Method for automatically controlling width of slab during hot rough-rolling thereof

A method for automatically controlling the width of a slab during hot rough-rolling thereof, which comprises: arranging a pair of horizontal broadening rolls each having at least one annular projection in a hot roughing mill train comprising a plurality of roll stands; calculating an amount of roll gap correction of said pair of broadening rolls on the basis of the variation in the width of said slab during hot rough-rolling on said hot roughing mill at the entry of said pair of broadening rolls; and, controlling the roll gap of said pair of broadening rolls in response to said amount of roll gap correction; thereby automatically controlling the width of said slab during hot rough-rolling thereof to a prescribed value at a high accuracy in accordance with the finishing width of a steel strip, and at the same time, automatically correcting variations in the width of said slab during hot rough-rolling thereof at a high accuracy.

FIELD OF THE INVENTION 
The present invention relates to a method for automatically controlling the 
width of a slab at a high accuracy to a prescribed value during hot 
rough-rolling thereof, and at the same time, automatically correcting 
variations in the width of the slab at a high accuracy during hot 
rough-rolling thereof. 
BACKGROUND OF THE INVENTION 
A slab fed as the material to be rolled to a hot roughing mill of a hot 
strip mill has conventionally been manufactured by slabbing a steel ingot. 
Since, in the slabbing process, the slab width has been determined with 
the finishing width of a steel strip in view, the amount of slab edging by 
a hot roughing mill (i.e., the difference between the width of the slab 
fed to the hot roughing mill and the finishing width of a steel strip) has 
been relatively small as from about 10 to about 20 mm. 
In the meantime, the continuous casting process which has various 
advantages over the slabbing process has recently been industrialized and 
has become popular in many applications, and this has made it difficult to 
feed many kinds of slabs with different widths to a hot roughing mill. The 
reason is that, in the continuous casting process, it is impossible to 
alter the slab width unless the mold is replaced, and this mold 
replacement causes a serious decrease in the productivity of slabs by the 
continuous casting process. As a result, the amount of slab edging by a 
hot roughing mill has largely increased to a value of from about 50 to 
about 75 mm. 
In order to manufacture a steel strip at a satisfactory width accuracy by a 
hot finishing mill under such circumstances, it is particularly important 
to control the width of a slab during hot rough-rolling thereof. Major 
factors causing the occurrence of variations in the slab width during hot 
rough-rolling of the slab include those based on the slab fed to the hot 
roughing mill, and those based on heating and hot rough-rolling of the 
slab. Factors based on the slab fed to the hot roughing mill include the 
variation in the thickness and the width of the slab, the variation in 
slab dimensions caused by the local scarfing of the slab, and the 
variation in deformation resistance caused by the variations in the 
chemical composition of the slab. Factors based on heating of the slab 
are, for example, skid marks and the variation in deformation resistance 
caused by the non-uniformity of heating temperature in the heating 
furnace. Factors based on hot rough-rolling of the slab include the 
broadening of the slab width during rolling by horizontal rolls of the hot 
roughing mill, and the local narrowing of the slab width at the top 
portion and the bottom portion of a slab caused by the metal flow during 
rolling by vertical rolls of the hot roughing mill. 
With reference to these various causes mentioned above, the state of 
variations in the slab width in the course of hot rough-rolling of a slab 
are shown in FIG. 1. In FIG. 1, (1) is the top portion of the slab; (2) is 
the middle portion of the slab; and, (3) is the bottom portion of the 
slab. As shown in FIG. 1, during hot rough-rolling in general, a serious 
narrowing of width occurs at the top portion (1) and the bottom portion 
(2) of the slab, and a variation in the width is observed also at the 
middle portion (2) of the slab. 
There is conventionally known a method for correcting variations in the 
slab width during hot rough-rolling which comprises controlling the slab 
width principally by adjusting the roll gap of the vertical rolls of a hot 
roughing mill in response to the variation in the slab width. The 
following methods and apparatus have been proposed: 
(1) A method, disclosed in Japanese Patent Provisional Publication No. 
