JP7021608B2 - Method for estimating the central solid phase ratio of continuously cast slabs - Google Patents

Description

The present invention relates to a method for estimating the central solid phase ratio of a continuously cast slab during continuous casting.

When a slab, bloom, or other slab is cast by a continuous casting method, so-called central segregation may occur in which components such as phosphorus and manganese segregate in the center of the slab. In addition, a hole called center porosity is generated in the center of the slab.

At the end of solidification during continuous casting, the unsolidified molten steel flows toward the solidification completion point of the final solidified portion as the molten steel solidifies and shrinks. During the flow of molten steel, impurity-concentrated molten steel at the solid-liquid interface accumulates in the final solidified portion. This causes central segregation. Therefore, in order to reduce the central segregation, it is effective to suppress the flow of the molten steel in the vicinity of the final solidified portion by reducing the solidified shell by the amount corresponding to the amount of solidification shrinkage of the molten steel in the vicinity of the final solidified portion. Based on this idea, a light reduction technique is used in which the slab is reduced by a support roll before the completion of solidification at the end of continuous casting. Further, the reduction for the purpose of crimping porosity is effective in the region where the solid phase ratio at the center of the thickness of the slab (hereinafter, also referred to as “central solid phase ratio”) is 0.8 or more.

For example, Patent Document 1 describes a light reduction method at the end of coagulation. Light reduction is started when the central solid phase ratio is 0.1 to 0.3, and light reduction is performed in the section up to the central solid phase ratio of 0.7. It is described that it will be improved. Further, Patent Document 2 discloses an invention in which a range of at least 2 m is lightly reduced from the crater end of the solid phase line toward the upstream side. The "crater end of the solid phase line" means a position where the central solid phase ratio is 1.0.

For the central solid phase ratio, the temperature T _C at the center in the thickness direction of the slab during continuous casting was obtained by one-dimensional heat transfer solidification calculation, and then the liquidus temperature T _Liq and the solid phase temperature T _Sol were used. It is calculated by the following formula. The enthalpy method and the equivalent specific heat method are known for heat transfer / solidification calculation.
Central solid phase ratio = (T _Liq - _TC ) / (T _Liq -T _Sol ) (A)

Patent Document 3 is characterized in that the presence or absence of solidification completion of a slab is detected based on the slab reduction amount when the slab reduction roll is reduced by a predetermined reduction force. The method is disclosed.

Patent Document 4 discloses a continuous casting apparatus capable of reducing slabs, which can be used in a laboratory experiment.

Japanese Unexamined Patent Publication No. 2005-193265 Special Publication No. 62-34460 Japanese Unexamined Patent Publication No. 2007-245168 International release WO2013 / 175536

In actual continuous casting, it is not uncommon for the central solid phase ratio at a predetermined site in the casting direction of the slab to fluctuate with respect to the estimated value. There is a case to do. Therefore, during casting, it is required to develop a highly accurate and simple method for estimating the central solid phase ratio at each part in the casting direction of the slab. In the invention described in Patent Document 3, the presence or absence of solidification of the slab is only detected, and the central solid phase ratio at each site in the casting direction of the slab cannot be accurately measured.

An object of the present invention is to provide a method for estimating the central solid phase ratio of a continuously cast slab, which can accurately estimate the central solid phase ratio at a predetermined portion in a casting direction of a slab in continuous casting.

