JPH10109151A - Method for calculating solidification thickness of continuously casting strand - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calculating method of solidification thickness in a continuously casting strand, which can calculate the thickness of the solidified part of the strand in high precision according to the change of operational condition even in the case of using a computer comparatively low in calculating speed and low in price. SOLUTION: The relation between the thickness of the solidified part of the strand in a suitable position in the drawing direction of a continuous caster and casting velocity, is beforehand obtd. in off-line by using a heat conductive model. The length of the strand 1 drawn from a mold M is measured in each prescribed time, and a time Tj needed for the strand 1 to arrive at the position is calculated based on each obtd. length and a historical casting velocity VEj at the position is obtd. by using the calculated time Tj . Then, a corrective historical casting velocity VMEj =αj , the historical casting velocity VEj +(1-αj ) and the actual casting velocity VC are calculated, and the thickness Dshell j in the solidified part at the position is decided. Further, the Dshell j is corrected with the change of molten metal temp. in the mold M and the change of cooling water temp.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calculating the thickness of a solidified portion of a strand continuously drawn from a continuous casting machine.

[0002]

2. Description of the Related Art In a continuous casting machine, a molten metal is supplied into a mold from an immersion nozzle, and a strand having a solidified shell formed around it by primary cooling by contact with a water-cooled casting wall is drawn out of the mold. Then, the secondary cooling by spray water is performed, and the strand solidified to the center is cut into required lengths to continuously cast a plurality of cast pieces. In the operation of such a continuous casting machine, center segregation in which a specific metal element segregates in the center of the strand, and suppression of center porosity in which voids are generated in the center of the strand, prevention of internal cracks in the strand, or For the purpose of coping with the direct charge in which the slab is directly fed to the rolling process, it is important to accurately determine the thickness of the solidified portion at an appropriate position in the strand drawing direction of the continuous casting machine.

For example, in order to prevent the above-mentioned center segregation and center porosity, electromagnetic stirring of the unsolidified portion inside the strand or reduction of the strand in the vicinity of a completely solidified position solidified to the center thereof is known. In the case of, it is necessary to accurately determine the thickness of the unsolidified part, that is, the thickness of the solidified part, in order to set the conditions of electromagnetic stirring.
In the latter case, it is necessary to accurately determine the complete solidification position.

[0004] Further, internal cracks in the strand are caused by tensile stress at a bending point in a vertical bending continuous casting machine and at a correction point in a curved continuous casting machine. To estimate the tensile stress, the thickness of the solidified portion of the strand at the stress generating position must be determined with high accuracy. Further, in a continuous casting machine having a plurality of bending points, it is necessary to determine the tensile stress at each bending point, and to determine the thickness of the solidified portion of the strand at each position.

[0005] On the other hand, in order to carry out direct charging, it is necessary to set the completely solidified position of the strand near the cutting position of the slab in order to feed the slab as hot as possible to the rolling process. Therefore, it is necessary to obtain the thickness of the solidified portion at a plurality of points in the strand drawing direction of the continuous casting machine, and to grasp the completely solidified position.

In order to determine the thickness of a solidified portion of a strand, a method of calculating the thickness by the following equation (1) has been used. S = k√t (1) where S: thickness of solidified portion of the strand (mm) k: solidification coefficient t: elapsed time after casting (minutes)

[0007]

However, in the conventional method, since the thickness of the solidified portion is calculated using the simple formula (1), the calculation accuracy is low, and the operating conditions are low. Cannot respond to changes in

For this reason, Japanese Patent Application Laid-Open No. 5-123842 discloses that
A method is disclosed in which a required physical quantity is measured during operation, and the thickness of the solidified portion of the strand is calculated by performing online heat transfer calculation of the strand using the measured value.

[0009] However, in order to perform heat transfer calculation online, it is necessary to introduce a large computer that performs calculations at a high speed. However, such a large computer is expensive and has a problem of high equipment cost.

The present invention has been made in view of such circumstances, and an object of the present invention is to transmit a first relationship between the thickness of a solidified portion of a strand and a drawing speed at an appropriate position in a drawing direction of a continuous casting machine. Using a thermal model, the history drawing speed at the position is obtained based on the length of the strand measured every predetermined time, and the history drawing speed is measured using the measured drawing speed and a preset parameter. To obtain the correction history withdrawal speed, and by determining the thickness of the solidified portion at the position from the obtained correction history withdrawal speed and the first relationship, even with an inexpensive computer whose calculation speed is relatively slow. It is another object of the present invention to provide a method for calculating a solidified thickness of a continuous cast strand, which can accurately calculate the thickness of a solidified portion of a strand in accordance with a change in operating conditions.

