JPS5816446B2 - How to measure roll eccentricity - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for measuring roll eccentricity in a rolling mill, in which the eccentricity of an upper back-up roll and the eccentricity of a lower back-up roll can be detected separately for each roll.

There are two drawbacks to the conventional method:

One is that the amount of roll eccentricity is detected without separating the eccentricity component of the upper back-up roll and the eccentricity component of the lower back-up roll, which prevents mechanical meshing between the upper roll and lower roll during rolling. The deviation occurs and the disturbance appears as a change in the resultant eccentricity, and it takes several cycles to correct this, which has the disadvantage that the plate thickness during this period is disturbed.

In other words, if the mechanical engagement angles of the upper and lower rolls do not deviate at all between the time when the amount of eccentricity is detected and the time during rolling, an ideal eccentricity component can be output. Similarly, when the upper and lower rolls are out of mesh, the phase of the combined eccentricity also shifts.

However, since the eccentric components of the upper and lower rolls are not detected separately, the amount of eccentricity that matches each phase of the upper and lower rolls cannot be immediately determined, so it takes several cycles to correct the phase shift. It requires.

The other problem is that even if the previous drawback is improved, if Fourier analysis is performed with the lower rolls in a kiss roll state because they have different diameters, an analysis error will occur when detecting the amount of eccentricity. be.

In other words, since the periods of the upper roll and the lower roll do not match, analysis errors as shown in the shaded area in FIG. 2 occur.

Therefore, this analysis shows that even if the eccentric component is separated into the upper roll and the lower roll, the error remains uncorrected.

In the present invention, when detecting the eccentricity of the upper back-up roll and the lower back-up roll, the eccentricity is detected separately while correcting the analysis error due to the diameter difference between the two rolls. This was designed to quickly absorb the change component of the amount of eccentricity and reduce the effect of eccentricity on the plate thickness.The upper back-up roll pulse generator and the lower back-up roll pulse generator generate sampling pulses and mark pulses. Then, the rolling mill is started with the upper work roll and the lower work roll in a kiss roll state, and when the mark pulse of the backup roll that has fallen down is transmitted, each For each sampling pulse of the backup roll, the first Fourier analysis is performed to obtain the composite amplitude of the upper and lower backup rolls until at least the next mark pulse signal is transmitted, and then the upper and lower backup rolls are analyzed.
A second Fourier analysis was performed by shifting the phase of the lower back up roll, and the combined amplitude of the upper and lower rolls was determined.
Furthermore, considering the amplitude error due to the diameter difference between the upper and lower rolls (natural slippage of the phase of both rolls), the true Fourier coefficient is calculated from the composite amplitude obtained in the first and second analysis, and above this, This method relates to a method for measuring roll eccentricity, which is characterized by separately determining the eccentricity component of the lower roll.Below, before describing the method for measuring roll eccentricity according to the present invention in detail, we will first outline its principle. do.

In the rolling mill, the rolling load P is based on one of the upper and lower back rolls, and has the same frequency as the roll rotation speed, twice the frequency, three times the frequency,..., n times the frequency, That is, it is a periodic function expressed by ωX: upper roll angular velocity, ωy: lower roll angular velocity t: time.

As an example of rolling load variation, if the fundamental wave component is ΔP, then ΔP = a xcO3ωx t+a ycO3ωy
t+b xsinωx t+bysinωyt ・
...(b).

Taking the fundamental waveform component as an example, the relationship between the eccentricity of the composite roll and the rolling load variation can be expressed as follows.

where ΔP: variation in rolling load based on synthetic roll eccentricity (axis deviation) ΔS: variation in roll gap due to roll eccentricity K; rigidity of the rolling mill M; plastic constant of the rolled material, therefore variation in rolling load By continuously detecting ΔP, a value ΔP(t) proportional to the amount of combined roll eccentricity can be obtained.

The CO8 component is A1, s when this rolling load variation is expanded using trigonometric functions using the lower roll period as a reference interval.
Assuming that the in component is B1, A and B1 can be found from the value of ΔP(t) using the following equation using the method of Fourier analysis.

Here, the nth-order wave component, which is half the sampling number of N; ΔP(t), can be similarly calculated.

Expanding this formula becomes.

(For details, refer to calculation formula (1) described later) where n;
Number of roll rotations ζω-ωX-ωy after starting the analysis In this way, A1. Find B1.

