Title of Invention	MODELING METHOD FOR A METAL
Abstract	The temperature (T) of a metal (1) can be influenced directly or indirectly by at least one actuator (2) which is actuated in accordance with a control variable (S) . The control variable (S) and starting values (TA, p1A, p2A) for a temperature of the metal (1) and phase proportions in which the metal (1) is at least in a first phase or a second phase, respectively, are predetermined for a material model (5) . A heat conduction equation and a transformation equation are solved in real time within the material model (5) , taking account of these variables (TA, p1A, p2A) , and in this way expected values (TE, p1E/ p2E) are determined for these variables. As part of the transformation equation, the Gibbs' free energies (G1, G2) of the phases of the metal (1) are determined, a transformation rate of the metal (1) from the first phase to the second phase is determined therefrom, and the expected proportions (p1E, p2E) are determined from the latter.

Title of Invention

MODELING METHOD FOR A METAL

Abstract

The temperature (T) of a metal (1) can be influenced directly or indirectly by at least one actuator (2) which is actuated in accordance with a control variable (S) . The control variable (S) and starting values (TA, p1A, p2A) for a temperature of the metal (1) and phase proportions in which the metal (1) is at least in a first phase or a second phase, respectively, are predetermined for a material model (5) . A heat conduction equation and a transformation equation are solved in real time within the material model (5) , taking account of these variables (TA, p1A, p2A) , and in this way expected values (TE, p1E/ p2E) are determined for these variables. As part of the transformation equation, the Gibbs' free energies (G1, G2) of the phases of the metal (1) are determined, a transformation rate of the metal (1) from the first phase to the second phase is determined therefrom, and the expected proportions (p1E, p2E) are determined from the latter.

