AU2010351732B2 - Gage controller, gage control method, and gage control program - Google Patents

Abstract

The disclosed device comprises: a rolling load detection means (6) which detects the rolling load on a metallic material; a rolling load vertical distribution means (10) which vertically distributes the detected rolling load on the basis of a comparison of an upper side rolling load being generated by an upper side roller set and a lower side rolling load being generated by a lower side roller set; a rolling load vertical change amount extraction means (11) which extracts an upper side rolling load change amount and a lower side rolling load change amount generated in relation to the rotational position of the upper side roller set and the lower side roller set, on the basis of the vertically distributed rolling loads of the upper side roller set and the lower side roller set; a manipulation amount calculation means (12) which calculates a work roller gap command amount between an upper side work roller (3a) and a lower side work roller (3b), on the basis of the extracted upper side rolling load change amount and lower side rolling load change amount; and a roller gap manipulation means (13) which manipulates the work roller gap between the upper side work roller (3a) and the lower side work roller (3b), on the basis of the calculated work roller gap command amount.

Description

1 JTSBME-19-PCT DESCRIPTION Title: GAGE CONTROLLER, GAGE CONTROL METHOD, AND GAGE CONTROL 5 PROGRAM Technical Field [0001] Embodiments described herein generally relate to a gage controller, a gage control method, and a gage control program for metallic material rolling mills, adapted to control 10 variations of gage such as those due to a so-called roll eccentricity developed in association with a position in rotation of a work roll or such in an implementation of gage controller, gage control method, or gage control program. Background Art [0002] 15 As one of quality controls performed in strip rolling or plate rolling, there is an automatic gage control (AGC) employed to control a gage at a transversely central zone of a rolling material. For the gage control, methods employed include a monitor AGC feeding back a process value on a gage meter installed at a rolling mill delivery side, a gage meter AGC (GM-AGC) using a gage meter thickness estimated from a rolling force or a roll gap (as a gap 20 between upper and lower work rolls), a mill modulus control (MMC) as a mill modulus variable control using rolling forces, etc. [0003] As disturbances inhibiting the enhancement of gage precision in the hot rolling there are variations in temperature of a rolling material. As disturbances common to the hot rolling 25 and the cold rolling, there are variations in tension due to a deterioration of another control, e.g., a tension control, changes in roll gap or speed due to an intervening manipulation by an operator, roll eccentricities due to non-conforming precisions in the structure of rolls or roll grinding, etc. [0004] Among them, roll eccentricities are caused when keyways at the backup rolls that 30 have oil bearings receive large rolling forces ranging from several hundred tons to two or three 2 thousand tons, whereby the shafts are moved up and down, making the roll gap vary as the rolls rotate. Though, even at rolls having no keyways, the roll gap varies in dependence on roll rotation from causes such as an asymmetric diversity in roll grinding, or a biased thermal expansion. 5 [0005] It is noted that the following discussion is likewise applicable to any one of those cases including the case of a so-called 21i mill composed of simply 2 work rolls being an upper and a lower, the case of a so-called 4Hi mill composed of 4 rolls having 2 work rolls being an upper and a lower and 2 backup rolls being a top and a bottom, and the case of a so-called 6Hi mill 10 composed of 6 rolls having 2 work rolls being an upper and a lower, 2 middle rolls being an upper and a lower, and 2 backup rolls being a top and a bottom, as well as other cases. For the sake of notation, work rolls are each referred to as a work roll (sometimes abbreviated to WR), and rolls other than work rolls are each referred to as a backup roll (sometimes abbreviated to BUR). 15 [0006] Roll gap detectors are unable to detect disturbances depending on axial run-outs of rolls, such as roll eccentricities. There is a device for setting up a roll gap by using a detection value fed back from a roll gap detector. This is done for a control to attain a given gap. However, since no axial run-outs of rolls appear in the detection value, the control gets 20 unsuccessful. Though, disturbances depending on axial run-outs of rolls give variations in actual roll gap, thus appearing in rolling forces. For this reason, they constitute significant disturbances such as those in the MMC and the GM-AGC making use of rolling forces. [0007] To reduce disturbances depending on axial run-outs of rolls, such as roll eccentricities, 25 there has been proposed a gage controller adapted for e.g. provision to a rolling mill for rolling a metallic material, to control gage variations due to roll eccentricities of upper and lower work rolls and upper and lower backup rolls (refer to e.g. PTL I below). The gage controller included a rolling force detector, a kissing roll force variation extractor, a rolling force upper and lower variation extractor, a manipulative variable calculator, and a roll gap manipulator. The 30 rolling force detector was operable to detect a kissing roll force and a rolling force. The 3 kissing roll force variation extractor was operable to take kissing roll forces detected by the rolling force detector at rotational positions of upper and lower work rolls and upper and lower backup rolls, as bases to separately extract, with respect to the kissing roll forces, variation components due to roll eccentricities of the upper work roll and the upper backup roll at 5 respective rotational positions and variation components due to roll eccentricities of the lower work roll and the lower backup roll at respective rotational positions. The rolling force upper and lower variation extractor was operable to take variation components of kissing roll forces separately extracted by the kissing roll force variation extractor, as bases to separately extract, with respect to rolling forces detected by the rolling force detector at respective rotational 10 positions, variation components due to roll eccentricities of the upper work roll and the upper backup roll at respective rotational positions and variation components due to roll eccentricities of the lower work roll and the lower backup roll at respective rotational positions. 'Te manipulative variable calculator was operable to take variation components of rolling forces separately extracted by the rolling force upper and lower variation extractor, as bases to calculate 15 roll gap command values associated with respective rotational positions to reduce gage variations of a rolling material being rolled. The roll gap manipulator was operable to take roll gap command values calculated by the manipulative variable calculator, as bases to manipulate roll gaps associated with respective rotational positions. The gage controller was thereby adapted for an ensured separation between rolling force variations developed as the upper rolls 20 rotate and rolling force variations developed as the lower rolls rotate, to control a roll gap in accordance with a respective separated rolling force variation. Citation List Patent Literature [0008] 25 PTL 1: W02008/090596 Summary Problem [0009] By the way, there may be upper and lower backup rolls having different diameters. 30 In that case, the upper and lower backup rolls have different rotation speeds, producing the 4 phenomena of a so-called beat, which deteriorates the control performance. [0010] Description is now made of the way how the beat is produced. Suppose upper and lower backup rolls having diameters different from each other. Letting owr [rad/s] be a rotation 5 frequency of the upper backup roll, and OB [rad/s] be a rotation frequency of the lower backup roll, set the upper and lower amplitudes to be a unity, assuming no initial phase difference, for simplicity. Then, superimposed rotations of the upper and lower backup rolls have a resultant signal Y, as follows: [Math 1] 10 Y = sin ot +sin oBt = 2sin 09T OfB t IcoST -B .. .(expression 1) [0011] The sine wave (as the 'sin' factor) has a frequency of r + OB [rad/s]. This is an increased frequency, at which small vibrations appear with a short period. On the other hand, the cosine wave (as the 'cos' factor) has a frequency of Wir- oB [rad/s]. This is a decreased 15 frequency, at which large vibrations appear with a long period. [0012] Fig. 8(A) shows waveforms of the sin (or t) (solid line) and the cos (o t) (broken line), as examples, respectively. The frequencies are assumed such that oyr = 5 rad/s, and OB = 4 rad/s. Fig. 8(B) shows a waveform of a superimposition (solid line) between the sin (wr t) 20 and the cos (o t), and a waveform of the factor cos{(r- oB) t/2} (broken line), as examples, respectively. The horizontal axes each represent a time (s). It will be seen that the waveform of the superimposition has an envelope curve constituting a long-period wave (broken line). [0013] However, the gage controller proposed in PTL I employed both of a so-called kissing 25 roll force produced by upper and lower work rolls brought into contact with each other in their non-rolling states, and a rolling force produced in their rolling states, to make a separation between roll eccentric components developed at an upper backup roll and roll eccentric components developed at a lower backup roll. This needed measuring a kissing roll force while non-roling, taking the more time and efforts, as a problem.

