EP4124400A1 - Method for determining a defect probability of a cast product section - Google Patents

Abstract

The present invention relates to the field of casting plants, preferably continuous casting plants for the production of slabs. The object of the present invention is to provide a method which provides a determination of quality-reducing defects before the cast product has left the casting plant. The task is solved by a method for determining a defect probability of a cast product section (7a-7d). A multi-stage product section calculation, which runs in real time, in a first calculation step at least changes in matrix phase proportions and an element concentration profile in phase areas are calculated for one temperature-time step .The results of the first calculation step are fed to a second calculation step, wherein in the second calculation step a change in precipitation proportions from at least one phase area is determined for the subsequent tempera tur-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

Description

field of technology

The present invention relates to the field of casting plants, preferably continuous casting plants for the production of slabs.

On the one hand, the invention relates to a method for determining a defect probability of a product section cast in a casting plant, preferably by means of a continuous casting plant. A temperature profile over time—for at least one position of a cross section of the product section—that was determined during the casting process is used as the input parameter. On the other hand, the invention relates to a computer program for carrying out the method, as well as a casting system and a computer-readable medium.

State of the art

When casting metal products, which are produced by a casting plant, a wide variety of suboptimal mechanical or thermal conditions can occur, which can lead to quality-reducing defects. If you are aware of these quality-reducing defects, you can react in different ways. For example, the cast metal product may be classified as low quality, post-processing may be arranged, a section may be cut out of the product and scrapped, or other actions may be taken. The problem - which has existed so far - is that the calculations are very complex and are time-consuming and a determination of defects is often only available at a late point in time. As a result, it is often no longer possible to take certain measures because they have already been completed.

Summary of the Invention

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

The task is solved by a multi-stage product section calculation. This is carried out with the help of characterizing parameters of the product section and selected operating parameters of the caster. The multi-stage product section calculation is divided into at least two calculation steps, since the partial calculations are easier to solve - two small equation systems compared to one large equation system. This is not exact but an approximation.

In the first calculation step, at least one change in matrix phase proportions is calculated for a temperature-time step i at time t _i and temperature T _i . The matrix phase components include matrix phases such as ferrite, austenite or bainite and carbide phase components such as primary carbides such as M23C6 or M7C3. For the calculation, physical thermodynamic calculations of the product section are preferably calculated using the input parameters and the temperature profile. The temperature profile over time is preferably taken over by an existing calculation system of the casting plant.

$$\frac{v_{\mathit{Phase}12,\mathit{grenz}}}{V_m}\ast \left(C_{\mathit{I\; Phase}1}-C_{\mathrm{I\; Phase}2}\right)=J_{\mathit{I\; Phase}1}-J_{\mathit{I\; Phase}2}$$

µI Phase1 ···

chemische Potential für Komponente I in der Phase 1

µI Phase2 ···

chemische Potential für Komponente I in der Phase 2

vPhase12,grenz ···

Geschwindigkeit der Grenzschicht zwischen Phasen 1 und 2

Vm ...

molares Volumen

CI Phase1 ···

Konzentration der Komponente I in Phase 1 an der Grenzschicht zu Phase 2

CI Phase2 ···

Konzentration der Komponente I in Phase 2 an der Grenzschicht zu Phase 1

JI Phase1 ···

Konzentrationsfluss der Komponente I in Phase 1

JI Phase2 ···

Konzentrationsfluss der Komponente I in Phase 2

The calculations are preferably based on a thermodynamic Gibbs energy approach with 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 laws) according to Equation 2. $${\mu }_{\mathit{I\; phase}1}\left(T_i,{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{1,\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1},{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{2\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1},...,C_{N,\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}\right)-{\mu }_{\mathit{I\; phase}2}\left(T_i,{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{1,\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2},...,C_{N,\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)=0$$

$$\frac{v_{\mathit{phase}12,\mathit{limit}}}{V_m}\ast \left(C_{\mathit{I\; <figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}-C_{\mathrm{I\; <figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)=J_{\mathit{I\; <figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}-J_{\mathit{I\; <figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}$$

µI Phase1 ···

chemical potential for component I in phase 1

µI Phase2 ···

chemical potential for component I in phase 2

vPhase12,limit ···

Velocity of the boundary layer between phases 1 and 2

vm...

molar volume

CI Phase1 ···

Concentration of component I in phase 1 at the interface to phase 2

CI Phase2 ···

Concentration of component I in phase 2 at the interface to phase 1

JI Phase1 ···

Component I concentration flow in phase 1

JI Phase2 ···

Component I concentration flow in phase 2

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

• Carbon-Nitride, beispielsweise Nb(CN) oder Ti(NC)
• Nitride, beispielsweise VN, AIN
• Carbide, beispielsweise NbC, TiC
• Sulfid, beispielsweise (MnCr)S, MnS
• Oxide
• Boride

bestimmt.In the second calculation step, a change in the proportion of precipitation in the phase regions is determined. In the case of excretion fractions, fractions of excretions such as:

• Carbon nitrides, for example Nb(CN) or Ti(NC)
• Nitrides, for example VN, AlN
• Carbides, for example NbC, TiC
• sulfide, e.g. (MnCr)S, MnS
• oxides
• borides

certainly.

