[0001]The present invention relates to a zigzagging control method for a workpiece.
BACKGROUND ART
10 [0002]
When a workpiece is rolled with a rolling mill, the workpiece may cause what is called zigzagging, in which a width-direction center of the workpiece deviates from a mill center while a tail portion of the workpiece is passing through the rolling mill. If a workpiece zigzags, a tail portion of the workpiece may hit a side guide that is placed
15 downstream of a rolling mill through which the workpiece passes; in this case, buckling can occur, in which the workpiece is rolled with a next rolling mill as the workpiece is buckled. The occurrence of buckling of a workpiece causes an excessively heavy rolling load on the rolling mill, which may result in damage to a roll and, in addition, suspension of operation for repair.
20 [0003]
Hence, techniques have been proposed for preventing zigzagging of a workpiece when a tail portion of the workpiece passes a rolling mill. For example, Patent Document 1 discloses a differential-load type zigzagging control method in which roll-axis-direction thrust counterforces of all of at least either upper rolls or lower rolls
25 other than backup rolls are measured, and an influence of an inter-roll thrust force on a differential load is taken into consideration. Patent Document 2 discloses a differential-load type zigzagging control method in which a work-roll thrust counterforce and a surface profile of a work roll are measured, and influences of an inter-roll thrust force and a material-roll thrust force on a differential load are taken into consideration.
30 Patent Document 3 discloses a differential-load type zigzagging control method in which
1

a skew angle of a roll is measured, and an influence of an inter-roll thrust force on a differential load is taken into consideration. Patent Document 4 discloses a method for controlling a rolling mill in which, before rolling, a roll gap is opened, and a bending force is applied while rollers are driven to identify an influence of an inter-roll thrust 5 force on a differential load, and reduction leveling control is performed with consideration given to the influence of the inter-roll thrust force on the differential load.
LIST OF PRIOR ART DOCUMENTS PATENT DOCUMENT 10 [0004]
Patent Document 1: JP2000-312911A Patent Document 2: JP2005-976A Patent Document 3: JP2014-4599A Patent Document 4: JP2009-178754A 15 NON PATENT DOCUMENT [0005]
Non Patent Document 1: Y. Liu et al. "Investigation of Hot Strip Mill 4 Hi Reversing Roughing Mill Main Drive Motor Thrust Bearing Damage", AISTech 2009 Proceedings-Volume II, 2009, p. 1091-1101 20
SUMMARY OF INVENTION TECHNICAL PROBLEM [0006]
Here, in the conventional differential-load type zigzagging control, work-side 25 and drive-side rolling loads of at least any one of upper and lower roll assemblies are measured to determine a rolling load difference or a rolling load difference ratio, and reduction leveling control is performed on a rolling mill based on this value. However, it is known that if inter-roll cross (a rotation tilt in a horizontal plane) occurs, an axial force between rolls (inter-roll thrust force) is generated. In addition, if material-roll cross 30 occurs, an axial force between a material and a roll (material-roll thrust force) is similarly
2

generated. The material-roll thrust force is small when compared with the inter-roll thrust force but has a significant influence particularly in a case of a low rolling reduction rate. These inter-roll thrust force and material-roll thrust force are supported by counterforces from roll chocks, which causes an overturning moment to act on a roll due 5 to a perpendicular distance between a support point and a line of action of the force (moment arm). Note that the overturning moment of a roll refers to a moment in a plane perpendicular to a longitudinal direction of rolling. It is considered that a difference in vertical direction load cell measured value between the work side and the drive side (differential load) fluctuates at this time so as to establish the balance with the overturning
10 moment. If a differential load attributable to these thrust forces occurs unintentionally, the differential load serves as a disturbance in the reduction leveling control, which becomes a cause of decreasing accuracy of leveling correction. [0007]
In the techniques described in the above Patent Documents 1, 3, and 4, no
15 consideration is given to an inference of a material-roll thrust force on a differential load; therefore, a differential load attributable to thrust forces cannot be estimated accurately, and thus accurate leveling correction as described above cannot be performed. In the technique described in the above Patent Document 2, influence coefficients of an inter-roll thrust force and a material-roll thrust force on a differential load are calculated,
20 and a sum of the influence coefficients is multiplied by a measured thrust counterforce to estimate a differential load attributable to thrust forces, by which reduction leveling control is performed. However, this technique lacks the number of parameters to determine the influence coefficients, and thus an accuracy of the estimation is not satisfactory. For this reason, as with the above Patent Documents 1,3, and 4, accurate
25 leveling correction cannot be performed. [0008]
In the technique described in the above Patent Document 4, it is necessary before rolling to open a roll gap and apply a bending force while rollers are driven to identify an influence of an inter-roll thrust force on a differential load, and this operation is required
30 to be performed in addition to a regular operation.
3

