JPH08276258A - Method for estimating solidified shell thickness of continuously cast slab - Google Patents

Abstract

PURPOSE: To drastically reduce the processing quantity of a computer by using the corrected casting velocity and calculating the solidified thickness at a prescribed position in the casting direction corresponding to the relational curve in on-line. CONSTITUTION: The relation between the set casting velocity and the solidified shell thickness 4 at the prescribed position 3 in the casting direction is found in advance with a heat transfer model in off-line. This relation is obtd. related to the plural setting velocity, and the relational curve between the set velocity and the shell thickness is drawn in on-line. A histrical casting velocities are obtd. during casting in on-line and the result is corrected according to the casting velocity at the present time to calculate the corrected casting velocity. The corrected casting velocity is used and the solidified shell thickness 4 at the prescribed position is calculated corresponding to the relational curve in on-line to estimate the solidified shell thickness. Thus, the solidified shell thickness can be estimated with high precision.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for highly accurately estimating the thickness of a solidified shell in a casting direction in a continuously cast slab being cast.

[0002]

2. Description of the Related Art Generally, in continuous casting, a molten metal poured into a mold is cooled by the mold to form a certain solidified shell, which is then passed through a large number of slab supporting rolls and spray cooling. With secondary cooling, it is drawn out by a pinch roll, completely solidified, and then cut into a certain length.

The highly accurate estimation of the thickness of the solidified shell at an arbitrary position in the casting direction of the slab being cast, and the position where the slab is completely filled with the solidified shell, that is, the completely solidified position, can be grasped from the following viewpoints. Is one of the important technical issues.

Measures for improving the quality of slabs cast by continuous casting (1) Suppression of center segregation and center porosity (2) Reduction of internal cracks ・ Measures for operation (3) High temperature in direct charge and direct rolling Next, a conventional method concerning the above (1) to (3) will be described.

(1) Suppression of center segregation and center porosity When a continuously cast slab is longitudinally cut along the center axis, holes may be found near the axis, which is called center porosity. At this time, elements such as C, P, and S may segregate in the central portion in a concentrated manner. This is called center segregation.

As a method of reducing these defects,
An electromagnetic stirring method for increasing the equiaxed crystal ratio and a rolling method at the end of solidification for preventing molten steel flow are known.

The conditions for applying electromagnetic stirring to a cast piece have an optimum value depending on the diameter of the unsolidified portion of the cast piece in a horizontal continuous casting machine, that is, the inner diameter of the unsolidified portion in the cross section of the round cast piece. It is important to estimate the solidified portion of the slab, that is, the thickness of the solidified shell.

In the slab reduction method, the reduction condition may be set based on the completely solidified position of the slab.

(2) Reduction of internal cracks Causes of internal cracks in cast slabs can be classified into those caused by bulging and those caused by unsolidified bending and straightening. It is known that this often occurs when a tensile stress is applied at a bending point in a vertical curved continuous casting machine and a straightening point in a curved continuous casting machine. Therefore, in order to estimate the internal crack, it is necessary to estimate this tensile stress, but for that purpose, it is necessary to estimate the thickness of the solidified shell of the slab at the stress generation site.

Recently, there is a continuous casting facility having a plurality of bending points. In this case, the solidified shell thickness at a plurality of points may be estimated according to the number of bending points.

(3) High-temperature slab in direct charge and direct rolling Understanding the final solidification position of the slab is important in the following cases in addition to the suppression of (1).

[0012] In recent years, a method (direct charging and direct rolling) of directly feeding a high temperature slab produced in continuous casting to a rolling process has been positively adopted. The slab temperature in should be kept as high as possible. However, for that purpose, it is necessary to move the completely solidified position to the machine end side as much as possible, and therefore it is necessary to highly accurately estimate the completely solidified position of the slab.

As a method for estimating the solidified shell thickness of a slab, the following equation (1) is conventionally known.

