METHOD FOR ESTABLISHING A LIKELIHOOD OF DEFECTS IN A CAST PRODUCT SECTION

Abstract

A method that allows quality-reducing defects to be detected before the cast product has left a casting plant by establishing a likelihood of defects in a cast product section with a multi-stage product section, the method including multi-step calculations performed in real time. In a first calculation step, at least changes in matrix phase proportions and an element concentration profile in phase regions are calculated in each case for a temperature-time step. The results of the first calculation step are fed to a second calculation step. In the second calculation step, a change in precipitation proportions out of at least one phase region is determined for the subsequent temperature-time step. The results of the second calculation step are used as input variables for the first calculation step. The results of the calculations are used to determine at least one defect index.

Description

FIELD OF THE TECHNOLOGY

The present invention relates to the field of casting plants, preferably continuous casting plants for producing slabs. On the one hand, the invention relates to a method for establishing a likelihood of defects in a product section cast in a casting plant, preferably by means of a continuous or semi-continuous casting plant, particularly preferably by means of a continuous casting plant. As an input parameter, a temperature curve over time—for at least one position of a cross section of the product section—is used, which was determined during the casting process.

On the other hand, the invention relates to a computer program for carrying out the method, and a casting plant and a computer-readable medium.

PRIOR ART

In the casting of metal products which are created by a casting plant, greatly varying suboptimal mechanical or thermal conditions can occur, which can result in quality-reducing defects. Different reactions can be taken to these quality-reducing defects if they are known. For example, the cast metal product can be assigned to a low quality, a posttreatment can be initiated, a section can be cut out of the product and scrapped, or other measures can be initiated. The problem—which has existed up to this point—is that the calculations are very complex and time-intensive and a determination of defects is often only provided at a later point in time. It is thus often no longer possible to perform certain measures, since they are already completed.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a method which supplies a determination of quality-reducing defects before the cast product has left the casting plant.

The object is achieved by a multistage product section calculation which is executed using a computer system having a computer-readable medium. This is carried out with the aid of characterizing parameters of the product section and selected operating parameters of the casting plant.

The selected operating parameters and the characterizing parameters are either transmitted directly from measuring instruments or can be transmitted from a higher-order automation system of the casting plant.

The multistage product section calculation is divided into at least two calculation steps, since the partial calculations are easier to solve—two small equation systems in relation to one large equation system. This is not exact, but rather an approximation.

In the first calculation step, at least one change of matrix phase components is calculated in each case for a temperature-time step i at the time t_i and temperature T_i. The matrix phase components comprise matrix phases such as ferrite, austenite, or bainite and carbide phase components, for example primary carbides such as M23C6 or M7C3. For the calculation, physically thermodynamic calculations of the product section are preferably calculated with the aid of the input parameters and the temperature curve. The temperature curve over time is preferably accepted from an existing calculation system of the casting plant.

The calculations are preferably performed on the basis of a thermodynamic Gibbs energy approach having thermodynamic equilibrium at one or more phase boundaries according to equation 1 and for different phases together with a material equilibrium approach at the phase boundary layer and diffusion (Fick's law) according to equation 2.

$\begin{array}{cc}{\mu }_{I\mathrm{Phase}1}\left(T_i,C_{1,\mathrm{Phase}1},C_{2\mathrm{Phase}1},\dots ,C_{N,Phase1}\right)-{\mu }_{I\mathrm{Phase}2}\left(T_i,C_{1,\mathrm{Phase}2},\dots ,C_{N,\mathrm{Phase}2}\right)=0& \mathrm{Equation}1\end{array}$ $\begin{array}{cc}\frac{v_{\mathrm{Phase}12,\mathrm{grenz}}}{V_m}*\left(C_{I\mathrm{Phase}1}-C_{I\mathrm{Phase}2}\right)=J_{I\mathrm{Phase}1}-J_{I\mathrm{Phase}2}& \mathrm{Equation}2\end{array}$

• • μ_{I Phase1} chemical potential for component I in phase 1
  • μ_{I Phase2} chemical potential for component I in phase 2
  • ν_{Phase12,grenz} speed of the boundary layer between phases 1 and 2
  • V_m molar volume
  • C_{I Phase1} concentration of component I in phase 1 at the boundary layer to phase 2
  • C_{I Phase2} concentration of component I in phase 2 at the boundary layer to phase 1
  • J_{I Phase1} concentration flow of component I in phase 1
  • J_{I Phase2} concentration flow of component I in phase 2

The results of the first calculation step are fed to a second calculation step.

