JPH115111A - Device for plate rolling - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make it possible to control accurately the warpage by estimating and operating the tip warpage generation rate in the pre-pass rolling based upon the amount of curvature therein, circumferential speed of the upper and lower workrolls and upper and lower surface temperatures of the rolled stock and that of the rolled stock before above-said pass rolling. SOLUTION: From the peripheral speed of the upper and lower work rolls at the pre-pass, the temperatures of the upper and lower surfaces of the rolled stock and the tip warpage rate, the warpage rate caused by the difference of the peripheral speed and the warpage rate caused by the temperature difference between the upper and lower surfaces of the rolled stock together with the warpage rate caused by the factors other than mentioned above are obtained. Then the temperature difference between the upper and lower surfaces of the rolled stock is measured and the warpage rate caused by this temperature difference is operated and estimated. Further, based on the non uniform circumferential and the warpage rate caused by factors other than the temperature difference between the upper and lower surfaces and the estimated warpage rate based upon the temperature and the estimated warpage rate based upon the temperature difference between the upper and lower surfaces, the warpage rate to come out at afore-said pass is obtained. The rolling is conducted by setting the peripheral speed so that the warpage is solved.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a rolling method for producing a sheet metal product.

[0002]

2. Description of the Related Art Warpage generated during rolling of a sheet material has a great effect on product productivity, such as a reduction in rolling efficiency, occurrence of equipment accidents, and an increase in the refining process. For example, in the refining process, it is necessary to correct a warp by a leveler, a press, or the like, and in an extreme case, it may be necessary to cut a defective portion. Further, when a larger warpage occurs, the rolling equipment may be damaged due to the collision of the plates. In this case, not only does the plate itself lose its product value, but it also causes enormous damage such as production stoppage and repair of rolling equipment.

It is generally said that the mechanism of occurrence of rolling warpage is caused by the following vertical asymmetry factor in rolling. Vertical difference in friction coefficient between work roll and rolled material: Δμ Vertical temperature difference in rolled material (vertical difference in deformation resistance): Δt Difference in circumferential speed of upper and lower work rolls: ΔV Geometric condition Radius difference between upper and lower work rolls .DELTA.R. Plate incident angle (difference between upper and lower pass lines) .alpha. However, the above vertical asymmetry factor does not always affect the warpage. It is not understood. Therefore, a method of controlling the warpage of the previous path by measuring the warp of the previous path is disclosed in Japanese Patent Application Laid-Open No. 63-60012,
JP-A-63-132708, JP-A-3-2343
No. 09 and Japanese Patent Application Laid-Open No. 4-26281. Each of these methods is a method of measuring the warpage of the preceding pass and performing control (for example, different peripheral speed rolling) for eliminating the warpage in the relevant pass.

[0004]

SUMMARY OF THE INVENTION The aforementioned Japanese Patent Application Laid-Open No. 63-6 / 1988
0012, JP-A-63-132708, JP-A-3-234309, JP-A-4-262711
In the above publication, it is assumed that the warpage of the previous pass continues in the pass in any of the methods. However, in actual rolling, the warping direction may be reversed between the preceding pass and the pass depending on conditions, and in the conventional method, warpage may be increased by controlling the conventional method.

An object of the present invention is to provide a method of controlling warpage with high accuracy in the manufacture of a plate-shaped metal product in view of the above points.

[0006]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems, the present invention provides an amount of warpage at the time of leading edge rolling in a previous pass, a peripheral speed of upper and lower work rolls, upper and lower surface temperatures of a rolled material, and rolling before the pass rolling. Measure the upper and lower surface temperature of the material, predict and calculate the tip warpage amount of the path from the measurement result,
The method is characterized in that different peripheral speed ratios of the upper and lower work rolls for solving the predicted warpage amount are calculated, and a difference between the upper and lower work roll peripheral speeds is set and controlled based on the calculation result of the different peripheral speed ratios.

That is, the subject of the present invention is as follows. In the method of rolling a plate material by a rolling mill having at least upper and lower work rolls, from the peripheral speed of the upper and lower work rolls in the previous pass, the upper and lower surface temperatures of the rolled material and the radius of curvature of the rolled material tip in the previous pass,
Determine the curvature due to the different peripheral speed in the previous pass and the curvature due to the temperature difference between the upper and lower surfaces of the rolled material in the previous pass, and calculate the curvature due to factors other than the different peripheral speed and the upper and lower surface differences in the front pass. The temperature of the upper and lower surfaces of the rolled material in the pass is measured, and the warp curvature in the pass due to the temperature difference between the upper and lower surfaces of the rolled material is obtained. Based on the warp curvature and the warp curvature caused by the temperature difference between the upper and lower surfaces of the rolled material in the pass, the warp curvature in the pass is determined, and the upper and lower work rolls in the pass are determined so as to eliminate the warp curvature. A plate rolling method characterized in that a plate material is rolled by setting a speed difference, and preferably, the warp curvature in the pass, the different peripheral speed in the previous pass and the upper and lower surfaces of the upper and lower surfaces. And warp curvature due to factors other than the time difference,
A sheet rolling method, wherein the rolling is performed by setting the peripheral speed difference between the upper and lower work rolls in the pass to be the sum of the warpage curvatures caused by the temperature difference between the upper and lower surfaces in the pass, and eliminating the warpage curvature. More preferably, the warp curvature in the path, the warp curvature due to factors other than the different peripheral speed and the temperature difference between the upper and lower surfaces in the previous path, the warp curvature in consideration of the change in the shape ratio between the previous path and the path. When,
A sheet rolling method, wherein the rolling is performed by setting the peripheral speed difference between the upper and lower work rolls in the pass to be the sum of the warpage curvatures caused by the temperature difference between the upper and lower surfaces in the pass, and eliminating the warpage curvature. It is.

Preferably, at least upper and lower work tubes are used.
Method of rolling a sheet material with a rolling mill having a roll
The peripheral speed of the upper and lower work rolls in the previous pass
(V^T _R1, V^B _R1), The temperature of the upper and lower surfaces of the rolled material (t^T ₁ ,
t^B ₁ ) And the curvature of the rolled material tip in the previous pass
Radius ρ₁ And measure the roll peripheral speed and warpage
Different peripheral speed ratio in the previous pass from the radius of curvature₁ And warp
Curvature κ_M1And the different peripheral speed ratio χ₁ Warpage caused by
Rate κ_V1And the temperature difference Δt between the upper and lower surfaces of the rolled material.₁ 
Curvature κ due to_T1And warp in the previous pass
Rate κ_M1Different peripheral speed ratio from₁ Curvature κ due to_V1And up and down
Warpage curvature κ caused by temperature difference between surfaces_T1And subtract
Due to factors other than the different peripheral speeds and the temperature difference between the upper and lower surfaces.
Curvature κ_Q1And rolling in the pass
Temperature of the upper and lower surfaces of the material (t^T _Two , T^B _Two ) Measure the temperature
Difference Δt_Two Curvature κ due to_T2To the path
Due to factors other than different peripheral speeds and temperature differences between the upper and lower surfaces
Curvature κ_Q2To κ_Q2= Κ_Q1And the curvature of the path
Rate κ_P2And κ_P2= Κ_Q2+ Κ_T2To eliminate this curvature
So that the peripheral speed of the upper and lower work rolls in the pass
A plate rolling method characterized by rolling with a set difference
And more preferably, the curvature κ in the path._P2
Other than the peripheral speed and the temperature difference between the upper and lower surfaces in the previous pass.
Curvature κ_Q1In addition, the shape ratio between the previous pass and the relevant pass
Calculated based on the following formula taking into account the effects of fluctuations in
Due to factors other than the different peripheral speeds in the pass and the temperature difference between the upper and lower surfaces.
Curvature κ_Q2And the temperature difference between the upper and lower surfaces in the path
Resulting curvature κ_T2Characterized by the sum of
It is a rolling method. κ_Q2= Δ₁ ・ Κ_Q1 δ₁ : Shape ratio (contact projection arc length between rolled material and work roll)
Divided by the average value of the thickness of the inlet and outlet plates) and the curvature
Learning coefficient indicating engagement

[0009] In addition, preferably, the warp curvature κ _P2 in the path is changed to the warp curvature κ _Q1 due to factors other than the different peripheral speed and the temperature difference between the upper and lower surfaces in the previous path, and the shape ratio of the front path and the path is calculated. This is a plate rolling method characterized by taking the sum of κ _Q2 obtained based on the following equation in consideration of the influence of fluctuation and the warp curvature κ _T2 caused by the temperature difference between the upper and lower surfaces in the pass.