5 [0014] To this point, it is an object of embodiments herein to provide a gage controller, a gage control method, and a gage control program adapted to manipulate a roll gap at a roll stand by using a rolling force measured while rolling, without using kissing roll forces. 5 Solution [0015] To achieve the object, according to a first aspect of embodiments of the gage controller, them is provided a gage controller adapted to control variations in a gage of a rolling material to be manufactured by rolling a metallic material between an upper roll set being a set of upper 10 rolls and a lower roll set of lower work roll and backup roll. This gage controller includes a rolling force detector, a rolling force upper and lower distributor, a rolling force upper and lower variation value extractor, a manipulative variable calculator, and a roll gap manipulator. The rolling force detector is configured to detect a rolling force to the metallic material. The rolling force upper and lower distributor is configured to make, with respect to a rolling force detected 15 by the rolling force detector, an upper and lower distribution based on a ratio between an upper rolling force being produced at the upper roll set and a lower rolling force being produced at the lower roll set. The rolling force upper and lower variation value extractor is configured to take the rolling forces of the upper roll set and the lower roll set distributed to be the upper and the lower by the rolling force upper and lower distributor, as bases to extract an upper rolling force 20 variation value and a lower rolling force variation value developed in association with a rotational position of the upper roll set and the lower roll set. The manipulative variable calculator is configured to take a combination of the upper rolling force variation value and the lower rolling force variation value extracted by the rolling force upper and lower variation value extractor, as a basis to calculate a work roll gap command value between the upper work roll 25 and the lower work roll. The roll gap manipulator is configured to take the work roll gap command value calculated by the manipulative variable calculator, as a basis to manipulate a work roll gap between the upper work roll and the lower work roll. [0016] To achieve the object, according to a second aspect of embodiments of the gage 30 controller, the manipulative variation calculator is configured to be operable until rotation of the 6 upper roll set and the lower roll set exceeds a prescribed time, to take a combination of the upper rolling force variation value and the lower rolling force variation value separately extracted by the rolling force upper and lower variation value extractor, as a basis to calculate a work roll gap command value between the upper work roll and the lower work roll, and after rotation of the 5 upper roll set and the lower roll set has exceeded the prescribed time, to identify respective roll eccentric amounts of upper and lower backup rolls based on integrated values of the rolling force variation values calculated by the rolling force upper and lower variation value extractor, and calculate a work roll gap command value between the upper work roll and the lower work roll based on identified roll eccentric amounts. 10 [0017] To achieve the object, according to a third aspect of embodiments of the gage controller, the rolling force upper and lower distributor is configured to have the ratio for the upper and lower distribution of the rolling force detected by the rolling force detector, set to a 0.5 immediately after a replacement of the backup rolls, and set up for a subsequent or later 15 rolling material after the replacement of the backup rolls, based on a deviation of the rolling force at the manipulative variable calculator with respect to a current rolling material. [0018] To achieve the object, according to a fourth aspect of embodiments of the gage controller, the rolling force upper and lower distributor is configured to have the ratio for the 20 upper and lower distribution of the rolling force detected by the rolling force detector, set to a 0.5 immediately after a replacement of the backup rolls, and set up for a subsequent or later rolling material after the replacement of the backup rolls, by using integrated values of the rolling force variation values at the manipulative variable calculator with respect to a current rolling material for identification of an amplitude of a periodic function, as a ratio to a sum in 25 value of an amplitude associated with the upper roll set and an amplitude associated with the lower roll set. [0019] To achieve the object, according to an aspect of embodiments of the gage control method, there is provided a gage control method of controlling variations in a gage of a rolling 30 material to be manufactured by rolling a metallic material between an upper roll set being a set 7 of upper rolls and a lower roll set of lower work roll and backup roll. This gage control method includes a step of detecting a rolling force to the metallic material, a step of making, with respect to a rolling force as detected, an upper and lower distribution based on a ratio between an upper rolling force being produced at the upper roll set and a lower rolling force 5 being produced at the lower roll set, a step of taking the rolling forces of the upper roll set and the lower roll set distributed to be the upper and the lower, as bases to extract an upper rolling force variation value and a lower rolling force variation value developed in association with a rotational position of the upper roll set and the lower roll set, a step of taking a combination of the upper rolling force variation value and the lower rolling force variation value as extracted, as 10 a basis to calculate a work roll gap command value between the upper work roll and the lower work roll, and a step of taking the work roll gap command value as calculated, as a basis to manipulate a work roll gap between the upper work roll and the lower work roll. [0020] To achieve the object, according to an aspect of embodiments of the gage control 15 program, there is provided a gage control program adapted to have a computer execute controlling variations in a gage of a rolling material to be manufactured by rolling a metallic material between an upper roll set being a set of upper rolls and a lower roll set of lower work roll and backup roll. This gage control program includes, for the computer to execute, a step of detecting a rolling force to the metallic material, a step of making, with respect to a rolling 20 force as detected, an upper and lower distribution based on a ratio between an upper rolling force being produced at the upper roll set and a lower rolling force being produced at the lower roll set, a step of taking the rolling forces of the upper roll set and the lower roll set distributed to be the upper and the lower, as bases to extract an upper rolling force variation value and a lower rolling force variation value developed in association with a rotational position of the upper roll 25 set and the lower roll set, a step of taking a combination of the upper rolling force variation value and the lower rolling force variation value as extracted, as a basis to calculate a work roll gap command value between the upper work roll and the lower work roll, and a step of taking the work roll gap command value as calculated, as a basis to manipulate a work roll gap between the upper work roll and the lower work roll. 30 Advantageous Effects 8 [0021] According to embodiments herein, it is allowed to extract rolling force variation components such as those due to roll eccentricities, i.e., variation components of rolling forces developed in association with roll rotational positions such as those due to roll eccentricities, by 5 using a rolling force measured while rolling a metallic material, without using kissing roll forces, Brief Description of Drawings [0022] Fig. 1 is a configuration diagram showing an entirety of a gage controller according to 10 an example I of embodiment. Fig. 2 is a graph showing the concept of a rolling force to be measured in the gage controller according to the example 1 of embodiment. Fig. 3 is an illustration showing divisions at upper and lower backup rolls and their relations to upper and lower work rolls, as they are provided in the gage controller according to 15 the example 1 of embodiment. Fig. 4 is a graph showing a rolling force varying with variations of a backup roll rotational angle in an example of method of extracting varying fractions of a rolling force such as those due to roll eccentricities. Fig. 5 is a diagram showing details of an example of configuration including a 20 combination of a rolling force upper and lower variation extractor and a manipulative variable calculator provided in the gage controller according to the example I of embodiment. Fig. 6 is a graph showing how upper and lower backup rolls rotate. Fig. 7 is an explanatory diagram showing variations of values stored in adders for an upper backup roll in a gage controller according to an example 2 of embodiment. 25 Fig. 8 is an explanatory diagram showing a state of beat. Description of Embodiments [00231 (Example 1) Fig. I shows in a configuration diagram an entirety of a gage controller according to 30 an example I of embodiment.