[0009]
The present invention is made in view of the problems described above and has an objective to provide a novel, improved zigzagging control method for a workpiece that enables leveling correction to be performed with an influence of thrust forces on a 5 differential load taken into consideration more accurately.
SOLUTION TO PROBLEM [0010]
In order to solve the problem described above, according to an aspect of the
10 present invention, there is provided a zigzagging control method for a workpiece in a rolling mill of four-high or more, the rolling mill including a plurality of rolls that include at least a pair of work rolls and at least a pair of backup rolls supporting the work rolls, an upper roll assembly including an upper work roll and an upper backup roll, a lower roll assembly including a lower work roll and a lower backup roll, the zigzagging control
15 method including: an estimation step of acquiring at least any one of an inter-roll thrust force estimated based on an inter-roll cross angle and an inter-roll friction coefficient that are acquired through measurement or estimation and a material-roll thrust force estimated based on a material-roll cross angle and a material-roll friction coefficient that are acquired through measurement or estimation, the estimation step being performed before
20 rolling of a tail portion of the workpiece; and a tail control step of measuring work-side and drive-side rolling loads of at least any one of the upper and lower roll assemblies, correcting rolling-load-difference information based on any two of acquired parameters including a roll-axis-direction thrust counterforce at the measurement of the rolling loads, the inter-roll thrust force, and the material-roll thrust force that act on a roll other than the
25 backup roll, the rolling-load-difference information being calculated based on the measured work-side and drive-side rolling loads, and performing reduction leveling control on the rolling mill based on the corrected rolling-load-difference information, the tail control step being performed during the rolling of the tail portion of the workpiece. [0011]
30 In the tail control step, the rolling-load-difference information may be corrected
4

based on the roll-axis-direction thrust counterforce measured at the measurement of the
rolling loads and the inter-roll thrust force or the material-roll thrust force acquired in the
estimation step.
[0012]
5 In the estimation step, the inter-roll cross angle, the material-roll cross angle, the
inter-roll friction coefficient, and the material-roll friction coefficient may be acquired through estimation based on rolling loads, rolling reduction rates, and thrust counterforces acting on the roll other than the backup roll at four levels or more acquired from at least any one of the upper and lower roll assemblies, and at least any one of the
10 inter-roll thrust force and the material-roll thrust force may be acquired through estimation based on the acquired inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and material-roll friction coefficient. [0013]
Alternatively, in the estimation step, the inter-roll friction coefficient and the
15 material-roll friction coefficient may be acquired through measurement, the inter-roll cross angle and the material-roll cross angle may be acquired through estimation based on rolling loads, rolling reduction rates, and thrust counterforces acting on the roll other than the backup roll at two levels or more acquired from at least any one of the upper and lower roll assemblies, and at least any one of the inter-roll thrust force and the material-roll
20 thrust force may be acquired through estimation based on the acquired inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and material-roll friction coefficient. [0014]
Alternatively, in the estimation step, the inter-roll cross angle and the
25 material-roll cross angle may be acquired through measurement, the inter-roll friction coefficient and the material-roll friction coefficient may be acquired through estimation based on rolling loads, rolling reduction rates, and thrust counterforces acting on the roll other than the backup roll at two levels or more acquired from at least any one of the upper and lower roll assemblies, and at least any one of the inter-roll thrust force and the
30 material-roll thrust force may be acquired through estimation based on the acquired
5

inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and
material-roll friction coefficient.
[0015]
In the estimation step described above, estimated values, which are acquired 5 through estimation out of the inter-roll cross angle, the material-roll cross angle, the inter-roll friction coefficient, and the material-roll friction coefficient, may be acquired in accordance with predicted values of variations of the estimated values of each workpiece estimated based on a result of past learning and a result of estimating estimated values in last rolling.
10 [0016]
In the estimation step, estimated values, which are acquired through estimation out of the inter-roll cross angle, the material-roll cross angle, the inter-roll friction coefficient, and the material-roll friction coefficient, may be corrected in accordance with a difference between an estimated value based on data on constant portions of workpieces
15 rolled in a past and an estimated value based on data on tail portions of the workpieces. [0017]
In the estimation step, rolling loads, rolling reduction rates, and thrust counterforces acting on a roll other than the backup roll for workpieces rolled recently may be used.
20 [0018]
Alternately, in the estimation step, the inter-roll friction coefficient, the material-roll friction coefficient, the inter-roll cross angle, and the material-roll cross angle may be acquired through measurement, and at least any one of the inter-roll thrust force and the material-roll thrust force may be acquired through estimation based on the
25 acquired inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and material-roll friction coefficient.
ADVANTAGEOUS EFFECTS OF INVENTION
[0019]
30 As described above, according to the present invention, leveling correction can
6

