JP2664572B2 - Temperature prediction method for unsolidified part of slab in continuous casting - Google Patents
Temperature prediction method for unsolidified part of slab in continuous castingInfo
- Publication number
- JP2664572B2 JP2664572B2 JP28985591A JP28985591A JP2664572B2 JP 2664572 B2 JP2664572 B2 JP 2664572B2 JP 28985591 A JP28985591 A JP 28985591A JP 28985591 A JP28985591 A JP 28985591A JP 2664572 B2 JP2664572 B2 JP 2664572B2
- Authority
- JP
- Japan
- Prior art keywords
- slab
- solidification
- temperature
- equation
- thickness
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims description 29
- 238000009749 continuous casting Methods 0.000 title claims description 15
- 238000007711 solidification Methods 0.000 claims description 94
- 230000008023 solidification Effects 0.000 claims description 91
- 238000004364 calculation method Methods 0.000 claims description 36
- 238000009826 distribution Methods 0.000 claims description 27
- 239000007790 solid phase Substances 0.000 claims description 26
- 238000001816 cooling Methods 0.000 claims description 21
- 238000005266 casting Methods 0.000 claims description 10
- 239000007787 solid Substances 0.000 claims description 10
- 239000007788 liquid Substances 0.000 claims description 9
- 238000006243 chemical reaction Methods 0.000 claims description 8
- 229910000831 Steel Inorganic materials 0.000 claims description 6
- 239000010959 steel Substances 0.000 claims description 6
- 239000000203 mixture Substances 0.000 claims description 2
- 238000013277 forecasting method Methods 0.000 claims 1
- 238000002844 melting Methods 0.000 claims 1
- 230000008018 melting Effects 0.000 claims 1
- 230000015271 coagulation Effects 0.000 description 6
- 238000005345 coagulation Methods 0.000 description 6
- 239000007791 liquid phase Substances 0.000 description 6
- 230000009467 reduction Effects 0.000 description 6
- 230000008859 change Effects 0.000 description 5
- 238000013178 mathematical model Methods 0.000 description 4
- 238000005204 segregation Methods 0.000 description 4
- 229910052698 phosphorus Inorganic materials 0.000 description 3
- 229910052799 carbon Inorganic materials 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000004907 flux Effects 0.000 description 2
- 229910052748 manganese Inorganic materials 0.000 description 2
- 239000011572 manganese Substances 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 1
- OAICVXFJPJFONN-UHFFFAOYSA-N Phosphorus Chemical compound [P] OAICVXFJPJFONN-UHFFFAOYSA-N 0.000 description 1
- 239000000498 cooling water Substances 0.000 description 1
- 238000007599 discharging Methods 0.000 description 1
- 239000004744 fabric Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 239000012535 impurity Substances 0.000 description 1
- WPBNNNQJVZRUHP-UHFFFAOYSA-L manganese(2+);methyl n-[[2-(methoxycarbonylcarbamothioylamino)phenyl]carbamothioyl]carbamate;n-[2-(sulfidocarbothioylamino)ethyl]carbamodithioate Chemical compound [Mn+2].[S-]C(=S)NCCNC([S-])=S.COC(=O)NC(=S)NC1=CC=CC=C1NC(=S)NC(=O)OC WPBNNNQJVZRUHP-UHFFFAOYSA-L 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 230000005499 meniscus Effects 0.000 description 1
- 239000003595 mist Substances 0.000 description 1
- 239000011574 phosphorus Substances 0.000 description 1
- 230000000704 physical effect Effects 0.000 description 1
- 239000000843 powder Substances 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 238000005096 rolling process Methods 0.000 description 1
- 238000013316 zoning Methods 0.000 description 1
Landscapes
- Continuous Casting (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Description
【０００１】[0001]
【産業上の利用分野】本発明は、連続鋳造鋳片の中心部
において不純物元素（例えば炭素、マンガン、燐等）が
偏析するのを防止すべく鋳片に対し軽圧下を行う際に、
この軽圧下を施すべき位置を決定するために用いて好適
の、鋳片未凝固部分の温度予測方法に関する。BACKGROUND OF THE INVENTION The present invention relates to a method for lightly reducing a slab in order to prevent segregation of impurity elements (eg, carbon, manganese, phosphorus, etc.) in the center of a continuous cast slab.
The present invention relates to a method for predicting the temperature of an unsolidified portion of a slab, which is preferably used for determining the position where the light reduction is to be performed.
【０００２】[0002]
【従来の技術】一般に、鋳型から鋳片を連続的に引き抜
いて鋳造を行う連続鋳造では、鋳片の厚さ方向中心部が
最後に凝固する。この最終凝固部分では、Ｃ、Ｍｎ、Ｐ
等の溶鋼成分濃度が高くなり偏析が生じる。2. Description of the Related Art Generally, in continuous casting in which a slab is continuously drawn from a mold to perform casting, a central portion in the thickness direction of the slab is solidified last. In this final solidification part, C, Mn, P
Etc., the concentration of the molten steel component increases, and segregation occurs.
