Title of Invention

" A COMPUTER-IMPLEMENTED METHOD FOR MODELLING THE PHASE CONVERSION OF A STEEL VOLUME WITH A VOLUMETRIC SURFACE IN A COOLING DOWN PROCESS".

Abstract The invention relates to a computer-implemented method for modelling the phase conversion of a steel volume (1) with a volumetric surface in a cooling down process, the method comprising the steps of determining in a computer apparatus (4) a subsequent state (ZF) of the steel volume (1), on the basis of an instantaneous initial state (ZA) of the steel volume (1) and at least one instantaneous influence quantity (W) operating via the volumetric surface of the steel volume (1), by resolving a thermal conduction equation and a phase change equation, the at least one influence quantity (W) comprising one local influence for a number of surface elements (10)of the volumetric surface in each case and the local influences operating via the relevant surface element (10) on the steel volume (1), the initial state (ZA) and the subsequent state (ZF) for a number of volume elements (9) of the steel volume (1) comprise local proportions (p1, p2, p3) of modeled phases of the steel and a quantity (H) describing a local energy content of the steel, the modeled phases of the steel comprise austenite and a first further phase, into which austenite can transform and which can transform into austenite, the initial state (ZA) and the subsequent state (ZF) for at least one of the volume elements (9) also comprise a local distribution in concentration (K) of at least one mobile alloy element in the steel, within the context of the phase change equation it is determined for the at least one volume element (9) which concentrations (k1, k3; k2, k4) of the at least one mobile alloy element are present on both sides of a first phase boundary (11,12)
Full Text

Description
Computer-assisted modelling method for the behavior of a steel
volume having a volumetric surface
The present invention relates to a computer-assisted modelling
method for the behavior of a steel volume having a volumetric
surface,
in which a computer, based on an instantaneous initial
state of the steel volume and at least one instantaneous
influence quantity operating via the volumetric surface on
the steel volume, by resolving an equation of thermal
conduction and a phase change equation, determines a subsequent state of the steel volume,
in which the at least one influence quantity comprises at
least one local influence in each case for a number of
surface elements of the volumetric surface and the local
influences operate via the relevant surface element on the
steel volume,
in which the initial state and the subsequent state for a
number of volume elements of the steel volume each comprise
local elements of modelled phases of the steel and a
quantity describing the local energy content of the steel,
in which the modelled phases of the steel comprise
austenite and a first further phase into which austenite
can be changed and which can be changed into austenite.
This type of mode]ling method is known for example from DE-A-
101 29 565. In this publication in particular an attempt was
made tor the first time to resolve the Fourier thermal
conductivity equation itself and not to resolve an incorrect
variation of this thermal conductivity equation, in order to
correctly describe the thermodynamic behavior of a steel band.
This publication is thus included by reference it in the

disclosed content of the present invention.
Such a modelling method is also described in the older German
Patent Application 102 51 716.9 not published at the time of
the present application. With this modelling method an attempt
is made to model the phase conversion of the steel on the
basis of the Gibbs free enthalpies of the steel. This
publication too is thus included by reference to it in the
disclosed content of the present invention.
This type of modelling method is also known from the paper
"Numerische Simulation der Warmeleitung in Stahlblechen -
Mathematik hilft bei der Steuerung von Kiihlstrecken"
(numerical simulation of thermal conductivity in steel sheets
- mathematics helps in the control of cooling lines) by W.
Borchers et al., published in the University periodical of the
Friedrich-Alexander University Erlangen-Nurnberg, Volume 102,
October 2001, 27th year.
Finally traditional approaches in accordance with the Scheilen
rule, according to Johnson-Mehl-Avrami and Brimacombe, are
known.
The exact modelling of the temperature curve of steel over
time during cooling down, especially of steel bands, is
decisive for the control of the required water or coolant
amounts of a cooling line for steel. This is because the
transformation of the steel which occurs during cooling down
decisively influences the thermal behavior of the steel as it
cools down. Major material properties of the steel are also
influenced by the cooling down process. Since the cooling down
does not occur in thermal equilibrium however, it is not
possible to describe the transformation simply by suitable
adaptation of the thermal capacity. Thus an exact modelling of
the phase change of the steel is also required in order to

enable the cooling line to be controlled correctly.
In practice the traditional approaches of the prior art do not
operate without errors in all cases. In particular they
exhibit a series of systematic disadvantages. First of all
separate parameters must be set for each material.
Interpolations between different materials are not possible or
at least only possible to a restricted extent. Secondly only
two phases are considered in the traditional method of the
prior art. An expansion to more than two phases is not
possible for system reasons. Thirdly the traditional prior art
methods only deliver a good match between model and reality
for a complete change of the metal observed. Fourthly the
traditional prior art methods do not provided any information
about the heat released during the phase change. The knowledge
of the phase change heat is however an absolute necessity for
a correct solution of the thermal conduction equation.
The methodologies according to DE-A-101 29 565 and the
technical paper "Numerische Simulation ..." already represent
a significant advance by comparison with such methods, since
they at least describe the thermal conduction completely
correctly. The older German Patent Application additionally
improves the modelling of the phase change. In particular it
supplies the change heat which occurs during the phase change.
However these methods are also not capable of improvement.
The object of the present invention is to create a modelling
method for a metal which delivers better modelling results.
The object is achieved,
by the initial state and the subsequent state for at least
one of the volume elements also including a local
concentration distribution of at least one mobile alloy
element in the steel,

within the context of the change equation it is determined
for at least one volume element which concentrations of the
at least one mobile alloy element are present on both sides
of a first phase boundary between austenite and the first
further phase,
by resolving a first Stefan problem it is determined whether
and how the concentration in distribution of the at least
one mobile alloy element changes in the austenite zone of
the volume element concerned and whether and by what
proportion the first phase boundary is thereby displaced,
and
the local proportions of the phases are determined on the
basis of a position of the first phase boundary specified by
the extent of the shift of the first phase boundary.
The mobile alloy element in steel is as a rule carbon. As an
alternative or in addition however it is also possible for the
alloy element to be nitrogen. It can also be another alloy
element which is preferably arranged in steel at intermediate
grid locations.
This modelling method already allows a clear advance compared
to the known prior art. This is because, with this process -
depending on whether the further phase is ferrite or cementite
- the change behavior of austenite into ferrite or austenite
into cementite and vice versa can be modelled very
realistically.
Preferably the modelled phases of the steel also comprise a
second further phase into which austenite can be converted and
which can be converted into austenite. This is because it is
then especia11y possible,
that, for the volume element considered, it is also
determined within the context of the change equation which

