JP3821664B2 - Prediction method of thermal crown of rolling roll, its prediction program, and its prediction system - Google Patents

Description

ここで，各前記等価境界熱伝達率α'，α''及び各前記等価境界温度Ｔ''，Ｔ''は，各々次式（２）〜（５）により，前記圧延ロールの周方向で平均化して求められる。

前記（２）〜（５）式において，α₂，α₃は，前記圧延ロールの周面における各々クーラントによる冷却部，前記被圧延材との接触部と前記冷却部とを除く残りの空冷部の各熱伝達率を，Ｓ₁，Ｓ₂，Ｓ₃は，各々前記圧延ロール周面における前記接触部，前記冷却部，前記空冷部の各周方向の長さを，Ｔ₁，Ｔ₂，Ｔ₃は，各々被圧延材温度，前記クーラントの温度，前記空冷部の雰囲気温度をそれぞれ表す。
前記（２）〜（５）式を前記（１）式に代入すると，次式のようになり，前記圧延ロールへの単位長さ当たりの入熱量ｑが，前記熱伝達率α₁と正の相関関係にあることがわかる。

従って，例えば，前記熱伝達率α₁に試験的に平均的な値を用いて熱の移動計算を行い，前記圧延ロール温度を予測計算すると，一般に，前記圧下量の大きい上流工程の圧延装置（上流スタンド）における実際の熱伝達率α₁は平均的な値より小さいため，前記圧延ロールへの計算上の入熱量ｑが実際よりも大きくなり，その結果前記圧延ロール温度の計算値が実測値よりも高く計算されてしまう。逆に前記圧下量の小さい下流スタンドでは前記圧延ロール温度が実測値よりも低く計算されてしまう。このようなことから，従来は，前記熱伝達率α₁に，スタンド毎及び被圧延材の種類（材質，厚み等）毎に，予め稼働条件と合わせた圧延条件での実測により求めた前記熱伝達率α₁を設定し，サーマルクラウン予測を行っていた（従来技術甲）。例えば，文献２（北浜ら：塑性と加工（日本塑性加工学会誌）第３６巻 第４１７号（１９９５−１０）ｐｐ．１１６３−１１６８）に示されるサーマルプロフィルモデルにおいても，前記熱伝達率α₁は実測値から決定される定数として扱われている。（従来技術乙）
【０００３】
【発明が解決しようとする課題】
しかし，前記従来技術甲及び乙では，例えば従来にない厚みの被圧延材の圧延を行う場合や，ある圧延工程を従来と異なるスタンドで行うような圧延スケジュールの組み替えを行う場合等，新たな圧延条件となった場合には，事前に実測により前記熱伝達率α₁を求めたときの圧延条件と異なるため，該熱伝達率α₁に誤差が生じ，これにより前記圧延ロールの予測温度に誤差が生じる。その結果サーマルクラウン予測にも誤差が生じて被圧延材のクラウン品質が悪化するという問題点があった。
したがって、本発明は上記事情に鑑みてなされたものであり、その目的とするところは、実測データのない新たな圧延条件となった場合でも，高精度に圧延ロールのサーマルクラウンを予測できるサーマルクラウン予測方法及びその予測プログラム並びその予測システムを提供することである。
【０００４】
【課題を解決するための手段】
上記目的を達成するために本発明は、被圧延材の熱間圧延における圧延ロールのサーマルクラウン予測方法において，前記圧延ロールと前記被圧延材との接触部の熱伝達率を，該圧延ロールが前記被圧延材と接触する周面の周方向の長さである接触弧長Ｓ₁ の関数である熱伝達率関数Ｆ（Ｓ₁ ）により求めることを特徴とするものである。
また，前記熱伝達率関数Ｆ（Ｓ₁ ）が，前記被圧延材の温度，定常状態の前記圧延ロールの温度，前記圧延ロールがクーラントによって冷却されているクーラント冷却部の熱伝達率，前記クーラントの温度，前記圧延ロールの前記クーラント冷却部以外の空冷部の熱伝達率，該空冷部の雰囲気温度，前記圧延ロールと前記被圧延材との摩擦発熱量，圧延パス時間，及びある圧延パス終了時から次の圧延パス開始時までの圧延パス間時間を含む定常パラメータに基づき決定されるものが考えられる。
また，前記熱伝達率関数Ｆ（Ｓ₁ ）が，複数の前記定常状態における前記定常パラメータと，これに対応する前記接触弧長Ｓ₁ とに基づき決定するものであってもよい。
また，前記熱伝達率関数Ｆ（Ｓ₁ ）が，前記定常パラメータ及びこれに対応する前記接触弧長Ｓ₁ に基づく統計計算により予め決定されるものも考えられる。また，被圧延材の熱間圧延における圧延ロールのサーマルクラウン予測工程を実行するための圧延ロールのサーマルクラウン予測プログラムにおいて，前記圧延ロールと前記被圧延材との接触部の熱伝達率を，該圧延ロールが前記被圧延材と接触する周面の周方向の長さである接触弧長Ｓ₁ の関数である熱伝達率関数Ｆ（Ｓ₁ ）により求める工程を実行するコンピュータ読み取り可能な圧延ロールのサーマルクラウン予測プログラムとして構成することも考えられる。
さらに，被圧延材の熱間圧延における圧延ロールのサーマルクラウン予測システムにおいて，前記圧延ロールと前記被圧延材との接触部の熱伝達率を，該圧延ロールが前記被圧延材と接触する周面の周方向の長さである接触弧長Ｓ₁ の関数である熱伝達率関数Ｆ（Ｓ₁ ）により求める圧延ロールのサーマルクラウン予測システムとして構成することも考えられる。
