Method for casting a metal strand and method for determining the temperature of a cast metal strand

Abstract

Method for determining the temperature of a metal strand (3) cast in a continuous casting plant (1), comprising the following steps: dividing the strand (3) into a plurality of rake segments (k), comprising rake segments (k) in the interior of the metal strand (3) and rake segments (k) adjacent to the surface of the metal strand (3); iteratively determining the temperature of each rake segment (k) by solving a heat conduction equation; characterized in that a scale layer forming on the surface of the metal strand (3) is taken into account when determining the temperature of the rake segments (k) adjacent to the surface of the metal strand (3).

Description

Field of the invention

[0001] The present invention is directed to a method for casting metal strands. In particular, steel or iron alloys can be cast. Furthermore, the invention encompasses a method for determining the temperature of cast metal, particularly in a continuous casting plant. State of the art

[0002] A variety of casting processes are known from the state of the art in which liquid metal is poured and begins to solidify.

[0003] Knowledge of temperature distribution is crucial for the safe operation of a continuous casting plant, for example. Excessively high temperatures of a cast metal strand, for example, lead to bulging between the rollers of the casting plant during continuous casting. Excessively low temperatures can cause defects on the strand surface during bending and straightening of the metal strand, which can lead to cracks.

[0004] The temperature distribution and solidification length of the strand are of interest, but cannot be determined directly at every location in a casting machine or plant. For example, pyrometers are often only available downstream of a secondary cooling zone and upstream of a shear. Moreover, temperatures at the strand surface can only be measured there.

[0005] The temperature distribution in a secondary cooling zone of a continuous casting plant is often of particular interest. Strand temperatures are difficult to measure due to the splashing cooling water. Furthermore, temperatures inside the strand cannot be measured with pyrometers; they can only be calculated. This is usually done by solving Fourier's heat conduction equation: ρcp∂∂s−(λ∂T∂s)=Q where ρ is the density, c p is the specific heat capacity, s is the spatial coordinate or a segment, λ is the thermal conductivity and T is the temperature of the material (e.g. the metal) and Q is the latent heat or in other words, the energy released during the phase transformation (e.g. from liquid to solid).

[0006] This heat conduction equation can, as is also well known, be expressed as a function of the enthalpy H in the following form: ρ∂H∂T−∂∂s(λ∂T∂s)=0

[0007] Furthermore, the determination of the sump tip position of the strand is also not possible using direct measuring methods due to the liquid core in the middle of the strand.

[0008] There are known programs for calculating the temperature of the strand. These programs are based on models that can determine the temperature distribution, shell thickness, and solidification length depending on the process conditions in the continuous casting plant. The models used in these programs can also be used for control purposes in a secondary cooling water zone of a continuous casting plant. Control variables such as the surface temperature or solidification length can be used. Given these set values, the model calculates the required water quantities. The results are preferably updated with each new cyclical calculation.

[0009] The calculation of the strand temperature and / or the solidification length can generally be performed using a finite-difference method. The strand is therefore divided into individual (calculation) elements or (calculation) segments. Boundary conditions can be formulated, for example, with the dimensions of the cooling zones, water quantities, and / or the temperature of the cooling water and / or the ambient temperature. Process variables such as casting speed and temperature can also be considered during the calculation.

[0010] Another well-known calculation model using the solution of the heat conduction equation is described, for example, in EP 1 289 691 B1.

[0011] Whichever model is chosen for the specific calculation of the temperature and / or solidification of the strand, the basis for this calculation is usually the solution of the aforementioned Fourier heat conduction equation.

[0012] In summary, the solution of the Fourier heat equation can be carried out using various numerical methods and ultimately yields a temperature result.

[0013] However, previous solutions to the Fourier heat equation do not always provide sufficiently satisfactory results. Calculated results may differ from actually measured temperatures.

[0014] In particular, significant deviations occur in the so-called "hot mode" of a continuous casting process in various known solutions. "Hot mode" refers, among other things, to the fact that during the casting of a metal strand in a casting machine, one or more guide segments (guide roller supports) at the end of a continuous casting guide located in the direction of continuous casting are cooled with less spray water than in the previous segments, or that no spray water cooling is used at all. This usually applies to at least the last two strand guide segments or the horizontal part of the strand guide.

