CONTROLE DE PLANEITE SUR LAMINOIR A CHAUD

FLATNESS CONTROL IN HOT STRIP MILL

Abrégé anglais

21-DSS-2505
FLATNESS CONTROL IN HOT STRIP MILL
ABSTRACT OF THE DISCLOSURE
The flatness of metal strip being rolled in a
hot strip mill is improved by applying higher than
normal interstand tensions with maximum permissible
tensions being based upon pre-established maximum
allowable width reductions due to interstand tensions.
The relationships between interstand tension and
interstand plastic deformation are predetermined
functions of strip material properties, strip
temperature, and assumed tensile stress distribution
across the strip width.

Revendications

- 23 - 21-DSS-2505
The embodiment of the invention in which an
exclusive property or privilege is claimed are defined
as follows:
1. In a hot strip mill having at least two mill
stands where a metal workpiece is compressed and reduced
in thickness to form a strip, each mill stand having rolls,
the rolls of each mill stand being rotatable at selected
speeds by means of a mill control system so that the strip
can be placed under tension during its passage between
mill stands, a method for improving strip flatness,
comprising the steps of:
a) selecting a predetermined maximum width
reduction which the strip will be permitted
to undergo during its passage between
adjacent mill stands;
b) calculating, from predetermined relationships
between stress and strain-rate, the tensile
stress which will produce this width
reduction; and,
c) regulating interstand tensile stress at or
below the calculated tensile stress level.
2. The method of Claim 1 wherein the relation-
ship between stress and strain-rate is defined by
equation:
.sigma.= K1 + R2 ln(?)
wherein,
.sigma. = stress
? = strain-rate
K1 and K2 = constants representing the intercept
and slope of the equation for a
particular material at a particular
temperature.
3. In a hot strip mill having at least two mill
stands where a metal workpiece is compressed and reduced
in thickness to form a strip, each mill stand having rolls,
the rolls of each mill stand being rotatable at selected
speeds by means of a mill control system so that the strip

21-DSS-2505
- 24 -
can be placed under tension during its passage between
mill stands, a method for improving strip flatness,
comprising the steps of:
a) selecting a predetermined maximum width
reduction which the strip will be permitted
to undergo during its passage between
adjacent mill stands;
b) calculating the transverse strain-rate in
the strip resulting from the selected width
reduction;
c) calculating the axial strain-rate in the
strip corresponding to the calculated
transverse strain-rate in the strip based
upon a predetermined relationship between
transverse strain-rate and axial strain-rate;
d) calculating the axial stress in the strip
which will produce the calculated axial
strain-rate; and,
e) regulating the speed of the rollers in
adjacent mill stands to apply axial stress
to the strip at a level at or below the
calculated axial stress.
4. The method of Claim 3 wherein the calculated
axial stress is calculated as a function of strain-rate,
strip material and strip temperature.
5. The method of Claim 3 wherein the relation-
ship between axial strain-rate and axial stress also is
corrected to allow for tension nonuniformity across the
strip width.
6. In a hot strip mill having at least two mill
stands where a metal workpiece is compressed and reduced
in thickness to form a strip, each mill stand having rolls,
the rolls of each mill stand being rotatable at a selected
speed so that the strip may be placed under tension during
its passage between mill stands, a method for improving
strip flatness during the rolling process, comprising the
steps of

21-DSS-2505
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a) selecting a predetermined maximum width
reduction which the strip will be permitted
to undergo during its passage between mill
stands;
b) establishing the degree of transverse strain-
rate in the strip needed to achieve the
selected width reduction as a function of
a fixed mill stand spacing and a predeter-
mined strip speed between adjacent mill
stands;
c) establishing the degree of axial strain-rate
in the strip corresponding to the
established transverse strain-rate in the
strip based on a predetermined relationship
between transverse strain-rate and axial
strain-rate;
d) establishing the axial stress in the strip
which will produce the established axial
strain-rate; and,
e) regulating the speed of the rollers in
adjacent mill stands to apply axial stress
to the strip such that the established
axial strain-rate is not exceeded.
7. The method of Claim 6, wherein the
relationship between axial stress (.sigma.) and axial strain-
rate (?a) is determined from a series of relationships
based on the equation:
.sigma.= K1 + K2 ln(?a)
where K1 and R2 are constants dependent upon the strip
material properties, the strip temperature, the strain
which the material experiences, and the nature of the
axial stress distribution across the strip width.
8. The method of Claim 7,wherein permissible
axial stress levels are recalculated during acceleration
of the mill to higher rolling speeds, and interstand
tension levels are raised to the maximum permissible
extent after each recalculation.

21-DSS-2505
- 26 -
9. In a hot strip mill having at least two mill
stands where a metal workpiece is compressed and reduced
in thickness to form a strip, each mill stand having rolls,
the rolls of each mill stand being rotatable at selected
speeds by means of a mill control system so that the strip
may be placed under tension during its passage between
mill stands, a method improving strip flatness during the
rolling process, comprising the steps of:
a) selecting a predetermined maximum width
reduction (.DELTA. W) which the strip will be
permitted to undergo between mill stands;
b) establishing the-maximum per unit width
reduction (.DELTA. W/W) acceptable in the strip,
wherein W is the strip width upon entering
an interstand space;
c) establishing the degree of axial per unit
strain (.DELTA. L/L) in the strip associated with
said maximum acceptable per unit width
reduction in accordance with the relationship
.DELTA. L/L = 2 .DELTA. W/W, wherein .DELTA. L equals the
elongation of a strip element of length L
while traversing an interstand space;
d) establishing the axial strain-rate (?a) in
accordance with the formula:
<IMG>
wherein, t equals the time required for a
point on the strip to transverse the inter-
stand space;
e) determining the axial stress (.sigma.) needed to
produce the established axial strain rate
(?a) from an equation of the form:
.sigma. = K1 + K2 ln(?a)
wherein K1 and K2 are constants dependent
upon the strip material properties, the
strip temperature, the strain which the
material experiences, and the nature of the