Full Text	Description Modeling method for a metal The present invention relates to a modeling method for a metal, the temperature of which can be influenced directly or indirectly by at least one actuator, a starting temperature of the metal and starting proportions, in which the metal is at least in a first phase or a second phase, respectively, being predetermined for a material model, a heat conduction equation and a transformation equation being solved in real time within the material model, taking account of the starting temperature, the starting proportions and a control variable for the actuator, so as to determine an expected temperature for the metal and expected proportions in which the metal is at least in the first phase or the second phase, respectively, the actuator being actuated in accordance with the control variable. Methods of this type are known, for example, from the article "Numerische Simulation der Warmeleitung in Stahlblechen - Mathematik hilft bei der Steuerung von Kuhlstrecken" [Numerical Simulation of the Heat Conduction in Steel Sheets - Mathematics helps to control cooling sections] by W. Borchers et al., published in Unikurier der Friedrich-Alexander- Universitat Erlangen-Nurnberg, Volume 102, October 2001, 27th edition. The known methods are used in particular to control coolant actuators in rolling mills. The coolant actuators may be arranged between the rolling stands. They may also be arranged downstream of the rolling stands. However, there are also other conceivable applications, for example in the context of calculating solidification processes in continuous casting or in the control of rolling mills per se. In the prior art, the Scheil rule or the Johnson-Mehl- Avrami or Brimacombe approaches are used to determine the proportions of the phases. The approaches used in the prior art in practice are not without faults in all cases. In particular, they have a range of systematic drawbacks. Firstly, each material has to be parameterized separately. Interpolations between different materials are not possible or at least are only possible to a limited extent. Secondly, the methods of the prior art consider only two phases. The system cannot be expanded to cover more than two phases. Thirdly, the methods of the prior art only provide good correspondence between model and reality if the metal under consideration is completely transformed. Fourthly, the method of the prior art does not give any information about the transformation heat released during the phase transformation. However, knowledge of the transformation heat is imperative if the heat conduction equation is to be correctly solved. The object of the present invention is to provide a modeling method for a metal which gives better modeling results. The object is achieved by virtue of the fact that as part of the transformation equation the Gibbs' free energies of the phases of the metal are determined, a transformation rate of the metal from the first phase to the second phase is determined on the basis of the Gibbs' free energies and the expected proportions are determined on the basis oC the transformation rate. In the simplest case of the present invention - as in the prior art - a purely two-phase system is considered, for example a transformation from austenite into ferrite and vice versa. However, the invention can also readily be expanded to multiphase systems, in particular to the ferrite-austenite- cementite system. In general, the proportions of the additives cannot be considered independently of one another. The - albeit linked - influence of additives on the Gibbs' free energy is known, however. By way of example, reference is made to the specialist articles "Approximate Thermodynamic Solution Phase Data for Steels" by Jyrki Miettinen, Calphad, Vol. 22, No. 2, pages 275 to 300, 1998, and "A Regular Solution Model for Phases with Several Components and Sublattices, Suitable for Computer Applications" by Bo Sundman and John Agren, Journal Phys. Chem. Solids, Vol. 42, pages 297 to 301. Therefore, for steel it is possible to determine the Gibbs' free energy of an iron-carbon mixture as a function of the proportion of carbon and the temperature and to take account of the effects of the additives, e.g. Ni, Si, P, as a function of the iron- carbon mixture, and also the temperature. If the material model is designed in such a manner that the proportions of the additives can also be predetermined for it, it is therefore possible to determine the Gibbs' free energies of the phases under consideration even for materials which are not explicitly predetermined. If specific Gibbs' free energies of the phases, i.e. Gibbs' free energies which are based on a uniform quantity of the metal, are determined, it is possible to determine the transformation rate in a particularly simple way, namely on the basis of the difference between the specific Gibbs' free energies. Alternatively, it is possible to determine the transformation rate :on the basis of the sum of the specific Gibbs' free energies of the phases, weighted with the proportions of the phases. Furthermore, it is possible to determine the transformation rate on the basis of the position integral over the specific Gibbs' free energies. This type of determination is advantageous in particular if the Gibbs' free energies of at least one of the phases are position-dependent. If the metal contains at least two chemically different constituents, the Gibbs' free energies can also be used to determine the distribution of the constituents between chemical compositions. The modeling method according to the invention can also be employed if at least one of the phases corresponds to a liquid state of the metal. However, it is also possible for at least one (and preferably all) of the phases to correspond to a solid state of the metal. It is possible for the method to be applied just once per metal. However, it is preferably applied at a multiplicity of locations in the metal which directly follow one another in terms of their position. If at least one desired temperature is predetermined for the material model, it is possible for the material model to automatically determine the control variable. The desired temperature may in this case in particular be a (temporal) desired temperature curve. The control variable may be a temporal control variable curve. In this case, it is possible in particular for the heat conduction equation and the transformation equation to be solved in steps using the control variable curve and in this way to determine an expected temperature curve for the metal and also expected proportion curves for the phases. In this case, the actuator is preferably only actuated after the heat conduction and transformation equations have been completely solved. However, the control variable may also be a single value. In this case, it is only used for one step in each case. In this case, the actuator is preferably actuated between the preceding step and the subsequent step. The modeling method operates particularly reliably if the starting temperature is an actual temperature recorded by a measuring element before the metal is influenced by the actuator. If a final temperature of the metal is recorded by a measuring element after the metal has been influenced by the actuator, the final temperature is compared with the expected temperature and the material model is adapted on the basis of the comparison, the material model becomes a self-teaching model. It is preferable for the heat conduction equation which is to be solved for the interior of the metal 1 to take the form where H is the enthalpy, t the time, *λthe thermal conductivity, p1 and p2 the proportions of the phases, p the density and T the temperature of the metal. q' is a heat quantity which is generated within the metal by external influences, e.g. deformation during rolling or inductive heating. The transformation heat produced on account of phase transformations, by contrast, is already taken into account in the left-hand part of the equation. The above, correct heat conduction equation can always be employed irrespective of the shape and state of the metal. If the. metal is in the form of a metal strip with a strip .thickness direction, it is possible to replace the equation given above by the simplified equation where x is the location in the strip thickness direction. Further advantages and details will emerge from the following description of an exemplary embodiment in conjunction with the accompanying drawings,in which in each case in outline form, FIG. 1 shows an installation for influencing the temperature of a metal, FIGS 2 and 3 show material models, FIG. 4 shows a block diagram for solving a transformation equation, FIGS 5 and 6 show examples of curves for Gibbs' free energies, and FIGS 7 to 9 show further installations for influencing the temperature of a metal. In accordance with FIG. 1, an installation for influencing the temperature of a metal 1 has an actuator 2. The temperature T of the metal 1 can be influenced directly or indirectly by means of the actuator 2, generally by cooling, but in some cases also by heating. By way of example, a defined quantity of a cooling.medium (typically water) can be applied to the metal 1. In the present case, the metal 1 is steel in solid state. However, it could also be in a liquid state. The metal 1 could also be a metal other than steel, e.g. aluminum or a nonferrous metal. According to FIG. 1, the metal 1 is -furthermore designed as a metal strip', with a strip thickness direction. However, other forms of the metal 1, e.g. profiled sections in rod form (e.g. wires), tubes or U-sections are also conceivable. The installation is controlled by a control computer 3. In particular, the actuator 2 is also actuated by the control computer 3 in accordance with a control variable S. The control computer 3 is programmed with a computer program 4. On account of the programming with the computer program 4, the control computer 3 - in addition to controlling the installation - also carries out a modeling method for the metal 1, which is described in more detail below. As part of the execution of the modeling method, as shown in FIG. 2 a starting temperature TA of the metal 1 and starting proportions plA, p2A, in which the metal 1 is in a first phase or a second phase, respectively, are predetermined for a material model 5 for the metal 1. The starting temperature TA may be an estimated value or a theoretically calculated value. Preferably, however - of. FIG. 1 - the installation has a measurement element 6. An actual temperature T of the metal can be recorded by means of the measuring element 6. In the present case, this recording of the actual temperature T takes place before the metal 1 is influenced by the actuator 2. The actual temperature T recorded at this instant is the starting temperature TA, which is fed to the material model 5. The starting proportion plA/ p2A are generally values which are determined on the basis of calculations or are known on account of process conditions. For example, it is already known that the metal 1 is entirely in a liquid phase prior to casting. Alternatively, it is known that the material is austenite if steel is held for long enough at a temperature above the transformation temperature of steel . Within the material model 5, in accordance with FIG. 2, the material equations are solved in real time for the interior of the metal 1 taking account of these starting values TA, plA, p2A, the control variable S and the efficiency of the actuator 2. The material equations comprise a heat conduction equation of the form and a transformation equation. In the equations, H is the enthalpy, t the time, A. the thermal conductivity, p1 and p2 the proportions of the phases, p the density and T the temperature of the metal 1. q' is a heat quantity which is generated within the metal 1 by external influences, e.g. deformation during rolling or inductive heating. The transformation heat produced on account of phase transformations, by contrast, is already taken into account in the left-hand part of the equation. Within the material model 5, therefore, an expected temperature TE for the metal 1 and expected proportions p1E P2E in which the metal 1 is in the first phase or the second phase, respectively, are determined in real time. The solution to the heat conduction equation and also the way of taking account of the control variable S and the efficiency of the actuator 2 are generally known to those skilled in the art. Therefore, these details will not be dealt with further in the text which follows. It should merely be noted that the abovementioned heat conduction equation is the general equation to be solved irrespective of the state and shape of the metal 1. In the present case, in which the metal 1 is in the form of a metal strip with a strip thickness direction, the heat conduction equation in accordance with FIG. 3 can be formulated in one-dimensional form, since the gradients in the strip movement direction and in the strip width are substantially zero. In this case, therefor'e, the heat conduction equation can be simplified to where x is additionally the location in the strip thickness direction. Solving the transformation equation involves using a method which is explained in more detail below in conjunction with FIG. 4. In the illustration shown in FIG. 4, the simplifying assumption was made that the metal 1 can adopt two phases. However, the method can readily be expanded to a metal 1 comprising more than two phases. In accordance with FIG. 4, a plurality of input variables are fed to an equation solution block 7. First of all, a heat quantity Q' is fed to the equation solution block 7. The heat quantity Q' comprises firstly the change in the heat balance on account of heat conduction and secondly if appropriate also the heat quantity q' generated within the metal 1 by external influences. Then, the proportion p1 in which the metal 1 is in the first phase is fed to the equation solution block 7. The temporal change p1' is also fed to the equation solution block 7. On account of the fact that FIG. 4 considers only a two-phase system, therefore, the proportion p2 of the second phase and its change p2' are also known. Finally, the enthalpies H1, H2 of the phases of the metal 1 are also fed to the equation solution block 7. The enthalpies H1, H2 are in this case based on a uniform quantity of the metal 1, for example one kilogram or one mol. The equation solution block 7 uses the linear equation system to determine the temporal changes H1', H2' in the enthalpies H1 and H2. These changes H1', H2' are fed to integrators 8, 9 which then determine the enthalpies H1, H2 as output signal. The integrators 8, 9 are suitably initialized with starting values Hl0, H20. The starting values Hl0, H20 in this case cannot be predetermined independently of one another. Rather, they have to be determined in such a way that the resulting specific Gibbs' free energies G1, G2 adopt the same value at the phase transformation temperature. In the linear equation system, T1' and T2' are to be understood as meaning the first derivatives of the corresponding temperatures Tl, T2 according to the respective enthalpy H1 or H2, i.e. not the temporal derivatives. As an alternative to the linear equation system given above, it is also possible to solve a nonlinear equation system of the form H0 is in this case a suitable starting value for the enthalpy H of the system. This equation system directly gives the enthalpies H1, H2. On the other hand, as has already been mentioned, it is not linear. The determined enthalpy H1 is fed to a temperature- determining means 10, which uses the enthalpy H1 for the phase under consideration to determine the expected temperature Tl. Furthermore, the enthalpy H1 is fed to an entropy-determining means 11, which uses the relationship to determine the entropy S1 for the phase under consideration. The expected temperature T1 and the determined entropy S1 are fed to a multiplier 12, the output signal of which is fed - with a negative sign - to an adder 13, which is also fed with the enthalpy H1. The output signal from the adder 13 corresponds to the specific Gibbs' free energy G1 of the phase under consideration. The corresponding specific Gibbs' free energy G2 is determined analogously for the second phase. Then, the difference AG between the two specific Gibbs' free energies G1, G2 is formed in an adder 14. The difference AG between the specific Gibbs' free energies Gl, G2 determined in this way is fed to a means 15 for determining the transformation rate. This means uses the difference ΔG and the proportion p1 to determine the transformation rate. The transformation rate is fed to an integrator 16, which is additionally fed with the starting proportion p1A as starting value. The output signal from the integrator 16, i.e. the expected proportion p1E determined, is then fed back to the equation solution block 7 and the means 15 for determining the transformation rate. As can be seen from FIG. 4, the transformation equation is solved in steps; in each step, the expected values previously determined are fed to the equation solution block 7. Similarly, the heat conduction equation is also solved in steps. Of course, the results of the heat conduction equation and transformation equation are adjusted after each step. The method is preferably applied for each reference point for the heat conduction equation. To save on calculation time, however, it is also possible to reduce the outlay involved in calculating the transformation model by combining reference points in the phase transformation. However, the heat conduction equation is always - i.e. in this case too - solved for each reference point. Furthermore, the temperatures T1, T2, if they are calculated correctly, have the same value, also referred to below as the expected temperature TE, at any instant. Any deviation between the temperatures Tl, T2 is therefore an indication that the material model 5 is less than optimum. It can therefore be used as part of the programming compilation of the material model 5 to optimize the material model 5 - in particular the entropy- and temperature- determining means 10, 11. The method shown in FIG. 4, therefore, determines the temporal curves for the expected temperature TE and the expected proportions p13, p2E. In the case of the method shown in FIG. 4, the control variable S does not have to have the same value at any given instant. Rather, the control variable S may have a temporal curve, referred to below as the control variable curve. Therefore, the current value of the control variable S is also updated at each step. In the event of the treatment of the metal 1 only acting on the surface, for example when water is applied to the metal, it forms part of the boundary conditions which are to be observed when solving the heat conduction equation. If a treatment of the metal 1 affects its volume, for example a rolling operation or an inductive heating step, by contrast, the control variable S in particular forms part of the heat quantity Q'. If the heat conduction and material equations are solved in steps, two alternative procedures are possible. Firstly, the actuator 2 can be actuated in accordance with the predetermined control variable curve S after the temporal curves for the expected temperature TE and the expected proportions plE, p2E have been determined. Secondly, however, it is also possible to use only the control variable S for the corresponding step and to actuate the actuator 2 in accordance with the control variable S between the preceding step and the subsequent step. In both cases, it is possible for only the control variable S to be predetermined for the material model 5. However, in accordance with FIGS 2 and 3, it is also possible for a desired temperature T - or preferably even a temporal curve of the desired temperature T* - to be predetermined for the material model 5. In this case, it is possible for the material model 5 to determine the control variable S automatically on the basis of the desired temperature T, the starting temperature TA and the efficiency of the actuator 2. After the metal 1 has been influenced by the actuator 2, the actual temperature T of the metal 1 is recorded once again - in accordance with FIG. 1 by means of a further measuring element 6'. This temperature T, referred to below as the final temperature, is compared, as shown in FIG. 5, with the expected temperature TE by an adapter element 5' . The adapter element 5' then adapts the material model 5 on the basis of the comparison. By way of example, it is possible to vary heat transfer variables in the heat conduction equation or influencing variables for the transformation rates. In accordance with the exemplary embodiment given, therefore, the specific Gibbs' free energies Gl, G2 of the phases, which are based on a uniform quantity of the metal 1, are determined. The transformation rate is then determined on the basis of the difference AG. In the simplest case, the transformation rate results as a product of a constant with the determined difference AG. In this case, however, it. is advantageous to employ a means 15 for determining the transformation rate which determines the transformation rate p1' from the difference AG and the instantaneous phase proportion p1. A means 15 of this type for determining the transformation rate may, for example, be parameterized on the basis of a data set from TTT diagrams for various steels. Furthermore, it would be entirely equivalent for the transformation rate to be determined on the basis of the sum of the specific Gibbs' free energies Gl, G2 weighted with the proportions p1, p2 of the phases. This makes use of the fact that the transformation, at a fixed temperature, automatically proceeds only in the direction of a decrease in the Gibbs' free energy G. The procedure described above in connection with FIG. 4 is appropriate in particular in the case of a pure phase transformation with the same chemical composition, for example a pure transformation from austenite to ferrite. It can also be employed if there is a pure transformation from a solid phase to a liquid phase or vice versa. The above description of the determination of the proportions p1, p2 has in each case used the current instantaneous values for the specific Gibbs' free energies G1, G2, for the specific entropies S1, S2, for the specific enthalpies H1, H2 and the expected temperatures T1, T2. However, the evaluation performed by the temperature- and entropy-determining means 10, 11 requires the functional curves or dependent relationships of the temperatures Tl, T2 and the specific entropies S1, S2 with respect to the corresponding specific enthalpies H1, H2 to be known. Therefore, in order to enable the phase transformations to be described successfully and correctly, it is necessary for basic functions which are dependent on the currently modeled metal 1, in particular on its chemical