JP2004174544A

JP2004174544A - Method for manufacturing continuously cast slab

Info

Publication number: JP2004174544A
Application number: JP2002342637A
Authority: JP
Inventors: 幸司 ▲高▼谷; Koji Takatani
Original assignee: Sumitomo Metal Industries Ltd
Current assignee: Nippon Steel Corp
Priority date: 2002-11-26
Filing date: 2002-11-26
Publication date: 2004-06-24
Anticipated expiration: 2022-11-26
Also published as: JP3896953B2

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for manufacturing a continuously cast slab of slight center segregation or the like and excellent property by analyzing an adequate rolling condition in advance when continuously casting molten metal by using a mathematical model with correctly described motion of a solidified shell, and rolling down the slab including a non-solidified portion under this adequate rolling condition. <P>SOLUTION: The quality of a slab in complete solidification is operated by using a mathematical model having at least an equation of motion including a constitutive equation to describe that an enriched liquid phase contained in a solid-liquid coexistent phase within a solidified shell is discharged by deformation of the solidified shell of the slab from a mold of a continuously casting machine under the external force. A rolling condition of the continuously casting machine capable of maintaining the quality at a desired level is obtained in advance. The continuously casting machine is operated based on the obtained rolling condition to manufacture a continuously cast slab. <P>COPYRIGHT: (C)2004,JPO

Description

【０００１】
【発明の属する技術分野】
本発明は、連続鋳造鋳片の製造法に関し、具体的には、連続鋳造機による鋳片の凝固時の現象を記述した数学モデルを用いて、溶融金属の連続鋳造の際の圧下ロールの適正な圧下の条件を実際の操業前に解析しておき、この連続鋳造機をこの適正な圧下の条件に基づいて実際に操業することにより、中心偏析等の鋳片品質の不良が極めて軽微であって性状が良好な連続鋳造鋳片を確実に製造可能な方法に関する。
【０００２】
【従来の技術】
連続鋳造機の適正な操業条件を解析する際に用いられる数学モデルは、溶融金属の流動のみを解析する数学モデル１と、溶融金属の流動と熱移動とを解析する数学モデル２と、溶融金属の流動は無視し、熱移動と生成した凝固シェルの変形とを解析する数学モデル３と、溶融金属の流動、熱移動、溶融金属および凝固シェル中の溶質成分の輸送、および凝固シェルの運動を解析する数学モデル４との４種に大別される。
【０００３】
数学モデル１、２は、溶融金属の流動現象に重きを置いているため、例えば浸漬ノズルの吐出孔形状や電磁攪拌装置等の、鋳型の内部における溶融金属の流動に影響する因子を設計する際に利用される。また、数学モデル３は、凝固シェルが生成するときに連続鋳造機の湾曲形状に合わせて変形を受けて歪みを蓄積し、場合によっては凝固シェルの内部で割れが発生するため、これを定量的に評価することにより連続鋳造機の引き抜き部の湾曲形状を設計する際に利用される。
【０００４】
これに対し、数学モデル４は、連続鋳造機を用いて連続鋳造を行う際に生じる殆ど全ての現象を最も精緻かつ的確に表現することができるものであり、連続鋳造機の適正な操業条件（例えば圧下ロールの圧下量等）を解析する場合に有効に利用できる。例えば、この数学モデル４によれば、連続鋳造における製品欠陥のひとつである中心偏析もモデル上で再現することができる。
【０００５】
非特許文献１〜３のいずれにも、細部には若干の違いはあるものの、連続鋳造機における溶融金属の流動、凝固および溶質成分の凝固偏析挙動を記述する数学モデルを用いて中心偏析の発生の程度を予測する方法が開示されている。
【０００６】
これらの発明は、凝固シェルの運動方程式からなる力学的な支配方程式を解かずに強制的に外部から凝固シェルの速度を与えて凝固シェルの運動を表現する点、すなわち凝固シェルの変形および移動挙動の推定を行わない点で共通する。すなわち、これらの発明では、固体である凝固シェルの大変形を伴う場合の溶融金属の流動、伝熱（凝固）および偏析現象の解析は、凝固シェルの変形を予め固定値として仮定することにより、中心偏析の発生の程度を予測していた。
【０００７】
【非特許文献１】
Ｋ．ＭｉｙａｚａｗａａｎｄＳｃｈｗｅｒｄｔｆｅｇｅｒ著「Ａｒｃｈ．Ｅｉｓｅｎｈｕｔｔｅｎｗｅｓ」ｖｏｌ．５２，（１９８１）、Ｐ４１６
【非特許文献２】
Ｉ．ＯｈｎａｋａａｎｄＴ．Ｓｈｉｍａｚｕ著「ＰｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅＳｉｘｔｈＩｎｔｅｒｎａｔｉｏｎａｌＩｒｏｎａｎｄＳｔｅｅｌＣｏｎｇｒｅｓｓ」１９９０、Ｎａｇｏｙａ、ＩＳＩＪ
