Wedge and Camber Control

Abstract

In this paper, we show that lateral forces and bending moments, respectively, acting on a slab during hot rolling can induce lateral material flow in the roll bite. Furthermore, we present an automation scheme that allows for reducing wedge in a roughing mill stand without generating camber. Thus, camber can be decoupled from wedge and hence roll tilting in the roughing mill stand can be used to control the wedge in the rolling process. A slab-to-slab control algorithm is presented using the measured wedge of the finished strip as input and the tilting of the roughing mill stand as actuator. As a key to success, we apply the edger to induce the required lateral forces in the upstream passes. Because only equipment is applied that is available anyway, no further investment in hardware is required to benefit from this automation scheme.

Full text

1

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
Wedge and Camber Control
M. Kurz, R. Döll, Primetals Technologies Germany GmbH, Schuhstr. 60, 91052 Erlangen Germany; A. Kainz,
T. Pumhössel, K. Zeman, Johannes-Kepler-University, Linz, Austria;
Siemens VAI Metals Technologies has now become part of Primetals Technologies, which is a joint venture
company of Siemens, Mitsubishi Heavy Industries and partners.
Contact data
Dr. Matthias Kurz, Primetals Technologies Germany GmbH, Schuhstr. 60, 91052 Erlangen, +49 (9131) 7-46534,
matthias.kurz@primetals.com
Summary
In this paper, we show that lateral forces and bending moments, respectively, acting on a slab during hot rolling
can induce lateral material flow in the roll bite. Furthermore, we present an automation scheme that allows for
reducing wedge in a roughing mill stand without generating camber. Thus, camber can be decoupled from wedge
and hence roll tilting in the roughing mill stand can be used to control the wedge in the rolling process. A slab-to-
slab control algorithm is presented using the measured wedge of the finished strip as input and the tilting of the
roughing mill stand as actuator.
As a key to success, we apply the edger to induce the required lateral forces in the upstream passes. Because only
equipment is applied that is available anyway, no further investment in hardware is required to benefit from this
automation scheme.
Key Words
Wedge, Camber, Roughing Mill, Edger, Straightening
Introduction
Rolled strip is ideally both straight (i.e. without
camber) and left-right-symmetrical with respect to
thickness (i.e. without wedge), respectively.
Unfortunately, if a wedge within the slab is removed
through swiveling of the rolls without further
countermeasures, a camber would result,
which - from a quality point of view – is even worse
than wedge.
Modern, so called “camber free rolling systems” apply
cameras to swivel mill stands in roughing or finishing
mill stands to minimize the lateral curvature (camber)
of the produced strip. Hence, all shape errors on the
slab, i.e. initial camber or wedge are transferred into
a wedge on the coil. This resulting wedge has to be
accepted, if no additional actuator is employed.
Reducing wedge without causing camber is a big
challenge for today’s production in hot strip mills.
Although camber has been treated as a problem for
many years, cf. e.g. [1–4], most of such studies are
based on qualitative camber assessment, pilot plant
trials and numerical simulation. However, if
automated control and suppression of wedge and
camber in a commercial hot mill has to be realized, a
vital prerequisite is a viable on-line method of
measurement.
In the following sections we want to first give some
definitions and then line out how to induce lateral
material flow and how to apply it to reduce both
camber and wedge, respectively.
Definitions
A slab, transfer bar of finished strip can show different
form defects. The asymmetric linear part of the
thickness profile over width is usually called wedge.
The lateral curvature of the material is known as
camber. It is characterized by the distance d between
a straight line of length l and the strip edge, where l is
typically around 5m in length.
Figure 1: Definition of absolute wedge Wabs and center
line thickness HC.
Figure 2: Definition of camber

.
Both, wedge and camber are characteristics of an
asymmetric material distribution in the lateral strip
dimension. So the total form error  for a strip of
width w can be defined as

2

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
.

w
H
W
C
abs 
(1)
For small aspect ratios h/w, which can be assumed
for the last passes of a finishing mill, lateral material
flow can be neglected. As a consequence, the lateral
material distribution cannot be changed and the total
form error remains constant
const.

w
H
W
C
abs
(2)
On the other hand, for high aspect ratios, as they
arise in a roughing stand, lateral material flow occurs
and the form error is subject to change,
const,

w
H
W
C
abs
(3)
either by natural or induced lateral flow.
Material Flow Induced by Lateral Forces
In the following, we investigate the behavior of a
wedged slab going through one horizontal pass with
aligned rolls. Due to the wedge on the entry side and
the alignment of the rolls, the material obtains
different reductions on the operator side and on the
drive side of the material. As a consequence, the side
with higher reduction shows higher elongation. This
results in a curvature of the material on the exit side
and camber develops.
Figure 3: Formation of camber due to
inhomogeneous elongation.
Figure 4: Induction of material flow due to lateral
force.
The impact of an externally applied lateral force
would cause an asymmetric tension regime, which
counteracts the different elongations by inducing
lateral material flow. Consequently, with the choice of
the right force, the wedge can be eliminated without
formation of camber.
Analytical Treatment of the Induced Lateral
Material Flow inside the Roll-bite
The empirical considerations as outlined above can
be analyzed to some extent analytically as follows.
The x-coordinate of the underlying Cartesian
coordinate system denotes the rolling direction,
whereas in this section y and z indicate the lateral
and thickness directions of the strip or slab,
respectively. A non-dimensional lateral coordinate is
introduced via
 
1, 1
2
w
y

   
. (4)
Within the frame of perturbation theory, the special
case of plane strain (i.e. no lateral material flow) can
be considered as “undisturbed” scenario of pure
thickness reduction with logarithmic strain values
 
