JP5949316B2 - Manufacturing method of continuous cast slab - Google Patents

Description

  The present invention relates to a technique for estimating and controlling a solidified state (slab temperature state) of a slab in secondary cooling control of a continuous casting process. The present invention also relates to a technique for accurately grasping at least the final solidification shape in the machine (in the strand) during continuous casting, estimating the state of the final solidification shape having a high correlation with the slab internal quality, and controlling it.

  Various methods have been proposed for on-line estimation calculation of the solidification state of a slab in continuous casting. For example, Patent Document 1 describes the following calculation method. That is, every time casting of a predetermined length progresses in the strand during continuous casting, a calculation (cutting) surface perpendicular to the casting direction (the slab longitudinal direction) is generated. Then, when each generated calculation surface passes through a plurality of zones set continuously in the casting direction and reaches the next zone entry boundary, the average of the zones that the calculation surface has passed immediately before Based on the cooling conditions, two-dimensional solidification calculation within the calculation surface is performed. Furthermore, the temperature distribution in the calculation plane is given as the initial value of the solidification calculation performed in the next zone and thereafter, and the solidification calculation in the calculation plane is sequentially performed to obtain the temperature distribution in the calculation plane at the final zone entry side boundary. .

Further, in Patent Document 2, the calculation means for simulating the solidified state in continuous casting uses a means for measuring the surface temperature of at least one slab so that the calculated value of the surface temperature matches the measured temperature. Discloses a solidification calculation method having calculation means for correcting the heat flux distribution.
Here, it is necessary to always grasp the final solidification position in order to prevent quality abnormalities such as segregation depending on the steel type and to perform appropriate slab reduction at an appropriate position in the slab longitudinal direction. Also, in order to improve productivity, in the steel grades that are cast just before the machine end position, the final solidification position of the final solidification position can be kept in the machine so that troubles such as slab bulge due to machine end loss can be prevented. A grasp is necessary.

  The final solidified shape is considered to have a strong correlation with quality abnormalities such as component segregation inside the slab. For example, the larger the unevenness of the solidified shape, the larger the component segregation. For this reason, in order to prevent quality abnormalities and quality control, it is necessary to constantly grasp the solidification shape.

JP 2002-178117 A Japanese Patent Laid-Open No. 10-291060

Although various methods have been proposed for measuring the internal temperature of slabs during continuous casting (hereinafter abbreviated as CC) for the purpose of estimating the final solidification position and solidification shape, the usage environment is high temperature and humidity. There is still nothing that can be used at all times during operation.
For example, in the method of estimating the final solidification state using an ultrasonic sensor, in order to obtain a sufficient signal strength, the ultrasonic sensor needs to be installed at a position within 8 mm from the slab. Exposed to high temperature environment of about ℃. Even if measures such as cooling with cooling water are taken, there are many cases where the sensor fails when used continuously. In order to measure the distribution in the width direction of the final solidified shape, it is necessary to install a large number of ultrasonic sensors in the width direction or to automatically operate the sensors in the width direction. In that case, it is difficult to automatically keep the sensor at an appropriate distance from the slab at each position in the width direction.
For this reason, it is the present condition that an internal state can be estimated only by the solidification calculation as described in Patent Document 1. In such adjustment of solidification calculation, strike the slab, etc. to confirm the solidification position and compensate for consistency with the actual situation, or temporarily measure the cross-sectional average temperature using ultrasonic waves, etc. Adjustment is carried out. And once adjustment is performed, the actual operation which trusted the calculation result is performed.

However, conditions such as changes in casting conditions, cooling equipment, aging deterioration, temporary failures, etc. occur differently from the time of calculation adjustment, and the estimation result of the solidification state by calculation differs from the actual solidification state There is a problem that the situation occurs.
Here, Patent Document 2 describes a method of correcting a deviation between a solidified state estimated by calculation as described above and an actual solidified state by using a surface temperature measurement value. However, although this Patent Document 2 describes a method of directly correcting the heat flux due to cooling based on the temperature error, the method described in Patent Document 2 cannot estimate the final solidification position and shape.

Also, in the flow rate control and secondary cooling control in the mold by magnetic field, the final solidification shape is flat at the solidification position, that is, the final solidification position in the longitudinal direction is uniform and uniform in the width direction. However, in actual operation, unevenness in the width direction and spray generated in the mold, that is, cooling unevenness in the longitudinal direction and width direction occurs due to the influence of flowing water between the rolls, and the final solidification position and shape change. To do. The final solidification position / shape is an index related to the slab quality, and its constant grasp is necessary for management control of the final solidification position / shape for quality control and quality improvement.
The present invention has been made paying attention to the problems as described above, and it is an object of the present invention to estimate the final solidification position and final solidification shape in continuous casting with higher accuracy and control casting based on the estimation result.

In order to solve the above-mentioned problem, one aspect of the method for producing a continuous cast slab of the present invention is the use of the operating conditions of a continuous caster equipped with a light reduction belt for lightly reducing the slab in the casting direction. Estimate and calculate the temperature distribution of multiple slab cross sections from the upstream side to the downstream side, predict the final solidification position and shape from the estimated calculation, and control the solidification completion position of the slab within the range of the light pressure zone And a continuous casting slab manufacturing method for continuously casting molten steel,
The surface temperature distribution in the slab width direction is measured, and the error between the measured surface temperature measured value and the estimated surface temperature value at the surface temperature distribution measurement position in the estimated calculation result of the temperature distribution of the slab cross section is minimized. By correcting the calculated value of the temperature distribution of the slab cross section and re-estimating, the final solidification position and shape prediction accuracy can be improved to predict the final solidification shape,
Based on the predicted shape of the final solidification, the control generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold for the molten steel discharge flow from the immersion nozzle. By adjusting the power, the width direction shape of the solidification completion position of the slab is controlled so that the difference between the solidification completion position on the most upstream side and the solidification completion position on the most downstream side is equal to or less than a preset length. ,
In correcting and recalculating the calculated temperature distribution of the slab cross section,
Determine the position upstream of the surface temperature distribution measurement position and upstream of the final solidification position, and correct the calculated value of the temperature distribution of the slab cross section at the determined upstream position so that the error is minimized , Re-estimation calculation is performed using the calculated value of the temperature distribution of the slab cross section at the corrected upstream position.

Further, one aspect of the method for producing a continuous cast slab of the present invention is that the upstream casting direction is used in the casting direction from the upstream side in the casting direction using the operating conditions of the continuous casting machine provided with the light reduction belt for lightly reducing the slab. Estimate and calculate the temperature distribution of multiple slab cross-sections, and predict the final solidification position and shape from the estimation calculation, while controlling the solidification completion position of the slab within the range of the light pressure zone and continuously casting molten steel A continuous casting slab manufacturing method comprising:
The surface temperature distribution in the slab width direction is measured, and the error between the measured surface temperature measured value and the estimated surface temperature value at the surface temperature distribution measurement position in the estimated calculation result of the temperature distribution of the slab cross section is minimized. By correcting the calculated value of the temperature distribution of the slab cross section and re-estimating, the final solidification position and shape prediction accuracy can be improved to predict the final solidification shape,
Based on the predicted shape of final solidification, the braking force generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold for the molten steel discharge flow from the immersion nozzle The difference between the most upstream solidification completion position and the most downstream solidification completion position is equal to or less than a preset set length. The width direction shape of the solidification completion position of the slab is controlled so that
In correcting and recalculating the calculated temperature distribution of the slab cross section,
Determine the position upstream of the surface temperature distribution measurement position and upstream of the final solidification position, and correct the calculated value of the temperature distribution of the slab cross section at the determined upstream position so that the error is minimized , Re-estimation calculation is performed using the calculated value of the temperature distribution of the slab cross section at the corrected upstream position.

Moreover, one aspect of the method for producing a continuous cast slab according to the present invention is a secondary casting process using a continuous casting machine provided with a light reduction belt for lightly reducing the slab while drawing the molten steel injected into the mold. It is a method for producing a continuous cast slab that solidifies by cooling, continuously casts molten steel by controlling the solidification completion position of the slab within the range of the light pressure lower zone,
By calculating the temperature distribution of a plurality of slab cross sections from the upstream side to the downstream side in the casting direction by a heat transfer model using a heat flux based on the cooling condition of at least the secondary cooling, the final solidification of the slab While estimating the position and shape, measure the temperature distribution in the slab width direction at a preset measurement position in the slab longitudinal direction,
The slab cross section is corrected by correcting the heat flux distribution in the slab width direction of the slab width direction so that the estimated temperature calculated by the heat transfer model at the measurement position matches the measured temperature distribution in the slab width direction. By recalculating the temperature distribution of the
Based on the estimated final solidification shape, the braking force generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold for the molten steel discharge flow from the immersion nozzle Adjusting the width direction shape of the solidification completion position of the slab so that the difference between the solidification completion position on the most upstream side and the solidification completion position on the most downstream side is equal to or less than a preset set length,
The secondary cooling is performed by a plurality of cooling zones,
A heat flux distribution correction coefficient di (i: width direction correction position) for correcting the magnification of the heat flux distribution is set individually for each of the cooling zones ,
The correction coefficient di is a coefficient by which the heat transfer coefficient of the heat flux is multiplied. By multiplying the correction coefficient di, the magnification of the heat flux is corrected, and the width direction correction position i is set to 2 or more. The bundle distribution magnification is corrected .