[0010] However _{κ Q2 = δ 2 · κ Q1} , δ 2: warp curvature shape ratio when Δμ does not change occurs when the Γ ₂ q (Γ ₂₎ and shape ratio occurs when the gamma ₁ The ratio to the warp curvature q (Γ ₁ ) (q (Γ ₂ ) /
q (Γ ₁ )) Δt: Vertical temperature difference of rolled material Δμ: Vertical difference of friction coefficient between work roll and rolled material Γ ₁ : Shape ratio of previous pass Γ ₂ : Shape ratio of relevant pass Γ: Shape ratio: Rolling The value obtained by dividing the contact projection arc length between the material and the work roll by the average value of the thickness of the entrance side and the thickness of the exit side. More preferably, the warpage curvature is obtained by using the curvature that is standardized as work roll radius / warpage curvature radius. This is a sheet rolling method.

[0011] In the present invention, more preferably, when rolling is performed by giving the upper and lower material temperature difference Δt ^C ₂ at the time of rolling of the pass, the difference between the different peripheral speed and the upper and lower surface temperature difference in the pass. The curvature curvature κ _Q'2 is _defined as κ _Q′2 = κ _M2 −κ _V2 −κ ^C _T2 , and the curvature curvature κ _Q3 other than the different peripheral speed and the upper and lower surface temperature differences in the next pass is _defined as κ _Q3 = κ _Q′2. , The upper and lower surface temperature of the rolled material in the next pass (t ^T ₃ , t ^B
₃ ) is measured, the curvature κ _T3 in the next pass due to the temperature difference Δt ₃ is obtained, and the curvature κ _P3 generated in the next pass is κ _P3 = κ _Q3 + κ _T3, preferably κ _P3 = κ _Q3 + η Rolling by predicting κ _T3 and setting any of the upper and lower work roll speed differences, upper and lower material temperature differences, and upper and lower friction coefficient differences alone or in combination in the next pass to eliminate this warpage This is a plate rolling method. Where κ
_M2 is the warp curvature at the path, kappa _V2 is the warp curvature of the upper and lower work rolls speed difference caused in the path, kappa ^C _T2 upper and lower surfaces temperature difference warping of resulting in a temperature difference Delta] t ^C ₂ after application of the path Is a curvature, and η is a correction coefficient obtained by learning, experiment, or calculation.

In addition, when rolling is performed by applying a vertical friction coefficient difference Δμ ^L ₂ during rolling of the pass, the warpage curvature κ _Q′2 other than the different peripheral speed and the upper and lower surface temperature difference in the _pass.
Κ _Q′2 = κ _M2 −κ _V2 −κ _T2 −κ _L2 , preferably, as κ _Q′2 = κ _M2 −κ _V2 −κ _T2 −γ · κ _L2 , _Assuming that the curvature κ _Q3 other than the upper and lower surface temperature difference is κ _Q3 = κ _Q′2 , the upper and lower surface temperatures of the rolled material in the next pass (t ^T ₃ , t ^B
₃ ) is measured, the curvature κ _T3 in the next pass due to the temperature difference Δt ₃ is obtained, and the curvature κ _P3 generated in the next pass is predicted as κ _P3 = κ _Q3 + κ _T3 to eliminate this curvature. As described above, the present invention provides a sheet rolling method in which any one of the difference between the upper and lower roll speeds, the difference between the upper and lower material temperatures, and the difference between the upper and lower friction coefficients is set alone or in combination in the next pass. Here, κ _L2 is a warpage curvature caused by Δμ ^L _{2 in the} path, and γ is a correction coefficient obtained by learning, experiment, or calculation.

Further, the influence of the change in the shape ratio between the current path and the next path is determined by changing the warp curvature κ _Q3 in the next path to the warp curvature κ _Q′2 due to factors other than the different peripheral speeds and the temperature difference between the upper and lower surfaces of the current path. Κ _Q3 = δ ₁ κ _Q'2, and _more preferably, a sheet rolling method characterized by being determined based on the following equation. κ _Q3 = δ ₂ · κ _Q'2 where δ ₁ : The _relationship between the shape ratio (the value obtained by dividing the contact projection arc length between the rolling mill and the work roll by the average value of the entrance and exit sheet thicknesses) and the warpage curvature Learning coefficient to indicate. [delta] _2: ratio of warp curvature q (gamma ₁₎ that Δμ warp curvature q (gamma ₂₎ a shape ratio shape ratio when no change occurs in the case of gamma ₂ occurs when the gamma ₁ (q ( Γ ₂ ) / q
(Γ ₁ )) Δt: Vertical temperature difference of rolled material Δμ: Vertical difference of friction coefficient between work roll and rolled material Γ ₁ : Shape ratio of previous pass Γ ₂ : Shape ratio of relevant pass ：: Shape ratio: Rolled material The value obtained by dividing the contact projection arc length between the workpiece and the work roll by the average value of the thicknesses of the entrance side and the exit side. In the present invention, the warpage curvature is defined as the work curvature radius / warpage curvature radius. Can also.

[0014]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the drawings. FIG. 1 shows an example of a rolling mill to which the present invention is applied. Roller tables 4 and 4 are provided before and after a rolling mill 7 having upper and lower work rolls 1 and 2, respectively.
The rolled material 3 illustrated on the roller table 4 is:
The upper work roll 1 and the lower work roll 2 are rolled to a predetermined thickness. The upper roll system is composed of an upper work roll 1 and an upper backup roll 5, and the lower roll system is composed of a lower work roll 2 and a lower backup roll 6. Hereinafter, unless otherwise specified, a roll refers to a work roll.

Further, the different peripheral speed χ, the warpage curvature κ, and the normalized warpage curvature κ ^* are defined as follows. Different peripheral speed ratio χ = (V _T −V _B ) / max (V _T , V _B ) × 10
0 (%) where, V _T is the circumferential speed of the upper roll, V _B is the peripheral speed of the lower roll. Warp curvature κ = 1 / Warp curvature radius ρ (warp warping upward from the rolling line is referred to as upward warpage, positive, and warping downward below the rolling line is referred to as downward warpage, negative.) Standardized warpage curvature κ ^* = Roll radius R / Warp radius of curvature ρ (upward warp: +, downward warp: −) Shape ratio を: The projected arc length of the contact between the rolled material and the work roll is the average value of the sheet thicknesses on the roll entry and exit sides. Divided by.

If warpage occurs when reverse rolling is performed in the rolling mill shown in FIG. 1, as described above, serious problems such as interruption of rolling and occurrence of a large accident occur. As a cause of the warpage, the following vertical asymmetry factors are considered from the above-described viewpoint. Vertical difference in friction coefficient between work roll and rolled material: Δμ Vertical temperature difference in rolled material (vertical difference in deformation resistance): Δt Difference in circumferential speed of upper and lower work rolls: ΔV Geometric condition Radius difference between upper and lower work rolls .DELTA.R. Plate incidence angle (upper and lower pass line differences) .alpha. Therefore, if all these values in the pass can be measured accurately, Warpage prediction is considered possible with considerable accuracy. However, it is practically almost impossible to accurately measure Δμ for each path, for example.

As a result of the ingenuity, the inventors of the present invention have determined, in addition to the warpage generated in the previous pass, the peripheral speeds of the upper and lower work rolls in the previous pass, the upper and lower surface temperatures of the rolled material, and the rolled material before the pass rolling. By measuring the upper and lower surface temperatures and calculating the amount of warpage due to factors other than the different peripheral speeds in the path based on those values, the warpage of the path can be accurately calculated without measuring Δμ for each path. It has been found that it can be predicted, and that accurate warpage control is possible. The details will be described below, taking the case of reverse rolling as an example. Note that the warpage curvature in the previous pass indicates the curvature of the warpage generated during the preceding pass rolling, and the warpage curvature in the relevant pass indicates the curvature of the warpage generated during the preceding rolling.

The inventors first performed a reverse rolling experiment using the rolling mill shown in FIG. 1 to examine the warpage generation behavior. As a result, when there is a vertical asymmetry condition such as Δt, Δμ, ΔV, etc., when the tip of the rolled material is rolled, warpage (both upward warp and downward warp may occur) occurs, It was found that no warping occurred when the center and rear end portions of the rolling direction were rolled, and the mechanism was clarified. The mechanism is as follows.

With respect to the definition of the front end and the rear end, when the rolled material moves by rolling, the front end is the front end and the rear end is the rear end. In the case of reverse rolling, the moving direction of the rolled material is reversed for each pass, and therefore, if attention is paid to the rolled material itself, the leading end and the rear end are switched for each pass. That is, in the reverse rolling, the same location in the rolled material is rolled at the leading end every two passes. Therefore, assuming that the path whose warpage is to be controlled is the N path, the previous path for which κ and 測定 are to be measured is N-2. On the other hand, in the case of unidirectional rolling, since the direction in which the rolled material moves by rolling is always constant, the positions of the leading end and the trailing end do not change even if attention is paid to the rolled material itself. That is, in one-way rolling, the same location in the rolled material is rolled at the leading end for each pass, so if the pass is N pass, the previous pass to measure κ and χ is
N-1.