In the second calculation step, a change of precipitant proportions in the phase areas is determined. In precipitant proportions, proportions of precipitants are determined, such as:

• • carbon nitrides, for example Nb(CN) or T_i(NC)
  • nitrides, for example VN, AlN
  • carbides, for example NbC, TiC
  • sulfide, for example (MnCr)S, MnS
  • oxides
  • borides.

In the second calculation step, the changes of the precipitant proportions in the phase areas are preferably calculated with the aid of a second thermodynamic equilibrium calculation between matrix phases of an alloy and nonmetallic precipitants. For this purpose, equations 3 and 4 are used for each component I. This equilibrium calculation supplies as a result new concentrations at the phase boundaries in the matrix phase areas.

$\begin{array}{cc}{\mu }_{I\mathrm{Matrix}}\left(T_i,C_{1,\mathrm{Matrix}},C_{2\mathrm{Matrix}},\dots ,C_{N,\mathrm{Matrix}}\right)-{\mu }_{I\mathrm{prec}}\left(T_i,C_{1,\mathrm{prec}},C_{2,\mathrm{prec}},C_{3,\mathrm{prec}}\right)=0& \mathrm{Equation}3\end{array}$ $\begin{array}{cc}\frac{v_{\mathrm{grenz}}}{V_m}*\left(C_{I\mathrm{Matrix}}-C_{I\mathrm{prec}}\right)=J_{I\mathrm{Matrix}}-J_{I\mathrm{prec}}& \mathrm{Equation}4\end{array}$

• • μ_{I Matrix} chemical potential for component I in the matrix phase
  • μ_{I prec} chemical potential for component I in the precipitant
  • ν_grenz speed of the boundary layer between matrix phase and precipitant
  • V_m molar volume
  • C_{I Matrix} concentration of component I in the matrix phase
  • C_{I prec} concentration of component I in the non-stoichiometric precipitant
  • J_{I Matrix} concentration flow of component I in the matrix phase
  • J_{I prec} concentration flow of component I in the non-stoichiometric precipitant

For the following temperature-time step, the results of the second calculation step are used as the input variable for the first calculation step.

The results of the product section calculation are used to determine at least one defect index, wherein the at least one determined defect index is available in real time, thus immediately before the product section leaves the casting plant, preferably before the product section reaches a cutting device of the casting plant.

As the starting condition for the calculation, a starting temperature and associated matrix phase proportions, as well as proportions of the precipitants and the chemical composition thereof have to be known. Preferably a temperature, which is above the liquidus temperature and a formation temperature of the precipitants to be considered of the material to be cast, due to which the liquid matrix phase proportion 100% corresponds to its composition of the incoming chemical analysis, and furthermore the proportion of each precipitant taken into consideration is 0%.

In one embodiment variant, assuming complete diffusion within a time step, the concentration flows J_I simply result from obtaining the mass balance and element concentration profiles are constant in each phase area.

In one preferred embodiment, C_{I Matrix} from equation 4 is entered in a third calculation step—the calculation of the element concentration profile by means of a diffusion equation. An element concentration profile x₁(r,t_i) at a point r and at a point in time t_i is initialized using the concentration of a melt. As a result, element concentrations of the converted area—between t_i-1 and t_i from a phase 1 into a phase 2—between R_Phase12(t_i-1) and R_Phase12(t_i) are estimated while maintaining the mass balance at the boundary layer with the aid of equation 5 and 6 and then the division equation (equation 7) is solved in consideration of corresponding boundary conditions to determine a new element concentration profile.

