JP6167856B2 - Continuous casting machine, secondary cooling control method and secondary cooling control device for continuous casting machine - Google Patents

Description

  The present invention relates to a continuous casting machine, a secondary cooling control method and a secondary cooling control apparatus for a continuous casting machine, and more particularly, continuous casting in which the surface temperature distribution in the full width direction of a slab is controlled symmetrically with respect to the center line of the slab. The present invention relates to a secondary cooling control method and a secondary cooling control device for a continuous casting machine.

  In continuous casting of steel, for example, in a vertical bending type continuous casting machine, a slab drawn from a vertical mold is once bent, then drawn at a constant radius of curvature, and then the slab with no bending in the correction part. Extract and cut. However, in the bending part of the strand (which means a set of “mold + secondary cooling zone group + roller group”, the same applies hereinafter), the lower surface of the slab and the upper part of the slab in the correction part Since tensile stress is applied to the surface, surface cracks called lateral cracks may occur when the temperature of the slab surface is in a range called an embrittlement region. For this reason, it is necessary to appropriately set the cooling water flow rate distribution so that the slab surface portion temperature avoids the above-described embrittlement region in the bending portion and the straightening portion of the strand. An appropriate setting of the cooling water flow rate distribution is, for example, in the case of a constant casting speed, cooling water in each cooling zone when the secondary cooling zone is divided into a plurality of regions (cooling zones) in the casting direction of the slab. This can be achieved by setting the flow distribution to an appropriate value in advance by simulation or the like.

  However, when the arrival of the next ladle in continuous casting is delayed, the casting speed needs to be changed during operation in order to wait for arrival by lowering the casting speed below a predetermined value so that continuous casting is not interrupted. At this time, in the conventional cascade water amount control in which the cooling water flow rate in each cooling zone set in advance with respect to the casting speed is set for the casting speed being changed, the time from the mold surface of the slab to the cutting is cut. The cooling history for the slab is disturbed, and slab quality defects such as lateral cracks on the surface occur.

  Moreover, the relationship between the cooling water flow rate and the surface heat transfer coefficient may change from that assumed in the previous simulation due to the influence of scale adhesion on the surface of the slab. Even in such a case, the surface temperature of the slab enters the embrittlement region, and lateral cracks may occur.

  So far, a control method by so-called model predictive control has been disclosed for such a problem. For example, in Patent Document 1, the drawn slab is tracked at regular intervals, the temperature distribution of each tracking surface is sequentially calculated based on the heat transfer model, and the slab drawn locus is divided into several zones. The above model is corrected by the heat transfer coefficient learned from the relationship between the calculated temperature and the actually measured temperature on the exit side of the zone, and the temperature distribution of each tracking surface at the temperature measuring point provided along the locus is corrected. The amount of water obtained by summing the amount of feedforward water obtained from the difference between the target temperature and the predicted temperature at the relevant position and the amount of feedback water obtained from the difference between the measured temperature and the target temperature is calculated. A method for controlling the surface temperature of spraying is disclosed.

JP-A-57-154364

In the method of calculating the feedforward water amount disclosed in Patent Document 1, for each tracking point existing in the cooling zone, the temperature at the time when each reaches the temperature measuring point at the cooling zone outlet is predicted. A predicted water amount density at which the temperature predicted value when the temperature measurement point is reached coincides with the target value is obtained, and the weighted average value of the predicted water density for all tracking surfaces of the cooling zone is set as the feed forward water amount. In this technology, in order from the cooling zone on the mold side, a procedure for obtaining the feedforward water amount, and a procedure for obtaining a recalculated temperature by recalculating the temperature distribution in the cooling zone using the feedforward water amount obtained in this procedure. And the procedure of setting the recalculated temperature as the initial temperature at the inlet of the cooling zone adjacent to the downstream side is repeated to determine the cooling water amount in all the cooling zones. However, in this technique, even if the recalculated temperature is the initial temperature at the cooling zone inlet adjacent to the downstream side, the temperature calculation of the tracking points other than the inlet of the cooling zone adjacent to the downstream side (recalculated temperature was obtained). The influence of the feedforward water amount does not appear in the calculation of the tracking point temperature in the cooling zone existing further downstream than the cooling zone adjacent to the downstream side of the cooling zone. Therefore, in the technique disclosed in Patent Document 1, the time required for the upstream water amount change to be correctly reflected in the temperature prediction calculation becomes long, and problems such as hunting of the water amount occur in some cases.
In addition, if the heat transfer coefficient of the slab becomes non-uniform in the width direction due to the scale adhesion on the slab surface or the inflow of mold powder in the mold, the surface of the slab can be obtained even if the cooling water density is uniform. The temperature distribution becomes non-uniform in the width direction of the slab. However, in the technique disclosed in Patent Document 1, since a plurality of surface thermometers are not provided in the width direction of the slab, there is a means for knowing whether or not the temperature distribution in the width direction of the slab is symmetric. Absent. Therefore, with the technique disclosed in Patent Document 1, it is difficult to control the surface temperature in the width direction of the slab symmetrically on both sides of the center line in the width direction of the slab.

  Accordingly, the present invention provides a continuous casting machine, a secondary cooling control method for a continuous casting machine, and a secondary cooling control apparatus capable of controlling the surface temperature distribution in the full width direction of the slab symmetrically with the center line of the slab. It is an issue to provide.

  The first aspect of the present invention is based on two surface temperature measuring devices for measuring the surface temperature of a slab, which are arranged so as to be paired at symmetrical positions on both sides of the slab with respect to the center line in the width direction. At least one surface temperature measuring device pair, and at least in the secondary cooling zone on the downstream side in the casting direction of the slab from the surface temperature measuring device, the cooling water flow rate is controlled independently on both sides of the center line in the width direction. Secondary cooling control device, and the secondary cooling control device controls the cooling water so as to control the actual surface temperature value of the slab to the same surface temperature target value on both sides of the center line in the width direction. It is a continuous casting machine characterized by controlling a flow rate.

