JP4352779B2 - Thick steel plate rolling method - Google Patents

Description

【００３０】
上記のように、ＬmaxとＷcrop（既知）および対称の５条件から、上記４次式の５個の係数Ｄ1〜Ｄ5を決定することができる。例えば、Ｌmaxとなる座標（ｘＬ，Ｌmax）と突出する部分のもう１点（変曲点）の座標（ｘａ，ｙａ）とを実験に基づいて予測する簡易式を作成し、その簡易式を用いて係数Ｄ1〜Ｄ5を決定する。この４次式（５）が板厚分布付与後の１パスでの予測平面形状Ｐrdaを与えるものとなる。つまり、本発明では平面形状のプロフィールをＷcropおよびＬmaxの２つの代表値で表現することとしている。
【００３１】
図８の（ａ）は最終平面形状が矩形となる理想的圧延状態を示す平面模式図、図８の（ｂ）は通常圧延で矩形から不足する部分に基づく幅出し完了後の目標形状の設定方法を説明する図である。
【００３２】
さらに高精度に幅出し完了後の形状ΔＰrcを求める場合は、幅端部の幅方向メタルフローも考慮に入れて、上記の一次近似で得られた幅出し完了時の平面形状から求められたΔＰr₁、ΔＰrc₁を用いて、従来の通常圧延における厚肉部の無い場合の平面形状予測式で最終平面形状を求め、不足する（または過剰となる）ΔＰr₂を再度求める。
【００３３】
上記と同様の方法で幅出し完了時に換算した形状（ΔＰrc₂）を求める。つまり、より精度の良いΔＰrc＝ΔＰrc₁＋ΔＰrc₂とすればよい。なお、符号Ｙ_f(x)は最終圧延後の不足分を表わし、符号Ｙ_w(x)は断面に厚肉部を有するときの１パス圧延後の不足分を表わす。上記の方法を繰り返すことにより精度が向上する。
【００３４】
図９は、次材以降へのフィードバックを説明する図である。図中にて実線で示す特性線Ｐは実測値を、破線で示す特性線Ｑは予測値をそれぞれ表わす。予測値と実測値との平面形状プロフィールを比較し、ＬmaxおよびＷcropそれぞれのずれ割合を算出した。前提条件として、予測値が次材でも同じようなずれを生じると仮定し、また、ベースとなる厚肉部を付与しない場合の従来の平面形状予測式の精度は良好であると仮定した。
【００３５】
ＲＬ＝δＬmax／Ｌmax
ＲＷ＝δＷcrop／Ｗcrop
そのずれ割合の何％（係数：ＣoeＲ，ＣoeＷ）かを次材の予測値に付加する。
【００３６】
次材の修正Ｌmax＝ＲＬ×ＣoeＲ×Ｌmax（次材の予測値）
次材の修正Ｗcrop＝ＲＬ×ＣoeＷ×Ｗcrop（次材の予測値）
これらの修正により図５のフローチャートから求まる厚肉部形状が変更される。
【００３７】
なお、上記の予測式（１）〜（４）の精度向上を目的として、多数の実測値（計測値）とそれぞれの圧延条件に基づき式中の係数Ｃ11〜Ｃ23を重回帰法のような統計的手法を用いて学習する。
【００３８】
図１０は、水平圧延による平面形状変化を説明するモデル図である。
【００３９】
（i）１パス水平圧延による平面形状変化モデルの例
矩形鋼板を水平圧延した場合の平面形状変化モデルを図１０に示す。幅異形量とクロップ長はそれぞれ式（６）と式（７）から得られる。板幅変動と先後端クロップ長は式（８）と式（９）で近似できる。但し、式中の記号はそれぞれ、Ｒ：ワークロール半径、Δｈ：水平圧延圧下量、Ｈｉ：入側板厚、Ｗｏ：板幅の中央値である。
【００４０】
【数２】

【００４１】
（ii）多パス圧延による平面形状変化モデルの例
多パス圧延後の形状は、各パスの積算値として取り扱われる。式（１０）と式（１１）に多パス圧延時の板幅変動と先後端クロップ形状を示す。但し、式中の記号はそれぞれ、ｙｗ(n)，ｙｗ(n-1)：ｎパス目，ｎ−１パス目の出側板幅変動、ｙｗ：ｎパス目で生じる板幅変動、ｙＬ(n)，ｙＬ(n-1)：ｎパス目，ｎ−１パス目の出側クロップ形状、ｙＬ：ｎパス目で生じるクロップ形状変化、α：伸び率補正係数、ｈ(n)，ｈ(n-1)：ｎパス目，ｎ−１パス目の出側板厚である。
【００４２】
【数３】

【００４３】
（iii）平面形状予測精度の検証
幅方向に厚肉部を付与した場合のエッジングによる平面形状変化モデルと水平圧延による平面形状変化モデルを重ね合わせて、矩形スラブから仕上圧延終了後の平面形状まで予測する一貫シミュレータを構成した。圧延終了後の平面形状予測精度は、例えば、板内幅偏差で±１０ｍｍ、クロップ長で±１００ｍｍであり、平面形状制御に適用するのに十分な予測精度が得られた。クロップ長の予測精度が板内幅偏差に比べて劣るのは、予測誤差が長手方向に延ばされて拡大されていくからである。
【００４４】
本発明は、圧延中に付与した板厚分布が、その後の水平圧延によりどのように変形するのかを検討する中でなされた。材料の変形を検討するにあたり、本発明者らは純鉛を用いたモデル圧延実験を行った。
【００４５】
図１１は横軸に板幅エッジからの距離（ｍｍ）をとり、縦軸に後端クロップのタング長さ（ｍｍ）をとって、板幅方向における後端クロップのタング長さ分布を示す特性線図である。図中にて特性線Ａはマスフロー一定則に基づいて計算した理論値曲線を示し、特性線Ｂは実際に試料を用いて測定した実験値曲線を示す。板厚１２mm×幅１８０mm×長さ３００mmサイズの素材に対してＬ＝４０ｍｍ、ΔＨ＝１．０ｍｍのような板厚分布を付与した。この板厚分布付与材料を板厚１０．５mmまで圧延したときの後端部クロップ形状について理論値と実験値をそれぞれ調べた。
【００４６】