90,560/75 dated July 19, 1975, which comprises: 
detecting the width of a slab transferred to a hot roughing mill provided 
with vertical rolls by means of a slab width detector installed at the 
entry or at the exit of said hot roughing mill; 
calculating the deviations of the values thus detected from the target slab 
width at the entry or at the exit of said hot roughing mill; and, 
controlling the slab width by adjusting the roll gap of said vertical rolls 
in response to said deviations (hereinafter referred to as the "prior art 
(I)"). 
(2) An apparatus, disclosed in Japanese Patent Publication No. 34,029/77 
dated Sept. 1, 1977, which comprises: 
a slab width measuring device for measuring the width of a slab at the exit 
of vertical rolls of a hot roughing mill in accordance with signals from a 
rolling load detector of said vertical rolls and a roll gap detector of 
said vertical rolls; 
a slab width calculating device for performing a predicting calculation of 
the slab width at the exit of horizontal rolls of the hot roughing mill in 
accordance with the amount of slab width broadening caused by said 
horizontal rolls previously calculated and the signal from said slab width 
measuring device; 
a slab width setting device for calculating a new slab width setting value, 
which predicts the effects acting on the finishing width of a steel strip 
at the final roll stand of a hot finishing mill, with the use of the width 
correcting coefficient of the steel strip at the exit of the final roll 
stand of the hot finishing mill and the width correcting coefficient of 
the slab at the exit of the final roll stand of the hot roughing mill; 
and, 
a roll gap correction calculating device for calculating a roll gap 
correction value for the vertical rolls on the basis of signals from said 
slab width calculating device and said slab width setting device 
(hereinafter referred to as the "prior art (II)"). 
However, both the prior arts (I) and (II) presented above, in which the 
slab width is controlled during hot rough-rolling by adjusting the roll 
gap of vertical rolls, have the following problems: 
(a) Control of the slab width by vertical rolls increases the ratio of crop 
loss occurring in the slab; 
(b) For the purpose of increasing the control accuracy of slab width, it is 
desirable to effect adjustment of the slab width by the vertical rolls in 
the downstream of the hot roughing mill train as far as possible. The slab 
thickness decreases, on the other hand, toward the downstream of the hot 
roughing mill train. Adjustment of the slab width by the vertical rolls in 
the downstream of the hot roughing mill train may therefore cause buckling 
of the slab under the effect of the vertical rolls; and, 
(c) As compared with horizontal rolls, vertical rolls are poor in the 
accuracy of roll gap adjustment and the roll gap response characteristics 
because of their structure. The control accuracy of slab width by the 
vertical rolls is therefore lower than that by the horizontal rolls. 
SUMMARY OF THE INVENTION 
A principal object of the present invention is to provide a method for 
automatically controlling the width of a slab during hot rough-rolling 
thereof to a prescribed value at a high accuracy in accordance with the 
finishing width of a steel strip. 
Another object of the present invention is to provide a method for 
automatically correcting variations in the slab width during hot 
rough-rolling at a high accuracy. 
An additional object of the present invention is to provide a method for 
hot rough-rolling a slab, which gives a smaller ratio of crop loss. 