composition, to be made available to the temperature-determining means 10 and the entropy- determining means 11. For this purpose, when the material model 5 is being developed, it is preferable first of all to determine the specific Gibbs' free energies Gl, G2 for the phases of the substance under consideration as a function of the temperature. Determination of the specific Gibbs' free energy as a function of the temperature is described, for example, in the specialist article "A Thermodynamic Evaluation of the Fe-C System" by Per Gustafson in the Scandinavian Journal of Metallurgy 14 (1985), pages 259 to 267. It is then readily possible to determine the functional curves of the temperatures T1, T2 or of the specific entropies S1, S2 as a function of the specific enthalpy H1, H2 on :'the basis of the specific Gibbs' free energy G1 or G2 determined in this way as a function of the corresponding' temperature T1 or T2, respectively - i.e. the functional curves of the specific Gibbs' free energies G1, G2. This form of determination is one with which those skilled in the art will be generally familiar. For details, reference is made once again to the abovementioned article by Per Gustafson. When the functional curves of the specific Gibbs' free energies G1, G2 and also the functional curves of the temperatures T1, T2 and of the specific entropies S1, S2 are being determined, it is necessary in particular also to take into account the changes in the specific Gibbs' free energies G1, G2 that are caused by additives. Therefore, the changes to the specific Gibbs' free energies G1, G2 as a function of the added quantities of the additives under consideration are determined for the additives to be considered. Although with regard to the quantity of additive under consideration these changes may be highly nonlinear, they may also be dependent on one another. Both their aqtion and their dependent relationships with respect to one another are known, however, cf. the abovementioned articles by J. Miettinen and by B. Sundman and J. Agren. As a result, therefore, the temperature-determining means 10 and the entropy- determining means 11 are also intended for unknown mixtures if the proportions of the additives are known. Therefore, it is also possible to model unknown mixtures (in particular unknown steel compositions) with a high degree of accuracy. In practice, the metal 1 often has two chemically different base constituents. In the case of steel, these two constituents are typically iron (as the main constituent in amounts of significantly over 50 atom %) and carbon. In this case, first of all the specific Gibbs' free energy G is determined as a function of the (relative) proportion n of one of the two constituents and the temperature. Then, it is once again determined how this function changes for the additives under consideration. In this case too, however, the changes may be highly nonlinear. This is true both with regard to the quantities of the additives and with regard to the effect of the same quantities of the additives at various iron and carbon mixing ratios. Therefore, it is quite possible for a specific quantity of additives (e.g. 1% of silicon and 2% of phosphorus) to have a completely different effect on the specific Gibbs' free energy of an iron-carbon mixture comprising 1% of carbon and 99% of iron than on an iron-carbon mixture comprising 4% of carbon and 96% of iron. The percentages are in this case atomic percentages. It is also quite possible, for example, for double the quantity of the additives to have a completely different effect on the specific Gibbs' free energy than the single quantity of the additives. However, it is moreover the case that the influences of. the additives are known or can be determined in a known way. The curve of the specific Gibbs' free energy G determined in, this way for the iron-carbon mixture can be used to determine the distribution of the metal 1 between chemical compositions of the constituents. This is explained in more detail below on the basis of the example of an iron-carbon mixture. Assume the presence of a mixture of iron and carbon. In this context, nA is the proportion of iron, nB the proportion of carbon in the mixture. The sum of the proportions nA, nB is of course one. Furthermore, assume that nA1 is the proportion of iron in a first chemical composition, nA2 is the proportion of iron in a second chemical composition. The sum of these proportions nA1, nA2 in this case of course corresponds to the total proportion nA of iron. Similarly, proportions nB1, nB2 of carbon are also contained in both compositions. The sum of these proportions nB1, nB2 once again results in the total proportion nB of carbon. With m1 = nA1 + nB1 and m2 = nA2 + nB2, proportions for the respective composition are introduced. Therefore, the Gibbs' free energy G of the overall system turns out to be (Complete) differentiation of this equation according to nA1 and nB1 and zeroing the derivatives gives two equations and therefore two conditions for the proportions nA1 and nB1- In this context, it must be borne in mind that in this equation m1, m2 and the argument of G2 implicitly include nA1 and nB1 as variables. If the Gibbs' free energy G of the iron-carbon mixture as a function of the proportion n of carbon has a convex curve, as illustrated by way of example in FIG. 5, it is not possible to divide it into two chemical compositions in which the proportionally weighted sum of the specific Gibbs' free energies G1, G2 is lower than the Gibbs' free energy of the uniformly mixed system. In this case, the equations are linearly dependent. The result is a uniform chemical composition of the metal 1. On the other hand, if, as illustrated by way of example in FIG. 6, the Gibbs' free energy G as a function of the carbon content is not exclusively convex, it is possible to perform this division into two different chemical compositions in which the proportionally weighted sum of the specific Gibbs' free energies Gl, G2 is lower than the Gibbs' free energy G of the uniform mixture. In this case, the equations are linearly independent. This results in unambiguous values for the proportions nA1, nA2, nB1 and nB2. In this case, the metal 1 is broken down into two different chemical compositions. The compositions have mixing ratios n1 or n2 . The mixing ratios n1, n2 are defined by the equations respectively. In practice, it is often necessary to employ mixtures of these two procedures. For example, a relatively large quantity of carbon is soluble in austenite. On the other hand, only a small quantity of carbon is sdluble in ferrite. Therefore, during cooling austenite breaks down into a mixture of ferrite and pearlite, wherein pearlite is a eutectic mix comprising cementite (Fe3C) and ferrite and has formed as a result of carbon-saturated austenite cooling to below the temperature of the surrounding walls. The phase transformation rate is described by what is known as a transformation diffusion model. In this case, the various phases are separated from one another by moveable phase boundaries. There are moveable and non-moveable elements within each phase. The non- moveable elements are distributed uniformly. The moveable elements are not generally distributed uniformly within the phase. The diffusion of the moveable elements in each phase is toward the negative gradient of the associated chemical potential. The diffusion rate of the moveable elements is in this case finite. The chemical potential is obtained by differentiation of the specific Gibbs' free energies (i.e. the Gibbs' free energies based on identical quantities) on the basis of the concentration of the moveable elements. The precise presentation of the diffusion for one or more moveable elements is known to those skilled in the art. To determine the speed at which the phase interface is moving, the difference between the specific Gibbs' free energies immediately in front of and immediately behind the phase interface is to be formed at the free phase interface. This task is referred to by those skilled in the art as the free boundary problem with diffusion or also as the Stefan problem and is generally known. An approximated solution is to be found, for example, in Kar, A. and Mazumder, J.: Analytic Solution of the Stefan Problem in Finite Mediums. Quart. Appl. Math., Vol. 52, 1994. In the context of the present invention, a dedicated transformation rate can be determined for each transformation - both for a phase transformation per se and for decomposition of a chemical composition into other. chemical compositions. Overall, it can be stated that the transformation phenomenon at any time is moving in the direction of a decrease in the Gibbs' free energy G of the overall system. Therefore, the above model proposal can also be formulated without explicit use of the difference between the specific Gibbs' free energies G1, G2 at the phase interfaces. In particular taking account of the cooling behavior of the metal 1, therefore, it is possible to make a statement not only on the phase state of the metal 1 but also on its microstructure and grain size. In accordance with FIG. 7, the installation is designed as a cooling device for the metal 1. The actuator 2 is designed as a' coolant actuator 2. It is either arranged between rolling stands of a rolling mill or downstream of the rolling stands. It can apply defined quantities of a . coolant, typically water, to the metal 1 via individually actuatable sections 2' . As has been stated above in connection with FIG. 1, the temperature T of the metal 1 is in each case recorded by means of measuring elements 6, 6' . If the cooling device is arranged exclusively downstream of the rolling stands, the measuring element 6 is arranged downstream of the final rolling stand and upstream of the cooling device. Otherwise, it is preferable for the measuring element 6 to be arranged upstream of the rolling stand (s) which precede (s) the cooling device and for the measuring element 6' to be arranged downstream of, the rolling stand (s) which precede(s) the cooling device. When the cooling section is operating, as part of the cycle, the starting temperature TA of the metal 1 is recorded by means of the measuring element 6 each time the heat conduction and transformation equations are being solved. Furthermore, a material velocity v is fed to the material model 5. This enables the material model 5 to carry out material monitoring with regard to the locations in the metal 1 at which the starting temperature TA was recorded, and in this way to actuate the individual sections 2' of the actuator 2 at the correct time. It is also possible for the final temperature . T to be recorded at the correct time by means of a further measuring element 6' at the end of the cooling section and for this temperature to be assigned to the corresponding location of the metal 1. In the embodiment shown in FIG. 7, therefore, the modeling method is applied at a multiplicity of locations in the metal 1 which directly follow one another in terms of their position. In the example shown in FIG. 7, the direction of flow of the material is always identical. However, it is also possible for the direction of flow of the material to change. For example, in the case of a plate mill train, the material can be returned to the rolling stand for cooling purposes and subjected to a further rolling operation with a subsequent cooling operation. FIGS 8 and 9 show further possible applications for the modeling method according to the invention. In accordance with FIG. 8, the installation is designed as a rolling mill train. In the present case, the actuator 2 is one of the rolling stands, and the corresponding control variable S is the rolling speed. If appropriate, the actuator 2 may also be a combination of a rolling stand and a cooling device. In this case, of course, the control variable S is also a combined control variable. In the embodiment shown in FIG. 9, the installation is designed as a continuous-casting installation. The actuator 2 is designed as a combined actuator, by means of which on the one hand the cooling of the permanent mold of the continuous-casting installation is influenced, and on the other hand the discharge velocity v at which the cast strand 1 is discharged from the permanent mold. The present invention has numerous advantages. Firstly, the material model 5 of the present invention, given complete parameterization with respect to the possible additives, makes it possible to obtain generally valid results which allow the treatment even of unknown material classes and individual materials. Furthermore - unlike with the approaches used by Scheil and Avrami - the transformation behavior is described correctly even in the case of incomplete transformation. In this case, unlike in the methods of the prior art, the transformation heat produced during the phase transformation is determined correctly and taken into account within the scope of the material model 5. In particular, however, the complicated topology of phase diagrams and TTT diagrams is returned to the parameterization of standard smooth curves. As a result, technical processing of the dependent relationship among alloying elements, which is extremely complex in the case of steel, becomes possible for the first time, since if the pressure and temperature T of the system under consideration - in this case of the metal 1 - are kept constant, the Gibbs' free energy G of the system seeks to adopt its minimum value. A comparison of the Gibbs' free energies G1, G2 of various phases therefore indicates the direction of the phase transformation. In this case, it is even possible to process the extremely difficult case of a metal with additives and compounds such as cementite (Fe3C) as phases in a physically correct manner. Finally, the approaches can be applied not only to temperature calculation but also to the calculation of microstructure and grain size. WE CLAIM : 1. A method for controlling a solidification process of metal (1) in continuous casting or a rolling mill by controlling coolant actuator in the mill, or the like, the temperature (T) of which can be influenced directly or indirectly by at least one actuator (2), said method comprising the steps of: predetermining for a material model (5) a starting temperature TA) of the metal (1) and starting proportions (p1A, P2A), in which the metal (1) is at least in a first phase or a second phase, respectively; solving in real time a heat conduction equation and a transformation equation within the material model (5), taking account of the starting temperature (TA), the starting proportions (p1 A. P2A) and a control variable (S) for actuator (2), so as to determine an expected temperature (TE) for the metal (1) and expected proportions (p1E, p2E) in which the metal (1) is at least in the first phase or the second phase respectively; and actuating said actuator (2) in accordance with said controlled variable/s; characterized in that as part ot the transformation equation the Gibbs' free energies (Gl, G2) of the phases of the metal (1) are determined, a transformation rate of the metal (1) from the first phase to the second phase is determined on the basis of the Gibbs' free energies (Gl, G2) and the expected proportions (p1E, P2E) are determined on the details of the transformation rate. 2.The modeling method as claimed in claim 1, wherein specific Gibbs' free energies (Gl, G2) of the phases, i.e. Gibbs' free energies which are based on a uniform quantity of the metal (1), are determined, and in that the transformation rate is determined on the basis of the difference between the specific Gibbs' free energies (Gl, G2). 3. The modeling method as claimed in claim 1, wherein specific Gibbs' free energies (Gl, G2), i.e. Gibbs' free energies which are based on a uniform quantity of the metal (1), are determined, and in that the transformation rate is determined on the basis of the sum of the specific Gibbs' free energies (G1, G2) of the phases, weighted with the proportions (p1, p2) of the phases. 4 The modeling method as claimed in claim 1, 2 or 3, wherein specific Gibbs' free energies (G1, G2), i.e. Gibbs' free energies which are based on a uniform quantity of the metal (1), are determined, in that the specific Gibbs' free energy (Gl, G2) of at least one of , the phases is position-dependent, and in that the transformation rate is determined on the basis of the position integral over the specific Gibbs' free energy (Gl, G2) of the phases. 5. The modeling method as claimed in one , of the wherein the preceding claims, the metal (1) contains at least two chemically different constituents (e.g. iron and carbon), and in that the Gibbs' free energies (Gl, G2) are also used to determine the distribution of the constituents between chemical compositions. 6. The modeling method, as . claimed in one of the wherein preceding claims, at least one of the phases corresponds to a liquid state of the metal (1) 7. The modeling method as claimed in one of the where in preceding claims, , at least one of the phases corresponds to a solid state of the metal (1) 8.' The modelinq method, as . claimed in one of the whereinpreceding claims, It is applied at a multiplicity of locations in the metal (1) which directly follow one another in terms of their position. 9. The modeling method as .claimed in one of the wherein preceding claims, characterized_at least one desired temperature (T) is predetermined for the material model (5), and in that the material model (5) automatically determines the control variable (S). 10. The modeling method as claimed in claim 9, the desired temperature (T) is a desired temperature curve (T). 11. The modeling method as claimed in one of claims 1 wherein to 10, the control variable (S) is a control variable curve (S) , in that the heat conduction equation and the transformation equation are solved in steps using the control variable curve (S) , and in this way an expected temperature curve (TE) for the metal (1) and expected proportion curves (p1E/ p2E) for the phases are determined, and in that the actuator (2) is only actuated in accordance with the control variable curve (S) after the expected temperature curve (TE) for the metal (1) and the expected proportion curves (plE, p2E) for the phases have been determined. 12. The modeling method as claimed in one of claims 1 wherein that "the heat conduction equation and the transformation equation are solved in steps, and in this way an expected temperature curve (TE) for the metal (1) and expected proportion curves (p1E, p2E) for the phases are determined, in that the control variable (S) is used only for the respective step, and in that the actuator (2) is actuated in accordance with the control variable (S:) between the preceding step and the subsequent step. 13. The modeling method as claimed in one of the wherein preceding claims,wherein the starting temperature (TA) is an actual temperature (T) of the metal (1) recorded by a measuring element (6) before the metal (1) is influenced by the actuator (2). 14. The modeling method as claimed in one of the wherein preceding claims, wherein after the metal (1) has been influenced by the actuator (2), a measuring element (6') records a final temperature (T) of the metal (1), in that the final temperature (T) is compared with the expected temperature (TE) , and in that the material model (5) is adapted on the basis of the comparison. 15. The modeling method as claimed in one of claims 1 to 14, wherein the heat conduction equation which is to be solved for the interior of the metal (1) takes the form where H is the enthalpy, t the time, λ the thermal conductivity, p1 and p2 the proportions of the phases, p the density and T the temperature of the metal (1) and q' is a heat quantity which is generated by external influences within the metal (1). 16. The modeling method as claimed in one of claims 1 wherein to 14, wherein metal (1) is in the form of a metal strip with a strip thickness direction, and in that the heat conduction equation which is to be solved for the interior of the metal (1) takes the' form where H is the enthalpy, t the time, x the location in the strip thickness direction, λ the thermal conductivity, p1 and p2 the proportions of the phases, p the density and T the temperature of the metal (1) and q' is a heat quantity which is generated by external influences within the metal (1). 17. The modeling method as claimed in one of the preceding claims, wherein the metal (1) contains iron as its main constituent. 18. A computer system (3) enabled to control a device having an actuator (2), to manipulate the temperature (T) of a metal (1) directly or indirectly. 19. A device having an actuator (2) by means of which the temperature (T) of a metal (1) can be manipulated directly or indirectly, wherein it is controlled by the computer system (3) as claimed in claim 18. 20. The device as claimed in claim 19, wherein it is configured as a cooling device for a metal (1), and wherein the actuator (2) is a coolant actuator (2). 21.The device as claimed in claim 20, comprising at least one rolling stand of a rolling mill disposed downstream of the cooling device 22. The device as claimed in claim 20, wherein the cooling device is disposed downstream of at least one rolling stand of a rolling mill. 23. The device as claimed in claim 19, wherein it is configured as a rolling mill train, and wherein the actuator (2) is designed as a rolling speed actuator (2). 24. The device as claimed in claim 19, wherein it is configured as a continuous-casting device. 25. The device as claimed in claim 19, wherein it is configured as a continuous-casting device for casting a strip (1) with a strip thickness (d) of between 40 and 100 mm, and having finishing train arranged directly downstream of the device. 26. The device as claimed in claim 19, wherein it is configured as a thin- strip casting device for casting a metal strip (1) with a maximum strip thickness (d) of 10 mm, and having two rolling stands arranged downstream of the device. The temperature (T) of a metal (1) can be influenced directly or indirectly by at least one actuator (2) which is actuated in accordance with a control variable (S) . The control variable (S) and starting values (TA, p1A, p2A) for a temperature of the metal (1) and phase proportions in which the metal (1) is at least in a first phase or a second phase, respectively, are predetermined for a material model (5) . A heat conduction equation and a transformation equation are solved in real time within the material model (5) , taking account of these variables (TA, p1A, p2A) , and in this way expected values (TE, p1E/ p2E) are determined for these variables. As part of the transformation equation, the Gibbs' free energies (G1, G2) of the phases of the metal (1) are determined, a transformation rate of the metal (1) from the first phase to the second phase is determined therefrom, and the expected proportions (p1E, p2E) are determined fromthe latter.