$\begin{array}{cc}{R}_{\mathrm{Phase}12}\left(t_i\right)=R_{\mathrm{Phase}12}\left(t_{i-1}\right)+v_{\mathrm{Phase}12,\mathrm{grenz}}\left(t_i-t_{i-1}\right)& \mathrm{Equation}5\end{array}$ $\begin{array}{cc}{x}_I^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\begin{array}{c}\mathrm{Init}(C_{I,\mathrm{matrix}},x_I,\\ R_{\mathrm{Phase}12},t_i,t_{i-1})\left(r\right)\end{array}& r\in \left[\begin{array}{c}{R}_{\mathrm{Phase}12}\left(t_{i-1}\right),\\ R_{\mathrm{Phase}12}\left(t_i\right)\end{array}\right]\\ x_I\left(r,t_{i-1}\right)& \mathrm{else}\end{array}& \mathrm{Equation}6\end{array}$

$\begin{array}{cc}{\nabla }^2{x}_I\left(r,t\right)-\frac{1}{D_I\left(r\right)}\frac{\partial }{\partial t}{x}_I\left(r,t\right)=0\mathrm{with}\mathrm{starting}\mathrm{condition}{x}_I^0\left(r,t_{i-1}\right)& \mathrm{Equation}7\end{array}$

• • D_I(r) a diffusion constant of the component I at the position r
  • Init a distribution of the concentration x in newly converted phase area while maintaining the mass balance
  • C_{I Matrix} from equation 4 and x_I from equation 7 are then entered as output variables in equation 1 and equation 2 for the next temperature/time step.

For the following temperature-time step, the results of the third calculation step are entered as an input variable for the first calculation step.

Calculation Example

• • calculation step 1: change of matrix phase proportions. Results used from calculation step 2 or 3 of the calculation of the temperature-time step t_i-1:
    • x_C(r),x_Ti(r) from calculation step 3
    • C_C,Phase1, C_Ti,Phase1, C_C,Phase2, C_Ti,Phase2 as the starting value from calculation step 2
  • Unknown variables:
    • C_Fe, C_C, C_Ti in each of the two phases (6 unknowns)
    • V_{phase12,grenz} between the two phases
  • Equations

C _Fe,Phase1=1−C_C,Phase1−C_Ti,Phase1

C _Fe,Phase2=1−C_C,Phase2−C_Ti,Phase2

μ_C,Phase1(T_i,C_C,Phase1,C_Ti,Phase1)−μ_C,Phase2(T_i,C_C,Phase2,C_Ti,Phase2)=0

μ_Fe,Phase1(T_i,C_C,Phase1,C_Ti,Phase1)−μ_Fe,Phase2(T_i,C_C,Phase2,C_Ti,Phase2)=0

μ_Ti,Phase1(T_i,C_C,Phase1,C_Ti,Phase1)−μ_Ti,Phase2(T_i,C_C,Phase2,C_Ti,Phase2)=0

$\frac{v_{\mathrm{Phase}12,\mathrm{grenz}}}{V_m}*\left(C_{C\mathrm{Phase}1}-C_{C\mathrm{Phase}2}\right)=-D_{C,\mathrm{Phase}1}\nabla x_C{❘}_{r=R_{\mathrm{Phase}1}}+D_{C,\mathrm{Phase}2}\nabla x_C{❘}_{r=R_{\mathrm{Phase}2}}$ $\frac{v_{\mathrm{Phase}12,\mathrm{grenz}}}{V_m}*\left(C_{\mathrm{Ti}\mathrm{Phase}1}-C_{\mathrm{Ti}\mathrm{Phase}2}\right)=-D_{\mathrm{Ti},\mathrm{Phase}1}\nabla x_{\mathrm{Ti}}{❘}_{r=R_{\mathrm{Phase}1}}+D_{\mathrm{Ti},\mathrm{Phase}2}\nabla x_{\mathrm{Ti}}{❘}_{r=R_{\mathrm{Phase}2}}$

• • calculation step 2: precipitants from phase 2 for TiC. Results used from calculation step 1:
    • x_C(r,ti) and starting value for C_C,Phase2
    • x_Ti(r,ti) and starting value for C_Ti,phase2
  • Unknown variables:
    • C_C, C_Ti in phase2 and as TiC (4 unknowns)
    • ν_{Phase2,TiC,grenz} between the two phases
  • Secondary condition:
    • J_TiC=0 (no back diffusion of precipitants)
  • Equations:

C _Ti,TiC=0.5 (stoichiometric ratio)

C _C,TiC=0.5 (stoichiometric ratio)