【０００３】偏析は強度等の機械的性質のバラツキ要因
となるため、このような鋳片の中心偏析を防止する手段
として、凝固末期に鋳片の未凝固部分を軽圧下し、Ｃ、
Ｍｎ、Ｐ等の高濃度溶鋼を鋳片中心部より排出し、均質
な鋳片を製造する技術が一般的に行われている。Since segregation causes a variation in mechanical properties such as strength, as a means for preventing such center segregation of the slab, the unsolidified portion of the slab is lightly reduced at the end of solidification , and C,
2. Description of the Related Art A technique of discharging a high-concentration molten steel such as Mn and P from a central portion of a slab and manufacturing a homogeneous slab is generally performed.
【０００４】[0004]
【発明が解決しようとする課題】ところで、凝固末期に
鋳片の未凝固部分を軽圧下する場合、凝固位置、未凝固
厚、固相率等の凝固情報に基づいて、圧下条件を適切に
選択することが重要になる。しかし、連続鋳造では、ト
ップ、ボトム、中間部で鋳造条件の変動があるため、常
に凝固状態が変化する。そのような状態変動に対応して
動的に圧下制御を行うべく、オンライで凝固状態を精度
よく予測することが必要となる。By the way, in the last stage of coagulation,
When the unsolidified portion of the slab is lightly reduced, it is important to appropriately select the rolling conditions based on solidification information such as solidification position, unsolidified thickness, and solid fraction. However, in continuous casting, the solidification state always changes due to fluctuations in casting conditions at the top, bottom, and intermediate portions . In order to dynamically perform the reduction control in response to such a state change, it is necessary to accurately predict the solidification state online.
【０００５】凝固状態を予測する手段としては、差分計
算が一般的に用いられてきているが、差分計算の場合、
計算断面に計算節点を設けるため、その処理が膨大にな
って、計算機負荷の制約によりプロセスコンピュータ等
でのオンライン計算が困難になる。逆に、オンライン計
算を行えるように計算節点と計算断面を減らすと、計算
精度が大きく低下し、オンライン制御に適用できなくな
る。つまり、オンラインで凝固状態を予測し軽圧下制御
を行うためには、計算精度と演算処理の高速化とを同時
に満足させる必要がある。As a means for predicting the solidification state, difference calculation has been generally used. In the case of difference calculation,
Since calculation nodes are provided in the calculation cross section, the processing becomes enormous, and it becomes difficult to perform online calculation with a process computer or the like due to the limitation of the computer load. Conversely, if the number of calculation nodes and the number of calculation cross sections are reduced so that online calculation can be performed, the calculation accuracy is greatly reduced, and the calculation cannot be applied to online control. That is, in order to predict the solidification state online and perform the light reduction control, it is necessary to simultaneously satisfy the calculation accuracy and the speeding up of the arithmetic processing.
【０００６】本発明は、このような課題を解決しようと
するもので、数式モデルによる凝固状態の予測計算の簡
易化と精度の向上とを実現し、高い精度の凝固状態予測
結果に基づいて、鋳片に対する軽圧下位置を高速で予測
できるようにした、連続鋳造における鋳片未凝固部分の
温度予測方法を提供することを目的とする。The present invention is intended to solve such a problem, and realizes simplification of calculation and prediction of solidification state using a mathematical model and improvement of accuracy. Based on a highly accurate solidification state prediction result, An object of the present invention is to provide a method for predicting a temperature of an unsolidified portion of a slab in continuous casting, in which a light reduction position with respect to a slab can be predicted at a high speed.
【０００７】[0007]
【課題を解決するための手段】上記目的を達成するため
に、本発明の連続鋳造における鋳片未凝固部分の温度予
測方法は、鋳型から鋳片を連続的に引き抜いて鋳造を行
う連続鋳造中に、オンラインで前記鋳片の未凝固部分の
温度を予測する方法であって、鋳片の凝固初期の鋳型近
傍では、含熱量−変換温度法を適用し差分計算により
求めた前記鋳片の温度分布と溶鋼成分から決まる固相温
度から鋳型近傍の鋳片の凝固厚を求め、鋳片の２次冷
却帯 では、固液界面での熱バランス式と、固相部温度
分布を２次方程式近似する積分プロファイル法とを適用
して前記鋳片の凝固速度式を求めた後、この凝固速度式
に前記鋳型近傍で求めた鋳片の凝固厚を初期値として
代入して、この凝固速度式を解くことにより２次冷却帯
の鋳片の凝固厚を求め、鋳片の凝固末期では、前記
２次冷却帯で求めた鋳片の凝固厚を用いた所定の境界
条件式を満足するように、この未凝固部分の温度分布を
仮定し、この温度分布に基づいて、凝固末期の鋳片の
中心温度を予測することを特徴としている。[MEANS FOR SOLVING THE PROBLEMS] To achieve the above object
In the continuous casting of the present invention, the temperature pre-
The measurement method is to continuously pull out the slab from the mold and perform casting.
During continuous casting, the unsolidified portion of the slab is
A method for predicting temperature,Near the mold at the early stage of solidification of the slab
BesideThen, apply the heat content-conversion temperature method and calculate the difference.
