Patent ID: 12226814

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

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.

FIG.1is a schematic representation of a cooling device10, implemented in the present exemplary embodiment as a so-called pre-strip cooler, between a roughing train1and a finishing train2.

The roughing train1and the finishing train2each have one or more roll stands1a,2afor 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 train1is preferably used to roll a pre-strip from a slab, which for example comes from a continuous caster. After passing through the cooling device10, the pre-strip is finish-rolled by the finishing train2to the desired final thickness.

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.

InFIG.1, the last roll stand1aof roughing train1and the first roll stand2aof finishing train2are 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.

The cooling device10has a nozzle arrangement11with a plurality of nozzles11a. The nozzle arrangement11defines 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 train1and ends immediately upstream of the finishing train2. 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 train1and the finishing train2.

The nozzle arrangement11has 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 nozzles11a. The nozzles11aare configured to spray the cooling medium onto the metal strip B, in particular the two strip surfaces. For this purpose, the nozzles11aare 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.

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 devices20,21are preferably located between roughing train1and finishing train2. In the present example, a first temperature measuring device20is located directly downstream of roughing train1and a second temperature measuring device21is arranged directly in upstream of finishing train2. Of course, alternative or further temperature measuring devices can be located in the cooling section, in roughing train1and/or finishing train2, as well as sensors for determining further physical variables, such as the conveying speed of metal strip B, for example. The temperature measuring devices20preferably 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 train1and the finishing train2, temperature measuring devices20,21can optionally be dispensed with.

The measurement data of the temperature measuring devices20,21and any other sensors are sent to a control device30, 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 device10. The control commands are also sent by cable or wirelessly to the corresponding actuators, such as pumps and/or valves, of the cooling device10, whereby the cooling performance of the cooling device10can 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 train2.

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 device10does not necessarily have to be arranged downstream of a roughing train1with roll stands1aor, in particular, between a roughing train1and a finishing train2. The cooling device10can, for example, also be arranged between two roll stands1aof a roughing train1or between two roll stands2aof a finishing train2.

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.

In the following, first the basic principle underlying the temperature calculation program are described. Subsequently, an exemplary process sequence for regulating the cooling device10is presented.

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 device10, which metal strip B may have previously passed through the roughing train1. 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 device10, the quantities and temperature of the cooling medium and the ambient temperature.

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.

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”):

ρ⁢d⁢Hd⁢t-δδ⁢s⁢(λ⁢δ⁢Tδ⁢s)=0(1)

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.

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

H=G-T⁡(∂G∂T)⁢p(2)

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

G=∑ifi⁢Gi(3)
Here fϕdenotes the phase portion of phase ϕ and Gϕdenotes the molar Gibbs energy of this phase ϕ. For the austenite, ferrite and liquid phase, the Gibbs energy is:

Gϕ=∑i=1nxiϕ⁢Giϕ+R⁢T⁢∑i=1nxi⁢ln⁢xi+EGϕ+magnGϕ(4)EGϕ=∑xi⁢xj⁢aLi,jϕ⁢(xi-xj)a+∑xi⁢xj⁢xk⁢Li,j,kϕ(5)magnGϕ=R⁢T⁢ln⁡(1+β)⁢f⁡(τ)(6)

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)).

In detail, Gϕdenotes the Gibbs energy of a phase ϕ, xiϕdenotes the mole fraction of the i-th component of the corresponding phase ϕ, Giϕdenotes 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,EGϕdenotes the Gibbs energy for a non-ideal mixture,magGϕdenotes the magnetic energy of the system, a denotes a correction term, andaLϕi,jandaLϕi,j,kdenote interaction parameters of different order of the metal band B. formed overall system. Furthermore, β denotes the magnetic moment, and f(τ) denotes the proportion of the overall system as a function of the normalized Curie temperature τ of the overall system formed by the metal strip B.

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.

FIG.2is a diagram showing the Gibbs energy as a function of temperature for pure iron. FromFIG.2it 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.

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.

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 device10, 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.

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

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:
Tφ=F(Analysis, austenite grain size, cooling rate)  (7)
{dot over (T)}=F(Analysis, austenite grain size)  (8)
More precisely:

TΦ=a0+∑i=1nai⁢Ci+∑i=1n∑j=inbij⁢Ci⁢Cj+c1⁢M+c2⁢T˙+c3⁢ln⁡(T˙)(9)log(T˙Φ)=a0+∑i=1nai⁢Ci+∑i=1n∑j=inbij⁢Ci⁢Cj+c1⁢M(10)
Here, Tϕdenotes 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)}ϕindicate 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), ai, bijand cidenote regression constants and Ci, Cjdenote 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.