Another object is to provide a second relation between the thickness of the solidified portion of the strand at an appropriate position in the drawing direction of the continuous casting machine and the temperature of the molten metal in the mold. A third relationship with the temperature of the cooling medium that cools the strand is obtained in advance, the thickness change amount of the solidified portion is calculated from the measurement result of the molten metal temperature and the second relationship, and the measurement result of the temperature of the cooling medium is obtained. And calculating the thickness change amount of the solidified portion from the third relationship, and correcting the thickness of the solidified portion determined based on the first relationship by using the obtained both thickness change amounts, thereby obtaining the temperature of the molten metal. It is an object of the present invention to provide a method for calculating the solidification thickness of a continuously cast strand, which can obtain the thickness of the solidified portion of the strand with higher calculation accuracy in consideration of the change and the change of the cooling water temperature.

[0012]

According to a first aspect of the present invention, there is provided a method for calculating a solidified thickness of a continuous cast strand, wherein a molten metal flows from one end of a mold, and a solidified portion is formed around the molten metal by contact with the mold. During the operation of a continuous casting machine that pulls the strand from the other end of the
In the method for calculating the thickness of the solidified portion of the strand at an appropriate position in the drawing direction of the continuous casting machine, a first relationship between the thickness of the solidified portion at the position and the drawing speed is obtained in advance using a heat transfer model. Measuring the length of the strand pulled out of the mold at predetermined intervals, calculating the time required for the strand to reach the position based on the measured lengths, and using the calculated time at the position. Determine the history pulling speed, and also measure the strand pulling speed, correct the history pulling speed using the measured pulling speed and the preset parameters to obtain a corrected history pulling speed, and obtain the corrected history pulling speed. And determining the thickness of the solidified portion at the position from the first relationship.

According to a second aspect of the present invention, there is provided a method for calculating a solidified thickness of a continuous cast strand according to the first aspect, wherein the corrected history drawing speed V _M is obtained by substituting the history drawing speed V _E , the drawing speed V _C and the parameter α into the following equation. It is characterized in that it is determined by: V _M = α · V _E + (1−α) · V _C where 0 <α <1

The first relationship between the thickness of the solidified portion of the strand and the drawing speed at an appropriate position in the drawing direction of the continuous casting machine is determined offline using a heat transfer model, and the strand is determined online using the first relationship. Since the thickness of the solidified portion is calculated as follows, even if an inexpensive computer having a relatively slow calculation speed is used, it is possible to cope with online calculations.

The length of the strand drawn from the mold is measured at predetermined intervals, and the total value of the obtained lengths and the distance from the meniscus to an appropriate position in the drawing direction of the continuous casting machine are determined. Then, the total number of times that the total value approximates the distance is obtained, and the time required for the strand to move from the meniscus to the position is calculated using the obtained total number. From the time thus calculated and the distance, the history drawing speed at an appropriate position in the drawing direction of the continuous casting machine is calculated. Thereby, the change in the drawing speed is taken into the history drawing speed. Also, based on the length obtained by measuring at regular intervals, to capture the change in the drawing speed, as in the case of actually measuring the drawing speed at the position, capture the change in the actual drawing speed with high accuracy. Can be.

Further, the drawing speed V _{C of the} strand is measured, and the drawing speed V _C , the history drawing speed V _E and the parameter α are substituted into the following equation (2) to obtain the corrected history drawing speed V _M.
Is calculated, and the obtained correction history extraction speed V _M and the first
From the relationship, the thickness of the solidified portion at the position is determined. V _M = α · V _E + (1−α) · V _C (2) where 0 <α <1

In the equation (2), the parameter α is empirically determined according to the relative relationship between the measurement position of the drawing speed V _C and the thickness calculation position for calculating the thickness of the solidified portion, the type of steel, the conditions of the casting equipment, and the like. The value of the parameter α is smaller as the thickness calculation position is closer to the measurement position, and is larger as the thickness calculation position is farther from the measurement position. In this way, in order to correct the history pull-out speed obtained at regular time intervals with the measured pull-out speed,
Errors due to so-called delays are reduced.