${\mu }_{\mathrm{TiC}}\left(T,C_{C,\mathrm{Tic}},C_{\mathrm{Ti},\mathrm{TiC}}\right)-{\mu }_{C,\mathrm{Phase}2}\left(T,C_{C,\mathrm{Phase}2},C_{\mathrm{Ti},\mathrm{Phase}2}\right)-{\mu }_{\mathrm{Ti},\mathrm{Phase}2}\left(T,C_{C,\mathrm{Phase}2},C_{\mathrm{Ti},\mathrm{Phase}2}\right)=0$ $\frac{v_{\mathrm{Phase}2,\mathrm{Tic},\mathrm{grenz}}}{V_m}*\left(C_{C\mathrm{TiC}}-C_{C\mathrm{Phase}2}\right)=J_{\mathrm{TiC}}+D_{\mathrm{Phase}2}\nabla x_C{❘}_{r=R_{\mathrm{Phase}2}}$ $\frac{v_{\mathrm{Phase}2,\mathrm{TiC},\mathrm{grenz}}}{V_m}*\left(C_{\mathrm{Ti}\mathrm{TiC}}-C_{\mathrm{Ti}\mathrm{Phase}2}\right)=J_{\mathrm{TiC}}+D_{\mathrm{Phase}2}\nabla x_{\mathrm{Ti}}{❘}_{r=R_{\mathrm{Phase}2}}$

• • calculation step 3: diffusion
  • Unknown variables:
    • x_C, x_Ti, x_Fe concentration profiles of the elements (3 unknowns)
  • Secondary conditions:

$R_{\mathrm{Phase}12}\left(t_i\right)=R_{\mathrm{Phase}12}\left(t_{i-1}\right)+v_{\mathrm{Phase}12,\mathrm{grenz}}\left(t_i-t_{i-1}\right)$ $x_C^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\begin{array}{c}\mathrm{Init}(C_{C,\mathrm{Phase}1},C_{C,\mathrm{Phase}2},\\ x_C,R_{\mathrm{Phase}12},t_i,t_{i-1})\left(r\right)\end{array}& r\in \begin{array}{c}[R_{\mathrm{Phase}12}\left(t_i\right),\\ R_{\mathrm{Phase}12}\left(t_{i+1}\right)]\end{array}\\ x_C\left(r,t_{i-1}\right)& \mathrm{else}\end{array}$ $x_{\mathrm{Ti}}^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\begin{array}{c}\mathrm{Init}(C_{\mathrm{Ti},\mathrm{Phase}1},C_{\mathrm{Ti},\mathrm{Phase}2},\\ x_{\mathrm{Ti}},R_{\mathrm{Phase}12},t_i,t_{i-1})\left(r\right)\end{array}& r\in \begin{array}{c}[R_{\mathrm{Phase}12}\left(t_i\right),\\ R_{\mathrm{Phase}12}\left(t_{i+1}\right)]\end{array}\\ x_{\mathrm{Ti}}\left(r,t_{i-1}\right)& \mathrm{else}\end{array}$ $x_{\mathrm{Fe}}^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\begin{array}{c}\mathrm{Init}(C_{\mathrm{Fe},\mathrm{Phase}1},C_{\mathrm{Fe},\mathrm{Phase}2},\\ x_{\mathrm{Fe}},R_{\mathrm{Phase}12},t_i,t_{i-1})\left(r\right)\end{array}& r\begin{array}{c}[R_{\mathrm{Phase}12}\left(t_i\right),\\ R_{\mathrm{Phase}12}\left(t_{i+1}\right)]\end{array}\\ x_{\mathrm{Fe}}\left(r,t_{i-1}\right)& \mathrm{else}\end{array}$

• • equations:

${\nabla }^2{x}_C\left(r,t\right)-\frac{1}{D}\frac{\partial }{\mathrm{\delta t}}{x}_C\left(r,t\right)=0$ $x_C^0\left(r,t=t_{i-1}\right)$

with starting condition

${\nabla }^2{x}_{\mathrm{Ti}}\left(r,t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_{\mathrm{Ti}}\left(r,t\right)=0$ $x_{\mathrm{Ti}}^0\left(r,t=t_{i-1}\right)$

with starting condition

${\nabla }^2{x}_{Fe}\left(r,t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_{Fe}\left(r,t\right)=0$ $x_{Fe}^0\left(r,t=t_{i-1}\right)$

with starting condition

A result of the product section calculation is used to determine, by means of a computer system having computer-readable medium, likelihoods of defects, in the cross section of the product section, by means of defined defect indices. A position in the cross section of the product section is given by the predetermined temperature curve. A separate temperature curve also has to be transferred as an input parameter to the method according to the invention for each position in the cross section. The defined defect indices are preferably a mathematical formula which indicates a high likelihood of a quality-reducing defect if a predetermined threshold value is exceeded. The product section has a specific cross section—thus a width and a height—and the defects can occur, for example, in the strand center or on the surface. The calculation is therefore preferably carried out at multiple positions in the cross section. One possible defect index is QI_PERI, by which an occurrence and an extent of peritectic behavior is indicated.

$\begin{array}{cc}Q{I}_{PERI}=\mathrm{factor}1\star (\mathrm{phase}{\mathrm{proportion}}_{\mathrm{Ferrite}}\left(\mathrm{Tsolidus}\right)-& \mathrm{Equation}8\end{array}$ $\mathrm{phase}{\mathrm{proportion}}_{\mathrm{Ferrite}}\left(\mathrm{Tsolidus}-\Delta T\right))$

• • Q_{I PERI} defect index
  • factor1 pilot factor
  • phase proportion_Ferrite(Tsolidus) ferrite phase proportion at solidus temperature. Volume proportion of the ferrite phase for R_Ferrite(t_Solidus) with T(t_Solidus)=T_Solidus
  • phase proportion_Ferrite(T_solidus−ΔT) ferrite phase proportion at temperature ΔT below the solidus temperature T_Solidus

The pilot factor is used to set the sensitivity so that the defect index is as much as possible in a range between 0 and 1. The phase proportions and the solidus temperature are determined in the above-described calculations. The temperature ΔT has to be empirically determined in a validation process. This temperature ΔT normally does not change further during the operation of the casting plant.

The defect indices are specified scaled in a range from 0 to 1, wherein values in the vicinity of 0 mean a very low likelihood of defects and values in the vicinity of 1 represent a very high likelihood of an occurrence of defects.

The determined defects are determined in real time, thus immediately before the product section leaves the casting plant, preferably before the product section reaches a cutting device of the casting plant.

The above-described calculation system enables a categorization of the susceptibility to defects for certain defects, which occur with a certain likelihood, to be provided during the passage through the casting plant. The determined defects can then be used, for example, to define a cutting position of the product segment, define the following processing, and/or define possible posttreatment steps.

One preferred embodiment provides that a selection from the following parameters are used as the selected operating parameters:

• • casting speeds,
  • status of the casting machine,
  • casting powder,
  • electromagnetic molds and/or casting stirrers,
  • temperature distribution of the metal within the mold

One expedient embodiment provides that the product section calculation has a third calculation step, in which the diffusion is calculated with the aid of the results of the second calculation step and its results are fed as the input variable to the following first calculation step.

One advantageous embodiment provides that the characterizing parameters of the product section comprise a selection of the following parameters:

• • chemical composition
  • histories of the mechanical tensions and deformations
  • stretching rates and stretches due to the bending in a bending facility
  • stretching rates and stretches due to the straightening in a bending facility
  • stretching rates and stretches due to soft reduction
  • thermal stretching rates and stretches of the product section within the casting plant

One expedient embodiment provides that at least the temperature curves of two, preferably four, particularly preferably six different positions of the cross section of the cast product section are transmitted as input parameters. In these at least two, preferably four, particularly preferably six positions of a cross section of the product section, defect probabilities are determined.

The calculation is therefore preferably carried out at multiple positions in the cross sections so that defects can also be identified at different positions in the cross section.

A further expedient embodiment provides that the characterizing parameters of the product section and the selected operating parameters of the casting plant are determined as a function of operating parameters which are partially or completely determined from the casting process or are calculated during the casting process and made available to the product section calculation in real time.

One advantageous embodiment provides that a change of carbide phase proportions in the first calculation step is calculated. This is important for those steel grades which form carbides to obtain an accurate calculation.