()
(0) (0)
()
ln 0
In
c
xx zz Out
c
H
H


 


. (5)
For simplicity, linear wedge-profiles are assumed
here for the strip entry- and exit profiles (In: before
roll-gap entry, Out: after roll-gap exit) according to
 
   
()
()
12
In
In
In abs
CIn
C
W
HHH





(6a)
 
   
()
()
12
Out
Out
Out abs
COut
C
W
HHH





. (6b)
Calculations taking into account more general strip-
profiles are straight forward. A systematic expansion
in series of Legendre-polynomials was accomplished
and will be treated in a subsequent publication. The
results presented here refer to first Legendre order P1.
By taking into account a small relative strip wedge
change, defined as the difference of the absolute
strip wedge values, divided by the respective nominal
(C: Centerline) thickness values,
 
 
 
 
1
Out In
abs abs
rel rel
Out In
CC
WW
W with W
HH

    


(7)
the corresponding induced logarithmic (i.e., “true”)
plastic strains inside the strip or slab at the roll gap
exit can approximately be assumed to be of the form
(in lowest order of ∆Wrel)
 
 
(0) (1 ) 2
xx xx rel
W
   
  
(8)

3

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
.

w
H
W
C
abs 
(1)
For small aspect ratios h/w, which can be assumed
for the last passes of a finishing mill, lateral material
flow can be neglected. As a consequence, the lateral
material distribution cannot be changed and the total
form error remains constant
const.

w
H
W
C
abs
(2)
On the other hand, for high aspect ratios, as they
arise in a roughing stand, lateral material flow occurs
and the form error is subject to change,
const,

w
H
W
C
abs
(3)
either by natural or induced lateral flow.
Material Flow Induced by Lateral Forces
In the following, we investigate the behavior of a
wedged slab going through one horizontal pass with
aligned rolls. Due to the wedge on the entry side and
the alignment of the rolls, the material obtains
different reductions on the operator side and on the
drive side of the material. As a consequence, the side
with higher reduction shows higher elongation. This
results in a curvature of the material on the exit side
and camber develops.
Figure 3: Formation of camber due to
inhomogeneous elongation.
Figure 4: Induction of material flow due to lateral
force.
The impact of an externally applied lateral force
would cause an asymmetric tension regime, which
counteracts the different elongations by inducing
lateral material flow. Consequently, with the choice of
the right force, the wedge can be eliminated without
formation of camber.
Analytical Treatment of the Induced Lateral
Material Flow inside the Roll-bite
The empirical considerations as outlined above can
be analyzed to some extent analytically as follows.
The x-coordinate of the underlying Cartesian
coordinate system denotes the rolling direction,
whereas in this section y and z indicate the lateral
and thickness directions of the strip or slab,
respectively. A non-dimensional lateral coordinate is
introduced via
 
1, 1
2
w
y

   
. (4)
Within the frame of perturbation theory, the special
case of plane strain (i.e. no lateral material flow) can
be considered as “undisturbed” scenario of pure
thickness reduction with logarithmic strain values
 
()
(0) (0)
()
ln 0
In
c
xx zz Out
c
H
H


 


. (5)
For simplicity, linear wedge-profiles are assumed
here for the strip entry- and exit profiles (In: before
roll-gap entry, Out: after roll-gap exit) according to
 
   
()
()
12
In
In
In abs
CIn
C
W
HHH





(6a)
 
   
()
()
12
Out
Out
Out abs
COut
C
W
HHH





. (6b)
Calculations taking into account more general strip-
profiles are straight forward. A systematic expansion
in series of Legendre-polynomials was accomplished
and will be treated in a subsequent publication. The
results presented here refer to first Legendre order P1.
By taking into account a small relative strip wedge
change, defined as the difference of the absolute
strip wedge values, divided by the respective nominal
(C: Centerline) thickness values,
 
 
 
 
1
Out In
abs abs
rel rel
Out In
CC
WW
W with W
HH

    


(7)
the corresponding induced logarithmic (i.e., “true”)
plastic strains inside the strip or slab at the roll gap
exit can approximately be assumed to be of the form
(in lowest order of ∆Wrel)
 
 
(0) (1 ) 2
xx xx rel
W
   
  
(8)
 
 
2
yy rel
W
  

(9)
 
 
(0) 2
zz zz rel
W
  
 
, (10)
where the scalar “material transfer factor”

is a
measure of the magnitude of the lateral material flow
involved. A value of zero indicates the case of plane
strain and zero lateral flow, whereas a value of
1


represents 100% lateral flow such that no longitudinal
strain inhomogenities are induced across the strip’s
width.
Note that shear strains are neglected here. The
plastic incompressibility constraint is fulfilled exactly
for the logarithmic strain tensor components (8-10)
     
11
0
xx yy zz


  

  

. (11)
The uniaxial equivalent plastic strain can be
determined according to
 
 
() 2 2 2
2
3
p
xx yy zz
 
 
. (12)
By neglecting higher orders in the relative strip wedge
change ∆Wrel, one is immediately led to
 
( ) (0)
(0)
21
11
22
3
prel
xx
xx
W

  








(13)
Within the frame of Levy-Mises [6, 7] the deviatoric
(i.e. trace-free) stress-components
ij


of the Cauchy
stress tensor are fully determined by the associated
plastic flow rule. To calculate the stresses itself, two
more conditions have to be taken into consideration.
The lateral force-equilibrium reduces here to
0
yy yy
p
y






 
(14)
i.e., the lateral change of the hydrostatic pressure p is
already prescribed. The longitudinal stress boundary
condition is given by
 