According to a third aspect of the present invention, there is provided a method for calculating a solidified thickness of a continuous cast strand according to the first or second aspect, wherein a second relationship between a thickness of a solidified portion at the position and a temperature of a molten metal in the mold is obtained in advance. In advance, the temperature of the molten metal is measured with time, and the temperature at the time when the thickness of the solidified portion is calculated and the temperature at the time immediately before the time by an appropriate time from the time are obtained. A thickness change amount of the solidified portion is calculated from the second relationship, and the thickness of the solidified portion determined based on the first relationship is corrected using the calculated thickness change amount.

According to a fourth aspect of the present invention, there is provided a method for calculating a solidified thickness of a continuous cast strand according to the first or second aspect, wherein a cooling medium is brought into contact with the strand to cool the strand, and the thickness of the solidified portion at the position and the cooling medium are determined. And the temperature at the time when the temperature of the cooling medium is measured over time to calculate the thickness of the solidified portion, and the time before the time as appropriate from the time. Is calculated from the obtained deviation and the third relationship, and the thickness change amount of the solidified portion is calculated from the obtained difference and the third relationship. Using the calculated thickness change amount, the thickness of the solidified portion determined based on the first relationship is calculated. Is corrected.

According to a fifth aspect of the present invention, in the method for calculating a solidified thickness of a continuous cast strand according to the first or second aspect, a second relationship between a thickness of a solidified portion at the position and a temperature of a molten metal in the mold is obtained in advance. In advance, the temperature of the molten metal is measured with time, and the first deviation between the temperature of the molten metal at the time when the thickness of the solidified portion is calculated and the temperature of the molten metal at a time immediately before the time by an appropriate time is determined. The thickness change amount of the solidified portion is calculated from the obtained first deviation and the second relationship, and the strand is cooled by contacting a cooling medium with the strand, and the thickness of the solidified portion and the temperature of the cooling medium at the position are cooled. Third
The relationship is obtained in advance, the temperature of the cooling medium is measured with time, and the temperature of the cooling medium at the time when the thickness of the solidified portion is calculated, and the temperature of the cooling medium at a time immediately before the time by an appropriate time. Of the solidified portion is calculated from the obtained second deviation and the third relationship, and the solidified portion determined based on the first relationship using both the obtained thickness change amounts. Is characterized in that the thickness is corrected.

The thickness of the solidified portion in the strand is affected by the temperature change of the molten metal flowing into the mold and the temperature change of the cooling water sprayed on the strand. Therefore, the second relationship between the temperature of the molten metal and the thickness of the solidified portion and the third relationship between the temperature of the cooling water and the thickness of the solidified portion are determined off-line. Then, online, the temperature of the molten metal, the temperature of the cooling water is measured over time, the two temperatures at the time when the thickness of the solidified portion is calculated, and the difference between the two temperatures measured immediately before the time, or The difference between the two temperatures at the time when the thickness of the solidified portion is calculated and the two temperatures at the time before the time required for the strand to reach the position from the time is calculated, and the calculated temperature deviation and the second relationship , And the third relationship, the amount of change in the thickness of the solidified portion is obtained,
In addition to the thickness of the solidified portion determined based on the first relationship. Thereby, the temperature change of the molten metal and the temperature change of the cooling water are taken into consideration, and the accuracy of calculating the thickness of the solidified portion is further improved.

[0022]

Embodiments of the present invention will be specifically described below with reference to the drawings. FIG. 1 is a schematic side view showing an example of a continuous casting machine used for carrying out the method of the present invention, in which L is a ladle for transporting molten metal (steel). The ladle L containing the molten metal is transferred onto the tundish T. An injection pipe IT is provided at the bottom of the ladle L, and the opening operation of the sliding gate interposed in the injection pipe IT causes
The molten metal flows from the ladle L into the tundish T.

