JP2018043255A - Meandering prediction system and meandering prediction method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a meandering prediction system capable of further accurately predicting meandering of a plate material causable in rolling time.SOLUTION: The meandering prediction system comprises an acceptance part for accepting an actual value ΔPof a difference load of rolling rolls 11 and 12 and an actual value Δσof difference tension of a plate material 2 on the outlet side of the rolling rolls 11 and 12 and an arithmetic operation part for calculating a calculation value ΔPof the difference load and a calculation value Δσof the difference tension. The arithmetic operation part is constituted to calculate a meandering quantity Yof the plate material 2 and a level difference ΔS of the roling rolls 11 and 12 by a numerical model. The meandering prediction system further comprises an output part for outputting a calculation result of the meandering quantity Yof the plate material 2 and the level difference ΔS of the rolling rolls 11 and 12 at a point of time of ΔP=ΔPand Δσ=Δσ.SELECTED DRAWING: Figure 4

Description

  The present invention relates to a meandering prediction system and a meandering prediction method, and more particularly to a meandering prediction system and a meandering prediction method for predicting meandering of a plate material on the entrance side of a rolling roll.

  Conventionally, a technique for processing a plate material to a desired thickness by passing the plate material between a pair of rolling rolls in a tandem rolling mill or the like is known. In such a rolling process, the plate material may meander so as to be shifted to the left and right with respect to the axial center of the rolling roll as the sheet passing time elapses. Thereby, there exists a problem of causing a rolling trouble, such as the edge part of the width direction of a board | plate colliding with both sides of a conveyance path.

  On the other hand, as disclosed in the following Patent Documents 1 to 3, various methods for controlling meandering of a plate material that may occur during rolling have been studied. The following Patent Documents 1 and 2 disclose a method of measuring the differential tension of the plate material on the entry side or exit side of the rolling roll and adjusting the leveling of the rolling roll based on the result. Patent Document 3 below discloses a method of calculating the leveling adjustment amount based on fuzzy inference using the differential tension of the plate material on the entry side of the rolling roll and the differential load received by the rolling roll from the plate material.

JP 7-124620 A Japanese Patent No. 4306273 Japanese Patent Laid-Open No. 4-118108

  In the methods proposed in Patent Documents 1 to 3 above, it is possible to predict to some extent the sheet meandering that occurs during rolling, but there is a large deviation from the actual meandering behavior as follows, and there is a problem in the accuracy of the prediction. was there.

  In Patent Documents 1 and 2, the leveling amount of the rolling roll is adjusted based only on the prediction that the plate material meanders to the side having the wider gap between the rolling rolls. However, in reality, the plate material may approach the side where the gap between the rolling rolls is narrow. In this case, the meandering stops without performing leveling adjustment. That is, even in a situation where the left and right level difference occurs in the rolling roll due to a difference in mill constant, etc., the meandering does not always progress, and the plate material is stabilized in a state slightly off-centered with respect to the axial center of the rolling roll. There is. For this reason, if leveling adjustment is performed based on a prediction that deviates from the actual meandering behavior, the meandering may be promoted.

  Further, the fuzzy inference used for meandering prediction in Patent Document 3 is not based on a dynamic model based on the meandering mechanism that occurs during actual rolling. Therefore, it is difficult to accurately predict the meandering of the plate material as in Patent Documents 1 and 2, and the leveling operation based on fuzzy inference may cause the progress of meandering.

  The present invention has been made in view of the above problems, and an object thereof is to provide a meandering prediction system and a meandering prediction method that can more accurately predict meandering of a plate material that may occur during rolling.

The meandering prediction system according to one aspect of the present invention is a system that predicts meandering of a plate material on the entry side of a pair of rolling rolls. The meandering prediction system includes a receiving unit that receives the actual value ΔP ^act of the differential load of the rolling roll and the actual value Δσ _D ^act of the differential tension of the plate material on the exit side of the rolling roll, and the calculation of the differential load An arithmetic unit for calculating a value ΔP ^cal and a calculated value Δσ _D ^cal of the differential tension. The calculation unit is configured to calculate a meandering amount Ys of the plate material and a level difference ΔS of the rolling rolls by a numerical model. The meander prediction system further includes an output unit for outputting the calculation result of [Delta] P ^act = [Delta] P ^cal and Δσ _D ^act = Δσ meandering amount of the plate at the time of _D ^cal _{Y S} and level difference of the rolling rolls [Delta] S.

In the meandering prediction system, the meandering amount Y _S of the plate material and the level difference ΔS of the rolling roll are calculated by a numerical model, and the calculated values of the differential load of the rolling roll and the delivery side differential tension of the rolling material are coincident with the actual values ( ΔP ^act = ΔP ^cal , Δσ _D ^act = Δσ _D ^cal ) is output. As a result, it becomes possible to output the calculated values of the meandering amount Y _S and the level difference ΔS corresponding to the actual values ΔP ^act and Δσ _D ^act of the differential load and the outgoing differential tension. Meander can be predicted more accurately. Thus, accurately calculate the amount of meandering Y _S and level difference [Delta] S, by appropriate meandering preventive measures based on this, it is possible to prevent the occurrence of rolling troubles due meandering in advance.

In the meandering prediction system, the calculation unit calculates Jacobians (Jacobi matrices) J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ of the following formulas (1) to (4), and the Jacobian J ₁₁ , J ₁₂ , J _21, the inverse matrix _J ¹¹ -1 of ^{_{J 22, J 12 -1, J}} 21 -1, with a _J ^{22 -1,} the following equation (5), meandering amount _{Y S} and the plate (6) The level difference ΔS of the rolling rolls may be calculated.

