METHOD FOR CONTROLLING A COOLING DEVICE IN A ROLLING TRAIN

Abstract

Method and control device for controlling a cooling device (10) which is set up to control the temperature of a rolling stock, preferably metal strip (B), which the cooling device (10) runs through along a conveying direction (F), the cooling device (10) preferably in front of a rolling train is arranged and the method comprises: determining a total enthalpy of the system formed by the rolling stock; Determining a measure for the formation of scale, which preferably comprises a scale factor that depends on the chemical composition and the surface temperature of the rolling stock; Calculating a temperature distribution and/or average temperature in the rolling stock on the basis of a temperature calculation model, in which the determined total enthalpy and the measure for the formation of scale are included; and setting a cooling capacity of the cooling device (10) taking into account the calculated temperature distribution and/or average temperature in the rolling stock.

Claims

1. Method for controlling a cooling device (10), which is configured to control the temperature of a rolling stock, preferably metal strip (B), which runs through the cooling device (10) along a conveying direction (F), the cooling device (10) being arranged upstream of a rolling train, the method comprising: determining a total enthalpy of the system formed by the rolling stock; determining a measure for the formation of scale, which preferably comprises a scale factor that depends on the chemical composition and the surface temperature of the rolling stock; calculating a temperature distribution and/or average temperature in the rolling stock on the basis of a temperature calculation model, in which the determined total enthalpy and the measure for the formation of scale are included; and setting a cooling performance of the cooling device (10) taking into account the calculated temperature distribution and/or average temperature in the rolling stock.

2. Method according to claim 1, characterized in that the total enthalpy of the rolling stock is calculated from the sum of the free molar enthalpies of all the pure phases and/or phase fractions present in the rolling stock.

3. Method according to claim 1, characterized in that the temperature calculation model is based on a non-stationary heat equation, preferably on a partial differential equation which relates the spatial temperature distribution in the rolling stock to the development of the total enthalpy over time.

4. Method according to claim 1, characterized in that the sequence of determining the total enthalpy, calculating the temperature distribution and/or average temperature and setting the cooling performance takes place iteratively, so that a desired temperature distribution and/or average temperature in the rolling stock is approximated.

5. Method according to claim 1, characterized in that the setting of the cooling capacity of the cooling device (10) takes place in such a way that the cooling performance is changed if the calculated temperature distribution or a temperature value therefrom, preferably an average temperature or surface temperature, deviates by a tolerance or more of from a corresponding setpoint, and the cooling performance is otherwise not changed.

6. Method according to claim 1, characterized in that the cooling device (10) has a nozzle arrangement (11) with several nozzles (11a) which is configured to supply the nozzles (11a) with a fluid cooling medium, preferably water or a water mixture, the cooling performance of the cooling device (10) being adjusted by the amount of cooling medium output by the nozzles (11a).

7. Method according to claim 1, characterized in that one or more temperature measuring devices (20, 21) are provided, the measured values of which are included in the determination of the total enthalpy and/or determination of the degree of scale formation and/or in some other way in the temperature calculation model.

8. Method according to claim 1, characterized in that the cooling device (10) is arranged between a roughing train (1) and a finishing train (2), each of which has one or more roll stands for rolling the rolling stock.

9. Method according to claim 1, characterized in that with the calculation of the temperature distribution and/or average temperature in the rolling stock based on the temperature calculation model, the inlet temperature of the rolling stock in a rolling train, preferably a finishing train (2), arranged downstream of the cooling device (10) is calculated.

10. Method according to claim 1, characterized in that, when calculating the total enthalpy, phase transition temperatures are determined by means of a regression method which uses regression coefficients which are preferably obtained from a calculated or empirically obtained TTT diagram.

11. Method according to claim 1, characterized in that, within the framework of the temperature calculation model, the total enthalpy as the free molar total enthalpy H of the rolling stock by means of the Gibbs energy G at constant pressure p according to the equation $H=G-T\left(\frac{\partial G}{\partial T}\right)p$ where T is the absolute temperature in Kelvin.