(0)
xx F F xx
   

(15)
for prescribed mean front tension stress. These two
conditions enable the unique determination of the
hydrostatic pressure p and of the Cauchy stresses,
which read in lowest order of ∆Wrel
 
(0)
12
3
frel
F
xx
kW
p

 




 




(16)
 
(0)
3
4
3
frel
xx F
xx
kW

  




  



(17)
 
3
f
yy F
k
 

 


(18)
 
(0)
23
4
33
ff rel
zz F
xx
kk W

  


 








(19)
where
f
k
denotes the yield-strength value.
When dealing with camber formation, the “material
transfer factor”

as introduced in Equ. (8) and (9),
is directly correlated to the camber-curvature

(1 )
rel
W
w


 
, (20)
as can be shown easily via elementary geometric
considerations. It takes its maximum value for zero
lateral flow
max
0
rel
W
w
 

 
. (21)
For the opposite scenario
1


the lateral flow
inside the roll-gap suffices to fully eliminate the
camber (i.e.  = 0). In that case longitudinal com-
pressive stresses (σxx < 0) and tensile stresses
(σxx > 0) are induced, as follows quantitatively from
Equ. (17). Moreover, the local roll separating force
proportional to ~[-σzz] (cf. Equ. (19)) decreases in
regions, where longitudinal tensile stresses occur.
The external bending moment MB corresponding to
the longitudinal stress distribution σxx(ɳ) in Equ. (17)
is determined by evaluating the integral
     
/2
()
/2
w
Out
B xx
w
M H y y y dy



 

(22)
()2
(0)
423
plast
Out
cf rel
B
xx
M
H wk W
M






. (23)
The corresponding plastic deformation work (per strip
unit length) reads
 
max
2
()
0
()
(0)
16 3
Out
c f rel
pl
z
xx
H wk W
W Md



 

(24)
It should be emphasized that the bending moment
Equ. (23) to eliminate camber is tiny (about 2-8%)
compared to the value Mplast, which is necessary for
“classical” strip bending. The underlying main reason
is that due to strip thickness reduction inside the roll
gap, plastification already occurs. Therefore, the
material flow merely has to be modulated, i.e. only
the stress-redistributions coupled to the additional
lateral material flow have to be induced by applying
this external bending moment.

4

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
Finite Element Simulation
To investigate the effect of an external lateral force,
applied to the strip according to Fig. 4, on the
formation of strip camber, Finite Element simulations
were carried out using the software package
©Abaqus Explicit. Figure 5 shows a sketch of the
corresponding Abaqus model. Due to the horizontal
symmetry of strip and roll stand, the simulations are
restricted to the top half. An elasto-viscoplastically
material law was implemented for the strip, whereas
work roll, edger and side-guides were modeled as
rigid bodies.
In the initial step, the upper work roll is located with
some gap above the strip, see Fig. 5 (top), and the
strip is in a rest position, i.e. no initial axial velocity
boundary condition is applied to the strip. Side guides
are used to prevent the strip from lateral movement
on the entry side.
Figure 5: Sketch of Abaqus model for investigating the
effect of a lateral edger force on the camber formation
of rolled strips with initial wedge.
To reduce the numerical simulation time, which is of
utmost importance if the effects of variations of
system parameters have to be investigated, the
edger is located closer to the roll stand than in the
real plant, i.e.
()
/3
r
we we
ll
, where the superscript
()
r
denotes the reduced quantity, see Fig. 5 (bottom).
Thus, the total length of the strip can be reduced
significantly in the simulation. Moreover, a mass
scaling factor of 10 is used, which enables a larger,
stable time-increment. Although, these measures are
simple in nature, the reduction in numerical
simulation time is considerable, and hence, the
reduced model is well suited to be exploited for
parameter studies.
The numerical simulation in Abaqus Explicit starts
with applying the required rotational speed to the
work roll. Simultaneously, a proper vertical velocity
induces a lowering of the work roll to the final
thickness of the strip, see Fig. 5 (top). Thereafter, the
vertical position of the work roll remains constant.
The position of the edger is fixed in x- and y-direction,
whereas in z-direction, a low-stiffness spring ensures
connection to the inertial frame. A lateral force
()r
zE
F
applied to the edger according to Fig. 5 (bottom)
results in a movement of the edger towards the strip.
A typical time-history of the force
()r
zE
F
, as
implemented in the Abaqus model is depicted in
Figure 6.
Figure 6: Time-history of lateral edger force to
influence the lateral material flow in the roll gap.
At the instant of time
s
tt
, where the front crop of
the strip has passed the center of the edger,
()r
zE
F
increases slightly according to a linear function until
r
tt
. The length of the interval
[, ]
sr
tt
is chosen in a
way that contact between edger and strip can be
guaranteed within this timespan. As the stiffness of
the spring, connecting the edger to the inertial frame
is very small, only a small force is required to ensure
the contact. At
r
tt
,
()r
zE
F
increases according to a
sine function to the value
()
,max
r
zE
F
, and remains
constant thereafter.
The chosen sequence of moving the edger to the
strip, until contact occurs, using a very low force, and
applying the significantly larger force, necessary for
suppressing camber after the contact, prevents the
edger from bouncing against the strip.
Table 1 shows some system parameters used for
establishing the Abaqus model.
Table 1: System parameters for establishing the
Abaqus model.
Parameter Symbol Value Unit
width of slab w 1200 mm
thickness of slab HC 180 mm
absolute wedge W abs 6 mm
draft