The present inventors diligently studied a policy for more accurately predicting the meandering of the plate material in accordance with the meandering behavior during actual rolling. As a result, the meandering model Jacobian J (J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ ) represented by the above equations (1) to (4) is calculated, and its inverse matrix J ⁻¹ (J ₁₁ ⁻¹ , J ₁₂ ⁻¹ , J ₂₁ ⁻¹ , J ₂₂ ⁻¹ ) and paying attention to a model for calculating the meandering amount Y _S of the plate material and the level difference ΔS of the rolling roll by the above formulas (5) and (6), The present invention has been conceived.

In the meandering prediction system, the meandering amount Y _S of the plate material and the level difference ΔS of the rolling roll can be calculated by the above equations (5) and (6) using the inverse matrix J ⁻¹ of the Jacobian J. As a result, unlike conventional systems, it is possible to calculate accurately in accordance with the actual meandering behavior including meandering stop and divergence.

The meandering prediction system includes a determination unit for determining whether a time change of the meandering amount Y _S of the plate material exceeds a predetermined threshold value, and a time change of the meandering amount Y _S of the plate material in the determination unit. An alarm generation unit that generates an alarm when it is determined that the threshold value exceeds the threshold value.

According to this configuration, the harmful serpentine beyond the time variation threshold in meandering amount Y _S has occurred, the operator can easily recognize the warning. As a result, it is possible to more reliably notify the operator that it is necessary to take a meandering prevention measure.

  The meandering prediction system predicts meandering of the plate material between the pair of rolling rolls arranged in the uppermost stream in the tandem rolling mill and the upstream roll arranged on the upstream side of the tandem rolling mill. It may be configured to.

  According to this configuration, it is possible to accurately predict the meandering of the plate material that may occur on the entry side of the rolling roll disposed in the uppermost stream of the tandem rolling mill.

The meandering prediction method according to another aspect of the present invention is a method for predicting meandering of a plate material on the entry side of a pair of rolling rolls. The meandering prediction method includes a step of inputting an actual value ΔP ^act of the differential load of the rolling roll and an actual value Δσ _D ^act of the differential tension of the plate material on the exit side of the rolling roll; and calculation of the differential load A step of calculating a value ΔP ^cal and a calculated value Δσ _D ^cal of the differential tension, a step of calculating a meandering amount Y _{S of the} plate material and a level difference ΔS of the rolling roll by a numerical model, and ΔP ^act = ΔP ^cal and Δσ _D ^act = Δσ _D ^cal , and outputting the calculation result of the meandering amount Y _{S of the} plate and the level difference ΔS of the rolling roll.

According to the meandering prediction method, the numerical model with calculating the meandering amount Y _S and level difference ΔS of the rolling rolls of sheet material, the calculated value of the outlet side differential tension differences load and plate rolling rolls coincide with each actual value (ΔP ^act = ΔP ^cal , Δσ _D ^act = Δσ _D ^cal ) is output. Thereby, the calculated values of the meandering amount Y _S and the level difference ΔS corresponding to the actual values ΔP ^act and Δσ _D ^act of the differential load and the outlet side differential tension can be obtained, and the meandering of the plate material that can occur during actual rolling can be obtained. It can be predicted accurately.

In the meandering prediction method, the steps of calculating include the steps of calculating Jacobians J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ of the following formulas (1) to (4), and the Jacobians J ₁₁ , J ₁₂ , J _21, the inverse matrix _J ¹¹ -1 of ^{_{J 22, J 12 -1, J}} 21 -1, with a _J ^{22 -1,} the following equation (5), meandering amount _{Y S} and the of the plate (6) Calculating a level difference ΔS of the rolling rolls.

In the meandering prediction method, the meandering amount Y _S of the plate material and the level difference ΔS of the rolling roll can be calculated by the above formulas (5) and (6) using the inverse matrix J ⁻¹ of the Jacobian J. Thus, unlike the conventional calculation method, it is possible to perform an accurate calculation according to the actual meandering behavior including the meandering stop and divergence.

In the above-described meander prediction method may generate an alarm when the time variation in the meandering amount Y _S of the plate exceeds a predetermined threshold.

  According to this method, the operator can easily recognize the occurrence of harmful meandering by an alarm. In response to this, the operator can prevent the occurrence of rolling troubles due to meandering by taking appropriate meandering prevention measures such as centering of the plate material.

  The meandering prediction method predicts meandering of the plate material between the pair of rolling rolls arranged in the uppermost stream in the tandem rolling mill and the upstream roll arranged on the upstream side of the tandem rolling mill. It may be a method to do.

  According to this method, it is possible to accurately predict the meandering of the plate material that may occur on the entry side of the rolling roll disposed in the uppermost stream of the tandem rolling mill.

  As is apparent from the above description, according to the present invention, it is possible to provide a meandering prediction system and a meandering prediction method capable of more accurately predicting meandering of a plate material that may occur during rolling.