$$\frac{v_{\mathit{grenz}}}{V_m}\ast \left(C_{\mathit{I\; Matrix}}-C_{\mathit{I\; prec}}\right)=J_{\mathit{I\; Matrix}}-J_{\mathit{I\; prec}}$$

µI Matrix ···

chemische Potential für Komponente I in der Matrix Phase

µI prec ···

chemische Potential für Komponente I in der Ausscheidung

vgrenz -

Geschwindigkeit der Grenzschicht zwischen Matrixphase und Ausscheidung

Vm ...

molares Volumen

CI Matrix ···

Konzentration der Komponente I in Matrixphase

CI prec -

Konzentration der Komponente I in der nicht stöchiometrischen Ausscheidung

JI Matrix ···

Konzentrationsfluss der Komponente I in die Matrixphase

JI prec -

Konzentrationsfluss der Komponente I in der nicht stöchiometrischen Ausscheidung

In the second calculation step, the changes in the proportions of precipitation in the phase areas are preferably calculated with the aid of a second thermodynamic equilibrium calculation between matrix phases of an alloy and non-metallic precipitations. The result of this equilibrium calculation is new concentrations at the phase boundaries in the matrix phase regions. $${\mu }_{\mathit{I\; Matrix}}\left(T_i,{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{1,\mathit{matrix}},{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{2\mathit{matrix}},...,C_{N,\mathit{matrix}}\right)-{\mu }_{\mathit{I\; prec}}\left({\mathrm{<figure-callout\; id="1"\; label="T\; i\; C"\; filenames="imgf0003.png"\; state="\{\{state\}\}">T</figure-callout>}}_i,C_{},{}_{1,\mathit{<figure-callout\; id="2"\; label="prec\; C"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">prec</figure-callout>}},C_{},{}_{2,\mathit{<figure-callout\; id="3"\; label="prec\; C"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">prec</figure-callout>}},C_{},{}_{3,\mathit{prec}}\right)=0$$

$$\frac{v_{\mathit{limit}}}{V_m}\ast \left(C_{\mathit{I\; Matrix}}-C_{\mathit{I\; prec}}\right)=J_{\mathit{I\; Matrix}}-J_{\mathit{I\; prec}}$$

µI Matrix ···

chemical potential for component I in the matrix phase

µI prec ···

chemical potential for component I in the excretion

vlimit -

Velocity of the boundary layer between matrix phase and precipitation

vm...

molar volume

CI Matrix ···

Concentration of component I in matrix phase

CI prec -

Concentration of component I in the non-stoichiometric excretion

JI Matrix ···

Component I concentration flow into the matrix phase

JI prec -

Flow of concentration of component I in the non-stoichiometric excretion

In an embodiment variant, assuming complete diffusion within one time step, the concentration fluxes J _I result simply from maintaining the mass balance and the element concentration profiles are constant in each phase region.

In a preferred embodiment, C _I,matrix from Equation 4 goes into a third calculation step—the calculation of the element concentration profile using a diffusion equation. An element concentration profile x _I ( r , t _i ) at a point r and a time t _i is initialized with the concentration of a melt. As a result, element concentrations of the - between t _{i -1} and t _i from a phase 1 to a phase 2 - converted area between R _{phase 12} ( t _{i -1} ) and R _{phase 12} ( t _i ) in compliance with the mass balance at the Boundary layer is estimated using Equations 5 and 6 and then the diffusion equation (Equation 7) is solved, taking into account the appropriate boundary conditions, to obtain a new

$$x_I^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\mathit{Init}\left(C_{I,\mathit{matrix}},x_I,R_{\mathit{Phase}12},t_i,t_{i-1}\right)\left(r\right)& r\in \left[R_{\mathit{Phase}12}\left(t_{i-1}\right),R_{\mathit{Phase}12}\left(t_i\right)\right]\\ x_I\left(r,t_{i-1}\right)& \mathrm{else}\end{array}$$

$${\nabla }^2{x}_I\left(r,t\right)-\frac{1}{D_I\left(r\right)}\frac{\partial }{\partial t}{x}_I\left(r,t\right)=0{\mathrm{mit\; Startbedingung}x}_I^0\left(r,t_{i-1}\right)$$

DI(r) ...

eine Diffusionskonstante der Komponente I an der Position r

Init ...

eine Verteilung der Konzentration x in neu umgewandelten Phasengebiet unter Beibehaltung der Massenbilanz

Determine element concentration profile. $$R_{\mathit{phase}12}\left(t_i\right)=R_{\mathit{phase}12}\left(t_{i-1}\right)+v_{\mathit{phase}12,\mathit{limit}}\left(t_i-t_{i-1}\right)$$

$$x_I^0\left(\mathrm{right},t_{i-1}\right)=\{\begin{array}{cc}\mathit{initial}\left(C_{I,\mathit{matrix}},x_I,R_{\mathit{phase}12},t_i,t_{i-1}\right)\left(\mathrm{right}\right)& \mathrm{right}\in \left[R_{\mathit{phase}12}\left(t_{i-1}\right),R_{\mathit{phase}12}\left(t_i\right)\right]\\ x_I\left(\mathrm{right},t_{i-1}\right)& \mathrm{else}\end{array}$$

$${\nabla }^2{x}_I\left(\mathrm{right},t\right)-\frac{1}{D_I\left(\mathrm{right}\right)}\frac{\partial }{\partial t}{x}_I\left(\mathrm{right},t\right)=0{\mathrm{with\; start\; condition}x}_I^0\left(\mathrm{right},t_{i-1}\right)$$

To you) ...

a diffusion constant of component I at position r

init...

a distribution of the concentration x in the newly transformed phase domain while maintaining the mass balance

C _{I matrix} from Equation 4 and x _I from Equation 7 are then used as output variables in Equation 1 and Equation 2 for the next temperature/time step.

