JP4105839B2 - In-mold casting abnormality detection method in continuous casting - Google Patents

Description

ここで、αは溶融金属対流による熱伝達係数、Ｔｘは凝固シェル内表面からΔｘの距離における凝固シェル温度、Ｔｂは溶融金属のバルク温度を示す。
（１６）式より

が熱対流起因の熱流束である。
【００３５】
上記熱流束などを求める演算は、図１に示すコンピューター１９により図８に示すフローチャートの命令に従って実行される。
【００３６】
ステップ１で時間ｔにゼロを設定し、ステップ２で時間ｔに微小時間間隔Δｔを加算し、時間を更新する。ステップ３にて鋳造方向に鋳型内設置された熱電対の計測値をコンピューター１９に読み込み、ステップ４にてステップ３で読み込んだ熱電対の計測値に基づき、鋳型表面の熱流束と鋳型内表面温度Ｔ_msを計算する。
【００３７】
具体的には、前述の（４）式を初期条件、（２）式および（３）式を境界条件にして（１）式を離散化して解く。（１）〜（４）式より計算した熱電対計測点に於ける鋳型温度Ｔ（Ｅ，ｔ）と計測温度Ｙ（ｔ）の２乗誤差を以下の前述の（５）式により計算する。
【００３８】
前述の（６）式に示すように２乗誤差Ｆ（ｑ）の熱流束ｑに関する偏微分係数がゼロに近づくように、仮定した熱流束値ｑ₀を以下の手順にしたがって修正する。
【００３９】
仮定した熱流束ｑ_０を境界条件にして計算した鋳型温度計測点における鋳型温度計算値をＴ（Ｅ，ｔ）０、修正した熱流束ｑ_１を境界条件にして計算した鋳型温度計測点における鋳型温度計算値をＴ（Ｅ，ｔ）１とすると、Ｔ（Ｅ，ｔ）１をΔｑ≡ｑ_１−ｑ_０に関してテーラー展開すると以下のようになる。
Ｔ（Ｅ，ｔ）１＝Ｔ（Ｅ，ｔ）０＋（∂Ｔ（Ｅ，ｔ）０／∂ｑ_０）
・（ｑ_１−ｑ_０） （１８）
ここで、感度係数β_０を次式のように定義する。
β_０≡∂Ｔ（Ｅ，ｔ）０／∂ｑ_０
＝（Ｔ（Ｅ，ｔ）１−Ｔ（Ｅ，ｔ）０）／εｑ_０ （１９）
ここで、εはｑの最適値を探索するために設定する微小値であり、例えば、０．００１とする。（１８）式と（１９）式を（６）式に代入し、ｑ_１に関して整理すると、
ｑ_１＝ｑ_０＋（Ｔ（Ｅ，ｔ）０−Ｙ（ｔ））／β_０ （２０）
ｑ_１とｑ _０ を比較し、下記の収束判定式を満足すればｑ_１が求める熱流束である。
（ｑ_１−ｑ_０）／ｑ_０＜０．００１ （２１）
【００４０】
（２１）式を満足しない場合は、ｑ₁を基準に上と同様の手順で以下の（２２）式に従ってｑ_iの計算を行い、（２３）式を満足するまで、計算を繰り返し、熱流束ｑを決定し、同時に鋳型内表面温度Ｔ（０，ｔ）が計算される。

【００４１】
ステップ５では、（７）〜（１１）式を使って凝固シェル厚みδおよび凝固シェル表面温度ＴLを求める。その際、（９）式に使用する熱流束値ｑ_mは、熱電対計測値から逆問題で求めた熱流束値の鋳造方向内外挿値を使用する。
【００４２】
ステップ６では、（１２）〜（１５）式により凝固シェル内表面熱流束を求める。その際、（１３）式のＹ（ｔ）は各熱電対位置におけるステップＳ５で求めた鋳片表面温度を使用し、（１４）式のｑ_mはステップＳ４で逆問題を解いて求めた鋳型内面熱流束値を使用する。
【００４３】
ステップ７で上記凝固シェル内表面熱流束により溶融金属流動に起因する対流熱伝達量を（１７）式より求める。
【００４４】
以上説明した発明の実施の形態では鋳片がスラブであったが、本発明はこれに限られるものではない。例えば、鋳片がビレット、厚板材、丸棒材などであってもよく、また水平連続鋳造にも適用することができる。
【００４５】
【発明の効果】
本発明方法では、鋳型内面と水冷溝間に配置した鋳型温度計測値から定常状態だけでなく非定常状態にある溶融金属鋳型表面または凝固シェル表面の熱流束を求め、鋳型表面温度その他を推定するので、溶融金属鋳型内の凝固状態を明確に検知することができる。この結果、オンラインかつ高い精度で鋳型内鋳造異常を検出でき、健全な凝固状態が得られるような鋳造操業方法を管理することが可能となる。また、鋳型表面温度を得るために、熱電対などの温度計測手段の先端を鋳型表面に露出する必要はない。
【図面の簡単な説明】
【図１】本発明方法を実施する際の装置構成図である。
【図２】（ａ）はブレイクアウトが発生した鋳片の熱電対温度変化の経時変化を示し、（ｂ）は同鋳片の熱流束の経時変化を示す線図である。
【図３】（ａ）は縦割れが発生した鋳片の熱電対温度変化の経時変化を示し、（ｂ）は同鋳片の熱流束の経時変化を示す線図である。
【図４】縦割れが発生した鋳片について、熱流束のウエーブレット解析結果を示す線図である。
【図５】健全な鋳片について、熱流束のウエーブレット解析結果を示す線図である。
【図６】鋳型内面と鋳型水冷溝間の熱移動を表す概念図である。
【図７】溶融金属内の熱移動を表す概念図である。
【図８】本発明に基づく演算フロー図である。
【符号の説明】
１：鋳片
２：溶融金属
３：メニスカス
５：凝固シェル
７：溶融スラグ
１１：鋳型
１２：鋳型内表面
１３：水冷溝
１４：流量計
１５：冷却水温度計測手段
１６：第１鋳型温度計測手段
１７：第２鋳型温度計測手段
１９：コンピューター[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for online detection of casting abnormalities in continuous casting, particularly breakouts, surface defects, abnormalities in molten metal flow, etc. occurring in a slab in a mold.
[0002]
[Prior art]