Here, “so that the estimated temperature at the measurement position matches the temperature distribution in the slab width direction measured by the temperature distribution measuring means” means that the matching state is processed, that is, the matching state It means to perform processing so as to approach.
Further, “match” means that the difference between the estimated temperature at the calculation position estimated by the heat transfer model and the temperature distribution in the slab width direction measured by the temperature distribution measuring means is, for example, the width of the slab. The state is within ± 10 ° C., preferably within ± 5 ° C., excluding the direction end of 50 mm.

Moreover, one aspect of the method for producing a continuous cast slab according to the present invention is a secondary casting process using a continuous casting machine provided with a light reduction belt for lightly reducing the slab while drawing the molten steel injected into the mold. It is a method for producing a continuous cast slab that solidifies by cooling, continuously casts molten steel by controlling the solidification completion position of the slab within the range of the light pressure lower zone,
By calculating the temperature distribution of a plurality of slab cross sections from the upstream side to the downstream side in the casting direction by a heat transfer model using a heat flux based on the cooling condition of at least the secondary cooling, the final solidification of the slab While estimating the position and shape, measure the temperature distribution in the slab width direction at a preset measurement position in the slab longitudinal direction,
The slab cross section is corrected by correcting the heat flux distribution in the slab width direction of the slab width direction so that the estimated temperature calculated by the heat transfer model at the measurement position matches the measured temperature distribution in the slab width direction. By recalculating the temperature distribution of the
Based on the estimated final solidification shape, the braking force generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold with respect to the molten steel discharge flow from the immersion nozzle. After adjusting at least one of the adjustment and the width adjustment amount of the secondary cooling, the difference between the solidification completion position on the most upstream side and the solidification completion position on the most downstream side is less than or equal to a preset set length. Control the width direction shape of the solidification completion position of the slab so that
The secondary cooling is performed by a plurality of cooling zones,
A heat flux distribution correction coefficient di (i: width direction correction position) for correcting the magnification of the heat flux distribution is set individually for each of the cooling zones ,
The correction coefficient di is a coefficient by which the heat transfer coefficient of the heat flux is multiplied. By multiplying the correction coefficient di, the magnification of the heat flux is corrected, and the width direction correction position i is set to 2 or more. The bundle distribution magnification is corrected .

At this time, two or more measurement positions are set along the slab longitudinal direction, the temperature distribution in the slab width direction is measured at each measurement position, and is estimated by the heat transfer model for each measurement position. as the temperature distribution of the estimated temperature and the measured the slab width direction that matches may be corrected heat flux distribution in the slab width direction of the heat flux.

Also, setting the length set above previously it may be set to 2m.

  According to the present invention, the estimated final solidification position and shape are monitored in real time by correcting the parameters of the model using the actually measured temperature in the slab width direction, and the magnetic field force installed in the mold and 2 By controlling the width of the next cooling, it is possible to cast while flattening the shape of the solidification completion position in the width direction of the slab.As a result, the casting conditions that do not cause quality abnormalities such as center segregation of the slab Can be modified.

It is a figure which shows the structural example of the vertical bending type continuous casting machine of 1st Embodiment to which this invention is applied. It is a figure which shows the view of the final solidification prediction method of the continuous casting which concerns on 1st Embodiment. It is a figure which shows the flow of a process which estimates optimization calculation and the position and shape of CE. It is a comparison figure of the predicted value of the surface temperature of the radiation thermometer measurement position of a machine end, and an actual measurement value. It is a comparison figure of the predicted value and actual value which applied the final coagulation prediction method concerning a 1st embodiment. It is a figure which shows the change of a crater end position and shape. It is a schematic diagram explaining the structure of the continuous casting machine which concerns on 2nd and 3rd embodiment based on this invention. It is a flowchart explaining the correction | amendment process in the coagulation | solidification state estimation part which concerns on 2nd Embodiment based on this invention. It is a figure which shows the example of a mesh division | segmentation. It is a figure which compares the calculation result in the thermometer in the case where correction | amendment is not implemented, and a measured value. It is a figure which compares the calculation result in the thermometer 4b which concerns on 2nd Embodiment based on this invention, and a measured value. It is a figure which shows the example of correction | amendment of the correction coefficient d _i . It is a figure which shows the last solidification position and shape in the case of not correct | amending. It is a figure which shows the last solidification position and shape at the time of implementing the correction | amendment which concerns on 2nd Embodiment based on this invention. The temperature in the same width direction when the heat transfer coefficient correction coefficient is provided for each zone according to the second embodiment of the present invention and when the heat transfer coefficient correction coefficient common to all the zones is used at the time of use. It is a figure which shows the difference of the last solidification position and shape. It is a flowchart explaining the correction | amendment process in the coagulation | solidification state estimation part which concerns on 3rd Embodiment based on this invention. It is a figure which shows the calculation cross-section temperature distribution after correction | amendment in the measurement position of the thermometer 4a. It is the figure which compared the model calculation temperature in the measurement position of the thermometer 4b at the time of correct | amending at the measurement value position of the thermometer 4a, and measured temperature. It is a figure which compares the calculation result in the thermometer 4b which concerns on 3rd Embodiment based on this invention, and a measured value. It is a figure which shows the final coagulation position and shape in case correction | amendment based on a thermometer measurement result is not performed. It is a figure which shows the last solidification position and shape at the time of implementing the correction | amendment which concerns on 3rd Embodiment based on this invention. It is a schematic perspective view of the casting_mold | template part of the slab continuous casting machine of this embodiment. It is a schematic front view of the casting_mold | template part of the slab continuous casting machine shown in FIG. It is a figure which shows typically the magnetic field application method in the case of applying a moving magnetic field in order to give a braking force to molten steel discharge flow. It is a figure which shows typically the magnetic field application method in the case of applying a moving magnetic field in order to give acceleration force to molten steel discharge flow. It is the schematic which shows the structure of the spray nozzle of a secondary cooling zone. It is a figure which shows one example of the width direction shape of a coagulation completion position.

Embodiments of the present invention will be described with reference to the drawings.
(First embodiment)
FIG. 1 is a diagram showing a configuration example of a vertical bending type continuous casting machine to which the present invention is applied. In the figure, 1 represents a tundish, 2 represents a mold, 3 represents an immersion nozzle, 4 represents a surface temperature distribution measuring instrument, 5 represents a cast piece, 6 represents a support roll, and 7 to 13 represent cooling zones.

In the vertical bending type continuous casting machine, a mold 2 is provided below the tundish 1, and an immersion nozzle 3 serving as a molten steel supply port to the mold 2 is provided at the bottom of the tundish 1. A support roll 6 is installed below the mold 2. The cooling zones 7 to 13 constitute a divided secondary cooling zone.
In each cooling zone, a plurality of spray or air mist spray nozzles are arranged, and secondary cooling water is sprayed from the spray nozzle to the surface of the slab. In the cooling zone, the cooling zone on the side opposite to the reference surface (upper surface side) is indicated by a, and the reference surface side (lower surface side) is indicated by b.

Further, FIG. 1 shows a total of seven cooling zones, but this is a conceptual diagram, and the number of zones of an actual continuous casting machine is divided into various numbers depending on the length of the machine.
Furthermore, a reduction roll (light reduction roll) for lightly reducing the slab 5 is installed. That is, in the continuous casting machine of this embodiment, as shown in FIG. 1, a light reduction belt 16 for lightly reducing the slab 5 as a part of the support roll 6 is installed. The light pressure lower belt 16 is composed of a plurality of sets of support rolls 6, and the interval between the opposed support rolls 6 is set so as to gradually narrow toward the downstream side in the casting direction of the slab 5. On the other hand, it has a structure capable of applying a rolling force.
The light pressure lower belt 16 is set so that the interval between the opposing support rolls 6 (referred to as “roll interval”) is gradually narrowed toward the downstream side in the casting direction of the slab 5. 5 is a group of support rolls 6 capable of applying a rolling force to 5.

  Further, as shown in FIGS. 22 and 23, the mold 2 is composed of a mold long side 2a opposed in the longitudinal direction and a mold short side 2b disposed in the mold long side 2a and opposed in the short direction. The tundish 1 is disposed at a predetermined position above the mold 2. An upper nozzle 21 is installed at the bottom of the tundish 1, and an immersion nozzle 3 including a fixed plate 22, a sliding plate 23, and a rectifying nozzle 24 is disposed in contact with the lower surface of the upper nozzle 21. An immersion nozzle 3 having a pair of discharge holes 19 in the lower part is disposed in contact with the lower surface of 3, and a molten steel outflow hole 25 from the tundish 1 to the mold 2 is formed. In order to prevent alumina from adhering to the inner wall surface of the immersion nozzle 3, non-oxidizing gas such as Ar gas and nitrogen gas is blown into the molten steel outflow hole 25 from the upper nozzle 21, the fixed plate 22, the immersion nozzle 3, and the like. .

  A moving magnetic field generator 40 is disposed on the back surface of the mold long side 2a. The moving magnetic field generator 40 is arranged in a total of four units divided into two on the left and right in the width direction of the mold long side 2a with the immersion nozzle 3 as a boundary. The moving magnetic field generator 40 is disposed so as to be opposed to the long side 2a of the mold with the center position in the casting direction as a position immediately below the discharge hole 19. Each moving magnetic field generator 40 is connected to a power source (not shown), and the magnetic field strength and the magnetic field moving direction applied from the moving magnetic field generator 40 are individually controlled by the power supplied from the power source. It is like that.

