Method for controlling meandering of plate to be rolled

Abstract

To properly control meandering and camber of a plate to be rolled in cross rolling.SOLUTION: In a method for controlling meandering of a plate to be rolled of the present disclosure, the meandering amount of the plate to be rolled is separated into the meandering amount due to wedge ratio change, the meandering amount due to left-right difference in friction coefficient, and the meandering amount due to upper-lower difference in friction coefficient from a rolling state of the plate to be rolled in cross rolling mill, and based on the meandering amount due to each cause, the meandering of the plate to be rolled of a control target is suppressed by performing at least one of leveling control, friction coefficient left-right difference control for controlling left-right difference in friction coefficient, and friction coefficient upper-lower difference control for controlling upper-lower difference in friction coefficient.SELECTED DRAWING: Figure 8

Description

[Technical Field]

[0001] The present invention relates to a method for controlling meandering of a rolled sheet in a cross rolling mill, for controlling the meandering and camber of the rolled sheet. [Background technology]

[0002] It is known that meandering (off-center behavior of the rolled sheet in the left-right direction from the pass line) and camber (left-right bending of the rolled sheet at the exit of the rolling pass) of a rolled sheet occur due to left-right asymmetry in the rolling state. Since meandering and camber of a rolled sheet impair sheet threadability in the rolling process, reduce productivity, and lower the straightness of the rolled product, thereby degrading quality, there is a need to control these. One factor that causes left-right asymmetry in the rolling state is the difference in the reduction rate between the left and right sides (i.e., a change in the wedge ratio). Numerous methods have been proposed to eliminate left-right asymmetry in the rolling state by adjusting the difference in the reduction amount between the left and right sides, i.e., by leveling adjustment, thereby bringing the change in the wedge ratio closer to zero (for example, Non-Patent Document 1).

[0003] However, meandering and camber in a rolled sheet can also occur due to factors other than changes in the wedge ratio. A typical example is known to be the occurrence of meandering and camber in a rolled sheet due to an asymmetric friction coefficient distribution (i.e., a difference between the left and right friction coefficients). Methods for controlling the occurrence of meandering and camber by adjusting the difference between the left and right friction coefficients have been proposed (e.g., Patent Documents 1 to 3). Furthermore, cross rolling mills, such as pair cross rolling mills, equipped with a pair of work rolls crossed in the rolling plane have high crown control capabilities. However, in cross rolling, meandering and camber are known to occur in the rolled sheet due to the difference between the upper and lower friction coefficients. Therefore, a method for controlling the occurrence of meandering and camber by adjusting the difference between the upper and lower friction coefficients so that the difference between the upper and lower thrust forces or torques is zero has also been proposed (e.g., Patent Document 4). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 60-250818 [Patent Document 2] Japanese Patent Application Publication No. 5-237528 [Patent Document 3] Japanese Patent Application Publication No. 6-99211 [Patent Document 4] Japanese Patent Application Laid-Open No. 2000-280015 [Non-patent literature]

[0005] [Non-Patent Document 1] Hiroe Nakajima and five others, "Study on the method of controlling meandering in hot strip rolling (1st report) - Theory on the mechanism of occurrence of meandering and camber -", Proceedings of the 1980 Spring Conference on the Technology of Plasticity, pp. 61-64, 1980 Summary of the Invention [Problem to be solved by the invention]

[0006] However, meandering and camber of the rolled sheet are not necessarily caused by a single factor, but may be caused by multiple factors among a change in wedge ratio, a difference in the coefficient of friction between the top and bottom, and a difference in the coefficient of friction between the left and right. For example, in cross rolling, meandering of the rolled sheet may be caused by two factors, a change in wedge ratio and a difference in the coefficient of friction between the top and bottom, or by three factors, a change in wedge ratio, a difference in the coefficient of friction between the top and bottom, and a difference in the coefficient of friction between the left and right. Since the behavior of meandering caused by these factors differs for each, it is difficult to appropriately suppress meandering of the rolled sheet.

[0007] Therefore, the present invention has been made in consideration of the above problems, and an object of the present invention is to provide a method for controlling the meandering of a rolled sheet, which is capable of appropriately controlling the meandering and camber of the rolled sheet in cross rolling. [Means for solving the problem]

[0008] In order to solve the above problems, according to one aspect of the present invention, a method for controlling the meandering of a rolled sheet is provided, which separates the amount of meandering of the rolled sheet from the rolling state of the rolled sheet in a cross rolling mill into an amount of meandering caused by a change in the wedge ratio, an amount of meandering caused by the difference in the left and right friction coefficients, and an amount of meandering caused by the difference in the top and bottom friction coefficients, and based on the amount of meandering caused by each cause, suppresses the meandering of the rolled sheet to be controlled by performing at least one of leveling control, left and right friction coefficient difference control that controls the difference in the left and right friction coefficients, and top and bottom friction coefficient difference control that controls the difference in the top and bottom friction coefficients.

[0009] The method for controlling the meandering of a rolled sheet may involve performing at least one of leveling control, which reduces the amount of meandering caused by a change in the wedge ratio to zero, left-right friction coefficient difference control, which reduces the amount of meandering caused by the difference in the friction coefficient between the left and right sides to zero, and top-bottom friction coefficient difference control, which reduces the amount of meandering caused by the difference in the friction coefficient between the top and bottom sides to zero, thereby suppressing the meandering of the rolled sheet being controlled.

[0010] In at least one of the left-right friction coefficient difference control and the top-bottom friction coefficient difference control, at least one of the concentration and supply amount of lubricating oil injected between the work roll and the rolled sheet may be adjusted.

[0011] Alternatively, at least one of the left-right friction coefficient difference control and the top-bottom friction coefficient difference control may adjust at least one of the roughness of the work rolls or the surface quality of the rolled sheet.

[0012] The meandering control method for the rolled sheet may be implemented by reducing the amount of meandering of the rolled sheet to zero by leveling control alone.

[0013] In this case, the leveling control amount at the front end of the rolled plate to be controlled and the leveling control amount at the tail end of the rolled plate to be controlled may be changed depending on the amount of meandering caused by a change in the wedge ratio, the amount of meandering caused by the difference in the left and right friction coefficients, and the amount of meandering caused by the difference in the top and bottom friction coefficients.

[0014] Alternatively, a leveling control amount may be applied based on the amount of meandering caused by a change in the wedge ratio, the amount of meandering caused by the difference in the left and right friction coefficients, and the amount of meandering caused by the difference in the top and bottom friction coefficients, so that the wedge remains constant over the entire length of the rolled plate to be controlled.

[0015] The rolling state of the rolled sheet may be determined based on at least one of the following factors: the amount of camber at the exit side of the rolling pass; a change in the wedge ratio in the rolling pass; a difference in the rolling load between the left and right sides; the amount of meandering on the entry side; and a difference in the load acting on the entry side edger device between the left and right sides or a difference in the load acting on the side guides between the left and right sides.

[0016] Furthermore, when the amount of meandering caused by the difference in the coefficient of friction between the left and right sides is within an allowable range, the meandering in the rolling pass may be separated as the rolling state of the rolled sheet based on at least two or more factors of the camber amount at the exit side of the rolling pass, or the change in the wedge ratio in the rolling pass, the difference in the rolling load between the left and right sides, the amount of meandering on the entry side, the amount of meandering on the exit side, and the difference in the load acting on the entry side edger device between the left and right sides or the difference in the load acting on the side guides between the left and right sides.

[0017] When the difference in rolling load between the left and right sides of the rolled sheet is included in the factors representing the rolling state of the rolled sheet, the difference in temperature between the left and right sides of the rolled sheet may be included in the factors to separate meandering. [Effects of the Invention]

[0018] As described above, according to the present invention, in a cross rolling mill, meandering caused by a change in the wedge ratio, meandering caused by a difference in the coefficient of friction between the top and bottom, and meandering caused by a difference in the coefficient of friction between the left and right sides can be appropriately separated, and meandering of the rolled sheet can be controlled. Note that camber occurs as a result of meandering of the rolled sheet due to a change in the wedge ratio or a difference in the coefficient of friction between the left and right sides. In other words, if meandering caused by a change in the wedge ratio, a difference in the coefficient of friction between the top and bottom, or a difference in the coefficient of friction between the left and right sides can be controlled, then naturally, camber caused by a change in the wedge ratio, a difference in the coefficient of friction between the top and bottom, or a difference in the coefficient of friction between the left and right sides can also be controlled. Therefore, the meandering control method according to the present invention can control not only the meandering of the rolled sheet, but also the camber. [Brief explanation of the drawings]

[0019] [Figure 1] 1 is an explanatory diagram showing a rolling apparatus according to an embodiment of the present invention; [Figure 2] FIG. 1 is a schematic plan view showing an edger installed on the entry side of a cross rolling mill. [Figure 3] FIG. 1 is a schematic plan view showing a state in which a side guide is installed on the inlet side of a cross rolling mill. [Figure 4] 1 is a graph showing an example of meandering behavior of a rolled sheet due to changes in wedge ratio. [Figure 5] 1 is a graph showing an example of meandering behavior of a rolled sheet due to a difference in friction coefficient between the top and bottom. [Figure 6] FIG. 1 is an explanatory diagram showing the meandering state of a rolled sheet when the lower friction coefficient is greater than the upper friction coefficient in a cross rolling mill. [Figure 7] 1 is a graph showing an example of meandering behavior of a rolled sheet due to a difference in friction coefficient between the left and right sides. [Figure 8] As an example of a method for controlling the meandering of a rolled sheet according to the embodiment, this is a flowchart for a case (control example 1) in which meandering is suppressed by different meandering controls depending on the cause of the meandering, and shows a case in which meandering or camber caused by three factors, namely, a change in wedge ratio, a difference in the friction coefficient between the top and bottom, and a difference in the friction coefficient between the left and right, is controlled. [Figure 9]As an example of a method for controlling the meandering of a rolled sheet according to the embodiment, this is a flowchart for a case (control example 1) in which meandering is suppressed by different meandering controls depending on the cause of the meandering, and shows a case in which meandering or camber caused by two factors, namely, a change in wedge ratio and a difference between the upper and lower friction coefficients, is controlled. [Figure 10] 10 is a flowchart showing an example of a method for controlling meandering of a rolled sheet according to the embodiment, illustrating a case (control example 2) in which meandering of the rolled sheet is suppressed only by leveling control. DETAILED DESCRIPTION OF THE INVENTION

[0020] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In this specification and drawings, components having substantially the same functional configurations are designated by the same reference numerals, and redundant explanations will be omitted.

[0021] [1. Configuration of rolling equipment] First, a schematic configuration of a rolling mill 1 equipped with a cross rolling mill 10 according to one embodiment of the present invention will be described with reference to Figures 1 to 3. Figure 1 is an explanatory diagram showing one example of the configuration of the rolling mill 1 according to this embodiment. Figure 2 is a schematic plan view showing a state in which an edger device 50 is installed on the entry side of the cross rolling mill 10. Figure 3 is a schematic plan view showing a state in which a side guide 60 is installed on the entry side of the cross rolling mill 10.

[0022] In the following description, the upstream side of the cross rolling mill 10 in the rolling direction (X direction) is also referred to as the "entrance side," and the downstream side of the cross rolling mill 10 in the rolling direction (X direction) is also referred to as the "exit side." The reference direction is the left-right direction of the cross rolling mill 10, i.e., the direction (Y direction) perpendicular to the rolling direction within the rolling plane (XY plane) on which the cross rolling mill 10 rolls the sheet S. The reference direction is the direction along the longitudinal direction of the barrels of the work rolls 11 and 12 (i.e., the roll axes). Here, when viewing the cross rolling mill 10 from the upstream side in the rolling direction, one side of the barrels of the work rolls 11 and 12 located on the right side (the front side of the paper in FIG. 1, and the bottom side of the paper in FIGS. 2 and 3) is also referred to as the "work side," and the other side of the barrels of the work rolls 11 and 12 located on the left side (the back side of the paper in FIG. 1, and the top side of the paper in FIGS. 2 and 3) is also referred to as the "drive side."

[0023] Note that Figure 1 shows a schematic configuration of the rolling mill 1, and the work rolls 11, 12 are shown in a state where they have no cross angle, but in the cross rolling mill 10, at least one of the work rolls 11, 12 is installed so that the roll axis on the rolling surface has an angle with respect to a reference direction.