According to a second aspect of the present invention, a secondary cooling zone for cooling a slab drawn from a mold of a continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slab, and injected toward the slab. In the method of controlling the surface temperature of the slab by controlling the cooling water flow rate in each cooling zone, the slab is arranged so as to be paired at symmetrical positions on both sides with the center line in the width direction as the axis. The slab surface temperature measurement process for measuring the surface temperature of the slab at the above-mentioned symmetrical position during casting, the casting speed grasping process for grasping the casting speed of the continuous casting machine, and the cross section of the slab temperature, the surface temperature of the slab, and a tracking surface is subject to calculate the solid fraction distribution of the slab, in the area from the mold molten steel surface position to the cooling zone outlet of at least the secondary cooling control target, predetermined Tracking surface setting to be set at regular intervals The slab target temperature setting step for setting the same target value of the surface temperature of the slab at each symmetrical position on both sides of the tracking surface, and the tracking surface in the casting direction of the slab as the casting proceeds. Each time a predetermined interval is reached, the heat transfer solidification model based on the heat transfer equation is used to determine the temperature within the cross section of the slab perpendicular to the casting direction, the surface temperature at each of the above symmetric positions of the slab, and the solidity of the slab. Thermal solid phase ratio estimation process for calculating and updating the phase distribution, and heat transfer coefficient for the surface of the slab used in the heat transfer solidification model, calculated using a heat transfer coefficient model using the cooling water flow rate A surface temperature at each of the symmetric positions of the slab measured in the estimation step, and a surface temperature at each of the symmetric positions of the slab estimated in the temperature solid phase ratio estimation step. Difference from Using the heat transfer coefficient model parameter correction step for correcting the parameters of the heat transfer coefficient model and the tracking surface set in the tracking surface setting step at a predetermined time in a predetermined casting direction at a future time A future prediction surface setting step for setting a future prediction surface for predicting a surface temperature at each of the above-mentioned symmetrical positions of the slab in the above-mentioned symmetrical position, a temperature in the cross section of the slab perpendicular to the casting direction, and a solid fraction distribution of the slab As the casting progresses, it is assumed that the casting speed does not change from the current time while any future prediction plane advances from the current time to the future prediction plane position adjacent to the downstream side. When the predicted surface position is reached, the surface temperature at each symmetrical position of the slab, the temperature in the cross section of the slab perpendicular to the casting direction, and the solid fraction distribution of the slab are The future prediction surface that repeatedly predicts and updates using the heat transfer solidification model at each interval used in the future prediction surface setting step, and any future prediction surface is downstream from the current time by the progress of casting. Assuming that the casting speed does not change from the current time every time it moves to the future predicted surface position adjacent to, each future predicted surface when the cooling water flow rate in each of the above cooling zones changes in a step function is The surface temperature at each of the symmetric positions of the slab at each tracking surface position that passes until reaching the predicted surface position is predicted using the heat transfer solidification model , and the symmetric of each of the predicted slabs. The deviation between the surface temperature at the position and the surface temperature at each symmetric position of the slab predicted in the future prediction step is obtained, and the deviation and the cooling function that changes in a step function form are obtained. A future temperature influence coefficient prediction process for obtaining a future temperature influence coefficient related to the water flow rate, and a surface at each symmetrical position of the slab predicted by the future prediction process when the future prediction surface reaches the tracking surface position. The slab surface, which is the intermediate target temperature at each of the slabs in the symmetric position, connecting the temperature and the target value of the surface temperature at each of the symmetric positions of the slabs determined in the slab target temperature setting step The slab surface reference temperature calculation step for calculating the reference temperature of the slab, and the cooling water flow rate of each cooling zone including the cooling water flow rate set independently on both sides of the center line in the width direction of the slab at the current time are determined variables The future temperature influence coefficient at each future prediction plane position through which each future prediction plane has passed in each of the future prediction process and the future temperature influence coefficient prediction process, The deviation between the reference temperature calculated in the slab surface reference temperature calculation step and the surface temperature of the slab predicted in the future prediction step is calculated, and the sum of the deviations calculated in the respective future prediction planes is minimized. An optimization problem coefficient matrix calculating step for specifying a quadratic programming problem of an optimization problem to be performed, calculating a coefficient matrix for a decision variable in the quadratic programming problem, and numerically solving the quadratic programming problem An optimization problem solving process for determining the optimum value of the amount of change in the cooling water flow rate at the current time of the cooling zone on each side of the slab width center line, which changes in a function, and the slab width center line A cooling water flow rate changing step for changing the cooling water flow rate by adding the optimum value on each side to the current cooling water flow rate of the cooling zone on each side of the slab width direction center line. Water flow change By repeatedly changing the cooling water flow rate in the process, while each tracking surface moves to the cooling zone exit of the secondary cooling control target at an arbitrary time during casting, the slab at the future predicted surface position of the future predicted surface The surface temperature at each of the symmetric positions is controlled to a target value of the surface temperature at each of the symmetric positions of the slab determined in the slab target temperature setting step. This is a cooling control method.

According to a third aspect of the present invention, a secondary cooling zone for cooling a slab drawn from a mold of a continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slab and injected toward the slab. Is a device for controlling the surface temperature of the slab by controlling the flow rate of the cooling water in each cooling zone so as to be paired at symmetrical positions on both sides with the center line in the width direction of the slab as an axis. And a slab surface temperature measuring unit for measuring the surface temperature of the slab at the above-mentioned symmetrical position during casting, a casting speed grasping unit for grasping the casting speed of the continuous casting machine, and the temperature in the cross section of the slab, the surface temperature of the slab, and a tracking surface is subject to calculate the solid fraction distribution of the slab, in the area from the mold molten steel surface position to the cooling zone outlet of at least the secondary cooling control target, predetermined intervals The tracking surface setting part set in step 1 and the tracking surface A slab target temperature setting unit that sets the same target value of the surface temperature of the slab at each symmetrical position on both sides, and every time the tracking surface advances by a predetermined interval in the casting direction of the slab as casting progresses. In addition, the heat transfer solidification model based on the heat transfer equation is used to calculate the cross-sectional temperature of the slab perpendicular to the casting direction, the surface temperature at each of the above symmetric positions of the slab, and the solid fraction distribution of the slab. A temperature solid phase ratio estimator to be updated, a heat transfer coefficient estimator for calculating the heat transfer coefficient of the surface of the slab used in the heat transfer solidification model by a heat transfer coefficient model using a cooling water flow rate, and the slab Using the difference between the surface temperature at each of the symmetric positions of the slab measured by the surface temperature measurement unit and the surface temperature at each of the symmetric positions of the slab estimated by the temperature solid phase ratio estimation unit, The heat transfer coefficient model From the tracking surface set by the heat transfer coefficient model parameter correcting unit for correcting the meter and the tracking surface setting unit, each symmetrical position of the slab at a future time at a predetermined interval in a predetermined casting direction A future prediction plane setting unit for setting a future prediction plane for predicting the surface temperature, the temperature in the cross section of the slab perpendicular to the casting direction, and the solid phase ratio distribution of the slab, and any future by casting Assuming that the casting speed does not change from the current time while the prediction surface advances from the current time to the future prediction surface position adjacent to the downstream side, when each future prediction surface reaches the future prediction surface position, The surface temperature at each symmetrical position of the slab, the temperature in the cross section of the slab perpendicular to the casting direction, and the solid fraction distribution of the slab for each interval used in the future prediction plane setting unit A future prediction unit that repeatedly predicts and updates using a heat transfer solidification model, and every time a future prediction plane advances from the current time to a future prediction plane position adjacent to the downstream side by casting, the casting speed Assuming that the cooling water flow rate in each of the above cooling zones changes in a step function, each tracking surface that passes by the time when each future prediction surface reaches the future prediction surface position is assumed. The surface temperature at each symmetrical position of the slab at the position is predicted using the heat transfer solidification model , and the predicted surface temperature at each symmetrical position of the slab and the casting predicted by the future prediction unit. The future in which the deviation from the surface temperature at each of the above symmetrical positions of the piece is obtained, and the future temperature influence coefficient related to the deviation and the cooling water flow rate changing in a step function is obtained. The surface temperature at each symmetrical position of the slab when the future prediction surface reaches the tracking surface position, predicted by the degree influence coefficient prediction unit and the future prediction unit, and determined by the slab target temperature setting unit Further, a slab surface reference temperature calculation for calculating a reference temperature of the slab surface, which is an intermediate target temperature at each of the symmetric positions of the slab, connecting the target value of the surface temperature at each of the symmetric positions of the slab. And the future temperature prediction coefficient and the future temperature influence coefficient, with the cooling water flow rate of each cooling zone including the cooling water flow rate set independently on both sides of the width direction center line of the slab at the current time In each of the prediction units, the future temperature influence coefficient at each future prediction surface position through which each future prediction surface has passed, the reference temperature calculated by the slab surface reference temperature calculation unit, and the general temperature The deviation from the surface temperature of the slab predicted by the prediction unit is calculated, the secondary planning problem of the optimization problem that minimizes the sum of the deviations calculated in the respective future prediction planes is specified, and the secondary planning problem An optimization problem coefficient matrix calculation unit for calculating a coefficient matrix for a decision variable in the above, and by solving the quadratic programming problem numerically, on each side of the center line in the width direction of the slab, which changes into a step function, The optimization problem solving unit for obtaining the optimum value of the change amount of the cooling water flow rate at the current time of the cooling zone, and the optimum value on both sides of the slab width direction center line are determined on each side of the slab width direction center line. A cooling water flow rate changing unit that changes the cooling water flow rate by adding to the current cooling water flow rate of the cooling zone, and by repeatedly changing the cooling water flow rate in the cooling water flow rate changing unit, At any time While each tracking surface moves to the cooling zone outlet of the secondary cooling control target, the surface temperature at the symmetric position of the slab at the future prediction surface position of the future prediction surface is determined by the slab target temperature setting unit. It is a secondary cooling control device for a continuous casting machine, characterized in that control is performed to a target value of a surface temperature at each of the above-described symmetrical positions of a defined slab.