9 [0024] In Fig. 1, the gage controller according to the example 1 of embodiment is provided as a controller involving a rolling mill to roll a rolling material I made of a metallic material. This controller includes a housing 2, a work roll composed of an upper work roll 3a and a lower 5 work roll 3b, and a backup roll 4 composed of an upper backup roll 4a and a lower backup roll 4b. The controller has a screw down device 5 for applying rolling forces to the rolling material 1, a rolling force detector 6 for detecting a rolling force, a roll revolution detector 7 for detecting a revolution number of a roll, a roll reference position detector 8 for detecting a prescribed reference position every cycle of one revolution of the backup roll 4a or 4b, and a roll gap 10 detector 9 for detecting a gap between the work rolls 3a and 3b, that is, a roll gap. Here, the upper work roll 3a and the upper backup roll 4a constitute an upper roll set in embodiments herein, and the lower work roll 3b and the lower backup roll 4b constitute a lower roll set in embodiments herein. [0025] 15 Further, as shown in Fig. 1, the gage controller according to the example I of embodiment includes a rolling force upper and lower distributor 10, a rolling force upper and lower variation extractor 11, a manipulative variable calculator 12, and a roll gap manipulator 13. [0026] 20 The rolling force upper and lower distributor 10 is operable to make, with respect to rolling forces detected by the rolling force detector 6 at rotational positions of the work rolls 3a and 3b and the backup rolls 4a and 4b, an upper and lower distribution based on ratios taken between upper rolling forces produced at the upper roll set being the upper work roll 3a and the upper backup roll 4a, and lower rolling forces produced at the lower roll set being the lower 25 work roll 3b and the lower backup roll 4b. [0027] The rolling force upper and lower variation extractor 11 is operable to take rolling forces at the upper roll set and the lower roll set, as they are distributed to be upper and lower by the rolling force upper and lower distributor 10, as bases to extract upper rolling force variation 30 values and lower rolling force variation values developed in association with rotational positions 10 of the upper roll set and the lower roll set, respectively. [0028] The manipulative variable calculator 12 is operable to take upper and lower variation components of rolling forces separately extracted by the rolling force upper and lower variation 5 extractor 11, as bases to calculate roll gap command values associated with the rotational positions so as to reduce gage variations of a rolling material I being rolled. [0029] The roll gap manipulator 13 is operable to take roll gap command values calculated by the manipulative variable calculator 12, as bases to manipulate roll gaps associated with the 10 rotational positions. Also, the roll gap manipulator 13 is operable for an addition between a magnitude of roll gap determined by e.g. an MMC or GM-AGC and a magnitude of roll gap correction calculated by the manipulative variable calculator 12, to take a resultant value as a set point of roll gap, to control the screw down device 5. [0030] 15 It is noted the description below is made of the case of a 4Hi mill composed of 4 rolls having 2 work rolls being an upper and a lower and 2 backup rolls being a top and a bottom. This is taken as an example that is in no way restrictive. Accordingly, the discussion is likewise applicable also to the case of a so-called 2Hi mill composed of simply 2 work rolls being an upper and a lower, and the case of a so-called 6Hi mill composed of 6 rolls having 2 20 work rolls being an upper and a lower, 2 middle rolls being an upper and a lower, and 2 backup rolls being a top and a bottom, as well as other cases. [0031] In the gage controller according to the example I of embodiment configured as described, the rolling material 1 is rolled between the work rolls 3a and 3b that have a roll gap 25 and a speed adjusted as necessary to provide a preferable thickness at the delivery side. Here, the work rolls 3a and 3b are arranged so that the work roll 3a, 3b is supported from above by the upper backup roll 4a and the lower work roll 3a, 3b is supported from below by the lower backup roll 4b, to minimize deflections in the roll width direction. Further, the backup rolls 4a and 4b are bom to be rotatable relative to the mill housing 2, with a structure sufficiently 30 endurable even to rolling forces to be exerted on the rolling material 1.

1 [0032] As implements available as the screw down device 5 there are two types: one using an electric motor control (referred to as an electric motor screw down device), the other using a hydraulic control (referred to as a hydraulic screw device). For the response to be faster, the 5 hydraulic reduction is easier to implement. It therefore is typical to employ the hydraulic reduction capable of a fast response for implementation of the rolling force control to be adaptive to handle wave components of as short periods as those in disturbances due to roll eccentricities. Moreover, the work rolls 3a and 3b have a gap in between, that is, a roll gap, which is adjusted by the screw down device 5. 10 [0033] The rolling force detector 6 detects a rolling force. For this, available manners include among others the manner of using a load cell embedded, e.g. between the mill housing 2 and the screw down device 5, for direct measurement of a rolling force, as well as the manner of using a pressure detected at a hydraulic presser as a basis to calculate a rolling force. 15 [0034] The roll revolution detector 7 is provided to the work roll 3a or 3b, or to a shaft (un-depicted) of an electric motor driving the work roll 3a or 3b, to detect the number of revolutions of the work roll 3a or 3b or such. Here, the roll revolution detector 7 may include a pulse outputting element for outputting pulses in accordance with a rotational angle of e.g. the 20 work roll 3a or 3b, and an angle calculator for detecting pulses output from the pulse outputting element to calculate a rotational angle of the work roll 3a or 3b, to thereby permit the detection of a revolution number of the work roll 3a or 3b, allowing for the more detail detection of a rotational angle. It is noted that, assuming a known ratio of diameters between the work rolls 3a and 3b and the backup rolls 4a and 4b, the revolution number as well as the rotational angle 25 of the work roll 3a or 3b detected by the roll revolution detector 7 can be based on to calculate a revolution number and a rotational angle of the backup rolls 4a and 4b with ease providing no slips developed between the work rolls 3a and 3b and the backup rolls 4a and 4b. [0035] The roll reference position detector 8 detects a reference position. Employable 30 arrangements may include a combination of an object of detection provided on e.g. the backup 12 roll 4a or 4b, and a sensor such as a proximity switch detecting the object every one-revolution of the backup roll 4a or 4b. There may be another arrangement making use of e.g. a pulse generator, for taking out pulses depending on rotational angles of the backup roll 4a or 4b to detect a rotational angle of the backup roll 4a or 4b, thereby detecting a reference position. It is 5 noted that the roll reference position detector 8 shown in Fig. I is provided simply to the upper backup roll 4a, as a case. There may be an arrangement including roll reference position detectors 8 provided to the backup rolls 4a and 4b, to detect respective reference positions of the backup rolls 4a and 4b. [0036] 10 The roll gap detector 9 is provided e.g. between the screw down device 5 and the backup roll 4a or 4b, for an indirect detection of a roll gap defined between the work rolls 3a and 3b. [0037] Description is now made of operations of the gage controller according to the example 15 1, with reference to Fig. 2 through Fig. 6. In particular, for the rolling force upper and lower distributor 10, the rolling force upper and lower variation extractor 11, and the manipulative variable calculator 12, their specific configurations and operations will be described. [0038] Fig. 2 is a diagram showing the concept of what is measured as a rolling force at the 20 gage controller according to the example 1. Fig. 2 illustrates a rolling force 101 in an event undergoing no roll eccentricities, and a rolling force 102 in an event undergoing roll eccentricities. There is an interval defined between a point of time t, and a point of time t 2 , which corresponds to one revolution of the backup rolls 4a and 4b. [0039] 25 As illustrated in Fig. 2, the rolling force 101 has variations such as those due to changes to be caused in temperature as well as in gage of a rolling material 1, with the time, i.e., as the rolls rotate, even when undergoing no roll eccentricities caused at the backup rolls 4a and 4b or such. [0040] 30 On the other hand, when undergoing roll eccentricities caused at the backup rolls 4a 13 and 4b or such, the rolling force 102 describes a superimposed combination of rolling force variations due to else other than roll eccentricities and components of rolling force variations due to roll eccentricities. Description made below is addressed to a specific control at the gage controller, which follows the basic concept of separating rolling force variations due to roll 5 eccentricities from rolling force variations due to else other than roll eccentricities, in an appropriate manner for use of the present gage controller to control rolling force variations due to roll eccentricities, affording for use of the MMC as well as the GM-AGC to control rolling force variations due to else other than roll eccentricities. [0041] 10 Description is now made of presuppositions as necessary to discuss configurations as well as operations of the rolling force upper and lower variation extractor 11 and the like, with reference being made to Fig. 3. [0042] Fig. 3 is a diagram for explanation of positional relations among work rolls (WR) 3a 15 and 3b and backup rolls (BUR) 4a and 4b. [0043] As shown in Fig. 3, the backup rolls (BUR) 4a and 4b are each provided with a positional scale 14 for use to detect rotational positions. Also, the backup rolls (BUR) 4a and 4b each have a rotative reference position 4c set up in advance in part thereof and interlocked 20 with rotation of the backup roll (BJR) 4a or 4b. [0044] The positional scale 14 is arranged outside the backup roll (BUR) 4a or 4b, close thereto, so as to e.g. enclose a periphery of the backup roll (BUR) 4a or 4b. It has graduation marks arrayed at intervals of a prescribed angle (360/n degrees) about an axis of rotation of the 25 backup roll (BUR) 4a or 4b, i.e., dividing a whole circumference of the backup roll (BUR) 4a or 4b into 'n' equal parts. Then, they are numbered up to an (n-1)-th, letting a reference position (as a fixed reference position) 14a of the positional scale 14 be a 0-th. For the 'n', there may be set a value within e.g. n = 30 to 40 or near. Here, the positional scale 14 is provided for description of the rolling force upper and lower variation extractor 11 and the like. The scale 30 itself may not be arranged in actual instruments.