Next, shift the engagement angle of the upper and lower rolls, and use the formula (to), (
Create an expression corresponding to

ax←a xcosα+ b X51nαbx←−aX
S1nα+bXCosαα; Since this is the shift angle, the eccentricity synthesized at this time is as follows.

If there is no diameter difference, Sω=0, so equation (to),
(G), ff-), and (IJ) are corrected using the following formula.

A1-aX+ay ”°B1=bx
+by −・・−・−Ql/)A2= a y+
a XC03(X + b xslna −・−・
<MB2 = b y-a xslna + b xc
O8a −・”('7).

However, since there is generally a difference in diameter, it is necessary to find the combined roll eccentricity by averaging n rotations, so the detected combined eccentricity An1jBn1
, An2, and Bn2 are as follows.

An1=ay+kcax+ksbx -(#)B
nl: by+kcbx-ks ax
-(Yo)An2 = ay+kc(axcO3α+
bxs1nα) + k s (-axs1nα+ bx
cO3α)-----(evening) B B2 = by+kc
(-axs1na+ bxcO3α)+k s (
a xcO3α+ b xslna) ・・, −(LJ
Here, An1 to Bn2 are the detected values (in the formula), (e)
α (shift angle) is known, kc.

Since PG is attached to each of the upper and lower rolls, ks can be found by calculating the diameter difference from this value. Therefore, by solving the four-dimensional linear simultaneous equations of equations (to) to (L)), ax, bx, You can find ay and by.

The ax, bx, ay, by obtained here are (nu) ~ (
By substituting into formula r7), A1. B1. A2. B2 can be found.

As mentioned earlier, in plate mills, the plate during rolling repeats biting and slipping, so there is a possibility that the relative positional relationship between the upper roll and lower roll will deviate between when the analysis is performed and during rolling. be.

Therefore, if the eccentricity is determined separately into the upper roll component and the lower roll component using these A1-B2 and the two components are combined in accordance with the respective phases, the correct combined eccentricity can be obtained at any time.

A method of separating the amount of eccentricity into upper and lower roll components will now be described.

(For details, refer to calculation formula (II) described later) Note that for convenience of explanation, vector quantities will be used in the explanation.

The eccentricity of the upper backup roll is now a hole, the eccentricity of the lower backup roll is Y, the first combined eccentricity when the upper work roll and lower work roll are kiss-rolled is Δ50, and further from this state , the second resultant eccentricity when the relative angle of the lower back up roll is shifted by α (shift angle) and the kiss roll is performed again is ΔS2, and the relative shift angle of the upper and lower back up rolls is α , the phase difference between ΔS1 and A52 is β, the initial phase of ΔS is 61, ΔS2
If the initial phase of is 62, the initial phase of death is θx, and the initial phase of "yl" is θy, then X and Y can be expressed as follows from the geometrical relationship in FIG.

This is A1- B instead of IΔS11.1Δg2+
It is expressed as 2.

(For details, refer to calculation formula (n) described later.) Now, the eccentricity of the upper back-up roll\ and the eccentricity Y of the lower back-up roll are values obtained when the upper work roll and the lower work roll are in a kiss roll state. However, these quantities are output as control signals during rolling of the plate.

Therefore, the control signal must be corrected during rolling based on Y, θX, and ey, which are obtained during kiss rolling.

This correction operation is called an integral operation and will be described next.

Assuming that the control signal for the upper backup roll eccentric component is ffX, and the control signal for the lower backup roll eccentric component is ey, these are expressed by the following equation.

ex = (IX' I ・cosθX)CO5ωxt
+ (1$l −sinθX)sinωxt,,
,,,,(@-ffy=(lYl ・cosθy)CO
5ωyt+(IYI-sinθy) Sinωyt
After the "" (+) plate is engaged, the above control signal is output for one cycle, and at the same time, the variation of the rolling load is sampled at every fixed machine angle, and after the sampling of the - cycle is completed, the resultant eccentricity IΔ$1 is calculated by the following formula. calculate.

Here, A and B are obtained from formulas) and (e).

be.