35 mm

5

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
Finite Element Simulation
To investigate the effect of an external lateral force,
applied to the strip according to Fig. 4, on the
formation of strip camber, Finite Element simulations
were carried out using the software package
©Abaqus Explicit. Figure 5 shows a sketch of the
corresponding Abaqus model. Due to the horizontal
symmetry of strip and roll stand, the simulations are
restricted to the top half. An elasto-viscoplastically
material law was implemented for the strip, whereas
work roll, edger and side-guides were modeled as
rigid bodies.
In the initial step, the upper work roll is located with
some gap above the strip, see Fig. 5 (top), and the
strip is in a rest position, i.e. no initial axial velocity
boundary condition is applied to the strip. Side guides
are used to prevent the strip from lateral movement
on the entry side.
Figure 5: Sketch of Abaqus model for investigating the
effect of a lateral edger force on the camber formation
of rolled strips with initial wedge.
To reduce the numerical simulation time, which is of
utmost importance if the effects of variations of
system parameters have to be investigated, the
edger is located closer to the roll stand than in the
real plant, i.e.
()
/3
r
we we
ll
, where the superscript
()r
denotes the reduced quantity, see Fig. 5 (bottom).
Thus, the total length of the strip can be reduced
significantly in the simulation. Moreover, a mass
scaling factor of 10 is used, which enables a larger,
stable time-increment. Although, these measures are
simple in nature, the reduction in numerical
simulation time is considerable, and hence, the
reduced model is well suited to be exploited for
parameter studies.
The numerical simulation in Abaqus Explicit starts
with applying the required rotational speed to the
work roll. Simultaneously, a proper vertical velocity
induces a lowering of the work roll to the final
thickness of the strip, see Fig. 5 (top). Thereafter, the
vertical position of the work roll remains constant.
The position of the edger is fixed in x- and y-direction,
whereas in z-direction, a low-stiffness spring ensures
connection to the inertial frame. A lateral force
()r
zE
F
applied to the edger according to Fig. 5 (bottom)
results in a movement of the edger towards the strip.
A typical time-history of the force
()r
zE
F
, as
implemented in the Abaqus model is depicted in
Figure 6.
Figure 6: Time-history of lateral edger force to
influence the lateral material flow in the roll gap.
At the instant of time
s
tt
, where the front crop of
the strip has passed the center of the edger,
()r
zE
F
increases slightly according to a linear function until
r
tt
. The length of the interval
[, ]
sr
tt
is chosen in a
way that contact between edger and strip can be
guaranteed within this timespan. As the stiffness of
the spring, connecting the edger to the inertial frame
is very small, only a small force is required to ensure
the contact. At
r
tt
,
()r
zE
F
increases according to a
sine function to the value
()
,max
r
zE
F
, and remains
constant thereafter.
The chosen sequence of moving the edger to the
strip, until contact occurs, using a very low force, and
applying the significantly larger force, necessary for
suppressing camber after the contact, prevents the
edger from bouncing against the strip.
Table 1 shows some system parameters used for
establishing the Abaqus model.
Table 1: System parameters for establishing the
Abaqus model.
Parameter
Symbol
Value
Unit
width of slab
w
1200
mm
thickness of slab
HC
180
mm
absolute wedge
Wabs
6
mm
draft

35
mm
Figure 7: Exemplary Abaqus result of rolling of a strip
with initial wedge. Free formation of camber due to no
contact between edger and strip.
Figures 7 and 8 depict first Abaqus Explicit results for
rolling of a strip with initial wedge until the front crop
of the strip reaches the center of the edger.
Figure 8: Top view of rolled strip depicting the evolved
camber due to initial wedge. Lateral edger force is
equal to zero.
Until now, there is no contact between edger and
strip, i.e. free formation of camber occurs, which is
clearly observed, see Fig. 8.
Applying the edger force
()r
zE
F
, see Fig. 6, induces a
lateral material flow in the roll gap caused by
modulating the axial stress distribution in the roll gap.
Figure 9 shows the typical effect of the external
lateral force, applied to the strip on the exit side of the
roll stand, on the axial stress distribution. Therein,
0,
E
xx xx xx


(25)
is shown as a function of the relative width coordinate
/zw
(z denotes the lateral coordinate in this section)
of the strip, representing the difference of the
averaged axial stress
E
xx

at the roll bite exit when a
lateral force
()r
zE
F
is applied, and the averaged axial
stress 0
xx

when
()
0
r
zE
F
throughout all the time. It is
worth to note that E
xx

as well as 0
xx

are based on
the formation of a well-defined steady state in the
strip. Obviously,
()r
zE
F
induces tensile stresses, i.e.
0
xx


in about the half of the strip adjacent to the
edger, and compressive stresses,
0
xx


, in the
opposite half.
Figure 9: Typical difference of axial stress distribution
at roll bite exit with and without lateral edger force.
The relation of the corresponding moment of the
lateral edger force
()
,max
r
zE
F
to the moment Mplast (see
Equ. (23)) required for plastification in the roll bite
without rolling force (pure bending) is given by
,max
11
() ()
()2 0.065
/4
zE
rr
we
Out
plast f c
Fl
M
M kH w

 
. (26)
This means that only 6.5% of the moment
plast
M
is
necessary to modulate the material flow in the roll
gap, as the plastification of the material in the roll gap
is already achieved by the work rolls.
Figure 10: Curvature
()
()
r
sc
x

of slab centerline of
the reduced model at t=2.7s. Evaluation zone of an
averaged curvature
()
,
r
s avg

in the quasi steady-state
after passing the edger.
It will be shown in the following that modulating this
axial stress distribution allows to suppress the
formation of strip camber by inducing a lateral
material flow in the roll gap.