Knowing the solidification state of the molten metal in the mold of a continuous casting machine during casting is the on-line detection of slab surface defects caused by non-uniform formation of solidified shells and prediction of operational abnormalities such as breakout and scene vibration. It is a necessary condition for performing the process and is important for continuous casting operation and quality control. Therefore, many methods for detecting abnormality in casting in the mold have been proposed.
[0003]
In order to know the solidification thickness of the molten metal and the temperature profile of the solidified shell, it is necessary to know the heat flux on the inner surface of the mold. Conventionally, the heat flux in the mold of the molten metal is divided into two thermocouples at different positions in the heat removal direction of the mold. The heat flux q is calculated from the temperature difference ΔT obtained from the thermal conductivity λ of the mold material, the distance d between the two thermocouples, and the temperature measured by the thermocouple,
q = (λ / d) · ΔT
There was an attempt to find it by the following formula. However, there is a problem that it is difficult to maintain and manage two thermocouples in a narrow space between the mold inner surface and the water cooling groove. Furthermore, the heat flux derived by this method is based on the premise that the temperature distribution in the mold is in a steady state, and the estimation error for the actual heat flux value increases as the degree of unsteady state increases. There is a problem.
[0004]
Further, in Japanese Patent Application No. 9-273745, “Method for determining in-mold abnormality in continuous casting equipment”, the tip of the thermocouple is exposed on the copper plate surface of the mold, and the temperature on the casting side of the copper plate surface of the mold is measured. Obtain the solidification state and powder lubrication state of the molten metal in the mold, and determine abnormalities during casting. As a result, the yield is improved by minimizing the occurrence of casting interruption (breakout) due to the outflow of molten metal and the occurrence of slab surface defects. In this in-mold abnormality determination method, the heat flux in the slab is not obtained, so the solidification state in the mold and the thickness of the solidified shell cannot be known. For this reason, surface defects, abnormalities in molten metal flow, etc. cannot be detected online. Further, it is necessary to attach a large number of thermocouples to the mold with their tips exposed on the mold surface.