  The magnetic field applied by the moving magnetic field generator 40 is a moving magnetic field. When a magnetic field is applied to apply a braking force to the molten steel discharge flow 31 from the immersion nozzle 3, as shown in FIG. In the case where the moving direction is from the mold short side 2b side to the immersion nozzle 3 side, and a magnetic field is applied to apply an acceleration force to the molten steel discharge flow 31 from the immersion nozzle 3, as shown in FIG. The moving direction is from the immersion nozzle 3 side to the mold short side 2b side. 24 and 25 are diagrams showing the moving direction of the magnetic field from directly above the mold 2, and the arrows in the drawings indicate the moving direction of the magnetic field.

Moreover, the secondary cooling spray nozzle for width cutting is provided.
As shown in FIG. 26, the secondary cooling spray nozzles 60 are installed at two positions in the width direction of the slab 5 in the gaps of the support rolls 6 arranged in the casting direction. The height position can be changed. In this case, when the spray angle of the spray nozzle 60 is 2θ, the spray nozzle 60 moves in the direction of the angle θ with respect to a line ZZ ′ passing through the center of the slab 5 and perpendicular to the long side surface of the slab. However, by changing the height position arbitrarily, it is possible to spray with an arbitrary cutting amount. For example, as shown in FIG. 26, when the tip position of the spray nozzle 60 is the height H1, the width cutting amount is the width W1, and when the height position is the height H2, the width cutting amount is the width W2. In FIG. 26, the spray nozzle on the opposite surface side (lower surface side) of the slab 5 is not shown, but the opposite side has the same structure. In addition, in FIG. 26, the spray nozzle 60 is described in the example of two places in the slab width direction, but the structure is slightly complicated also in the case of three or more places, but the width cutting amount is adjusted by the same method. be able to. The method of adjusting the width cutting amount is not limited to the method of moving the spray nozzle 60 as described above. For example, a number of spray nozzles are installed in the slab width direction, and the spray corresponding to the width cutting position is set. It is possible to stop spraying from the nozzle, and it is also possible to install a movable shielding plate between the slab surface and the spray nozzle.

  The slab surface temperature distribution measuring instrument 4 is, for example, a thermometer that measures the surface temperature distribution in the width direction of the slab at the machine end. The thermometer used for this is a radiation thermometer that can directly measure the temperature distribution or a method that scans a partial measurement thermometer, and also uses the temperature dependence of ultrasonic transmission time using longitudinal and transverse ultrasonic waves. Even if it is the steel plate inside thermometer which was made, if the temperature distribution of the width direction can be measured, a measuring system will not be ask | required.

  The secondary cooling calculation of CC (continuous casting machine) considers, for example, the cross section of a slab sliced in unit length (casting direction), and depending on the location in the strand during casting, water cooling, air cooling, mist cooling, It is implemented by giving a heat flux of boundary conditions in various situations such as heat removal from a roll and solving a two-dimensional heat transfer equation shown in the following equation (1).

  At this time, unsteady temperature calculation can also be realized by generating and calculating sliced cross sections of unit length one after another. Currently, the calculation capability is dramatically improved, and it is possible to import the operating conditions such as water cooling performance data, casting speed, tundish (T / D) molten steel temperature online and perform secondary cooling calculation in real time. It has become. By this calculation, it is possible to calculate where the final solidification position of the slab is by using the solidus temperature.

In the present embodiment, first, a method for correcting the secondary cooling calculation using the estimated temperature value of the secondary cooling calculation and the actually measured temperature is provided. FIG. 2 is a diagram showing the concept of the method for predicting the final solidification of continuous casting according to the embodiment of the present invention. Here, the temperature measurement location is described as the slab surface temperature at a position close to the machine end, but temperature measurement in the machine may be used.
First, the temperature is calculated continuously from the meniscus to the machine end for each two-dimensional cross-sectional slice of the unit length in the casting direction. That is, the entire secondary cooling calculation is executed once to calculate the upstream boundary condition and the end surface temperature distribution.

Next, the surface temperature distribution in the width direction is measured with an in-machine or end-of-machine thermometer.
Then, the difference between the slab surface temperature calculated value and the surface temperature actual measurement value at the surface temperature observation position is used as an evaluation function based on an error area or the like, and evaluation is performed using the value. An appropriate position upstream of the position of the final solidification, that is, the crater end (hereinafter also abbreviated as CE) is determined upstream of the temperature measurement position so that the evaluation function value becomes small, and the temperature distribution of the cross section is corrected. The temperature distribution that minimizes the evaluation function is calculated (optimization calculation) by correcting the temperature distribution of the cross section and evaluating the temperature error repeatedly, and the result of recalculation based on the temperature distribution is the most error-free. Reduce the temperature.
In this way, when the cross-sectional temperature distribution at the upstream position that minimizes the evaluation function is obtained, the cooling calculation according to the operation conditions is performed again from the position downstream to calculate the final solidification position and shape. To do.

FIG. 3 is a diagram showing a flow of processing for performing shape control in the slab width direction while predicting optimization calculation and the position and shape of CE.
In Step 100, a position upstream from the CE position is determined and given a temperature distribution. In Step 101, the end surface temperature distribution based on the temperature model is estimated and calculated. The estimated surface temperature distribution is compared with the actually measured surface temperature distribution, and the error is evaluated using an evaluation function (Step 102).

Then, the convergence of the evaluation function is determined. If the convergence is not determined, the upstream temperature distribution is corrected (Step 103).
After the correction, the process returns to Step 101 and is repeated until it is determined at Step 102 that convergence has occurred. If it is determined that convergence has occurred, recalculation is performed under the converged temperature condition, and finally the CE position / shape prediction is terminated (Step 104). In this way, if the cross-sectional temperature distribution at the upstream position that satisfies the constraints and minimizes the evaluation function is obtained, the cooling calculation is performed again according to the operation condition from the position toward the downstream, and the final calculation is performed. Prediction accuracy of solidification position and shape can be improved.
An example of a specific method for correcting the cross-sectional temperature distribution at the upstream position in Step 103 is shown below.

First, the width direction is divided by a specified number coarser than the calculation mesh, and the divided section is given a width direction surface temperature by a method of approximating it as a constant temperature, and this is used as a variable to be obtained.
Next, as for the distribution in the thickness direction, the temperature up to the central portion in the thickness direction is determined using a function that approximates the distribution in the thickness direction at the specified upstream position of the slab temperature calculated at first with a quadratic function. . Although quadratic function approximation is used here, the temperature distribution in the thickness direction may use the distribution shape obtained by calculation according to the surface cooling state as it is, or make an appropriate correction. (A specific method may include a method of storing a temperature ratio between meshes in the thickness direction).

  Any optimization method may be used as long as it is a nonlinear optimization method. For example, sequential quadratic programming can be considered. As the evaluation function, the width direction temperature distribution actual measurement data at the machine end designated location and the error area of the surface temperature calculation result at the same position, the square sum of the divided temperature errors in the width direction, and the like can be considered. In addition, it is also possible to give a temperature constraint to the convergence condition, and to give a constraint that the error between the observation data and the calculation data appropriately falls within the temperature range. Furthermore, upper and lower limits can also be placed on the upstream surface temperature and the center temperature in the thickness direction, which are variables.

In this embodiment, further, in Step 105, the shortest solidification completion position and the longest solidification completion position are obtained from the predicted final solidification shape in the slab width direction, and the difference between the shortest solidification completion position and the longest solidification completion position, that is, In accordance with the distance between the two, the following processing (1) to (3) is performed so that the difference becomes smaller than the set length.
(1) A magnetic field is applied by the linear AC moving magnetic field generator 40, or the strength or application pattern of the magnetic field is changed to adjust the flow of molten steel in the mold.
(2) Change the width of secondary cooling.
(3) Adjusting the flow of molten steel in the mold by the linear AC moving magnetic field generator 40 and simultaneously changing the width of the secondary cooling.

(Example)
Next, a specific example to which the first embodiment based on the present invention is applied will be described.
FIG. 4 is a comparison diagram between the predicted value and the actual measurement value of the surface temperature at the radiation thermometer measurement position at the aircraft end.
This example is an example in which optimization calculation, that is, correction of the upstream temperature distribution is not performed, there is a difference in the temperature value between the actual measurement and calculation of the surface temperature, and the distribution method in the width direction is also different. I understand. In such a situation, even if the CE position shape is predicted from the calculation result, there is no guarantee that it matches the actual situation.
On the other hand, FIG. 5 is a comparison diagram between a predicted value and an actually measured value to which the final coagulation prediction method according to the present invention is applied. According to the algorithm described above, the slab cross-section temperature distribution at the upstream boundary is corrected so that the error between the actual measurement value and the calculation value is minimized by performing optimization calculation (sequential quadratic programming) with 15 variables in the width direction. It is a thing.

