JP5906992B2 - Method for estimating solidification state of slab and continuous casting method - Google Patents

Description

  The present invention relates to a method for predicting final solidification of continuous casting, a method for estimating a solidification state of a slab, and a continuous casting method, and in particular, accurately estimates the final solidification position and final solidification shape of a slab in a continuous casting machine. It relates to technology that makes it possible.

In the continuous casting process, 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. Therefore, there is a demand for a technique for constantly grasping the solidified shape and controlling based on the solidified shape for preventing quality abnormality and quality control.
In order to deal with the above, various methods have been proposed for online estimation calculation of the solidification state of a slab in continuous casting. For example, Patent Document 1 describes the following calculation method. That is, a calculation surface (cross section) perpendicular to the casting direction (the slab longitudinal direction) is generated each time casting of a predetermined length proceeds in the strand during continuous casting. Then, each generated calculation surface passes through a plurality of zones set continuously in the casting direction, and when the next zone entry boundary is reached, 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. In the above calculation means for simulating the solidification state, the surface temperature and surface temperature distribution of the slab during casting are important calculation data, and it is desirable to continuously measure the temperature distribution of the slab. It is rare.
In general, there are two methods for measuring temperature, a contact method such as a thermocouple and a non-contact method such as a radiation thermometer. Of these, the contact type is not practical when the object moves like a slab, and a method of using a radiation thermometer can be considered to continuously measure the slab surface.

  As a typical example of a radiation thermometer, there is a method of installing a thermography so that a slab can be observed. Thermography can measure a two-dimensional temperature distribution easily and continuously. However, in the machine of the continuous casting process, there is water that accumulates on the slab surface as cooling water for cooling the slab. In addition, there is what is called mist or water smoke in which the cooling water evaporates due to the heat of the slab and once becomes water vapor, and is cooled again to form small water droplets in the air. If this water paste or mist is present in the optical path of the radiation temperature measurement, infrared absorption or scattering occurs, resulting in a measurement error.

  As a method for measuring the surface temperature without being influenced by this, for example, there is a method disclosed in Patent Document 3. In this method, a water column as an optical waveguide is formed between the temperature-measured steel material and the radiation thermometer, and the radiation light from the surface of the temperature-measured steel material is detected by the radiation thermometer via the water column, Measure the surface temperature of the hot steel material. However, since this method is a point measurement, information on the temperature distribution cannot be obtained.

  As a method for measuring the distribution of the surface temperature, for example, there is a method disclosed in Patent Document 4. In this method, a radiation thermometer called a scanning radiation thermometer is scanned along the stage, and a mist is collected by bringing a lens for collecting infrared light from the slab close to the slab through a fiber. The measurement is performed by blowing off the water by injecting gas onto the surface of the slab. However, since this method is a scanning method, if the scanning speed of the radiation thermometer is slow relative to the moving speed of the slab, measurement may be lost. In order to increase the scanning speed, the equipment must be scaled up. Further, since the sensor is brought close to the slab, there is a possibility that the sensor contacts the slab and breaks.

JP 2002-178117 A Japanese Patent Laid-Open No. 10-291060 JP 2008-164626 A JP 2012-071330 A

  For the purpose of estimating the final solidification position and solidification shape, various methods such as ultrasonic measurement methods for measuring the internal temperature of the slab during continuous casting have been proposed, but because the operating environment is hot and humid, There is still nothing that can be used continuously and at low cost during operation. 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. In Patent Document 2, a specific temperature measurement method is not clearly described.

In the secondary cooling control, the design and setting are performed so that the final solidification shape is flat at the solidification position, that is, the final solidification position in the longitudinal direction is uniform in the width direction without unevenness. However, in actual operation, unevenness in the width direction and spray generated in the mold, that is, uneven cooling in the longitudinal direction and width direction occur due to the influence of flowing water between the rolls, and the final solidification position and shape change. 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 in view of such circumstances, and accurately estimates the final solidification position and final solidification shape of a slab in a continuous casting machine (hereinafter also referred to as a continuous casting machine). It is an object of the present invention to provide a method for predicting the final solidification of a continuous casting, a method for estimating a solidification state of a slab, and a continuous casting method.

  In order to solve the above-described problem, a continuous casting final solidification prediction method according to an aspect of the present invention is a continuous casting in which a solidification state is estimated and calculated using operating conditions of a continuous casting machine, and a final solidification position and shape are predicted. In the final solidification prediction method, 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 at the surface temperature distribution measurement position in the solidification state estimation calculation result is The prediction value of the final solidification position and shape is improved by correcting the calculated value of the slab cross-section temperature distribution and re-estimating the calculation so that the surface temperature distribution is minimized. The surface to be measured is imaged, the surface temperature distribution of the surface to be measured is obtained based on the luminance at each surface position of the imaged image, and the image used for obtaining the surface temperature distribution is a light receiving unit of the imaging device. When Serial imaging angle between the normal of the line and 該被 measurement plane connecting the measurement surface is 40 ° or more, characterized in that it is an image of an imaging range of the 65 ° or less.

Further, in the above-described method for predicting the final solidification of continuous casting, the position calculated upstream of the surface temperature distribution measurement position and upstream of the final solidification position is used for correcting and re-estimating the calculation value of the slab cross-section temperature distribution. The temperature distribution of the cross section at the determined upstream position may be corrected using an optimization method, and reestimation calculation may be performed using the temperature distribution of the cross section at the corrected upstream position.
In the method for predicting the final solidification of the continuous casting, the imaging angle at the near end of the measurement surface closest to the imaging device is 40 ° or more, and the measurement surface of the measurement surface farthest from the imaging device is used. The imaging angle at the far end may be 65 ° or less.