S = k√ (t) ····· (1) Where, S: slab solidification shell thickness (mm) k: solidification coefficient (-) t: from casting As a technique for estimating the temperature inside the slab, for example, Japanese Patent Laid-Open No. 5-1
Some use a method for predicting the temperature of an unsolidified portion as disclosed in Japanese Patent No. 23842. Particularly, as a method for detecting the completely solidified position of a slab, there is a method disclosed in Japanese Patent Publication No. 4-61742.

[0015]

When determining the electromagnetic stirring site, the reduction position, the internal crack generation condition estimation and the complete solidification position estimation for the cast piece during casting, the casting speed, etc. It is necessary to estimate the thickness of the solidified shell in consideration of casting conditions and steel grade and determine these.

Further, during the operation, it is necessary to flexibly cope with the casting speed, etc., which changes every moment.

The above formula (1) is a simple formula, and highly accurate estimation of the solidified shell thickness is impossible.

In the method disclosed in the above-mentioned Japanese Patent Laid-Open No. 5-123842, it is necessary to perform heat transfer calculation online, which increases the cost of the computer.

Since the method disclosed in Japanese Patent Publication No. 4-61742 is intended to grasp the position of complete solidification, it is impossible to estimate the thickness of the solidified shell at any slab site.

The present invention has been made in view of the above problems, and an object of the present invention is to determine the thickness of the solidified shell at an arbitrary slab portion in the casting direction of the slab during casting, and further the final solidification position. In consideration of the steel type, it flexibly responds to operating conditions such as pouring speed, which changes momentarily during operation, and provides a method that can be estimated online with high accuracy without requiring a large calculation load. To do.

[0021]

The gist of the present invention is the following method for estimating the solidified shell thickness of continuously cast slabs.

A continuous casting machine characterized by estimating the solidified shell thickness in the casting direction of the slab being cast in a continuous casting machine for continuously casting the slab from the mold for casting. Method for estimating solidified shell thickness of piece.

The relationship between the "set casting speed" and the "solidified shell thickness at a predetermined position in the casting direction" is obtained off-line in advance by a heat transfer model.

The above relationship is obtained for a plurality of set casting speeds, and a relationship curve (table) between the "set casting speed" and the "solidified shell thickness at a predetermined position in the casting direction"
Is created off-line in advance.

During casting, the history casting speed is calculated online from the casting length at regular time intervals and the average arrival time of the slab at a predetermined position in the casting direction. Correct according to the casting speed (actual casting speed at the current time sampled online during casting),
Calculate the corrected pouring speed.

The corrected pouring speed obtained above is used as the pouring speed, and the solidified shell thickness at a predetermined position in the pouring direction is calculated online corresponding to the relational curve obtained above.

[0027]

[Function] The most variable factor of the thickness of the solidified shell is the casting speed. Therefore, in the method of the present invention, the relationship between a plurality of set casting speeds and the thickness of the solidified shell at a predetermined position in the casting direction is obtained in advance by a heat transfer model in advance, and a relationship curve between the two is created.

During casting of the slab, ie online,
The history casting speed is obtained from the casting length at regular time intervals and the average arrival time of the slab at a predetermined position in the casting direction, and this is corrected according to the actual casting speed at the present time. Further, by using this modified casting speed as the casting speed, and by corresponding to the relationship curve between the set casting speed and the solidified shell thickness at the predetermined position in the casting direction, the solidified shell at the predetermined position Calculate the thickness.

Here, the above-mentioned "predetermined position in the casting direction" is a position in the casting direction of the target continuous casting machine. Just set it. In addition, there are no particular restrictions on the number of positions, and any position where the solidified shell thickness should be obtained may be considered.

A specific example of the method of the present invention will be described below with reference to FIGS.

First, a method for obtaining the relationship between the set casting speed and the thickness of the solidified shell at a predetermined position in the casting direction by a heat transfer model in the off-line will be shown.

FIG. 1 is a schematic diagram showing a heat transfer model. Figure 1 (a) shows the case of a round slab and Figure 1 (b) shows the case of a slab. The heat transfer calculation in the thickness direction or radial direction of the slab is obtained using a one-dimensional heat transfer model in which the thickness direction of the slab 2 is one-dimensional from the viewpoint of heat transfer, as shown in FIG.