21-DSS-2505
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tension distribution to which the strip is
subjected; and,
f) regulating the speed of the rollers in
adjacent mill stands to apply axial stress
to the strip so that the calculated axial
stress is approached or attained.
10. The method of Claim 9 wherein permissible
axial stress levels are recalculated during acceleration
of the mill to higher rolling speeds, and interstand
tension levels are raised to the maximum permissible
extent after each recalculation.
11. The method of Claim 9, wherein the method
is applied only to the latter mill stands of a multiple
mill stand finishing train.
12. In a hot strip mill having at least two mill
stands where a steel workpiece is compressed and reduced
in thickness to form a strip, each mill stand having rolls,
the rolls of each mill stand being rotatable at selected
speeds by means of a mill control system so that the strip
may be placed under tension during its passage between
mill stands, a method for improving strip flatness during
the rolling process, comprising the steps of:
a) selecting a predetermined maximum width
reduction (.DELTA. W) which the strip will be
permitted to undergo between the latter
mill stands of a multiple mill stand
finishing train;
b) establishing the maximum per unit width
reduction (.DELTA. W/W) acceptable in the strip,
wherein W is the strip width upon entering
an interstand space;
c) establishing the degree of axial per unit
strain (.DELTA. L/L) in the strip associated with
said maximum acceptable per unit width
reduction in accordance with a value of

21-DSS-2505
- 28 -
Claim 12 cont'd....
Poisson's Ratio of approximately 1/2
whereby .DELTA. L/L - 2 .DELTA. W/W, wherein .DELTA.L equals
the elongation of a strip element of length
L while traversing an interstand space;
d) establishing the axial strain-rate (?a) in
accordance with the formula;
<IMG>
wherein, t equals the time required for a
point on the strip to transverse the
interstand space;
e) determining the axial stress (.sigma.) needed to
produce the established axial strain rate
(?a) from an equation of the form:
.sigma. = K1 + K2 ln(?a)
where K1 and K2 are constants dependent
upon strip material properties, the strip
temperature, the strain which the material
experiences, and the nature of the tension
distribution to which the strip is
subjected;
f) calculating the interstand tension value
corresponding to said axial stress;
g) applying the calculated interstand
tension value to interstand tension
regulation means;

21-DSS-2505
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Claim 12 continued ...
h) recalculating permissable interstand
tension levels during acceleration of
the mill to higher rolling speeds and
raising interstand tension levels to
the maximum permissible extent after
each recalculation.

Description

- 1 - 21-DSS-2505
FLATNESS CONTROL IN HOT STRIP MILL
WORKPIECE SHAPE CONTROL, U.S. Patent No.
4,137,741 - issued February 6, 1979 - Fapiano et al
and assigned to the assignee of the present invention.
COMPUTER CONTROLLED SYSTEM FOR METALS ROLLING
MILL, U.S. Reissue Patent No. 26,996 - issued December
8, 1970 - Beadle et al and assigned to the assignee of
the present invention.
The present invention relates to the rolling
of metal strips and, more particularly, to techniques
for maintaining the strips flat during the rolling
process.
Sheet metal is produced by rolling slabs, bars,
or other relatively massive workpieces into thin,
elongated strips. Although finish rolling often occurs
near room temperature (cold rolling), the intial
workpiece reduction from its slab form is done at
elevated temperature in a facility known as a hot strip
mill. The product of the hot strip mill
may be further processed and further reduced in
thickness, or it may be sold directly for applications
requiring thicker strip materials. Where hot-rolled strip

~517~8
- 2 _ 21-DSS-2505
is an intermediate produce subject to furthér rolling, its
width and thickness dimensions may be somewhat less critical
than where it is the final product. In either case, however,
its flatness, or freedom from waviness, is important since
excess waviness interfers with both subsequent processing
and eventual fabrication of the strip into a finished
product.
waviness in rolled strip results from unequal
elongation across the strip width due to une~ual percentage
thickness reduction across the strip width. A region of
strip which is elongated more-than other strip regions
will exhibit waviness.
In order to reduce the thickness of the strip,
the strip is passed between successive stands having two
opposed rolls which are designed to support large rolling
forces. In a "two high" stand only two rolls are present,
while in a "four high" stand upper and lower work rolls
contact the strip and are themselves contacted by upper
and lower backup rolls of much larger diameter. Even the
relatively rigid "four high" assembly experiences deflect-
ion under the bending effort of rolling forces which rangerom 500 to 3000 tons in strip rolling applications. To
compensate for deflection the work rolls may be ground,
or contoured, so that their diameters at mid-length are
greater than their diameters at the ends. This diameter
difference is referred to as roll "crown".
Roll crown is not constant during a rolling
operation, but varies as the roll temperature increases or
decreases through contact with (a) the hot workpiece and
(b) cooling water used in the process. Roll crown changes
due to nonuniform temperature variations across the roll
may exceed 0.01 inch. During the rolling process, the roll
crown is further altered by surface wear in the regions of
contact with the workpiece. Work rolls are changed relatively
frequently to maintain good surface conditions but may
exhibit wear in excess of 0.01 inch. In addition
rA~ t