It is a schematic diagram which shows a mode that a board | plate material approachs between a pair of rolling rolls of a tandem rolling mill. It is a schematic diagram which shows the rolling load which a rolling roll receives from a board | plate material in the said tandem-type rolling mill. It is a schematic diagram for demonstrating the contact arc length which is the length which a rolling roll and a board | plate material contact in the said tandem-type rolling mill. It is a schematic diagram which shows a mode that a board | plate material is sent to the said tandem-type rolling mill from a steering roll. It is a schematic diagram for demonstrating the mechanism in which the meandering of a board | plate material stops. It is a schematic diagram which shows the differential load of a rolling roll when the meandering of a board | plate material stops. It is a schematic diagram for demonstrating the mechanism by which the meandering of a board | plate material diverges. It is a schematic diagram which shows the differential load of a rolling roll when the meandering of a board | plate material diverges. It is a block diagram for demonstrating each function of the meandering prediction system which concerns on Embodiment 1 of this invention. It is a figure which shows the flow of the meandering prediction method which concerns on Embodiment 1 of this invention. It is a graph which shows an example of the calculation result of the amount of meandering and level difference by the said meandering prediction method. It is a schematic diagram which shows a mode that a board | plate material is sent to # 2 stand from # 1 stand of the said tandem-type rolling mill.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
[Tandem type rolling mill]
First, a tandem rolling mill 10 to which a meandering prediction system and a meandering prediction method according to the present embodiment are applied will be described with reference to FIGS. The tandem rolling mill 10 is for processing a plate material 2 such as a steel plate into a desired thickness by a pair of rolling rolls 11 and 12. In the tandem rolling mill 10, a plurality of rolling stands having a pair of rolling rolls 11 and 12 are arranged from upstream to downstream, but FIG. 1 is arranged at the most upstream position. Only one stand 10A is shown.

The # 1 stand 10A has a pair of upper and lower rolling rolls 11 and 12 arranged with a gap (gap) through which the plate material 2 can enter, and a pair of upper and lower backup rolls 13 and 14 that support the rolling rolls 11 and 12, Is provided. As shown in FIG. 1, the plate material 2 having a thickness h _E is made to have a desired thickness by causing the plate material 2 to enter the gap between the rolls while rotating the rolling rolls 11 and 12 counterclockwise by a motor (not shown). It can be processed into h _D (<h _E ). Hereinafter, h _E is also referred to as “entrance side plate thickness” of the plate member 2, and h _D is also referred to as “exit side plate thickness” of the plate member 2.

  As shown in FIG. 2, the # 1 stand 10A has a working side (Work Side; WS) on the left side in the drawing, and a driving side (Drive Side; DS) on the right side in the drawing. The WS side is an area for the operator to work, and the DS side is an area where a drive mechanism such as a motor for rotating the rolls 11 to 14 is arranged.

The # 1 stand 10A includes hydraulic cylinders (not shown) as means for adjusting the left and right rolling positions (leveling amounts) of the rolling rolls 11 and 12. Thereby, it can be moved up and down by pushing the right and left parts of the rolling rolls 11 and 12 with the piston of the said cylinder. Therefore, the level difference ΔS between the rolling rolls 11 and 12 is adjusted by adjusting the left and right gaps while maintaining a constant gap between the rolls at the mill center C (the center of the rolling rolls 11 and 12 in the roll axis direction). be able to. The level difference [Delta] S, which is the difference between the gap _{S L} between the rolling rolls 11 and 12 in the WS side, and the gap _{S R} between the rolling rolls 11 and 12 in the DS side _(S L -S _R). Therefore, when the DS side reduction amount is large (S _L > S _R ), the level difference ΔS is a positive value, and when the WS side reduction amount is large (S _L <S _R ), the level difference ΔS is a negative value. It becomes.

As shown in FIG. 2, the rolling rolls 11 and 12 receive a rolling load P as a reaction force from the plate material 2 during rolling. The # 1 stand 10A is provided with load cells 15 and 16 on the left and right as means for detecting the rolling load P. Thereby, the rolling load P which the rolling rolls 11 and 12 receive from the board | plate material 2 can be detected separately in each of the DS side and WS side. And actual value (DELTA) ^Pact of the differential load of the rolling rolls 11 and 12 can be measured by the difference of these detection values. That is, the “rolling roll differential load” is a difference between the rolling load P applied to the WS side and the rolling load P applied to the DS side, which is obtained by subtracting the DS side rolling load P from the WS side rolling load P. is there. Therefore, when the WS-side rolling load P is larger than the DS-side rolling load P, the differential load has a positive value, and in the opposite case, the differential load has a negative value.

The delivery side plate thickness h _D is expressed as follows. That is, assuming that the gap between the rolling rolls 11 and 12 is S, the rolling load is P, and the mill constant of the stand is M, the outlet side thickness h _D is expressed by the following formula (7). The mill constant is a longitudinal rigidity coefficient of the stand, and is a ratio of the rolling load to the amount of deformation in the vertical direction of the entire stand. Note that the entry side and the delivery side of the rolling rolls 11 and 12 is provided with an unillustrated plate thickness sensor, thereby respectively measuring the thickness at entrance side h _E and delivery side thickness h _D.

As shown in FIG. 3, the plate 2 is in contact with the rolling rolls 11 and 12 by the length of the contact arc length l (l _L , l _R ). This contact arc length l is expressed as follows. That is, when the radius of the rolling rolls 11 and 12 is R, the entry side plate thickness is h _E , and the exit side plate thickness is h _D , the contact arc length l is expressed by the following equation (8).

As shown in FIG. 4, exit side tension sensors 17 and 19 are provided on the exit side of the rolling rolls 11 and 12 as means for detecting the tension of the plate material 2. The exit side tension sensors 17 and 19 are provided on the DS side and the WS side, respectively. The tension sensors 17 and 19 can detect the respective tensions on the DS side and WS side of the plate 2 on the exit side of the rolling rolls 11 and 12. The actual value Δσ _D ^act of the differential tension (hereinafter also referred to as “exit differential tension”) of the plate 2 on the exit side of the rolling rolls 11 and 12 can be measured from the difference between these detected values. That is, the exit differential tension is a difference between the WS side tension and the DS side tension on the exit side of the rolling rolls 11 and 12, and is obtained by subtracting the DS side tension from the WS side tension. Therefore, when the WS-side exit tension is larger than the DS-side exit tension, the exit-side differential tension has a positive value, and vice versa. In addition, a tension sensor (entrance tension sensor) is also provided on the entry side of the rolling rolls 11 and 12, whereby the differential tension (entrance difference tension) of the plate material 2 on the entry side of the rolls 11 and 12 can be measured. It may be.

