JP3821665B2 - Sheet crown prediction method and hot rolling method in hot rolling - Google Patents

Description

ただし，前記（Ａ）式において，ζ及びηは，各々予め与えられる前記メカニカルクラウンＣ_Mの転写率及び前記パス前板のクラウンＣｒ_inの転写率であり，前記（Ｂ）式において，α_P，α_B，α_CW，α_CB，α_CHは，各々前記メカニカルクラウンＣ_Mへの影響係数であり，前記被圧延材の幅Ｗ，前記圧延荷重Ｐ，前記ワークロールの直径Ｄ_w，前記バックアップロールの直径Ｄ_B，次のパスとその前のパスとの前記被圧延材の幅の差ΔＷ，及び前記ロール形状可変機構により決定される前記バックアップロールのプロフィル形状を表す無次元パラメータτのうち，少なくとも１つ以上のパラメータの関数である。
【００１０】
さらに，前記各影響係数α_P，α_B，α_CW，α_CB，α_CHを，前記パラメータＷ，Ｐ，Ｄ_w，Ｄ_B，ΔＷ，τの以下の各関数としてもよい。
α_P ＝Ｆα_P（Ｗ，Ｐ，Ｄ_w，τ）
α_B ＝Ｆα_B（Ｗ，Ｐ，Ｄ_B，τ）
α_CW＝Ｆα_CW（Ｗ，Ｐ）
α_CB＝Ｆα_CB（Ｗ，Ｐ）
α_CH＝Ｆα_CH（Ｗ，Ｐ，ΔＷ）
【００１１】
また，前記各関数Ｆα_P，Ｆα_B，Ｆα_CW，Ｆα_CB，Ｆα_CHを，複数の圧延条件下において，前記接触領域情報を仮定し，該仮定に基づき分割モデルにより前記ワークロールと前記バックアップロールとの間の軸方向の接触荷重分布を計算し，該接触荷重分布に負の値の接触荷重が存在する場合は前記接触領域情報の仮定を修正して前記接触荷重分布の計算を順次繰り返し，前記接触荷重分布に負の値の前記接触荷重が存在しなくなった場合に，該接触荷重分布の計算結果に基づいて前記パス後の板クラウンのサンプル値を計算し，前記複数の圧延条件下で求めた前記サンプル値の重回帰分析に基づいて決定することが考えられる。
【００１２】
また，熱間圧延における前記板クラウン予測方法を用いた熱間圧延方法として捉えたものも考えられる。
即ち，前記ベンディング機構によるベンディング力及び前記ロール形状可変機構による前記バックアップロールのプロフィル形状を仮定し，該仮定に基づいて，前記板クラウン予測方法により決定される板クラウン予測式によりパス後の板クラウンＣｒ_outを計算し，該パス後の板クラウンＣｒ_outと予め設定された目標板クラウンとの差が所定の誤差範囲内にない場合は，前記ベンディング力及び前記バックアップロールのプロフィル形状の少なくとも一方の仮定を修正して前記板クラウン予測方法による前記パス後の板クラウンの計算を順次繰り返し，前記差が前記誤差範囲内となった場合に，そのときの前記ベンディング力及び前記バックアップロールのプロフィル形状を前記圧延装置に設定する熱間圧延方法である。
【００１３】
【発明の実施の形態】
以下添付図面を参照しながら、本発明の実施の形態について説明し、本発明の理解に供する。尚、以下の実施の形態は、本発明を具体化した一例であって、本発明の技術的範囲を限定する性格のものではない。
ここに、図１は一般的な熱間圧延に用いられる圧延装置の構成例を示す図，図２は一般的な熱間圧延に用いられる圧延装置のロール両端部に非接触領域が生じた場合を示す図，図３は一般的な圧延方法の手順を示すブロック図，図４は本発明の実施の形態に係る板クラウン予測方法に用いられる板クラウン予測式を求める手順を示すフローチャート，図５は本発明の実施の形態に係る板クラウン予測方法に用いられるバックアップロールのプロフィル形状を表す無次元パラメータについて説明するグラフ，図６は本発明の実施の形態に係る板クラウン予測方法を用いて計算した板クラウン計算値と従来手法により計算した板クラウン計算値とを比較する図である。
【００１４】
本発明の実施の形態に係る板クラウン予測方法は，前述した図３に示す一般的な圧延方法において，Ｓ２１の板クラウン予測モデル３０に適用され，パス後の板クラウンＣｒ_outを計算するための板クラウン予測式（前記（１）式）に含まれる前記メカニカルクラウンＣ_Mの計算式に特徴を有するものである。従って，該メカニカルクラウンＣ_Mの計算式以外の範囲の計算方法等については，前記文献１に示されるものの他，周知のものがあるのでここでは説明を省略する。
【００１５】
本実施の形態に係る板クラウン予測方法に用いられる前記板クラウン予測式は，パス前及びパス後の各板クラウンＣｒ_in及びＣｒ_outと，被圧延材のパス前及びパス後の各板厚Ｈ_in及びＨ_outと，前記ワークロールのメカニカルクラウンＣ_Mとの関係を表す次式（Ａ）によって与えられる。これは，前記従来手法における（１）式と同じである。
Ｃｒ_out／Ｈ_out＝ζＣ_M／Ｈ_out＋ηＣｒ_in／Ｈ_in …（Ａ）
ここで，ζ及びηは，各々予め与えられる前記メカニカルクラウンＣ_Mの転写率及び前記パス前板のクラウンＣｒ_inの転写率である。このζ及びηの具体的内容については，例えば文献３（粟津ら：３３回塑性加工連合講演会講演論文集（１９８２）ｐ．１４３）等により周知であるのでここでは説明を省略する。
【００１６】
さらに，前記メカニカルクラウンＣ_Mは，圧延荷重Ｐ，ベンディング力Ｆ_B，ワークロールイニシャルクラウンＣ_RW，バックアップロールイニシャルクラウンＣ_RB，及びワークロールサーマルクラウンＣ_RHとの関係を表す次式（Ｂ）によって与えられる。

ここで，α_P，α_B，α_CW，α_CB，α_CHは，各々前記メカニカルクラウンＣ_Mへの影響係数である。（Ｂ）式が，前記従来手法における（２）式と異なる点は，前記ワークロールイニシャルクラウンＣ_RW，及び前記ワークロールサーマルクラウンＣ_RHの前記影響係数α_CW，α_CHを各々個別に設けた点である。
これにより，一般的にその形状が略放物線状となる前記ワークロールイニシャルクラウンＣ_RW，及び略台形状となる前記ワークロールサーマルクラウンＣ_RHが前記メカニカルクラウンＣ_Mに及ぼす影響ついて，その形状の違いにより生じる影響の違いを反映することができる。
【００１７】
また，前記影響係数α_P，α_B，α_CW，α_CB，α_CHは，次式（Ｃ１）〜（Ｃ５）に示される各関数で与える。
α_P ＝Ｆα_P（Ｗ，Ｐ，Ｄ_w，τ） …（Ｃ１）
α_B ＝Ｆα_B（Ｗ，Ｐ，Ｄ_B，τ） …（Ｃ２）
α_CW＝Ｆα_CW（Ｗ，Ｐ） …（Ｃ３）
α_CB＝Ｆα_CB（Ｗ，Ｐ） …（Ｃ４）
α_CH＝Ｆα_CH（Ｗ，Ｐ，ΔＷ） …（Ｃ５）
