JP3944002B2 - Rolling load prediction method for sheet metal rolling - Google Patents

Rolling load prediction method for sheet metal rolling Download PDF

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Publication number
JP3944002B2
JP3944002B2 JP2002173623A JP2002173623A JP3944002B2 JP 3944002 B2 JP3944002 B2 JP 3944002B2 JP 2002173623 A JP2002173623 A JP 2002173623A JP 2002173623 A JP2002173623 A JP 2002173623A JP 3944002 B2 JP3944002 B2 JP 3944002B2
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Prior art keywords
rolling
force function
formula
prediction method
rolling load
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JP2004017073A (en
JP2004017073A5 (en
Inventor
康宏 東田
茂 小川
健二 山田
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Nippon Steel Corp
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Nippon Steel Corp
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Description

【0001】
【発明の属する技術分野】
本発明は、板状の金属製品を圧延によって製造する圧延方法に関し、さらに詳しくは、金属板圧延の圧延荷重予測方法に関するものである。
【0002】
【従来の技術】
金属板圧延において、高精度の板厚、板形状、板クラウンを得るためには、圧延荷重を正確に予測した上で、ロールを含めた圧延機(ミル)の変形量を計算し、圧下設定値、ロールベンダー値などの各種設定値を決める必要がある。
この圧延荷重の予測精度が悪いと、圧延後の板厚およびクラウン精度も悪化し、板形状も大きく乱れる結果となる。したがって、圧延荷重を予め、正確に予測計算することは、板圧延において、極めて重要なことである。
【0003】
ところで、一般に、圧延荷重Pの予測には下記の式(2)が用いられる。
P=k・B・ld・Q ・・・・・・(2)
ここで、 P:圧延荷重、k:圧延材の変形抵抗、B:板幅、ld:接触弧長
Q:圧下力関数
式(2)において、変形抵抗kは、圧縮試験等の実験から求めることができ、板幅B、接触弧長ldは、幾何学的に求めることができるので、圧下力関数Qを正確に求めることが、圧延荷重Pの精度向上に極めて重要であることが分かる。
【0004】
この圧下力関数に関しては、従来より、種々の検討がなされ、特に、厚板圧延のような板厚の厚い板から薄板のような薄い板までの圧下力関数Qを表す式として、斉藤の式、中島の式等が提案されている(例えば、「最新塑性加工要覧」社団法人日本塑性加工学会 昭和61年8月発行 147ページ参照)。両式とも、式の形は式(3)の通りであり、形状比Γをパラメータとして、圧下力関数Qを表現するものである。
Q=a0+b0・Γ+c0/Γ ・・・・・・(3)
ここで、
0、b0、c0:定数
形状比Γ=接触弧長/平均板厚
平均板厚=(入側板厚+2・出側板厚)/3
≒(入側板厚+出側板厚)/2
【0005】
【発明が解決しようとする課題】
上記の斉藤の式ないし中島の式は、形状比のみをパラメータとしているために、板厚と圧下量が異なっても、形状比Γが同一であれば、同一の圧下力関数Qの値を示すことになる。しかしながら、後述するように、形状比Γが同一であっても板厚と圧下量が異なれば、圧下力関数Qの値は異なる場合があり、上記の斉藤の式ないし中島の式を用いた場合、予測される圧下力関数Qが大きな誤差を持つために、圧延荷重の計算値の誤差も大きくなり、結果として、板厚不良、形状不良などが発生するという問題があった。
【0006】
そこで、本発明は、かかる課題を有利に解決するために新たな圧下力関数Qを用いて、より精度の高い予測を可能とする金属板圧延の圧延荷重予測方法を提供することを目的とする。
【0007】
【課題を解決するための手段】
本発明の要旨とするところは、以下の通りである。
(1) 少なくとも上下2本のロールを用いることによって所定の板厚とする金属板の圧延において、圧延荷重式の構成要素である圧下力関数Qのパラメータに形状比Γ、板の噛込角φを用いて、圧延荷重を予測計算することを特徴とする、金属板圧延の圧延荷重予測方法。
(2) 前記圧下力関数Qを計算する式が、下記(1)式を満足することを特徴とする、前記(1)に記載の金属板圧延の圧延荷重予測方法。
Q=a+b・xn+c/xm ・・・・・・(1)
ここで、
a、b、c、n、m:少なくとも一つは板の噛込角φをパラメータとする変数であり、該変数以外は定数である。
x=α(Γ+β)
α、β:定数
Γ:形状比
(3) 前記(1)式中のnを、板の噛込角φのパラメータとする変数とすることを特徴とする、前記(2)に記載の金属板圧延の圧延荷重予測方法。
【0008】
【発明の実施の形態】
以下、本発明を図面に基づいて、詳細に説明する。
一般に、圧延解析に関して、計算時間を十分長くとることができる場合には、三次元有限要素法と呼ばれる解析手法(例えば、「板圧延の理論と実際」社団法人日本鉄鋼協会 昭和59年9月1日発行 67〜72ページ参照)を用いれば、正確な圧延荷重が計算できることが知られている。
【0009】