[Meandering behavior of plate material in tandem rolling mill]
Next, meandering behavior of the plate 2 that can actually occur during rolling by the tandem rolling mill 10 will be described with reference to FIGS. 5 and 6 show a case where the meandering of the plate material 2 stops, that is, a case where the amount of meandering of the plate material 2 does not increase with the passing time and becomes constant. 7 and 8 show a case where the meandering amount of the plate material 2 increases with the passing time and the meandering diverges.

  As shown in FIG. 5, the plate 2 is restrained in a state of being wound around a steering roll 18 (upstream roll) disposed on the upstream side of the tandem rolling mill 10, while the rolling roll 11 of the # 1 stand 10 </ b> A, Enter between twelve. And the board | plate material 2 which passed # 1 stand 10A is sent to # 2 stand 10B arrange | positioned downstream.

In the # 1 stand 10A, when the gap between rolls on the DS side is wider than that on the WS side, the plate 2 tends to meander to the DS side. More specifically, when the plate 2 enters with the DS side gap wide, a difference occurs between the left and right contact arc lengths l _L and l _R (l _L > l _R ) as shown in FIG. When the plate material 2 enters in this state, an incident angle θ is formed between the traveling direction D1 of the plate material 2 and the rotation direction D2 of the rolling rolls 11 and 12 (direction perpendicular to the roll axis direction). As a result, a velocity component V toward the DS side is generated, and the plate member 2 tries to meander toward the DS side due to the velocity component V.

In this state, when the plate material 2 enters between the rolling rolls 11 and 12 of the # 2 stand 10B as shown in FIG. 5, tensile stress P1 is generated on the DS side and compressive stress P2 is generated on the WS side. The tensile stress P1 and the compressive stress P2 act in the longitudinal direction of the plate material 2, respectively. In this way, by applying stresses P1 and P2 in opposite directions to the DS side and WS side of the plate material 2, a moment M1 that attempts to rotate the plate material 2 counterclockwise from the center in the width direction. Will occur. In order to balance this moment M1, in the # 1 stand 10A, a force P3 that brings the plate 2 to the WS side is generated. For this reason, the meandering to the DS side does not occur and the meandering stops. In this case, the rolling load P received by the rolling rolls 11 and 12 of the # 1 stand 10A is larger on the WS side than the DS side as shown in FIG. 6, and the exit side tension σ _D of the # 1 stand 10A is shown in FIG. As shown, the DS side is larger than the WS side.

  Further, the restraint of the plate material 2 by the steering roll 18 also works to stop the meandering of the plate material 2 in the same manner as the moment M1. Specifically, the entry side differential tension of the # 1 stand 10A is changed by winding the plate material 2 around the steering roll 18 and restraining the feed direction and feed position of the plate material 2. In response to this change, the level difference ΔS between the rolling rolls 11 and 12 in the # 1 stand 10A is reduced and the incident angle θ is reduced, whereby the meandering stops.

On the other hand, when the plate 2 to meander to the DS side enters straight into the # 2 stand 10B, the WS side portion of the plate 2 on the entry side of the # 2 stand 10B as shown by the wavy line in FIG. May buckle. In this case, unlike the case of FIG. 5, the moment to rotate the plate member 2 is reduced or the moment is not generated. For this reason, in the # 1 stand 10A, the force P4 that moves the plate 2 toward the WS side is reduced. Therefore, the meandering component to the DS side cannot be suppressed, and the meandering diverges to the DS side. In this case, the rolling load P received by the rolling rolls 11 and 12 is larger on the DS side than on the WS side as shown in FIG. 8, and the exit side tension σ _D of the # 1 stand 10A is on the DS side as shown in FIG. It becomes larger than the WS side.

  Thus, in actual rolling, the meandering of the plate 2 may stop even in the same situation where the gap between the rolls on the WS side is narrower than that on the DS side (FIG. 5), while meandering diverges. In some cases (FIG. 7). According to the meandering prediction system and the meandering prediction method according to this embodiment described below, accurate meandering prediction according to such actual meandering behavior becomes possible.

[Meander prediction system]
Next, the meandering prediction system 1 according to the present embodiment will be described with reference to FIG. FIG. 9 is a functional block diagram of the meandering prediction system 1. The meandering prediction system 1 is a system for predicting meandering of the plate 2 on the entrance side of the pair of rolling rolls 11 and 12 of the # 1 stand 10A. That is, the meandering prediction system 1 is used to predict meandering of the plate 2 between the pair of rolling rolls 11 and 12 and the steering roll 18 of the # 1 stand 10A. The meandering prediction system 1 is composed of, for example, a computer attached to a rolling line, and includes a calculation unit 21, a reception unit 22, an output unit 23, a storage unit 24, a determination unit 25, and an alarm generation unit 26. .

The accepting unit 22 is a part that accepts various data necessary for calculation by the computing unit 21. As the received data, for example, the entry side plate thickness h _E , the exit side plate thickness h _D , the plate width W, the rolling load P, the WR bending force J, the entry side tension σ _E , the exit side tension σ _D , the rolling rolls 11, 12. ^Examples include the actual value ΔP ^act of the differential load and the actual value Δσ _D ^act of the outlet side differential tension of the plate member 2. These performance data are acquired by the specifications of the plate material 2 and various sensors (tension sensor, load cell, plate thickness sensor) attached to the rolling mill, and transmitted to the receiving unit 22.