concentrations of the at least one mobile alloy element are
present on both sides of a second phase boundary between
austenite and the second further phase,
through additionally resolving a second Stefan problem it is
determined whether and how the concentration distribution of
the at least one mobile alloy element changes in the
austenitic zone of the volume element considered and whether
and by what extent the second phase boundary' is thereby
displaced,
the Stefan problems are coupled to each other,
square measures are assigned to the phase boundaries,
a proportion of the square measure assigned to the second
phase boundary of the total of the square measures is
determined and
the local proportions of the phases also depend on the
proportion of the square measure of the total of the square
measures assigned to the second phase boundary.
With this method not only can the change between austenite on
the one side and ferrite or cementite on the other be
described very realistically, but especially also the change
of austenite into perlite and vice versa. This means that
total significant change behaviors of steel in the fixed state
can be described correctly. Furthermore this procedure makes
it possible to establish whether perlite is formed or not.
The proportion of the square measure of the total of the
square measures assigned to the second phase boundary can be
determined by the phase boundaries always remaining arranged
next to each other. Alternatively it is however also possible
to adjust this proportion such that the phase boundaries tend
towards each other. On the basis of this proportion it can
then also be deduced whether austenite only changes in the
first further phase, only in the second further phase or both

into the first and also into the second further phase.
In principle it is also possible to determine the embodiment
of the first phase boundary three-dimensionally. However this
demands a significant computing effort. Preferably the
computation is thus undertaken one-dimensionally. This is
possible more simply if the volume element is a space-filling
Aristotle body, especially a cuboid It is also preferable,
for the observed volume element to be embodied as a cuboid
and to have three' basic dimensions,
for the first phase boundary to be embodied as a rectangle
with a first longitudinal side and a first transverse side
and
for the first longitudinal side- to correspond to the first
of the basic dimensions, for the first transverse side to
run in parallel to a second of the basic dimensions and for
displacements of the first phase boundary to occur in
parallel to the third of the basic dimensions.
If the second further phase is also taken into account then
the following applies,
that the second phase boundary is embodied as a rectangle
with a second longitudinal side and a second transverse side
and
that the second longitudinal side corresponds to the first
of the basic dimensions, the second transverse side runs in
parallel to the second of the basic dimensions and
displacements of the second phase boundary occur in parallel
to the third of the basic dimensions.
If the sum of the transverse sides of the phase boundaries is
approximately equal to 1.5 to 3 times a critical lamella
spacing in which an energy balance which on the on hand takes
account of the phase changes of the steel corresponding to the

displacement of the phase boundaries and on the other hand
takes account changes to the surface of a boundary layer
between the first and the second further phase corresponding
to the displacement of the phase boundaries, the grain spacing
of the perlite can also be determined using the model. The
lamella spacing (meaning the sum of the transverse sides of
the phase boundaries) can in this case especially be
approximately equal to double the critical lamella spacing.
Despite the only one-dimensional computation, the inventive
modelling method delivers very realistic results if the
proportion of austenite based on a non-linear function
determines the position of the phase boundary or of the phase
boundaries.
If the concentrations in which the at least one mobile alloy
element are present on both sides of the first phase boundary
or on both sides of the first and on both sides of the second
phase boundary are determined on the basis of the Gibbs free
enthalpies of the phases, the determination of the
concentrations of the at least one mobile alloy element at the
phase boundaries is especially simple.
It is possible to always resolve the coupled Stefan problems
and to deduce from this which phases are formed in what
volume. In many cases this is even irrefutable. Sometimes
however it is possible, before resolving the phase change
equation, on the basis of the phases already available in the
initial state and on the basis of the Gibbs free enthalpies,
to determine in advance, whether both austenite and also the
first further phase are present or whether in addition to
austenite and the first further phase: the second further
phase is present.
In individual cases the number of volume elements can be

small. In an extreme case they are equal to one. Usually
however the steel volume comprises a plurality of volume
elements. If the Stefan problem or the Stefan problems are
only resolved for a. part of the volume elements and the local
proportions of the phases of the other volume elements are
determined on the basis of the local proportions of the phases
of the part of the volume element, the computing power
required for modelling the behavior of the steel volume can
thus be greatly reduced without having any great detrimental
effect on the expressiveness of the model computation. The
thermal conduction equation on the other hand is generally
resolved individually for each volume element.
The modelling method can alternatively be executed online and
in real time but also offline.
It is possible for example,
for an initial status and at least one desired end quantity
to be specified to the computer,
for the above modelling method to be applied iteratively,
for the initial state of the first iteration to correspond
to the initial state and the initial state of each further
iteration to correspond to the subsequent state determined
immediately beforehand, and
that, on the basis of the subsequent state determined after
a last iteration an expected final quantity is determined
and is compared with the desired final quantity.
In this case the inventive modelling method can be
alternatively executed online and in real time or offline.
With offline execution in particular it is possible in this
case that the influence quantities of the iteration correspond
in their totality to a sequence of influence quantities, that
the computer on the basis of the comparison of the expected

end quantity with the desired end quantity varies the
influence quantity sequence and starting from the initial
status again, executes the above modelling method until at
least the expected end quantity corresponds to the desired end
quantity.
It is however also possible for the computer to determine the
influence quantities on the basis of an initial quantity
determined from the initial state and a desired subsequent
quantity and to control an influence device such that the
steel volume is influenced in accordance with the influence
quantity determined. In this case the modelling method must be
executed online and in real time. The influencing device can
be controlled in this case alternatively immediately or in the
subsequent iteration.
Further advantages and details emerqe from the subsequent
description of an exemplary embodiment in conjunction with the accompanying
drawings. The Figures show the following basic diagrams
FIG 1 a cooling line for a steel band,
FIG 2 the steel band from FIG. 1 in detail,
FIG 3 a volume element in a perspective diagram,
FIG 4 a flowchart,for what
FIG 5 a further flowchart,
FIG 6 a thermal conduction equation and a phase change
equation,
FIG 7 a further thermal conduction equation and a phase
change equation, FIG 8 a (further flowchart, FIG 9 the Gibbs free enthalpies of the phases of this steel
as a function of the proportion of carbon at a first
temperature,
FIG 10 the Gibbs free enthalpies as a function of the