Here, with respect to the variable in the width direction (width direction mesh) used for temperature matching, the distance between the dots may be 50 to 100 mm. In this example, since the number of points is 15 for a half width of 1000 mm, the distance between the points is about 70 mm. This is because there is heat transfer in the width direction inside, so that if the measured temperature appearing on the surface is set to a pitch of 50 to 100 mm or less in the width direction, an extreme difference does not occur. On the other hand, when a fine pitch is set, there is a problem that the calculation load increases and there is a case where the calculation does not end within a desired calculation time.
The calculation result of the surface temperature generally increases, and a temperature calculation that matches the numerical calculation result is realized at a part where the temperature measurement point is present. It can be seen that calculation that steadily reduces the difference in surface temperature specified by the evaluation function can be realized by nonlinear optimization calculation.

And FIG. 6 is a figure which shows the change of a crater end position and shape. 6 (a) shows the CE position after optimization corresponding to FIG. 4, FIG. 6 (b) shows the CE position after optimization corresponding to FIG. 5, the horizontal axis is the distance from the meniscus, and The vertical axis indicates the solidification completion position in the width direction position.
Since the first calculated temperature is lower than the actually measured surface temperature, the calculated temperature rises by correcting the temperature by optimization calculation, and as a result, the crater end position also extends downstream. Thus, if the calculation result at the surface temperature measurement position matches the actual measurement value, the validity of the CE position / shape prediction determined by the temperature state inside the slab is expected.

  In this way, if the CE position and shape can be predicted with high accuracy, the casting conditions (spray conditions, light rolling conditions, casting speed, mold electromagnetic stirring strength, etc.) can be changed in various ways, and how these shapes change. You can figure out how it will go. This makes it possible to define the slab manufacturing conditions with a flat crater end shape and little center segregation, and to provide an excellent quality slab.

In the present embodiment, the shortest solidification completion position and the longest solidification completion position are obtained from the predicted final solidification shape in the slab width direction, and the difference between the shortest solidification completion position and the longest solidification completion position, that is, the distance between the two. Depending on the above, any one of the following processes (1) to (3) is performed in consideration of a margin of the operation amount of each device in the current operation state so that the difference becomes smaller than the set length. I do.
(1) A magnetic field is applied by the linear AC moving magnetic field generator 40, or the strength or application pattern of the magnetic field is changed to adjust the flow of molten steel in the mold.
(2) Change the width of secondary cooling.
(3) Adjusting the flow of molten steel in the mold by the linear AC moving magnetic field generator 40 and simultaneously changing the width of the secondary cooling.

  Specifically, when the longest solidification completion position exists near the short side surface in the width direction of the slab 5, a moving magnetic field is applied so as to decelerate the discharge flow from the immersion nozzle or the magnetic field strength is increased. Or reduce the width cut amount. Conversely, when the longest solidification completion position exists near the center of the width direction of the slab 5, a moving magnetic field is applied or the magnetic field strength is increased so as to accelerate the discharge flow from the immersion nozzle. Alternatively, this is dealt with by increasing the width cutting amount. Since the molten steel flow in the mold depends on the discharge flow from the immersion nozzle, the overall flow of the molten steel in the mold can be controlled by controlling the flow rate of the discharge flow. When reducing the width cutting amount, the solidification completion position length may be adjusted without zeroing the width cutting amount, that is, when the slab 5 for direct rolling is cast, From the viewpoint of securing the temperature of the corner portion of the slab 5, it is preferable that the minimum amount of width cutting is about 100 mm.

  Normally, the shortest solidification completion position and the position of the longest solidification completion position in the slab width direction also change during casting. However, when the slab 5 is cooled in a state where the spray nozzle 60 is not clogged, the shortest solidification completion position generally exists at the center of the slab width, while the longest solidification completion position is In many cases, it exists at a position about 200 mm away from one short side surface. Therefore, the shape in the width direction of the solidification completion position is W-shaped as shown in FIG. However, in this case, the solidification completion position shape is not symmetrical on the left and right with respect to the center of the slab 5, and as shown in FIG. In such a case, the difference between the shortest solidification completion position and the longest solidification completion position is strictly the difference L1 in the figure, but when changing the strength of the magnetic field and the application pattern, or the width cut amount, the difference Either L1 or difference L2 may be used as a reference. In such a case, the countermeasures for the molten steel flow and the width cutting amount are the same regardless of which is used as a reference.

In addition, when the slab 5 is lightly reduced to further reduce the center segregation, the casting speed and the secondary cooling are performed so that the shortest solidification completion position is at the center or the outlet side of the light reduction zone 16 of the continuous casting machine. Adjust the amount of water, and further adjust the flow control of the molten steel in the mold by moving magnetic field and / or the width cutting amount to reduce the difference between the shortest solidification completion position and the longest solidification completion position. Control within the range of the light pressure lower belt 16. In this case, since the center segregation is reduced as the difference between the shortest solidification completion position and the longest solidification completion position is smaller, it is preferable to control the difference between the shortest solidification completion position and the longest solidification completion position to 2 m or less.
As described above, according to the present invention, it is possible to manufacture the slab 5 while flattening the shape of the solidification completion position in the slab width direction, improving the center segregation and improving the productivity of the continuous casting machine. Such secondary effects can be obtained.

(Second Embodiment)
Next, 2nd Embodiment based on this invention is described with reference to drawings.
FIG. 7 is a schematic diagram showing an example of a continuous casting machine to which the solidification state estimation device for the slab 5 based on the present invention is applied. In FIG. 7, a vertical bending type continuous casting machine is illustrated as a continuous casting machine. However, the same reference numerals are used for the same components as in FIG.

(Configuration of continuous casting machine)
As shown in FIG. 7, in the continuous casting machine, a mold 2 is provided below the tundish 1, and an immersion nozzle 3 serving as a molten steel supply port to the mold 2 is provided at the bottom of the tundish 1. A plurality of support rolls 6 are installed below the mold 2, and the slab 5 is drawn along the plurality of support rolls 6 at a predetermined drawing speed. Reference numerals 7 to 15 denote divided cooling zones, which constitute secondary cooling zones. Cooling nozzles (not shown) such as a plurality of spray or air mist spray nozzles are arranged in each cooling zone, and secondary cooling water is sprayed on the surface of the slab 5 from each cooling nozzle, Secondary cooling of the target slab 5 is performed. In FIG. 7, the cooling zone on the side opposite to the reference surface (upper surface side) is indicated by a, and the reference surface side (lower surface side) is indicated by b. In addition, FIG. 7 illustrates a case where the cooling zone is a total of 9 zones, but the number of zones is not limited to this. The actual number of zones in a continuous casting machine varies depending on how long the machine is divided.

  Further, a reduction roll (light reduction roll) for lightly reducing the slab 5 is installed. That is, in the continuous casting machine of this embodiment, as shown in FIG. 1, a light reduction belt 16 for lightly reducing the slab 5 as a part of the support roll 6 is installed. The light pressure lower belt 16 is composed of a plurality of sets of support rolls 6, and the interval between the opposed support rolls 6 is set so as to gradually narrow toward the downstream side in the casting direction of the slab 5. On the other hand, it has a structure capable of applying a rolling force. The light pressure lower belt 16 is set so that the interval between the opposing support rolls 6 (referred to as “roll interval”) is gradually narrowed toward the downstream side in the casting direction of the slab 5. 5 is a group of support rolls 6 capable of applying a rolling force to 5.

The mold and the surrounding structure are the same as in the first embodiment (see FIGS. 22 and 23).
That is, four moving magnetic field generators 40 are arranged on the back surface of the mold long side 2a, and each moving magnetic field generator 40 is connected to a power source (not shown), and based on a command from the moving magnetic field controller, The magnetic field strength and the magnetic field moving direction applied from the moving magnetic field generator 40 are individually controlled by the power supplied from the power source.

  The magnetic field applied by the moving magnetic field generator 40 is a moving magnetic field. When a magnetic field is applied to apply a braking force to the molten steel discharge flow 31 from the immersion nozzle 3, as shown in FIG. In the case where the moving direction is from the mold short side 2b side to the immersion nozzle 3 side, and a magnetic field is applied to apply an acceleration force to the molten steel discharge flow 31 from the immersion nozzle 3, as shown in FIG. The moving direction is from the immersion nozzle 3 side to the mold short side 2b side. 24 and 25 are diagrams showing the moving direction of the magnetic field from directly above the mold 2, and the arrows in the drawings indicate the moving direction of the magnetic field.

Moreover, the secondary cooling spray nozzle 60 for width cutting is provided with the same structure as 1st Embodiment (refer FIG. 26).
Moreover, the thermometer 4b which comprises a temperature distribution measurement means is arrange | positioned with respect to one place preset in the slab longitudinal direction. The thermometer 4b measures the surface temperature distribution in the width direction of the slab 5 in the machine. Examples of the thermometer 4b include a radiation thermometer and a thermography that can directly measure the temperature distribution, and any instrument may be used as long as the temperature distribution in the width direction can be measured.
In addition, in FIG. 7, the case where the thermometers 4a and 4b which respectively comprise a temperature distribution measurement means are arrange | positioned with respect to two places along a slab longitudinal direction is illustrated. This is because two thermometers 4a and 4b used in a third embodiment to be described later are shown together with FIG. Of course, the thermometer used in the first embodiment may be the thermometer of reference numeral 4a.