When the tip is rolled, as described above, both upward warpage and downward warpage can occur. This is because, in the case of rolling at the leading end, there is nothing to restrict the deformation (warpage) of the material until the material reaches the table roller, and the material length on the exit side, that is, the leading end of the material in the rolling direction from the roll bite exit. This is because the influence of the material's own weight is small because the distance to the rolled material is short, and when the warp starts to occur due to the vertical asymmetry such as the temperature difference between the upper and lower sides of the rolled material, the curvature of the warp expands to the limit.

On the other hand, no warpage occurs at the time of rolling the central portion and the rear end portion of the rolled material in the rolling direction. First, with respect to the downward warpage, even if the downward warpage is to occur, the material is restrained by the table roller on the output side, and the material cannot be largely deformed downward. The mechanism of occurrence of warpage is as follows. Here, a temperature difference between the upper and lower surfaces of a rolled material is exemplified as a vertical asymmetry factor. FIG. 2 shows the rolling behavior when the lower surface of the material is at a high temperature.
Since the lower surface is at a high temperature, the stretching of the material on the lower surface becomes large, and first, the warp of the tip portion in the upward direction occurs (FIG. 2A). As rolling proceeds, warpage does not occur due to the restraint of the material before and after the roll bite (FIG. 2B). As the rolling further proceeds, the material on the rear end side becomes shorter and the rear end becomes free, so that an upward warpage is likely to occur again. However, since there is a long material that has already been rolled on the roll tool exit side, there is a large difference in tension on the upper and lower surfaces of the material due to its own weight, which eliminates non-uniformity of the exit speed at the roll tool exit on the upper and lower surfaces of the material. Acting, no warping occurs at the rear end (FIG. 2 (c)). From the above results, it was found that the warp to be controlled was the warpage of the tip.

Next, the inventors conducted a rolling experiment using a twin-drive reverse rolling mill to determine the warpage generation behavior and the upper and lower rolls in the front pass (first pass) and the front pass (third pass) during tip rolling. The peripheral speed and the upper and lower surface temperatures of the rolled material were examined in detail. Table 1 shows the warpage generation behavior of the first pass and the third pass in three steel materials (conditions 1, 2, and 3) having different plate thicknesses. From this result, it can be seen that the curvature radius κ _M of the generated warp greatly differs between the first pass and the third pass under any conditions. For example, condition 2
In the figure, the first pass is upwardly warped, whereas the third pass is downwardly warped.

The inventors have determined that the curvature produced after each pass.
κ_MFrom the warpage curvature κ due to the different peripheral speed_VAnd pressure
Warp curvature κ due to difference in temperature between upper and lower surfaces of rolled material_TReduced warpage
Rate κ _Q= Κ_M−κ_V−κ_TIs one pass under any conditions
It was found that the eye and the third pass matched very well. You
In other words, the continuation to the pass (third pass) is the previous pass
(First pass) Warpage curvature κ observed during rolling_MThen
Κ_MCurvature curvature κ due to different peripheral speed_VAnd rolled material
Warpage curvature κ caused by temperature difference_TLess curvature
κ_QIt turns out that.

Therefore, the resistance generated during the preceding pass rolling is reduced.
Curvature κ_M1, Different peripheral speedχ₁ And the upper and lower surface temperature t of the rolled material
^T ₁ , T^B ₁ Measure χ₁ Warpage curvature κ_V1and
Δt ₁ (T^T ₁ And t^B ₁ Curvature κ due to_T1To
Factors other than the different peripheral speed and upper and lower surface temperature difference in the previous pass
Curvature κ_Q1To κ_Q1= Κ_M1−κ_V1−κ_T1Calculated from
And Δt in the path_Two Warpage curvature κ_T2Sought
If the warpage is due to factors other than the different peripheral speed in the path,
κ_P2Is κ_P2= Κ_Q2+ Κ_T2Can accurately predict
become.

[0025]

[Table 1]

Based on the above results, the inventors of the present invention
The amount of warpage in rolling at the front end of the rolled material,
Lower work roll peripheral speed and upper and lower surface temperature of rolled material,
Measure the upper and lower surface temperature of the rolled material before the pass rolling,
Predict and calculate the amount of tip warpage of the path from the measurement result,
Top and bottom work rolls with different circumferences to eliminate the predicted warpage
The speed ratio is calculated, and the upper and lower
Method for setting and controlling the crawl peripheral speed difference, and better
More preferably, the peripheral speed of the upper and lower work rolls in the previous pass
(V^T _R1, V^B _R1), The temperature of the upper and lower surfaces of the rolled material (t^T ₁ ,
t^B ₁ ) And the curvature of the rolled material tip in the previous pass
Radius ρ₁ And measure the roll peripheral speed and warpage
Different peripheral speed ratio in the previous pass from the radius of curvature₁ And warp
Curvature κ_M1And the different peripheral speed ratio χ₁ Warpage caused by
Rate κ_V1And the temperature difference Δt between the upper and lower surfaces of the rolled material.₁ 
Curvature κ due to_T1And warp in the previous pass
Rate κ _M1Different peripheral speed ratio from₁ Curvature κ due to_V1And up and down
Warpage curvature κ caused by temperature difference between surfaces_T1And subtract
Due to factors other than the different peripheral speeds and the temperature difference between the upper and lower surfaces.
Curvature κ_Q1And rolling in the pass
Temperature of the upper and lower surfaces of the material (t ^T _Two , T^B _Two ) Measure the temperature
Difference Δt_Two Curvature κ due to_T2To the path
Due to factors other than different peripheral speeds and temperature differences between the upper and lower surfaces
Curvature κ_Q2To κ _Q2= Κ_Q1And the curvature of the path
Rate κ_P2And κ_P2= Κ_Q2+ Κ_T2To eliminate this curvature
So that the peripheral speed of the upper and lower work rolls in the pass
A sheet rolling method for rolling with a set difference was found.

That is, if the present method is used, accurate warpage control can be performed even when the warping directions of the preceding pass and the relevant pass are reversed. Hereinafter, an example procedure of the present control method will be described. Table 2 shows the flowchart.

[0028]

[Table 2]

(1) Measurement of Rolling Data in Previous Pass Warp radius of curvature ρ ₁ and vertical roll speed V during tip rolling
^T _R1, V ^B _R1, the upper and lower temperature t ^T ₁ of the rolled material, t ^B ₁ (after pre-rolling or rolling) was measured, the warpage curvature kappa _M1, obtaining the differential speed ratio chi ₁ and upper and lower temperature difference Delta] t _1. Regarding the warpage curvature κ _M1 , it is preferable to normalize the curvature κ _{M1 as} shown in Expression (1.1) so that the results at different roll radii can be used. If it is difficult to measure the curvature itself, the curvature may be calculated from the height of the curvature. In equation (1.2),
An example of how to obtain the different peripheral speed ratio will be described.

Κ_M1 ^*= Roll radius R / ρ₁ (Upward warpage: +, downward warp:-) ... (1.1) χ₁ = (V^T _R1-V^B _R1) / Max (V^T _R1, V^B _R1) × 100 (%) (1.2) Δt₁ = T^T ₁ -T^B ₁ ... (1.3) (2) Warpage analysis of previous path Warp curvature κ caused by different peripheral speed_V1 ^*Derivation of different peripheral speed χ and warpage curvature κ under the condition of Δt = 0 and Δμ = 0
_V ^*From the relationship, the warpage curvature κ caused by different peripheral speeds_V1 ^*Ask for
You. χ and κ_V ^*For example, the relation of Δt =
Experiment or finite element method calculation under the condition of 0, Δμ = 0
Is performed, and a regression curve, for example, an equation (2.1) is obtained from the result.
Or create a table etc. corresponding to Γ and ask
deep. If there is an effect of sheet thickness, steel type, etc.
Χ and κ for each case _V ^*Experiment or calculation of the result
May be considered in equation (2.1) or a table.
FIG. 3A shows an experiment when Δt = 0 and Δμ = 0.
From the shape ratio Γ and the curvature κ^*Relationship with different peripheral speed ratios
It is shown.