【０００５】
【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及び実施例について説明し、本発明の理解に供する。尚、以下の実施の形態及び実施例は、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は実測データから求められた熱伝達率と接触弧長との相関図，図２は本発明の実施の形態に係るサーマルクラウン予測方法を使用する場合としない場合の圧延ロールの予測温度と実測温度の相関図である。
【０００６】
本発明の実施の形態に係る圧延ロールのサーマルクラウン予測方法は，例えば前記従来技術乙（前記文献２）に示されるサーマルプロフィルモデル等の手法を用いて圧延ロールのサーマルクラウン予測を行う際に，鉄鋼，アルミ，アルミ合金等の被圧延材と前記圧延ロールとの間の熱の移動計算に用いる主要な入力変数の１つである，前記圧延ロールと前記被圧延材との接触部の熱伝達率α₁を高精度に予測する方法に特徴を有するものである。従って，前記サーマルクラウン予測における前記熱伝達率α₁の計算以外の範囲の計算方法については，前記従来技術乙の他，知られたものがあるのでここでは説明を省略する。
即ち，この実施の形態における前記熱伝達率α₁の計算方法は，圧延の際に前記圧延ロールが前記被圧延材と接触する周面の周方向の長さである接触弧長Ｓ₁ を入力として前記熱伝達率α₁を求める関数である熱伝達率関数Ｆ（Ｓ₁ ）によって計算するものである。以下，前記熱伝達関数Ｆ（Ｓ₁）の導出方法について説明する。
前記熱伝達率関数Ｆ（Ｓ₁）は，複数の圧延条件下での定常状態において，後述する定常パラメータにより求められる前記熱伝達率α₁と，前記圧延条件から求められる前記接触弧長Ｓ₁ との相関関係を統計計算することによって導出する。ここで，前記定常状態とは，前記被圧延材の材質，厚み，温度や前記圧下量等の圧延条件を同一にして圧延を継続したときに，前記圧延ロールが前記被圧延材から受ける熱量と，該圧延ロールがこれを冷却するクーラント等により奪われる熱量とが釣り合い，前記圧延ロール温度がほぼ一定の値に収束する状態をいう。従って，該定常状態では，前記（６）式において前記圧延ロールへの単位長さ当たりの入熱量ｑ＝０となることから，次式が成り立つ。
α₁(Ｔ_R−Ｔ₁)τ'・Ｓ₁＋α₂(Ｔ_R−Ｔ₂)τ'・Ｓ₂＋α₃(Ｔ_R−Ｔ₃)τ'・Ｓ₃
＋Ｑ_F ・τ'
＋α₂(Ｔ_R−Ｔ₂)τ''・Ｓ₂＋α₃(Ｔ_R−Ｔ₃)τ''・Ｓ₃＝０ …(６)
従って，前記定常状態における前記各温度Ｔ_R，Ｔ₁，Ｔ₂，Ｔ₃を実測すれば，前記（６）式中，前記熱伝達率α₁以外の他のパラメータは既知の値又は知られた方法により求められる値であるので，前記熱伝達率α₁を求めることができる。この（６）式中，前記熱伝達率α₁を除く残りのパラメータτ'，τ''，α₂，α₃，Ｔ_R，Ｔ₁，Ｔ₂，Ｔ₃，Ｑ_Fが前述した定常パラメータである。
一方，前記接触弧長Ｓ₁は，前記圧延条件として与えられる，１パスの入側の前記被圧延材の厚みｈ１と，同出側の厚みｈ０と，前記圧延ロールの半径Ｒとにより表される次式，
Ｓ₁＝√［Ｒ（ｈ１―ｈ０）］ …(７)により求めることができる。
【０００７】
ここに図１は，前記被圧延材の厚みや温度，前記圧下量，前記スタンド等，種々異なる圧延条件下で，前記定常状態における前記各温度Ｔ_R，Ｔ₁，Ｔ₂，Ｔ₃を実測し，これを含む前記定常パラメータから前記（６）式を用いて前記熱伝達率α₁を求め，これと前記（７）式で求まる前記接触弧長Ｓ₁との相関を示したグラフである。なお，前記各圧延条件において，前記圧延ロール及び前記被圧延材の材質については同一条件である。
図１から明らかなように，前記熱伝達率α₁と前記接触弧長Ｓ₁との間には高い相関関係があることがわかる。この図１に示される相関関係から，例えば指数関数や２次式による近似や累乗近似等により前記接触弧長Ｓ₁と前記熱伝達率α₁との関係を表す近似式を求め，これを前記熱伝達率関数Ｆ（Ｓ₁）とする。
【０００８】
次に，このようにして求めた前記熱伝達率関数Ｆ（Ｓ₁）の有効性を確認した結果について説明する。実際の圧延における前記圧延ロールの変形は，サーマルクラウン以外の要因によっても生じ，前記圧延ロールの変形量の実測値から，サーマルクラウンによる変形量のみを抽出することは困難であるため，ここでは，圧延中の圧延ロール温度の実測値と計算値との比較によって評価する。
図２（ａ）は，前記被圧延材の厚みや温度，前記圧下量，前記スタンド等，種々異なる圧延条件下における圧延ロール温度実測値と，前記各圧延条件において前記熱伝達率α₁を定数で与えることにより計算した圧延ロール温度計算値とを比較した散布図，図２（ｂ）は，同じく前記圧延ロール温度実測値と，前記各圧延条件において前記熱伝達率α₁を前述の手順で指数関数（ｋ／Ｓ₁ ^p，ここでｋ，ｐは所定の係数）による近似によって導出した前記熱伝達率関数Ｆ（Ｓ₁）を用いて算出した結果を与えることにより計算した圧延ロール温度計算値とを比較した散布図である。該圧延ロール温度計算値は，例えば前記従来技術甲（前記文献１）に示される温度シミュレーションモデルによって求めることができる。