【非特許文献３】
Ｈ．ＥｉｓｅｒｍａｎａｎｄＫ．Ｓｃｈｗｅｒｄｔｆｅｇｅｒ著「ＰｒｏｃｅｅｄｉｎｇｓｏｆＴｈｅＪｕｌｉａｎＳｚｅｋｅｌｙｍｅｍｏｒｉａｌＳｙｍｐｏｓｉｕｍｏｎｍａｔｅｒｉａｌｓＰｒｏｃｅｓｓｉｎｇＥｄｉｔｅｄｂｙＨ．Ｙ．Ｓｏ」ｈｎ．Ｊ．Ｗ．ＥｖａｎｔｓａｎｄＤ．Ａｐｅｌｉａｎ，ＴｈｅＭｉｎｅｒａｌｓ＆ＭａｔｅｒｉａｌｓＳｏｃｉｅｔｙ（１９８７）、ｐ３８３〜３９２
【０００８】
【発明が解決しようとする課題】
上述したように、連続鋳造機の適正な操業条件（例えば圧下ロールの圧下量等）を合理的に解析しようとすると、溶融金属の流動、熱移動、溶融金属および凝固シェル中の溶質成分の輸送だけではなく、さらに、凝固シェルの運動を詳細に把握する必要がある。
【０００９】
しかし、これらの非特許文献１〜３に記載された数学モデルでは、凝固シェルの変形や移動挙動の推定を行わないため、凝固シェルの正確な移動や変形現象を記述することができない。すなわち、凝固シェルの運動の推定手段として上述した数学モデルが従来より用いられているものの、例えば凝固シェルが変形することにより凝固シェルの内部の固液共存相に含まれる濃化液相が排出されるという現象を記述できる数学モデルは、これまでのところ存在しない。
【００１０】
本発明の目的は、連続鋳造機による鋳片の凝固時の現象を記述した数学モデルを用いて溶融金属の連続鋳造の際の適正な操業条件（例えば圧下ロールの圧下条件）を実際の操業前に解析しておき、この連続鋳造機をこの適正な圧下の条件に基づいて実際に操業することにより、中心偏析等の鋳片品質不良が極めて軽微であるとともに性状が良好な連続鋳造鋳片を確実に製造することができる方法を提供することである。
【００１１】
【課題を解決するための手段】
本発明者は、従来から用いられてきた全ての数学モデルには、凝固シェルの運動を正確に記述する運動方程式が組み込まれていないため、中心偏析の発生を抑制できる程度に実際の現象を正確に示すことができないと考えた。
【００１２】
そして、未凝固部を含む鋳片を圧下する場合の凝固シェルの運動を正確に記述するためには、固液共存相を含む凝固シェルを剛塑性体として近似するとともに固液共存相を多孔質体として近似することにより凝固シェルの変形および移動挙動を少なくとも記述する運動方程式を含む数学モデルを用いれば、凝固シェルが変形した時の固液共存相内の濃化液相の排出挙動を正確に記述することができ、これにより、上述した課題を解決することができることを知見し、さらに検討を重ねて、本発明を完成した。
【００１３】
本発明は、連続鋳造機の鋳型を出た鋳片の凝固シェルが外力を受けて変形することにより凝固シェルの内部に存在する固液共存相に含まれる濃化液相が排出されることを記述する構成方程式を含む運動方程式を少なくとも有する数学モデルを用いて、完全凝固時の鋳片の品質を演算により求め、この品質を所望のレベルに維持可能な連続鋳造機の、未凝固部を含む鋳片に対する圧下の条件を予め求めておき、求められた圧下の条件にしたがって連続鋳造機を操業することにより連続鋳造鋳片を製造することを特徴とする連続鋳造鋳片の製造法である。
【００１４】
この本発明にかかる連続鋳造鋳片の製造法では、運動方程式が、さらに、凝固シェルが引き抜き方向へ移動することを記述することが、例示される。この場合に、運動方程式が、固液共存相を含む凝固シェルの変形及び引き抜き方向への移動を記述し、変形に起因した固液共存相の体積変化を記述する構成方程式を少なくとも有することが、例示される。具体的には、運動方程式が固液共存相を含む凝固シェルを剛塑性体または弾塑性体として近似するとともに、構成方程式が固液共存相を多孔質体として近似することが、例示される。
【００１５】
これらの本発明にかかる連続鋳造鋳片の製造法では、所望のレベルが、連続鋳造鋳片の溶質成分分布、温度分布及び応力・歪分布のうちの少なくとも一つに基づいて、決定されることが、例示される。
【００１６】
これらの本発明にかかる連続鋳造鋳片の製造法では、数学モデルが、連続鋳造機における溶融金属の流動、凝固および溶質成分の凝固偏析を記述することが例示される。この場合に、数学モデルが、溶融金属の流動を記述するナビエ・ストークス式、熱移動を記述する凝固現象を考慮したエネルギー収支式、溶融金属と凝固シェル中の溶質成分の輸送を記述する溶質成分の物質収支式を有することが例示される。さらに、鋳片の品質が、ナビエ・ストークス式、エネルギー収支式、物質収支式および運動方程式からなる支配方程式群を連成解析することにより、求められることが例示される。
【００１７】
【発明の実施の形態】
以下、本発明にかかる連続鋳造鋳片の製造法の実施の形態を、添付図面を参照しながら詳細に説明する。
【００１８】
本実施の形態では、連続鋳造機の鋳型を出た鋳片の凝固シェルが外力を受けて変形することにより凝固シェルの内部に存在する固液共存相に含まれる濃化液相が排出されることを記述する構成方程式を含む運動方程式を少なくとも有する数学モデルを用いて、完全凝固時の鋳片の品質を演算により求め、この品質を所望のレベルに維持可能な連続鋳造機の操業条件、例えば、未凝固部を含む鋳片に対する圧下の条件を予め求めておき、求められた圧下の条件にしたがって連続鋳造機を操業することにより連続鋳造鋳片を製造する。そこで、（Ｉ）この数学モデルと、（ＩＩ）完全凝固時の鋳片の品質の演算による把握と、（ＩＩＩ）圧下の条件の事前決定および適正な操業条件にしたがった圧下とを、以下に順次説明する。
【００１９】
（Ｉ）数学モデル
本実施の形態で用いる数学モデルの内容を以下に詳細に記述する。なお、後述する（１）式〜（１１）式において用いる符合を、以下にまとめて示す。
ｃ_ｌ ^ｍ：未凝固部中ｍ成分濃度（ｃ_ｓ ^ｍ）’：凝固シェル中ｍ成分平均濃度
Ｃ_ｐｌ：未凝固部比熱Ｃ_ｐｓ：凝固シェル比熱
Ｄ_２：デンドライト２次アーム間隔Ｄ_ｌ ^ｍ：未凝固部内ｍ成分拡散係数
Ｄ_ｓ ^ｍ：凝固シェル内ｍ成分拡散係数ｆ_ｌ：未凝固部体積分率
ｆ_ｓ：凝固シェル体積分率ｇ：重力加速度
ｋ^ｍ：固液間溶質平衡分配係数ｋ_ｌｅ：未凝固部有効熱伝導度
ｋ_ｓｅ：凝固シェル有効熱伝導度ｌ_ｓ ^ｍ：ｍ成分の凝固シェル内有効拡散距離
ｍ_ｌ ^ｍ：ｍ成分の液相線降下温度係数ｐ：圧力
ｔ：時間Ｔ：温度
Ｔ_ｏ：純物質の溶融温度Ｕ_ｌ：未凝固部流速ベクトル
Ｕ_ｓ：凝固シェル流速ベクトルＹ_ｓ：凝固シェルの降伏応力
Ｒ_ｖ：体積凝固速度 μ ：粘性係数
ρ ：密度 τ ：未凝固部内粘性応力テンソル
σ ：凝固シェル内応力テンソル ΔＨ：凝固潜熱
δ_ｉｊ：クロネッカーのデルタ
【００２０】
【数１】