  According to the present invention, a continuous casting machine, a secondary cooling control method for a continuous casting machine, and a secondary cooling control apparatus capable of controlling the surface temperature distribution in the full width direction of the slab symmetrically with respect to the center line of the slab. Can be provided. As a result, it is possible to control the surface temperature of the entire slab so as to always coincide with a predetermined target temperature, so that continuous casting is possible at any casting speed and even when the casting speed changes during casting. In the bending and straightening segments of the machine, the surface temperature can be controlled so as to avoid the steel embrittlement zone. Therefore, according to the present invention, it is possible to produce a slab free from defects due to surface defects.

It is a figure explaining the continuous casting machine 9 and the secondary cooling control apparatus 10 of this invention. It is a figure which shows the example of arrangement | positioning of a surface temperature measuring apparatus, division | segmentation of a slab cross section perpendicular | vertical to a casting direction, and a lattice point. It is a figure explaining one control cycle of the secondary cooling control method of the present invention. It is a figure explaining the relationship between the position of the tracking surface which evaluates surface temperature, and the relative time which estimates temperature while each future prediction surface moves to the future prediction surface position adjacent to the downstream. FIG. 2 is a block diagram for explaining the relationship between each part provided in the cooling control device 10. It is a graph showing the result at the time of controlling the surface temperature of a slab by optimally controlling the cooling water flow rate by the secondary cooling control method of the present invention. It is a graph showing the result at the time of controlling the surface temperature of a slab by adjusting a cooling water flow rate by the conventional control method, when a casting speed is changed during casting.

  Embodiments of the present invention will be described below. In addition, the form demonstrated below is an illustration of this invention and this invention is not limited to the form demonstrated below.

FIG. 1 is a diagram for explaining a continuous casting machine 9 of the present invention and a secondary cooling control device (hereinafter sometimes referred to as “cooling control device”) 10 of the continuous casting machine of the present invention. In FIG. 1, the continuous casting machine 9 and the cooling control device 10 are shown in a simplified manner, and for convenience, only one surface temperature measuring device 7 is shown as a surface temperature measuring device that should constitute the surface temperature measuring device pair.
In the continuous casting machine 9 of the present invention, the strand is drawn from the mold 1 at a predetermined drawing speed (casting speed) by a pinch roll provided with a driving device while supporting the strand solidified on the outside with a pair of rolls. Reference numeral 4 denotes a molten steel meniscus. A mist spray 2 (or spray 2) for spraying cooling water toward the slab 5 between adjacent support rolls arranged on both sides in the width direction of the slab at a predetermined interval in the casting direction. A spout is installed. The sprayed cooling water is supplied to the mist spray 2 through the cooling water pipes installed corresponding to the respective cooling zones in which the casting direction length of the slab 5 is divided into a plurality of pieces. It is controlled by a flow rate adjusting valve 3 installed in the water pipe. The opening degree of the flow rate adjusting valve 3 is adjusted based on a flow rate instruction value given from the cooling control device 10. Since the cooling water pipe is installed corresponding to a cooling zone (a cooling zone divided by the cooling zone boundary line 6) in which the casting direction length of the slab 5 is divided into a plurality of pieces, The flow distribution is controlled for each cooling zone. In the following description, the cooling zone may be referred to as a first cooling zone, a second cooling zone,.

  In the continuous casting machine 9, in some or all cooling zones, cooling water pipes are independently installed on both sides of the slab width direction center line, and the cooling water flow rate is also independently on both sides of the slab width direction center line. Be controlled. Hereinafter, in the description of the present invention, one side of the center line in the width direction of the slab may be referred to as the L side, and the opposite side may be referred to as the R side. In the continuous casting machine 9, at the exit of the fourth cooling zone, positions on the L side and the R side that are separated by 2/3 of the slab width from the center line in the width direction of the slab (1/6 width of the slab width). Surface temperature measuring device 7 is provided at the position and the 5/6 width position). In the following description, the surface temperature measuring device 7 provided on the L side is referred to as “L side temperature measuring device 7L”, and the surface temperature measuring device 7 provided on the R side is referred to as “R side temperature measuring device 7R”. There is. FIG. 2 shows an arrangement example of the L-side temperature measuring device 7L and the R-side temperature measuring device 7R.

  The distribution of the slab 5 temperature and solid phase ratio in the strand is a calculation point set at regular intervals in the casting direction from the molten metal surface in the mold to the final roll exit side. Is calculated by solving the discrete heat conduction equation under the boundary condition of the heat transfer coefficient reflecting the cooling condition at each calculation point. In the initial condition of the heat conduction equation, set the calculation result of the temperature and solid phase ratio of the cross section adjacent to the upstream side of the cross section existing at the calculation target position, from the calculation point adjacent to the upstream side to the target calculation position, By repeating the calculation until the cross section moves by drawing the slab, the temperature and the solid phase ratio of the entire slab can be calculated.

In order to discretize the heat conduction equation, for example, a two-dimensional model shown in FIG. 2 is used in which half of the slab thickness direction is set as a calculation region and divided by a grid parallel to and perpendicular to each side of the slab. . In the following, according to FIG. 2, on the width direction axis of the slab cross section, i = 0 at the lattice point on the short side surface of the slab on the L side, and i = I at the lattice point on the short side surface of the slab on the R side. To do. On the other hand, on the thickness direction axis, j = 0 at a lattice point on the surface of the slab long side, and j = J on the opposite thickness direction center line. Using the temperature T _{ij at} each lattice point (i, j), the enthalpy H _ij per unit mass, and the solid phase ratio f _ij per unit mass as variables, the physical constants at each lattice point (i, j) Considering the dependency, it is expressed as density ρ _ij , specific heat C _ij , and thermal conductivity λ _ij . At this time, the relationship among the enthalpy H _ij , the temperature T _ij , and the solid phase rate f _ij is expressed by the following equation (1).

In the above formula (1), L _ij is the solidification latent heat at the lattice point (i, j).

During the time step Δt, the time variation of the distribution of the enthalpy H _ij and the solid phase ratio f _ij of the cross section drawn from the casting direction position z to z + Δz is expressed by the discrete heat conduction equations (2), (3), (4 ), Initial conditional expression (5), and boundary conditional expressions (6), (7), (8), and (9). In the following formula, the superscript z represents the position in the casting direction, and the molten metal surface position in the mold is set to z = 0. The time step Δt in the heat conduction equation is converted into Δt = Δz / v (t−1) using the cross-section setting step Δz in the casting direction and the casting speed v (t−1) at time t−1. The heat removal from the slab surface reflects boundary conditions that take into account the difference in cooling method depending on the cross-section position in the casting direction, such as cooling with cooling water sprayed toward the slab 5, contact with the roll, and radiation. Here, the heat transfer coefficient K _x when expressed by the linear expression of the difference between the temperature T _E representing the outside and the surface temperature T _ij ^z shown in the equations (6) and (7) or it was represented by _{K y.}

In the above formula (2), Δx _i is the distance from the lattice point (i−1 / 2, j) to the lattice point (i + 1/2, j), and Δy _i is the lattice point (i, j−1 / 2). ) To the lattice point (i, j + 1/2). Q _{i + 1/2, j} ^z is the heat flux from the lattice point (i, j) in the width direction to the lattice point (i + 1, j) at the casting direction position z−1, and i = 1,. In the case of a lattice point inside one slab, it is represented by the following formula (3).

In the above equation (3), λ _{i + 1/2, j} is λ _{i + 1/2, j} = (λ _{i + 1, j} + λ _ij ) / 2, and Δx is the lattice point (i + 1, j) from the lattice point (i, j). ).

In the above formula (2), q _{i, j + 1/2} ^z is the heat flux from the lattice point (i, j) in the thickness direction of the slab to the lattice point (i, j + 1), j = 1, In the case of a lattice point inside the slab of J-1, it is represented by the following formula (4).

In the above equation (4), λ _{i, j + 1/2} is λ _{i, j + 1/2} = (λ _{i, j + 1} + λ _ij ) / 2, and Δy is the lattice point (i, j + 1) from the lattice point (i, j). ).

  The initial condition is expressed by the following formula (5).

Also, boundary conditions, in the slab on the short side surface lattice points of i = 0, represented by the following formula (6) with a heat transfer coefficient K _x and the external representative temperature T _E in the casting direction position z-1 .

Further, in the slab short side surface on the lattice points of the i = I, represented by the following formula (7) using a heat transfer coefficient K _x and the external representative temperature T _E in the casting direction position z-1.