図１１から明らかなように、いわゆるフィッシュテール形状となっており、伸びの最大値（Ｌmax）はほぼ幅端部で生じている。ここで、特許文献３に記載されたマスフロー一定則に基づいて予測した形状を図中に示すが、幅端部についてはマスフロー一定則での予測値よりも伸びは小さいことが判明した。これは幅端部では幅広がりの影響が大きいためである。また、伸びが大きい領域の幅（Ｗcrop）はＬ（＝４０ｍｍ）よりも大きいことが判明した。
【００４７】
以上の実験結果より、このような板厚分布を有した材料を圧延した場合に発生する平面形状変化を予測するためには）代表寸法として、少なくとも図２の（ａ）に示す最大伸び長さＬmaxと厚肉部の影響により伸びが大きくなっている領域の幅Ｗcropを用いる必要がある。例えば、４次曲線等を利用して形状を近似することにより、フィッシュテール形状を予測することが可能である。
【００４８】
さらに、部分的に厚肉部を付与した後の圧延パス後において、圧延材の平面形状Ｐrdrを測定し、この平面形状Ｐrdrの測定値と上記予測平面形状Ｐrdaの値との差分を、次材以降の圧延にフィードバックするようにしてもよい。
【００４９】
【発明の実施の形態】
以下、添付の図面を参照しながら本発明の好ましい実施の形態について説明する。
図５のフローチャートを用いて本発明の実施形態を説明する。
先ず通常圧延でのクロップ形状Ｐruを図中に実線で示すように予測する（工程Ｓ１）。このクロップ形状Ｐruの予測には、例えば特許文献３に記載された所定の実験式を用いてもよいし、数値解析法（Finite Element Method；ＦＥＭ）を用いるようにしてもよい。
【００５０】
次いで、通常圧延クロップ予測形状Ｐruを目標とする矩形の平面形状Ｐro（図中の破線）と比較し、前者が後者から外れる部分の形状ΔＰrを算出する（工程Ｓ２）。
【００５１】
算出した矩形から外れる部分の形状ΔＰrを幅出し圧延完了したときに予測される形状に換算する（工程Ｓ３）。この換算工程Ｓ３では、幅出し圧延完了パスで板厚分布を付与する場合を考えると、図１の（ａ）に示すパターンＡの形状を仕上圧延圧下比（＝幅出し完了板厚／製品板厚）で割り戻し、パターンＡの形状を幅出し圧延完了時点での図１の（ｂ）に示すパターンＢに近似する形状Ａ´に換算する。この一次近似形状Ａ´は、厚肉部を付与しない場合に不足する部分の形状を圧下比分だけ圧延方向に縮小した形状を算出し、この算出形状を通常圧延における幅出し圧延完了時の平面形状にプラスした平面形状が、最終の仕上圧延で平面形状が矩形となる平面形状Ｐro（幅出し圧延完了時の形状）となる。
【００５２】
なお、本実施例では一次近似形状Ａ´を用いるようにしているが、さらに精度良く目標平面形状を求める手法としてＦＥＭを採用してもよい。すなわち、ＦＥＭを用いて線形計画法に準じた演算を何回も繰り返すことにより、最終的に目標平面形状を求めることができる。また、ＦＥＭから加工の最終段階までを逆に溯って帰納的に演算して形状を求めるようにしてもよい。
【００５３】
換算した一次近似の予測形状Ａ´に基いて幅出し圧延完了時の厚肉部を付与しない場合の平面形状Ｐruaを求める（工程Ｓ４）。
【００５４】
この幅出し圧延完了時の厚肉部を付与しない場合の平面形状Ｐruaに基いて初期の板厚分布を仮定する（工程Ｓ５）。この仮定した板厚分布を厚鋼板端部に板厚分布を付与するときに用いる。
【００５５】
板厚分布付与後に、１パスでの予測平面形状Ｐrdaを算出する（工程Ｓ６）。板厚分布付与後の１パスでは、ほとんど厚肉部のみを圧下して平らにするように圧延する。このとき、板厚が厚い部分は圧延方向に伸びようとするが、ほとんど圧下されない部分は伸ばされずに伸びようとする厚肉部を拘束し、かつ幅端部に近いメタルは幅方向にも流れ、その結果、（ｉ）厚肉部の圧延方向に突出する長さ（クロップ長さ）は短くなり、（ii）伸びようとする厚肉部に圧下されない部分が引っ張られて、突出する幅Ｗcropは厚肉部を付与した幅Ｌより大きくなる。すなわち図６の（ａ）に示すように、素材断面において厚肉部の占める部分（断面積Ｓ２）とそれ以外の部分（断面積Ｓ１）との割合、例えばＳ１／（Ｓ１＋Ｓ２）、Ｓ２／（Ｓ１＋Ｓ２）、および厚肉部の圧下率ε２（圧下歪み：伸びようとする大きさ）とそれ以外の圧下率ε１とが、ＷcropとＬmaxを予測する主要なパラメータであり、これらを用いて予測式として上記の２つの式（１）と式（２）を作成した。なお、断面積Ｓ１，Ｓ２は上記の式（３）と式（４）に示すようにΔＨとＷ／Ｌを用いて表わすことができる。
【００５６】
図７に示すように、平面形状のプロフィールを４次式（５）で近似すると、ＷcropとＬmaxから平面形状のプロフィールを決定することができる。この４次式（５）が板厚分布付与後の１パスでの予測平面形状Ｐrdaを与えるものとなる。
【００５７】
１パスでの予測平面形状Ｐrdaから厚肉部を付与しない場合の平面形状Ｐruaを差し引き、その差分を差形状ΔＰrdとする（工程Ｓ７）。
【００５８】
形状ΔＰrcの面積Ａ１から差形状ΔＰrdの面積Ａ２を差し引き、その差分を面積差ΔＡd（＝Ａ１−Ａ２）とする（工程Ｓ８）。
【００５９】
求めた面積差ΔＡdを所定の許容面積差Ａｓと比較し、その大小を判定する（工程Ｓ９）。面積差ΔＡdが許容面積差Ａｓより小さいか又は等しい場合は合格判定とし、演算を終了する。なお、所定の許容面積差Ａｓは、ゼロではないが限りなくゼロに近い値であり、板厚と板幅との組合せごとに予め実験により求めておいたものである。
【００６０】