In the case of a slab, the symbol i in FIG. 1 is the number of a point representing a mesh assumed from the surface in the thickness direction of the slab 2 to the inside in the thickness direction of the slab 2. Similarly, in the case of a round cast slab, it is the number of a point representing a mesh assumed from the surface in the thickness direction of the cast at a certain point (for example, the top side) on the circumference of the cast slab.

When the surface of the cast slab is 1, the above-mentioned i represents the number of all mesh points, and corresponds to the number of the center point in the thickness direction.

In this heat transfer model, the enthalpy method is used for calculation in order to handle the solidification phenomenon.
This basic equation is shown in the following equations (2) to (5).

H _i '= {Δt / (ρΔV _i }  (Q _i −Q _{i + 1} ) + H _i (2) where i = 1, n−1 Δt = A _i / V H _i '= {Δt / (ρ ・ ΔV _i } ・ Q _i + H _i (3) where i = n (center of slab) Q _i = _{A i · (K i / △} L i) · (T i-1 -T i) ······· (4) where, i = 2~n (slab inside) Q _i = A _i · h ・ (Tw −T _i ) ・ ・ ・ ・ ・ ・ ・ ・ ・ (5) where i = 1 (the surface of the slab) where H _i : enthalpy (kJ / kg) H _i ′: Enthalpy after △ t time (kJ / kg) △ t: Time mesh interval (sec) A _i : Boundary area of mesh volume (m) or (m ² ) V: Set casting speed (m / min) ρ: Molten steel Specific gravity (kg / m ³ ) ΔV _i : Mesh volume (m ³ ) Q _i : Inflow / outflow heat amount (W) in mesh K _i : Thermal conductivity of mesh volume [W / (m · K)] T _i : Temperature at mesh point i (K) ΔL _i : Distance between meshes (m) Tw: Cooling water temperature (K) (Ambient temperature in the part where cooling water is not sprinkled) h: Heat transfer on the surface of the slab Rate [W / (m ² · K)] n: number of meshes Using the above heat transfer model, the temperatures of the surface and the inside of the cast slab are obtained, and these are sequentially calculated in the casting direction.

FIG. 2 is a schematic view for explaining the solidified shell thickness at a predetermined position in the casting direction. (a) is a vertical cross-sectional view in the side direction, and (b) is an enlarged view of a portion A of (a). In FIG. 2, reference numeral 1 is a mold, 2 is a slab being cast, 3 is a predetermined position in the casting direction, 4 is a slab solidified portion region in the slab thickness direction, that is, a solidified shell thickness, and T shell is a slab. It is the boundary temperature between the solidified portion and the non-solidified portion in the thickness direction.
This boundary temperature (Tshell) is expressed by the following equation (6).

Tshell = (1-fs). (TL-Ts) + Ts (6) where Tshell is the boundary temperature (K between the solidified portion and the non-solidified portion in the thickness direction of the slab). ) Fs: solid phase ratio (-) TL: liquidus temperature (K) Ts: solidus temperature (K) Solidified shell thickness (Dshel) at a predetermined position in the casting direction
l) is determined as follows at a cast piece site at a predetermined position in the casting direction. In the thickness direction of the target slab, the temperature at an arbitrary distance from the surface of the slab can be determined based on the temperature calculation result of each mesh point in the heat transfer model shown in FIG. That is, as a result of the inverse calculation, an arbitrary point (position) in the thickness direction of the cast piece can be converted as a distance from the surface of the cast piece based on the temperature at that point.

Therefore, from the temperature distribution in the thickness direction of the cast piece, the position from the surface of the cast piece at the point satisfying the above expression (6) is determined, and the result is defined as the solidified shell thickness (D shell).