be performed with an influence of the thrust forces on the differential load taken into consideration more accurately.
BRIEF DESCRIPTION OF DRAWINGS 5 [0020]
[Figure 1] Figure 1 is an explanatory diagram illustrating a configuration example of a
four-high rolling mill and a processing device for performing zigzagging control on a
workpiece according to an embodiment of the present invention.
[Figure 2] Figure 2 is a schematic diagram illustrating forces that act in a rolling mill 10 illustrated in Figure 1.
[Figure 3] Figure 3 is a flowchart illustrating an outline of a zigzagging control method
for a workpiece according to an embodiment of the present invention.
[Figure 4] Figure 4 is a flowchart illustrating an example of the zigzagging control
method for a workpiece according to the embodiment. 15 [Figure 5] Figure 5 is a flowchart illustrating a zigzagging control method for a workpiece
in a case where UWM, UWB, <|)WM, and <|)WB are all acquired through estimation (Case 1).
[Figure 6] Figure 6 is a flowchart illustrating a zigzagging control method for a workpiece
in a case where UWM and UWB are acquired through measurement, and <|)WM and (|)WB are
acquired through estimation (Case 6). 20 [Figure 7] Figure 7 is an explanatory diagram illustrating an example of a method for
measuring a friction coefficient.
[Figure 8] Figure 8 is an explanatory diagram illustrating another example of the method
for measuring a friction coefficient.
[Figure 9] Figure 9 is a flowchart illustrating a zigzagging control method for a workpiece 25 in a case where UWM and UWB are acquired through estimation, and <|)WM and <|)WB are
acquired through measurement (Case 11).
[Figure 10] Figure 10 is an explanatory diagram illustrating an example of a method for
measuring a cross angle.
[Figure 11] Figure 11 is a flowchart illustrating a zigzagging control method for a 30 workpiece in a case where UWM, UWB, <|)WM, and (|)WB are all acquired through
7

measurement (Case 16).
DESCRIPTION OF EMBODIMENT
[0021]
5 A preferred embodiment of the present invention will be described below in
detail with reference to the accompanying drawings. In the present specification and drawings, components having substantially the same functions and structures are denoted by the same reference characters, and the repeated description thereof will be omitted. [0022]
10 [1. Configuration of Rolling Mill]
First, a schematic configuration of a rolling mill to which a zigzagging control method for a workpiece according to an embodiment of the present invention is applied will be described with reference to Figure 1. Figure 1 is an explanatory diagram illustrating a configuration example of a four-high rolling mill and a processing device for
15 performing zigzagging control on a workpiece S according to the present embodiment. Although Figure 1 illustrates a four-high rolling mill, the present invention is applicable to a rolling mill of four-high or more with a plurality of rolls including at least a pair of work rolls and at least a pair of backup rolls supporting the work rolls. In Figure 1, in a roll-axis direction, a work side is denoted as WS, and a drive side is denoted as DS. The
20 work side is an operation side and is opposite to the drive side across the rolling mill. [0023]
A rolling mill 10 illustrated in Figure 1 is a four-high rolling mill that includes a pair of work rolls 1 and 2 and a pair of backup rolls 3 and 4 supporting the work rolls 1 and 2. The upper work roll 1 is supported by upper work roll chocks 5a and 5b, and the
25 lower work roll 2 is supported by lower work roll chocks 6a and 6b. The upper backup roll 3 is supported by upper backup roll chocks 7a and 7b, and the lower backup roll 4 is supported by lower backup roll chocks 8a and 8b. The upper work roll 1 and the upper backup roll 3 form an upper roll assembly, and the lower work roll 2 and the lower backup roll 4 form a lower roll assembly. The upper backup roll chocks 7a and 7b, and the lower
30 backup roll chocks 8a and 8b are held by a housing 15.
8

