Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02305401 2000-03-31
~~ 72118
Method for deterrlining and controlling the material flow of
continuous-cast slabs
Description
The invention relates to a method for determining and
controlling the material flow of continuous-cast slabs, in
particular steel :labs, by monitoring and optimizing the
temperature on the>ir transport path between the continuous-
casting installation and the rolling mill.
For the operator of a continuous-casting installation
with connected rolling mill, and for projecting slab
continuous-casting finishing bays as a link between the
continuous-casting installation and the rolling mill, it is
becoming increasingly important to know the heat content
which is present i.n the slab which has just been cast or is
being temporarily stored, in order to bring the slab into a
material flow which corresponds to the heat content still
present therein in an economical optimum manner. Since a slab
which has just been cast has an inhomogeneous temperature
profile which, over a prolonged period, strives to achieve a
more homogenous temperature profile, it is not possible to
draw conclusions about the mean slab temperature using
measurable surface temperatures. Therefore, it is also
impossible to be certain of the slab temperature profile
CA 02305401 2000-03-31
' - 2 -
after a certain time, for example in order to bring the slab
to an optimum, homogenous rolling temperature via a reheating
fixture. Finally, the solidified slab which leaves the caster
passes through different transport and processing paths,
which each lead to different slab temperature profiles.
Differences in the' temperature profile arise depending on
whether the slab is transported on a roller table with or
without thermal insulation, whether one or more slabs are
stored in the stack, whether the slabs are stored in an open
slab yard or in an open or closed holding pit. Different
temperature profiles also result for slabs which have
undergone accelerated cooling in a water immersion basin
compared to those which have undergone slower cooling in a
water-spraying in~;tallation. It is therefore clear that it is
desirable to find and be aware of the cooling profile of the
various slabs, in order to use this knowledge in a targeted
manner for material monitoring and controlling the material
flow, which were hitherto carried out predominantly on the
basis of experience and tests.
In view of the above problems, the object of the
present invention is to find a method for determining and
controlling the material flow of continuous-cast slabs, in
particular steel ,labs, which enables the amount of heat and
the temperature profile of a continuous-cast slab on its path
between the contir..uous-casting installation and the rolling
mill to be determined and used in a targeted manner, in order
CA 02305401 2000-03-31
' _ 3 _
for the values found to be used in an existing
slab-monitoring s~~stem, in order to obtain a material flow
which is optimum in terms of energy, i.e. is economical and
safe.
To achieve' the object, it is proposed, according to
the invention, that to determine the amount of heat and the
temperature profile of the slab, starting from the known
temperature of the liquid phase at the mold exit of the
continuous-casting installation and given knowledge of the
physical parameters of the slab, the convective mixing of the
amount of heat contained in the slab and the time-dependent
heat loss from the inhomogeneously cooling slab to the
surrounding medium are calculated by means of a mathematical-
physical model, and the result of the calculation, if
appropriate together with the measured surface temperature of
the slab, is used to control the material flow in an existing
slab-monitoring system.
The proposal of the invention makes it possible to
guide a slab in a controlled manner through the various
material flows, such as warm charge rolling, hot charge
rolling, cold charge rolling or hot direct rolling, from the
continuous-casting installation into the rolling mill. It is
possible both to find the cooling profile of various slabs in
the stack and to determine the profile of cooling at the
surface of various slabs, in order to draw a conclusion
concerning the temperature in the interior of the slab using
CA 02305401 2000-03-31
_ 4 _
control measurements. The calculated values and additional
production data of. the installation can be used, for example,
to determine the size of the holding pit and, in operation,
to predict hot batches at different mean temperatures.
In a preferred configuration of the method according
to the invention, there is provision for the two-dimensional
finite element method to be used to calculate the
mathematical-physical model. Finite element calculation
methods enable a zTery wide range of operations to be
simulated, thus a~~sisting with design developments, handling
operations, sales and, in the present case, also the future
plant operator. In the design phase, the method is frequently
used to reveal anct minimize possible risks through structural
mechanics analyses>. It can be used to carry out deformation
and stress analyses, temperature calculations,
thermomechanical ~>imulations and also to determine
eigenfrequencies wind eigenforms, with the aim of structural
optimization. Simulations based on finite element
calculations are often demanded by plant operators as early
as the project phase and are frequently included in the
supply contract of: the plant as a fixed component of the
contract.