[0015] It has been shown that calculations using known numerical methods for solving the heat conduction equation, for example, in this case in particular, lead to surface temperatures that can deviate by more than 50°C from the actual measured temperatures. However, such deviations are unacceptable in many cases and can result, for example, in incorrect regulation of the cooling water flow.

[0016] Similar phenomena are particularly evident in billet and round continuous casting plants, where splash water cooling is often only carried out in the first half (relative to the casting direction) of the strand guide.

[0017] Furthermore, the position of the sump tip is often not specified accurately enough. This can result in inaccurate adjustment of the strand guide segments during soft reduction, meaning that potential quality improvements through soft reduction are not achieved.

[0018] The technical problem is therefore to overcome at least one of the above-mentioned disadvantages and / or to provide a method in which the temperature of a cast metal or a cast metal strand can be determined with greater accuracy than before. Disclosure of the invention

[0019] The present invention, according to claim 1, is directed to a method for determining the temperature of a metal strand cast in a continuous casting plant. The method generically comprises dividing the strand into a plurality of rake segments, comprising rake segments inside the metal strand and rake segments adjacent to the surface of the metal strand. For each of the segments, the temperature of each segment is determined by iteratively solving a heat conduction equation (Fourier's heat conduction equation). According to the invention, a forming scale layer is taken into account when determining the temperature for the rake segments adjacent to the surface of the metal strand.

[0020] Because, according to the invention, a scale layer forming on the strand surface is taken into account at least when determining the temperature for the surface segments of the metal strand, this determination can be carried out more accurately than before, i.e. in comparison to a temperature calculation without taking a scale layer into account.

[0021] In a preferred embodiment, both the thickness and the thermal conductivity of the scale are included in the temperature calculation.

[0022] In a further preferred embodiment, the thickness D Z of the scale or a forming scale layer according to the calculation formula DZ(t+dt)=DZ(t)2+FZ⋅dt, dt=dzvGIES be determined, where dt is a time step, F Z the tinder factor, d z a stretch of road and v GIESThe casting speed is the same. Scale factor and casting speed are generally known. Alternatively, the thickness of the scale layer could be estimated. This estimate could be based on empirical values ​​or optical images, for example.

[0023] In a further preferred embodiment of the method, the cast metal strand in the continuous casting plant is cooled at least in sections by spray water cooling. Furthermore, the temperature of the metal strand or the tip position, i.e., the position at which the metal strand is completely solidified for the first time, can serve as control variables. The temperature determined by iteratively solving the heat conduction equation can be used as the actual value for temperature control, which can be offset against desired temperature setpoints, allowing a controller to influence the controlled system via actuators in the form of spray water cooling.

[0024] In a further preferred embodiment, the metal strand is cast using a mold and then passes through a strand guide having a plurality of strand guide segments, wherein each of the strand guide segments comprises a plurality of guide or bending rollers on both sides of the metal strand for guiding or bending the metal strand, and the metal strand is subjected to splash water cooling as it passes through a plurality of the strand guide segments. However, according to the embodiment, the strand is not subjected to splash water cooling as viewed in the casting direction, at least as it passes through the last two strand guide segments of the plurality of strand guide segments. Strand guide segments can, for example, each comprise between 2 and 10 pairs of rollers, or preferably each comprise between 3 and 6 pairs of rollers, wherein one roller of each pair of rollers is arranged above the strand and the second roller of the pair of rollers is arranged below the strand.For example, a strand guide can comprise between 5 and 15 strand guide segments.

[0025] In a further preferred embodiment of the method, the metal strand is not subject to any splash water cooling, at least in the last four strand guide segments viewed in the casting direction.

[0026] In a further preferred embodiment, the metal strand, viewed in the casting direction, is not subject to any splash water cooling in the second half of the plurality of strand guide segments.

[0027] In a further preferred embodiment, the metal strand is cast vertically using a mold and subsequently bent in a horizontal direction, whereby the metal strand is not subjected to any cooling or splash water cooling, at least during its horizontal run. The section of the strand run behind the mold up to the end of the water cooling can be referred to as secondary cooling.