Solid phase temperature determined from the temperature distribution of the slab and the molten steel component
The solidification thickness of the slab near the mold from the degree, Secondary cooling of slab
Rejection Now, the heat balance formula at the solid-liquid interface and the solid phase temperature
distributionApply integral profile method to approximate quadratic equation
Then, after determining the solidification rate equation of the slab,This solidification rate formula
The solidification thickness of the slab determined near the mold as the initial value
Substitute,thisBy solving the solidification rate equationSecondary cooling zone
ofFind the solidification thickness of the slab,In the final stage of solidification of the slab,
Of the slab found in the secondary cooling zonePredefined boundary using solidification thickness
In order to satisfy the conditional expression, the temperature distribution of this unsolidified part is
Assuming,thisBased on the temperature distribution,In the last stage of solidification
It is characterized by predicting the center temperature.
【０００８】[0008]
【作用】上述した本発明の連続鋳造における鋳片未凝固
部分の温度予測方法によれば、凝固初期の鋳型近傍で
は、熱流束の変化が激しいため、含熱量−変換温度法を
適用し差分計算により鋳片の温度分布を求め、この温度
分布と溶鋼成分から決まる固相温度から鋳片の凝固厚が
求められ、鋳片の２次冷却帯 以降では、鋳片の凝固速
度の変化が小さくなるので、固液界面での熱バランス式
と固相部温度分布を２次方程式近似する積分プロファイ
ル法とを適用し、鋳片の凝固速度式を求め、さらに、こ
の凝固速度式から２次冷却帯の鋳片の凝固厚が求めら
れる。前記凝固速度式では、既知の凝固厚を用いて凝固
速度を求めるため、前記鋳型近傍で得られた鋳片の凝
固厚を初期値として代入する。The slab is not solidified in the continuous casting of the present invention described above.
According to the temperature prediction method of the part,Near the moldso
Uses the heat content-conversion temperature method because the heat flux changes drastically.
By applying the difference calculation,Find the temperature distribution and calculate this temperature
The solidification thickness of the slab is determined from the solid phase temperature determined by the distribution and the molten steel composition.
Required, Secondary cooling zone of slab Hereinafter, the solidification speed of the slab
Since the change in degree is small, the heat balance type at the solid-liquid interface
And solid phase temperaturedistributionIntegral profile that approximates the quadratic equation
And apply the lawFind the solidification rate equation for the slabAnd more
From the solidification rate equationOf the secondary cooling zoneThe solidification thickness of the slab is required
It is.In the solidification rate equation, solidification is performed using a known solidification thickness.
In order to determine the speed, the coagulation of the slab obtained near the mold was performed.
Substitute solid thickness as initial value.
【０００９】そして、鋳片の凝固末期では、前記２次
冷却帯で求めた鋳片の凝固厚を用いた所定の境界条件
式を満足するように、鋳片の未凝固部分の温度分布が仮
定され、その温度分布に基づき鋳片の中心温度が予測さ
れる。In the final stage of solidification of the slab, the secondary
The temperature distribution of the unsolidified portion of the slab is assumed to satisfy a predetermined boundary condition equation using the solidified thickness of the slab obtained in the cooling zone, and the center temperature of the slab is predicted based on the temperature distribution. You.
【００１０】凝固初期の鋳型近傍における極短い区間
では、差分計算を行うために計算断面の数をある程度多
く設定する必要はあるが、２次冷却帯 以降では、固液
界面での熱バランス式と固相部温度分布を２次方程式近
似する積分プロファイル法とを適用することで、数式モ
デルによる凝固状態の予測計算が簡易化されると同時
に、十分な予測精度も得られる。In the early stage of solidificationNear the moldExtremely short interval at
Now, we need to increase the number of calculation cross sections to
It is necessary to set it well, but the secondary cooling zone In the following, solid-liquid
Heat balance equation at interface and solid phase temperaturedistributionTo the quadratic equation
By applying a similar integral profile method,
Simultaneous with Dell's simplified calculation of solidification state
In addition, sufficient prediction accuracy can be obtained.
【００１１】[0011]
【実施例】以下に、図面により本発明の一実施例として
の連続鋳造における鋳片未凝固部分の温度予測方法につ
いて説明する。図１は本方法を適用される連続鋳造中の
鋳片モデルおよびその座標系を示す図であり、この図１
において、１は鋳型、２はこの鋳型１から下方へ連続的
に引き抜かれる鋳片で、この鋳片２は、引き抜きに伴い
徐々に形成されてゆく凝固部分（固相部）２ａと、凝固
部分２ａ内方の未凝固部分（液相部）２ｂとを有してい
る。また、鋳片凝固初期の鋳型近傍を、鋳片の２次冷
却帯を、鋳片の凝固末期をで示す。 DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A method for predicting the temperature of an unsolidified portion of a slab in continuous casting as an embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a view showing a slab model and its coordinate system during continuous casting to which the present method is applied.
In the figure, 1 is a mold, 2 is a cast piece that is continuously drawn downward from the mold 1, and the cast piece 2 is composed of a solidified portion (solid phase portion) 2a and a solidified portion that are gradually formed with the drawing. 2a and an unsolidified portion (liquid phase portion) 2b inside. Further, the vicinity of the mold at the initial stage of solidification of the slab is subjected to secondary cooling of the slab.
The zoning is indicated by the last stage of solidification of the slab.