[0005]
[Problems to be solved by the invention]
The present invention estimates the heat flux of the molten metal mold surface not only in the steady state but also in the unsteady state from the measured temperature value of the mold disposed between the inner surface of the mold and the water cooling groove, and based on this, breakout and surface defects with high accuracy are estimated. It is another object of the present invention to provide a method for detecting an in-mold casting abnormality such as a molten metal flow abnormality.
[0006]
[Means for Solving the Problems]
According to the present invention , there is provided a method for detecting abnormality in casting in a mold by measuring a mold temperature with temperature measuring means embedded in a plurality of locations of the mold at intervals in the casting direction, and measuring the mold at each measurement point based on the measured mold temperature. The heat flux on the inner surface is estimated from the numerical solution of the unsteady heat transfer equation using the inverse heat transfer problem method. Then, from the estimated change in the elapsed time of the heat flux, the estimated value of the heat flux is set in advance for each measurement point at or near the elapsed time when an arbitrary point of the in- mold slab passes two measurement points. A breakout or vertical crack is detected when the value falls below the value and in the order of measurement points.
[0007]
The breakout occurs when a portion where the thickness of the slab solidified layer is partially thin due to a foreign matter caught between the mold and the slab or a crack of the slab is broken and the molten metal flows out. When the solidified layer that leads to breakout passes through the mold, the heat transfer from the solidified layer to the mold is hindered by the influence of foreign matters or cracks that cause the solidified layer, resulting in a decrease in heat flux. Therefore, the occurrence of breakout can be detected from the amount of decrease in heat flux at each measurement point obtained by the above method.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
The embodiment of the present invention will be described by taking slab continuous casting as an example. FIG. 1 schematically shows a mold and an in-mold slab (consisting of a molten metal and a solidified shell) in a longitudinal section along the slab width direction.
[0013]
As shown in FIG. 1, a water cooling groove 13 is formed in the mold 11, and the water cooling groove 13 is provided with cooling water temperature measuring means 15 for measuring the cooling water temperature. The amount of cooling water is measured by the flow meter 14. The mold 11 is cooled with cooling water passing through the water-cooling groove 13, and heat is extracted from the in-mold slab 1. The first mold temperature measuring means 16 and the second mold temperature measuring means 17 are embedded between the mold inner surface 12 and the water cooling groove 13 with a space d in the vertical (casting) direction. In order to accurately determine the heat flux, mold temperature distribution, etc., the first mold temperature measuring means 16 is preferably arranged at the molten slag liquid phase portion 7 or at or near the solidification start point, and the second mold temperature measuring means 17. Is placed in the solidified shell 5 portion. The distance d between the temperature measuring means 16 and 17 is set to an interval suitable for detecting a casting abnormality based on the operation results in accordance with the casting conditions, the slab size and the like. In FIG. 1, two mold temperature measuring means are arranged in the vertical direction. However, for example, 3 to 5 mold temperature measuring means may be arranged in the vertical direction as needed. The distribution of the heat flux and the mold surface temperature in the casting direction can be obtained with higher accuracy as the number of mold temperature measuring means (temperature measurement points) is increased. Moreover, you may make it arrange | position 2-6 sets of mold temperature measuring means 16 and 17 which became the upper and lower pairs according to the width | variety of the slab 1, for example in the slab width direction. In addition, regarding the direction perpendicular to the casting direction, only one temperature measuring means may be used. As the cooling water temperature measuring means 15 and the mold temperature measuring means 16 and 17, for example, a thermocouple, a thermistor or the like is used. The temperature measurement value and the flow rate measurement value are transmitted to the computer 19. The computer 19 is preliminarily inputted with data and a calculation program necessary for calculation such as casting conditions, heat conductivity of the mold material, distance of the temperature measurement point from the inner surface of the mold and other heat fluxes, temperature distribution, convection heat transfer amount and the like. .
[0014]
In the present invention , the mold temperature is measured by temperature measuring means 16 and 17 embedded in a plurality of locations of the mold 11 at intervals d in the casting direction, and the heat flow on the mold inner surface 12 at each measurement point based on the measured mold temperature. Each bundle is estimated using the inverse heat transfer method. The heat flux estimation method will be described later together with estimation of temperature distribution and the like.