[0028] In a further preferred embodiment of the method, the heat transfer coefficient of the scale can be determined by αZ(DZ,λZ)=λZDZ be taken into account, where α Z (D Z ,λ Z ) the heat transfer coefficient of the scale, D Z the thickness of the scale and λ Z is the thermal conductivity of the scale.

[0029] Furthermore, the invention can be directed to a method for casting a metal strand in a continuous casting plant, comprising the following steps: casting the metal strand using a mold; guiding the cast metal strand with a plurality of strand guide segments, each of the strand guide segments comprising a plurality of guide or bending rollers on both sides of the metal strand for guiding or bending the metal strand; and cooling the metal strand with a spray water cooling system as it passes through a plurality of the strand guide segments. Finally, the method preferably comprises determining the temperature of the metal strand in the continuous casting plant according to the above-mentioned method according to the invention or according to one of the aforementioned embodiments.

[0030] All features of the embodiments or methods described above can be combined with one another or exchanged for one another. Short description of the characters

[0031] The figures of the exemplary embodiments are briefly described below. Further details can be found in the detailed description of the exemplary embodiments. They show: Fig. 1 shows an example of a cross-section through a continuous casting plant with spray water cooling arranged between the guide rollers; Fig. 2 shows an example of a cross-section through the continuous casting plant according to Fig. 1, with no splash water cooling in the horizontal guide area; Fig. 3 a schematic example of a strand segmentation for temperature calculation; Fig. 4 a schematic comparison between measured temperatures and calculated temperatures; and Fig. 5 a schematic representation of the relationships between strand temperature, scale layer thickness and the continuous casting plant length. Detailed description of the implementation examples

[0032] The Fig. 1 shows a schematic cross-section through a continuous casting plant 1, which comprises a strand guide 2 with strand guide and / or bending rollers 9. Strand guide and / or bending rollers 9 can be arranged in strand guide segments (not explicitly shown), which can serve as supports for several of these rollers 9. Such strand guide segments are, of course, known to those skilled in the art.

[0033] Strand 3 is cast, for example, using a mold 10 and begins to solidify from its surface. However, in the first half of strand guide 2, strand 3 still has a liquid core 5. The solidification of strand 3 is preferably assisted by cooling, for example, by spray water cooling 11. At the end of strand guide 2 located in the casting direction, strand 3 is completely solidified.

[0034] According to Fig. 1, a spray water cooling system 11 extends into a horizontal guide area of ​​system 1. In practice, this type of cooling is often referred to as the "cold mode" of system 1. During this operation of system 1, the cooling of strand 3 occurs across the entire strand guide 2, or in other words, in all strand guide segments. The pressure of the spray water during a spray water cooling system can typically be between 1 and 4 bar.

[0035] The Fig. 2 shows a Fig. 1 similar or identical Annex 1. Therefore, the same reference numerals as in the Fig. 1 used.

[0036] The fundamental difference between the Fig. 1 and the one in the Fig. 2 is that in the horizontal area of ​​the strand guide 2 according to Fig. 2, no spray water cooling 11 is performed. This is also referred to as the "hot mode." In other words, no spray water cooling 11 is performed in some of the last strand guide segments in the casting direction. The same applies to spray water cooling in these segments at pressures below 0.5 bar.

[0037] Especially when cooling according to Fig. 2 problems arise in standard temperature calculations by solving the heat conduction equation.

[0038] The inventors have recognized that one cause of the calculation deviations lies in a scale layer forming on the surface of the strand 3 and that this scale layer can significantly influence the cooling process of the strand 3.

[0039] In accordance with Fig. 1 used (secondary) cooling with spray water in all segments, the so-called cold operating mode, the problem often does not occur significantly, since the scale formed immediately flakes off and is washed away by the spray water. However, with the aforementioned hot operating mode, a thicker scale layer forms due to the comparatively higher surface temperatures, which does not flake off due to the lack of spray water. In billet and round continuous casting plants, for example, cooling with spray water is only used in the first half of the strand guide, so that a non-flaking scale layer subsequently forms.