Further, the cast strip long side surface on the lattice points of j = 0, represented by the following formula (8) with a heat transfer coefficient K _y and external representative temperature T _E in the casting direction position z-1.

Further, in the slab thickness direction central line grid point of j = J, represented by the following formula (9) with a heat transfer coefficient K _x and the external representative temperature T _E in the casting direction position z-1.

After calculating the enthalpy H _ij ^{z + Δz} at the casting direction position z + Δz, when f _ij ^{z + Δz} = 0 of the complete liquid phase or f _ij ^{z + Δz} = 1 of the complete solid phase, the respective values are substituted into the above formula (1). Thus, the temperature T _ij ^{z + Δz} is obtained. On the other hand, when 0 <f _ij ^{z + Δz} <1, the temperature T _ij ^{z + Δz} is the liquidus temperature T _L (C _k ) (C _k is the solute component k) represented by a phase diagram determined by the solute concentration in the liquid phase. The concentration). Here, since the solute concentration in the liquid phase depends on the solid phase ratio as known from the Scheil equation, the model represented by the following equation (10) is used, and the equation (10) and the above equation ( 1) and f _ij ^{z + Δz} and T _ij ^{z + Δz} are obtained as solutions of the simultaneous equations.

  When the heat transfer coefficient K on the surface of the slab where the cooling water sprayed from the mist spray 2 collides is expressed by the model of the following equation (11), the heat flux q is obtained by the following equation (12).

Each Here, _{T S} is the surface temperature [℃], _{D w} is the surface water flow rate _{^{[l / m 2], v}} a is the spray air flow rate [m / s], α, β, γ, and, c is It is a constant.

  The cooling control device 10 uses the drawing speed of the slab 5, the molten steel temperature in the tundish, and the cooling water temperature to determine a future predicted value of the slab surface temperature at a predetermined temperature evaluation point in the casting direction. And the deviation between this future predicted value and the target value of the slab surface temperature at the temperature evaluation point in each cooling zone, and the cooling water flow rate (the cooling water flow rate is independently on both sides of the center line in the width direction of the slab. In the cooling zone to be adjusted, the cooling water flow rate on the L side, the cooling water flow rate on the R side, and the cooling water flow rate in the cooling zone where the cooling water flow rate is not adjusted independently on both sides of the center line in the width direction of the slab. The cooling water flow rate of each cooling zone (for example, in the cooling zone where the cooling water flow rate is independently adjusted on both sides of the center line in the width direction of the slab, the width of the slab is minimized. The optimum value of the flow rate of the cooling water sprayed from the spray groups arranged on both sides of the direction center line to the cooling zone is calculated. In the secondary cooling control method of the continuous casting machine according to the present invention (hereinafter sometimes referred to as “the cooling control method of the present invention”), the calculation described below is repeated within one control cycle. Thus, the slab surface temperature on each tracking surface is controlled to a predetermined target value of the slab surface temperature. The cooling control method of the present invention will be described below with reference to FIG. 3 illustrating the cooling control method of the present invention.

  As shown in FIG. 3, the cooling control method of the present invention includes a slab surface temperature measuring step (S1), a casting speed grasping step (S2), a tracking surface setting step (S3), and a slab target temperature setting. Step (S4), temperature solid phase ratio estimation step (S5), heat transfer coefficient estimation step (S6), heat transfer coefficient model parameter correction step (S7), future prediction plane setting step (S8), and future Prediction step (S9), future temperature influence coefficient prediction step (S10), slab surface reference temperature calculation step (S11), optimization problem coefficient matrix calculation step (S12), and optimization problem solving step (S13) And a cooling water flow rate changing step (S14).

  The slab surface temperature measuring step (hereinafter, sometimes referred to as “S1”) is a surface temperature measuring device for measuring a slab surface temperature at a temperature measurement point on a slab surface in a predetermined strand during casting. 7 (L-side temperature measuring device 7L and R-side temperature measuring device 7R).

  The casting speed grasping step (hereinafter, sometimes referred to as “S2”) uses the casting speed measuring roll 8 to sequentially measure the slab drawing speed (casting speed) of the continuous casting machine 9, thereby casting speed. It is a process to grasp. In addition, S2 can be a process of grasping the casting speed by receiving data related to the setting value of the casting speed from, for example, a host computer (not shown) of the cooling control device 10.

  The tracking surface setting step (hereinafter sometimes referred to as “S3”) is a method of calculating the tracking surface, the surface temperature of the slab, the surface temperature of the slab, and the solid fraction distribution, and the position of the molten metal surface in the mold. Is a step of setting at a predetermined interval in a region from at least to the cooling zone outlet of the secondary cooling control target.

  The slab target temperature setting step (hereinafter, sometimes referred to as “S4”) is performed on the tracking surface set in S3 on both sides of the slab with respect to the width direction center line. This is a step of determining the same target value of the slab surface temperature.

The temperature solid phase ratio estimation step (hereinafter sometimes referred to as “S5”) is transmitted each time the tracking surface determined in S3 advances by a predetermined interval in the casting direction of the slab as casting progresses. This is a step of calculating and updating the slab cross-sectional temperature perpendicular to the casting direction, the surface temperature at each symmetric position of the slab, and the solid fraction distribution by a heat transfer solidification model based on the heat equation.
In S5, the amount of change from the previous control cycle of the temperature and solid phase ratio distribution in the vertical cross section set at regular intervals in the casting direction of the slab is changed to the heat conduction equation considering the transformation heat generated when the steel solidifies. Calculate by solving.
More specifically, assuming that the current time is t, the above formulas (2) to (10) are regarded as relational expressions between variables between time t-1 and time t, and calculation adjacent to the mold surface in the mold is performed. The temperature of the cross section and the solid fraction distribution at each calculation point from the point to the cooling zone outlet of the secondary cooling control target are calculated.

  The heat transfer coefficient estimation step (hereinafter also referred to as “S6”) is a heat transfer coefficient (the heat transfer coefficient represented by the above formulas (6) to (9)) used in the heat transfer solidification model. ) Is calculated using the estimated value of the heat transfer coefficient model parameter at the current time t and the casting conditions such as the cooling water flow rate at the time t-1.

  The heat transfer coefficient model parameter correction step (hereinafter sometimes referred to as “S7”) includes the surface temperature at each of the symmetric positions of the slab measured at S1 and each of the symmetries of the slab estimated at S5. This is a step of correcting the parameter in the heat transfer coefficient model using the difference from the surface temperature at the position.

  The correction of the parameter of the heat transfer coefficient model is performed by correcting the error between the surface temperature at each symmetric position of the slab measured at S1 and the estimated value of the surface temperature at each symmetric position of the slab estimated at S5. Is added to the parameter of the heat transfer coefficient model as a model parameter correction amount. When there are a plurality of measurement points of the surface temperature of the slab (hereinafter sometimes referred to as “temperature measurement points” or “temperature measurement positions”), the correction coefficient is represented by a matrix or a vector. The correction coefficient used for correcting the parameters of the heat transfer coefficient model is obtained for each parameter to be estimated by the following procedure.

1) For the parameter to be corrected, a value slightly changed from the current value is set.
2) The temperature and the solid phase ratio cross section at the casting direction position z _k (t-Ta) where the cross section at the temperature measurement position z _k at the current time t goes back from the present at a predetermined time Ta. The internal distribution is the initial value. Then, by giving a history of cooling conditions from the position z _k (t-Ta) at the time t-Ta to the temperature measurement position z _k at the current time t, and repeating the calculations of the above equations (2) to (10). Then, the estimated temperature value at the temperature measurement point when the parameter is slightly changed at the current time t is calculated. Retroactive time range Ta is corrected target parameters may be limited to a range affected in the state of the cross section in the temperature measurement position z _k.
3) A linear relational expression representing the relationship of the temperature change amount to each parameter correction amount is obtained by the following procedure.
When the parameter θ _i is changed by Δθ _i , the estimated surface temperature calculated in 2) above changes to T _k + ΔT _{k, i} with respect to the surface temperature T _k (t) at the current time t estimated in S5. Assuming that, ΔT _{k, i} can be expressed by the following equation (13).