l9 21 -DS S - 2 5 0 5
-- 3 --
to work roll dimension changes, backup rolls wear due to
friction from their contact with the work rolls. Although
backup roll wear rates are much lower than work roll wear
rates, the time between bac~up roll changes is sufficiently
S greater that the accumulated wear may be of the same order
as work roll wear.
These roll crown-influencing facto~s combine at
each mill stand to produce some strip thickness variation
across strip width. The difference between strip thickness
near its edge and at its center is referred to as "strip
crown". With the exception of roll wear, all of the factors
which influence roll crown and roll deflection can be used
to control strip crown. Roll temperature can be controlled
by the use of roll coolant. ~eflection can be controlled
by proper choice of thickness reduction which determines
the associated roll separating force. Roll grinding
practices normally are chosen to be compatible with the
planned rolling practice. Finally, supplementary roll
' bending sys~ems can be provided to alter the effective roll
crown by applying bending moments to the work rolls or
backup rolls with hydraulic cylinders.
Whatever the method of controlling roll crown
and strip crown, the strip crowns in successive rolling
~tands must result in essentially equal elongation of all
elements of the strip across its width or waviness
eventually will result. Equal element elongation will be
achieved if all strip elements receive identical percentage
thickness reductions in each rolling stand. Expressed
another way, the percent strip crown must be maintained
essentially constant during the successive reductions in
thickness.
These concepts are well understood in the context
of both cold rolling and hot rolling. In hot rolling, most
recent techniques have attempted to meet the constant per-
centage thickness reduction require.~ent by proper choice ofthickness reduction and associated rolling force. These

748
21-DSS-2505
_ 4 _
methods attempt to model mathematically the thermal roll
crown changes in the work rolls, the wear pattern in the
work rolls and backup rolls, and the deflection of the
work rolls under nonuniform roll separating forces. These
5 methods then attempt to choose a thickness reduction such
that the combination of roll crown factors and roll
deflection factors produces a delivery strip crown which
bears the proper relationship to the entry strip crown at
each rolling stand. In some variations of this strategy,
the calculations are limited to the last three or four
rolling stands.
While this prior art strategy produces somewhat
better results than strategies which take no account of
entry and delivery strip crown relationships~ it is obvious
that in the absence of flatness feedback, the results often
will be unreliable. That is, the prior techniques are
"predictive" because they calculate in advance the expected
regult8 of a rolling schedule and do not rely on measured
values to determine if in fact the proper strip crown
relationghips are being produced. The difficulties
lnherent in a predictive approach can be appreciated by
recognizing that a workpiece 0.1 inch thick produced with
a ~trip crown 0.001 inch greater than a crown produced
under conditions of uniform elongation will experience
approximately 0.1 percent less eiongation at the center
than at the edges. The extra edge elongation will produce
an edge waviness of about 0.8 inch amplitude, in the
abgence of tension.- Since uncertainties in the actual
loaded roll surface configuration will often exceed 0.001
3~ inch, it is clear that waviness easily can occur with even
the most sophisticated predictive technigue.
Prior art strip crown control techniques in hot
strip mills have analyzed the waviness problem without
taking tension between roll stands into account or by
assuming that interstand tension is negligible. It is
well known in cold rolling to provide substantial tension
, , . _ ...... ........ ..
- ~ , . ~ , .. .

` 1~51748
21--DSS--2505
_ 5 _
between successive roll stands. This is done primarily to
reduce the roll force required to effect the desired
thickness reduction. It also is recognized that in.erstand
tension acts as an aid to fla~ness control. The use of
relatively high interstan~ tension has been possible in
cold rolling because the elastic lim~ts of a typical
workpiece at or near room temperature are very high.
Interstand tensile stresses m2y therefore be maintained
correspondingly high without exceeding the elastic limits
of the strip and, therefore, without causing undesirable
interstand plastic deformation.
It ia fur~her known in cold rolling applications
that nonuni~orm tension distributions which would have
resulted from nonuniform elongation across stri~ width
are attenuated by an amount which depends upon the length
of the arc of contact, the thickness of the wor~piece and
the elastic moduli of the workpiece and rolls. Davies
~"Preduction and Control of Strip Flatness in Cold Rolling~
-W. E. Davies, et al, etals Technology, October 1975)
give~ the following expression for attenuation, A, o' roll
crown errors in the presence of tension:
Q E5
A ~ 1 + 6 ~ E
wherein:
Q = arc of contact
h = outgoing thic~ness
ES = elastic modulus of strip
ER = elastic modulus of roll.
In this res~ect, interstand tenfiion influences are ~i~ilar for
hot and cold rolling ~pplications. The fact that interstznd
tension exhibits this flatness correcting e ect in hot
rolling applications has probably been neglected because
(1) it has been generally assumed that interstand tension
levels are negligible in hot rolling, and (2) it has been
incorrectly assumea that the mo2ulus of elasticity of the
3~ workpiece at rolling tempera.ures is too low to sisnif}cantly