[0040] Heat dissipation at the strand surface can be considered as input variables for the heat conduction equation, as this variable influences the temperature result. To describe heat dissipation, one or more of the following variables can preferably be considered: convection, radiation, and a temperature drop due to contact between a strand and rollers of a strand guide. The inventors have also recognized that this heat dissipation is affected by any scale layer present. In particular, the scale layer impedes convection and radiation from the hot strand surface.

[0041] Therefore, the thickness of the forming scale is preferably determined. By determining the thickness of the forming scale layer, the temperature calculation and / or the determination of the sump tip position can be carried out with greater accuracy.

[0042] The increase in scale thickness D Zin a time step dt can be calculated, for example, as follows: DZ(t+dt)=DZ(t)2+FZ⋅dt where D Z (t) the scale thickness at time t, F Z is the scale factor and dt is the scaling time. The scaling time represents the time interval between two calculation points. Thus, the scaling time can be defined as dt=dZvGIES where v GIES The casting speed, or rather the speed of the cast strand 3, and thus the speed of a strand element. This speed is known and / or measurable. The variable dz indicates the distance traveled in the casting direction in time dt.

[0043] The tinder factor F Z can be specified depending on the surface temperature of strand 3 and the metal analysis. For example, it is as follows: FZ=9.8⋅107⋅e−2.8C⋅e−17780 / TM where T Mwhere 3 is the surface temperature of strand in °K, and C represents the unitless concentration of carbon in the metal. This concentration is known during continuous casting. Equation (4), for example, provides particularly good results for metal with silicon contents of less than 2%.

[0044] As the carbon content increases, the scale thickness decreases. Given a known scale density, the scale mass can also be calculated from the scale thickness. Further calculations could therefore also be based on the scale mass.

[0045] As already described, three types of heat transfer can be considered to solve the heat conduction equation. First, the convection of a rake segment at the surface of the strand; second, the thermal radiation of a rake segment at the surface of the strand through the rollers; and third, the heat transfer of a rake segment by thermal radiation against the rollers of a strand guide.

[0046] This relationship is shown schematically in the Fig. 3. The Fig. 3 shows a cross-section of a strand 3 divided into cuboid-shaped rake segments or elements k, on the surface of which a scale layer with the thickness D Z The segments k, which border the surface of the strand 3, have, for example, the thicknesses or heights D k, which, as shown, can be identical for all surface elements k. However, they could also be chosen differently. For a surface element k, during the cooling process, heat transfer takes place by radiation against an adjacent roll 9, which has the temperature T obtained from the previous calculation step. rolle of the roll 9. The corresponding radiation can be determined by a heat transfer coefficient α srolle,k Similarly, heat radiation also enters a gap between two rollers 9 against the temperature T Lücke (The temperature T Lücke = air temperature is only slightly changed, but the strand releases heat). The corresponding radiation influence can be determined by a further heat transfer coefficient α sluecke,k Finally, the influence of convection can also be taken into account in the form of an additional heat transfer coefficient αkonv,k This acts against the ambient temperature T konv . (The ambient temperature is only slightly changed, but the heat emission is always calculated from a temperature difference, so here from T Strang - T konv ). In order to additionally take into account the influence of the scale, a heat transfer coefficient of the scale α Z (D Z ,λ Z ), where αZ(DZ,λZ)=λZDZ holds. Where λ Z the generally known thermal conductivity or thermal conductivity of the scale and D Z the previously mentioned scale thickness. The thermal conductivity λ Z of the scale can be calculated, for example, as a function of the surface temperature of the metal strand T m taken from the literature.

[0047] For the sake of clarity, it is pointed out at this point that the term heat transfer coefficient is equivalent to the terms heat transfer number or “alpha number”.

[0048] Heat transfer coefficients α s for radiation can be determined, for example, as follows: as∼TA3+TA2⋅TB+TB2⋅TA+TB3 where T A the surface temperature of a first radiator A and T B represents the surface temperature of the irradiated medium or body B.

[0049] The sizes T rolle , T luecke are generally available from the solution of the heat conduction equation in the previous calculation step, so that the heat transfer coefficients can be easily determined. T konv can also be easily determined using standard calculation methods (for example, taking into account the amount of cooling water used).