That is, the gist of the present invention is as follows.
(1) Roll reduction of unsolidified slabs is performed during continuous casting, the reduction force and reduction amount at the time of roll reduction are measured, the average deformation resistance AR per unit area of the slabs due to roll reduction is calculated, and casting is in progress. A method for estimating the central solid phase ratio during continuous casting, which comprises measuring the slab surface temperature T _Su in the above and calculating the central solid phase ratio fs at the roll reduction position based on the following equation (1).
fs = (AR-β-γ × (T _Su -calculated surface temperature)) / α (1)
α, β, and γ are constants and are determined in advance by heat transfer calculation and deformation analysis. The calculated surface temperature is determined in advance by heat transfer calculation and deformation analysis as a function of the average deformation resistance.
(2) Roll reduction of unsolidified slabs is performed during continuous casting, the reduction force and reduction amount at the time of roll reduction are measured, the average deformation resistance AR per unit area of the slabs due to roll reduction is calculated, and casting is in progress. A method for estimating the central solid phase ratio during continuous casting, which comprises measuring the slab surface temperature T _Su in the above and calculating the central solid phase ratio fs at the roll reduction position based on the following equation (2).
fs = (AR-β-γ (T _Su- (T _Liq -ΔT))) / (α-γ ・ (T _Liq -T _Sol )) (2)
T _Liq is the liquidus temperature (° C.), and T _Sol is the solidus phase temperature (° C.). α, β, and γ are constants and are determined in advance by heat transfer calculation and deformation analysis. ΔT (° C.) is the difference between the center temperature and the surface temperature of the slab, and is a constant determined in advance by heat transfer calculation.
(3) The casting direction position at which solidification is completed (fs = 1.0) is calculated based on the central solid phase ratio fs at the roll reduction position, which is the above-mentioned (1) or (2). ). The method for estimating the central solid phase ratio during continuous casting.
(4) The method for estimating the central solid phase ratio during continuous casting according to any one of (1) to (3) above, wherein the slab shape is a bloom shape.

In the present invention, the unsolidified slab is rolled down during continuous casting, and the average deformation resistance and the slab surface temperature due to the roll rolling are measured to accurately determine the central solid phase ratio at a predetermined portion in the casting direction of the slab. Can be estimated.

It is a figure which shows the situation which the unsolidified slab is reduced by the reduction roll, (A) is the side sectional view, (B) is the front sectional view. It is a figure which shows the correlation between the measured central solid phase ratio and the predicted central solid phase ratio, and is the case where the surface temperature correction is not performed. It is a figure which shows the correlation between the measured central solid phase ratio and the predicted central solid phase ratio, and is the case of this invention which performs the surface temperature correction when the equation (2) of this invention is used. It is a figure which shows the correlation between the measured central solid phase ratio and the predicted central solid phase ratio, and is the case of this invention which performs the surface temperature correction when the equation (1) of this invention is used.

During continuous casting, the slab portion that has started solidification in the mold is pulled downward from the mold (primary cooling) over time and is cooled while passing through the secondary cooling zone at a predetermined casting speed. Coagulation progresses. FIG. 1A is a side sectional view showing an unsolidified slab during casting, in which the slab progresses from left to right in the figure, and the solid phase portion 3 on the surface side, the solid-liquid coexisting layer 4, and the liquid phase portion. 5 is separated by a solid phase line position 6 and a liquid phase line position 7, respectively. The position where the solid phase line positions on the upper surface side and the lower surface side of the slab match is the solidification completion position 9. Regarding the progress of such solidification, the shape (width, thickness) of the slab, casting speed, primary cooling conditions, and secondary cooling conditions are determined, and the heat transfer calculation is performed to determine the time lapse of the slab and the slab. The temperature distribution of can be calculated. Both the surface temperature and the center temperature of the slab part of interest decrease with the passage of time (progress in the casting direction).

During continuous casting, as shown in FIG. 1, the slab 1 can be reduced by the reduction roll 2 in the unsolidified stage. When the reduction force of the reduction roll 2 is a predetermined reduction force, the thickness reduction margin (reduction amount) of the slab due to the reduction roll differs depending on the deformation resistance of the slab when reduced, and the deformation resistance of the slab is large. The smaller the amount of reduction when the same reduction force is applied.

From the reduction amount d (mm), reduction force F (kgf), slab width w (mm), and reduction roll radius r (mm), the average deformation resistance AR (kgf / mm ² ) at the reduction portion is as follows. Can be calculated as follows. The roll contact arc length L (mm) at the time of reduction is
L = r · cos ^-1 {(rd) / r} (3A)
(The angle of the trigonometric function is displayed in radians), and the roll contact area S (mm ² ) is
S = L × w (3B)
Will be. Since the rolling force F (kgf) is applied to the roll contact area S, the average deformation resistance AR (kgf / mm ² ) per unit area is
AR = F / S (3C)
Can be obtained as.

