WO1990000450A1

WO1990000450A1 - Rolling of strip material

Info

Publication number: WO1990000450A1
Application number: PCT/GB1989/000772
Authority: WO
Inventors: Rolf Lehmann; Heinz Güttinger; Eugen Schnyder
Original assignee: DAVID McKEE (POOLE) LIMITED
Priority date: 1988-07-11
Filing date: 1989-07-07
Publication date: 1990-01-25

Abstract

A device for either hot or cold rolling of strip material, particularly metal strip, comprises a control deflection roll (7) having elements spaced apart along its length for individually controlling the pressure applied by the roll at the spaced apart positions and a second roll (8) which has a variable effective crown. The strip material (1) is rolled between these rolls or between a pair of work rolls and the above-mentioned rolls act as respective back-up rolls. The thickness or shape of the material being rolled is detected across its width and is subjected to harmonic analysis which provides outputs for controlling the deflection roll (7) and the roll (8) which has a variable effective crown.

Description

ROLLING OF STRIP MATERIAL

This invention relates to the rolling of strip material. In particular the invention relates to a device for rolling strip material and to a method of operating the device in order to roll metal strip.

According to the present invention, a device for rolling strip material comprises a controlled deflection roll having elements spaced apart along its length for individually controlling the pressure applied by the roll at said spaced apart positions and a roll having a variable effective crown, said strip material being rolled between said rolls or said rolls serving as respective back-up rolls for a pair of work rolls between which the strip material is rolled.

A controlled deflection roll is known, for example, from US-3885283 and US-3802044. Hydrostatic support elements, or other types of analogue individually controlled support elements, are employed in this type of roll. The control deflection roll may comprise a non-rotatable carrier shaft, a roll shell rotatable about the carrier shaft and a plurality of support elements disposed between the carrier shaft' and the shell at positions spaced apart along the length of the shaft, said support elements being individually controllable to apply pressure to the roll shell]

The roll which has a variable effective crown may be as described in US-34576517 or US-3604086, or EP-A-19737. Alternatively, it may have at least one pressure chamber with controllable pressure on the pressure side of the roll, as described, for example, in US-3043211 and US-3494675. Conveniently, the roll comprises a carrier shaft, a roll shell surrounding the carrier shaft with a space defined by the carrier shaft and the roll shell and means for introducing fluid under pressure into the space to vary the crown of the roll. The advantage with this type of roll is that the crown of the roll responds relatively fast to the pressure change of the hydraulic fluid.

Other means may be used to change the effective deflection curve of the roll, for example, roll bending. A similar effect is achieved by angular adjustment of the axis of the roll relative to the axis of the controlled deflection roll whereby variation of the ratio of the roll distance at the roll centre and at the end of the roll and the gap can be effected. This has an effect similar to a real curvature change and thereby achieves also a change of effective camber. A similar effect can also be achieved by laterally adjusting the position of the roll or differentially heating the roll or employing a roll with strength reducable ends, for instance, with axial displacement of a wedge-shaped insert into the end faces of the rolls.

It is known that, in the hot rolling process of metal strip, the thickness of the strip is successively reduced at each pass until a certain thickness profile across the width of the strip is obtained. As long as the temperature of the metal strip is sufficiently high and the material is still plastically deformable without creating mechanical tension, the thickness profile across the width of the strip can be influenced. However, as soon as the temperature of the metal strip falls below a certain value, i.e., into the cold rolling state, every deformation is connected with the generation of tensions. A change of the thickness profile within this temperature range results, therefore, in a change of the longitudinal tension distribution leading to flatness errors of the rolled strip. The thickness profile that has been rolled in the hot rolling stage cannot be changed in the cold rolling stage, but the force distribution in the roll gap has to be controlled in the subsequent rolling stands to maintain the thickness profile and the longitudinal tension profile to prevent flatness deviations.

The device according to the present invention may be operated to hot roll metal strip and, in this process, the thickness profile of the rolled strip is determined at positions across its width downstream of the rolling device; the measured thickness profile is subjected to harmonic analysis and the amplitude of the fundamental of the harmonic analysis is used to control the effective crown of the roll which has a variable effective crown and the amplitude of the higher harmonics are used for the individual control of the elements of the controlled deflection roll.-

Alternatively, if the metal strip is placed under longitudinal tension, the tension profile of the rolled strip may be determined at positions across its width downstream of the device; and the measured tension profile is subjected to harmonic analysis, the amplitude of the fundamental of the harmonic analysis is essentially used to control the effective crown of the roll which has a variable effective crown and the amplitudes of higher harmonics are used for the individial control of the pressure force of the controlled deflection roll across its width.