ここで，Ｗは被圧延材の幅，Ｐは前記圧延荷重，Ｄ_wは前記ワークロールの直径，Ｄ_Bは前記バックアップロールの直径，ΔＷは次のパスとその前のパスとの被圧延材の幅の差，τは前記ロール形状可変機構により決定される前記バックアップロールのプロフィル形状を表す無次元パラメータである。
【００１８】
ここで，図５を用いて，前記バックアップロールのプロフィル形状を表す無次元パラメータτについて説明する。
図５のグラフにおいて，Ｘ軸は前記バックアップロールの軸方向の中心からの距離，Ｙ軸（左側）は前記形状可変機構により前記バックアップロール２に変形を加えたときの表面の半径方向の変位量であり，変形を与えないときの位置を０（ゼロ）とした相対変位量である。図５に示す前記バックアップロール２は，変形を加えないフラットな状態を含め，そのプロフィル形状を１１段階に可変な可変機構を有する。
前記無次元パラメータτは，前記バックアップロール２に変形を与えないフラットな状態を０（ゼロ），最も変形量（表面の変位量）の大きい変形状態を１とし，その間の９段階の変形状態を０．１から０．９まで０．１刻みで表す（図５のＹ軸右側）ことにより，前記バックアップロールのプロフィル形状を無次元化したパラメータである。
これにより，前記バックアップロールのプロフィル形状の変化が前記メカニカルクラウンＣ_Mに与える影響を与える要素として，前記影響係数α_P，α_Bの各関数Ｆα_P，Ｆα_Bに含められるので，前記バックアップロール２のプロフィル形状毎に前記前記影響係数α_P，α_Bを個別に求める必要がなくなる。
【００１９】
また，前記影響係数α_P，α_B，α_CW，α_CB，α_CHを求める関数Ｆα_P，Ｆα_B，Ｆα_CW，Ｆα_CB，Ｆα_CHは，各々次式（Ｄ１）〜（Ｄ５）で与えられる。

ここで，ａ１〜ａ５，ｂ１〜ｂ５，ｃ１，ｃ２，ｄ５，ｔ１〜ｔ２は，未知係数であり，ｋ，ｌ，ｍ，ｎは，前記未知係数の所定の展開次数である。
これら未知係数を求めることにより，前記影響係数α_P，α_B，α_CW，α_CB，α_CHが求まり，その結果前記（Ｂ）式が求まり，さらに前記（Ａ）式，即ち，板クラウンの予測式が求まる。
【００２０】
次に，図４を用いて前記影響係数α_P，α_B，α_CW，α_CB，α_CHを求める手順について説明する。
ここで，図４の手順が開始される前に，予め定められた複数（１〜Ｎ）の圧延条件が与えられているものとする。
まず，複数の前記圧延条件の中から１番目（ｉ＝１）の前記圧延条件を選択（Ｓ１０１→Ｓ１０２）する。ここで前記圧延条件とは，パス前の板クラウンＣｒ_in，被圧延材４のパス前の温度Ｔ_i及び板形状，被圧延材４のパス前及びパス後の各板厚Ｈ_in及びＨ_out，被圧延材４の前記板幅Ｗ，前記ワークロール１のベンディング力Ｆ_B，前記ワークロール１及び前記バックアップロール２の各初期形状である。
【００２１】
次に，選択された前記圧延条件に基づいて，圧延開始時の前記ワークロールイニシャルクラウンＣ_RW，及び前記バックアップロールクラウンＣ_RBを計算（Ｓ１０３）する。
次に，前記圧延条件に基づいて，熱収支計算により当該圧延における被圧延材４のパス後の上昇温度を計算し，該上昇温度と，Ｓ１０３で求めた前記各イニシャルクラウンＣ_RW及びＣ_RBとに基づいて，前記サーマルプロフィルモデル３１を用いて前記バックアップロール１及び前記ワークロール２の各サーマルクラウンを計算（Ｓ１０４）する。
次に，Ｓ１０４で求めた前記各サーマルクラウンに基づいて，前記圧延荷重Ｐによる前記ワークロール１及び前記バックアップロール２の変形プロフィルを計算（Ｓ１０５）する。
前記Ｓ１０２〜Ｓ１０５の具体的内容については，前記文献２に示される他，周知であるのでここでは説明を省略する。
【００２２】
次に，Ｓ１０５で求められた前記各変形プロフィルに基づいて，前記ワークロール１と前記バックアップロール２との間の接触領域情報を仮定（Ｓ１０６）する。該仮定の初期状態は，例えば，前記ワークロール１と前記バックアップロール２とがオーバーラップする領域は全て接触するものとして仮定する等の方法が考えられる。
次に，前記接触領域情報により接触すると仮定した領域にのみ圧延荷重Ｐが作用するものとして，前記文献２等に示される前記分割モデルを用いて前記ワークロール１及び前記バックアップロール２の変形，前記ワークロール１と前記バックアップロール２との間の軸方向の接触荷重分布ｑ（ｘ）を計算（Ｓ１０７）する。（ｘは軸方向の位置を表す。）
次に，計算された前記接触荷重分布ｑ（ｘ）において，軸方向のいずれかの位置ｘにおける荷重が負の値になっている場合（Ｓ１０８のＹｅｓ側）は，Ｓ１０６で仮定した前記接触領域情報を変更（Ｓ１０９）した後，再度，前記接触荷重分布ｑ（ｘ）を計算（Ｓ１０７）する。ここで，前記接触領域情報の変更は，例えば，前記接触荷重分布ｑ（ｘ）に基づいて，その荷重値が所定の値以上である位置ｘのみが接触するものとして変更する等の方法が考えられる。
【００２３】
このようにして，前記接触荷重分布ｑ（ｘ）において，軸方向のいずれの位置ｘにも負の値の荷重が存在しなくなるまで，前記接触領域情報の変更及び前記接触荷重分布ｑ（ｘ）の計算（Ｓ１０９→Ｓ１０７）を繰り返す。
そして，軸方向のいずれの位置ｘにも負の値の荷重が存在しなくなった場合（Ｓ１０８のＮｏ側）に，そのときの前記接触荷重分布ｑ（ｘ）に基づいて，被圧延材の所定の評価点（例えば，板幅方向の中央部と両端部等）における板クラウンを計算（Ｓ１１０）する。
次に，順次別の前記圧延条件を選択（ｉ番目の圧延条件を選択，ｉ＝２，３，，，）して（Ｓ１１２→Ｓ１０２），前述したＳ１０３〜Ｓ１１０の手順を繰り返し，予め与えられた全ての前記圧延条件について前記板クラウンの計算値を求める（Ｓ１０２〜Ｓ１１１→Ｓ１１２）。
そして，このようにして求められた複数の前記板クラウンの計算値を，前記式（Ｄ１）〜（Ｄ５）を用いて重回帰処理を行うことにより，前記未知係数ａ１〜ａ５，ｂ１〜ｂ５，ｃ１，ｃ２，ｄ５，ｔ１〜ｔ２を求め，これにより前記影響係数α_P，α_B，α_CW，α_CB，α_CHが求まる（Ｓ１１３）。このとき，前記展開次数ｋ，ｌ，ｍ，ｎは，例えば２次とする。
【００２４】
次に，図６を用いて，前記従来手法により求めた板クラウンの予測式（（１）式，（２）式）を用いて計算した板クラウン計算値Ａと，図４に示す手順に従って求めた板クラウンの予測式（（Ａ）式，（Ｂ）式）を用いて計算した板クラウン計算値Ｂとを比較する。ここで，多数の圧延条件下における板クラウンの実測値を収集することは困難であるため，前記分割モデルにより厳密に計算したパス後の板クラウンの厳密解を実測値に代わるものとし，前記各板クラウンの計算値と前記厳密解との相関を評価した。
【００２５】