図1に、その三次元有限要素法の計算に基づく圧下力関数Qと前述の従来法である式(3)による圧下力関数Qとを、形状比Γとの関係で比較して示す。なお、図1での計算条件は、ワークロール直径1200mm、板厚15〜300mm、圧下率5〜40%とし、また、式(3)中の定数a0、b0、c0は、最小自乗法で最適化した。この場合、パラメータが形状比Γのみである式(3)では、形状比Γが1を越えるあたりから正確な圧下力関数Qを算出できなくなることが分かる。
【0010】
そこで、本発明者らは鋭意検討した結果、図2で説明するような噛込角φを考慮すれば、正確な圧下力関数Qを求められることを見出した。例えば、図3に、図1で示した有限要素法による圧下力関数Qを噛込角φ別に層別して再整理した結果を示すように、噛込角φをパラメータとすれば、圧下力関数Qを正確に予測できることが分かる。本発明者らは、さらに、創意工夫を重ね、圧下力関数Qを計算する式を下記の式(1)とすれば、噛込角φをパラメータとして圧下力関数Qが正確に計算できることを見出した。
Q=a+b・xn+c/xm ・・・・・・(1)
ここで、
a、b、c、n、m:少なくとも一つは板の噛込角φをパラメータとする変数であり、該変数以外は定数である。
x=α(Γ+β) ・・・・・・(4)
ここで、α、β:定数
形状比Γ=接触弧長/平均板厚
平均板厚=(入側板厚+2・出側板厚)/3
≒(入側板厚+出側板厚)/2
【0011】
なお、a、b、c、n、mのいずれを噛込角φのパラメータとするかは、各圧延条件に応じた有限要素法の計算結果に応じて選択すれば良いが、通常、圧下力関数Qは図3に示すような挙動を示す(形状比Γが大きくなるにつれて噛込角φの影響が増加する。)ので、nを噛込角φの主パラメータとするのが好ましい。もし、有限要素法の結果が、形状比Γが小さくなるにつれて噛込角φの影響が増加する場合には、cを噛込角φの主パラメータとすれば良い。さらに、形状比Γの全範囲で噛込角φの影響を受ける場合には、aを主パラメータにするのが良く、微調整をn、b、c、mで行えば良い。
また、式(4)は、通常、α=1,β=0で十分な精度が得られるが、より精度を高める場合には、α、βをチューニングすれば良い。
【0012】
以下、例として、図1の結果を、噛込角φのパラメータとして式(1)のnを用いて整理した場合について述べる(α=1,β=0とした。)。この場合、a、b、c、mを表1に示す定数とし、噛込角φとnとの関係は表2の通りとすれば良い。その結果を図4に示す。同図から明らかなように、本発明によれば、非常に高精度で、圧下力関数Qが予測計算できることが分かる。なお、噛込角φとnとの関係は、表2のようにテーブル化しても良いし、適当な関数で近似しても良い。
【0013】
【表1】

Figure 0003944002
【0014】
【表2】
Figure 0003944002
【0015】
【実施例】
板厚、圧下率の異なるスラブ1000本を対象として、圧延荷重を予測し、その荷重予測値に基づいて計算した圧下設定値で、鋼の熱間圧延を実施した。圧延荷重予測には、式(2)を用い、圧下力関数モデルとしては、式(1)を用いた。式(4)においては、α=1,β=0とした。また、式(1)のa、b、c、mは表1に示す定数を用い、nを噛込角φのパラメータとした。nと噛込角φの関係は、表2の結果を回帰計算し、n=−0.03179φ+1.11678とした。
【0016】
比較例として、実施例と同様に、板厚、圧下率の異なるスラブ1000本を対象として、圧延荷重を予測し、その荷重予測値に基づいて計算した圧下設定値で、鋼の熱間圧延を実施した。圧下力関数モデルは式(3)を用いた。式(3)の定数a0、b0、c0に関しては、図1に示す有限要素法の結果に基づいて、回帰計算により求めた。
【0017】
表3に、本発明の実施例と比較例の板厚の予測誤差(計算値−実測値)の標準偏差σを示す。圧延荷重が高精度に予測できる本発明の実施例では、板厚予測誤差の標準偏差が非常に小さいことが分かる。一方、圧延荷重の予測誤差が大きい比較例では、大きな板厚の予測誤差を示した。
【0018】
【表3】
Figure 0003944002
【0019】
【発明の効果】
本発明の金属板圧延の圧延荷重予測方法により、従来技術より著しく改善された高い精度で圧延荷重を予測することができることから、ひいてはより高精度の板厚、板形状および板クラウンを有する高品質の金属板を有利に提供できるだけでなく、圧延コストを大幅に低減できるという有利な効果が得られる。
【図面の簡単な説明】
【図1】従来法である式(3)による圧下力関数Qと有限要素法による計算結果から算出した圧下力関数Qとを、形状比Γとの関係で比較して示す図である。
【図2】板圧延における噛込角φを説明する図である。
【図3】有限要素法の計算結果から算出される圧下力関数Qを、噛込角φと形状比Γとをパラメータにして示す図である。
【図4】本発明による圧下力関数Qと有限要素法の計算結果から算出した圧下力関数Qとを、形状比Γとの関係で比較して示す図である。
【符号の説明】
1、1′ ワークロール
2 被圧延材[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a rolling method for producing a plate-shaped metal product by rolling, and more particularly to a rolling load prediction method for metal plate rolling.
[0002]
[Prior art]
In metal sheet rolling, in order to obtain high-precision sheet thickness, sheet shape, and sheet crown, the rolling load is accurately predicted, the amount of deformation of the rolling mill (mill) including the roll is calculated, and the reduction is set. It is necessary to determine various setting values such as value and roll vendor value.