In accordance with one of the features of the present invention, there is 
provided a method for automatically controlling the width of a slab during 
hot rough-rolling thereof, which comprises: 
arranging a pair of horizontal broadening rolls each having at least one 
annular projection in a hot roughing mill train comprising a plurality of 
roll stands each having a pair of vertical rolls and a pair of horizontal 
rolls; 
calculating an amount of roll gap correction of said pair of broadening 
rolls on the basis of the variation in the width of said slab during hot 
rough-rolling by said hot roughing mill, at the entry of said pair of 
broadening rolls; and, 
controlling the roll gap of said pair of broadening rolls in response to 
said amount of roll gap correction; 
thereby automatically controlling the width of said slab during hot 
rough-rolling thereof to a prescribed value in accordance with the 
finishing width of a steel strip, and at the same time, automatically 
correcting variations in the width of said slab during hot rough-rolling 
thereof.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
With a view to solving the above-mentioned problems involved in the 
conventional method and apparatus for automatically controlling the width 
of a slab during hot rough-rolling thereof, we carried out extensive 
studies, and as a result, obtained the following finding: 
When locally reducing a slab by horizontal rolls of a hot roughing mill, 
metal flow in the longitudinal direction of the slab is restrained by the 
portion of slab not rolled. Consequently, the slab is hardly rolled in the 
longitudinal direction, but mostly rolled in the width direction. It is 
therefore possible to conduct broadening of a slab width and correction of 
the slab width, easily and accurately, by locally reducing the slab during 
hot rough-rolling thereof, by a pair of horizontal rolls each having at 
least one annular projection. 
The present invention was made with reference to the above-mentioned 
finding, and the method of the present invention comprises: arranging a 
pair of horizontal broadening rolls each having at least one annular 
projection in a hot roughing mill train comprising a plurality of roll 
stands, and, during hot rough-rolling of a slab by said hot roughing mill, 
adjusting the roll gap of said pair of broadening rolls in response to 
variations in the width of said slab, thereby automatically controlling 
the width of said slab during hot rough-rolling thereof to a prescribed 
value at a high accuracy in accordance with the finishing width of a steel 
strip, and at the same time, automatically correcting variations in the 
width of said slab during hot rough-rolling thereof at a high accuracy. 
The method for automatically controlling the width of a slab during hot 
rough-rolling thereof of the present invention is described in detail with 
reference to the drawings. 
FIG. 2 is a schematic descriptive drawing illustrating an embodiment of the 
method of the present invention. In FIG. 2, 1 is a heating furnace; 2 is a 
slab heated to a prescribed temperature in the heating furnace 1; 12 is a 
conventional hot roughing mill comprising a plurality of roll stands; and 
6 is a conventional hot finishing mill, comprising a plurality of roll 
stands, arranged on the exit side of the final roll stand of the hot 
roughing mill 12. Each of the roll stands of the hot roughing mill 12 
includes a pair of vertical rolls 3 and a pair of horizontal rolls 4, and 
the pair of horizontal rolls 4 are located downstream of the pair of 
vertical rolls 3. Some of the pairs of horizontal rolls 4 are equipped 
with backup rolls 4'. FIG. 2 shows a hot roughing mill comprising five 
roll stands, but it is needless to mention that the number of roll stands 
is not limited to five. The slab 2 heated to a prescribed temperature in 
the heating furnace 1 is rough-rolled by the hot roughing mill 12 into a 
bar, an intermediate product, and the bar thus obtained is then rolled by 
the hot finishing mill 6 into a steel strip, the final product. 
In FIG. 2, 5 are a pair of horizontal broadening rolls each having at least 
one annular projection (hereinafter referred to as the "broadening 
rolls"), arranged in the train of the hot roughing mill 12; 7 is a slab 
width detector for measuring the width of the slab 2 at the entry of the 
pair of broadening rolls 5, provided upstream of the pair of broadening 
rolls 5; 8 is a rolling pass schedule calculating device; 9 is a roll gap 
correction calculating device; and 10 is a roll gap controller for the 
pair of broadening rolls 5. 
Use of the horizontal broadening rolls each having at least an annular 
projection is emphasized. The pair of broadening rolls 5 is the most 
important feature of the present invention. 
FIG. 3 (A) is a front view illustrating the broadening roll 5 having one 
annular projection 11, for use in the present invention. The annular 
projection 11 is formed at right angles to the axial center of the 
broadening roll 5 along the circumference of the broadening roll 5. As 
shown in FIG. 3 (B), two annular projections 11 as mentioned above may be 
formed. In all cases, in order to effectively control the broadening of 
the width of the slab 2, the annular projection(s) 11 should satisfy the 
following two formulae: 
EQU .SIGMA.W.ltoreq.(Bar width)/2, and 
EQU H.gtoreq.(Reduction)/2, 
where, 
.SIGMA.W: total of the width "W" of at least one annular projection 11 of 
the broadening roll 5; and 
H: height of the annular projection 11. 