[0015]
Breaks when the estimated value of heat flux falls below the preset limit value for each measurement point and in the order of measurement points at or near the elapsed time when any point of the in-mold slab 1 passes through two measurement points Detect out. The elapsed time or the time τ nearby is expressed by the following equation.
d / v _c ≦ τ ≦ (1 + α) d / v _c
Here, d is the interval between the upper and lower temperature measurement points, and _vc is the casting speed. α is a margin coefficient and is about 0.01 to 0.1. The margin coefficient α is a coefficient that takes into account the delay time when the movement of the foreign matter biting portion of the cast in the mold is delayed from the first measurement point to the second measurement point. The limit value is set based on the operation results according to casting conditions, slab dimensions, and the like.
[0016]
FIG. 2A shows the relationship between the elapsed casting time and the mold temperature measured by the thermocouple, and FIG. 2B shows the relationship between the elapsed casting time and the heat flux estimated from the measured mold temperature. The first temperature measurement point is 180 mm from the upper surface of the mold, and the second temperature measurement point is 340 mm. From these figures, it can be seen that the change in heat flux is finer and sharper than the change in mold temperature and is clear. Therefore, detection of breakout due to a change in heat flux can detect a smaller breakout with higher reliability than change in mold temperature.
[0017]
In FIG. 2 (b), when the heat flux estimated value at the first measurement point falls below the limit value a, and then the heat flux estimated value at the first measurement point falls below the limit value b within the elapsed time, Determine that a breakout has occurred. In addition, as shown by a portion surrounded by a circle in FIG. 2B, foreign object biting can also be detected.
[0018]
In the reference form , surface defects such as vertical cracks are detected based on the heat flux. The crack of the slab can be regarded as having a small degree of breakout. Therefore, by changing the limit values a and b of the breakout determination described above, a large crack can be detected. However, as the crack size decreases, the determination becomes difficult due to the influence of a disturbance or the like.
[0019]
FIG. 3A shows the relationship between the elapsed casting time and the mold temperature measured by a thermocouple when vertical cracking occurs. FIG. 3B shows the relationship between the casting elapsed time and the heat flux estimated from the mold measurement temperature in the same case as above. Due to the heat transfer delay due to the heat transfer resistance from the temperature measuring means to the mold inner surface, it can be detected only when the heat transfer change on the mold inner surface is dull as shown in FIG. Similarly to FIG. 2, in FIG. 3B, it can be seen that the change in the heat flux is finer and sharper than the change in the mold temperature and is clear. However, if the crack becomes small as described above, it is difficult to detect the small crack as shown in FIG.
[0020]
In the reference mode , small cracks are detected by performing wavelet analysis on the temporal change of the heat flux estimation value shown in FIG. 4 (a) to 4 (d) and FIGS. 5 (a) to 5 (d) show the fluctuation results of the heat flux period of 8 seconds, 16 seconds, 32 seconds and 64 seconds, respectively, by wavelet analysis. 4 shows a case where there is a vertical crack in the slab, and FIG. 5 shows a case where the slab is healthy. The vertical crack maintenance rate of the slab, that is, the occurrence rate of vertical cracks is shown below FIG. From these wavelet analysis results, it can be seen that the fluctuation of the heat flux fluctuation in the period between 8 seconds and 32 seconds is larger in the longitudinal crack occurrence slab than in the case of the sound slab. The magnitude (amplitude) and frequency of these fluctuations correspond well to the extent of the vertical crack maintenance rate, and vertical cracks can be detected by managing the heat flux fluctuations in these periodic bands. The size of the vertical crack can be determined by the above-mentioned amplitude, and the position in the slab length direction can be determined by the elapsed casting time. Longitudinal cracking slabs have the same up and down heat flux behavior in the 64-second period, and are considered to represent the slab's lifting behavior from the mold. Yes.
[0021]
In FIG. 4, there are two measurement points, the upper thermocouple position and the lower thermocouple position. Although surface defects such as vertical cracks can be detected based on the heat flux fluctuation amount measured at one location, the accuracy of defect detection is higher when measured at two locations. In the case of measurement at two places, the presence / absence of a defect, the size, and the position in the slab length direction are determined based on the one with the larger amplitude of the heat flux fluctuation amount.