図２から明らかなように，本発明に係る前記熱伝達率関数Ｆ（Ｓ₁）を用いた場合（図２（ｂ）），これを用いない場合（図２（ａ））に比べ，前記圧延ロー温度実測値（図２の横軸）に対する計算値（図２の縦軸）の誤差がはるかに小さくなり，計算精度が向上していることがわかる。図２（ａ）と図２（ｂ）とに示されるデータは，各々実設備稼働中のオンライン制御データであるため，各々同じ条件下で同時に実測及び計算されたものではないが，本発明を用いて計算された図２（ｂ）のデータの方が，用いなかった図２（ａ）のデータよりも，より広範囲の圧延ロール温度域のデータであるにもかかわらず，前記誤差が小さく抑えられており，前記圧延条件により圧延状態が広範囲に変化しても本発明が有効に機能することがわかる。しかも，図２（ａ）及び図２（ｂ）に示すデータは，前記定常状態以外の非定常状態におけるデータを含むものであり，前記定常状態における前記定常パラメータに基づいて得た前記熱伝達率関数Ｆ（Ｓ₁）が，前記非定常状態においても有効に機能することを示している。圧延ロールのサーマルクラウン予測では，圧延ロール温度の予測結果に基づいて熱膨張による変形量が求められるので，圧延ロール温度の予測精度が向上すれば，サーマルクラウンの予測精度も向上することは明らかである。
このようにして求められた前記熱伝達率関数Ｆ（Ｓ₁）を用いたサーマルクラウン予測システムは，例えば前記従来技術乙（前記文献２）に示されるサーマルクラウン計算方法において，定数で与えられている前記熱伝達率α₁を前記熱伝達関数Ｆ（Ｓ₁）によって求めるよう変更された計算方法を実現するプログラムをコンピュータに組み込むことによって実現できる。
このように，前記統計計算が行える程度の数の圧延条件について，予め前記定常パラメータ等を実測しておけば，少なくとも圧延ロール及び前記被圧延材の材質が同条件であれば，実測データのない新たな圧延条件となった場合でも，高精度に圧延ロールのサーマルクラウン予測が行える。
【０００９】
【発明の効果】
以上説明したように、本発明によれば、圧延ロールによる鉄鋼，アルミ，アルミ合金等の被圧延材の圧延において，実測データのない新たな圧延条件となった場合でも，圧延ロールと被圧延材との間の熱伝達率が高精度に求められ，圧延ロールのサーマルクラウンの予測精度が向上し，その結果，被圧延材のクラウン品質が向上する。
【図面の簡単な説明】
【図１】実測データから求められた熱伝達率と接触弧長との相関図。
【図２】本発明の実施の形態に係るサーマルクラウン予測方法を使用する場合としない場合の圧延ロールの予測温度と実測温度の相関図。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a thermal roll prediction method, a prediction program thereof, and a prediction system thereof for use in controlling a crown control actuator in hot rolling of a material to be rolled such as steel, aluminum, and an aluminum alloy.
[0002]
[Prior art]
Until now, in the hot rolling of rolled materials such as steel, aluminum and aluminum alloys, the crown of the rolled material is controlled by predicting the thermal crown of the rolling roll using a computer in order to improve the crown quality. Control of a control actuator or the like is performed. In particular, the thermal crown of a rolling roll has a direct effect on the crown quality of the material to be rolled, so it must be predicted with high accuracy. In order to improve the accuracy of the thermal crown prediction, it is necessary to predict the temperature of the rolling roll with high accuracy, and one of the main parameters used for heat transfer calculation in the temperature prediction is the rolling roll and It is important to