JP4099915B2 - Control method of reversible rolling mill - Google Patents

Control method of reversible rolling mill Download PDF

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JP4099915B2
JP4099915B2 JP37447499A JP37447499A JP4099915B2 JP 4099915 B2 JP4099915 B2 JP 4099915B2 JP 37447499 A JP37447499 A JP 37447499A JP 37447499 A JP37447499 A JP 37447499A JP 4099915 B2 JP4099915 B2 JP 4099915B2
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pass
rolling
plate thickness
steepness
sign
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JP2001191103A (en
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武男 矢澤
裕之 古川
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Sumitomo Metal Industries Ltd
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Sumitomo Metal Industries Ltd
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Description

【0001】
【発明の属する技術分野】
本発明は金属板材を複数回のパスで開始板厚から目標板厚に圧延する場合の可逆式圧延機の制御方法に関する。
【0002】
【従来の技術】
以下では金属板材として厚鋼板を例に説明する。可逆式圧延機を用いた厚鋼板の圧延においては、少ないパス回数で平坦な形状の鋼板に仕上げることが重要である。パス回数を少なくするには圧延荷重を大きくするのが有効であるが、圧延荷重を大きくすると、ワークロールに撓みが発生し、板幅端部が過剰に圧延され耳波と呼ばれる形状不良が発生する。
【0003】
このような形状不良が発生すると、圧延途中では絞り込み等のトラブルが発生し、生産性を阻害することになり、また最終パス完了後に発生した場合には次工程で手入れ等の余分な作業が発生し、製造コストの増加を招く。
【0004】
板端部が過剰にのばされて発生する耳波や、逆に板幅中央部が過剰にのばされ発生する中伸びなどの形状不良の程度の指標として、下記(5) 式で示す急峻度λが用いられる。
【0005】
λ=t/l (5)
ただし、tは波高さ、lは波長である。
【0006】
また、前述のワークロールの撓みは形状不良の発生以外に、板厚の幅方向の偏差を発生させる。
【0007】
この幅方向の板厚偏差の程度を示す指標として下記(6) 式で示す板クラウンCrが用いられる。
【0008】
Cr=Hc−He (6)
ただし、Hcは幅方向中央部の板厚、Heは幅端部の板厚である。
【0009】
通常、ワークロールの撓みにより発生する板クラウンを低減するため、ワークロールのバレル方向のロール径を一定ではなく、端部より中央部の直径が大きい形状に成形する。このワークロールのバレル方向の直径差はワークロールクラウンと呼ばれ、中央部とバレル端部の直径差で定義される。
【0010】
形状不良を防止し、少ないパス回数で圧延するため、被圧延材の板厚が厚い前段のパスでは、圧延荷重を大きくしてパス回数を少なくし、板厚が薄くなって形状不良が発生しやすい後段のパスでは、圧延荷重を小さくして被圧延材を平坦な形状に整える。このためには、圧延荷重等の圧延条件をパス毎に設定したパススケジュールを算出しなければならない。
【0011】
パス毎の圧延条件を算出する方法としては、以下に示す方法が特公昭61−32086号公報に開示されている。
【0012】
図8は前記公報に開示された圧延条件の算出方法を説明するグラフである。同図においては、横軸に被圧延材の板厚をとり、縦軸に被圧延材の板クラウンをとって、n回のパスでHnの目標板厚に圧延するための板厚と板クラウンとの関係を示している。
【0013】
同図中の△印は前段のパスで圧延機の許容値内の最大荷重で圧延した場合の板厚と板クラウンとの関係を示している。この計算方法は、開始板厚Hsから下記(7) 式を用いて、各パスにおける許容最大荷重P(i)に対するiパス目の出側板厚H(i)を求め、(8) 式を用いて許容最大トルクTr(i)に対するiパス目の出側板厚H(i)を求めて、2つの出側板厚H(i)を比較し、大きい方を目標とする出側板厚H(i)とし、該出側板厚H(i)から(9) 式を用いてiパス目の出側板クラウンCr(i)を算出するという方法である。
【0014】
圧延条件を許容最大荷重または許容最大トルクに基づいて求めることから、この段階のパスを全負荷パスと呼び1パス目から順に計算する。
【0015】
P(i)=F1(H(i),H(i-1),Kfm(i),B) (7)
ただし、P(i)はiパス目の荷重、H(i)はiパス目の出側板厚、H(i−1)はiパス目の入側板厚(i−1パス目の出側板厚と同じ)、Kfmはiパス目の変形抵抗、Bは板幅である。
【0016】
Tr(i)=F2(P(i),H(i),H(i-1)) (8)
ただしTr(i)はiパス目のトルクである。
【0017】
Cr(i)=F3(P(i),B,Cwr) (9)
ただし、Cr(i)は板クラウン、Cwrはワークロールクラウンである。
【0018】
図8の○印は後段のパスで被圧延材の許容急峻度を維持できる範囲内で最大荷重で圧延した場合の板厚と板クラウンとの関係を示しており、目標板厚Hnから(7) 式、(9) 式、および下記の(10)式、(11)式を用いて、各パスにおける急峻度が最大急峻度λ(i)となる出側板厚H(i)及び出側板クラウンCr(i)を算出してプロットしたものである。このパスを形状調整パスと呼び、最終パスであるnパス目から溯って計算する。
【0019】
Δγ(i)=Cr(i)/H(i)−Cr(i-1)/H(i-1) (10)
ただし、Δγ(i)はiパス目の板クラウン比率変化である。
【0020】
λ(i)=F4(H(i),B)×√|Δγ(i)| (11)
ただし、λ(i)はiパス目の急峻度である。
【0021】
このように、可逆式圧延機では前段のパスでは全負荷パスにより圧延し、後段のパスでは形状調整パスにより圧延する。全負荷パスから形状調整パスへ切り替わるパスをつなぎパスと呼び図8では(n−3)パス目がこれに当たる。
【0022】
全負荷パスの計算により求めたつなぎパスと、形状調整パスの計算により求めたつなぎパスとは通常一致することはなく、圧延条件を調整してこれらのつなぎパスを一致させなければならない。
【0023】
すなわち、全負荷パス及び形状調整パスにおいて負荷する荷重を小さくして再計算をする。この再計算を図中●印で示すようにつなぎパスが一致するまで繰り返し、一致した条件を最適なパススケジュールとする。
【0024】
【発明が解決しようとする課題】
前記特公昭61−32086号公報に開示された方法においては、計算負荷の点で問題がある。
【0025】
すなわち、全パスについて全負荷パスを対称としたパススケジュール計算と、形状調整パスを対称としたパススケジュール計算の2通りの計算を実施しなければならず、さらに、全負荷パスと形状調整パスのつなぎパスの差異を丸める(一致させる)処理をするために、再度全パスについて全負荷パスのスケジュール計算と形状調整パスのスケジュール計算の2通りの計算を実施し、これをつなぎパスでの差異が無くなるまで複数回繰り返す必要がある。このため、計算に要する負荷が大きく計算時間は長くなり、厚鋼板の圧延のように被圧延材の開始板厚及び/または目標板厚が毎回変わるような操業に対して適用すると、被圧延材毎にパススケジュールを算出する必要があり、計算時間の長さは生産サイクルの延長及び算出装置の独占等の悪影響をもたらす場合がある。
【0026】
また、従来の算出方法で可逆式圧延プロセスにオンラインで適用する場合、計算時間を短縮するため高性能な計算機が必要なり、システムのコストアップにつながるという問題がある。
【0027】
前記特公昭61−32086号公報に開示された方法にはさらに以下の問題がある。
【0028】
前記の形状調整パスで、目標急峻度から出側板クラウンCr(i)を算出する段階では、板クラウン比率変化Δγと急峻度λの関係を板厚と板幅を変数とした関数F4 (H(i),B)で求めているが、実操業においてはこれらの関係式の予測精度が不十分で、目標通りの急峻度を達成することは困難であり、形状不良の発生に伴う絞り込み等が発生するおそれがある。
【0029】
本発明は上記の問題を解決すべくなされたものであり、その課題は全負荷パスと形状調整パスのつなぎパスの調整をする際に、計算負荷を軽減し、制御用計算機の有効利用を図るとともに、形状調整パスでの圧延条件を算出する際の高精度の急峻度計算モデルを導入して平坦形状の制御精度を向上させる制御方法を提供することにある。
【0030】
【課題を解決するための手段】