【００２１】
【数２】

【００２２】
【数３】

【００２３】
【数４】

【００２４】
（１）式および（２）式は、それぞれ凝固シェル（固相）および未凝固部（液相）の質量収支式であり、（３）式および（４）式は、それぞれ凝固シェルおよび未凝固部内の溶質成分の質量収支式であり、（５）式および（６）式は、それぞれ未凝固部および凝固シェルの運動量収支式であり、（７）式はエネルギー収支式であり、さらに（８）式は凝固温度に及ぼす溶質濃度の影響を示す補助方程式であり、これらの方程式群により、本実施の形態の数学モデルは完結する。以下、（１）〜（８）式の物理的意義を説明する。
【００２５】
（１）式の左辺の第一項は凝固シェルの蓄積速度を示し、同じく第二項は凝固シェルの対流による移動速度を示す。一方、右辺の第一項は凝固に伴う凝固シェルの増加速度を示す。すなわち、（１）式は全体として凝固シェルの物質収支を示すものである。
【００２６】
（２）式の左辺の第一項は未凝固部の蓄積速度を示し、同じく第二項は未凝固部の対流による移動速度を示す。一方、右辺の第一項は凝固に伴う未凝固部の減少速度を示す。すなわち、（２）式は全体として未凝固部の物質収支を示す。
【００２７】
（３）式の左辺の第一項は凝固シェル中の溶質成分ｍの蓄積速度を示し、同じく第二項は対流による凝固シェル中の溶質成分ｍの移動速度を示す。一方、右辺の第一項は凝固に伴う凝固シェル中の溶質成分ｍの増加速度を示し、第二項は凝固シェル中の溶質成分ｍの未凝固部から凝固シェルへの凝固シェル内拡散速度を示す。すなわち、（３）式は全体として凝固シェル中の溶質成分ｍの物質収支を示している。
【００２８】
（４）式の左辺の第一項は未凝固部中の溶質成分ｍに蓄積速度を示し、第二項は対流による未凝固部中の溶質成分ｍの移動速度を示す。一方、右辺の第一項は凝固に伴う未凝固部中の溶質成分ｍの減少速度を示し、第二項は未凝固部中の溶質成分ｍの未凝固部から凝固シェルへの拡散速度を示し、第三項は未凝固部中の溶質成の未凝固部内拡散速度を示す。すなわち、（４）式は全体として未凝固部中の溶質成分ｍの物質収支を示す。
【００２９】
（５）式の左辺の第一項は未凝固部の運動量の蓄積速度を示し、第二項は対流による未凝固部の運動量の移動速度を示す。一方、右辺の第一項は圧力勾配項を示し、第二項は未凝固部内の粘性による応力項を示し、第三項は重力項を示し、第四項は未凝固部と凝固シェルの相対速度差による流体抵抗の項を示す。そして、（５）式は全体として未凝固部の運動量の収支を示す。
【００３０】
（６）式の左辺の第一項は凝固シェルの運動量の蓄積速度を示し、第二項は対流による凝固シェルの運動量の移動速度を示す。一方、右辺の第一項は凝固シェル内の変形による応力項を示し、第二項は重力項を示し、第三項は未凝固部と凝固シェルの相対速度差による流体抵抗の項を示す。そして、（６）式は全体として凝固シェルの運動量の収支を示す。
【００３１】
（７）式の左辺の第一項は未凝固部および凝固シェルの熱量の蓄積速度を示し、第二項は対流による未凝固部および凝固シェルの熱量の移動速度を示す。一方、右辺の第一項は未凝固部の有効な熱拡散速度を示し、第二項は凝固シェルの有効な熱拡散速度を示し、第三項は凝固潜熱の項を示す。そして、（７）式は全体として未凝固部および凝固シェルの熱量収支を示す。
【００３２】
さらに、（８）式は補助的な式であって、純物資の融点Ｔ_０に対して溶質成分ｍが存在したときの融点の降下を近似的に示す。
ここで、（６）式を除く支配方程式、すなわち（１）〜（５）、（７）および（８）式からなる支配方程式群は、上述した従来法においても用いられているものと基本的に同じである。すなわち、（６）式を導入したことが本実施の形態の本質であるため、この（６）式について詳しく説明する。
【００３３】
上述したように、（６）式は、凝固シェルの運動量の収支を表している。そして、応力と歪速度との関係は、多孔質体の挙動を記述する公知の方法（例えばＳ．ＳｈｉｍａｄａａｎｄＭ．Ｏｙａｎｅ著「ＩＮＴ．Ｊ．ＭｅｃｈａｎｉｃａｌＳｃｉｅｎｃｅ」ｖｏｌ．１８（１９７６）ｐ２８５〜２９１参照。）により定式化すると、（９）式により示す構成方程式が得られる。
【００３４】
【数５】

【００３５】
この構成方程式からｘ、ｙ、ｚ方向の応力と歪速度との関係より、（１０）式により表される関係が導かれる。
【００３６】
【数６】

【００３７】
したがって、（１１）式に示す式
【００３８】
【数７】

【００３９】
は零とはならず、非圧縮性条件（体積一定条件）を満たさないことが分かる。つまり、静水圧（σ_ｘｘ＋σ_ｙｙ＋σ_ｚｚ）／３に応じて圧縮されることを意味しており、圧縮されると空隙が潰れて体積収縮を生じるという多孔質体の特徴が、的確に表現されている。
【００４０】
一方、固相率ｆ_ｓが１となる完全固体領域では、Ｆ＝∞となり、（１０）式を満足するにはｅ_ｋｋ＝０とならなければならない。すなわち、非圧縮性条件（体積一定条件）が満足され、通常の金属材料の特徴が、的確に表現されている。
【００４１】
したがって、（９）式により示す構成方程式を用いて（６）式の運動方程式を記述すれば、固液共存相から完全固体までの領域を統一的に表現でき、これにより、完全固体領域における凝固シェルの塑性変形から、凝固シェルの変形に起因して固液共存相から濃化液相が排出される現象までを全て記述することが可能となる。このため、この数学モデルを用いれば、濃化液相の移動が支配するマクロ偏析等の問題を、実際の現象に則して取り扱うことができるようになる。
【００４２】
上述した支配方程式群を解く手順は種々あるが、例えば以下のような時間進展に基づいた手順▲１▼〜▲６▼により解くことができる。
▲１▼各未知数に初期値を与える。
▲２▼ （１）、（２）、（５）式を解いて△ｔ秒後の未凝固部の流速ｕ_ｌを得る。
▲３▼ （６）式を解いて△ｔ秒後の凝固シェルの流速ｕ_ｓを得る。
▲４▼ （７）式および（８）式を解いて△ｔ秒後の温度Ｔを得る。
▲５▼ （３）式および（４）式を解いて△ｔ秒後の未凝固部および凝固シェル中の溶質成分ｃ_ｌ ^ｍ、（ｃ_ｓ ^ｍ）’を得る。
▲６▼上記▲２▼〜▲５▼の手順を繰り返して、未知数の時間変化を求める。
【００４３】
（ＩＩ）完全凝固時の鋳片の品質の演算による把握
本実施の形態では、このように、連続鋳造機の鋳型を出た鋳片の凝固シェルが外力を受けて変形することにより凝固シェルの内部に存在する固液共存相に含まれる濃化液相が排出されることを記述する構成方程式を含む運動方程式を少なくとも有する、上述した数学モデルを用いて、完全凝固時の鋳片の品質を演算により求める。
【００４４】
以下、鋳片条件が中心部負偏析である場合を例にとって、鋳片の品質の把握手法を説明する。
本例は、図１に示す大きさを有する連続鋳造鋳片の連続鋳造装置において、鋳造方向の中央部においてテーパ状に鋳片厚みを圧下により２０ｍｍ薄くし、鋳片中心部の濃化溶鋼を排出して中心部を負偏析とする場合である。
【００４５】
溶鋼は、図１における鋳片の左端部から一様に供給される。そのときの設定条件（引き抜き速度、溶鋼成分、溶鋼供給温度および熱伝達係数ｈ）を表１にまとめて示す。
【００４６】
【表１】