[0024]
The rolling mill 10 illustrated in Figure 1 includes lower load sensors 11a and lib each of which senses a vertical roll load relating to the lower roll assembly. The rolling mill 10 may include, in place of the lower load sensors 11a and lib, upper load 5 sensors each of which senses a vertical roll load relating to the upper roll assembly or may include the upper load sensors together with the lower load sensors 11a and lib. The lower load sensor 11a senses a vertical roll load (rolling load) on the drive side, and the lower load sensor lib senses a vertical roll load (rolling load) on the work side. [0025]
10 Below the lower load sensors 11a and lib, leveling devices 13a and 13b that
apply perpendicularly upward loads to the lower backup roll chocks 8a and 8b, respectively, are provided. The leveling devices 13a and 13b are each constituted by, for example, a hydraulic cylinder and can adjust leveling by moving their hydraulic cylinders in a perpendicular direction.
15 [0026]
In addition, thrust counterforce measurement apparatuses 12a and 12b that measure roll-axis-direction thrust counterforces are installed on the work rolls 1 and 2 of the rolling mill 10, respectively. In the rolling mill 10 illustrated in Figure 1, the thrust counterforce measurement apparatus 12a is provided between the upper work roll chock
20 5a on the work side and the work roll shift device 14a, and the thrust counterforce measurement apparatus 12b is provided between the lower work roll chock 6a on the work side and the work roll shift device 14b. The work roll shift devices 14a and 14b are driving devices for moving the work rolls 1 and 2 in the roll-axis direction, support the upper work roll chock 5a and the lower work roll chock 6a, respectively, and generate
25 counterforces (roll-axis-direction thrust counterforces) that support the inter-roll thrust force and the material-roll thrust force. The roll-axis-direction thrust counterforces measured by the thrust counterforce measurement apparatuses 12a and 12b are output to a differential-load thrust-counterforce acquisition unit 120. [0027]
30 The rolling mill 10 according to the present embodiment includes, as illustrated
9

in Figure 1, an estimation unit 110, the differential-load thrust-counterforce acquisition unit 120, a correction unit 130, and a leveling control unit 140, as a device that performs information processing for performing reduction leveling control by the leveling devices 13a and 13b. The processing device having these functional units may be constituted by 5 generic members and circuits or may be constituted by pieces of hardware that are specialized in the functions of the constituent components. Alternatively, the functions of the constituent components of the processing device may be all fulfilled by a CPU or the like. A configuration used for the processing device can be altered as appropriate in accordance with a technological standard of a time at which the present embodiment is
10 carried out. In addition, a computer program for implementing the functions of the processing device can be fabricated and installed in a personal computer or the like. In addition, a computer-readable recording medium that stores such a computer program can be also provided. The computer program may be distributed, for example, over a network without using a recording medium.
15 [0028]
The estimation unit 110 estimates at least any one of an inter-roll thrust force and a material-roll thrust force generated in the rolling mill before a tail portion of the workpiece S is rolled. The estimation unit 110 calculates an inter-roll cross angle, a material-roll cross angle, an inter-roll friction coefficient, and a material-roll friction
20 coefficient based on rolling loads, rolling reduction rates, and thrust counterforces acting on a roll other than the backup roll at four levels or more acquired from at least any one of the upper and lower roll assemblies and calculates at least any one of the inter-roll thrust force and the material-roll thrust force. As the rolling loads, the rolling reduction rates, and the thrust counterforces acting on the roll other than the backup roll at four levels or
25 more used by the estimation unit 110, actual rolling result data stored in an actual rolling result database 200 may be used. [0029]
The differential-load thrust-counterforce acquisition unit 120 acquires a drive-side rolling load sensed by the lower load sensor 11a and a work-side rolling load
30 sensed by the lower load sensor lib and calculates a rolling load difference or a rolling
10

load difference ratio as rolling-load-difference information. The rolling load difference is a difference between the drive-side rolling load and the work-side rolling load, and the rolling load difference ratio is a ratio of the load difference to a total load (i.e., a sum of the drive-side rolling load and the work-side rolling load) (load difference/total load). 5 The rolling load difference ratio enables elimination of a sensing error attributable to a difference in characteristics between right and left load sensors. With the same centerline deviation, the sensed rolling load difference ratio does not fluctuate if the rolling loads fluctuate due to changes in temperature, sheet width, sheet thickness, and the like. Therefore, by using the rolling load difference ratio, a centerline deviation can be
10 corrected more accurately as compared with a case of using the rolling load difference. [0030]
The correction unit 130 corrects the rolling load difference or the rolling load difference ratio calculated by the differential-load thrust-counterforce acquisition unit 120 based on the measured roll-axis-direction thrust counterforces and the inter-roll
15 thrust force or the material-roll thrust force calculated by the estimation unit 110. This removes a rolling load difference or a rolling load difference ratio attributable to the thrust forces from a rolling load difference or a rolling load difference ratio used in the reduction leveling control. [0031]
20 The leveling control unit 140 controls the leveling devices 13a and 13b. The
leveling control unit 140 performs the reduction leveling control using the rolling load difference or the rolling load difference ratio corrected by the correction unit 130. The reduction leveling control can be performed by using a well-known method such as reduction leveling control described in Patent Document 1 described above.
25 [0032]
[2. Calculation of Rolling Load Difference attributable to Thrust Forces]
In the zigzagging control method for a workpiece according to the present embodiment, the reduction leveling control is performed with a rolling load difference or a rolling load difference ratio from which a component attributable to the thrust forces
30 serving as disturbance is removed. To take the load difference attributable to the thrust
11