6

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
Figure 10 depicts the curvature
()r

of the reduced
model at the instant of time
2.7ts
as a function of
the strip centerline coordinate
sc
x
. The maximum
edger force
()
,max
400kN
r
zE
F
, as displayed in the
diagram. The positions of the work roll, respectively
the edger, are indicated as CL WR (centerline work
roll), and CL E (centerline edger). One clearly
observes the unsteady behaviour near the front crop
of the strip, where the work roll is lowered to the final
strip thickness. In the following, a short quasi-steady
state area of the curvature occurs, corresponding to
free formation of camber, as the strip has not yet
reached the edger, i.e. no lateral force is applied until
now. The node Nr is the first node in the roll gap exit,
where the edger gets in contact with the strip, i.e.
corresponds to the instant of time
r
t
in Fig. 6.
Subsequently, the lateral edger force increases, and
is equal to
()
,max
400kN
r
zE
F
at
r
tt
for the first time.
At this instant of time, the node Nc enters the roll gap.
From node Nc to node Nr, a drastic reduction of the
strip curvature occurs, as the edger force induces a
lateral material flow in the roll gap. A quasi steady-
state behaviour of the curvature is reached when
node Nc has passed the roll gap, and hence, has fully
participated in the lateral material flow in the roll gap.
Thereafter, a well pronounced steady-state behaviour
of the curvature is observed. For the following
investigations, an averaged curvature
()
,
r
s avg

is
defined within spatial area which is constant with
respect to the inertial frame, see Fig. 10. Compared
to the case where no edger is used, and therefore,
free formation of the camber takes place,
()
,
r
s avg

has
reduced to about 27.6%.
Figure 11: Averaged curvature
()
,
r
s avg

for different
values of the maximum lateral edger force
()
,max
r
zE
F
.
Determination of the required lateral force where the
strip curvature will vanish
It can be expected that, increasing the maximum
lateral edger force
()
,max
r
zE
F
, will result in a further
decrease of the strip curvature
()
,
r
s avg

, and possibly in
a total suppression of strip camber. Hence, the effect
of
()
,max
r
zE
F
on
()
,
r
s avg

was investigated systematically in
the following by executing several Abaqus
simulations with
()
,max
[0, 150 :50 :800] kN
r
zE
F
. The
resulting function
() ()
,
,ma x
()
rr
s avg
zE
F

is presented in
Fig. 11. For
()
,max 0
r
zE
F
, i.e. free formation of camber,
( ) -1
,
0.024 m
r
s avg

 
. With increasing edger force
()
,max
r
zE
F
, the averaged strip curvature
()
,
r
s avg

tends to
zero. A strip with zero curvature is achieved for
()
,max 524.4 kN
r
zE
F
. In this case, the lateral material
flow in the roll gap, induced by the edger,
compensates the camber formation initiated by the
incoming wedge of the strip. If
()
,max 524.4 kN
r
zE
F
in
this test-case, the averaged curvature
()
,
r
s avg

becomes positive, i.e. the direction of the strip
camber changes to the opposite direction, and
()
,
r
s avg

increases. This means, that a strip with zero
curvature can only be achieved if the lateral edger
force is equal to a certain level, which depends on
the geometry and the material of the strip, as well as
on the rolling conditions. This is computationally
expensive, and hence, reduced models, which
approximate the behaviour of an original model in a
satisfactory manner, are required. In the present
case, the calculation time of the reduced model is
about 4% of the corresponding ©Abaqus Standard
calculation time of the full model.
To evaluate the accuracy of the reduced model, the
full model is solved, where
() ()
,ma x ,
,ma x
( 0) / 3
rr
zE s avg
zE
FF

 
(27)
is used, as the edger is on its original position in this
model. Figure 12 presents the corresponding results
of the strip curvature.
Figure 12: Curvature of full model for applying the
lateral edger force
()
,ma x ,
( 0)
r
zE s avg
F


, where the
curvature of the reduced model is equal to zero.
The anterior part of the strip, that passes the roll gap
without contact between edger and strip shows free
formation of camber with a curvature
-1
0.024 m


.
A well pronounced steady state area is observed.
Applying the lateral force, when the front crop of the

7

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
Figure 10 depicts the curvature
()r

of the reduced
model at the instant of time
2.7ts
as a function of
the strip centerline coordinate
sc
x
. The maximum
edger force
()
,max
400kN
r
zE
F
, as displayed in the
diagram. The positions of the work roll, respectively
the edger, are indicated as CL WR (centerline work
roll), and CL E (centerline edger). One clearly
observes the unsteady behaviour near the front crop
of the strip, where the work roll is lowered to the final
strip thickness. In the following, a short quasi-steady
state area of the curvature occurs, corresponding to
free formation of camber, as the strip has not yet
reached the edger, i.e. no lateral force is applied until
now. The node Nr is the first node in the roll gap exit,
where the edger gets in contact with the strip, i.e.
corresponds to the instant of time
r
t
in Fig. 6.
Subsequently, the lateral edger force increases, and
is equal to
()
,max
400kN
r
zE
F
at
r
tt
for the first time.
At this instant of time, the node Nc enters the roll gap.
From node Nc to node Nr, a drastic reduction of the
strip curvature occurs, as the edger force induces a
lateral material flow in the roll gap. A quasi steady-
state behaviour of the curvature is reached when
node Nc has passed the roll gap, and hence, has fully
participated in the lateral material flow in the roll gap.
Thereafter, a well pronounced steady-state behaviour
of the curvature is observed. For the following
investigations, an averaged curvature
()
,
r
s avg

is
defined within spatial area which is constant with
respect to the inertial frame, see Fig. 10. Compared
to the case where no edger is used, and therefore,
free formation of the camber takes place,
()
,
r
s avg

has
reduced to about 27.6%.
Figure 11: Averaged curvature
()
,
r
s avg

for different
values of the maximum lateral edger force
()
,max
r
zE
F
.
Determination of the required lateral force where the
strip curvature will vanish
It can be expected that, increasing the maximum
lateral edger force
()
,max
r
zE
F
, will result in a further
decrease of the strip curvature
()
,
r
s avg

