KR101573666B1 - Method for the continuous casting of a metal strand - Google Patents

Method for the continuous casting of a metal strand Download PDF

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KR101573666B1
KR101573666B1 KR1020107028210A KR20107028210A KR101573666B1 KR 101573666 B1 KR101573666 B1 KR 101573666B1 KR 1020107028210 A KR1020107028210 A KR 1020107028210A KR 20107028210 A KR20107028210 A KR 20107028210A KR 101573666 B1 KR101573666 B1 KR 101573666B1
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strand
continuous casting
metal
account
thermal conduction
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KR20110020828A (en
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쿠르트 디텐베르거
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지멘스 브이에이아이 메탈스 테크놀로지스 게엠베하
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
    • B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
    • B22D11/16—Controlling or regulating processes or operations
    • B22D11/22—Controlling or regulating processes or operations for cooling cast stock or mould
    • B22D11/225—Controlling or regulating processes or operations for cooling cast stock or mould for secondary cooling

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  • Mechanical Engineering (AREA)
  • Continuous Casting (AREA)

Abstract

The present invention relates to a method for continuous casting of metal strands, in particular steel strands, in a continuous casting plant wherein the strand having a liquid core surrounded by a strand sheath is drawn from a cooled in-line mold, Supported in a support and cooled using a coolant, wherein the thermodynamic state change of the entire strand is co-computed in a mathematical simulation model taking into account the physical parameters of the metal, the strand thickness and the continuously measured output speed. It is an object of the present invention to provide a method of the aforementioned type which can be used to increase the accuracy of the simulation of the change of thermodynamic state of the whole strand and in combination with the strand cooling, The productivity of the process can be improved. This objective is achieved by a method in which a three-dimensional thermal conduction equation is numerically interpreted in real time in a mathematical simulation model and the cooling of the strand is controlled while taking into account the calculated state change.

Description

[0001] METHOD FOR THE CONTINUOUS CASTING OF A METAL STRAND [0002]

The present invention relates to a continuous casting method of metal strands.

More particularly, the present invention relates to a method for continuous casting of metal strands, in particular steel strands, in a continuous casting plant wherein a strand having a liquid core surrounded by a strand shell is cooled in- line mold, supported in a strand support device downstream of the mold and cooled using a coolant, wherein the thermodynamic state change of the entire strand is determined by physical parameters of the metal, the thickness of the strand and the constantly measured (Co-calculated) in the mathematical simulation model, taking into account the output speed.

DE 4417808 A1 discloses a process for the continuous casting of metal strands wherein a strand having a liquid core surrounded by a strand sheath is drawn from a cooled mold and subsequently supported in a strand support device and used And cooled. The change in state that occurs during the continuous casting process is co-calculated in real time for the entire strand by a mathematical simulation model that includes a two-dimensional thermal conduction equation, Adjust the cooling of the strand while considering.

Due to the two-dimensional nature of the thermal conduction equation used, it has not yet been possible to calculate the thermal conduction and concomitant relative changes in all directions of the metal strand (strand thickness, strand width and strand output direction) The temperature profile could not be conveniently adjusted by strand cooling as the temperature changed. Also, due to thermodynamic effects (not considered in the simulation model), a deviation occurs between the calculated freezing point and the actual freezing point.

It is an object of the present invention to provide a method of the aforementioned type which can be used to increase the accuracy of the simulation of the change of thermodynamic state of the whole strand and in combination with the strand cooling, The productivity of the process can be improved.

This object is achieved by a method of the type described above, in which a three-dimensional thermal conduction equation is numerically analyzed in real time in a mathematical simulation model and the cooling of the strand is taken into account, taking into account the calculated state changes.

By the method of DE 4417808 A1, the thermodynamic state change can be calculated in real time according to two-dimensional thermal conduction, and the strand's temperature profile can be influenced by the strand cooling. According to the method according to the invention, the non-linear, non-steady state heat (or non-steady state) heat is generated according to the three-dimensional heat conduction i.e. the heat conduction in the strand thickness direction, The conduction equation makes it possible to easily influence the thermodynamic state change. By doing this, the thermodynamic state change can be calculated with higher accuracy and can be very easily affected by the strand cooling that is tailored to it. In a mathematical simulation model, the strands are divided into separate volume elements, that is, "discretized ", wherein each intermittent volume element is oriented in the strand length direction, And extend in the strand width direction.