For the subsequent temperature-time step, the results of the third calculation step flow in as an input variable for the first calculation step.

• Berechnungsschritt 1: Veränderung von Matrixphasenanteilen.
  • Verwendete Ergebnisse aus Berechnungsschritt 2 bzw. 3 der Berechnung des Temperatur-Zeitschrittes t _i-1:
    • ∘ x_C (r), x_Ti (r) aus Berechnungsschritt 3
    • ∘ C _C,Phase1, C _Ti,Phase1, C _C,Phase2, C _Ti,Phase2 als Startwert aus Berechnungsschritt 2
  • Unbekannte Variablen:
    • ∘ C_Fe, C_C, C_Ti in jeder der zwei Phasen (6 Unbekannte)
    • ∘ v _{Phase12,grenz} zwischen den beiden Phasen
• Gleichungen
  • ∘ $$C_{\mathit{Fe},\mathit{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}=1-C_{C,\mathit{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}-C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}$$
    
  • ∘ $$C_{\mathit{Fe},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}=1-C_{C,\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}-C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}$$
    
  • ∘ $${\mu }_{C,\mathit{Phase}1}\left(T_i,C_{C,\mathit{Phase}1},C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}\right)-{\mu }_{C,\mathit{Phase}2}\left(T_i,C_{C,\mathit{Phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\right)=0$$
    
  • ∘ $${\mu }_{\mathit{Fe},\mathit{Phase}1}\left(T_i,C_{C,\mathit{Phase}1},C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}\right)-{\mu }_{\mathit{Fe},\mathit{Phase}2}\left(T_i,C_{C,\mathit{Phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\right)=0$$
    
  • ∘ $${\mu }_{\mathit{Ti},\mathit{Phase}1}\left(T_i,C_{C,\mathit{Phase}1},C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}\right)-{\mu }_{\mathit{Ti},\mathit{Phase}2}\left(T_i,C_{C,\mathit{Phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\right)=0$$
    
  • ∘ $$\frac{v_{\mathit{Phase}12,\mathit{grenz}}}{V_m}\ast \left({\mathrm{<figure-callout\; id="1"\; label="C\; C\; Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{C\; Phase}}-{\mathrm{<figure-callout\; id="2"\; label="C\; C\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{C\; Phase}}\right)=-{\mathrm{D}}_{\mathrm{C},\mathrm{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}\nabla x_C{|}_{r={\mathrm{<figure-callout\; id="1"\; label="R\; Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{Phase}}+{\mathrm{D}}_{\mathrm{C},\mathrm{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\nabla x_C{|}_{r={\mathrm{<figure-callout\; id="2"\; label="R\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{Phase}}}}$$
    
  • ∘ $$\frac{v_{\mathit{Phase}12,\mathit{grenz}}}{V_m}\ast \left({\mathrm{<figure-callout\; id="1"\; label="C\; TiPhase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{TiPhase}}-{\mathrm{<figure-callout\; id="2"\; label="C\; TiPhase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{TiPhase}}\right)=-{\mathrm{D}}_{\mathrm{Ti},\mathrm{<figure-callout\; id="1"\; label="Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}1}\nabla x_{\mathit{Ti}}{|}_{r={\mathrm{<figure-callout\; id="1"\; label="R\; Phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{Phase}}+{\mathrm{D}}_{\mathrm{Ti},\mathrm{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\nabla x_{\mathit{Ti}}{|}_{r={\mathrm{<figure-callout\; id="2"\; label="R\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{Phase}}}}$$
    
• Berechnungsschritt 2: Ausscheidungen aus Phase 2 für TiC.
  • Verwendete Ergebnisse aus Berechnungsschritt 1:
    • ∘ x _{C(r,ti )} und Startwert für C _C,Phase2
    • ∘ x _{Ti(r,ti )} und Startwert für C _Ti,Phase2
  • Unbekannte Variablen:
    • ∘ C_C, C_Ti in der Phase2 und als TiC (4 Unbekannte)
    • ∘ v _{Phase2,TiC,grenz} zwischen den beiden Phasen
• Nebenbedingung:
  • ∘ J_TiC = 0 (kein Rückdiffusion von Ausscheidungen)
• Gleichungen:
  • ∘ C_Ti,TiC = 0.5 (stöchiometrisches Verhältnis)
  • ∘ C_C,TiC = 0.5 (stöchiometrisches Verhältnis)
  • ∘ $${\mu }_{\mathit{TiC}}\left(T,C_{C,\mathit{TiC}},C_{\mathit{Ti},\mathit{TiC}}\right)-{\mu }_{C,\mathit{Phase}2}\left(T,C_{C,\mathit{Phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\right)-{\mu }_{\mathit{Ti},\mathit{Phase}2}\left(T,C_{C,\mathit{Phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\right)=0$$
    