This 1ΔS'1 upper roll component is 1Δ3. 'lx, and if the lower roll component is 1Δ$'1 y, then from Figure 4, 1Δcf, /+ 2= +Δ$'12x+IΔS'1
2y2゜+21Δ$'I X・1Δ5'l y-C...
Looking down, C=C03((θX-θy)±Δθ), θX,
ey is "1st X1=1me1 2nd X2-X1±1ΔS I X1 3rd X3-X2±1ΔS I X2 nth X n = X n-1±1Δ51x(n-1
) Here, Xl, X2,... Xl, X2, ..., Xn and ¥1.Y2 of the value formula (b) to be substituted n times,
..., if Yn is calculated and output, it refers to the initial phase when x and Y are calculated at the biased kiss roll of the upper backup roll, and Δθ is the current initial phase difference (θX'-θy and the kiss roll) This is a deviation from the initial phase difference, and Δθ is zero if there is no deviation in the upper roll phase and lower roll phase between the kiss roll analysis and the current state.

(Δθ=(θX-θy)=(θX'-θy')) Each amplitude of × and Y analyzed by kiss roll (1×1, I
Since the ratio (m) of YI) remains constant as long as the shape of the roll does not change, IXI: l'71=lΔ$Jx:lΔS' ly
Therefore, if 1Δf)' ly=m ・lΔ$Jx, equation (6) becomes 1Δ(j, / + 2 = +3%' l 2x (
1+m" +2mc) Therefore, here, 1ΔSlx; upper roll component 1ΔSly of composite eccentricity 1ΔS1; lower roll component 1 to n times of composite eccentricity 1ΔS1, calculate the following, and calculate the following equations, (1), (J+)
Assign to .

The amount of center X and the amount of eccentricity Y of the lower back up roll can be determined.

Embodiments of the present invention will be described in detail below with reference to the drawings.

FIG. 5 is a block diagram of a device for removing the effect of roll eccentricity used in the method for measuring roll eccentricity according to the present invention, and FIG. 6 is an explanatory diagram of a rolling mill using the method for measuring roll eccentricity according to the present invention. .

In Fig. 5, 1 is a roll pressure transducer (load cell) for detecting the total pressure of the upper and lower rolls, 2 is an upper backup roll pulse generator, 3 is a lower backup roll pulse generator, and 4 is an analysis start push button switch. , 5
is a coat roll on/off switch, 6 is a coat roll mode selection push button switch, 7 is an interlock contact signal,
8 is a roll eccentricity effect removal control panel, 9 is a phase shift request lamp, 10-1 is an analysis A lamp, 10-2 is an analysis B lamp, 11 is a control display lamp, and 12 to 24 are roll eccentricity effect removal control panels. 12 is a roll pressure eccentric component calculation circuit, 13 is a direction determination circuit, and 14
Input buffer 15 is an A/D converter, 16 is a position check circuit, 17 is an interrupt circuit, 18 is an input/output circuit, 19 is a central processing unit (CPU), 20 is an upper roll/A converter, and 21 is an input/output circuit. A/A converter for the lower roll, 22, 23, and 24 a potentiometer or gain adjustment device, and 25 a rolling mill control device consisting of a hydraulic pressure reduction control device, a roll position control actuator, and the like.

In Fig. 6, 26 is an upper work roll, 27 is a lower work roll, 28 is an upper back-up roll, 29 is a lower back-up roll, 30 is a servo valve, and 31 is a servo amplifier. Items with the same symbol indicate the same item.

Regarding operation: Eccentricity with the same period as the roll rotation (fundamental wave)
will be explained as an example.

This measurement method requires offline analysis and online control.

To perform offline analysis, first press the analysis start push button switch 4 with the upper workpiece opening roll 26 and lower workroll 27 in a kiss-roll state.

An interrupt occurs in the central processing unit 19 via the input buffer 14 and the interrupt circuit 17, and offline analysis is requested.

Further, in order to check the conditions for starting the analysis, the interlock contact signal 7 enters the input/output circuit 18 via the input buffer 14, and is then input to the central processing unit 19.

If the conditions of the input input to the central processing unit 19 are satisfied, the next operation, the first Fourier analysis, is performed and at the same time the analysis A lamp 10-1 is lit.

Fourier analysis is performed using either the upper or lower back-up roll pulse generator 2 or 3 of the upper or lower back-up roll 2829 as a reference, but in the method for measuring roll eccentricity of the present invention, the lower back-up roll is used as a reference. explain.

Both the upper roll pulse generator 2 and the lower roll pulse generator 3 output two types of output pulse signals: 60 pulses/rotation and /pulse/revolution.

