DE102012224502A1 - Rolling method for rolling metallic rolled stock in hot strip mill, involves determining dynamic course of total enthalpy, and processing as input variable in temperature computation model - Google Patents

Abstract

The method involves computing rolled temperature distribution by using a temperature computation model. The total enthalpy of the system formed by rolled stock is determined, and is processed as an input variable in the temperature computation model. An output of the temperature computation model is used for the regulation and/or control of the rolling process. The dynamic course of the total enthalpy is determined, and is processed as an input variable in the temperature computation model. An independent claim is included for a rolled strip or metal sheet.

Description

Field of the invention

The present invention relates to a rolling method, preferably a rolling method, which can be applied to a plate mill or a hot strip mill.

State of the art

In order to accurately control or regulate a hot strip mill or plate, and to produce the resulting rolled product with a high quality, it is of great importance to be able to track the temperature distribution in the rolled product within the respective rolling line and then the rolling parameters accordingly to adjust. In particular, too high or too low temperatures of the rolled product and the possibly resulting too high or too low cooling rates within a rolling mill possibly undesirably alter the mechanical properties of the rolled product, in particular a rolled steel sheet.

The process conditions during rolling, such as the final rolling temperature, the cooling rates or the respective rolling speeds influence the temperature distribution in the rolled product. If the speeds are greater or the final rolling temperature higher, then take the required amounts of water to achieve the desired cooling rates accordingly. The maximum possible rolling speed is limited by the maximum available amount of water and the correspondingly providable maximum cooling capacity, since at higher speeds no longer the desired reel temperature or a desired cooling stop temperature can be achieved. On the other hand, very low rolling speeds lead to low temperatures of the rolled product, which are at least then no longer manageable if the cooling water quantities can not be switched below a certain volume flow, so that too low reel temperatures or too low cooling stop temperatures would be achieved.

The temperature distribution of the rolling stock, so in particular the band or the sheet is very important for the control or regulation of the rolling process, but it can not be determined directly at any point within the rolling process. Usually pyrometers are provided in front of and behind the cooling section and preferably also at least one intermediate point. By means of these pyrometers, the surface temperatures of the rolling stock can be determined. It goes without saying, however, that the temperatures present in the interior of the rolling stock, that is to say in particular those inside the strip or sheet, can not be measured by means of a pyrometer.

Furthermore, it is known to calculate the temperature distribution within the rolled product by means of simulation methods. For example, a CSC (Cooling Section Control) program is known, which determines the temperature distribution within the rolled product depending on the process conditions in the respective cooling section. This model is also suitable for regulatory purposes.

As controlled variables in the CSC program, the surface temperature at an intermediate pyrometer or the surface temperature after cooling can be used. Given a specification of these set values, the CSC model then calculates the necessary cooling water quantities. The results obtained by this program are immediately visible and updated with each new cyclic calculation.

In the described CSC program, the temperature distribution in the rolled product is calculated or simulated. This calculation is done according to the finite differences method. In this case, the rolled product for the calculation is modeled in accordance with divided into small elements, so that the geometry of the different cooling zones and the dimensions of the rolled product can be considered. The boundary conditions can be formulated via the dimensions of the cooling zones, the supply of water, as well as the temperature of the cooling water and the ambient temperature. During the calculation, the process variables, such as the rolling speed and the rolling temperature, are taken into account and, if the parameters are changed, are immediately included in the new calculation.

As a result, the CSC program indicates a temperature distribution in the rolling stock, for example the strip or sheet, and thus a corresponding coiler temperature in the hot rolling mill or a cooling stop temperature in the plate mill can be determined. The process conditions, such as the rolling speed or the cooling water supply, can be adjusted accordingly, that a desired reel temperature or a desired cooling stop temperature in the rolling stock is achieved.

In the known CSC program, the temperature calculation is calculated on the basis of the Fourier heat equation. A necessary input in this heat equation is the total enthalpy of the system, which is not measurable. For certain metal compositions, especially of iron or steel alloys, the total enthalpy can only be described in an inaccurate manner by means of approximate equations.