[0024] As shown in FIG. 1 , the rolling mill 1 according to this embodiment includes a cross rolling mill 10, a meander gauge 20, lubricant supply devices 31 and 32, a screw down device 40, and a control device 100. The cross rolling mill 10 has a top work roll 11 and a bottom work roll 12. The cross rolling mill 10 rolls the sheet S passing between the top work roll 11 and the bottom work roll 12 to a predetermined thickness. The roll gap between the top work roll 11 and the bottom work roll 12 can be adjusted by a screw down device 40 that presses down the top work roll 11 in the reduction direction (negative side in the Z direction). The screw down device may also be arranged to press up the bottom work roll 12 in the reduction direction (positive side in the Z direction).

[0025] A meandering meter 20 for measuring the meandering amount of the rolled sheet S is installed on the delivery side of the cross rolling mill 10 shown in FIG. 1 . The meandering meter 20 according to this embodiment measures the meandering amount of the rolled sheet S at multiple positions on the delivery side of the cross rolling mill 10 so as to measure the amount of outlet camber at the delivery side of the cross rolling mill 10. The amount of outlet camber is expressed as the difference between the amount of meandering at a reference position on the delivery side of the cross rolling mill 10 and the amount of meandering at an outlet other than the reference position. The meandering meter 20 may also be installed on the entry side of the cross rolling mill 10. The type of meandering meter 20 is not particularly limited. For example, an image of the rolled sheet S may be captured by a CCD camera, and the edge position of the rolled sheet S may be detected by image processing to calculate the amount of meandering. Measurement information from the meandering meter 20 is output to the control device 100.

[0026] At the entry side of the cross rolling mill 10, there are disposed a lubricant supply device 31 that supplies lubricant to the top work roll 11, and a lubricant supply device 32 that supplies lubricant to the bottom work roll 12. The lubricant supply devices 31, 32 are configured to distribute the amount and concentration of lubricant supplied in the width direction, for example, by arranging multiple flat spray nozzles across the length of the roll barrels of the work rolls 11, 12. Furthermore, although this embodiment shows the case where lubricant is sprayed onto the work rolls 11, 12, the lubricant may also be sprayed onto the rolled sheet S or auxiliary rolls. As the lubricant, for example, a synthetic ester-based lubricant oil that is commonly used as hot rolling oil may be used.

[0027] Furthermore, as shown in FIG. 2, an edger device 50 that reduces the width of the rolled sheet S may be installed on the entry side of the cross rolling mill 10. The edger device 50 presses the rolled sheet S in the width direction (Y direction) using a pair of edger rolls 51, 52, thereby adjusting the rolled sheet S to a predetermined width. Alternatively, as shown in FIG. 3, a side guide 60 may be installed on the entry side of the cross rolling mill 10. The side guide 60 is composed of a pair of guides 61, 62 installed opposite each other in the width direction (Y direction) and is installed to center the rolled sheet S passing through the sheet threading line. The load or torque with which the edger device 50 presses the rolled sheet S and the load (repulsion force) that the side guide 60 receives from the rolled sheet S can be measured. The measured horizontal load or torque of the edger device 50 or the load that the side guide 60 receives from the rolled sheet S are output to the control device 100.

[0028] The control device 100 performs various controls of the rolling mill 1. In this embodiment, for example, when the control device 100 determines that the rolled sheet S is meandering based on the detection results of the meander meter 20, it controls the rolling mill 1 so that the amount of meandering is zero, thereby controlling the meandering of the rolled sheet S. At this time, the control device 100 appropriately controls the meandering or camber of the rolled sheet S by performing at least one of leveling control, top-bottom friction coefficient difference control, and left-right friction coefficient difference control, depending on the cause of the meandering or camber of the rolled sheet. The meandering control method according to this embodiment will be described in detail later.

[0029] An example of the configuration of the rolling mill 1 according to this embodiment has been described above.

[0030] [2. Controlling the meandering of rolled sheets] [2-1. Overview] In a cross rolling mill, the causes of meandering or camber in the rolled sheet S are, as mentioned above, asymmetries in the rolling state between the top and bottom and the left and right, such as changes in the wedge ratio, differences in the coefficient of friction between the top and bottom, and differences in the coefficient of friction between the left and right. Here, the inventors of the present application have found that the behavior of meandering caused by changes in the wedge ratio, meandering caused by differences in the coefficient of friction between the top and bottom, and meandering caused by differences in the coefficient of friction between the left and right, are different.

[0031] Figure 4 is a graph showing an example of the meandering behavior of the rolled sheet S due to a wedge ratio change ΔΨ. Figure 4 shows the rolling analysis results for cases where the wedge ratio change ΔΨ is positive and negative, and shows the trajectory of the center of the cross section of the rolled sheet S. The solid line represents the case where the wedge ratio change ΔΨ is negative (ΔΨ<0), and the dashed line represents the case where the wedge ratio change ΔΨ is positive (ΔΨ>0). Here, in this specification, wedge refers to the difference in thickness between the work side and drive side of the rolled sheet, and is considered positive when the work side thickness is thicker than the drive side thickness. The wedge ratio is the value obtained by dividing the wedge by the sheet thickness. The wedge ratio change refers to the difference between the wedge ratio at the exit side of the rolling pass and the wedge ratio at the entry side of the same rolling pass. In Figure 4, there is no difference in the friction coefficient between the top, bottom, left, and right.

[0032] As shown in Figure 4, whether the wedge ratio change ΔΨ is positive or negative, the trajectory of the rolled sheet S is linear at the entry side of the rolling mill and quadratic at the exit side. It can also be seen that the meandering direction is the same on the entry side and the exit side. That is, in the example of Figure 4, when the wedge ratio change ΔΨ is negative, the sheet meanders in the positive direction (drive side) at the entry side and the exit side of the rolling mill, and when the wedge ratio change ΔΨ is positive, the sheet meanders in the negative direction (work side) at the entry side and the exit side of the rolling mill.

[0033] 5 is a graph showing an example of the meandering behavior of the rolled sheet S due to the difference in the coefficient of friction between the top and bottom of a cross rolling mill. The coefficient of friction between the top work roll 11 and the rolled sheet S (hereinafter also referred to as the "upper coefficient of friction") μ T and the coefficient of friction between the bottom work roll 12 and the sheet S to be rolled (hereinafter also referred to as the "lower side coefficient of friction") μ BIf there is a difference between the two, the direction of travel of the rolled sheet S will be inclined in a direction perpendicular to the rotation axis of the work roll on the side with the larger coefficient of friction.

[0034] For example, consider a pair cross rolling mill in which the drive side (DS) of the barrel of the top work roll 11 is located downstream in the rolling direction and the work side (WS) of the barrel is located upstream in the rolling direction, and the drive side (DS) of the barrel of the bottom work roll 12 is located upstream in the rolling direction and the work side (WS) of the barrel is located downstream in the rolling direction, as shown in Figure 6. In this case, it is assumed that there is no difference in the coefficient of friction between the work rolls 11, 12 and the sheet S to be rolled on the left and right, and that there is no change in the wedge ratio of the sheet S to be rolled. Furthermore, the amount of meandering of the sheet S to be rolled is set to zero when there is no meandering.

[0035] In such a pair cross rolling mill, the lower friction coefficient μ B is the upper friction coefficient μ T 5, the rolled sheet S snakes toward the drive side (DS) at the exit side of the pair cross rolling mill so as to approach a direction perpendicular to the rotation axis of the bottom work roll 12. On the other hand, if the upper friction coefficient μ T is the lower friction coefficient μ B When the rolling speed is larger than 1 / 2, the sheet S to be rolled snakes toward the work side (WS) at the exit side of the pair cross rolling mill so as to approach a direction perpendicular to the rotation axis of the upper work roll 11. In either case, the trajectory of the sheet S to be rolled is a straight line from the entry side to the exit side of the pair cross rolling mill.

[0036] However, unlike the case of the wedge ratio change shown in Figure 4, the meandering direction is opposite on the entry side and the exit side. That is, in the example of Figure 5, the lower friction coefficient μ B is the upper friction coefficient μ T When the upper friction coefficient μ is larger than , the material snakes in the negative direction (work side) at the entry side of the pair cross rolling mill, but snakes in the positive direction (drive side) at the exit side. T is the lower friction coefficient μ B When the rolling speed is larger than , the material snakes in the positive direction (drive side) at the entry side of the pair cross rolling mill, but snakes in the negative direction (work side) at the exit side.

[0037] If the crossing direction of the work rolls in pair cross rolling is opposite to that of the pair cross rolling mill shown in Figure 6, that is, if the drive side (DS) of the barrel of the upper work roll 11 is located upstream in the rolling direction and the work side (WS) of the barrel is located downstream in the rolling direction, and if the drive side (DS) of the barrel of the lower work roll 12 is located downstream in the rolling direction and the work side (WS) of the barrel is located upstream in the rolling direction, then the direction of meandering of the rolled sheet S due to the difference in the upper and lower friction coefficients will be opposite to that shown in Figure 5. In other words, if the lower friction coefficient μ B is the upper friction coefficient μ T When the upper friction coefficient μ is larger than 1 / μm, the rolled sheet S snakes toward the work side (WS) at the exit side of the pair cross rolling mill so as to approach a direction perpendicular to the rotation axis of the bottom work roll 12. On the other hand, when the upper friction coefficient μ T is the lower friction coefficient μ B If the rolling speed is larger than 1 / 2, the rolled sheet S will snake toward the drive side (DS) so as to approach a direction perpendicular to the rotation axis of the upper work roll 11 on the delivery side of the pair cross rolling mill.

[0038] Fig. 7 is a graph showing an example of the meandering behavior of the rolled sheet S due to the difference in the coefficient of friction between the left and right. DW (=μ DS -μ WS ) and shows the locus of the center of the cross section of the rolled sheet S. Here, the coefficient of friction between the work rolls 11, 12 and the rolled sheet S on the drive side (DS) from the center of the width direction of the rolled sheet S (hereinafter also referred to as the "drive side friction coefficient") is μ DS The coefficient of friction between the work rolls 11, 12 and the rolled sheet S on the work side (WS) from the center of the width direction of the rolled sheet S (hereinafter also referred to as the "work side coefficient of friction") is μ WS In Figure 7, the solid line represents the difference in the coefficient of friction between the left and right, Δμ DW When is negative (i.e. μ DS <μ WS The dashed line indicates the difference in the friction coefficient between the left and right, Δμ DW When is positive (i.e. μ DS >μ WS (In the case of

[0039] In the rolling analysis of Fig. 7, it was assumed that there was no difference between the coefficient of friction between the top work roll 11 and the rolled sheet S and the coefficient of friction between the bottom work roll 12 and the rolled sheet S on either the drive side (DS) or the work side (WS) with respect to the width center of the rolled sheet S. It was also assumed that there was no change in the wedge ratio of the rolled sheet S.

[0040] As shown in Fig. 7, the difference in the friction coefficient between the left and right, Δμ DW Whether the value of is positive or negative, the trajectory of the rolled sheet S is linear on the entry side of the rolling mill and quadratic on the exit side. However, unlike the case of the wedge ratio change shown in Figure 4, the direction of meandering is opposite on the entry side and the exit side. That is, in the example of Figure 7, the difference in the friction coefficient between the left and right, Δμ DW When is negative, the rolling mill will snake in the negative direction (work side) on the entry side, but will snake in the positive direction (drive side) on the exit side. DW When is positive, the rolling mill meanders in the positive direction (drive side) at the entry side, but in the negative direction (work side) at the exit side.

[0041] As described above, the meandering caused by the change in the wedge ratio has the same direction at the entry side and the exit side of the cross rolling mill, whereas the meandering caused by the difference in the coefficient of friction between the top and bottom sides and the difference in the coefficient of friction between the left and right sides have different directions at the entry side and the exit side of the cross rolling mill. For this reason, for example, when attempting to eliminate meandering occurring in a cross rolling mill, even if the meandering is actually caused by the difference in the coefficient of friction between the top and bottom sides or the difference in the coefficient of friction between the left and right sides, if the meandering occurring at the exit side of the cross rolling mill is assumed to be caused by a change in the wedge ratio and leveling control is attempted to control the meandering occurring at the entry side of the cross rolling mill, the meandering actually becomes larger. Similarly, if the meandering occurring at the entry side of the cross rolling mill due to the difference in the coefficient of friction between the top and bottom sides or the difference in the coefficient of friction between the left and right sides is assumed to be caused by a change in the wedge ratio and leveling control is attempted to suppress the meandering, the meandering actually becomes larger at the exit side of the cross rolling mill.