前述のように、厚鋼板の圧延では能率を高め平坦形状を良好に保つには、前段の全負荷パスと後段の形状制御パスで構成されるパススケジュールが用いられる。
【0031】
その場合、圧延機の能力制約による全負荷パススケジュール計算から平坦形状に制約される形状制御パススケジュール計算への切換えはつなぎパスで行われ、つなぎパスでは双方の制約条件を満足する必要がある。
【0032】
前記特公昭61−32086号公報に記載の計算方法では、つなぎパスの圧延条件を満たすべく、前段の全負荷パスと後段の形状制御パスの両方を調整する方法を用いているため、計算の負荷が大きい。
【0033】
本発明者らは、形状調整パスでは圧延機の能力の制約がないこと、全負荷パスでは平坦形状の制約がないことに着目し下記の計算方法を想到した。
【0034】
まず、後段の形状調整パススケジュールを最終パスから先行パスに遡り、圧延機能力の制約を受ける寸前のパスまで計算し、形状調整パススケジュールを決定する。次いで圧延機能力制約の範囲内でさらに先行パスに遡ってパス入側板厚を求めて行く。求められた入側板厚が素材の厚さ(圧延開始の厚さ)を超えたときに全負荷パスのパス回数を決定する。この時計算された第1パスの入側板厚は素材厚より厚いため、第1パスの入側板厚がちょうど素材厚と等しくなるよう全負荷パスの各パス圧下量を軽減する調整(丸め)を行う。この調整計算は平坦形状の制約がないため、計算負荷が少ない。
【0035】
このように、形状調整パスを先に決定し、全負荷パスの圧延条件のみを調整すれば、前記特公昭61−32086号公報に記載の方法のように2通りの計算をする必要が無く計算負荷が軽減できる。また、前記特公昭61−32086号公報に記載の方法で問題のあった板クラウン比率変化Δγと急峻度λの関係式を、板厚と板幅だけでなく、材料温度も考慮した関数式とするのがよい。この着想からさらにその数式化を試みた。
【0036】
急峻度λは圧延後の形状不良の程度を示す指標であり、文献(「板圧延の理論と実際」日本鉄鋼協会編、1984、pp96)に記載されているとおり、板厚方向ひずみの幅方向偏差、すなわち板クラウン比率変化と相関がある。
【0037】
本発明者らはまず、この急峻度λと板クラウン比率変化の関係を、広範囲に変化する実操業のデータを詳細に解析することで、多様な条件下でも精度良く表現できるモデルを定式化した。
【0038】
同一の圧延条件での板クラウン比率変化Δγと急峻度λの関係は前記文献にもあるように下記の式で表現することができる。
【0039】
λ=sign(Δγ)a√|Δγ| (1)
a=E(X) (20)
ここで、sign()は符号を付け替える関数で
Δγ<0の時、sign(Δγ)=−1、
Δγ>0の時、sign(Δγ)=+1であり、
Δγ=(CO/HO)-(CI/HI) (4)
HOは出側板厚、HIは入側板厚、COは出側板クラウン、CIは入側板クラウンである。通常HO,HIは幅中央部の板厚である。また、aは形状換算係数と呼ばれる形状不良の発生のしやすさを示す係数で圧延条件(圧延パラメータ:X)の関数である。
【0040】
板クラウン比率変化と急峻度の関係は、被圧延材の寸法、及び圧延条件により大きく変化する。本発明者らは(1) および(20)式の形状換算係数を正確に定式化するため、表1に示す仕様の可逆式圧延機を用い、表2に示すように広範囲の条件で圧延実験を実施した。
【0041】
【表1】

Figure 0004099915
【0042】
【表2】
Figure 0004099915
【0043】
図3は形状換算計数aを、特公昭61−32086号公報に記載された方法(従来法)に基づきプロットした結果を示すグラフである。同図の縦軸は形状換算計数aを示し、横軸は従来法で用いられている圧延パラメータX’(=板幅B/入側板厚HI)を示している。図3から従来法で用いられている圧延パラメータX’では形状換算係数が大きくばらつく結果となり、形状換算係数aと圧延パラメータX’の間の相関が小さいことがわかる。
【0044】
すなわち、従来法では板クラウン比率変化と急峻度の関係を精度良く表現できていないために、圧延途中で耳波等の圧延形状不良が発生し、絞り込み等の操業トラブルが多発していたことがわかった。
【0045】
本発明者らは図3の結果をさらに詳細に分析して形状換算係数に影響を及ぼす圧延条件因子を抽出した。
【0046】
その結果、形状換算係数aは、入側板厚、出側板厚、板幅、圧延温度の4条件によって支配されることが判明し、入出側板厚が薄いほど、板幅が広いほど、圧下率が大きいほど、圧延温度が低いほど形状換算係数aが大きくなることがわかった。すなわち、高精度の圧延形状予測を行うには、従来法で用いていた入側板厚および板幅の変数に加えて、出側板厚、圧延温度を考慮して圧延パラメータXを定義しなければならない。
【0047】
本発明者らは圧延パラメータXを入側板厚HI、出側板厚HO、板幅B及び圧延温度Tの関数Fとして定義して、下記(30)式
X=F(R,B,HI,HO,T) (30)
のように形状換算係数の定式化を図った。
【0048】
さらに、(30)式の具体的な関数式として、下記(31)式を定めた。
【0049】
【数2】
Figure 0004099915
【0050】
ここで、G(T)は実験式として求めた材料の変形抵抗を表す係数で、Tの多項式(a0 +a1 T+a22 )または多項式の分数{(b0 +b1 T+b22 )/(a0 +a1 T+a22 )}等で例示される。
【0051】
図4は圧延パラメータXに対して形状換算係数aの関係を示すグラフである。同図に示すように、形状換算係数aは材料寸法、圧延条件によらずパラメータXで整理することができた。同図に示す結果を最小二乗回帰することで、(21)式に示すように形状換算係数の定式化を図った。
【0052】
a=A(X-b)C (21)
ここで、A,b,Cは定数である。
【0053】
なお、(21)式に記載した関数以外にも、いくつかの関数型が考えられるが、ここでは本発明者らが詳細な検討の上最も精度のよい(21)式を用いた例で説明する。
【0054】
図5は本発明の(1) 式、(21)式および(31)式を用いて計算した計算急峻度と、実測急峻度の関係を示すグラフである。同図に示すように、計算値と実測値とは±0.5%の精度で一致しており、急峻度の予測が可能であることがわかる。
【0055】
本検討により、従来困難であった急峻度の予測が高精度で実現できることになり、以下で述べる圧延パススケジュールを高精度に設計することができ、圧延能率の向上および平坦不良防止が可能となる見通しを得た。
【0056】
本発明は上記の知見に基づきなされたものであり、その要旨は以下の(1) 及び(2) にある。
【0057】
(1) 可逆式圧延機による金属板材の圧延制御におけるパススケジュール計算をする際、急峻度λと板クラウン比率変化Δγとの関係を下記の(1) 、(20)および(30)式で表すことによって、急峻度λの計算式を予め作成しておき、各パスで許容される平坦度制約内で目標急峻度を設定し、目標板厚を出側板厚とする最終パスから前方側のパスに向かって順次前記急峻度計算式を用いて各パスの圧延条件を計算し、前記圧延条件が予め与えられた圧延機の許容値を超える場合には、当該パスの圧延条件を許容値内に納めるべく再計算し、当該パスの入側板厚が圧延開始厚より厚くなったときに、入側板厚および開始板厚の差を吸収すべく、前記再計算したパスの圧延条件を調整する可逆式圧延機の制御方法。
【0058】
λ=sign(Δγ)a√|Δγ| (1)
a=E(X) (20)
X=F(R,B,HI,HO,T) (30)
Δγ=(CO/HO)-(CI/HI) (4)
ここで、sign()は符号を付け替える関数で、
Δγ<0の時、sign(Δγ)=−1、
Δγ>0の時、sign(Δγ)=+1、
であり、Rはワークロール半径、Bは板幅、HOは出側板厚、HIは入側板厚、COは出側板クラウン、CIは入側板クラウン、Tは圧延温度である。
【0059】
(2) 可逆式圧延機にて板材を圧延する際のパススケジュール計算において、急峻度λと板クラウン比率変化Δγとの関係を下記の(1) 、(21)および(31)式で表すことによって、急峻度λの計算式を予め作成しておき、各パスで許容される平坦度制約内で目標急峻度を設定し、目標板厚を出側板厚とする最終パスから前方側のパスに向かって順次前記急峻度計算式を用いて各パスの圧延条件を計算し、前記圧延条件が予め与えられた圧延機の許容値を超える場合には、当該パスの圧延条件を許容値内に納めるべく再計算し、当該パスの入側板厚が圧延開始厚より厚くなったときに、入側板厚および開始板厚の差を吸収すべく、前記再計算したパスの圧延条件を調整する可逆式圧延機の制御方法。
【0060】
λ=sign(Δγ)a√|Δγ| (1)
a=A(X-b)C (21)
【0061】
【数3】
Figure 0004099915
【0062】
Δγ=(CO/HO)-(CI/HI) (4)
ここで、sign()は符号を付け替える関数で、
Δγ<0の時、sign(Δγ)=−1、
Δγ>0の時、sign(Δγ)=+1、
であり、Rはワークロール半径、Bは板幅、HOは出側板厚、HIは入側板厚、COは出側板クラウン、CIは入側板クラウン、Tは圧延温度、G(T)は温度Tの関数、A、bおよびCは定数である。
【0063】
【発明の実施の形態】