12. Method according to claim 1, characterized in that, within the framework of the temperature calculation model, the Gibbs energy G of the overall system as the sum of the Gibbs energies of the pure phases and their phase proportions according to the equation $G=\underset{i}{.Math.}{f}^i{G}^i$ where f.sup.i denotes the Gibbs energy fraction of the respective phase or the respective phase fraction in the overall system and Gi denotes the Gibbs energy of the respective pure phase or the respective phase fraction of the system, where the rolling stock preferably consists of steel, with proportions of austenite, ferrite and liquid phase, and the Gibbs energy of the respective phases in this case according to the following equation $G^{\varphi }=\underset{i=1}{\overset{n}{.Math.}}{x}_i^{\varphi }{G}_i^{\varphi }+RT\underset{i=1}{\overset{n}{.Math.}}{x}_i\ln x_i+{ }^E{G}^{\varphi }+{ }^{\mathrm{magn}}{G}^{\varphi }$ where G.sup.ϕ denotes the Gibbs energy of a respective phase ϕ, x.sub.i.sup.ϕ the mole fraction of the i-th component of the respective phase ϕ, G.sub.i.sup.ϕ the Gibbs energy of the i-th component of the respective phase ϕ, R the general gas constant, T the absolute temperature in Kelvin, .sup.EG.sup.ϕ the Gibbs energy for a non-ideal mixture and .sup.magG.sup.ϕ the magnetic energy of the system, where the Gibbs energy for a non-ideal mixture .sup.EG.sup.ϕ is preferably determined according to the equation
.sup.EG.sup.ϕ=Σx.sub.ix.sub.j.sup.aL.sup.ϕ.sub.i,j(x.sub.i−x.sub.j).sup.a+Σx.sub.ix.sub.jx.sub.kL.sub.i,j,k.sup.ϕ where x.sub.i is the mole fraction of the i-th component, xj is the mole fraction of the j.sup.th component, x.sub.k is the mole fraction of the k-.sup.th component, a is a correction term, .sup.aL.sup.ϕ.sub.i, j and .sup.aL.sup.ϕ.sub.i, j, k designate interaction parameters of various orders of the overall system formed by the rolling stock, whereby the component of the magnetic energy .sup.magG.sup.ϕ is preferably determined according to the equation
.sup.magG.sup.ϕ=RTln(1+β)f(τ) where R is the general gas constant, T is the absolute temperature in Kelvin, β is the magnetic moment and f(T) is the proportion of the overall system as a function of the normalized Curie temperature T of the overall system formed by the rolling stock, and preferably the conversion kinetics of the phases is determined via a diffusion-controlled approach according to the Enomoto equation.

13. Method according to claim 1, characterized in that, within the framework of the temperature calculation model, the thickness of the scale formed on the rolling stock after a period of time according to the following calculation formula $\begin{array}{c}{D}_Z\left(t+\mathrm{dt}\right)=\sqrt{{D_Z\left(t\right)}^2+F_Z.Math.\mathrm{dt}}\end{array}$ $\mathrm{with}\mathrm{dt}=\frac{d_Z}{\upsilon }$ where D.sub.Z(t) is the thickness of the scale, t is the time, dt is the period of time, F.sub.Z is the scale factor, v is the conveying speed of the rolling stock and d.sub.Z denotes a distance covered at the conveying speed v in the period dt, where the scale factor F.sub.Z is determined as a function of the surface temperature of the rolling stock and its chemical composition, preferably according to the equation
F.sub.Z=a.Math.e.sup.−b.Math.c %.Math.e.sup.−c/T.sub.0 where T.sub.o is the surface temperature of the rolling stock and C % is the dimensionless concentration of carbon in the material of the rolling stock, a, b and c denote coefficients, preferably with a=9.8*107, b=2.08, c=17780, and the heat transfer coefficient of the scale is preferably taken into account according to the equation ${\alpha }_z\left(D_z,{\lambda }_z\right)=\left(\frac{{\lambda }_z}{D_z}\right)$ α.sub.Z(D.sub.Z, λ.sub.Z) denoting the heat transfer coefficient of the scale, D.sub.Z the thickness of the scale and λ.sub.Z the coefficient of thermal conductivity of the scale.

14. Control device (30) for controlling a cooling device (10) which is configured to control the temperature of a rolling stock, preferably metal strip (B), which passes through the cooling device (10) along a conveying direction (F), the control device (30) being configured for carrying out a method according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] FIG. 1 is a schematic representation of a cooling device arranged between a roughing train and a finishing train.