proportion of carbon of the steel at a second
temperature,
FIG 11 a volume element in a perspective diagram,
FTG 12 the volume element of FIG. 11 viewed from the side,
FIG 13 a volume element similar to that depicted in FIG. 12,
FIG 14 a volume element in a perspective diagram,
FIG 15 the volume element of FIG. 14 seen from above,
FIG 16 the volume element of FIG. 15 shown in cross section
along the line XVI - XVI of FIG. 15
FIG 17 the volume element of FIG. 15 shown in cross section
along the line XVII - XVII of FIG. 5, FIG 18 a further flowchart and W^T
FIG 19 a detail of FIG. 15.
In accordance with FIG 1 a steel band 1 for example is to be
cooled off so that it assumes specified final properties. To
this end the steel band 1 is treated in a cooling line 2 with
a cooling medium 3 - as a rule water.
The steel band 1 has a breadth b and a depth d. It also has -
basically' any - band length. It passes through the cooling
line 2 at a velocity v.
The band velocity v is continuously recorded and fed to a
computer 4 which controls the cooling line 2. The computer 4
is thus able in a known way to implement a path trace of the
steel band 1. The zones of the steel band 1 which are affected
are also known to the computer 4 if the cooling medium 3 is
applied to the steel band 1 by means of delivery devices 5 of
the cooling line 2.
The computer 4 is programmed with a computer program 6 which
is supplied to the computer 4 via a data medium 7, e.g. a CD-
ROM 7. The computer program 6 is stored in (exclusively)
machine-readable form on the data medium 7. The computer

program 6 is accepted by the computer 4 and stored in bulk
storage 8, e.g. on a hard disk 8, of the computer 4. This
enables the computer 4, when the computer program 6 is called,
to execute a modelling method for the steel band 1 or for its
individual zones (= the steel volume 1) which will be
described in more detail below.
As shown in FIG 2 the steel volume 1 is broken down within the
computer 4 into volume elements 9. Where a volume element 9 is
not surrounded in this case on all sides by other volume
elements 9, one or two surface elements 10 are assigned to the
relevant volume element 9. The surface elements 10 in their
entirety form a volumetric surface of the steel band 1 or of
the zone of the steel band 1 observed
On the basis of the programming with the computer program 6
the computer 4 especially implements a mode in which for each
volume element 9 the thermal couplings with its environment
are taken into account. Each volume element 9 in this case -
see FIG 3 - is embodied in the shape of a cube It thus has
three basic dimensions A, B, C which as a rule are oriented in
parallel to the direction of the band velocity v, the band
breadth b and the band depth d.
In a first embodiment of the inventive modelling method the
computer 4 is supplied in accordance with FIG 4 in a step S1
with a first state Z. The first Z comprises for each volume
element 9 of the steel band 1 initially local proportions p1,
p2, p3 of modelled phases of the steel. The phases can
especially be ferrite (proportion p1), cementite (proportion
p2) and austenite (proportion p3).
The first state Z also comprises for each volume element 9 of
the steel band 1 a quantity H which describes the local energy
content of the 'steel of the volume element 9. For example this

quantity H can be the enthalpy H of the volume element 9.
Alternatively the temperature or the entropy are also
considered .
Finally the first state Z, for at least one of the volume
elements 9 of the steel band 1, preferably for each volume
element 9 of the steel band, also comprises a local
distribution in concentration K of at least one mobile alloy
element in the steel. The mobile alloy element can in
particular be carbon. Nitrogen can also be considered for
example as a alternative or in addition.
As part of step S1 the computer 4 is further supplied with at
least a desired end value f'*. If necessary the computer 4 can
also be supplied as part of step S1 with intermediate
quantities, so that if necessary even a desired timing curve
of the quantity can be specified to the computer 4.
In accordance with FIG 4 an influence quantity sequence is now
defined in a step S2. The influence quantities sequence
comprises an influence quantity W for a plurality of directly
consecutive points in time. The influence quantity W
corresponds for example to the volume of coolant to be applied
to the steel volume 1 (i.e. the steel band or its observed
zone) taking into account other influences on the steel volume
such as the transport rollers, heat convection, heat radiation
etc. for example. It comprises a local influence in each case
for the plurality of surface elements 10 of the steel volume 1
(see FIG 2). The local influences then operate via the
relevant surface element 10 on the steel volume 1.
In accordance with FIG 4, in a step S3 an initial state ZA of
the steel volume 1 is now set equal to the first state Z and a
time base t at a start time t0. The start time tO as a rule
corresponds in this case to the point in time at which the

observed steel volume 1, that is a section of the steel band 1
for example enters the cooling line 2.
Then in a step S4, on the basis of the influence quantity
sequence, the influence quantity to be applied at the point
determined by the time base t is determined. In a step S5 the
computer 4 then determines on the basis of the instantaneous
initial state ZA of the steel volume 1 and of the
instantaneous influence quantity W operating over the
volumetric surface on the steel volume 1 a subsequent state ZF
of the steel volume The computer 4 resolves a thermal
conduction equation and a phase change equation in this case.
The subsequent state ZF comprises these same elements K, p1,
p2, p3, H as the initial state ZA.
Then in a step S6 the time base t is incremented by the time
increment Δt. Next', in a step S7 a check is made as to whether
the time base t has reached an end time tl. The end time t1 in
this case generally corresponds to the time at which the
observed steel volume 1 leaves the cooling line 2 again.
If end time tl is not yet reached, in a step S8 the initial
state ZA is set equal to the subsequent state ZF determined
immediately beforehand and then a branch is made back to step
S4.
If on the other hand the end time tl was reached, the program
exits from the loop consisting of steps S4 to S8. If no
further measures are taken thereafter, only a so-called
process observer is realized. Preferably however, as shown in
FIG 4, an expected final value f', e.g. the temperature or the
material hardness is determined in a step S9 on the basis of
the subsequent state ZA now determines and is compared to the
desired final quantity f'*. If the expected final quantity f'
does not correspond to the desired final quantity f'* -