[0042] On the other hand, meandering caused by a change in the wedge ratio and a difference in the coefficient of friction between the left and right sides is a quadratic curve at the exit of the cross rolling mill, but meandering caused by a difference in the coefficient of friction between the top and bottom of the cross rolling mill is a linear shape at the exit of the cross rolling mill. Therefore, for example, linear meandering at the exit of the cross rolling mill caused by a difference in the coefficient of friction between the top and bottom cannot be compensated for by leveling control.

[0043] From this, the inventors of the present application have found that by focusing on the meandering profile at the delivery side of the cross rolling mill, it is possible to separate meandering caused by a change in the wedge ratio and a difference in the friction coefficient between the left and right sides, from meandering caused by a difference in the friction coefficient between the top and bottom sides. Furthermore, they have also found that by focusing on the direction of meandering at the entry side and the direction of meandering at the delivery side of the cross rolling mill, it is possible to separate meandering caused by a change in the wedge ratio from meandering caused by a difference in the friction coefficient between the top and bottom sides and a difference in the friction coefficient between the left and right sides.

[0044] Therefore, in the method for controlling the meandering of the rolled sheet S according to this embodiment, the meandering or camber of the rolled sheet S is appropriately controlled by performing at least one of leveling control, top-bottom friction coefficient difference control, and left-right friction coefficient difference control, depending on the factor causing the meandering or camber of the rolled sheet S.

[0045] [2-2. Control method] In the method for controlling the meandering of a rolled sheet S according to this embodiment, the meandering amount of the rolled sheet S is first separated into a meandering amount due to a change in the wedge ratio, a meandering amount due to a difference in the left-right friction coefficient, and a meandering amount due to a difference in the top-bottom friction coefficient based on the rolling state of the rolled sheet S in a cross rolling mill. Then, based on the meandering amount due to each cause, the meandering of the rolled sheet S to be controlled is suppressed by performing at least one of leveling control, left-right friction coefficient difference control to control the difference in the left-right friction coefficient, and top-bottom friction coefficient difference control to control the difference in the top-bottom friction coefficient. The rolled sheet S to be controlled may be the same as the rolled sheet S when the meandering amount occurring for each cause of meandering is identified, or it may be the rolled sheet S to be rolled next after the rolled sheet S when the meandering amount occurring for each cause of meandering is identified. In the following description, the rolled sheet S to be controlled is assumed to be the same as the rolled sheet S when the meandering amount occurring for each cause of meandering is identified.

[0046] Ideally, it is desirable to perform control to suppress meandering so that the amount of meandering caused by each factor approaches 0. Taking these circumstances into consideration, a specific meandering control method for separating the amount of meandering of the rolled sheet S that has occurred into each factor and appropriately suppressing the amount of meandering caused by each factor will be described below.

[0047] [2-2-1. Suppressing meandering by different meandering control methods for each cause of meandering (Control Example 1)] First, as an example of a method for controlling meandering of the rolled sheet S according to this embodiment, a case where meandering is suppressed by different meandering controls depending on the cause of the meandering (control example 1) will be described in detail. In control example 1, meandering occurring in the rolled sheet S is suppressed by performing at least one of leveling control, which reduces the amount of meandering caused by a change in wedge ratio to zero, left-right friction coefficient difference control, which reduces the amount of meandering caused by the difference in friction coefficient between the left and right sides to zero, and top-bottom friction coefficient difference control, which reduces the amount of meandering caused by the difference in friction coefficient between the top and bottom sides to zero.

[0048] The meandering or camber of the rolled sheet S that occurs in cross rolling can be caused by three factors: a change in wedge ratio, a difference in the coefficient of friction between the top and bottom, and a difference in the coefficient of friction between the left and right, or by two factors: a change in wedge ratio and a difference in the coefficient of friction between the top and bottom. Below, the method for controlling the meandering of the rolled sheet S according to this embodiment for each case will be described in detail.

[0049] [2-2-1-1. Control of meandering or camber caused by three factors] FIG. 8 is a flowchart showing a method for controlling meandering of the rolled sheet S when controlling meandering or camber caused by three factors: a change in wedge ratio, a difference in the coefficient of friction between the top and bottom, and a difference in the coefficient of friction between the left and right.

[0050] (S100: Measurement of the rolling state of the rolled plate) First, the rolling condition of the sheet S to be rolled is measured (S100). The rolling condition of the sheet S to be rolled can be expressed, for example, by the camber amount at the delivery side of the rolling mill, the change in wedge ratio, the difference in rolling load between the left and right sides, the amount of meandering at the entry side, the difference in load acting on the entry side edger device between the left and right sides, or the difference in load acting on the side guides between the left and right sides. The camber amount of the sheet S to be rolled at the delivery side of the rolling mill can also be calculated by, for example, capturing images of the sheet S to be rolled with a CCD camera at the delivery side of a cross rolling mill, and processing the images to detect the edge positions of the sheet S to be rolled, thereby obtaining the amount of meandering at multiple positions. The measured rolling condition of the sheet S to be rolled can be output to the control device 100.

[0051] (S110: Separation of meandering amount according to the cause) Next, the control device 100 separates the meandering that has occurred in the rolled sheet S from the rolling state of the rolled sheet S measured in step S100 into meandering caused by changes in the wedge ratio, meandering caused by the difference in the friction coefficient between the top and bottom, and meandering caused by the difference in the friction coefficient between the left and right (S110).

[0052] In step S110, among the factors that represent the rolling state of the rolled sheet S, the amount of outlet camber is used, as well as at least one of the following factors: the change in wedge ratio in the rolling pass, the difference in rolling load between the left and right sides, the amount of entry meandering, and the difference in load acting on the entry edger device between the left and right sides or the difference in load acting on the side guide between the left and right sides.

[0053] Based on two or more factors including these delivery camber amounts, meandering occurring in the rolled sheet S is separated into meandering caused by a change in the wedge ratio, meandering caused by a difference in the coefficient of friction between the top and bottom, and meandering caused by a difference in the coefficient of friction between the left and right. Specifically, the processing of step S110 may be performed by, for example, the following separation methods (A) to (D).

[0054] (A) Separation based on wedge ratio change and exit camber amount For example, by using the change in wedge ratio and the actual measured value of the camber amount on the delivery side as the rolling state of the rolled sheet S, the meandering occurring in the rolled sheet S can be separated into the amount of meandering caused by the change in wedge ratio, the amount of meandering caused by the difference in the coefficient of friction between the top and bottom, and the amount of meandering caused by the difference in the coefficient of friction between the left and right. Separation method (A) can be applied regardless of whether the rolled sheet S is restrained on the entry side of the cross rolling mill.

[0055] The delivery camber amount is acquired in step S100. When the rolled sheet S meanders on the delivery side of the cross rolling mill 10 due to a change in the wedge ratio or a difference in the coefficient of friction between the left and right sides, the trajectory is approximately parabolic, as shown in Figures 4 and 7. On the other hand, when the sheet S meanders due to a difference in the coefficient of friction between the top and bottom sides, the trajectory is linear, as shown in Figure 5. Therefore, if the delivery camber amount is separated into a second-order component representing a substantially parabolic meandering and a first-order component representing a linear meandering, it is possible to extract, from the delivery camber amount measured in step S100, the amount of meandering due to a change in the wedge ratio and a difference in the coefficient of friction between the left and right sides (second-order component) and the amount of meandering due to the difference in the coefficient of friction between the top and bottom sides (first-order component).

[0056] The wedge ratio change may be calculated based on measured values ​​of the wedge at the entry and exit sides of the rolling pass. Alternatively, the wedge ratio change may be calculated using an estimated value of the wedge at the exit side of the rolling pass based on the difference in rolling load between the left and right sides and the difference in mill rigidity between the left and right sides in the rolling pass. The wedge at the entry side of the rolling pass can also be estimated based on the difference in rolling load between the left and right sides and the difference in mill rigidity between the left and right sides in the rolling pass immediately before the rolling pass.

[0057] Once a measured or estimated value of the wedge ratio change in the rolling pass is obtained, it is possible to estimate the amount of exit meandering due to a wedge ratio change based on a method for estimating the camber curvature change due to a wedge ratio change. A known method can be used to estimate the camber curvature change due to a wedge ratio change, and for example, the method described in Non-Patent Document 1 (relationship between wedge ratio change ΔΨ and camber curvature change Δκ) may be used. In this way, the exit camber curvature due to a wedge ratio change can be estimated. If the exit camber curvature due to a wedge ratio change can be estimated, the amount of meandering can be estimated at a meander meter position installed a predetermined distance downstream from the cross rolling mill, based on the fact that the trajectory of the rolled sheet downstream of the cross rolling mill is approximately parabolic.

[0058] The difference between the estimated value of the amount of meandering on the delivery side estimated from the change in wedge ratio and the amount of meandering on the delivery side (secondary component) extracted from the actual measured value is extracted as the amount of meandering caused by the difference in the coefficient of friction between the left and right sides. For example, suppose the estimated value of the amount of meandering on the delivery side at a predetermined distance from the cross rolling mill estimated from the change in wedge ratio is 80 mm, and the amount of meandering on the delivery side (secondary component) extracted from the actual measured value at the same position is 150 mm. In this case, of the actual measured value of the amount of meandering on the delivery side (secondary component) of 150 mm, the amount of meandering caused by the change in the wedge ratio is estimated to be 80 mm, and the difference between the two (70 mm) can be estimated to be caused by the difference in the coefficient of friction between the left and right sides. In this way, based on the measured or estimated value of the change in the wedge ratio in the rolling pass and the amount of meandering on the delivery side of the rolling pass (secondary component), the secondary component of the meandering occurring in the rolled sheet S can be separated into meandering caused by the change in the wedge ratio and meandering caused by the difference in the coefficient of friction between the left and right sides.

[0059] (B) Separation based on the amount of meandering on the entry side and the amount of camber on the exit side Furthermore, for example, by using the amount of entry-side meandering and the amount of delivery-side camber as the rolling state of the rolled sheet S, it is possible to separate the meandering occurring in the rolled sheet S into meandering caused by a change in the wedge ratio, meandering caused by the difference in the coefficient of friction between the top and bottom, and meandering caused by the difference in the coefficient of friction between the left and right. Separation method (B) can be applied when the rolled sheet S is not constrained at the entry side of the cross rolling mill. Separation method (B) does not require measurement and estimation of wedges at the entry and delivery sides of the cross rolling mill. However, it is preferable to obtain in advance the relationship between the meandering measurement position and the amount of meandering according to the change in the wedge ratio as shown in FIG. 4 (hereinafter also referred to as "wedge ratio change-meandering amount information"), and the relationship between the meandering measurement position and the amount of meandering according to the difference in the coefficient of friction between the left and right as shown in FIG. 7 (hereinafter also referred to as "left and right difference in the coefficient of friction-meandering amount information").

[0060] First, as in separation method (A), the exit camber amount is separated into a second-order component representing an approximately parabolic meandering and a first-order component representing a linear meandering. This makes it possible to extract, from the exit camber amount measured in step S100, the amount of meandering (second-order component) due to a change in the wedge ratio or a difference in the left-right friction coefficient, and the amount of meandering (first-order component) due to a difference in the top-bottom friction coefficient.

[0061] Next, based on the amount of meandering (secondary component) extracted from the actual measurements and the amount of entry-side meandering, the secondary component of the meandering occurring in the rolled sheet S is separated into meandering caused by changes in the wedge ratio and meandering caused by the difference in the coefficient of friction between the left and right sides. The amount of entry-side meandering can be determined by using the amount of meandering measured at the entry side of the rolling pass. In this case, since meandering caused by the difference in the coefficient of friction between the top and bottom of a cross rolling mill will be linear, it is possible to separate the amount of meandering caused by the difference in the coefficient of friction between the top and bottom for the amount of entry-side meandering.

[0062] Then, for example, a combination is searched for in which the sum of the exit-side meandering amount based on the wedge ratio change-meandering amount information and the exit-side meandering amount based on the friction coefficient left-right difference-meandering amount information matches the meandering amount (secondary component) extracted from the actual measurement value, or a combination in which the error between the two is minimum. There are multiple such combinations, but for each combination, there is only one combination in which the sum of the entry-side meandering amount based on the wedge ratio change-meandering amount information and the entry-side meandering amount based on the friction coefficient left-right difference-meandering amount information matches the actual measurement value of the entry-side meandering amount, or a combination in which the error between the two is minimum. From a combination in which both the entry-side meandering amount and the exit-side meandering amount found in this way match the actual measurement value, or a combination in which the sum of the squares of the errors between the two is minimum, the wedge ratio change and the left-right difference in the friction coefficient in the rolling pass can be estimated. Then, based on the estimated wedge ratio change and the difference in the friction coefficient between the left and right sides, the secondary component of the meandering occurring in the rolled sheet S can be separated into meandering caused by the change in the wedge ratio and meandering caused by the difference in the friction coefficient between the left and right sides.