  • ∘ $$\frac{v_{\mathit{Phase}}}{}$$$$\frac{{\mathit{}2,\mathit{TiC},\mathit{grenz}}_{}}{V_m}\ast \left(C_{\mathit{C\; TiC}}-C_{\mathit{C\; <figure-callout\; id="2"\; label="Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Phase</figure-callout>}2}\right)=J_{\mathit{TiC}}+{\mathrm{<figure-callout\; id="2"\; label="D\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{Phase}}\nabla x_C{|}_{r={\mathrm{<figure-callout\; id="2"\; label="R\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{Phase}}}$$
    
  • ∘ $$\frac{v_{\mathit{Phase}}}{}$$$$\frac{{\mathit{}2,\mathit{TiC},\mathit{grenz}}_{}}{V_m}\ast \left(C_{\mathit{Ti\; TiC}}-{\mathrm{<figure-callout\; id="2"\; label="C\; Ti\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{Ti\; Phase}}\right)=J_{\mathit{TiC}}+{\mathrm{<figure-callout\; id="2"\; label="D\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{Phase}}\nabla x_{\mathit{Ti}}{|}_{r={\mathrm{<figure-callout\; id="2"\; label="R\; Phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{Phase}}}$$
    
• Berechnungsschritt 3: Diffusion
  • Unbekannte Variablen:
    • ∘ x_C, x_Ti, x_Fe Konzentrationsprofile der Elemente (3 Unbekannte)
• Nebenbedingungen:
  • ∘ $$R_{\mathit{Phase}12}\left(t_i\right)=R_{\mathit{Phase}12}\left(t_{i-1}\right)+v_{\mathit{Phase}12,\mathit{grenz}}\left(t_i-t_{i-1}\right)$$
    
  • ∘ $$x_C^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\mathit{Init}\left(C_{C,\mathit{Phase}1},C_{\mathit{C},\mathit{Phase}2},x_C,R_{\mathit{Phase}12},t_i,t_{i-1}\right)\left(r\right)& r\in \left[R_{\mathit{Phase}12}\left(t_i\right),R_{\mathit{Phase}12}\left(t_{i+1}\right)\right]\\ x_C\left(r,t_{i-1}\right)& \mathrm{sonst}\end{array}$$
    
  • ∘ $$x_{\mathit{Ti}}^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\mathit{Init}\left(C_{\mathit{Ti},\mathit{Phase}1},C_{\mathit{Ti},\mathit{Phase}2},x_{\mathit{Ti}},R_{\mathit{Phase}12},t_i,t_{i-1}\right)\left(r\right)& r\in \left[R_{\mathit{Phase}12}\left(t_i\right),R_{\mathit{Phase}12}\left(t_{i+1}\right)\right]\\ x_{\mathit{Ti}}\left(r,t_{i-1}\right)& \mathrm{sonst}\end{array}$$
    
  • ∘ $$x_{\mathit{Fe}}^0\left(r,t_{i-1}\right)=\{\begin{array}{cc}\mathit{Init}\left(C_{\mathit{Fe},\mathit{Phase}1},C_{\mathit{Fe},\mathit{Phase}2},x_{\mathit{Fe}},R_{\mathit{Phase}12},t_i,t_{i-1}\right)\left(r\right)& r\in \left[R_{\mathit{Phase}12}\left(t_i\right),R_{\mathit{Phase}12}\left(t_{i+1}\right)\right]\\ x_{\mathit{Fe}}\left(r,t_{i-1}\right)& \mathrm{sonst}\end{array}$$
    
• Gleichungen:
  • ∘ $${\nabla }^2{x}_C\left(r,t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_C\left(r,t\right)=0$$
    
  • mit Startbedingung $x_C^0\left(r,t=t_{i-1}\right)$
    
  • ∘ $${\nabla }^2{x}_{\mathit{Ti}}\left(r,t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_{\mathit{Ti}}\left(r,t\right)=0$$
    
  • mit Startbedingung $x_{\mathit{Ti}}^0\left(r,t=t_{i-1}\right)$
    
  • ∘ $${\nabla }^2{x}_{\mathit{Fe}}\left(r,t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_{\mathit{Fe}}\left(r,t\right)=0$$
    
    mit Startbedingung $x_{\mathit{Fe}}^0\left(r,t=t_{i-1}\right)$
    

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,phase 1} , C _{Ti,phase 1} , C _{C,phase 2} , C _{Ti,phase 2} as start value from calculation step 2
  • Unknown variables:
    • ∘ C _Fe , C _C , C _Ti in each of the two phases (6 unknowns)
    • ∘ v _{phase 12 , boundary} between the two phases
• equations
  • ∘ $$C_{\mathit{feet},\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}=1-C_{C,\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}-C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}$$
    
  • ∘ $$C_{\mathit{feet},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}=1-C_{C,\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}-C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}$$
    
  • ∘ $${\mu }_{C,\mathit{phase}1}\left(T_i,C_{C,\mathit{phase}1},C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}\right)-{\mu }_{C,\mathit{phase}2}\left(T_i,C_{C,\mathit{phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)=0$$
    