By modifying the equation (13), A ^a _ki in the above equation (13) can be expressed by the following equation (14).

When ^a matrix having A ^a _ki as a component of k rows and i columns is expressed as A ^a , a temperature change estimated value that combines the effects on the surface temperature at the temperature measurement point by all the correction target parameters is Δθ _i as the i-th component. The vector Δθ = [Δθ ₁ Δθ ₂ ... Δθ _k ] ^T is expressed as A ^a Δθ.

The optimum correction amount of the parameter is the deviation ψ ^a _k (t) between the temperature measurement values T ^a _k (t) and T _k (t) of the respective temperature measuring points expressed by the following formula (15). When the vector is ψ ^a (t), the estimated temperature change value A ^a Δθ based on the corrected parameter is determined so as to best approximate the temperature change in consideration of numerical calculation errors and data variations.

In this step, for example, when ^a matrix representing an error of each component of the gain matrix A ^a is ΔA ^a ,

Find the value that minimizes. Here, <x> represents an expected value of the variable x.

  The minimum value of J represented by the above equation (16) can be solved analytically, and the optimal correction amount Δθ (t) of the parameter that minimizes J can be represented by the following equation (17).

Here, it is assumed that <ΔA ^a > = 0. <ΔA ^aT ΔA ^a > is represented by a matrix having the variances of the diagonal components ΔA ^a _ii as diagonal components at the same position, assuming that the correlation of each component of the gain matrix is zero. Predetermined by knowledge such as
The parameter correction amount Δθ (t) obtained as described above is added to the current parameter.

Is used to calculate the control operation amount after the next time.

  The future prediction plane setting step (hereinafter sometimes referred to as “S8”) is the above-described symmetry of the slab at a future time at a predetermined interval in a predetermined casting direction from the tracking plane set in S3. This is a step of setting a future prediction surface for predicting the surface temperature at the position, the temperature within the slab cross section, and the solid fraction distribution.

  In the future prediction process (hereinafter, sometimes referred to as “S9”), as the casting proceeds, any future prediction plane set in S8 advances from the current time to the future prediction plane position adjacent to the downstream side. Assuming that the casting speed does not change from the current time, the surface temperature at each symmetrical position of the slab when each future predicted surface set in S8 reaches the future predicted surface position adjacent to the downstream side, This is a step of repeatedly predicting and updating the temperature in the single cross section and the solid phase ratio distribution using the heat transfer solidification model at intervals determined in S8. In S9, using the casting speed at the current time, the amount of cooling water in each cooling zone, and the value of the parameter of the heat transfer coefficient model corrected in S7, the surface temperature at each of the symmetric positions of the slab, the slab cross-section temperature And predict the solid fraction distribution. As the initial value of the prediction calculation, the values of the surface temperature, the slab cross-sectional temperature, and the solid phase ratio distribution at each of the symmetric positions of the slab of the future prediction surface at the current time t obtained in S5 are used.

FIG. 4 shows the relationship between the position of the tracking surface for evaluating the surface temperature and the relative time for predicting the temperature while each future prediction surface set in S8 moves to the future prediction surface position adjacent to the downstream side. It is a figure explaining. FIG. 4 shows that the surface temperature is predicted at the time indicated by “●”. The inclination of the oblique straight line connecting a plurality of “●” shown in FIG. 4 corresponds to the casting speed v (t) at the current time t. In S9, the slab surface temperature predicted value at the tracking surface position z _j of the future predicted surface i is set as a future predicted temperature T _ij ^pred .

The future temperature influence coefficient prediction step (hereinafter, sometimes referred to as “S10”) is performed every time the future prediction plane set in S8 advances from the current time to the future prediction plane position adjacent to the downstream side as casting progresses. Furthermore, assuming that the casting speed does not change from the current time, each future prediction plane reaches the future prediction plane position adjacent to the downstream side when the cooling water flow rate in each cooling zone changes in a step function. The surface temperature at each of the symmetric positions of the slab at each tracking surface position passing through is predicted, and the surface temperature at each of the symmetric positions of the predicted slab and the surface at each of the symmetric positions of the slab predicted at S9. In this step, a deviation from the temperature is obtained, and a future temperature influence coefficient related to the deviation and the cooling water flow rate changing in a step function is obtained. In the following description, the variable on the R side of the center line in the width direction of the slab is expressed using a superscript ^(R), and the variable on the L side of the center line in the width direction of the slab is expressed as a superscript ^{( L)} .

In S10, for each cooling zone k, on the R side of the center line in the width direction of the slab, each cooling water flow rate q ^(R) _k (t) is changed in a step function by Δq ^(R) _k at the current time t. In this case, the surface temperature T _ij ^{(R) k} of the slab when the future predicted surface i reaches the future predicted surface position z _j adjacent to the downstream side is predicted. Then, a difference ΔT _ij ^{(R) k} (t) = T _ij ^{(R) k−} T _ij ^{(R) pred} between T _ij ^{(R) pred} predicted in S9 and the above Δq ^(R) _k Relationship

The coefficient M ^{(R) k} _ij is expressed as a future temperature influence coefficient. In S10, a surface temperature change gain matrix M ^(R) _{i in} which the future temperature influence coefficient M ^{(R) k} _ij is arranged in the j row and k column components is calculated for each future prediction plane.

Similarly, on the L side of the center line in the width direction of the slab, if each cooling water flow rate q ^(L) _k (t) is changed in a step function by Δq ^(L) _k at the current time t, the future The surface temperature T _ij ^{(L) k} of the slab when the predicted surface i reaches the future predicted surface position z _j adjacent to the downstream side is predicted. Then, the difference ΔT _ij ^{(L) k} (t) = T _ij ^{(L) k−} T _ij ^{(L) pred} between T _ij ^{(L) pred} predicted in S9 and the above Δq ^(L) _k Relationship

The coefficient M _ij ^{(L) k} is expressed as a future temperature influence coefficient. In S10, a surface temperature change gain matrix M _i ^{(L) in} which the future temperature influence coefficient M _ij ^{(L) k} is arranged in the j row and k column components is calculated for each future prediction plane.

The slab surface reference temperature calculation step (hereinafter sometimes referred to as “S11”) is a target value of the slab surface temperature set in S4 for each of the R side and the L side of the center line in the width direction of the slab. And an intermediate target value determined according to time (prediction calculation of S10), which is a value between the predicted value of the slab surface temperature at the time when the future prediction surface reaches the future prediction surface position predicted in S10 This is a step of calculating a reference target temperature that is asymptotic to the target value of the slab surface temperature set in S4 each time the process is repeated.
In S11, for example, with respect to the R side, the reference target temperature T _ij ^{(R) ref at} the temperature evaluation point z _j of the cross section at the entrance of the i-th cooling zone at the current time is the future as shown in the following equation (21). It can be defined as a temperature that internally ^divides between the predicted temperature T _ij ^{(R) pred} and the target temperature T _j ^{(R) tgt} by a ratio according to an exponential function of time t _ij . S11 is a step of obtaining a reference target temperature trajectory T _ij ^{(R) ref} represented by a function of time and obtaining a reference target temperature trajectory T _ij ^{(L) ref} represented by a function of time in the same manner. , And can be. T _ij ^{(L) ref} can be expressed by the following formula (22).

In Equation (21) and Equation (22), _Tr is a time constant corresponding to a predetermined attenuation parameter.

The optimization problem coefficient matrix calculation step (hereinafter, sometimes referred to as “S12”) is the cooling of each cooling zone including the cooling water flow rates set independently on the R side and the L side at the current time t. With the water flow rate as a decision variable, the future temperature influence coefficient at each future prediction plane position through which each future prediction plane passed in each of S9 and S10, the reference temperature calculated in S11 and the surface temperature of the slab predicted in S9 And calculating a coefficient matrix for a decision variable in the quadratic programming problem, specifying a quadratic programming problem of an optimization problem that minimizes the sum of the deviations calculated on each of the future prediction planes. .
In S12, the optimum values of the change step widths Δq ^(R) _k and Δq ^(L) _k on the R side and the L side of the cooling water flow rate in each cooling zone are determined according to the casting at each evaluation position z _j at the evaluation time t. Weighted sum of squares of deviation between single surface temperature response T _ij ^pred (t) + ΔT _ij (t) and reference temperature T _ij ^ref (t), and sum of squares of change step width Δq _k of cooling water flow rate in each cooling zone The evaluation function represented by the sum of the R-side evaluation function J ^(R) represented by the following formula (23) and the L-side evaluation function J ^(L) represented by the following formula (24) Δq = [Δq ^(R) ₁ Δq ^(R) ₂ ... Δq ^(R) _K Δq ^(L) ₁ Δq ^(L) ₂ ... Δq ^(L) _K ] that minimizes J = J ^(R) + J ^{(L) Calculate} as ^T.