Full Text

Description
Modeling method for a metal
The present invention relates to a modeling method for
a metal, the temperature of which can be influenced
directly or indirectly by at least one actuator,
a starting temperature of the metal and starting
proportions, in which the metal is at least in a
first phase or a second phase, respectively, being
predetermined for a material model,
a heat conduction equation and a transformation
equation being solved in real time within the
material model, taking account of the starting
temperature, the starting proportions and a control
variable for the actuator, so as to determine an
expected temperature for the metal and expected
proportions in which the metal is at least in the
first phase or the second phase, respectively,
the actuator being actuated in accordance with the
control variable.
Methods of this type are known, for example, from the
article "Numerische Simulation der Warmeleitung in
Stahlblechen - Mathematik hilft bei der Steuerung von
Kuhlstrecken" [Numerical Simulation of the Heat
Conduction in Steel Sheets - Mathematics helps to
control cooling sections] by W. Borchers et al.,
published in Unikurier der Friedrich-Alexander-
Universitat Erlangen-Nurnberg, Volume 102, October
2001, 27th edition.
The known methods are used in particular to control
coolant actuators in rolling mills. The coolant
actuators may be arranged between the rolling stands.
They may also be arranged downstream of the rolling
stands. However, there are also other conceivable
applications, for example in the context of calculating
solidification processes in continuous casting or in

the control of rolling mills per se.