[0050] By solving the heat conduction equation in a previous calculation step, the surface temperature of the strand T M (i.e. the metal under the scale) is known, but not directly the surface temperature of the scale T Z .. Alternatively, for example, a starting value for the surface temperature of the strand T M be specified.

[0051] The surface temperature of the scale T Z can therefore be easily determined by taking into account the scale thickness, the heat transfer coefficient and the thermal conductivity of the scale.

[0052] Alternatively or additionally, the surface temperature of the scale T Z be measured.

[0053] If all the above-mentioned radiation and convection losses are taken into account, which is not absolutely necessary, the temperature of the scale can be preferably specified using the quantities already listed above, for example as follows: TZ(DZ,λZ)=αsrollek⋅TRolle+αsluckek⋅Tluecke+αkonvk⋅Tkonv+TMαZ(DZλZ)αsrollek+αsluckek+αkonvk+1αZ(DZλZ). If the surface temperature of the scale T Z . and in particular its thickness D Z known, the new enthalpy H(k,t+dt) can be determined based on the enthalpy H(k,t) of the previous time step or calculation step, so that, for example, according to the following equation (8): H(k,t+dt)=H(k,t)+dtρ⋅(λk+λk+1)⋅(−Dk)⋅ΔTkk+1+2Dk⋅(akonvk⋅(Tkonv−TZ(DZ,λZ))+αarollek⋅(Trolle−TZ(Dz,λZ))+aalueckek⋅(Tluecke−TZ(DZ,λZ)))

[0054] This equation includes all correction summands (however, this is not necessary; alternatively, only one or two of the summands of the last three summands could be included), where t is the time, H(k,t) is the enthalpy before the time step dt, ρ is the density of the scale, λ k the thermal conductivity of the surface element k, λ k+1 the thermal conductivity of a neighboring surface element k+1, D k , the thickness (height) of the surface element k, ΔT k,k+1 the temperature difference between the surface elements k and k+1 α konv,k the heat transfer coefficient of convection of the element k, T Z (D Z , λ Z ) which is of thickness D Z of the scale and the thermal conductivity of the scale λ Z dependent temperature at the scale surface, T konv for example, the temperature of air, water and rolls, which is caused by convection, α srolle,kthe heat transfer coefficient of radiation against a roll, T rolle the temperature of the roll caused by thermal radiation, α sluecke,k the heat transfer coefficient of the thermal radiation emitted into a gap between two adjacent rolls, T luecke the temperature of the gap caused by the thermal radiation of the segment k. The above calculation formulas represent only preferred and advantageous examples and are not to be understood as limiting.

[0055] The Fig. 4 shows a schematic representation of the calculation of the surface temperature of a strand as a function of time or the distance traveled by the strand 3 in a continuous casting plant 1. The Fig. 4 was based on a casting system 1, at the end of which scale formation occurs, for example, during hot operation. Therefore, a temperature calculation without taking scale formation into account leads to unsatisfactory results, deviating by more than 50°C from the measured temperatures. However, if the forming scale layer is taken into account, the calculated temperatures exhibit deviations of less than 10°C.

[0056] The Fig.Figure 5 shows an example of the development of a scale layer thickness as a function of water cooling, strand temperature, and location. Shown are, among other things, the strand temperature at the strand surface during cold operation and the strand temperature at the strand surface during hot operation. In addition, the scale layer thickness is given for both cold operation and hot operation. During hot operation, the strand surface temperature rises again after cooling is interrupted. During cold operation, it decreases due to continuous cooling. During hot operation, the scale layer thickness increases between 10 m and 12 m after cooling is interrupted. During cold operation, where cooling is only interrupted between 29 and 31 meters, the formation of a scale layer only begins at this length. The length specifications given refer to the length of the cast strand, measured from the mold along the strand.

[0057] Apart from the fact that scale growth starts later in cold operation than in hot operation, it is also lower because at the time of cooling interruption in cold operation, the surface temperature of the strand is lower than that at the time of cooling shutdown in hot operation.

[0058] The exemplary embodiments described above serve primarily to better understand the invention and should not be construed as limiting. The scope of protection of the present patent application is derived from the patent claims.