面積差ΔＡdが許容面積差Ａｓより大きい場合は、不合格と判定し、先の初期板厚分布を修正し（工程Ｓ１０）、工程Ｓ５に戻る。工程Ｓ５では修正板厚分布を実圧延の板厚分布と仮定する。そして、この修正板厚分布を用いて上記工程Ｓ６〜Ｓ８の手順に従って面積差ΔＡdを求め、求めた面積差ΔＡdと許容面積差Ａｓとの大小を繰り返し比較判定する（工程Ｓ９）。具体的には、厚肉部形状（長さＬ、高さΔＨ）の初期値に対してこれを圧延したときの形状Ｂを予測し、形状Ｂが一次近似形状Ａ´に近づくように、厚肉部形状の修正を繰り返す。この処理により、クロップロスが最小となるような、長さＬ、高さΔＨの最適値が算出可能である。なお、本発明では、厚肉部形状の修正量および修正方法については特に問わない。
【００６１】
なお、部分的に厚肉部を付与した後の圧延パス後に、圧延材の平面形状（Ｐrdr）を測定し、この測定値と予測した平面形状（Ｐrda）との差を、次材以降の圧延にフィードバックするようにしてもよい。
【００６２】
【実施例】
次に、本発明方法を適用した実施例について説明する。
【００６３】
本発明方法に従って平面形状を制御した厚板サンプルを実施例とし、上記特許文献３の方法に従って平面形状を制御した厚板サンプルを比較例として、両者に生じるクロップロスの比較を行った。
【００６４】
厚板サンプルとして初期サイズが板厚２５１mm×幅１３２０mm×長さ２０９５mmのスラブを採用し、このスラブから板厚９．８mm×幅２３９４mm×長さ２９５００mmの圧延製品を得ることを想定した。厚板に付与する板厚分布は図２（ｂ）に示す断面形状とした。
【００６５】
表１に調整圧延、幅出圧延、仕上圧延のパススケジュールをそれぞれ示す。調整圧延は３パス、幅出圧延は４パス、仕上圧延は９パスとした。調整圧延の３パス目では厚板を９０°回転させてクロスロールを行った。幅出圧延の４パス目では、１〜３パスで厚板に板厚分布を付与した後に、これを９０°回転させてクロスロールを行った。
【００６６】
通常圧延時のクロップ長Ｌｃは４３０mm、肩落ち幅Ｗは４００mmであるため、比較例では長さＬｃ＝Ｗ＝４００mm、高さΔＨ＝７．０mmであった。これに対して、本発明方法を適用した実施例では、長さＬｃ＝３５０mm、高さΔＨ＝１６．２mmであった。
【００６７】
【表１】

【００６８】
図１２に通常圧延時のクロップロスＣＲ１に対する、従来法（特許文献３の方法を用いた比較例）と本発明方法（上記の実施例）をそれぞれ適用した場合のクロップロスＣＲ２の比（ＣＲ２／ＣＲ１）を示す。この図から明らかなように、従来法を適用した場合にはクロップロスが約３５％低減するが、本発明方法を適用すればクロップロスを約６５％も削減することができた。
【００６９】
【発明の効果】
本発明は、材料の幅方向に薄肉部と厚肉部を有する板厚分布を付与することにより、平面形状を制御して圧延する厚鋼板の圧延方法において、付与する板厚分布を決定するにあたり、板厚分布を付与した後の圧延における平面形状変化を予測することにより、最終平面形状を矩形に近づけるために必要な厚肉部の断面形状を高精度に算出することができる。このため、クロップロスが従来に比べて大幅に低減され、製品歩留りを飛躍的に向上させることができる。
【図面の簡単な説明】
【図１】（ａ）は通常圧延時における厚鋼板の後端部（パターンＡ）を示す断面模式図、（ｂ）は通常圧延時における他の厚鋼板の後端部（パターンＢ）を示す断面模式図。
【図２】（ａ）は厚鋼板の後端部を示す平面模式図、（ｂ）は厚鋼板の後端部を示す断面模式図。
【図３】厚鋼板の後端部を示す断面模式図。
【図４】通常圧延されたクロップ形状を示す平面模式図。
【図５】（ａ）は本発明の厚鋼板の圧延方法を示すフローチャート、（ｂ）は各工程に対応する厚鋼板の断面をそれぞれ示す模式図。
【図６】（ａ）は平坦部の拘束が無いと仮定した場合に厚肉部がすべて圧延方向に伸びた状態を示す平面模式図、（ｂ）は平坦部の拘束が有ると仮定した場合に厚肉部を１パス圧延後の実際の状態を示す平面模式図。
【図７】ＷcropとＬmaxから後端部の平面形状プロフィールの計算予測方法を説明する図。
【図８】（ａ）は最終平面形状が矩形となる理想的圧延状態を示す平面模式図、（ｂ）は通常圧延で矩形から不足する部分に基づく幅出し完了後の目標形状の設定方法を説明する図。
【図９】次材以降へのフィードバックを説明する図。
【図１０】水平圧延による平面形状変化を説明するモデル図。
【図１１】板幅方向における後端クロップのタング長さ分布を示す特性線図。
【図１２】クロップロスについて本発明方法と従来法とを比較して示すグラフ図。
【符号の説明】
２…厚鋼板、
３…クロップ、
Ｐru…通常圧延でのクロップ形状（予測平面形状）、
Ｐro…目標とする矩形の平面形状、
ΔＰr…矩形から外れる部分の形状、
ΔＰrc…１パス後の予測換算形状、
Ｐrua…厚肉部を付与しない場合の１パス後の予測平面形状、
Ｐrda…板厚分布付与後の１パスでの予測平面形状、
ΔＰrd…差形状（＝Ｐrda−Ｐrua）、
Ａ１…予測換算形状ΔＰrcの面積、
Ａ２…差形状ΔＰrdの面積、
ΔＡｄ…面積差（＝Ａ１−Ａ２）。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method of rolling a thick steel plate that is rolled while controlling a planar shape by providing a plate thickness distribution in the width direction of the thick steel plate.