  The solidification state estimation method for a slab according to another aspect of the present invention is the above-described continuous casting in which the molten steel injected into the mold is solidified by performing secondary cooling while being drawn to continuously produce the slab. In the solidification state estimation method for estimating a solidification state of a slab, the solidification state of the slab is estimated by a heat transfer model using a heat flux based on at least the cooling condition of the secondary cooling, and in the slab longitudinal direction in advance. The temperature distribution in the slab width direction at the set measurement position is measured, and the heat flow is measured so that the estimated temperature estimated by the heat transfer model at the measurement position matches the measured temperature distribution in the slab width direction. By correcting the heat flux distribution in the slab width direction of the bundle, the output of the heat transfer model is corrected, and the temperature distribution is measured by imaging the surface to be measured of the slab with an imaging device, and capturing the image. Each table The temperature distribution of the surface to be measured is obtained based on the luminance at the position, and the image used when obtaining the temperature distribution is a line connecting the light receiving unit of the imaging device and the surface to be measured and the method of the surface to be measured. It is an image of an imaging range in which an imaging angle formed by a line is 40 ° or more and 65 ° or less.

Further, in the solidification state estimation method of the slab, two or more measurement positions are set along the slab longitudinal direction, and the temperature distribution in the slab width direction is measured at each measurement position, and each measurement is performed. For each position, the correction of the heat flux distribution in the slab width direction of the heat flux is repeated so that the estimated temperature estimated by the heat transfer model matches the measured temperature distribution in the slab width direction. It is good.
In the above method for estimating the solidification state of a slab, the secondary cooling is performed by a plurality of cooling zones, and a correction coefficient of the heat flux distribution for correcting the heat flux distribution is individually set for each cooling zone. It is good also as a feature to set to.

Further, in the solidification state estimation method of the slab, the imaging angle at the near end of the measurement surface closest to the imaging device is 40 ° or more, and the measurement surface farthest from the imaging device The imaging angle at the far end may be 65 ° or less.
In the solidification state estimation method for the slab, the temperature distribution may be measured by imaging the measurement target surface using at least two imaging devices as the imaging device.

Further, in the solidification state estimation method for the slab, two imaging devices are arranged on both sides in the slab width direction, the same imaged surface is imaged by the two imaging devices, and each imaging device The temperature distribution of the surface to be measured may be obtained based on the luminance of each captured image.
Further, in the solidification state estimation method of the slab, the imaging optical path from the measurement surface to the imaging device passes through a gap between segments of a continuous casting machine, and the stroke of 80% or more of the optical path is It may be characterized by passing below the upper end of the segment.

Further, in the solidification state estimation method of the slab, when measuring the temperature distribution, the surface to be measured of the slab is imaged in a wavelength region of 0.85 μm or more and 1.0 μm or less. This may be a feature.
Further, in the solidification state estimation method of the slab, when measuring the temperature distribution, while blowing a gas of 30 Nm ³ / min or more from above the measurement surface of the slab toward the measurement surface, The measurement target surface may be imaged.

Moreover, in the solidification state estimation method of the above slab, when the temperature distribution is measured, while blowing a gas of 30 Nm ³ / min or more to a pipe through which a cooling medium for cooling the segments of the continuous casting machine is blown, The measurement target surface may be imaged.
A continuous casting method according to still another aspect of the present invention is based on the solidification state estimated by the above-described solidification state estimation method of a slab, and includes at least one of secondary cooling conditions, light reduction conditions, casting speed, and mold electromagnetic stirring strength. It is characterized by operating one.

According to one aspect of the present invention, the surface to be measured of the slab is imaged by an imaging device, and the temperature distribution of the surface to be measured is obtained based on the luminance at each surface position of the captured image. The image used for obtaining the temperature distribution has an imaging angle of 40 ° or more and 65 ° or less formed by a line connecting the light receiving unit of the imaging device and the measurement surface and a normal line of the measurement surface. It is an image of an imaging range.
This eliminates the need to scan the slab with an image pickup device and does not require a large-scale traverse device, and thus it is possible to measure the temperature distribution of the slab from a remote location by a simple method. Moreover, it is possible to accurately estimate the final solidification position and final solidification shape of the slab by correcting the model parameters using the measured temperature in the slab width direction measured by this method.

  In addition, by performing production and quality control using these highly accurate positions and shapes, it is possible to correct casting conditions that do not cause quality abnormalities such as segregation or end-of-machine flaws. At this time, according to the fourth aspect of the present invention, even if an unsteady operation such as a change in casting conditions occurs, the final solidification position / shape can be estimated with higher accuracy.

It is a conceptual diagram which shows the structural example of the continuous casting machine which concerns on 1st Embodiment of this invention. 3 is a side view showing a configuration example of a thermometer 4. FIG. It is the top view which looked at the same form as FIG. 2 from the top. It is a conceptual diagram which shows the method of the signal processing which concerns on 1st Embodiment of this invention. It is a figure which shows the relationship between temperature and a brightness | luminance. It is a figure which shows the temperature measurement method which concerns on Example 1. FIG. It is a figure which shows the temperature change of the same location in the width direction of slab. It is a side view which shows the temperature measurement method when the result of FIG.6 (b) is obtained. It is a side view which shows the temperature measurement method when the result of FIG.6 (c) is obtained. It is a top view which shows the temperature measurement method when the result of FIG.6 (c) is obtained. 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 of this invention. It is a flowchart explaining the correction | amendment process in the coagulation | solidification state estimation part which concerns on 2nd Embodiment of 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 of this invention, and a measured value. It is a figure which shows the example of correction | amendment of the correction coefficient di. 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 of this invention. When the correction coefficient of the heat transfer coefficient is provided for each zone according to the second embodiment of the present invention and when the correction coefficient of the heat transfer coefficient common to all the zones is provided, the final temperature in use in the same width direction is used. It is a figure which shows the difference in a solidification position and a shape. It is a flowchart explaining the correction process in the coagulation state estimation part which concerns on 3rd Embodiment of 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 of 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 of this invention. It is a figure which shows the omnidirectional emissivity of a non-metal surface and an oxide film metal surface.