forces into consideration for such reduction leveling control, it is necessary to acquire two or more values of the inter-roll thrust force, the material-roll thrust force, and the roll-axis-direction thrust counterforce acting on the work roll through measurement or estimation. Of these, the roll-axis-direction thrust counterforce is measurable. In 5 contrast, the inter-roll thrust force and the material-roll thrust force cannot be measured, and thus it is necessary to acquire at least any one of them through estimation. To do so, it is necessary to acquire the inter-roll cross angle, the material-roll cross angle, the inter-roll friction coefficient, and the material-roll friction coefficient through measurement or estimation.
10 [0033]
Hereinafter, a method for calculating the rolling load difference attributable to the thrust forces in accordance with patterns of acquiring the material-roll cross angle, the inter-roll cross angle, the material-roll friction coefficient, and the inter-roll friction coefficient will be described in detail with reference to Figure 2. Figure 2 is a schematic
15 diagram illustrating forces that act in the rolling mill 10 illustrated in Figure 1. Although Figure 2 illustrates only forces that act in the lower roll assembly, the description holds true for the upper roll assembly. [0034]
A material-roll friction coefficient UWM, an inter-roll friction coefficient OWB, a
20 material-roll cross angle <|>WM, and an inter-roll cross angle <|)WB are acquired through estimation or measurement. Specifically, 16 cases shown in Table 1 below are possible. Table 1 also shows formulas for determining a material-roll thrust force TWM3, an inter-roll thrust force TWBB, and a thrust counterforce Tw8 acting on the lower work roll chocks 6a and 6b.
25 [0035] [Table 1] Table 1

Case U WM A* WB 0WM 0WB T B 1 WM T B 1 WB T B 1 w
1 • • • • Formula(5a) Formula(6a) Formula(7a)
2 o • • • Formula(5b) Formula(6a) Formula(7e)
3 • o • • Formula(5a) Formula(6b) Formula(7f)
12

4 • • o • Formula(5c) Formula(6a) Formula(7g)
5 • • • o Formula(5a) Formula(6c) Formula(7h)
6 o o • • Formula(5b) Formula(6b) Formula(7b)
7 o • o • Formula(5d) Formula(6a) Formula(7i)
8 o • • o Formula(5b) Formula(6c) Formula(7j)
9 • o o • Formula(5c) Formula(6b) Formula(7k)
10 • o • o Formula(5a) Formula(6d) Formula(71)
11 • • o o Formula(5c) Formula(6c) Formula(7c)
12 o o o • Formula(5d) Formula(6b) Formula(7m)
13 o o • o Formula(5b) Formula(6d) Formula(7n)
14 o • o o Formula(5d) Formula(6c) Formula(7o)
15 • o o o Formula(5c) Formula(6d) Formula(7p)
16 o o o o Formusla(5d) Formula(6d) Formula(7d)
• :estimation, O :measurement
[0036]
The following four cases will be described below.
(Case 1) UWM, UWB, <|>WM, and (|)WB are all acquired through estimation
5 (Case 6) UWM and UWB are acquired through measurement, and <|)WM and (|)WB are
acquired through estimation
(Case 11) UWM and UWB are acquired through estimation, and <|)WM and (|)WB are acquired through measurement
(Case 16) UWM, UWB, <|>WM, and (|>WB are all acquired through measurement
10 After these four cases have been described, the other cases will be described.
[0037]
[2-1. Case where UWM, UWB, <|>WM, and (|)WB are all acquired through estimation (Case 1)] First, a method for calculating the rolling load difference attributable to the thrust forces in a case where UWM, UWB, <|>WM, and <|>WB are all acquired through estimation 15 (Case 1) will be described. In Figure 2, equilibrium of forces in the roll-axis direction acting on the lower work roll 2, equilibrium of forces in the roll-axis direction acting on the lower backup roll 4, and equilibrium of moments in the lower roll assembly are expressed by the following Formulas (1) to (3). [0038] 20 [Expression 1]
13

*WB — l w "•"i tew ,,.

r
5 TT £

(2) (3)

[0039]
5 Symbols represent the following components.
TWBB: Thrust force that acts between the lower work roll 2 and the lower backup roll 4 (inter-roll thrust force)
TWM3: Thrust force that acts between the lower work roll 2 and the workpiece S
(material-roll thrust force)
10 Tw8: Thrust counterforce that acts on the lower work roll chocks 6a and 6b
TBB: Thrust counterforce that acts on the lower backup roll chocks 8a and 8b PTdfB: Load difference attributable to the thrust forces a: span between rolling supports
1IBB: Working point position of a thrust counterforce that acts on the lower 15 backup roll chocks 8a and 8b
DB: Diameter of the lower backup roll 4 Dw: Diameter of the lower work roll 2 [0040]
By removing TBB from the above Formulas (1) to (3), PTdfB can be expressed by 20 any one of the following Formulas (4-1) to (4-3). [0041]
[Expression 2]
PL" = aTWMB + PTWBB ...(4-1)
P&B = (a + fi)TWBB - (1TWB ... (4-2)
25 PTJ = (a + fl)TWMB + $TWB ■ ■ ■ (4-3)
Here,
14

