FIELD OF THE INVENTION
The present invention relates to required determination of no load gap for finishing
stands in hot strip mills and ,in particular, to a method for determining such no load roll
gap for finishing stands in roiling mills in order to obtain the desired thickness in a hot
strip mill. The method advantageously and effectively utilizes the provision of no load roll
gap (mill set up) residing in a computer (PC) and acquiring rolling parameters as inputs
from a data acquisition system based on which the no load roll gap is calculated. The
calculated roll gap identified following the method as above can be further displayed to
the speed cabin operator for adjusting the roll gap so as to ensure that the desired
target thickness is achieved during operation of the roll mill.

BACKGROUND ART
It is well known that in a hot strip mill, strips of different thicknesses and width are
rolled from slabs. Usually the hot strip mills are known to consist of three roughing
stands and six finishing stands. The first roughing stand is usually provided as a
combination horizontal stand and vertical stand while the other two roughing stands are
four high horizontal stands. There is a delay table after the roughing stand, one coil box
and a crop shear at the end of the delay table. The finishing stand usually comprise of
six numbers of four high finishing stands and two hydraulic down coders.
It is also known in the art that the roll gaps for finishing stands in such conventional
rolling mills are usually set based on human judgment. Such use of human judgment to
set the roll gap to the finishing stands is necessarily subject to human error and
consequently, after the rolling is completed the thickness achieved are usually found to
have deviated from the desired target thickness. Moreover, in the conventional practice
it was not possible to ascertain or monitor that the roll force develop during rolling does
not exceed the rated capacity of the rolling stand which in turn can lead to tripping of
the rolling stand drive due to excess load and consequential loss of mil! availability.
Thus in a conventional rolling mill the no load gap is determined either based on
operator's judgment or based on other types of similar non-reliable manner of
determination of the no load roll gap. Accordingly therefore, such conventional manner
of determining the no load roll gap is found to suffer from drawback /disadvantages
which include the following:-

a) the operator has no idea about finishing stand entry temperature and he
adjusts the roll gap based on his own perception;
b) since the roll gap is required to be set in a short interval of time, operator
can commit error in mentally calculating the roll gap;
c) no provision for desired predicting whether the rolling stand motor will trip
due to such roiling load;
d) unequal distribution of roll force in the finishing stands;
e) provision of retrieving the data for strips rolled earlier was not possible;
f) when rolling new grade of steel there is huge stabilization time as there is no
prediction of roll force.
It is thus apparent from the above that the conventional method of providing no roll gap
in finishing stands of rolling mills which is basically carried out based on operator's
judgment is subject to various limitations and concerns which lead to failure in achieving
the desired target thickness during the rolling operation. There is thus a continuing need
in the art to develop method whereby the no load gap of the finishing stands could be
ascertained reliably to favour setting of the mill to achieve the target thickness.
OBJECT OF THE INVENTION
It is the thus the basic object of the invention to provide for a method for ascertaining
the no load roil gap for different finishing stand in roiling mills to obtain the desired
target thickness and which would avoid the conventional manner of roil gap setting
based on human judgment.
Yet further object of the present invention is directed to a method for calculating for no
load roll gap in such a way that all the rolling stands are equally loaded and the full
capacity is utilized.
Yet further object of the present invention is directed to calculate the roll gap based on
finishing stand entry temperature which is preferably measured by a pyrometer or
calculated in response to the roughing stand exit temperature.
Another object of the present invention is directed to provide a method for calculating
the no load roll gap in hot strip mill during hot rolling process which could be carried out
to favour achieving target thickness by way of providing the operator with the required
inputs about finishing stand entry temperature and favour necessary adjustment in the
roil gap based thereon.