It is of advantage to apply a harmonic analysis to the measured shape profile, at least approximately, for instance, in the form of a Fourier series of trigonometric functions with a wave length of the fundamental according to the width of the strip, or with other orthogonal functions, for instance, Legrendre polynomials. It is advantageous in this case to control the coefficient of the first term, which is a measure of the degree of tilt via the difference of the screwdown forces at the roll ends, while the amplitude of the second term of the Fourier series which is a measure of the crown of the profile, i.e., essentially the fundamental, is controlled by controlling the effective crown of the opposing roll. To control the remaining harmonics with shorter wavelength, particularly the amplitudes of the third term which indicates the asymmetric crowns as well as the fourth term, representing the quarter buckles, the particularly fine control facilities of the controlled deflection roll are used. With a sufficient number of control zones of the controlled deflection roll, it is possible to respond to harmonics of high order.

By using the described combinations of two rolls of different types on the same roll stand and by assigning the control functions for harmonics of different order to both rolls, the application range of such a rolling device is clearly improved.

Due to the small masses that have to be moved in a controlled deflection roll, the control rate is also clearly improved in particular when acting in conjunction with a controllable opposing roll, e.g., a hydraulically inflatable roll which also has a small time delay. However, even when operating in conjunction with a slower controllable roll, a certain advantage can be achieved, if the control equipment is designed or programmed that also at the fundamental rapid changes are at first compensated and are then transmitted to the generally controllable opposing roll.

In order that the invention may be more readily understood, a first embodiment thereof will now be described, by way of example only, with reference to the accompanying drawings, in which:-

Figure 1 is a perspective view of a rolling device in accordance with the embodiment:

Figure 2 is a schematic diagram of the rolling device with the relevant control circuit;

Figure 3 gives an example of a harmonic analysis of a shape profile; and

Figure 4 is a control diagram.

The rolling device is schematically illustrated in Figure 1 omitting details which are unimportant to the invention, such as bearings, drive and seals. The four-high rolling device is for cold rolling of metal strip 1 between two work rolls 2, 3 through a roll gap 6 with a rolling load acting on the strip. Each of the work rolls 2, 3 has a back-up roll 7, 8 acting on the side opposite to the roll gap. The rolling load can be chosen to result in a strip reduction, that means that the strip is further reduced to foil thickness, or the rolling load is chosen to even out any irregularities only, i.e., skin pass rolling.

The upper back-up roll 7 is designed as a ' controlled deflection roll with a non-rotating carrier shaft and a roll shell rotating about the carrier shaft supported with adjustable pressure force by a number of support elements positioned across the length of the roll, as described, for example, in ϋS-A-3885283 or US- A-3802044 with hydrostatic support elements, or in another known manner with analogue acting, individually controllable support elements. This makes it possible that not only a total rolling load can be applied across the width of the strip but also different individual pressure forces with an adjustable width profile creating a certain rolling load profile in the roll gap 6 via the work roll 2 across the width.

The opposing roll on the opposite side, i.e. the back up roll 8 designed as roll with a generally controllable crown or camber described_t for instance, in US-A-3 457 617, US-A-3 604 086 or E A-19 737, or in another suitable manner. Designs are preferr where the crowning can be controlled rapidly and with little ti delay. The change of the crown is transferred to the roll gap 6 v the work roll 3 and superimposed on the pressure forces of t support elements respectively on the deformations of the roll she of the controlled deflection roll 7. A. device for roll bending c also be provided which is not illustrated here.

After the metal strip has passed the roll gap 6 it is guided ov a shape meter 9, as described, for instance, in GB-A-1 160 11

1 2 3 This consists of a number of measuring ring^'s 9 , 9 , 9 , .. distributed across the width of the strip. These rings are used measure the longitudinal tension distribution across the width the rolled metal strip via the bearing pressure of the individu segments. This longitudinal tension distribution is a dire -measure of the shape error of the metal strip, respective deformations and faults.