【００４７】
本例では、鋳片の表面の冷却の熱伝達係数ｈの設定を、０．３５、０．６５（ｋｃａｌ／ｍ・ｓ・ｋ）の２水準で変化させて、圧下位置における凝固シェル厚みを２０ｍｍ変更した場合に、完全凝固時の鋳片の品質（中心部における負偏析）をどの程度制御できるかを、上述した数学モデルを用いて、品質を演算により求めた。
【００４８】
本実施の形態の数学モデルを用いて行った演算結果を、図２および図３に示す。また、装置出口部（右端部）での鋳片厚み方向の凝固シェル中Ｃ濃度を図４にグラフで示す。
【００４９】
まず、図２（ａ）〜図２（ｅ）は表面における熱伝達係数ｈが０．６５（ｋｃａｌ／ｍ・ｓ・ｋ）の場合であり、図３（ａ）〜図３（ｅ）は熱伝達係数ｈが０．３５（ｋｃａｌ／ｍ・ｓ・ｋ）の場合であって、図２（ａ）〜図２（ｅ）に示す場合が図３（ａ）〜図３（ｅ）に示す場合よりも冷却速度が速く設定されている。
【００５０】
なお、上述した数学モデルを用いた今回の解析では、鋳片の各部位に一様な熱伝達係数ｈを与えているが、連続鋳造機の実際の操業では、一般的に、冷却水の噴出速度や水量を鋳片の各部位毎に変化させるため、鋳片の各部位に応じて熱伝達係数ｈの大きさを変更して設定するようにしてもよい。
【００５１】
また、図２および図３において、（ａ）図は未凝固部の溶質成分であるＣの濃度分布を示し、（ｂ）図は凝固シェルのＣの濃度分布を示し、（ｃ）図は未凝固部の速度を示し、（ｄ）図は凝固シェルの速度を示し、さらに（ｅ）図は固液間の相対速度を示す。以下、図２および図３における各図面の説明を行う。
【００５２】
上述したように、図２（ａ）および図３（ａ）は、未凝固部の溶質成分であるＣの濃度分布を示す。本例で設定した条件では、供給溶鋼の温度が液相線温度と同じ温度（１４８６℃）であるため、溶鋼が鋳型に入ると直ちに凝固が開始されるが、固相率が非常に小さな領域では、未凝固部の初期濃度である０．６質量％に略近くなっているが、固液共存相内（０＜ｆ_ｓ＜１）では、凝固に伴って固液間の溶質の分配が起り、固相率が大きくなるにしたがい濃度が上昇し、いわゆる濃化が発生する。そして、完全な固体部分（ｆ_ｓ＝１）では、未凝固部が存在しないため、濃度は０となる。
【００５３】
上述したように、図２（ｂ）および図３（ｂ）は、凝固シェル内のＣの濃度分布を示す。完全液相部分（ｆ_ｓ＝０）では凝固シェルが存在しないため、濃度は０となる。また、固液共存相内において徐々に濃度が増加し、完全な固体領域においてほぼ初期の未凝固部内のＣ濃度である０．６質量％になる。そして、固液共存相内において、凝固シェルと未凝固部との間に速度差が存在した部分では、マクロ偏析が生じ、完全な固体領域に濃度の濃淡が生じる。
【００５４】
上述したように、図２（ｃ）および図３（ｃ）は、未凝固部の速度成分を示す。ただし、完全固体内にも速度ベクトルが描かれているが、ここには未凝固部が存在しないので、本来は０とすべきであるが、未凝固部が限りなく０に近い場合、凝固シェルと同じ速度を示すため、便宜的に極値を表示してある。
【００５５】
上述したように、図２（ｄ）および図３（ｄ）は、凝固シェルの速度成分を示す。この図にも完全未凝固部領域に速度ベクトルが描かれているが、これも限りなく、凝固シェルが０に近い場合の極値を表示してある。
【００５６】
さらに、図２（ｅ）および図３（ｅ）は、固液間、すなわち凝固シェルと未凝固部との間の相対速度を示しており、未凝固部の速度から凝固シェルの速度を差し引いて示している。この図は、移動する凝固シェルから見た未凝固部の速度である。速度が表示されている部分では、凝固シェルと未凝固部とが相対速度を持って移動しており、固液共存相内で相対速度を有するときにマクロ偏析が生じる。この場合、テーパ状に圧下された凝固末期の部分において相対速度が存在し、板厚の中心部にマクロ偏析が発生している。
【００５７】
図２〜図４に示す結果から、凝固シェルは圧下部を除き、ほぼ同一流速で運動し、圧下部では固液共存相にある濃化溶鋼が上部に排出され、その結果として厚み中央部で負偏析となっている。
【００５８】
このとき、図２および図３に示すように、未凝固部内のＣ濃度は、固液共存相内で濃化する一方、凝固シェル内のＣ濃度は、固液共存相から濃度が高くなり、凝固完了とともに凍結される。また、凝固シェルと未凝固部との相対速度（液体速度から固体速度を差し引いた速度）を見れば、固体に乗って移動した場合の液体の動きを観察できるが、圧下部位において溶鋼が上部に排出される様子が見て取れる。このとき、下部から上部に排出される溶鋼は、固液共存相内で濃化しており、上部の温度の高い領域に移動すると凝固シェルを再溶解することになる。本例では、楕円状に完全な未凝固部領域が形成されている。
【００５９】
そして、本実施の形態では、操業条件として圧下の条件、すなわち圧下ロールの圧下量を変更したり、鋳片表面の熱伝達係数ｈを変更したり、あるいは圧下位置での凝固シェル厚みを変更することにより、図２および図３を対比すれば、中心部の負偏析の程度を制御可能であることが分かる。また、装置形状やその他の操業条件（例えば引き抜き速度、鋼種、溶鋼供給温度等）を変更した場合における中心部の負偏析の予測も同様に行うことができる。
【００６０】
本実施の形態では、以下このような操作を繰り返すことにより、凝固時の鋳片の品質（鋳片の溶質成分分布および鋳片温度分布）を、その際の操業条件（本実施の形態では圧下ロールの圧下量であるが、引き抜き速度、鋼種さらには溶鋼供給温度等も用いてもよい）とともに演算により把握しておく。
【００６１】
（ＩＩＩ）圧下の条件の事前決定、および適正な操業条件にしたがった圧下
そして、本実施の形態では、鋳片のこの品質を所望のレベルに維持可能な連続鋳造機の圧下の条件を、予め求めておく。そして、求められた圧下の条件にしたがって連続鋳造機を操業することにより連続鋳造鋳片を製造する。
【００６２】
すなわち、連続鋳造を行う前に予め求めた、鋳片の品質を所望のレベルに維持可能な連続鋳造機の圧下の条件に基づいて連続鋳造機を操業する。
本実施の形態によれば、上述したように、連続鋳造機の鋳型を出た鋳片の凝固シェルが圧下ロールにより圧下の際に外力を受けて変形することにより凝固シェルの内部に存在する固液共存相に含まれる濃化液相が排出されることを記述する構成方程式を含む運動方程式を少なくとも有する数学モデルを用いるため、圧下ロールによる圧下により凝固シェルが圧縮されたときにまず空隙が縮み、この縮んだ量だけ濃化溶鋼が排出されるという実際の連続鋳造における濃化溶鋼の排出状況を極めて忠実に記述できる。
【００６３】
このように、本実施の形態によれば、連続鋳造機による鋳片の凝固時の現象を記述した数学モデルを用いて溶融金属の連続鋳造の際の適正な圧下の条件を実際の操業前に解析しておき、この連続鋳造機をこの適正な圧下の条件に基づいて実際に操業することにより、中心偏析等の鋳片品質不良が極めて軽微であって性状が良好な連続鋳造鋳片を確実に製造することができる。
【００６４】
【発明の効果】
以上詳細に説明したように、本発明によれば、連続鋳造機による鋳片の凝固時の現象を記述した数学モデルを用いて溶融金属の連続鋳造の際の適正な圧下の条件を実際の操業前に解析しておき、この連続鋳造機をこの適正な圧下の条件に基づいて実際に操業することにより、中心偏析等の鋳片品質不良が極めて軽微であって性状が良好な連続鋳造鋳片を確実に製造可能な方法を提供できる。
【００６５】
連続鋳造における大きな課題である中心偏析を、迅速かつ確実な抑制または低減することができる本発明の意義は、極めて著しい。
【図面の簡単な説明】
【図１】実施の形態の連続鋳造鋳片の大きさを示す説明図である。
【図２】実施の形態の数学モデルを用いて行った演算結果を示す説明図であり、図２（ａ）〜図２（ｅ）は表面における総括熱伝達係数ｈが０．６５（ｋｃａｌ／ｍ・ｓ・ｋ）の場合を示す。
【図３】実施の形態の数学モデルを用いて行った演算結果を示す説明図であり、図３（ａ）〜図３（ｅ）は表面における総括熱伝達係数ｈが０．３５（ｋｃａｌ／ｍ・ｓ・ｋ）の場合を示す。
【図４】実施の形態の装置出口部（右端部）での鋳片厚み方向の固体中Ｃ濃度を示すグラフである。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for producing a continuous cast slab, specifically, using a mathematical model describing a phenomenon at the time of solidification of a slab by a continuous caster, the appropriateness of a rolling roll during continuous casting of molten metal. By analyzing the conditions of proper reduction before the actual operation and actually operating the continuous casting machine based on the appropriate conditions of the reduction, the quality of cast slabs such as center segregation is extremely small. The present invention relates to a method for reliably producing a continuously cast slab having good properties.
[0002]
[Prior art]
The mathematical model used when analyzing the appropriate operating conditions of the continuous casting machine is a mathematical model 1 for analyzing only the flow of the molten metal, a mathematical model 2 for analyzing the flow and heat transfer of the molten metal, and a mathematical model 2 for analyzing the flow and heat transfer of the molten metal. Neglecting the flow of heat, the mathematical model 3 that analyzes the heat transfer and the deformation of the formed solidified shell, and the flow of the molten metal, the heat transfer, the transport of the solute component in the molten metal and the solidified shell, and the movement of the solidified shell. The mathematical model 4 to be analyzed is roughly divided into four types.
[0003]
Since the mathematical models 1 and 2 place importance on the flow phenomenon of the molten metal, when designing factors that influence the flow of the molten metal inside the mold, for example, the shape of the discharge hole of an immersion nozzle or an electromagnetic stirrer. Used for In addition, the mathematical model 3 is characterized in that when a solidified shell is formed, it undergoes deformation according to the curved shape of the continuous casting machine and accumulates strain, and in some cases cracks occur inside the solidified shell. It is used when designing the curved shape of the drawing part of the continuous casting machine by evaluating the above.
[0004]
On the other hand, the mathematical model 4 can express almost all phenomena occurring when performing continuous casting using a continuous casting machine in the most precise and accurate manner. For example, it can be effectively used when analyzing the reduction amount of a reduction roll. For example, according to the mathematical model 4, center segregation, which is one of the product defects in continuous casting, can be reproduced on the model.
[0005]
Although there are slight differences in details in each of Non-Patent Documents 1 to 3, the occurrence of central segregation using a mathematical model that describes the flow of molten metal, solidification and solidification segregation behavior of solute components in a continuous casting machine A method for estimating the degree of is disclosed.
[0006]
These inventions express the movement of the solidified shell by forcibly giving the speed of the solidified shell from the outside without solving the dynamic governing equation consisting of the equation of motion of the solidified shell, that is, the deformation and movement behavior of the solidified shell Is common in that the estimation is not performed. In other words, in these inventions, the analysis of the flow, heat transfer (solidification) and segregation of the molten metal in the case of large deformation of the solidified solidified shell is performed by assuming the deformation of the solidified shell as a fixed value in advance. The degree of occurrence of center segregation was predicted.
[0007]
[Non-patent document 1]
K. Miyazawa and Schwerdtfeger, “Arch. Eisenhuttenwees” vol. 52, (1981), P416
[Non-patent document 2]
I. Ohnaka and T.S. "Proceedings of the Sixth International Iron and Steel Congress" by Shimazu, 1990, Nagoya, ISIJ.
[Non-Patent Document 3]
H. Eiserman and K.C. Schwerdtfeger, "Proceedings of The Julian Szekelly memorial Symposium on materials Processing Edited by H. Y. So." J. W. Events and D.E. Apelian, The Minerals & Materials Society (1987), p383-392.
[0008]
[Problems to be solved by the invention]
As described above, in order to rationally analyze the appropriate operating conditions of the continuous casting machine (for example, the amount of reduction of the reduction roll), it is necessary to consider the flow of molten metal, heat transfer, transport of molten metal and solute components in the solidified shell. Not only that, it is necessary to understand the movement of the solidified shell in detail.
[0009]