図６（ａ）に示すグラフは，前記従来手法により求めた前記（３）式の前記影響係数α_P ，α_B ，α_CWに基づいて，前記（１）式及び（２）式を用いて計算したパス後の板クラウンの計算結果ＡをＹ軸に，パス後の板クラウンの前記厳密解をＸ軸にとった散布図である。
また，図６（ａ）に示すグラフは，前記図４の手順に従い，前記（Ｄ１）〜（Ｄ５）式の展開次数ｋ，ｌ，ｍ，ｎを２次までとって前記影響係数α_P，α_B，α_CW，α_CB，α_CHを求め，これに基づいて前記（Ｂ）式及び（Ａ）式を用いて計算したパス後の板クラウンの計算結果ＢをＹ軸に，パス後の板クラウンの前記厳密解をＸ軸にとった散布図である。
図６（ａ），（ｂ）を比較して明らかなように，本発明による板クラウンの計算値Ｂの方が，前記従来手法による板クラウンの計算値Ａよりも，広範囲に渡って前記厳密解に近似していることがわかる。
また，図６（ｃ）は，図６（ａ），（ｂ）の各々について，前記厳密解に対する前記板クラウンの計算値Ａ，Ｂの各誤差を示した棒グラフである。本発明による板クラウンの計算値Ｂの誤差（２５．９μｍ）は，前記従来手法による板クラウンの計算値Ａの誤差（６７．１μｍ）の４０％以下に抑えられており，本発明による効果が大きいことがわかる。
また，このように予測精度の高い板クラウンの予測式（予測モデル）を，図３に示す板クラウン予測モデル３０に適用して圧延制御を行えば，板クラウンの品質が向上することは明らかである。
【００２６】
【発明の効果】
以上説明したように、本発明によれば，ワークロールとバックアップロールとの間に非接触領域が生じるような圧延条件下であっても，高精度で，かつ小さい計算負荷で板クラウンを予測でき，その結果，板クラウンの品質を向上することができる。
【図面の簡単な説明】
【図１】一般的な熱間圧延に用いられる圧延装置の構成例を示す図。
【図２】一般的な熱間圧延に用いられる圧延装置のロール両端部に非接触領域が生じた場合を示す図。
【図３】一般的な圧延方法の手順を示すブロック図。
【図４】本発明の実施の形態に係る板クラウン予測方法に用いられる板クラウン予測式を求める手順を示すフローチャート。
【図５】本発明の実施の形態に係る板クラウン予測方法に用いられるバックアップロールのプロフィル形状を表す無次元パラメータについて説明するグラフ。
【図６】本発明の実施の形態に係る板クラウン予測方法を用いて計算した板クラウン計算値と従来手法により計算した板クラウン計算値とを比較する図。
【符号の説明】
１…ワークロール
２…バックアップロール
４…被圧延材
２１…非接触領域
３０…板クラウン予測モデル
３１…サーマルプロフィルモデル
Ｆ_B…ベンディング力
Ｐ…圧延荷重
ｑ…接触荷重
Ｓ１１，Ｓ１２，，，…ステップ（手順）の番号[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a sheet crown prediction method in hot rolling of a material to be rolled such as steel, aluminum, and an aluminum alloy, and a hot rolling method using the same.
[0002]
[Prior art]
In general, in hot rolling of rolled materials such as steel, aluminum, and aluminum alloys, the sheet crown after the rolling pass is predicted using a computer in order to improve the sheet crown quality of the rolled material, and based on the predicted results. The rolling apparatus is controlled. A configuration of a four-stage rolling apparatus, which is an example of the rolling apparatus, is shown in FIG. The rolling device directly acts on the material to be rolled 4 to roll the work roll 1, which reinforces the work roll 1, and the backup roll 2 having a shape variable mechanism, and the work roll and the backup roll to bend the bending force F _B. A roll bending mechanism (not shown) that generates When the material to be rolled 4 is passed (rolled) to such a rolling device, the work roll 1 receives a rolling load P of several hundred tons or more from the material to be rolled 4 and also receives a contact load q from the backup roll, The work roll 1 is bent, and a plate crown is formed on the rolled material 4 after the pass. At that time, in order to obtain a desirable plate crown from both the quality and operational aspects, the profile shape of the backup roll 2 by the shape variable mechanism and the bending force by the roll bending mechanism are based on the predicted result of the plate crown after the pass. to control the F _B.
[0003]
A general control procedure of such a rolling apparatus is as shown in FIG. 3, for example. Hereinafter, S11, S12,... Represent step numbers.