Another important input of Fourier's heat equation is the thermal conductivity, which is a function of temperature, chemical composition and phase content, and which can be determined experimentally.

Due to the non-measurable enthalpy and the correspondingly inaccurate approximations for the enthalpy, the subsequent numerical solution of the Fourier heat equation can accordingly lead to inaccurate temperature results. In particular, the numerical solution of the Fourier heat equation can lead to an inaccurate temperature result in the case of faulty enthalpy input data.

In the WO 2009/106423 A1 describes an operating method for a cooling section for cooling a rolling stock with temperature-separated cooling to a final enthalpy value.

Schwerdtfeger gives as publisher in his book "Metallurgy of Continuous Casting", Verlag Stahleisen mbH, 1992 empirical regression equations for the enthalpy of unalloyed carbon steels, which can be used within certain narrow analytical limits with reasonable accuracy. However, these regression equations are approximate equations and have no physical basis. Judge "The most important physical properties of 52 iron materials", Verlag Stahleisen Düsseldorf, 1973 For pure iron, gives an exact thermodynamic relationship for the enthalpy of each phase. However, pure iron has no technical significance. For steel materials there is no exact thermodynamic data for the total enthalpy of a system.

The disadvantage of this prior art is therefore that the solution of the Fourier heat equation is performed by numerical methods which, depending on the quality of the input data, provide a temperature result, that is to say a temperature distribution in the metal strand, so that the result obtained is faulty or inaccurate enthalpy input data leads to deviations between the calculated temperature distribution or temperature and the actual existing, possibly occupied by measurements, temperature distribution.

Presentation of the invention

Based on the cited prior art, it is an object of the present invention to further improve the calculation of the temperature data.

This object is achieved by means of a method having the features of claim 1. Advantageous developments of the method will become apparent from the dependent claims.

Accordingly, a rolling method for rolling metallic rolling stock, preferably in a hot strip mill or a heavy plate road, proposed, wherein the temperature distribution within the rolling material is calculated by means of a temperature calculation model, the total enthalpy of the system formed by the rolling stock is determined and as an input in the Temperature calculation model is processed, and at least one output of the temperature calculation model is used to control and / or control of the rolling process. According to the invention, the dynamic course of the total enthalpy is determined and processed as an input variable in the temperature calculation model.

Characterized in that is determined in the determination of the temperature distribution within the rolling the dynamic course of the total enthalpy and is taken into account in the temperature determination via the temperature calculation model, a temperature calculation is carried out with higher accuracy.

In a rolling process of the type described in more detail above, the total enthalpy is calculated from the sum of the free molar enthalpies (Gibbs energies) of all the phases and / or phase fractions currently present in the rolling stock.

The dynamic behavior of the total enthalpy is correspondingly influenced by the transformation kinetics of the phase transformations in the ferrite, perlite, bainite, and martensite phases in the rolling stock. This conversion kinetics had not been taken into account in the hitherto known approaches, so that the approach proposed here allows a more accurate temperature calculation.

Furthermore, the calculation or consideration of the dynamic curve of the total enthalpy over the entire temperature course during the rolling process makes it possible to take into account also the corresponding cooling rates and the resulting changes in the total enthalpy. In the known rolling processes are usually cooling rates in the range of 10 K / s up to about 100 K / s application. Accordingly, the phase transition temperatures must be determined not only for the equilibrium state, but also for the dynamic case when using the appropriate cooling rates.

The start and end temperatures of the phase transformation in the ferrite, perlite, bainite, and martensite phases determine the area in which the corresponding heat is released. Within these ranges, the conversion kinetics determines at what time which portions of the phase transformation take place. Since the phase contributions of the system are known at all times by the proposed dynamic consideration, the exact knowledge of the enthalpy of the corresponding pure phases then enables the calculation of the course of the total enthalpy of the system.