[0023]
As described above, in the present invention and the reference embodiment , the heat flux on the inner surface of the mold is estimated from the mold temperature measured by the temperature measuring means embedded between the inner surface of the mold and the water cooling groove, and a breakout or a surface defect is detected. . Hereinafter, a method for obtaining the heat flux and the convective heat transfer amount based on the mold temperature measurement value will be described.
[0024]
The heat flux on the inner surface of the mold is applied to the non-stationary heat transfer equation by applying James. V. BECK's nonlinear inverse heat transfer method [Int. J. Mass s Transfer, vol. 13, pp703-716 (1970)]. From this numerical solution, the heat flux that can best explain the one-point mold temperature measurement value embedded between the mold surface and the water cooling groove is sequentially obtained in time series. In addition, the mold inner surface temperature obtained as a solution of the heat flux and the unsteady heat transfer difference equation is determined simultaneously.
[0025]
FIG. 6 is a conceptual diagram showing heat transfer between the mold inner surface 12 and the mold water cooling groove 13. The heat flux flowing from the molten metal 2 into the mold 11 passes through the mold 11 and is removed by the cooling water w flowing through the mold water cooling groove 13. In order to detect the heat flux, a thermocouple 16 is installed at a position of a vertical distance E from the mold inner surface 12 to the mold water cooling groove.
[0026]
In FIG. 6, considering only the one-dimensional heat transfer in the mold thickness direction, an equation governing the heat transfer from the mold inner surface to the mold water cooling groove is expressed by the following formula.
ρc _p ∂T / ∂t = −∂ (λ∂T / ∂x) / ∂x (1)
T (E, t) = Y (t) (2)
λ∂T (F, t) / ∂x = hw (T (F, t) −Tw) (3)
T (x, 0) = T0 (x) (4)
Here, the density of ρ is the template material, c _p is the specific heat of the mold material, x is the vertical distance at an arbitrary position from the mold inner surface to the water cooling groove, the vertical distance E from the mold inner surface to mold thermocouple installation point , Y indicates the measured value. F is the vertical distance from the mold inner surface 12 to the mold water cooling groove 13, and hw and Tw are the overall heat transfer coefficient and water temperature for water side cooling, respectively. T0 (x) represents the initial temperature distribution in the vertical direction between the mold inner surface 12 and the mold water cooling groove 13, and is set to room temperature immediately before the start of casting.
[0027]
The square error between the mold temperature T (E, t) and the measured temperature Y (t) at the thermocouple measurement point calculated from the equations (1), (3), and (4) is defined by the following equation (5). Then, the heat flux q (t, 0) ≡λ∂T / ∂xx _{= 0} where this is minimized is determined from the equation (6).
F (q) = (T (E, t) −Y (t)) ² (5)
∂F (q) / ∂q = 0 (6)
[0028]
In the above description, the heat flux is obtained for the upper temperature measurement point (the position of the temperature measurement means 16) in FIG. 6, but there are three or more lower temperature measurement points (the position of the temperature 17 in FIG. 1) or measurement points. Even in this case, the heat flux at the measurement point can be obtained in the same manner. The heat flux distribution in the casting direction is obtained by interpolating with the obtained heat flux. The heat flux is a function of the casting direction position and time, and is simply expressed as q _m below.
[0029]
Next, the solidified shell thickness, the solidified shell temperature distribution, and the solidified shell surface temperature are determined based on the heat flux.
[0030]
FIG. 7 is a conceptual diagram showing heat transfer in the molten metal. When the molten metal 2 in the molten metal pool is drawn downward from the meniscus 3 at a speed corresponding to the casting speed, it is cooled by the heat flux by the mold 11 to form a solidified shell 5. The x-dimensional one-dimensional unsteady heat transfer calculation of the molten metal 2 is performed using the molten metal temperature in the meniscus 3 as an initial condition and the mold surface heat flux obtained above as a boundary condition. For convenience of calculation, the x direction is opposite to that in FIG. Here, since the thermal inertia of the powder layer is small, it is assumed that the heat transfer in the powder layer between the solidified shell and the mold surface is in a quasi-steady state, and the mold surface heat flux is equal to the solid shell surface heat flux.