Calculatic>ns using the finite element method are also
carried out during the development of mathematical-physical
models which have to provide accurate results on-line within
CA 02305401 2000-03-31
- 5 -
a very short time, predominantly parameter studies, from the
results of which analytic formulae are then derived.
For the present invention, the two-dimensional finite
element method, tree finite difference method or software
using formulae derived from off-line studies are used to
calculate the mathematical-physical model.
A universal, commercially available finite element
package can be usE>d in off-line studies to implement the
method. On line, this package is probably too large and too
slow. Therefore, i_t is appropriate to use, i.e. program, a
method (this may also be a finite element method or the
finite difference method) which is specifically adapted to
the slab geometry (rectangular) and is therefore quick
enough. The on-line method can be checked using the off-line
finite element package.
The physical parameters of the slab used are
preferably the ter~iperature-dependent material values density
p, the specific heat cP, the thermal conductivity ~, and scale
properties.
According to the invention, to optimize the method,
the result of the calculation and the measured surface
temperature of the slab are linked to automation of the
material flow in the slab-monitoring system.
The invention advantageously makes it possible, by
means of the mathematical-physical model, preferably using a
finite element sirr~ulation or finite difference method, to
CA 02305401 2000-03-31
- 6 -
determine the temperature profile of slabs and stacks of
slabs of different. dimensions under specific cooling
conditions. Through evaluation of the profiles of the mean
slab temperature and selected surface temperatures over time,
it is subsequentl~r possible to make a good estimation of the
mean slab temperatures by measuring the surface temperature.
For example, the result of the method according to the
invention can be used to draw conclusions as to how many
hours a fixed mean slab temperature is maintained in the
finishing bay; it is possible to draw conclusions concerning
the entire temperature spectrum in the slab-monitoring
system. It has emerged that the method according to the
invention and the above-described calculation method are very
flexible in use and are suitable for achieving the object of
the invention, i.e. that of enabling economical and reliable
material flow between the continuous-casting installation and
the rolling mill. The invention is able to replace the
previous slab control method which was based on experience
and empirical values. The installations no longer have to be
overdimensioned for safety reasons, because with the method
according to the invention it is now possible to determine
and control the actual conditions for the material flow
between continuous;-casting installation and rolling mill.
The invention is easiest to explain with reference to
a practical example. In the example, it is assumed that a
plurality of continuous-cast slabs are stored in a stack in
CA 02305401 2000-03-31
an open holding p=Lt. The mean cooling profile of the various
slabs in the stag; is to be determined, as is the profile of
cooling at the surfaces of various slabs in the stack. The
aim of an application could be to determine the size of a
holding pit or to predict hot batches of slabs at different
mean temperatures during ongoing production.
Working on the basis of a model as described above,
by way of example thirteen slabs each with 420 elements are
discretized. It i:~ sufficient to model one half of a slab
given symmetrical boundary conditions and, for example, to
generate the finite element network in such a way that the
mean temperature and the time-dependent control of the
stacking operation can subsequently be determined with ease.
The simulation can be divided up as follows:
1. Monitoring of the temperature of the slab cross
section a~; it passes through the caster,
corresponding to the starting temperature profile for
each individual slab at the start of the stack.
2. Simulation of the stack of the individual slabs.
3. Simulation: of the cooling of the stack of slabs.
In the first substep, the solidification of the slab
in the caster is simulated in order to generate an entry
temperature profile of the slabs in the holding pit which is
close to reality. The material density, specific heat and
thermal conductivity are temperature-dependent.