The former is called a sampling pulse, and the latter is called a mark pulse.

The first mark pulse of the lower backup roll 28 is input as an interrupt signal to the central processing unit 19 via the direction discrimination circuit 13 and the interrupt circuit 17, and then Fourier analysis is started.

Further, the sampling pulse generated next to the mark pulse is similarly input to the central processing unit 19, and the next calculation is performed for each sampling pulse.

(In the case of N=30) Here, ΔP(X); A1.F!1 after one rotation of the lower backup roll 28 is determined from the read value formula (m, ()) for the variation in rolling load at the X-th pulse.

[However, as mentioned above, this includes a phase error if there is a diameter difference between the upper and lower backup rolls.

Therefore, the true values of these A, , B1 are determined after performing the second analysis. It is determined by performing phase correction calculation simultaneously with B2.

The calculation method will be explained in detail in the second analysis. ] At this point, the first analysis ends and the analysis parump 10-1 disappears.

When the first Fourier analysis is completed, the central processing unit 1
The phase shift request lamp 9 is turned on by the output signal from the phase shift request lamp 9.

At the same time, the output signal from the central processing unit 19 causes the phase angle to be shifted (
(number of sampling pulses).

The roll shift is performed by once separating the upper work roll 26 and the lower work roll 27 from the kissing roll state and speeding up one of the work rolls (for example, the upper work roll 26).

Upper backup roll 28 and lower backup roll 29
The shifted phase angle is checked by the phase check circuit 16, and when it matches the preset phase angle, a signal is input to the central processing unit 19 via the interrupt circuit 17.

At this time, the output from the central processing unit 19 turns off the phase shift request lamp 9, so the operator stops the shift operation by turning off the lamp 9 and returns the upper and lower work rolls 26 and 27 to the kiss roll state. Perform operations.

When the upper and lower work rolls are in the kiss roll state, the analysis start push button switch 4 is pressed again and the central processing unit 19 performs a second Fourier analysis in the same manner as described above to obtain the next value.

At this time, the analysis B lamp 10-2 lights up.

A1- found from the formula (m, ()), (ko), ((1)
B2 is the formula (a)) (yo), (evening), (- Am1~Bm
2 to find ax-by, and use this as the formula (nu), (/L
), (wo), and (wa) to find the true A1-B2 with the phase error corrected.

In order to obtain the eccentricity of the upper back-up roll 28 and the lower back-up roll 29 from the results of the first and second Fourier analysis, the central processing unit 19 calculates the component 1×1 of the upper back-up roll 28 and the lower back-up roll 28. Atsuprol 2
The component I Y 1 of 9 is determined by the above-mentioned equations (n) and (t).

Also, the formula (,t), CtJ). (U) (Determine the sin and cos functions of the initial phases θX and θy from the gradients.

When these calculations are completed, the analysis B lamp 10-2 is turned off by the output signal from the central processing unit 19.

The above analysis start operation, the first Fourier analysis,
The roll shift operation and the second Fourier analysis are performed twice or more, and the components of the upper backup roll 28 and lower backup roll 29 in the maximum case are adopted as the final values to obtain accurate values. data can be obtained.

Next, the case of online control will be explained.

The start of online control (from board biting to before mark pulse input) is started by pressing the control on/off switch 5 after the offline analysis is completed, and the signal enters the interrupt circuit 17 via the input buffer 14 and enters the central processing unit 19. This is an interrupt signal, and the central processing unit 19 checks whether online control can be performed.

When the biting signal of the interlock contact signal 7 is turned on, the biting signal is input to the central processing unit 19 via the input buffer 14 and the input/output circuit 18, and the central processing unit 19 calculates the next value. do.

#x = (IX l −cosθx)CO3ωXt+
(l, gl-sin θX)S1nωXt・・・・・・(
Force ty-(IYl・cosθy)CO3O)y i+
(l'Y'l -5inθv')S1nωXt -...
...(A□ Here, PX: Upper backup roll eccentricity removal control signal (fundamental wave) 4y: Lower backup roll eccentricity removal control signal (fundamental wave) 1×1; Amplitude of upper backup roll eccentricity component (offline IYI: Amplitude of the eccentric component of the lower back up roll (offline analysis value) ωX, ωy: Angular velocity of the upper and lower back up roll θX, θy: Initial phase of the eccentric component of the upper and lower back up roll Calculated using the above formula The value is sent to the input/output circuit 18 as a control output.
The signals from the D/A converters 20 and 21 are added together and then added to the output signal of the rolling mill control device 25 as an eccentricity removal control signal.