An immersion nozzle I is provided at the bottom of the tundish T.
N is provided, and the immersion nozzle IN extends into a cylindrical mold M having a cooling water channel provided in the wall. The molten metal that has flowed into the tundish T is temporarily stored there and becomes a stable flow, and is guided into the mold M from the immersion nozzle IN. This molten metal is primarily cooled by contact with the casting wall of the mold M, becomes a strand 1 around which a solidified shell is formed, and is pulled out of the mold M. A spray roll band SR for spraying cooling water is arranged below the mold M. The strand 1 is secondarily cooled by the spray roll band SR, and the thickness of the solidified shell increases. Following the spray roll band SR, a plurality of roll segments RS ₁ , RS ₂ ,.
The pinch roll band PIR is arranged so as to have a predetermined curvature, and the strand 1 is further air-cooled while being corrected horizontally, and solidifies to its center. Pinch roll band PIR
A cutting machine 2 is arranged at a predetermined distance from the pinch roll band PIR, and the strand 1 solidified to the center is cut by the cutting machine 2 into a slab of a required length. In this way, a plurality of cast pieces are continuously cast.

In such a continuous casting machine, the opening of the sliding gate interposed in the immersion nozzle IN is adjusted so that the height of the meniscus 3 which is the surface of the molten metal in the mold M becomes constant. I have. Then, the thickness of the solidified portion of the strand 1 at an appropriate position in the drawing direction of the continuous casting machine is calculated as follows.

FIGS. 2A and 2B are explanatory diagrams for explaining a heat transfer model used in the embodiment of the present invention. FIG. 2A shows a case where the present invention is applied to a columnar strand, and FIG. Are respectively shown. As shown in FIG. 2 (a), in the case of a cylindrical strand, i = 1 is set at an appropriate position on the peripheral surface of the strand 1 and i = n at the center, i.e., in the thickness direction of the strand 1. Set multiple meshes. In the case of a slab or a bloom as shown in FIG.
1 and a plurality of meshes are set between the two with the center being i = n. Thus, the thickness SA direction of both strands 1 is set to 1
A one-dimensional heat transfer model as a dimension is set.

Then, a one-dimensional heat transfer model is represented by the following equations (3) to (6) by applying the enthalpy method. _{H i '= {Δt / (} ρ · ΔV i)} · (Q i -Q i + 1) + H i; i = 1, n-1 ... (3) H i' = {Δt / (ρ · ΔV i )｝ · Q _i + H _i ; i = n (center of slab) (4) Q _i = A _i · (K _i / ΔL _i ) · (T _i−1 −H _i ); i = 2 to n ( slab _{internal) ... (5) Q i =} a i · h · (T w -H i); ( slab surface) ... (6) However, H _i: enthalpy H _i ': enthalpy after Δt time Δt: time grid interval [rho: density [Delta] V _i: mesh volume Q _i: heat output flows in the mesh K _i: thermal conductivity T _i: temperature [Delta] L _i at the mesh points i: mesh distance T _w: the coolant temperature (cooling water H: heat transfer coefficient on the surface n: number of meshes

An appropriate casting speed (drawing speed) is set,
The temperature at each mesh point is calculated by using the equations (3) to (6), and the same calculation is performed by sequentially changing the position in the drawing direction of the continuous casting machine, so that the strand 1 at the set casting speed is set. Is obtained. Further, the same calculation is performed by changing the casting speed variously to obtain the temperature distribution of the strand 1 for each casting speed. When modeling a slab or bloom at an appropriate position in the width direction of the strand 1, the expressions (3) to (6) may be expressed in two dimensions.

On the other hand, boundary temperature T _{sh ell} the solidified portion and the non-solidified portion in the thickness direction of the strand is determined by the following equation (7). T _shell = (1−fs) · (Tl−Ts) + Ts (7) where fs: solid fraction Tl: liquidus temperature Ts: solidus temperature

[0029] Then, the temperature distribution of the strand was as calculated as described above, determine the position of the mesh is a boundary temperature T _shell, from the surface of the strand thickness to the position of the boundary temperature T _shell and the solidified thickness D _shell determined I do.

FIG. 3 is a graph showing an example of the relationship between the position in the drawing direction of the continuous casting machine and the thickness of the solidified portion of the strand, calculated by a one-dimensional heat transfer model. The horizontal axis represents the distance from the meniscus. The vertical axis indicates the thickness of the solidified shell. In FIG. 3, a and b show the cases where appropriate casting speeds V ₁ and V ₂ (V ₁ <V ₂ ) are set, respectively. In both cases, the solid phase ratio was 0.1.
The calculation was performed with the temperature of the molten metal and the temperature of the cooling water to be sprayed kept constant.