^{_{Here, T i (R) pred,}} T i (R) ref, ΔT i (R), T i (L) pred, T i (L) ref, and, [Delta] T _{i ^(L),} respectively, wherein (25), Formula (26), Formula (27), Formula (28), Formula (29), and Formula (30).

  The term of temperature deviation of the evaluation function can be rewritten as the following equation (31) using the gain matrix obtained in S10.

Further, except for a term irrelevant to the change step width of the cooling water flow rate, the minimization of the evaluation function of the above equation (23) is equivalent to the minimization of J _R ′ represented by the following equation (32).

Further, the minimization of the evaluation function of the above equation (24) is equivalent to the minimization of the evaluation function J _L ′ when the subscript ^(R) of the above equation (32 ⁾ is replaced with ^(L) . Therefore, minimization of the evaluation function is equivalent to minimization of J ′ = _JR ′ + _JL ′.

  J 'minimization is a quadratic programming problem with Δq as a decision variable. Q is an I × I-dimensional non-negative definite matrix, and R is a K × K-dimensional positive definite matrix. For example, a diagonal matrix whose diagonal component is a non-negative constant is used for Q, and a diagonal matrix whose diagonal component is a positive constant is used for R. Furthermore, physical constraints in the mist spray 2 can be reflected by adding constraint conditions based on the upper and lower limits of the change step width of the cooling water flow rate and the upper and lower limits of the cooling water flow rate.

The optimization problem solving process (hereinafter, sometimes referred to as “S13”) is a step function function by numerically solving the quadratic programming problem in S12. This is a step of obtaining the optimum value Δq ^* of the change amount Δq of the cooling water flow rate at the current time t in the cooling zone. Since the quadratic programming problem identified in S12 is a convex quadratic programming problem, when Δq is not restricted, the optimum value Δq ^* is obtained by the following equation (33). When Δq is constrained, the optimum solution Δq ^* can be easily obtained by using an effective constraint method or the like.

The cooling water flow rate changing step (hereinafter sometimes referred to as “S14”) is performed by adding the optimum solution Δq ^* obtained in S13 to the cooling water flow rate q (t) of the current cooling zone.

Change to The coolant flow rate q (t + 1) thus changed is used in the next control cycle.

  According to the cooling control method of the present invention having S1 to S14, the influence of the change in the cooling water amount is immediately applied to a position other than the inlet of the cooling zone adjacent to the downstream side in the casting direction of the tracking surface for evaluating the surface temperature. Can be reflected. Furthermore, since the same target temperature is given to each of the R side and the L side, and the cooling water flow rate is controlled independently on each of the R side and the L side, the temperatures on the R side and the L side can be kept symmetrical. Become. That is, according to the cooling control method of the present invention, the surface temperature distribution in the full width direction of the slab can be controlled symmetrically with respect to the center line of the slab. Therefore, according to the cooling control method of the present invention, it is possible to improve the accuracy when the surface temperature of the entire slab is controlled to a predetermined target temperature. By accurately controlling the surface temperature of the entire slab to the target temperature, the surface temperature of the continuous casting machine in the bending segment and the straightening segment at any casting speed and even when the casting speed changes during casting. Since it becomes possible to control so as to avoid the embrittlement region, it becomes possible to manufacture a slab free from defects due to surface defects.

  The cooling control method of the present invention described above can be implemented using, for example, the cooling control device 10 shown in FIGS. As shown in FIG. 5, the cooling control device 10 includes a surface temperature measuring device 7 (L side temperature measuring device 7L and R side temperature measuring device 7R) functioning as a slab surface temperature measuring unit, and a casting speed grasping unit. A functioning casting speed measuring roll 8 (casting speed grasping part 8), a tracking surface setting part 10a, a slab target temperature setting part 10b, a temperature solid phase ratio estimating part 10c, and an L functioning as a heat transfer coefficient estimating part. Side heat transfer coefficient estimation unit 10dL and R side heat transfer coefficient estimation unit 10dR, L side heat transfer coefficient model parameter correction unit 10eL and R side heat transfer coefficient model parameter correction unit 10eR functioning as a heat transfer coefficient model parameter correction unit, The future prediction plane setting unit 10f, the L-side future prediction unit 10gL and the R-side future prediction unit 10gR functioning as the future prediction unit, and the future temperature influence coefficient prediction unit L-side future temperature influence coefficient prediction unit 10hL and R-side future temperature influence coefficient prediction unit 10hR, L-side slab surface reference temperature calculation unit 10iL and R-side slab surface reference temperature that function as a slab surface reference temperature calculation unit A calculation unit 10iR, an optimization problem coefficient matrix calculation unit 10j, an optimization problem solution unit 10k, a cooling water flow rate change unit 101, an L-side cooling water flow rate control unit 10mL, and an R-side cooling water flow rate control unit 10mR, have. As described above, the L-side temperature measuring device 7L and the R-side temperature measuring device 7R are used in S1, and the casting speed measuring roll 8 (casting speed grasping portion 8) is used in S2. Further, S3 is in the tracking surface setting unit 10a, S4 is in the slab target temperature setting unit 10b, S5 is in the temperature solid phase ratio estimation unit 10c, and the L side heat transfer coefficient estimation unit 10dL and the R side heat transfer coefficient estimation unit 10dR. In S6, S7 is performed in the L-side heat transfer coefficient model parameter correction unit 10eL and the R-side heat transfer coefficient model parameter correction unit 10eR, respectively. Further, S8 in the future prediction plane setting unit 10f, S9 in the L side future prediction unit 10gL and the R side future prediction unit 10gR, and S10 in the L side future temperature influence coefficient prediction unit 10hL and the R side future temperature influence coefficient prediction unit 10hR. However, S11 is performed in the L-side slab surface reference temperature calculation unit 10iL and the R-side slab surface reference temperature calculation unit 10iR, respectively. Further, S12 is performed in the optimization problem coefficient matrix calculation unit 10j, S13 is performed in the optimization problem solving unit 10k, and S14 is performed in the cooling water flow rate changing unit 10l. And the information regarding the change width of the L side cooling water flow rate specified by the cooling water flow rate changing unit 10l controls the cooling water flow rate injected from the mist spray 2 arranged on the L side. Cooling water that is sent from the mist spray 2 that is sent to the flow rate control device unit 10mL and that is specified by the cooling water flow rate changing unit 10l and that is related to the change amount of the R side cooling water flow rate is arranged on the R side It is sent to the R-side cooling water flow rate controller 10mR that controls the flow rate. And the information regarding the actual value of the L-side cooling water flow rate controlled by the L-side cooling water flow rate control unit 10 mL is sent to the L-side heat transfer coefficient estimation unit 10 dL, and the R-side cooling water flow rate control unit 10 mR. Is sent to the R-side heat transfer coefficient estimator 10dR, and this information is used in the next control cycle. By using the cooling control device 10 configured as described above, the cooling control method of the present invention can be implemented. Therefore, according to this invention, the secondary cooling control apparatus of a continuous casting machine which can control the surface temperature distribution of the full width direction of a slab symmetrically with the centerline of a slab can be provided.

  Moreover, as shown in FIG.1, FIG.2 and FIG.5, the continuous casting machine 9 of this invention is equipped with the L side temperature measuring device 7L and R side temperature measuring device 7R which make a pair, Cooling control of this invention. Since the apparatus 10 is provided, the cooling control method of the present invention can be implemented. Therefore, according to this invention, the continuous casting machine which can control the surface temperature distribution of the full width direction of a slab symmetrically with the centerline of a slab can be provided.