[0059] The features of the described embodiments can also be combined with one another or exchanged for one another.

[0060] Furthermore, the described features can be adapted by the person skilled in the art to existing circumstances or requirements. List of reference symbols 1 continuous casting plant 2 strand guide 3 strand 5 liquid core of the strand 9 Support, guide or bending roller 10 molds 11 Splash water cooling k (calculation) segment D k Thickness or height of the rake segment k D Z Thickness of the scale layer T M Temperature on the metal surface T konv a temperature taking convection into account T luecke Temperature of a gap between two rollers adjacent to segment k T rolle Temperature of a roll adjacent to segment k α srolle,k Heat transfer coefficient with respect to the radiation caused by segment k to an adjacent roll α sluecke,k Heat transfer coefficient with respect to the radiation caused by segment k into a gap between two rolls adjacent to segment k α konv,kHeat transfer coefficient related to the convection caused by segment k

Claims

[1] Method for determining the temperature of a metal strand (3) cast in a continuous casting plant (1), comprising the following steps: Dividing the strand (3) into a plurality of rake segments (k), comprising rake segments (k) in the interior of the metal strand (3) and rake segments (k) adjacent to the surface of the metal strand (3); iteratively determining the temperature of each computational segment (k) by solving a heat conduction equation; characterized by , that When determining the temperature of the rake segments (k) adjacent to the surface of the metal strand (3), a scale layer forming on the surface of the metal strand (3) is taken into account. [2] The method according to claim 1, wherein the thickness of the scale layer and the thermal conductivity of the scale are taken into account to determine the temperature of the rake segments (k) adjacent to the surface of the metal strand. [3] The method according to claim 2, wherein the thickness of the scale formed after a period of time is determined according to the following calculation formula: DZ(t+dt)=DZ(t)2+FZ⋅dt,dt=dzvGIES where D Z the thickness of the scale, t the time, dt the time period, F Z the tinder factor, v GIES the casting speed of the metal strand (3) and d Z one in the time period dt with the casting speed V Gies distance traveled. [4] The method according to one of the preceding claims, wherein the cast metal strand (3) in the continuous casting plant (1) is cooled at least in sections by a spray water cooling system (11). [5] The method according to one of the preceding claims, wherein the metal strand (3) is cast by means of a mold (10) and then passes through a strand guide (2) having a plurality of strand guide segments, wherein each of the strand guide segments comprises a plurality of guide or bending rollers (9) on both sides of the metal strand (3) for guiding or bending the metal strand (3), and the metal strand (3) is subject to splash water cooling (11) when passing through a plurality of the strand guide segments, but, viewed in the casting direction, is not subject to splash water cooling (11) at least when passing through the last two strand guide segments of the plurality of strand guide segments. [6] The method according to claim 5, wherein the metal strand (3) is not subjected to any spray water cooling (11) at least in the last four strand guide segments viewed in the casting direction. [7] The method according to claim 5, wherein the metal strand (3), viewed in the casting direction, is not subject to any splash water cooling (11) in the second half of the plurality of strand guide segments. [8] The method according to any one of the preceding claims, wherein the metal strand (3) is cast vertically by means of a mold (11) and then bent in a horizontal direction. [9] The method according to claim 8, wherein the metal strand (3) is not subjected to any splash water cooling (11) at least during its course in the horizontal direction. [10] The method according to any one of the preceding claims, wherein the heat transfer coefficient of the scale is αZ(DZ,λZ)=λZDZ is taken into account, where α Z (D Z ,λ Z ) the heat transfer coefficient of the scale, D Z the thickness of the scale and λ Z is the thermal conductivity of the scale. [11] A method for casting a metal strand (3) in a continuous casting plant, comprising the steps: Casting the metal strand (3) by means of a mold (10); Guiding the cast metal strand (3) with a plurality of strand guide segments, each of the strand guide segments comprising a plurality of guide or bending rollers (9) on both sides of the metal strand (3) for guiding or bending the metal strand (3); Cooling the metal strand (3) with a splash water cooling system when passing through several of the strand guide segments by means of a splash water cooling system (11); Determination of the temperature of the metal strand in the continuous casting plant (1) according to the method of claim 1.

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