14 [0045] Here, designated at 0 wro is a rotational angle that a work roll 3 has when the reference position 4c at the backup roll (BUR) 4a or 4b is coincident with the fixed reference position 14a, and 0 wr is a rotational angle that the work roll 3 has when the backup roll (BUR) 5 4a or 4b is rotated by a 0 BT. Here, denoted by 0 is an angle. At the left of suffix, W is a work roll 3, and B is a backup roll 4. At the right of suffix, T is the top side, and B is the bottom side. As used herein, with respect to the backup roll (BUR) 4a or 4b, the rotational angle means an angle by which the reference position 4c of the backup roll (BUR) 4a or 4b is moved from the fixed reference position 14a in conjunction with rotation of the backup roll 10 (BUR) 4a or 4b. For instance, that the backup roll (BUR) 4a or 4b has a rotational angle of 90 degrees means that the reference position 4c of the backup roll (BUR) 4a or 4b resides in a position where it is rotated at 90 degrees from the fixed reference position 14a in a rotational direction of the backup roll (BUR) 4a or 4b. Also, when the backup roll (BUR) 4a or 4b has a rotational angle nearest to a certain one of graduation marks in the positional scale 14 (for 15 instance, to a j-th mark in the positional scale 14), this state is referred to as the backup roll (BUR) 4a or 4b having a rotational angle number 'j'. [0046] It is noted that the roll reference position detector 8 may be composed of a sensor such as a proximity sensor and an object of detection to be detected by the sensor, the sensor and the 20 detection object being embedded at the reference position 4c of the backup roll (BUR) 4a or 4b and the fixed reference position 14a. In such a case, for instance, a proximity sensor provided at the reference position 4c of the backup roll (BUR) 4a or 4b is rotated together with the backup roll 4, getting at the fixed reference position 14a, whereby a detection object embedded at the reference position 14a is detected by the proximity sensor. Namely, the reference 25 position 4c of the backup roll (BUR) 4a or 4b is recognized as passing the fixed reference position 14a. It is noted that the roll reference position detector 8 is not material to embodiments herein. [0047) The divisions numbered from the 0-th at the fixed reference position up to the (n-1)-th 30 have their positions, which are associated with an equal number of sections defined, in Fig. 5 to 15 be described later on, as rolling force record areas (Po to Pa 1 in Fig. 5), so that rolling forces at those divisional positions are stored in the record areas. Typical used values range within n = 30 to 90 or near. Increasing 'n' requires devices for control to exhibit an enhanced calculation performance. The control to be precise and the capacity for calculation thus have conflicting 5 relations to each other, as a matter to be careful. [0048] As will be seen, for a backup roll 4a or 4b, the rotational angle represents an angle by which a reference position of the backup roll is moved, following rotation of the backup roll, relative to a fixed reference position. For instance, for the backup roll 4a or 4b, if the rotational 10 angle reads 90 degrees, this represents the reference position of the backup roll residing in a position where it is rotated at 90 degrees from the fixed reference position in a rotational direction of the backup roll. Also, when a backup roll rotational angle is nearest to a graduation mark in a positional scale (for instance, to an i-th mark in the positional scale), this state is taken as having a backup roll rotational angle number' i'. 15 [0049] Description is now made of a method of extracting variation components of rolling forces due to roll eccentricities, with reference to Fig. 4. [0050] Fig. 4 is a graph showing a rolling force varying with a changing rotational angle of a 20 backup roll. In Fig. 4, with respect to either backup roll 4, when the reference position 4c is coincident with the reference position 14a, that is, when the rotational angle number of the backup roll 4 is '0', the rolling force shown has a value P10. The rolling force is varied to P 1 1 ,

P

12 , P 13 , ..., as the rotational angle number of the backup roll 4 is changed to 1, 2, 3, ...as it proceeds. In due course, the backup roll 4 makes one revolution, with a rotational angle 25 number changed from '(n-1)' again to '0', having a rolling force P 2 0 then sampled. At this point of time, the rolling forces P 1 o and P 20 can be connected with each other by a straight line 130, to take this straight line 130 as a set of rolling forces excluding rolling force variations due to roll eccentricities. Accordingly, one can detenrine rolling force variations due to roll eccentricities from differences between the straight line and rolling forces P 1 , P 12 , P 13 , ... , P 20 30 measured at respective rotational angle numbers.