As described above, after calculating the temperature distribution in the slab by heat transfer calculation, deformation analysis is used based on the calculated temperature distribution in the slab C cross section at a predetermined elapsed time or the position in the casting direction. The average deformation resistance AR defined above can be calculated. Here, the C cross section means a cross section perpendicular to the casting direction. As the deformation analysis method, for example, ABAQUS, which is a general-purpose finite element analysis code, can be used. Since the center temperature T _C in the cross section of the slab decreases and the average deformation resistance AR increases with the passage of time, the center temperature T _C and the average deformation resistance AR have a one-to-one correspondence. The surface temperature T _Su also has a one-to-one correspondence at the same time. Then, it became clear from the results of deformation analysis and laboratory experiments that the relationship between the center temperature _TC and the average deformation resistance AR is a linear relationship. Further, the relationship between the central solid phase ratio and the central temperature _TC is also a linear relationship as shown in the above equation (A). From the above, the relationship between the central solid phase ratio and the average deformation resistance AR can be expressed as the following equation (4). Here, the central solid phase ratio is expressed as fs. α and β are constants.
AR = α ・ fs + β (4)

Therefore, it was decided to confirm the prediction accuracy of the central solid phase ratio fs by the above equation (4) by conducting a laboratory experiment. In the laboratory experiment, molten steel was injected into a mold for casting slabs with a width of 400 mm and a thickness of 200 mm, the solidified shell was pulled out from the mold when the initial solidified shell was formed, and solidification proceeded with the lower part of the mold as the secondary cooling zone. Then, after a lapse of a predetermined time, the slab is unsolidified and reduced by a reduction roll (see Patent Document 4). The molten steel component is C: 0.55% by mass and Mn: 1.0% by mass. In the laboratory experiment, a thermocouple was inserted into the part corresponding to the center of the thickness of the slab, and the time course of the center temperature _TC was measured. Based on the results of heat transfer calculation and deformation analysis (ABAQUS) calculated under the conditions of the laboratory experiment, the values of the constants α and β in Eq. (4) were determined. It was calculated as α = 0.45 and β = −0.6. In the laboratory experiment, the reduction amount d when the reduction was performed by the reduction roll with the reduction force F was measured, the average deformation resistance AR was obtained based on the equations (3A) to (3C), and the center was further calculated from the AR by the equation (4). The solid phase ratio fs was obtained and used as the "predicted central solid phase ratio".
On the other hand, the central temperature _TC of the slab was measured at the time when the reduction was performed with the reduction roll, and the central solid phase ratio fs was obtained based on the formula (A), which was used as the “measured central solid phase ratio”. The correlation between the measured central solid phase ratio and the predicted central solid phase ratio is shown in FIG. The correlation coefficient R is 0.78, and the relationship between the two varies widely, and it was found that it is difficult to predict the central solid phase ratio with high accuracy as it is.

In the calculation result obtained by combining the heat transfer calculation and the deformation analysis, the average deformation resistance, the center temperature, and the surface temperature are determined as one combination. In other words, the center temperature and surface temperature are determined as a function of the average deformation resistance. Therefore, when determining the center temperature _TC of the slab from the measured value of the average deformation resistance AR, the surface temperature is also automatically determined. Therefore, in the laboratory experiment, the surface temperature of the slab was measured when the roll was reduced. As a result, it was found that there was a difference between the calculated surface temperature calculated based on the measured average deformation resistance and the measured surface temperature. Then, when the difference between the calculated surface temperature and the measured surface temperature and the difference between the predicted central solid phase ratio and the measured central solid phase ratio are compared, it is clear that there is a correlation between the two. became.

Therefore, it was decided to add a correction term based on the difference between the actual measurement and the calculation of the slab surface temperature to the above equation (4), and the following equation (5) was derived.
AR = α ・ fs + β + γ × (measured surface temperature-calculated surface temperature) (5)
γ is a constant and can be calculated by combining heat transfer calculation and deformation analysis. The actual measurement of the surface temperature can be performed at a position immediately before or immediately after the reduction by the rolling roll, or after the complete reheat after the reduction, and the calculated surface temperature means the calculated surface temperature at the actual measurement position of the surface temperature. It is preferable to actually measure the surface temperature immediately before or immediately after the reduction by the reduction roll. Hereinafter, a case where the surface temperature is actually measured immediately before or immediately after the reduction by the reduction roll will be described. The surface temperature measurement portion on the outer periphery of the slab is preferably measured at the center of the width of the long side, but the surface temperature may be measured at a portion other than the center of the width on the long side or at the short side. When measuring the surface temperature at any part, the surface temperature of the part corresponding to the surface temperature measurement position is calculated for the calculated surface temperature.