l~S179~8
21-DSS--2505
-- 6 --
influence tension profiles.
In hot rolling, moreover, prior attempts to employ
other than minimal interstand tensions, insufficient to
have any noticeable effect on strip flatness, have met
with inconsistent and sometimes highly unsatisfactory
results. Because the factors governing interstand plastic
deformation have been insufficiently understood, the
results of these prior attempts have varied so that in
some instances no appreciable effect was observed, while
at other times severe reductions in width, or nec~ing
resulted. In extreme cases, interstand plastic deformation
has been so drastic as to result in breaking of the strip.
Summ æ~ of the Invention
It is, therefore, an object of the present
invention to provide a method for employing interstand
tension as an active flatness control parameter in a hot
metal rolling mill.
It is another object to provide a method of
flatness control in a hot metal rolling process which
employs relatively high controlled interstand tensions
derived as a unction of determinable workpiece
characteristic3.
It is a further object to provide a method of
flatness control in a hot metal rolling mill which employs
appreciable interstand tension in a controlled and pre-
dictable manner.
The foregoing and other objects are achieved in
accordance with the method of the present invention which
overcomes the major problems associated with the use of
high interstand tensions and provides an effective,
controllable technique for improving strip flatness in
hot strip mills. Essentially, the invention first
determines an acceptable wor~piece width reduction due
to plastic flow between each pair of roll stands. Based
on (a~ the acceptable width reduction, (b) the initial
strip width, (c) the transport time between each pair of
. .

J~lS1748
21-DSS-2505
roll stands, and (d) an assumed relationship between
transverse and longitudinal strain, longitudinal strain
rates are calculated. These strain rates then are used
to select allowable tension levels from stored
S relationships between stress and strain rate for the
particular grade of material and for the average
temperature in each interstand space. The selected
tensile stresses are converted to interstand tensile
force and applied as references to a conve~tionally
supplied interstand tension regulation system.
In a preferred em~odiment, interstand stress
levels are stored as linear functions o~ the logarithm
of strain rate for representative opesating temperatures
and for material groups having similar tension-strain
rate characteristics. Preferably, the stress levels are
reduced to compensate for some amount of tension non-
uniformity, since nonuniform tension produces more width
reduction than does uniform tension.
Brie~ Description of the Drawing
While the present invention is described in
particularity in the claims annexed to and forming a part
o~ thls spe~ification, a better understanding of the
~nvention can be had ~y reference to th~ following
description t~ken in conjunction with the accompanying
drawing in which:
Fig. 1 is a simplified schematic view of a hot
strip mill in which the present invention may be
practiced;
Fig. 2 is a schematic representation of the
interaction between interstand ten9ion distribution and
rolling force distribution;
Fig. 3 schematically represents the relationship
between interstand tension distribution and interstand
plastic ~low;
Fig. 4 is a plot of stress versus logarithm of
strain rate for a metal strip under uniform tension across
its width;

115174~
21-DSS-2505
- 8 -
Fig. ; is a plot of percent strip width
reduction ~ersus tension at a 2,000 foot per munute strip
delivery speed for a uniform strip tension profile;
Fig. 6 is a plot of tension in the strip across
the width of the strip when the center of the strip is
under greatest tension;
Fig. 7 is a plot of tension in the strip across
the width of the strip when the edges of the strip are
under greatest tension;
Fig. 8 is a plot of percent strip width
reduction versus tension at a 2,000 foot per minute strip
delivery speed for different strip tension profiles;
Fig. 9 is a plot of strip tension versus mill
stand location, a typical prior art tension level being
plotted and a tension level according to the invention
being plotted; and,
Fig. 10 is a block diagram representing the
methodology of the present invention and its implementation
in a hot strip mill.
Description of the Preferred Embodiment
In a hot strip mill, the initial reductions of
the thickness of a metal slab are taken in a set of
tandem mill stands known collectively as a roughing train.
Fig. 1 shows in greatly simplified form the last stand
of a roughing train 10 along with other components in a
hot strip mill. As the slab emerges Erom the stand ~ ,
it moves across a mill table 12 toward a finishing train
20 consisting of mill stands Fl, F2, F3, F4, F5, F6 and F7
arranged in tandem. The final reductions in thickness are
taken in the finishing train 20 to produce a metal strip
22 which may be, for example, 1,000 or more feet in length,
two to seven feet in width, and 0.05 to 0.5 inch in
thickness.
As a typical example, during its passage through
the roughing train 10 and the finishing train ~0, the strip

~.~517~fl
21-DSS-2505
_ g _
22 gradually is cooled from its initial temperature of
about 2200 degrees Fahrenheit (F). By the time the
strip 22 reaches stand F7, it has cooled to around 1600~
to 1700F. As the strip 22 emerges from the last stand
F7 in the finishing train 20, it traverses a cooling or
runout table 24 before being coiled by a coiler 26.
Strip tension during the coiling operation is maintained
a pair of pinch rolls 28, 30 located at the coiler end
of the runout table 24.
As illustrated in Fig. 1, each stand in the
finishing train 20 includes an upper work roll 40 and a
lower work roll 42. Upper and-lower backup rolls 44, 46
are pressed against the upper and lower work rolls 40, 42,
respectively, during a rolling operation to prevent
excessive distortion of the work rolls 40, 42. This
configuration is known as a four high mill. Each mill
stand includes roll-adjusting screws 48 to regulate the
opening between the upper and lower work rolls 40, 42.
The rolls of each mill stand are rotated by independently
controllable electric motors having motor controls, all
indicated schematically by the numeral 50. By rotating
the motors 50 at different speeds with respect to each
other, the tension applied to a strip 22 passing through
the finishing train 20 can be controlled. Customarily,
in a modern autcmated mill, the determination of the
individual motor ~roll) speeds is the result of
computations performe~ by a suitable computer 51 (for
x/p ~ example, a ~oneywell 4000 Series). The computations
employ various parameters of the strip itself tfor example,
composition, size, temperature, etc.) as well as operating
parameters of the mill tfor example, roll force, thickness
reduction, etc.) all as is well known in the art. As an
example, reference is made to the Computer Control Patent.
The control link between the motors and their controls 5~
and the computer 51 is schematically illustrated by a bus
49.