10

Dw DB+Dw + 2hBB
a = —,P =
a a
[0042]
This shows that, as described above, at least any one of the material-roll thrust force TWM8 and the inter-roll thrust force TWBB needs to be estimated to determine the rolling load difference PTdfB attributable to the thrust forces. [0043]
Here, the material-roll thrust force TWM8 and the inter-roll thrust force TWBB are expressed by, for example, the following Formulas (5a) and (6a) according to Non Patent Document 1. [0044] [Expression 3]

TWM — ZH-WMQWMYL*1

'Q.5 + V(0^My)2 + O.25N \4>WMY
P = Tl
WM yH-WM' 0WM' P> r)
...(5a)

WB
PWBPO
TWB — ih/B"

1-

1-

tan0
\GW GBJ

2
► P — TWB \}LWB> P)

15

(6a)

[0045]

20 roll 4
roll 4
25

Symbols represent the following components.
UWM: Friction coefficient between the lower work roll 2 and the workpiece S
OWB: Friction coefficient between the lower work roll 2 and the lower backup
<|>WM: Cross angle between the lower work roll 2 and the workpiece S
(|)WB: Inter-roll cross angle between the lower work roll 2 and the lower backup
y = (l-r)/r (r: rolling reduction rate) Gw: Modulus of rigidity of a work roll GB: Modulus of rigidity of a backup roll

15

po: Maximum contact pressure between rolls
P: Rolling load [0046]
That is, it is understood that calculation of the material-roll thrust force TWM8 5 requires the friction coefficient UWM between the lower work roll 2 and the workpiece S, the cross angle <|)WM between the lower work roll 2 and the workpiece S, the rolling load P, and the rolling reduction rate r. It is also understood that calculation of the inter-roll thrust force TWBB requires the friction coefficient UWB between the lower work roll 2 and the lower backup roll 4, the inter-roll cross angle <|)WB between the lower work roll 2 and 10 the lower backup roll 4, and the rolling load P. [0047]
Therefore, with Formula (1), the thrust counterforce Tw8 acting on the lower work roll chocks 6a and 6b can be expressed by the following Formula (7a). [0048] 15 [Expression 4]
Tw = TWB — TWM = f \}IWM> H-WB> 0WM' $WB> P> r)
...(7a) [0049]
In Formula (7a), the rolling load P and the rolling reduction rate r can be
20 acquired in a form of their actual values or their setting values. In contrast, the friction coefficient UWM between the lower work roll 2 and the workpiece S, the friction coefficient UWB between the lower work roll 2 and the lower backup roll 4, the cross angle <|)WM between the lower work roll 2 and the workpiece S, and the inter-roll cross angle <|)WB between the lower work roll 2 and the lower backup roll 4 are unknowns. In order to
25 determine the four unknowns, the thrust counterforce Tw8 acting on the lower work roll chocks 6a and 6b is to be measured for combinations of the rolling load P and the rolling reduction rate r at four levels or more. At fifth and subsequent levels, the material-roll thrust force TWM8 and the inter-roll thrust force TWBB can be acquired from the above Formulas (5a) and (6a) with values of the unknowns determined at the four levels and the
30 rolling load P and the rolling reduction rate r at the fifth and subsequent levels.
16

10
15

[0050]
By using the material-roll thrust force TWM3 and the inter-roll thrust force TWBB acquired in this manner, and the measured roll-axis-direction thrust counterforce, the load difference PTdfB attributable to the thrust forces can be calculated from any one of the above Formulas (4-1) to (4-3). [0051]
[2-2. Case where (IWM and (IWB are acquired through measurement, and <|)WM and (|)WB are acquired through estimation (Case 6)]
Next, a method for calculating the rolling load difference attributable to the thrust forces in a case where \IWM and \IWB are acquired through measurement, and <|>WM and (|)WB are acquired through estimation (Case 6) will be described. In this case, the material-roll thrust force TWM8 and the inter-roll thrust force TWBB that are expressed by Formulas (5a) and (6a) in Case 1 are expressed by the following Formulas (5b) and (6b). [0052] [Expression 5]

WM
TWM — 2^%M0wM7m

'Q.5 + V(0^My)2 + O.25N \4>WMY
P = Tl

\WM> P> r)

(5b)