Regarding the calculated surface temperature, in the combination of the heat transfer calculation and the deformation analysis, the average deformation resistance, the center temperature, and the surface temperature are determined as one combination, so the average deformation resistance is actually measured and the measured value is used. The surface temperature determined by the combination of may be used as the calculated surface temperature.

More simply, the following calculations can be performed. First, let ΔT be the difference between the calculated center temperature and the calculated surface temperature of the slab. ΔT can be obtained as a constant from the heat transfer calculation. The calculated center temperature of the slab is calculated by the central solid phase ratio fs according to the formula (A). Center temperature = T _{Liq- (T Liq -} T _Sol ) fs (6A)
It is expressed as. Then, using ΔT,
Calculated surface temperature = Calculated center temperature-ΔT (6B)
= T _{Liq-(T Liq -} T _Sol ) fs-ΔT (6)
To guide. After expressing the measured surface temperature as T _Su , substituting equation (6) into equation (5),
AR = α ・ fs + β + γ (T _{Su-(T Liq- (T Liq - T Sol} ) fs-ΔT))
= (Α-γ ・ (T _Liq －T _Sol )) ・ fs ＋ β ＋ γ (T _Su － (T _Liq －ΔT)) (7)
Will be. Replacing the equation (7) with the equation for fs,
fs = (AR-β-γ (T _Su- (T _Liq -ΔT))) / (α-γ ・ (T _Liq -T _Sol )) (2)
Is guided. In equation (2), T _Liq and T _Sol are physical property values determined from the steel composition, and α, β, γ, and ΔT are constants obtained in advance from heat transfer calculation and deformation analysis. By actually measuring the temperature T _Su , the central solid phase ratio fs at the reduction site can be determined.

Therefore, verification was performed in the same laboratory experiment as above. α, β, γ, and ΔT were determined in advance from heat transfer calculation and deformation analysis. It was calculated as α = 0.45, β = −0.6, and γ = 0.0086. Further, ΔT was determined to be ΔT = 380 ° C. using the difference between the center temperature and the surface temperature at the position where the central solid phase ratio = 1.0 (the crater end of the solid phase). The central solid phase ratio obtained by substituting these values into Eq. (2) was defined as the "improved predicted central solid phase ratio", and the correlation with the measured central solid phase ratio based on the measured center temperature measured in the laboratory experiment was evaluated. .. The results are shown in FIG. The correlation coefficient R is 0.92. As is clear from the comparison with FIG. 2, it was found that the correlation between the measured central solid phase ratio and the predicted improvement central solid phase ratio was good.

The present invention can be applied during continuous casting of an actual machine. In the support roll band for continuous casting, a reduction roll 2 is provided at the position where the central solid phase ratio fs is desired (central solid phase ratio evaluation position 8) or near the position as shown in FIG. Roll down the slab 1. The reduction roll 2 is provided with a measuring instrument for measuring the reduction force F. The roll reduction force F can be measured from the pinch roll hydraulic pressure. Further, strain sensors can be provided on the upstream side and the downstream side of the roll reduction to measure the reduction amount d due to the roll reduction. The average deformation resistance AR can be obtained by the above equations (3A) to (3C), where r is the rolling radius and w is the width of the slab. Further, a thermometer for measuring the surface temperature of the slab is provided immediately before or immediately after the rolling roll, and the surface temperature T _Su is measured.

Heat transfer calculation is performed in advance based on the shape (width, thickness) of the slab, casting speed, primary cooling conditions, and secondary cooling conditions. Calculate the temperature distribution of, and calculate the calculated surface temperature and the calculated center temperature. Further, based on the calculated temperature distribution, the calculated average deformation resistance AR when the unsolidified portion is reduced by the reduction roll at an arbitrary position in the unsolidified portion in the casting direction is calculated by deformation analysis. The constants α, β, γ in equation (5) and ΔT, which is the constant in equation (6), are also obtained from heat transfer calculation and deformation analysis.