[0002]
[Prior art]
In general, the rolling process for thick steel plates is to maintain the surface care or width accuracy of the slab, so that the adjustment rolling phase for adjusting the plate thickness and the width rolling phase for obtaining a predetermined product width by rotating the rolling direction 90 degrees on a flat surface. The finish rolling phase is composed of three rolling phases, which are rotated 90 degrees again to obtain a predetermined product sheet thickness. Rolling of thick steel plates is performed by lever rolling, and a total of 10 or more passes of rolling is applied in combination of these three phases.
[0003]
The planar shape of the product obtained through such a process changes with the width ratio (product width / slab width) or the longitudinal reduction ratio (product length / slab length) as one of the parameters. For example, it is generally known that when the tenter ratio is small and the longitudinal reduction ratio is large, a drum shape is obtained, and conversely, when the tenter ratio is large and the longitudinal reduction ratio is small, a drum shape is obtained. In the plate cutting after the completion of rolling, all of these planar shapes that are out of the rectangle are cut off, resulting in a decrease in product yield.
[0004]
As countermeasures against these planar shape defects, several methods have been proposed in which rolling is performed by predicting a final planar shape in advance.
[0005]
For example, Patent Document 1 discloses that a planar shape of a thick plate that is subjected to tenth rolling or finish rolling by turning 90 ° after giving a predetermined thickness distribution to the material to be rolled by changing the roll interval during rolling. A control method has been proposed. In the control of the planar shape disclosed in Patent Document 1, the tongue or fishtail is brought close to a rectangle as follows.
[0006]
When the longitudinal end face becomes a tongue, in the final pass of the tenter rolling phase, a thickness distribution is imparted so that the thickness of the front and rear end portions in the longitudinal direction is thicker than the central portion, and then finish rolling is performed. When the width end face becomes a tongue, in the final pass of the adjustment rolling phase, a plate thickness distribution is given so that the plate thickness of the front and rear end portions in the longitudinal direction is thicker than the central portion, and then tentering rolling may be performed. It is said.
[0007]
In addition, as a method of determining the thickness distribution to be applied, for example, in Patent Document 2, it is assumed that the volume deviated from the rectangle in normal rolling and the volume of the thick part are the same, that is, the volume of the thick part flows in the rolling direction. The law of constant mass flow should be used.
[0008]
Moreover, in patent document 3, in addition to the idea of the above-mentioned law of constant mass flow, the influence of width direction plastic flow is taken into account using a regression equation using the plate thickness and plate width.
[0009]
Further, in Non-Patent Documents 1 to 3, based on the actual measured values of the planar shape of the material to be rolled when a slab (lead model) that does not give a thick part is actually rolled, the entry side plate thickness, plate width, roll Methods for obtaining a prediction formula (empirical formula) including parameters such as diameter and rolling reduction and predicting the planar shape of the material to be rolled by the prediction formula are described.
[0010]
[Patent Document 1]
Japanese Patent Laid-Open No. 52-57061 (pages 2 to 4, FIGS. 1 to 4)
[0011]
[Patent Document 2]
Japanese Unexamined Patent Publication No. 55-77907 (pages 2 to 4, FIGS. 1 to 5)
[0012]
[Patent Document 3]
JP-A-57-097803 (pages 2 to 5, FIGS. 1 to 3)
[0013]
[Non-Patent Document 1]
Okado, Nakauchi et al .: Iron and steel (1976), p. 236
[Non-Patent Document 2]
Okado, Nakauchi et al .: Iron and steel (1978), p. 278
[Non-Patent Document 3]
Okado, Nakauchi et al .: Iron and Steel, 66 (1980), page 964.
[Problems to be solved by the invention]
In the above prior art, the shape of the thick part is determined so that the volume deviated from the rectangle by normal rolling and the volume of the thick part flowing at the front and rear ends coincide.
[0017]
However, when the planar shape is made close to a rectangle, it is not sufficient to consider the volume of the portion outside the rectangle. For example, when considering the shape of the tip crop 3 at the time of normal rolling as shown in (a) and (b) of FIG. 1, when the material to be rolled 2 provided with a thickness distribution in the width direction is rolled, Even if the volume A and the pattern B have the same volume flowing at the tip (SA = SB), the cut-off volume of the crop 3 is larger in the pattern B and the product yield is different. In other words, unless the fishtail shape generated when the material to be rolled having a thickness distribution in the width direction as shown in FIG. 2 is rolled is accurately predicted, a portion (crop) deviated from a rectangle generated during normal rolling. There is a problem that it cannot be reduced efficiently.
[0018]
For example, when considering a case where a tapered plate thickness distribution (length L, height ΔH) as shown in FIG. 3 is applied, Patent Document 3 discloses a method for determining the applied plate thickness distribution as follows. ing.
