hR

Nzzzz

i.e.

2

1

1

22

2

2

11.Ln.

Rh

41Arctg

21tan

TT

hh

hhS f

IVIII60

III0

60 MPa0 MPat1t2

Neutral point, forward slip

« Friction hill »

Nor

mal

stre

ss (M

Pa)

inlet outlet


20/42

• Tensions are therefore used to decrease the contact stresses (see previous slide), the roll force, and consequently the roll deformation.

• They also help keep the strip in line and centered

• They keep the strip flat during rolling

Note: on the wire rod mills, tensions are used also to control spread

Tension in the range 0.1 – 0.2 x 0 are most common. The regulation is based on tension loops.

Tensions are applied either by pay-off reel / coiler (single stand reversing mills),

Paper coilsCoiler


Paper coils

Roller levelling

Pay-off reel

Paper coil

Paper coilsCoiler


Paper coils

Roller levelling

Pay-off reel

Paper coil

Flyingshear

coilers

Flyingshear

coilers

or by the velocity sequence on tandem mills (Vi+1 > Vi.hi/hi+1)

Strip tensions

zkT .sin.2


21/42

Criticism and limits of the 1D model

1 – 2D vision: neglected shear strain & stress, z-heterogeneity

Aluminium 6,35 mm, reduction 14%, L/h = 1,4

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12x (mm)

Nor

mal

str

ess

(MPa

)

0

5

10

15

20

25

30

35

40

Tang

entia

l str

ess

(MPa

)

Exp,sig_n SM, sig_nFEM, sig_n Exp, TauSM, Tau FEM, Tau


0

50

100

150

200

250

0 2 4 6 8 10 12 14 16x (mm)

Nor

mal

stre

ss

(MPa

)0

20

40

60

80

100

Tang

entia

l St

ress

(MPa

)

Exp, Sig_n SM, sig_n, 0.20/.03FEM, Sig_n, 0.20/0.03 Exp, TauSM, Tau, 0.20/.03 FEM, Tau, 0.20/0.03

Copper 1,6 mm, reduction 28%, L/h = 4,3

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10x (mm)

Nor

mal

Str

ess

(MPa

)

Exp, Sig_nSM, Sig_nSM, TauFEM, Sig_nFEM, Tau

Measurementof normal and tangential stresses, comparison with the slab method

and with the FEM

The validity of the 1D model scales with the value of L/h


22/42


0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12x (mm)

Nor

mal

str

ess

(MPa

)

0

5

10

15

20

25

30

35

40

Tang

entia

l str

ess

(MPa

)

Exp,sig_n SM, sig_nFEM, sig_n Exp, TauSM, Tau FEM, Tau


0

50

100

150

200

250

0 2 4 6 8 10 12 14 16x (mm)

Nor

mal

stre

ss

(MPa

)

0

20

40

60

80

100

Tang

entia

l St

ress

(MPa

)

Exp, Sig_n SM, sig_n, 0.20/.03FEM, Sig_n, 0.20/0.03 Exp, TauSM, Tau, 0.20/.03 FEM, Tau, 0.20/0.03

Copper 1,6 mm, reduction 28%, L/h = 4,3

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10x (mm)

Nor

mal

Str

ess

(MPa

)


Where shear bands are dominant, the 1D model fails because it neglects shear components

Heterogeneity is governed by a geometric ratio: bite length / average thickness: hL /


23/42

-40

-20

0

20

40

60

-0,4 -0,2 0 0,2 0,4z(m m )

Res

idua

l Str

ess

xx

(MPa

)

0,41

0,415

0,42

0,425

0,43

0,435

0,44

Stra

in

sig-xx, E=210 GPa, sig01=300 MPa

Eps, E=210 GPa, sig01=300 MPa

From strain-rate to strain to residual stress Copper 1,6 mm, reduction 28%, L/h = 4,3

0

100

200

300

400

500

600

700

800

0 2 4 6 8 10x (mm)

Nor

mal

Str

ess

(MPa

)


• The strain is always larger near the surface due to the strain rate concentration at the entry point

• the difference increases when L/h decreases

• xx(z) residual stress heterogeneity is connected with the strain gradient


24/42

2 – Plane strain vs 3D

p'(y) (Tons / meter) = rolling load profileInitial thickness h1 = 2 mm; Roll radius R 250 mm. L/h 4.

The stress transducer is located successively at different positions along Oy

y (= width)

• Edges introduce 3D effects (edge = free surface decreased p hence n)

• But most of the profile comes from roll deformation (bending + flattening) resulting in (slightly) y-dependent reduction


25/42

Influence of width on edge effects (FEM, rigid rolls)

0

5

10

15

20

0 20 40 60 80 100 120y (mm)

F (k

N/m

)

0

1,5

3

4,5

6

Dy

(mm

)

200 x 200, F 200 x 20, F200 x 2, F 200 x 200, Dy200 x 20, Dy 200 x 2, Dy.10

• When W/H ≈ 1 (long products), edge effects extend on the whole width: * n decreases consistantly from centre to edge, * transverse flow starts from the centreline (Vy quasi-linear)

• When W/H >> 1, edge effects extend on near-edge area only (more or less, depending on friction) * n is constant on the central part (Vy ≈ 0), then decreases towards the edge, * transverse flow is restricted to the edge area


26/42

On roll deformation: profile and flatness actuators


27/42

Profile and flatness actuators are many, with different complexity

Non-adaptative actuators (1)

• Against roll bending : grinding crown

• Against roll bending : complex styands with back-up rolls

R)R)