C _s ρ _s ∂T / ∂t _meni = ∂ (−λ _s ∂T / ∂x) / ∂x (7)
T = T0 where t _meni = 0 (8)
−λ _s ∂T / ∂x = q _m where x = 0 (9)
T = TL where x = δ (10)
−λ _s ∂T / ∂x = ρ _s L (dδ / dt) where x = 0 (11)
Where t _meni is the elapsed time from the meniscus, x is the distance from the mold surface at any position within the solidified shell, δ is the solidified shell thickness, L is the latent heat of solidification, λ _s is the thermal conductivity of the solidified shell, and C _s is The specific heat of the solidified shell, TL, indicates the solidification temperature.
[0031]
By solving the equations (7) to (11), the temperature distribution in the solidified shell is obtained simultaneously with the thickness of the solidified shell, and the solidified shell surface temperature at an arbitrary position in the casting direction can be determined from the meniscus.
[0032]
Next, a method of estimating the solidified shell surface heat flux and determining the heat flux due to thermal convection (molten metal flow) will be described. As before, we use JVBECK's nonlinear inverse heat transfer method.
[0033]
Considering only one-dimensional heat transfer in the solidified shell thickness direction as shown in FIG. 7, the governing equation can be expressed by the following equation.
ρ _s C _s ∂T / ∂t = −∂ (λ _s ∂T / ∂x) / ∂x (12)
T (0, t) = Y (t) (13)
λ _s ∂T (0, t) / ∂t = q _m (14)
T (x, 0) = Ti (x) (15)
Here, t represents an arbitrary time and is different from t _meni indicating the elapsed time from the meniscus.
[0034]
Assuming a certain solidified shell thickness, the above equations (12) to (15) are solved to obtain the assumed heat flux and temperature on the inner surface of the solidified shell. By setting the solidified shell thickness to an appropriate value, the solidified shell inner surface temperature and the molten metal solidified temperature obtained by calculation can be made to coincide with each other, and the heat flux at this time is the heat flux q on the solidified shell inner surface. _m . The heat flux q _m is composed of the heat flux caused by the thermal convection of the molten metal, the heat flux that is transferred to the solidified shell by heat conduction, and the amount of heat used as the latent heat of solidification of the molten metal. expressed.

Here, α is a heat transfer coefficient by molten metal convection, Tx is a solidified shell temperature at a distance Δx from the inner surface of the solidified shell, and Tb is a bulk temperature of the molten metal.
From equation (16)

Is the heat flux due to thermal convection.
[0035]
The calculation for obtaining the heat flux and the like is executed by the computer 19 shown in FIG. 1 in accordance with the instructions of the flowchart shown in FIG.
[0036]
In step 1, time t is set to zero, and in step 2, the minute time interval Δt is added to time t to update the time. In step 3, the measured value of the thermocouple installed in the casting direction in the casting direction is read into the computer 19, and in step 4, based on the measured value of the thermocouple read in step 3, the heat flux on the mold surface and the temperature inside the mold Calculate T _ms .
[0037]
Specifically, equation (1) is discretized and solved using equation (4) as an initial condition and equations (2) and (3) as boundary conditions. The square error between the mold temperature T (E, t) and the measured temperature Y (t) at the thermocouple measurement point calculated from the equations (1) to (4) is calculated by the following equation (5).
[0038]
As shown in the above equation (6), the assumed heat flux value q ₀ is corrected according to the following procedure so that the partial differential coefficient related to the heat flux q of the square error F (q) approaches zero.
[0039]
The mold temperature calculated at the mold temperature measurement point calculated using the assumed heat flux q ₀ as the boundary condition is T (E, t) 0, and the mold at the mold temperature measurement point calculated using the corrected heat flux q ₁ as the boundary condition. When the temperature calculated value T (E, t) 1 and, T (E, t) become 1 as follows to Taylor expansion with respect Δq≡q ₁ -q _0.
T (E, t) 1 = T (E, t) 0+ (∂T (E, t) 0 / ∂q 0)
・ (Q ₁ −q ₀ ) (18)
Here, the sensitivity coefficient β ₀ is defined as follows:
β ₀ ≡∂T (E, t) 0 / ∂q ₀
= (T (E, t) 1-T (E, t) 0) / εq ₀ (19)
Here, ε is a minute value set to search for the optimum value of q, and is set to 0.001, for example. Substituting Equation (18) and Equation (19) into Equation (6) and rearranging with respect to q ₁ ,
q ₁ = q ₀ + (T (E, t) 0−Y (t)) / β ₀ (20)
When q ₁ is compared with q ₀ and the following convergence determination formula is satisfied, q ₁ is the heat flux obtained.