If the prediction accuracy of the rolling load is poor, the plate thickness and crown accuracy after rolling are also deteriorated, and the plate shape is greatly disturbed. Therefore, accurately predicting and calculating the rolling load in advance is extremely important in sheet rolling.
[0003]
By the way, the following formula (2) is generally used for predicting the rolling load P.
P = k · B · ld · Q (2)
Here, P: rolling load, k: deformation resistance of the rolled material, B: plate width, ld: contact arc length Q: in the rolling force function equation (2), the deformation resistance k is obtained from an experiment such as a compression test. Since the sheet width B and the contact arc length ld can be obtained geometrically, it can be seen that obtaining the rolling force function Q accurately is extremely important for improving the accuracy of the rolling load P.
[0004]
Various studies have been made on this rolling force function, and in particular, Saito's formula as a formula representing the rolling force function Q from a thick plate such as thick plate rolling to a thin plate such as a thin plate. Nakajima's formula has been proposed (see, for example, “Newest Plastic Working Manual”, Japan Society for Technology of Plasticity, published August 1986, page 147). In both equations, the form of the equation is as shown in Equation (3), and expresses the rolling force function Q using the shape ratio Γ as a parameter.
Q = a 0 + b 0 · Γ + c 0 / Γ (3)
here,
a 0 , b 0 , c 0 : Constant shape ratio Γ = contact arc length / average plate thickness average plate thickness = (input side plate thickness + 2 · outside plate thickness) / 3
≒ (Incoming side plate thickness + Outer side plate thickness) / 2
[0005]
[Problems to be solved by the invention]
The above Saito's formula or Nakajima's formula uses only the shape ratio as a parameter. Therefore, even if the plate thickness and the amount of rolling are different, the same rolling force function Q is shown if the shape ratio Γ is the same. It will be. However, as will be described later, even when the shape ratio Γ is the same, the value of the rolling force function Q may be different if the plate thickness and the rolling amount are different, and the above-mentioned Saito formula or Nakajima formula is used. Since the predicted rolling force function Q has a large error, an error in the calculated value of the rolling load also increases, resulting in problems such as a defective thickness and a defective shape.
[0006]
Then, this invention aims at providing the rolling load prediction method of the metal plate rolling which enables a more accurate prediction using the new rolling force function Q in order to solve this subject advantageously. .