  • ∘ $${\mu }_{\mathit{feet},\mathit{phase}1}\left(T_i,C_{C,\mathit{phase}1},C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}\right)-{\mu }_{\mathit{feet},\mathit{phase}2}\left(T_i,C_{C,\mathit{phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)=0$$
    
  • ∘ $${\mu }_{\mathit{Ti},\mathit{phase}1}\left(T_i,C_{C,\mathit{phase}1},C_{\mathit{Ti},\mathit{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}\right)-{\mu }_{\mathit{Ti},\mathit{phase}2}\left(T_i,C_{C,\mathit{phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)=0$$
    
  • ∘ $$\frac{v_{\mathit{phase}12,\mathit{limit}}}{V_m}\ast \left({\mathrm{<figure-callout\; id="1"\; label="C\; C\; phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{C\; phase}}-{\mathrm{<figure-callout\; id="2"\; label="C\; C\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{C\; phase}}\right)=-{\mathrm{D}}_{\mathrm{C},\mathrm{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}\nabla x_C{|}_{\mathrm{right}={\mathrm{<figure-callout\; id="1"\; label="R\; phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{phase}}+{\mathrm{D}}_{\mathrm{C},\mathrm{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\nabla x_C{|}_{\mathrm{right}={\mathrm{<figure-callout\; id="2"\; label="R\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{phase}}}}$$
    
  • ∘ $$\frac{v_{\mathit{phase}12,\mathit{limit}}}{V_m}\ast \left({\mathrm{<figure-callout\; id="1"\; label="C\; TiPhase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{TiPhase}}-{\mathrm{<figure-callout\; id="2"\; label="C\; TiPhase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{TiPhase}}\right)=-{\mathrm{D}}_{\mathrm{Ti},\mathrm{<figure-callout\; id="1"\; label="phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}1}\nabla x_{\mathit{Ti}}{|}_{\mathrm{right}={\mathrm{<figure-callout\; id="1"\; label="R\; phase"\; filenames="imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{phase}}+{\mathrm{D}}_{\mathrm{Ti},\mathrm{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\nabla x_{\mathit{Ti}}{|}_{\mathrm{right}={\mathrm{<figure-callout\; id="2"\; label="R\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{phase}}}}$$
    
• Calculation Step 2: Phase 2 precipitates for TiC.
  • Results used from calculation step 1:
    • ∘ x _{C ( r,t i )} and initial value for C _{C,phase 2}
    • ∘ x _{Ti ( r,t i )} and initial value for C _{Ti,phase 2}
  • Unknown variables:
    • ∘ C _C , C _Ti in phase2 and as TiC (4 unknowns)
    • ∘ v _{Phase 2 ,TiC,limit} between the two phases
• constraint:
  • ∘ J _TiC = 0 (no back-diffusion of precipitates)
• Equations:
  • ∘ C _Ti,TiC = 0.5 (stoichiometric ratio)
  • ∘ C _C,TiC = 0.5 (stoichiometric ratio)
  • ∘ $${\mu }_{\mathit{TiC}}\left(T,C_{C,\mathit{TiC}},C_{\mathit{Ti},\mathit{TiC}}\right)-{\mu }_{C,\mathit{phase}2}\left(T,C_{C,\mathit{phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)-{\mu }_{\mathit{Ti},\mathit{phase}2}\left(T,C_{C,\mathit{phase}2},C_{\mathit{Ti},\mathit{<figure-callout\; id="2"\; label="phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">phase</figure-callout>}2}\right)=0$$
    
  • ∘ $$\frac{{\mathrm{<figure-callout\; id="2"\; label="v\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">v</figure-callout>}}_{\mathit{phase}}}{V_m}\ast \left(C_{\mathit{CTiC}}-{\mathrm{<figure-callout\; id="2"\; label="C\; C\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{C\; phase}}\right)=J_{\mathit{TiC}}+{\mathrm{<figure-callout\; id="2"\; label="D\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{phase}}\nabla x_C{|}_{\mathrm{right}={\mathrm{<figure-callout\; id="2"\; label="R\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{phase}}}$$
    
  • ∘ $$\frac{{\mathrm{<figure-callout\; id="2"\; label="v\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">v</figure-callout>}}_{\mathit{phase}}}{V_m}\ast \left(C_{\mathit{TiTiC}}-{\mathrm{<figure-callout\; id="2"\; label="C\; Ti\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">C</figure-callout>}}_{\mathit{Ti\; phase}}\right)=J_{\mathit{TiC}}+{\mathrm{<figure-callout\; id="2"\; label="D\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{phase}}\nabla x_{\mathit{Ti}}{|}_{\mathrm{right}={\mathrm{<figure-callout\; id="2"\; label="R\; phase"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathit{phase}}}$$
    
• Calculation step 3: Diffusion
  • Unknown variables:
    • ∘ x _C, x _Ti , x _Fe concentration profiles of the elements (3 unknowns)
• Constraints:
  • ∘ $$R_{\mathit{phase}12}\left(t_i\right)=R_{\mathit{phase}12}\left(t_{i-1}\right)+v_{\mathit{phase}12,\mathit{limit}}\left(t_i-t_{i-1}\right)$$
    