By this interruption, individual strand cooling nozzles can be assigned to one or more intermittent volume elements of the strand, thereby eliminating it on the one hand by thermal conduction and strand cooling in all spatial dimensions The thermodynamic state changes in these volumetric elements can be determined with high accuracy while taking into account the calories, and on the other hand the thermodynamic properties of the strands can be very conveniently and very effectively influenced by these nozzles.

In a particularly preferred embodiment, the three-dimensional thermal conduction equation is numerically interpreted in real time in a mathematical simulation model of the method according to the invention, taking into account the temperature-dependent density variation of the metal strands. It is well known to those skilled in the art that the density of the metal can vary considerably with temperature. In a continuous casting process, for example, the density of steel is increased from about 7000 kg / m 3 to about 7800 kg / m 3 at 300 ° C (solidified strand) at 1550 ° C (the temperature of the melt in the tundish) do. The density variation is also related to the thermal conduction equation for determining the solidification point in the continuous casting process. The solidification point refers to the point at which the metal strands completely solidify past the direction of strand output, i. E., The point at which the metal strand no longer contains the liquid core. It is highly desirable in any case to calculate the freezing point to the maximum accuracy. If the position of the freezing point is underestimated, that is, not far from the mold than there is a real point along the output direction, this could result in a very dangerous casting situation (e.g. strand breakage). On the other hand, if the freezing point is overestimated, acceptable casting speeds will be unnecessarily limited, thereby reducing the productivity of the equipment.

In interpreting the numerical value of the heat conduction equation taking into account the temperature-dependent density variation of the metal strands, the approximated equation for the enthalpy with correct mass and correct enthalpy for the entire strand is used Another particularly preferred embodiment of the method according to the invention can be achieved. Here, it should be noted that no three-dimensional non-linear and non-steady state thermal conduction equations have been analyzed so far, taking into account temperature-dependent density variations. Without taking temperature-dependent density changes into account, the thermal conduction equation currently in use is merely a rough approximation of the exact equation, and such a solution can be quite different from the exact interpretation. However, using an estimated equation for the enthalpy with the correct mass and the correct enthalpy as a whole (i.e., when the entire strand is taken into account) ensures that these essential thermodynamic state variables correspond to the correct values.

When the thermal conduction equation is numerically analyzed by a finite volume method or a finite volume method or by a finite element method, the method according to the present invention may be particularly preferably carried out. The thermal conduction equation is a parabolic partial differential equation which can be interpreted by standard methods of numerical mathematics and can be interpreted in particular by finite volume methods or finite element methods : Numerische Mathematik [numerical mathematics] by IN Bronstein, KA Semendjajew, G. Musiol, H. Muehlig: Taschenbuch der Mathematik [handbook of mathematics], Verlag Harri Deutsch, 6 th edition, 2005).

The method according to the invention can be particularly advantageously practiced when the thermodynamic state change is calculated for only one quarter of the strand cross section based on spatial symmetry. This simplification can be accomplished without loss of accuracy due to spatial symmetry and time-varying boundary conditions of the strand cross-section, so that even with relatively low-power process computers, three-dimensional thermal conduction equations Can be interpreted.

The method according to the invention can be used to improve the quality of the cast metal strands without the limitation of casting metal strands having billet, bloom, slab or slab-slab cross-sections of any dimensions It will be possible.

Other features and advantages of the present invention will become apparent from the following non-limiting exemplary embodiments, with reference to the accompanying drawings.

1 is a side view of a continuous casting installation;
Fig. 2 is a view showing interrupted metal strands. Fig.
Figure 3 is a graph comparing the analysis of different formulations of thermal conduction equations.