The pair of broadening rolls 5 are arranged within the train of the hot 
roughing mill 12. According to our experience, installation thereof before 
the roll stand in the downstream of the hot roughing mill train 12 as far 
as possible, gives better results when the manufactured bar has a larger 
thickness. FIG. 2 shows the case where the pair of broadening rolls 5 are 
arranged upstream of the No. 3 roll stand. 
The slab width detector 7 provided upstream of the pair of broadening rolls 
5 measures the width of the slab 2 at the entry of the pair of broadening 
rolls 5. As the slab width detector 7, an infrared type width gauge meter 
or a backlight type width gauge meter may be used to directly detect the 
width of the slab 2, or, as the slab width detector 7, a pair of vertical 
rolls (not shown) may be provided upstream of the pair of broadening rolls 
5 to indirectly detect the width of the slab 2 from the rolling load 
acting on said pair of vertical rolls and the roll gap of said pair of 
vertical rolls. In the latter case, the slab width, "B.sub.M in ", at the 
entry of the pair of broadening rolls 5 is calculated by the following 
formula: 
##EQU1## 
where, 
B.sub.M in : roll gap of the pair of vertical rolls, 
P.sub.E : rolling load acting on the pair of vertical rolls, and 
M: mill constant for the pair of vertical rolls. 
The rolling pass schedule calculating device 8 calculates a rolling pass 
schedule composed of a vertical reduction schedule for the several pairs 
of vertical rolls 3 of the hot roughing mill 12, a horizontal reduction 
schedule for the several pairs of horizontal rolls 4 of the hot roughing 
mill 12, and another horizontal reduction schedule for the pair of 
broadening rolls 5, from such parameters as the measured thickness and the 
measured width of the slab 2 to be fed to the hot roughing mill 12, the 
steel grade of the slab 2, the extraction temperature of the slab 2 from 
the heating furnace 1, and the target thickness and the target width of 
the bar to be manufactured, and stores the rolling pass schedule thus 
calculated. 
The roll gap correction calculating device 9 calculates the amount of 
correction of the roll gap for the pair of broadening rolls 5, established 
by the rolling pass schedule calculating device 8, on the basis of the 
deviations of the measured width of the slab 2 at the entry of the pair of 
broadening rolls 5, sent from the slab width detector 7, from the 
predicted slab width of the slab 2 at the entry of the pair of broadening 
rolls 5, included in the horizontal reduction schedule for the pair of 
broadening rolls 5, sent from the rolling pass schedule calculating device 
8. 
The roll gap controller 10 controls the roll gap of the pair of broadening 
rolls 5 in response to signals sent from the roll gap correction 
calculating device 9. 
In the method of the present invention, as shown in FIG. 4, the roll gap of 
the pair of broadening rolls 5 is adjusted on the basis of the deviations, 
".DELTA.B", of the measured width, "B.sub.M in ", of the slab 2 at the 
entry of the pair of broadening rolls 5, and the predicted width, "B.sub.C 
in ", of the slab 2 at the entry of the pair of broadening rolls 5, so 
that the width of the slab 2 at the exit of the pair of broadening rolls 5 
matches with the target width, "B.sub.C out ". 