Reference numeral 20 denotes a continuous casting control unit.
The continuous casting control unit 20 includes a secondary cooling control unit 20A, a solidification state estimation unit 20B, a moving magnetic field control unit 20C, and a secondary cooling width cut control unit 20D.
The secondary cooling control unit 20A controls the secondary cooling in each of the cooling zones based on a command from the manufacturing management control unit 21. For example, the cooling conditions are set so that the outlet temperature in each cooling zone becomes the target temperature at that position. This cooling condition is also input to the solidification state estimation unit 20B.

The solidification state estimation unit 20B includes a solidification state estimation unit main body 20Ba and a heat flux distribution correction unit 20Bb.
The solidification state estimation part main body 20Ba estimates the solidification state (temperature state) of the slab 5 based on the heat transfer model using the obtained heat flux while obtaining the heat flux based on at least the cooling condition of the secondary cooling.

Further, the heat flux distribution correction unit 20Bb corrects the width direction distribution of the heat flux used in the solidified state estimation unit body 20Ba. Specifically, the estimated temperature of the slab surface calculated by the heat transfer model at the measurement position of the thermometer 4b matches the surface temperature distribution in the slab width direction measured by the thermometer 4b. The heat flux distribution in the slab width direction of the heat flux is corrected.
The solidification state estimation unit body 20Ba operates again each time the correction coefficient is changed by the heat flux distribution correction unit 20Bb, and corrects the output value by performing recalculation.

  Here, the secondary cooling calculation of normal continuous casting is, for example, considering a cross section of a slab sliced at a unit length along the slab longitudinal direction (casting direction), and depending on the location in the strand during casting. The heat flux is obtained based on the equation (2) indicating the boundary condition on the slab surface by the secondary cooling condition comprising water cooling, air cooling, mist cooling, heat removal from the roll, etc., and using the obtained heat flux, the equation ( This is performed by solving the two-dimensional heat transfer equation of 4).

  However, φ, which is a value related to temperature in the equation (2), can be expressed by the following equation (3). For this reason, when formula (2) is applied to formula (4) described later, the temperature is replaced as in formula (3).

here,
Q: heat flux κ: thermal conductivity κ _d : thermal conductivity at reference temperature h: heat transfer coefficient T: model surface temperature Ta: ambient temperature

here,
c: Specific heat ρ: Density κ: Thermal conductivity T: Temperature t: Time x, y: Coordinates

And the heat transfer coefficient h in Formula (2) is determined by secondary cooling conditions, such as cooling methods, such as water cooling, air cooling, and mist cooling, the amount of cooling operations, and heat removal from a roll. Obtain the internal temperature distribution of the slab 5 by the secondary cooling calculation by the expression (4) based on the above expression (2), and further calculate the complete solidification position from the solidus temperature determined by the internal temperature distribution and the molten steel components. To do.
In addition, by using the above formulas (2) to (4), the sliced unit length of the cross section is continuously generated along the slab longitudinal direction one after another, and calculated, thereby changing the casting speed and the like. Unsteady temperature calculation can also be realized. At present, the calculation capability has improved dramatically, and the operating conditions such as water cooling performance data, casting speed and tundish molten steel temperature can be taken online, and the secondary cooling calculation and final solidification calculation can be performed in real time.

In the present embodiment, the following equation (5) is used instead of the equation (2) as the equation of the heat flux due to the boundary condition due to the secondary cooling condition.
Q _ij = d _i h (T−Ta) (5)
here,
d _i : Heat transfer coefficient correction coefficient (initial value is “1”)
i: width direction correction position j: longitudinal direction position

Next, the process of the solidification state estimation unit 20B will be described with reference to FIG.
In the present embodiment, the parameters of the slab 5 are adjusted by adjusting the parameters used for the secondary cooling calculation using the surface temperature calculation value of the secondary cooling model (heat transfer model) and the surface temperature actual measurement value in the width direction. Estimate the temperature distribution and estimate the final solidification position and shape. Specifically, the correction coefficient d _i which is a parameter for correcting the heat flux distribution in the width direction or the heat transfer coefficient distribution at the secondary cooling position is corrected.

The position of the actually measured thermometer 4b used in this embodiment is preferably the slab surface temperature at a position close to the final solidification position in the machine, but in principle, any position in the longitudinal direction position may be used.
First, in step S10, the solidification state estimation unit body 20Ba performs secondary cooling calculation by the above-described processing. The correction coefficient d _i is set to “1” as an initial value.
In the secondary cooling calculation, the temperature is first calculated at the casting speed corresponding to the casting history at that time for one two-dimensional cross-sectional slice having a unit length in the casting direction, using the above formulas (5) and (4). . The sliced unit length cross-sections are successively generated along the slab longitudinal direction and calculated.

Next, in step S20, the slab surface temperature (temperature distribution in the width direction) at the measurement position of the surface temperature observation by the thermometer 4b is obtained from the calculation by the secondary cooling calculation in step S10.
Next, in step S30, the measured temperature distribution in the slab width direction at the measurement position is obtained from the measurement value of the thermometer 4b that is continuously input. For example, an average value of measured values in a preset time interval is set as an actually measured temperature distribution in the slab width direction.

Next, in Step S40, the heat flux distribution correction unit 20Bb calculates the calculated value (estimated temperature) of the slab surface temperature obtained in Step S20 and the actual surface temperature value measured by the thermometer 4b obtained in Step S30. It is determined whether or not the difference is equal to or larger than a preset threshold value. If the difference is equal to or larger than the threshold value, the process proceeds to step S50. If it is less than the threshold value, the process proceeds to step S60, the recalculation of the secondary cooling calculation is terminated, and the final solidification position and the final solidification shape (profile) are obtained based on the corrected secondary cooling calculation.
Here, a plurality of correction points n in the slab width direction are set, for example, 20 points (n = 20), and a deviation between the estimated temperature and the actual measurement value is obtained at each correction point position. It is determined whether or not it is equal to or less than the threshold value.

On the other hand, in step S50, the difference between the calculated value of the slab surface temperature obtained in step S20 and the actual measured surface temperature measured by the thermometer 4b obtained in step S30 is small or zero. The correction coefficient d _i (i = 1 to n) is changed so that When the correction coefficient d _i is changed, the process proceeds to step S10 and recalculation of the secondary cooling calculation is performed.
The correction coefficient d _i of the width direction heat transfer coefficient h is uniformly changed in the longitudinal cooling zone. For the sake of convenience, the thermometer 4b that can be measured in the width direction is installed in only one place in the longitudinal direction, and is uniformly changed in the longitudinal direction.

  As a specific calculation method, using the error area of the temperature distribution measurement data at the specified location and the surface temperature calculation result at the same position as the evaluation function, the evaluation function value is reduced, that is, the error area is minimized. Calculation may be performed as follows. A general optimization method may be used as the method. In addition, when a restriction is imposed on the correction coefficient, a nonlinear optimization method such as a sequential quadratic programming method may be used.

  Further, the moving magnetic field control unit 20C determines a magnetic force command based on the solidification state information estimated by the solidification state estimation unit 20B, and controls the magnetic field force in the mold. The moving magnetic field control unit 20C obtains the shortest solidification completion position and the longest solidification completion position from the estimated final solidification shape in the slab width direction, and the difference between the shortest solidification completion position and the longest solidification completion position, that is, the distance between the two. Accordingly, the flow of molten steel in the mold is adjusted by applying a magnetic field by the linear AC moving magnetic field generator 40 or changing the strength or application pattern of the magnetic field so that the difference becomes as small as the set length.

  Specifically, when the longest solidification completion position exists near the short side surface in the width direction of the slab 5, a moving magnetic field is applied so as to decelerate the discharge flow from the immersion nozzle or this magnetic field. Increase strength. Conversely, when the longest solidification completion position exists near the center of the slab 5 in the width direction, a moving magnetic field is applied or the magnetic field strength is increased so as to accelerate the discharge flow from the immersion nozzle. Since the molten steel flow in the mold depends on the discharge flow from the immersion nozzle, the overall flow of the molten steel in the mold can be controlled by controlling the flow rate of the discharge flow.

  The secondary cooling width cutting control unit 20D determines the width cutting amount based on the solidification state information estimated by the solidification state estimation unit 20B, and outputs the width cutting amount to the manufacturing management control device 41. Control. The manufacturing management control device 41 adjusts the width cut based on the width cut amount output from the secondary cooling width cut control unit 20D. The secondary cooling width cutting control unit 20D obtains the shortest solidification completion position and the longest solidification completion position from the estimated final solidification shape in the slab width direction, and the difference between the shortest solidification completion position and the longest solidification completion position, that is, both The width cut amount for changing the width cut amount of the secondary cooling is determined so that this difference becomes smaller than the set length according to the distance between them.

  Specifically, when the longest solidification completion position exists near the short side surface in the width direction of the slab 5, the width cutting amount is reduced. On the contrary, when the longest solidification completion position exists near the center of the slab 5 in the width direction, this is dealt with by increasing the width cutting amount. Since the molten steel flow in the mold depends on the discharge flow from the immersion nozzle, the overall flow of the molten steel in the mold can be controlled by controlling the flow rate of the discharge flow. When reducing the width cutting amount, the solidification completion position length may be adjusted without zeroing the width cutting amount, that is, when the slab 5 for direct rolling is cast, From the viewpoint of securing the temperature of the corner portion of the slab 5, it is preferable that the minimum amount of width cutting is about 100 mm.