[0007]
[Means for Solving the Problems]
The gist of the present invention is as follows.
(1) In rolling a metal plate having a predetermined thickness by using at least two upper and lower rolls, the shape ratio Γ and the biting angle φ of the plate are included in the parameters of the rolling force function Q that is a component of the rolling load type. A rolling load prediction method for metal plate rolling, characterized in that the rolling load is predicted and calculated using
(2) The rolling plate load prediction method for metal sheet rolling according to (1), wherein the formula for calculating the rolling force function Q satisfies the following formula (1).
Q = a + b · x n + c / x m (1)
here,
a, b, c, n, m: At least one is a variable having the biting angle φ of the plate as a parameter, and other than the variable is a constant.
x = α (Γ + β)
α, β: constant Γ: shape ratio (3) The metal plate according to (2), wherein n in the formula (1) is a variable that is a parameter of the biting angle φ of the plate. Rolling load prediction method for rolling.
[0008]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the present invention will be described in detail with reference to the drawings.
In general, if the calculation time can be sufficiently long for the rolling analysis, an analysis method called a three-dimensional finite element method (for example, “Theory and Practice of Sheet Rolling” Japan Iron and Steel Institute, September 1, 1984) It is known that an accurate rolling load can be calculated by using a daily issue (see pages 67 to 72).
[0009]
FIG. 1 shows a comparison between the rolling force function Q based on the calculation of the three-dimensional finite element method and the rolling force function Q according to the above-mentioned conventional method (3) in relation to the shape ratio Γ. The calculation conditions in FIG. 1 are a work roll diameter of 1200 mm, a plate thickness of 15 to 300 mm, a rolling reduction of 5 to 40%, and the constants a 0 , b 0 and c 0 in equation (3) are the minimum Optimized by multiplication. In this case, it can be seen that in Formula (3) in which the parameter is only the shape ratio Γ, the accurate rolling force function Q cannot be calculated when the shape ratio Γ exceeds 1.
[0010]
Therefore, as a result of intensive studies, the present inventors have found that an accurate rolling force function Q can be obtained in consideration of the biting angle φ described with reference to FIG. For example, FIG. 3 shows the result of rearranging the rolling force function Q by the finite element method shown in FIG. 1 by layering according to the biting angle φ, and if the biting angle φ is used as a parameter, the rolling force function Q It can be seen that can be accurately predicted. The present inventors have further found out that the reduction force function Q can be accurately calculated using the bite angle φ as a parameter if the following formula (1) is used as an expression for calculating the reduction force function Q through repeated ingenuity. It was.
Q = a + b · x n + c / x m (1)
here,
a, b, c, n, m: At least one is a variable having the biting angle φ of the plate as a parameter, and other than the variable is a constant.
x = α (Γ + β) (4)
Here, α, β: constant shape ratio Γ = contact arc length / average plate thickness average plate thickness = (input side plate thickness + 2 · outside plate thickness) / 3
≒ (Incoming side plate thickness + Outer side plate thickness) / 2
[0011]
It should be noted that which of a, b, c, n, and m is used as the parameter of the biting angle φ may be selected according to the calculation result of the finite element method corresponding to each rolling condition. The function Q behaves as shown in FIG. 3 (the influence of the biting angle φ increases as the shape ratio Γ increases), so it is preferable to set n as the main parameter of the biting angle φ. If the result of the finite element method shows that the influence of the biting angle φ increases as the shape ratio Γ decreases, c may be set as the main parameter of the biting angle φ. Further, when the shape angle Γ is affected by the biting angle φ over the entire range, it is preferable to use a as a main parameter, and fine adjustment may be performed using n, b, c, and m.
In addition, in Formula (4), sufficient accuracy is usually obtained when α = 1 and β = 0 , but α and β may be tuned for higher accuracy.
[0012]
Hereinafter, as an example, a case where the result of FIG. 1 is arranged using n in the equation (1) as a parameter of the biting angle φ will be described ( α = 1, β = 0 ). In this case, a, b, c, and m may be constants shown in Table 1, and the relationship between the biting angle φ and n may be as shown in Table 2. The result is shown in FIG. As can be seen from the figure, according to the present invention, the rolling force function Q can be predicted and calculated with very high accuracy. The relationship between the biting angle φ and n may be tabulated as shown in Table 2 or approximated by an appropriate function.