【００１２】ただし、図１において、鋳型１からの鋳片
２の引き抜き方向が水平に描かれているが、図１の左右
方向は鋳片の長さ方向位置を示している。また、凝固部
分２ａの厚さ（凝固厚）は、鋳片２の最外殻位置を０と
し鋳片厚中心線（一点鎖線）に直交する方向を正とする
Ｘ軸により表され、時刻ｔにおける凝固厚をＸ（ｔ）と
する。同様に、未凝固部分２ｂの厚さ（未凝固厚）は、
鋳片厚中心位置を０とし鋳片２の最外殻面に直交する方
向を正とするε軸により表され、時刻ｔにおける未凝固
厚をＥ（ｔ）とする。However, in FIG. 1, the drawing direction of the slab 2 from the mold 1 is drawn horizontally, but the horizontal direction in FIG. 1 indicates the longitudinal position of the slab . The thickness (solidified thickness) of the solidified portion 2a is represented by an X-axis with the outermost shell position of the slab 2 set to 0 and the direction orthogonal to the slab thickness center line (dashed line) to be positive. Let X (t) be the solidification thickness at. Similarly, the thickness of the unsolidified portion 2b (unsolidified thickness) is
The unsolidified thickness at time t is represented by E (t), which is represented by an ε-axis in which the slab thickness center position is 0 and the direction orthogonal to the outermost shell surface of the slab 2 is positive.
【００１３】本実施例では、図１に示すように、鋳型１
から鋳片２を連続的に引き抜きながら鋳造を行う連続鋳
造中に、オンラインで鋳片２の未凝固部分２ｂの中心温
度Ｔｃｎｔを予測して、凝固末期における鋳片２の中心
温度に基づいて鋳片２の固相率を知り、鋳片２に対する
軽圧下位置を決定しようとするもので、以下に、本発明
によるその未凝固部分２ｂの中心温度Ｔｃｎｔの予測手
順を説明する。In this embodiment, as shown in FIG.
During continuous casting in which casting is continuously performed while continuously drawing the slab 2 from the slab, the center temperature Tcnt of the unsolidified portion 2b of the slab 2 is predicted online, and based on the center temperature of the slab 2 in the final stage of solidification. The procedure for estimating the center temperature T cnt of the unsolidified portion 2b according to the present invention will be described below.
【００１４】本実施例の数式モデル（凝固速度式）につ
いて説明する。まず、凝固初期で鋳型１の近傍区間（鋳
型近傍）では、熱流束の変化が激しいため、含熱量−
変換温度法による下記（１）式を適用し、差分計算によ
り鋳片２の凝固状態、つまり鋳片（液相、固相）２の温
度分布を求め、溶鋼成分から決まる固相温度となる鋳片
厚さ方向位置（凝固厚Ｘ）をこの温度分布より求める。 A mathematical model ( solidification rate equation ) of this embodiment will be described. First, in the early stage of solidification, the section near the mold 1 ( casting
(Near the mold ), the heat flux changes drastically,
The solidification state of the slab 2, that is, the temperature distribution of the slab (liquid phase, solid phase) 2, is calculated by the difference calculation using the following equation (1) based on the conversion temperature method, and the solid phase temperature is determined by the molten steel component. Piece
The position in the thickness direction (solidified thickness X) is determined from this temperature distribution.
【００１５】[0015]
【数１】 (Equation 1)
【００１６】ここで、ρは比重量、Ｔは温度、Ｈは含熱
量、λｄは基準温度（０℃）における熱伝導率、φは変
換温度（熱伝導率を温度に変換した物性値）、λは熱伝
導率、ｔは時間である。Here, ρ is specific weight , T is temperature, H is heat content, λ d is thermal conductivity at a reference temperature (0 ° C.), and φ is conversion temperature (physical property value obtained by converting thermal conductivity into temperature). , Λ is the thermal conductivity and t is the time .
【００１７】そして、鋳型近傍での（１）式による差
分計算結果の温度分布と固相温度から求まる凝固厚Ｘを
踏まえて、鋳片２の凝固速度の変化が小さい２次冷却帯
では、固液界面（凝固部分２ａと未凝固部分２ｂとの
境界面）での熱バランス式と固相部温度分布Ｔ ｓ を２次
方程式近似する積分プロファイル法とを適用している。
つまり、固相部（凝固部分）温度分布Ｔｓを下記（２）
式に示す２次方程式で近似し、下記（３）式に示す境界
条件式を用いて、（２）式における各係数Ｚ０、Ｚ１、
Ｚ２を下記（４）式の通り求める。AndNear the moldBy equation (1)
Minute calculation resultSolidification thickness X obtained from the temperature distribution of solid and the solidus temperatureTo
Based on this, the change in the solidification rate of the slab 2 is smallSecondary cooling zone
Then, the solid-liquid interface (the solidified portion 2a and the unsolidified portion 2b
Thermal balance equation at the boundary surface) and solid phase temperatureDistribution T s Is secondary
The integral profile method for approximating equations is applied.
In other words, the solid phase (solidification) temperaturedistributionTsThe following (2)
Approximate by the quadratic equation shown in the equation,Equation (3) belowBoundaries shown
Using a conditional expression, each coefficient Z in the expression (2)0, Z1,
Z2Is determined according to the following equation (4).