The computing unit 21 is configured by a processing device such as a CPU (Central Processing Unit). Based on the various data transmitted from the receiving unit 22, the calculation unit 21 performs various calculations necessary for calculating the meandering amount Y _S of the plate material 2 and the level difference ΔS of the rolling rolls 11 and 12 using a numerical model. Each calculation function of the calculation unit 21 will be described for each block. The calculation unit 21 includes an entry side tension calculation unit 21A, a differential load calculation unit 21B, a plate thickness calculation unit 21C, an exit side tension calculation unit 21D, and an incident angle. A calculation unit 21E, a Jacobian calculation unit 21F, a meandering amount calculation unit 21G, and a level difference calculation unit 21H are included.

The details of the calculation processing by the calculation unit 21 will be described later, but the outline is as follows. The entry side tension computing unit 21A is rolled and the incident angle θ and the amount of meandering of the sheet material 2 into between rolls 11, 12 Y _{S (off-center} amount of the sheet material 2 from the mill center C), constrained by the steering roller 18 of the sheet material 2 Based on the conditions, the entry side differential tension of the plate member 2 is calculated. The differential load calculation unit 21B calculates the differential load of the rolling rolls 11 and 12 based on the entry side differential tension of the plate 2 calculated by the entry side tension calculation unit 21A. The plate thickness calculator 21C includes factors (for example, level difference ΔS, left and right) that affect the difference in rolling reduction between the left and right rolling rolls 11 and 12, including the calculated value ΔP ^cal of the differential load calculated by the differential load calculator 21B. difference thickness at entrance side h _E of, by using the difference, etc.) of the left and right of the mill constant, calculates the distribution of the delivery thickness h _D out. The exit side tension calculating unit 21D calculates the exit side differential tension Δσ _D ^cal of the plate member 2 based on the entry side differential tension calculated by the entry side tension calculating unit 21A. Incidence angle calculating section 21E, based on the distribution of the delivery thickness h _D out is calculated by the thickness calculating section 21C, to calculate the θ angle of incidence of the plate 2. The Jacobian computation unit 21F calculates the meandering model Jacobians J ₁₁ , J ₁₂ , J ₂₁ , and J _{22 represented} by the following formulas (1) to (4). Meandering amount calculation unit 21G is Jacobian _{J 11,} the inverse matrix _J ¹¹ of _{J 12 -1,} with a _J ^{12 -1,} calculates the amount of meandering _{Y S} by the following equation (5). The level difference calculation unit 21H calculates the level difference ΔS by the following formula (6) using the inverse matrices J ₂₁ ⁻¹ and J ₂₂ ⁻¹ of the Jacobians J ₂₁ and J ₂₂ .

In the above formulas (1) to (4), ΔP is the differential load of the rolling rolls, Y _S is the meandering amount, dY _S is the minute change amount of the meandering amount, Y _S ⁰ is the initial value of the meandering amount, and ΔS is the level difference. , DΔS represents a minute change amount of the level difference, ΔS ⁰ represents an initial value of the level difference, and Δσ _D represents an exit side differential tension.

The output unit 23 is a part for outputting a calculation result by the calculation unit 21. Specifically, the output unit 23 is a plate material at a time point (ΔP ^act = ΔP ^cal and Δσ _D ^act = Δσ _D ^cal ) when the actual value and the calculated value coincide with each other in the differential load and the outlet side differential tension of the rolling rolls 11 and 12. and it outputs the calculation result of the level difference between the second meandering amount _{Y S} and rolling rolls 11, 12 [Delta] S. The output unit 23 includes a display device such as a display.

The determination unit 25 determines whether the time change of the meandering amount Y _S of the plate 2 calculated by the calculation unit 21 exceeds a predetermined threshold value. This threshold value can be arbitrarily set by the operator and is stored in the storage unit 24. The alarm generation unit 26 generates an alarm when the determination unit 25 determines that the time change of the meandering amount Y _S of the plate material exceeds the threshold value. This makes the operator recognize that harmful meandering has occurred. The alarm generation unit 26 may be configured by, for example, a voice type that sounds an alarm buzzer, or may be configured by a lighting type that displays a warning light.

  The storage unit 24 stores information on various arithmetic expressions necessary for calculation by the arithmetic unit 21, and is configured by a storage device such as a memory or a hard disk. Specifically, the off-center amount and level difference using the arithmetic expression for the Jacobian calculation of the above formulas (1) to (4) and the Jacobian inverse matrix of the above formulas (5) and (6) An arithmetic expression for calculation is stored in the storage unit 24. The calculation unit 21 executes calculation processing according to these calculation programs stored in the storage unit 24.

[Meander prediction method]
Next, a meandering prediction method according to this embodiment implemented using the meandering prediction system 1 will be described according to the flow shown in FIG. In this meandering prediction method, meandering of the plate material 2 on the entrance side of the pair of rolling rolls 11 and 12 of the # 1 stand 10A is predicted. That is, the meandering of the plate material 2 between the rolling rolls 11 and 12 of the # 1 stand 10A and the steering roll 18 is predicted. FIG. 10 shows a flow of calculation processing by PAD (Problem Analysis Diagram).

First, step S10 for inputting the rolling record is executed. In this step S10, the entry side plate thickness h _E , the exit side plate thickness h _D , the plate width W, the rolling load P, the WR bending force J, the entry side tension σ _E , the exit side tension σ _D , the actual value ΔP _{act of the} differential load and The actual value Δσ _D ^act of the delivery-side differential tension is transmitted to the receiving unit 22 as the actual rolling value. These data are automatically acquired from various sensors provided in the rolling mill.