図1は本発明の圧延条件算出装置を適用した可逆式圧延機を示す模式図である。同図において符号10はプロセスコンピュータ、11は被圧延材、12は複数のロールを有する第1テーブルローラ、13は第2テーブルローラ、14は上下一対のワークロール、14aはワークロール14の回転軸、15は上下一対のバックアップロール、20はプロセスコンピュータ10に計算結果を与える圧延条件算出装置である。ワークロール14等、圧延に供する設備を圧延機16と総称する。
【0064】
第1テーブルローラ、第2テーブルローラおよびワークロール14を同じ方向へ回転させることにより、被圧延材11は第1テーブルローラ12側から第2テーブルローラ13側へ、または第2テーブルローラ13側から第1テーブルローラ12側へ搬送される。このとき、ワークロール14で被圧延材11を圧延すると一回の圧延を1パスという。
【0065】
被圧延材11は所定回数圧延機16を往復させて圧延を繰り返し、被圧延材11を目標板厚に仕上げる。圧延機16の各制御機器はプロセスコンピュータ10で制御されており、プロセスコンピュータ10の制御は、圧延条件算出装置20から送信されるパススケジュールに基づいている。
【0066】
図2は本発明の圧延条件算出装置を示すブロック図である。圧延条件算出装置20は各パスの圧延条件を算出するためのプログラムを実行するCPU21を備え、CPU21にはプログラム及びデータ等の情報を記録するハードディスク22,CPU21の処理中に発生するデータを一時的に記憶するRAM23,マウス及びキーボード等の入力手段24,モニタ及びプリンタ等の出力手段25,並びに算出した圧延条件をプロセスコンピュータ10へ送信する通信インターフェース26が接続されている。なお、決定したパススケジュールは、出力手段25からも出力され、作業者が算出結果を確認できるようにしてもよい。
【0067】
図6は本発明の計算処理内容を示すフローチャートである。同図において各処理ステップをS1、S2・・・のように記述する。
【0068】
S1では、計算に用いる目標板厚H0及び目標板クラウンCr0の入力を受け付け、S2で最終パスの出側板厚H(1)及び出側板クラウンCr(1)として設定し、最終パスから計数したパス回数を示すカウンタJに「1」を初期設定する。
【0069】
次いで、S3より後段パスから順に遡る各パス計算に入る。S3では(8) 式:Cr(i)=F3 (P(i),B,Cwr)を用いてJパス目の出側板クラウンCr(J)、板幅B、及びワークロールクラウンCwrからJパス目の圧延荷重P(J)計算する。最初の段階ではJ=1であるため最終パスにおける製品板クラウンCr(1)等のパラメータの数値から圧延荷重P(1)を計算することになる。
【0070】
S4では、(6) :P(i)=F(H(i),H(i−1),Kfm,B)を用いてJパス目の出側板厚H(J)、圧延荷重P(J)、変形抵抗Kfm(J)、及び板幅BからJパス目の入側板厚H(i+1)を計算する。最初の段階ではJ=1であるため最終パスの入側板厚、すなわち最終パスから1つ前の出側板厚を計算することになる。
【0071】
次いで、S5では、(7) 式:Tr(i)=F2(P(i),H(i),H(i−1))を用いてJパス目の圧延荷重P(J)、Jパス目の入側板厚H(i+1)、及びJパス目の出側板厚H(J)からJパス目の圧延トルクTr(J)を計算する。
【0072】
S6では、それまでのS3〜S5で計算された圧延荷重P(J)及び圧延トルクTr(J)、並びに入側板厚と出側板厚との差である圧下量H(J+1)−H(J)のすべての圧延条件が、予め設定されている可逆式圧延機の許容値内であるか否かを判定する。すべての圧延条件の値が予め設定されている可逆式圧延機の許容値内である場合、Jパス目の圧延設定は設備能力上可能と判断する(S6のY分岐)。最終パス近傍すなわち形状調整パスでは通常圧延機の許容値内(Yes分岐)となる。
【0073】
S6において、圧延荷重P(J)、圧延トルクTr(J)、及び圧下量H(J+1)−H(J)の値の内いずれか一つでも可逆式圧延機の許容値からはずれる場合、Jパス目の圧延設定は設備能力上不可能と判断する(S6のNo分岐)。このケースは通常圧延開始後のパス、すなわち全負荷パスで起きる。
【0074】
その場合S7で、当該パス番号Jを限界パスJmaxとして記憶する。限界パスJmaxは特公昭61−32086号公報に開示された方法のつなぎパスに相当する。
【0075】
次いで、S8では、圧延荷重P(J)、圧延トルクTr(J)、及び圧下量H(J+1)−H(J)が小さくなるように入側板厚H(J+1)を小さくして、これらの値がすべて許容値内に収まる最大の入側板厚H(J+1)を求めるように再計算する。この再計算は許容値からはずれる項目の値を許容値の値にして入側板厚H(J+1)を求めればよいので許容値と比較する圧延条件の数、すなわち3回より多く再計算することはなく、計算回数が著しく増加することはない。
【0076】
S9では、入側板厚H(J+1)が圧延開始板厚Hsより大きいか否かを判定する。入側板厚H(J+1)が圧延開始板厚Hsより大きくなるのは全負荷パスの場合であり、S8の再計算を行った場合に判定結果がYesとなる。この判定は各パス計算の終了条件判定である。
【0077】
S9において入側板厚H(J+1)が圧延開始板厚Hsより小さい場合(S9のNo分岐)、J+1回以上の圧延が必要と判断する。
【0078】
S10では、(8) 式:Δγ(i)=Cr(i)/H(i)−Cr(i−1)/H(i−1)、(11)式、(21)式、および(31)式の急峻度計算モデルを用いて出側板厚H(J)、出側板クラウンCr(J)、入側板厚H(J+1)、及び許容急峻度λ(J)から入側板クラウンCr(J+1)を算出する。
【0079】
S10における計算では、必ずCr(J+1)>Cr(J)の関係が成り立ち、S3における(8) 式でCr(J)はP(J)に比例していて必ずP(J+1)>P(J)となり、カウンタJが増加する方向、すなわち後行パスから先行パスへ行くほど圧延荷重P(J)は増加する。これによりJmaxパス目以降の計算ではすべてのパスがS6における圧延荷重P(J)及び/または圧延トルクTr(J)の許容値を超えることになり、S8において再計算が行われる。このためJmaxパス目より先行側のパスは特公昭61−32086号公報に開示された方法の全負荷パスに相当し、後行側のパスは形状調整パスに相当する。
【0080】
S11では、カウンタJに「1」を加えて、S3に戻り、一つ先行側のパスについての圧延条件を計算する。
【0081】
S9において入側板厚H(J+1)が圧延開始板厚Hsより大きい場合(S9のYes分岐)、圧延はJ回で完了と判断してS12に至る。
【0082】
S12において、入側板厚H(J+1)と圧延開始板厚Hsとの差である過剰圧下量ΔHを吸収すべく、S8における再計算により最大荷重で圧下するように設定されているJmaxパス目からJパス目までの各パス(全負荷パス)に、予め設定されている所定の規則にしたがって過剰圧下量ΔH(=H(J+1)−Hs)を振り分けることにより、過剰圧下量ΔHを吸収し、Jmaxパス目からJパス目までの圧下量を調整する丸め処理を行う。
【0083】
図7は、本発明の圧延条件算出方法における圧下量を調整する丸め処理を概念的に示す説明図である。図7には縦軸に板厚をとり、圧延開始板厚Hsから成品板厚H0までの板厚の変化を階段状のグラフで示したものであり、階段状のグラフ(a) が丸め処理前の板厚の変化を示し、階段状グラフ(b) が丸め処理後の板厚の変化を示す。
【0084】
グラフ(a) に示すように丸め処理前では、成品板厚H0から溯って計算したJパス目の出側板厚H(J)は圧延開始板厚Hsより薄く、Jパス目の入側板厚H(J+1)は圧延開始板厚HsよりΔH厚い。この過剰圧下量ΔHを吸収すべく、Jmaxパス目からJパス目までの各々のパスに予め設定されている所定の規則にしたがって過剰圧下量ΔHを振り分ける丸め処理を行ったのがグラフ(b) である。グラフ(b) はグラフ(a) に比べてJmaxパス目以降の板厚がそれぞれ丸め処理前の板厚より薄くなっており、丸め処理後のJパス目の入側板厚H’(J+1)は圧延開始厚Hsに一致する。
【0085】
以上の処理によって、前段の全負荷パスが決定し、全パススケジュールが求められる。
【0086】
【実施例】
表1に示す可逆式圧延機を用いて本発明例にしたがって圧延を行った。なお、前提条件は、スラブサイズ:板厚105mm×板幅2084mm×板長2000mm、製品サイズ:板厚5.76mm×板幅2084mm×板長41100mm、製品板クラウン:0.1mm、途中パス許容急峻度:−2.0%、最終パス狙い急峻度:0.0%、最大許容荷重5000tonf、最大許容トルク:600tonf・m、仕上温度750℃に設定している。
【0087】
また比較例として、従来法を用いて上記条件と同一条件にてパススケジュールを算出し、圧延を行った。
【0088】
表3は全10回のパスにおける出側板厚、圧延荷重、トルク、及び急峻度をパス毎に示したものであり、表3においてJmaxパスは4パス目である。
【0089】
すなわち1パス目から3パス目までが全負荷パス、4パス目から10パス目までが形状調整パスにあたる。
【0090】
本発明例では、最終パスを除く形状調整パスの急峻度はほぼ設定した急峻度(−2.0%)となっており、また最終パス完了後の急峻度もほぼ狙い通りフラットの製品となっている。
【0091】
一方従来例では、形状調整パスの急峻度は設定と大きくずれており、最終パスの急峻度も−2%を超え、次工程にて手入れ作業を余儀なくされた。
【0092】