FIG. 3 shows the solidified shell thickness (D shell) in the casting direction of the slab obtained by the above calculation method when the solid fraction is 0.8.
It is a figure which shows the example which calculated | required the distribution of. In FIG. 3, reference numerals 5 and 6 are solidified shell thickness distribution calculation values in the casting direction, which are calculated by changing the set casting speed. The set pouring speed used when calculating the solidified shell thickness shown by reference numeral 5 here is slower than the set pouring speed used when calculating the solidified shell thickness shown by reference numeral 6 (set pouring speed 1 <Set casting speed 2).

Solidified shell thicknesses at position 7 in the casting direction (horizontal axis in FIG. 3) are 8, 9 respectively, and solidified shell thicknesses at position 10 in the casting direction are 11, 12 respectively. . Reference numerals 13 and 14 indicate the completely solidified positions at the respective casting speeds.

FIG. 4 is a diagram showing an example of the above calculation results as a relationship curve between the set casting speed and the solidified shell thickness (D shell) at a predetermined position in the casting direction. FIG.
In the above, reference numerals [1] and [2] are curves showing the above relationship at the positions 7 and 10 in the casting direction shown in FIG. 3, respectively.

In both the slab and the round cast slab, the thickness of the solidified shell (D shell) at an arbitrary site in the slab cross section
In that case, the above equation (2) ~
(5) should be expressed in two dimensions.

As described above, the solidified shell thickness (Dsh) at a predetermined position in the casting direction is off-line by the means.
ell) is calculated in advance, offline by means, the calculation is performed for a plurality of set casting speed, to create a relationship curve between the set casting speed and the solidified shell thickness at a predetermined position in the casting direction, In the following means, the historical casting speed (VEj) and the casting speed obtained by modifying it, that is, the corrected casting speed (VMEj) are calculated online.

The historical pouring speed (VEj) and the corrected pouring speed (VMEj) are obtained in consideration of the temporal fluctuation of the pouring speed, and the actual casting speed (V) at the current time.
By prioritizing the casting speed before reaching c), that is, the amount of fluctuation of the past speed with respect to time, the increase / decrease relationship per hour with the actual casting speed (Vc) at the current time is obtained, and according to this relationship The thickness of the solidified shell is estimated with high accuracy.

The history casting speed (VEj) is a casting speed determined based on the history of past casting speeds. In order to obtain this, first, the average arrival time Tj to the position where the solidified shell thickness is to be calculated in the casting direction is calculated by
Calculate by the procedure of (c).

(A) First, a fixed time interval Δ from the start of casting
For each S (for example, 10 seconds, 20 seconds, etc.), the distance cast within that time is obtained.

FIG. 5 is a diagram for explaining this method. Each △
The casting distances L1, L2, ..., Lm for each S are always the first ΔS1 as shown in FIG. 5, that is, the casting distance at the nearest ΔS immediately after casting is always ΔS. Assuming L1, the second casting distance at ΔS2 is represented by a new casting distance L1 and L2 where the distance at ΔS1 was L1. Similarly, the mth ΔS
The casting distance at m is represented by the newest L1, L2 which was L1 at ΔSm−1, ..., The distance Lm cast at the first ΔS1.

(B) Next, the casting length from the meniscus, that is, the head positions L1, L2, ...
· Find Lm. This is L1 when the casting length in the first ΔS1 is L1 using the result of (a) above.
= L1. The casting length in the second ΔS2 is L1
Becomes a new L1, and L2 is the sum L1 + L2 of the new L1 and L2 which was L1 in ΔS1. Similarly, the casting length Lm at the m-th ΔSm is given by the following equation (7).

[0050]

[Equation 1]

(C) Next, letting Dj be a predetermined position in the casting direction of the slab from the meniscus, the m-th one satisfying the condition of the following expression (8) is obtained.

Lm <Dj <Lm + 1 (8) where Dj is a predetermined position in the casting direction of the slab from the meniscus j : Average arrival time Tj from the j-th predetermined position in the casting direction of the slab to the position where the solidified shell thickness is to be calculated is given by the following formula (9).