provided the corresponding computing power is available - the
sequence of the influence quantities W is varied in a step
S10. A branch is then made back to a step S3. Otherwise the
required coolant amount sequence is determined so that the
computer 4 can now accordingly control the cooling line 2 in a
step Sll.
For the sake of completeness it should be mentioned here that
the computer 4, if as well as the desired end quantity f'*,
desired intermediate quantities are also specified to it,
obviously determines the coolant sequence up to the first
desired intermediate quantity, then up to the second desired
intermediate quantity etc., until the entire coolant amount
sequence up to the desired end quantity f'* is determined.
In accordance with FIG 1 and 4 the model method described
above is executed online and in real time. An offline
execution is obviously easily possible too. This is indicated
in FIG 1 by the fact that the connection of the cooling line 2
to the computer 4 is shown as an openable connection, that is
there does not have to be a direct control of the cooling line
2. Furthermore step Sll in FIG 4 is only shown by dashed
lines ..
The procedure in accordance with FIG 4 demands a very great
computing effort. If the computing power required for
execution of the method in accordance with FIG 4 is not
available, but online control using the inventive modelling
method is still to be undertaken, a method is executed online
and in real time which is described below in greater detail in
conjunction with FIG. 5.
In accordance with FIG 5 the computer 4 accepts the first
state Z in a step S12 similar to step S1. In a step S13
similar to step S3 the computer 4 sets the initial state ZA

equal to the first state Z and the time base t to time t0.
Then the computer 4 in a step S14 determines a desired
subsequent quantity f* or accepts this quantity.
In a step S15 similar to step S9 the computer 4 determines an
initial quantity t on the basis of an initial state ZA. On the
basis of the initial quantity f and the desired subsequent
quantity f* determined in step S15, the computer 4 then
determines the influence quantities W in a step S16. In a step
S17, which corresponds to the step Sll, the computer 4 finally
controls the cooling line 2 in accordance with the influence
quantity W determined. In this case the control is preferably
undertaken immediately, as in FIG. 5. If necessary however an
activation can also be undertaken in the next cycle.
The subsequent steps S18 to S21 correspond to the steps S5 to
S8 of FIG 4. A detailed description of these steps S18 to S21
is thus dispensed with.
The method in accordance with FIG 5 a is preferably used for
example for a control of a steel band 1 running through the
cooling line 1 for expiry of the desired subsequent quantity
f* . In this case the method described above in connection with
FIG 5 must obviously be executed individually for each
individual section of the steel band 1. Also for each section
those of the supply devices 5 must be activated in the area of
influence of which the observed section is currently located.
This is guaranteed by the path tracing mentioned at the start.
The method in accordance with FIG 5 is in this case
furthermore executed in parallel for all the sections of the
steel band 1 located in the cooling line 2.
The desired subsequent quantity f* in each case can be
explicitly specified to the computer 4. It is however also
possible for the computer merely to have the desired

subsequent quantity f* specified to it, e.g. on exit of the
steel band 1 from the cooling line 2 or on reaching a coiler
on which the steel band 1 is coiled. In this case the computer
4 determines independently on the basis of a pre-specified
determination specification the desired subsequent quantities
f* for the individual iterations.
The controlling in accordance with FIG 5 can of course also be
structured in a different manner, as is described in the older
DE 103 21 792.4 for example.
As mentioned in the steps S5 and S18 a thermal conduction
equation and a phase change equation are resolved.
An example of a thermal conduction equation and of a phase
change equation are shown in FIG 6. A one-dimensional approach
for thermal conduction is adopted there. For bands however
this approach can in every likelihood also be simplified to
the one-dimensional approach depicted in FIG 7, since the heat
flow in the longitudinal band direction and the transverse
band direction is negligible. 5/ 5x is in this case the local
derivation in the band breadth direction.
The thermal conduction equation and the phase change equation
are evidently coupled to one another. To resolve the thermal
conduction equation and the phase change equation (step SS,
S18) the procedure in accordance with FIG 8 is thus as
follows:
The local temperature T is first determined in a step S22. The
temperature is determined on the basis of the enthalpy H and
the proportions p1, p2, p3 of the phases ferrite, cementite
and austenite. Because of the small size of the observed
volume element 9 it can namely be assumed that the local
temperature T is constant within the volume element 9. This

means that the phases of the steel within this volume element
9 also exhibit this same local temperature T. The enthalpy H
of the volume element 9 can thus be written as
H = p1H1(T) + p2H2(T) + p3H3(T) (1)
Since furthermore for each of the phases of the enthalpies H1,
H2 or H3 the relevant phase as function of the local
temperature T - where necessary for austenite taking into
consideration the proportion of carbon - are uniquely
determined, the local temperature T is able to be easily
determined by the equation 1.
For the local temperature T determined in the step S22 the
Gibbs free enthalpies G 1 to G3 of the individual phases are
then determined in a step S2 3 - separately for the phase
ferrite, cementite and austenite - as a function of the
proportion of the mobile alloy element. Examples of these
types of curve are shown in FIG 9 and 10. In the example
depicted in FIG] 9 the local temperature T in this case lies
above the temperature at which austenite changes into perlite,
in the example depicted in FIG. 10 it lies below this
temperature.
It is possible to always assume that all three phases ferrite,
cementite and austenite are present and only later - see the
explanations for FIG 18 below - to decide which phases are
present and which phase changes are taking place. In
accordance with FIG 8 however the number of phases to be
observed is initially determined in a step S24. This is done
using the following procedure:
Initially the system ferrite-austenite is extracted. A check
is made for this system whether the overall proportion of the
mobile alloy element present in the volume element 9 is purely

ferritic, purely austenitic or mixed stable and which phase
distribution is present in the stable state where necessary.
The overall proportion of the mobile alloy element can easily
be determined on the basis of the concentration in
distribution.
The stable phase(s) is (are) determined and if necessary
distributed by an attempt being made to determine a minimum
for the total Gibbs free enthalpy G of such a system. The
concrete procedure is produced in this case as described on
pages 16 to 18 of the older German Patent Application 102 51
716.9. This procedure simultaneously also delivers
concentrations K1 and K3 in which the mobile alloy element - a
typically carbon - is present at any phase boundary 11 between
ferrite and austenite in the ferritic or the austenitic zone.
The mixture systems ferrite-cementite (=perlite) and
austenite-cementite are then investigated in a similar manner.
The investigation of the mixture system austenite-cementite
simultaneously also delivers concentrations K2 and K4 in this
case in which the mobile alloy element is present at any phase
boundary 12 between cementite and austenite in the cementitic
or the austenitic zone.
The three Gibbs free enthalpies G determined for the three
two-phase systems are compared to one another and the two-
phase system with the overall minimum Gibbs free enthalpy G is
obtained. If this two-phase system contains austenite, it is
possible to determine on the basis of the Gibbs free
enthalpies whether the stable state comprises one or two
phases, which phase this might necessarily be or which phases
these might necessarily be and which concentrations k1, k3 or.
k2, k4 of the mobile alloy element are present on both sides
of the phase boundary 11 from austenite to ferrite or the