First, the initial value of the bending force F _B and the profile shape of the backup roll, the target plate crown after the pass (target plate crown), the next coil such as the thickness, width and load of the material 4 to be passed next. The rolling conditions such as information are input (S11 to S13). Further, a rolling history such as the temperature of the material to be rolled 4 and the cooling temperature of the work roll 1 is input (S14), and the axial direction of the work roll 1 due to thermal expansion by a predetermined thermal profile model 31 based on the rolling history. Is obtained (S15). Then, based on the rolling condition and the thermal profile, a predicted value of the sheet crown after the pass is calculated using a predetermined sheet crown prediction model 30 (S21), and this is within a predetermined error range of the target sheet crown. If there is not (No in S22), the prediction calculation (S21) of the plate crown after the pass is sequentially repeated (S23 → S21) while correcting the bending force F _B and the profile shape of the backup roll (S23). → S22). The profile shape of the bending force F _B and the backup when the calculated value of the strip crown after the pass falls within the predetermined error range (Yes side at S22) is set to the rolling device (S31).
[0004]
Here, the thermal profile model 31 includes, for example, the thermal profile shown in Reference 1 (Kitahama et al .: Plasticity and Processing (Journal of the Japan Society for Technology of Plasticity) Vol. 36, No. 417 (1995-10) pp. 1163-1168). Models etc. are applicable.
The plate crown prediction model 30 for obtaining the plate crown after the pass is generally given by the following equation (1).
Cr _out / H _out = ζ C _M / H _out + ηCr _in / H _in (1)
Here, Cr _in and Cr _out each strip crown after path before and paths, H _in and H _out each plate thickness after the pass before and path of the rolled material 4, C _M is the mechanical crown of the work rolls 1 (crown work roll 1 in the case of uniform load in the width direction is applied from the material to be rolled) is a transcription factor of the ζ and η are each previously given the mechanical crown C _M and the path before the sheet crown Cr _in.
[0005]
Further, the mechanical crown C _M is conventionally given by the following equation (2).
C _M = α _P · P + α _B · F _B + α _CW (C _RW + C _RH ) + α _CB · C _RB (2)
Here, P is the rolling load, F _B is the bending force, C _RW is the initial crown of the work roll 1, C _RH is the thermal crown of the work roll 1, and C _RB is the initial crown of the backup roll 2.
Α _P , α _B , α _CW , and α _CB are influence coefficients on the mechanical crown C _M , respectively. As shown in the following equation (3), for example, the width W of the material 4 to be rolled, It is given as a function of the diameter of the work roll 1 and the diameter of the backup roll 2.