Specifically, the calculation of the temperature behavior is carried out according to the Fourier equation, as follows:

Here, c _{p is} the specific heat capacity of the system, λ the thermal conductivity, ρ the density and s the spatial coordinate. T indicates the calculated temperature accordingly. The term Q on the right takes into account the released energies during the phase transformation, which are given as follows: Q = ρL ∂ / ∂tf _s where Q = the released energy during the phase transformation, ρ = the density, L = the latent heat of transformation, t = the time, and f _s = the phase transition degree of the system.

During cooling, the transition from the γ-phase into the α-phase and the resulting heat are of great interest for the exact determination of the temperature behavior. From the calculation of the specific heat capacity, the total enthalpy H follows: H = ∫ c _p ∂T

Specifically, the calculation step for determining the total enthalpy in embodiment of the invention is characterized in that in the temperature calculation model, the total enthalpy as the total free enthalpy (H) of the system by means of the Gibbs energy (G) at constant pressure (p) according to the equation H = G - T (∂G / ∂T) _p where H = the molar enthalpy of the system, G = the Gibbs energy of the system, T = the absolute temperature in Kelvin and p = the pressure of the system.

For a phase mixture, as it is present in all alloys over the course of temperature, the Gibbs energy of the entire system can then be calculated by the Gibbs energies of the pure phases and their phase components as follows: G = f ^l G ^l + f ^γ G ^γ + f ^pα G ^pα + f ^eα G ^eα + f ^ec G ^ec

ermittelt wird, wobei G^Φ = die Gibbs-Energie einer jeweiligen Phase Φ, x_i ^Φ = der Molenbruch der i-ten Komponente der jeweiligen Phase Φ, G_i ^Φ = die Gibbs-Energie der i-ten Komponente der jeweiligen Phase Φ, R = die allgemeine Gaskonstante, T = die absolute Temperatur in Kelvin, ^EG^Φ = die Gibbs-Energie für eine nicht ideale Mischung und ^magnG^Φ = die magentische Energie des Systems bedeuten. Here f ^{Φ are} the phase components of the respective phase Φ and G ^Φ is the Gibbs energy of this corresponding phase Φ. For the austenite, ferrite and liquid phases, the Gibbs energy advantageously results from the fact that in the temperature calculation model for a system with proportions of austenite, ferrite and liquid phase, the Gibbs energy according to the following equation

where G ^Φ = the Gibbs energy of a respective phase Φ, x _i ^Φ = the mole fraction of the ith component of the respective phase Φ, G _i ^Φ = the Gibbs energy of the ith component of the respective phase Φ, R = the general gas constant, T = the absolute temperature in Kelvin, ^E G ^Φ = the Gibbs energy for a non-ideal mixture and ^magn G ^Φ = the magenta energy of the system.

ermittelt wird, wobei ^EG^Φ = die Gibbs-Energie für eine nicht ideale Mischung, x_i = den Molenbruch der i-ten Komponente, x_j = den Molenbruch der j-ten Komponente, x_k = den Molenbruch der k-ten Komponente, a = einen Korrekturterm, ^aL^Φ _i,j = Wechselwirkungsparameter verschiedener Ordnung und ^aL^Φ _i,j,k = ^aL^Φ _i,j = Wechselwirkungsparameter verschiedener Ordnung des Gesamtsystems bedeuten.Furthermore, in an embodiment of the invention, it is expediently taken into consideration that in the context of the temperature calculation model the Gibbs energy for a non-ideal mixture ( ^E G ^Φ ) is ^calculated according to the equation

where ^E G ^Φ = the Gibbs energy for a non-ideal mixture, x _i = the mole fraction of the i-th component, x _j = the mole fraction of the j-th component, x _k = the mole fraction of the k-th component , a = a correction term, ^a L ^Φ _{i, j} = interaction parameters of different order and ^a L ^Φ _{i, j, k} = ^a L ^Φ _{i, j} = mean interaction parameters of different order of the total system.