[0040] FIG. 2 is a graph showing Gibbs energy as a function of temperature for pure iron.

[0041] FIG. 3 is a diagram showing the course of the total enthalpy according to Gibbs for a low-carbon steel with known phase boundaries.

[0042] FIG. 4 is a TTT diagram that was determined for a low-carbon material using regression equations.

[0043] FIG. 5 is a diagram showing the scale thickness as a function of the scaling time at different surface temperatures.

[0044] FIG. 6 is a diagram showing the scale thickness as a function of the plant length for various carbon contents.

[0045] FIG. 7a is a diagram showing, by way of example, a calculated and measured temperature profile as a function of time without taking the influence of scale into account.

[0046] FIG. 7b is a showing, by way of example, a calculated and measured temperature profile as a function of time, taking into account the influence of scale.

[0047] FIG. 8 is a flow chart illustrating an exemplary process sequence for regulating the cooling device according to FIG. 1.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0048] In the following, preferred exemplary embodiments are described with reference to the Figures. Identical, similar or identically acting elements are provided with identical reference symbols, and a repetitive description of these elements is in some cases omitted to avoid redundancies.

[0049] FIG. 1 is a schematic representation of a cooling device 10, implemented in the present exemplary embodiment as a so-called pre-strip cooler, between a roughing train 1 and a finishing train 2.

[0050] The roughing train 1 and the finishing train 2 each have one or more roll stands 1a, 2a for rolling a rolling stock that is transported through the system along a conveying direction F. In the following, a metal strip B is used as the rolling stock. The roughing train 1 is preferably used to roll a pre-strip from a slab, which for example comes from a continuous caster. After passing through the cooling device 10, the pre-strip is finish-rolled by the finishing train 2 to the desired final thickness.

[0051] The finished sheet, the pre-strip and all intermediate products fall under the term “metal strip”. Furthermore, the term “metal strip” includes all metals and alloys suitable for rolling in sheet form, in particular steel and non-ferrous metals such as aluminum or nickel alloys.

[0052] In FIG. 1, the last roll stand 1a of roughing train 1 and the first roll stand 2a of finishing train 2 are shown by way of example. Here, spatial relationships such as “upstream of”, “downstream of”, “first”, “last” etc. are to be understood in relation to the conveying direction F.

[0053] The cooling device 10 has a nozzle arrangement 11 with a plurality of nozzles 11a. The nozzle arrangement 11 defines a continuous cooling section in which the metal strip B is cooled in a targeted manner and which preferably begins immediately downstream of the roughing train 1 and ends immediately upstream of the finishing train 2. It should be pointed out, however, that other units, such as a descaling machine, a heat insulating hood, scissors and the like, can also be installed in the area between the roughing train 1 and the finishing train 2.

[0054] The nozzle arrangement 11 has a fluid system with pump(s), distribution line(s), valve(s) and the like, not shown in detail in the Figure which is configured to supply a cooling medium, preferably water or a water mixture, to the nozzles 11a. The nozzles 11a are configured to spray the cooling medium onto the metal strip B, in particular the two strip surfaces. For this purpose, the nozzles 11a are suitably positioned and aligned in order to apply a variable amount of cooling medium to the metal strip B, preferably controllable in sections along the cooling path.

[0055] In order to be able to control the cooling performance in the cooling section in a targeted manner, as explained in detail below, one or more temperature measuring devices 20, 21 are preferably located between roughing train 1 and finishing train 2. In the present example, a first temperature measuring device 20 is located directly downstream of roughing train 1 and a second temperature measuring device 21 is arranged directly in upstream of finishing train 2. Of course, alternative or further temperature measuring devices can be located in the cooling section, in roughing train 1 and/or finishing train 2, as well as sensors for determining further physical variables, such as the conveying speed of metal strip B, for example. The temperature measuring devices 20 preferably work without contact and are generally designed to essentially determine the surface temperature of the metal strip B. If the surface temperature is known at one or more points between the roughing train 1 and the finishing train 2, temperature measuring devices 20, 21 can optionally be dispensed with.