However, the mathematical models described in these Non-Patent Documents 1 to 3 do not estimate the deformation and movement behavior of the solidified shell, and thus cannot describe the accurate movement and deformation phenomenon of the solidified shell. That is, although the above-described mathematical model has been conventionally used as a means for estimating the movement of the solidified shell, for example, the concentrated liquid phase contained in the solid-liquid coexisting phase inside the solidified shell is discharged by deformation of the solidified shell. So far, there is no mathematical model that can describe this phenomenon.
[0010]
An object of the present invention is to use a mathematical model describing a phenomenon during solidification of a slab by a continuous casting machine to determine an appropriate operating condition (for example, a rolling-down condition of a rolling roll) at the time of continuous casting of molten metal before an actual operation. By continuously operating this continuous casting machine on the basis of this appropriate rolling condition, it is possible to produce a continuous cast slab with extremely low cast slab quality defects such as center segregation and good properties. An object is to provide a method that can be reliably manufactured.
[0011]
[Means for Solving the Problems]
The present inventor has argued that all mathematical models that have been used in the past do not incorporate equations of motion that accurately describe the motion of the solidified shell, so that actual phenomena can be accurately analyzed to the extent that center segregation can be suppressed. Thought it could not be shown.
[0012]
In order to accurately describe the motion of the solidified shell when rolling down the slab including the unsolidified part, the solidified shell containing the solid-liquid coexisting phase is approximated as a rigid plastic body, and the solid-liquid coexisting phase is made porous. By using a mathematical model that includes the equation of motion that at least describes the deformation and movement behavior of the solidified shell by approximating it as a body, the discharge behavior of the concentrated liquid phase in the solid-liquid coexisting phase when the solidified shell is deformed can be accurately determined. The present inventors have found that the above-mentioned problems can be solved by the above description, and have further studied and completed the present invention.
[0013]
The present invention provides that a solidified shell contained in a solid-liquid coexisting phase present inside a solidified shell is discharged by deforming a solidified shell of a slab that has exited a mold of a continuous casting machine under external force. Using a mathematical model having at least an equation of motion including a constitutive equation to be described, the quality of the slab at the time of complete solidification is calculated and calculated, including the unsolidified portion of a continuous casting machine capable of maintaining this quality at a desired level. This is a method for producing a continuous cast slab, characterized in that rolling conditions for a slab are determined in advance, and a continuous casting slab is manufactured by operating a continuous casting machine in accordance with the determined rolling conditions.
[0014]
In the method of manufacturing a continuous cast slab according to the present invention, it is exemplified that the equation of motion further describes that the solidified shell moves in the drawing direction. In this case, the equation of motion describes at least the constitutive equation describing the deformation of the solidified shell including the solid-liquid coexisting phase and the movement in the drawing direction, and describing the volume change of the solid-liquid coexisting phase due to the deformation. Is exemplified. Specifically, it is exemplified that the equation of motion approximates a solidified shell including a solid-liquid coexisting phase as a rigid plastic body or an elasto-plastic body, and the constitutive equation approximates a solid-liquid coexisting phase as a porous body.
[0015]
In the method for producing a continuous cast slab according to the present invention, the desired level is determined based on at least one of a solute component distribution, a temperature distribution, and a stress / strain distribution of the continuous cast slab. Is exemplified.
[0016]
In the method for producing a continuous cast slab according to the present invention, it is exemplified that the mathematical model describes the flow, solidification, and solidification segregation of a solute component in a continuous caster. In this case, the mathematical model is the Navier-Stokes equation that describes the flow of the molten metal, the energy balance equation that takes into account the solidification phenomenon that describes the heat transfer, the solute component that describes the transport of the solute component in the molten metal and the solidified shell It is exemplified to have a material balance equation of Further, it is exemplified that the quality of the slab is obtained by coupled analysis of a governing equation group including a Navier-Stokes equation, an energy balance equation, a material balance equation, and a motion equation.
[0017]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, an embodiment of a method of manufacturing a continuous cast slab according to the present invention will be described in detail with reference to the accompanying drawings.
[0018]
In the present embodiment, the concentrated liquid phase contained in the solid-liquid coexisting phase present inside the solidified shell is discharged by deforming the solidified shell of the slab that has exited the mold of the continuous casting machine under external force. Using a mathematical model having at least an equation of motion including a constitutive equation describing that, the quality of the slab during complete solidification is obtained by calculation, and the operating conditions of a continuous casting machine capable of maintaining this quality at a desired level, for example, The rolling conditions for the slab including the unsolidified portion are determined in advance, and the continuous casting slab is manufactured by operating the continuous casting machine in accordance with the determined rolling condition. Therefore, the following describes (I) this mathematical model, (II) grasp by calculation of the quality of the slab at the time of complete solidification, and (III) prior determination of the rolling conditions and rolling according to appropriate operating conditions. It will be described sequentially.
[0019]
(I) Mathematical Model The content of the mathematical model used in the present embodiment will be described in detail below. The symbols used in the expressions (1) to (11) described below are collectively shown below.
c _l ^m: unsolidified portion in m component concentration _(c ^{s m)} ': solidified shell in m components mean concentration _{C pl:} unsolidified portion specific heat C _ps: solidified shell specific heat _{D 2:} dendrite secondary arm spacing D _l ^m: unsolidified portion m component diffusion coefficient _D ^{s m:} solidified shell m component diffusion coefficient f _l: unsolidified portion volume fraction _{f s:} solidified shell volume fraction g: gravitational acceleration ^{k m:} solid-liquid between the solute equilibrium distribution coefficient k _le: unsolidified portion effective thermal conductivity _{k se:} solidified shell effective thermal conductivity l _s ^m: the solidified shell of the m components effective diffusion length _m ^l m: m components liquidus temperature lowering coefficient p: pressure t: time T: temperature _{T o:} the melting temperature of the pure substance U _l: unsolidified portion velocity vector _{U s:} solidified shell velocity vector Y _s: yield stress of the solidified shell _{R v:} volume solidification rate mu: viscosity coefficient [rho: density tau: Viscous stress tensor σ in the unsolidified part: Solid shell within the stress tensor ΔH: latent heat of solidification δ _ij: Kronecker delta [0020]
(Equation 1)