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

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

xC0-xCαxCγ-xC0⁢fα={1-6π2⁢∑n=1∞1n2*exp[-n2⁢π2⁢4⁢(T0-T)⁢DCγ(1-fα)23⁢d2⁢T.]}⁢(1-fα)(11)

Here, xc0denotes the carbon concentration in the volume, xcαthe carbon concentration at the phase boundary on the ferrite side and xcλthe 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. T0denotes 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. Dcydenotes the diffusion constant of carbon in austenite according to

DCγ=(1+yCγ)*[1+yCγ*(1-yCγ)*8339.9T]*0.00453*exp[-(1T-0.0002221)*(1⁢7⁢7⁢6⁢7-2⁢6⁢436*yCγ)](12)
with d as austenite grain size.

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.

For an exact temperature calculation and control of the quantities of cooling medium required, i.e. to be sprayed, in the cooling device10, knowledge of these material quantities is important.

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:

The increase in the scale thickness DZin a time increment dt is calculated according to
DZ(t+dt)==√{square root over (DZ(t)2+FZ·dt)}  (13)
where DZ(t) denotes the scale thickness at time t, FZdenotes 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=DZ/ν, where v indicates the known and/or measurable conveying speed of the metal strip B. The variable dZdenotes the distance covered in the time dt. The scale factor FZis dependent on the surface temperature of the metal strip B and the chemical analysis of its material composition (steel)
FZ=a·e−b·c %·e−c/T0(14)
where Tois 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.

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.

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

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.

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

TABLE 1Lambda- ScaleLambda-Steel[W/m*K][W/m*K]900° C.1.35281000° C.1.6291200° C.2.131

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:

αz(Dz,λz)=(λzDz)(15)
Here αZ(DZ, λZ) denote the heat transfer coefficient of the scale, DZthe thickness of the scale and λZthe coefficient of thermal conductivity (thermal conductivity) of the scale.

With the heat transfer coefficient of the scale, the surface temperature of the scale layer TZcan 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.

A precise knowledge of the behavior of the scale layer is important for the correct calculation of the temperature development in the cooling device10.

FIG.7ais 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.7bshows 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.

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 device10, is described using the flow chart inFIG.8:

The input or control variables of the model are the surface temperatures of the metal strip B, which are determined by the temperature measuring devices20,21. If a surface temperature is specified as the setpoint at the outlet of the cooling device10, the temperature calculation model in the control device30calculates the amount of cooling water required to achieve the desired surface temperature of the metal strip B passing through the cooling device10. 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 device10and, if necessary, the downstream finishing train2of the rolling train. The values for the temperature distribution are updated with each new cyclical or iterative calculation.

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.

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

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 train1is set to an initial value T0for 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.

The iteration begins with step A4with: 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.

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

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

Subsequently, the deviation of the setpoint value from the actual value of the surface temperature is determined in F1and 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 device10takes place before the next iteration step according to A8, preferably an adaptation of the amount of cooling medium output by the nozzles11a.

The method presented here makes it possible to set the optimum inlet temperature of the metal strip B into the finishing train2by regulating the cooling device10during rolling without pauses. Depending on the application, i.e., depending on the forming process, this means avoiding unnecessary productivity losses. The cooling device10, in particular as a pre-strip cooling, reduces surface defects due to the formation of scale.

The temperature calculation model and its implementation as a method or in the control device30enables the temperature distribution within the metal strip B in the cooling device10to 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 device10. 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.

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 device10that can be set in a defined manner.

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.

The data calculated to regulate the cooling device10can be passed on to a preset model of a possible subsequent finishing train2(for example caloric mean temperature, grain size, or the like).

With the disclosed method, the cooling medium quantities required for cooling can be determined and regulated in the cooling device10in such a way that the inlet temperature required in the inlet of the finishing train2is reached exactly. In addition, low inlet temperatures can be used in a targeted manner to increase the rolling speed and thus increase production.

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 device30can also be applied to metal strips B of such materials.

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

1roughing train1aroll stand2finishing train2aroll stand10cooling device11nozzle arrangement11anozzle20temperature measuring device21temperature measuring device30control deviceB metal stripF direction of conveyance