In other words, when the slab 2 fed to the hot roughing mill 12 reaches the 
position of the slab width detector 7, the measured width, "B.sub.M in " 
of the slab 2 at the entry of the pair of broadening rolls 5 is detected 
by the slab width detector 7, and said detected value of the measured 
width, "B.sub.M in ", is sent to the roll gap correction calculating 
device 9. On the other hand, the predicted width, "B.sub.C in ", of the 
slab 2 at the entry of the pair of broadening rolls 5, set by the rolling 
pass schedule calculating device 8, is also sent to the roll gap 
correction calculating device 9, where the deviations, ".DELTA.B", of said 
measured width, "B.sub.M in ", from said predicted width, "B.sub.C in ", 
are calculated, and then, the amount of roll gap correction for the pair 
of broadening rolls 5 is calculated on the basis of said deviations, 
".DELTA.B". The amount of roll gap correction is calculated by the 
following formula: 
##EQU2## 
In the formula (1), ".DELTA.B.sub.C " is the amount of width broadening of 
the slab 2 at the exit of the pair of broadening rolls 5, and is 
calculated by the following formula: 
##EQU3## 
In the formulae (1) and (2): 
.DELTA.H.sub.C set : initially set reduction of the pair of broadening 
rolls 5; 
h: thickness of the slab 2 at the entry of the pair of broadening rolls 5; 
B: width of the slab 2 at the entry of the pair of broadening rolls 5; 
D: outside diameter of the broadening roll 5 including the annular 
projection thereof; and, 
C, n.sub.0 : constants dependent on the steel grade and the extraction 
temperature from the heating furnace 1 of the slab 2. 
The calculated value thus obtained of the amount of roll gap correction for 
the pair of broadening rolls 5 is sent to the roll gap controller 10, and 
the roll gap of the pair of broadening rolls 5 set by the rolling pass 
schedule calculating device 8 is controlled by the roll gap controller 10 
in response to said calculated value of the amount of roll gap correction, 
thereby accurately controlling the width of the slab during hot 
rough-rolling thereof to a prescribed value, and at the same time, 
accurately correcting variations in the slab width. 
FIG. 5 is a graph illustrating the experimental data showing the 
relationship between the amount of reduction and the amount of width 
broadening of the slab 2 in the case where the slab 2 is reduced by the 
pair of broadening rolls 5. Table 1 shows the rolling conditions of the 
slab 2 in this experiment. 
TABLE 1 
______________________________________ 
Rolling Rolling 
conditions 
conditions 
A B 
______________________________________ 
Steel grade of slab 
Low carbon Low carbon 
steel (C: steel (C: 
0.06 wt.%) 0.06 wt.%) 
Extraction temperature of 
slab from heating 1,250 1,280 
furnace (.degree.C.) 
Slab thickness (mm) 
190 205 
Slab width (mm) 900 1,250 
Outside diameter of broadening 
roll including annular 
1,100 1,160 
projection(s) (mm) 
Number of annular projections 
1 2 
Height of annular 
projection (mm) 40 30 
Width of annular production 
(mm) 300 400 
Revolutions of broadening 
roll having annular 
18.4 18.4 
projection(s) (rpm) 
______________________________________ 
In FIG. 5, the line connecting the marks "o" indicates the case where the 
slab is reduced under the rolling conditions "A" as given in Table 1, and 
the line connecting the marks ".cndot." represents the case where the slab 
is reduced under the rolling conditions "B" as given in Table 1. As is 
clear from FIG. 5, use of the pair of broadening rolls 5 permits effective 
broadening of the slab width in proportion to the amount of reduction in 
the both cases. 
The combination "a" (the portion enclosed by dotted lines in FIG. 2) of the 
slab width detector 7 and the pair of broadening rolls 5 may be any of the 
following combinations, in addition to that described above: 
(1) A width gauge meter or a pair of vertical rolls as the slab width 
detector 7; a pair of broadening rolls 5 capable of adjusting the roll 
gap, installed downstream of the slab width detector 7; and another pair 
of broadening rolls (not shown) not capable of adjusting the roll gap, 
installed downstream of said pair of broadening rolls capable of adjusting 
the roll gap; 
(2) A pair of broadening rolls not capable of adjusting the roll gap (not 
shown); a width gauge meter or a pair of vertical rolls, as the slab width 
detector 7, installed in the downstream of said pair of broadening rolls; 
and, another pair of broadening rolls capable of adjusting the roll gap, 
installed downstream of said slab width detector 7; and 
(3) A width gauge meter or a vertical roll as the slab width detector 7; a 
pair of horizontal rolls installed in the downstream of said slab width 
detector 7; and a pair of broadening rolls capable of adjusting the roll 
gap, installed in the downstream of said pair of horizontal rolls. 