Liquid steel 2 is supplied to the cooled mold 1, and such liquid steel is supplied from the turn-dish 3. The strand 6 which is formed in the mold 1 with the liquid core 4 and the initial only thin strand sheath 5 is guided by the curved strand supporting device 7, And supports the strand in the upper and lower sides until it is leveled and the strand is further transported or divided as a continuous strand after solidification. In order to cool the strand 6, a nozzle 10 for supplying a coolant is provided along the strand supporting device 7 and only the nozzles on the strand upper side are shown at the beginning of the strand supporting device 7 . One or more nozzles 10 are connected to the supply line 11, respectively. The amount of refrigerant applied to the strand by the nozzle may be changed by a continuously adjustable valve 12, and a flow metering device 13 is located downstream of the valve. Each valve 12 can be adjusted by an actuator 14 which can be actuated by a control element 16 which is driven by a central processing computer 15. Each flow metering device is coupled to the process computer 15 by an input unit 17 so that the computer drives all of the control elements 16 by an output unit 18. For example, the input unit 17 of the process computer 15 also receives the physical parameters of the metal being cast (steel 2 in this case) and, in other words, the temperature-dependent density value, the specific heat capacity ) And thermal conductivity, as well as the flow-dependent spray pattern of the nozzles 10 arranged in a position-dependent manner, the position-dependent roller spacing 9, the similar position-dependent strand thickness, the strand width and the continuous casting equipment ) Receives the measured casting speed.

According to the invention, the strands (6) are cooled in a controlled manner at fixed or variable specific locations of the strand supporting device (7). The three dimensional thermal conduction equation is analyzed in real time with the help of the process computer 15 to control the strand cooling while taking into account the thermodynamic state changes of the entire strand 6.

The three-dimensional non-linear and non-steady state heat transfer equations of the enthalpy formulations can be described, for example, as follows:

Figure 112010082716616-pct00001

At this time

t is the time in seconds,

x is the coordinates of the strand thickness direction in m,

y is a coordinate in the strand width direction in units of m,

z is the output direction in m, that is, the coordinates of the strand longitudinal axis,

Figure 112010082716616-pct00002
Is a partial derivative of the time t,

Figure 112010082716616-pct00003
Is a partial derivative of the position (x, y, z)

Figure 112010082716616-pct00004
Is a position vector in a right-angled coordinate system of m,

ρ is the density in kg / m 3 ,

Figure 112010082716616-pct00005
Is the mass-related enthalpy at time (t) and position (x) in J / kg,

ξ is a dimensionless dummy variable,

Figure 112010082716616-pct00006

Figure 112010082716616-pct00007
Is the output speed of the strand in m / s at time t.

In this heat conduction equation, the temperature-dependent density variation of the strand 6 is still ignored. Since the density of steel 2 increases from 7000 kg / m 3 at 1550 ° C to 7800 kg / m 3 at 300 ° C, this simplification causes inaccuracies in the calculation of thermodynamic state changes. It has been found that the freezing point is underestimated in this thermal conduction equation, that is to say that the actual freezing point is farther away from the mold 1 than the calculated freezing point. In order to avoid disadvantages and sometimes even to avoid dangerous casting situations, it is necessary to use the density value p within the maximum density range of the steel 2, and as a result significantly reduces the maximum allowable casting speed.

The second formulation of non-linear three-dimensional and non-steady state heat conduction equations is as follows:

Figure 112014030918134-pct00008

At this time,

Figure 112010082716616-pct00009
Is the temperature in K units at time (t) and position (x)

Figure 112010082716616-pct00010
Denotes the density of the metal strands in the unit of kg / m 3 at the temperature (T).

This formulation of the thermal conduction equation is mass-correct in its entirety, that is, considering the entire strand, but it is inaccurate with respect to enthalpy. It can be seen that the solidification point is overestimated in this thermal conduction equation, that is, the actual solidification point is not farther away from the mold than the calculated solidification point. Accordingly, although the use of these equations is not a problem with respect to any adverse casting situation, the maximum allowable casting speed is nevertheless unnecessarily limited, which leads to a reduction in productivity of the equipment.

The following thermal conduction equations may preferably be used:

Figure 112010082716616-pct00011

At this time,

Figure 112010082716616-pct00012
Is the mass-related enthalpy transformed at time (t) and position (x).

In this case, the overall correct modified enthalpy < RTI ID = 0.0 >

Figure 112010082716616-pct00013
Use two expressions. The thermodynamic conditions in the strand 6 change significantly at the freezing point 19 because the strand 6 is located above the freezing point (as viewed in the casting direction) from the liquid core 4 connected to the liquid steel 2 of the mold 1 ). The ferrostatic pressure in this region presses the already solidified strand jacket 5 against the roll 8 of the strand support device 7 and thereby the steel (2) 2) are compensated in this region. Below the freezing point (19), such compensation no longer occurs.