[0063] (C) Separation based on the amount of exit camber and the load on the edger or side guide Furthermore, for example, the rolling state of the rolled sheet S can be determined by using the amount of camber on the delivery side, the difference in the load (weight or torque) acting on the edger device 50 between the left and right sides, or the difference in the load acting on the side guides 60, to separate the meandering of the rolled sheet S into three types: meandering caused by a change in the wedge ratio, meandering caused by a difference in the coefficient of friction between the top and bottom, and meandering caused by a difference in the coefficient of friction between the top and bottom. Separation method (C) can be applied when the rolled sheet S is constrained by the edger device 50 or side guides 60 installed on the entry side of the cross rolling mill 10. While separation method (C) does not require measurement or estimation of the wedges at the entry and exit sides of the cross rolling mill, it is preferable to obtain in advance the relationship between the change in the wedge ratio, the difference in the coefficient of friction between the left and right sides, and the difference in the coefficient of friction between the top and bottom and the difference in the load (weight or torque) acting on the edger device or the difference in the load acting on the side guides.

[0064] First, as in separation method (A), the exit camber amount is separated into a second-order component representing an approximately parabolic meandering and a first-order component representing a linear meandering. This makes it possible to extract from the exit camber amount measured in step S100 the amount of meandering (second-order component) due to a change in the wedge ratio or the difference in the left and right friction coefficient, and the amount of meandering (first-order component) due to the difference in the top and bottom friction coefficient.

[0065] Next, based on the amount of meandering (secondary component) extracted from the actual measurements and the load on the edger device or side guide, the secondary component of the meandering occurring in the rolled sheet S is separated into meandering caused by changes in the wedge ratio and meandering caused by the difference in the left-right friction coefficient. At this time, the difference in the load on the edger device or side guide caused by the difference in the friction coefficient between the top and bottom is subtracted from the actual measurements. Here, in separation method (C), the difference in the friction coefficient between the top and bottom is assumed to be zero, and the difference in the load (load or torque) acting on the edger device 50 or the difference in the load acting on the side guide 60 caused by changes in the wedge ratio alone is calculated.

[0066] When it is assumed that the difference in the coefficient of friction between the left and right sides is zero, the amount of meandering (secondary component) extracted from the actual measurement value and the estimated value of the amount of meandering on the outlet side match, but the estimated value of the difference in the load (weight or torque) acting on the edger device 50 between the left and right sides or the difference in the load acting on the side guides 60 between the left and right sides do not necessarily match the actual measurement value. Therefore, this estimated value is compared with the actual measurement value of the difference in the load (weight or torque) acting on the edger device 50 between the left and right sides or the difference in the load acting on the side guides 60 between the left and right sides. Then, the difference in the coefficient of friction between the left and right sides is corrected so that the estimated value of the difference in the load (weight or torque) acting on the edger device 50 between the left and right sides or the difference in the load acting on the side guides 60 between the left and right sides approaches the actual measurement value.

[0067] The amount of exit meandering is then estimated in the presence of the corrected left-right difference in the friction coefficient and the current wedge ratio change. The difference between the calculated (estimated) value of the left-right difference in the load (weight or torque) acting on the edger device 50 or the left-right difference in the load acting on the side guide 60 and the actual measurement value is considered to be the effect of the left-right difference in the friction coefficient. In other words, the amount of deviation from the amount of meandering (secondary component) extracted from the actual measurement value occurs by the amount of correction of the left-right difference in the friction coefficient. For this reason, the assumed wedge ratio change and the left-right difference in the friction coefficient are corrected so that the amount of meandering (secondary component) extracted from the actual measurement value approaches the estimated amount of exit meandering in the presence of the corrected left-right difference in the friction coefficient.

[0068] The values ​​of the wedge ratio change and the difference in the friction coefficient between the left and right sides are corrected and repeatedly calculated until the estimated value of the outlet side meandering amount and the meandering amount (secondary component) extracted from the actual measurement values ​​match, for the outlet side meandering amount and the left and right difference in the load (load or torque) acting on the edger device 50 or the left and right difference in the load acting on the side guide 60. Then, for the outlet side meandering amount and the left and right difference in the load (load or torque) acting on the edger device 50 or the left and right difference in the load acting on the side guide 60, the values ​​of the wedge ratio change and the difference in the friction coefficient between the left and right sides when the estimated value of the outlet side meandering amount and the meandering amount (secondary component) extracted from the actual measurement values ​​match are taken as the estimated values ​​of the wedge ratio change and the difference in the friction coefficient between the left and right sides for that rolling pass.

[0069] In this way, it is possible to estimate the wedge ratio change and the difference in the friction coefficient between the left and right sides in the rolling pass. Then, from the estimated wedge ratio change and the difference in the friction coefficient between the left and right sides, it is possible to separate the meandering occurring in the rolled sheet S into meandering caused by the wedge ratio change and meandering caused by the difference in the friction coefficient between the left and right sides.

[0070] (D) Separation based on the amount of camber on the delivery side and the difference in rolling load between the left and right sides Furthermore, for example, by using the amount of exit camber and the difference in rolling load between the left and right sides as the rolling state of the rolled sheet S, the meandering occurring in the rolled sheet S can be separated into meandering caused by changes in the wedge ratio, meandering caused by the difference in the friction coefficient between the top and bottom, and meandering caused by the difference in the friction coefficient between the left and right.

[0071] First, as in separation method (A), the exit camber amount is separated into a second-order component representing an approximately parabolic meandering and a first-order component representing a linear meandering. This makes it possible to extract from the exit camber amount measured in step S100 the amount of meandering (second-order component) due to a change in the wedge ratio or the difference in the left and right friction coefficient, and the amount of meandering (first-order component) due to the difference in the top and bottom friction coefficient.

[0072] Next, based on the difference in rolling load between the left and right sides, the secondary component of meandering extracted from the actual measured values ​​occurring in the rolled sheet S is separated into meandering caused by a change in the wedge ratio and meandering caused by a difference in the left and right friction coefficient. The difference in rolling load between the left and right sides is the difference between the rolling load on the work side and the rolling load on the drive side of the rolling mill. A difference in rolling load between the left and right sides occurs when there is a change in the wedge ratio or a difference in the left and right friction coefficient. Therefore, in separation method (D), a difference in the left and right friction coefficient and a change in the wedge ratio are assumed, and the amount of meandering on the delivery side and the difference in rolling load between the left and right sides are estimated for the assumed difference in the left and right friction coefficient and the change in the wedge ratio. Then, based on the estimated change in the wedge ratio and the difference in the left and right friction coefficient, the secondary component of meandering occurring in the rolled sheet S extracted from the actual measured values ​​can be separated into meandering caused by a difference in the left and right friction coefficient and meandering caused by a change in the wedge ratio.

[0073] By using these separation methods (A) to (D), it is possible to separate the meandering occurring in the rolled sheet S into the following: meandering caused by a change in the wedge ratio, meandering caused by a difference in the coefficient of friction between the top and bottom, and meandering caused by a difference in the coefficient of friction between the left and right. Note that in the above explanation, the case has been described in which the meandering is separated for each factor causing the meandering using one factor as the rolling state of the rolled sheet S other than the amount of delivery camber: the change in the wedge ratio, the difference in the rolling load between the left and right, the amount of entry-side meandering, and the difference in the load acting on the entry-side edger device between the left and right, or the difference in the load acting on the side guides between the left and right. However, the present invention is not limited to this example, and the meandering may be separated using two or more factors.

[0074] Furthermore, methods for estimating the left-right difference in friction coefficients or meandering caused by the left-right difference in friction coefficients, the top-bottom difference in friction coefficients or meandering caused by the top-bottom difference in friction coefficients, and the wedge ratio change or meandering caused by the wedge ratio change using these factors are not limited to the examples described in the separation methods (A) to (D). In other words, the above description illustrates a method for separating the meandering caused by the wedge ratio change, the meandering caused by the left-right difference in friction coefficients, and the meandering caused by the top-bottom difference in friction coefficients using convergence calculation, but the convergence calculation method is not limited to the above example. Furthermore, for example, by previously determining the amount of meandering for various combinations of the wedge ratio change, the left-right difference in friction coefficients, and the top-bottom difference in friction coefficients, it is also possible to separate the meandering caused by the wedge ratio change, the meandering caused by the left-right difference in friction coefficients, and the meandering caused by the top-bottom difference in friction coefficients without using convergence calculation.

[0075] Furthermore, in separation method (D), which uses the difference in rolling load between the left and right sides as the rolling state of the rolled sheet S, the difference in rolling temperature between the left and right sides may be included as a factor. For example, in hot rolling, if a difference in rolling temperature between the left and right sides occurs, that is, if a temperature difference occurs between the work side and the drive side of the rolled sheet S, the hardness of the material (i.e., deformation resistance) differs between the work side and the drive side of the rolled sheet S, resulting in a difference in rolling load between the left and right sides. Therefore, the difference in rolling temperature between the left and right sides is taken into consideration as the rolling state of the rolled sheet S, and the difference in rolling load between the left and right sides caused by the difference in rolling temperature between the left and right sides is removed from the actual or estimated value of the difference in rolling load between the left and right sides. This makes it possible to accurately separate meandering caused by a change in wedge ratio, meandering caused by a difference in the left and right friction coefficient, and meandering caused by a difference in the top and bottom friction coefficient.

[0076] (S120-S140: Meandering control implemented) Returning to the explanation of Figure 8, in step S110, the amount of camber on the delivery side of the rolled sheet S measured in step S100 is separated into the amount of meandering caused by the change in wedge ratio, the amount of meandering caused by the difference in the friction coefficient between the top and bottom, and the amount of meandering caused by the difference in the friction coefficient between the left and right, and the rolling device 1 is controlled to control each of the separated amounts of meandering.

[0077] (Leveling control) The control device 100 controls the amount of meandering caused by the change in wedge ratio by leveling control (S120). The control device 100 controls the screw down device 40 and adjusts the difference in the amount of reduction of the rolled sheet S between the left and right sides so that the amount of meandering caused by the change in wedge ratio approaches zero.

[0078] (friction coefficient difference control) The control device 100 also controls the amount of meandering caused by the difference in friction coefficient between the top and bottom using upper and lower friction coefficient difference control (S130). The control device 100 adjusts the difference in friction coefficient between the top and bottom so that the amount of meandering caused by the difference in friction coefficient between the top and bottom approaches zero. The difference in friction coefficient between the top and bottom can be adjusted, for example, by changing the amount or concentration of lubricant supplied by the lubricant supply devices 31, 32 between the top and bottom, or by changing at least one of the surface roughness of the work rolls 11, 12 or the surface texture of the rolled sheet S between the top and bottom.

[0079] Increasing the amount of lubricant supplied by the lubricant supply devices 31, 32 reduces the coefficient of friction between the work rolls 11, 12 and the rolled sheet S. In addition, increasing the concentration of the lubricant supplied by the lubricant supply devices 31, 32 reduces the coefficient of friction between the work rolls 11, 12 and the rolled sheet S. Therefore, in step S130, lubricant is supplied by the lubricant supply devices 31, 32 in accordance with the direction of meandering caused by the difference in the coefficient of friction between the top and bottom of the rolled sheet S, and the lower friction coefficient μ B or upper friction coefficient μ T At least one of these may be adjusted.

[0080] For example, in the pair cross rolling mill shown in Figure 6, the upper friction coefficient μ T is the lower friction coefficient μ B When the lower friction coefficient μ is larger than 1 / μ, the rolled sheet S snakes toward the work side (WS) at the exit side of the pair cross rolling mill. B is the upper friction coefficient μ T , the rolled sheet S will meander toward the drive side (DS) at the delivery side of the pair cross rolling mill. Therefore, when the meandering direction of the rolled sheet S at the delivery side of the cross rolling mill 10 due to the difference between the upper and lower friction coefficients is toward the work side (WS), the control device 100 determines whether the lower friction coefficient μ B is the upper friction coefficient μ T The lower friction coefficient μ B Adjustment to increase the upper friction coefficient μ T On the other hand, when the meandering direction of the rolled sheet S at the delivery side of the cross rolling mill 10 due to the difference between the upper and lower friction coefficients is the drive side (DS), the control device 100 adjusts the upper friction coefficient μ T is the lower friction coefficient μ B The lower friction coefficient μ B Adjustment to reduce the upper friction coefficient μ T At least one of the adjustments to increase the

[0081] The coefficient of friction between the work rolls 11, 12 and the sheet S to be rolled can also be adjusted by changing the surface roughness of the work rolls 11, 12 or the surface properties of the sheet S to be rolled. For example, by grinding the surfaces of the work rolls 11, 12 using a roll grinding device (not shown) installed in the rolling mill 10, the surface roughness of the work rolls 11, 12 can be reduced, thereby reducing the coefficient of friction between the work rolls 11, 12 and the sheet S to be rolled. Therefore, the lower coefficient of friction μ B is the upper friction coefficient μ T If it is desired to adjust the upper friction coefficient μ to be larger than 1, for example, the roll surface of the upper work roll 11 may be ground to adjust the upper friction coefficient μ T On the other hand, the upper friction coefficient μ T is the lower friction coefficient μ B If it is desired to adjust the lower friction coefficient μ to be larger than 1 / 2, for example, the roll surface of the bottom work roll 12 may be ground to adjust the lower friction coefficient μ B can be made smaller.