【００１８】ここで、固相部温度分布Ｔｓは、凝固厚、
凝固速度、熱伝導率が求められた場合の定常状態の温度
分布を表す。また、鋳型近傍での（１）式による差分
計算結果である凝固厚Ｘは、凝固速度式、下記（６）式
における凝固厚Ｘの初期値として代入される。[0018] In this case, the solid phase portion temperature distribution T s is, coagulation thickness,
It shows the steady-state temperature distribution when the solidification rate and the thermal conductivity are determined. Further, the solidification thickness X, which is the result of the difference calculation by the equation (1) in the vicinity of the mold , is substituted as an initial value of the solidification thickness X in the solidification rate equation and the following equation (6) .
【００１９】凝固速度ｄＸ／ｄｔは（２）式〜（４）式
および凝固厚Ｘの位置で固相温度Ｔｓｌ一定の条件
（５）式のもと下記（６）式で計算される。この（６）
式において、Ｃは凝固速度係数で、（６）式での計算値
を（１）式に整合させるためのものである。また、凝固
厚Ｘの計算精度を高めるため、本実施例では（６）式を
Ｒｕｎｇｅ−Ｋｕｔｔａ法により解いて凝固厚Ｘを求め
る。The solidification speed dX / dt is given by the formulas (2) to (4).
Of solid phase temperature T sl constant at the position of solidification thickness X
It is calculated by the following equation (6) based on the equation (5) . This (6)
In the formula, C is a solidification rate coefficient, which is used to match the calculated value in the formula (6) to the formula (1). Further, in order to increase the calculation accuracy of the solidified thickness X, in the present embodiment, the solidified thickness X is obtained by solving the equation (6) by the Runge-Kutta method.
【００２０】 Ｔｓ＝Ｚ２・Ｘ２＋Ｚ１・Ｘ＋Ｚ０ （２）T s = Z 2 · X 2 + Z 1 · X + Z 0 (2)
【００２１】[0021]
【数２】 (Equation 2)
【００２２】[0022]
【数３】 (Equation 3)
【００２３】ここで、Ｔｓｌは固相温度、Ｔ０は冷却側
温度（水温）、Ｌは固相温度Ｔｓｌに対する液相含熱
量、Ｃは凝固速度係数、ｈは鋳片２外表面での熱伝達率
〔ｋｃａｌ／（ｍ２・ｈ・℃）〕、ｔは時間、Ｃｐｓは
固相比熱、λｓは固相熱伝導率〔ｋｃａｌ／（ｍ・ｈ・
℃）〕、ρｓは固相比重量、ρｌは液相比重量、Ｂｉ＝
ｈ／λｓ、ａ ｓ ＝λ ｓ ／ρ ｓ Ｃ ｐｓ である。なお、２次
冷却帯 でのミストの熱伝達率については、例えば、下
記（７）式に示す熱伝達率ｈを用いて計算を行う。Where TslIs the solidus temperature, T0Is the cooling side
Temperature (water temperature), L is solid phase temperature TslLiquid heat content for
Quantity, C is the solidification rate coefficient, h is the heat transfer coefficient on the outer surface of the slab 2
[Kcal / (m2H · ° C)], t is time, CpsIs
Solid phase specific heat, λsIs the solid thermal conductivity [kcal / (m · h ·
℃)], ρsIs the solid phase specific weight, ρlIs the liquid phase specific weight, Bi=
h / λs,a s = Λ s / Ρ s C ps It is. The secondary
Cooling zone Mist inHeat transfer coefficientFor example,under
Note (7)The calculation is performed using the heat transfer coefficient h shown in the equation.
【００２４】[0024]
【数４】 (Equation 4)
【００２５】ここで、Ｗは冷却水量密度、Ｑａは空気流
量、Ｔｗは水温、Ｔｓは鋳片２の固相部（凝固部２ａ）
の温度分布で、ｘ＝０を付したＴｓはｘ＝０位置つまり
鋳片２の固相部の外表面位置の温度である。[0025] Here, W is the amount of cooling water density, Q a is the air flow rate, T w is the water temperature, T s is the solid phase portion of the slab 2 (solidified portion 2a)
In the temperature distribution, T s marked with x = 0 is the temperature of the outer surface position of the solid phase portion of the x = 0 position ie the slab 2.
【００２６】図１に示す２次冷却帯 では、上述した
（２）〜（７）式を用いて凝固厚Ｘの演算が行われる。
ただし、上述した鋳型近傍での（１）式による差分計
算結果の温度分布と固相温度から求めた凝固厚Ｘが初期
値として（６）式に代入される。さらに下流側の凝固末
期 では、鋳片２の両側からの凝固の影響が現れ、凝固
厚とともに凝固速度が急速に大きくなる。この現象を数
式化するため、下記（８）式の形を導入した。ここで、
定数Ｄは（６）、（８）式で得られる凝固速度を一致・
整合させるためのものである。また、（６）式中のＣお
よび（８）式中のｎは、（１）式の差分計算を凝固初期
から凝固末期まで一貫して行った場合の凝固速度と、
（６）式、（８）式を用いて求められる凝固速度とを互
いに整合させるべく算出されたものである。The secondary cooling zone shown in FIG. So, as mentioned above
(2)-(7)Calculation of solidification thickness X is performed using the formula.