Above the freezing point (19), the expression is:

Figure 112010082716616-pct00014
.

On the other hand, below the freezing point 19, the following expressions are used:

Figure 112010082716616-pct00015
.

From here,

Figure 112010082716616-pct00016
(Arbitrary) but a constant reference temperature (typically 25 ° C)

Figure 112010082716616-pct00017
Is the temperature (K) of the metal in the casting bath,

Figure 112010082716616-pct00018
Is the derivative of the mass-related enthalpy over time.

The thermal conduction equation is based on Lagrangian coordinates,

Figure 112010082716616-pct00019
Lt; / RTI > to be observed by an observer moving with the strand output movement. These variations are as follows:

Figure 112010082716616-pct00020

At this time,

Figure 112010082716616-pct00021
Represents the time (in seconds) when an intermittent volumetric element is formed in the mold.

The thermal conduction equation in the Lagrangian coordinates is:

Figure 112010082716616-pct00022

This thermal conduction equation is interpreted in real time by the process computer 15 using a finite volume method. This standard method of computational mathematics is known to those skilled in the art and can be operated using intermittent volume elements of the strand 6. [ Thereby, for each volume element 20,

Figure 112015073936110-pct00023
Dimensional thermal conduction equation described in an element-fixed coordinate system that moves to a three-dimensional (3-D) In order to obtain the time-variable temperature field of the entire strand 6, this is done periodically for a number of the volume elements 20. It can be seen in FIG. 2 that the strand 6 is divided into intermittent volume elements 19 having an edge length of, for example, 10 cm. A volume element 19 is formed in the mold and is followed by a continuous casting installation according to the casting speed.

As shown in Fig. 2, the strand thickness axis x and the strand width axis y are symmetrical with respect to the edge of the coagulating strand 6. This spatial symmetry along the strand width and strand thickness direction provides the advantage that the thermodynamic state change can be calculated for only one quarter of a quadrant 20, i. E., The strand section section.

However, in order to interpret the thermal conduction equations, boundary conditions are still required, both initial conditions and time-varying (due to movement of the volume elements through the mold and through the various cooling zones).

The initial conditions for the newly formed volume element are:

Figure 112010082716616-pct00024

The boundary conditions are roughly as follows:

Figure 112010082716616-pct00025

At this time,

Figure 112010082716616-pct00026
The
Figure 112010082716616-pct00027
Lt; / RTI > is the temperature-dependent thermal conductivity,

Figure 112010082716616-pct00028
Is a temperature gradient perpendicular to the surface,

Figure 112010082716616-pct00029
Is the specific heat flux at time t.

To model the thermal flux q (t), the following expressions are used inside the cooled mold 1:

Figure 112010082716616-pct00030

Outside the mold,

Figure 112010082716616-pct00031

At this time,

a mold (T surf (t)) is the heat dissipation function of the mold,

α water (sw (t)) is the heat dissipation function of strand cooling,

(sw (t)) is the amount of cooling water for strand cooling,

α roll (t) is the heat dissipation function of the support roll,

σ is a Stefan-Boltzmann constant,

is the emissivity,

T surf (t) is the surface temperature of the strand 6,

T amb Is the ambient temperature.

Since the three-dimensional thermal conduction equation has not been interpreted so far, the high accuracy of the formulation of the thermal conduction equation with the modified enthalpy E trans according to the invention should be checked with the aid of a one-dimensional example. An accurate interpretation of the thermal conduction equation considering the temperature-dependent density variation (solid line) is known as a one-dimensional case and in Figure 3 a mass-accurate formulation (dotted line) and mass- and enthalpy- As shown in Fig. In Fig. 3, the distance from the mold in the strand output direction is denoted in the ordinate and the thickness of the metal strand along the strand thickness direction is denoted in abscissa. As shown in Figure 3, when using the mass- and enthalpy-accurate formulation of the thermal conduction equation, the actual freezing point is located slightly further from the mold than the calculated freezing point, i. E., The freezing point is slightly overestimated. By comparison, the freezing point is significantly underestimated when using the mass-exact formulation of the thermal conduction equation, which can lead to a hazardous situation in the continuous casting process.