Then potentiometer or gain adjustment devices 22, 23
, 24, the gain can be adjusted to find the optimum value of the control output signal.

At this time, the control indicator lamp 11 lights up.

Equation (7-), (1χ1 obtained by off-line analysis until the first mark pulse is input after board biting as in (71),
zX and #y are calculated using l'rr'l and used as a control output signal.

From the time the first mark pulse is input until the upper and lower backup rolls 28 and 29 make one revolution, the control signal is 4
At the same time as outputting ly, A and B are generated in the same way as offline analysis.
The following equation is calculated in the central processing unit 19 at the same time as the next mark pulse is input.

1Δ$1=J Shikomimi Ward...The following calculation is performed based on the value obtained by formula (7) and (s) in the judgment.

Assuming that the ratio of the amplitude of the upper back-up roll eccentric component and the amplitude of the lower back-up roll eccentric component determined by the offline analysis does not change during online operation, the following equation holds from the results of the offline analysis and FIG. 7.

1Δ51=1Δ1512x+1Δ$12y+21Δ$l
xiΔ$+y−c ...(-1) where I) Sl: Amplitude of the upper back-up roll component determined by offline analysis lYl: Amplitude of the lower back-up roll component determined by offline analysis m: l'71 and IYI ratio C=C03((θX-θy)±Δθ)...)' (Δθ is the difference between the initial phase difference between the current father and Y and the initial phase difference at the time of kiss roll) Above formula (1), 1Δ512=lΔ512x+(mlΔ51x)2+21
ΔSlx−mlΔ51x−C −1ΔS I2x (1+m2+2m−C)"H"H"Hence, 1ΔSly=mlΔS l x ""('J''desirably m\1, C\).

When m=1 and C=-1, it becomes 1Δ51-0.

(Eccentricity up and down cancellation) At this time, the control signal is not corrected.

1ΔSlx and 1Δsty determined by the formula (wing, ni) are then added to the control output signal determined last time as described below and used as the next control signal.

(Bite) → (before mark pulse input) (1st mark pulse) → (before 2nd mark pulse input) (2nd mark pulse) → (before 3rd mark pulse input) (0th mark pulse)→(before inputting the n+1 mark pulse) Therefore, the output signals -ex, 7y from the central processing unit 19 are as follows.

J! zo=(lχl cosθx )cosωx t+
(1) 31 sinθx )Sinω)(i4x 1=
(Xl-cosθX)CO8ωXt+(Xl・Sinθ
X)S1nωxt-eX2=((X1±Δ$X1)-C
O3θx ) C08(1)X t+(CXI±Δ5x
1) -5inθX)SinωXt4xn=((Xn-
1±Δ$X(n→)-CO3CX)CO3(1)X t
+ ((Xn-1)) -sinθX)sin>(t
.

Xo=1×1, Y(,=lYl x1=1'7+, Y1=lYI X2-X1±IΔ$IX1, ¥2=¥1±1Δ$1yt
X n = X n-1±1Δ$1x(n-i), Yn
=Yn-1±1Δ$ly(n-1) Roll pressure transducer (
The output signal of the load cell 1 includes a rolling load, a roll eccentricity component, and a pressure fluctuation component due to its disturbance.

Therefore, the roll pressure eccentricity component calculation circuit 12 performs the following calculation to extract the fluctuation component with respect to the value when there is a rolling load as a reference.

ΔpR=pRPRO where PR, ;Output signal of roll pressure transducer 1]-aO
: Output signal ΔPR of the held roll pressure transducer 1 at a certain moment; variation in rolling load (output signal of eccentric component calculation circuit) This result is input to the central processing unit 19 via the A/D converter 15 be done.

In addition, although the above-mentioned operation has been explained using the fundamental wave as an example, it originally includes up to the n-th harmonic if expanded into a Fourier series.

Therefore, it is determined in advance which harmonics are to be analyzed, and the control mode selection push button switch 6 is used to determine which harmonics to combine.