First, a method of obtaining the central solid phase ratio fs based on the equation (5) will be described. After setting the measured surface temperature of Eq. (5) to T _Su , the Eq. (5) is modified.
fs = (AR-β-γ × (T _Su -calculated surface temperature)) / α (1)
And.

As a result of the deformation analysis performed in advance, the relationship between the calculated average deformation resistance and the calculated slab surface temperature has been clarified. In other words, the calculated surface temperature is determined as a function of the average deformation resistance. Therefore, the calculated slab surface temperature when the calculated deformation resistance equal to the measured average deformation resistance AR is obtained is derived, and the value is used as the calculated surface temperature in Eq. (1). As a result, the central solid phase ratio fs is calculated based on the equation (1).
The case of using the above equation (1) of the present invention was verified in the same laboratory experiment as above. α, β, and γ are the same as when the above equation (2) is used. The calculated surface temperature at the position (solid phase crater end) where the central solid phase ratio = 1.0 determined in advance by heat transfer calculation and deformation analysis was determined to be 1026 ° C. The central solid phase ratio obtained by substituting these values into Eq. (1) was defined as the "improved predicted central solid phase ratio", and the correlation with the measured central solid phase ratio based on the measured center temperature measured in the laboratory experiment was evaluated. .. The results are shown in FIG. The correlation coefficient R is 0.88. Although it does not reach the correlation coefficient of (Fig. 3) when Eq. (2) is used, as is clear from the comparison with Fig. 2, the correlation between the measured central solid phase ratio and the predicted improvement central solid phase ratio. Turned out to be good.

Next, a method of obtaining the central solid phase ratio fs based on the equation (2) will be described. Since the variables and constants used in the equation (2) are obtained as described above, the central solid phase ratio fs is calculated by substituting these numerical values into the equation (2) (see FIG. 3 above). As shown in FIG. 2, the central solid phase ratio fs calculated above at the roll reduction position was obtained as an approximation of Eq. (5) under the conditions of 0.4 or more and 1.0 or less. It is preferable to use it in.

In the present invention, after calculating the central solid phase ratio fs at the roll reduction position as described above, solidification is completed (fs = 1.0) based on the calculated central solid phase ratio fs. Crater end position) can be calculated. In this case, before and after the position expected to be the crater end position, roll reduction is performed with a plurality of roll pairs in the casting direction, and the central solid phase ratio of the present invention is estimated. For each roll pair under roll reduction, the reduction amount, reduction force, and slab surface temperature are measured, and the central solid phase ratio is estimated based on the measured values. Then, the roll pair at the position where the estimated central solid phase ratio is smaller than 1.0 and is closest to 1.0 is defined as the nearest roll pair on the upstream side of the crater end, and the estimated central solid phase ratio is larger than 1.0. The roll pair at the position closest to 1.0 is defined as the nearest roll pair on the downstream side of the crater end. Further, the average deformation resistance at the crater end position is fs = 1.0 in the equation (7) in which the constant is determined in advance by the deformation analysis, and the moment when fs = 1.0 obtained from the heat transfer calculation result ( It is obtained from the surface temperature T _Su whose center temperature is the solidus temperature T _Sol ).
On top of that, the difference between the average deformation resistance at the position of the nearest roll pair on the upstream side of the crater end and the average deformation resistance at the position of the latest roll pair on the downstream side of the crater end, and the deformation resistance at the crater end position and the latest roll pair on the upstream side of the crater end. By interpolating the pitch between both rolls by the ratio of the difference from the deformation resistance of the position of, the crater end position can be estimated from the position of the nearest roll pair on the upstream side of the crater end.
The average deformation resistance at the position of the roll pair is directly determined by the equation (3) by directly measuring the rolling reaction force and the rolling amount.