計算機の負荷については、本発明例は従来例に比較し約50%の計算時間短縮ができた。
【0093】
【表3】
Figure 0004099915
【0094】
【発明の効果】
本発明の制御方法により、可逆式圧延機による金属板材圧延のパススケジュールの計算時間を大幅に短縮することができ、安価な制御用計算機で高能率の圧延が可能になる。また、後段の形状調整パスでの急峻度予測の精度が向上し、絞り込み等の事故防止を図るとともに、最終製品の平坦度が向上し、品質の向上を図ることができる。
【図面の簡単な説明】
【図1】本発明の圧延条件算出装置を適用した可逆式圧延機を示す模式図である。
【図2】本発明の圧延条件算出装置を示すブロック図である。
【図3】形状換算計数aを、特公昭61−32086号公報に記載された方法に基づきプロットした結果を示すグラフである。
【図4】圧延パラメータXに対して形状換算係数aの関係を示すグラフである。
【図5】本発明に係る計算式を用いて計算した計算急峻度と、実測急峻度の関係を示すグラフである。
【図6】本発明の計算処理内容を示すフローチャートである。
【図7】本発明の圧延条件算出方法における圧下量を調整する丸め処理を概念的に示す説明図である。
【図8】特公昭61−32086号公報に開示された圧延条件の算出方法を説明するグラフである。
【符号の説明】
10:プロセスコンピュータ
11:被圧延材
12:第1テーブルローラ
13:第2テーブルローラ
14:ワークロール
14a:回転軸
15:バックアップロール
16:圧延機
20:圧延条件算出装置
21:CPU
22:ハードディスク
23:RAM
24:入力手段
25:出力手段
26:通信インターフェース[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a control method for a reversible rolling mill when a metal plate is rolled from a starting plate thickness to a target plate thickness in a plurality of passes.
[0002]
[Prior art]
Hereinafter, a thick steel plate will be described as an example of the metal plate material. In rolling thick steel plates using a reversible rolling mill, it is important to finish the steel plate into a flat shape with a small number of passes. To reduce the number of passes, it is effective to increase the rolling load. However, if the rolling load is increased, the work roll will bend and the end of the plate width will be excessively rolled, resulting in a shape defect called ear waves. To do.
[0003]
If such a shape defect occurs, troubles such as narrowing occur during rolling, which will impede productivity, and if it occurs after the final pass is completed, extra work such as care will occur in the next process In addition, the manufacturing cost increases.
[0004]
The steepness shown in the following formula (5) is used as an indicator of the degree of shape defects such as an ear wave that is generated when the end of the plate is excessively stretched, and conversely that the middle portion of the plate width that is excessively stretched is generated. A degree λ is used.
[0005]
λ = t / l (5)
Where t is the wave height and l is the wavelength.
[0006]
Further, the aforementioned bending of the work roll causes a deviation in the width direction of the plate thickness in addition to the occurrence of the shape defect.
[0007]
A plate crown Cr represented by the following equation (6) is used as an index indicating the degree of the thickness deviation in the width direction.
[0008]
Cr = Hc−He (6)
However, Hc is the plate thickness at the center in the width direction, and He is the plate thickness at the width end.
[0009]
Usually, in order to reduce the plate crown generated by the bending of the work roll, the roll diameter in the barrel direction of the work roll is not constant, but is formed into a shape having a larger diameter at the center than at the end. This diameter difference in the barrel direction of the work roll is called a work roll crown, and is defined by the difference in diameter between the center and the end of the barrel.
[0010]
In order to prevent shape defects and perform rolling with a small number of passes, in the previous pass where the plate thickness of the material to be rolled is thick, the rolling load is increased to reduce the number of passes, and the plate thickness becomes thin and shape defects occur. In an easy subsequent pass, the rolling load is reduced to adjust the material to be rolled into a flat shape. For this purpose, a pass schedule in which rolling conditions such as rolling load are set for each pass must be calculated.
[0011]
As a method for calculating the rolling conditions for each pass, the following method is disclosed in Japanese Patent Publication No. 61-32086.
[0012]
FIG. 8 is a graph for explaining the rolling condition calculation method disclosed in the publication. In this figure, the plate thickness and the plate crown for rolling to the target plate thickness of Hn in n passes, with the plate thickness of the material to be rolled on the horizontal axis and the plate crown of the material to be rolled on the vertical axis. Shows the relationship.