In the prior art, the Scheil rule or the Johnson-Mehl-
Avrami or Brimacombe approaches are used to determine
the proportions of the phases.
The approaches used in the prior art in practice are
not without faults in all cases. In particular, they
have a range of systematic drawbacks. Firstly, each
material has to be parameterized separately.
Interpolations between different materials are not
possible or at least are only possible to a limited
extent. Secondly, the methods of the prior art consider
only two phases. The system cannot be expanded to cover
more than two phases. Thirdly, the methods of the prior
art only provide good correspondence between model and
reality if the metal under consideration is completely
transformed. Fourthly, the method of the prior art does
not give any information about the transformation heat
released during the phase transformation. However,
knowledge of the transformation heat is imperative if
the heat conduction equation is to be correctly solved.
The object of the present invention is to provide a
modeling method for a metal which gives better modeling
results.
The object is achieved by virtue of the fact that as
part of the transformation equation the Gibbs' free
energies of the phases of the metal are determined, a
transformation rate of the metal from the first phase
to the second phase is determined on the basis of the
Gibbs' free energies and the expected proportions are
determined on the basis oC the transformation rate.
In the simplest case of the present invention - as in
the prior art - a purely two-phase system is
considered, for example a transformation from austenite
into ferrite and vice versa. However, the invention can
also readily be expanded to multiphase

systems, in particular to the ferrite-austenite-
cementite system.
In general, the proportions of the additives cannot be
considered independently of one another. The - albeit
linked - influence of additives on the Gibbs' free
energy is known, however. By way of example, reference
is made to the specialist articles "Approximate
Thermodynamic Solution Phase Data for Steels" by Jyrki
Miettinen, Calphad, Vol. 22, No. 2, pages 275 to 300,
1998, and "A Regular Solution Model for Phases with
Several Components and Sublattices, Suitable for
Computer Applications" by Bo Sundman and John Agren,
Journal Phys. Chem. Solids, Vol. 42, pages 297 to 301.
Therefore, for steel it is possible to determine the
Gibbs' free energy of an iron-carbon mixture as a
function of the proportion of carbon and the
temperature and to take account of the effects of the
additives, e.g. Ni, Si, P, as a function of the iron-
carbon mixture, and also the temperature. If the
material model is designed in such a manner that the
proportions of the additives can also be predetermined
for it, it is therefore possible to determine the
Gibbs' free energies of the phases under consideration
even for materials which are not explicitly
predetermined.
If specific Gibbs' free energies of the phases, i.e.
Gibbs' free energies which are based on a uniform
quantity of the metal, are determined, it is possible
to determine the transformation rate in a particularly
simple way, namely on the basis of the difference
between the specific Gibbs' free energies.
Alternatively, it is possible to determine the
transformation rate :on the basis of the sum of the
specific Gibbs' free energies of the phases, weighted
with the proportions of the phases.

Furthermore, it is possible to determine the
transformation rate on the basis of the position
integral over the specific Gibbs' free energies. This
type of determination is advantageous in particular if

the Gibbs' free energies of at least one of the phases
are position-dependent.
If the metal contains at least two chemically different
constituents, the Gibbs' free energies can also be used
to determine the distribution of the constituents
between chemical compositions.
The modeling method according to the invention can also
be employed if at least one of the phases corresponds
to a liquid state of the metal. However, it is also
possible for at least one (and preferably all) of the
phases to correspond to a solid state of the metal.
It is possible for the method to be applied just once
per metal. However, it is preferably applied at a
multiplicity of locations in the metal which directly
follow one another in terms of their position.
If at least one desired temperature is predetermined
for the material model, it is possible for the material
model to automatically determine the control variable.
The desired temperature may in this case in particular
be a (temporal) desired temperature curve.
The control variable may be a temporal control variable
curve. In this case, it is possible in particular for
the heat conduction equation and the transformation
equation to be solved in steps using the control
variable curve and in this way to determine an expected
temperature curve for the metal and also expected
proportion curves for the phases. In this case, the
actuator is preferably only actuated after the heat
conduction and transformation equations have been
completely solved.
However, the control variable may also be a single
value. In this case, it is only used for one step in each

case. In this case, the actuator is preferably actuated
between the preceding step and the subsequent step.
The modeling method operates particularly reliably if
the starting temperature is an actual temperature
recorded by a measuring element before the metal is
influenced by the actuator.
If a final temperature of the metal is recorded by a
measuring element after the metal has been influenced
by the actuator, the final temperature is compared with
the expected temperature and the material model is
adapted on the basis of the comparison, the material
model becomes a self-teaching model.
It is preferable for the heat conduction equation which
is to be solved for the interior of the metal 1 to take
the form

where H is the enthalpy, t the time, **λthe thermal
conductivity, p1 and p2 the proportions of the phases, p
the density and T the temperature of the metal. q' is a
heat quantity which is generated within the metal by
external influences, e.g. deformation during rolling or
inductive heating. The transformation heat produced on
account of phase transformations, by contrast, is already
taken into account in the left-hand part of the equation.
The above, correct heat conduction equation can always
be employed irrespective of the shape and state of the
metal. If the. metal is in the form of a metal strip
with a strip .thickness direction, it is possible to
replace the equation given above by the simplified
equation

where x is the location in the strip thickness
direction.
Further advantages and details will emerge from the
following description of an exemplary embodiment in
conjunction with the accompanying drawings,in which in each case
in outline form,
FIG. 1 shows an installation for influencing
the temperature of a metal,
FIGS 2 and 3 show material models,
FIG. 4 shows a block diagram for solving a
transformation equation,
FIGS 5 and 6 show examples of curves for Gibbs' free
energies, and
FIGS 7 to 9 show further installations for
influencing the temperature of a metal.
In accordance with FIG. 1, an installation for
influencing the temperature of a metal 1 has an
actuator 2. The temperature T of the metal 1 can be
influenced directly or indirectly by means of the
actuator 2, generally by cooling, but in some cases
also by heating. By way of example, a defined quantity
of a cooling.medium (typically water) can be applied to
the metal 1.
In the present case, the metal 1 is steel in solid
state. However, it could also be in a liquid state. The
metal 1 could also be a metal other than steel, e.g.
aluminum or a nonferrous metal. According to FIG. 1,
the metal 1 is -furthermore designed as a metal strip',
with a strip thickness direction. However, other forms
of the metal 1, e.g. profiled sections in rod form

(e.g. wires), tubes or U-sections are also conceivable.

The installation is controlled by a control computer 3.
In particular, the actuator 2 is also actuated by the
control computer 3 in accordance with a control
variable S. The control computer 3 is programmed with a
computer program 4. On account of the programming with
the computer program 4, the control computer 3 - in
addition to controlling the installation - also carries
out a modeling method for the metal 1, which is
described in more detail below.
As part of the execution of the modeling method, as
shown in FIG. 2 a starting temperature TA of the metal
1 and starting proportions plA, p2A, in which the metal
1 is in a first phase or a second phase, respectively,
are predetermined for a material model 5 for the metal
1. The starting temperature TA may be an estimated
value or a theoretically calculated value. Preferably,
however - of. FIG. 1 - the installation has a
measurement element 6. An actual temperature T of the
metal can be recorded by means of the measuring element
6. In the present case, this recording of the actual
temperature T takes place before the metal 1 is
influenced by the actuator 2. The actual temperature T
recorded at this instant is the starting temperature
TA, which is fed to the material model 5.
The starting proportion plA/ p2A are generally values
which are determined on the basis of calculations or
are known on account of process conditions. For
example, it is already known that the metal 1 is
entirely in a liquid phase prior to casting.
Alternatively, it is known that the material is
austenite if steel is held for long enough at a
temperature above the transformation temperature of
steel .
Within the material model 5, in accordance with FIG. 2,
the material equations are solved in real time for the

interior of the metal 1 taking account of these
starting values TA, plA, p2A, the control variable S and
the efficiency of the actuator 2. The material
equations comprise a heat conduction equation of the
form

and a transformation equation. In the equations, H is
the enthalpy, t the time, A. the thermal conductivity,
p1 and p2 the proportions of the phases, p the density
and T the temperature of the metal 1. q' is a heat
quantity which is generated within the metal 1 by
external influences, e.g. deformation during rolling or
inductive heating. The transformation heat produced on
account of phase transformations, by contrast, is
already taken into account in the left-hand part of the
equation. Within the material model 5, therefore, an
expected temperature TE for the metal 1 and expected
proportions p1E P2E in which the metal 1 is in the
first phase or the second phase, respectively, are
determined in real time.
The solution to the heat conduction equation and also
the way of taking account of the control variable S and
the efficiency of the actuator 2 are generally known to
those skilled in the art. Therefore, these details will
not be dealt with further in the text which follows. It
should merely be noted that the abovementioned heat
conduction equation is the general equation to be
solved irrespective of the state and shape of the metal
1. In the present case, in which the metal 1 is in the
form of a metal strip with a strip thickness direction,
the heat conduction equation in accordance with FIG. 3
can be formulated in one-dimensional form, since the
gradients in the strip movement direction and in the
strip width are substantially zero. In this case,
therefor'e, the heat conduction equation can be
simplified to

where x is additionally the location in the strip
thickness direction.
Solving the transformation equation involves using a
method which is explained in more detail below in
conjunction with FIG. 4.