[0019]
First, as the final crop shape at the time of normal rolling, as shown in FIG. 4, a shoulder drop width W _f and a crop length Lc are predicted, and an area to be supplemented (SO = W _f × Lc) is calculated. Next, after calculating the height ΔH * from the mass flow constant law with the length L = W _f , ΔH * is corrected to ΔH by the width direction plastic flow coefficient. In this way, the conventional method of Patent Document 3 calculates the length L and the height ΔH that minimize the crop loss.
[0020]
However, the premise of L = W _f in the conventional method, a material having a thickness distribution as shown in FIG. 4, 90 ° C. rotated width of the fishtail which occurs when the horizontally rolled after (wcrop in Figure 2) shoulder It is determined based on the assumption that it coincides with the falling width W _f, and if the assumption that supports this precondition is broken, the optimum thickness distribution (length L and height ΔH) is not necessarily calculated. There is no problem.
[0021]
In the methods of Non-Patent Documents 1 to 3, when rolling a simple cross-sectional slab having a uniform thickness, the planar shape can be predicted with a certain degree of accuracy, but a thickness distribution is given in advance in the width direction. When rolling a slab, the planar shape after rolling cannot be predicted.
[0022]
The present invention has been made to solve the above problems, and provides a method for rolling a thick steel plate capable of calculating with high accuracy the cross-sectional shape of a thick portion necessary for making the final planar shape close to a rectangle. The purpose is to do.
[0023]
[Means for Solving the Problems]
The rolling method of a thick steel plate according to the present invention is a rolling method for controlling the planar shape of a thick steel plate by providing a plate thickness distribution partially having a thick portion in the width direction of the thick steel plate. A step of predicting the planar shape Pru after normal finish rolling in the case where the meat part is not provided, and (b) a step of calculating a shape ΔPr of a portion where the predicted planar shape Pru deviates from the target rectangular planar shape Pro. (C) converting the shape ΔPr of the disengaged portion into a predicted conversion shape ΔPrc after giving a plate thickness distribution partially having a thick portion and subjected to at least one pass rolling; (D) The difference between the predicted planar shape Prda after one-pass rolling and the predicted planar shape Prua after one-pass rolling after the thick-walled portion is partially applied and the thick-walled portion is not applied. Calculating the shape ΔPrd; and (e) the prediction. A step of calculating an area difference ΔAd as a difference between the area A1 of the calculation shape ΔPrc and the area A2 of the difference shape ΔPrd; and (f) a plate thickness distribution that minimizes the area difference ΔAd is given. And a step of determining the dimension and shape of the thick part, respectively.
[0024]
In the step (d), when compared with the predicted planar shape Prua in the case where the thick portion is not provided, the amount Lmax that is most greatly extended by adding the thick portion and the width Wcrop of the region in which the elongation increases are determined. Predict the predicted planar shape Prda using these predictions Lmax and Wcrop, respectively. In the prediction of the amount Lmax that is most greatly extended by adding the thick part and the width Wcrop of the region where the elongation is increased, at least the thick part width with respect to the width L of the thick part, the thickness distribution ΔH, and the plate width W It is desirable to use a ratio W / L of L. In addition, since many data can be obtained from the past rolling performance regarding the maximum elongation amount Lmax and the elongation increase region width Wcrop shown in FIG. 2, the predicted planar shape Prda can be predicted with higher accuracy.
[0025]
In the step (d), the predicted Lmax and Wcrop are predicted using the width L of the thick portion, the thickness distribution ΔH, and the ratio (W / L) of the thick portion width L to the plate width W. Is preferred. Thickness distribution is given by these parameters (Lmax, Wcrop, L, ΔH, W, W / L) and numerical analysis method (Finite Element Method; FEM) using predetermined formulas and / or by lead model rolling simulation test The predicted planar shape Prda in the subsequent one pass can be predicted with higher accuracy.
[0026]
Hereinafter, a method for obtaining the predicted planar shape Prda will be described with reference to FIGS.
FIG. 6A is a schematic plan view showing a state in which all the thick portions extend in the rolling direction when it is assumed that there is no constraint on the flat portion, and FIG. 6B assumes that there is a constraint on the flat portion. It is a plane schematic diagram which shows the actual state after 1-pass rolling a thick part in the case of doing.
[0027]
Assuming that the cross-sectional shape of the thick-walled portion is a triangle, the relationships of equations (1) to (4) are established. However, C11 to C23 are coefficients obtained from the experimental conditions (plate thickness, plate width, reduction condition, roll diameter, etc.) and the planar shape measurement result after rolling.
[0028]
FIG. 7 is a diagram for explaining a method for calculating and predicting the planar shape profile of the rear end portion from Wcrop and Lmax. Assuming that the planar shape curve is fourth-order, the planar shape y is given by equation (5).
[0029]
[Expression 1]

[0030]
As described above, the five coefficients D1 to D5 of the above-mentioned quaternary equation can be determined from Lmax, Wcrop (known), and five symmetrical conditions. For example, a simple formula for predicting the coordinates (xL, Lmax) that becomes Lmax and the coordinates (xa, ya) of another point (inflection point) of the protruding portion is created based on an experiment, and the simple formula is used. To determine the coefficients D1 to D5 . This quartic equation (5) gives the predicted planar shape Prda in one pass after the plate thickness distribution is given. That is, in the present invention, the planar profile is expressed by two representative values of Wcrop and Lmax.
[0031]
FIG. 8 (a) is a schematic plan view showing an ideal rolling state in which the final planar shape is a rectangle, and FIG. 8 (b) is a setting of a target shape after completion of the tentering based on a portion that is insufficient from the rectangle in normal rolling. It is a figure explaining a method.
[0032]
Further, when the shape ΔPrc after the completion of the width finding is obtained with high accuracy, ΔPr obtained from the planar shape at the time of the completion of the width finding obtained by the above-mentioned first approximation, taking into account the width direction metal flow at the width end portion. ₁ , ΔPrc ₁ is used to determine the final planar shape using a planar shape prediction formula when there is no thick portion in conventional normal rolling, and ΔPr ₂ that is insufficient (or excessive) is obtained again.