For this operation, the same number of pushbutton switches as the number of harmonics are provided, and the operator can select the pushbutton switch arbitrarily by pressing the pushbutton switch.Calculation formula (I) P(t)-ag +a XC03(cJX t+a y
cO3ωy t+ b xs1nωx t+b ys1
nωy t〈CO8 component〉 (ωX-
ωy + ζω) P (eliminate O8ωytdt ωX Upper roll angular velocity ωy: Lower roll angular velocity B2= ) (sinθx + YSln (θM+(1
)ysinθy (cos a-1)+Ycosθys
ina=B2-E31 (Force (6) is determined for Y and substituted into equation (7), (2)
, Calculate XCO3θX, X5inθX using equation (3) and substitute them into equations (4) and (5;
Separate na=A2-A1 (6) sinθy, CO39) into both sides and find tanθy. Similarly, calculate cosθy and Slnθy from equation (8), and cosθX and sinθX from equation (9), and use equation (1). According to equation (1) 7, FIG. 9 is a graph in which the present invention was confirmed using the simulation circuit shown in FIG. 8.

According to the above-mentioned method for measuring the roll eccentricity state of the present invention, various excellent effects are exhibited as shown below.

(1) Even if there is a diameter difference between the upper and lower back up rolls, roll eccentricity control can be performed, and the influence of eccentricity on the plate thickness can be reduced.

(11) Even if the phases of the upper and lower rolls shift during analysis of the composite eccentricity, this can be correctly analyzed and separated into the eccentric components of the upper and lower rolls.

+m) Even if the phase of the upper and lower rolls shifts during rolling, each eccentric component is output as a control signal synchronized with the sampling pulse of each PG, so the change in eccentricity caused by this phase shift can be quickly corrected. can respond to

lψ Since an eccentric component unique to the phase of each roll can be calculated, continuous control is possible even when the rolls repeatedly rotate forward and reverse.

]■ At the same time as outputting the control amount (eccentricity component), the rolling load in each phase is Fourier analyzed for each rotation.

Since the amount that could not be controlled (or controlled too much) is analyzed and this is added as a control correction amount in the next rotation, the convergence of the control signal (integral operation) is fast, and it is suitable for machines such as plate mills that quickly remove metal. It's suitable.

[Brief explanation of the drawing]

FIGS. 1 and 2 are explanatory diagrams showing problems with the conventional method in an easy-to-understand manner, FIGS. 3 and 4 are vector diagrams for explaining the present invention in detail, and FIG. A block diagram of a roll eccentricity effect removing device used in the method for measuring roll eccentricity of the present invention, FIG. 6 is an explanatory diagram of a rolling mill to which the present invention is applied, and FIG. 7 is for performing calculations in the measuring method of the present invention. 8 is an explanatory diagram of the simulation circuit, FIG. 9 is a diagram confirming the present invention using the circuit of FIG. 8, and FIG. 10 is a diagram for calculating the measurement method of the present invention. It is a vector diagram used. 1 is a roll pressure transducer, 2 and 3 are upper and lower back-up roll pulse generators, 8 is a roll eccentricity effect removal control panel, 12 is a roll pressure eccentricity component calculation circuit, 13 is a direction determination circuit, 14 is an input buffer, 15 is A/D
Converk, 16 is a position check circuit, 17 is an interrupt circuit, 18 is an input/output circuit, 13 is a central processing unit, 20 and 21 are for upper and lower rolls/A converk, 25 is a rolling mill control device, 26 and 27 are upper and lower work rolls;
28 and 29 are upper and lower backup rolls, and 30 is a servo valve.

Claims (1)

[Claims] 1 Generate two types of output pulse signals: sampling pulses (number + pulses/1 rotation) and mark pulses (1 pulse/1 rotation) from the pulse generators attached to the upper backup roll and lower backup roll, respectively. Then, the rolling mill is started with the upper work roll and the lower work roll in a kiss roll state, and when the mark pulse of any backup roll is transmitted, at least the following The first Fourier analysis was performed until the mark pulse signal was transmitted, and the composite amplitude of the upper and lower back-up rolls was determined.Then, the second Fourier analysis was performed by shifting the phase of the upper and lower back-up rolls. The composite amplitude of the upper and lower rolls was calculated, and the composite amplitude was calculated in the first and second analysis by taking into account the amplitude error due to the difference in diameter of the lower roll (natural slip in the phase of both rolls). A method for measuring roll eccentricity, characterized in that the true Fourier coefficient is determined from the true Fourier coefficient, and eccentric components of upper and lower rolls are determined separately.