In the illustration shown in FIG. 4, the simplifying
assumption was made that the metal 1 can adopt two
phases. However, the method can readily be expanded to
a metal 1 comprising more than two phases.
In accordance with FIG. 4, a plurality of input variables
are fed to an equation solution block 7. First of all, a
heat quantity Q' is fed to the equation solution block 7.
The heat quantity Q' comprises firstly the change in the
heat balance on account of heat conduction and secondly if
appropriate also the heat quantity q' generated within the
metal 1 by external influences.
Then, the proportion p1 in which the metal 1 is in the
first phase is fed to the equation solution block 7.
The temporal change p1' is also fed to the equation
solution block 7. On account of the fact that FIG. 4
considers only a two-phase system, therefore, the
proportion p2 of the second phase and its change p2'
are also known.
Finally, the enthalpies H1, H2 of the phases of the
metal 1 are also fed to the equation solution block 7.
The enthalpies H1, H2 are in this case based on a
uniform quantity of the metal 1, for example one
kilogram or one mol.
The equation solution block 7 uses the linear equation
system

to determine the temporal changes H1', H2' in the
enthalpies H1 and H2. These changes H1', H2' are fed to
integrators 8, 9 which then determine the enthalpies
H1, H2 as output signal.

The integrators 8, 9 are suitably initialized with
starting values Hl0, H20. The starting values Hl0, H20
in this case cannot be predetermined independently of
one another. Rather, they have to be determined in such
a way

that the resulting specific Gibbs' free energies G1, G2
adopt the same value at the phase transformation
temperature.
In the linear equation system, T1' and T2' are to be
understood as meaning the first derivatives of the
corresponding temperatures Tl, T2 according to the
respective enthalpy H1 or H2, i.e. not the temporal
derivatives.
As an alternative to the linear equation system given
above, it is also possible to solve a nonlinear
equation system of the form

H0 is in this case a suitable starting value for the
enthalpy H of the system. This equation system directly
gives the enthalpies H1, H2. On the other hand, as has
already been mentioned, it is not linear.
The determined enthalpy H1 is fed to a temperature-
determining means 10, which uses the enthalpy H1 for
the phase under consideration to determine the expected
temperature Tl. Furthermore, the enthalpy H1 is fed to
an entropy-determining means 11, which uses the
relationship

to determine the entropy S1 for the phase under
consideration.
The expected temperature T1 and the determined entropy
S1 are fed to a multiplier 12, the output signal of
which is fed - with a negative sign - to an adder 13,
which is also fed with the enthalpy H1. The output
signal from the adder 13 corresponds to the specific
Gibbs' free energy G1 of the phase under consideration.

The corresponding specific Gibbs' free energy G2 is
determined analogously for the second phase. Then, the
difference AG between the two specific Gibbs' free
energies G1, G2 is formed in an adder 14.
The difference AG between the specific Gibbs' free
energies Gl, G2 determined in this way is fed to a
means 15 for determining the transformation rate. This
means uses the difference ΔG and the proportion p1 to
determine the transformation rate. The transformation
rate is fed to an integrator 16, which is additionally
fed with the starting proportion p1A as starting value.
The output signal from the integrator 16, i.e. the
expected proportion p1E determined, is then fed back to
the equation solution block 7 and the means 15 for
determining the transformation rate.
As can be seen from FIG. 4, the transformation equation is
solved in steps; in each step, the expected values
previously determined are fed to the equation solution
block 7. Similarly, the heat conduction equation is also
solved in steps. Of course, the results of the heat
conduction equation and transformation equation are
adjusted after each step. The method is preferably applied
for each reference point for the heat conduction equation.
To save on calculation time, however, it is also possible
to reduce the outlay involved in calculating the
transformation model by combining reference points in the
phase transformation. However, the heat conduction
equation is always - i.e. in this case too - solved for
each reference point.
Furthermore, the temperatures T1, T2, if they are
calculated correctly, have the same value, also referred
to below as the expected temperature TE, at any instant.
Any deviation between the temperatures Tl, T2 is therefore
an indication that the material model 5 is less than
optimum. It can therefore be used as part of the

programming compilation of the material model 5 to
optimize the material model 5

- in particular the entropy- and temperature-
determining means 10, 11.
The method shown in FIG. 4, therefore, determines the
temporal curves for the expected temperature TE and the
expected proportions p13, p2E.
In the case of the method shown in FIG. 4, the control
variable S does not have to have the same value at any
given instant. Rather, the control variable S may have
a temporal curve, referred to below as the control
variable curve. Therefore, the current value of the
control variable S is also updated at each step. In the
event of the treatment of the metal 1 only acting on
the surface, for example when water is applied to the
metal, it forms part of the boundary conditions which
are to be observed when solving the heat conduction
equation. If a treatment of the metal 1 affects its
volume, for example a rolling operation or an inductive
heating step, by contrast, the control variable S in
particular forms part of the heat quantity Q'.
If the heat conduction and material equations are
solved in steps, two alternative procedures are
possible. Firstly, the actuator 2 can be actuated in
accordance with the predetermined control variable
curve S after the temporal curves for the expected
temperature TE and the expected proportions plE, p2E
have been determined. Secondly, however, it is also
possible to use only the control variable S for the
corresponding step and to actuate the actuator 2 in
accordance with the control variable S between the
preceding step and the subsequent step.
In both cases, it is possible for only the control
variable S to be predetermined for the material model
5. However, in accordance with FIGS 2 and 3, it is also
possible for a desired temperature T* - or preferably

even a temporal curve of the desired temperature
T* - to be predetermined for the material model 5. In
this case, it is possible for the material model 5 to
determine the control variable S automatically on the
basis of the desired temperature

T*, the starting temperature TA and the efficiency of
the actuator 2.
After the metal 1 has been influenced by the actuator
2, the actual temperature T of the metal 1 is recorded
once again - in accordance with FIG. 1 by means of a
further measuring element 6'. This temperature T,
referred to below as the final temperature, is
compared, as shown in FIG. 5, with the expected
temperature TE by an adapter element 5' . The adapter
element 5' then adapts the material model 5 on the
basis of the comparison. By way of example, it is
possible to vary heat transfer variables in the heat
conduction equation or influencing variables for the
transformation rates.
In accordance with the exemplary embodiment given,
therefore, the specific Gibbs' free energies Gl, G2 of
the phases, which are based on a uniform quantity of
the metal 1, are determined. The transformation rate is
then determined on the basis of the difference AG. In
the simplest case, the transformation rate results as a
product of a constant with the determined difference
AG. In this case, however, it. is advantageous to employ
a means 15 for determining the transformation rate
which determines the transformation rate p1' from the
difference AG and the instantaneous phase proportion
p1. A means 15 of this type for determining the
transformation rate may, for example, be parameterized
on the basis of a data set from TTT diagrams for
various steels.
Furthermore, it would be entirely equivalent for the
transformation rate to be determined on the basis of
the sum of the specific Gibbs' free energies Gl, G2
weighted with the proportions p1, p2 of the phases.
This makes use of the fact that the transformation, at
a fixed temperature, automatically proceeds only in the

direction of a decrease in the Gibbs' free energy G.
The procedure described above in connection with FIG. 4
is appropriate in particular in the case of a pure
phase transformation with the same chemical
composition, for example a pure transformation from
austenite

to ferrite. It can also be employed if there is a pure
transformation from a solid phase to a liquid phase or
vice versa.
The above description of the determination of the
proportions p1, p2 has in each case used the current
instantaneous values for the specific Gibbs' free
energies G1, G2, for the specific entropies S1, S2, for
the specific enthalpies H1, H2 and the expected
temperatures T1, T2. However, the evaluation performed
by the temperature- and entropy-determining means 10,
11 requires the functional curves or dependent
relationships of the temperatures Tl, T2 and the
specific entropies S1, S2 with respect to the
corresponding specific enthalpies H1, H2 to be known.
Therefore, in order to enable the phase transformations
to be described successfully and correctly, it is
necessary for basic functions which are dependent on
the currently modeled metal 1, in particular on its
chemical composition, to be made available to the
temperature-determining means 10 and the entropy-
determining means 11. For this purpose, when the
material model 5 is being developed, it is preferable
first of all to determine the specific Gibbs' free
energies Gl, G2 for the phases of the substance under
consideration as a function of the temperature.
Determination of the specific Gibbs' free energy as a
function of the temperature is described, for example, in
the specialist article "A Thermodynamic Evaluation of the
Fe-C System" by Per Gustafson in the Scandinavian Journal
of Metallurgy 14 (1985), pages 259 to 267.
It is then readily possible to determine the functional
curves of the temperatures T1, T2 or of the specific
entropies S1, S2 as a function of the specific enthalpy
H1, H2 on :'the basis of the specific Gibbs' free energy
G1 or G2 determined in this way as a function of the
corresponding' temperature T1 or T2, respectively - i.e.