  • ∘ $$x_C^{}$$$${}_0^{}\left(\mathrm{right},t_{i-1}\right)=\{\begin{array}{cc}\mathit{initial}\left(C_{C,\mathit{phase}1},C_{\mathit{C},\mathit{phase}2},x_C,R_{\mathit{phase}12},t_i,t_{i-1}\right)\left(\mathrm{right}\right)& \mathrm{right}\in \left[R_{\mathit{phase}12}\left(t_i\right),R_{\mathit{phase}12}\left(t_{i+1}\right)\right]\\ x_C\left(\mathrm{right},t_{i-1}\right)& \mathrm{otherwise}\end{array}$$
    
  • ∘ $$x_{\mathit{Ti}}^{}$$$${\mathit{}}_0^{}\left(\mathrm{right},t_{i-1}\right)=\{\begin{array}{cc}\mathit{initial}\left(C_{\mathit{Ti},\mathit{phase}1},C_{\mathit{Ti},\mathit{phase}2},x_{\mathit{Ti}},R_{\mathit{phase}12},t_i,t_{i-1}\right)\left(\mathrm{right}\right)& \mathrm{right}\in \left[R_{\mathit{phase}12}\left(t_i\right),R_{\mathit{phase}12}\left(t_{i+1}\right)\right]\\ x_{\mathit{Ti}}\left(\mathrm{right},t_{i-1}\right)& \mathrm{otherwise}\end{array}$$
    
  • ∘ $$x_{\mathit{feet}}^{}$$$${\mathit{}}_0^{}\left(\mathrm{right},t_{i-1}\right)=\{\begin{array}{cc}\mathit{initial}\left(C_{\mathit{feet},\mathit{phase}1},C_{\mathit{feet},\mathit{phase}2},x_{\mathit{feet}},R_{\mathit{phase}12},t_i,t_{i-1}\right)\left(\mathrm{right}\right)& \mathrm{right}\in \left[R_{\mathit{phase}12}\left(t_i\right),R_{\mathit{phase}12}\left(t_{i+1}\right)\right]\\ x_{\mathit{feet}}\left(\mathrm{right},t_{i-1}\right)& \mathrm{otherwise}\end{array}$$
    
• Equations:
  • ∘ $${\nabla }^2{x}_C\left(\mathrm{right},t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_C\left(\mathrm{right},t\right)=0$$
    
  • with start condition $x_C^{}$${}_0^{}\left(\mathrm{right},t=t_{i-1}\right)$
    
  • ∘ $${\nabla }^2{x}_{\mathit{Ti}}\left(\mathrm{right},t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_{\mathit{Ti}}\left(\mathrm{right},t\right)=0$$
    
  • with start condition $x_{\mathit{<figure-callout\; id="0"\; label="Ti"\; filenames="imgf0003.png"\; state="\{\{state\}\}">Ti</figure-callout>}}^0\left(\mathrm{right},t=t_{i-1}\right)$
    
  • ∘ $${\nabla }^2{x}_{\mathit{feet}}\left(\mathrm{right},t\right)-\frac{1}{D}\frac{\partial }{\partial t}{x}_{\mathit{feet}}\left(\mathrm{right},t\right)=0$$
    
    with start condition $x_{\mathit{<figure-callout\; id="0"\; label="feet"\; filenames="imgf0003.png"\; state="\{\{state\}\}">feet</figure-callout>}}^0\left(\mathrm{right},t=t_{i-1}\right)$
    

A result of the product section calculation is used to determine defect probabilities in the cross section of the product section using fixed defect indices. A position in the cross section of the product section is given by the predetermined temperature profile. For each position in the cross section, the inventive method must also be given its own temperature profile as an input parameter.

QI PERI ···

Defektindex

factor1 ...

Vorfaktor

PhasenanteilFerrit(Tsolidus) ...

Ferrit Phasenanteil bei Solidus Temperatur. Volumenanteil der Ferrit-Phase für RFerrit(tsolidus) mit T(tSolidus) = TSolidus

PhasenanteilFerrit(Tsolidus - ΔT)

Ferrit Phasenanteil bei Temperatur ΔT unterhalb der Solidus Temperatur Tsolidus

The specified defect indices are preferably a mathematical formula which indicates a high probability of a quality-reducing defect when a predetermined threshold value is exceeded. The product section has a specific cross-section - that is, a width and a height - and the defects can occur, for example, in the middle of the strand or on the surface. The calculation is therefore preferably carried out at several positions in the cross section. A possible defect index is QI _PERI , which indicates the occurrence and extent of peritectic behavior. $${\mathit{QI}}_{\mathit{PERI}}=\mathit{<figure-callout\; id="1"\; label="factor"\; filenames="imgf0003.png"\; state="\{\{state\}\}">factor</figure-callout>}1\ast ({\mathit{phase\; fraction}}_{\mathit{ferrite}}\left(\mathit{Tsolidus}\right)-{\mathit{phase\; fraction}}_{\mathit{ferrite}}\left(\mathit{Tsolidus}-\mathrm{\Delta }\mathit{T}\right)$$

QI PERI ···

defect index

factor1 ...

prefactor

Phase fraction ferrite(Tsolidus) ...