phase boundary 12 from austenite to cementite in each case.
It is further known from initial state ZA which phases are
initially present for which proportions p1 to p3.
If the two-phase system with the minimum Gibbs enthalpy G
contains austenite, it can thus be determined by looking at
the initially present phases and the phases determined as
stable where they are a pure system with only one of the
phases ferrite, austenite and cementite or a mixed system with
two or even three of the phases ferrite, austenite and
cementite have to be observed. Because of the fact that it can
also be determined on the basis of the Gibbs free enthalpies
G, G1 which phase is stable or which phases are stable in
addition the direction of any phase change is also known.
If the two-phase system with the total minimum Gibbs free
enthalpy G is the perlite system and the initial state ZA does
not contain any austenite (p3 = 0), a completely changed
framework, that is a two=phase system ferrite-cementite is
present that is not subject to any further phase change, if on
the other hand the initial state ZA contains austenite (p3 >
0) and the perlite system features the minimum Gibbs free
enthalpy G it cannot simply be decided whether one or both of
the phases ferrite and cementite will now be formed, in this
case it is thus provisionally assumed that both phases are
formed, that is that a three-phase system ferrite-cementite-
austenite is to be observed.
A next check is made in a step S25 as to whether there is more
than one phase present in the observed volume element 9. If
this is not the case, there is obviously no phase change.
Despite this, in a step S26 a diffusion equation for the
mobile alloy element is started and resolved for the volume
element 9 in order to compensate for any concentration

variations of the mobile alloy element within the observed
volume element 9. This process is especially of significance
for austenite, in which the carbon content can vary greatly.
The approach and the solution of such a diffusion equation is
generally known to those skilled in the art. The use of the
diffusion equation and its solution will thus not be dealt
with in any greater detail here.
If there is more than one phase present in the observed volume
element 9, a check is made in a next step S27 as to whether
all three phases are present. If they are not the system is a
two-phase system. In this case a check is made in a step S28
whether one of the two phases present is austenite. If this is
not the case, the system is a complete perlite system, that is
a layer structure made from ferrite and cementite. This
structure is essentially stable. In this case no further
measures must thus be taken.
If on the other hand one of the phases is austenite and thus
the other phase is ferrite or cementite, a phase boundary 11
exists between austenite and ferrite (see FIG 11 and 12) or a
phase boundary 12 between austenite and cementite (see FIG. 11
and 13). In this case it is assumed as a simplifying measure
that the phase boundary 11 or 12 is embodied as a rectangle
which has a longitudinal side and a transverse side. The
longitudinal side and the transverse side of the rectangle
correspond in this case to the basic dimensions A and B of the
observed volume element 9. Displacements of the phase boundary
11, 12 occur in this case, as is especially evident from FIG
11, in parallel to basic dimension C.
As is generally known to those skilled in the art, and can
also be seen from FIG 12, only very little carbon is contained
in ferrite. By contrast, at the phase boundary 11 to the

austenitic zone there is a jump in concentration. The
concentrations k1, k3, in which the mobile alloy element is
present at the phase boundary 11 are in this case the
concentrations k1, k3, which were determined above in the step
S24 for the ferrite-austenite system.
If, as shown in FIG 12, a change is to take place from
austenite into ferrite, the "concentration peak" of the mobile
alloy element must diffuse down in the austenitic zone in the
vicinity of the phase boundary 11. Conversely, if a change is
to occur from ferrite into austenite, the "concentration
trough" of the mobile alloy element in the austenitic zone in
the vicinity of the phase boundary 11 must be constantly
filled up. The numerical or analytical solution to this task
is generally known as the Stefan problem. It is undertaken in
a step S29. In the present case the Stefan problem can be
formulated as follows:
K't-DK'xx=0 (2)
D is in this case the - where necessary temperature-dependent
- diffusion constant of the mobile alloy element in the
austenite. K' is the concentration K. The indices t and x mean
the derivation according to the time or the location in the
direction of displacement of the phase boundary 11. The
displacement direction of the phase boundary 11 in this case
does not necessarily have to be the band breadth direction.
The initial conditions for the equation 2 are defined by the
local distribution in concentration K' of the mobile alloy
element in the initial state ZA. For resolution of the Stefan
problem only the peripheral conditions then have to be
considered, that in the ferritic or austenitic zone at the
phase boundary 11 the concentrations kl or k3 are present,
that the mobile alloy element cannot leave the volume element

9 concerned and that the displacement δx' of the phase
boundary 11 in accordance with the Stefan condition produces

with 5t being the timing step sizes used in the resolution of
the Stefan problem. In this case this can be a fraction (1/2,
1/3, 1/4 ...) of the time step width At or equal to the time
step width Δt.
By resolving the Stefan problem in the step S29 it is also
determined whether and how the distribution in concentration K
or. K' of the mobile alloy element changes in the austenitic
zone of the volume element 9 observed. At the same time it is
also determined in this case, whether and by what extent δx'
the phase boundary 11 is displaced thereby.
If the further phase is not ferrite, but cementite is,
basically the same type of approach to the solution is
produced and also basically a solution of the same type. The
difference is only that for the. formation of cementite carbon
is greatly enriched in the cementite and in the austenitic
zone in the vicinity of the phase boundary 12 carbon is
degraded from the cementite. This too is generally known to
persons skilled in the art and is shown in FIG 13. The
peripheral conditions thus change. The displacement δx" of the
phase boundary 11 in accordance with the Stefan condition in
this case is produced for

K" is in this case again the concentration K.
If on the other hand in the step S28 it was established that
all three phases are present or could be present, a more
complicated problem is produced. The approach which must then

be selected is that a layer structure exists, which - see FIG
14 and 15 - consists of an alternate ferrite layer 13 and a
cementite layer 14. The layer structure borders an austenitic
zone 15. FIG 16 and 17 each show a curve of the concentration
K' or. K" of the mobile alloy element in a ferrite layer 13 or
a cementite layer t 14 and in the austenitic zone 15 in front
of these layers 13, 14.
Within the framework of the model it is still assumed in this
case, that the phase boundaries 11, 12 are embodied as
rectangles each having a longitudinal side and a transverse
side. The longitudinal sides continue to correspond to the
first basic measurement A. The transverse sides still run in
parallel to the second basic dimension B. It is also still
assumed that displacements of the phase boundaries 11, 12
occur in parallel to the third basic dimension C.
For each of the phase boundaries 11 and 12 a Stefan problem is
now formulated and resolved in a step S30. The step S30 is
shown in greater detail in FIG 18.
The Stefan problem for the phase boundary 11 between ferrite
and austenite obeys in accordance with FIG 18, see step S31
there, the following law:

K' is in this case the concentration of the mobile alloy
element before the phase boundary 11.
The Stefan problem for the phase boundary 12 between cementite
and austenite obeys the following law:

K" in this case - like K' - is the concentration of the mobile

alloy element before the phase boundary 12.
L1 and L2 are coupling terms. They are - see FIG 14 -
functions of a lamella spacing 1 of the layer structure and of
a proportion q of the cementite phase at the layer structure
as well as its time derivation. Written out they can for
example be as follows:

As can be seen from the equations 5 to 8, the two Stefan
problems are coupled to each other because of the coupling
terms L1, L2 on the right side of the equations 5 and 6.
In the equations 5 to 8 as well the indices t and x again
stand for the derivation in accordance with the time or the
location in the direction of displacement of the phase
boundary 11 or 12.
The Stefan conditions continue to apply for the displacements δx', 6x" of the phase boundaries 11, 12 (see equations 3 and
4). It is thus possible to set the displacements δx', δx"
equal in accordance with the equations 3 and 4 in a step S32 .
The proportion q is then to be determined such that the
displacement 6x' of the phase boundary 11 in accordance with
equation 3 and the displacement δx" of the phase boundary 12
in accordance with equation 4 assume the same value. The
proportion q in this case is also to be defined such that the
phase boundaries 11, 12 always remain arranged next to one
another.
The equivalence of the displacements δx' , δx" of the phase

boundaries 11, 12 can also be obtained by the proportion q of
the cementite phase in the layer structure of the perlite
being suitably selected. One can also determine - e.g. by
trial and error, for which proportion q of the cementite phase
the displacements δx', δx" of the phase boundaries 11, 12
match.
On the basis of the proportion q thus determined it can also
then be determined, whether perlite will actually be formed or
whether only one of the two phases ferrite and cementite will
be formed. Perlite will only be formed if the proportion q
lies between zero and one. If the proportion q on the other
hand is greater than one, exclusively cementite is formed. If
on the other hand it is less than zero, exclusively ferrite is
formed.
The proportion q can with the procedure assume any values for
numeric reasons, that is especially also less than zero or
greater than one. These values however make no sense
physically. The proportion q is thus corrected accordingly in
steps S33 to S36 where necessary.
The procedure according to step 32 can lead to numerical
problems. Alternatively it is thus possible to allow differing
displacements δx', δx". In this case the proportion q of the
cementite in the layer structure in accordance with

is adjusted in steps S32a and S32b so that the positions of
the phase boundaries 11, 12 tend towards one another. The
steps S32a and S32b are executed in this case in accordance
with FIG 18 instead of step S32. a is a suitable
proportionality constant. Its value is greater than zero.

In this case an average displacement 5x the phase boundaries
11, 12 for

is defined.
Regardless of which of these two procedures (step S32 or steps
S32a, S32b) is followed, in both case however it is only
determined and deduced from the determination of the
proportion q which phases will be formed in what volume.
If perlite will be formed proportion q thus lies between zero
and one, the lamella spacing 1 must still be determined. This
is done in accordance with FIG 19 as follows:
With the displacement 5x the phase boundaries 11, 12 and the
proportion q it is known which phase changes take place and in
which proportions they take place. The phase changes deliver
an amount 5E1 for energy balance. The amount 5E1 depends on
the volume in which the phase changes occur. The following
thus applies

(3 is in this case a proportionality constant that can be
determined in advance.
This further produces a change of the surface of a boundary
layer 16 between ferrite and cementite. The change of this
surface also delivers an amount δE2 for energy balance. This
amount δE2 is proportional to the change in the surface of the
boundary layer 16. The following thus applies


γ is in this case again a proportionality constant that can be
determined in advance. The factor 2 is produced by the fact
that, for each phase boundary 11, 12 or for each layer 13, 14
one boundary layer 16 respectively is present and two phase
boundaries 11, 12 or two layers 13, 14 are observed.
On the basis of the equations 11 and 12 it is thus possible to
determine a critical lamella spacing 1', in which the energy
balance, which takes account of the two amounts 5E1 and δE2 is
balanced. The following then applies for this critical lamella
spacing 1'

The lamella spacing 1, that is the sum of the layer
thicknesses 11 and 12, is now set to appr. one and a half
times to three times this critical lamella spacing 1', e.g. to
appr. twice The layer thicknesses 11 or 12 are then produced
for

The layer thicknesses 11, 12 are proportional to square
measures F1, F2, which the phase boundaries 11, 12 exhibit.
Each one of the square measures Fl, F2 in FIG 14 is
highlighted accordingly by shading.
If in one of the steps S2 9, S30 a displacement δx', δx" of a
phase boundary 11, 12, was determined, the position of the
phase boundary 12 has thus changed. I this case in a step S37
(obviously taking account of the leading sign of the average
displacement 6x) a new position of the phase boundaries 11, 12
or 11 and 12 is determined. In a step S38, on the basis of a

non-linear function the position of the phase boundary 11, 12
or the phase boundaries 11, 12 of the proportion p3 of the
austenite is determined. The non-linear function in this case
especially takes account of the fact that the Stefan problem
of the step S29 or the Stefan problem of the step S30 were
started and resolved one-dimensionally but in reality a three
dimensional change occurs.
In a step S39 the changes of the proportions p1, p2 of the two
other phases ferrite and cementite will then be determined. If
in this case the steps S37 to S39 are reached from step S29,
the proportion q is obviously one or zero.
With the average displacement 5x of the phase boundaries 11,
12 and the proportion q of the cementite in the layer
structure (0 manner which changes are produced for the proportions p1, p2,
p3 of the phases of the steel as regards the volume element 9
observed.
Despite the simplifying assumptions of the above modeling
methods a significant computing effort is produced. Thus in
accordance with FIG 8 before step S22 steps S40 and S41 and
after step S39 a step S42 are inserted.
In the step S40 the volume element 9 is assembled into groups.
For example there can be a grouping together of a number of
volume elements 9 which in the direction of the band breadth
b, the band depth d and/or the band velocity v adjoin each
other. Combinations of these are also possible. In the step
S41 a single one of the volume elements 9 in each case is then
selected per group of volume elements 9. Only for the selected
elements of the volume elements 9 are in steps S22 to S39 the
differential equation, the Stefan problem or the Stefan
problems resolved and the proportions p1 p2, p3 of the phases