α _P = F ₁ α _P (W, D _w , D _B )
α _B = F ₁ α _B (W, D _w , D _B ) (3)
α _CW = F ₁ α _CW (W, D _w , D _B )
Here, each function expressed by the equation (3) is obtained by virtually dividing the work roll 1 and the backup roll 2 in the axial direction by several tens of minutes, and the force for each divided area under a plurality of given rolling conditions. And a calculation result of the mechanical crown C _M obtained by a so-called division model that precisely solves the deflection and flat deformation of each roll, and finds the balance between the rolls and the surface displacement matching conditions between the work roll 1 and the backup roll 2, and each rolling conditions (sample data), the parameters W, D _w, is determined by multiple regression with factors such as D _B (conventional method). The division model is well known as shown in, for example, Reference 2 (Shohet, KN & Townsend, NA: J. Iron and Steel Inst. 206-11 (1968), p. 1088).
[0006]
Here, for example, when the material 4 to be rolled is steel or the like, the rolling load P is very large, for example, about 1000 t. Therefore, the peripheral surfaces of the work roll 1 and the backup roll 2 overlap in the width direction. For the area to be touched, all areas usually touch. Therefore, in the conventional method, the sample data is obtained on the condition that the entire area is in contact as shown in the document 1.
[0007]
[Problems to be solved by the invention]
However, when the material to be rolled 4 is, for example, aluminum or an aluminum alloy, the rolling load P is relatively small, for example, about 200 t, and the gap originally formed between the work roll 1 and the backup roll. The flat deformation of each roll does not become so large that it is erased over the entire area, and a non-contact area is formed between both rolls. FIG. 2 shows a state in which the non-contact area 21 is formed at both ends of the work roll 1. In such a case, the conventional method based on the premise that the entire region is in contact has a problem that an error in the calculation result of the plate crown after the pass becomes large.
In order to solve such problems, a method for calculating the contact area between both rolls is disclosed in Japanese Patent No. 2980661. However, in this method, convergence calculation is required to obtain the contact area. If this is executed in S21 of FIG. 3, the convergence calculation is performed in the convergence calculation, and the calculation load increases, and depending on the ability of the computer to perform the calculation, online control may not be in time. Obtained.
Accordingly, the present invention has been made in view of the above circumstances, and the object of the present invention is to achieve high accuracy even under rolling conditions in which a non-contact region is generated between the work roll and the backup roll. Another object of the present invention is to provide a plate crown prediction method capable of predicting a plate crown after a pass with a small calculation load and a rolling method using the same.
[0008]
[Means for Solving the Problems]
In order to achieve the above object, the present invention provides a method for predicting a sheet crown in hot rolling of a material to be rolled by a rolling apparatus having a work roll, a roll having a roll shape variable mechanism, and a roll bending mechanism. in strip crown Cr _out after path found through the work roll and the backup roll with a plurality of strip crown prediction expression which is determined on the basis of the strip crown calculation results calculated based upon certain parameters, including the contact region information This is a method for predicting a sheet crown in hot rolling.
[0009]
Further, it is conceivable to determine the contact area information based on the profile shapes of the work roll and the backup roll.
Further, the strip crown prediction formula, and each strip crown Cr _in and Cr _out after the path before and paths, wherein each plate thickness H _in and H _out after the path before and path of the rolled material, the work roll It is given by the following equation (A) representing the relationship with the mechanical crown C _M ,
Cr _out / H _out = ζ C _M / H _out + ηCr _in / H _in (A)
The mechanical crown C _M is given by the following equation (B) representing the relationship between the rolling load P, bending force F _B , work roll initial crown C _RW , backup roll crown C _RB , and work roll thermal crown C _RH. Conceivable.

However, in the formula (A), the ζ and eta, are each transfer ratio and the transfer rate of the crown Cr _in the path front plate in advance given the mechanical crown C _M in the formula (B), alpha _{P , α B, α CW, α} CB, α CH are each influence coefficient to the mechanical crown C _M, the width W of the material to be rolled, the rolling load P, the work roll diameter D _w, said backup Of dimensionless parameter τ representing roll diameter D _B , difference ΔW in width of material to be rolled between next pass and previous pass, and profile shape of backup roll determined by roll shape variable mechanism , A function of at least one or more parameters.
[0010]
Further, the influence coefficients α _P , α _B , α _CW , α _CB , α _CH may be used as the following functions of the parameters W, P, D _w , D _B , ΔW, τ.
α _P = Fα _P (W, P, D _w , τ)
α _B = Fα _B (W, P, D _B , τ)
α _CW = Fα _CW (W, P)
α _CB = Fα _CB (W, P)
α _CH = Fα _CH (W, P, ΔW)
[0011]
The functions Fα _P , Fα _B , Fα _CW , Fα _CB , and Fα _CH are assumed to be the contact area information under a plurality of rolling conditions, and based on the assumption, the work roll and the backup roll are divided according to a division model. And when the contact load distribution has a negative contact load, the assumption of the contact area information is corrected and the calculation of the contact load distribution is sequentially repeated. When the contact load having a negative value no longer exists in the contact load distribution, a sample value of the plate crown after the pass is calculated based on the calculation result of the contact load distribution, and It may be determined based on the multiple regression analysis of the obtained sample values.
[0012]
Moreover, what was considered as a hot rolling method using the said plate crown prediction method in hot rolling is also considered.