In the present invention, the reduction roll for performing roll reduction on the unsolidified slab includes a flat roll (see FIG. 1 (B)) having a constant diameter in the longitudinal direction of the roll and a radius of the center in the longitudinal direction of the roll. A disc roll larger than the radius on both ends can be used. Regardless of whether a flat roll or a disc roll is used as the rolling roll, the shape of the rolling roll is input and analyzed when performing the deformation analysis. In the unsolidified slab at the site where the roll is reduced, the short sides at both ends in the width direction have already been solidified to the center of the thickness. When a disc roll is used as the reduction roll, the length of the portion having a large roll radius can be made equal to the length of the unsolidified region, and only the unsolidified portion is compressed, so that the reduction amount d becomes large at a specific reduction force F. .. On the other hand, when a flat roll is used as the reduction roll, the reduction is performed including the solidification complete portion on the short side. Therefore, when the reduction is performed with the same reduction force F, the reduction amount d as compared with the disc roll. Becomes smaller. Therefore, in order to improve the estimation accuracy of the central solid phase ratio fs, it is preferable to use a disk roll. When one roll of the reduction roll pair is a disc roll and the other roll is a flat roll, the reduction amount d is obtained from the roll interval of the upper and lower roll pairs immediately before the reduction roll by the difference in the roll interval of the upper and lower reduction rolls. Can be done.

The slab shape targeted by the present invention can be either a slab or a bloom. Above all, it is preferable to target Bloom. Bloom has a stable crater end shape that is convex toward the casting direction, and the temperature gradient in the width direction at the center of the slab thickness is a negative function from the center of the slab toward the surface of the short side of the slab. This means that the correlation between the center temperature and the surface temperature is large, which is advantageous for estimating the solid phase ratio. On the other hand, in slab slabs, the temperature distribution in the width direction becomes complicated due to solidification delay, etc., and there are cases where there are two temperature peaks at locations other than the center, and the central solid phase ratio is determined only by the two variables of rolling reaction force and surface temperature. Then, the accuracy may be insufficient. Further, in the case of a slab, the width of the slab is mixed from narrow to wide in the same continuous casting device, but in the case of Bloom, the width of the slab is constant in the same continuous casting device. Even when a disk roll is used, a single disk roll can be used, which is preferable.

1 slab 2 reduced roll 3 solid phase part 4 solid-liquid coexisting layer 5 liquid phase part 6 solid phase line position 7 liquid phase line position 8 central solid phase ratio evaluation position 9 solidification completion position

Claims (4)

Roll reduction of unsolidified slab during continuous casting is performed, the reduction force and reduction amount at the time of roll reduction are measured, the average deformation resistance AR per unit area of the slab due to roll reduction is calculated, and the slab during casting is calculated. A method for estimating the central solid phase ratio during continuous casting, which comprises measuring the surface temperature T _Su and calculating the central solid phase ratio fs at the roll reduction position based on the following equation (1).
fs = (AR-β-γ × (T _Su -calculated surface temperature)) / α (1)
α, β, and γ are constants and are determined in advance by heat transfer calculation and deformation analysis. The calculated surface temperature is determined in advance by heat transfer calculation and deformation analysis as a function of the average deformation resistance. Roll reduction of unsolidified slab during continuous casting is performed, the reduction force and reduction amount at the time of roll reduction are measured, the average deformation resistance AR per unit area of the slab due to roll reduction is calculated, and the slab during casting is calculated. A method for estimating the central solid phase ratio during continuous casting, which comprises measuring the surface temperature T _Su and calculating the central solid phase ratio fs at the roll reduction position based on the following equation (2).
fs = (AR-β-γ (T _Su- (T _Liq -ΔT))) / (α-γ ・ (T _Liq -T _Sol )) (2)
T _Liq is the liquidus temperature (° C.), and T _Sol is the solidus phase temperature (° C.). α, β, and γ are constants and are determined in advance by heat transfer calculation and deformation analysis. ΔT (° C.) is the difference between the center temperature and the surface temperature of the slab, and is a constant determined in advance by heat transfer calculation. The first or second aspect of the present invention, wherein the casting direction position at which solidification is completed (fs = 1.0) is calculated based on the calculated central solid phase ratio fs at the roll reduction position. A method for estimating the central solid phase ratio during continuous casting. The method for estimating the central solid phase ratio during continuous casting according to any one of claims 1 to 3, wherein the slab shape is a bloom shape.

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