Embodiments of the present invention will be described with reference to the drawings. Note that, in each drawing described below, parts having the same configuration are denoted by the same reference numerals, and repeated description thereof is omitted.
<First Embodiment>
(Configuration of continuous casting machine)
FIG. 1 is a conceptual diagram showing a configuration example of a vertical bending type continuous casting machine according to a first embodiment of the present invention. As shown in FIG. 1, 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 a cast piece (for example, slab) 5 is drawn along the support rolls 6 at a predetermined drawing speed. Reference numerals 7 to 13 denote divided cooling zones, which constitute secondary cooling zones.

  In each cooling zone, a plurality of cooling nozzles (not shown) such as spray or air mist spray nozzles are arranged, and the secondary cooling water is sprayed from the respective cooling nozzles onto the surface of the slab 5, thereby achieving the target. Secondary cooling of the slab 5 is performed. In FIG. 1, 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. 1 illustrates a case where the cooling zone has a total of 7 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.

Moreover, although there are cases where a rolling roll (light rolling roll) for lightly rolling down the slab 5 is installed depending on the continuous casting machine, the present invention is not affected by the presence or absence of light rolling.
Further, this continuous casting machine is provided with a temperature measuring device 4 that measures the surface temperature distribution in the width direction of the slab 5 at a predetermined location (for example, the machine end) in the longitudinal direction of the slab. The temperature measuring device 4 includes an imaging device such as a CCD (Charge Coupled Device) image sensor or a CMOS (Complementary Metal Oxide Semiconductor) image sensor.

(Temperature measurement method)
FIG. 2 is a side view showing a configuration example of the temperature measuring device 4. As shown in FIG. 2, support rolls 6 are installed on the upper surface side and the lower surface side of each segment (for example, the same as each cooling zone). The slab 5 is disposed in a gap between the support rolls 6 on the upper surface side and the lower surface side, and proceeds in the normal direction of the paper surface.

  In FIG. 2, as the temperature measuring device 4, two imaging devices (that is, cameras) 32 a and 32 b and tripods 33 a and 33 b that support the imaging devices 32 a and 32 b are illustrated. The cameras 32a and 32b are disposed on the passages 34a and 34b located on both sides of the slab 5 via tripods 33a and 33b, and are located at substantially the same distance with the slab 5 interposed therebetween. It is installed so as to image (photograph) from the substantially same angle with respect to the upper surface (that is, the surface to be measured) 5a.

  The reason for arranging two cameras with the slab 5 interposed therebetween is to reduce the influence of mist. For example, even when the mist blocks the optical path from one camera 32a to the slab 5, the camera 32b accurately captures the slab 5 if the optical path from the other camera 32b to the slab 5 is not affected. be able to. According to the knowledge of the present inventor, mist tends to be generated on one side in the slab width direction, particularly under the influence of the external environment (wind and temperature). For this reason, it is possible to effectively reduce the influence of mist by arranging two cameras with the slab 5 interposed therebetween.

Further, when measuring the temperature of the measurement surface of the slab, the temperature of the measurement surface can be measured by combining images obtained from the two cameras 32a and 32b. As a method of combining, for example, a method of determining the temperature of the measurement target surface based on the luminance information having the higher luminance value for two pieces of luminance information of the same measurement target image simultaneously captured by the cameras 32a and 32b. It is done.
In the camera 32a, an imaging angle formed by a line connecting the light receiving unit of the camera 32a and the measurement target surface 5a and a normal line of the measurement target surface 5a is 0 ° or more and 65 ° or less (40 ° to 65 °). The imaging range which becomes is imaged. Similarly, the camera 32b images an imaging range in which an imaging angle formed by a line connecting the light receiving unit of the camera 32b and the measurement target surface 5a and a normal line of the measurement target surface 5a is 40 ° to 65 °.

  In FIG. 2, the angle formed by the imaging direction of the camera 32a and the normal direction of the measurement target surface 5a of the slab 5 (that is, the direction along the normal line) is the slab end on the near side as viewed from the camera 32a. It is set to be 40 ° and 65 ° at the end of the cast slab on the back side. Similarly, the angle formed by the imaging direction of the camera 32b and the normal direction of the surface 5a to be measured of the slab 5 is 40 ° at the slab end on the front side as viewed from the camera 32b, and 65 at the slab end on the back side. It is set to be °.

  That is, when viewed from the cameras 32a and 32b, the imaging angle at the near end of the closest measured surface 5a is θ1. The imaging angle at the far end of the farthest measurement target surface 5a when viewed from the cameras 32a and 32b is θ2. The imaging angles θ1 and θ2 are set within a range of 40 ° to 65 ° on condition that θ1 <θ2. In FIG. 2, θ1 is set to 40 °, for example, and θ2 is set to 65 °, for example.

  In addition, said imaging angle 40 degrees-65 degrees is the range which this inventor discovered through experiment etc. That is, there is a problem that the emissivity decreases when the angle formed by the normal direction of the surface to be measured of the slab and the imaging direction of the camera is increased. This is because the influence of the surface roughness of the slab is reduced and the reflectance is increased when the above angle is increased. It is known that an object that does not transmit light such as a cast slab has a relationship of reflectance + emissivity = 1, so that the reflectivity increases and the emissivity decreases as the angle increases.