[0056] The measurement data of the temperature measuring devices 20, 21 and any other sensors are sent to a control device 30, via cable or wirelessly, where they are further processed with the aid of a physical model in order to obtain control variables for controlling the cooling device 10. The control commands are also sent by cable or wirelessly to the corresponding actuators, such as pumps and/or valves, of the cooling device 10, whereby the cooling performance of the cooling device 10 can be varied in terms of time and/or space along the cooling path, around the metal strip B as precisely as possible to bring to the temperature required for the finishing train 2.

[0057] It should be noted that the system structure described above is only exemplary. The process control described herein can be used for cooling devices of any kind, the task of which is to cool a metallic product, in particular rolled stock, in a targeted manner to a desired final temperature. The cooling device 10 does not necessarily have to be arranged downstream of a roughing train 1 with roll stands 1a or, in particular, between a roughing train 1 and a finishing train 2. The cooling device 10 can, for example, also be arranged between two roll stands 1a of a roughing train 1 or between two roll stands 2a of a finishing train 2.

[0058] Since the temperatures inside the metal strip B cannot be measured, a physical model is used to determine the temperatures. With the help of the model, the temperature distribution in the metal strip B can be determined as a function of the process conditions using a temperature calculation program.

[0059] In the following, first the basic principle underlying the temperature calculation program are t described. Subsequently, an exemplary process sequence for regulating the cooling device 10 is presented.

[0060] The core task of the temperature calculation program relates to the calculation of the pre-strip temperature, that is to say the temperature distribution in the metal strip B at the moment of entry into the cooling device 10, which metal strip B may have previously passed through the roughing train 1. The calculation is preferably carried out using a finite difference method. For this purpose, the metal strip B is mathematically divided into thin strips. The boundary conditions are formulated taking into account the dimensions of the cooling zones of the cooling device 10, the quantities and temperature of the cooling medium and the ambient temperature.

[0061] The calculation of the temperature distribution also includes process variables such as the strip speed and the surface temperature of the strip as well as the thickness and/or the chemical composition of the metal strip B, and are therefore immediately and instantaneously included in the calculation in the event of a change. The result is a temperature distribution in the metal strip B.

[0062] The basis of the temperature calculation is the transient heat equation, see equation (1) below, which takes thermal boundary conditions and Fourier's law into account, according to which a heat flow in the direction of the temperature gradient is established depending on the thermal conductivity λ. The density ρ and the enthalpy H of the material are included in the equation. The energy released during the conversion can be combined with the heat capacity to form a total enthalpy H. Let s denote the position coordinate along the thickness direction, and T indicates the calculated temperature. Then the following applies (cf. Miettinen, S. Louhenkilpi; 1994; “Calculation of Thermophysical Properties of Carbon and Low Alloyed Steels for Modeling of Solidifaction Processes”):

[00008]$\begin{array}{cc}\rho \frac{dH}{dt}-\frac{\delta }{\delta s}\left(\lambda \frac{\delta T}{\delta s}\right)=0& \left(1\right)\end{array}$

[0063] As necessary input variables for the calculation of the temperature distribution, the heat conduction or thermal conductivity λ and the total enthalpy H are particularly important, since these variables have a decisive influence on the temperature result. The thermal conductivity λ is a function of the temperature, the chemical composition and the phase proportion and can be determined experimentally for the pure phases. However, the enthalpy H cannot be measured and for certain chemical compositions of the metal strip B can only be described imprecisely with approximate equations. Any numerical solution to the above differential equation (1) can therefore lead to inaccurate temperature results. The energy flowing in or out from outside (heat transfer by convection) is taken into account in the thermal boundary conditions.

[0064] In order to increase the accuracy of the calculation, the aim is to determine the overall enthalpy curve with phase boundaries that are as exact as possible. For this purpose, the molar enthalpy of the system, here of the metal strip B, is calculated using the Gibbs energy according to the following equation

[00009]$\begin{array}{cc}H=G-T\left(\frac{\partial G}{\partial T}\right)p& \left(2\right)\end{array}$

[0065] Here H denotes the molar enthalpy of the system, G the molar Gibbs energy of the entire system and T the absolute temperature in Kelvin. For a phase mixture, the Gibbs energy of the overall system can be calculated using the Gibbs energies of the pure phases and their phase proportions according to the following equation

[00010]$\begin{array}{cc}G=\underset{i}{.Math.}{f}^i{G}^i& \left(3\right)\end{array}$