16 [0051] It is noted that in most cases actual measured rolling forces Pj have values (as actual values) containing components of noises, in addition to rolling force variations due to roll eccentricities, and rolling force variations due to temperature variations, gage variations, tension 5 variations, and the like. As a result actual values of actual rolling forces Pi are unlikely to show distributions along such smooth curves as illustrated in Fig. 4. Some cases involve the difficulty to identify a combination of a rolling force Pio and a rolling force Pgi+lo constituting a start point and an end point to be connected with each other to thereby determine a straight line. To this point assuming the combination of the rolling force Pio and the rolling force P(,Io to be 10 insignificant in the magnitude of change, one can obtain an average of n rolling forces Pio, Pii, P2, P 3 , ... ,Pi(n-i), for use to determine differences APg between the average and respective measured rolling forces Pio, Pit, Pi 2 , Pi 3 , ...,Pi, ) to take them as variation components of rolling forces due to roll eccentricities. This method is advantageous in that the number of sampled actual values of rolling forces can be reduced to the (n-1)-th division, and that it is 15 robust to variations of rolling forces such as those due to noises, as well. It is noted that actual values of rolling forces may be filtering-processed to reduce noise components, as an additional effective measure. [0052] <Operations of gage controller> 20 Description is now made of the gage controller according to the example 1 of embodiment [0053] In the gage controller according to the example 1 of embodiment, a rolling material I is rolled between the upper and lower work rolls 3a and 3b that have a gap and a speed adjusted 25 as necessary to provide a preferable thickness at the delivery side of this device. The work rolls 3a and 3b are supported on the backup rolls 4a and 4b, and arranged to minimize deflections in the roll width direction. The backup rolls 4a and 4b are bom by the mill housing 2, with a structure endurable to rolling forces to the rolling material 1. [0054] 30 The upper and lower work rolls 3a and 3b have a gap in between, which is adjusted by 17 the screw down device 5. As available implements as the screw down device 5 there are two types: one using an electric motor control (called an electric reduction), the other using a hydraulic control (called a hydraulic reduction), while the latter is easier to implement a fast response. Generally, controlling disturbances such as roll eccentricities that have short periods 5 needs a fast response, so the hydraulic reduction is employed in most cases. [0055] The rolling force detector 6 is operable to detect a rolling force. Available manners include among others the manner of using a load cell embedded between the mill housing 2 and the screw down device 5 to directly measure a rolling force, and the manner of calculating a 10 rolling force from pressures detected at a hydraulic presser. [0056] The roll revolution detector 7 is fixed to the work roll 3a or 3b, or to an electric motor shaft driving the work roll 3a or 3b, to detect the revolution number. It may be adapted to output pulses in accordance with a roll rotational angle, or may be used to detect a roll rotational 15 angle. In a situation given a known ratio of diameters between the work rolls 3a and 3b and the backup rolls 4a and 4b, the revolution number as well as the rotational angle of the work roll 3a or 3b can be used to determine a revolution number and a rotational angle of the backup rolls 4a and 4b with ease, providing no slips between the work rolls 3a and 3b and the backup rolls 4a and 4b. 20 [0057] Next, the roll reference position detector 8 detects a reference position every one-revolution of the backup roll 4a or 4b, by using a proximity switch or such. Alternately, there may be arranged a pulse generator or such for taking out pulses depending on rotational angles to detect a rotational angle itself, providing the adaptation to detect the reference position 25 every one-revolution or more frequently. Shown in Fig. 1 is the case of provision to either or both of the backup rolls 4a and 4b. Though even in a situation no roll reference position detector 8 is provided, rotational angles of the work roll 3a or 3b can be used, if given, to calculate rotational angles of the backup roll 4a or 4b based on a ratio of diameters between the work rolls 3a and 3b and the backup rolls 4a and 4b, by an expression below, such that: 30 [Math 2] 18 6B = D" Ow B (expression 2) [0058] Here, denoted by 0 B is a rotational angle [rad] of the backup roll 4a or 4b, 0 w is a rotational angle [rad] of the work roll 3a or 3b, DB is a diameter [mm] of the backup roll 4a or 5 4b, and Dw is a diameter [mm] of the work roll 3a or 3b. It is noted that the roll reference position detector 8 in Fig. 1 is not material to embodiments herein, as described. [0059] The roll gap detector 9 is installed between the screw down device 5 and the backup roll 4a or 4b, to indirectly detect a gap between the work rolls 3a and 3b. 10 [0060] Then, the rolling force upper and lower distributor 10 is operable, assuming rolling forces P detected by the rolling force detector 6 as being individually produced at the upper backup roll 4a and the lower backup roll 4b, for separating them into rolling forces PT being produced at the upper backup roll 4a and rolling forces PB being produced at the lower backup roll 4b, to output 15 to the rolling force upper and lower variation extractor 11. [0061] Description is now made of specific configurations and operations of the rolling force upper and lower variation extractor 11 and the manipulative variable calculator 12, with reference to Fig. 5. 20 (0062] Fig. 5 is an explanatory diagram showing an example of configuration of a combination of the rolling force upper and lower variation extractor 11 and the manipulative variable calculator 12 in the gage controller according to the example 1. [0063] 25 In Fig. 5, the rolling force upper and lower variation extractor 11 includes an upper load variation extractor 111, and a lower load variation extractor 112. [0064] The upper load variation extractor Ill is operable to take rolling forces PT separated by the rolling force upper and lower distributor 10, as bases to extract variation components due 19 to roll eccentricities of rolling forces PTj at rotational positions of the upper backup roll 4a. [0065] The lower load variation extractor 112 is operable to take rolling forces PB separated by the rolling force upper and lower distributor 10, as bases to extract variation components due 5 to roll eccentricities of rolling forces PBj at rotational positions of the lower backup roll 4b. [0066] Further, the upper load variation extractor 111 includes rolling force recorders lIla, an average calculator 11 Ib, and deviation calculators 11 Ic. Likewise, the lower load variation extractor 112 also includes rolling force recorders 112a, an average calculator 112b, and 10 deviation calculators II 2c. [0067] The rolling force recorders lila are provided as rolling force recorders, n in total, associated with the rotational angle numbers of the backup roll 4a or 4b, respectively. Each rolling force recorder 11 Ia is adapted to store therein a rolling force P-rj when the backup roll 4a 15 or 4b has reached an associated rotational angle, to hold for a prescribed period. [0068] The average calculator 111 b is operable to take rolling forces PTj stored in the rolling force recorders lIla, as bases to calculate an average of n rolling forces P-j (J = 0 to (n-1)) detected during one revolution of the backup roll 4a or 4b. 20 [0069] The deviation calculators 11I c are provided in correspondence to the rolling force recorders l la, respectively. They are each operable every one revolution of the backup roll 4a or 4b, to calculate and output a deviation APTj that a rolling force PTj stored in a corresponding rolling force recorder lIla has relative to the above-noted average. It is noted 25 that the rolling force recorders 11 2a, average calculator II 2b, and deviation calculators l I2c of the lower load variation extractor 112 also work in similar manners. [0070] The manipulative variable calculator 12 includes an upper adder set 121, a lower adder set 122, an upper switch set 123, a lower switch set 124, and a roll gap correction amount 30 calculator 125.