the functional curves of the specific Gibbs' free
energies G1, G2. This form of determination is one with
which those skilled in the art will be generally
familiar. For details,

reference is made once again to the abovementioned
article by Per Gustafson.
When the functional curves of the specific Gibbs' free
energies G1, G2 and also the functional curves of the
temperatures T1, T2 and of the specific entropies S1,
S2 are being determined, it is necessary in particular
also to take into account the changes in the specific
Gibbs' free energies G1, G2 that are caused by
additives. Therefore, the changes to the specific
Gibbs' free energies G1, G2 as a function of the added
quantities of the additives under consideration are
determined for the additives to be considered. Although
with regard to the quantity of additive under
consideration these changes may be highly nonlinear,
they may also be dependent on one another. Both their
aqtion and their dependent relationships with respect
to one another are known, however, cf. the
abovementioned articles by J. Miettinen and by
B. Sundman and J. Agren. As a result, therefore, the
temperature-determining means 10 and the entropy-
determining means 11 are also intended for unknown
mixtures if the proportions of the additives are known.
Therefore, it is also possible to model unknown
mixtures (in particular unknown steel compositions)
with a high degree of accuracy.
In practice, the metal 1 often has two chemically
different base constituents. In the case of steel,
these two constituents are typically iron (as the main
constituent in amounts of significantly over 50 atom %)
and carbon. In this case, first of all the specific
Gibbs' free energy G is determined as a function of the
(relative) proportion n of one of the two constituents
and the temperature. Then, it is once again determined
how this function changes for the additives under
consideration. In this case too, however, the changes
may be highly nonlinear. This is true both with regard

to the quantities of the additives and with regard to
the effect of the same quantities of the additives at
various iron and carbon mixing ratios. Therefore, it is

quite possible for a specific quantity of additives
(e.g. 1% of silicon and 2% of phosphorus) to have a
completely different effect on the specific Gibbs' free
energy of an iron-carbon mixture comprising 1% of
carbon and 99% of iron than on an iron-carbon mixture
comprising 4% of carbon and 96% of iron. The percentages
are in this case atomic percentages. It is also quite
possible, for example, for double the quantity of the
additives to have a completely different effect on the
specific Gibbs' free energy than the single quantity of
the additives. However, it is moreover the case that the
influences of. the additives are known or can be
determined in a known way.
The curve of the specific Gibbs' free energy G
determined in, this way for the iron-carbon mixture can
be used to determine the distribution of the metal 1
between chemical compositions of the constituents. This
is explained in more detail below on the basis of the
example of an iron-carbon mixture.
Assume the presence of a mixture of iron and carbon. In
this context, nA is the proportion of iron, nB the
proportion of carbon in the mixture. The sum of the
proportions nA, nB is of course one. Furthermore, assume
that nA1 is the proportion of iron in a first chemical
composition, nA2 is the proportion of iron in a second
chemical composition. The sum of these proportions nA1,
nA2 in this case of course corresponds to the total
proportion nA of iron. Similarly, proportions nB1, nB2 of
carbon are also contained in both compositions. The sum
of these proportions nB1, nB2 once again results in the
total proportion nB of carbon. With m1 = nA1 + nB1 and
m2 = nA2 + nB2, proportions for the respective
composition are introduced. Therefore, the Gibbs' free
energy G of the overall system turns out to be

(Complete) differentiation of this equation according to
nA1 and nB1 and zeroing the derivatives gives two
equations and therefore two conditions for the
proportions nA1 and nB1- In this context, it must be borne
in mind that in this equation m1, m2 and the argument of
G2 implicitly include nA1 and nB1 as variables.
If the Gibbs' free energy G of the iron-carbon mixture
as a function of the proportion n of carbon has a
convex curve, as illustrated by way of example in
FIG. 5, it is not possible to divide it into two
chemical compositions in which the proportionally
weighted sum of the specific Gibbs' free energies G1,
G2 is lower than the Gibbs' free energy of the
uniformly mixed system. In this case, the equations are
linearly dependent. The result is a uniform chemical
composition of the metal 1.
On the other hand, if, as illustrated by way of example
in FIG. 6, the Gibbs' free energy G as a function of the
carbon content is not exclusively convex, it is possible
to perform this division into two different chemical
compositions in which the proportionally weighted sum of
the specific Gibbs' free energies Gl, G2 is lower than
the Gibbs' free energy G of the uniform mixture. In this
case, the equations are linearly independent. This
results in unambiguous values for the proportions nA1,
nA2, nB1 and nB2. In this case, the metal 1 is broken down
into two different chemical compositions. The
compositions have mixing ratios n1 or n2 . The mixing
ratios n1, n2 are defined by the equations

respectively.
In practice, it is often necessary to employ mixtures
of these two procedures. For example, a relatively
large quantity of carbon is soluble in austenite. On
the other hand, only a small quantity of carbon is
sdluble in ferrite. Therefore, during cooling austenite
breaks down into a mixture of ferrite and pearlite,
wherein pearlite is a eutectic mix comprising cementite
(Fe3C) and ferrite and has formed as a result of
carbon-saturated austenite cooling to below the
temperature of the surrounding walls.
The phase transformation rate is described by what is
known as a transformation diffusion model. In this
case, the various phases are separated from one another
by moveable phase boundaries. There are moveable and
non-moveable elements within each phase. The non-
moveable elements are distributed uniformly. The
moveable elements are not generally distributed
uniformly within the phase. The diffusion of the
moveable elements in each phase is toward the negative
gradient of the associated chemical potential. The
diffusion rate of the moveable elements is in this case
finite. The chemical potential is obtained by
differentiation of the specific Gibbs' free energies
(i.e. the Gibbs' free energies based on identical
quantities) on the basis of the concentration of the
moveable elements. The precise presentation of the
diffusion for one or more moveable elements is known to
those skilled in the art. To determine the speed at
which the phase interface is moving, the difference

between the specific Gibbs' free energies immediately
in front of and immediately behind the phase interface
is to be formed at the free phase interface. This task
is referred to by those skilled in the art as the free
boundary problem with diffusion or also as the Stefan
problem and is generally known. An

approximated solution is to be found, for example, in
Kar, A. and Mazumder, J.: Analytic Solution of the
Stefan Problem in Finite Mediums. Quart. Appl. Math.,
Vol. 52, 1994.
In the context of the present invention, a dedicated
transformation rate can be determined for each
transformation - both for a phase transformation per se
and for decomposition of a chemical composition into
other. chemical compositions. Overall, it can be stated
that the transformation phenomenon at any time is
moving in the direction of a decrease in the Gibbs'
free energy G of the overall system. Therefore, the
above model proposal can also be formulated without
explicit use of the difference between the specific
Gibbs' free energies G1, G2 at the phase interfaces. In
particular taking account of the cooling behavior of
the metal 1, therefore, it is possible to make a
statement not only on the phase state of the metal 1
but also on its microstructure and grain size.
In accordance with FIG. 7, the installation is designed
as a cooling device for the metal 1. The actuator 2 is
designed as a' coolant actuator 2. It is either arranged
between rolling stands of a rolling mill or downstream
of the rolling stands. It can apply defined quantities
of a . coolant, typically water, to the metal 1 via
individually actuatable sections 2' .
As has been stated above in connection with FIG. 1, the
temperature T of the metal 1 is in each case recorded
by means of measuring elements 6, 6' . If the cooling
device is arranged exclusively downstream of the
rolling stands, the measuring element 6 is arranged
downstream of the final rolling stand and upstream of
the cooling device. Otherwise, it is preferable for the
measuring element 6 to be arranged upstream of the
rolling stand (s) which precede (s) the cooling device

and for the measuring element 6' to be arranged
downstream of, the rolling stand (s) which precede(s) the
cooling device.

When the cooling section is operating, as part of the
cycle, the starting temperature TA of the metal 1 is
recorded by means of the measuring element 6 each time
the heat conduction and transformation equations are
being solved. Furthermore, a material velocity v is fed
to the material model 5. This enables the material
model 5 to carry out material monitoring with regard to
the locations in the metal 1 at which the starting
temperature TA was recorded, and in this way to actuate
the individual sections 2' of the actuator 2 at the
correct time. It is also possible for the final
temperature . T to be recorded at the correct time by
means of a further measuring element 6' at the end of
the cooling section and for this temperature to be
assigned to the corresponding location of the metal 1.
In the embodiment shown in FIG. 7, therefore, the
modeling method is applied at a multiplicity of
locations in the metal 1 which directly follow one
another in terms of their position.
In the example shown in FIG. 7, the direction of flow
of the material is always identical. However, it is
also possible for the direction of flow of the material
to change. For example, in the case of a plate mill
train, the material can be returned to the rolling
stand for cooling purposes and subjected to a further
rolling operation with a subsequent cooling operation.
FIGS 8 and 9 show further possible applications for the
modeling method according to the invention.
In accordance with FIG. 8, the installation is designed
as a rolling mill train. In the present case, the
actuator 2 is one of the rolling stands, and the
corresponding control variable S is the rolling speed.
If appropriate, the actuator 2 may also be a
combination of a rolling stand and a cooling device. In
this case, of course, the control variable S is also a

combined control variable.
In the embodiment shown in FIG. 9, the installation is
designed as a continuous-casting installation. The
actuator 2 is designed as a combined actuator, by means
of which on the one hand the

cooling of the permanent mold of the continuous-casting
installation is influenced, and on the other hand the
discharge velocity v at which the cast strand 1 is
discharged from the permanent mold.
The present invention has numerous advantages. Firstly,
the material model 5 of the present invention, given
complete parameterization with respect to the possible
additives, makes it possible to obtain generally valid
results which allow the treatment even of unknown
material classes and individual materials.
Furthermore - unlike with the approaches used by Scheil
and Avrami - the transformation behavior is described
correctly even in the case of incomplete
transformation. In this case, unlike in the methods of
the prior art, the transformation heat produced during
the phase transformation is determined correctly and
taken into account within the scope of the material
model 5. In particular, however, the complicated
topology of phase diagrams and TTT diagrams is returned
to the parameterization of standard smooth curves. As a
result, technical processing of the dependent
relationship among alloying elements, which is
extremely complex in the case of steel, becomes
possible for the first time, since if the pressure and
temperature T of the system under consideration - in
this case of the metal 1 - are kept constant, the
Gibbs' free energy G of the system seeks to adopt its
minimum value. A comparison of the Gibbs' free energies
G1, G2 of various phases therefore indicates the
direction of the phase transformation. In this case, it
is even possible to process the extremely difficult
case of a metal with additives and compounds such as
cementite (Fe3C) as phases in a physically correct
manner. Finally, the approaches can be applied not only
to temperature calculation but also to the calculation
of microstructure and grain size.