Fig. 2 shows a similar rolling device but where the controll deflection roll 7 and the opposing roll with variable cro directly form the roll gap 6 without two intermediate work rol acting on the rolled strip 1. The section shows the arrangement the controlled deflection roll 7 with the non rotating carri shaft 11, the roll shell 12 rotating about the carrier shaft a a number of support rolls 13 supporting the roll shell 12 again he carrier shaft 11 and fed by supply lines 4 controll individually by a control device 5. The opposing roll 8 with controllable crown consists of a carr shaft 20 and a rotatable roll shell 18 and a pressure chamber between the carrier shaft 20 and the roll shell 18. The press chamber which is closed and sealed against the outside is suppl via supply line 19 with a hydraulic medium with controlla pressure. A pressure change in the pressure chamber 22 changes crown of the opposing roll 8.

It is of advantage here that only certain masses have to be mo making a rapid control possible. It is, however, possible to u other rolls instead with variable effective crown, for instan inflatable hollow rolls without non rotating carrier shaft, rol with at least on pressure chamber on the load side only, or it possible to make the axis of the opposing roll rotatable in a pla at right angles to the plane of applied load (axis crossing) or is possible to make the roll as a whole bendable in the plane the applied load (roll bending). Rolls with variable crowns differential heating of the roll core or rolls with end that c be made weaker (taper piston rolls) could be suitable.

The evaluation of the measured values of the longitudinal tensi distribution of the rolled strip 1 across the width of the stri

1 2 3 provided by the shape meter segments 9 , 9 , 9 .... is carried o by means of a number of transducers 16 whose output signals a converted by a central computer into a width profile which displayed on a monitor 17. The transducers 16 convert t

1 2 3 temperature measured at the shape meter rotors 9 , 9 ,9 ....by mea

1 2 3 of suitable temperature sensors 15 , 15 , 15 ....to tension valu according to the known temperature expansion laws. Therefore t output signals represent longitudinal tension values aft temperature compensation. The longitudinal tension width profile derived by the computer i fed to the evaluation unit 5 which undertakes an harmonic analysi of the profile across the width of the strip, for instance by Fourier analysis with trigonometric functions, or with polynomials e.g. Legrendre polynomials, or -other linearly independent orthogonal systems of functions of increasing order and wit decreasing wave lengths. By this method the amplitudes of th various terms are determined, i.e. the tilt, the fundamental an the various harmonics. It is advantageous to use osculatin functions to the deflection line of the rolls. If discrete measure values are available it is advisable to use digital processing o the signals to achieve an approximate harmonic analysis, fo instance according to the known Bessel functions to derive th Fourier coefficients.

Fig. 3 shows an example of such an analysis of a tension profil P between the boundaries 0 and L of the metal strip. The profil P(x) represents here the deviations of the measured longitudina tensions from the mean value ag. It is known that each continuou

profile P(x) within the range 0 - L can be expanded into a Fourie series, consisting only of cosine terms if a boundary is chosen a origin. This can be achieved in the following manner:

P = a_j^ cos(-7x/L) + a₂ cos(2^x/L) + a₃ cosθTx/L)

+ a^ cos(4_Fx/L) + ....

with the coefficients:

or with Legrendre polynomials :

2 . 3

P⁽ x ) = a^ x/L ) + [ 3 /L ) - 1 ] + a₃[ 5 ( x/L ) - 3 ( x/L ) ] + Here the amplitude &^ of the first term represents the tilt of the

profile, the amplitude a₂ of the fundamental the camber, the

amplitude of the third term tfhe asymmetric buckles and the amplitude a^ of the firs harmonic the quarter buckle. Further

coefficients ag whose amplitude, as a rule, is constantly

declining, represents the waviness of higher order.

Now the evaluation unit 5 controls the various correcting elements according to the amplitudes a^, a₂, ag, a^, ag .... of the harmonic

analysis derived from the tension profile P. The amplitude a-^

indicating the tilt of the profile controls, if a controlled deflection roll is used with a free movable roll shell 12 along the complete length of the roll, preferably the two outer support elements at the ends, of the roll shell via the- supply lines 14 and the inner support elements via the supply lines 4 with decreasing intensity. When using a roll with a supported shell the difference of the screw down forces at the roll end is controlled via the supply lines 14. The crown represented by amplitude a₂ serves as

a control signal for the lower back up roll 8 with variable crown via line 19. To achieve better osculation to the deflection line of the roll some small part of the amplitude of certain harmonics can be added, e.g. a^. As the amplitude a₂. as a rule, has the

greatest value, the control of the deviations with the greatest amplitude is not used for the roll bend stabilisation roll, so that the control range can be utilised to compensate deviations of higher order. In particular the support elements 13 of the controlled deflection roll 7 receive individual signals according to the amplitudes ag of the asymmetric buckle and the amplitude a^

of the^" quarter buckle via lines 4 and these shape deviations are thereby fully compensated. It becomes apparent that a controlled deflection roll with fi individually controlled support elements or support zones adequate to remove deviations up to the fourth order. If t controlled deflection roll 7 has more than five zones waviness a higher order can also be fully compensated. With a roll with on five zones waviness of fifth or higher order can however be remov by the control of spray nozzles 24 which are distributed acro the width of a strip using a coolant supplied via line 23.