Κ _V1 ^* = fa (χ ₁ , Γ ₁ ) (2.1) Next, the curvature ratio κ _V1 ^* corresponding to the shape ratio Γ ₁ and the different peripheral speed ratio χ ₁ in the previous pass is calculated by the equation (2. 1) or from a table or FIG. 3 (a). The temperature difference caused by the warp curvature κ _T1 ^* of derivation Δμ = 0, χ = Δt and from warping curvature κ _T ^* of the relationship between the 0 of conditions, determine the warp curvature of the resulting temperature difference κ _T1 ^*. χ and κ
Similar to the above, the relationship of _T ^* is obtained, for example, by performing an experiment or calculation by the finite element method in advance, and forming a regression curve, for example, equation (2.2) or a table from the result. Here, as in the case of equation (2.1), the plate thickness,
If there is an effect of the type of steel or the like, the result may be considered in equation (2.2) or the like. FIG. 3 (c) shows the relationship between the shape ratio Γ and the curvature κ ^* with respect to the material temperature difference by an experiment in which χ = 0 and Δμ = 0.

Κ _T1 ^* = fb (Δt ₁ , Γ ₁ ) (2.2) Next, the curvature ratio κ _V1 ^* corresponding to the shape ratio Γ ₁ and the temperature difference Δt ₁ in the previous pass is calculated by the equation (2.2). ) Or from a table or FIG. 3 (c). In accordance with Equation calculation following differential speed chi _1, below and temperature difference Delta] t ₁ warpage curvature due to factors other than kappa _Q1 ^*, to calculate a warped curvature kappa _Q1 ^* due to factors other than chi ₁ and Delta] t _1.

Κ _Q1 ^* = κ _M1 ^* −κ _V1 ^* −κ _T1 ^* (2.3) (3) Prediction of Warpage Curvature κ _P2 ^* of the Path Other than Differential Speed χ ₂ and Upper and Lower Surface Temperature Difference Δt ₂ Of the curvature κ _Q2 ^* due to the factors of ₁ and Δt ₁ , the curvature κ _Q1 ^*
Since the continuation to the path (third pass), the curvature κ due to factors other than χ ₂ and Δt ₂ in the path
_Q2 ^* can be predicted by the following equation.

Κ _Q2 ^* = κ _Q1 ^* (3.1) Derivation of Warpage Curvature κ _T2 ^* Caused by Temperature Difference By measuring the vertical temperatures t ^T ₂ and t ^B ₂ of the rolled material, the above equation (2) is obtained. From 2), κ _T2 ^* can be predicted. ^{_{κ T2 * = fb (Δt 2}} , Γ 2) in accordance with ... (3.2) wherein the warp curvature kappa _P2 ^* calculated following the path, calculates the kappa _P2 ^* due to factors other than differential speed in the path.

Κ _P2 ^* = κ _Q2 ^* + κ _T2 ^* (3.3) (4) Calculation of Roll Speed Setting Value of the Passes Calculation of Different Peripheral Speed Rate χ ₂ to be Secured During Tip Rolling differential speed ratio chi ₂ required for eliminating the expected kappa _P2 ^* warpage, the shape ratio of the path gamma ₂ and kappa _P2 ^*, can be calculated from equation (4.1). Equation (4.1) can be easily obtained by simply modifying equation (2.1).

Χ ₂ = fc (κ _P2 ^* , Γ ₂ ) (%) (4.1) When χ ₂ is obtained, the equation (2.1) is back-calculated to obtain a value during the tip rolling in the pass. V ^T _R2 to be secured, V ^B
_R2 is found. V ^T _R2, V ^B _R2 calculation above said upper and lower required to obtain a roll speed roll set speed V ^T _S2, V ^B _S2 is a roll speed to be secured at the tip rolling. Therefore, if the speed control highly mill, in the case of ^{_{V T S2 = V T R2,}} V B S2 = may be the V ^B _R2, but the speed controllability is poor mill, V ^T _R2 ,
Roll set speed V ^T _S2 for ensuring V ^B _R2, V ^B _S2
Is obtained through experiments.

The warpage can be controlled by setting the roll speed thus obtained and performing the pass (パ ス₂ ). By the way, FIG. 3B shows Δt = 0, ΔV =
The relationship between the shape ratio Γ and the warpage curvature κ ^* is shown in relation to Δμ by an experiment when it is set to 0, and FIG. 3C shows the relationship between the shape ratio Γ and the warpage curvature κ by an experiment when Δμ = 0 and ΔV = 0.
The relationship with ^* is shown with respect to Δt. From these relationships, it can be seen that factors other than the different peripheral speed and the vertical temperature difference, that is, the warpage curvature caused by Δμ are affected by Γ as shown in FIG.

In the above equation (3), the warpage curvature κ _Q2 ^* continued on the path is κ _Q1 ^* as shown in the equation (3.1) ^.
It is said to be equivalent to. This is assumed in the equation (3) because, in normal rolling, the variation width of Γ for each pass is small, and as can be seen from FIG. 3 (b), the change in the curvature caused by Δμ with respect to the change in 小 さ い is small. As described above (3.1)
The peripheral speed may be set as κ _Q2 ^* = κ _Q1 ^{* in the} equation. However, in the case where 大 き く greatly changes for each pass, a method of considering the relationship between the warpage curvature due to Δμ and Γ will be described below.

That is, in the above equation (3), (3.
It is preferable to estimate κ _Q2 ^* assumed in the expression (1) by the expression (5). ^{_{κ Q2 * = δ · κ Q1}} * ... (5) δ , as shown in equation (6), when Δμ is constant, warp curvature q and shape ratio shape ratio occurs when the gamma ₂ There is the ratio of the warp curvature q that occurs when the gamma _1.

Δ = q (Γ ₂ ) / q (Γ ₁ ) (6) where Γ ₁ is the shape ratio of the previous path, and Γ ₂ is the shape ratio of the path. The specific method of obtaining q (求 め) is shown in FIG.
It may be read from an arbitrary curve of (b), for example, a curve in the case of Δμ = 0.10, or it may be obtained from a mathematical expression.

[0041]

(Equation 1)

As can be seen from FIG.
(Γ) itself varies depending on Δμ, so strictly speaking, an approximate expression of a curve corresponding to each Δμ should be used. However, as can be seen from FIG. 3 (b), it is possible to display:

[0043]

(Equation 2)

Also, what is ultimately needed is not q (Γ) itself, but q (Γ ₂ ) / q (Γ ₁ ).

[0045]

(Equation 3)

Is as follows. Therefore, it suffices to use equation (7). Note that δ is simply the warpage curvature κ _M1 −κ _V1 − due to factors other than the shape ratios Γ ₁ , Γ ₂ of the previous pass and the relevant pass and the different peripheral speeds and the temperature difference between the upper and lower surfaces at that time.
κ _T1 , κ _M2 −κ _V2 −κ _T2 may be determined by measuring and learning in actual production. For the above δ, Δ
Considering only μ and not considering the effect of the incident angle α,
Regarding α, there is almost no influence on warpage under the conditions of actual production, as described below, so there is no need to particularly consider it.

In the range of -1 ° <α <1 °, even if α is changed, the curve in FIG. 3A has no change, and α has no influence on the warpage in this range. Under normal rolling conditions, even if the pass line is not adjusted, it is almost impossible that α becomes 1 ° or more due to the dimensions of the plate. Particularly, in the present invention, the change in the amount of warpage due to the change amount Δα of the incident angle of the plate between the previous pass and the pass is most important, but the actual value of Δα is very small (for example, the roll radius 50
In the case of 0 mm and a board length of 1000 mm, it is 130 at the N-2th pass.
Rolled from mm to 110mm, N-passed from 50mm to 30mm
mm, very extreme conditions (Γ ₁ = 0.
83, Γ ₂ = 2.49), even if the difference Δα between the plate incident angles is constant without adjusting the pass line,
Only Δα = about 0.1 °).

The above description is based on reverse rolling as an example.
Has been measured, but the measurement and
With control, one single stand rolling mill
When rolling down only in the direction or rolling with a tandem rolling mill
In this case, the present invention can be used. this
In this case, if the path is the N-th path, the previous path is N-1.
It will be an eye. In the above description, the control means
Although different peripheral speed rolling was used,
Warping can also be achieved by forcibly applying a lower friction coefficient difference.
Can be controlled. The method is described below. [Control by upper and lower material temperature difference] Table 3 shows the previous pass (subscript
₁) Is measured in the rolling data,
Character _Two), The warpage is controlled by the material temperature difference.
In the next pass, measure the rolling data in the
Character_Three) Is shown until the warpage is predicted and controlled.