[0033]
The shape (ΔPrc ₂ ) converted at the time of completion of width finding is obtained by the same method as described above. That is, more accurate ΔPrc = ΔPrc ₁ + ΔPrc ₂ may be set. Reference numeral Y _f (x) represents the shortage after the final rolling, the code Y _w (x) denotes the shortfall after one pass rolling when having a thick portion in the cross section. The accuracy is improved by repeating the above method.
[0034]
FIG. 9 is a diagram for explaining feedback to subsequent materials. In the figure, a characteristic line P indicated by a solid line represents an actual measurement value, and a characteristic line Q indicated by a broken line represents a predicted value. The planar shape profiles of the predicted value and the actually measured value were compared, and the deviation ratios of Lmax and Wcrop were calculated. As a precondition, it is assumed that the same deviation occurs in the predicted value even in the next material, and that the accuracy of the conventional planar shape prediction formula when the thick portion serving as the base is not given is assumed to be good.
[0035]
RL = δLmax / Lmax
RW = δWcrop / Wcrop
What percentage (coefficient: CoeR, CoeW) of the deviation ratio is added to the predicted value of the next material.
[0036]
Correction of next material Lmax = RL × CoeR × Lmax (predicted value of next material)
Next material correction Wcrop = RL × CoeW × Wcrop (predicted value of next material)
With these corrections, the thick part shape obtained from the flowchart of FIG. 5 is changed.
[0037]
For the purpose of improving the accuracy of the above prediction formulas (1) to (4), the coefficients C11 to C23 in the formulas are calculated as in the multiple regression method based on a large number of actually measured values (measured values) and respective rolling conditions. To learn using traditional techniques.
[0038]
FIG. 10 is a model diagram for explaining a planar shape change due to horizontal rolling.
[0039]
(I) Example of planar shape change model by 1-pass horizontal rolling FIG. 10 shows a planar shape change model when a rectangular steel plate is horizontally rolled. The width variation amount and the crop length are obtained from the equations (6) and (7), respectively. The plate width variation and the leading and trailing end crop length can be approximated by Equations (8) and (9). However, the symbols in the formula are R: work roll radius, Δh: horizontal rolling reduction, Hi: entry side plate thickness, Wo: median plate width.
[0040]
[Expression 2]

[0041]
(Ii) Example of planar shape change model by multi-pass rolling The shape after multi-pass rolling is handled as an integrated value of each pass. Equation (10) and Equation (11) show the sheet width variation and the leading and trailing edge crop shape during multi-pass rolling. However, the symbols in the equations are yw (n), yw (n-1): fluctuation of the exit side plate width in the nth pass and n-1th pass, yw: plate width variation generated in the nth pass, yL (n ), YL (n−1): n-th pass, n−1-th exit side crop shape, yL: crop shape change occurring in the n-th pass, α: elongation correction coefficient, h (n), h (n -1): Thickness of the exit side of the nth and n-1th passes.
[0042]
[Equation 3]

[0043]
(Iii) Verification of planar shape prediction accuracy From the rectangular slab to the planar shape after finishing rolling by superimposing the planar shape variation model due to edging and the planar shape variation model due to horizontal rolling when a thick part is added in the width direction An integrated simulator to predict was constructed. The planar shape prediction accuracy after the rolling is, for example, ± 10 mm in the in-plate width deviation and ± 100 mm in the crop length, and sufficient prediction accuracy to be applied to the planar shape control was obtained. The reason why the crop length prediction accuracy is inferior to the in-plate width deviation is that the prediction error is extended in the longitudinal direction and enlarged.
[0044]
The present invention has been made in examining how the plate thickness distribution imparted during rolling is deformed by subsequent horizontal rolling. In examining the deformation of the material, the present inventors conducted a model rolling experiment using pure lead.
[0045]
In FIG. 11, the horizontal axis indicates the distance (mm) from the plate width edge, and the vertical axis indicates the tongue length (mm) of the trailing end crop, and shows the tongue length distribution of the trailing end crop in the plate width direction. FIG. In the figure, a characteristic line A shows a theoretical value curve calculated based on a constant mass flow rule, and a characteristic line B shows an experimental value curve actually measured using a sample. A thickness distribution such as L = 40 mm and ΔH = 1.0 mm was applied to a material having a thickness of 12 mm × width of 180 mm × length of 300 mm. The theoretical value and the experimental value were examined for the shape of the rear end crop when the thickness distribution imparting material was rolled to a thickness of 10.5 mm.
[0046]
As is apparent from FIG. 11, the so-called fishtail shape is obtained, and the maximum value (Lmax) of elongation occurs almost at the width end. Here, the shape predicted based on the mass flow constant law described in Patent Document 3 is shown in the figure, but it has been found that the elongation at the width end is smaller than the predicted value based on the mass flow constant law. This is because the influence of the width expansion is large at the width end portion. Further, it was found that the width (Wcrop) of the region having a large elongation is larger than L (= 40 mm).
[0047]
From the above experimental results, in order to predict a change in the planar shape that occurs when a material having such a thickness distribution is rolled, as a representative dimension, at least the maximum stretch length shown in FIG. It is necessary to use the width Wcrop of the region where the elongation is large due to the influence of Lmax and the thick portion. For example, the fishtail shape can be predicted by approximating the shape using a quartic curve or the like.
[0048]
Furthermore, after the rolling pass after partially giving the thick part, the planar shape Prdr of the rolled material is measured, and the difference between the measured value of the planar shape Prdr and the value of the predicted planar shape Prda is determined as the next material. You may make it feed back to subsequent rolling.
[0049]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings.
The embodiment of the present invention will be described with reference to the flowchart of FIG.