Another object of the present invention is directed to provide a method for calculating
the no roll gap in hot strip mill which would avoid problems of human judgment based no
load roll gap settings and enable setting the roll gap effectively in a short interval of time
without concerns of human error.
Another object of the present invention is directed to provide a method for calculating
the no load roll gap in a hot strip mill, which would favour prediction of whether the
rolling stand motor can be subjected to tripping due to excess rolling load.
Yet another object of the present invention is directed to a method of ascertaining the
no load roll gap of finishing stands in a rolling mill, which would avoid problems of
unequal distribution of roil force in the finishing stands.
Yet further object of the present invention is directed to the development of a method
for ascertaining the no load roll gap of finishing stand in rolling mill which would have
provision for retrieving data of strips rolled earlier for effective achievement of target
thickness during the subsequent rolling operations.
A further object of the present invention is directed to a method for ascertaining the no
load roll gap in finishing stands of hot strip mills which would enable the prediction of roll
force and favour reduction of stabilization time when roiling of new grade of steel.
SUMMARY OF THE INVENTION:
Thus according to the basic aspect of the present invention there is provided a method
for determining no load roll gap in a hot strip mill for achieving target thickness during
rolling operations comprising:
(i) using a reference mill set-up based on roughing stand exit temperature finishing
entry temperature, roll force and stand exit temperature for each stand in a suitably
programmable PC;
(ii) acquiring inputs form a data acquisition system on the roll mill performance and
based thereon,
(iii) determining the no load gap for the finishing strands in order to obtain the desired
target thickness in a hot strip mill.

Importantly, in the above method the roll gap is determined such that all the rolling
stands are equally loaded and the full capacity is utilized. Moreover, the roll gap is
determined based on the finishing stand entry temperature which is calculated based on
the roughing stand exit temperature or measured by a pyrometer.
In accordance with a preferred aspect the method further comprises:
determining the roil force at each stand based on parameters for determining pressure
distribution at roll bite for a single stand, determining strain rate and formulation for
rolling load, derivation of torque and power;
determining temperature before entry of finishing roll, determining temperature after
each stand ;
obtaining there from the roll force and temperature of entry for each stand of the
finishing stands.
In the above method the finishing entry temperature can be determined for coilbox and
non-coilbox mode using radiation heat transfer and convection cooling. Also importantly,
the method takes into account the mill spring when setting strip thickness after each
stand.
Also in the above method the reduction at different stands are varied within mill safe
limits preferably maximum allowable force, torque and power such that desired output
gauge is obtained as per specified target thickness which is displayed as the output.
In accordance with a preferred aspect the method is carried out in a roll mill having
three roughing stands and six numbers of finishing, the first roughing stand (RO/VO)
being a combination horizontal stand and a vertical stand and other two roughing stands
(R1 & R2) and four high horizontal stands, a delay table after R2 stand , one coil box and
a crop shear at the end of the delay table , six numbers of four high finishing stands (F1
to F6) and two hydraulic down coilers,
Importantfy, the operative parameters relevant to determining the no load roll gap in
the rolling mill indude F3 stand position reference. Motor (Rear) side in Hydraulic screw
down position regulation system, F3 stand position reference, Works (Front) side, in
Hydraulic screw down position regulation system, F4 stand position reference- Motor
(Rear) side in Hydraulic screw down position regulation system, F4 stand position
reference- Works (Front) side in Hydraulic screw down position regulation system, F5