appropriately set the heat transfer coefficient α ₁ at the contact portion with the material to be rolled. However, the heat transfer coefficient α ₁ is different even when the combination of the material of the rolling roll and the material to be rolled is the same, for example, the difference in the diameter of the rolling roll and the thickness of the material to be rolled, and the rolling material before and after rolling. It is known that the difference is caused by a difference in the amount of reduction, which is a difference in thickness. The influence of the non-constant heat transfer coefficient α _{1 on the} prediction of the thermal crown of the rolling roll will be described below.
When predicting the thermal crown of a rolling roll with a computer, usually the rolling roll is divided into differential meshes, the appropriate boundary conditions are given, the rolling roll temperature is calculated for each mesh, and the thermal expansion of each mesh is calculated. The amount of displacement in the radial direction, that is, the thermal crown is obtained by adding the rolling rolls in the radial direction. Actually, in the rolling roll during rolling, temperature distribution occurs in the circumferential direction in addition to the rotation axis direction and radial direction, but in the thermal crown prediction calculation, the temperature distribution in the circumferential direction of the rolling roll is averaged. As a matter of fact, only the axial and radial temperature distributions are solved. Therefore, the boundary condition in the circumferential direction of the rolling roll is averaged in the circumferential direction. For example, according to Reference 1 (Iwaki et al .: Ishikawajima Harima Technique, Vol. 17, No. 2, March, 1978, pp. 95-104), the heat input q per unit length to the rolling roll is in the pass (rolling Middle) and the equivalent boundary temperatures T _eq ′, T _eq ″ between the paths from the end of one path to the start of the next path, the equivalent boundary heat transfer coefficients α _eq ′, α _eq ″, Each time τ ′, τ ″, the frictional heating value Q _{F of} the rolling roll, and the radius R of the rolling roll are obtained by the following equation (1).