[0082] Similarly, by improving the surface quality of the rolled sheet S by increasing the pressure and flow rate of the descaling water in the descaling device (not shown) installed upstream of the rolling mill 10, it is possible to reduce the coefficient of friction between the work rolls 11, 12 and the rolled sheet S. By applying this principle, the coefficient of friction μ T , μ B Just change the following.

[0083] In step S130, the control device 100 generates, from the amount of meandering caused by the difference in the coefficient of friction between the top and bottom, control information such as the position at which to change the amount and concentration of lubricant supplied, the amount and concentration of lubricant supplied after the change, the amount of grinding on the surfaces of the work rolls 11 and 12, or the descaling conditions for the rolled sheet S. The control device 100 then outputs the control information to the lubricant supply devices 31 and 32, the roll grinding device, or the descaling device, and drives these devices to adjust the difference in the coefficient of friction between the top and bottom.

[0084] In this case, it is preferable to obtain in advance the relationship between the amount of lubricant supplied, the concentration, the surface roughness of the work rolls 11 and 12, or the descaling conditions, and the amount of meandering of the rolled sheet S. However, even if these relationships are unknown, the amount of lubricant supplied, the concentration, the amount of surface grinding of the work rolls 11 and 12, or the descaling conditions may be adjusted by referring to the amount of meandering caused by the difference in the coefficient of friction between the top and bottom.

[0085] (friction coefficient difference control) The control device 100 also controls the amount of meandering caused by the difference in the left and right friction coefficients by controlling the difference in the left and right friction coefficients (S140). The control device 100 adjusts the difference in the left and right friction coefficients so that the amount of meandering caused by the difference in the left and right friction coefficients approaches zero. The difference in the left and right friction coefficients can be adjusted, for example, by changing the amount or concentration of lubricant supplied by the lubricant supply devices 31, 32 between the work side and the drive side, or by changing at least one of the surface roughness of the work rolls 11, 12 or the surface texture of the rolled sheet S between the work side and the drive side.

[0086] Increasing the amount of lubricant supplied by the lubricant supply devices 31, 32 reduces the coefficient of friction between the work rolls 11, 12 and the rolled sheet S. In addition, increasing the concentration of the lubricant supplied by the lubricant supply devices 31, 32 reduces the coefficient of friction between the work rolls 11, 12 and the rolled sheet S. Therefore, in step S140, the difference Δμ between the left and right friction coefficients is calculated. DW (=μ DS -μ WS ), it is possible to increase the lubricant supply rate or concentration supplied to the work side (WS) of the work rolls 11, 12, for example. Alternatively, it is possible to decrease the lubricant supply rate or concentration supplied to the drive side (DS) of the work rolls 11, 12, for example.

[0087] In the present invention, the lubricant supply amount or concentration is not limited to being changed only on the work side or the drive side of the roll barrel length, but may be changed at multiple positions along the roll barrel length. DW (=μ DS -μWS ), the amount of lubricant supplied to the work side (WS) of the work rolls 11 and 12 can be increased or the concentration can be increased to increase the work side friction coefficient μ WS The driving side friction coefficient μ is reduced by reducing the amount of lubricant supplied to the driving side (DS) of the work rolls 11 and 12 or by lowering the concentration. DS may be increased.

[0088] The coefficient of friction between the work rolls 11, 12 and the sheet S to be rolled can also be adjusted by changing the surface roughness of the work rolls 11, 12 or the surface properties of the sheet S to be rolled. For example, by grinding the surfaces of the work rolls 11, 12 using a roll grinding device (not shown) installed in the rolling mill 10, the surface roughness of the work rolls 11, 12 can be reduced, thereby reducing the coefficient of friction between the work rolls 11, 12 and the sheet S to be rolled. Therefore, in step S40, the difference Δμ between the left and right friction coefficients is calculated. DW (=μ DS -μ WS ), for example, the roll surfaces of the work side (WS) of the work rolls 11 and 12 are ground to increase the work side friction coefficient μ WS On the other hand, in step S40, the difference Δμ DW (=μ DS -μ WS ) is desired to be smaller, for example, the roll surfaces of the driving side (DS) of the work rolls 11 and 12 are ground to reduce the driving side friction coefficient μ DS can be made smaller.

[0089] Similarly, by improving the surface quality of the rolled sheet S by increasing the pressure and flow rate of the descaling water in the descaling device (not shown) installed upstream of the rolling mill 10, it is possible to reduce the coefficient of friction between the work rolls 11, 12 and the rolled sheet S. By applying this principle, the difference Δμ DW (=μ DS -μ WS ) can be changed.

[0090] In step S140, the control device 100 generates, from the amount of meandering caused by the difference in the coefficient of friction between the left and right sides, control information such as the amount of lubricant supplied, the position at which the concentration is changed and the amount of lubricant supplied and the concentration after the change, the position and amount of grinding for the surfaces of the work rolls 11, 12, or the descaling conditions for the rolled sheet S. The control device 100 then outputs the control information to the lubricant supply devices 31, 32, the roll grinding device, or the descaling device, and drives these devices to adjust the difference in the coefficient of friction between the left and right sides.

[0091] In this case, it is preferable to obtain in advance the relationship between the amount of lubricant supplied, the concentration, the surface roughness of the work rolls 11 and 12, or the descaling conditions, and the amount of meandering of the rolled sheet S. However, even if these relationships are unknown, the amount of lubricant supplied, the concentration, the amount of surface grinding of the work rolls 11 and 12, or the descaling conditions may be adjusted by referring to the amount of meandering caused by the difference in the coefficient of friction between the left and right sides.

[0092] The above has described a method for controlling meandering of the rolled sheet S when controlling meandering or camber caused by three factors: a change in wedge ratio, a difference in the friction coefficient between the top and bottom, and a difference in the friction coefficient between the left and right.

[0093] In the above explanation, a case has been described in which leveling control, top-bottom friction coefficient difference control, and left-right friction coefficient difference control are performed to suppress meandering or camber caused by three factors, respectively, but the present invention is not limited to such an example. When meandering caused in the rolled sheet S is separated into meandering caused by three factors, it is preferable to perform all three controls and control the meandering caused by each factor separately in order to control the meandering with high precision. However, it is not necessary to perform all three controls; it is sufficient to perform at least one of leveling control, top-bottom friction coefficient difference control, and left-right friction coefficient difference control.

[0094] For example, if one of the meanderings caused by a change in the wedge ratio, the meanderings caused by a difference in the left-right friction coefficient, and the meanderings caused by a difference in the top-bottom friction coefficient is clearly larger than the others, only the control to control the clearly larger meandering may be performed. Also, if two meanderings are clearly larger than the remaining one, only the two controls to control the clearly larger meanderings may be performed. Note that "clearly larger meandering" may be, for example, a case where an amount of meandering that is unacceptable in actual operation is occurring.

[0095] [2-2-1-2. Control of meandering or camber caused by two factors] Next, a method for controlling the meandering of the rolled sheet S when controlling the meandering or camber caused by two factors, namely, a change in wedge ratio and a difference in the coefficient of friction between the top and bottom, will be described with reference to Fig. 9. Fig. 9 is a flowchart showing a method for controlling the meandering of the rolled sheet S when controlling the meandering or camber caused by two factors, namely, a change in wedge ratio and a difference in the coefficient of friction between the top and bottom. In the following explanation, detailed explanation of the same processes as in Fig. 8 will be omitted.

[0096] The method for controlling the meandering of the rolled sheet S shown in Figure 9 is applicable when meandering caused by the difference in the left and right friction coefficient is within an acceptable range. In other words, the method for controlling the meandering of the rolled sheet S shown in Figure 9 is applicable when the difference in the left and right friction coefficient is small and the effect of this on meandering can be ignored, for example, because sufficient measures have been taken to suppress the left and right deviations in the amount and concentration of lubricant supplied. In this case, the factors that cause meandering or camber in the rolled sheet are considered to be changes in the wedge ratio and the difference in the top and bottom friction coefficients.

[0097] (S200: Measurement of the rolling state of the rolled plate) First, the rolling condition of the sheet S to be rolled is measured (S200). The rolling condition of the sheet S to be rolled can be expressed, for example, by the amount of camber or meandering at the delivery side of the rolling mill, the change in wedge ratio, the difference in rolling load between the left and right sides, the amount of meandering at the entry side, the difference in load acting on the entry side edger device between the left and right sides, or the difference in load acting on the side guides between the left and right sides. Measurement of the rolling condition of the sheet S to be rolled can be performed in the same manner as in step S100 of FIG. 8. Note that the amount of camber of the sheet S to be rolled at the delivery side of the rolling mill can be determined, for example, by capturing images of the sheet S to be rolled with a CCD camera at the delivery side of a cross rolling mill, and then processing the images to detect the edge positions of the sheet S to be rolled, thereby calculating the amount of meandering at multiple positions. The measured rolling condition of the sheet S to be rolled is output to the control device 100.

[0098] (S210: Separation of meandering amount according to the cause) Next, the control device 100 separates the meandering of the rolled sheet S into meandering caused by a change in the wedge ratio and meandering caused by a difference in the coefficient of friction between the top and bottom of the rolled sheet S based on the rolling state of the rolled sheet S measured in step S200 (S210). In step S210, among factors representing the rolling state of the rolled sheet S, the control device 100 uses the amount of delivery camber, i.e., the amount of meandering at multiple points on the delivery side of the rolling mill, or at least two or more factors from among the following: a change in wedge ratio in the rolling pass, a difference in rolling load between the left and right sides, the amount of entry-side meandering, the amount of exit-side meandering, and a difference in load acting on the entry-side edger device between the left and right sides or a difference in load acting on the side guides between the left and right sides to separate the meandering of the rolled sheet S into meandering caused by a change in the wedge ratio and meandering caused by a difference in the coefficient of friction between the top and bottom of the rolled sheet S. Specifically, the processing of step S210 may be performed, for example, by the following separation methods (E) to (N).

[0099] (E) Separation based on exit camber For example, by using the actual measured value of the camber amount on the delivery side as the rolling state of the rolled sheet S, it is possible to separate the meandering occurring in the rolled sheet S into the amount of meandering caused by a change in the wedge ratio and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom. Separation method (E) can be applied regardless of whether the rolled sheet S is restrained on the entry side of the cross rolling mill.

[0100] The delivery camber amount is acquired in step S200. When the rolled sheet S meanders on the delivery side of the cross rolling mill 10 due to a change in the wedge ratio, the trajectory is approximately parabolic, as shown in FIG. 4. On the other hand, when the rolled sheet S meanders due to a difference in the coefficient of friction between the top and bottom, the trajectory is linear, as shown in FIG. 5. Therefore, if the delivery camber amount is separated into a second-order component representing a substantially parabolic meandering and a first-order component representing a linear meandering, it is possible to extract the amount of meandering due to a change in the wedge ratio (second-order component) and the amount of meandering due to a difference in the coefficient of friction between the top and bottom (first-order component) from the delivery camber amount measured in step S200.

[0101] (F) Separation based on wedge ratio change and exit meander amount Furthermore, by using the change in wedge ratio and the actual measured value of the amount of meandering on the delivery side as the rolling state of the rolled sheet S, the amount of meandering can be separated into the amount of meandering caused by the change in wedge ratio and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom. Separation method (F) can be applied regardless of whether the rolled sheet S is restrained on the entry side of the rolling mill.