In the continuous casting machine for slabs, an embodiment in which the present invention is applied is shown below from the first cooling zone immediately below the mold outlet to the final tenth cooling zone.
As the temperature target value, the slab surface temperature calculated value at the tracking surface position by the strand heat transfer solidification calculation when the cooling water flow rate in each cooling zone was optimized was assumed, assuming that the casting speed was constant. The continuous casting machine used in this example has a slab width of 2300 mm, a slab thickness of 300 mm, a distance from the meniscus position in the mold to the outlet of the secondary cooling zone, and a casting direction more than the surface temperature measuring device. Is a continuous casting machine for slabs equipped with a secondary cooling control device that can independently adjust the cooling water flow rate on both sides of the center line in the width direction of the slab on the downstream side of the slab. In the following, when standing on the upper surface of the slab and looking at the upstream side in the casting direction, the secondary cooling zone on the right side of the center line in the width direction of the slab is the R side and 2 on the left side of the center line in the width direction of the slab. The next cooling zone is referred to as the L side.
The update interval of the heat transfer calculation in this example was 25 mm, the tracking surface interval was 125 mm, and the future temperature prediction surface interval was 1.25 m. On the tracking surface, a half section obtained by dividing the cross section of the slab by the center line of the short side was divided into 20 sections in the thickness direction and 40 sections in the width direction, and the calculation using the heat transfer solidification model was performed.
The surface temperature of the slab is measured on the exit side of the fourth cooling zone. The temperature measurement position on the L side of the slab and the temperature measurement position on the R side are the 1/6 width position of the slab width of 2300 mm and 5 The surface temperature of the slab was measured with a radiation thermometer.

[Example]
After changing the casting speed from 0.7 m / min to 0.8 m / min during casting, the surface temperature on the L side and R side of the slab was controlled by applying the cooling control method of the present invention. FIG. 6 shows the results of the target temperature of the slab, the actual value of the surface temperature of the slab, the cooling water flow rate, and the casting speed on the L side and the R side.
When cooling was performed at the cooling water flow rate set in the calculation of the cooling water flow rate in advance, the surface temperature on the R side was kept constant, but the surface temperature on the L side was 742 as shown at time 0 in FIG. The surface temperature was 16 ° C. higher than the 726 ° C., which is the surface temperature on the R side, and the surface temperature was asymmetric between the L side and the R side of the slab.
Therefore, while sequentially estimating the actual heat transfer coefficient by the method described above, the cooling water flow rate is optimally controlled while changing the cooling water flow rate only on the L side in a step function without changing the cooling water flow rate on the R side. . As a result, as shown in FIG. 6, on the L side, the cooling water flow rate increased from the initial set value, and the temperature at the temperature measuring point on the L side coincided with the target value after 350 seconds. From the above, according to the present invention, it was confirmed that the surface temperature distribution in the full width direction of the slab can be controlled to the target value symmetrically with the center line of the slab even if the casting speed is changed midway. .

[Comparative example]
On the other hand, after changing from 0.7 m / min to 0.8 m / min during casting, the cooling water flow rate in the entire width direction of the slab is optimized based on the L side temperature measurement value and the temperature prediction result, The surface temperature of the slab was controlled by applying a conventional cooling control method that uniformly changes the cooling water flow rate in the width direction of the slab. FIG. 7 shows the results of the target temperature of the slab on the L side and the actual values of the surface temperature of the slab, the actual values of the target temperature of the slab of the R side and the surface temperature of the slab, the cooling water flow rate, and the casting speed. Show. Unlike the example, in the comparative example, the cooling water flow rate is not controlled independently on the L side and the R side, and therefore there is only one line representing the result of the cooling water flow rate shown in FIG.
As a result of controlling the cooling water flow rate by the conventional method, the cooling water flow rate in the fourth cooling zone gradually increases after the casting speed is increased, and the surface temperature on the R side of the fourth cooling zone is controlled without greatly deviating from the target value. It was.
On the other hand, as shown in FIG. 7, the surface temperature on the L side decreased as the cooling water flow rate was increased. This is probably because the L side had less scale adhesion than the R side and had a larger heat transfer coefficient, and therefore could not perform the same temperature control as the R side.

DESCRIPTION OF SYMBOLS 1 ... Mold 2 ... Mist spray 3 ... Cooling water flow rate adjustment valve 4 ... Molten steel meniscus 5 ... Slab 6 ... Cooling zone boundary line (inlet or outlet position)
7 ... Surface temperature measuring device (surface temperature measuring unit)
7L ... L side temperature measuring device (surface temperature measuring device, surface temperature measuring unit)
7R ... R side temperature measuring device (surface temperature measuring device, surface temperature measuring unit)
8 ... Casting speed measuring roll (Casting speed grasping part)
9 ... Continuous casting machine 10 ... Cooling control device (secondary cooling control device)
DESCRIPTION OF SYMBOLS 10a ... Tracking surface setting part 10b ... Slab target temperature setting part 10c ... Temperature solid phase ratio estimation part 10dL ... L side heat transfer coefficient estimation part (heat transfer coefficient estimation part)
10dR ... R side heat transfer coefficient estimator (heat transfer coefficient estimator)
10eL ... L-side heat transfer coefficient model parameter correction unit (heat transfer coefficient model parameter correction unit)
10eR ... R side heat transfer coefficient model parameter correction section (heat transfer coefficient model parameter correction section)
10f ... Future prediction plane setting unit 10gL ... L side future prediction unit (future prediction unit)
10gR ... R side future prediction part (future prediction part)
10hL ... L side future temperature influence coefficient prediction part (future temperature influence coefficient prediction part)
10hR ... R side future temperature influence coefficient prediction section (future temperature influence coefficient prediction section)
10iL ... L-side slab surface reference temperature calculation unit (slab surface reference temperature calculation unit)
10iR ... R side slab surface reference temperature calculation unit (slab surface reference temperature calculation unit)
10j ... Optimization problem coefficient matrix calculation unit 10k ... Optimization problem solving unit 10l ... Cooling water flow rate changing unit 10mL ... L side cooling water flow rate control unit 10mR ... R side cooling water flow rate control unit

Claims (2)