Here, the equivalent boundary heat transfer coefficients α ′ and α ″ and the equivalent boundary temperatures T ″ and T ″ are respectively expressed in the circumferential direction of the rolling roll by the following equations (2) to (5). Obtained by averaging.

In the formulas (2) to (5), α ₂ and α ₃ are the cooling portions by the coolant on the peripheral surface of the rolling roll, the remaining air cooling portions excluding the contact portion with the material to be rolled and the cooling portions, respectively. , S ₁ , S ₂ , S ₃ are the respective circumferential lengths of the contact portion, the cooling portion, and the air cooling portion on the peripheral surface of the rolling roll, respectively, T ₁ , T ₂ , T ₃ represents the temperature of the material to be rolled, the temperature of the coolant, and the ambient temperature of the air-cooled part, respectively.
When the equations (2) to (5) are substituted into the equation (1), the following equation is obtained, and the heat input q per unit length to the rolling roll is positive with the heat transfer coefficient α ₁ . It can be seen that there is a correlation.

Therefore, for example, when heat transfer calculation is performed using an experimentally average value for the heat transfer coefficient α ₁ and the rolling roll temperature is predicted and calculated, generally, the upstream rolling mill with a large rolling reduction ( Since the actual heat transfer coefficient α ₁ in the upstream stand) is smaller than the average value, the calculated heat input q to the rolling roll is larger than the actual value, and as a result, the calculated value of the rolling roll temperature is the actual measured value. Will be calculated higher than. Conversely, in the downstream stand with a small reduction amount, the rolling roll temperature is calculated to be lower than the actual measurement value. For this reason, conventionally, the heat transfer coefficient α ₁ is determined by the actual measurement under the rolling conditions in combination with the operating conditions in advance for each stand and for each type of rolled material (material, thickness, etc.). The transmission coefficient α ₁ was set to predict the thermal crown (conventional technology A). For example, in the thermal profile model shown in Reference 2 (Kitahama et al .: Plasticity and processing (Journal of the Japan Society for Technology of Plasticity) Vol. 36, No. 417 (1995-10) pp. 1163-1168), the heat transfer coefficient α ₁ Is treated as a constant determined from actual measurement values. (Conventional technology B)
[0003]
[Problems to be solved by the invention]
However, in the above-mentioned conventional technology A and B, for example, when rolling a material to be rolled having an unprecedented thickness, or when changing a rolling schedule such that a certain rolling process is performed on a stand different from the conventional one, a new rolling when a condition is different and the rolling conditions when determined the heat transfer coefficient alpha ₁ by actual measurement in advance, an error occurs in the heat transfer coefficient alpha _1, thereby errors in predicted temperature of the rolling rolls Occurs. As a result, there is a problem that an error occurs in the thermal crown prediction and the crown quality of the material to be rolled deteriorates.
Accordingly, the present invention has been made in view of the above circumstances, and the object of the present invention is to provide a thermal crown capable of predicting the thermal crown of the rolling roll with high accuracy even when new rolling conditions without actual measurement data are obtained. To provide a prediction method, a prediction program thereof, and a prediction system thereof.
[0004]
[Means for Solving the Problems]
In order to achieve the above object, the present invention provides a method for predicting a thermal crown of a rolling roll in hot rolling of a material to be rolled, wherein the rolling roll has a heat transfer coefficient at a contact portion between the rolling roll and the material to be rolled. It is obtained by a heat transfer coefficient function F (S ₁ ) which is a function of a contact arc length S ₁ which is a circumferential length of a peripheral surface in contact with the material to be rolled.