[0102] The wedge ratio change may be calculated based on measured values ​​of the wedge at the entry and exit sides of the rolling pass. Alternatively, the wedge ratio change may be calculated using an estimated value of the wedge at the exit side of the rolling pass based on the difference in rolling load between the left and right sides and the difference in mill rigidity between the left and right sides in the rolling pass. The wedge at the entry side of the rolling pass can also be estimated based on the difference in rolling load between the left and right sides and the difference in mill rigidity between the left and right sides in the rolling pass immediately before the rolling pass.

[0103] Once a measured or estimated value of the wedge ratio change in the rolling pass is obtained, it is possible to estimate the amount of exit meandering due to a wedge ratio change based on a method for estimating a camber curvature change due to a wedge ratio change. A known method can be used to estimate a camber curvature change due to a wedge ratio change, and for example, the method described in Non-Patent Document 1 (relationship between wedge ratio change ΔΨ and camber curvature change Δκ) may be used. In this way, the exit camber curvature due to a wedge ratio change can be estimated. If the exit camber curvature due to a wedge ratio change can be estimated, the amount of meandering can be estimated at a meander meter position installed a predetermined distance downstream from the rolling mill, based on the fact that the trajectory of the rolled sheet downstream of the rolling mill is approximately parabolic.

[0104] The difference between the estimated value of the amount of outlet meandering estimated from the change in wedge ratio and the actual measured value of the amount of outlet meandering is extracted as the amount of meandering caused by the difference in the coefficient of friction between the top and bottom. For example, assume that the estimated value of the amount of outlet meandering estimated from the change in wedge ratio is 80 mm, and the actual measured value of the amount of outlet meandering is 150 mm. In this case, of the actual measured value of the amount of outlet meandering of 150 mm, the amount of meandering caused by the change in wedge ratio is estimated to be 80 mm, and the difference between the two (70 mm) can be estimated to be caused by the difference in the coefficient of friction between the top and bottom. In this way, based on the measured or estimated value of the change in wedge ratio in the rolling pass and the amount of meandering on the outlet side of the rolling pass, it is possible to separate the meandering occurring in the rolled sheet S into meandering caused by the change in wedge ratio and meandering caused by the difference in the coefficient of friction between the top and bottom.

[0105] Although it has been described here that the amount of meandering of the rolled sheet can be measured using a meander meter, it goes without saying that this technology can also be applied to cases where the camber curvature can be measured using a camber meter.

[0106] (G) Separation based on wedge ratio change and inlet meander amount Furthermore, for example, by using the change in wedge ratio and the actual measured value of the entry-side meandering amount as the rolling state of the rolled sheet S, the meandering amount can be separated into the amount of meandering caused by the change in wedge ratio and the amount of meandering caused by the difference in the upper and lower friction coefficients. Separation method (G) can be applied when the rolled sheet S is not restrained on the entry side of the rolling mill.

[0107] Separation method (G) is a case where the entry-side meandering amount is used instead of the delivery-side meandering amount used in separation method (F), and can be carried out in the same manner as separation method (F). That is, the difference between the estimated entry-side meandering amount, which is estimated from the measured or estimated value of the wedge ratio change in the rolling pass, and the entry-side meandering amount, which is the actual measured value, is extracted as the meandering amount caused by the difference in friction coefficient between the top and bottom. In this way, the meandering occurring in the rolled sheet S can be separated into meandering caused by the change in wedge ratio and meandering caused by the difference in friction coefficient between the top and bottom.

[0108] (H) Separation based on wedge ratio change and load on side guide Furthermore, for example, by using the change in wedge ratio and the load on the side guide 60 as the rolling state of the rolled sheet S, the amount of meandering can be separated into the amount of meandering caused by the change in wedge ratio and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom. Separation method (H) can be applied when the rolled sheet S is restrained by the side guide 60 installed on the inlet side of the rolling mill.

[0109] As shown in Fig. 4, a side guide 60 is installed on the entry side of the rolling mill 10. If the sheet S to be rolled meanders during rolling, the sheet S comes into contact with the guide 61 (or guide 62), and the guide 61 (or guide 62) receives a load from the sheet S to be rolled.

[0110] Then, the difference between the estimated value of the difference in the load between the left and right sides of the side guides 60 received from the rolled sheet S, estimated from the measured or estimated value of the wedge ratio change in that rolling pass, and the actual measured value, is extracted as the effect of meandering caused by the difference in the friction coefficient between the top and bottom. In this way, the meandering occurring in the rolled sheet S can be separated into meandering caused by the change in the wedge ratio and meandering caused by the difference in the friction coefficient between the top and bottom.

[0111] (I) Separation based on the amount of meandering on the exit side and the amount of meandering on the entry side Furthermore, for example, by using the amount of meandering on the delivery side and the amount of meandering on the entry side as the rolling state of the rolled sheet S, the amount of meandering can be separated into the amount of meandering caused by a change in the wedge ratio and the amount of meandering caused by the difference in the friction coefficient between the top and bottom. Separation method (I) can be applied when the rolled sheet S is not constrained on the entry side of the rolling mill. Separation method (I) does not require measurement or estimation of the wedge on the entry side and the delivery side of the rolling mill, but it is preferable to acquire in advance information on wedge ratio change versus meandering amount as shown in Figure 4 and information on left-right difference in friction coefficient versus meandering amount as shown in Figure 5.

[0112] The actual measured values ​​of the meandering amounts at the entry and exit of the rolling pass measured in step S200 may be used for the exit-side meandering amount and the entry-side meandering amount. Then, for example, a combination is searched for in which the sum of the exit-side meandering amount based on the wedge ratio change-meandering amount information and the exit-side meandering amount based on the friction coefficient left-right difference-meandering amount information matches the actual measured value of the exit-side meandering amount, or a combination in which the error between the two is minimized. There are multiple such combinations, but for each combination, there is only one combination in which the sum of the entry-side meandering amount based on the wedge ratio change-meandering amount information and the entry-side meandering amount based on the friction coefficient left-right difference-meandering amount information matches the actual measured value of the entry-side meandering amount, or a combination in which the error between the two is minimized. The wedge ratio change and the difference between the top and bottom of the friction coefficient in the rolling pass can be estimated from a combination in which both the entry-side meandering amount and the exit-side meandering amount found in this way match the actual measured values, or a combination in which the sum of the squares of the errors between the two is minimized. Then, based on the estimated wedge ratio change and the difference between the upper and lower friction coefficients, the meandering occurring in the rolled sheet S can be separated into meandering caused by the change in wedge ratio and meandering caused by the difference between the upper and lower friction coefficients.

[0113] (J) Separation based on the amount of meandering on the exit side and the load on the edger device or side guide Furthermore, for example, by using the amount of meandering on the delivery side and the difference between the left and right loads (weight or torque) acting on the edger device 50 or the difference between the left and right loads acting on the side guides 60 as the rolling state of the rolled sheet S, the amount of meandering can be separated into the amount of meandering caused by a change in the wedge ratio and the amount of meandering caused by the difference between the top and bottom friction coefficients. Separation method (J) can be applied when the rolled sheet S is restrained by the edger device 50 or side guides 60 installed on the entry side of the rolling mill. Separation method (J) does not require measurement or estimation of the wedge on the entry and exit sides of the rolling mill.

[0114] In separation method (J), for example, the amount of meandering at the exit side of the rolling pass measured in step S200 is assumed to have zero difference in the friction coefficient between the top and bottom, and the difference between the left and right loads (weight or torque) acting on the edger device 50 or the difference between the left and right loads acting on the side guides 60 when caused only by a change in the wedge ratio is calculated.

[0115] When the difference in the coefficient of friction between the top and bottom is assumed to be zero, the actual measurement and estimated values ​​of the amount of meandering on the delivery side match, but the estimated value of the difference in the load (load or torque) acting on the edger device 50 between the left and right sides or the difference in the load acting on the side guides 60 between the left and right sides does not necessarily match the actual measurement. Therefore, this estimated value is compared with the actual measurement value of the difference in the load (load or torque) acting on the edger device 50 between the left and right sides or the difference in the load acting on the side guides 60 between the left and right sides. Then, the difference in the coefficient of friction between the top and bottom is corrected so that the estimated value of the difference in the load (load or torque) acting on the edger device 50 between the left and right sides or the difference in the load acting on the side guides 60 between the left and right sides matches the actual measurement value, or so that the error between the two is minimized.

[0116] The amount of exit meandering is then estimated in the presence of the corrected difference between the upper and lower friction coefficients and the current wedge ratio change. The difference between the calculated (estimated) value of the difference between the left and right loads (weight or torque) acting on the edger device 50 or the left and right loads acting on the side guides 60 and the actual measured value is considered to be the effect of the difference between the upper and lower friction coefficients. In other words, the amount of deviation from the actual measured value of the amount of exit meandering occurs by the amount of correction of the difference between the upper and lower friction coefficients. For this reason, the assumed wedge ratio change and the difference between the upper and lower friction coefficients are corrected so that the actual measured value and estimated value of the amount of exit meandering match or the error between them is minimized in the presence of the corrected difference between the upper and lower friction coefficients.

[0117] The values ​​of the wedge ratio change and the difference between the upper and lower friction coefficients are corrected and repeatedly calculated until the estimated values ​​and the actually measured values ​​for the amount of delivery side meandering and the left-right difference in the load (load or torque) acting on the edger device 50 or the left-right difference in the load acting on the side guide 60 match, or the error between the two falls below a predetermined threshold. Then, the values ​​of the wedge ratio change and the difference between the upper and lower friction coefficients when the estimated values ​​and the actually measured values ​​for the amount of delivery side meandering and the left-right difference in the load (load or torque) acting on the edger device 50 or the left-right difference in the load acting on the side guide 60 match, or the error between the two falls below the threshold, are taken as the estimated values ​​of the wedge ratio change and the difference between the upper and lower friction coefficients for that rolling pass.

[0118] In this way, it is possible to estimate the wedge ratio change and the difference between the upper and lower friction coefficients in the rolling pass. Then, from the estimated wedge ratio change and the difference between the upper and lower friction coefficients, it is possible to separate the meandering occurring in the rolled sheet S into meandering caused by the wedge ratio change and meandering caused by the difference between the upper and lower friction coefficients.

[0119] (K) Separation based on wedge ratio change and left / right rolling load difference Furthermore, for example, by using the measured values ​​of the wedge ratio change and the difference in rolling load between the left and right sides as the rolling state of the rolled sheet S, the amount of meandering can be separated into the amount of meandering caused by the change in wedge ratio and the amount of meandering caused by the difference in the upper and lower friction coefficients. The difference in rolling load between the left and right sides is the difference between the rolling load on the working side and the rolling load on the driving side of the rolling mill. When there is a change in the wedge ratio or a difference in the upper and lower friction coefficients, a difference in rolling load between the left and right sides occurs. Therefore, in separation method (K), for example, the difference in rolling load between the left and right sides due to the change in wedge ratio is calculated, assuming that there is no difference in the upper and lower friction coefficients. Then, the calculated difference in rolling load between the left and right sides is compared with the measured value, and the difference between the two is considered to be due to the difference in the upper and lower friction coefficients, and the assumed value of the difference in the upper and lower friction coefficients is corrected.

[0120] In this way, the difference in the friction coefficient between the upper and lower sides can be estimated by repeatedly performing the calculation until the estimated value of the difference in rolling load between the left and right sides and the actually measured value match, or until the error between the two falls below a predetermined threshold. Then, from the estimated wedge ratio change and the difference in the friction coefficient between the upper and lower sides, the meandering occurring in the rolled sheet S can be separated into meandering caused by the change in the wedge ratio and meandering caused by the difference in the friction coefficient between the upper and lower sides.

[0121] (L) Separation based on the amount of meandering on the delivery side and the difference in rolling load between the left and right Furthermore, for example, the amount of meandering on the delivery side and the difference in rolling load between the left and right sides can be used as the rolling state of the rolled sheet S to separate the amount of meandering into the amount of meandering due to a change in the wedge ratio and the amount of meandering due to a difference in the friction coefficient between the top and bottom. Separation method (L) is a case in which the amount of meandering on the delivery side is used instead of the change in the wedge ratio used in separation method (K), and can be performed in the same manner as separation method (K). That is, the difference in the friction coefficient between the top and bottom and the change in the wedge ratio are assumed, and estimated values ​​of the amount of meandering on the delivery side and the difference in the rolling load between the left and right sides for the assumed difference in the friction coefficient between the top and bottom and the change in the wedge ratio are obtained. The difference in the friction coefficient between the top and bottom and the change in the wedge ratio can be estimated by performing a convergence calculation on the assumed difference in the friction coefficient between the top and bottom and the change in the wedge ratio until the estimated values ​​match the actually measured values ​​or the error between the two falls below a predetermined threshold. Then, based on the estimated change in the wedge ratio and the difference in the friction coefficient between the top and bottom, the meandering occurring in the rolled sheet S can be separated into the amount of meandering due to the difference in the friction coefficient between the top and bottom and the amount of meandering due to a change in the wedge ratio.