Here, normally, the shortest solidification completion position and the position of the longest solidification completion position in the slab width direction also change during casting. However, when the slab 5 is cooled in a state where the spray nozzle 60 is not clogged, the shortest solidification completion position generally exists at the center of the slab width, while the longest solidification completion position is In many cases, it exists at a position about 200 mm away from one short side surface. Therefore, the shape in the width direction of the solidification completion position is W-shaped as shown in FIG. However, in this case, the solidification completion position shape is not symmetrical on the left and right with respect to the center of the slab 5, and as shown in FIG. In such a case, the difference between the shortest solidification completion position and the longest solidification completion position is strictly the difference L1 in the figure, but when changing the strength of the magnetic field and the application pattern, or the width cut amount, the difference Either L1 or difference L2 may be used as a reference. In such a case, the countermeasures for the molten steel flow and the width cutting amount are the same regardless of which is used as a reference.
Here, at least one of the magnetic field control performed by the moving magnetic field control unit 20C and the secondary cooling width cutting control performed by the secondary cooling width cutting control unit 20D may be executed.

  In addition, when the slab 5 is lightly reduced to further reduce the center segregation, the casting speed and the secondary cooling are performed so that the shortest solidification completion position is at the center or the outlet side of the light reduction zone 16 of the continuous casting machine. Adjust the amount of water, and further adjust the flow control of the molten steel in the mold by moving magnetic field or the adjustment of the width cutting amount, or both, to reduce the difference between the shortest solidification completion position and the longest solidification completion position to the set length or less, The longest solidification completion position is controlled within the range of the light pressure lower belt 16. In this case, since the center segregation is reduced as the difference between the shortest solidification completion position and the longest solidification completion position is smaller, it is preferable to control the difference between the shortest solidification completion position and the longest solidification completion position to 2 m or less.

(About secondary cooling calculation)
The above secondary cooling calculation will be supplementarily described below.
The secondary cooling calculation of normal continuous casting is, for example, considering a slab cross-section sliced by unit length along the slab longitudinal direction (casting direction), depending on the location in the strand during casting, water cooling, The heat flux is obtained based on the above equation (2) indicating the boundary condition on the slab surface by the secondary cooling conditions including air cooling, mist cooling, heat removal from the roll, etc., and using the obtained heat flux, the above equation (4 ) To solve the two-dimensional heat transfer equation.

Here, the two-dimensional heat conduction equation represented by the equation (4) is an equation assuming that there is no heat conduction in the casting direction of the slab in the slab cross section.
In general, the physical property values of specific heat, density, and thermal conductivity change with the temperature change of the slab, so it is necessary to solve equation (4) by changing the physical property values as a function of temperature. When the physical property value has temperature dependence, Equation (4) cannot be developed into a difference equation as it is.
Therefore, in the actual calculation, the “temperature-conversion temperature method”, which is a well-known method, is used to linearize the temperature as follows.

  Then, when Expressions (6) and (7) are substituted into Expression (4), the following Expression (8) is obtained.

By differentiating this equation (8), the heat transfer calculation for each slice can be numerically analyzed.
Here, the difference formula differs between the internal point and the surface point of the slice.
On the slab surface, it is expressed by the following formula (9):

  Based on these formulas (9) and (10), when formula (8) is differentiated (discretized) at each of the internal points and surface points, the following formula is obtained.

In the above equation, l represents a calculation time step, and the value of (l + 1) of the next calculation step (time) is obtained from each value of l.
Using these difference formulas (11) and (12), the actual heat transfer calculation is performed by the difference method.
In this actual calculation process, the three-dimensional calculation is traced through the following procedures (1) to (9).
(1) As the analysis starts, one two-dimensional sheet enters the mold and proceeds.
(2) This sheet is calculated only by external boundary conditions and two-dimensional internal heat conduction. (The heat conduction in the traveling direction is not considered.)
(3) On the way, the speed changes at each time according to the speed data.
(4) In the middle, the spray pattern is switched by the external cooling pattern data.
(5) This one sheet is calculated until the end time of the analysis time.
(6) When moving to the next sheet, change the physical property value and initial temperature according to the input.
(7) When the calculation of one sheet is completed, the calculation of the next sheet is started after the time step, and is calculated until the analysis time end time.
(8) The above calculation is performed for each sheet until the drawing end time.
(9) File output is performed as needed during the process.

[About mesh division]
In the calculation of the heat transfer calculation, the heat conduction in the slab is analyzed using a difference method, and the portion in the thickness direction 1/2 is analyzed from the structural objectivity. For example, when the short side and the long side are divided into m and n, the mesh is as shown in FIG.
[About heat transfer coefficient used]
Further, the heat transfer coefficient h in the equation (9) is determined by a secondary cooling condition such as a cooling method such as water cooling, air cooling, mist cooling, a cooling operation amount, a roll heat removal amount, or the like. Moreover, the heat transfer coefficient h changes a calculation formula according to the cooling method (only water, water and air, only air, and each flow rate).
The heat removal actually used adopts a larger value by comparing these with radiant cooling.

[About solid phase ratio]
The calculation of the solid phase ratio is as follows. When the temperature of each cell is lower than the liquidus temperature, the solid phase ratio = 1, and when the temperature is higher than the solidus temperature, the solid phase ratio = 0. When it is between the temperature and the solidus temperature, the following formula is used.

[Calculating heat removal in the mold]
In the mold, the amount of heat removed from the surface is determined by the time required for the slice to pass through the mold.
The heat removal is determined to be uniform on both the long side and the short side.
[Examples of calculation conditions]
The calculation conditions are set as follows, for example.
・ Simulation time step: 0.02 sec
・ Casting speed: 1.4 mpm
・ Analysis thickness: 125 mm (half thickness, total thickness 250 mm)
・ Analysis width: 1050 mm (half width, full width 2100 mm)
・ Atmosphere temperature: 30 ℃
・ Secondary cooling water temperature: 28 ℃
-Molten steel temperature: 1555 ° C
・ Thermal conductivity at the reference temperature: Determined based on the components of the target material ・ Liquid phase temperature and solid phase temperature determined from the above components: Determined by experiments and others ・ Conversion temperature φ-temperature relationship: Determined by experiments and others ・Heat content H-temperature relationship: determined by experiment, etc. Density ρ-temperature relationship: determined by experiment, etc. Example of mesh width direction division number width (n) = 66
Thickness (n) = 25

(Operation other)
FIG. 10 shows the thermometer installation position (measurement position) using only the secondary cooling calculation after taking in the operating conditions at the time of surface temperature measurement without correcting the heat flux distribution in the width direction according to the present embodiment. It is the figure which compared the model calculation temperature in FIG. In FIG. 10, the state of one side from the center of the width direction of the slab 5 is illustrated. The same applies to FIGS. 11 to 14 described later.
As shown in FIG. 10, the temperature distribution of the calculated temperature (estimated temperature) is flat in the slab width direction, and there is a difference between the measured surface temperature values. Then, the way of distribution in the width direction is also different. In such a situation, even if the final solidification position shape is predicted from the calculation result, there is no guarantee that it matches the actual situation.

An example of applying this embodiment to this is shown in FIG. 11, the width direction correction point as 20 mesh (n = 20), so that the error of the measured value and the calculated value after optimization calculation is reduced, modifying the magnification of the heat transfer coefficient in the width direction (d _i It is a figure which shows the example of the calculation result of the surface temperature when adjusting. In addition, FIG. 12 shows the correction magnification (value of the correction coefficient d _i ) of the heat transfer coefficient before and after correction at this time.

In the calculation, the temperature measurement by the model and the actually measured temperature average are calculated for each mesh and used for the calculation. As a result, by changing the correction factor of the heat transfer coefficient in the slab width direction as shown in FIG. 12, temperature calculation that matches the numerical calculation result is realized at a portion where the temperature measurement point is present. It can be seen that the optimization calculation can realize a calculation that steadily reduces the difference in surface temperature specified by the evaluation function.
FIG. 13 (Comparative Example) and FIG. 14 (Example) show the final solidification position (CE position) and shape in these two cases (see FIGS. 10 and 11). 13 and 14, the vertical axis indicates the distance in the slab longitudinal direction from the mold 2, and the horizontal axis indicates the solidification completion position at the slab width direction position.

In FIG. 13 (comparative example), since the temperature distribution in the width direction is based on a flat calculated temperature, the final solidified shape is flat with no irregularities except at the end. On the other hand, in the case where the heat transfer coefficient in the width direction is corrected using the actual surface temperature in the width direction in FIG. 14 (Example), the unevenness in the width direction can be expressed and the surface temperature distributions match. It is thought that the final coagulation state close to reality can be expressed. Thus, if the calculation result at the surface temperature measurement position matches the actual measurement value, it is expected to improve the estimation accuracy of the final solidification position and shape determined by the temperature state in the slab.
Thus, if the calculation result at the surface temperature measurement position matches the actual measurement value, the validity of the estimated value of the final solidification position / shape determined by the temperature state inside the slab is further improved.

As described above, the model surface temperature in the width direction at the measurement position by the thermometer 4b is made to match or approach the measured surface temperature by correcting the distribution of the heat transfer coefficient based on the measured surface temperature. As a result, it is possible to reflect the actual operation state more, and it is possible to improve the estimation accuracy of the final solidification position / shape.
Here, in the above-described embodiment, the heat flux distribution is corrected by adjusting the heat transfer coefficient. However, the width direction distribution of the heat flux may be corrected by adjusting other parameters.