[Table 3](1) Rolling data measurement of the front end of the plate in the previous pass As in the case of the control at the different peripheral speed rolling described above, the rolling data at the front end rolling is used.
Warp curvature κ_M1 ^*, Different peripheral speedχ₁, The upper and lower surface temperature t of the rolled material
^T ₁, T^B ₁Is measured. Curvature of generated warpage κ_M1 ^* Different peripheral speed rate during rolling χ₁ Upper and lower surface temperature of rolled material t^T ₁, T^B ₁ (2) Analysis of Warpage of Previous Pass Just like the control in the above-mentioned different peripheral speed rolling, the equation (1) is used.
0.1), (10.2), (10.3), κ_V1 ^*,
κ_T1 ^*, Κ_Q1 ^*Ask for. Warpage curvature κ caused by different peripheral speed rolling_V1 ^*Derivation κ_V1 ^*= Fa (χ₁, Γ₁) ... (10.1) Warp curvature κ caused by temperature difference_T1 ^*Derivation κ_T1 ^*= Fb (Δt₁, Γ₁…… (10.2) Warpage curvature due to factors other than different peripheral speeds and temperature difference between upper and lower surfaces
κ_Q1 ^* κ_Q1 ^*= Κ_M1 ^*−κ_V1 ^*−κ_T1 ^* ... (10.3) (3) Warp curvature κ generated in the path_P2 ^*In this case, too, just as in the case of control with different peripheral speed rolling,
From equations (10.4), (10.5), and (10.6), κ
_Q2 ^*, Κ_T2 ^*, Κ_P2 ^*Ask for. In this case, the expression
As in the case of (5), (10.4) 'is more preferable. Warpage curvature due to factors other than different peripheral speeds and upper and lower surface temperature differences
κ_Q2 ^* κ_Q2 ^*= Κ_Q1 ^* … (10.4) κ_Q2 ^*= Δ · κ_Q1 ^* ... (10.4) 'Warp curvature κ caused by temperature difference_T2 ^*(T^T _Two, T^B _Two
Measurement) κ_T2 ^*= Fb (Δt_Two, Γ_Two) (10.5) Warpage curvature κ due to factors other than the different peripheral speed of the path_P2 ^*of
Calculation κ_P2 ^*= Κ_Q2 ^*+ Κ_T2 ^* ... (10.6) (4) Warpage control in the relevant path Temperature difference Δt between upper and lower materials to be given^C _TwoThe curvature generated in the path is κ_P2 ^*From
κ_P2 ^*Δt to be given in order to eliminate^C _TwoTo the formula (1
0.7). Equation (10.7) is calculated by using equation (10.
It can be easily obtained by back calculation of 5). Δt^C _Two= Fe (κ_P2 ^*, Γ_Two) (10.7) Δt^C _TwoΔt determined above^C _TwoTo the material being rolled. Method
The upper or lower surface of the material before rolling is cooled
Or by heating, cooling with a water cooling device, etc.
It is only necessary to use a heater or the like. Required Δt^C _TwoTo get
Adjustment of cooling capacity etc. (for example, cooling water flow rate)
What is necessary is just to obtain | require by calculation by a finite element method etc. or experiment. (5) Measurement of rolling data at the end of the plate in the relevant pass In order to predict the curvature of the next pass, the following measurements were performed.
U. Curvature of generated warpage κ_M2 ^* Different peripheral speed rate during tip rolling χ_Two (T^T _Two, T^B _Two(6) Analysis of the warpage of the path From equations (10.8), (10.9) and (10.10),
Other than the different peripheral speed and temperature difference between the upper and lower surfaces
Curvature κ_Q'2 ^*Is calculated. (With '
Different peripheral speed and upper and lower surface temperatures expected to occur in this pass
Warpage curvature κ due to factors other than difference_Q2 ^*And distinguished. )
In addition, the upper and lower materials after the application of the temperature difference in the equation (10.9)
Temperature difference Δt_Two+ Δt^C _TwoThe value is the upper and lower surface temperature after cooling.
It may be determined by direct measurement. Warpage curvature κ caused by different peripheral speed rolling_V2 ^*Derivation κ_V2 ^*= Fa (χ_Two, Γ_Two) ... (10.8) Warpage curvature κ caused by temperature difference between upper and lower materials after applying temperature difference^C _T2
^*Derivation κ^C _T2 ^*= Fb (Δt_Two+ Δt^C _Two, Γ_Two…… (10.9) Warpage curvature due to factors other than different peripheral speeds and temperature difference between upper and lower surfaces
κ_Q'2 ^*Calculation κ_Q'2 ^*= Κ_M2 ^*−κ_V2 ^*−κ^C _T2 ^* ... (10.10) (7) Warp curvature κ generated in the next pass_P3 ^*Equations (10.11), (10.12), (10.13)
From the next pass, the curvature κ_P3 ^*Ask for. In addition,
As shown in equation (7), κ_Q3 ^*Is given by the equation (10.1
1) 'is more preferable. Further, Δt^C _TwoAttached
The temperature distribution in the sheet thickness direction by applying
It can be different, so κ_P3 ^*As for (1)
0.13) '. Where η is
It is a correction coefficient obtained by learning, experiment, or calculation. Warpage curvature due to factors other than different peripheral speeds and upper and lower surface temperature differences
κ_Q3 ^* κ_Q3 ^*= Κ_Q'2 ^* ... (10.11) κ_Q3 ^*= Δ · κ_Q'2 ^* ... (10.11) 'Warp curvature κ caused by temperature difference_T2 ^*(T^T _Three, T^B _Three
Measurement) κ_T3 ^*= Fb (Δt_Three, Γ_Three) (10.12) Warpage curvature κ due to factors other than the different peripheral speed of the next pass_P3 ^*Calculation
Out κ_P3 ^*= Κ_Q3 ^*+ Κ_T3 ^* ... (10.13) κ_P3 ^*= Κ_Q3 ^*+ Η ・ κ_T3 ^* ... (10.13) '(8) Warpage control of next path (κ_P3 ^*The curvature κ generated in the next pass in equation (10.13)_P3 ^*But
From what can be predicted, κ_P3 ^*In order to eliminate
The warpage may be controlled again by one of the methods described above. What
The warpage control based on the difference between the upper and lower friction coefficients will be described later.
You. Warpage control by different peripheral speed rolling Warpage control by upper and lower material temperature difference Warpage control by upper and lower friction coefficient difference (described later) [Control by upper and lower friction coefficient difference]
₁) Is measured in the rolling data,
Character _Two), Warpage control is performed based on the friction coefficient difference.
In the next pass, measure the rolling data in the
Character_Three) Is shown until the warpage is predicted and controlled.