~ ~S~7413
(
21-DSS-2505
-- 10 --
A metal sensor 52 is located a short distance
upstream of the first mill stand Fl. The metal sensor 52
is positioned above the mill table 12 and senses when the
beginning and the end of a strip 22 are approaching the
first mill stand Fl. The metal sensor 52 generates a
signal which is sent to the computer Sl via a line 53.
A looper 54 is positioned midway between each mill stand
and is in contact with the underside of a strip 22 during
its passagé through the finishing train 20. The loopers
54 are in communication with the computer 51 by way of a
line 55. The loopers 54 serve to maintain a desired strip
loop between mill stands as well as a desired preset
tension. Looper positions are maintained through
adjustments of the adjacent work roll speeds. The strip
tension is determined by the looper and strip geometry
and by looper torque motor current. Alternatively, a
suitable tensiometer such as is known in the art may be
used to sense interstand tension and provide the requisite
feedback signals.
29 Fig. 2 is a schematic representation of a metal
strip 22 as it i9 deformed during its passage through the
finishing train 20. Only the lower work roll 42 is shown
for purposes of clarity. Under normal rolling conditions,
the work rolls 40, 42 are subjected to roll separating
~5 forces of between 500-3,000 tons. The work rolls 40, 42
are supported along their entire length by the backup
rolls 44, 46 to prevent excessive bending. Even though
the resulting roll assembly is relatively rigid, the
large roll separating forces produce roll deflections which
are signiicant when compared with the thickness of the
strip being rolled. Since the backup rolls 44, 46 are
supported only at their ends by the roll adjusting screws
48, deflections tend to be greater near the center of the
workpiece than near the edge of the workpiece. Typically,
the work rolls 40, 42 are contoured to have a slightl~
larger diameter at their midlength than at their ends in

1.~51~4~3
21-DSS-2505
-- 11 --
an attempt to compensate for expected roll deflections.
Furthermore, the combined action of roll cooling water,
which is distributed over the full length of the work
rolls 40, 42, as well as heat conducted from the strip 22
causes relatively more thermal expansion at the mid-length
of the rolls 40, 42 than at the ends of the rolls 40, 42.
This th~rmal expansion is influenced by the length of the
rolling contact arc, the temperature of the strip 22, the
temperaturé of the rolls 40, 42, the temperature of the
cooling water, the rolling speed, and the width of the
strip 22, among other factors. The effective roll crown
is ~urther influenced by surface wear of the work rolls
40, 42 which also is nonuniform and is influenced by many
unpredictable factors. The backup rolls 44, 46 wear more
slowly than the work rolls 40, 42 but the backup rolls
40, 46 are retained longer in the mill stand and experience
accumulated wear comparable to that of the work rolls 4~,
42. Although mathematical models have been proposed for
calculating roll thermal crowns, none of these models
have been completely effective in the presence of the
unmeasurable variations in many of the controlling factors.
All of the foregoing actors combine to produce
a thickness variation across the width of the strip 22 as
the strip Z2 is reduced in thickness between the work
rolls 40, 42. It is well known that the crown imparted
to the strip 22 (strip crown) as the strip 22 exits the
work rolls 40, 42 must bear a specific relationship to
the strip crown upon entry to the work rolls 40, 42 if
good strip flatness is to be maintained. Specifically,
the percentage strip crown must be maintained approximately
constant at each stage of strip thickness reduction from
the initial to final thickness in the hot strip mill. In
the earlier stands, some deviation from constant percent
crown is permissible, the amount of deviation depending
upon the thickness, width and temperature of the strip 22.
.

21-DSS-2505
- 12 -
In the latter stands, particularly when rolling thin,
wide strips, ver~ little deviation from constant percent
crown is permissible.
As earlier indicated, interstand tension can
improve strip flatness in a rolling mill through inter-
action with r~ll gap forces. In hot rolling, the gap
force tension interaction is supplemented by two
additional mechanisms associated with interstand flow.
~ig. 2 illustrates the relationship between
interstànd tension and roll force profiles when the roll
gap configuration is such as to produce more elongation
at workpiece center than at workpiece edges. In the
presence of interstand tension this condition will reduce
the tension at workpiece center and increase the tension
at workpiece edges as illustrated by the arrows 58.
Since the wor~piece yields when the combined stress equals
the yield stress, the tension profile will produce the
nonuniform force profile illustrated by the arrows 57.
The higher roll separating force in the workpiece central
region will produce more roll deformation there than in
the regions corresponding to the workpiece edge~. As a
result, the wor~piece crown will be increased and the
elongation at workpiece center reduced compared to that
which would have occurred in the absence of tension. ~he
2S reduced elongation is re~resented in Fig. 2 by dimension
~, the dotted line representing the condition which would
have occurred in the absence of intérstand tension. This
is similar to that occurring in cold rolling, as previously
noted.
It will be understood from the previous
illustration that the average interstand tension level
is significant since higher tension will accommodate
larger tension differéntials before any element of wor~-
piece width falls to zero tension and manifest waviness
appears.