However, the difference meter based on the equation (1) near the mold described above is used.
The solidification thickness X obtained from the calculated temperature distribution and solidus temperature is the initial value.
The value is substituted into equation (6).Solidification powder further downstream
Period Then, the effect of solidification from both sides of the slab 2 appears,
The solidification rate increases rapidly with thickness. This phenomenon
To formulate,Equation (8) belowThe shape was introduced. here,
The constant D is(6), (8)Match the solidification rate obtained by the formula
This is for matching. Also,(6) C in the formula
And n in equation (8) is the difference calculation of equation (1)
To the coagulation rate when performed consistently from to the end of coagulation,
The solidification rate obtained by using the equations (6) and (8) is interchanged.
InIt is calculated to match.
【００２７】[0027]
【数５】 (Equation 5)
【００２８】ここで、Ｓｔは鋳片２の厚さの２分の１、
Ｘは凝固末期での凝固厚、ｎは凝固末期凝固速度指数
である。[0028] In this case, one half of the thickness of the S t is the slab 2,
X is the solidification thickness at the end of solidification , and n is the solidification rate index at the end of solidification.
【００２９】上述した（２）〜（８）式により、２次冷
却帯、凝固末期における鋳片２の凝固速度ｄＸ／ｄ
ｔ、凝固厚Ｘ、鋳片２の表面温度Ｔｓ（ｘ＝０）が算出
される。ただし、（６）式には上述した鋳型近傍での
（１）式による差分計算結果の温度分布と固相温度から
求めた凝固厚Ｘを初期値として代入する。 According to the above equations (2) to (8) , the secondary cooling
Solidification speed dX / d of slab 2 at the end of solidification and solidification
t, the solidified thickness X, and the surface temperature T s (x = 0) of the slab 2 are calculated. However, the equation (6) shows that
From the temperature distribution and solid phase temperature of the difference calculation result by equation (1)
The obtained solidified thickness X is substituted as an initial value.
【００３０】さて、鋳片２に対する軽圧下の制御では、
鋳片２の未凝固部分２ｂの中心付近の温度と固相率を知
る必要がある。そこで、本実施例では、（２）〜（８）
式に基づき算出された凝固厚データを用い下記（９）式
により示すような境界条件式を満足するように、ある時
間ｔにおける未凝固部分２ｂの温度分布ｆ（ε）を仮定
し、この温度分布ｆ（ε）を（１０）式に代入して未凝
固部分２ｂの中心温度Ｔｃｎｔを求める。つまり、
（２）〜（８）式を用いて凝固厚Ｘ（未凝固厚Ｅ）、鋳
片表面温度、固液界面での固相部温度勾配、鋳片表面熱
伝達率を計算し、これらを下記（９）、（１０）式に代
入して、未凝固部分２ｂの中心温度Ｔｃｎｔを求める。In the control of the slab 2 under light pressure,
It is necessary to know the temperature near the center of the unsolidified portion 2b of the slab 2 and the solid fraction. Therefore, in this embodiment, (2) to (8)
Using the solidification thickness data calculated based on the expression , a temperature distribution f (ε) of the unsolidified portion 2b at a certain time t is assumed so as to satisfy the boundary condition expression as shown by the following expression (9). The center temperature Tcnt of the unsolidified portion 2b is obtained by substituting the distribution f (ε) into the equation (10) . That is,
The solidification thickness X (unsolidified thickness E), the slab surface temperature, the solid phase temperature gradient at the solid- liquid interface , and the slab surface heat transfer coefficient were calculated using the equations (2) to (8). By substituting into the equations (9) and (10) , the center temperature Tcnt of the unsolidified portion 2b is obtained.
【００３１】[0031]
【数６】 (Equation 6)
【００３２】ここで、ｍ、Ｍは次数、Δｔは時間増分、
Ｃｐｌは液相比熱、αｍはπ／２、３π／２、５π／
２、……、ρｌは液相比重量、λｌは液相熱伝導率であ
る。なお、上記（１０）式は、未凝固部分２ｂに対する
熱伝導方程式についてフーリェ級数展開して導出したも
のである。Where m and M are orders, Δt is a time increment,
C pl is liquid phase specific heat, α m is π / 2, 3π / 2, 5π /
2, ..., the [rho l liquid phase specific weight, the lambda l is Ekishonetsu conductivity. The above equation (10) is derived by expanding the Fourier series of the heat conduction equation for the unsolidified portion 2b.
【００３３】このようにして算出・予測された未凝固部
分２ｂの中心温度Ｔｃｎｔに基づいて、凝固末期の鋳
片２の固相率を知り、鋳片２に対する軽圧下位置が決定
される。固相率は（Ｔ ｌｌ −Ｔ ｃｎｔ ）／（Ｔ ｌｌ −Ｔ
ｓｌ ）で近似し、Ｔ ｌｌ は液相温度、Ｔ ｓｌ は固相温度
である。 Based on the calculated and predicted center temperature Tcnt of the unsolidified portion 2b, the solid phase ratio of the slab 2 at the final stage of solidification is known, and the position of the light reduction with respect to the slab 2 is determined. The solid fraction is ( Tll - Tcnt ) / ( Tll- T
approximated by sl), T ll the liquidus temperature, T sl solid phase temperature
It is.