Ferrite phase fraction at solidus temperature. Volume fraction of the ferrite phase for RFerrit(tsolidus) with T(tSolidus) = TSolidus

Phase fraction ferrite(Tsolidus - ΔT)

Ferrite phase fraction at temperature ΔT below the solidus temperature Tsolidus

The prefactor is used to set the sensitivity so that the defect index is in a range between 0 and 1 if possible. The phase fractions and the solidus temperature are determined in the calculations described above. The temperature Δ T must be determined empirically in a validation process. Normally, this temperature ΔT no longer changes during the operation of the casting installation.

The defect indices are normalized in a range from 0 to 1, with values close to 0 meaning a very low probability of defects and values close to 1 representing a very high probability of defects occurring.

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

The calculation system described above makes it possible to provide a categorization of the susceptibility to defects for specific defects that occur with a specific probability during the run through the casting plant. The defects determined can then be used, for example, to determine a cutting position of the product segment, to determine subsequent processing and/or to determine possible post-processing steps.

• Gießgeschwindigkeiten,
• Zustand der Gießmaschine,
• Gießpulver,
• Elektromagnetischer Kokillen und/oder Strangrührer,
• Temperaturverteilung des Metalls innerhalb der Kokille

A preferred embodiment provides that a selection from the following parameters is used as selected operating parameters:

• casting speeds,
• state of the casting machine,
• casting powder,
• Electromagnetic molds and/or strand stirrers,
• Temperature distribution of the metal within the mold

An expedient embodiment provides that the product section calculation has a third calculation step, in which the diffusion is calculated using the results of the second calculation step and the results of which are supplied as input variables to the following first calculation step.

• Chemische Zusammensetzung
• Geschichte der mechanischen Spannungen und Verformungen
• Dehnraten und Dehnungen aufgrund des Biegens in einer Bogenanlage
• Dehnraten und Dehnungen aufgrund des Richtens in einer Bogenanlage
• Dehnraten und Dehnungen aufgrund von Softreduction
• Thermische Dehnraten und Dehnungen des Produktabschnittes innerhalb der Gießanlage

An advantageous embodiment provides that the characterizing parameters of the product section include a selection of the following parameters:

• Chemical composition
• History of mechanical stresses and deformations
• Strain rates and strains due to flexing in an arch facility
• Strain rates and elongations due to straightening in an arch facility
• Strain rates and elongations due to soft reduction
• Thermal strain rates and elongations of the product section within the caster

An 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. Defect probabilities are determined in these at least two, preferably four, particularly preferably six positions of a cross section of the product section.

The calculation is therefore preferably carried out at a number of positions in the cross section, so that defects at different positions in the cross section can also be identified.

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

An advantageous embodiment provides that a change in carbide phase components is calculated in the first calculation step. This is important for those steel grades that form carbides in order to get an accurate calculation.

The object is also achieved by a computer program including instructions for carrying out the method described above.

The object is also achieved by a casting installation, preferably a continuous casting installation, for producing cast products, preferably slabs. This includes a computer system which includes the computer program described above.

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

Fig. 1

eine schematische Darstellung einer Stranggußanlage

Fig. 2

ein schematischer Ablauf des Verfahrens

Fig. 3

Querschnitt eines Stranges

Fig. 4a

Temperaturverlauf einer vergossenen Stahlschmelze

Fig. 4b

Defektindex für verschiedene Temperaturverläufe

Brief description of the drawings

1

a schematic representation of a continuous casting plant

2

a schematic flow of the procedure

3

cross section of a strand

Figure 4a

Temperature profile of a cast steel melt

Figure 4b

Defect index for different temperature curves

Description of the embodiments

In the 1 a continuous casting plant 1 is shown schematically. Liquid metal 6 is poured into a mold 2 and a cast strand 7 is then drawn off from the mold. A computer system 3, which is connected to a memory 4, calculates defects in the cast strand 7. 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 . On the one hand, these input parameters can be transferred from measuring instruments 5a, from memory 4, via storage line 5b and/or from a higher-level control system of the industrial plant. The parameters recorded by measuring instruments 5a are, for example, the temperature of the melt, casting speed and/or parameters of the cooling section. A cutting device 10 can be controlled, for example, by the production planning system 9, which has created a corresponding cutting plan based on the defects determined. However, the production planning system 9 can also specify subsequent treatment steps and/or products to be produced. A composition of the melt can either be stored in the memory or transmitted by the higher-level control system of the industrial plant. In addition to specific data of the continuous casting plant 1, measurement data can also be stored in memory 4.

In the 2 a schematic flow of a method for determining defects of a cast product section is shown. In step S1, the process data for the currently generated product section are collected and used as input parameters for a subsequent two-stage product section calculation. An input parameter is at least the temperature profile of the product section during the casting process. Furthermore, for example, the casting speed, the format, elongation and strain rate in bending and straightening zones, chemical composition of the melt can be used as input parameters flow in. In step S2, a change in matrix phase proportions and an element concentration profile in phase regions are calculated for a temperature-time step using the input parameters.

The result from step S2 is used in step S3 to determine a change in precipitation proportions in the phase regions.

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

In the next step S4, possible defects at specific locations of the product segment are then determined using criteria for defect indices. The defects and their specific location are then forwarded in step S5 to a subsequent production planning system, for example.