[Table 4] (1) Rolling data measurement at the front end of the plate in the previous pass As in the case of the above-mentioned control at the different peripheral speed rolling, the warpage curvature κ _M1 ^{* at} the front end rolling, the different peripheral speed ratio χ ₁ , the upper and lower surface temperatures t of the rolled material t
Measure ^T ₁ and t ^B ₁ . Curvature of generated warpage κ _M1 ^* Different peripheral speed rate during rolling χ ₁ Upper and lower surface temperature of rolled material t ^T ₁ , t ^B ₁ (2) Analysis of warpage of previous pass Completely same as control at the above-mentioned different peripheral speed rolling Similarly, equation (1)
1.1), (11.2) and (11.3), κ _V1 ^* ,
Find κ _T1 ^* , κ _Q1 ^* . Derivation of warpage curvature κ _V1 ^* caused by different peripheral speed rolling κ _V1 ^* = fa (χ ₁ , Γ ₁ ) (11.1) Derivation of warpage curvature κ _T1 ^* caused by temperature difference κ _T1 ^* = fb (Δt ₁ , Γ ₁ ) ... (11.2) Warpage curvature κ _Q1 ^* κ _Q1 ^* = κ _M1 ^* -κ _V1 ^* -κ _T1 ^* … (11.3) (3) ) Prediction of the warpage curvature κ _P2 ^{* in which} the path occurs In this case as well, in the same way as in the case of control at different peripheral speed rolling,
From equations (11.4), (11.5) and (11.6), κ
_Q2 ^{*, κ} _T2 ^*, determine the κ _P2 ^*. Note that, in this case as well, as in the case of the equation (5), it is preferable to obtain κ _Q2 ^* by the equation (11.4) ′. Warp curvature κ _Q2 ^* κ _Q2 ^* = κ _Q1 ^* ... (11.4) κ _Q2 ^* = δ · κ _Q1 ^* ... (11.4) 'due to temperature difference Derivation of the warpage curvature κ _T2 ^* (t ^T ₂ , t ^B ₂
Κ _T2 ^* = fb (Δt ₂ , Γ ₂ ) (11.5) Calculation of warpage curvature κ _P2 ^* due to factors other than the different peripheral speed of the path κ _P2 ^* = κ _Q2 ^* + κ _T2 ^* ( 11.6) (4) calculated chi = 0 of the upper and lower coefficient of friction difference [Delta] [mu ^L ₂ should warpage control granted in the path, from [Delta] [mu and warp curvature Kappamyu ^* relationship in terms of Delta] t = 0, the kappa _P2 ^* A difference Δμ ^L ₂ between the upper and lower friction coefficients to be given to eliminate the difference is obtained. The relationship between Δμ and κμ ^* can be determined, for example, by performing an experiment or calculation by the finite element method in advance under the conditions of χ = 0 and Δt = 0,
For example, formula (11.7) or a table or the like is created and determined in association with Γ. In addition, if there is an effect of sheet thickness, steel type, etc., conduct experiments or calculations for each of these conditions,
The result may be considered in equation (11.7), a table, or the like. FIG. 3B shows the relationship between the shape ratio Γ and the curvature κμ ^* with respect to Δμ by an experiment in which χ = 0 and Δt = 0. ^{_{Δμ L 2 = fg (κ P2}} *, Γ 2) ... (11.7) to give the Δμ Δμ ^L ₂ obtained in the given above of ^L _2. As an example of the method, the upper surface or the lower surface may be lubricated. Required Δμ ^L
Adjustment of lubrication to obtain ₂ (for example, lubricating oil flow rate)
May be obtained in advance by calculation using a finite element method or the like or by experiment. (5) Rolling data measurement at the end of the plate in the relevant pass Curvature of generated warpage κ _M2 ^* Peripheral velocity during tip rolling χ ₂ Δμ ^L ₂ Upper and lower surface temperatures t ^T ₂ ', t ^B ₂ ' (6) path search of warp curvature kappa _V2 ^* analysis above chi ₂ and formula of warpage (11.8) of the differential speed rolling caused a further ^{_{Δt 2 '= t T 2'}} -t B 2 '
From Equation (11.9), the warpage curvature κ _T2 ^* resulting from the temperature difference between the upper and lower materials is obtained. In equation (11.10), κ _L2 ^*
Represents the warpage curvature caused by Δμ ^L ₂ given by the warpage control.
Since Δμ ^L ₂ is generally given by the difference between the upper and lower lubrication, in that case, the lubricating oil is flowed by the cooling water by the next pass, and Δμ ^L ₂ ≒ It is considered to be 0. Therefore, the warpage curvature κ _Q′2 ^* that continues in the next pass is represented by Expression (11.10).
However, since the effect of Δμ ^L ₂ may remain, in such a case, the effect of Δμ ^L ₂ may be considered as shown in Expression (11.11). Although γ is a correction coefficient, it may be obtained by learning, or may be obtained by experiment, calculation by the finite element method, or the like. Derivation of warpage curvature κ _V2 ^* caused by different peripheral speed rolling κ _V2 ^* = fa (χ ₂ , Γ ₂ ) (11.8) Derivation of warpage curvature κ _T2 ^* caused by temperature difference between upper and lower materials κ _T2 ' ^* = fb (Δt ₂ ′, Γ ₂ )… (11.9) Calculation of warpage curvature κ _Q′2 ^* due to factors other than different peripheral speeds and upper and lower surface temperature differences κ _Q′2 ^* = κ _M2 ^* −κ _V2 ^* −κ ^{_{T2 '* -κ L2 * ... (}} 11.10) κ Q'2 * = κ M2 * -κ V2 * -κ T2' * -γ · κ L2 * ... (11.11) here, κ _L2 ^* is warp curvature of the [Delta] [mu ^L ₂ due imparted by the warp control, gamma correction coefficient (7) warp curvature kappa _P3 ^* of prediction expression which occurs in the next pass (11.12), (11.13), (11.14) Then, the curvature κ _P3 ^* generated in the next pass is obtained. In addition,
As shown by the equation (7), κ _Q3 ^* is _calculated by the equation (11.1)
2) 'is more preferable. Calculation of the warpage curvature κ _Q3 ^* due to factors other than the different peripheral speeds and the temperature difference between the upper and lower surfaces κ _Q3 ^* = κ _Q'2 ^* ... (11.12) κ _Q3 ^* = δ · κ _Q'2 ^* ... (11.12) ) 'Derivation of warpage curvature κ _T2 ^* due to temperature difference (t ^T ₃ , t ^B ₃
Κ _T3 ^* = fb (Δt ₃ , Γ ₃ ) (11.13) Calculation of warpage curvature κ _P3 ^* generated in the next pass κ _P3 ^* = κ _Q3 ^* + κ _T3 ^* (11.14) ( 8) Warp Control of Next Path (Control to Eliminate κ _P3 ^* ) Since the curvature κ _P3 ^* generated in the next path can be predicted by equation (11.14), to eliminate κ _P3 ^* , The warpage may be controlled again by one of the methods. Warpage control by different peripheral speed rolling Warpage control by upper and lower material temperature difference Warpage control by upper and lower friction coefficient difference

[0049]

【Example】

Example 1 A slab having a thickness of 100 mm and a width of 1760 mm was cut into a slab having a thickness of 55 mm using a rolling mill having a work roll diameter of 1000 mm.
mm was reverse-rolled according to the pass schedule shown in Table 5.

[0050]

[Table 5]

Table 6 shows Examples and Comparative Examples. The present invention
In the example, first, the tip at the time of rolling in the previous pass (first pass)
Radius of curvature, roll peripheral speed, upper and lower surface temperature of rolled material
As a result, the curvature of the tip is κ_M1 ^*= -0.3
33 and the peripheral speed ratio at the tip is χ₁ = 4.0%
Temperature difference Δt at the tip₁ = 42 ° C. This χ
₁ And Δt₁ Curvature κ in the previous pass due to_V1
^*, Κ_T1 ^*From the regression equation determined in advance by experiments
When calculated, κ_V1 ^*= −0.142, κ_T1 ^*= −
0.088. Next, the different peripheral speed and
Curvature κ due to factors other than temperature and temperature difference κ_Q2 ^*= Κ_Q1 ^*=
κ_Q1 ^*= Κ_M1 ^*−κ_V1 ^*−κ_T1 ^*= −0.333 − (−
0.142)-(-0.088) = -0.103
Was. Further, the upper and lower surface temperatures of the rolled material in the pass are measured.
As a result, the temperature difference Δt_Two = 24 ° C. This
Δt_Two Curvature κ in the previous pass due to_T2 ^*Oh
Calculated from the regression equation previously determined in the experiment
Κ_T2 ^*= -0.051. Based on this result,
Κ due to factors other than the different peripheral speed in the path_P2 ^*To κ_P2
^*= Κ_Q2 ^*+ Κ_T2 ^*= -0.103-0.051 =-
0.154 is obtained, and the different peripheral speed ratio す る for solving this is obtained._Two = −
4.2% is calculated from the above regression equation,
Eye). As a result, a plate with almost no warpage is rolled.
I was able to.

On the other hand, in the comparative example, the warpage curvature κ _M1 ^* = − 0.333 (downward warpage) of the front end in the previous pass (first pass) is measured, and it is assumed that the warpage continues in the previous pass ( κ _P2
^* = -0.333: under warp), χ ₂ to eliminate the warp
= -9.2% (lower high speed) was given in the pass (third pass). Having overestimated the amount of warpage in the path, applying the chi ₂ is too large, a large cambered occurs.

[0053]

[Table 6] [Embodiment 2] In the above-mentioned Embodiment 1, an example of control by different peripheral speed rolling was shown. The following describes a method for controlling warpage by forcibly giving a difference between upper and lower material temperatures and a difference between upper and lower friction coefficients. The following shows an example. In both cases, using a rolling mill with a work roll diameter of 1000 mm, the sheet thickness is 100 m.
A slab having a width of 1760 mm and a width of 1760 mm was reverse-rolled to a thickness of 42 mm according to the pass schedule shown in Table 7.