20 [0071] The upper adder set 121 is operable to add variation components due to roll eccentricities of rolling forces P-rj output from the upper load variation extractor 111, for each rotational angle number. 5 [0072] The lower adder set 122 is operable to add variation components due to roll eccentricities of rolling forces Paj output from the lower load variation extractor 112, for each rotational angle number. [0073] 10 The upper switch set 123 is operable to handle variation components due to roll eccentricities of rolling forces PTj as added for each rotational angle number by the upper adder set 121, i.e., upper rolling force variation values being deviations of rolling forces P-rj, to output in accordance with the rotational angle number of the backup roll 4a. [0074] 15 The lower switch set 124 is operable to handle variation components due to roll eccentricities of rolling forces PBj as added for each rotational angle number by the lower adder set 122, i.e., lower rolling force variation values being deviations of rolling forces Paj, to output in accordance with the rotational angle number of the backup roll 4b. [0075] 20 The roll gap correction amount calculator 125 is operable to take an output value of the upper switch set 123 and an output value of the lower switch set 124, as bases to calculate a correction amount of roll gap in accordance with a rotational angle number of the backup rolls 4a and 4b. [0076] 25 Here, the upper adder set 121 and the lower adder set 122 have similar configurations to each other, as well as the upper switch set 123 and the lower switch set 124. For instance, the upper adder set 121 includes a limiter 121a, switches 121b, and adders 121c. Here, the limiter 121a checks upper and lower limits of a deviation APTj input from each deviation calculator 111. The switches 121b are turned on every one revolution of the upper backup roll 30 4a, that is, each time when the average calculation at the average calculator 11 lb has come to an 21 end, so that deviations APTj input from the limiter 121a are concurrently output. The adders 121 c are provided in correspondence to the rotational angle numbers of the upper backup roll 4a, to add deviations output from the switches 121b for each rotational angle number. Also the upper switch set 123 and the lower switch set 124 have similar configurations. 5 [0077] Description is now made of operations of the rolling force upper and lower variation extractor 11 and the manipulative variable calculator 12. [0078] The rolling force detector 6 is allowed to simply have a single value sampled as a 10 rolling force for one stand. To this point, the rolling force upper and lower distributor 10 is adapted to separate a rolling force detected by the rolling force detector 6 into a rolling force PT produced at the upper backup roll 4a and a rolling force PB produced at the lower backup roll 4b, by using e.g. expressions below, such that: [Math 3] 15 P 7 =R-P ... (expression 3), and [Math 4] P = (1 - R)P ... (expression 4). 20 [0079] Here, PT: a rolling force produced at the upper backup roll 4a, PB: a rolling force produced at the lower backup roll 4b, P: a total rolling force actual value (as a value detected by the rolling force detector), 25 and R: a ratio to be set relative to the total rolling force P, for distribution to the rolling force PT produced at the upper backup roll 4a. [0080] Here, in the example 1, as the ratio R to be set to the total rolling force P for 30 distribution to the rolling force PT produced at the upper backup roll 4a, there is given a specific 22 value in the vicinity of 0.5, so that when distributing the total rolling force actual value P to the rolling forces produced at the backup rolls 4a and 4b, the values distributed to be an upper and a lower get vicinal to half the P. By doing so, either upper or lower set of adders 121c or 122c can serve to substantially cancel out rolling force variation components such as those due to roll 5 eccentricities at the opposing back up roll 4a or 4b. The reason why will be discussed later on. [0081] Next, at the rolling force upper and lower variation extractor 11, the rolling force recorders lIla hold rolling forces at the backup roll rotational angle numbers 0, 1, 2,..., n-I during one revolution of the upper backup roll 4a, and the average calculator 111 b operates to 10 calculate an average when it has reached the rotational angle number n-i. Then, the deviation calculators I lc outputs differences between the average and the rolling forces at the backup roll rotational angle numbers 0, 1, 2,..., n-1, as rolling force variations such as those due to roll eccentricities to the manipulative variable calculator 12. In this case, differences may not be taken relative to an average, but may be calculated, after an operation to determine an 15 expression of a straight line from a combination of Po at a start point and P, at an end point, in terms of differences between the straight line and rolling forces at respective positions. [0082] Rolling force variations such as those due to roll eccentricities at backup roll rotational angle numbers are checked for upper and lower limits at the limiters 121a and 122a, and when 20 average calculations are ended, the switches 121b and 122b are simultaneously turned on, whereby rolling force variation values APO, API, ... , APnj being deviations of rolling forces are concurrently sent to the adders (E 0 , Ei, > 2 ,..., EI) 121c and 122c, respectively, for their additions, such that: [Math 5] 25 Z--[k+1]-Z[k]-Aj (expression 5) [0083] Here, Zj: a value at an adder 2i, k: the number of times of addition (generally, coincident with the revolution 30 number of the backup roll 4a or 4b), and 23 j =0 to n-l. The adders (Yo, E-, Y2,..., Yn- 1 ) 121c and 122c are cleared to a zero prior to the rolling of a rolling material 1, and have deviations of rolling forces added thereto one time each every end of average calculation following one revolution of each backup roll 4a or 4b. This 5 procedure is carried out at the upper adder set 121 and the lower adder set 122. [0084] The switch sets 123 and 124 are operable to take out an upper rolling force variation value APAr and a lower rolling force variation value APBT being deviations of rolling forces added in association with rotational angles of the backup rolls 4a and 4b, respectively. 10 [0085] Namely, at the point of time when the backup roll reference position has passed the fixed reference position '0', simply a SWo is tuned on, whereby a APAO is taken out of a o at an adder 121 c. At the point of time when the backup roll reference position has reached a rotational angle number 'l', simply a SWi is tuned on, whereby a APAI is taken out of a Y 1 at an 15 adder 121c. Such an action is repeated at the switch sets 123 and 124 of rolling force variation values such as those due to roll eccentricities associated with backup roll rotational angles. [0086] It is noted that the additions are made at respective positions, as can be led with ease from a general control law. In other words, for control objects provided with no integration 20 systems as the present control objects are, it is reasonable from the control law to provide integrators at the controller end, to thereby remove steady-state deviations. Here, the system of control objects is not continuous, but discrete, so instead of integrators, the adders 121c and 122c are provided. [0087] 25 Then, as constituents of the manipulative variable calculator 12 in Fig. 5, the upper adder set 121 and the upper switch set 123 serve to calculate a deviation of rolling force (as an upper rolling force variation value) APAT due to the upper backup roll 4a, while the lower adder set 122 and the lower switch set 124 serve to calculate a deviation of rolling force (as a lower rolling force variation value) APBT due to the lower backup roll 4b, and the roll gap correction 30 amount calculator 125 calculates a roll gap correction value AST for the upper backup roll and a 24 roll gap correction value ASB for the lower backup roll, by using an expression 6 and an expression 7 below, such that: [Math 6] AS -(M+Q) MQ ---(expression 6) 5 [Math 7] AS, = ~(M+Q) MQ ---(expression 7) [0088] The roll gap correction amount AS is a manipulative variable. Since the roll gap is unable to separately manipulate at the upper side and the lower side, the roll gap correction 10 amount calculator 125 calculates, to output, a sum of upper and lower roll gap correction amounts AST and ASB, by using an expression 8 below, such that: [Math 8] AS = KT -(AST + ASI.) (exprssion 8) [0089] 15 Here, M: a mill modulus, Q: a coefficient of plastic viscosity of the rolling material, KT: an adjustment factor, ASr: a roll gap correction amount for the upper backup roll, 20 ASB : a roll gap correction amount for the lower backup roll, AS: the roll gap correction amount, APAr: a deviation of rolling force due to the upper backup roll (as an upper rolling force variation value), and APBT: a deviation of rolling force due to the lower backup roll (as a lower rolling force 25 variation value). Then, the roll gap manipulator 13 is operable to add the roll gap correction amount AS determined by the expression 8 to a roll gap amount of MMC, GM-AGC, or such, to give the result to the screw down device 5.