That is, the bending force by the bending mechanism and the profile shape of the backup roll by the roll shape variable mechanism are assumed, and the plate crown after the pass is determined by the plate crown prediction formula determined by the plate crown prediction method based on the assumption. Cr _out is calculated, and if the difference between the plate crown Cr _out after the pass and the preset target plate crown is not within a predetermined error range, at least one of the bending force and the profile shape of the backup roll is selected. The assumption is corrected and the calculation of the plate crown after the pass by the plate crown prediction method is sequentially repeated. When the difference falls within the error range, the bending force and the profile shape of the backup roll at that time are calculated. It is a hot rolling method set in the rolling device.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the accompanying drawings for understanding of the present invention. In addition, the following embodiment is an example which actualized this invention, Comprising: It is not the thing of the character which limits the technical scope of this invention.
Here, FIG. 1 is a diagram showing a configuration example of a rolling device used for general hot rolling, and FIG. 2 is a case where non-contact areas are generated at both ends of the roll of the rolling device used for general hot rolling. FIG. 3 is a block diagram showing a procedure of a general rolling method, FIG. 4 is a flowchart showing a procedure for obtaining a plate crown prediction formula used in the plate crown prediction method according to the embodiment of the present invention, and FIG. FIG. 6 is a graph for explaining dimensionless parameters representing the profile shape of the backup roll used in the plate crown prediction method according to the embodiment of the present invention, and FIG. 6 is calculated using the plate crown prediction method according to the embodiment of the present invention. It is a figure which compares the plate crown calculated value and the plate crown calculated value calculated by the conventional method.
[0014]
The plate crown prediction method according to the embodiment of the present invention is applied to the plate crown prediction model 30 of S21 in the general rolling method shown in FIG. 3 described above, and is used for calculating the plate crown Cr _out after the pass. those characterized by a calculation formula of the mechanical crown C _M contained in the plate crown prediction expression (expression (1) above). Accordingly, the calculation method of the range other than the calculation formula of the mechanical crown C _M is well-known in addition to the one shown in the above-mentioned document 1, and the description thereof is omitted here.
[0015]
The plate crown prediction formula used in the plate crown prediction method according to the present embodiment includes the plate crowns Cr _in and Cr _out before and after the pass, and the plate thicknesses H before and after the pass of the material to be rolled. and _in and H _out, given by the following expression representing the relation between the mechanical crown C _M of the work roll (a). This is the same as equation (1) in the conventional method.
Cr _out / H _out = ζ C _M / H _out + ηCr _in / H _in (A)
Here, ζ and eta, are each transfer ratio and the transfer rate of the crown Cr _in the path front plate in advance given the mechanical crown C _M. The specific contents of ζ and η are well known, for example, from Document 3 (Awazu et al .: Proceedings of the 33rd Plastic Working Joint Lecture (1982) p. 143), and the description thereof is omitted here.
[0016]
Further, the mechanical crown C _M is expressed by the following equation (B) representing the relationship between the rolling load P, bending force F _B , work roll initial crown C _RW , backup roll initial crown C _RB , and work roll thermal crown C _RH . Given.

Here, α _P , α _B , α _CW , α _CB , and α _CH are coefficients of influence on the mechanical crown C _M , respectively. The difference between the formula (B) and the formula (2) in the conventional method is that the influence coefficients α _CW and α _CH of the work roll initial crown C _RW and the work roll thermal crown C _RH are individually provided. Is a point.
Thus, the work roll initial crown C _RW, and the work roll thermal crown C _RH as a substantially trapezoidal shape with influence on the mechanical crown C _M generally its shape is substantially parabolic, difference in shape It is possible to reflect the difference in the effects caused by.
[0017]
The influence coefficients α _P , α _B , α _CW , α _CB , and α _CH are given by the functions shown in the following equations (C1) to (C5).
α _P = Fα _P (W, P, D _w , τ) (C1)
α _B = Fα _B (W, P, D _B , τ) (C2)
α _CW = Fα _CW (W, P) (C3)
α _CB = Fα _CB (W, P) (C4)
α _CH = Fα _CH (W, P, ΔW) (C5)
Here, W is the width of the rolled material, P is the rolling load, D _w is the work roll diameter, D _B is the diameter of the backup roll, the material to be rolled in ΔW is the following path and the previous path Is a dimensionless parameter representing the profile shape of the backup roll determined by the roll shape variable mechanism.
[0018]
Here, the dimensionless parameter τ representing the profile shape of the backup roll will be described with reference to FIG.
In the graph of FIG. 5, the X-axis is the distance from the center of the backup roll in the axial direction, and the Y-axis (left side) is the amount of radial displacement of the surface when the backup roll 2 is deformed by the shape variable mechanism. The relative displacement is 0 (zero) when the position is not deformed. The backup roll 2 shown in FIG. 5 has a variable mechanism whose profile shape can be varied in 11 steps including a flat state without deformation.
The dimensionless parameter τ is set to 0 (zero) for a flat state where the backup roll 2 is not deformed, 1 for a deformation state having the largest deformation amount (surface displacement amount), and nine stages of deformation states therebetween. By expressing in 0.1 increments from 0.1 to 0.9 (on the right side of the Y axis in FIG. 5), it is a parameter obtained by making the profile shape of the backup roll dimensionless.
As a result, the influence of the change in the profile shape of the backup roll on the mechanical crown C _M is included in the functions Fα _P and Fα _B of the influence coefficients α _P and α _B. It is not necessary to separately determine the influence coefficients α _P and α _B for each profile shape.
[0019]
The functions Fα _P , Fα _B , Fα _CW , Fα _CB , Fα _CH for obtaining the influence coefficients α _P , α _B , α _CW , α _CB , α _CH are given by the following equations (D1) to (D5), respectively. It is done.