Further, the heat transfer coefficient function F (S ₁ ) is the temperature of the material to be rolled, the temperature of the rolling roll in a steady state, the heat transfer coefficient of the coolant cooling part in which the rolling roll is cooled by the coolant, the coolant Temperature, heat transfer coefficient of air cooling part other than the coolant cooling part of the rolling roll, atmospheric temperature of the air cooling part, frictional heat generation between the rolling roll and the material to be rolled, rolling pass time, and end of certain rolling pass One that is determined based on steady-state parameters including the time between rolling passes from time to the start of the next rolling pass can be considered.
Further, the heat transfer coefficient function F (S ₁ ) may be determined based on the steady parameter in the plurality of steady states and the corresponding contact arc length S ₁ .
It is also conceivable that the heat transfer coefficient function F (S ₁ ) is determined in advance by statistical calculation based on the steady parameter and the corresponding contact arc length S ₁ . Further, in a thermal roll prediction program for a rolling roll for executing a thermal roll prediction process for a rolling roll in hot rolling of the material to be rolled, the heat transfer coefficient of a contact portion between the rolling roll and the material to be rolled is calculated as follows: A computer-readable rolling roll that performs a step of obtaining by a heat transfer coefficient function F (S ₁ ) that is a function of a contact arc length S ₁ that is a circumferential length of a circumferential surface that is in contact with the material to be rolled. It is also possible to configure as a thermal crown prediction program.
Furthermore, in the thermal crown prediction system of the rolling roll in the hot rolling of the material to be rolled, the heat transfer coefficient of the contact portion between the rolling roll and the material to be rolled is defined as the peripheral surface where the rolling roll contacts the material to be rolled. It is also conceivable to constitute a thermal roll prediction system for a rolling roll obtained by a heat transfer coefficient function F (S ₁ ) that is a function of the contact arc length S ₁ that is the circumferential length of the rolling roll.
[0005]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments and examples of the present invention will be described with reference to the accompanying drawings to provide an understanding of the present invention. The following embodiments and examples are examples embodying the present invention, and do not limit the technical scope of the present invention.
Here, FIG. 1 is a correlation diagram between the heat transfer coefficient obtained from the measured data and the contact arc length, and FIG. 2 is the case of using the rolling roll with and without using the thermal crown prediction method according to the embodiment of the present invention. It is a correlation diagram of predicted temperature and measured temperature.
[0006]
The method for predicting the thermal crown of the rolling roll according to the embodiment of the present invention, for example, when performing the thermal crown prediction of the rolling roll using a technique such as a thermal profile model shown in the prior art B (Reference 2), Heat transfer at the contact portion between the rolling roll and the material to be rolled, which is one of the main input variables used for calculating the heat transfer between the rolling material such as steel, aluminum and aluminum alloy and the rolling roll. It is characterized by a method for predicting the rate α ₁ with high accuracy. Accordingly, the calculation methods in the range other than the calculation of the heat transfer coefficient α ₁ in the thermal crown prediction are known in addition to the prior art B, and the description thereof is omitted here.
That is, in the calculation method of the heat transfer coefficient α ₁ in this embodiment, a contact arc length S ₁ which is a circumferential length of a peripheral surface where the rolling roll contacts the material to be rolled during rolling is input. Is calculated by a heat transfer coefficient function F (S ₁ ) which is a function for obtaining the heat transfer coefficient α ₁ . Hereinafter, a method for deriving the heat transfer function F (S ₁ ) will be described.
The heat transfer coefficient function F (S ₁ ) is the steady state under a plurality of rolling conditions, and the contact arc length S ₁ obtained from the heat transfer coefficient α ₁ obtained from steady parameters described later and the rolling conditions. The correlation is derived by statistical calculation. Here, the steady state is the amount of heat that the rolling roll receives from the material to be rolled when rolling is continued with the same rolling conditions such as the material, thickness, temperature, and amount of reduction of the material to be rolled. , The state where the rolling roll temperature converges to a substantially constant value by balancing the amount of heat taken by the coolant etc. that cools the rolling roll. Therefore, in the steady state, since the heat input q = 0 per unit length to the rolling roll in the equation (6), the following equation is established.