[Table 7]Table 8 shows examples of the control method based on the temperature difference between the upper and lower materials.
Is shown. First, the tip at the time of rolling in the previous pass (first pass)
Radius of curvature, roll peripheral speed, and upper and lower surface temperature of rolled material
As a result of measurement, the curvature of the tip is κ_M1 ^*= -0.33
3. Different peripheral speed ratio at the tip₁= 4.0%, tip temperature
Difference Δt₁= 42 ° C. This χ₁And Δt₁To
Curvature κ in the previous pass due to_V1 ^*, Κ_T1 ^*Oh
When calculated from the regression equation obtained in the preliminary experiment,
κ_V1 ^*= −0.142, κ_T1 ^*= −0.088
Was. Next, the different peripheral speed in the pass (third pass) and
Warpage curvature κ due to factors other than temperature difference κ_Q2 ^*= Κ_Q1 ^*= Κ_M1
^*−κ_V1 ^*−κ_T1 ^*= -0.333-(-0.142)
− (− 0.088) = − 0.103 was determined. further,
As a result of measuring the upper and lower surface temperatures of the rolled material in the pass,
Temperature difference Δt_Two= 24 ° C. This Δt_TwoKi
Curvature κ in the previous pass_T2 ^*Experiment in advance
Calculated from the regression equation obtained in_T2 ^*= −
0.051. Based on this result,
Curvature due to factors other than the different peripheral speed
Predicted curvature κ in_P2 ^*To κ_P2 ^*= Κ_Q2 ^*+ Κ_T2 ^*
= −0.103−0.051 = −0.154
Material temperature difference Δt to be given in order to eliminate this^C _Two
= -71 ° C (top surface cooling) is obtained from a separately calculated regression equation.
Was. Next, Δt^C _Two= Cooling water strip to which -71 ° C can be applied
Parameters (flow rate, flow velocity, time, etc.) are calculated from the regression equation.
In the third pass, the upper surface is cooled under that condition
And rolled at the same speed (χ_Two= 0%). The result
As a result, a board with almost no warpage (κ_M2 ^*= -0.003)
We were able to. Regarding the upper and lower surface temperature difference, cool the upper surface
The temperature difference between the upper and lower materials after the temperature difference was applied (after control)
Is Δt_Two+ Δt^C _Two= 24 + (− 71) = − 47 ° C.
And the warpage caused by this temperature difference (-47 ° C)
Is, from the regression equation, κ^C _T2 ^*= 0.102 was calculated.
Therefore, the different peripheral speed and the
Curvature κ due to factors other than temperature difference between upper and lower surfaces_Q'2 ^*Is calculated
When I put out, κ_Q'2 ^*= Κ_M2 ^*−κ_V2 ^*−κ^C _T2 ^*=
−0.003-0−0.102 = −0.105
Was. Therefore, in the next pass (fifth pass),
Curvature κ due to factors other than temperature difference between upper and lower surfaces_Q3 ^*And κ
_Q3 ^*= Κ_Q'2 ^*= -0.105. Here, the next
As a result of measuring the upper and lower surface temperatures of
Temperature difference Δt_Three= -32 ° C was obtained. Δt_Three= -32
Warpage due to ° C_T3 ^*From the regression equation, κ_T3 ^*= 0.
070 was obtained. Therefore, in the next pass (fifth pass)
The generated curvature κ_P3 ^*To κ_P3 ^*= Κ_Q3 ^*+ Κ_T3 ^*= −
0.105 + 0.070 = -0.035
Different peripheral speed ratio to eliminate warpageχ_Three= -0.95% from the regression equation
Different peripheral speed rolling was carried out. As a result, the next pass
(Fifth pass), a plate with almost no warpage (κ_M3 ^*=
0.001) could be rolled.

[Table 8]

[Table 9]Next, Table 9 shows the control method based on the difference between the upper and lower friction coefficients.
An example will be described. First, when rolling in the previous pass (first pass)
Tip radius of curvature, roll peripheral speed, upper and lower surfaces of rolled material
As a result of measuring the temperature, the curvature of the tip is κ_M1 ^*= −
0.333, Different peripheral speed ratio at tip₁= 4.0%, tip
Temperature difference Δt₁= 42 ° C. This χ₁and
Δt₁Curvature κ in the previous pass due to_V1 ^*, Κ_T1
^*Was calculated from the regression equation determined in advance by experiments.
Where κ_V1 ^*= −0.142, κ _T1 ^*= -0.088
It became. Next, the different peripheral speed in the pass (third pass)
Curvature due to factors other than temperature and temperature difference κ_Q2 ^*= Κ_Q1 ^*
= Κ_M1 ^*−κ_V1 ^*−κ_T1 ^*= −0.333 − (− 0.1
42) − (− 0.088) = − 0.103. Sa
Furthermore, the results of measuring the upper and lower surface temperatures of the rolled material in the pass
As a result, the temperature difference Δt at the tip _Two= 24 ° C. This Δ
t_TwoCurvature κ in the previous pass due to_T2 ^*Clear
When calculated from the regression equation obtained in the first experiment, κ
_T2 ^*= -0.051. Based on this result,
Curvature due to factors other than different peripheral speeds,
Predicted curvature κ for the path_P2 ^*To κ_P2 ^*= Κ_Q2 ^*
+ Κ_T2 ^*= -0.103-0.051 = -0.154
Vertical friction coefficient difference to be obtained and given to eliminate this
Δμ^L _Two= 0.071 (lower surface lubrication) calculated separately
It was determined from the equation. Next, the vertical friction coefficient difference Δμ^L _Two= 0.0
Lubrication conditions (type of lubricating oil, flow rate, time
Is calculated from the regression equation, and the path (third pass)
After lubrication under the same conditions,_Two
= 0%). As a result, a plate with almost no warpage (κ
_M2 ^*= 0.002). Upper and lower surface temperature
Regarding the degree of difference, the amount of lubricating oil used was small.
The temperature difference between the upper and lower materials after the friction coefficient difference is applied (after control) is Δ
t_Two ^'Is the same as before control, Δt_Two ^'= Δt_Two= 24
° C. Therefore, in the pass (third pass)
Curvature due to factors other than different peripheral speeds and upper and lower surface temperature differences
κ_Q'2 ^*Is calculated, κ_Q'2 ^*= Κ_M2 ^*−κ_V2 ^*
−κ_T2 ^'*−κ_L2 ^*= 0.002-0-(-0.051)
-0.154 = -0.101. Therefore, the next pass
Other than the different peripheral speed and the temperature difference between the upper and lower surfaces in (5th pass)
Curvature κ due to the factor of_Q3 ^*And κ_Q3 ^*= Κ_Q'2 ^*= −
It was determined to be 0.101. Here, the rolled material in the next pass
As a result of measuring the upper and lower surface temperatures, the temperature difference Δt_Three= 1
8 ° C. was obtained. Δt_Three= Warp due to 18 ° C κ _T3 ^*To
Calculated from regression equation, κ_T3 ^*= -0.040 was obtained. I
Therefore, the curvature κ generated in the next pass (fifth pass)_P3
^*And κ_P3 ^*= Κ_Q3 ^*+ Κ_T3 ^*= -0.101-0.0
Predicts 40 = -0.141 and eliminates warpage
Speed χ_Three= −3.84% obtained from the regression equation
Nobu was carried out. As a result, in the next pass (fifth pass)
Also, a board with almost no warpage (κ_M3 ^*= -0.001)
We were able to.

[Table 10]

[Table 11]

[0054]

As described above, according to the present invention, it is possible to easily manufacture a plate having no warpage, so that a plate-shaped metal product having an excellent shape can be efficiently produced.

[Brief description of the drawings]

FIG. 1 is a diagram showing an example of a rolling mill to which the present invention is applied.

FIG. 2 is a view showing a warpage generation behavior during rolling when the lower surface of a rolled material is at a high temperature.

FIG. 3 is a diagram showing the effect of the asymmetry factor and the shape ratio that the shape ratio has on the curvature of curvature.

[Explanation of symbols]

 Reference Signs List 1 upper work roll 2 lower work roll 3 rolled material 4 roller table 5 upper backup roll 6 lower backup roll 7 rolling mill

Claims (10)