Next, step S20 for setting an initial value is executed. In this step S20, the initial value ΔS ⁰ of the level difference, the initial value Y _S ⁰ of the meandering amount, and the initial value θ ^{0 of the} incident angle are set and transmitted to the accepting unit 22.

Next, step S30 for continuously calculating the meandering amount Y _S ^j and the level difference ΔS ^j (j = 1 to max) is executed. In step S30, first, continuous calculation of the incident angle θ ⁱ (i = 1 to max) is executed as follows.

First, the stress distribution of the plate 2 between the steering roll 18 and the # 1 stand 10A is analyzed (S31). Specifically, the initial value θ ⁰ of the incident angle and the initial value Y _S ⁰ of the meandering amount are set as one boundary condition, and the constraint condition of the plate member 2 by the steering roll 18 is set as the other boundary condition. And the differential tension | tensile_strength of the board | plate material 2 in the entrance side of the rolling rolls 11 and 12 of # 1 stand 10A is calculated by analysis methods, such as a two-dimensional finite element method (2D-FEM (Finite Element Method)). At this time, as a constraint condition by the steering roll 18, a direction in which the plate material 2 is fed from the steering roll 18 toward the # 1 stand 10A, a feed position of the plate material 2, and the like are used. This calculation is executed by the entry-side tension calculation unit 21A.

Next, calculation of the differential load ΔP ^cal of the rolling rolls 11 and 12 based on the entry side differential tension (differential load calculation unit 21B), and the outlet side thickness distribution h _{D of the} rolling rolls 11 and 12 based on the calculated differential load value ΔP ^cal The calculation of (z) (sheet thickness calculation unit 21C) and the calculation of the outlet side differential tension Δσ _D ^cal of the plate member 2 (output side tension calculation unit 21D) are sequentially executed (S32). The differential load ΔP ^cal is calculated so that the rolling load P becomes smaller on the side having the larger entry side tension and the rolling load P becomes larger on the side having the smaller entry side tension. Further, the outlet side plate thickness distribution h _D (z) is calculated based on the roll deflection after calculating the deflection of the rolling rolls 11 and 12 based on the differential load ΔP ^cal . Further, the outgoing differential tension Δσ _D ^cal is calculated in consideration of the interference coefficient between the incoming tension σ _E and the outgoing tension σ _D based on the incoming differential tension calculated in step S31.

Next, the incident angle θ ⁱ is calculated (S33). Specifically, first, the contact arc lengths l _L and l _R of the plate material 2 are calculated using the outlet side plate thickness distribution h _D (z) (FIG. 3). Specifically, the contact arc lengths l _L and l _R are calculated by the above equation (8) using the roll diameter R, the left and right inlet side plate thickness h _E, and the left and right outlet side plate thickness h _D , respectively. And, as shown in FIG. 3, since the following formula (9) is established between the difference l _L -l _R of the contact arc length and the width W at which the plate material 2 contacts the rolling rolls 11 and 12, The incident angle θ ⁱ of the plate material 2 is calculated by using this.

Next, it is determined whether or not the relational expression of θ ⁱ = θ ⁱ⁻¹ is satisfied (S34). When θ ⁱ ≠ θ ⁱ⁻¹ (“NO” in the figure), θ ^{i + 1} is calculated by the following equation (10) (S36). This equation (10) is an exponential smoothing equation for determining the value of θ ^{i + 1} , “g” is a coefficient indicating the weight of θ ⁱ obtained this time, and “1-g” is obtained last time. This is a coefficient indicating the weight of θ ⁱ⁻¹ .

Thereafter, the process proceeds to the calculation of the incident angle θ ^{i + 2 in} the next step (S37). Then, the differential tension of the plate 2 on the entrance side of the # 1 stand 10A is recalculated using θ ^{i + 1} obtained by the above equation (10) (S31), and the differential load ΔP ^cal is calculated in the same manner as described above. The calculation of the thickness distribution h _D (z) and the calculation of the outlet differential tension Δσ _D ^cal are performed in order (S32), and then the incident angle θ ^{i + 2} is calculated (S33). Such calculation of the incident angle θ ⁱ is repeated.

When the relational expression of θ ⁱ = θ ⁱ⁻¹ is satisfied in the determination in step S34 (“YES” in the figure), the process proceeds to the next determination step S38. In this step S38, with respect to the differential load ΔP of the rolling rolls 11 and 12 and the outlet side differential tension Δσ _D of the sheet material 2, whether the actual value input in step S10 matches the calculated value obtained in step S32 or not. Determine. That is, it is determined whether or not the relational expressions ΔP ^cal = ΔP ^act and Δσ _D ^cal = Δσ _D ^act are satisfied.

When ΔP ^cal ≠ ΔP ^act or Δσ _D ^cal ≠ Δσ _D ^act (“NO” in the figure) in the above determination, the meandering amount Y _S of the sheet 2 and the level difference ΔS of the rolling rolls 11 and 12 are calculated by a numerical model. Move to the step to do. This step includes a Jacobian calculation step (S39) and a step (S40) of calculating the meandering amount Y _S of the plate 2 and the level difference ΔS of the rolling rolls 11 and 12 using the inverse Jacobian matrix. In step S39, the Jacobian computing unit 21F calculates Jacobians J ₁₁ , J ₁₂ , J ₂₁ , and J ₂₂ shown in the following formulas (1) to (4), respectively.

Then, in step S40, the Jacobian _{J 11, J 12, J 21} , the inverse matrix _J ¹¹ -1 of ^{_{J 22, J 12 -1, J}} 21 -1, with a _J ^{22 -1,} the following equation (5) , (6), the correction amount of the meandering amount Y _S and the level difference ΔS is calculated. In this calculation, the values of ΔP ^act and Δσ _D ^act input in step S10 and the values of ΔP ^cal and Δσ _D ^cal calculated in step S32 are used. These calculations are executed in the meandering amount calculation unit 21G and the level difference calculation unit 21H, respectively.