With the control process as described it is advantageous that t individual control facilities of a controlled deflection roll c best be utilised by compensating the fundamental of the tensi profile deviation by the opposing roll with variable crown camber while the waviness of higher order can be compensat without limitations by the controlled deflection roll. The contr range of such a combination of a controlled deflection roll and roll with variable crown together with a control based on harmonic analysis has clearly been extended compared to existi known devices for cold rolling metal strips or foil.

Fig. 4 shows a control diagram of a rolling device according to t invention, showing, for the sake of clarity only, the two lowe symmetrical amplitudes a of the total curvature and a^ of t

quarter buckle. The control fields of the controlled deflecti roll alone are indicated by the almost rectangular fields DE whi cover a larger area due to the individual controllability of t support elements, i.e it is easier to compensate the camber as we as the quarter buckle than with previously known .rolling devic which have only a straight line as control characteristic as wi a single roll with controllable camber or a narrow parallelogr achieved by a combination of one roll with controllable camber a work roll bending. The control range of a controlled deflecti roll which is already relatively wide is further widened by use the opposing roll with controllable camber, as indicated in figure by a number of quadrilaterals VC, creating a control ra that has hitherto not been achieved. This ensures that for a w range of pressure forces the origin, indicating ideal flatness the rolled strip, will practically always be within the cont field. That means a flatness of rolled strip or foil can achieved even under unfavourable conditions.

A further advantage in the described process is the particular short control time of a controlled deflection roll especially conjunction with an opposing roll which can also be rapid controlled. This makes a higher strip speed possible witho qual

In order that a further aspect of the invention may be more readily understood, it will now be described, by way of example only, with reference to the accompanying drawings, in which:-

Figure 5 is a perspective view of a rolling device with four rolls;

Figure 6 is a sectional view of two rolls; and

Figure 7 is an example of flatness analysis across the width of a rolled metal strip.

Figure 5 shows a schematic rolling device, omitting details which are nor essential for the invention, e.g. bearings, drive and seals. A strip 1 is being rolled, for example, a metal strip, at a temperature at which the metal experiences plastic deformation without creation of tensions, or another rolled strip being subjected to plastic deformation between two work rolls 2, 3 in a roll gap under the influence of a rolling load, whereby the thickness of the strip is being reduced due to the pressure force between the work rolls 2, 3. On each side of the work rolls 2, 3, back-up rolls 7, 8 are acting in the direction of the applied pressure.

The upper back-up roll 7 is designed as a controlled deflection roll with a non-rotating carrier shaft 11 and a roll shell 12 which rotates about it. ^• -.'- The roll shell 12 is supported by a mu ber of support elements 13 which are distributed along the length of the roll and whose pressure force can be individually controlled via a number of supply lines 4, so that different forces can be applied across the width of the roll, i.e., a pressure force distribution with a controllable width profile creating a certain roll force profile across the width in the roll gap 6 via the work roll 2. This causes a relevant change of the thickness profile of the rolled strip 1.

The opposing roll situated on the opposite side, i.e., the back-up roll 8 has been designed as a roll with a general changeable crown or camber, whose crown or camber can be varied via a supply line 19. This camber change is transferred via the work roll 3 to the roll gap 6 and is superimposed on to the pressure forces of the individual support elements 13 of the controlled deflection roll

IL

7 . Additional equipment to achieve work roll bending can be used, which is not illustrated here.