α ₁ (T _R −T ₁ ) τ ′ · S ₁ + α ₂ (T _R −T ₂ ) τ ′ · S ₂ + α ₃ (T _R −T ₃ ) τ ′ · S ₃
+ Q _F・ τ '
+ Α ₂ (T _R −T ₂ ) τ ″ · S ₂ + α ₃ (T _R −T ₃ ) τ ″ · S ₃ = 0 (6)
Accordingly, if the respective temperatures T _R , T ₁ , T ₂ , T ₃ in the steady state are measured, parameters other than the heat transfer coefficient α _{1 in the} equation (6) are known values or known. Therefore, the heat transfer coefficient α ₁ can be obtained. In this equation (6), the remaining parameters τ ′, τ ″, α ₂ , α ₃ , T _R , T ₁ , T ₂ , T ₃ , Q _F excluding the heat transfer coefficient α ₁ are the steady parameters described above. It is.
Meanwhile, the contact arc length S _1, the given as rolling conditions, the thickness h1 of the material to be rolled in the inlet side of the one-pass, the same exit side thickness h0, represented by the radius R of the rolling rolls The following formula,
S ₁ = √ [R (h1−h0)] (7).
[0007]
Here, FIG. 1 shows the measured temperatures T _R , T ₁ , T ₂ , and T ₃ in the steady state under various rolling conditions such as the thickness and temperature of the material to be rolled, the amount of reduction, and the stand. Then, the heat transfer coefficient α ₁ is obtained from the steady parameter including this using the equation (6), and this is a graph showing the correlation between the heat transfer coefficient α ₁ and the contact arc length S ₁ obtained by the equation (7). . In addition, in each said rolling condition, it is the same conditions about the material of the said rolling roll and the said to-be-rolled material.
As is apparent from FIG. 1, it can be seen that there is a high correlation between the heat transfer coefficient α ₁ and the contact arc length S ₁ . From the correlation shown in FIG. 1, for example, an approximate expression representing the relationship between the contact arc length S ₁ and the heat transfer coefficient α ₁ is obtained by approximation by exponential function or quadratic expression or power approximation, etc. It is assumed that the heat transfer coefficient function F (S ₁ ).
[0008]
Next, the result of confirming the effectiveness of the heat transfer coefficient function F (S ₁ ) thus obtained will be described. The deformation of the rolling roll in actual rolling is caused by factors other than the thermal crown, and it is difficult to extract only the deformation amount due to the thermal crown from the measured value of the deformation amount of the rolling roll. Evaluation is made by comparing the measured value and the calculated value of the rolling roll temperature during rolling.
2 (a) is above the material to be rolled thickness and temperature, the reduction rate, the stand etc., different to the rolling roll temperature measured value in the rolling conditions, said constant the heat transfer coefficient alpha ₁ in each rolling conditions FIG. 2 (b) is a scatter diagram comparing the calculated rolling roll temperature calculated by giving the calculated value of the rolling roll temperature, and the heat transfer coefficient α ₁ in the above rolling conditions in the same manner as described above. Rolling roll temperature calculation calculated by giving a result calculated using the heat transfer coefficient function F (S ₁ ) derived by approximation with an exponential function (k / S ₁ ^p , where k and p are predetermined coefficients) It is a scatter diagram which compared the value. The calculated value of the rolling roll temperature can be obtained, for example, by a temperature simulation model shown in the above-mentioned prior art A (Reference 1).
As is apparent from FIG. 2, the heat transfer coefficient function F (S ₁ ) according to the present invention is used (FIG. 2 (b)), compared with the case where this is not used (FIG. 2 (a)). It can be seen that the error of the calculated value (vertical axis in FIG. 2) with respect to the measured value of the rolling low temperature (horizontal axis in FIG. 2) is much smaller, and the calculation accuracy is improved. Since the data shown in FIG. 2 (a) and FIG. 2 (b) are online control data during actual operation, they are not actually measured and calculated simultaneously under the same conditions. Although the data of FIG. 2 (b) calculated using the data is a data of a wider range of rolling roll temperatures than the data of FIG. 2 (a) not used, the error is suppressed to be smaller. Thus, it can be seen that the present invention functions effectively even if the rolling state changes over a wide range depending on the rolling conditions. In addition, the data shown in FIGS. 2A and 2B includes data in an unsteady state other than the steady state, and the heat transfer coefficient obtained based on the steady parameter in the steady state. This shows that the function F (S ₁ ) functions effectively even in the unsteady state. In the thermal crown prediction of a rolling roll, the amount of deformation due to thermal expansion is obtained based on the prediction result of the rolling roll temperature, so it is clear that if the prediction accuracy of the rolling roll temperature is improved, the prediction accuracy of the thermal crown is also improved. is there.