Here f.sup.ϕ denotes the phase portion of phase ϕ and G.sup.ϕ denotes the molar Gibbs energy of this phase ϕ. For the austenite, ferrite and liquid phase, the Gibbs energy is:

[00011]$\begin{array}{cc}{G}^{\varphi }=\underset{i=1}{\overset{n}{.Math.}}{x}_i^{\varphi }{G}_i^{\varphi }+RT\underset{i=1}{\overset{n}{.Math.}}{x}_i\ln x_i+{ }^E{G}^{\varphi }+{ }^{\mathrm{magn}}{G}^{\varphi }& \left(4\right)\end{array}$$\begin{array}{cc}{ }^E{G}^{\varphi }=.Math.x_i{x}_j{ }^a{L}_{i,j}^{\varphi }{\left(x_i-x_j\right)}^a+.Math.x_i{x}_j{x}_k{L}_{i,j,k}^{\varphi }& \left(5\right)\end{array}$$\begin{array}{cc}{ }^{\mathrm{magn}}{G}^{\varphi }=RT\ln \left(1+\beta \right)f\left(\tau \right)& \left(6\right)\end{array}$

[0066] In the equation (4), the terms correspond to the single element energy, a contribution for the ideal mixture and a contribution for the non-ideal mixture (equation 5)) and the magnetic energy (equation (6)).

[0067] In detail, G.sup.ϕ denotes the Gibbs energy of a phase ϕ, x.sub.i.sup.ϕ denotes the mole fraction of the i-th component of the corresponding phase ϕ, G.sub.i.sup.ϕ denotes the Gibbs energy of the i-th component of the corresponding phase ϕ, R denotes the general gas constant, T denotes the absolute temperature in Kelvin, .sup.EG.sup.ϕ denotes the Gibbs energy for a non-ideal mixture, .sup.magG.sup.ϕ denotes the magnetic energy of the system, a denotes a correction term, and .sup.aL.sup.ϕ.sub.i,j and .sup.aL.sup.ϕ.sub.i,j,k denote interaction parameters of different order of the metal band B. formed overall system. Furthermore, β denotes the magnetic moment, and f(T) denotes the proportion of the overall system as a function of the normalized Curie temperature T of the overall system formed by the metal strip B.

[0068] The parameters of the terms of equations (6) to (8) can be obtained from a database, for example, and used to determine the Gibbs energies of a steel composition of the metal strip B, for example. With the help of a mathematical derivation, this gives the total enthalpy of this steel composition.

[0069] FIG. 2 is a diagram showing the Gibbs energy as a function of temperature for pure iron. From FIG. 2 it can be seen that the individual phases ferrite, austenite and the liquid phase assume a minimum for a characteristic temperature range at which these phases are stable.

[0070] In principle, it is thus possible to create a phase diagram for every steel composition. With the Gibbs energies, the phase transitions are determined exactly and the stable phase components are represented.

[0071] Such a phase diagram is correct for the state of equilibrium. Since the rolling process in connection with the cooling process is not a state of equilibrium but a dynamic process, the phase transition temperatures must also be calculated in the dynamic case. In the cooling device 10, for example, a cooling rate of 5 to 20° C./s, for steel of 5 to 10° C./s, is achieved. For such cooling rates and higher cooling rates, the phase transition temperatures can no longer be derived from the respective equilibrium diagram. The so-called TTT diagrams (time-temperature transformation diagrams) are therefore used.

[0072] FIG. 3 shows the course of the total enthalpy according to Gibbs for a low-carbon steel with known phase boundaries.

[0073] The phase transition temperatures are now determined using regression methods. The regression coefficients are preferably derived from a large number of different ZTU diagrams. The equations for a metal strip B made of steel have the form:

T.sup.φ=F (Analysis, austenite grain size, cooling rate)  (7)

{dot over (T)}=F (Analysis, austenite grain size)  (8)

More precisely:

[00012]$\begin{array}{cc}{T}^{\Phi }=a_0+\underset{i=1}{\overset{n}{.Math.}}{a}_i{C}_i+\underset{i=1}{\overset{n}{.Math.}}\underset{j=i}{\overset{n}{.Math.}}{b}_{\mathrm{ij}}{C}_i{C}_j+c_{1}M+c_2\sqrt{\dot{T}}+c_3\ln \left(\dot{T}\right)& \left(9\right)\end{array}$$\begin{array}{cc}\log \left({\dot{T}}^{\Phi }\right)=a_0+\underset{i=1}{\overset{n}{.Math.}}{a}_i{C}_i+\underset{i=1}{\overset{n}{.Math.}}\stackrel{n}{\underset{j=i}{.Math.}}{b}_{\mathrm{ij}}{C}_i{C}_j+c_{1}M& \left(10\right)\end{array}$

Here, T.sup.ϕ denotes the transformation temperatures at which the structure of ferrite, pearlite, bainite or martensite is formed or the formation of pearlite is terminated. {dot over (T)} and {dot over (T)}.sup.ϕ indicate the maximum cooling rate at which ferrite or pearlite is formed, whether the structure contains 100% ferrite and pearlite, or whether 20, 80 or 100% martensite is formed. In equations (9) and (10), a.sub.i, b.sub.ij and c.sub.i denote regression constants and C.sub.i, C.sub.j denote the concentrations of the individual elements in percent by weight. The number of analysis components of the chemical composition of the metal strip B taken into account is denoted by n. M is the ASTM grain size and can have values in the range from 1 to 10. With these parameters it is possible to construct a TTT diagram or TTT diagram.

[0074] FIG. 4 shows an exemplary TTT diagram for a low-carbon material that was determined using the specified regression equations.

[0075] The transformation kinetics between the individual phases can be described using a diffusion-controlled approach with an Enomoto equation as follows:

[00013]$\begin{array}{cc}\frac{x_C^0-x_C^{\alpha }}{x_C^{\gamma }-x_C^0}{f}^{\alpha }=\left\{1-\frac{6}{{\pi }^2}{.Math.}_{n=1}^{\infty }\frac{1}{n^2}*\exp \left[-\frac{n^2{\pi }^{2}4\left(T_0-T\right)D_C^{\gamma }}{{\left(1-f^{\alpha }\right)}^{\frac{2}{3}}{d}^2\stackrel{.}{T}}\right]\right\}\left(1-f^{\alpha }\right)& \left(11\right)\end{array}$

[0076] Here, x.sub.c.sup.0 denotes the carbon concentration in the volume, x.sub.c.sup.α the carbon concentration at the phase boundary on the ferrite side and x.sub.c.sup.λ the carbon concentration at the phase boundary on the austenite side. The carbon concentrations are calculated from the equilibrium concentrations, which in turn result from the equilibrium of the chemical potentials at the phase boundaries. T.sub.0 denotes the start temperature of the phase transition, T the current temperature of the metal strip B, here the steel pre-strip, and denotes the cooling rate. The starting temperature for the phase transition is determined from the regression equations of the TTT diagrams. D.sub.c.sup.y denotes the diffusion constant of carbon in austenite according to

[00014]$\begin{array}{cc}{D}_C^{\gamma }=\left(1+y_C^{\gamma }\right)*\left[1+y_C^{\gamma }*\left(1-y_C^{\gamma }\right)*\frac{8339.9}{T}\right]*0.00453*\exp \left[-\left(\frac{1}{T}-0.0002221\right)*\left(17767-26436*y_C^{\gamma }\right)\right]& \left(12\right)\end{array}$

with d as austenite grain size.

[0077] With the thus obtained phase boundaries and the structural proportions, the total enthalpy can be determined. In Fourier's heat conduction equation, in addition to enthalpy, temperature-dependent and phase-dependent heat conduction or thermal conductivity and density also appear. These material-dependent values are determined for each structural phase of the metal strip B using regression equations.

[0078] For an exact temperature calculation and control of the quantities of cooling medium required, i.e. to be sprayed, in the cooling device 10, knowledge of these material quantities is important.