WB
WB
PWBPO
TWB — V-WB H

1-

1-

tan0
\GW GBJ

>P = T

'(bra, p)

(6b)
20 [0053]

25

That is, it is understood that calculation of the material-roll thrust force TWM8 requires the cross angle <|)WM between the lower work roll 2 and the workpiece S, the rolling load P, and the rolling reduction rate r. It is also understood that calculation of the inter-roll thrust force TWBB requires the inter-roll cross angle <|)WB between the lower work roll 2 and the lower backup roll 4, and the rolling load P. [0054]
Therefore, with Formula (1), the thrust counterforce Tw3 acting on the lower

17

work roll chocks 6a and 6b can be expressed by the following Formula (7b).
[0055]
[Expression 6]
Tw = TWB — TWM = f \jt>wM> QWB* P> r)
5 ...(7b)
[0056]
In Formula (7b), the rolling load P and the rolling reduction rate r can be acquired in a form of their actual values or their setting values. In contrast, the cross angle <|)WM between the lower work roll 2 and the workpiece S, and the inter-roll cross
10 angle <|)WB between the lower work roll 2 and the lower backup roll 4 are unknowns. In order to determine the two unknowns, the thrust counterforce Tw3 acting on the lower work roll chocks 6a and 6b is to be measured for combinations of the rolling load P and the rolling reduction rate r at two levels or more. At third and subsequent levels, the material-roll thrust force TWM8 and the inter-roll thrust force TWBB can be acquired from
15 the above Formulas (5b) and (6b) with values of the unknowns determined at the two levels and the rolling load P and the rolling reduction rate r at the third and subsequent levels. [0057]
By using the material-roll thrust force TWM8 and the inter-roll thrust force TWBB
20 acquired in this manner, and the measured roll-axis-direction thrust counterforce, the load difference PTdfB attributable to the thrust forces can be calculated from any one of the above Formulas (4-1) to (4-3). [0058] [2-3. Case where UWM and UWB are acquired through estimation, and <|>WM and <|)WB are
25 acquired through measurement (Case 11)]
Next, a method for calculating the rolling load difference attributable to the thrust forces in a case where UWM and UWB are acquired through estimation, and <|)WM and <|)WB are acquired through measurement (Case 11) will be described. In this case, the material-roll thrust force TWM8 and the inter-roll thrust force TWBB that are expressed by
30 Formulas (5a) and (6a) in Case 1 are expressed by the following Formulas (5c) and (6c).
18

[0059] [Expression 7]
\ H-WB> P > r)
...(7c) [0063]
In Formula (7c), the rolling load P and the rolling reduction rate r can be acquired in a form of their actual values or their setting values. In contrast, the friction coefficient UWM between the lower work roll 2 and the workpiece S, and the friction coefficient UWB between the lower work roll 2 and the lower backup roll 4 are unknowns. In order to determine the two unknowns, the thrust counterforce Tw8 acting on the lower work roll chocks 6a and 6b is to be measured for combinations of the rolling load P and the rolling reduction rate r at two levels or more. At third and subsequent levels, the

19

material-roll thrust force TWM8 and the inter-roll thrust force TWBB can be acquired from
the above Formulas (5c) and (6c) with values of the unknowns determined at the two
levels and the rolling load P and the rolling reduction rate r at the third and subsequent
levels. 5 [0064]
By using the material-roll thrust force TWM8 and the inter-roll thrust force TWBB
acquired in this manner, and the measured roll-axis-direction thrust counterforce, the load
difference PTdfB attributable to the thrust forces can be calculated from any one of the
above Formulas (4-1) to (4-3). 10 [0065]
[2-4. Case where UWM, UWB, <|>WM, and (|)WB are all acquired through measurement (Case
16)]
Next, a method for calculating the rolling load difference attributable to the
thrust forces in a case where UWM, UWB, <|)WM, and (|)WB are all acquired through 15 measurement (Case 16) will be described. In this case, the material-roll thrust force
TWM8 and the inter-roll thrust force TWBB that are expressed by Formulas (5a) and (6a) in
Case 1 are expressed by the following Formulas (5d) and (6d).
[0066]
[Expression 9]

WM
20 TWM = 2nWM(J)WMY\n

'Q.5 + V(0^My)2 + O.25N \4>WMY
P = T<

'{P. r)

(5d)