[0013]
The Δ mark in the figure shows the relationship between the plate thickness and the plate crown when rolling is performed with the maximum load within the allowable value of the rolling mill in the previous pass. This calculation method uses the following equation (7) from the starting plate thickness Hs to obtain the exit side plate thickness H (i) for the i-th pass with respect to the allowable maximum load P (i) in each pass, and uses the equation (8). Then, the outlet thickness H (i) of the i-th pass with respect to the allowable maximum torque Tr (i) is obtained, the two outlet thicknesses H (i) are compared, and the larger outlet side thickness H (i) is targeted. And the i-th-pass exit plate crown Cr (i) is calculated from the exit plate thickness H (i) using the equation (9).
[0014]
Since the rolling condition is obtained based on the allowable maximum load or the allowable maximum torque, the pass at this stage is called the full load pass and is calculated in order from the first pass.
[0015]
P (i) = F 1 (H (i), H (i-1), Kfm (i), B) (7)
Where P (i) is the load of the i-th pass, H (i) is the thickness of the exit side of the i-th pass, and H (i-1) is the thickness of the entrance side of the i-th pass (the thickness of the exit side of the i-1th pass). Kfm is the deformation resistance of the i-th pass, and B is the plate width.
[0016]
Tr (i) = F 2 (P (i), H (i), H (i-1)) (8)
However, Tr (i) is the i-th pass torque.
[0017]
Cr (i) = F Three (P (i), B, Cwr) (9)
However, Cr (i) is a plate crown and Cwr is a work roll crown.
[0018]
The circles in FIG. 8 indicate the relationship between the plate thickness and the plate crown when rolled at the maximum load within a range in which the allowable steepness of the material to be rolled can be maintained in the subsequent pass. ), (9), and the following expressions (10) and (11), the exit plate thickness H (i) and the exit plate crown at which the steepness in each path is the maximum steepness λ (i) Cr (i) is calculated and plotted. This pass is called a shape adjustment pass and is calculated from the nth pass which is the final pass.
[0019]
Δγ (i) = Cr (i) / H (i) −Cr (i-1) / H (i-1) (10)
However, Δγ (i) is the plate crown ratio change of the i-th pass.
[0020]
λ (i) = F Four (H (i), B) × √ | Δγ (i) | (11)
However, λ (i) is the steepness of the i-th pass.
[0021]
Thus, in the reversible rolling mill, rolling is performed by the full load pass in the first pass, and by the shape adjustment pass in the second pass. A path that switches from the full load path to the shape adjustment path is called a connection path, and this is the (n-3) th path in FIG.
[0022]
The joint path obtained by the calculation of the total load path and the joint path obtained by the calculation of the shape adjustment path usually do not coincide with each other, and the joining conditions must be adjusted by adjusting the rolling conditions.
[0023]
That is, recalculation is performed by reducing the load applied in the full load path and the shape adjustment path. This recalculation is repeated until the connecting paths match as indicated by the mark ● in the figure, and the matched condition is set as the optimum path schedule.
[0024]
[Problems to be solved by the invention]
The method disclosed in Japanese Patent Publication No. 61-32086 has a problem in terms of calculation load.
[0025]
That is, for all paths, two types of calculations are required: a path schedule calculation in which all load paths are symmetric, and a path schedule calculation in which shape adjustment paths are symmetric. In order to round (match) the difference in the connection path, the calculation of the schedule for the full load path and the schedule calculation for the shape adjustment path is performed again for all paths. It is necessary to repeat several times until it disappears. For this reason, when the load required for calculation is large and the calculation time is long, and it is applied to an operation in which the starting plate thickness and / or the target plate thickness of the rolled material changes every time, such as rolling of a thick steel plate, the rolled material It is necessary to calculate the pass schedule every time, and the length of the calculation time may cause adverse effects such as an extension of the production cycle and monopolization of the calculation device.
[0026]
In addition, when applying to the reversible rolling process online by the conventional calculation method, there is a problem that a high-performance computer is required to shorten the calculation time, leading to an increase in system cost.
[0027]
The method disclosed in Japanese Patent Publication No. 61-32086 has the following problems.
[0028]
In the step of calculating the exit side plate crown Cr (i) from the target steepness in the shape adjustment pass, the function F with the plate thickness and the plate width as variables is the relationship between the plate crown ratio change Δγ and the steepness λ. Four (H (i), B), but in the actual operation, the prediction accuracy of these relational expressions is insufficient, and it is difficult to achieve the desired steepness, which is accompanied by the occurrence of shape defects. There is a risk of narrowing down.
[0029]
The present invention has been made to solve the above problems, and its problem is to reduce the calculation load and make effective use of the control computer when adjusting the connecting path of the full load path and the shape adjustment path. Another object is to provide a control method for improving the control accuracy of a flat shape by introducing a high-accuracy steepness calculation model when calculating rolling conditions in a shape adjustment pass.
[0030]
[Means for Solving the Problems]
As described above, in order to increase the efficiency and keep the flat shape good in the rolling of thick steel plates, a path schedule composed of the full load path at the front stage and the shape control path at the rear stage is used.
[0031]
In that case, switching from the full load path schedule calculation due to the rolling mill capacity constraint to the shape control path schedule calculation constrained to a flat shape is performed in the connection path, and both conditions must be satisfied in the connection path.
[0032]
In the calculation method described in Japanese Patent Publication No. 61-32086, a method of adjusting both the full load path in the preceding stage and the shape control path in the subsequent stage is used in order to satisfy the rolling condition of the connecting path. Is big.
[0033]
The inventors of the present invention have conceived the following calculation method by paying attention to the fact that there is no restriction on the capacity of the rolling mill in the shape adjustment pass and that there is no restriction in the flat shape in the full load pass.
[0034]
First, the shape adjustment pass schedule in the subsequent stage is traced back from the final pass to the preceding pass, and calculated up to the pass immediately before the restriction of the rolling function force, thereby determining the shape adjustment pass schedule. Next, the pass entry side plate thickness is further determined by going back to the preceding pass within the range of the rolling functional force constraint. When the obtained entry side plate thickness exceeds the thickness of the material (thickness at the start of rolling), the number of passes of the full load pass is determined. At this time, the calculated thickness of the entrance side of the first pass is thicker than the material thickness. Therefore, the adjustment (rounding) is performed to reduce the amount of path reduction in each full-load path so that the thickness of the entrance side of the first pass is exactly equal to the material thickness. Do. Since this adjustment calculation is not limited by a flat shape, the calculation load is small.
[0035]
Thus, if the shape adjustment pass is determined first and only the rolling conditions of the full load pass are adjusted, there is no need to perform two kinds of calculations as in the method described in Japanese Patent Publication No. 61-32086. The load can be reduced. In addition, the relational expression between the plate crown ratio change Δγ and the steepness λ, which has been problematic in the method described in the above Japanese Patent Publication No. 61-32086, is a function equation considering not only the plate thickness and the plate width but also the material temperature. It is good to do. From this idea, I tried to formulate it further.
[0036]
The steepness λ is an index indicating the degree of shape defect after rolling, and as described in the literature ("Theory and Practice of Sheet Rolling" edited by the Japan Iron and Steel Institute, 1984, pp96), the width direction of strain in the sheet thickness direction. There is a correlation with the deviation, that is, the change in the plate crown ratio.
[0037]
The inventors first formulated a model that can accurately represent the relationship between the steepness λ and the plate crown ratio change by accurately analyzing the actual operation data that varies widely. .
[0038]
The relationship between the plate crown ratio change Δγ and the steepness λ under the same rolling conditions can be expressed by the following equation as described in the above document.
[0039]
λ = sign (Δγ) a√ | Δγ | (1)
a = E (X) (20)
Here, sign () is a function for changing the sign.
When Δγ <0, sign (Δγ) = − 1,
When Δγ> 0, sign (Δγ) = + 1,
Δγ = (CO / HO)-(CI / HI) (4)
HO is the exit side plate thickness, HI is the entry side plate thickness, CO is the exit side plate crown, and CI is the entry side plate crown. Usually, HO and HI are plate thicknesses in the center of the width. Moreover, a is a coefficient which shows the easiness of generation | occurrence | production of the shape defect called a shape conversion coefficient, and is a function of rolling conditions (rolling parameter: X).