In one preferred embodiment, the temperature curve is made available by a calculation and/or a measurement, preferably a temperature measurement. The calculation of the temperature curve takes place with the aid of a corresponding temperature model.

The object is furthermore achieved by a computer program comprising commands which, upon the execution of the program by a computer, prompt it to carry out the method as claimed in claims 1-9.

The object is also achieved by a casting plant, preferably a continuous casting plant for producing cast products, preferably slabs. This comprises a computer system having a computer-readable medium which comprises the above-described computer program.

The object is furthermore achieved by a computer-readable medium on which the above-described computer program is stored.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic representation of a continuous casting plant

FIG. 2 shows a schematic sequence of the method

FIG. 3 shows a cross section of a strand

FIG. 4a shows a temperature curve of a cast steel melt

FIG. 4b shows a defect index for various temperature curves

DESCRIPTION OF THE EMBODIMENTS

FIG. 1 schematically shows a continuous casting plant 1. Liquid metal 6 is cast in a mold 2 and then a cast strand 7 is drawn from the mold. Defects of the cast strand 7 are calculated by a computer system 3, which is connected to a memory 4. The strand is divided into different product sections 7a-7d for the calculation. The defects are fed to a production planning system 9 and/or a display unit 8. The computer system 3 receives input parameters via inputs 5. These input parameters can be transferred, on the one hand, from measuring instruments 5a, from the memory 4, via the memory line 5b, and/or from a higher-order control system of the industrial plant. The parameters detected by measuring instruments 5a are, for example, the temperature of the melt, casting speed, and/or parameters of the cooling line. A cutting device 10 can be controlled, for example, by the production planning system 9, which has prepared a corresponding cutting plan on the basis of the determined defects. The production planning system 9 can also define, however, following treatment steps and/or products to be produced. A composition of the melt can either be stored in the memory or can be transmitted by the higher-order control system of the industrial plant. In addition to specific data of the continuous casting plant 1, measurement data can also be stored in the memory 4.

FIG. 2 shows a schematic sequence of a method for determining defects of a cast product section. In step S1, the process data for the currently produced product section are collected and used as input parameters for a following two-stage product section calculation. One input parameter is at least the temperature curve of the product section during the casting process, furthermore, for example, the casting speed, the format, stretching and stretching rate in bending and straightening zones, and chemical composition of the melt can be incorporated as input parameters. In step S2, a change of matrix phase components and an element concentration profile in phase areas is calculated in each case for a temperature-time step with the aid of the input parameters.

The result from step S2 is used in step S3 to determine a change of precipitant proportions in the phase areas.

The results from step S3 are used to carry out the calculations in step S2 for a next temperature-time step.

In next step S4, possible defects at specific locations of the product segment are then determined on the basis of criteria for defect indices. The defects and the determined locations thereof are then passed on in step S5, for example, to a downstream production planning system.

FIG. 3 shows a cross section of a strand 7. Various positions 11a-11d are shown here at which a likelihood of defects is calculated. The points are dependent, inter alia, on which position resolution the temperature curve which is made available has.

FIG. 4a shows by way of example for a cast steel melt a temperature curve 20a-20c over the time t, which was achieved with the aid of different cooling rates. All other parameters were the same. A smaller amount of cooling water was applied for the temperature curve 20a than for the temperature curves 20b and 20c, wherein the greatest amount of cooling water was applied to the observed product section for the temperature curve 20c. In FIG. 4b, a defect index O_{I com} for the above-mentioned different temperature curves—using different coolant amounts KM—was shown on the y axis. This defect index O_{I com} is dependent on the following parameters:

Q _{I com} =f(ε,f_decomp,Ar3,Ar1)

ε stretching

• • f_decomp phase proportion of the already converted austenite
  • Ar3 temperature of the ferrite formation
  • Ar1 starting temperature of the perlite formation

The calculated defect index 21a corresponds to temperature curve 20a, the defect index 21b resulted by way of a temperature curve 20b, and the defect index 21c by way of the temperature curve 21c. The defect indices 21a-21c are scaled and are specified in a range from 0 to 1, wherein a greater value corresponds to a higher likelihood of defects.

Although the invention was illustrated and described in more detail by the preferred exemplary embodiments, the invention is not thus restricted by the disclosed examples and other variations can be derived therefrom by a person skilled in the art without leaving the scope of protection of the invention.