As shown in FIG. 3, in both cases a and b, as the distance from the meniscus increases, the thickness of the solidified portion gradually increases, and the thickness of the solidified portion rapidly increases to the center of the strand. Although it becomes constant after the increase, the extent to which the thickness of the solidified portion increases is a> b. In other words, even when the distance from the meniscus is the same, the degree to which the strand is cooled in a unit time is larger in the case where the casting speed is low than in the case where the casting speed is high. The solidified portion is thicker when the casting speed is faster. In FIG. 3, points P ₁ and P ₂ indicate the completely solidified positions of the strand at the pouring speeds V ₁ and V ₂ , respectively.

Such a graph is obtained for a plurality of casting speeds, and the relationship between the casting speed and the thickness of the solidified portion is obtained using the results.

FIG. 4 is a graph showing an example of the relationship between the casting speed and the thickness of the solidified portion of the strand. The horizontal axis shows the casting speed, and the vertical axis shows the thickness of the solidified shell. In FIG. 4, c is shorter than d from the meniscus.
As apparent from FIG. 4, at an appropriate position in the drawing direction of the continuous casting machine, there is a one-to-one relationship between the casting speed and the solidified thickness.
It can be seen that there is a corresponding relationship.

The above calculations are performed in advance offline, and FIG.
As described above, the relationship between the casting speed and the solidified thickness of the strand at an appropriate position in the drawing direction of the continuous casting machine is determined in advance. Then, the casting speed at the position is determined on-line as follows in consideration of the time-dependent speed change, and from the relationship between the determined casting speed and the casting speed determined offline and the solidification thickness of the strand, , Calculate the thickness of the solidified portion of the strand at said position.

FIG. 5 is an explanatory diagram for explaining a method of calculating the time required for the strand drawn from the mold to reach an appropriate position in the drawing direction of the continuous casting machine. At fixed time intervals ΔS ₁ , ΔS ₂ ,..., ΔS _m (for example, 10 seconds or 20 seconds), the head positions of the strands drawn from the mold are detected, and the length L ₁ from the meniscus to each head position is detected. , L ₂ ,..., L _m .

Now, assuming that the length that has increased within the time interval ΔS closest to the current time is l ₁ , after the elapse of the time interval ΔS _1,
The length L ₁ at the first time before the lapse of S ₂ is L ₁ = l ₁
It can be expressed as. Further, the length L ₂ at the second time after the elapse of the time interval ΔS _{2 and} before the elapse of the time interval ΔS ₃ is the first length L ₂ .
L ₂ , which was l ₁ at the time, and the time interval Δ
Due to the increased length l ₁ during S ₂ , L ₂ = l ₁ +
l ₂ . Accordingly, the length L _m of the m-th time before the time interval [Delta] S m _{+ 1} has elapsed after the time interval [Delta] S _m elapsed
Is the length l ₁ increased during the time interval ΔS _m and the (m
And l ₂ of the place was a l ₁ in -1) time, ...,
By the l _m where was l ₁ at the first time, it can be expressed as the following equation (8).

[0037]

(Equation 1)

Then, the continuous casting machine is pulled from the meniscus.
The length to the appropriate position in the pulling direction is D _jAnd the following (9)
Find m that satisfies the expression and substitute it for the following expression (10).
Depending on the method, how to pull out the continuous casting machine from the meniscus
Time required for the strand to move to the appropriate position in the direction
_jCan be requested. With this, within a certain time
Fluctuations in the casting speed can be captured. L_m<D_j<L_{m + 1} … (9) T_j= ΔS × ｛m + (D_j-L_m) / (L_{m + 1}-L_m) ... (10)

From the time T _j and the length D _j , the following (1)
The hysteresis casting speed V _Ej is calculated by the equation 1). V _Ej = D _j / T _j (11)

The above-mentioned time T _j is obtained by measuring the actual pouring speed with time, and the measurement result and the above-mentioned distance D _j
Can also be obtained from However, when the measurement position of the actual casting speed is different from the position at which the thickness of the solidified portion is determined, the measured actual casting speed is different from the actual casting speed at the position at which the thickness of the solidified portion is determined. _Therefore , the time T _j cannot be obtained accurately. In many cases, the actual casting speed cannot be measured directly at the position where the thickness of the solidified portion is determined. On the other hand, as described above, when using the casting length of the strand obtained at a predetermined time interval, at an appropriate position in the drawing direction of the continuous casting machine, with substantially the same accuracy as when directly measuring the actual casting speed at that position. Time T _j can be calculated.