Fig. © shows a similar rolling device where the controlle deflection roll 7 and the opposing roll 8 with variable crown for the roll gap and act directly on to the rolled strip Withou intermediate work rolls. The section shows the arrangement of th support elements 13 of the controlled defection roll 7 in greate detail. For the individual support elements 13 cylindrical bore 15 are provided which form with the support elements 13 a piston cylinder guide. The cylinders are supplied with hydraulic fluid vi a supply line .14 positioned in the carrier shaft. The pressure o the hydraulic fluid can be controlled via a control valve 4' . O the bearing surfaces of the support elements 13 hydrostati bearing pockets 16 are provided connected to the cylinder by chok bores 17 and act by known methods, hydrostatically and moveabl as support and bearing for the roll shell 12 in relation to th carrier shaft 11 in the direction of the pressure PP. Othe versions of controlled deflection roll can, of course, also be use if its pressure force can be individually controlled across th width at a plurality of positions independent of each other.

The opposing roll 8 is designed with a general, controllable crow also with a non rotating carrier shaft 20 and with a roll shell 1 rotating about the carrier shaft, the space between carrier shaf 20 and roll shell 18 forms a closed and sealed pressure chamber 22 It is supplied with a hydraulic fluid via a supply line 19 and control valve 19' and then through a further supply line 21 in th carrier shaft. The pressure of the hydraulic fluid is controllable A change of pressure in the pressure chamber 22 results in a chang n

of crown of the opposing roll 8, shown by broken line in fig. —

Different rolls with variable effective crown can also be use instead of the roll described here, for instance inflatable hollo rolls without non rotatable carrier shafts, rolls with at least on pressure chamber with controllable pressure on the side of the rol acting towards the strip or rolls with strength reducible end (taper piston rolls). It is also possible to have the axis of th opposing roll rotatable in a plane at right angles to the pressur plane (crossed axis), or bending of the roll as a whole in th pressure plane (roll bending), or the roll can be internall heated.

To regulate the thickness profile of the rolled strip 1 there ar thickness sensors 9 distributed across the width of the strip o which only few are shown for the sake of clarity. It is possibl to use various separate sensors whose number, as a rule, shoul correspond to the number of individually controllable suppor elements 13 or groups of support elements of the controlle deflection roll 7. It is also possible to use a sensor 9 traversin across the width of the strip giving a thickness , signal, continuously or at certain positions to a decoder 10. The decode collects measured values of the sensors 9 or of the sensor 9 a various points, or the signal spectrum during one travel acros the strip and generates an actual-thickness-profile-signal whic is fed to the evaluation unit 5 for the control of the suppor elements 13 of the controlled deflection roll 7 and the crownin of the opposing roll 8. The evaluation unit 5 carries out a harmonic analysis of the thickness profile across the width of the strip, for instance by Fourier analysis of trigonometric functions, or polynomials, for instance Legrende polynomials or other linearly independent orthogonal systems of functions in ascending order, i.e. with decreasing wave lengths and derives the amplitude of the constant term, the slope, the fundamental and the various higher harmonics. Functions conforming to the deflection characteristics of the rolls are used advantageously. If discrete measured values are available a digital signal processing to an approximate harmonic analysis is recommended, for instance according to the known Bessel formulae for the derivation of the Fourier coefficients.

In fig. ^'~^~~j an example of such an analysis can be seen, of a thickness profile P(x) across the width of the strip between the boundaries 0 and L of the strip. It is known that a continuous function P(x) can be resolved into a Fourier series, which consists only of cosine terms, if one border is chosen as origin in the following manner:

P = a₀ + a₁cos(«Tx/L) + a₂cos(

+ a₃cos(3 ^"x/L)

with coefficients :

or with Legrendre polynomials:

2 3 P(x) = a^ /D + a₂[3(x/L) - 1] + a₃[5(x/L) - 3{x/L)] +

The constant term BQ represents the total load, the amplitude a^ of

the first term the tilt of the profile, the amplitude a₂ of the

fundamental the camber, the amplitude of the third term as^ymmetrical buckles and the amplitude a₄ of the first harmonic quarter buckles and further coefficients a₅ ..... whose amplitude

decreases successively as a rule, represent waviness of a hi^gher order.