~1517~8 21-~SS-2505
-- 13 --
It is in the interstand wor~piece behavior that
~he differences between hot and cold rolling applications
become most significant Interstand flow in the presence
of tension is nonexistent in cola rolling but may be
~ 5 significant in hot rolling. ~his interstand flow
influences width, which is generally considered
undesirable, while it has two be~eficial i~fluences on
flatness. Fig.3 illustrates one of these actions. Consider an
element of strip le2~ing one or a pa_, of mill stands
io with excessi~e elongation as shown by section 56 Tensile
s'.ress at the workpiece edges woul2 be grezter than at
the centerline, the tension distribution taking the for~
illustsated ~y the ærrows 60 During the t~me interval
in which the workpiece section proceeds from a first to a
second o the stand pairs all of the workpiece section
expesiences some flow~or creep, the regions of the sections
under greater tension experiencing greater flow When the
wor~piece element arri~es at the second stand, its edges
have been elongated more than its center and the conditions
which would have given rise to waviness thus have been
partially compensated as demonstrated at 61 wherein the
dotted lines again show the condition in the absence of
tension.
While not shown in Fig 3, it will be understood
that the edge regions of the workpiece in this example
will not only have undergone more elonsation that the
central regions, but additionally the edge thic~ness will
have been reduced more than the central thickness and the
transverse flow or width reduction in the edge regions will
be sreater than that in the cent-al resions
The thickness changing ~n'luence o' _he in~erstznd
tension differenti21 acts to 'ur.her ampli'y the roll force
pattern illustr2ted in ~ig 2 The s~eater ~eduction of
edge gzuge reduces the relative reduction and associated
roll separating force in the edge regions, assisting the
b)~ ,

~5~74l9
21-DSS-2505
- 14 -
previously described action of the tension profile.
A quantitative understanding of these phenomena
requires knowledge of the "creep" or strain~rate behavior
of the workpiece at rolling temperatures and practical
interstand tensile stress levels. The Journal of Applied
Mechanics, June 1941, "High-Speed Tension Tests at Elevated
Temperatures - Parts II and III" by Nadai et al gives some
data for mild steel. Additional laboratory results
performed by the assignee of the present invention are in
general agreement with the earlier published results but
cover a broader range of materials.
Fig. 4 shows typical-actual experimental results
for mild steel at temperatures of 1700F and 1800F.
These data can be expressed as a log-linear equation.
For stresses in the 1000 to 10,000 psi range, the stress
V8. strain-rate (i.e., time rate of change of strain)
relation can be expressed as a log-linear equation of the
form:
(1) C~ = Rl + K2 ln(e)
20 wherein,
a= stress (psi)
e - strain-rate (in/in/sec)
Kl & R2 = constants representing the intercept
and slope of the equation for a
particular material at a particular
temperature.
For mild steel at 1700F, as an exa~ple, and in the
region of 1% strain, the relationship is approximately:
(2) cr = 10200 1 1100 l~e)
For mild steel at 1800F, the relationship will be
approximately:
(3) CJ , 8600 1 1040 ln(e).
Experimental data for the values of Kl and K2 have been
developed for a range of temperatures and materials and
such data can be duplicated in any metallurgical

~S174~
21-DSS-2505
- 15 -
testing facility by well-known methods such as that set
forth in the l~adai et al article cited above.
These relationships can be stored in a computer
(i.e., computer 51 in Fig 1) in any convenient form such
as tabular or as equations such as those cited above.
Equations (1), (2) and (3) describe the
relationship between stress and axial strain rate for
conditions of axial tension. It is necessary that this
information be correlated to width reductions for various
conditions of interest. An assumption can be made that,
for small interstand strains, the percent width reduction
and percent thickness reduction are each half of the
percent length increase. This is a reasonable assum~tion
because Poisson's Ratio, the ratio of transverse strain
to axial strain, approaches one-half because volume
remains substantially constant in plastic deformation.
~aving thus determined the relationship between axial
tension and trans~erse strain rate, the percent width
reduction due to axial tension also can be determined.
Fig. 5 is derived from equation (2) and is a
plot of percent width reduction between mill stands
versus average interstand tension for an average inter-
stand temperature of 1700aF and a transit time
corresponding to a wor~piece speed of 2,000 feet per
minute. In order to plot the cur~e of Fig. 5, it has
been assumed that the mill stands are spaced a known
constant distance and that the tensiGn applied across
the width of the strip 22 is uni~orm. A significant
problem exists, however, because it is difficult, if not
impossible, to achieve uniform tension across the width
of the strip under day to day operating conditions. It
therefore is necessary to determine the effect of non-
uniform tensile stresses on width reduction before high
interstand tension levels can be effectively applied.
Figs. 6 and 7 illustrate "tight center" and "tight edge"

~iS3~7~19
21-DSS-2505
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conditions, respectively, of a typical strip 22 being
roll~ed in a hot strip mill. The distributions are
assumed to be parabolic and the depictions indicate that
for a strip being rolled at a mean tension of 2000 psi,
and under greatest tension at its center, the maximum
tension differential which can be tolerated before
waviness appears is 3000 psi. wa~iness will appear in
a strip being rolled whenever tension in a portion of
the-strip drops to zero. Fig. 7 illustrates that a
'10 strip having more tension at its edges than at its center
can tolerate a maximum tension differential of 6000 psi
before waviness appears.
The importance of these curves becomes apparent
when the width reduction for a given strip under different
tensile loadings is explored. In Fig. 8, a family of
curves is plotted for a particular grade of strip steel
at 1700F and under three different tensile loadings:
uniform loading, tight edge loading and tight center
' loading. It has been assumed that the strip is being
rolled at a speed of 2000 feet per minute and that the
mill stands are spaced a known constant distance.
Because the temperature of the strip decreases as it
passes through the mill, a temperature of 1700F
approximates that in a ty,pical strip mill in the last
interstand space
The cuxves of Fig. 8 for the tight center and
tight edge conditions are derived from the uniform width
reduction case, for example, by integration by parts.
According to thls technique, the percentage width reduction
at each element of the strip due to the local tension
there is calculated from a cur~e similar to that of Fig. 5
for the particular material and temperature under
consideration. The calculated percentage width reduction
at that particular element is multiplied by the width of
that element. The calculation is repeated for each of