(Q ₁ -q ₀ ) / q ₀ <0.001 (21)
[0040]
If the equation (21) is not satisfied, q _i is calculated according to the following equation (22) in the same procedure as above with reference to q ₁ , and the calculation is repeated until the equation (23) is satisfied. q is determined, and at the same time, the mold inner surface temperature T (0, t) is calculated.

[0041]
In step 5, the solidified shell thickness δ and the solidified shell surface temperature TL are obtained using the equations (7) to (11). At that time, the heat flux value q _m used in the equation (9) uses a value in the casting direction extrapolated value of the heat flux value obtained from the thermocouple measurement value by an inverse problem.
[0042]
In step 6, the solidified shell inner surface heat flux is obtained by the equations (12) to (15). At that time, Y (t) in equation (13) uses the slab surface temperature obtained in step S5 at each thermocouple position, and q _{m in} equation (14) represents the mold obtained by solving the inverse problem in step S4. Use internal heat flux values.
[0043]
In step 7, the amount of convective heat transfer caused by the molten metal flow is determined from the equation (17) by the surface heat flux in the solidified shell.
[0044]
In the embodiment of the invention described above, the slab is a slab, but the present invention is not limited to this. For example, the slab may be a billet, a thick plate material, a round bar, or the like, and can also be applied to horizontal continuous casting.
[0045]
【The invention's effect】
In the method of the present invention, the heat flux of the molten metal mold surface or solidified shell surface not only in the steady state but also in the unsteady state is obtained from the mold temperature measurement value arranged between the mold inner surface and the water cooling groove, and the mold surface temperature and the like are estimated. Therefore, the solidification state in the molten metal mold can be clearly detected. As a result, it is possible to detect a casting abnormality in the mold with high accuracy on-line and to manage a casting operation method that can obtain a sound solidified state. Further, it is not necessary to expose the tip of a temperature measuring means such as a thermocouple to the mold surface in order to obtain the mold surface temperature.
[Brief description of the drawings]
FIG. 1 is an apparatus configuration diagram when carrying out a method of the present invention.
FIG. 2 (a) shows a change with time of thermocouple temperature change of a slab where breakout occurred, and FIG. 2 (b) is a diagram showing a change with time of heat flux of the slab.
FIG. 3 (a) shows a change with time of thermocouple temperature change of a slab where vertical cracking occurred, and FIG. 3 (b) is a diagram showing a change with time of heat flux of the slab.
FIG. 4 is a diagram showing the results of wavelet analysis of heat flux for a slab in which vertical cracks have occurred.
FIG. 5 is a diagram showing the results of wavelet analysis of heat flux for a healthy slab.
FIG. 6 is a conceptual diagram showing heat transfer between a mold inner surface and a mold water cooling groove.
FIG. 7 is a conceptual diagram showing heat transfer in molten metal.
FIG. 8 is a calculation flowchart according to the present invention.
[Explanation of symbols]
1: cast slab 2: molten metal 3: meniscus 5: solidified shell 7: molten slag 11: mold 12: mold inner surface 13: water cooling groove 14: flow meter 15: cooling water temperature measuring means 16: first mold temperature measuring means 17: Second mold temperature measuring means 19: Computer

Claims (1)

In the method of measuring the mold temperature with a plurality of temperature measuring means embedded in the mold and detecting the casting abnormality in the mold based on the mold temperature measurement value, the temperature measuring means embedded at a plurality of locations in the mold at intervals in the casting direction. the mold temperature is measured, the heat flux in a mold inner surface at each measurement point based on the mold temperature measured value, estimated respectively from numerical solutions of unsteady heat transfer equation using the heat transfer inverse problem techniques, heat flow and the estimated From the change in the elapsed time of the bundle, the estimated heat flux is below the preset limit value for each measurement point at or near the elapsed time when any point of the slab in the mold passes the two measurement points, and the measurement point A method for detecting an abnormality in casting in a mold in continuous casting, wherein breakout or longitudinal crack is detected by decreasing in order.

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