stand position reference- Motor (Rear) side, in Hydraulic screw down position regulation
system, F5 stand position reference- Works (Front) side, in Hydraulic screw down
position regulation system, F6 stand position reference- Motor (Rear) side, in Hydraulic
screw down position regulation system, F6 stand position reference- Works (Front) side,
in Hydraulic screw down position regulation system, F3 stand actual position- Motor
(Rear) side. Signal from LVOT, F4 stand actual position- Works (Front) side. Signal from
LVDT, F5 stand actual position. Motor (Rear) side. Signal from LVDT, F5 stand actual
position- Work (front) side. Signal from LVDT, F6 stand actual position, Motor (Rear)
side. Signal from LVOT, F6 stand actual position, Works (Front) side. Signal from LVDT,
F1 stand total roll force, F2 stand total roll force, F3 stand total roll force, F4 stand total
roll force, F5 stand total roll force, F6 stand total roll force, F1 stand speed, F2 stand
speed, F3 stand speed, F4 stand speed, F5 stand speed, F6 stand speed, F6 Thickness,
R2 temperature, F1 temperature, F6 temperature, Thickness at the entry of finishing
stand, Target thickness, Width at the entry of finishing stand, Material grade (slab
Chemistry),and Work roll diameter for F1 to F6 stand.
The method thus effectively carries out (a) roll force determination involving pressure
distribution equations at roll bite for a single stand including (i) determination of strain
rate , (ii) using formulations for expressions for rolling load and (iii) derivations of
expressions for torque and power , (b) thermal determinations involving (i)
determination of temperature before entry to finishing group (ii) determination of
temperature after each stand and (c) combination of roil force and thermal
determinations parameters for each stand and extending the single stand determinants
to all other of the finishing stands.
Advantageously, the reductions at different stands are varied within mill safe limits
preferably the maximum allowable force, torque and power such that desired output
gauge is obtained as per the specified target thickness which is displayed as the output.
Thus, it is possible by way of the present invention to provide for a rolling mill having an
improved method avoiding complete reliance on human judgment to calculate the no
load roll gap based on various rolling parameters, comprising Roll Force , Thermal
temperature determination, combination of roll force and thermal determination for
finishing stands to achieve no load roll gap setting for desired thickness. The method of
the invention can be advantageously carried out in a hot rolling mill having required
data acquisition system based on preferably a fast programmable controller.

DETAILED DESCRIPTION OF THE INVENTION:
The details of the invention, its object and advantages are explained hereunder in
greater details in relation to the non-limiting exemplary illustrations as per the following
accompanying figures wherein :
Figure 1: is a lay out of a conventional hot strip mill; and
Figure 2: is a schematic diagram of hot rolling deformation.
Reference is first invited to Figure 1 which illustrates a conventional hot strip mill, which
is adapted to provide strips of different thicknesses and width rolled from slabs. As
illustrated in the figure such a hot strip mill usually consists of three roughing stands and
six finishing stands. Figure 1 shows the layout of a typical conventional hot strip mill.
The typical layout shows three different roughing stands consisting of Horizontal-Vertical
Stand combination (1), Reversing Roughing Stand (2), Non-reversing roughing stand
(3), Coil Box (4), Crop Shear (5) and six numbers of non-reversing Finishing Stands (6).
Last four finishing stands hydraulic cylinders (7) along with mechanical screw-down for
roll gap adjustment whereas the first two finishing stands have only mechanical screw-
down systems for roll gap adjustment. The First roughing stand (Ro/V0) is a combination
horizontal stand and a vertical stand. The other two roughing stands (R1) and (R2) are
four high horizontal stands. There is a delay table after R2 stand, one coil box and a crop
shear at the end of the delay table. There are six numbers of four high finishing stands
(F1) to (F6) and two hydraulic down coilers.
In such conventional roll mills as illustrated in Figure 1, the roll gaps for F1 to F6 are set
based on human judgment. Consequently therefore after the rolling is completed the
thickness achieved is found to deviate from the target thickness.
In order to avoid the above limitations and disadvantages of such human error prone
manner of setting of no load roll gap in finishing stands of rolling mills, the method of
the invention advantageously and effectively provides for selective relevant input
parameter based calculation of no load roll gap to be set so as to achieve the desired
target thickness. The manner of effecting the no load roll gap in accordance with the
invention is further detailed hereunder.
The method of the invention is described hereunder under the following sections:

i) Parameters required for the calculation of no load roll gap in accordance
with the invention;
II) Roll Force determination (Determination of strain rate, Formulation of
expressions for rolling load and expression for torque and power);
in) Thermal determination (Determination of Temperature before entry to
Finishing Group, Determination of temperature after each stand;
iv) Combination of roll force and thermal model for finishing stands

v) Formulation of Methodology
vi) Mill Schedule determination.
Parameters required for model calculation are as detailed hereunder in Table 1