  FIG. 31 is a diagram showing the omnidirectional emissivity of a non-metal surface and an oxide-coated metal surface (from Heat Transfer Engineering (Science and Engineering), Kaneyasu Nishikawa, Masanobu Fujita, page 298). As shown in FIG. 31, in a normal substance, the emissivity is in a certain range from 0 ° to about 50 ° to 60 °. However, as a result of experiments, the present inventors found that the slab may be regarded as the same emissivity up to 65 °. The above imaging angles of 40 ° to 65 ° are based on such knowledge of the present inventors.

Further, as shown in FIG. 2, when the distance between the light receiving portions of the cameras 32a and 32b (for example, the lens closest to the slab 5) and the measured surface 5a of the slab 5 is h1, h1 Is, for example, 1.8 m. When the camera 32a, the distance between the upper end of the light receiving portion and the segment 35a and 32b and h2, h 2 is 0.3m, for example.
FIG. 3 is a plan view of the same form as FIG. 2 as seen from above. The cameras 32a and 32b are installed in the gap between the two segments 35a and 35b, and image the slab 5 from between the segments. As described above, the height h1 of the cameras 32a and 32b from the measured surface 5a is set to 1.8 m, for example, and the height h2 from the upper end of the segment is set to 0.3 m, for example. At this time, 83% of the optical path when the camera 32a, 32b to image the slab 5 (= (1.8-0.3) /1.8 × 100), and below the segment upper i.e. above about 80% It has become.

  Thus, in this embodiment, it is preferable that about 80% or more of each optical path of the cameras 32a and 32b is below the upper end of the segment. The reason is as follows. That is, the temperature between the segments is high, and the superheated steam is not easily misted (white smoke). Therefore, it is desirable that there are many segments in the optical path length between the camera and the slab surface. On the other hand, in order to protect the camera, it is not desirable to leave the camera exposed to a hot and humid environment, so it is necessary to prevent the vicinity of the camera from entering the segment. For these reasons, it is preferable to install the cameras 32a and 32b so that a length of 80% or more of the optical path length is lower than the segment height.

Moreover, when measuring said temperature distribution, it is preferable to image the to-be-measured surface 5a of the slab 5 in a wavelength region of 0.85 μm or more and 1.0 μm or less, and a wavelength of 0.9 μm in the wavelength region. It is more preferable to take an image. The reason is as follows.
That is, there are a plurality of wavelength bands called “atmosphere windows” that are not easily absorbed by water vapor, which is a measurement disturbance, with minimums of 0.9 μm, 3.9 μm, and 10 μm, respectively. Among these zones, the zone near 0.9 μm is the strongest against water glue in which liquid phase water is accumulated on the slab. This is because infrared absorption is caused by a large amount of water (liquid phase), and the absorption spectrum value of water (liquid phase → water) is the smallest in the band near 0.9 μm.

  FIG. 4 is a conceptual diagram showing a signal processing method according to the first embodiment of the present invention. As shown in FIG. 4A, the cameras 32a and 32b simultaneously image the same measured surface 5a of the slab 5 through the gaps between the segments. And the brightness | luminance on the straight line in alignment with the slab width direction of the to-be-measured surface 5a is extracted from each image which the cameras 32a and 32b imaged. For example, for the luminance information at each surface position of each image captured by the cameras 32a and 32b, the luminance information with the higher luminance value is extracted as the luminance information at each surface position.

Since the images are taken continuously, as shown in FIG. 4B, the extracted luminance information in the slab width direction is arranged in the time axis direction. Since the slab 5 flows along the slab longitudinal direction orthogonal to the slab width direction in plan view, the luminance information on the flow direction of the slab 5 (that is, the direction parallel to the slab longitudinal direction) is obtained by this processing. Can be obtained.
That is, the original imaged image shows only a small part between the segments in the flow direction of the slab 5, but the luminance information of the entire length of the slab 5 can be obtained by this processing. For example, a relationship between temperature and luminance is measured in advance using a black body furnace, and a graph representing the relationship between temperature and luminance is created based on the result of the preliminary measurement. An example of the graph created in this way is shown in FIG. Here, the relationship between the luminance X and the temperature T can be simply expressed as in Expression (1) with A and B as constants.

Based on this equation (1), the luminance information of the full width of the slab 5 obtained in FIG. 4 is converted into temperature information, thereby obtaining the temperature of the full width of the slab 5 (that is, actually measuring). Can do.
Thus, according to the temperature measurement method according to the present embodiment, the surface to be measured 5a of the slab 5 is imaged by the cameras 32a and 32b, and the surface to be measured 5a is measured based on the luminance at each surface position of the captured image. Obtain the surface temperature distribution. The image used when calculating the surface temperature distribution is such that the imaging angle formed by the line connecting the light receiving portions of the cameras 32a and 32b and the measured surface 5a and the normal line of the measured surface 5a is 40 ° or more and 65 ° or less. It is an image of the imaging range which becomes. This eliminates the need to scan the slab 5 with an image pickup device and does not require a large-scale traverse device, so that the temperature distribution of the slab 5 can be measured remotely by a simple method. .

(Example 1)
The above-described temperature measurement method will be described in more detail with reference to Example 1 as a specific example.
FIG. 6 is a diagram illustrating a temperature measurement method according to the first embodiment of the present invention.
FIG. 6A is an example in which the temperature is measured by the method described in the embodiment. FIG. 7 is a graph showing the temperature change at the same location in the width direction of the slab 5 of FIG. 6 (a) and FIGS. 6 (b) and 6 (c) described later. That is, FIG. 7 is a diagram showing the temperatures along the broken lines in FIGS. 6A, 6B, and 6C. 6A, 6B, and 6C are not measured at the same timing, and there is actually a difference in the slab temperature. For this reason, in FIG. 7, each temperature of FIG. 6 (a), (b), (c) does not correspond.

  In FIG. 6A and the corresponding FIG. 7, there are places where the temperature is lowered over the entire width in some places of the slab 5. This coincides with the timing at which mist is generated. The infrared rays are scattered by the mist, the brightness of the image is lowered, and the temperature is lowered and displayed. Thus, although the part where temperature is not measured in part is seen, it can measure over the whole range.