, and possibly in
a total suppression of strip camber. Hence, the effect
of
()
,max
r
zE
F
on
()
,
r
s avg

was investigated systematically in
the following by executing several Abaqus
simulations with
()
,max
[0, 150 :50 :800] kN
r
zE
F
. The
resulting function
() ()
,
,ma x
()
rr
s avg
zE
F

is presented in
Fig. 11. For
()
,max 0
r
zE
F
, i.e. free formation of camber,
( ) -1
,
0.024 m
r
s avg

 
. With increasing edger force
()
,max
r
zE
F
, the averaged strip curvature
()
,
r
s avg

tends to
zero. A strip with zero curvature is achieved for
()
,max 524.4 kN
r
zE
F
. In this case, the lateral material
flow in the roll gap, induced by the edger,
compensates the camber formation initiated by the
incoming wedge of the strip. If
()
,max 524.4 kN
r
zE
F
in
this test-case, the averaged curvature
()
,
r
s avg

becomes positive, i.e. the direction of the strip
camber changes to the opposite direction, and
()
,
r
s avg

increases. This means, that a strip with zero
curvature can only be achieved if the lateral edger
force is equal to a certain level, which depends on
the geometry and the material of the strip, as well as
on the rolling conditions. This is computationally
expensive, and hence, reduced models, which
approximate the behaviour of an original model in a
satisfactory manner, are required. In the present
case, the calculation time of the reduced model is
about 4% of the corresponding ©Abaqus Standard
calculation time of the full model.
To evaluate the accuracy of the reduced model, the
full model is solved, where
() ()
,ma x ,
,ma x
( 0) / 3
rr
zE s avg
zE
FF

 
(27)
is used, as the edger is on its original position in this
model. Figure 12 presents the corresponding results
of the strip curvature.
Figure 12: Curvature of full model for applying the
lateral edger force
()
,ma x ,
( 0)
r
zE s avg
F


, where the
curvature of the reduced model is equal to zero.
The anterior part of the strip, that passes the roll gap
without contact between edger and strip shows free
formation of camber with a curvature
-1
0.024 m


.
A well pronounced steady state area is observed.
Applying the lateral force, when the front crop of the
strip has passed the edger, finally leads to a
reduction of the curvature to almost zero for the
subsequently rolled strip. This result underlines the
accuracy and validity of the reduced model.
Figure 13 depicts the associated screenshot from
Abaqus Explicit. It is clearly observed that the camber
in the anterior part of the strip, in which the curvature
0


, is followed by the a steady state area, where
the camber is suppressed.
Figure 13: Result of Abaqus simulation for
suppressing camber formation applying the lateral
edger force
()
,ma x ,
( 0)
r
zE s avg
F


.
To assist a comparison with the analytical results,
slabs with different initial widths were investigated.
Figure 14 presents the material transfer factor

according to Equ. (20) for slabs of 800, 1200 and
1600 mm width. For each slab, Abaqus Explicit
simulations were carried out for several values of the
lateral edger force
,maxzE
F
, and from these results the
material transfer factor

was calculated.
Figure 14: Lateral material transfer factor for strips
with different initial width w and for different values of
the lateral edger force
,maxzE
F
.
As stated in the analytical section, total suppression
of camber is achieved if
1


, whereas
0


indicates undisturbed formation of camber
corresponding to zero lateral material flow.
It should be emphasized that a lateral material
transfer factor
1


refers to a scenario, where the
induced lateral material flow is capable of changing
the sign of the strip camber curvature, hence, the
material is over-bent to the other direction.
Camber Control
In [5] a so-called heavy side guide solution is
introduced to apply a lateral force to the strip on the
exit side of the roll stand. When the strip threads into
the horizontal stand, the side guide is opened as
usual. After tracking and as soon as hot metal
detectors indicate that the side guide is occupied, the
side guide would close and press against the
material.
This procedure has proven to straighten the material,
but might show two drawbacks:
 Large wear results in frequent changes of wear
plates of the side guides.
 The strip head cannot be straightened and shows
the full camber. The closing side guide over-
bends the material in the roll gap to the other
direction so that an S-shape develops, which is
difficult to handle in the finishing mill and the
subsequent run-out table.
Figure 15: Side guides closing and applying lateral
force.
An alternative to the procedure described in [5] is
presented here: an edger roll applies the lateral force
to the strip as follows. As before, the edger is wide
opened, when the material threads into the horizontal
stand. When the material enters the edger, the
vertical gap is closed. As soon as one roll has
touched the material, the position control is switched
over to force control. The edger gap is employed as
actuator, where the sum of both, the operator side
force and drive side force in the vertical stand is used
as target value.
With this scheme we can overcome the problems of
side guides:

8

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
 Since the edger rolls can turn with the strip
speed, the additional wear is negligible.
 Even if the very strip tail cannot be treated, the
lateral force acts on a defined position and would
not over-bend the material to an S-form.
Figure 16: Possible S-shape due to a reverse
bending of the material after contact as in Figure 15.
In addition, the employment of the edger gap as
actuator simplifies the modelling effort. In principle,
an almost arbitrary force set-point can be handed
over to force control. If the material tends to bend,
one roll touches it first, while closing the gap, and
starts applying the lateral force to induce the lateral
material flow in the roll bite. As a result, this roll would
move further to the centerline of the mill. If the force
was chosen too high, this roll would start to over-
bend the material to the wrong direction, i.e. the
applied lateral force would start to produce a camber
to the wrong side. However, this is prevented by the
other edger roll, which in this case moves towards
the centerline as well. Thus it would start to hold
against the material from the other side and would
avoid over-bending.
Figure 17: Straightening by application of the edger.
As described in the previous sections, the forces
needed to straighten are small as compared to those
required for edging. So in case there is no curvature
to be eliminated, an additional edger pass is taken at
negligible edging force and draft. Up to now, no
negative impact on the width performance was
observed through this automation concept.
Wedge Control
To a certain extent, the principle presented above
avoids the material from developing camber,
regardless of the root cause of it. Of course, the main
application is to reduce a form error coming with the
slab. While camber on slabs is generally well-known,
wedge can be observed mostly on longitudinally slit
slabs. Anyway, it is obvious that for an improvement
of the final product quality, camber control must be
combined with wedge control: otherwise – with only
camber control - if e.g. a perfect slab is processed
with a wrong work roll tilt, a wedge would be induced
on the material, while the camber would be
suppressed.
With activated camber control as described above,
the roll stack of the associated roll stand can be
swiveled to – almost – arbitrary values. The scheme
will prevent the material from developing camber.
However, without lateral forces as actuators, the
swivel value has to be adjusted to minimize the
curvature of the material for operational stability, i.e.
there is no free actuator to manipulate the wedge.
This was the situation before camber control with
lateral forces as actuators.
For getting mill feedback, the first idea might be to
install a profile gauge behind the roughing mill. Thus,
we could control the swivel value of the roughing mill
stand according to the measured wedge after the
roughing mill. However, this would entail additional
investment and maintenance cost. Furthermore, it is
not easy to reliably measure the wedge at a typical
transfer bar thickness of 30mm - 40mm.
A second thought reveals that the operators of the
finishing mill would always swivel the roll stacks of
the finishing mill stands to avoid curvature of the
material. Results can still be improved when they are
supported by camera based strip steering controllers.
If the strip enters the finishing mill without camber,
the relative wedge on the transfer bar will not be
changed in the finishing mill. Therefore, the
measured wedge in the profile gauge after the
finishing mill is an appropriate feedback for the
control of the roughing mill swiveling. On the other
hand, this quantity is exactly the criterion for the
quality of the produced coil.
rolling direction
3: force control for the gap.
F
OS
F
DS

9

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
 Since the edger rolls can turn with the strip
speed, the additional wear is negligible.
 Even if the very strip tail cannot be treated, the
lateral force acts on a defined position and would
not over-bend the material to an S-form.
Figure 16: Possible S-shape due to a reverse
bending of the material after contact as in Figure 15.
In addition, the employment of the edger gap as
actuator simplifies the modelling effort. In principle,
an almost arbitrary force set-point can be handed
over to force control. If the material tends to bend,
one roll touches it first, while closing the gap, and
starts applying the lateral force to induce the lateral
material flow in the roll bite. As a result, this roll would
move further to the centerline of the mill. If the force
was chosen too high, this roll would start to over-
bend the material to the wrong direction, i.e. the
applied lateral force would start to produce a camber
to the wrong side. However, this is prevented by the
other edger roll, which in this case moves towards
the centerline as well. Thus it would start to hold
against the material from the other side and would
avoid over-bending.
Figure 17: Straightening by application of the edger.
As described in the previous sections, the forces
needed to straighten are small as compared to those
required for edging. So in case there is no curvature
to be eliminated, an additional edger pass is taken at
negligible edging force and draft. Up to now, no
negative impact on the width performance was
observed through this automation concept.
Wedge Control
To a certain extent, the principle presented above
avoids the material from developing camber,
regardless of the root cause of it. Of course, the main
application is to reduce a form error coming with the
slab. While camber on slabs is generally well-known,
wedge can be observed mostly on longitudinally slit
slabs. Anyway, it is obvious that for an improvement
of the final product quality, camber control must be
combined with wedge control: otherwise – with only
camber control - if e.g. a perfect slab is processed
with a wrong work roll tilt, a wedge would be induced
on the material, while the camber would be
suppressed.
With activated camber control as described above,
the roll stack of the associated roll stand can be
swiveled to – almost – arbitrary values. The scheme
will prevent the material from developing camber.
However, without lateral forces as actuators, the
swivel value has to be adjusted to minimize the
curvature of the material for operational stability, i.e.
there is no free actuator to manipulate the wedge.
This was the situation before camber control with
lateral forces as actuators.
For getting mill feedback, the first idea might be to
install a profile gauge behind the roughing mill. Thus,
we could control the swivel value of the roughing mill
stand according to the measured wedge after the
roughing mill. However, this would entail additional
investment and maintenance cost. Furthermore, it is
not easy to reliably measure the wedge at a typical
transfer bar thickness of 30mm - 40mm.
A second thought reveals that the operators of the
finishing mill would always swivel the roll stacks of
the finishing mill stands to avoid curvature of the
material. Results can still be improved when they are
supported by camera based strip steering controllers.
If the strip enters the finishing mill without camber,
the relative wedge on the transfer bar will not be
changed in the finishing mill. Therefore, the
measured wedge in the profile gauge after the
finishing mill is an appropriate feedback for the
control of the roughing mill swiveling. On the other
hand, this quantity is exactly the criterion for the
quality of the produced coil.
rolling direction
3: force control for the gap.
F
OS
F
DS
Figure 18: Basic principle of wedge control.
Figure 18 shows the basic principle of the wedge
control: for each strip, the mean measured wedge is
sent to the wedge control algorithm. Based on this, a
change of the swivel set-point is calculated
considering the elongation in the finishing mill, the
ratio of strip width to lever arm of the screw down
system and an amplification factor p < 1. The new
swivel set-point will be available for the subsequent
strip at the earliest.
The current implementation is more sophisticated
than the above presented basic principle. Just to
mention a few features:
 For safety reasons the change rate of the swivel
value from piece to piece is constrained.
 The measured wedge is checked for plausibility.
 In order to allow for ‘mixed rolling’, where
different steel grades from different furnaces/
casters are charged to related furnace lines, a
furnace dependent swivel value treatment is
available.
 The change of the swivel value is balanced to an
operator’s manual intervention during rolling.
Conclusions and Outline
A novel approach has been presented to minimize
both camber and wedge, respectively, with negligible
need for mechanical modifications. In this paper, we
have shown the principle of inducing lateral flow in
the roll gap by lateral forces or bending moments,
respectively. The application within a camber control
and associated wedge control has been outlined.
With this approach, a significant reduction of the
wedge issues on hot rolled coil is expected compared
to only manual interventions by mill operators. First
results from a hot rolling mill look promising.
Abbreviations
HC
Nominal strip
thickness
(C: Centreline)
d
Distance
l
Length  Form error