The thermal crown prediction system using the heat transfer coefficient function F (S ₁ ) thus obtained is given by a constant in the thermal crown calculation method shown in the prior art B (reference 2), for example. The heat transfer coefficient α ₁ can be realized by incorporating in a computer a program that realizes a calculation method modified to obtain the heat transfer coefficient α ₁ by the heat transfer function F (S ₁ ).
In this way, if the steady-state parameters and the like are measured in advance for a number of rolling conditions that can perform the statistical calculation, there is no measured data if at least the material of the rolling roll and the material to be rolled are the same. Even when new rolling conditions are met, the thermal crown of the roll can be predicted with high accuracy.
[0009]
【The invention's effect】
As described above, according to the present invention, in rolling a material to be rolled such as steel, aluminum, and aluminum alloy by a rolling roll, even when new rolling conditions without actual measurement data are obtained, the rolling roll and the material to be rolled are used. The heat transfer coefficient between the roll and the roll is calculated with high accuracy, and the prediction accuracy of the thermal crown of the rolling roll is improved. As a result, the crown quality of the material to be rolled is improved.
[Brief description of the drawings]
FIG. 1 is a correlation diagram between a heat transfer coefficient obtained from measured data and a contact arc length.
FIG. 2 is a correlation diagram between a predicted temperature of a rolling roll and an actually measured temperature when a thermal crown prediction method according to an embodiment of the present invention is used and when it is not used.

Claims (6)

In the method for predicting the thermal crown of a rolling roll in hot rolling of a material to be rolled,
The heat transfer rate of the contact portion of the rolling rolls and the material to be rolled, heat transfer the rolling roll is circumferential direction of the function of the contact arc length S ₁ is the length of the peripheral surface in contact with the material to be rolled A method for predicting the thermal crown of a rolling roll, characterized by being obtained by a rate function F (S ₁ ). The heat transfer coefficient function F (S ₁ ) is the temperature of the material to be rolled, the temperature of the rolling roll in a steady state, the heat transfer coefficient of the coolant cooling part where the rolling roll is cooled by the coolant, and the temperature of the coolant. , The heat transfer coefficient of the air cooling part other than the coolant cooling part of the rolling roll, the ambient temperature of the air cooling part, the amount of heat generated by friction between the rolling roll and the material to be rolled, the rolling pass time, and the end of a certain rolling pass The method for predicting a thermal crown of a rolling roll according to claim 1, wherein the thermal crown predicting method is determined based on a steady parameter including a time between rolling passes until the start of the next rolling pass. The thermal crown of the rolling roll according to claim 2, wherein the heat transfer coefficient function F (S ₁ ) is determined based on a plurality of the steady parameters in the steady state and the corresponding contact arc length S _1. Prediction method. The heat transfer coefficient function F (S ₁₎ is the constant parameter and thermal crown prediction method of the rolling roll according to claim 3 which is predetermined by statistical calculation based on the contact arc length S ₁ corresponding thereto. In the roll roll thermal crown prediction program for executing the roll roll thermal crown prediction process in hot rolling of the material to be rolled,
The heat transfer coefficient of the contact part of the rolling rolls and the material to be rolled, heat transfer the rolling roll is circumferential direction of the function of the contact arc length S ₁ is the length of the peripheral surface in contact with the material to be rolled A computer-readable thermal roll prediction program for a rolling roll, characterized by executing a step obtained by a rate function F (S ₁ ). In the thermal crown prediction system for rolling rolls in hot rolling of work materials,
The heat transfer rate of the contact portion of the rolling rolls and the material to be rolled, heat transfer the rolling roll is circumferential direction of the function of the contact arc length S ₁ is the length of the peripheral surface in contact with the material to be rolled A thermal crown prediction system for a rolling roll, characterized by being obtained by a rate function F (S ₁ ).

Images