llS174~3
--- 21-DSS-2505
- 17 -
the other elements across the width of the strip and a
family of curves li~e thzt in Fig. 8 can be plo'ted.
The curves thus plotted can be stored in tzbular
form or can be converted back into log-linear relationships
like thzt o' equation (l). For example, mild steel in the
region of one percent strain and under tisnt center
conditions, will yield zn approximate relationship.
(4) a = 7830 1 800 ln(e~, at 1700~F.
Various relationships like those of equations (2), (3) and
(4) can be calculated and s.ored by the computer 51.
Three zspects of these relationships are of
particular interest. Firs., there is a pronounced "~nee"
in these curves, above which strain inc~eases sharply with
- tension. Second, the allowable s~ress levels drop quickly
as the ups~ream stands are approached due to the com~ined
effects of increasing temperature and increasing transit
time between mill stands. The third aspect relates to
the uniform tension assumption. All nonuniform tension
distributions produce greater width reductions than
uni.orm tension distributions because of the nonlinear
stress-strain rate relationship. Because the tight edse
tension distribution produces more extreme stress
concentration than the tisht center condition, the
corresponding width reduction may be substantizlly greater.
For example, at a mean tension of 3000 psi, z uniform
tension distribution shows only a ~.04 percent width
reduction, while a tisht center tension distribution
shows a 0.07 percent width reduction. A tisht edse
tension distribution, however, shows a 0.56 percent width
_eduction. Clearly, i' a strip is being rolled under
tight edge conditions and ~nte_stand tensions z~e
permitted to reach even into the 3000 psi .ange, width
reductions of one percent or more are possi~le. 3ased on
~he foregoing phenomenon, which until the present invention
3~ hzs not been understood, at least in the context o' hot
., ~pJ .
......... . .. ........ . .. . . .. ...... . .... ........... ................................................................. ...

4~9
(
21-DSS-2505
- 18 -
strip mill operation, hot strip mill practice has been
to reduce interstand tension levels to the order of a
maximum of 1500 psi in order to avoid any tension-induced
problems. Stated differently, in the absence of a
clearer understanding of interstand plastic flow relation-
ships, the only reliable recourse has been to reduce
interstand tension to levels which produce acceptable
width reduction under the most unfavorable combinations
of tension distribution, temperature and rolling speed.
As a result, the flatness-producing mechanisms which
require the presence of high interstand tension have been
substantially unused.
The invention contemplates a technique for
calculating optimum interstand tension levels for the
conditions which exist at each interstand space, and for
controlling the interstand tension regulation means to
produce the calculated optimum tension levels. Essentially,
an acceptable width reduction of a strip 22 due to tension
lmposed between roll stands is sought from predetermined
conBiderations. In a typical hot strip mill, an
acceptable width reduction might be 0.5 inch from the mill
stand Fl through the mill stand F7. Because the rolling
process might widen the strip 22 about 0.25 inch, the
total acceptable tension-induced width reduction from
mill stand Fl through mill stand F7 might be about 0.75
inch. The tension~induced reduction is distributed over
the interstand spaces, favoring the~latter stands where
the percentage elongation errors and flatness problems are
most troublesome. A typical distribution of tension-
induced width reduction might be, for example, 50 percentin the F6-F7 space, 30 percent in the F5-F6 space, and
20 percent in the F4-F5 space. Tension levels upstream
of mill stand F4 would remain at their normal, low levels.
Rolling speeds and temperatures are determined
in advance of workpiece arrival at the finishing train 22.

17~8
21-DSS-2505
-- 19 --
The Computer Control Patent describes one such technique.
For a typical steel wor~piece, rolling speeds leaving the
last mill stand F7 will be 1000 to 3000 feet per minute
and corresponding temperatures will range from 1600F to
170pF. The transit times for the F6-F7 space typically
- are 0.~ to 1.5 seconds. For each interstand space, values
for the workpiece temperature entering that space and the
workpiece velocity while traversing that space can be
calculated and stored by the computer 51.
A further objective of the rolling schedule
calculation is to achieve approximately uniform elongation
in the successive reductions. A method for accomplishing
this through proper choice of (strip) reductions is
- described in the Shape Control PatentO Computer calculated
reduction schedules employing this or similar strategies
can avoid (extreme) tight e~dge tension distributions.
Manually controlled ~ cannot be relied upon to
avoid undesirable tension distributions.
The thickness reduction schedule and/or roll
bending techniques are usually employed in a manner to
produce a desired tension distribution. By erring in
the direction of tight center conditions, excessively
high local tensions are avoided.
Mean tension levels have been calculated for each
interstand location. Referring to Fig. 9, typical
conventional interstand tension levels are illustrated
by the line marked "An. These tens~ion levels between mill
stands Fl and F2 are approximately 500 psi and increase
tp approximately 1050 psi between mill stands F6 and F7.
Presently available mill control equipment automatically
maintains tension in the strip at preselected low levels
such as that shown in Fig. 9. Ten~ions calculated and
used in accordance with this invention will fall into the
range illustrated by the shaded area bounded by curves C
and D in Fig. 9.