  The present inventors evaluated the generation | occurrence | production condition of the mist which inhibits this measurement. As a result, it was confirmed that a large amount of mist was generated around the pipes for cooling water (ie, water cooling pipes) arranged above the segments to cool the segments, and a part of them was flowing between the segments. . Mist is a very small drop of water in the air as water vapor is cooled or saturated. It is similar to clouds and fog. The reason why this mist is often generated in the vicinity of the pipe for cooling water in the segment is considered as follows.

  First, the cooling water for cooling the slab 5 is evaporated by the heat of the slab 5. At this time, since water vapor is present near the slab, it is very hot due to the heat of the slab 5. This water vapor moves upward between the segments because of its high temperature. Since it is a narrow space between the segments, it is kept at a relatively high temperature, so that the state of water vapor is maintained. When this air escapes above the segment, the temperature is lowered and the mist is changed. In particular, it is considered that the vicinity of the pipe for cooling water disposed above the segment is likely to be misted because the temperature is lower than that of the periphery.

As described above, by making the optical path above the segment 20% or less of the whole, it is possible to realize measurement that is hardly affected by mist. However, as seen in FIG. 6A, when a mist is generated above the segment, this mist flows into the segment and hinders measurement.
Therefore, the present inventor conducted temperature measurement experiments while supplying dry air (for example, the same temperature as room temperature) to the cooling water pipe disposed above the segment by a blower. FIG. 6B shows the result of this experiment. FIG. 8 is a side view showing a temperature measurement method when the result of FIG. 6B is obtained.

  As shown in FIG. 8, pipes 36a and 36b for flowing a cooling medium for cooling the segment are arranged above both sides of the segment. These pipes 36a and 36b are water-cooled tubes through which, for example, cooling water flows as a cooling medium. These pipes 36a and 36b cool the segment located immediately below the pipes 36a and 36b or other segments adjacent to the segments.

  Also, blowers 37a and 37b are respectively disposed on the passages 34a and 34b which are obliquely above both sides of the segment and located outside the pipes 36a and 36b. For example, the blower 37a is fixed on the passage 34a, and the direction of the air blowing is directed to the pipe 36a. Further, when viewed from the segment, the blower 37a is disposed outside the camera 32a. This is to prevent the blower 37a from entering the field of view of the camera 32a. Similarly, the blower 37b is fixed on the passage 34a, and the direction of the air blowing is directed to the pipe 36b. Further, when viewed from the segment, the blower 37b is disposed outside the camera 32b.

In FIG. 8, while the air dried toward the cooling pipes 36a and 36b is supplied by the blowers 37a and 37b, the measurement surface 5a of the slab 5 is imaged by the cameras 32a and 32b. In this way, the dried air is supplied to the pipes 36a and 36b so that air containing a large amount of water vapor from the vicinity of the slab 5 does not flow into the vicinity of the pipes 36a and 36b. As a result, as can be seen from FIGS. 6B and 7, it was possible to measure the temperature while reducing the influence of the mist seen in FIG. In addition, the present inventor has confirmed that the influence of mist can be sufficiently removed by setting the air supply amount (air volume) by the blowers 37a and 37b to 30 Nm ³ / min or more, respectively.
In FIG. 6A, a temperature decrease in a very narrow range is partially observed. This is consistent with the position of the water glue, which is considered to be the effect of heat absorption by the water glue. According to the calculation that takes the maximum value in the flow direction shown in FIG. 4, the temperature before and after the water can be taken and the influence of the water is reduced. However, some influence remains.

Therefore, the present inventor, in addition to supplying the dried air to the pipes 36a and 36b for cooling the segments with the blowers 37a and 37b, supplies the dried air between the segments from directly above with the blower. The experiment of temperature measurement was conducted while flying water on the surface of the slab 5. FIG. 6C shows the results of this experiment. 9 and 10 are a side view and a plan view showing a temperature measurement method when the result of FIG. 6C is obtained.
As shown in FIGS. 9 and 10, blowers 38 a and 38 b are arranged above the segments as well as on both sides of the segments. These blowers 38a and 38b are fixed upward between the segments by a fixing tool (not shown), and the direction of the air blowing is directed to the measurement surface 5a (that is, the downward direction) of the slab 5.

And while the air dried from each blower 37a, 37b, 38a, 38b is supplied between pipe 36a, 36b and a segment, the to-be-measured surface 5a of the slab 5 is imaged with the cameras 32a, 32b. Thus, the dry air was supplied also between the segments, and the water on the surface of the slab 5 was blown away. As a result, as can be seen from FIG. 6C and FIG. 7, the temperature measurement can be performed while reducing the influence of water glue (small temperature drop in a narrow range) seen in FIG. 6B. . In addition, the present inventor has confirmed that the influence of water residue can be sufficiently removed by setting the air supply amount (air volume) by the blowers 37a, 37b, 38a, and 38b to 30 Nm ³ / min or more, respectively.
9 and 10 are the contents including the configuration of FIG. 8, but the present embodiment is not limited to this. 9 and 10, there may be a configuration in which only the blowers 38a and 38b are provided without the blowers 37a and 37b. Even with such a configuration, it is possible to remove the influence of water.

(Final solidification prediction method)
Next, a final solidification prediction method for predicting the final solidification position and shape of the slab 5 using the temperature measurement method will be described. The secondary cooling calculation of the continuous casting machine is, for example, considering a 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, roll heat removal For example, the heat flux of the boundary condition in various situations is given and the two-dimensional heat transfer equation shown in the following equation (2) is solved.