The evaluation unit 5 of the control unit regulates various control elements according to the amplitudes β , a^, a₂, ... derived by the

harmonic analysis of the thickness profile P. The basic load according to &Q is fed as a total force to the support elements 13

of the controlled deflection roll 7 or fed as screw down force to the roll ends should the controlled deflection roll consist of a roll shell supported at its ends. The amplitude a^ which indicates

the tilt of the pressure profile controls preferably the two outer support elements and the inner support elements with decreasing intensity if a controlled deflection roll with a moveable roll shell 12 across the total width is used or if a controlled deflection roll with a supported roll shell is used the amplitude a_ji controls the difference of the screw down forces.The camber

indicated by the amplitude a is used as a control signal for the

lower back up roll 8 with variable crown. To conform to the deflection line of the roll certain small parts of the amplitude of higher harmonics, e.g. a^ can be added. As the amplitude a has,

as a rule, the highest value the feedback control of the deviation with the largest amplitude is not fed to the controlled deviation roll so that the control range can best be utilised for the control of the deviations of higher order. Particularly the support elements 13 of the controlled deflection roll 7 are individually fed with position signals according to the amplitudes a₃ of the

asymmetric buckle and the amplitude a₄ of the quarterbuckle to

control these deviations-. One can see that a controlled deviation roll with five individually controllable support elements or support element zones is sufficient for removal of deviations up to the fourth order. If the controlled deviation roll 7 has been designed with more than five zones, waviness of higher order can still be removed, that has to be achieved by other means on a roll with five zones, as for instance with individually roll cooling distributed across the width.

In the described procedure not only the more accurate and the finer control of the actual profile of a rolled strip to a required profile is beneficial but also the very short control time of a controlled deflection roll, particularly when interacting with a controllable opposing roll whose response time is similar. This permits higher rolling speeds without reduction in quality, a feature which is of special advantage when hot rolling metal strips.

In roll stands with at least four rolls where work roll bending with the known methods is provided to conform to a changed total rolling load, the wear and the variable change of shape of the work rolls across the width can advantageously compensated in such a way that here the basic change of the camber can also be responded to by the generally controllable opposing roll while the deviations from the fundamental can be removed by the controlled deflection roll. The service life of the work rolls can thereby be extended without replacement or re-grinding.

Claims

Claims :

1. A device for rolling strip material comprising a controlled deflection roll having elements spaced apart along its length for individually controlling the pressure applied by the roll at said spaced apart positions and a roll having a variable effective crown, said strip material being rolled between said rolls or said rolls serving as respective back-up rolls for a pair of work rolls between which the strip material is rolled.

2. A device as claimed in claim 1 in which the controlled deflection roll comprises a non-rotatable carrier shaft, a roll shell rotatable about the carrier shaft and a plurality of support elements disposed between the carrier shaft and the shell at positions spaced apart along the length of the shaft, said support elements being individually controllable to apply pressure to the roll shell.

3. A device as claimed in claim 1 or 2, in which the roll having a variable effective crown comprises a carrier shaft, a roll shell surrounding the carrier shaft with a space defined by the carrier shaft and the roll shell and means for introducing fluid under pressure into the space to vary the crown of the roll.

4. A device as claimed in claim 1 or 2, in which the roll having a variable effective crown is provided with means for either bending the roll, or angularly adjusting the longitudinal axis of the roll, or laterally adjusting the position of the roll, or differentially heating the roll, or intentionally weakening the ends of the roll in order to vary the effective crown of the roll.

5. A method of operating the device claimed in any preceding claim to hot roll metal strip with a desired thickness profile in which the actual thickness profile of the rolled strip is determined at positions across its width downstream of the device; that the measured thickness profile is subjected to harmonic analysis and that the amplitude of the fundamental of the harmonic analysis is used to control the effective crown of the roll having a variable effective crown and the amplitudes of the higher harmonics are used for the individual control of the elements of the controlled deflection roll.

6. A method of operating the device claimed in any of the claims 1 to 4 to cold roll metal strip with a desired flatness in which the rolled strip is placed under longitudinal tension and that the tension profile of the rolled strip is determined at positions across its width downstream of the device; that the measured tension profile is subjected to harmonic analysis and that the amplitude of the fundamental of the harmonic analysis is essentially used to control the effective crown of the roll having a variable effective crown and the amplitudes of higher order are used for the individual control of the pressure force of the controlled deflection roll across its width.

7. The method according to claim 5 or 6, in which the harmonic analysis is carried, out in the form of a Fourier series of trigonometric functions, particularly cosine functions, with the wavelength of the fundamental according to the width of the strip.

8. The method according to claim 7, in which the constant term (a_Q) of the Fourier series is used to control the total force applied to the strip by the rolls, the amplitude (a-^) of the first term of the series being used to control the steer of the rolls, the amplitude (a₂) of the second term of the series being used to control the effective crown of the roll having variable effective crown and the amplitude (33

& a₄) being used to control the controlled deflection roll to control those deviations which have not been controlled by the opposing roll.

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