On the other hand, for example, the rotation speed of the pinch roll is detected, and the actual casting speed V _C is obtained from the detected rotation speed.
Then, the history casting speed V _Ej , the actual casting speed V _C, and the preset parameter α _j are substituted into the following equation (12),
History pouring velocity V _Ej calculates the corrected correction history casting speed V _{MEj. V MEj = α j × V Ej} + (1-α j) × V C ... (12) However, alpha _j: parameter 0 <α _j <1 Note at appropriate positions in the drawing direction of the continuous casting machine, the parameter alpha _j is It is determined in advance in consideration of the operating conditions of the continuous casting facility, steel type, and the like.

By the way, the thickness D _{shell j} of the solidified portion of the strand calculated by using the corrected hysteresis _pouring speed V _MEj obtained in this manner _indicates the variation of the temperature of the molten metal in the mold and the temperature of the cooling water to be sprayed. Affected by change. Therefore, taking these factors into consideration, the thickness D of the solidified portion
Modify _{shell j} as follows.

FIG. 6 is an explanatory view for explaining a method for correcting the thickness of the solidified portion due to the change in the temperature of the molten metal. The horizontal axis represents the temperature of the molten metal in the mold, and the vertical axis represents the temperature in the drawing direction of the continuous casting machine. The thickness of the solidified portion of the strand at an appropriate position is shown. As is apparent from FIG. 6, the thickness of the solidified portion decreases as the temperature of the molten metal increases.

Now, the molten metal temperature at time k is represented by T
_Sj (k), the thickness of the solidified shell at that time is S _Sj (k), and the melt temperature at time (k + 1) is T _Sj (k +
1) Assuming that the thickness of the solidified shell at that time is S _Sj (k + 1), the molten metal temperature change amount δ (T _Sj ) between time k and time (k + 1) is expressed by the following equation (13). You. δ (T _Sj ) = T _Sj (k + 1) −T _Sj (k) (13)

On the other hand, the rate of change β _j of the curve shown in FIG. 6 is obtained in advance off-line. This change rate β _j is given by the following (1)
Equation (4) can be expressed as in Equation (13), and Equation (13) and (1)
From equation (4), the correction amount δ (S _Sj ) ｛δ (S
_Sj ) = S _Sj (k + 1) -S _Sj (k)} can be calculated by the following equation (15). β _j = δ (S _Sj ) / δ (T _Sj ) (14) δ (S _Sj ) = β _j · δ (T _Sj ) = β _j · {T _Sj (k + 1) -T _Sj (k)} (15)

Therefore, the molten metal temperature is measured at predetermined time intervals, the molten metal temperature {T _Sj (k + 1)} at the current time when the thickness of the solidified portion is determined, and the molten metal temperature _{ΔT Sj} measured one time before that. (K) The deviation from｝ is obtained, and the obtained deviation is (1)
By substituting into the expression 5), the correction amount δ (S _Sj ) of the thickness of the solidified portion is calculated. On the other hand, the molten metal temperature _{{T Sj (k + 1)} } at the current time to determine the thickness of the solidified portion, molten metal temperature {T _Sj at time T _j only before time required for the strand reaches the position from the current time ( k) The deviation from｝ may be obtained, and the obtained deviation may be substituted into Expression (15) to calculate the correction amount δ (S _Sj ) of the thickness of the solidified portion. In the former case, the change in the molten metal temperature at the measured time interval can be captured. You can capture change.

FIG. 7 is an explanatory diagram for explaining a method of correcting the thickness of the solidified portion due to the fluctuation of the cooling water temperature. The horizontal axis represents the temperature of the cooling water, and the vertical axis represents the drawing direction of the continuous casting machine. The thickness of the solidified portion of the strand at an appropriate position is shown. As is clear from FIG. 7, the thickness of the solidified portion decreases as the temperature of the cooling water increases.