[0079] At high temperatures, scale formation occurs on the strip surface of the metal strip B, which is increased by longer idle or pause times of the metal strip B during the forming process. The layer of scale that forms reduces the heat given off by the metal strip B through radiation. When calculating the temperature distribution in metal strip B, this reduced heat transfer to the environment due to the scale layer is taken into account. To do this, it is necessary to determine the scale layer that forms, which can be done as follows:

[0080] The increase in the scale thickness D.sub.Z in a time increment dt is calculated according to

D.sub.Z(t+dt)==√{square root over (D.sub.Z(t).sup.2+F.sub.Z.Math.dt)}  (13)

where D.sub.Z(t) denotes the scale thickness at time t, F.sub.Z denotes the scale factor and dt denotes the scale time. The “scaling time” denotes the time interval between two calculation points in the longitudinal direction of the metal strip B. Thus, the scaling time can be specified as dt=D.sub.Z/ν, where v indicates the known and/or measurable conveying speed of the metal strip B. The variable d.sub.Z denotes the distance covered in the time dt. The scale factor F.sub.Z is dependent on the surface temperature of the metal strip B and the chemical analysis of its material composition (steel)

F.sub.Z=a.Math.e.sup.−b.Math.c %.Math.—e.sup.−c/T.sub.0  (14)

where T.sub.o is the surface temperature of the metal strip B and C % is the dimensionless concentration of carbon in the material. a, b and c are coefficients known from the literature; See, for example, R. Viscorova, Investigation of the heat transfer in spray water cooling with special consideration of the influence of scaling, TU Clausthal, dissertation, 2007.

[0081] Equation (14) given above yields particularly good results for metal, in particular steel, with small silicon contents, in particular less than 2% by weight. For example, in this case the coefficients are: a=9.8*107, b=2.08, c=17780.

[0082] FIG. 5 is a diagram showing the scale thickness as a function of the scaling time at different surface temperatures. FIG. 6 is a diagram showing the scale thickness as a function of the plant length for various carbon contents.

[0083] The formation of scale therefore depends heavily on the analysis, in particular on the carbon content of the material. A low carbon content results in more scale formation than a higher carbon content. Pure iron scales more strongly than steel with a higher carbon content. In addition to the scaling time, the scale growth also depends heavily on the surface temperature of the metal strip B. The layer of scale hinders heat dissipation of the metal strip B.

[0084] The thermal conductivity of the scale depends on the temperature. Table 1 contains exemplary values, including thermal conductivity values lambda (2) at different temperatures, on the one hand for the scale layer and on the other hand for a material made of steel:

TABLE-US-00001 TABLE 1 Lambda- Scale Lambda-Steel [W/m*K] [W/m*K]  900° C. 1.35 28 1000° C. 1.6 29 1200° C. 2.1 31

[0085] The thermal conductivity of the scale layer is much smaller than that of the steel material. The heat transfer coefficient of the scale is defined as:

[00015]$\begin{array}{cc}{\alpha }_z\left(D_z,{\lambda }_z\right)=\left(\frac{{\lambda }_z}{D_z}\right)& \left(15\right)\end{array}$

Here α.sub.Z(D.sub.Z, λ.sub.Z) denote the heat transfer coefficient of the scale, D.sub.Z the thickness of the scale and λ.sub.Z the coefficient of thermal conductivity (thermal conductivity) of the scale.

[0086] With the heat transfer coefficient of the scale, the surface temperature of the scale layer T.sub.Z can be calculated via the heat balance and from this the heat radiation of the metal strip B to the environment can be determined. The layer of scale thus reduces cooling of the metal strip B.

[0087] A precise knowledge of the behavior of the scale layer is important for the correct calculation of the temperature development in the cooling device 10.

[0088] FIG. 7a is a diagram which shows, by way of example, a calculated and measured temperature profile as a function of time without taking the influence of scale into account. A large discrepancy between measurement and calculation can be seen here. In contrast, FIG. 7b shows the calculated and measured temperature profile as a function of time, taking into account the influence of scale. A good correspondence between calculation and experiment can be seen.

[0089] In the following, an exemplary process sequence for using the model, i.e., for determining the temperature distribution in the metal strip B, and for regulating or activating the cooling device 10, is described using the flow chart in FIG. 8:

[0090] The input or control variables of the model are the surface temperatures of the metal strip B, which are determined by the temperature measuring devices 20, 21. If a surface temperature is specified as the setpoint at the outlet of the cooling device 10, the temperature calculation model in the control device 30 calculates the amount of cooling water required to achieve the desired surface temperature of the metal strip B passing through the cooling device 10. The calculated values of the temperature distribution in the metal strip B are immediately visible and can be used for the control and/or regulation of the cooling device 10 and, if necessary, the downstream finishing train 2 of the rolling train. The values for the temperature distribution are updated with each new cyclical or iterative calculation.