The method of the present invention described above, which comprises 
measuring variations in the slab width at the entry of the pair of 
broadening rolls 5 by the slab width detector 7, and controlling the roll 
gap of the pair of broadening rolls 5 installed in the downstream of the 
slab width detector 7 in response to said variations in the slab width, is 
called the feed-forward control method. Now, the following paragraphs 
explain another control method called the preset control method, which 
comprises controlling the roll gap of the pair of broadening rolls 5 by 
predicting by calculation the variations in the slab width at the entry of 
the pair of broadening rolls 5 from such rolling conditions as the 
measured thickness and the measured width of the slab at the entry of the 
hot roughing mill 12, the steel grade of the slab, the extraction 
temperature of the slab from the heating furnace 1, the target thickness 
and the target width of the bar, and by presetting the roll gap of the 
pair of broadening rolls 5 on the basis of the result of said predicting 
calculation. In the preset control method, a slab width detector 7 is not 
necessary, since the slab width at the entry of the pair of broadening 
rolls 5 is predicted by calculation. 
The preset control method includes the following two control methods: 
(1) The tabulation of method, which comprises tabulation variations in the 
predicted slab width at the entry of the pair of broadening rolls 5, and 
presetting the roll gap of the pair of broadening rolls 5 on the basis of 
this tabulation; and, 
(2) The pattern calculation method, which comprises converting variations 
in the predicted slab width at the entry of the pair of broadening rolls 5 
into a pattern, and presetting the roll gap of the pair of broadening 
rolls 5 on the basis of this pattern. 
Both the tabulating method and the pattern calculation method are slab 
width control methods adapted to correct the narrowing of slab width 
occurring in top and bottom portions of a slab. 
The tabulation method is first described. 
The tabulation method comprises predicting by calculation the variation in 
the width of the slab 2 at the entry of the pair of broadening rolls 5 in 
accordance with the predicting formulae of slab width variation (3), (4), 
(5) and (6) described later; preparing a table on the basis of the results 
of said predicting calculation; entering said table into the rolling pass 
schedule calculating device 8 for storage; calculating the amount of 
necessary width broadening at the top portion and the bottom portion of 
the slab at the exit of the pair of broadening rolls 5 and the amount of 
roll gap correction for the pair of broadening rolls 5, by the roll gap 
correction calculating device 9, in accordance with the formulae (7), (8) 
and (9) described later, on the basis of the table stored in the rolling 
pass schedule calculating device 8; and, controlling the roll gap of the 
pair of broadening rolls 5 by the roll gap controller 10, on the basis of 
said amount of roll gap correction; thereby automatically controlling the 
width of the slab during hot rough-rolling thereof to a prescribed value 
at a high accuracy, and at the same time, automatically correcting 
variations in the width of the slab during hot rough-rolling thereof at a 
high accuracy. 