computed.
In accordance with FIG 8, for each group the solution result
of the volume element 9 observed is accepted in the step S42
for the other volume elements 9 of the relevant group. This
represents the simplest procedure. It would however also be
conceivable to determine the proportions p1, p2, p3 of the
phases of volume elements 9, for which the phase distribution
has not been explicitly computed through linear or non-linear
interpolation.
Because of the circumstance, namely that for each group of
volume elements 9 only the distribution in concentration K of
one of the volume elements 9 is calculated and for the
resolution of the thermal conduction equation not the
concentration in distribution K, but only the proportions p1,
p2, p3 of the available phases are needed if necessary the
concentration in distribution K can only be specified for this
one volume element 9 of each group.
The thermal conduction equation on the other hand is resolved
in a step S43 individually for each of the volume elements 9.
The step S43 can in this case alternatively be executed before
or after the resolution of the phase change equation in the
steps S22 to S42.
The resolution of the thermal conduction equation is possible
in any event. This is because the temperatures T of the
individual volume elements 9 - see above explanations for step
S22 - can be determined in any event, so that their location
gradient can also be determined immediately. Since the
proportions p1, p2, p3 of the phases of the individual volume
elements 9 are also known, the thermal conductivity A of the
individual volume elements 9 can also be easily determined.
Since finally the density p is essentially a constant and the

enthalpy H of the individual volume elements 9 is given
directly the thermal conduction equation is thus also soluble
as a whole.
Using the present invention a physical model is thus created
in which, on the basis of the Gibbs free enthalpy G and of the
diffusion law (Stefan problem) the change process as regards
phase proportions p1, p2, p3 arising and speed of change can
be described with very high accuracy. Generally valid results
are made possible which also allow the handling of as yet
unknown substances and materials. The approaches can also be
used not only for temperature calculation, but also for
computing the framework structure and particle size.
The inventive modelling method can be employed at any point,
that is especially for example also for cooling processes
between roller frames of a roller track or with so-called
ferrite rollers. It is also suitable for description of the
change back when the steel is heated up.

WE CLAIM
1. A computer-implemented method for modelling the phase conversion of a
steel volume (1) with a volumetric surface in a cooling down process, the
method comprising the steps of:
- determining in a computer apparatus (4) a subsequent state (ZF) of the steel
volume (1), on the basis of an instantaneous initial state (ZA) of the steel
volume (1) and at least one instantaneous influence quantity (W) operating
via the volumetric surface of the steel volume (1), by resolving a thermal
conduction equation and a phase change equation, the at least one influence
quantity (W) comprising one local influence for a number of surface elements
(10)of the volumetric surface in each case and the local influences operating
via the relevant surface element (10) on the steel volume (1),
- the initial state (ZA) and the subsequent state (ZF) for a number of volume
elements (9) of the steel volume (1) comprise local proportions (p1, p2, p3)
of modeled phases of the steel and a quantity (H) describing a local energy
content of the steel,
- the modeled phases of the steel comprise austenite and a first further phase,
into which austenite can transform and which can transform into austenite,
characterized in that
- the initial state (ZA) and the subsequent state (ZF) for at least one of the
volume elements (9) also comprise a local distribution in concentration (K) of

at least one mobile alloy element in the steel,
- within the context of the phase change equation it is determined for the at
least one volume element (9) which concentrations (k1, k3; k2, k4) of the at
least one mobile alloy element are present on both sides of a first phase
boundary (11,12) between austenite and the first further phase,
- by resolving a first Stefan problem it is determined whether and how the
distribution in concentration (K) of the at least one mobile alloy element
changes in the austenitic zone of the volume element (9) observed and
whether and to what extent (δx, δx', δx") the first phase boundary (11,12) is
displaced thereby, and
- the local proportions (p1, p2, p3) of the phases are determined on the basis
of the position of the first phase boundary (5, 5) defined by the extent (5x) of
the displacement of the first phase boundary (11,12).
2. The method as claimed in claim 1, wherein
- the modelled phases of the steel comprise a second further phase into which
austenite can transform and which can transform into austenite,
- for the volume element (9) observed, it is also determined within the context
of the phase change equation which concentrations (k2,k4; k1, k3) of the at

least one mobile alloy element are present on both sides of a second phase
boundary (12,11) between austenite and the second further phase,
- through additional resolution of a second Stefan problem it is determined
whether and how the distribution in concentration (K) of the at least one
•. mobile alloy element changes in the austenitic zone of the volume element
(9) observed and whether and to what extent ( δx'; δx") the second phase
boundary (12,11) is displaced by this,
- the Stefen problems are coupled to each other,
- area measures (F1,F2) are assigned to the phase boundaries (11,12),
- a proportion (q) of the area measure (F2) assigned to the second phase
boundary (12) is determined from the sum of the area measures (F1,F2) and
- the local proportion (p1,p2,p3) depending on the proportion (q) of the area
measure (F2) assigned to the second phase boundary (12) in the sum of the
square measures (F1, F2).
3. The method as claimed in claim 2, wherein the proportion (q) of the area
measure (F2) assigned to the second phase boundary (12) in the sum of the
area measures (F1, F2) is determined such that the phase boundaries (11,12)
always remain arranged alongside one another.

4. The method as claimed in claim 2, wherein the proportion (q) of the area
measure (F2) assigned to the second phase boundary (12) in the sum of the
area measures (F1,F2) is adjusted such that the phase boundaries (11,12)
move towards each other.
5. The method as claimed in claim 2, 3, or 4, wherein, on the basis of the
proportion (q) of the area measure (F2) assigned to the second phase
boundary (12) of the sum of the area measures (F1,F2) it is deduced whether
austensite changes only in the first further phase, only in the second further
phase or both in the first and also in the second further phase.
6. The method as claimed in one of the preceding claims, wherein:

- the volume element (9) observed is embodied as a cuboid and has three
basic dimensions (A, B, C),
- the first phase boundary (11,12) is embodied as a rectangle with a first
longitudinal side and a first transverse side and
- the first longitudinal side corresponds to one of the first basic dimensions (A,
B, C), the first transverse side runs in parallel to a second of the basis
dimensions (A, B, C) and displacements (δx', δx") of the first phase boundary
(11,12) occur in parallel to the third of the basic dimensions (A, B, C).
7. The method as claimed in claim 6 and one of claims 2 to 5, wherein:

- the second phase boundary (12,11) is embodied as a rectangle with a second
longitudinal side and a second transverse side and
- the second longitudinal side corresponds to the first of the basic dimensions
(A, B, C), the second transverse side runs in parallel to the second of the
basic dimensions (A, B, C) and displacement ( δx", δx') of the second phase
boundary (12,11) occur in parallel to the third of the basic dimensions (A, B,
C).
8. The method as claimed in claim 7, wherein the sum (1) of the transverse
sides of the phase boundaries (11,12) is roughly the same as 1.5 to 3 times a
critical lamella spacing (I'), in which an energy balance which takes accounts
on the one hand of the phase changes of the steel corresponding to the
displacement of the phase boundaries (11,12) and on the other hand takes
account of the changes in the surface of a boundary layer (16) between the
first and the second further phase corresponding to the displacement of the
phase boundaries (11,12) is zero.
9. The method as claimed in one of the preceding claims, wherein the Stefan
problems is formulated and resolved in one dimension or the Stefan problem
are formulated and resolved in one dimension and that the proportion (p3) of
austenite is determined on the basis of a non-linear function of the position of
the phase boundary (11,12) or the phase boundaries (11,12).

10.The method as claimed in one of the preceding claims, wherein the
concentrations (k1 to k4) in which the at least one mobile alloy element is
present on both sides of the first phase boundary (11,12) or on both sides of
the first and both sides of the second phase boundary (11,12) are determined
on the basis of the Gibbs free enthalpies (G1, G2, G3) of the phases.
11.The method as claimed in one of the preceding claims, wherein on the basis
of the phases already present in the initial state (ZA) and on the basis of the
Gibbs free enthalpies (G1, G2, G3) of the phases, it is determined whether
both austenite and also the first further phase are present or whether in
addition to austenite and the first further phase, the second further phase is.
also present.
12.The method as claimed in one of the preceding claims, wherein the steel
volume (1) comprises a multiple of the volume elements (9), and wherein the
Stefan problem or the Stefan problems are only resolved for a part of the
volume elements (9) and that the local proportions (p1, p2, p3) of the phases
of the other volume elements (9) are determined on the basis of the local
proportions (p1, p2, p3) of the phases of the part of the volume elements
(9).
13.The method as claimed in claim 12, wherein the thermal conduction equation
is resolved individually for each volume element (9).
14.The method as claimed in one of claims 1 to 13, wherein

- an initial state (Z) and at least one desired end value (f *) are specified to
the computer (4),
- the method is applied iteratively in accordance with one of the claims 1 to 10,
- the initial state (ZA) of the first iteration corresponds to the first state (Z) and
the initial state (ZA) of each further iteration to the subsequent state (ZF)
determined immediately beforehand and
- on the basis of the subsequent state (ZF) determined after a last iteration, an
expected end quantity (f) is determined and compared with the desired end
quantity (P *).
15.The method as claimed in claim 14, wherein the method is executed online
and in real time or offline.
16.The method as claimed in claim 14 or 15, wherein the influence quantities
(W) of the iterations correspond in their entirety to an influence quantity
sequence, wherein the computer (4) varies the influence quantity sequence
on the basis of the comparison of the expected end quantity (f) with the
desired end quantity (f *) and starting from the first state (Z) executes the
modeling method again in accordance with claim 12 until at least the
expected end quantity (f) correspond to the desired end quantity (f *.).

17.The method as claimed in one of the claims 1 to 13, wherein the method
is executed online and in real time, wherein the computer (4) determines
the influence quantity (W) on the basis of an initial quantity (f)
determined from the initial state (ZA) and a desired subsequent quantity
(f*) and wherein the computer (4) controls an influencing device (2) such
that the steel volume (1) is influenced in accordance with the influence
quantity (W) determined.
18.A computer apparatus with a storage device (8) for implementing the
method as claimed in claim 1.


The invention relates to a computer-implemented method for modelling the
phase conversion of a steel volume (1) with a volumetric surface in a cooling
down process, the method comprising the steps of determining in a computer
apparatus (4) a subsequent state (ZF) of the steel volume (1), on the basis of an
instantaneous initial state (ZA) of the steel volume (1) and at least one
instantaneous influence quantity (W) operating via the volumetric surface of the
steel volume (1), by resolving a thermal conduction equation and a phase
change equation, the at least one influence quantity (W) comprising one local
influence for a number of surface elements (10)of the volumetric surface in each
case and the local influences operating via the relevant surface element (10) on
the steel volume (1), the initial state (ZA) and the subsequent state (ZF) for a
number of volume elements (9) of the steel volume (1) comprise local
proportions (p1, p2, p3) of modeled phases of the steel and a quantity (H)
describing a local energy content of the steel, the modeled phases of the steel
comprise austenite and a first further phase, into which austenite can transform
and which can transform into austenite, the initial state (ZA) and the subsequent
state (ZF) for at least one of the volume elements (9) also comprise a local
distribution in concentration (K) of at least one mobile alloy element in the steel,
within the context of the phase change equation it is determined for the at least
one volume element (9) which concentrations (k1, k3; k2, k4) of the at least one
mobile alloy element are present on both sides of a first phase boundary (11,12)

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1996-KOLNP-2006-EXAMINATION REPORT.pdf

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1996-KOLNP-2007-CORRESPONDENCE 1.1.pdf

1996-KOLNP-2007-OTHERS.pdf

abstract-01996-kolnp-2006.jpg


Patent Number 252372
Indian Patent Application Number 1996/KOLNP/2006
PG Journal Number 19/2012
Publication Date 11-May-2012
Grant Date 10-May-2012
Date of Filing 17-Jul-2006
Name of Patentee SIEMENS AKTIENGESELLSCHAFT
Applicant Address WITTELSBACHERPLATZ 2, 80333 MUNCHEN
Inventors:
# Inventor's Name Inventor's Address
1 KLAUS WEINZIERL EISENSTEINER ATR.12 90480 NÜRNBERG
2 WOLFGANG BORCHERS NATURBADSTR.49 91056 ERLANGEN
3 KLAUS FRANZ TÜRKHEIMER STR.1 90455 NÜRNBERG
PCT International Classification Number B21B37/74; G05B17/02
PCT International Application Number PCT/EP2004/053709
PCT International Filing date 2004-12-27
PCT Conventions:
# PCT Application Number Date of Convention Priority Country
1 102004005919.5 2004-02-06 Germany