CA 02305401 2000-03-31
_ g _
In the li<~uid phase, there is also convective heat
exchange, but thi;~ was not modeled. In order nevertheless to
simulate the temperature homogenization on the basis of the
convective mixing, instead the thermal conductivity was
increased by a fa<:tor of 100 compared to the solid phase. The
various water coo=ing operations in the areas of the primary
and secondary coo~_ing zones represent important boundary
conditions. The temperature range of possible surface
temperatures is d~_vided into sections of various heat
transfer types (st:able film evaporation, unstable area,
burn-out point, et:c.) on the basis of a heat transfer model,
since different approaches apply with regard to the heat
transfer coefficient for these areas. In some of these areas,
the heat transfer coefficient is also dependent on the
materials value of: the surface of the cooling body, this
applying, in the present case, in particular to highly
oxidized surfaces, for which the materials values of scale
are to be used.
The simul~~tion of the stack of slabs begins with the
introduction of tree first slab into the holding pit.
Thereafter, every 60 seconds the next slab is stacked on top
of the previous slab. The stacking operation ends when a cold
slab is laid on top of the twelve slabs which have hitherto
been stacked. The inherent weight of the cold slab reduces
the curvature of t:he top hot slab.
CA 02305401 2000-03-31
_ g _
After the first slab has been introduced into the
store, the corresponding elements of this slab are activated,
and the finite element simulation for this slab takes place
as early as in the holding pit. The second slab follows, and
the elements of s7_ab two are activated. This procedure
continues in a similar manner until the final, cold slab is
introduced into the store. The simulation of the entire stack
of slabs in the holding pit then begins. Here as well, the
heat transfer coefficients between the slab surfaces and the
environment form ~~ignificant boundary conditions. With the
exception of the bottom support surface, heat transfer
through air convection plus radiation is assumed for all
surfaces of the stack of slabs.
The air convection is calculated using specific
functions, since different heat transfer coefficients apply
for the horizonta7_ and vertical surfaces. At high
temperatures, there coefficients are still low compared to
the heat transfer coefficients of radiation, but at low
temperatures the convection coefficients become dominant.
Furthermore, the ambient temperature throughout the wider
environment of thEe hall and the walls of the holding pit form
part of the calcu7_ation. However, in a representative stack,
these parameters c:an only be seen in a particular part of the
solid angle, while in other parts of the solid angle there
are adjacent stac~a, which are at a similar temperature.
CA 02305401 2000-03-31
- 10 -
The bottom horizontal surface of the stack is in
contact with the pit floor. The pit floor itself could be
included in the finite element calculation, but in a
simplified version it is also possible to model the pit floor
as a semi-infinite' body which remains constantly at its
starting temperature, at which there is then a time-dependent
heat transfer coef=f icient .
For given slab dimensions, it is then possible to
determine the temperature profile over the cross section of
the slab or the stack of slabs. To be reintegrated into the
material flow between caster and rolling mill, the mean
temperature of a :steel slab should lie between 500 and 600°C.
At the start of cooling, the first slab still has the
temperature profile corresponding to when it leaves the
caster. At the encL of the stacking operation, it is found
that there is a me>re homogenous temperature distribution in
the stack if the floor is appropriately well insulated. As a
result of the cold slab being laid on top, the top slab in
the stack loses a relatively large amount of heat in the
first hour, and the bottom slab in the stack cools rapidly
during a short initial period, until the floor acts as an
insulator.
By linking a physical-mathematical model to the
automation of a standard slab material flow, the method
according to the invention makes it possible to control the
individual slabs between continuous-casting installation and
CA 02305401 2000-03-31
- 11 -
rolling mill in an economical and reliable manner. By
carrying out control measurements on the surface of the
slabs, including t:he values obtained through the calculation
model, it is possuble to draw conclusions as to the amount of
heat and the temperature profile of the slab in a simple
manner, provided that the appropriate boundary conditions are
included. In this way it is possible to determine, at any
location between continuous-casting installation and rolling
mill and, in particular, in storage yards, how much heat is
associated with tree particular slab and what level of energy
has to be supplied or dissipated in order to reach the
temperature profiles which are optimum for the further
process. The invention provides a design engineer with a
means of designing the installation optimally, so that it is
economical to produce and run.