First, a crop shape Pru in normal rolling is predicted as indicated by a solid line in the drawing (step S1). For the prediction of the crop shape Pru, for example, a predetermined empirical formula described in Patent Document 3 may be used, or a numerical analysis method (Finite Element Method; FEM) may be used.
[0050]
Next, the normal rolling crop predicted shape Pru is compared with the target rectangular planar shape Pro (broken line in the figure), and the shape ΔPr of the portion where the former deviates from the latter is calculated (step S2).
[0051]
The shape ΔPr of the portion deviating from the calculated rectangle is converted into a shape predicted when the tenter rolling is completed (step S3). In this conversion step S3, considering the case where the sheet thickness distribution is given in the tenth rolling completion pass, the shape of the pattern A shown in FIG. The thickness of the pattern A is converted to a shape A ′ that approximates the pattern B shown in FIG. The primary approximate shape A ′ is a shape obtained by reducing the shape of the portion that is insufficient when the thick-walled portion is not provided in the rolling direction by the reduction ratio, and this calculated shape is a planar shape at the completion of tenter rolling in normal rolling. The planar shape added to is the planar shape Pro (the shape when the tenter rolling is completed) in which the planar shape becomes rectangular in the final finish rolling.
[0052]
In the present embodiment, the primary approximate shape A ′ is used, but FEM may be employed as a method for obtaining the target plane shape with higher accuracy. That is, the target plane shape can be finally obtained by repeating the calculation according to the linear programming method many times using FEM. Alternatively, the shape may be obtained by performing a recursive calculation from the FEM to the final stage of machining.
[0053]
A planar shape Prua in the case where the thick part at the completion of tentering rolling is not given is obtained based on the converted primary approximate predicted shape A ′ (step S4).
[0054]
An initial plate thickness distribution is assumed based on the planar shape Prua in the case where the thick portion at the time of completion of the tentering rolling is not given (step S5). This assumed plate thickness distribution is used when the plate thickness distribution is given to the end of the thick steel plate.
[0055]
After providing the plate thickness distribution, the predicted planar shape Prda in one pass is calculated (step S6). In one pass after the plate thickness distribution is imparted, almost only the thick wall portion is rolled down so as to be flattened. At this time, the thick part tends to extend in the rolling direction, but the part that is hardly crushed restrains the thick part that is not stretched, and the metal near the width end also flows in the width direction. As a result, (i) the length (crop length) protruding in the rolling direction of the thick portion is shortened, and (ii) the width Wcrop where the portion that is not crushed by the thick portion to be stretched is pulled and protruded Becomes larger than the width L to which the thick portion is provided. That is, as shown in FIG. 6A, the ratio of the portion occupied by the thick portion (cross-sectional area S2) to the other portion (cross-sectional area S1) in the material cross section, for example, S1 / (S1 + S2), S2 / ( S1 + S2), the reduction ratio ε2 of the thick wall portion (the reduction strain: the size to be stretched) and the other reduction ratio ε1 are the main parameters for predicting Wcrop and Lmax. The above two formulas (1) and (2) were created. The cross-sectional areas S1 and S2 can be expressed using ΔH and W / L as shown in the above formulas (3) and (4).
[0056]
As shown in FIG. 7, when a planar profile is approximated by a quartic equation (5), the planar profile can be determined from Wcrop and Lmax. This quartic equation (5) gives the predicted planar shape Prda in one pass after the plate thickness distribution is given.
[0057]
The planar shape Prua in the case where the thick portion is not applied is subtracted from the predicted planar shape Prda in one pass, and the difference is set as a difference shape ΔPrd (step S7).
[0058]
The area A2 of the difference shape ΔPrd is subtracted from the area A1 of the shape ΔPrc, and the difference is defined as an area difference ΔAd (= A1−A2) (step S8).
[0059]
The obtained area difference ΔAd is compared with a predetermined allowable area difference As to determine the magnitude (step S9). When the area difference ΔAd is smaller than or equal to the allowable area difference As, it is determined to be acceptable and the calculation is terminated. The predetermined allowable area difference As is not limited to zero but is a value close to zero, and is obtained in advance by experiment for each combination of the plate thickness and the plate width.
[0060]
If the area difference ΔAd is larger than the allowable area difference As, it is determined to be unacceptable, the previous initial plate thickness distribution is corrected (step S10), and the process returns to step S5. In step S5, the corrected sheet thickness distribution is assumed to be the actual rolled sheet thickness distribution. Then, using this corrected plate thickness distribution, the area difference ΔAd is obtained according to the procedure of the above steps S6 to S8, and the magnitude of the obtained area difference ΔAd and the allowable area difference As is repeatedly compared and determined (step S9). Specifically, the thickness B is predicted so that the shape B when the thick portion shape (length L, height ΔH) is rolled with respect to the initial values of the thick portion shape (the length L and the height ΔH) is approximated to the primary approximate shape A ′. Repeat the flesh shape correction. By this processing, it is possible to calculate the optimum values of the length L and the height ΔH so that the crop loss is minimized. In the present invention, there is no particular limitation on the correction amount and correction method for the thick-walled portion shape.
[0061]
In addition, after the rolling pass after giving a thick part partly, the planar shape (Prdr) of a rolling material is measured, and the difference between this measured value and the predicted planar shape (Prda) is the rolling after the next material. You may make it feed back to.
[0062]
【Example】
Next, examples to which the method of the present invention is applied will be described.
[0063]
Crop loss generated in both cases was compared using a thick plate sample whose planar shape was controlled according to the method of the present invention as an example and a thick plate sample whose planar shape was controlled according to the method of Patent Document 3 as a comparative example.
[0064]
As a thick plate sample, a slab having an initial size of 251 mm × width 1320 mm × length 2095 mm was adopted, and it was assumed that a rolled product having a thickness of 9.8 mm × width 2394 mm × length 29500 mm was obtained from this slab. The plate thickness distribution to be given to the thick plate is the cross-sectional shape shown in FIG.