The predicting formulae of width variation of the slab 2 at the entry of 
the pair of broadening rolls 5 described above are as follows: 
##EQU4## 
in the above-mentioned formulae (3), (4), (5) and (6): 
i: pass number of the hot roughing mill; 
.DELTA.B.sub.Ti : width shortage in the slab width direction at the top 
portion of said slab after horizontal reduction in the i-th pass; 
.DELTA.B.sub.Bi : width shortage in the slab width direction at the bottom 
portion of said slab after horizontal reduction in the i-th pass; 
.DELTA.B.sub.E Ti : width shortage in the slab width direction at the top 
portion of said slab after slab width reduction in the i-th pass; 
.DELTA.B.sub.E Bi : width shortage in the slab width direction at the 
bottom portion of said slab after slab width reduction in the i-th pass; 
.DELTA.b.sub.Ti : width broadening in the slab width direction at the top 
portion of said slab after horizontal reduction in the i-th pass; 
.DELTA.b.sub.Bi : width broadening in the slab width direction at the 
bottom portion of said slab after horizontal reduction in the i-th pass; 
.DELTA.L.sub.Ti : width shortage in the slab longitudinal direction at the 
top portion of said slab after horizontal reduction in the i-th pass; 
.DELTA.L.sub.Bi : width shortage in the slab longitudinal direction at the 
bottom portion of said slab after horizontal reduction in the i-th pass; 
.DELTA.L.sub.E Ti : length of the dog bone at the non-stationary portion of 
the slab top portion after width reduction of said slab in the i-th pass; 
.DELTA.L.sub.E Bi : length of the dog bone at the non-stationary portion of 
the slab bottom portion after width reduction of said slab in the i-th 
pass; 
H.sub.i-1 : slab thickness at the entry in the i-th pass; 
B.sub.i-1 : slab width at the entry in the i-th pass; 
.DELTA.B.sub.Ei : slab width reduction in the i-th pass; 
.DELTA.H.sub.i : slab horizontal reduction in the i-th pass; 
.DELTA.B.sub.i : width broadening in the slab width direction at the 
stationary portion of said slab by horizontal reduction in the i-th pass; 
C.sub.1 .about.C.sub.8 : constants dependent on the steel grade of the 
slab, the slab extraction temperature from the heating furnace, the 
diameter of the vertical roll and other conditions; 
n.sub.1 .about.n.sub.10 : constants dependent on the steel grade of the 
slab, the slab extraction temperature from the heating furnace and other 
conditions; 
.alpha..sub.Ti : correction coefficient of elongation at the top portion of 
said slab; and, 
.alpha..sub.Bi : correction coefficient of elongation at the bottom portion 
of said slab. 
In ".DELTA.L.sub.E Ti " and ".DELTA.L.sub.E Bi ", the length of the dog 
bone at the non-stationary portion means the slab longitudinal length at 
the top and the bottom portions where the dog bone height varies. 
In ".DELTA.Bi", the width broadening in the slab width direction at the 
stationary portion of the slab means the amount of width broadening at 
portions other than the top and the bottom portions. 
The formula for calculating the amount of necessary width broadening at the 
top portion and the bottom portion of the slab at the exit of the pair of 
broadening rolls 5, and the formula for calculating the amount of roll gap 
correction for the pair of broadening rolls 5 mentioned above are as 
follows: 
The formula for calculating the amount of necessary width broadening at 
slab top portion ".DELTA.B.sub.C (lx)": 
##EQU5## 
The formula of the amount of necessary width broadening at slab bottom 
portion, ".DELTA.B.sub.C (lx)": 
##EQU6## 
provided that, in the above-mentioned formulae (7) and (8), the amount of 
width broadening at the exit of the pair of broadening rolls 5, 
".DELTA.B.sub.C ", is calculated by the following formula, as in the case 
of the aforementioned feed-forward control method: 
##EQU7## 
The formula for calculating the amount of roll gap correction for the pair 
of broadening rolls 5: 
##EQU8## 
In the formulae (7), (8) and (9) (refer to FIG. 6): 
.DELTA.B.sub.C : amount of width broadening at the stationary portion of 
the slab; 
.DELTA.B.sub.T : width shortage in the slab width direction at the top 
portion of the slab; 
.DELTA.B.sub.B : width shortage in the slab width direction at the bottom 
portion of the slab; 
.DELTA.L.sub.T : width shortage in the slab longitudinal direction at the 
top portion of the slab; 
.DELTA.L.sub.B : width shortage in the slab longitudinal direction at the 
bottom portion of the slab; 
L: longitudinal length of the slab; 
lx: longitudinal length of the top portion of the slab from the top end 
thereof; and, 
n: index approximating variations in the slab width at the top portion and 
the bottom portion of the slab. 