~5J~74~3
21-DSS-2505
- 20 -
Fig. 10 is a block diagram representation of
the technique by which the tension levels according to
the invention are calculated and by which the hot strip
mill is controlled to achieve desirable flatness properties
in a strip 22. The computer 51 is indicated in outline
form. As part of the computer 51, a calculator 62
determines the maximum allowable per uni~ width
reduction (~ W/W) based on a predetermined acceptable
width change ~ W. A calculator 64 determines the maximum
allowable length increase (~ L/L) based on the equation:
(5) ~ L/L = 2 (~ W~W).
Rnowing the properties of the material being
rolled, its temperature, and its rolling speed, axial
strain rate, ea,can be determuned from the equation-
(6) ea= 2 (~tW/W) = (~ L/L)
wherein,
t - time required for a point on the strip
to traverse the interstand space.
Equation (6) ~g solved by the calculator 66.
Ba~ed on the value of eacalculated by the
calculator 66, a calculator 68 solves an equation like
that of equation (1) to determine axial stress. The
calculator 6a can be programmed in advance for different
values of Rl and K2 depending upon the properties of the
particular material being rolled, i'ts temperature, its
strain level and so forth. In essence, equations (2),
(3), (4) and other similar appropriate equations can be
developed for all expected operating temperatures and
materials and the equations, or equivalent tables, can be
stored in the computer 51. Accordingly, during rolling
of a particular strip 22, the calculator 68 will only
ha~e to select the proper stored relationship to determine
axial stress as a function of axial strain rate.

~151~4~3 ~
- 21-DSS-2505
- 21 -
Axial stress is tra~slated into ir.terstand
tension through multiplication, in calculator 70, by the
cross sectional area of the strip. The interstand
tension is then applied as a re'erence to a normally
included tension cont~ol means o' any suitable type
~nown in the art, for example, cons'~nt .ension loopers
54 ~Fig. 1). The tension establishea ~y ~he constant
tension loopers is deten~ined by torque motors and by
the zngle made by the looper znd stri?. This angle is
io maintained constant by adjustins crive motor speed with
speed control means 50 to maintain co~s'ant loo?er
position. Other means such as airect control o' tension
by interstand tensiometer working through stand speed
control can also be employed . During acceleration of the mill
to stezdy -~tzte rolling speeds, the permissible in~er-
stand tension levels are recalculated and tension levels
zre raised to the maximum permissible extent after ezch
recalculation. The ~ethodology described schematically
in Fig. 9 is repezted separztely for each interstand
space in which high tension levels are desired. Typioally,
this woula ~e between mill stands F4-F5, F5-F6 and F6-F7.
Tension levels between the ~receedi~g m~ll stands would
be set accoraing to presently eY~isting techniques.
Exam~le
-
Steel having 0.09~ car~on and 0.~0% mzng2nese
exhibited the 'ollowins s.ress ve~sus strain-rate
relationship at 1700F, for uni'orm tension:
(7) cr = 10200 + 11001n(ea).
Allowing ~or the worst czse tension profile simil2r to thzt
~o in ~ig. 6, t~e re7ztionship is ~djusted ~o:
(8) C~ = 7830 + 8001n(ea).
It will ~e assumed thzt 50% o~ a ~otal width
reduction of 0.;0 inch is allowab~e in s?ace F6-~7 and
that the strip 22 is 80 inches wide, C~lculator 62 will
determ~ne the max_mum allowzble pe--~nit width reduction
.*~
,, .. , .......... ,, .. .. ... , .......... ,. _ ._ .....................................................

- ~151748
(
21-DSS-2505
- 22 -
as 0.003125. Calculator 6~ will compute the maximum per-
unit allowable length increase as 0.00625. Assuming that
mill stands F6 and F7 are 18 feet apart and strip is
traversing the F6-F7 space at 2000 feet per minute, an
element of strip would require 0.54 seconds to travel
from F6 to F7. The calculator 66 will calculate the
axial strain-rate during this interval as 0.01157 per-
unit per second.
Rnowing the material and temperature, the
calculator 68 will select from among stored relationships
the relationship given by equation (8), in this example,
and calculate the allowable axial stress at 4263 psi.
Accordingly, an interstand tension reference corresponding
to an axial stress of 4263 psi could be applied to the
interstand tension regulating means 54. This procedure
would be repeated for all interstand spaces, resulting
in a tension practice illustrated as curve B in Fig. 7.
Provided the interstand tension levels are
m2intained at or slightly below the tension levels
calculated in this manner, width reductions will be
acceptable and waviness problems will be reduced. Since
width reductions due to tension are predictable, they
ob~iously may be compensated by corresponding increases
in the strip width produced in the roughing mill 10.
Equally obvious is the fact that higher tensions
need not be employed where strip dimensions are such that
flatness problems are not usually e'ncountered.
Although the invention has been described in
its prçferred form with a certain degree of particularity,
it will be understood that the present disclosure of the
preferred embodiment has been made only by way of example
and that numerous changes may be resorted to without
departing fxom the true spirit and scope o~ the invention
as hereinafter claimed. It is intended that the patent
shall cover, by suitable expression in the appended claims,
whatever features of patentable novelty exist in the
invention disclosed.