Likewise, it is expediently taken into account in the temperature calculation model in an embodiment of the invention that, as part of the temperature ^{calculation model} , the proportion of the magnetic energy ( ^magn G ^Φ ) according to the equation ^magn G ^Φ = RTIn (1 + β) f (τ) where ^magn G ^Φ = the magnetic energy, R = the general gas constant, T = the absolute temperature in Kelvin, β = the magnetic moment and f (τ) = the proportion of the total system as a function of the normalized Curie temperature (τ) mean the entire system.

The parameters of the terms in the aforementioned equations are known from the literature and can be used accordingly to determine the Gibbs energy in any steel composition. With the aid of a numerical derivative, this results in the total enthalpy of precisely this steel composition.

With a known Gibbs energy of the system, the molar specific heat capacity can be calculated from this:

• • C < 5%
• • Mn <20%
• • Si < 5%
• • Cr < 30%
• • Ni < 10%
• • Mo < 10%
• • Cu < 1%
• • Nb < 5%
• • Ti < 2%
• • V < 5%
• • Al < 5%
• • S Spuren
• • P Spuren

The advantage of using the Gibbs energy is that there are hardly any restrictions for any analysis of a steel composition. The corresponding scopes for applying the Gibbs energies for the corresponding chemical compositions are as follows:

• • C <5%
• • Mn <20%
• • Si <5%
• • Cr <30%
• • Ni <10%
• • Mo <10%
• • Cu <1%
• • Nb <5%
• Ti <2%
• • V <5%
• • Al <5%
• • S tracks
• • P tracks

This table gives the scope of the Gibbs model. Accordingly, it can be seen immediately that the scope of Gibbs model includes a very large analysis area. These limits, which are provided, for example, in the known MatCalc databases, thus almost completely cover the carbon steels and stainless steels produced worldwide today. With these input data, the enthalpy profiles of the pure phases as well as the knowledge of the phase components can be used to determine the dynamic development of the total enthalpy of a material under investigation with the greatest possible accuracy.

To determine the dynamic course of the total enthalpy, the phase transition temperatures at a dynamic cooling rate are preferably determined. In this way, the phase transition temperatures can be determined at given cooling rates and thus the composition of the individual phases in the alloy can be determined.

The phase transition temperatures are preferably determined by a regression method, and the regression parameters are most preferably determined from ZTU graphs.

wobei

• x_c ⁰ = die Kohlenstoffkonzentrationen im Volumen
• x_c ^α = die Kohlenstoffkonzentrationen an der Phasengrenze auf der Ferritseite
• x_c ^γ = die Kohlenstoffkonzentrationen an der Phasengrenze an der Austenitseite
• T₀ = die Starttemperatur der Phasenumwandlung
• T = die aktuelle Temperatur, und
• T . = die Abkühlrate bedeuten.

In a further preferred embodiment, the transformation kinetics of the phases is determined by a diffusion-controlled approach, preferably for austenite-ferrite decay. It is particularly preferred to determine the conversion kinetics via the Enomoto equation:

in which

• x _c ⁰ = the carbon concentrations in the volume
• x _c ^α = the carbon concentrations at the phase boundary on the ferrite side
• x _c ^γ = the carbon concentrations at the phase boundary on the austenite side
• T ₀ = the start temperature of the phase transformation
• T = the current temperature, and
• T. = mean the cooling rate.

In a preferred embodiment, the carbon concentrations are calculated from the equilibrium concentrations resulting from the equilibrium of the chemical potentials at the phase boundaries.

It is further preferred to determine the conversion kinetics by numerical solution of the Enomoto equation according to the phase fraction of the ferrite, preferably for each volume element and particularly preferably for each temperature step.

The cooling capacity and / or the rolling speed is used to achieve predetermined temperatures, preferably to achieve a predetermined reel temperature in a hot strip mill or the cooling stop temperature in a heavy plate road, can be controlled according to the temperature calculation model.