In 3 a cross section of a strand 7 is shown. Various positions 11a-11d are shown at which a defect probability is calculated. The points depend, among other things, on the local resolution of the temperature curve that is made available.

In the Figure 4a a temperature curve 20a-20c over time t, which was achieved with the help of different cooling rates, is shown as an example for a cast steel melt. All other parameters were the same. A smaller amount of cooling water was used for the temperature profile 20a than for the temperature profiles 20b and 20c, with the greatest amount of cooling water being applied to the product section under consideration for the temperature profile 20c.

ε

Dehnung

fdecomp···

Phasenanteil des bereits umgewandelten Austenits

Ar3

Temperatur der Ferritbildung

Ar1

Start Temperatur der Perlitbildung

In Figure 4b a defect index Q _{I com} was shown on the y-axis for the various temperature curves mentioned above—with different amounts of coolant KM. This defect index Q _{I com} depends on the following parameters: $$Q_{\mathit{I\; com}}=f\left(e,f_{\mathit{decomp}},\mathit{are}3,\mathit{are}1\right)$$

e

strain

fdecomp

Phase portion of the already transformed austenite

Ar3

temperature of ferrite formation

Ar1

Start temperature of pearlite formation

The calculated defect index 21a corresponds to the temperature curve 20a, the defect index 21b resulted from a temperature curve 20b and the defect index 21c from the temperature curve 21c. The defect indices 21a-21c are normalized and are specified in a range from 0 to 1, with a larger value corresponding to a higher defect probability.

Although the invention has been illustrated and described in detail by the preferred embodiments, the invention is not limited by the disclosed examples and other variations can be derived therefrom by those skilled in the art without departing from the scope of the invention.

Reference List

1

continuous casting plant

2

mold

3

computer system

4

Storage

5

inputs

5a

measuring instruments

5b

storage line

6

liquid metal

7

strand

7a - 7d

product sections

8th

display unit

9

production planning system

10

cutting device

11a - 11d

positions

20a - 20c

temperature curve

S1 - S5

Step

QI com

defect index

KM

amount of coolant

t

time

T

temperature

Claims (10)

Procedure for determining a
Probability of defects in a product section (7a-7d) cast in a casting plant, preferably by means of a continuous casting plant (1), with a temperature profile (20a-20c) over time for at least one position of a cross section of the product section (7a-7d) during the casting process has been determined and is used as an input parameter, characterized in that
a multi-stage product section calculation is carried out using characterizing parameters of the product section (7a-7d) and selected operating parameters of the casting plant, with the product section calculation taking place in real time, the multi-stage product section calculation consisting of at least the following calculation steps: - a first calculation step, in which at least changes in matrix phase proportions are calculated for one temperature-time step, - Results of the first calculation step are fed to a second calculation step, - a change in precipitation proportions from at least one phase region being determined in the second calculation step, - for the subsequent 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 being used to determine at least one defect index, - wherein the at least one determined defect index is available in real time, i.e. immediately before the product section (7a-7d) leaves the casting plant, preferably before the product section reaches a cutting device (10) of the casting plant. Procedure for determining a
Probability of defects in a product section (7a-7d) cast in a casting plant according to Claim 1, characterized in that a selection from the following parameters is used as selected operating parameters: - casting speeds, - condition of the casting machine, - casting powder, - Electromagnetic molds and/or strand stirrers, - Temperature distribution of the metal inside the mold. Procedure for determining a
Defect probability of a product section (7a-7d) cast in a casting plant according to Claim 1 or 2, characterized in that the product section calculation has a third calculation step in which the diffusion is calculated using the results of the second calculation step and the results of which are used as input variables for the following first calculation step be supplied. Procedure for determining a
Probability of defects in a product section (7a-7d) cast in a casting plant according to one of Claims 1-3, characterized in that the characterizing parameters of the product section include a selection of the following parameters: - Chemical composition - History of mechanical stresses and deformations - Strain rates and strains due to bending in an arch facility - Strain rates and elongations due to straightening in an arch facility - Strain rates and elongations due to soft reduction - Thermal strain rates and elongations of the product section within the caster. Procedure for determining a
Probability of defect of a product section (7a-7d) cast in a casting plant according to one of Claims 1-4, characterized in that at least the temperature profiles of two, preferably four, particularly preferably six different positions of the cross section of the cast product section (7a-7d) as Input parameters are transmitted and defect probabilities are determined at least in these two, preferably four, particularly preferably six positions of the cross section. Procedure for determining a
Probability of defects in a product section (7a-7d) cast in a casting plant according to one of Claims 1-5, characterized in that the characterizing parameters of the product section and the selected operating parameters of the casting plant as a function of operating parameters which are partially or completely determined from the casting process, or calculated during the casting process and made available to product section calculation in real time. Procedure for determining a
Probability of defects in a product section cast in a casting plant according to one of Claims 1-6, characterized in that a change in carbide phase proportions is calculated in the first calculation step. Computer program comprising instructions for performing the method according to claims 1-7. Casting plant, preferably a continuous casting plant for producing cast products, preferably slabs, comprising a computer system which comprises a computer program according to claim 8. A computer-readable medium storing the computer program of claim 8.

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