[0040]
The relationship between the change in the plate crown ratio and the steepness varies greatly depending on the dimensions of the material to be rolled and the rolling conditions. In order to accurately formulate the shape conversion coefficients of the equations (1) and (20), the present inventors used a reversible rolling mill having the specifications shown in Table 1 and performed rolling experiments under a wide range of conditions as shown in Table 2. Carried out.
[0041]
[Table 1]
Figure 0004099915
[0042]
[Table 2]
Figure 0004099915
[0043]
FIG. 3 is a graph showing the result of plotting the shape conversion count a based on the method (conventional method) described in Japanese Patent Publication No. 61-32086. In the figure, the vertical axis represents the shape conversion count a, and the horizontal axis represents the rolling parameter X ′ (= sheet width B / entrance side plate thickness HI) used in the conventional method. FIG. 3 shows that the rolling conversion factor X ′ used in the conventional method results in a large variation in the shape conversion coefficient, and the correlation between the rolling conversion factor a and the rolling parameter X ′ is small.
[0044]
In other words, since the conventional method cannot accurately represent the relationship between the change in the plate crown ratio and the steepness, a rolling shape defect such as an ear wave has occurred during rolling, and operation troubles such as narrowing have occurred frequently. all right.
[0045]
The present inventors analyzed the results of FIG. 3 in more detail and extracted rolling condition factors that affect the shape conversion factor.
[0046]
As a result, it has been found that the shape conversion factor a is governed by four conditions of the entry side plate thickness, the exit side plate thickness, the plate width, and the rolling temperature. The thinner the entry / exit side plate thickness, the wider the plate width, the lower the reduction rate. It was found that the shape conversion factor a increases as the rolling temperature decreases and the rolling temperature decreases. That is, in order to predict the rolling shape with high accuracy, the rolling parameter X must be defined in consideration of the outlet side plate thickness and the rolling temperature in addition to the variables of the inlet side plate thickness and the plate width used in the conventional method. .
[0047]
The present inventors define the rolling parameter X as a function F of the inlet side plate thickness HI, the outlet side plate thickness HO, the plate width B, and the rolling temperature T, and the following equation (30)
X = F (R, B, HI, HO, T) (30)
In this way, the shape conversion coefficient was formulated.
[0048]
Furthermore, the following equation (31) was determined as a specific function equation of equation (30).
[0049]
[Expression 2]
Figure 0004099915
[0050]
Here, G (T) is a coefficient representing the deformation resistance of the material obtained as an empirical formula, and is a polynomial of T (a 0 + A 1 T + a 2 T 2 ) Or a fraction of a polynomial {(b 0 + B 1 T + b 2 T 2 ) / (A 0 + A 1 T + a 2 T 2 )} Etc.
[0051]
FIG. 4 is a graph showing the relationship of the shape conversion coefficient a to the rolling parameter X. As shown in the figure, the shape conversion factor a can be arranged by the parameter X regardless of the material dimensions and rolling conditions. The shape conversion coefficient was formulated as shown in Equation (21) by performing least square regression on the results shown in FIG.
[0052]
a = A (Xb) C (twenty one)
Here, A, b, and C are constants.
[0053]
In addition to the function described in equation (21), several functional types are conceivable, but here we will explain with examples using the most accurate equation (21) after detailed examination. To do.
[0054]
FIG. 5 is a graph showing the relationship between the calculated steepness calculated using the equations (1), (21), and (31) of the present invention and the measured steepness. As shown in the figure, the calculated value and the actually measured value coincide with each other with an accuracy of ± 0.5%, and it is understood that the steepness can be predicted.
[0055]
This study makes it possible to predict the steepness, which has been difficult in the past, with high accuracy, and to design the rolling pass schedule described below with high accuracy, improving the rolling efficiency and preventing flat defects. Got a prospect.
[0056]
The present invention has been made on the basis of the above findings, and the gist thereof is in the following (1) and (2).
[0057]
(1) When calculating the pass schedule in rolling control of a metal sheet with a reversible rolling mill, the relationship between the steepness λ and the sheet crown ratio change Δγ is expressed by the following expressions (1), (20) and (30) Thus, a formula for calculating the steepness λ is created in advance, the target steepness is set within the flatness constraint allowed for each pass, and the path from the final pass to the target thickness is the front pass. The rolling condition of each pass is calculated sequentially using the steepness calculation formula toward the direction, and when the rolling condition exceeds the allowable value of the rolling mill given in advance, the rolling condition of the pass is within the allowable value. A reversible formula that adjusts the rolling conditions of the recalculated path to absorb the difference between the inlet side thickness and the starting thickness when the entry side thickness of the pass becomes thicker than the rolling start thickness. Control method of rolling mill.
[0058]
λ = sign (Δγ) a√ | Δγ | (1)
a = E (X) (20)
X = F (R, B, HI, HO, T) (30)
Δγ = (CO / HO)-(CI / HI) (4)
Here, sign () is a function for changing the sign,
When Δγ <0, sign (Δγ) = − 1,
When Δγ> 0, sign (Δγ) = + 1,
Where R is the work roll radius, B is the plate width, HO is the exit plate thickness, HI is the entry plate thickness, CO is the exit plate crown, CI is the entry plate crown, and T is the rolling temperature.
[0059]
(2) In the pass schedule calculation when rolling a plate with a reversible rolling mill, the relationship between the steepness λ and the plate crown ratio change Δγ should be expressed by the following equations (1), (21) and (31) To create a formula for calculating the steepness λ in advance, set the target steepness within the flatness constraint allowed for each pass, and change from the final pass to the front pass with the target plate thickness as the outgoing plate thickness. Then, the rolling conditions of each pass are calculated sequentially using the steepness calculation formula, and when the rolling conditions exceed the allowable value of the rolling mill given in advance, the rolling conditions of the pass are kept within the allowable value. Reversible rolling to adjust the rolling conditions of the recalculated pass to absorb the difference between the entry side plate thickness and the starting plate thickness when the entry side plate thickness of the pass becomes thicker than the rolling start thickness. How to control the machine.
[0060]
λ = sign (Δγ) a√ | Δγ | (1)
a = A (Xb) C (twenty one)
[0061]
[Equation 3]
Figure 0004099915
[0062]
Δγ = (CO / HO)-(CI / HI) (4)
Here, sign () is a function for changing the sign,
When Δγ <0, sign (Δγ) = − 1,
When Δγ> 0, sign (Δγ) = + 1,
Where R is the work roll radius, B is the plate width, HO is the exit side plate thickness, HI is the entrance side plate thickness, CO is the exit side plate crown, CI is the entry side plate crown, T is the rolling temperature, and G (T) is the temperature T. The functions A, b and C are constants.
[0063]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a schematic diagram showing a reversible rolling machine to which a rolling condition calculation apparatus of the present invention is applied. In the figure, reference numeral 10 is a process computer, 11 is a material to be rolled, 12 is a first table roller having a plurality of rolls, 13 is a second table roller, 14 is a pair of upper and lower work rolls, 14a is a rotation axis of the work roll 14 , 15 is a pair of upper and lower backup rolls, and 20 is a rolling condition calculation device for giving a calculation result to the process computer 10. Facilities used for rolling, such as the work roll 14, are collectively referred to as a rolling mill 16.
[0064]
By rotating the first table roller, the second table roller, and the work roll 14 in the same direction, the material to be rolled 11 is moved from the first table roller 12 side to the second table roller 13 side or from the second table roller 13 side. It is conveyed to the first table roller 12 side. At this time, when the material to be rolled 11 is rolled with the work roll 14, one rolling is referred to as one pass.
[0065]
The material to be rolled 11 is repeatedly rolled by reciprocating the rolling mill 16 a predetermined number of times, and the material to be rolled 11 is finished to a target plate thickness. Each control device of the rolling mill 16 is controlled by the process computer 10, and the control of the process computer 10 is based on a pass schedule transmitted from the rolling condition calculation device 20.