[0021]
(Equation 2)

[0022]
[Equation 3]

[0023]
(Equation 4)

[0024]
Equations (1) and (2) are the mass balance equations for the solidified shell (solid phase) and unsolidified portion (liquid phase), respectively, and Equations (3) and (4) are the solidified shell and unsolidified respectively. Equations (5) and (6) are the momentum balance equations of the unsolidified part and the solidified shell, respectively, and Equation (7) is the energy balance equation of the solute component in the part. The equations are auxiliary equations showing the effect of the solute concentration on the solidification temperature, and these equations complete the mathematical model of the present embodiment. Hereinafter, the physical significance of the expressions (1) to (8) will be described.
[0025]
The first term on the left side of the equation (1) indicates the accumulation speed of the solidified shell, and the second term indicates the moving speed of the solidified shell by convection. On the other hand, the first term on the right side shows the rate of increase of the solidified shell due to solidification. That is, equation (1) indicates the material balance of the solidified shell as a whole.
[0026]
The first term on the left side of the equation (2) indicates the accumulation speed of the unsolidified portion, and the second term indicates the moving speed of the unsolidified portion by convection. On the other hand, the first term on the right-hand side shows the rate of reduction of the unsolidified portion due to solidification. That is, equation (2) shows the mass balance of the unsolidified portion as a whole.
[0027]
The first term on the left side of the equation (3) indicates the accumulation speed of the solute component m in the solidified shell, and the second term indicates the moving speed of the solute component m in the solidified shell by convection. On the other hand, the first term on the right side indicates the rate of increase of the solute component m in the solidified shell due to solidification, and the second term indicates the rate of diffusion of the solute component m in the solidified shell from the unsolidified portion to the solidified shell. Show. That is, equation (3) shows the mass balance of the solute component m in the solidified shell as a whole.
[0028]
The first term on the left side of the equation (4) indicates the accumulation speed of the solute component m in the unsolidified portion, and the second term indicates the moving speed of the solute component m in the unsolidified portion by convection. On the other hand, the first term on the right side shows the rate of decrease of the solute component m in the unsolidified part due to solidification, and the second term shows the diffusion rate of the solute component m in the unsolidified part from the unsolidified part to the solidified shell. The third term indicates the rate of diffusion of solute formation in the unsolidified portion. That is, Equation (4) shows the mass balance of the solute component m in the unsolidified portion as a whole.
[0029]
The first term on the left side of the equation (5) indicates the accumulation speed of the momentum of the uncoagulated portion, and the second term indicates the moving speed of the momentum of the uncoagulated portion due to convection. On the other hand, the first term on the right side indicates a pressure gradient term, the second term indicates a stress term due to viscosity in the unsolidified part, the third term indicates a gravity term, and the fourth term indicates the relative distance between the unsolidified part and the solidified shell. The term of the fluid resistance due to the speed difference is shown. Equation (5) shows the balance of the momentum of the unsolidified portion as a whole.
[0030]
The first term on the left side of the equation (6) indicates the accumulation speed of the momentum of the solidified shell, and the second term indicates the moving speed of the momentum of the solidified shell due to convection. On the other hand, the first term on the right side indicates a stress term due to deformation in the solidified shell, the second term indicates a gravitational term, and the third term indicates a term of fluid resistance due to a relative speed difference between the unsolidified portion and the solidified shell. Equation (6) shows the balance of the momentum of the solidified shell as a whole.
[0031]
The first term on the left side of the equation (7) indicates the rate of accumulation of heat in the unsolidified portion and the solidified shell, and the second term indicates the speed of movement of heat in the unsolidified portion and the solidified shell due to convection. On the other hand, the first term on the right side shows the effective heat diffusion rate of the unsolidified portion, the second term shows the effective heat diffusion rate of the solidified shell, and the third term shows the latent heat of solidification. Equation (7) shows the heat balance of the unsolidified portion and the solidified shell as a whole.
[0032]
Further, (8) is a supplementary wherein approximately a melting point of descent when solute components m were present for the melting point T ₀ of the pure materials.
Here, the governing equations except the equation (6), that is, the governing equations consisting of the equations (1) to (5), (7) and (8) are basically the same as those used in the conventional method described above. Is the same as That is, since the introduction of the expression (6) is the essence of the present embodiment, the expression (6) will be described in detail.
[0033]
As described above, equation (6) represents the balance of the momentum of the solidified shell. The relationship between the stress and the strain rate can be determined by a known method for describing the behavior of the porous body (for example, see S. Shimada and M. Oyane, “INT. J. Mechanical Science” vol. 18 (1976) p. 285-291). ), The constitutive equation shown by equation (9) is obtained.
[0034]
(Equation 5)