Tj = ΔS × {m + (Dj−Lm) / (Lm + 1−Lm)} (9) where Tj is the average arrival time to the position where the solidified shell thickness is to be calculated. In (8), the range of the average arrival time Tj is limited by obtaining the number of the predetermined position Dj in the casting direction of the cast piece corresponding to the casting length L from the meniscus, and the expression (9 ), The average arrival time Tj is specified by averaging the fluctuation of the casting speed within ΔSm, that is, assuming that it is constant. What is obtained using this result is the hysteresis pouring speed VEj shown in the following formula (10), which is obtained for each point at a predetermined position in the casting direction of the slab.

VEj = Dj / Tj ... (10) Where, VEj: History casting speed obtained from arrival time of the slab at a predetermined position Using this equation (10), the corrected casting speed VMEj shown in the following equation (11) is determined for each point at a predetermined position in the casting direction of the cast slab.

VMEj = αj × VEj + (1-αj) × Vc ... (11) where VMEj: Corrected casting speed Vc: Actual casting speed at current time sampled online αj: Casting Correction coefficient for each predetermined position in the casting direction (0 ≦ αj ≦ 1) The correction coefficient αj is the correction casting speed VMEj for each predetermined position in the casting direction of the casting steel type, the casting equipment or the target cast piece. Since the optimum values are different, various casting speed changes and steel grades are determined by off-line simulation using a heat transfer model.

As described above, the relationship between the set casting speed and the thickness of the solidified shell at a predetermined position in the casting direction of the slab is obtained by heat transfer calculation in the above-described means off-line, and the above-mentioned relationship is set in plural by the means as described above The casting speed is obtained, and a relational curve between the "set casting speed" and the "solidified shell thickness at a predetermined position in the casting direction" is created.

Then, online, the corrected casting speed VMEj is calculated by the above-mentioned means, and the solidified shell thickness is calculated at the step of the means.

FIG. 6 is a diagram for explaining a method of calculating the solidified shell thickness by using the corrected casting speed VMEj as the casting speed and corresponding to the relational curve shown in FIG. As shown in FIG. 6, the thickness of the solidified shell (Dsh
ell j) is the solidified shell thickness (Dsh) at each predetermined position in the casting direction.
ell) and the set pouring speed in the relationship curve as shown in FIG. 4, the modified pouring speed VM in which the speed fluctuation is temporally taken into consideration.
The value of Ej is used as the casting speed and is calculated by making it correspond to the above relational curve.

In the above-mentioned method of the present invention, since the relationship between the set casting speed and the thickness of the solidified shell at a predetermined position is based on the heat transfer calculation performed off-line in advance, it is possible to easily cope with a change in operation and to solidify the solidified shell. It is possible to estimate the thickness with high accuracy. Furthermore, because it is possible to determine the solidified shell thickness at any position in the casting direction, not limited to estimation of the final solidified position of the slab,
It is possible to obtain excellent effects on quality improvement measures performed during casting of a slab, such as electromagnetic stirring position, reduction position determination, estimation of internal crack generation condition, determination of complete solidification position, and the like.

[0060]

EXAMPLE A continuous casting test was carried out using the method shown in FIGS. 1 to 6, and the relationship between the actual casting speed at the present time and the solidified shell thickness was investigated by tacking. The casting conditions were as follows.

Model: Slab continuous casting machine Steel type: Low carbon steel Molten steel Superheat: 20 ° C Slab size: 1800 mm width x 250 mm thickness Set casting speed: 0.7-1.0 m / min Secondary cooling conditions: Constant Figure 7 shows the actual casting speed (Vc) at the current time of the above test
It is a figure which shows the time transition of the solidification shell thickness (Dshellj). In FIG. 7, reference numeral 15 is a calculated value of the solidified shell thickness according to the method of the present invention, and reference numerals 16, 17, and 18 are measured values of the solidified shell thickness by rivet driving, respectively. It can be seen from FIG. 7 that the solidified shell thickness of the slab during casting can be estimated with high accuracy according to the method of the present invention.