Brief description of the figures

Preferred further embodiments and aspects of the present invention will be explained in more detail by the following description of the figure. Show

1 Representation of Gibbs energy for pure iron,

2a) Calculated ZTU chart of a common carbon steel Ck15,

2 B) Experimentally determined ZTU chart of a common, carbon steel Ck15,

3 Gibbs total enthalpy for a Ck15 low carbon steel,

4 Course of the carbon concentration at the phase boundary in austenite, and

5 Course of the transformation kinetics of the Enomoto equation.

Detailed description of preferred embodiments

In the following, preferred embodiments will be described with reference to the figures. In this case, identical, similar or equivalent elements in the different figures are denoted by identical reference numerals and a repeated description of these elements will be omitted in the following description in part in order to avoid redundancies.

From the 1 results accordingly a representation of the Gibbs energy for pure iron. It can be seen that the individual phases ferrite, austenite and the liquidus phase occupy a minimum in a certain characteristic temperature range in which these phases are stable.

However, since the rolling process in connection with the cooling process is not a state of equilibrium in which the rolling stock could cool without external influence, but by the rolling process and the cooling process is a dynamic process, here also dynamic cooling rates in the field from about 10 K / s to over 100 K / s, the phase transition temperatures at which heat is released accordingly must also be calculated or determined in the dynamic case.

For this purpose, empirical compensation formulas are used, which allow a determination of all transformation temperatures in the phases ferrite, pearlite, bainite and martensite. These formulas are listed below:

Here, T ^{Φ means} the transformation temperature at which ferrite, pearlite, bainite or martensite is formed or the formation of perlite is terminated. T .φ indicates the maximum cooling rate at which ferrite or pearlite is formed, or if the structure contains, for example, 100% ferrite and pearlite, or if, for example, 20, 80 or 100% martensite is formed. In the equations, the parameters a _i , b _i , c _{i represent} corresponding regression constants and C _c , C _i the concentrations of the individual elements in percent by weight. M is the ASTM grain size and may assume values between 1 and 10.

With these parameters, it is possible to construct a time-temperature conversion chart ("ZTU" chart).

In the 2a) and 2 B) Schematics of a common, unalloyed carbon steel Ck15 with the structural components ferrite, pearlite, bainite and martensite are shown. The components are limited by the transformation temperatures and are marked accordingly flat.

As is clear from the 2a) and 2 B) Immediately results in small cooling rates, only the constituents of ferrite and perlite. At high cooling rates, bainite and martensite are also produced from the transformation structure.

In the 2a) and 2 B) is correspondingly in the area of I. martensite formation, in area II bainite formation, in area III. a ferrite formation as well as in area IV. to observe a perlite formation.

The calculations with the corresponding cooling rates are in 2a) shown schematically with the cooling lines A. The experimentally completed cooling lines a) -e) are in 2 B) represented and carry the appropriate cooling rates.

When comparing the 2a and 2 B) a good match of the calculated and measured values can be seen. The phase boundaries for all phases in the technologically relevant range between 10 K / s to 100 K / s and beyond are given in good agreement with the experiments.

• • C < 1.2%
• • MN < 2%
• • Si < 2%
• • Cr < 2%
• • Ni < 3.5%
• • Mo < 0.5%

The above-mentioned regression parameters can be optimized on the basis of different ZTU diagrams and allow a determination of further ZTU diagrams over a wide range of steels with different chemical compositions. The limits for calculating the respective transformation temperatures with a precisely acceptable accuracy are:

• • C <1.2%
• MN <2%
• • Si <2%
• • Cr <2%
• • Ni <3.5%
• • Mo <0.5%

Within these validity limits of the model, a prediction of the transformation temperatures as well as a precise determination of the areas in which the transformation of austenite into the phases ferrite, perlite, bainite and martensite takes place can be carried out.

Example becomes in 3 According to Gibbs, the overall enthalpy is shown as a function of temperature for a low-carbon steel Ck15, as well as the enthalpy of the pure phases austenite, ferrite, cementite and the melt. This results in a corresponding dynamic course of the total enthalpy according to Gibbs over the course of the temperature and accordingly also over the course of the rolling process, in which cooling takes place correspondingly through the rolling processes and the cooling processes.