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 5 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. 11 is a diagram showing the concept of the method for predicting the final solidification of continuous casting according to the first 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.
In the calculation, first, the temperature is calculated continuously from the meniscus to the end of the machine for every two-dimensional cross-sectional slice of a 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 by an in-machine or end-of-machine temperature measuring device.
Then, the difference between the slab surface temperature calculated value and the surface temperature measured value at the surface temperature observation position is used as an evaluation function based on the 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. 12 is a diagram illustrating a flow of processing for predicting the optimization calculation and the position / shape of the 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).

  Further, any optimization technique may be used as long as it is a nonlinear optimization technique. 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 be placed on the surface temperature at the upstream position and the center temperature in the thickness direction, which are variables.

(Example 2)
The above-mentioned final coagulation prediction method will be described in more detail with reference to Example 2 as a specific example.
FIG. 13 is a comparison diagram between the predicted value of the surface temperature at the measurement position of the radiation thermometer at the machine end and the measured value.
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. Recognize. 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. 14 is a comparison diagram between a predicted value to which the final coagulation prediction method according to the present invention is applied and an actual measurement value. According to the above algorithm, the slab cross-section temperature distribution at the upstream boundary is set so that the error in 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 has been corrected.
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. 15 is a figure which shows the change of a crater end position and shape. 15 (a) shows the CE position after optimization corresponding to FIG. 13, FIG. 15 (b) shows the CE position after optimization corresponding to FIG. 14, 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 a slab 5 of excellent quality.

Second Embodiment
Next, a second embodiment of the present invention will be described with reference to the drawings.
FIG. 16 is a schematic diagram showing an example of a continuous casting machine according to the second embodiment of the present invention. FIG. 16 illustrates a vertical bending type continuous casting machine as the continuous casting machine. However, the same reference numerals are used for the same components as in FIG. The continuous casting machine is applied with a solidification state estimating device for the slab 5.

(Configuration of continuous casting machine)
As shown in FIG. 16, 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. 16, 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. 16 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.

Moreover, although there are cases where a rolling roll (light rolling roll) for lightly rolling down the slab 5 is installed depending on the continuous casting machine, the present invention is not affected by the presence or absence of light rolling.
Moreover, the temperature measuring device 4b which comprises a temperature distribution measurement means is arrange | positioned with respect to one place preset in the slab longitudinal direction. The temperature measuring device 4b measures the surface temperature distribution in the width direction of the slab 5 in the machine.

  Here, the temperature measuring devices 4a and 4b have the same configuration and the same function as the temperature measuring device 4 described in the first embodiment. Moreover, the temperature measuring method by the temperature measuring devices 4a and 4b is the same as the method described in the column of (Temperature measuring method) and (Example 1) of the first embodiment, and the width direction temperature distribution of the slab 5 is the same. It can be measured. Therefore, repeated description of the configuration of the temperature measuring devices 4a and 4b and the temperature measuring method thereof will be omitted.

  Moreover, in FIG. 16, the case where the temperature measurement apparatuses 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 temperature measuring devices 4a and 4b used in a third embodiment to be described later are shown together with FIG. Of course, the temperature measuring device used in the present embodiment may be the temperature measuring device 4a.

The continuous casting control unit 20 includes a secondary cooling control unit 20A and a solidification state estimation unit 20B. 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 temperature measuring device 4b matches the surface temperature distribution in the slab width direction measured by the temperature measuring device 4b. In addition, 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 (3) indicating the boundary condition on the slab surface by the secondary cooling condition consisting of water cooling, air cooling, mist cooling, heat removal from the roll, etc., and using the obtained heat flux, the equation This is implemented by solving the two-dimensional heat transfer equation (5).

  However, φ, which is a value related to the temperature in the equation (3), can be expressed by the following equation (4). For this reason, when formula (3) is applied to formula (5) described later, the temperature is replaced as in formula (4).

here,
Q: heat flux κ: thermal conductivity κd: 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 (3) is determined by secondary cooling conditions, such as cooling methods, such as water cooling, air cooling, and mist cooling, the amount of cooling operation, and heat removal amount of a roll. Obtain the internal temperature distribution of the slab 5 by the secondary cooling calculation by the equation (5) based on the above equation (3), and further calculate the complete solidification position from the solidus temperature determined by the internal temperature distribution and molten steel components To do.
Further, by using the above formulas (3) to (5), the slices of the unit length are 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 formula (6) is used instead of formula (3) as the formula of the heat flux by the boundary condition by the secondary cooling condition.
Qij = dih (T−Ta) (6)
here,
di: Correction coefficient of heat transfer 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 di, 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 temperature measuring device 4b used in this embodiment is more 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 di is set to “1” as an initial value.
In the secondary cooling calculation, using the above formulas (6) and (5), the temperature is first calculated at a 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. . 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 temperature measuring device 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 temperature measurement device 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 slab surface temperature calculated in step S20 (estimated temperature), and the actual surface temperature measured by the temperature measuring device 4b obtained in step S30. It is determined whether or not the difference is equal to or greater than a preset threshold value. 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 by the heat flux distribution correction unit 20Bb and the actual measured surface temperature value measured by the temperature measuring device 4b obtained in step S30 is small. The correction coefficient di (i = 1 to n) is changed so as to be zero. When the correction coefficient di is changed, the process proceeds to step S10, and recalculation of the secondary cooling calculation is performed.

In addition, the change of the correction coefficient di of the width direction heat transfer coefficient h is assumed to be uniform in the cooling zone in the longitudinal direction. For the sake of convenience, the temperature measuring device 4b capable of measuring 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.

(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 (3) indicating the boundary condition on the surface of the slab by the secondary cooling condition including air cooling, mist cooling, heat removal from the roll, etc., and using the obtained heat flux, the above equation ( This is implemented by solving the two-dimensional heat transfer equation of 5).