[0035]
From this constitutive equation, the relationship expressed by the expression (10) is derived from the relationship between the stress in the x, y, and z directions and the strain rate.
[0036]
(Equation 6)

[0037]
Therefore, the equation shown in equation (11)
(Equation 7)

[0039]
Does not become zero and does not satisfy the incompressibility condition (constant volume condition). In other words, it means that the porous body is compressed according to the hydrostatic pressure ( _σxx + _σyy + _σzz ) / 3, and the feature of the porous body that the void is collapsed and the volume shrinks when compressed is accurately expressed. Have been.
[0040]
On the other hand, in the full solid area fraction solid f _s is 1, F = ∞, and the must become _{e kk} = 0 to satisfy the expression (10). That is, the incompressibility condition (constant volume condition) is satisfied, and the characteristics of ordinary metal materials are accurately expressed.
[0041]
Therefore, by describing the equation of motion of equation (6) using the constitutive equation expressed by equation (9), the region from the solid-liquid coexisting phase to the complete solid can be expressed in a unified manner. It is possible to describe everything from plastic deformation of the shell to the phenomenon that the concentrated liquid phase is discharged from the solid-liquid coexisting phase due to the deformation of the solidified shell. Therefore, if this mathematical model is used, problems such as macro-segregation dominated by the movement of the concentrated liquid phase can be handled according to actual phenomena.
[0042]
There are various procedures for solving the above-mentioned governing equations. For example, they can be solved by the following procedures (1) to (6) based on time evolution.
(1) Give an initial value to each unknown.
▲ 2 ▼ (1), ( 2), to obtain the flow velocity _{u l} unsolidified portion after (5) by solving the equation △ t seconds.
▲ 3 ▼ obtain the flow velocity u _s of the solidified shell after (6) by solving the equation △ t seconds.
(4) By solving the equations (7) and (8), the temperature T after Δt seconds is obtained.
▲ 5 ▼ (3) and Equation (4) solute c _l ^m in non-solidified portion and the solidified shell after solved △ t seconds equation to obtain _(c ^{s m)} '.
(6) Repeat the above steps (2) to (5) to determine the time change of the unknown.
[0043]
(II) Grasping by Computation of Slab Quality at Complete Solidification In this embodiment, the solidification shell of the slab that has exited the mold of the continuous casting machine is deformed by an external force as described above. Using the mathematical model described above, which has at least an equation of motion including a constitutive equation describing that the concentrated liquid phase contained in the solid-liquid coexisting phase present inside is discharged, the quality of the slab during complete solidification is determined. Obtained by calculation.
[0044]
Hereinafter, a method of ascertaining the quality of a slab will be described, taking as an example the case where the slab condition is negative central segregation.
This example is a continuous casting apparatus for continuous casting slab having the size shown in FIG. 1, in which the thickness of the slab is reduced by 20 mm in a tapered shape at the center in the casting direction by rolling, and the concentrated molten steel at the center of the slab is removed. This is the case where the center is negatively segregated by discharging.
[0045]
The molten steel is supplied uniformly from the left end of the slab in FIG. Table 1 summarizes the setting conditions (drawing speed, molten steel component, molten steel supply temperature, and heat transfer coefficient h) at that time.
[0046]
[Table 1]