[0066]
FIG. 2 is a block diagram showing the rolling condition calculation apparatus of the present invention. The rolling condition calculation device 20 includes a CPU 21 that executes a program for calculating rolling conditions for each pass. The CPU 21 temporarily stores data such as a hard disk 22 that records information such as programs and data, and data generated during the processing of the CPU 21. Are connected to the RAM 23, input means 24 such as a mouse and keyboard, output means 25 such as a monitor and printer, and a communication interface 26 for transmitting the calculated rolling conditions to the process computer 10. The determined pass schedule may also be output from the output means 25 so that the operator can check the calculation result.
[0067]
FIG. 6 is a flowchart showing the contents of calculation processing of the present invention. In the figure, each processing step is described as S1, S2,.
[0068]
In S1, the input of the target plate thickness H0 and the target plate crown Cr0 used for the calculation is received, and in S2, the exit side plate thickness H (1) and the exit side plate crown Cr (1) are set and the paths counted from the final pass are counted. “1” is initially set in the counter J indicating the number of times.
[0069]
Next, each path calculation that goes back in order from the succeeding path from S3 is entered. In S3, equation (8): Cr (i) = F Three Using (P (i), B, Cwr), the rolling load P (J) for the J pass is calculated from the exit side plate crown Cr (J) for the J pass, the plate width B, and the work roll crown Cwr. Since J = 1 at the first stage, the rolling load P (1) is calculated from the numerical values of the parameters such as the product sheet crown Cr (1) in the final pass.
[0070]
In S4, using (6): P (i) = F (H (i), H (i-1), Kfm, B), the exit side plate thickness H (J) and rolling load P (J ), The deformation resistance Kfm (J), and the plate width B, the entry side plate thickness H (i + 1) of the J-th pass is calculated. Since J = 1 at the first stage, the entry side plate thickness of the final pass, that is, the exit side plate thickness one before the final pass is calculated.
[0071]
Next, in S5, the rolling load P (J) of the J pass and the J pass using the equation (7): Tr (i) = F2 (P (i), H (i), H (i-1)) The rolling torque Tr (J) of the J pass is calculated from the entry side plate thickness H (i + 1) of the eye and the exit side plate thickness H (J) of the J pass.
[0072]
In S6, the rolling load P (J) and the rolling torque Tr (J) calculated in S3 to S5 so far, and the reduction amount H (J + 1) −H (J It is determined whether all the rolling conditions are within the allowable values of the reversible rolling mill set in advance. If the values of all the rolling conditions are within the preset allowable values of the reversible rolling mill, it is determined that the rolling setting for the J pass is possible in terms of equipment capacity (Y branch of S6). In the vicinity of the final pass, that is, the shape adjustment pass, it is normally within the allowable value of the rolling mill (Yes branch).
[0073]
In S6, if any one of the values of the rolling load P (J), the rolling torque Tr (J), and the reduction amount H (J + 1) −H (J) deviates from the allowable value of the reversible rolling mill, It is determined that the rolling setting for the pass is impossible due to the equipment capacity (No branch in S6). This case usually occurs in the pass after the start of rolling, that is, the full load pass.
[0074]
In that case, the pass number J is stored as a limit pass Jmax in S7. The limit path Jmax corresponds to a connection path of the method disclosed in Japanese Patent Publication No. 61-32086.
[0075]
Next, in S8, the entry side plate thickness H (J + 1) is reduced so that the rolling load P (J), the rolling torque Tr (J), and the reduction amount H (J + 1) −H (J) are reduced. Recalculation is performed so as to obtain the maximum entry side thickness H (J + 1) in which all the values are within the allowable value. In this recalculation, the value of the item deviating from the permissible value should be set to the permissible value, and the entry side thickness H (J + 1) may be obtained. The number of calculations does not increase significantly.
[0076]
In S9, it is determined whether the entry side plate thickness H (J + 1) is larger than the rolling start plate thickness Hs. The entry side plate thickness H (J + 1) is larger than the rolling start plate thickness Hs in the full load pass, and the determination result is Yes when the recalculation of S8 is performed. This determination is an end condition determination for each path calculation.
[0077]
If the entry side plate thickness H (J + 1) is smaller than the rolling start plate thickness Hs in S9 (No branch of S9), it is determined that J + 1 or more rollings are necessary.
[0078]
In S10, equation (8): Δγ (i) = Cr (i) / H (i) −Cr (i−1) / H (i−1), equation (11), equation (21), and (31 ) Type steepness calculation model, the exit side plate thickness H (J), the exit side plate crown Cr (J), the entrance side plate thickness H (J + 1), and the allowable steepness λ (J), the entrance side plate crown Cr (J + 1) Is calculated.
[0079]
In the calculation in S10, the relationship of Cr (J + 1)> Cr (J) always holds, and in the equation (8) in S3, Cr (J) is proportional to P (J) and is always P (J + 1)> P (J ), And the rolling load P (J) increases in the direction in which the counter J increases, that is, from the subsequent pass to the preceding pass. Accordingly, in the calculation after the Jmax pass, all passes exceed the allowable value of the rolling load P (J) and / or the rolling torque Tr (J) in S6, and recalculation is performed in S8. For this reason, the path on the leading side from the Jmax path corresponds to the full load path of the method disclosed in Japanese Patent Publication No. 61-32086, and the path on the following side corresponds to the shape adjustment path.
[0080]
In S11, “1” is added to the counter J, and the process returns to S3 to calculate the rolling condition for one preceding pass.
[0081]
If the entry side plate thickness H (J + 1) is larger than the rolling start plate thickness Hs in S9 (Yes branch of S9), it is determined that the rolling is completed J times, and S12 is reached.
[0082]
In S12, from the Jmax pass set to reduce the maximum load by recalculation in S8 in order to absorb the excessive reduction amount ΔH which is the difference between the entry side thickness H (J + 1) and the rolling start thickness Hs. The excess reduction amount ΔH is absorbed by distributing the excess reduction amount ΔH (= H (J + 1) −Hs) in accordance with a predetermined rule set in advance to each path (all load paths) up to the J-th pass, A rounding process is performed to adjust the amount of reduction from the Jmax pass to the J pass.
[0083]
FIG. 7 is an explanatory diagram conceptually showing a rounding process for adjusting the reduction amount in the rolling condition calculation method of the present invention. In FIG. 7, the vertical axis indicates the plate thickness, and the change in the plate thickness from the rolling start plate thickness Hs to the product plate thickness H0 is shown in a stepped graph. The stepped graph (a) is rounded. The change in plate thickness before is shown, and stepped graph (b) shows the change in plate thickness after rounding.
[0084]
As shown in the graph (a), before the rounding process, the exit side plate thickness H (J) calculated from the product plate thickness H0 is thinner than the rolling start plate thickness Hs, and the entrance side plate thickness H of the J pass. (J + 1) is ΔH thicker than the rolling start plate thickness Hs. Graph (b) is a graph (b) in which the excessive reduction amount ΔH is distributed according to a predetermined rule set in advance in each pass from the Jmax pass to the J pass in order to absorb this excessive reduction amount ΔH. It is. In the graph (b), the plate thickness after the Jmax pass is thinner than the plate thickness before the rounding process compared to the graph (a), and the entry side plate thickness H ′ (J + 1) of the J pass after the rounding processing is It corresponds to the rolling start thickness Hs.
[0085]
Through the above processing, the full load path in the previous stage is determined, and the full path schedule is obtained.
[0086]
【Example】
Using the reversible rolling mill shown in Table 1, rolling was performed according to the example of the present invention. The preconditions are: slab size: plate thickness 105 mm × plate width 2084 mm × plate length 2000 mm, product size: plate thickness 5.76 mm × plate width 2084 mm × plate length 41100 mm, product plate crown: 0.1 mm, midway path allowable steepness Degree: -2.0%, steepness aiming at final pass: 0.0%, maximum permissible load 5000tonf, maximum permissible torque: 600tonf · m, finishing temperature 750 ° C.