In addition, based on the prediction result of the final solidification position / shape obtained above, the final solidification position and shape can be controlled by adjusting the secondary cooling condition, light pressure reduction condition, casting speed, and mold electromagnetic stirring strength. The efficiency and quality may be improved by controlling to approach the target shape.
Furthermore, in this embodiment, the shortest solidification completion position and the longest solidification completion position are obtained from the estimated final solidification shape in the slab width direction, and the difference between the shortest solidification completion position and the longest solidification completion position, that is, the distance between the two. Accordingly, at least one of the magnetic field control and the width-cutting control is performed so that the difference becomes smaller than the set length.

In addition, when the slab 5 is lightly reduced to further reduce the center segregation, the casting speed and the secondary cooling are performed so that the shortest solidification completion position is at the center or the outlet side of the light reduction zone 16 of the continuous casting machine. Adjust the amount of water, and further adjust the flow control of the molten steel in the mold by moving magnetic field and / or the width cutting amount to reduce the difference between the shortest solidification completion position and the longest solidification completion position. Control within the range of the light pressure lower belt 16.
As a result, according to the present invention, it is possible to manufacture the slab 5 while flattening the shape of the solidification completion position in the slab width direction, and it is possible to improve the center segregation and the productivity of the continuous casting machine. The following effects can be obtained.

(Modification)
In FIGS. 11 to 14 described above, and the value of the correction coefficient d _i of the heat transfer coefficient (correction factor) is changed uniformly for each zone of the plurality of cooling zones.
Specifically, the correction coefficient d _i is calculated based on the equation (20).
Correction coefficient update value = (model temperature-measured temperature) x gain + previous correction coefficient value (20)
Further, this may be expanded so as to be individually adjustable (setting can be changed) for each cooling zone in the longitudinal direction, as shown in Expression (21).
Correction coefficient update value for cooling zone n = (model temperature-measured temperature) x gain n + (correction coefficient previous value for cooling zone n)
(21)
Here, n indicates the number of the cooling zone.

In Expression (21), the gain n is changed depending on the cooling zone.
The gain n is, for example, a gain for a zone set as a reference as a reference gain, and in a zone where cooling is stronger than the zone set as the reference, the gain n is set to a value larger than the reference gain and set as a reference. In a zone where cooling is weaker than the zone, the gain n is set to a value smaller than the reference gain.
Thus, when adjusting for every cooling zone individually, even if there is a case where there is a cooling nonuniformity for every cooling zone, it becomes possible to obtain the prediction result of the final solidification position and shape with high accuracy.

Next, an individual adjustment example for each cooling zone of the present modification will be specifically described.
In this example, the case where the thermometer 4a is used is shown.
In the correction using the equation (20), as shown in Table 1, the gain n common to all the cooling zones is used.

  On the other hand, in the correction using the equation (21), as shown in Table 2, the gain n for each zone is adjusted. As an example, the gain values in Table 2 are as follows. In the zone 7a-8a, where the cooling is strong, the gain n is large because the occurrence of temperature unevenness due to cooling is large, and in the zone 9a-13a, where the cooling is weak, the temperature unevenness due to cooling. Therefore, the correction gain is set to be small. Further, in the zone 14a-15a after the thermometer installation position, the correction gain is set to 0 and correction by the thermometer is not performed.

FIG. 15 shows the result of estimating the final solidification position using the gain n and the same temperature measurement value of the thermometer 4a.
As shown in FIG. 15, even when the same thermometer value is used, the difference between the peaks and valleys of the final solidification shape becomes larger when individual gain n is used for each zone as shown in Table 2 based on the modification. ing. This is because the surface temperature is strongly corrected in a zone where the temperature is far from the thermometer and the cooling is strong. Thus, it can be seen that the degree of freedom of adjustment is improved as compared with the case of the equation (20). This makes it possible to make adjustments that are more practical.

(Third embodiment)
Next, a third embodiment will be described with reference to the drawings. In addition, the same code | symbol is attached | subjected and demonstrated to the structure similar to the said 2nd Embodiment.
The basic configuration of the present embodiment is the same as that of the second embodiment.
However, two or more measurement positions are set along the slab longitudinal direction, the surface temperature distribution in the slab width direction is measured at each measurement position, and the measurement is performed using the heat transfer model for each measurement position. Each time the correction of the heat flux distribution in the slab width direction of the heat flux is repeated and corrected so that the estimated temperature temperature and the measured temperature distribution in the slab width direction coincide with each other, the solidification state estimation unit body 20Ba The secondary cooling calculation is performed again.

In the present embodiment, the case where the measurement position is set to two places will be described, but the measurement position may be three or more.
In the present embodiment, each measurement position is divided as a boundary along the slab longitudinal direction, and when the measurement position is the first measurement position and the second measurement position from the upstream side, A measurement section up to the measurement position, a measurement section from the first measurement position to the second measurement position,... Are divided into a plurality of measurement sections based on the measurement position. Then, the heat flux distribution in the casting width direction of the heat transfer model is corrected for each measurement section, and the calculation using the model is performed again each time correction is performed.
At this time, in the second and subsequent measurement intervals, the heat flux distribution obtained in the immediately preceding measurement interval is used as the initial value.

The heat transfer coefficient correction process in the solidification state estimation unit 20B of the present embodiment will be described with reference to FIG.
Steps S10 to S50 and S60 in FIG. 16 perform the same processing as steps S10 to S50 and S60 in the first embodiment (FIG. 8). In step S30, the thermometer 4a is adopted, and the measurement position of the thermometer 4a is set as the temperature comparison position.
In the present embodiment, the correction coefficient d _i is changed uniformly in the slab longitudinal direction every time the thermometer is installed.

Also, steps S110 to S150 in FIG. 16 perform the same processing as steps S10 to S50 in the first embodiment (FIG. 8). In step S130, the thermometer 4b is employed, and the measurement position of the thermometer 4b is set as the temperature comparison position.
However, the correction coefficient d _i (i = 1 to n), which is the initial value of the heat flux distribution in the calculation in step S110, is the value corrected in steps S10 to S50.

Further, in the calculation in step S110, the correction coefficient d _i (i = 1 to n) adjusted in step S150 is reflected on the measurement section from the first measurement position to the second measurement position.
That is, in the calculation in step S110, in the range up to a first measurement position, the correction coefficient d _i using the value obtained in step S50 as the first measurement position and the second measurement section to the measurement position On the other hand, the correction coefficient d _i (i = n) adjusted in step S150 is used.
Other processes are the same as those in the second embodiment.

(Operation other)
The operation when the present embodiment is adopted up to the first measurement position (the position of the thermometer 4a) is the same as that of the first embodiment (see FIGS. 10 to 12).
FIG. 17 is an example of the slice cross-section temperature distribution at the measurement position of the thermometer 4a after correction based on the measurement position of the thermometer 4a by the processing of steps S10 to S50.
When the width-direction surface temperature at the measurement position of the thermometer 4b calculated based on the slice cross-section temperature distribution shown in FIG. 18 is compared with the actually measured temperature at the measurement position of the thermometer 4b, the result shown in FIG. Become. As shown in FIG. 18, there may be a slight deviation even when the temperature distribution in the width direction is corrected at the measurement position of the thermometer 4a.
To eliminate this deviation, similarly to the correction based on the measurement result of the aforementioned thermometer 4a, the magnification of the heat transfer coefficient in the width direction of the interval between the measurement positions of the thermometers 4a-4b (the value of the correction coefficient d _i) Is corrected based on the measurement result of the thermometer 4b, the calculation result of the surface temperature as shown in FIG. 19 can be obtained at the measurement position of the thermometer 4b.

Next, how the position and shape of the final coagulation change between the case where no correction is made by the measurement value by the thermometer and the case where the correction is made based on this embodiment by the measurement value of the two thermometers 4a and 4b. As a result, the results shown in FIG. 20 (comparative example) and FIG. 21 (example) were obtained.
20 and 21, the vertical axis represents the distance in the longitudinal direction from the mold 2, and the horizontal axis represents the position in the width direction, indicating the solidification completion position. Here, by performing model temperature correction twice using two thermometer values, the calculated temperature rises, and as a result, the final solidification position also extends toward the machine end. As described above, if the calculation results at the two surface temperature measurement positions and the actual measurement values match, it can be expected to ensure the accuracy of the estimated value of the final solidification position and shape determined by the temperature state in the slab. Moreover, further improvement in accuracy can be expected by installing three or more thermometers and applying the same method.

  That is, when an unsteady operation such as a change in casting conditions occurs, the cooling conditions change dynamically, so that it is difficult to accurately represent the temperature distribution change of the slab 5 due to the cooling history with a model. When such an unsteady operation occurs, there is a high possibility that a deviation occurs between the model and the actual slab temperature distribution. By installing a width direction thermometer in the middle and using the value, the deviation of the model can be corrected, but if the cooling condition change is repeated multiple times, the value of the thermometer at one location in the slab longitudinal direction In the case of this correction, the deviation due to the cooling condition downstream from the measurement position by the thermometer cannot be corrected, and there is a possibility that the estimation accuracy of the final solidification position / shape is lowered accordingly. Moreover, even if a thermometer is installed at one location downstream from the final solidification position, there is a possibility that a deviation due to a change in cooling conditions generated upstream from the thermometer position cannot be corrected sufficiently.