20-roll Sendzimir stand

4-high stand


28/42

• Against thermal crown (differential dilatation) and its time evolution: pre-heating of rolls to avoid excessive variations along one roll mounting

• Against wear profile : the « rolling cone » : less and less wide strips are rolled

Note: to counter wear (by abrasion, fatigue), rolls are changed regularly. Frequency depends on load severity, requested surface quality(each new shift for carbon steel, each new coil for stainless steel, each new day for light alloys…)


Non-adaptative actuators (2)


29/42


Adaptative actuators (1)

Roll (counter)bendingis present on most stands of most rolling mills(light alloys and steel)

Efficient to correct near-edge defects


30/42


Adaptative actuators (2)


31/42

On roll deformation:roll deformation models

(2D approach)


32/42

hF

E )1(161 R R

2

0

Analytical estimate of roll flatteningHitchcock’s formula (1935)

Based on Hertz’s elastic contact theory, it assumes a circular deformed roll profile

R 0

R L0

L

This approximation may be grossly erroneous if R/R0 > 2


33/42

299,65

299,7

299,75

299,8

299,85

299,9

299,95

300

-8 -6 -4 -2 0 2 4 6

x (mm)

z (m

m) Undeformed roll profile

Reduction : 5%

Reduction: 10%

Reduction: 15%

Reduction: 20%

Reduction: 25%

Reduction:30%

Reduction: 35%

0

400

800

1200

1600

2000

2400

2800

3200

-8 -6 -4 -2 0 2 4 6

x (mm)

Nor

mal

stre

ss (M

Pa)

Reduction : 5%

Reduction: 10%

Reduction: 15%

Reduction: 20%

Reduction: 25%

Reduction:30%

Reduction: 35%

Coupled roll / strip modelling

Strip : 1D, slab model

n, (x)

Roll : 2D FEM or IFM

Converged ?

END

Rol

l pro

file

h1 = 0.3 mm, R = 300 mm, variable reduction. Steel strip, , Friction coefficient µ = 0.05

1.00 ).501(300

IFM = Influence Function Method

Deformed roll profile

Normal stress profile (« friction hill »)


34/42

0

5000

10000

15000

20000

0 10 20 30 40 50Reduction (%)

Forc

e (k

N/m

)

0

5000

10000

15000

20000

100*

Rol

l fla

tteni

ng (µ

m)

Force (Deform ed roll)Force (Rigid roll)100 x Roll flattening

0

5000

10000

15000

20000

0 50 100 150 200

Roll Radius (mm)

Forc

e (k

N/m

)0

0,05

0,1

0,15

0,2

Rol

l fla

tteni

ng (m

m)

Force

Flattening

Influence of roll deformation on roll load (through contact length)

Roll flattening (local decrease of the radius) is roughly proportional to the load and to the radius

Small rolls give less flatteningand lower edge-drop defect


35/42

On roll deformation:roll deformation models

(3D approach)


36/42

3D approach #1: iterative modeling of roll flattening and roll bending

Strip : y-seriesof slabs

n, (x,y)

Roll : 3D IFM

Converged ?

END

Rol

l sur

face

yi


37/42

An application: understanding the 6-high mill

Byw

wy

wyy ||2/expA -

2/ a

2/ a )(

4

4

2

2

Description of strip profile by a 4th-order polynomial(1 I-unit (IU) = 10-5)

Relative differential elongation


38/42

Effect of the WR and IR bending forces on reduction profile and strip flatness

• Fi is found to influence mainly a2• Fw changes firstly a4

Changing Fi and Fw builds a quadrilateral, the centre of which should be close to a2 = a4 = 0 for optimal performance

Roll shifting can be used for this:

- < 0 (outside strip edge) has little effect- > 0 (inside strip edge) is more effective


39/42

And what about edge-drop ?

• Edge drop is mostly sensitive to Fw and . • Thanks to the redundancy of these 2 parameters, a combination can be selected which gives

(1) a flat strip (a2 and a4 small)(2) a moderate edge-drop


40/42

3D approach #2: FEM

Strip : 3D FEM,

n, (x,y)

Roll : 3D IFM

Converged ?

END

Rol

l sur

face

FEM / IFM All FEM


41/42

Application: effect of roll grinding crown on strip profile

Small dots = measurements ; Empty circles = strip FEM / roll flattening FEM + roll bending IFMFull triangles = strip FEM / IFM (with end effect corrections)


42/42

3 references

W.L. Roberts an old, but irreplaceable 2500 pages…

I - Cold Rolling of steels. Manufacturing Engineering and Materials Processing Series, Vol. 2. Marcel Dekker, New York, 1978

II - Hot Rolling of steels. Manufacturing Engineering and Materials Processing Series, Vol. 10.Marcel Dekker, New York, 1983

J.G. Lenard a summary of a 40-y long work on most facets of rolling processes

Primer on Flat RollingElsevier, Oxford, 2007 (2nd edition is on its way)

P. Montmitonnet easy access, short – in French

in Les Techniques de l'Ingénieur:

I - Laminage. Objectifs et modélisation - (M 3065) (2002) (metal rolling : objectives and modelling)

II - Laminage. Analyses thermomécaniques et applications and applications) - (M 3066) (2003)(Metal rolling : thermomechanical analyses

Rolling versus other processes: a brief analysismetallurgie2012.sciencesconf.org/conference/metallurgie2012/pages/... · Rolling versus other processes: a brief analysis. ... for

Documents