[0122] (M) Separation based on the amount of meandering on the entry side and the difference in rolling load between the left and right Furthermore, for example, the amount of meandering can be separated into the amount of meandering caused by a change in the wedge ratio and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom, using the amount of meandering on the entry side and the difference in rolling load between the left and right sides as the rolling state of the rolled sheet S. Separation method (M) is a case where the amount of meandering on the entry side is used instead of the change in the wedge ratio used in separation method (K), and may be carried out in the same manner as separation method (K).

[0123] That is, the difference between the top and bottom friction coefficients and the change in the wedge ratio are assumed, and estimated values ​​of the inlet meandering amount and the left-right difference in rolling load for the assumed difference between the top and bottom friction coefficients and the change in the wedge ratio are obtained. The difference between the top and bottom friction coefficients and the change in the wedge ratio can be estimated by performing a convergence calculation on the assumed difference between the top and bottom friction coefficients and the change in the wedge ratio until the estimated values ​​match the actually measured values ​​or the error between the two falls below a predetermined threshold. Then, from the estimated change in the wedge ratio and the difference between the top and bottom friction coefficients, the meandering occurring in the rolled sheet S can be separated into meandering caused by the difference between the top and bottom friction coefficients and meandering caused by the change in the wedge ratio.

[0124] (N) Separation based on the load on the edger device or side guide and the difference in rolling load between the left and right sides Furthermore, for example, the amount of meandering can be separated into the amount of meandering caused by a change in the wedge ratio and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom, using the load on the edger device or side guide and the difference in rolling load between the left and right sides as the rolling state of the rolled sheet S. Separation method (N) is a case in which the load on the edger device or side guide is used instead of the change in wedge ratio used in separation method (K), and can be carried out in the same way as separation method (K).

[0125] That is, the difference in the coefficient of friction between the top and bottom and the change in the wedge ratio are assumed, and an estimate is obtained of the difference in the horizontal load or torque between the left and right sides of the edger rolls 51, 52 of the edger device 50, or the load that the side guide 60 receives from the rolled sheet S, for the assumed difference in the coefficient of friction between the top and bottom and the change in the wedge ratio. The difference in the coefficient of friction between the top and bottom and the change in the wedge ratio can be estimated by performing a convergence calculation on the assumed difference in the coefficient of friction between the top and bottom and the change in the wedge ratio until the estimated value matches the actually measured value or the error between the two falls below a predetermined threshold. Then, from the estimated change in the wedge ratio and difference in the coefficient of friction between the top and bottom, the meandering occurring in the rolled sheet S can be separated into meandering caused by the difference in the coefficient of friction between the top and bottom and meandering caused by the change in the wedge ratio.

[0126] By using these separation methods (E) to (N), it is possible to separate the meandering occurring in the rolled sheet S into the amount of meandering caused by a change in the wedge ratio and the amount of meandering caused by a difference in the coefficient of friction between the top and bottom. Note that in the above explanation, a case has been described in which the meandering occurring due to a difference in the coefficient of friction between the top and bottom and the amount of meandering caused by a change in the wedge ratio is separated using two factors as the rolling state of the rolled sheet S, namely, the amount of delivery camber or the change in the wedge ratio, the difference in rolling load between the left and right, the amount of entry meandering, the amount of delivery meandering, and the difference in load acting on the entry edger device between the left and right or the difference in load acting on the side guides between the left and right, but the present invention is not limited to such an example, and the meandering may be separated using three or more factors.

[0127] Furthermore, the method of estimating the difference between the upper and lower friction coefficients or meandering caused by the difference between the upper and lower friction coefficients, and the wedge ratio change or meandering caused by the difference between the upper and lower friction coefficients using these factors is not limited to the examples described in the above separation methods (E) to (N). In other words, the above explanation exemplified a method of separating meandering caused by wedge ratio change and meandering caused by the difference between the upper and lower friction coefficients using convergence calculation, but the method of convergence calculation is not limited to the above example. Furthermore, for example, by determining the amount of meandering for various combinations of wedge ratio change and difference between the upper and lower friction coefficients in advance, it is also possible to separate meandering caused by wedge ratio change and meandering caused by the difference between the upper and lower friction coefficients without using convergence calculation.

[0128] Furthermore, in the separation methods (K) to (N) that use the difference in rolling load between the left and right sides as the rolling state of the rolled sheet S, the difference in rolling temperature between the left and right sides may be included as a factor. For example, in hot rolling, if a difference in rolling temperature between the left and right sides occurs, that is, if a temperature difference occurs between the work side and the drive side of the rolled sheet S, the hardness of the material (i.e., deformation resistance) differs between the work side and the drive side of the rolled sheet S, resulting in a difference in rolling load between the left and right sides. Therefore, the difference in rolling temperature between the left and right sides is taken into consideration as the rolling state of the rolled sheet S, and the difference in rolling load between the left and right sides caused by the difference in rolling temperature between the left and right sides is removed from the actual measured or estimated value of the difference in rolling load between the left and right sides. This makes it possible to accurately separate meandering caused by a change in wedge ratio from meandering caused by a difference in the friction coefficient between the top and bottom.

[0129] (S220, S230: Snake control) Returning to the explanation of Figure 9, in step S210, based on the rolling state of the rolled sheet S measured in step S200, the meandering that has occurred in the rolled sheet S is separated into the amount of meandering caused by the change in wedge ratio and the amount of meandering caused by the difference in the upper and lower friction coefficients, and the rolling device 1 is controlled to control each of the separated amounts of meandering.

[0130] (Leveling control) The control device 100 controls the amount of meandering caused by the change in wedge ratio by leveling control (S220). The processing of step S220 may be performed in the same manner as step S120. The control device 100 controls the screw down device 40 and adjusts the difference in the amount of reduction of the rolled sheet S between the left and right sides so that the amount of meandering caused by the change in wedge ratio approaches zero.

[0131] (friction coefficient difference control) The control device 100 also controls the amount of meandering caused by the difference in the coefficient of friction between the top and bottom by controlling the difference in the coefficient of friction between the top and bottom (S230). The processing of step S230 may be performed in the same manner as step S130. The control device 100 changes the amount or concentration of lubricant supplied, or changes the surface roughness of the work rolls 11, 12 or the surface properties of the rolled sheet S, so that the amount of meandering caused by the difference in the coefficient of friction between the top and bottom approaches zero.

[0132] The above has described a method for controlling meandering of the rolled sheet S when controlling meandering or camber caused by two factors, namely, a change in wedge ratio and a difference in the coefficient of friction between the upper and lower sides. In the above explanation, leveling control and upper and lower friction coefficient difference control are performed to suppress meandering or camber caused by two factors, namely, a change in wedge ratio and a difference in the coefficient of friction between the upper and lower sides, respectively. However, the present invention is not limited to this example. For example, if one of the meandering caused by a change in wedge ratio and the meandering caused by a difference in the coefficient of friction between the upper and lower sides is clearly larger than the other, only the control to control the clearly larger meandering may be performed.

[0133] As an example of the method for controlling meandering of a rolled sheet according to one embodiment of the present invention, a case where meandering is suppressed by different meandering controls depending on the cause of meandering (control example 1) has been described above.

[0134] [2-2-2. Suppressing meandering of the rolled sheet S only by leveling control (control example 2)] Next, with reference to Fig. 10, a case where meandering of the rolled sheet S is suppressed only by leveling control (control example 2) will be described in detail as an example of the method for controlling meandering of the rolled sheet S according to this embodiment. Fig. 10 is a flowchart showing a case where meandering of the rolled sheet S is suppressed only by leveling control as an example of the method for controlling meandering of the rolled sheet S according to this embodiment. In the description of Fig. 10, detailed description of the same processes as those in Fig. 8 or 9 will be omitted.

[0135] Leveling control is relatively easy to implement because the screw down devices 40 are independent on the left and right sides of the work side and drive side of the rolling mill 10, whereas left-right friction coefficient difference control and top-bottom friction coefficient difference control are relatively difficult to implement because, for example, a mechanism must be provided that can set and control the concentration and injection amount of lubricant to different values ​​on the left and right or top and bottom. Therefore, in Control Example 2, left-right friction coefficient difference control and top-bottom friction coefficient difference control are not performed, and only leveling control is used to bring the meandering amount of the rolled sheet S to be controlled (i.e., the sum of the meandering amount due to a change in the wedge ratio, the meandering amount due to the difference in the left-right friction coefficient, and the meandering amount due to the difference in the top-bottom friction coefficient) close to zero.

[0136] Here, leveling control has the advantage that it is relatively easy to implement, as described above. However, while meandering caused by changes in the wedge ratio is in the same direction at the entry side of the rolling mill (the tail end of the rolled sheet S) and the exit side of the rolling mill (the front end of the rolled sheet S), meandering caused by a difference in the left-right friction coefficient and the amount of meandering caused by a difference in the top-bottom friction coefficient are in the opposite direction. For this reason, if an attempt is made to suppress meandering at the exit side of the rolling mill (the front end of the rolled sheet S) caused by a difference in the left-right friction coefficient or a difference in the top-bottom friction coefficient using leveling control while maintaining the same rolling conditions, very large meandering will occur at the entry side of the rolling mill (the tail end of the rolled sheet S). In order to appropriately suppress meandering of the rolled sheet S, it is important to identify the amount of meandering caused by each factor before implementing leveling control.

[0137] (S300: Meandering amount measurement) As shown in Fig. 10, first, the amount of meandering of the sheet S to be rolled is measured (S300). Measurement of the amount of meandering of the sheet S to be rolled may be performed in the same manner as step S100 in Fig. 8. That is, for example, an image of the sheet S to be rolled may be taken with a CCD camera, and the edge position of the sheet S to be rolled may be detected by image processing, and the amount of meandering may be calculated. Measurement of the amount of meandering may be performed at least on either the entry side or exit side of the rolling mill 10, and the measurement position may be determined depending on a method of separating the amount of meandering depending on the cause of occurrence, which will be described later. The measured amount of meandering of the sheet S to be rolled is output to the control device 100.

[0138] (S310: Separation of meandering amount according to the cause) Next, the control device 100 separates the meandering amount measured in step S300 from the rolling state of the rolled sheet S into a meandering amount caused by a change in the wedge ratio, a meandering amount caused by a difference in the left-right friction coefficient, and a meandering amount caused by a difference in the top-bottom friction coefficient (S310). The separation of the meandering amount according to the cause may be performed in the same manner as step S110 in FIG. 8.

[0139] That is, based on at least one or more factors from the rolling state of the rolled sheet S, which is represented by values ​​of factors related to the occurrence of meandering (for example, change in wedge ratio, difference in rolling load between left and right, amount of entry-side meandering, difference in load acting on the entry-side edger device between left and right, or difference in load acting on the side guide between left and right), meandering occurring in the rolled sheet S is separated into meandering caused by change in wedge ratio, meandering caused by difference in friction coefficient between left and right, and meandering caused by difference in friction coefficient between top and bottom. Specifically, the processing of step S310 may be performed by the above-mentioned separation methods (A) to (D).

[0140] (S320: Snake control) Then, in step S310, the meandering amount of the rolled sheet S is separated into the meandering amount due to a change in the wedge ratio, the meandering amount due to the difference in the left-right friction coefficient, and the meandering amount due to the difference in the top-bottom friction coefficient, and the rolling device 1 is controlled based on the separated meandering amounts to suppress the meandering amount of the rolled sheet S by leveling control (S320). There are, for example, the following two methods as a method for bringing the meandering amount of the rolled sheet S (i.e., the sum of the meandering amount due to a change in the wedge ratio, the meandering amount due to the difference in the left-right friction coefficient, and the meandering amount due to the difference in the top-bottom friction coefficient) close to zero by leveling control alone.

[0141] (1) A method of changing the amount of leveling control at the leading and trailing ends of the rolled sheet S. For example, the leveling control amount at the front end of the rolled sheet S and the leveling control amount at the tail end of the rolled sheet S may be changed depending on the amount of meandering due to each factor, so that the amount of meandering of the rolled sheet S (i.e., the sum of the amount of meandering due to a change in the wedge ratio, the amount of meandering due to the difference in the coefficient of friction between the left and right sides, and the amount of meandering due to the difference in the coefficient of friction between the top and bottom) approaches zero. Specifically, when the front end of the rolled sheet S is bitten (hereinafter also referred to as "when the front end is threaded"), leveling control is performed so that the amount of meandering at the delivery side of the rolling mill approaches zero, and when the tail end of the rolled sheet S passes through the rolling mill (hereinafter also referred to as "when the tail end is threaded"), leveling control is performed so that the meandering at the entry side of the rolling mill approaches zero.