Roll Force Determination
(a) Formulation of pressure distribution equations at roll bite for a single stand
Reference is invited to accompanying Figure 2 which illustrates the flat rolling hot
deformation process of strip in a single stand.
Figure 2 is a schematic diagram of hot rolling deformation process. In this figure, the
rolled material strip (8) is deformed between two rolls (9). The distance between centre
of roll (10) and exit section of strip (11) is the roll radius. The strip is rolled between the
entry Section (12) and exit section (11). The angle between the entry and exit section is
called angle of bite (13) which is represented by symbol 9. At the entry of the feed
material to roll bite, the tangential speed of roll is more than strip speed. At the exit, the
tangential speed of roll is less than strip speed. There is a section in the bite zone where
both tangential speed of roll and strip speed are equal. This section is called neutral
section. The zone of roll bite from entry to neutral point is called entry zone and from
neutral point to exit is called exit zone. The angle between exit section and neutral
section is called neutral angle (14). The thickness of rolled strip before entry to the roll
bite (15) is represented by symbol hi. The thickness of strip after exit from the roll bite
(16) is represented by symbol h2. The difference between hi and h2 is called draft which
is represented by symbol Ah. The roll radius (17) is represented by symbol R. Thickness
of strip at an analysis section (18) is represented by symbol h. The angle between the
exit section and analysis section (20) is represented by symbol . An infinitesimally small
angle (21) is taken from the analysis section towards entry zone for calculation of
pressure. The pressure of roll on the strip at this infinitesimally small section (22) is
represented by symbol, s.
The roll bite angle 9 is given by:

At the entry of the feed material to roll bite, the tangential speed of roll is more than
strip speed At the exit, the tangential speed of roll is less than strip speed. There is a
section in the bite zone where both tangential speed of roll and strip speed are equal.
This section is called neutral section. The zone of roll bite from entry to neutral point is
called entry zone and from neutral point to exit is called exit zone.
The pressure distribution equations for hot rolling as given by Sim's is given by


where
k= mean resistance to plane homogeneous deformation
h= thickness at any section of roll bite
Equation (2) is valid for exit zone and equation (3) is valid for entry zone
(i) Determination of strain Rate
Strain rate is given by the expression,

(n) Formulation of expressions for rolling load
Rolling load can be expressed mathematically as

Where b is the width of the material. After substituting values of s/k given in equation
(2) and (3) and taking k as mean resistance to deformation, the equation for P become, -,


Q is a geometric factor. ..umeric values of Q for different R/h2 and reductions are
available in tabular form.
Value of k at different strain rate for CRNO grade has already experimentally determined
in Thermo-mechanical simulator (Gleeble) at R & D Centre for Iron and Steel, RanchL If
new material is used, then its flow stress characteristics curves can be experimentally
determined in Gleeble.
In place of Roll radius R, the deformed roll radius R' is taken. The deformed roll radius is
given by Kitchkok's equation as

(As, for steel rolls E= 2.07X106 Kg/cm2 and v =0.35)
It can be noted here that Equation (6) and (7) are inter-dependant. An iterative method
is used to determine the roll force. Initial calculations are made with R' = R and then R'
is determined. Again roll force is calculated based on new R and R' is calculated again
and so on. This method is repeated till there is a very negligible difference between the
previous and new values of roll radius is obtained.
(iii) Derivations of expressions for torque and power
Orowan's torque equation is given by

where

g is the modified resistance to deformation given by g=xk. The value of x for different
reductions is experimentally determined and is available in literature.
Horse power is given by


where, N= trpm and m is the iever arm.
m is the length of (ever arm and is given by,

where r is the reduction.
Thermal Determination:
For setting model, temperature at tail end of strip is considered. This is because
temperature at tail end of strip is minimum, whether coil box is used or not. Designing
setting speed based on minimum temperature will give the desired gauge at higher
temperature also unless metallurgical phase transformation takes place (as in HRNO
grade).
(a) Determination of Temperature before entry to Finishing Group:
There is radiation heat transfer between R2 and Finishing stand. Coil passes Delay table,
coil box (not always), crop shear and Descaler before it reaches finishing stands.
Let TR2 = Temp, of hot bar at tail end at R2 in °C
Temperature drop due to radiation heat loss is given by,

where 1= length of delay table = 65m
vd= speed of bar delay table = 3.5 m/sec
tcB= time delay in coil box. This time is very less. An approximate value will be assumed.
t