One; Mold
2; steal
3; Turn Dish
4; Strand liquid core
5; Strand sheath
6; Strand
7; Strand support device
8; Support roll
9; Roll interval
10; Cooling nozzle
11; Refrigerant supply line
12; valve
13; Flow meter
14; Actuator
15; Process computer
16; Control element
17; Input unit
18; Output unit
19; Intermittent bulk factor
20; Strand powder

Claims (4)

A method for continuous casting of metal strands in a continuous casting plant comprising the steps of drawing a metal strand having a liquid core surrounded by a strand shell from a cooled inline mold, Wherein the thermodynamic state change of the entire metal strand is supported in the apparatus and cooled using the refrigerant and is calculated together in a mathematical simulation model taking into account the physical parameters of the metal, the thickness of the metal strand and the continuously measured output speed, In the continuous casting method,
Three-dimensional thermal conduction equations are numerically analyzed in real-time in a mathematical simulation model, taking into account temperature-dependent density variations of metal strands, and the cooling of the metal strands is controlled
Continuous casting method.
The method according to claim 1,
Taking account of the temperature-dependent density variation of the metal strands, an estimate of enthalpy, with an accurate mass and an accurate enthalpy for the entire metal strand, is used in a numerical solution of the thermal conductivity equation
Continuous casting method.
3. The method according to claim 1 or 2,
The thermal conduction equation is numerically interpreted by a finite volume method or a finite element method
Continuous casting method.
The method of claim 3,
The thermodynamic state change is calculated only for one quarter of the metal strand cross section based on the spatial symmetry
Continuous casting method.
KR1020107028210A 2008-05-21 2009-04-22 Method for the continuous casting of a metal strand KR101573666B1 (en)

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AT8152008A AT506847B1 (en) 2008-05-21 2008-05-21 METHOD FOR CONTINUOUSLY GASING A METAL STRUCTURE
ATA815/2008 2008-05-21

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KR102098023B1 (en) 2018-10-24 2020-04-07 주식회사 포스코 Apparatus for setting temperature of continuous casting device

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WO2012107143A1 (en) * 2011-02-07 2012-08-16 Siemens Vai Metals Technologies Gmbh Method for regulating a temperature of a strand by positioning a movable cooling nozzle in a strand guide of a strand casting system
DE102011082158A1 (en) 2011-09-06 2013-03-07 Sms Siemag Ag Casting, in particular continuous casting
EP3437756B1 (en) 2017-08-04 2021-12-22 Primetals Technologies Austria GmbH Continuous casting of a metallic strand
EP3437759B1 (en) 2017-08-04 2022-10-12 Primetals Technologies Austria GmbH Continuous casting of a metallic strand
EP3437757A1 (en) 2017-08-04 2019-02-06 Primetals Technologies Austria GmbH Continuous casting of a metallic strand

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DE4417808A1 (en) * 1993-05-24 1994-12-01 Voest Alpine Ind Anlagen Method for the continuous casting of a metal billet
JP2004506515A (en) * 2000-07-01 2004-03-04 エイ・イー・エム・ピー・コーポレーション Heat flow simulation for casting / forming process

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DE19850253A1 (en) * 1998-10-31 2000-05-04 Schloemann Siemag Ag Method and system for controlling cooling sections
AT409352B (en) * 2000-06-02 2002-07-25 Voest Alpine Ind Anlagen METHOD FOR CONTINUOUSLY casting a METAL STRAND
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Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE4417808A1 (en) * 1993-05-24 1994-12-01 Voest Alpine Ind Anlagen Method for the continuous casting of a metal billet
JP2004506515A (en) * 2000-07-01 2004-03-04 エイ・イー・エム・ピー・コーポレーション Heat flow simulation for casting / forming process

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR102098023B1 (en) 2018-10-24 2020-04-07 주식회사 포스코 Apparatus for setting temperature of continuous casting device

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SI2279053T1 (en) 2015-12-31
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EP2279053B1 (en) 2015-08-26
ES2548978T3 (en) 2015-10-22

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