The procedure for preparing a table to be stored in the rolling pass 
schedule calculating device 8 is as follows. More specifically, rolling 
conditions such as the steel grade of the slab, the type of slab, the 
width of the slab, and the amount of slab edging, are classified, for 
example, as follows: 
______________________________________ 
Carbon steel 
Steel grade 
of slab Alloy steel 
Ingot-cast slab (slab manufactured by 
the slabbing process) 
Type of 
slab Continuously cast slab (slab manufactured 
by the continuous casting process) 
from 600 mm to under 900 mm 
from 900 mm to under 1,200 mm 
Slab width from 1,200 mm to under 1,500 mm 
from 1,500 mm to under 1,800 mm 
from 1,800 mm to under 2,100 mm 
from -25 mm to under 0 mm 
from 0 mm to under 25 mm 
Amount of from 25 mm to under 50 mm 
slab edging from 50 mm to under 75 mm 
______________________________________ 
A table is prepared on the basis of the rolling conditions as classified as 
mentioned above. Table 2 gives an example of a thus prepared table. 
TABLE 2 
______________________________________ 
Variation in width at 
slab top and bottom 
Rolling (mm) 
conditions .DELTA.B.sub.T 
.DELTA.L.sub.T 
.DELTA.B.sub.B 
.DELTA.L.sub.B 
______________________________________ 
amount from 50 to under 75 
20 1100 15 1000 
of from 25 to under 50 
10 900 7 850 
slab from 0 to under 25 
5 700 0 0 
edging from -25 to under 0 
0 0 0 0 
(mm) 
Steel grade of slab 
Carbon steel 
Type of slab Continuously cast slab 
Slab width (mm) from 1200 to under 1500 
______________________________________ 
Now, the pattern calculation method is described below. 
In the pattern calculation method, variations in the width of the slab 2 at 
the entry of the pair of broadening rolls 5 are calculated and converted 
into a pattern, by the rolling pass schedule calculating device 8, on the 
basis of the rolling conditions stored in the rolling pass schedule 
calculating device 8 and in accordance with the above-mentioned formulae 
for prediction (3) to (6). Furthermore, the amounts of necessary width 
broadening at the top portion and the bottom portion of the slab 2 at the 
exit of the pair of broadening rolls 5 are calculated and stored by the 
rolling pass schedule calculating device 8, on the basis of said 
variations in the width of the slab 2 converted into the pattern as 
mentioned above, and in accordance with the above-mentioned formulae (7) 
and (8). Then, the amount of roll gap correction for the pair of 
broadening rolls 5 is calculated by the roll gap correction calculating 
device 9 on the basis of said amounts of necessary width broadening at the 
top portion and the bottom portion of the slab 2 stored in the rolling 
pass schedule calculating device 8, and in accordance with the 
above-mentioned formula (9). Then, the roll gap of the pair of broadening 
rolls 5 is controlled by the roll gap controller 10 on the basis of said 
amount of roll gap correction, thereby automatically controlling the width 
of the slab during hot rough-rolling thereof to a prescribed value at a 
high accuracy, and at the same time, automatically correcting variations 
in the width of the slab during hot rough-rolling thereof at a high 
accuracy. 
The pattern calculation method, which calculates the amounts of necessary 
width broadening at the top portion and the bottom portion of the slab at 
the exit of the pair of broadening rolls 5 on the basis of the variations 
in the slab width converted into a pattern, permits more accurate control 
of the slab width than in the tabulation method. 
According to the method of the present invention, as mentioned above in 
detail, it is possible to accurately and automatically control the width 
of a slab during hot rough-rolling thereof to a prescribed value in 
accordance with the finishing width of the steel strip, and at the same 
time, accurately and automatically correcting variations in the width of 
the slab during hot rough-rolling thereof, thus providing industrially 
useful effects.