WB
TwB — V-WB H

1-

1-

A zigzagging control method for a workpiece in a rolling mill of four-high or 5 more,
the rolling mill including a plurality of rolls that include at least a pair of work rolls and at least a pair of backup rolls supporting the work rolls,
an upper roll assembly including an upper work roll and an upper backup roll,
a lower roll assembly including a lower work roll and a lower backup roll,
10 the zigzagging control method comprising:
an estimation step of acquiring at least any one of an inter-roll thrust force estimated based on an inter-roll cross angle and an inter-roll friction coefficient that are acquired through measurement or estimation and a material-roll thrust force estimated based on a material-roll cross angle and a material-roll friction coefficient that are 15 acquired through measurement or estimation, the estimation step being performed before rolling of a tail portion of the workpiece; and
a tail control step of measuring work-side and drive-side rolling loads of at least any one of the upper and lower roll assemblies, correcting rolling-load-difference information based on any two of acquired parameters including a roll-axis-direction 20 thrust counterforce at the measurement of the rolling loads, the inter-roll thrust force, and the material-roll thrust force that act on a roll other than the backup roll, the rolling-load-difference information being calculated based on the measured work-side and drive-side rolling loads, and performing reduction leveling control on the rolling mill based on the corrected rolling-load-difference information, the tail control step being 25 performed during the rolling of the tail portion of the workpiece.
[Claim 2]
The zigzagging control method for a workpiece according to claim 1, wherein in the tail control step, the rolling-load-difference information is corrected based 30 on the roll-axis-direction thrust counterforce measured at the measurement of the rolling
47

loads and the inter-roll thrust force or the material-roll thrust force acquired in the estimation step.
[Claim 3]
5 The zigzagging control method for a workpiece according to claim 1 or 2,
wherein
in the estimation step, the inter-roll cross angle, the material-roll cross angle, the
inter-roll friction coefficient, and the material-roll friction coefficient are acquired
through estimation based on rolling loads, rolling reduction rates, and thrust
10 counterforces acting on a roll other than the backup roll at four levels or more acquired
from at least any one of the upper and lower roll assemblies, and
at least one of an inter-roll thrust force and a material-roll thrust force is acquired through estimation based on the acquired inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and material-roll friction coefficient. 15
[Claim 4]
The zigzagging control method for a workpiece according to claim 1 or 2, wherein
in the estimation step,
20 an inter-roll friction coefficient and a material-roll friction coefficient are
acquired through measurement, and an inter-roll cross angle and a material-roll cross
angle are acquired through estimation based on rolling loads, rolling reduction rates, and
thrust counterforces acting on a roll other than the backup roll at two levels or more
acquired from at least any one of the upper and lower roll assemblies, and
25 at least one of an inter-roll thrust force and a material-roll thrust force is acquired
through estimation based on the acquired inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and material-roll friction coefficient.
[Claim 5]
30 The zigzagging control method for a workpiece according to claim 1 or 2,
48

wherein
in the estimation step,
an inter-roll cross angle and a material-roll cross angle are acquired through
measurement, and an inter-roll friction coefficient and a material-roll friction coefficient
5 are acquired through estimation based on rolling loads, rolling reduction rates, and thrust
counterforces acting on a roll other than the backup roll at two levels or more acquired
from at least any one of the upper and lower roll assemblies, and
at least one of an inter-roll thrust force and a material-roll thrust force is acquired through estimation based on the acquired inter-roll cross angle, material-roll cross angle, 10 inter-roll friction coefficient, and material-roll friction coefficient.
[Claim 6]
The zigzagging control method for a workpiece according to any one of claims 1 to 5, wherein
15 in the estimation step, estimated values, which are acquired through estimation
out of the inter-roll cross angle, the material-roll cross angle, the inter-roll friction coefficient, and the material-roll friction coefficient, are acquired in accordance with predicted values of variations of the estimated values of each workpiece estimated based on a result of past learning and a result of estimating estimated values in last rolling.
20
[Claim 7]
The zigzagging control method for a workpiece according to any one of claims 1 to 6, wherein
in the estimation step, estimated values, which are acquired through estimation
25 out of the inter-roll cross angle, the material-roll cross angle, the inter-roll friction coefficient, and the material-roll friction coefficient, are corrected in accordance with a difference between an estimated value based on data on constant portions of workpieces rolled in a past and an estimated value based on data on tail portions of the workpieces.
30 [Claim 8]
49

The zigzagging control method for a workpiece according to any one of claims 1 to 7, wherein
in the estimation step, rolling loads, rolling reduction rates, and thrust counterforces acting on a roll other than the backup roll for workpieces rolled recently are 5 used.
[Claim 9]
The zigzagging control method for a workpiece according to claim 1 or 2,
wherein
10 in the estimation step,
the inter-roll friction coefficient, the material-roll friction coefficient, the inter-roll cross angle, and the material-roll cross angle are acquired through measurement, and
at least any one of an inter-roll thrust force and a material-roll thrust force is 15 acquired through estimation based on the acquired inter-roll cross angle, material-roll cross angle, inter-roll friction coefficient, and material-roll friction coefficient.