【００３４】上述のごとく行われた本実施例（凝固速度
式）による計算結果と、凝固初期の鋳型近傍、２次冷
却帯、凝固末期を通して含熱量−変換温度法による
差分計算による計算結果との比較結果を図３（ａ）、
（ｂ）に示す。なお、この比較計算に際しては、図２に
示すような鋳造速度を設定した。つまり、鋳造速度１．
６２ｍ／分から０．５０ｍ／分の変化を時間経過５〜１
１分に与え、凝固厚と未凝固部分２ｂの中心での固相率
を計算した結果を図３（ａ）、（ｂ）に示す。In this embodiment performed as described above ( solidification speed
Formula ), near the mold in the early stage of solidification, secondary cooling
FIG. 3 (a) shows the results of comparison with the calculation results obtained by the difference calculation based on the heat content-conversion temperature method throughout the final stage of solidification and solidification .
(B). In this comparison calculation, a casting speed as shown in FIG. 2 was set. That is, casting speed 1.
Change from 62m / min to 0.50m / min with time 5-1
The results obtained by calculating the solidification thickness and the solid fraction at the center of the unsolidified portion 2b at one minute are shown in FIGS. 3 (a) and 3 (b) .
【００３５】図３（ａ）、（ｂ）を比較して明らかなよ
うに、鋳造速度が変化するメニスカス位置からの距離１
０ｍ付近および凝固末期においても、両計算による凝固
厚はよく一致している。また、未凝固部分２ｂの中心で
の固相率は、最終凝固位置での変化割合が多少異なるも
のの、その差はわずか０．０５ほどで、十分にオンライ
ンモデルとして使用できるものである。As apparent from comparison of FIGS. 3A and 3B, the distance from the meniscus position at which the casting speed changes is 1
At around 0 m and at the end of solidification, the calculated solidification thicknesses are in good agreement. Further, the solid phase ratio at the center of the unsolidified portion 2b is slightly different in the rate of change at the final solidification position, but the difference is only about 0.05, and can be sufficiently used as an online model.
【００３６】このように、本実施例の予測方法によれ
ば、凝固初期の鋳型１部分における極短い区間の鋳型近
傍では、差分計算を行うために計算断面の数をある程
度多く設定する必要はあるが、２次冷却帯以降の２次冷
却帯、凝固末期では、固液界面での熱バランス式と
固相部温度分布を２次方程式近似する積分プロファイル
法とを適用することで、数式モデルによる凝固状態の予
測計算が大幅に簡易化されると同時に、十分な予測精度
も得られることが実証され、実機オンラインモデルへの
適用性が確認された。従って、高い精度の凝固状態予測
結果に基づいて、鋳片２に対する軽圧下位置を高速で且
つ精度よく予測できるものである。As described above, according to the prediction method of the present embodiment, the mold near the extremely short section of the mold 1 in the early stage of solidification.
In near, there is necessary to set a certain extent increase the number of calculations section for performing differential calculations, 2 after the secondary cooling zone Tsugihiya
At the end of cooling zone and final solidification , the heat balance equation at the solid-liquid interface and the integral profile method that approximates the temperature distribution of the solid phase to a quadratic equation greatly simplify the prediction calculation of the solidification state using a mathematical model. At the same time, it was verified that sufficient prediction accuracy was obtained, and its applicability to the online model of the actual machine was confirmed. Therefore, based on the highly accurate solidification state prediction result, it is possible to quickly and accurately predict the lightly reduced position on the slab 2.
【００３７】[0037]
【発明の効果】以上詳述したように、本発明の連続鋳造
における鋳片未凝固部分の温度予測方法によれば、凝固
初期の鋳型部分では、差分計算を行いながら、２次冷却
帯以降では、固液界面での熱バランス式と固相部温度分
布を２次方程式近似する積分プロファイル法とを適用す
ることで、数式モデルによる凝固状態の予測計算を大幅
に簡易化できるとともに、予測精度を向上でき、鋳片に
対する軽圧下位置を高速かつ高精度で予測できる効果が
ある。As described above in detail, according to the method for predicting the temperature of the unsolidified portion of a slab in continuous casting according to the present invention, the difference calculation is performed in the mold portion in the early stage of solidification while the difference is calculated in the secondary cooling zone and thereafter. , the thermal balance equation in the solid-liquid interface and the solid portion temperature min
By applying the integral profile method that approximates the cloth to the quadratic equation, the prediction calculation of the solidification state by the mathematical model can be greatly simplified, the prediction accuracy can be improved, and the light reduction position on the slab can be determined at high speed and with high accuracy. Has a predictable effect.
【図１】本発明の一実施例としての連続鋳造における鋳
片未凝固部分の温度予測方法を適用される連続鋳造中の
鋳片モデルおよびその座標系を示す図である。FIG. 1 is a view showing a slab model during continuous casting to which a method for predicting the temperature of an unsolidified portion of a slab in continuous casting as one embodiment of the present invention and a coordinate system thereof.