25 [0090] As the ratio R to be set to the total rolling force P for distribution to the rolling force PT produced at the upper backup roll 4a, there is given a value in the vicinity of 0.5. This is reasonable, the mason why follows. 5 [0091] With respect to the backup rolls 4a and 4b, letting Wr and oB be their rotation frequencies [rad/s], and TT and TB be their rotation periods [s], it so follows as shown by an expression 9 below, such that: [Math 9] T ;r 2;r Tr T TB 10 Or OB - (expression 9) [0092] Further, r is introduced as a ratio defined by an expression 10 below, such that: [Math 10] TT DT r = - TB DB ''(expression 10) 15 [0093] Here, it is assumed that Dr < DB, that is, r < 1. However, this assumption is made for the sake of convenience in description, and does not constitute any constraint to why it is reasonable that the R is set as a value in the vicinity of0.5. It may be that r > 1. [0094] 20 Then, with respect to the backup rolls 4a and 4b, letting yi and y2 be their roll deviation amounts [mm], and 02 be a phase difference in between, while assuming the amplitudes be 1.0 for simplification, it so follows as described by an expression 11 below, such that: [Math 11] { y. =sin cort 25 Y2 = sin(wt + 0 2 ) .- (expression 11) [0095] Now focused is the distance of axial movement The axial movement distance is 26 directly coupled with a variation of rolling force, so the rolling force variation may substitute in the discussion. [0096] The expression 11 above involves a relation, which is shown in Fig. 6. 5 [0097] Fig. 6 shows in a graph an example of combination of roll deviation amounts yj and y2 [mm] of the backup rolls 4a and 4b varying with time. [0098] The upper backup roll rotational angle stats from a fixed reference position, and 10 reaches a rotational angle number 'j'(j =0 to n-1) at a time To. This time To can be represented by an expression below, such that: [Math 12] T = 0rn -- (expression 12) [0099] 15 The adders 121c for the upper roll each have an integrated value, which is a sum of an integrated value Yirj) taken of axial movements of the upper backup roll 4a at a position 'j' of the upper backup roll 4a, and an integrated value YB(j) likewise taken of axial movements of the lower backup roll 4b at a position 'j' of the lower backup roll 4b. The Y-rj) is a value of integration over periods TT from To as an initial value, and can be calculated by an expression 20 13 below, such that: [Math 13] Yr (j)= sin OrTTO + sin Or (To + Tr) + sin r (TO + 2 TT)+ -. - (expression 13) [0100] Likewise, the YB(j) also is a value of integration over periods TT from To as an initial 25 value, and can be calculated by an expression 14 below, more specifically by an expression 15 below, such that: [Math 14] YB(j) = sin(afBT 0 +0 2 ) +sin{)B + T) + 2 -+sin aiB (To 2T) +0 2 }) + - (expression 14) 27 [Math 15] substituting a = B TO+0 2 u TB =2 , Y,(j) sina +sin(a+ cT,.)+sin(a +2w 8

T.)+--

=sina + sin(a + w)rTB) + sin(a + 2 B~rTB) + =sin a+sin(a+2nr)+sin(a+4nzr)+---+sin{a+2(n--1)nzr}+sina +sin{a -27f(1-r)}+sin{a-47r(1-r)}+--+sin{a +2(n-1)r(1 -r)}+-- -(expoession 15) 5 [0101] Here, it is assumed that an integer m can be determined, such that: [Math 16] m = 1/(1- r) ---(expression 16) [0102 10 Then, substituting the expression 16 into the expression 15, this expression 15 can be changed as shown in an expression 17, such that: [Math 17] 1 2 Y, (j) = sin a + sin(a - 2r -) + sin(a -2-) + m m i-1 .rm-i +sin(a -2;r )+-+sin(a -2.r m m 15 (expression 17) [0103] Here, with respect to a circle, suppose a total angle 2a [rad] multiplied by -1/n and added to a. A sin of a resultant angle gives a 0, when integrated. That is, the integrated value YBO) of axial movement amounts of the lower backup roll 4b becomes a 0 every integration of 20 m sin values. [0104] Further, in the expression 16, depending on the ratio of diameters of the backup rolls 4a and 4b, 1/(1-r) has a value, which is not always an integer. Though, in some cases, 1/(1-r) has a value close to an integer. In such a case, the YBO) has a value near to 0 every integration 25 of a number of sin values equal to the integer.