[0013]
[Table 1]
Figure 0003944002
[0014]
[Table 2]
Figure 0003944002
[0015]
【Example】
The rolling load was predicted for 1000 slabs with different plate thicknesses and rolling reductions, and the steel was hot-rolled with the rolling reduction set value calculated based on the predicted load value. Formula (2) was used for rolling load prediction, and Formula (1) was used as a rolling force function model. In the formula (4), α = 1 and β = 0 . In addition, the constants shown in Table 1 were used for a, b, c, and m in Equation (1), and n was a parameter for the biting angle φ. Regarding the relationship between n and the biting angle φ, the results of Table 2 were calculated by regression, and n = −0.03179φ + 11.1678.
[0016]
As a comparative example, in the same manner as in the example, the rolling load was predicted for 1000 slabs having different thicknesses and rolling reductions, and the steel was hot rolled at the rolling setting value calculated based on the predicted load value. Carried out. Formula (3) was used for the rolling force function model. The constants a 0 , b 0 , and c 0 in Equation (3) were obtained by regression calculation based on the result of the finite element method shown in FIG.
[0017]
Table 3 shows the standard deviation σ of the plate thickness prediction error (calculated value−actually measured value) of the example of the present invention and the comparative example. In the embodiment of the present invention in which the rolling load can be predicted with high accuracy, it can be seen that the standard deviation of the plate thickness prediction error is very small. On the other hand, the comparative example having a large rolling load prediction error showed a large plate thickness prediction error.
[0018]
[Table 3]
Figure 0003944002
[0019]
【The invention's effect】
The rolling load prediction method of the metal plate rolling according to the present invention can predict the rolling load with high accuracy significantly improved over the prior art, and consequently high quality having a more accurate plate thickness, plate shape, and plate crown. The advantageous effect that not only the metal plate can be advantageously provided but also the rolling cost can be greatly reduced is obtained.
[Brief description of the drawings]
FIG. 1 is a diagram showing a comparison of a rolling force function Q according to Equation (3), which is a conventional method, and a rolling force function Q calculated from a calculation result by a finite element method in relation to a shape ratio Γ.
FIG. 2 is a diagram for explaining a biting angle φ in plate rolling.
FIG. 3 is a diagram showing a rolling force function Q calculated from the calculation result of the finite element method using the bite angle φ and the shape ratio Γ as parameters.
FIG. 4 is a diagram showing a reduction force function Q according to the present invention and a reduction force function Q calculated from the calculation result of the finite element method in comparison with the shape ratio Γ.
[Explanation of symbols]
1, 1 'Work roll 2 Material to be rolled

Claims (3)

少なくとも上下2本のロールを用いることによって所定の板厚とする金属板の圧延において、圧延荷重式の構成要素である圧下力関数Qのパラメータに形状比Γ、板の噛込角φを用いて、圧延荷重を予測計算することを特徴とする、金属板圧延の圧延荷重予測方法。In rolling a metal sheet having a predetermined thickness by using at least two upper and lower rolls, the shape ratio Γ and the biting angle φ of the sheet are used as parameters of the rolling force function Q, which is a component of the rolling load formula. A rolling load prediction method for rolling a metal sheet, characterized by predicting and calculating a rolling load. 前記圧下力関数Qを計算する式が、下記(1)式を満足することを特徴とする、請求項1に記載の金属板圧延の圧延荷重予測方法。
Q=a+b・xn+c/xm ・・・・・・(1)
ここで、
a、b、c、n、m:少なくとも一つは板の噛込角φをパラメータとする変数であり、該変数以外は定数である。
x=α(Γ+β)
α、β:定数
Γ:形状比
The rolling load prediction method for metal sheet rolling according to claim 1, wherein the formula for calculating the rolling force function Q satisfies the following formula (1).
Q = a + b · x n + c / x m (1)
here,
a, b, c, n, m: At least one is a variable having the biting angle φ of the plate as a parameter, and other than the variable is a constant.
x = α (Γ + β)
α, β: Constant Γ: Shape ratio
前記(1)式中のnを、板の噛込角φのパラメータとする変数とすることを特徴とする、請求項2に記載の金属板圧延の圧延荷重予測方法。3. The rolling load prediction method for metal sheet rolling according to claim 2, wherein n in the equation (1) is a variable having a parameter of the biting angle φ of the sheet.
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