s
Swivel value
spt
Set-point
FM
Finishing mill
RM
Roughing mill
p Amplification
factor
D
x
Lever arm of
the screw
down system

Non-dimens.
lateral coord.

Material
transfer factor
()In
c
H
Nominal strip
entry
thickness
(C: Centreline)
ij

Cauchy stress
tensor
()Out
c
H
Nominal strip
exit thickness
ij


Deviatoric
Cauchy stress
()In
abs
W
Absolute strip
entry wedge
p
Hydrostatic
pressure
()Out
abs
W
Absolute strip
exit wedge

Strip
curvature
rel
W
Change of rel.
strip wedge
w
Width of strip
f
k
Yield strength
ij

(Logarithmic)
Strain tensor
F

Mean front
tension stress
(0)
ij

Strains w.r.t.
undisturbed
ref. state
()p

Uniaxial
plastic equiv.
strain
B
M
Bending
moment
()pl
W
Plastic defor-
mation work
(per unit strip
length)
we
l
Distance work
roll to edger
()r
we
l
Distance work
roll to edger of
reduced model
, maxzE
F
Maximum
lateral edger
force
()
, max
r
zE
F
Maximum
lateral edger
force of
reduced model
E
xx

Average axial
stress
distribution
with edger
0
xx

Average axial
stress
distribution
without edger
xx

Difference of
averaged
axial stresses
xx
M

Moment of
averaged axial
stresses
plast
M
Bending
moment for
plastification
CL WR
Centerline
work roll
CL E
Centerline
edger
()r

Strip curvature
of reduced
model
()
,
r
s avg

Averaged
strip curvature
of reduced
model
Acknowledgments
This project is carried out within the framework of the
Austrian COMET-K2 programme “Austrian Center of
Competence in Mechatronics” (ACCM). We gratefully
acknowledge the continuous and comprehensive
collaboration and support of voestalpine Stahl.

10

QG
(67$'
PHWHF



Düsseldorf, 15 – 19 June 2015
References
[1] Montague, R. J.; Watton, J.; Brown, K. J.: A ma-
chine vision measurement of slab camber in hot strip
rolling; J. of Materials Processing Technology, 168
(2005), P. 172–180
[2] Knight, C. W.; Hardy, S. J.; Lees, A. W.; Brown, K.
J.: Investigations into the influence of asymmetric
factors and rolling parameters on strip curvature
during hot rolling; J. of Materials Processing Tech-
nology, 134 (2003), P. 180–189
[3] Nilsson, A.: FE simulations of camber in hot strip
rolling; J. of Materials Processing Technology, 80-81
(1998), P. 325-329
[4] Shiraishi, T.; Ibata, H.; Mizuta, A.; Nomura, S.;
Yoneda, E.; Hirata, K.: Relation between camber and
wedge in flat rolling under restrictions of lateral
movement; ISIJ Int. 31 (No. 6) (1991), P. 583–587
[5] Jepsen, O.; Müller, H.-A.; Immekus, J.: Verfahren
und Vorrichtung zur gezielten Beeinflussung der
Vorbandgeometrie in einem Vorgerüst; WO
2006/119984 A1
[6] Belytschko, T; Liu, W. K.; Moran, B.: Nonlinear
Finite Elements for Continua and Structures, John
Wiley & Sons, Chichester, New York, 2002
[7] Simo, J. C.; Hughes, T. J. R.: Computational In-
elasticity, Springer, New York, 1998.
Primetals Technologies, Limited, headquartered in London,
United Kingdom, is a worldwide leading engineering, plant-building
and lifecycle partner for the metals industry. The company offers a
complete technology, product and service portfolio that includes
the integrated electrics, automation and environmental solutions.
This covers every step of the iron and steel production chain that
extends from the raw materials to the finished product – in addition
to the latest rolling solutions for the nonferrous metals sector.
Primetals Technologies is a joint venture of Mitsubishi Heavy
Industries (MHI) and Siemens. Mitsubishi-Hitachi Metals
Machinery (MHMM) - an MHI consolidated group company with
equity participation by Hitachi, Ltd. and IHI Corporation - holds a
51% stake and Siemens a 49% stake in the company. The
company employs around 9,000 employees worldwide. Further
information is available on the Internet at www.primetals.com.