Here, a1 to a5, b1 to b5, c1, c2, d5, and t1 to t2 are unknown coefficients, and k, l, m, and n are predetermined expansion orders of the unknown coefficients.
By obtaining these unknown coefficients, the influence coefficients α _P , α _B , α _CW , α _CB , and α _CH are obtained. As a result, the above equation (B) is obtained, and further, the above equation (A), that is, the plate crown A prediction formula is obtained.
[0020]
Next, a procedure for _obtaining the influence coefficients α _P , α _B , α _CW , α _CB and α _CH will be described with reference to FIG.
Here, it is assumed that a plurality of predetermined (1-N) rolling conditions are given before the procedure of FIG. 4 is started.
First, the first (i = 1) rolling condition is selected from a plurality of the rolling conditions (S101 → S102). Wherein the the rolling conditions, the path before the sheet crown Cr _in, the temperature T _i and the plate shape of the pass before the rolled material 4, the plate thickness after the pass before and path of the rolled material 4 H _in and H _out , The sheet width W of the material 4 to be rolled, the bending force F _{B of} the work roll 1, and the initial shapes of the work roll 1 and the backup roll 2.
[0021]
Next, based on the selected rolling conditions, the work roll initial crown C _RW and the backup roll crown C _RB at the start of rolling are calculated (S103).
Then, based on the rolling conditions, the temperature rise after the path of the rolled material 4 in the rolled calculated by heat balance calculation, and the temperature rise, and each initial crown C _RW and C _RB obtained in S103 Based on the above, thermal crowns of the backup roll 1 and the work roll 2 are calculated using the thermal profile model 31 (S104).
Next, based on the thermal crowns obtained in S104, the deformation profiles of the work roll 1 and the backup roll 2 with the rolling load P are calculated (S105).
The specific contents of S102 to S105 are well known in addition to those described in Document 2, and will not be described here.
[0022]
Next, based on each deformation profile obtained in S105, contact area information between the work roll 1 and the backup roll 2 is assumed (S106). As the assumed initial state, for example, a method is assumed in which it is assumed that all the areas where the work roll 1 and the backup roll 2 overlap are in contact with each other.
Next, assuming that the rolling load P acts only on the area assumed to be in contact with the contact area information, the deformation of the work roll 1 and the backup roll 2 using the division model shown in the literature 2 and the like, A contact load distribution q (x) in the axial direction between the work roll 1 and the backup roll 2 is calculated (S107). (X represents the position in the axial direction.)
Next, in the calculated contact load distribution q (x), when the load at any position x in the axial direction has a negative value (Yes side of S108), the contact region assumed in S106 is assumed. After changing the information (S109), the contact load distribution q (x) is calculated again (S107). Here, the contact area information can be changed, for example, based on the contact load distribution q (x), in which the load value is changed so that only a position x where the load value is a predetermined value or more is in contact. It is done.
[0023]
In this manner, in the contact load distribution q (x), the change of the contact area information and the contact load distribution q (x) until no negative load exists at any position x in the axial direction. (S109 → S107) is repeated.
And when the negative load no longer exists at any position x in the axial direction (No side of S108), based on the contact load distribution q (x) at that time, the predetermined material of the material to be rolled is determined. The plate crown at the evaluation points (for example, the center and both ends in the plate width direction) is calculated (S110).
Next, the other rolling conditions are sequentially selected (the i-th rolling condition is selected, i = 2, 3,...) (S112 → S102), and the above-described steps S103 to S110 are repeated and given in advance. The calculated values of the plate crown are obtained for all the rolling conditions (S102 to S111 → S112).
Then, the unknown coefficients a1 to a5, b1 to b5 are calculated by performing multiple regression processing on the calculated values of the plurality of plate crowns thus obtained using the equations (D1) to (D5). c1, c2, d5, t1 to t2 are obtained, and thereby the influence coefficients α _P , α _B , α _CW , α _CB , α _CH are obtained (S113). At this time, the expansion orders k, l, m, and n are, for example, secondary.
[0024]
Next, with reference to FIG. 6, the plate crown calculation value A calculated using the plate crown prediction formula (equation (1), (2)) obtained by the conventional method and the procedure shown in FIG. The plate crown calculated value B calculated using the prediction formula (Equation (A), Equation (B)) of the plate crown is compared. Here, since it is difficult to collect the measured values of the sheet crown under a large number of rolling conditions, the exact solution of the sheet crown after the pass calculated strictly by the division model is substituted for the measured values. The correlation between the calculated value of the plate crown and the exact solution was evaluated.
[0025]
The graph shown in FIG. 6 (a) is obtained by using the equations (1) and (2) based on the influence coefficients α _P , α _B , α _CW of the equation (3) obtained by the conventional method. FIG. 6 is a scatter diagram in which the calculated result A of the plate crown after the pass is taken on the Y axis and the exact solution of the plate crown after the pass is taken on the X axis.
Further, the graph shown in FIG. 6A is obtained by following the procedure shown in FIG. 4 and taking the expansion orders k, l, m, n of the equations (D1) to (D5) up to the second order, and the influence coefficients α _P , α _B , α _CW , α _CB , α _CH are obtained, and based on this, the calculation result B of the plate crown after the pass calculated by using the formulas (B) and (A) is used as the Y axis, It is a scatter diagram which took the exact solution of a plate crown as an X-axis.
6A and 6B, the calculated value B of the plate crown according to the present invention is more accurate than the calculated value A of the plate crown according to the conventional method over a wider range. You can see that it approximates the solution.