The conversion kinetics between the individual phases is carried out according to the proposed method via a diffusion-controlled approach for austenite-ferrite decay. According to the Enomoto equation:

Here, x _c ⁰ , x _c ^α , x _c ^{γ are} the carbon concentrations in the volume, at the phase boundary on the ferrite side and on the austenite side. The carbon concentrations are calculated from the equilibrium concentrations, which in turn derive from the equilibrium of the chemical

Potentials at the phase boundaries result. T ₀ , T and T. are the start temperature of the phase transformation, the current temperature, and the cooling rate. The start temperature of the phase transformation has already been explained above and the cooling rate can also be calculated with the CSC program.

D _c ^γ is the diffusion constant of carbon in austenite, using the following formula:

Where d is the austenite grain size.

By means of these parameters, it is now possible to calculate the phase transformation by solving numerically the above-mentioned Enomoto equation for the phase fraction of the ferrite f ^α . This solution must be done individually for each temperature step and for each volume element.

In 4 is shown the course of the carbon concentration at the phase boundary in austenite, both a calculation by means of the CSC, as well as a calculation with the software DICTA, which was carried out by means of the presented diffusion-controlled approach.

In 5 Furthermore, the course of the conversion kinetics of the Enomoto equation for a low carbon steel is shown using three different cooling rates, namely 1 K / s, 10 K / s and 70 K / s. On the one hand, the solid line shows Enomoto modeling and, on the other hand, experimental values are plotted. The kinetics calculated using the Enomoto equation thus correspond very well to the experimental data.

By means of the described method, it is thus possible to calculate the calculation of the temperature distribution in a rolling mill, in particular a hot strip mill or a plate mill more accurately, whereby a predetermined material-dependent optimal reel temperature or a cooling stop temperature can be set and controlled improved.

Since the total enthalpy can be given as input for the temperature calculation for a large part of today's materials produced worldwide with the Gibbs energy, the temperature calculation can also be carried out with the utmost security of the input data.

Due to the above-described description of the conversion by optimized calculation of the start and end temperatures of the respective phase transformation as well as a physically based kinetics, precise temperature calculations can also be carried out in the respective conversion regions.

Where applicable, all individual features illustrated in the individual embodiments may be combined and / or interchanged without departing from the scope of the invention.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• WO 2009/106423 A1 [0012]

Cited non-patent literature

• "Metallurgy of Continuous Casting", Verlag Stahleisen mbH, 1992 [0013]
• "The most important physical properties of 52 ferrous materials", Verlag Stahleisen Düsseldorf, 1973 [0013]

Claims (17)

Rolling process for rolling metallic rolling stock, preferably in a hot strip mill or a heavy plate road, wherein the temperature distribution within the rolling stock is calculated by means of a temperature calculation model, the total enthalpy of the system formed by the rolling stock is determined and processed as an input in the temperature calculation model, and at least one output of the temperature calculation model is used to control and / or control the rolling process, characterized in that the dynamic curve of the total enthalpy is determined and processed as an input in the temperature calculation model. Rolling process according to claim 1, characterized in that to determine the dynamic curve of the total enthalpy, the phase transformation temperatures are determined at a dynamic cooling rate. Rolling method according to claim 1 or 2, characterized in that the phase transformation temperatures are determined by means of a regression method and the regression parameters are preferably determined from ZTU graphs. Rolling process according to one of the preceding claims, characterized in that the transformation kinetics of the phases via a diffusion-controlled approach, preferably for the austenite-ferrite decay, is determined. Rolling process according to claim 4, characterized in that the conversion kinetics is determined by the Enomoto equation:

where x _c ⁰ = the carbon concentrations in the volume x _c ^α = the carbon concentrations at the phase boundary on the ferrite side x _c ^γ = the carbon concentrations at the phase boundary on the austenite side T ₀ = the start temperature of the phase transformation T = the current temperature, and T. = mean the cooling rate. Rolling process according to claim 5, characterized in that the carbon concentrations are calculated from the equilibrium concentrations resulting from the equilibrium of the chemical potentials at the phase boundaries. Rolling process according to one of claims 4 to 6, characterized in that the conversion kinetics is determined by numerical solution of the Enomoto equation according to the phase fraction of the ferrite, preferably for each volume element and particularly preferably for each temperature step. Rolling process according to one of the preceding claims, characterized in that the cooling capacity and / or the rolling speed to reach predetermined temperatures, preferably to achieve a predetermined reel temperature in a hot strip mill or the cooling stop temperature in a plate mill road is controlled by the temperature calculation model. Rolling process according to one of the preceding claims, characterized in that for the temperature calculation model, the total enthalpy as total free enthalpy (H) of the system by means of the Gibbs energy (G) at constant pressure (p) according to the equation H = G - T (∂G / ∂T) _p where H = the molar enthalpy of the system, G = the Gibbs energy of the system, T = the absolute temperature in Kelvin and p = the pressure of the system. Rolling method according to one of the preceding claims, characterized in that in the temperature calculation model, the temperature distribution by means of the Fourier heat equation

where ρ = the density, c _p = the specific heat capacity at constant pressure, T = the calculated absolute temperature in Kelvin, λ = the thermal conductivity, s = the associated spatial coordinate, t = the time and Q = the during the phase transformation mean free energy of the system. Rolling process according to one of the preceding claims, characterized in that in the temperature calculation model the energy (Q) released during the phase transformation is determined by means of the equation

where Q = the energy released during the phase transformation, ρ = the density, L = the latent heat of transformation, t = the time, and f _s = the phase transformation degree of the system. Rolling process according to one of the preceding claims, characterized in that in the temperature calculation model for a phase mixture, the free energy (G) of the total system as a sum of the Gibbs energies of the pure phases and their phase components according to the equation G = f ^l G ^l + f ^γ G ^γ + f ^pα G ^pα + f ^eα G ^eα + f ^ec G ^ec where G = the Gibbs energy of the system, f ⁱ = the Gibbs energy portion of the respective phase or of the respective phase portion of the overall system, and G ⁱ = the Gibbs energy of the respective pure phase or the respective phase portion of the system. Rolling process according to one of the preceding claims, characterized in that in the temperature calculation model for a system with portions of austenite, ferrite and liquid phase, the Gibbs energy according to the following equation

where G ^Φ = the Gibbs energy of a respective phase Φ, x _i ^Φ = the mole fraction of the ith component of the respective phase Φ, G _i ^Φ = the Gibbs energy of the ith component of the respective phase Φ, R = the general gas constant, T = the absolute temperature in Kelvin, ^E G ^Φ = the Gibbs energy for a non-ideal mixture and ^magn G ^Φ = the magenta energy of the system. Rolling method according to claim 13, characterized in that in the temperature calculation model the Gibbs energy for a non-ideal mixture ( ^E G ^Φ ) according to the equation

where ^E G ^Φ = the Gibbs energy for a non-ideal mixture, x _i = the mole fraction of the i-th component, x _j = the mole fraction of the j-th component, x _k = the mole fraction of the k-th component , a = a correction term, ^a L ^Φ _{i, j} = ^a L ^Φ _{i, j} = interaction parameters of different order and ^a L ^Φ _{i, j, k} = ^a L ^Φ _{i, j} = mean interaction parameters of different order of the total system. ^{Rolling method} according to claim 14, characterized in that in the temperature ^{calculation model} , the proportion of the magnetic energy ( ^magn G ^Φ ) according to the equation ^magn G ^Φ = RTIn (1 + β) f (τ) where ^magn G ^Φ = the magnetic energy, R = the general gas constant, T = the absolute temperature in Kelvin, β = magnetic moment and f (τ) = the proportion of the total system as a function of the normalized Curie temperature (τ) of the Mean complete system. Use of the rolling process according to one of the preceding claims, characterized in that it serves for the online determination of the temperature distribution in rolling stock. Rolled strip or sheet obtained by the rolling method of any one of claims 1-15.

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