A secondary cooling zone for cooling the slab drawn from the mold of the continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slab, and the flow rate of the cooling water injected toward the slab is changed to each In the method of controlling the surface temperature of the slab by controlling in the cooling zone,
The surface temperature of the slab at the symmetrical position is measured during casting by a surface temperature measuring device arranged so as to be paired with a symmetrical position on both sides of the slab as a center in the width direction. A single surface temperature measurement step;
A casting speed grasping step for grasping a casting speed of the continuous casting machine;
The slab cross-section in the temperature, the surface temperature of the slab, and the cooling zone of at least 2 primary cooling control Target tracking surface which is subject to calculate the solid fraction distribution of the cast piece, from the mold molten steel surface position In the area to the exit, setting at a predetermined interval, a tracking surface setting step,
A slab target temperature setting step for determining the same target value of the surface temperature of the slab at each symmetrical position on both sides of the tracking surface;
Each time the tracking surface advances by a predetermined interval in the casting direction of the slab as casting progresses, the temperature in the cross section of the slab perpendicular to the casting direction is determined by a heat transfer solidification model based on a heat transfer equation. A temperature solid phase ratio estimating step of calculating and updating the surface temperature at each of the symmetrical positions of the slab and the solid phase ratio distribution of the slab,
A heat transfer coefficient estimation step of calculating a heat transfer coefficient of the surface of the slab used in the heat transfer solidification model by a heat transfer coefficient model using the cooling water flow rate; and
The surface temperature at each symmetrical position of the slab measured in the slab surface temperature measuring step and the surface temperature at each symmetrical position of the slab estimated in the temperature solid phase ratio estimating step. A heat transfer coefficient model parameter correction step of correcting the parameter of the heat transfer coefficient model using the difference; and
Among the tracking surfaces set in the tracking surface setting step, a surface temperature at each symmetrical position of the slab at a future time at a predetermined interval in a predetermined casting direction, the perpendicular to the casting direction. A future prediction surface setting step for setting a future prediction surface for predicting the temperature in the cross section of the slab and the solid phase ratio distribution of the slab,
As the casting progresses, it is assumed that the casting speed does not change from the current time while any future prediction plane advances from the current time to the future prediction plane position adjacent to the downstream side. Is the surface temperature at each of the symmetric positions of the slab, the temperature in the cross section of the slab perpendicular to the casting direction, and the solid fraction distribution of the slab when the predicted surface position is reached , For each interval used in the future prediction surface setting step, repeatedly predicting and updating using the heat transfer solidification model, a future prediction step,
As the casting progresses, every time the future prediction plane advances from the current time to the future prediction plane position adjacent to the downstream side, it is assumed that the casting speed does not change from the current time. The surface temperature at each symmetrical position of the slab at each tracking surface position, through which each of the future prediction surfaces reaches the future prediction surface position when the water flow rate changes in a step function. Predicting using the heat transfer solidification model, the predicted surface temperature of each of the slabs at the symmetrical position, and the predicted surface temperature of each of the slabs at the symmetrical position predicted in the future prediction step. A future temperature influence coefficient predicting step for obtaining a deviation and obtaining a future temperature influence coefficient related to the deviation and the cooling water flow rate changing in a step function;
The casting temperature determined at the slab target temperature setting step and the surface temperature at each symmetrical position of the slab when the future prediction surface reaches the tracking surface position, predicted at the future prediction step. A slab surface reference temperature calculation step for calculating a reference temperature of a slab surface, which is an intermediate target temperature at each of the symmetric positions of the slab, connecting a target value of the surface temperature at each of the symmetric positions of the slab. When,
With the cooling water flow rate of each cooling zone including the cooling water flow rate set independently on both sides of the center line in the width direction of the slab at the current time as a decision variable, the future prediction step and the future temperature influence coefficient prediction The future temperature influence coefficient at each future prediction plane position through which each of the future prediction planes passes in each of the processes, the reference temperature calculated in the slab surface reference temperature calculation process, and the casting predicted in the future prediction process A deviation from the surface temperature of the piece is calculated, a quadratic programming problem of an optimization problem that minimizes the sum of the deviations calculated in the respective future prediction planes is specified, and a coefficient for a decision variable in the quadratic programming problem An optimization problem coefficient matrix calculation step for calculating a matrix;
By solving the secondary planning problem numerically, an optimum value of the change amount of the cooling water flow rate at the current time of the cooling zone on each side of the center line in the width direction of the slab, which changes in a step function shape, is obtained. Find the optimization problem solving process,
Changing the cooling water flow rate by adding the optimum value on each side of the width direction center line of the slab to the current cooling water flow rate of the cooling zone on each side of the width direction center line of the slab, A cooling water flow rate changing step,
By repeating the change of the cooling water flow rate in the cooling water flow rate changing step, the future prediction surface is changed while each tracking surface moves to the cooling zone outlet of the secondary cooling control target at an arbitrary time during casting. The surface temperature at each symmetrical position of the slab at the future predicted surface position is controlled to the target value of the surface temperature at each symmetrical position of the slab determined in the slab target temperature setting step. A secondary cooling control method for a continuous casting machine. A secondary cooling zone for cooling the slab drawn from the mold of the continuous casting machine is divided into a plurality of cooling zones in the casting direction of the slab, and the flow rate of the cooling water injected toward the slab is changed to each A device for controlling the surface temperature of the slab by controlling in the cooling zone,
The slab surface temperature measurement is performed such that the surface temperature at the symmetrical position of the slab is measured during casting, with the center line in the width direction of the slab as an axis. And
A casting speed grasping unit for grasping a casting speed of the continuous casting machine;
The slab cross-section in the temperature, the surface temperature of the slab, and the cooling zone of at least 2 primary cooling control Target tracking surface which is subject to calculate the solid fraction distribution of the cast piece, from the mold molten steel surface position A tracking surface setting unit that is set at predetermined intervals in the area to the exit;
A slab target temperature setting unit that defines the same target value of the surface temperature of the slab at each symmetrical position on both sides of the tracking surface,
Each time the tracking surface advances by a predetermined interval in the casting direction of the slab as casting progresses, the temperature in the cross section of the slab perpendicular to the casting direction is determined by a heat transfer solidification model based on a heat transfer equation. A surface temperature at each symmetrical position of the slab, and a solid phase ratio estimator for calculating and updating the solid fraction distribution of the slab, and
A heat transfer coefficient estimating unit for calculating a heat transfer coefficient of the surface of the slab used in the heat transfer solidification model by a heat transfer coefficient model using the cooling water flow rate;
The surface temperature at each symmetric position of the slab measured by the slab surface temperature measuring unit, and the surface temperature at each symmetric position of the slab estimated by the temperature solid phase ratio estimating unit A heat transfer coefficient model parameter correction unit for correcting the parameter of the heat transfer coefficient model using the difference;
Among the tracking surfaces set by the tracking surface setting unit, a surface temperature at each symmetrical position of the slab at a future time at a predetermined interval in a predetermined casting direction, and perpendicular to the casting direction. A future prediction surface setting unit for setting a future prediction surface for predicting the temperature in the cross section of the slab and the solid phase ratio distribution of the slab,
As the casting progresses, it is assumed that the casting speed does not change from the current time while any future prediction plane advances from the current time to the future prediction plane position adjacent to the downstream side. Is the surface temperature at each of the symmetric positions of the slab, the temperature in the cross section of the slab perpendicular to the casting direction, and the solid fraction distribution of the slab when the predicted surface position is reached , For each interval used in the future prediction plane setting unit, repeatedly predicting and updating using the heat transfer solidification model, a future prediction unit,
As the casting progresses, every time the future prediction plane advances from the current time to the future prediction plane position adjacent to the downstream side, it is assumed that the casting speed does not change from the current time. The surface temperature at each symmetrical position of the slab at each tracking surface position, through which each of the future prediction surfaces reaches the future prediction surface position when the water flow rate changes in a step function. Predicting using the heat transfer solidification model, the predicted surface temperature of each of the slabs at the symmetrical position and the predicted surface temperature of each of the slabs of the slab predicted by the future prediction unit A future temperature influence coefficient prediction unit that obtains a deviation and obtains a future temperature influence coefficient related to the deviation and the cooling water flow rate that changes in a step function;
The casting temperature determined by the future prediction unit, the surface temperature at each symmetrical position of the slab when the future prediction surface reaches the tracking surface position, and the slab target temperature setting unit. A slab surface reference temperature calculation unit that calculates a reference temperature of a slab surface that is an intermediate target temperature at each of the symmetrical positions of the slab, connecting the target value of the surface temperature at each of the symmetric positions of the slab. When,
With the cooling water flow rate of each cooling zone including the cooling water flow rate set independently on both sides of the center line in the width direction of the slab at the current time as a decision variable, the future prediction unit and the future temperature influence coefficient prediction The future temperature influence coefficient at each future prediction plane position through which each of the future prediction planes passes in each of the sections, the reference temperature calculated by the slab surface reference temperature calculation section, and the casting predicted by the future prediction section A deviation from the surface temperature of the piece is calculated, a quadratic programming problem of an optimization problem that minimizes the sum of the deviations calculated in the respective future prediction planes is specified, and a coefficient for a decision variable in the quadratic programming problem An optimization problem coefficient matrix calculation unit for calculating a matrix;
By solving the secondary planning problem numerically, an optimum value of the change amount of the cooling water flow rate at the current time of the cooling zone on each side of the center line in the width direction of the slab, which changes in a step function shape, is obtained. The optimization problem solving section
Changing the cooling water flow rate by adding the optimum value on each side of the width direction center line of the slab to the current cooling water flow rate of the cooling zone on each side of the width direction center line of the slab, A cooling water flow rate changing unit,
By repeating the change of the cooling water flow rate in the cooling water flow rate changing unit, the future prediction surface is changed while each tracking surface moves to the cooling zone outlet of the secondary cooling control target at an arbitrary time during casting. The surface temperature at each symmetric position of the slab at the predicted future surface position is controlled to the target value of the surface temperature at each symmetric position of the slab determined by the slab target temperature setting unit. A secondary cooling control device for a continuous casting machine.