On the other hand, in the present embodiment, the above disadvantages can be reduced or eliminated.
From the above consideration, when the secondary cooling control is different for each of a plurality of zones, it is preferable to perform the above correction by installing a thermometer at the boundary value position.

  In addition, as described above, the final solidification position and shape can be observed with higher accuracy compared to the conventional calculation, so various casting conditions (cooling conditions, light rolling conditions, casting speed, mold electromagnetic stirring strength, etc.) were changed by simulation. It is possible to grasp how the shape changes. This makes it possible to define the slab manufacturing conditions with a flat final solidification shape and little center segregation. For example, according to the final solidification position and shape calculated based on the surface temperature, the final solidification position and shape can be changed by changing the secondary cooling conditions such as changing the spray flow rate installed in the width direction for each spray. The efficiency and quality may be improved by controlling to approach a preset target position and target shape (such as flattening of the final solidified shape).

Further, in the present embodiment, as in the first embodiment, the shortest solidification completion position and the longest solidification completion position are obtained from the estimated final solidification shape in the slab width direction, and the shortest solidification completion position and the longest solidification completion position are determined. In accordance with the difference, that is, the distance between the two, at least one of the magnetic field control and the width cutting control is performed so that the difference becomes smaller than the set length.
In addition, when the slab 5 is lightly reduced to further reduce the center segregation, the casting speed and the secondary cooling are performed so that the shortest solidification completion position is at the center or the outlet side of the light reduction zone 16 of the continuous casting machine. Adjust the amount of water, and further adjust the flow control of the molten steel in the mold by moving magnetic field and / or the width cutting amount to reduce the difference between the shortest solidification completion position and the longest solidification completion position. Control within the range of the light pressure lower belt 16.

As a result, according to the present invention, it is possible to manufacture the slab 5 while flattening the shape of the solidification completion position in the slab width direction, and it is possible to improve the center segregation and the productivity of the continuous casting machine. The following effects can be obtained.
Other configurations and the like are the same as those in the second embodiment.

2 Mold 2a Mold long side 2b Mold short side 3 Immersion nozzle 4, 4a, 4b Thermometer 5 Cast piece 20 Continuous casting control unit 20A Next cooling control unit 20B Solidification state estimation unit 20Ba Solidification state estimation unit body 20Bb Heat flux distribution correction unit 20C moving magnetic field control section 20D 2 primary cooling width cutting control unit 40 moves the magnetic field generating device 60 spray nozzles _{d i} correction coefficient h heat transfer coefficient

Claims (6)

Estimate and calculate the temperature distribution of multiple slab cross sections from the upstream side to the downstream side in the casting direction using the operating conditions of a continuous casting machine equipped with a light reduction belt for lightly reducing the slab. A method for producing a continuous cast slab in which molten steel is continuously cast by controlling the solidification completion position of the slab within the range of the light pressure lowering zone while predicting the final solidification position and shape from the calculation,
The surface temperature distribution in the slab width direction is measured, and the error between the measured surface temperature measured value and the estimated surface temperature value at the surface temperature distribution measurement position in the estimated calculation result of the temperature distribution of the slab cross section is minimized. By correcting the calculated value of the temperature distribution of the slab cross section and re-estimating, the final solidification position and shape prediction accuracy can be improved to predict the final solidification shape,
Based on the predicted shape of the final solidification, the control generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold for the molten steel discharge flow from the immersion nozzle. By adjusting the power, the width direction shape of the solidification completion position of the slab is controlled so that the difference between the solidification completion position on the most upstream side and the solidification completion position on the most downstream side is equal to or less than a preset length. ,
In correcting and recalculating the calculated temperature distribution of the slab cross section,
Determine the position upstream of the surface temperature distribution measurement position and upstream of the final solidification position, and correct the calculated value of the temperature distribution of the slab cross section at the determined upstream position so that the error is minimized , A method for producing a continuous cast slab characterized by performing re-estimation calculation using a calculated value of a temperature distribution of a cross section of the slab at the corrected upstream position. Estimate and calculate the temperature distribution of multiple slab cross sections from the upstream side to the downstream side in the casting direction using the operating conditions of a continuous casting machine equipped with a light reduction belt for lightly reducing the slab. A method for producing a continuous cast slab in which molten steel is continuously cast by controlling the solidification completion position of the slab within the range of the light pressure lowering zone while predicting the final solidification position and shape from the calculation,
The surface temperature distribution in the slab width direction is measured, and the error between the measured surface temperature measured value and the estimated surface temperature value at the surface temperature distribution measurement position in the estimated calculation result of the temperature distribution of the slab cross section is minimized. By correcting the calculated value of the temperature distribution of the slab cross section and re-estimating, the final solidification position and shape prediction accuracy can be improved to predict the final solidification shape,
Based on the predicted shape of final solidification, the braking force generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold for the molten steel discharge flow from the immersion nozzle The difference between the most upstream solidification completion position and the most downstream solidification completion position is equal to or less than a preset set length. The width direction shape of the solidification completion position of the slab is controlled so that
In correcting and recalculating the calculated temperature distribution of the slab cross section,
Determine the position upstream of the surface temperature distribution measurement position and upstream of the final solidification position, and correct the calculated value of the temperature distribution of the slab cross section at the determined upstream position so that the error is minimized , A method for producing a continuous cast slab characterized by performing re-estimation calculation using a calculated value of a temperature distribution of a cross section of the slab at the corrected upstream position. Using a continuous casting machine equipped with a light reduction belt for lightly reducing the slab, the molten steel injected into the mold is solidified by performing secondary cooling while being drawn, and the solidification completion position of the slab is reduced lightly. A method for producing a continuous cast slab in which molten steel is continuously cast within a range of a strip,
By calculating the temperature distribution of a plurality of slab cross sections from the upstream side to the downstream side in the casting direction by a heat transfer model using a heat flux based on the cooling condition of at least the secondary cooling, the final solidification of the slab While estimating the position and shape, measure the temperature distribution in the slab width direction at a preset measurement position in the slab longitudinal direction,
The slab cross section is corrected by correcting the heat flux distribution in the slab width direction of the slab width direction so that the estimated temperature calculated by the heat transfer model at the measurement position matches the measured temperature distribution in the slab width direction. By recalculating the temperature distribution of the
Based on the estimated final solidification shape, the braking force generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold for the molten steel discharge flow from the immersion nozzle Adjusting the width direction shape of the solidification completion position of the slab so that the difference between the solidification completion position on the most upstream side and the solidification completion position on the most downstream side is equal to or less than a preset set length,
The secondary cooling is performed by a plurality of cooling zones,
A heat flux distribution correction coefficient di (i: width direction correction position) for correcting the magnification of the heat flux distribution is set individually for each of the cooling zones ,
The correction coefficient di is a coefficient by which the heat transfer coefficient of the heat flux is multiplied. By multiplying the correction coefficient di, the magnification of the heat flux is corrected, and the width direction correction position i is set to 2 or more. A method for producing a continuous cast slab, wherein the magnification of the bundle distribution is corrected . Using a continuous casting machine equipped with a light reduction belt for lightly reducing the slab, the molten steel injected into the mold is solidified by performing secondary cooling while being drawn, and the solidification completion position of the slab is reduced lightly. A method for producing a continuous cast slab in which molten steel is continuously cast within a range of a strip,
By calculating the temperature distribution of a plurality of slab cross sections from the upstream side to the downstream side in the casting direction by a heat transfer model using a heat flux based on the cooling condition of at least the secondary cooling, the final solidification of the slab While estimating the position and shape, measure the temperature distribution in the slab width direction at a preset measurement position in the slab longitudinal direction,
The slab cross section is corrected by correcting the heat flux distribution in the slab width direction of the slab width direction so that the estimated temperature calculated by the heat transfer model at the measurement position matches the measured temperature distribution in the slab width direction. By recalculating the temperature distribution of the
Based on the estimated final solidification shape, the braking force generated by moving the magnetic field in the horizontal direction from the short side of the mold toward the immersion nozzle along the long side of the mold with respect to the molten steel discharge flow from the immersion nozzle. After adjusting at least one of the adjustment and the width adjustment amount of the secondary cooling, the difference between the solidification completion position on the most upstream side and the solidification completion position on the most downstream side is less than or equal to a preset set length. Control the width direction shape of the solidification completion position of the slab so that
The secondary cooling is performed by a plurality of cooling zones,
A heat flux distribution correction coefficient di (i: width direction correction position) for correcting the magnification of the heat flux distribution is set individually for each of the cooling zones ,
The correction coefficient di is a coefficient by which the heat transfer coefficient of the heat flux is multiplied. By multiplying the correction coefficient di, the magnification of the heat flux is corrected, and the width direction correction position i is set to 2 or more. A method for producing a continuous cast slab, wherein the magnification of the bundle distribution is corrected .   Two or more measurement positions are set along the slab longitudinal direction, the temperature distribution in the slab width direction is measured at each measurement position, and the estimated temperature estimated by the heat transfer model for each measurement position. 5. The continuous casting according to claim 3, wherein the heat flux distribution in the slab width direction of the heat flux is corrected so that the measured temperature distribution in the slab width direction matches. A method for producing a slab.   The method for manufacturing a continuous cast slab according to any one of claims 1 to 5, wherein the preset length is 2 m.

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