WE CLAIM :
1. A method for controlling a solidification process of metal (1) in
continuous casting or a rolling mill by controlling coolant actuator in the
mill, or the like, the temperature (T) of which can be influenced directly or
indirectly by at least one actuator (2), said method comprising the steps
of:
predetermining for a material model (5) a starting temperature TA) of the
metal (1) and starting proportions (p1A, P2A), in which the metal (1) is at
least in a first phase or a second phase, respectively;
solving in real time a heat conduction equation and a transformation
equation within the material model (5), taking account of the starting
temperature (TA), the starting proportions (p1 A. P2A) and a control variable
(S) for actuator (2), so as to determine an expected temperature (TE) for
the metal (1) and expected proportions (p1E, p2E) in which the metal (1) is
at least in the first phase or the second phase respectively; and
actuating said actuator (2) in accordance with said controlled variable/s;

characterized in that as part ot the transformation equation the Gibbs'
free energies (Gl, G2) of the phases of the metal (1) are determined, a
transformation rate of the metal (1) from the first phase to the second
phase is determined on the basis of the Gibbs' free energies (Gl, G2) and
the expected proportions (p1E, P2E) are determined on the details of the
transformation rate.
2.The modeling method as claimed in claim 1, wherein specific Gibbs'
free energies (Gl, G2) of the phases, i.e. Gibbs' free energies which are
based on a uniform quantity of the metal (1), are determined, and in that
the transformation rate is determined on the basis of the difference
between the specific Gibbs' free energies (Gl, G2).
3. The modeling method as claimed in claim 1, wherein

specific Gibbs' free energies (Gl, G2), i.e.
Gibbs' free energies which are based on a uniform
quantity of the metal (1), are determined, and in that
the transformation rate is determined on the basis of
the sum of the specific Gibbs' free energies (G1, G2)
of the phases, weighted with the proportions (p1, p2)
of the phases.
4 The modeling method as claimed in claim 1, 2 or 3,
wherein
specific Gibbs' free energies
(G1, G2), i.e. Gibbs' free energies which are based on
a uniform quantity of the metal (1), are determined, in
that the specific Gibbs' free energy (Gl, G2) of at
least one of , the phases is position-dependent, and in
that the transformation rate is determined on the basis
of the position integral over the specific Gibbs' free
energy (Gl, G2) of the phases.
5. The modeling method as claimed in one , of the
wherein the preceding claims, the metal (1)
contains at least two chemically different constituents
(e.g. iron and carbon), and in that the Gibbs' free
energies (Gl, G2) are also used to determine the
distribution of the constituents between chemical
compositions.
6. The modeling method, as . claimed in one of the
wherein preceding claims, at least one of
the phases corresponds to a liquid state of the metal
(1)
7. The modeling method as claimed in one of the
where in preceding claims, , at least one of
the phases corresponds to a solid state of the metal
(1)
8.' The modelinq method, as . claimed in one of the
whereinpreceding claims,

It is applied at a multiplicity of locations in
the metal (1) which directly follow one another in
terms of their position.
9. The modeling method as .claimed in one of the
wherein
preceding claims, characterized_at least one
desired temperature (T*) is predetermined for the
material model (5), and in that the material model (5)
automatically determines the control variable (S).
10. The modeling method as claimed in claim 9,
the desired temperature (T*) is a
desired temperature curve (T*).
11. The modeling method as claimed in one of claims 1
wherein
to 10, the control variable (S)
is a control variable curve (S) , in that the heat
conduction equation and the transformation equation are
solved in steps using the control variable curve (S) ,
and in this way an expected temperature curve (TE) for
the metal (1) and expected proportion curves (p1E/ p2E)
for the phases are determined, and in that the actuator
(2) is only actuated in accordance with the control
variable curve (S) after the expected temperature curve
(TE) for the metal (1) and the expected proportion
curves (plE, p2E) for the phases have been determined.
12. The modeling method as claimed in one of claims 1
wherein that "the heat conduction
equation and the transformation equation are solved in
steps, and in this way an expected temperature curve
(TE) for the metal (1) and expected proportion curves
(p1E, p2E) for the phases are determined, in that the
control variable (S) is used only for the respective
step, and in that the actuator (2) is actuated in
accordance with the control variable (S:) between the
preceding step and the subsequent step.

13. The modeling method as claimed in one of the
wherein preceding claims,wherein the starting
temperature (TA) is an actual temperature (T) of the
metal (1) recorded by a measuring element (6) before
the metal (1) is influenced by the actuator (2).
14. The modeling method as claimed in one of the
wherein preceding claims, wherein after the metal
(1) has been influenced by the actuator (2), a
measuring element (6') records a final temperature (T)
of the metal (1), in that the final temperature (T) is
compared with the expected temperature (TE) , and in
that the material model (5) is adapted on the basis of
the comparison.
15. The modeling method as claimed in one of claims 1
to 14, wherein the heat conduction
equation which is to be solved for the interior of the
metal (1) takes the form

where H is the enthalpy, t the time, λ the thermal
conductivity, p1 and p2 the proportions of the phases,
p the density and T the temperature of the metal (1)
and q' is a heat quantity which is generated by
external influences within the metal (1).
16. The modeling method as claimed in one of claims 1
wherein to 14, wherein metal (1) is in the
form of a metal strip with a strip thickness direction,
and in that the heat conduction equation which is to be
solved for the interior of the metal (1) takes the' form

where H is the enthalpy, t the time, x the location in the strip thickness
direction, λ the thermal conductivity, p1 and p2 the proportions of the
phases, p the density and T the temperature of the metal (1) and q' is a
heat quantity which is generated by external influences within the metal
(1).
17. The modeling method as claimed in one of the preceding claims,
wherein the metal (1) contains iron as its main constituent.
18. A computer system (3) enabled to control a device having an actuator
(2), to manipulate the temperature (T) of a metal (1) directly or indirectly.
19. A device having an actuator (2) by means of which the temperature
(T) of a metal (1) can be manipulated directly or indirectly, wherein it is
controlled by the computer system (3) as claimed in claim 18.
20. The device as claimed in claim 19, wherein it is configured as a
cooling device for a metal (1), and wherein the actuator (2) is a coolant
actuator (2).
21.The device as claimed in claim 20, comprising at least one rolling
stand of a rolling mill disposed downstream of the cooling device

22. The device as claimed in claim 20, wherein the cooling device is
disposed downstream of at least one rolling stand of a rolling mill.
23. The device as claimed in claim 19, wherein it is configured as a
rolling mill train, and wherein the actuator (2) is designed as a rolling
speed actuator (2).
24. The device as claimed in claim 19, wherein it is configured as a
continuous-casting device.
25. The device as claimed in claim 19, wherein it is configured as a
continuous-casting device for casting a strip (1) with a strip thickness (d)
of between 40 and 100 mm, and having finishing train arranged directly
downstream of the device.
26. The device as claimed in claim 19, wherein it is configured as a thin-
strip casting device for casting a metal strip (1) with a maximum strip
thickness (d) of 10 mm, and having two rolling stands arranged
downstream of the device.

The temperature (T) of a metal (1) can be influenced
directly or indirectly by at least one actuator (2)
which is actuated in accordance with a control variable
(S) . The control variable (S) and starting values (TA,
p1A, p2A) for a temperature of the metal (1) and phase
proportions in which the metal (1) is at least in a
first phase or a second phase, respectively, are
predetermined for a material model (5) . A heat
conduction equation and a transformation equation are
solved in real time within the material model (5) ,
taking account of these variables (TA, p1A, p2A) , and in
this way expected values (TE, p1E/ p2E) are determined
for these variables. As part of the transformation
equation, the Gibbs' free energies (G1, G2) of the
phases of the metal (1) are determined, a
transformation rate of the metal (1) from the first
phase to the second phase is determined therefrom, and the expected proportions (p1E, p2E) are determined fromthe latter.

Documents:

1088-KOLNP-2004-FORM-27.pdf

1088-kolnp-2004-granted-abstract.pdf

1088-kolnp-2004-granted-claims.pdf

1088-kolnp-2004-granted-correspondence.pdf

1088-kolnp-2004-granted-description (complete).pdf

1088-kolnp-2004-granted-drawings.pdf

1088-kolnp-2004-granted-examination report.pdf

1088-kolnp-2004-granted-form 1.pdf

1088-kolnp-2004-granted-form 18.pdf

1088-kolnp-2004-granted-form 2.pdf

1088-kolnp-2004-granted-form 3.pdf

1088-kolnp-2004-granted-form 5.pdf

1088-kolnp-2004-granted-gpa.pdf

1088-kolnp-2004-granted-reply to examination report.pdf

1088-kolnp-2004-granted-specification.pdf

1088-kolnp-2004-granted-translated copy of priority document.pdf

1088-KOLNP-2004-OTHER PATENT DOCUMENTS.pdf

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Patent Number

231374

Indian Patent Application Number

1088/KOLNP/2004

PG Journal Number

10/2009

Publication Date

06-Mar-2009

Grant Date

04-Mar-2009

Date of Filing

29-Jul-2004

Name of Patentee

SIEMENS AKTIENGESELLSCHAFT

Applicant Address

WITTELSBACHERPLATZ 2, 8033 MUNCHEN

Inventors:

#	Inventor's Name	Inventor's Address
1	WEINZIERL KLAUS	EISSENSTEINER STR.12 90480 NURNBERG
2	FRANZ KLAUS	TURKHEIMER STR.1, 90455 NURNBERG

PCT International Classification Number

G05B 17/02

PCT International Application Number

PCT/DE03/003542

PCT International Filing date

2003-10-24

PCT Conventions:

#	PCT Application Number	Date of Convention	Priority Country
1	10251716.9	2002-11-06	Germany