[0087]
As a comparative example, a pass schedule was calculated using the conventional method under the same conditions as described above, and rolling was performed.
[0088]
Table 3 shows the exit side plate thickness, rolling load, torque, and steepness for each pass in all 10 passes. In Table 3, the Jmax pass is the fourth pass.
[0089]
That is, the first to third passes correspond to the full load pass, and the fourth to tenth passes correspond to the shape adjustment pass.
[0090]
In the example of the present invention, the steepness of the shape adjustment path excluding the final pass is almost the set steepness (−2.0%), and the steepness after completion of the final pass is a flat product almost as intended. ing.
[0091]
On the other hand, in the conventional example, the steepness of the shape adjustment pass is greatly different from the setting, and the steepness of the final pass exceeds -2%, which necessitates maintenance work in the next process.
[0092]
Regarding the load on the computer, the calculation time of the present invention example was reduced by about 50% compared to the conventional example.
[0093]
[Table 3]
Figure 0004099915
[0094]
【The invention's effect】
According to the control method of the present invention, it is possible to greatly reduce the calculation time of the pass schedule for rolling a metal sheet using a reversible rolling mill, and it is possible to perform highly efficient rolling with an inexpensive control computer. In addition, the accuracy of the steepness prediction in the subsequent shape adjustment pass can be improved to prevent accidents such as narrowing down, the flatness of the final product can be improved, and the quality can be improved.
[Brief description of the drawings]
FIG. 1 is a schematic diagram showing a reversible rolling machine to which a rolling condition calculation apparatus of the present invention is applied.
FIG. 2 is a block diagram showing a rolling condition calculation apparatus according to the present invention.
FIG. 3 is a graph showing the results of plotting the shape conversion count a based on the method described in Japanese Patent Publication No. 61-32086.
FIG. 4 is a graph showing a relationship of a shape conversion coefficient a with respect to a rolling parameter X.
FIG. 5 is a graph showing the relationship between the calculated steepness calculated using the calculation formula according to the present invention and the measured steepness.
FIG. 6 is a flowchart showing details of calculation processing according to the present invention.
FIG. 7 is an explanatory diagram conceptually showing a rounding process for adjusting a reduction amount in the rolling condition calculation method of the present invention.
FIG. 8 is a graph for explaining a calculation method of rolling conditions disclosed in Japanese Patent Publication No. 61-32086.
[Explanation of symbols]
10: Process computer
11: Rolled material
12: First table roller
13: Second table roller
14: Work roll
14a: Rotating shaft
15: Backup roll
16: Rolling mill
20: Rolling condition calculation device
21: CPU
22: Hard disk
23: RAM
24: Input means
25: Output means
26: Communication interface

Claims (2)

可逆式圧延機による金属板材の圧延制御におけるパススケジュール計算をする際、急峻度λと板クラウン比率変化Δγとの関係を下記の(1) 、(20)および(30)式で表すことによって、急峻度λの計算式を予め作成しておき、各パスで許容される平坦度制約内で目標急峻度を設定し、目標板厚を出側板厚とする最終パスから前方側のパスに向かって順次前記急峻度計算式を用いて各パスの圧延条件を計算し、前記圧延条件が予め与えられた圧延機の許容値を超える場合には、当該パスの圧延条件を許容値内に納めるべく再計算し、当該パスの入側板厚が圧延開始厚より厚くなったときに、入側板厚および開始板厚の差を吸収すべく、前記再計算したパスの圧延条件を調整することを特徴とする可逆式圧延機の制御方法。
λ=sign(Δγ)a√|Δγ| (1)
a=E(X) (20)
X=F(R,B,HI,HO,T) (30)
Δγ=(CO/HO)-(CI/HI) (4)
ここで、sign()は符号を付け替える関数で、
Δγ<0の時、sign(Δγ)=−1、
Δγ>0の時、sign(Δγ)=+1、
であり、Rはワークロール半径、Bは板幅、HOは出側板厚、HIは入側板厚、COは出側板クラウン、CIは入側板クラウン、Tは圧延温度である。
When calculating the pass schedule in the rolling control of the metal plate material by the reversible rolling mill, the relationship between the steepness λ and the plate crown ratio change Δγ is expressed by the following formulas (1), (20) and (30): Create a formula for calculating the steepness λ in advance, set the target steepness within the flatness constraint allowed for each pass, and move from the final pass to the front pass with the target plate thickness as the outgoing plate thickness The rolling conditions for each pass are calculated sequentially using the steepness calculation formula, and if the rolling conditions exceed the allowable value of the rolling mill given in advance, the rolling conditions for that pass are re-established within the allowable value. Calculate and adjust the rolling condition of the recalculated pass to absorb the difference between the entry side plate thickness and the start plate thickness when the entry side plate thickness of the pass becomes thicker than the rolling start thickness. Control method for reversible rolling mill.
λ = sign (Δγ) a√ | Δγ | (1)
a = E (X) (20)
X = F (R, B, HI, HO, T) (30)
Δγ = (CO / HO)-(CI / HI) (4)
Here, sign () is a function for changing the sign,
When Δγ <0, sign (Δγ) = − 1,
When Δγ> 0, sign (Δγ) = + 1,
Where R is the work roll radius, B is the plate width, HO is the exit plate thickness, HI is the entry plate thickness, CO is the exit plate crown, CI is the entry plate crown, and T is the rolling temperature.
可逆式圧延機による金属板材の圧延制御におけるパススケジュール計算をする際、急峻度λと板クラウン比率変化Δγとの関係を下記の(1) 、(21)および(31)式で表すことによって、急峻度λの計算式を予め作成しておき、各パスで許容される平坦度制約内で目標急峻度を設定し、目標板厚を出側板厚とする最終パスから前方側のパスに向かって順次前記急峻度計算式を用いて各パスの圧延条件を計算し、前記圧延条件が予め与えられた圧延機の許容値を超える場合には、当該パスの圧延条件を許容値内に納めるべく再計算し、当該パスの入側板厚が圧延開始厚より厚くなったときに、入側板厚および開始板厚の差を吸収すべく、前記再計算したパスの圧延条件を調整することを特徴とする可逆式圧延機の制御方法。
λ=sign(Δγ)a√|Δγ| (1)
a=A(X-b)C (21)
Figure 0004099915
Δγ=(CO/HO)-(CI/HI) (4)
ここで、sign()は符号を付け替える関数で、
Δγ<0の時、sign(Δγ)=−1、
Δγ>0の時、sign(Δγ)=+1、
であり、Rはワークロール半径、Bは板幅、HOは出側板厚、HIは入側板厚、COは出側板クラウン、CIは入側板クラウン、Tは圧延温度、G(T)は温度Tの関数、A、bおよびCは定数である。
When calculating the pass schedule in rolling control of a metal sheet with a reversible rolling mill, the relationship between the steepness λ and the sheet crown ratio change Δγ is expressed by the following formulas (1), (21) and (31): Create a formula for calculating the steepness λ in advance, set the target steepness within the flatness constraint allowed for each pass, and move from the final pass to the front pass with the target plate thickness as the outgoing plate thickness The rolling conditions for each pass are calculated sequentially using the steepness calculation formula, and if the rolling conditions exceed the allowable value of the rolling mill given in advance, the rolling conditions for that pass are re-established within the allowable value. Calculate and adjust the rolling condition of the recalculated pass to absorb the difference between the entry side plate thickness and the start plate thickness when the entry side plate thickness of the pass becomes thicker than the rolling start thickness. Control method for reversible rolling mill.
λ = sign (Δγ) a√ | Δγ | (1)
a = A (Xb) C (21)
Figure 0004099915
Δγ = (CO / HO)-(CI / HI) (4)
Here, sign () is a function for changing the sign,
When Δγ <0, sign (Δγ) = − 1,
When Δγ> 0, sign (Δγ) = + 1,
Where R is the work roll radius, B is the plate width, HO is the exit side plate thickness, HI is the entrance side plate thickness, CO is the exit side plate crown, CI is the entry side plate crown, T is the rolling temperature, and G (T) is the temperature T. The functions A, b and C are constants.
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