[0142] When the leading edge of the rolled sheet S is threaded, meandering on the delivery side (i.e., the downstream side of the rolling mill) becomes an issue in threading, while when the tail end of the rolled sheet S is threaded, meandering on the entry side (i.e., the upstream side of the rolling mill) becomes an issue in threading. This is because, for example, when the leading edge of the rolled sheet S is threaded, the length of the rolled sheet S downstream of the rolling mill is still short and the constraint due to its own weight is small, so it can meander easily, whereas when the leading edge of the rolled sheet S is threaded, the length of the rolled sheet S upstream of the rolling mill is long and it cannot meander easily due to constraints such as its own weight. For this reason, it is preferable to perform leveling control so as to suppress meandering on the delivery side (i.e., the downstream side of the rolling mill) when the leading edge is threaded, and to suppress meandering on the entry side (i.e., the upstream side of the rolling mill) when the tail end is threaded.

[0143] As a specific example, suppose the entry-side meandering amount is 10 mm, broken down as follows: 60 mm entry-side meandering amount due to a change in the wedge ratio, -30 mm entry-side meandering amount due to the difference in the left-right friction coefficient, and -20 mm entry-side meandering amount due to the difference in the top-bottom friction coefficient. Also, suppose the exit-side meandering amount is 170 mm, broken down as follows: 80 mm exit-side meandering amount due to a change in the wedge ratio, 70 mm exit-side meandering amount due to the difference in the left-right friction coefficient, and 20 mm exit-side meandering amount due to the difference in the top-bottom friction coefficient.

[0144] In this case, even if leveling control is performed to suppress only the meandering caused by the change in wedge ratio, meandering caused by the difference in the friction coefficient between the left and right sides (-50 mm on the entry side, 90 mm on the delivery side) will remain. Therefore, a leveling control amount can be applied during threading of the leading edge of the rolled sheet S to suppress the amount of meandering on the delivery side by 170 mm, and during threading of the tail edge of the rolled sheet S to suppress the amount of meandering on the entry side by 10 mm. Note that in the middle portion of the rolled sheet S (between the leading edge and the tail edge), a leveling control amount can be applied to bring the change in the wedge ratio close to zero, for example.

[0145] (2) A method of controlling the leveling amount to a constant value over the entire length of the rolled sheet S. In the above-mentioned method of changing the leveling control amount between the front and rear ends of the rolled sheet S, the wedge of the rolled sheet S to be controlled does not remain constant over the entire length. For this reason, if the leveling control amount is changed when the front end, middle section, and tail end of the rolled sheet S are threaded, meandering may occur unless the leveling control amount is appropriately applied to subsequent passes or subsequent rolling mills when the front end, middle section, and tail end of the rolled sheet S are threaded. For this reason, there is a possibility that control that keeps the leveling control amount constant over the entire length is preferred.

[0146] Therefore, the meandering amount of the rolled sheet S may be separated into the amount of meandering caused by a change in the wedge ratio, the amount of meandering caused by the difference in the coefficient of friction between the left and right sides, and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom sides. Then, a leveling control amount may be applied based on the amount of meandering caused by each factor to keep the wedge constant over the entire length of the rolled sheet S. This may bring the amount of meandering of the rolled sheet S (i.e., the sum of the amount of meandering caused by a change in the wedge ratio, the amount of meandering caused by the difference in the coefficient of friction between the left and right sides, and the amount of meandering caused by the difference in the coefficient of friction between the top and bottom sides) closer to zero. Specifically, a leveling control amount is applied so that the absolute value of the sum of the meandering amount at the entry side of the rolling mill and the meandering amount at the exit side of the rolling mill approaches zero. For example, a leveling control amount may be applied so that the absolute value of the sum of the amount of meandering at the exit side when the front end of the rolled sheet S is threaded and the amount of meandering at the entry side when the tail end is threaded is minimized. This control keeps the wedge of the rolled sheet S constant over the entire length.

[0147] In the example shown in (1) above, it is predicted that if the entry-side meandering amount is changed by 30 mm with a constant leveling control amount over the entire length, the delivery-side meandering amount will change by 40 mm. Furthermore, if only the meandering caused by the change in wedge ratio is suppressed by applying a constant leveling control amount over the entire length, it is predicted that meandering caused by the difference in the friction coefficient between the left and right sides (-50 mm on the entry side, 90 mm on the delivery side) will remain. From this, the relationship between the delivery-side meandering amount when the leading edge is threaded and the entry-side meandering amount when the tail edge is threaded for multiple leveling control amounts (constant leveling control amounts over the entire length) can be determined in advance, and from this relationship, it is possible to determine the leveling control amount that minimizes the absolute value of the sum of the delivery-side meandering amount when the leading edge is threaded and the entry-side meandering amount when the tail edge is threaded.

[0148] For example, in this example, when a leveling control amount was applied that minimized the absolute value of the sum of the delivery meandering amount when the leading edge is threaded and the entry-side meandering amount when the tail edge is threaded, the delivery meandering amount when the leading edge is threaded was 70 mm, and the entry-side meandering amount when the tail edge is threaded was -70 mm. By performing this leveling control, it is possible to optimize the suppression of the delivery meandering amount when the leading edge of the rolled sheet S is threaded and the entry-side meandering amount when the tail edge is threaded, under the constraint that the leveling control amount must be constant over the entire length.

[0149] The above describes a case where the meandering of the rolled sheet S is suppressed by leveling control alone (control example 2) as an example of a method for controlling the meandering of a rolled sheet according to one embodiment of the present invention. In the above description, the meandering amount of the rolled sheet is separated into three parts: a meandering amount due to a change in the wedge ratio, a meandering amount due to a difference in the coefficient of friction between the left and right sides, and a meandering amount due to a difference in the coefficient of friction between the top and bottom sides. However, the present invention is not limited to this example. For example, as described in step S210 of FIG. 9, the meandering amount of the rolled sheet may be separated into two parts: a meandering amount due to a change in the wedge ratio and a meandering amount due to a difference in the coefficient of friction between the top and bottom sides. In this case, meandering control may be performed in the same manner as in step S320 described above.

[0150] Thus, according to the method for controlling the meandering of the rolled sheet S of this embodiment, the meandering or camber of the rolled sheet S can be appropriately controlled by performing at least one of leveling control, top-bottom friction coefficient difference control, and left-right friction coefficient difference control, depending on the factor causing the meandering or camber of the rolled sheet S.

[0151] Although the preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, the present invention is not limited to these examples. It is clear that a person skilled in the art to which the present invention pertains can conceive of various modifications and alterations within the scope of the technical ideas set forth in the claims, and it is understood that these also naturally fall within the technical scope of the present invention.

[0152] For example, in the above description, the amount of meandering caused by a change in the wedge ratio in rolling, the amount of meandering caused by the difference in the left-right friction coefficient, and the amount of meandering caused by the difference in the top-bottom friction coefficient are determined based on the actual meandering data in the rolling process, and the rolling control amount for the rolled material is determined based on this, but the present invention is not limited to this example. For example, the rolling control amount for the next rolled sheet may be determined based on the amount of meandering caused by a change in the wedge ratio, the amount of meandering caused by the difference in the left-right friction coefficient, and the amount of meandering caused by the difference in the top-bottom friction coefficient determined in the rolling process. In other words, the rolled sheet to be controlled may be the same as the rolled sheet when the amount of meandering caused by each cause of meandering is determined, or it may be the rolled sheet to be rolled next after the rolled sheet when the amount of meandering caused by each cause of meandering is determined. Alternatively, for example, the rolling control amount for the next rolled sheet may be determined on the assumption that the difference in the friction coefficient between the left and right sides of the rolled sheet, or the difference in the friction coefficient between the top and bottom, when the amount of meandering occurring for each cause of meandering is understood will be maintained in the next rolled sheet to be rolled. [Explanation of symbols]

[0153] 1. Rolling equipment 10. Rolling Mill 11 Upper work roll 12 Lower work roll 20 Meandering meter 31, 32 Lubricant supply device 40 Screw down device 50 Edger device 51, 52 Edger roll 60 Side guide 61, 62 Guide 100 control device

Claims

1. Based on the rolling state of the rolled plate in the cross rolling mill, the meandering amount of the rolled plate is separated into a meandering amount due to a change in the wedge ratio, a meandering amount due to a difference in the left and right friction coefficients, and a meandering amount due to a difference in the top and bottom friction coefficients, A method for controlling the meandering of a rolled sheet, which suppresses the meandering of the rolled sheet to be controlled based on the amount of meandering due to each cause by performing at least one of leveling control, left-right friction coefficient difference control which controls the difference in the friction coefficient between the left and right sides, and up-down friction coefficient difference control which controls the difference in the friction coefficient between the top and bottom.

2. 2. The method for controlling meandering of a rolled sheet according to claim 1, wherein at least one of the leveling control for reducing the amount of meandering caused by a change in the wedge ratio to zero, the left-right friction coefficient difference control for reducing the amount of meandering caused by the left-right difference in the friction coefficient to zero, and the top-bottom friction coefficient difference control for reducing the amount of meandering caused by the top-bottom difference in the friction coefficient to zero is performed to suppress meandering of the rolled sheet to be controlled.

3. 2. The method for controlling meandering of a rolled sheet according to claim 1, wherein at least one of the left-right friction coefficient difference control and the top-bottom friction coefficient difference control adjusts at least one of the concentration or supply amount of lubricating oil injected between the work roll and the rolled sheet.

4. 2. The method for controlling meandering of a rolled sheet according to claim 1, wherein at least one of the left-right friction coefficient difference control and the top-bottom friction coefficient difference control adjusts at least one of the roughness of the work rolls or the surface properties of the rolled sheet.

5. 2. The method for controlling meandering of a rolled sheet according to claim 1, wherein the amount of meandering of the controlled rolled sheet is made to approach zero by only the leveling control.

6. 6. A method for controlling the meandering of a rolled plate as described in claim 5, wherein the leveling control amount at the front end of the rolled plate to be controlled and the leveling control amount at the tail end of the rolled plate to be controlled are changed according to the amount of meandering caused by the change in the wedge ratio, the amount of meandering caused by the difference in the left and right friction coefficients, and the amount of meandering caused by the difference in the top and bottom friction coefficients.

7. 6. A method for controlling the meandering of a rolled plate according to claim 5, wherein a leveling control amount is applied so that the wedge is constant over the entire length of the rolled plate to be controlled, based on the amount of meandering caused by a change in the wedge ratio, the amount of meandering caused by the difference in the left and right friction coefficients, and the amount of meandering caused by the difference in the top and bottom friction coefficients.

8. As a rolling state of the rolled plate, The camber amount at the exit side of the rolling pass, 8. The method for controlling meandering of a rolled sheet according to claim 1, wherein meandering in the rolling pass is separated based on at least one factor selected from the group consisting of a change in wedge ratio in the rolling pass, a difference in rolling load between the left and right sides, an amount of entry-side meandering, and a difference in load acting on an entry-side edger device between the left and right sides or a difference in load acting on a side guide between the left and right sides.

9. 9. The method for controlling meandering of a rolled sheet according to claim 8, wherein when the factor representing the rolling state of the rolled sheet includes the difference in rolling load between the left and right sides, the factor also includes the difference in temperature between the left and right sides of the rolled sheet, and the meandering is separated.

10. When the amount of meandering caused by the difference in the coefficient of friction between the left and right wheels is within the allowable range, As a rolling state of the rolled plate, The amount of camber at the exit side of the rolling pass, or 8. The method for controlling meandering of a rolled sheet according to claim 1, wherein meandering in the rolling pass is separated based on at least two or more factors among a change in wedge ratio in the rolling pass, a difference in rolling load between the left and right, an amount of entry-side meandering, an amount of exit-side meandering, and a difference in load acting on an entry-side edger device between the left and right, or a difference in load acting on a side guide between the left and right.

11. 11. The method for controlling meandering of a rolled sheet according to claim 10, wherein when the factor representing the rolling state of the rolled sheet includes the difference in rolling load between the left and right sides, the factor also includes the difference in temperature between the left and right sides of the rolled sheet, and the meandering is separated.

Images