【図２】含熱量−変換温度法による差分計算結果と凝固
速度式による計算結果との比較に用いた鋳造速度を示す
図である。Fig. 2 Difference calculation result by heat content-conversion temperature method and solidification
It is a figure which shows the casting speed used for the comparison with the calculation result by a speed formula .
【図３】（ａ）は含熱量−変換温度法による差分計算結
果を凝固厚および固相率について示すグラフ、（ｂ）は
凝固速度式による計算結果を凝固厚および固相率につい
て示すグラフである。FIG. 3 (a) is a graph showing the difference calculation result by the heat content-conversion temperature method with respect to the solidification thickness and the solid fraction, and FIG.
It is a graph which shows the calculation result by a solidification rate formula about solidification thickness and solid phase ratio.
１ 鋳型 ２ 鋳片 ２ａ凝固部分（固相部） ２ｂ未凝固部分（液相部） 鋳型近傍 ２次冷却帯 凝固末期 1 mold 2 cast slab 2a solidified portion (solid phase portion) 2b unsolidified portion (liquid phase part) mold near the secondary cooling zone coagulation end
Claims (1)
を行う連続鋳造中に、オンラインで前記鋳片の未凝固部
分の温度を予測する方法であって、鋳片の凝固初期の鋳型近傍 では、含熱量−変換温度法
を適用し差分計算により求めた前記鋳片の温度分布と溶
鋼成分から決まる固相温度から鋳型近傍の鋳片の凝固
厚を求め、 前記鋳片の２次冷却帯 では、固液界面での熱バランス
式と、固相部温度分布を２次方程式近似する積分プロフ
ァイル法とを適用して前記鋳片の凝固速度式を求めた
後、この凝固速度式に前記鋳型近傍で求めた鋳片の凝
固厚を初期値として代入して、この凝固速度式を解くこ
とにより２次冷却帯の鋳片の凝固厚を求め、前記鋳片の凝固末期では、前記２次冷却帯で求めた
鋳片の 凝固厚を用いた所定の境界条件式を満足するよう
に、この未凝固部分の温度分布を仮定し、この温度分布
に基づいて、凝固末期の鋳片の中心温度を予測するこ
とを特徴とする連続鋳造における鋳片未凝固部分の温度
予測方法。1. Casting by continuously drawing a slab from a mold
During continuous casting, the unsolidified portion of the slab is
A method of predicting the temperature of a minute,Near the mold at the early stage of solidification of the slab Then, the heat content-conversion temperature method
And apply the difference calculationThe temperature distribution and melting
Solidification of slab near mold from solidus temperature determined by steel composition
Find the thicknessSecondary cooling zone of the slab Now, the heat balance at the solid-liquid interface
Equation and solid phase temperaturedistributionIs an integral profile that approximates a quadratic equation
The solidification rate equation of the slab was obtained by applying the file method
rear,The solidification rate of the slab obtained near the mold was calculated using this solidification rate equation.
Substituting the solid thickness as the initial value,thisSolve the solidification rate equation
And byOf the secondary cooling zoneFind the solidification thickness of the slab,In the final stage of solidification of the slab, it was determined in the secondary cooling zone.
Slab Satisfy predetermined boundary condition formula using solidification thickness
Assuming the temperature distribution of this unsolidified part,thisTemperature distribution
On the basis of,In the last stage of solidificationPredict the center temperature
Temperature of unsolidified portion of slab in continuous casting characterized by
Forecasting method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP28985591A JP2664572B2 (en) | 1991-11-06 | 1991-11-06 | Temperature prediction method for unsolidified part of slab in continuous casting |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP28985591A JP2664572B2 (en) | 1991-11-06 | 1991-11-06 | Temperature prediction method for unsolidified part of slab in continuous casting |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH05123842A JPH05123842A (en) | 1993-05-21 |
| JP2664572B2 true JP2664572B2 (en) | 1997-10-15 |
Family
ID=17748638
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|---|---|---|---|
| JP28985591A Expired - Fee Related JP2664572B2 (en) | 1991-11-06 | 1991-11-06 | Temperature prediction method for unsolidified part of slab in continuous casting |
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| Country | Link |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| AT408197B (en) * | 1993-05-24 | 2001-09-25 | Voest Alpine Ind Anlagen | METHOD FOR CONTINUOUSLY casting a METAL STRAND |
| JP4501236B2 (en) * | 2000-06-30 | 2010-07-14 | Ｊｆｅスチール株式会社 | Continuous casting method |
| KR100889290B1 (en) * | 2002-08-30 | 2009-03-17 | 재단법인 포항산업과학연구원 | A Method for Calculating the Roll Life in a Continuous Casting |
| WO2005051569A1 (en) | 2003-11-27 | 2005-06-09 | Jfe Steel Corporation | Method for detecting solidification completion position of continuous casting cast piece, detector, and method for producing continuous casting cast piece |
| CN107790662B (en) * | 2017-10-16 | 2021-01-15 | 首钢集团有限公司 | Method and device for controlling center segregation of plate blank |
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1991
- 1991-11-06 JP JP28985591A patent/JP2664572B2/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| JPH05123842A (en) | 1993-05-21 |
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