Here, the two-dimensional heat conduction equation represented by Expression (5) is an expression that assumes that there is no heat conduction in the casting direction of the slab in the cross section of the slab.
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 the equation (5) by changing the physical property value as a function of temperature. If the physical property value has temperature dependence, Equation (5) 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.

Here, φ is the conversion temperature, H is the heat content, T _{d is the} reference temperature, and κ _d is the thermal conductivity at the reference temperature.
Then, when Expressions (7) and (8) are substituted into Expression (5), the following Expression (9) is obtained.

By differentiating this equation (9), 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 represented by the following formula (10):

Here, h: heat transfer coefficient, T _a : ambient temperature.
If the speed in the slab casting direction is v (z direction), the following formula (11) is satisfied.

Based on these equations (10) and (11), when equation (9) is differentiated (discretized) at each of the internal points and surface points, the following equation is obtained.

Here, Q is the heat flow rate.
In the above formula, l represents a calculation time step, and from each value of l, the next calculation step (
(L + 1) value of (time) is obtained.
The actual heat transfer calculation is performed by the difference method using the difference formulas of (12) and (13).
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 the analysis object because of 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 to be used]
In addition, the heat transfer coefficient h in the equation (10) 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.

[Solid fraction]
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.

C _O : Carbon concentration C _S : Carbon concentration at which a certain temperature is equal to the solidus temperature C _L : Carbon concentration at which a certain temperature is equal to the liquidus temperature

[Calculation of heat removal in 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 1.4mpm
・ 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. 19 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. 19, the state of one side from the center of the width direction of the slab 5 is illustrated. The same applies to FIGS. 20 to 14 described later.
As shown in FIG. 19, 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 and the calculated temperature and the measured temperature. 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. In FIG. 20, the width direction correction point is set to 20 mesh (n = 20), and the calculation of the optimization is performed, and the magnification of the heat transfer coefficient in the width direction is corrected so that the error between the actually measured value and the calculated value becomes small (di is adjusted) It is a figure which shows the example of the calculation result of the surface temperature when doing. In addition, FIG. 21 shows the correction magnification (value of the correction coefficient di) 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. 21, a 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 in which the difference in surface temperature specified by the evaluation function is steadily reduced.
FIG. 22 (Comparative Example) and FIG. 23 (Example) show the final solidification position (CE position) and shape in these two cases (see FIGS. 19 and 20). 22 and 23, the vertical axis represents the distance in the slab longitudinal direction from the mold 2, and the horizontal axis represents the solidification completion position at the slab width direction position.

  In FIG. 22 (comparative example), since the temperature distribution in the width direction is based on a flat calculation temperature, the final solidified shape is flat with no irregularities except for the end portions. On the other hand, when the heat transfer coefficient in the width direction is corrected using the actual surface temperature in the width direction in FIG. 23 (Example), the unevenness in the width direction can be expressed and the surface temperature distributions are consistent. It is thought that the final coagulation state close to reality can be expressed. In this way, 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 inside 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 temperature measuring device 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.

(Modification)
In FIGS. 20 to 23 described above, the value (correction magnification) of the heat transfer coefficient correction coefficient di is uniformly changed for each of the plurality of cooling zones.
Specifically, the correction coefficient di is calculated based on the equation (20).
Correction coefficient update value = (model temperature−actual temperature) × gain + correction coefficient previous 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 of cooling zone n = (model temperature−actual temperature) × gain n + (previous value of correction coefficient of 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, a case where the temperature measuring device 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 the cooling is large, and in the zone 9a-13a, where the cooling is weak, Therefore, the correction gain is set to be small. In the zone 14a-15a after the thermometer installation position, the correction gain is set to 0, and correction by the temperature measuring device is not performed.

FIG. 24 shows the result of estimating the final solidification position using the gain n and the same temperature measurement value of the temperature measuring device 4a.
As shown in FIG. 24, even when the same thermometer value is used, the difference between the peaks and valleys of the final solidification shape becomes larger when individual gains n are 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 far from the temperature measuring device and strong in cooling. 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 is estimated by 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. 25 perform the same processes as steps S10 to S50 and S60 in the first embodiment (FIG. 17). In step S30, the temperature measuring device 4a is employed, and the measurement position of the temperature measuring device 4a is set as the temperature comparison position.

In the present embodiment, the correction coefficient di is changed uniformly in the slab longitudinal direction every time the thermometer is installed.
Also, steps S110 to S150 in FIG. 25 perform the same processing as steps S10 to S50 in the first embodiment (FIG. 17). In step S130, the temperature measuring device 4b is adopted, and the measurement position of the temperature measuring device 4b is set as the temperature comparison position.
However, the correction coefficient di (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.

In the calculation in step S110, the correction coefficient di (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 the first measurement position, the value obtained in step S50 is used as the correction coefficient di, and the measurement interval from the first measurement position to the second measurement position is used. On the other hand, the correction coefficient di (i = n) adjusted in step S150 is used.

(Operation other)
The operation when this embodiment is adopted up to the first measurement position (position of the temperature measuring device 4a) is the same as that of the first embodiment (see FIGS. 19 to 21).
FIG. 26 is an example of the slice cross-section temperature distribution at the measurement position of the temperature measurement device 4a after correction based on the measurement position of the temperature measurement device 4a by the processing of steps S10 to S50.

When the surface temperature in the width direction at the measurement position of the temperature measuring device 4b calculated based on the slice cross-section temperature distribution shown in FIG. 27 is compared with the actually measured temperature at the measurement position of the temperature measuring device 4b, as shown in FIG. Result. As shown in FIG. 27, there may be a slight deviation even when the temperature distribution in the width direction is corrected at the measurement position of the temperature measuring device 4a.
In order to eliminate this deviation, similarly to the correction based on the measurement result of the temperature measurement device 4a, the magnification of the heat transfer coefficient in the width direction (the value of the correction coefficient di) in the section between the measurement positions of the temperature measurement devices 4a to 4b. ) Is corrected based on the measurement result of the temperature measurement device 4b, the calculation result of the surface temperature as shown in FIG. 28 can be obtained at the measurement position of the temperature measurement device 4b.