[0062]

According to the method of the present invention, since the heat transfer calculation is not performed online, the processing amount of the computer can be greatly reduced. Therefore, a large computer is not required, and the equipment cost can be kept low.

Since the relationship between the set casting speed and the thickness of the solidified shell at a predetermined position is based on heat transfer calculation, it is possible to easily cope with changes in operation and to accurately estimate the thickness of the solidified shell.

The method of the present invention is not limited to the estimation of the final solidification position of the slab, but the thickness of the solidification shell can be estimated at any position in the casting direction. Therefore, the electromagnetic stirring position, the reduction position, the internal crack generation condition estimation, It has an excellent effect on quality improvement measures taken during casting, such as determining the position of complete solidification.

[Brief description of drawings]

FIG. 1 is a schematic diagram showing a heat transfer model. (a) is the case of round slab and (b) is the case of slab.

FIG. 2 is a schematic diagram for explaining a solidified shell thickness at a predetermined position in a casting method. (a) is a vertical cross-sectional view in the side direction, and (b) is an enlarged view of a portion A of (a).

FIG. 3 is a diagram showing an example in which a distribution of solidified shell thickness in a casting direction of a slab is obtained when the solid fraction is 0.8.

FIG. 4 is a diagram showing an example of a relationship curve between a set casting speed and a solidified shell thickness at a predetermined position in a casting direction. [1] is the relationship at the pouring direction position 7 in FIG. 3, and [2] is the relationship at the pouring direction position 10 in FIG.

FIG. 5 is a diagram illustrating a method of calculating an average arrival time Tj to a position where the solidified shell thickness is to be calculated.

FIG. 6 is a diagram illustrating a method of calculating a solidified shell thickness using a corrected casting speed VMEj.

FIG. 7 is a diagram showing a time transition of an actual casting speed and a solidified shell thickness.

[Explanation of symbols]

1: mold, 2: cast piece, 3: predetermined position in casting direction, 4: region of cast solidified portion (solidified shell thickness) in cast thickness direction, 5: measured value of solidified shell thickness at set casting speed 1, 6: Measured value of solidified shell thickness at set casting speed 2, 7: predetermined position in casting direction, 8: solidified shell thickness at predetermined position 7 at set casting speed 1, 9: predetermined position at set casting speed 2 7, solidified shell thickness at 10: predetermined position in casting direction, 11: solidified shell thickness at predetermined position 10 at set casting speed 1, 12: solidified shell thickness at predetermined position 10 at set casting speed 2, 13: Complete solidification position at set casting speed 1 14: Complete solidification position at set casting speed 2 15: Calculated solidified shell thickness by the method of the present invention 16, 17, 18: Measured actual solidified shell thickness , Tshell: boundary temperature between a solidified portion and a non-solidified portion in the thickness direction of the slab, Dshell j: finally calculated solidified shell thickness, VME
j: corrected pouring speed, ΔS: constant time interval from the start of pouring, L: pouring distance for each ΔS, L: pouring length from meniscus

Claims (1)

[Claims] 1. A continuous casting machine for continuously casting a slab from a mold for casting, wherein the relationship between the set casting speed and the thickness of the solidified shell at a predetermined position in the casting direction is previously transferred off-line. Obtained from the model, this relationship is obtained for a plurality of set casting speeds, and the relationship curve between the set casting speed and the solidified shell thickness at a predetermined position in the casting direction is created offline in advance. Online, the historical casting speed was calculated from the casting length at regular time intervals and the average arrival time of the slab at a predetermined position in the casting direction, and this historical casting speed was calculated as the current casting speed (casting speed). The actual pouring speed at the current time sampled online during pouring is corrected to calculate the corrected pouring speed, and this corrected pouring speed is used as the pouring speed to correspond to the above relation curve. Casting Solidified shell thickness by calculating online, solidified shell thickness estimation method of the continuous casting slab, characterized by estimating the solidified shell thickness at casting direction of cast piece in the casting at a predetermined position in the direction.