Thereafter, Y _S ^{j + 1} and ΔS ^{j + 1} are respectively calculated as estimated disturbances for the next calculation by the following formulas (11) and (12) (S41). Then, returning to step S31, steps S31 to S41 described above are repeatedly performed using Y _S ^{j + 1} and ΔS ^{j + 1} .

When the relational expression of ΔP ^cal = ΔP ^act and Δσ _D ^cal = Δσ _D ^act is satisfied in the determination of step S38, the calculation result of the meandering amount Y _S and the level difference ΔS is output to the output unit 23 (S60). ). By performing the above calculation continuously while changing the rolling record data input in step S10, the time change of the meandering amount Y _S and the level difference ΔS can be calculated.

Then, it is determined that when the time variation of the calculated amount of meandering Y _S exceeds a predetermined threshold, harmful serpentine occurs in the determination unit 25. Then, a signal is sent from the determination unit 25 to the alarm generation unit 26, and the alarm generation unit 26 generates an alarm. In response to this alarm, the operator can take measures such as leveling adjustment of the rolling rolls 11 and 12 to prevent occurrence of rolling trouble due to meandering of the plate material 2.

[Calculation result by meandering prediction method]
Next, an example of the calculation result by the meandering prediction method will be described with reference to the graph of FIG. FIG. 11 shows a result of calculating the time variation of the meandering amount Y _S and the level difference ΔS from the actual value ΔP ^act of the differential load of the rolling rolls 11 and 12 and the actual value Δσ _D ^act of the outlet side differential tension.

In FIG. 11, (A) shows the time change of the motor speed of the MRH circuit that drives the rolling mill. (B) shows the time change of the actual value of the level difference ΔS (μm). (C) has shown the time change of the track load value (DELTA) ^Pact (Ton) of a differential load. (D) shows the time change of the actual value Δσ _D ^act (kg / mm ² ) of the outlet side differential tension. (E) shows the time change of the calculated value of the level difference ΔS (μm). (F) shows the change over time of the calculated value of the meandering amount Y _S (mm). In each of the graphs (A) to (F), the horizontal axis indicates the sheet passing time (seconds) for passing the plate 2 between the rolling rolls 11 and 12.

In FIG. 11, in the time period of about 780 to 1320 seconds, the level difference ΔS is a negative value as shown in the graph (E), and the WS side reduction amount is larger than the DS side reduction amount. As shown in the graph (C), the differential load ΔP ^act is a positive value, and the rolling load on the WS side is larger than that on the DS side as shown in FIG. In this case, as shown in the graph (D), the differential tension Δσ _D ^act temporarily becomes a negative value, and even if the DS side outlet tension becomes larger than the WS side as shown in FIG. as meandering amount Y _S is substantially constant. That is, the meandering stop behavior described with reference to FIGS. 5 and 6 is accurately expressed by the above calculation.

On the other hand, in the region of about 1320 to 1440 seconds, the differential load ΔP ^act and the differential tension Δσ _D ^act are both negative values as shown in the graphs (C) and (D), as shown in FIGS. any of the rolling load P and the exit-side tension sigma _D is DS side is larger. In this case, as meandering amount Y _S of the graph (F) is turned negative side, meandering amount of the DS side increases. Therefore, the meandering divergence behavior described with reference to FIGS. 7 and 8 is also accurately expressed by the above calculation.

As described above, in this embodiment, it is possible to accurately predict the meandering of the sheet material 2 which changes depending on the difference between the load ΔP and the outlet side differential tension .DELTA..sigma _D of the rolling rolls 11 and 12. As a result, the operator can perform meandering prevention measures such as centering of the plate material 2 at an appropriate timing, and the occurrence of rolling troubles due to the meandering of the plate material 2 can be prevented.

(Other embodiments)
Finally, other embodiments of the present invention will be described.

In the first embodiment, the method of calculating the meandering amount Y _S of the plate material 2 and the level difference ΔS of the rolling rolls 11 and 12 based on the differential load ΔP and the differential tension Δσ _D using the Jacobian and its inverse matrix has been described. However, it is not limited to this. For example, the following calculation method can be employed.

First, assuming appropriate initial values of meandering amount Y _S and level difference ΔS, a calculated value ΔP ^cal of a differential load and a calculated value Δσ _D ^cal of a delivery side differential tension are respectively calculated using a rolling model. As the rolling model, a model in which the relation among ΔP, Δσ, ΔS, and Y _S is appropriately numerically modeled based on a physical relational expression in the rolling process can be used.

When ΔP ^cal and Δσ _D ^cal are different from ΔP ^act and Δσ _D ^act which are actual rolling results, Y _S and ΔS are slightly changed in a direction in which the error is reduced. Then, ΔP ^cal and Δσ _D ^cal are calculated again.

This calculation step may be repeated until the difference between the calculated values (ΔP ^cal , Δσ _D ^cal ) and the actual values (ΔP ^act , Δσ _D ^act ) becomes sufficiently small. Further, _{Y S} and ΔS when which only slightly changed, numerical methods such as hill-climbing method (Simplex Method) may be used.