Now, let the cooling water temperature at time k be T
_Wj (k), the thickness of the solidified shell at that time is S _Wj (k), the cooling water temperature at time k + 1 is T _Wj (k + 1),
_Assuming that the thickness of the solidified shell at that time is S _Wj (k + 1), the temperature change amount δ between time k and time (k + 1)
(T _Wj ) is represented by the following equation (16). δ (T _Wj ) = T _Wj (k + 1) −T _Wj (k) (16)

On the other hand, the rate of change γ _j of the curve shown in FIG. 7 is obtained in advance off-line. This change rate γ _j is given by the following (1)
Equation (7) can be expressed as follows: Equation (16) and (1)
From equation (7), the correction amount δ (S _Wj ) ｛δ (S
_{wW) = S wj (k +} 1) -S Wj a (k)} can be calculated by the following equation (18). γ _j = δ (S _Wj ) / δ (T _Wj ) (17) δ (S _Wj ) = γ _j · δ (T _Wj ) = γ _j · {T _Wj (k + 1) −T _Wj (k)} (18)

Therefore, the cooling water temperature {T _Wj (k + 1)} at the current time when the cooling water temperature is measured at a predetermined time interval and the thickness of the solidified portion is obtained, and the cooling water temperature measured one time before that The deviation from {T _Wj (k)} is obtained, and the obtained deviation is substituted into equation (18) to calculate the correction amount δ (S _Wj ) of the thickness of the solidified portion. On the other hand, the cooling water temperature {T _Wj (k + 1)} at the current time for _obtaining the thickness of the solidified portion
And the cooling water temperature ΔT at a time earlier by the time T _j required for the strand to reach the position from the current time.
_Wj (k)｝, and by substituting the obtained deviation into the equation (18), the correction amount δ (S
_Wj ) may be calculated.

The correction amounts δ (S _Sj ) and δ (S _Wj ) thus obtained are substituted into the following equation (19), and the above-mentioned thickness D _{shell j} of the solidified portion is corrected and corrected. The thickness S _{total j} of the solidified portion is determined. S _{total j} = D _{shell j} + δ (S _Sj ) + δ (S _Wj ) (19)

[0052]

Next, the results of implementing the method according to the present invention will be described. FIG. 8 is a graph showing measurement results of actual casting speed, molten metal temperature, and cooling water temperature, and results of verifying the thickness of the solidified portion of the strand calculated by the method of the present invention using the measurement results. The horizontal axis represents the time, and the vertical axis represents the thickness of the solidified portion, the actual casting speed, the molten metal temperature, or the cooling water temperature. As shown in FIG.
When the temperature of the molten metal and the temperature of the cooling water changed over time, the thickness of the solidified portion was calculated as indicated by a line g by the method of the present invention. Then, at the position of the calculation target, when the tacking test was performed at a plurality of times to actually measure the thickness of the solidified portion,
The values are indicated by points B ₁ , B ₂ , and B ₃ , and as is apparent from FIG. 8, all points B ₁ , B ₂ , and B ₃ were on line g.

[0053]

As described in detail above, the method for calculating the solidified thickness of a continuous cast strand according to the first invention can be applied to online calculation even if an inexpensive computer having a relatively slow calculation speed is used. be able to. Further, the change in the actual drawing speed is taken into the history drawing speed, and the thickness of the solidified portion can be obtained with high accuracy according to the operation state. Further, the history drawing speed is calculated based on the length obtained by measuring at regular intervals, and the change in the actual drawing speed is taken into the history drawing speed. In addition, a change in the actual drawing speed can be captured with high accuracy.

In the method for calculating the solidified thickness of a continuous cast strand according to the second invention, the history drawing speed obtained at regular time intervals is corrected using the actual drawing speed and parameters, so that an error due to a so-called delay is generated. Is reduced, and the thickness of the solidified portion of the strand can be accurately calculated at an appropriate position in the drawing direction of the continuous casting machine.

In the method for calculating the solidification thickness of a continuous cast strand according to the third to fifth aspects of the present invention, when the thickness of the solidification part is calculated using the first relation obtained off-line,
The present invention has excellent effects, for example, taking into account the temperature change of the molten metal and the temperature change of the cooling water, and further improving the calculation accuracy of the thickness of the solidified portion of the strand.

[Brief description of the drawings]

FIG. 1 is a schematic side view showing an example of a continuous casting machine used for carrying out the method of the present invention.

FIG. 2 is an explanatory diagram illustrating a heat transfer model used for implementing the present invention.