Next, what is the position and shape of the final solidification in the case where no correction is made by the measured values by the temperature measuring device and the case where correction is made based on the present embodiment by the measured values of the two temperature measuring devices 4a and 4b. As a result, the results shown in FIG. 29 (comparative example) and FIG. 30 (example) were obtained.
29 and 30, 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. In this way, if the calculation results at the two surface temperature measurement positions agree with the actual measurement values, it can be expected to ensure the accuracy of the estimated values of the final solidification position and shape determined by the temperature state inside the slab. Further, further accuracy improvement can be expected by installing three or more temperature measuring devices 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 temperature measurement device 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 temperature measurement device at one location in the slab longitudinal direction In the case of correction by value, the deviation due to the cooling condition downstream from the measurement position by the temperature measuring device cannot be corrected, and the estimation accuracy of the final solidification position / shape may be lowered by that amount. Even if the temperature measuring device is installed at one location downstream from the final solidification position, there is a possibility that the deviation due to the fluctuation of the cooling condition generated upstream from the position of the temperature measuring device 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 temperature measuring device 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).
Other configurations and the like are the same as those in the second embodiment.

DESCRIPTION OF SYMBOLS 1 Tundish 2 Mold 3 Immersion nozzle 4, 4a, 4b Temperature measuring device 5 Slab 5a Measurement surface 6 Support rolls 7a-15b Cooling zone (segment)
20 Continuous casting control unit 20A Secondary cooling control unit 20B Solidification state estimation unit 20Ba Solidification state estimation unit body 20Bb Heat flux distribution correction unit 21 Manufacturing control unit 32a, 32b Camera 33a, 33b Tripod 34a, 34b Passage 35a, 35b Segment di Correction coefficient h Heat transfer coefficient

Claims (10)

In the solidification state estimation method for estimating the final solidification position and shape of the slab in continuous casting in which the molten steel injected into the mold is solidified by performing secondary cooling while being drawn and continuously producing the slab,
The final solidification position and shape of the slab are estimated by a heat transfer model using a heat flux based on the cooling condition of at least the secondary cooling, and the slab width direction at a preset measurement position in the slab longitudinal direction is estimated. Measure the temperature distribution,
As the temperature distribution of the slab width direction estimated temperature and the measured estimated by the heat transfer model in the measurement position coincides, by correcting the heat flux distribution in the slab width direction of the heat flux, the Correct the estimated temperature by the above heat transfer model upstream from the measurement position ,
The measurement of the temperature distribution is performed by imaging the surface to be measured of the slab with an imaging device, obtaining the temperature distribution of the surface to be measured based on the luminance at each surface position of the captured image,
The image used to determine the temperature distribution is
An imaging angle at one end of the measurement target surface in the slab width direction as viewed from the imaging device is θ1, and an imaging angle at the other end of the measurement surface in the slab width direction as viewed from the imaging device is θ2. when the θ1 and the θ2 each 40 ° or more, 65 ° Ri follows Do that image Zodea,
The secondary cooling is performed by a plurality of cooling zones,
A method for estimating a solidification state of a slab, wherein a correction coefficient of a heat flux distribution for correcting the heat flux distribution is individually set for each cooling zone . 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 heat transfer model is used for each of the two or more measurement positions. 2. The casting according to claim 1 , wherein correction of the heat flux distribution in the slab width direction of the heat flux is repeated so that the estimated temperature estimated matches the measured temperature distribution in the slab width direction. Method for estimating the solidification state of a piece. The imaging angle at the near end of the measured surface closest to the imaging device is 40 ° or more, and the imaging angle at the far end of the measured surface furthest from the imaging device is 65 ° or less. The solidification state estimation method of the slab of Claim 1 or Claim 2 characterized by these. Measurement of the temperature distribution, using at least two or more imaging devices as the imaging apparatus, cast as described in any one of claims 1 to 3, characterized in that the imaging the object surface Method for estimating the solidification state of a piece. Two imaging devices are arranged on both sides of the slab width direction,
5. The slab according to claim 4 , wherein the two image pickup devices pick up an image of the same surface to be measured, and obtain a temperature distribution of the surface to be measured based on the luminance of each image picked up by each image pickup device. Solidification state estimation method. The imaging device is located above the segment of the continuous casting machine,
As the gap of the segment the image path of imaging leading to the imaging device from the object surface, and 80% or more of the optical path, wherein the claim 1, characterized in that through the at no higher than the top of the segment The solidification state estimation method of the slab as described in any one of claim | item 5 . When measuring the temperature distribution over 0.85μm the measurement surface of the slab, with a wavelength range 1.0μm of claims 1 to 6, characterized in that imaging the該被measurement plane The solidification state estimation method of the slab described in any one of the items. When measuring the temperature distribution, the surface to be measured is imaged while blowing a gas of 30 Nm ³ / min or more toward the surface to be measured from above the surface to be measured of the slab. slab of solidified state estimation method according to any one of claims 7 to claim 1. When measuring the temperature distribution, the surface to be measured is imaged while blowing a gas of 30 Nm ³ / min or more to a pipe through which a cooling medium for cooling a segment of a continuous casting machine flows. The slab solidification state estimation method according to any one of claims 1 to 8 . Based claims 1 to final solidification position and shape of the slab estimated solidification state estimation method of the slab according to either one of claims 9, secondary cooling conditions, soft reduction conditions, the casting speed, mold A continuous casting method comprising operating at least one of electromagnetic stirring strengths.