28 [0105] Further, here, as a superimposition of y' and y2, a beat Y can be represented like he expression 1, by an expression 18 below, such that: [Math 18] 5 Y = sin aT +sin at = 2sin . cos( Wtj (expression 18) [0106] When oyr > oB, the long period frequency or- os /2 can be given, using TB= TT/r, [Math 19] Or-0, 1 1 TT 1--r 1 2 Tr , -- I I TB Tm T ( 2T TB TB TT(expression 19) 10 [0107] As above. [0108] Namely, m in the expression 16 gives a long period m -TT of beat, whereby the integrated value YB(j) of axial movement amounts of the lower backup roll 4b becomes a 0 15 every m -TT. [0109] Further, as seen from the expression 13, the integrated value Yr(j) of axial movement amounts of the upper backup roll 4a monotonically increases, unless a roll deviation control is made. The integrated value YB(j) of axial movement amounts of the lower backup roll 4b has 20 a ratio to the Y-r(j), which is decreased every revolution of the upper backup roll 4a. Therefore, at the adders 121c in Fig. 5, upper roll deviation components of the upper backup roll 4a are mainly integrated. [0110] In a similar view, at the adders 122c for lower roll, roll deviation components of the 25 lower backup roll 4b are mainly integrated. [0111] Therefore, as the ratio R to be set to the total rolling force P for distribution to the upper rolling force Pr, a value in the vicinity of 0.5 is successfully set, so that when distributing 29 the total rolling force actual value P to the rolling forces produced at the backup rolls 4a and 4b, the values distributed to be an upper and a lower get vicinal to half the P. [0112] As will be seen from the foregoing, the gage controller according to the example 1 is 5 adapted to extract variation components of rolling forces developed in association with roll rotational positions such as those due to roll eccentricities, i.e., rolling force variation components such as those due to roll eccentricities, for use to manipulate a roll gap of the roll stand, so as to reduce the rolling force variation, by making use of a rolling force to be measured when rolling a metallic material, without using kissing roll forces. 10 [0113] By doing so, the gage controller according to the example 1 is operable, when undergoing variations in rolling force such as those due to roll eccentricities, to suppress the rolling force variation, thus suppressing variations in gage due to rolling force variations. This affords to control such variation components, as well, that are unable to analyze by frequency 15 analyses under non-rolling conditions, needing no gage meter, and free from debasement of precision due to tracking errors. It permits a highly precise control, even with differences between diameters of the backup rolls 4a and 4b. In addition, it can eliminate the need to measure kissing roll forces. As a result, the gage controller according to the example of embodiment facilitates the roll management, eliminating constraints from the installation, 20 allowing for provision of highly precise gage controller, gage control method, and gage control program. [0114) In particular, the gage controller according to the example I has, as the ratio R to be set to the total rolling force P for distribution to the upper rolling force PT, a value set in the vicinity 25 of 0.5, so that when distributing the total rolling force actual value P to the rolling forces produced at the backup rolls 4a and 4b, the values distributed to be an upper and a lower get vicinal to half the P, whereby either upper or lower set of adders 121c or 122c can serve to substantially cancel out rolling force variation components such as those due to roll eccentricities at the opposing back up roll 4a or 4b. 30 [0115] 30 (Example 2) After sufficient rotation of the backup rolls 4a and 4b, the upper adder set 121 and the lower adder set 122 shown in Fig. 5 have values stored in some of adders 121c and 122c depending on eccentricities of the upper backup roll 4a or 4b, as is apparent. 5 [0116] Namely, there is a j-th adder 121c having a large stored value, informing that the j-th position experienced large eccentricities. Such is the case with a lower adder 121c. [0117] In this regard, in this example 2 of embodiment, the gage controller making use of this 10 operates after sufficient rotation of the backup rolls 4a and 4b, to identify values in upper and lower sets of adders 121c and 122c, i.e., roll eccentricities of the backup rolls 4a and 4b. Then, on this basis, it takes rotation speeds to calculate therefrom frequencies as well as periods of roll eccentricities. [0118] 15 Fig. 7 is an explanatory diagram showing a variation of values stored in adders 121c in the upper adder set 121. [0119] In Fig. 7, the horizontal axis represents numbers of adders among the adders 121c., and the vertical axis represents added values at the adders 121c. There are shown added values 20 201 (histograms) at the adders 121c, and a sine wave 202 identified by added values at respective positions. [0120] The adders 121c may contain noises or such, and a sine wave can be determined by using a least-square method or he like. 25 [0121] Then, the manipulative variable calculator 12 operates by using the expression 8 for a conversion from load to roll gap in the example 2, to calculate from values of loads stored in the adders 121 c a work roll gap command value between the upper work roll 3a and the lower work roll 3b, and the roll gap manipulator 13 takes the work roll gap command value calculated by 30 the manipulative variable calculator 12, as a basis to manipulate the work roll gap between the 31 upper work roll 3a and the lower work roll 3b. [0122] As will be seen from the foregoing, the gage controller according to the example I is adapted, like the example 1, to extract variation components of rolling forces developed in 5 association with roll rotational positions such as those due to roll eccentricities, i.e., rolling force variation components such as those due to roll eccentricities, for use to manipulate a roll gap of the roll stand, so as to reduce the rolling force variation, by making use of a rolling force to be measured when rolling a metallic material, without using kissing roll forces. [0123] 10 In particular, the gage controller according to the example 2 is operable to take rotation speeds of upper and lower backup rolls 4a and 4b to calculate therefrom frequencies as well as periods of roll eccentricities, after sufficient rotation of backup rolls 4a and 4b, by which values in upper and lower sets of adders 121c and 122c, i.e., roll eccentricities of both of upper and lower backup rolls 4a and 4b are matured to be identifiable. This permits the frequencies as 15 well as the periods of roll eccentricities to be determined with ease, affording to manipulate a roll gap of the roll stand, so as to reduce the rolling force variation. In addition, it has a value set in the vicinity of 0.5 as the ratio R to be set to the total rolling force P for distribution to the upper rolling force PT, so that when distributing the total rolling force actual value P to the rolling forces produced at the backup rolls 4a and 4b, the values distributed to be an upper and a 20 lower get vicinal to half the P, whereby either upper or lower set of adders 121c or 122c can serve to substantially cancel out rolling force variation components such as those due to roll eccentricities at the opposing back up roll 4a or 4b. [0124] (Example 3) 25 According to an example 3 of embodiment, the ratio R to be set to the total rolling force P for distribution to the upper rolling force PT is set to a value in the vicinity of 0.5 immediately after replacement of the backup rolls 4a and 4b. Though, after sufficient rotation of backup rolls 4a and 4b, for instance, after a rolling of one rolling material, by which values in upper and lower sets of adders 121c, as well as roll eccentricities of both upper and lower 30 backup rolls 4a and 4b, are matured to identify by using periodic functions such as sine waves, 32 there is taken a ratio of amplitudes of sine waves identified with respect to the backup rolls 4a and 4b, to set up as the ratio R for the next material. [0125] For instance, suppose a rolling performed immediately after replacement of backup 5 rolls 4a and 4b, resulting in a combination of a sine wave identified by adders 121c of the upper backup roll 4a, to be 0.9 in amplitude, and a sine wave identified by adders 121c of the lower backup roll 4b, to be 1.1 in amplitude. In this case, the ratio R to be used for the next material can be determined such that R = 0.9 /(0.9 + 1.1) =0. 45. [0126] 10 Further, instead of using periodic functions for identification, there may be calculations of absolute values of values stored in additions, for use to determine a ratio of roll eccentricities of the backup rolls 4a and 4b. For instance, suppose a rolling performed immediately after replacement of backup rolls 4a and 4b, resulting in a combination of 0.9 as a result of a sum taken over absolute values of values at respective positions of backup rolls 4a and 4b with 15 respect to adders 121c of the upper backup roll 4a, and 1.1 as a result of a sum taken over absolute values of values at respective positions of backup rolls 4a and 4b with respect to adders 121c of the lower backup roll 4b. In this case, the ratio Rto be used for the next material can be determined such that R =0.9 /(0.9+ 1.1)=0. 45. [0127] 20 In other words, in the example 3, the rolling force upper and lower distributor 10 is operable, immediately after replacement of the backup rolls 4a and 4b, to set the ratio R for upper and lower distribution of rolling forces detected by the rolling force detector 6, to 0.5. For the next or subsequent material after the backup roll replacement, the rolling force upper and lower distributor 10 may use integrated values of upper and lower rolling force variation 25 values APAT and APBT being deviations of rolling forces at the manipulative variable calculator 12 with respect to the current rolling material, for identifying amplitudes of periodic functions to set up a ratio to a sum of an amplitude for the upper work roll 3a and the upper backup roll 4a and an amplitude for the lower work roll 3b and the lower backup roll 4b. Or alternately, the rolling force upper and lower distributor 10 may operate to have the ratio R for upper and lower 30 distribution of rolling forces detected by the rolling force detector 6, set to 0.5 immediately after 33 the backup roll replacement, and set up depending on the rolling force variation values APAr and APBT being deviations of rolling forces at the manipulative variable calculator 12 with respect to the current rolling material, for the next or subsequent material after the backup roll replacement. 5 [0128] This ratio may well contain noises, and may be processed by using a filter defined by an expression below, to reduce influences of noises, such that: [Math 20] R(k + 1) = cR(k) + (1 - c)R(k -1) --- (expression 20) 10 [0129] Here, in the expression 20, k : an index indicating a current time, k+1: an index indicating the next time of use, k-1: an index indicating the one-previous time of the current time, and 15 c : a gain for filtering. [0130] As will be seen from the foregoing, the gage controller according to the example 3 is adapted, like the examples I and 2, to extract variation components of rolling forces developed in association with roll rotational positions such as those due to roll eccentricities, for use to 20 manipulate a roll gap of the roll stand, so as to reduce the rolling force variation, by making use of a rolling force to be measured when rolling a metallic material, without using kissing roll forces. Further, it is operable immediately after replacement of the backup rolls 4a and 4b, to have a value set in the vicinity of 0.5 as the ratio R to be set to the total rolling force P for distribution to the upper rolling force PT, so that when distributing the total rolling force actual 25 value P to the rolling forces produced at the backup rolls 4a and 4b, the values distributed to be an upper and a lower get vicinal to half the P, whereby either upper or lower set of adders 121c or 122c can serve to substantially cancel out rolling force variation components such as those due to roll eccentricities at the opposing back up roll 4a or 4b. [0131] 30 In particular, the gage controller according to the example 3 is operable, immediately 34 after replacement of the backup rolls 4a and 4b, to set the ratio R to be set to the total rolling force P for distribution to the upper rolling force PT,to 0.5. Though, after sufficient rotation of backup rolls 4a and 4b, for instance, after a rolling of one rolling material, by which values in upper and lower sets of adders 121c, as well as roll eccentricities of both upper and lower 5 backup rolls 4a and 4b, are matured to identify by using periodic functions such as sine waves, it is possible to take a ratio of amplitudes of sine waves identified with respect to the backup rolls 4a and 4b, to set up as the ratio R for the next material. This permits the frequencies as well as the periods of roll eccentricities to be determined with ease, affording to manipulate a roll gap of the roll stand, so as to reduce the rolling force variation. 10 Reference Signs List [0132] 3...a work roll 3a... an upper work roll 3b... a lower work roll 15 4...a backup roll 4a... a upper backup roll 4b... a lower backup roll 5.. .a presser 6.. .a rolling force detector 20 7.. .a roll revolution number detector 8... a roll reference position detector 9.. .a roll gap detector 10.. .a rolling force upper and lower distributor 11.. .a rolling force upper and lower variation extractor 25 12... a manipulative variable calculator 13... a roll gap manipulator Industrial Applicability [0133] Embodiments described herein are applicable to hot rolling mills for hot-rolling a 30 metallic material.