[0091] First, in a first step A1, the process is prepared, which includes: calculating the Gibbs energy and the enthalpy curve for each phase and each temperature; Determining the scale factor; Creation of a TTT diagram; and determining the coefficient of thermal conductivity and density for all pure phases as a function of temperature from regression equations.

[0092] The calculation network for the current strip geometry (strip width and strip thickness) is then created in a step A2.

[0093] In the following step A3, the initial conditions for the subsequent iteration are established. The workpiece temperature or the rolled stock temperature T downstream of the roughing train 1 is set to an initial value T.sub.0 for all calculation nodes. The scale thickness is set to 0 mm and the average cooling rate, for example, to 5 K/s as a default value.

[0094] The iteration begins with step A4 with: determining the phase boundaries and microstructural proportions from the TTT diagram for the current mean cooling rate; Calculating the enthalpy as a function of the temperature from the enthalpies of the pure phases and the phase distribution; and calculating the coefficients of thermal conductivity and densities from the pure phases and the phase distribution.

[0095] In step A5, the enthalpy H is determined from the current node temperature T for all calculation nodes.

[0096] In step A6, equation (1) is numerically solved to calculate the entire course of enthalpy and temperature over time.

[0097] Subsequently, the deviation of the setpoint value from the actual value of the surface temperature is determined in F1 and compared with a threshold value or a tolerance (for example ±2° C.). If the deviation is within the tolerance (“yes”), the next iteration step takes place in step A8. If the deviation is outside the tolerance (“no”), an adaptation/change of the operation of the cooling device 10 takes place before the next iteration step according to A8, preferably an adaptation of the amount of cooling medium output by the nozzles 11a.

[0098] The method presented here makes it possible to set the optimum inlet temperature of the metal strip B into the finishing train 2 by regulating the cooling device 10 during rolling without pauses. Depending on the application, i.e., depending on the forming process, this means avoiding unnecessary productivity losses. The cooling device 10, in particular as a pre-strip cooling, reduces surface defects due to the formation of scale.

[0099] The temperature calculation model and its implementation as a method or in the control device 30 enables the temperature distribution within the metal strip B in the cooling device 10 to be calculated with greater accuracy, whereby a material-dependent, optimal amount of the cooling medium, preferably water, can be set and controlled in the cooling device 10. Since the total enthalpy can be specified as an input variable in the temperature calculation for almost all materials currently produced worldwide with the Gibbs energies and the conversion temperatures can be determined very precisely using calculated TTT diagrams, the temperature calculation can be carried out particularly precisely and with the greatest possible reliability of the input data.

[0100] Furthermore, the method enables a homogenization of temperature irregularities in the metal strip B (pre-strip) over the length and/or the width via a cooling performance of the cooling device 10 that can be set in a defined manner.

[0101] Furthermore, the method takes into account the formation of scale and includes a calculation of the scale layer thickness on the metal strip B, as a result of which the calculation of the heat output of the metal strip B before and after cooling is optimized.

[0102] The data calculated to regulate the cooling device 10 can be passed on to a preset model of a possible subsequent finishing train 2 (for example caloric mean temperature, grain size, or the like).

[0103] With the disclosed method, the cooling medium quantities required for cooling can be determined and regulated in the cooling device 10 in such a way that the inlet temperature required in the inlet of the finishing train 2 is reached exactly. In addition, low inlet temperatures can be used in a targeted manner to increase the rolling speed and thus increase production.

[0104] While many of the features and numerical examples given herein relate to a metal strip B made of steel, all types of suitable metal strips B, for example made of an aluminum, nickel or copper alloy, are included. The model presented here and its application as a method and in the control device 30 can also be applied to metal strips B of such materials.

[0105] As far as applicable, all of the individual features set out in the exemplary embodiments can be combined with one another and/or exchanged without departing from the scope of the invention.

LIST OF REFERENCE SYMBOLS

[0106] 1 roughing train [0107] 1a roll stand [0108] 2 finishing train [0109] 2a roll stand [0110] 10 cooling device [0111] 11 nozzle arrangement [0112] 11a nozzle [0113] 20 temperature measuring device [0114] 21 temperature measuring device [0115] 30 control device [0116] B metal strip [0117] F direction of conveyance