In the first embodiment, the case where the meandering of the plate 2 between the rolling rolls 11 and 12 of the # 1 stand 10A and the steering roll 18 arranged in the uppermost stream in the tandem rolling mill 10 has been described. However, the present invention is not limited to this. For example, as shown in FIG. 12, based on the differential load ΔP of the rolling rolls 11 and 12 in the # 2 stand 10B and the outlet differential tension Δσ _{D of the} # 2 stand 10B, between the # 1 and # 2 stands. This may be applied when predicting meandering of the plate material 2. Similarly, the stands after # 3 may be applied to the meandering prediction of the plate 2 between adjacent stands.

  In the meandering prediction system 1 of the first embodiment, the determination unit 25 and the alarm generation unit 26 are not essential components and may be omitted.

In the meandering prediction method of the first embodiment, at least ΔP ^act and Δσ _D ^act may be input as rolling performance data, and other input data include h _E , h _D , W, P, J, σ _E , σ may be only a part of the data are used of _D.

  In the meandering prediction method of the first embodiment, the case where the calculation is repeated until the incident angle θ becomes constant in steps S31 to S37 has been described. However, the present invention is not limited to this, and the process proceeds to the next step S38 without performing the repetition calculation. May be.

  In the said Embodiment 1, although the meandering prediction in the tandem-type rolling mill 10 which consists of a plurality of stands was demonstrated, it is not limited to this, It can apply also to the meandering prediction of the rolling mill comprised only with one stand. . Moreover, it can be applied not only to the quadruple rolling mill shown in FIG. 1 but also to meandering prediction in a double rolling mill, a sixfold rolling mill, a cluster rolling mill or the like. Further, it can be applied to both hot rolling and cold rolling.

  It should be understood that the embodiments disclosed herein are illustrative and non-restrictive in every respect. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

DESCRIPTION OF SYMBOLS 1 Meander meander system 2 Sheet material 10 Tandem rolling mill 11,12 Roll roll 18 Steering roll (upstream roll)
21 arithmetic unit 22 receiving unit 23 output unit 25 determination unit 26 alarm generation unit J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ Jacobian J ₁₁ ⁻¹ , J ₁₂ ⁻¹ , J ₂₁ ⁻¹ , J ₂₂ ⁻¹ inverse matrix ΔP Actual value of ^act differential load ΔP Calculated value of ^cal differential load ΔS Level difference Y _S Meandering amount (off-center amount)
Actual value of Δσ _D ^act differential tension ΔCalculated value of Δσ _D ^cal differential tension

Claims (8)

A meandering prediction system for predicting meandering of a plate material on the entry side of a pair of rolling rolls,
A receiving unit that receives the actual value ΔP ^act of the differential load of the rolling roll and the actual value Δσ _D ^act of the differential tension of the plate material on the exit side of the rolling roll;
A calculation unit for calculating the calculated value ΔP ^{cal of the} differential load and the calculated value Δσ _D ^cal of the differential tension,
The calculation unit is configured to calculate a meandering amount Y _{S of the} plate material and a level difference ΔS of the rolling roll by a numerical model,
ΔP ^act = ΔP ^cal equipped and Δσ _D ^act = Δσ _D meandering amount of the plate at the time of ^cal _{Y S} and further an output unit for outputting the calculation result of the level difference ΔS of said rolling roll, meander prediction system. The arithmetic unit calculates Jacobians J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ of the formulas (1) to (4), and an inverse matrix J ₁₁ ^{−1 of the} Jacobians J ₁₁ , J ₁₂ , J ₂₁ , J _22. , J ₁₂ ⁻¹ , J ₂₁ ⁻¹ , J ₂₂ ⁻¹ are used to calculate the meandering amount Y _{S of the} plate material and the level difference ΔS of the rolling roll according to equations (5) and (6). The meandering prediction system according to claim 1.

A determination unit for determining whether the time change of the meandering amount Y _S of the plate material exceeds a predetermined threshold;
An alarm generating unit time changes in the meandering amount Y _S of the plate in the evaluation unit generates an alarm when it is determined that exceeds the threshold value, further comprising a meandering prediction system according to claim 1 or 2 .   It is configured to predict meandering of the plate material between the pair of rolling rolls arranged in the uppermost stream in the tandem rolling mill and the upstream roll arranged on the upstream side of the tandem rolling mill. The meandering prediction system according to any one of claims 1 to 3. A meandering prediction method for predicting meandering of a plate material on the entry side of a pair of rolling rolls,
Inputting the actual value ΔP ^act of the differential load of the rolling roll and the actual value Δσ _D ^act of the differential tension of the plate material on the exit side of the rolling roll;
Calculating a calculated value ΔP ^{cal of the} differential load and a calculated value Δσ _D ^{cal of the} differential tension;
Calculating a meandering amount Ys of the plate material and a level difference ΔS of the rolling roll by a numerical model;
And outputting ΔP ^act = ΔP ^cal and Δσ _D ^act = Δσ meandering amount of the plate at the time of _D ^cal _{Y S} and the calculation result of the level difference ΔS of said rolling rolls, with a meandering prediction method. The calculating step includes:
Calculating Jacobians J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ of equations (1)-(4);
Using the inverse matrix J ₁₁ ⁻¹ , J ₁₂ ⁻¹ , J ₂₁ ⁻¹ , J ₂₂ ⁻¹ of the Jacobian J ₁₁ , J ₁₂ , J ₂₁ , J ₂₂ , the plate material according to the formulas (5) and (6). meandering amount Y _S and and calculating the level difference ΔS of said rolling roll, meandering prediction method according to claim 5.

Generating an alarm when the time variation in the meandering amount Y _S of the plate exceeds a predetermined threshold, meandering prediction method according to claim 5 or 6.   Predicting meandering of the plate material between the pair of rolling rolls arranged in the uppermost stream in the tandem rolling mill and the upstream roll arranged on the upstream side of the tandem rolling mill. The meandering prediction method according to any one of 7.

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