LIST OF REFERENCE SIGNS

• • 1 continuous casting plant
  • 2 mold
  • 3 computer system
  • 4 memory
  • 5 inputs
  • 5 a measuring instruments
  • 5 b memory line
  • 6 liquid metal
  • 7 strand
  • 7 a-7d product sections
  • 8 display unit
  • 9 production planning system
  • 10 cutting device
  • 11 a-11d positions
  • 20 a-20c temperature curve
  • S1-S5 step
  • Q_{I com} defect index
  • KM coolant amount
  • t time
  • T temperature

Claims

1. A method for establishing a likelihood of defects in a product section cast in a casting plant, wherein a temperature curve over time, for at least one position of a cross section of the product section, was determined during the casting process and is used as an input parameter, wherein a multistage product section calculation is carried out on a computer system having a non-transitory computer-readable medium, with the aid of characterizing parameters of the product section and selected operating parameters of the casting plant, wherein the product section calculation runs in real time, the multistage product section calculation comprise of at least the following calculation steps:a first calculation step, in which at least changes of matrix phase proportions are each calculated for a temperature-time step,results of the first calculation step are fed to a second calculation step,wherein in the second calculation step a change of precipitant proportions from at least one phase area is determined,for the following temperature-time step, results of the second calculation step are used as an input variable for the first calculation step,wherein results of the product section calculation are used to determine at least one defect index by means of the computer system having the computer-readable medium,wherein the at least one determined defect index is available in real time, thus immediately before the product section leaves the casting plant.

2. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein a selection from the following parameters are used as the selected operating parameters: casting speeds,status of the casting machine,casting powder,electromagnetic molds and/or casting stirrers,temperature distribution of the metal within the mold.

3. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the product section calculation has a third calculation step in which the diffusion is calculated with the aid of the results of the second calculation step and its results are fed as an input variable to the following first calculation step.

4. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claimed in claim 1, wherein the characterizing parameters of the product section comprise a selection of the following parameters: chemical compositionhistories of the mechanical tensions and deformationsstretching rates and stretches due to the bending in a bending facilitystretching rates and stretches due to the straightening in a bending facilitystretching rates and stretches due to soft reductionthermal stretching rates and stretches of the product section within the casting plant.

5. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein at least the temperature curves of two different positions of the cross section of the cast product section are transmitted as input parameters and likelihoods of defects are determined at least the two positions of the cross section.

6. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the characterizing parameters of the product section and the selected operating parameters of the casting plant are determined as a function of operating parameters which are partially or completely determined from the casting process or are calculated during the casting process and made available in real-time to the product section calculation.

7. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein a change of carbide phase proportions is calculated in the first calculation step.

8. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the changes of the precipitant proportions in the phase areas are calculated with the aid of a second thermodynamic equilibrium calculation between matrix phases of an alloy and nonmetallic precipitants.

9. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the matrix phase proportions are calculated on the basis of a thermodynamic Gibbs energy approach having thermodynamic equilibrium at one or more phase boundaries and for different phases together with a material equilibrium approach at the phase boundary layer and diffusion.

10. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the temperature curve was determined by a calculation and/or a measurement.

11. A computer program product comprising a non-transitory computer readable-medium having commands recorded thereon which, upon execution by a computer, prompt the computer to carry out the method as claimed in claim 1.

12. A casting plant, preferably a continuous casting plant for producing cast products, preferably slabs, comprising a computer system having a computer-readable medium which comprises a computer program as claimed in claim 10.

13. A computer-readable medium on which the computer program as claimed in claim 11 is stored.

14. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the casting plant is a continuous casting plant.

15. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the casting plant is a semi-continuous casting plant.

16. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein at least four different positions of the cross section of the cast product section are transmitted as input parameters and likelihoods of defects are determined at least in the four positions of the cross section.

17. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein at least six different positions of the cross section of the cast product section are transmitted as input parameters and likelihoods of defects are determined at least in the six positions of the cross section.

18. The method for establishing a likelihood of defects in a product section cast in a casting plant as claimed in claim 1, wherein the at least one determined defect index is available in real time, thus immediately before the product section reaches a cutting device of the casting plant.