FIG. 3 is a graph showing an example of a relationship between a position in a drawing direction of a continuous casting machine and a thickness of a solidified portion of a strand, calculated by a one-dimensional heat transfer model.

FIG. 4 is a graph showing an example of a relationship between a casting speed and a thickness of a solidified portion of a strand.

FIG. 5 is an explanatory diagram illustrating a method of calculating a time required for a strand drawn from a mold to reach an appropriate position in a drawing direction of a continuous casting machine.

FIG. 6 is an explanatory diagram for explaining a method of correcting the thickness of a solidified portion due to a change in molten metal temperature.

FIG. 7 is an explanatory diagram illustrating a method of correcting the thickness of a solidified portion due to a change in cooling water temperature.

FIG. 8 is a graph showing measurement results of actual casting speed, molten metal temperature, and cooling water temperature, and a result of verifying the thickness of a solidified portion of a strand calculated by the method of the present invention using the measurement results.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Strand 2 Cutting machine 3 Meniscus M mold

Claims (5)

[Claims] 1. During the operation of a continuous casting machine, a molten metal flows in from one end of a mold, draws a strand from the other end of the mold while forming a solidified portion around the mold by contact with the mold, and solidifies to the center. In a method of calculating the thickness of the solidified portion of the strand at an appropriate position in the drawing direction of the continuous casting machine, a first relationship between the thickness of the solidified portion at the position and the drawing speed is obtained in advance using a heat transfer model, The length of the strand pulled out of the mold is measured every predetermined time, the time required for the strand to reach the position is calculated based on the measured length, and the history at the position is calculated using the calculated time. The drawing speed of the strand is determined, and the drawing speed of the strand is measured, and the history drawing speed is supplemented by using the measured drawing speed and a preset parameter. A method for calculating a solidification thickness of a continuous cast strand, wherein a correction history drawing speed is corrected, and a thickness of a solidified portion at the position is determined from the obtained correction history drawing speed and the first relationship. 2. A correction history drawing speed V _M is history drawing speed V _E, pulling velocity V _C and parameters α coagulation thickness calculation method for the continuous casting strand according to claim 1, wherein determining by substituting the following equation. V _M = α · V _E + (1−α) · V _C where 0 <α <1 3. A second relationship between the thickness of the solidified portion at the position and the temperature of the molten metal in the mold is determined in advance, and the temperature of the molten metal is measured over a predetermined period of time to determine the thickness of the solidified portion. Determine the difference between the temperature at the time to be calculated and the temperature at a time immediately before the time by an appropriate time,
The thickness variation of the solidified portion is calculated from the obtained deviation and the second relationship, and the thickness of the solidified portion determined based on the first relationship is corrected using the calculated thickness variation. 2
The method for calculating the solidification thickness of the continuous cast strand described. 4. Cooling by bringing a cooling medium into contact with the strands, a third relationship between the thickness of the solidified portion at the position and the temperature of the cooling medium is determined in advance, and the temperature of the cooling medium is measured over time. And the temperature at the time when the thickness of the solidified portion is calculated, and the temperature at the time immediately before the time by an appropriate time from the time are obtained, and the thickness of the solidified portion is obtained from the obtained deviation and the third relationship. 3. The method for calculating a solidified thickness of a continuous cast strand according to claim 1, wherein the change amount is calculated, and the thickness of the solidified portion determined based on the first relationship is corrected using the calculated thickness change amount. 5. A second relationship between the thickness of the solidified portion at the position and the temperature of the molten metal in the mold is determined in advance, and the temperature of the molten metal is measured over time to calculate the thickness of the solidified portion. Calculating a first deviation between the temperature of the molten metal at the time and the temperature of the molten metal at a time immediately before the time by an appropriate time, calculating a thickness change amount of the solidified portion from the determined first deviation and the second relationship; Cooling the strand by contacting a cooling medium with the strand,
A third relationship between the thickness of the solidified portion at the position and the temperature of the cooling medium is determined in advance, and the temperature of the cooling medium is measured with time to calculate the thickness of the solidified portion. And a second deviation from the temperature of the cooling medium at a time immediately before the above time by an appropriate time is calculated, and a thickness change amount of the solidified portion is calculated from the obtained second deviation and the third relationship. The method according to claim 1 or 2, wherein the thickness of the solidified portion determined based on the first relationship is corrected using the amount of change in the thickness.