[0047]
In this example, the setting of the heat transfer coefficient h for cooling the surface of the slab is changed at two levels of 0.35 and 0.65 (kcal / m · s · k) to reduce the thickness of the solidified shell at the rolling-down position. The quality of the cast slab at the time of complete solidification (negative segregation at the center) can be controlled by using the above-described mathematical model when the length is changed by 20 mm.
[0048]
FIGS. 2 and 3 show the results of calculations performed using the mathematical model of the present embodiment. In addition, FIG. 4 is a graph showing the C concentration in the solidified shell in the thickness direction of the slab at the outlet (right end) of the apparatus.
[0049]
First, FIGS. 2A to 2E show the case where the heat transfer coefficient h on the surface is 0.65 (kcal / m · s · k), and FIGS. 3A to 3E show When the heat transfer coefficient h is 0.35 (kcal / m · s · k), the cases shown in FIGS. 2 (a) to 2 (e) are shown in FIGS. 3 (a) to 3 (e). The cooling rate is set faster than the case shown.
[0050]
In this analysis using the above-described mathematical model, a uniform heat transfer coefficient h is given to each part of the cast slab. However, in actual operation of a continuous casting machine, generally, the injection of cooling water is performed. In order to change the speed and the amount of water for each part of the slab, the magnitude of the heat transfer coefficient h may be changed and set according to each part of the slab.
[0051]
2 and 3, (a) shows the concentration distribution of C which is a solute component in the unsolidified portion, (b) shows the concentration distribution of C in the solidified shell, and (c) shows the undistributed concentration. (D) shows the speed of the solidified shell, and (e) shows the relative speed between solid and liquid. Hereinafter, each drawing in FIGS. 2 and 3 will be described.
[0052]
As described above, FIGS. 2A and 3A show the concentration distribution of C, which is a solute component in the unsolidified portion. Under the conditions set in this example, the temperature of the supplied molten steel is the same as the liquidus temperature (1486 ° C), so solidification starts immediately after the molten steel enters the mold, but in the region where the solid fraction is very small. So although substantially closer to 0.6 wt% which is the initial concentration of the unsolidified portion, the solid-liquid coexisting phase in the _{(0 <f s <1)} , the distribution of the solute between the solid with the coagulating liquid As the solid fraction increases, the concentration increases and so-called thickening occurs. Then, the complete solid part (f s _{= 1),} since the unsolidified portion is not present, the concentration is zero.
[0053]
As described above, FIGS. 2 (b) and 3 (b) show the concentration distribution of C in the solidified shell. Since the complete liquid phase portion (f s _{= 0)} in the not solidified shell is present, the concentration is zero. Further, the concentration gradually increases in the solid-liquid coexisting phase, and reaches 0.6% by mass, which is the C concentration in the unsolidified portion almost at the initial stage in the complete solid region. Then, in the solid-liquid coexisting phase, macrosegregation occurs in a portion where the velocity difference exists between the solidified shell and the unsolidified portion, and the density varies in a complete solid region.
[0054]
As described above, FIGS. 2C and 3C show the velocity component of the unsolidified portion. However, although the velocity vector is also drawn in the complete solid, there is no unsolidified part here, so it should be set to 0 originally. In order to show the same speed as above, the extremum is displayed for convenience.
[0055]
As mentioned above, FIGS. 2 (d) and 3 (d) show the velocity component of the solidified shell. In this figure as well, a velocity vector is drawn in the completely unsolidified portion region, but this is not limited and the extreme value when the solidified shell is close to 0 is displayed.
[0056]
Further, FIGS. 2 (e) and 3 (e) show the relative velocity between the solid and liquid, that is, between the solidified shell and the unsolidified portion, and the speed of the solidified shell is subtracted from the speed of the unsolidified portion. Is shown. This figure shows the velocity of the unsolidified portion as viewed from the moving solidified shell. In the portion where the speed is indicated, the solidified shell and the unsolidified portion move with a relative speed, and macro segregation occurs when the solidified shell has a relative speed in the solid-liquid coexisting phase. In this case, there is a relative velocity in a portion at the end of solidification which is reduced in a tapered shape, and macro segregation occurs in a central portion of the plate thickness.
[0057]
From the results shown in FIG. 2 to FIG. 4, the solidified shell moves at almost the same flow rate except for the consolidation, and in the consolidation, the concentrated molten steel in the solid-liquid coexisting phase is discharged to the upper part. It has negative segregation.
[0058]
At this time, as shown in FIG. 2 and FIG. 3, the C concentration in the unsolidified portion increases in the solid-liquid coexisting phase, while the C concentration in the solidified shell increases from the solid-liquid coexisting phase. Freezes upon completion of coagulation. In addition, by observing the relative speed between the solidified shell and the unsolidified portion (the speed obtained by subtracting the solid speed from the liquid speed), the movement of the liquid when it moves on the solid can be observed. You can see how they are discharged. At this time, the molten steel discharged from the lower part to the upper part is concentrated in the solid-liquid coexisting phase, and when it moves to the upper part where the temperature is high, the solidified shell is re-dissolved. In this example, a complete unsolidified region is formed in an elliptical shape.
[0059]
In the present embodiment, the operating condition is a rolling condition, that is, a rolling amount of a rolling roll is changed, a heat transfer coefficient h of a slab surface is changed, or a solidified shell thickness at a rolling position is changed. Thus, comparing FIGS. 2 and 3, it can be seen that the degree of negative segregation at the center can be controlled. In addition, prediction of negative segregation at the center when the apparatus shape and other operating conditions (for example, drawing speed, steel type, molten steel supply temperature, and the like) are changed can be similarly performed.
[0060]
In the present embodiment, the quality of the slab at the time of solidification (solute component distribution and slab temperature distribution) at the time of solidification is reduced by repeating the above-described operations to reduce the operating conditions (in this embodiment, the rolling reduction). The amount of reduction of the roll is used, but the drawing speed, the steel type, and the molten steel supply temperature may also be used.
[0061]
(III) Predetermination of rolling conditions and rolling in accordance with appropriate operating conditions In the present embodiment, the rolling conditions of the continuous casting machine capable of maintaining this quality of the slab at a desired level are determined in advance. Ask for it. Then, a continuous cast slab is manufactured by operating a continuous caster in accordance with the determined rolling conditions.
[0062]
That is, the continuous casting machine is operated on the basis of the condition of the reduction of the continuous casting machine that can maintain the quality of the slab at a desired level, which is obtained in advance before performing the continuous casting.
According to the present embodiment, as described above, the solidified shell of the slab that has exited the mold of the continuous casting machine is deformed by receiving an external force during rolling down by the rolling rolls, and the solidified shell existing inside the solidified shell is deformed. To use a mathematical model that has at least the equation of motion including the constitutive equation describing that the concentrated liquid phase contained in the liquid coexisting phase is discharged, the gap first shrinks when the solidified shell is compressed by the reduction by the reduction roll. Thus, the discharge state of the concentrated molten steel in the actual continuous casting in which the concentrated molten steel is discharged by the reduced amount can be described very faithfully.
[0063]
Thus, according to the present embodiment, the appropriate rolling conditions during continuous casting of molten metal using a mathematical model describing the phenomenon during solidification of a slab by a continuous casting machine before the actual operation. Analyze and run this continuous casting machine under the conditions of the appropriate rolling reduction to ensure continuous casting slabs with very small cast slab quality defects such as center segregation and good properties. Can be manufactured.
[0064]
【The invention's effect】
As described in detail above, according to the present invention, an appropriate rolling condition during continuous casting of molten metal is determined by using a mathematical model that describes a phenomenon during solidification of a slab by a continuous casting machine. Analyzing beforehand, this continuous casting machine is actually operated based on the conditions of this appropriate reduction, so that the quality of the cast slab such as center segregation is extremely slight and the properties of the continuous cast slab are good. Can be provided reliably.
[0065]
The significance of the present invention, which can quickly and surely suppress or reduce center segregation, which is a major problem in continuous casting, is extremely significant.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram showing the size of a continuous cast slab according to an embodiment.
FIGS. 2A to 2E are explanatory diagrams showing calculation results performed using the mathematical model according to the embodiment. FIG. 2A to FIG. 2E show that the overall heat transfer coefficient h on the surface is 0.65 (kcal / m · s · k).
3 (a) to 3 (e) are explanatory diagrams showing calculation results performed using the mathematical model according to the embodiment. FIG. 3 (a) to FIG. m · s · k).
FIG. 4 is a graph showing the C concentration in the solid in the thickness direction of the slab at the outlet (right end) of the apparatus according to the embodiment.

Claims

A structure that describes that a solidified shell of a slab that has exited a mold of a continuous casting machine is deformed by an external force, thereby discharging a concentrated liquid phase contained in a solid-liquid coexisting phase existing inside the solidified shell. Using a mathematical model having at least an equation of motion including an equation, the quality of the slab at the time of complete solidification is obtained by calculation,
The quality of the continuous casting machine capable of maintaining the quality at a desired level, the conditions for the reduction of the slab including the unsolidified portion is determined in advance,
A continuous cast slab is produced by operating the continuous caster according to the determined rolling conditions.

The method of claim 1, wherein the equation of motion further describes that the solidified shell moves in a drawing direction.

The equation of motion describes at least the deformation of the solidified shell including the solid-liquid coexisting phase and the movement in the withdrawal direction, and has at least a constitutive equation describing the volume change of the solid-liquid coexisting phase due to the deformation. A method for producing a continuous cast slab according to claim 2.

4. The method according to claim 3, wherein the equation of motion approximates the solidified shell including the solid-liquid coexisting phase as a rigid plastic body or an elasto-plastic body, and the constitutive equation approximates the solid-liquid coexisting phase as a porous body. A method for producing continuous cast slabs.

The method according to claim 1, wherein the desired level is determined based on at least one of a solute component distribution, a temperature distribution, and a stress / strain distribution of the continuous cast slab. The described method for producing a continuous cast slab.