[0065]
Table 1 shows the pass schedules for adjustment rolling, tentering rolling, and finishing rolling, respectively. Adjusted rolling was 3 passes, widening rolling was 4 passes, and finish rolling was 9 passes. In the third pass of adjustment rolling, the thick plate was rotated 90 ° to perform cross roll. In the fourth pass of the tenter rolling, a plate thickness distribution was given to the thick plate by 1-3 passes, and then this was rotated 90 ° to perform cross roll.
[0066]
Since the crop length Lc during normal rolling is 430 mm and the shoulder drop width W is 400 mm, in the comparative example, the length Lc = W = 400 mm and the height ΔH = 7.0 mm. On the other hand, in the example to which the method of the present invention was applied, the length Lc = 350 mm and the height ΔH = 16.2 mm.
[0067]
[Table 1]

[0068]
FIG. 12 shows the ratio of the crop loss CR2 when the conventional method (comparative example using the method of Patent Document 3) and the method of the present invention (the above-mentioned embodiment) are applied to the crop loss CR1 during normal rolling (CR2 / CR1). As is apparent from this figure, the crop loss is reduced by about 35% when the conventional method is applied, but the crop loss can be reduced by about 65% when the method of the present invention is applied.
[0069]
【The invention's effect】
The present invention provides a plate thickness distribution having a thin portion and a thick portion in the width direction of the material, thereby determining the thickness distribution to be applied in a rolling method of a thick steel plate that is rolled while controlling the planar shape. By predicting the planar shape change in rolling after imparting the plate thickness distribution, the cross-sectional shape of the thick part necessary to make the final planar shape close to a rectangle can be calculated with high accuracy. For this reason, crop loss is significantly reduced as compared with the prior art, and the product yield can be dramatically improved.
[Brief description of the drawings]
1A is a schematic cross-sectional view showing a rear end portion (pattern A) of a thick steel plate during normal rolling, and FIG. 1B shows a rear end portion (pattern B) of another thick steel plate during normal rolling. FIG.
2A is a schematic plan view showing a rear end portion of a thick steel plate, and FIG. 2B is a schematic cross-sectional view showing a rear end portion of the thick steel plate.
FIG. 3 is a schematic cross-sectional view showing a rear end portion of a thick steel plate.
FIG. 4 is a schematic plan view showing a normally rolled crop shape.
FIG. 5A is a flowchart showing a method for rolling a thick steel plate according to the present invention, and FIG. 5B is a schematic diagram showing a cross section of the thick steel plate corresponding to each step.
FIG. 6A is a schematic plan view showing a state in which all thick portions are extended in the rolling direction when it is assumed that there is no flat portion constraint, and FIG. 6B is a case where there is a flat portion constraint. The plane schematic diagram which shows the actual state after 1-pass rolling a thick part.
FIG. 7 is a diagram for explaining a calculation prediction method of a planar shape profile of a rear end portion from Wcrop and Lmax.
FIG. 8A is a schematic plan view showing an ideal rolling state in which the final planar shape is a rectangle, and FIG. 8B is a method for setting a target shape after the completion of the tentering based on a portion that is insufficient from the rectangle in normal rolling. Illustration to explain.
FIG. 9 is a diagram for explaining feedback to subsequent materials.
FIG. 10 is a model diagram illustrating a change in planar shape due to horizontal rolling.
FIG. 11 is a characteristic diagram showing a tongue length distribution of a trailing end crop in a plate width direction.
FIG. 12 is a graph showing a comparison of the crop loss between the method of the present invention and the conventional method.
[Explanation of symbols]
2. Thick steel plate,
3 ... Crop,
Pru ... Crop shape in normal rolling (predicted plane shape),
Pro: Target rectangular planar shape,
ΔPr: the shape of the part out of the rectangle,
ΔPrc: Predicted conversion shape after 1 pass,
Prua: Predicted planar shape after one pass when no thick part is given,
Prda: Predicted plane shape in one pass after plate thickness distribution is given,
ΔPrd ... difference shape (= Prda-Prua),
A1: Area of the predicted conversion shape ΔPrc,
A2: Area of the difference shape ΔPrd,
ΔAd: Area difference (= A1-A2).

Claims (3)

In the rolling method for controlling the planar shape of the thick steel plate by giving a plate thickness distribution having a thick part partly in the width direction of the thick steel plate,
(A) a step of predicting a planar shape Pru after normal finish rolling in the case where a thick part is not provided;
(B) calculating a shape ΔPr of a portion where the predicted planar shape Pru deviates from the target rectangular planar shape Pr0;
(C) a step of converting the shape ΔPr of the disengaged portion into a predicted conversion shape ΔPrc after giving a plate thickness distribution partially having a thick portion and subjected to at least one pass rolling;
(D) The difference between the predicted planar shape Prda after one-pass rolling and the predicted planar shape Prua after one-pass rolling after the thick-walled portion is partially applied and the thick-walled portion is not applied. Calculating the shape ΔPrd;
(E) calculating an area difference ΔAd as a difference between the area A1 of the predicted conversion shape ΔPrc and the area A2 of the difference shape ΔPrd;
(F) determining the dimensions and the shape of the thick portion so that a plate thickness distribution is provided so that the area difference ΔAd is minimized;
A method of rolling a thick steel plate, comprising:   In the step (d), when compared with the predicted planar shape Prua in the case where the thick part is not provided, the amount Lmax which is most greatly extended by providing the thick part and the width Wcrop of the region where the increase in elongation is obtained. The method according to claim 1, wherein each prediction is performed and the predicted planar shape Prda is predicted using these predictions Lmax and Wcrop. In the step (d), the predicted Lmax and Wcrop are predicted using the width L of the thick portion, the thickness distribution ΔH, and the ratio (W / L) of the thick portion width L to the plate width W. The method according to claim 2.

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