FIG. 6C is a bar graph showing errors of the calculated values A and B of the plate crown with respect to the exact solution for each of FIGS. 6A and 6B. The error (25.9 μm) in the calculated value B of the plate crown according to the present invention is suppressed to 40% or less of the error (67.1 μm) in the calculated value A of the plate crown according to the conventional method. You can see that it ’s big.
In addition, it is clear that the quality of the plate crown can be improved by performing rolling control by applying the prediction formula (prediction model) of the plate crown having high prediction accuracy to the plate crown prediction model 30 shown in FIG. is there.
[0026]
【The invention's effect】
As described above, according to the present invention, the plate crown can be predicted with high accuracy and a small calculation load even under rolling conditions in which a non-contact area is generated between the work roll and the backup roll. As a result, the quality of the plate crown can be improved.
[Brief description of the drawings]
FIG. 1 is a diagram showing a configuration example of a rolling apparatus used for general hot rolling.
FIG. 2 is a view showing a case where non-contact areas are generated at both ends of a roll of a rolling apparatus used for general hot rolling.
FIG. 3 is a block diagram showing a procedure of a general rolling method.
FIG. 4 is a flowchart showing a procedure for obtaining a plate crown prediction formula used in the plate crown prediction method according to the embodiment of the present invention.
FIG. 5 is a graph for explaining a dimensionless parameter representing a profile shape of a backup roll used in the plate crown prediction method according to the embodiment of the present invention.
FIG. 6 is a diagram comparing a plate crown calculation value calculated using a plate crown prediction method according to an embodiment of the present invention and a plate crown calculation value calculated using a conventional method.
[Explanation of symbols]
1 ... work roll 2 ... backup roll 4 ... the material to be rolled 21 ... non-contact area 30 ... plate crown prediction model 31 ... thermal profile model F _B ... Bending force P ... rolling load q ... contact load S11, S12 ,,, ... Step (Procedure) number

Claims (6)

In a method for predicting a sheet crown in hot rolling of a material to be rolled by a rolling device equipped with a work roll and a roll having a roll shape variable mechanism and a roll bending mechanism,
Plate crown prediction determined based on a plurality of plate crown calculation results obtained by calculating the plate crown Cr _out after the pass in the hot rolling based on predetermined parameters including contact area information between the work roll and the backup roll A method for predicting a sheet crown in hot rolling, which is obtained by an equation. The method for predicting a sheet crown in hot rolling according to claim 1, wherein the contact area information is determined based on profile shapes of the work roll and the backup roll. The plate crown prediction formula is
Represents the path before and each strip crown Cr _in and Cr _out after the path, the each thickness H _in and H _out after the path before and path of the rolled material, the relationship between the mechanical crown C _M of the work roll Given by the following equation (A),
Cr _out / H _out = ζ C _M / H _out + ηCr _in / H _in (A)
The mechanical crown C _M is given by the following equation (B) representing the relationship between the rolling load P, bending force F _B , work roll initial crown C _RW , backup roll crown C _RB , and work roll thermal crown C _RH. The plate crown prediction method in the hot rolling according to claim 1 or 2.

However, in the formula (A), the ζ and eta, are each transfer ratio and the transfer rate of the crown Cr _in the path front plate in advance given the mechanical crown C _M in the formula (B), alpha _{P , α B, α CW, α} CB, α CH are each influence coefficient to the mechanical crown C _M, the width W of the material to be rolled, the rolling load P, the work roll diameter D _w, said backup Of dimensionless parameter τ representing roll diameter D _B , difference ΔW in width of material to be rolled between next pass and previous pass, and profile shape of backup roll determined by roll shape variable mechanism , A function of at least one or more parameters. The hot influence according to claim 3, wherein the influence coefficients α _P , α _B , α _CW , α _CB , α _CH are the following functions of the parameters W, P, D _w , D _B , ΔW, τ. Sheet crown prediction method in rolling.
α _P = Fα _P (W, P, D _w , τ)
α _B = Fα _B (W, P, D _B , τ)
α _CW = Fα _CW (W, P)
α _CB = Fα _CB (W, P)
α _CH = Fα _CH (W, P, ΔW) The functions Fα _P (W, P, D _w , τ), Fα _B (W, P, D _B , τ), Fα _CW (W, P), Fα _CB (W, P), and Fα _CH (W , P, ΔW) assuming the contact area information under a plurality of rolling conditions, and calculating an axial contact load distribution between the work roll and the backup roll by a split model based on the assumption, If the contact load distribution has a negative contact load, the assumption of the contact area information is corrected and the calculation of the contact load distribution is sequentially repeated, and the contact load distribution has a negative contact load. If it does not, the sample value of the plate crown after the pass is calculated based on the calculation result of the contact load distribution, and is determined based on the multiple regression analysis of the sample value obtained under the plurality of rolling conditions. The sheet crown pre-treatment in hot rolling according to claim 4. Measuring method. In a hot rolling method of a material to be rolled by a rolling device having a work roll and a roll having a roll shape variable mechanism and a roll bending mechanism,
Assuming the bending force by the bending mechanism and the profile shape of the backup roll by the roll shape variable mechanism,
Based on the assumption, the plate crown Cr _out after the pass is determined by a plate crown prediction formula determined based on a plurality of plate crown calculation results obtained based on parameters including contact area information between the work roll and the backup roll. Calculate,
If the difference between the plate crown Cr _out after the pass and the preset target plate crown is not within a predetermined error range, the assumption of at least one of the bending force and the profile shape of the backup roll is corrected. The calculation of the plate crown after the pass by the plate crown prediction method is sequentially repeated,
When the difference falls within the error range, the bending force and the profile shape of the backup roll at that time are set in the rolling device, and the hot rolling method is characterized in that:

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