[Claims] 1. A method of rolling a sheet material by a rolling mill having at least upper and lower work rolls, wherein a peripheral speed of upper and lower work rolls in a previous pass, upper and lower surface temperatures of the rolled material, a curvature radius of curvature of a rolled material tip in the previous pass, and From
The warp curvature caused by the different peripheral speed in the previous pass and the warp curvature caused by the temperature difference between the upper and lower surfaces of the rolled material in the previous pass and the warp curvature caused by factors other than the different peripheral speed and the upper and lower surface temperatures in the previous pass are determined. Measure the temperature of the upper and lower surfaces of the rolled material in the pass, find the curvature of the roll due to the temperature difference between the upper and lower surfaces of the rolled material, and calculate the curvature due to factors other than the different peripheral speed and the temperature difference between the upper and lower surfaces in the previous pass. And the warp curvature caused by the temperature difference between the upper and lower surfaces of the rolled material in the pass, the warp curvature in the pass is determined, and the peripheral speed difference between the upper and lower work rolls in the pass is determined so as to eliminate the warp curvature. A sheet rolling method, wherein the sheet material is rolled by setting the difference between the upper and lower material temperatures and the difference between the upper and lower materials independently or in combination. 2. The warp curvature in the path is equal to the sum of the warp curvature due to factors other than the different peripheral speed and the temperature difference between the upper and lower surfaces in the previous pass and the warp curvature due to the temperature difference between the upper and lower surfaces in the pass. 2. The rolling method according to claim 1, wherein the rolling is performed by setting the speed difference between the upper and lower work rolls, the temperature difference between the upper and lower work rolls, the difference between the upper and lower material temperatures, and the difference between the upper and lower friction coefficients alone or in combination so as to eliminate the warpage.
Sheet rolling method. 3. The warp curvature in the path, the warp curvature due to factors other than the different peripheral speed and the temperature difference between the upper and lower surfaces of the front path, the warp curvature in consideration of the change in the shape ratio between the front path and the path, Predicted to be equal to the sum of the warp curvatures due to the temperature difference between the upper and lower surfaces in the pass, and to eliminate the warp curvature, the speed difference between the upper and lower work rolls, the upper and lower material temperature difference, and the upper and lower friction coefficient difference in the pass are considered. 3. The sheet rolling method according to claim 1, wherein the rolling is performed by setting one or a combination thereof. 4. A pressure having at least upper and lower work rolls.
In the method of rolling a sheet material by a rolling machine,
Peripheral speed (V^T _R1, V^B _R1),rolling
Temperature of the upper and lower surfaces of the material (t^T ₁ , T^B ₁ ) And the previous pass
Radius of curvature of the tip of rolled material₁ Measure
In the previous pass from the roll peripheral speed and the curvature radius of curvature
Different peripheral speed ratio け る₁ And curvature κ_M1And ask for this difference
Circumferential rateχ₁ Curvature κ due to_V1And the pressure
Temperature difference Δt between upper and lower surfaces of rolled material₁ Curvature κ due to_T1To
And the curvature κ of the previous pass_M1Different peripheral speed ratio from₁ To
Resulting curvature κ_V1Caused by temperature difference between the upper and lower surfaces
Curvature κ_T1Subtract the different peripheral speed in the previous pass and
Warpage curvature κ due to factors other than temperature difference on the lower surface_Q1Ask for
In addition, the temperature of the upper and lower surfaces of the rolled material in the pass (t)
^T _Two , T^B _Two ) And the temperature difference Δt_Two caused by
Warp curvature κ_T2And the different peripheral speed and
Warpage curvature κ due to factors other than temperature difference on the lower surface_Q2To κ_Q2= Κ
_Q1And the curvature κ of the path_P2And κ_P2= Κ_Q2
+ Κ_T2And warp curvature κ_P2To eliminate
Speed difference between upper and lower work rolls in this pass, upper and lower materials
Temperature difference and vertical friction coefficient difference can be set individually or in combination.
3. The plate according to claim 1, wherein the plate is rolled.
Rolling method. 5. A warp curvature kappa _P2 in the path, the warp curvature kappa _Q1 due to factors other than the temperature difference between the differential speed and the upper and lower surfaces of the front path, the effects of changes in the path and the shape ratio of the path The sum of the warpage curvature κ _Q2 due to factors other than the different peripheral speed and the temperature difference between the upper and lower surfaces in the path obtained based on the following equation considered, and the curvature κ _T2 due to the temperature difference between the upper and lower surfaces in the path. The sheet rolling method according to claim 1, wherein the sheet is rolled. κ _Q2 = δ ₁ · κ _Q1 δ ₁ : Learning coefficient indicating the relationship between the shape ratio (the value obtained by dividing the projected arc length of the contact between the rolled material and the work roll by the average value of the entrance and exit sheet thicknesses) and the curvature. 6. A warp curvature kappa _P2 in the path, the warp curvature kappa _Q1 due to factors other than the temperature difference between the differential speed and the upper and lower surfaces of the front path, the effects of changes in the path and the shape ratio of the path Κ _Q2 calculated based on the following formula,
Warp curvature κ due to temperature difference between upper and lower surfaces in the path
The sheet rolling method according to claim 1 or 3, wherein the sum is equal to _T2 . κ _Q2 = δ ₂ κ _Q1 , where δ ₂ : warpage curvature q (Γ ₂ ) generated when the shape ratio is Γ ₂ when Δμ does not change and warpage curvature q generated when the shape ratio is Γ ₁ (gamma ₁₎ the ratio of (q (Γ ₂₎ /
q (Γ ₁ )) Δt: Vertical temperature difference of rolled material Δμ: Vertical difference of friction coefficient between work roll and rolled material Γ ₁ : Shape ratio of previous pass Γ ₂ : Shape ratio of relevant pass Γ: Shape ratio: Rolling The value obtained by dividing the projected arc length of the contact between the material and the work roll by the average value of the entry and exit plate thicknesses 7. A temperature difference Δt between upper and lower materials during rolling of the pass.
In case of performing rolling by applying a ^C _2, the warp curvature kappa _Q'2 other than the upper and lower surfaces temperature difference differential speed and in the path as _{κ Q'2 = κ M2 -κ V2 -κ} C T2, The warpage curvature κ _Q3 other than the different peripheral speed and the upper and lower surface temperature difference in the next pass is _defined as κ _Q3 = κ _Q′2 , and the upper and lower surface temperatures of the rolled material in the next pass (t ^T ₃ , t ^B
₃ ) is measured, the curvature κ _T3 in the next pass due to the temperature difference Δt ₃ is obtained, and the curvature κ _P3 generated in the next pass is κ _P3 = κ _Q3 + κ _T3, preferably κ _P3 = κ _Q3 + η Rolling by predicting κ _T3 and setting any of the upper and lower work roll speed differences, upper and lower material temperature differences, and upper and lower friction coefficient differences alone or in combination in the next pass to eliminate this warpage The sheet rolling method according to claim 4. Here, κ _M2 is the curvature of curvature in the pass, κ _V2 is the curvature of curvature due to the difference between the upper and lower work roll velocities in the pass, and κ ^C _T2
Is the warp curvature of the upper and lower surfaces temperature difference due to the temperature difference Delta] t ^C ₂ after application of the path, eta learning, a correction coefficient determined by experiments or calculation. 8. A difference Δμ in vertical friction coefficient during rolling of the pass.
^In the case where rolling is performed with ^L _{2 added} , the warpage curvature κ _Q′2 other than the different peripheral speed and the upper and lower surface temperature difference in the pass is _given by κ _Q′2 = κ _M2 −κ _V2 −κ _T2 −κ _L2 Preferably, as κ _Q′2 = κ _M2 −κ _V2 −κ _T2 −γ · κ _L2 , the curvature κ _Q3 other than the different peripheral speed and the upper and lower surface temperature difference in the next pass is κ _Q3 = κ _{Q ′. The} temperature of the upper and lower surfaces of the rolled material in the next pass (t ^T ₃ , t ^B
₃ ) is measured, the curvature κ _T3 in the next pass due to the temperature difference Δt ₃ is obtained, and the curvature κ _P3 generated in the next pass is predicted as κ _P3 = κ _Q3 + κ _T3 to eliminate this curvature. 5. The sheet rolling method according to claim 4, wherein in the next pass, any one of the difference between the upper and lower roll speeds, the difference between the upper and lower material temperatures, and the difference between the upper and lower friction coefficients is set alone or in combination, and the rolling is performed. Here, κ _L2 is a warpage curvature caused by Δμ ^L _{2 in the} path, and γ is a correction coefficient obtained by learning, experiment, or calculation. 9. A warp curvature kappa _Q3 in the next pass, the warp curvature kappa _Q'2 due to factors other than the upper and lower surfaces temperature difference and differential speed in the path, the influence of variations in the shape ratio of the path and the next path The sheet rolling according to claim 7 or 8, characterized in that it is determined on the basis of the following equation considering κ _Q3 = δ ₁ · κ _Q'2. Method. κ _Q3 = δ ₂ · κ _Q'2 where δ ₁ : The _relationship between the shape ratio (the value obtained by dividing the contact projection arc length between the rolling mill and the work roll by the average value of the entrance and exit sheet thicknesses) and the warpage curvature Learning coefficient to indicate. [delta] _2: ratio of warp curvature q (gamma ₁₎ that Δμ warp curvature q (gamma ₂₎ a shape ratio shape ratio when no change occurs in the case of gamma ₂ occurs when the gamma ₁ (q ( Γ ₂ ) / q
(Γ ₁ )) Δt: Vertical temperature difference of rolled material Δμ: Vertical difference of friction coefficient between work roll and rolled material Γ ₁ : Shape ratio of previous pass Γ ₂ : Shape ratio of relevant pass ：: Shape ratio: Rolled material Value obtained by dividing the contact projection arc length between the workpiece and the work roll by the average value of the entrance and exit sheet thicknesses 10. The sheet rolling method according to claim 1, wherein a warpage curvature standardized as a work roll radius / warpage curvature radius is used as the warpage curvature.