JPS649087B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Field of Application] The present invention relates to a method for measuring the eccentricity of a rolling roll. [Prior Art] Generally, in sheet thickness control during rolling, the rolling load and the gap between work rolls (work roll gap) are controlled in a correlated manner. In the case of plate thickness fluctuations caused by so-called skid marks, automatic gauge control (AGC) operates to narrow the work roll gap when the monitored rolling load increases. By the way, plate thickness control using automatic gauge control cannot fully meet the strict accuracy requirements of users, so various other factors that contribute to plate thickness accuracy have been studied, and eccentricity of the rolling roll has been considered as an important factor. It has been pointed out. Such eccentricity of the rolling roll is caused by thermal deformation during rolling,
This is caused by uneven wear or deviation from the perfect circle during regrinding of the work roll. In response to an increase in rolling load caused by roll eccentricity, it is necessary to control the work roll gap to widen it, and control characteristics that are opposite to those caused by plate thickness fluctuations due to skid marks, etc., are required. Ru. in this case,
Variations in rolling load caused by eccentricity of rolling rolls are superimposed on rolling loads caused by variations in plate thickness due to skid marks, etc., and are detected as superimposed rolling loads. When the gauge control is performed, the variation due to the eccentricity of the rolling rolls is added in the opposite direction with respect to the control of the work roll gap, which significantly reduces the accuracy of the control. For this reason, several methods have been proposed for measuring or estimating eccentricity parameters (eccentricity amplitude, eccentricity phase) of rolling rolls. The typical method is that rolling load fluctuations due to eccentricity of the rolling rolls appear at relatively short cycles (relatively high frequency) synchronized with the rotation of the rolling rolls, whereas fluctuations in plate thickness due to skid marks, etc. Since rolling load fluctuations appear in a relatively long cycle (relatively low frequency), the rolling load fluctuations detected by superimposing these are sampled over a rotation range of one or more rotations of the rolling roll.
This is a method of subjecting these sampled values to frequency analysis (Fourier analysis) to separate and extract rolling load fluctuations resulting from eccentricity of individual rolling rolls obtained as high frequency components. However, the above-mentioned Fourier analysis method requires a huge amount of calculations and a long calculation time, and it is practically impossible to execute the above-mentioned method during online control of plate thickness. In order to improve this problem, the Special Publication No. 56-22281
The publication focuses on the eccentricity of the upper and lower back-up rolls, and performs the first Fourier analysis and the second Fourier analysis with the upper and lower back-up rolls out of phase. A method has been proposed in which the amplitudes of the upper and lower back-up rolls are separated and extracted from the relative amplitudes obtained by the first and second Fourier analysis. However, this method does not solve any of the essential problems of the Fourier analysis method.
Since only the eccentricity of the upper and lower back-up rolls can be estimated, and the phases of the upper and lower back-up rolls need to be changed during the measurement, this method can only be performed offline, and is also inefficient. On the other hand, Japanese Patent Publication No. 56-43803 discloses a signal obtained by detecting a rolling load or a work roll gap, and delaying this detection output by a delay time τ, a roll rotation fundamental wave signal, its high frequency signal, and a signal of the upper and lower rolls. An eccentricity measurement method has been proposed in which the correlation with the beat wave signal determined from the sum of the rotational fundamental wave signals is determined for each signal by varying the delay time τ, and the amount of roll eccentricity and the eccentricity phase are determined from the correlation results. ing. This method has the advantage of being able to detect the eccentricity of the rolling roll without using Fourier analysis, but only takes into account the fundamental frequency of the reference back-up roll, its harmonics, and the beats of the upper and lower back-up rolls. Therefore, the model is simplified and the obtained eccentricity etc. may not necessarily represent the actual value, so it is difficult to expect high accuracy. Furthermore, since the above two methods perform calculations based on multi-point data obtained, for example, during one rotation of the back-up roll, the time interval between one control operation and the next control operation becomes long. The basic drawback is that continuous control cannot be performed. [Object of the Invention] The object of the present invention is to develop an eccentric state of a rolling roll that allows accurate calculation of the eccentric amplitude and eccentric phase of each rolling roll for each measurement of rolling load or work roll gap. The objective is to provide a measurement method. [Structure of the Invention] The basic feature of the present invention is to calculate the vector quantity, which can be called an eccentricity vector, with respect to all the rolls constituting a rolling mill, assuming that each roll has its own eccentricity amplitude and eccentricity phase. introduced,
Focusing on the fact that the rolling load fluctuation or work roll gap fluctuation that appears as a synergistic result of the eccentricity of all the rolling rolls can be linearly expanded by each component of the above vector, this vector quantity can be calculated based on the sequential form identification rule. The reason is that estimation is performed sequentially each time measurement data is obtained. Once each component of the vector is obtained, the eccentricity amplitude and eccentricity phase of each rolling roll can be determined by simple calculations. [Effects of the Invention] According to the present invention, the eccentricity parameters (eccentricity amplitude, eccentricity phase) of the rolling roll can be obtained for each measurement, so during online control, feedforward control can be performed continuously and with good responsiveness. can be done. Further, according to the present invention, since the sequential identification rule is used, the accuracy of the obtained estimated value of the roll eccentricity parameter can be calculated at the same time. Therefore, it is possible to determine the number of measured values required to obtain desired accuracy in off-line roll eccentricity parameter measurement performed during kiss roll operation before the start of rolling operation.
Furthermore, by determining the convergence of such accuracy, the validity of the adopted roll eccentricity model can be evaluated, and the eccentricity model can be switched as necessary. [Embodiments] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. As shown in FIG. 1, in this embodiment, a rolling mill 5 in which work rolls 1 and 2 are supported by upper and lower back up rolls 3 and 4 will be considered. A load cell 6 for detecting the rolling load P is provided for the upper back up roll 3, and a roll gap adjustment means 7 for adjusting the roll gap of the work rolls 1 and 2 is provided for the lower back up roll 4. is provided. Also,
The rotation angles θ ₁ , θ 2 , θ 3 , θ 4 of the upper and lower work rolls and the upper and lower back up rolls 1, ₂ , ₃ , and ₄ are as follows:
The signals are detected by pulse generators 8, 9, 10, and 11, respectively. The rolling load P detected by the load cell 6 and the rotation angles θ 1 , θ 2 of the upper and lower work rolls and the upper and lower back up rolls ₁ , 2, 3, ₄ ,
θ ₃ , θ ₄ , and the control output ΔSc for the roll gap adjustment means 7 are input to the computer,
The computer performs the following processing based on these input data. <Data processing> [] Signal processing routine Data is read at a predetermined sampling timing (for example, the pulse generator 10 of the upper backup roll 3
pulses can be used. ), and the read data is subjected to preprocessing such as removing the DC component of the rolling load signal P, for example. Now, generally speaking, in rolling using a rolling mill,
The amount of change ΔP in rolling load when the work roll gap changes by ΔS is: ΔP=-(MQ/M+Q)ΔS...(1) However, M...Equivalent mill constant of the rolling mill Q...Rolled material This is the plasticity coefficient of the material. However, since Q=∞ during kiss rolling before rolling operation, MQ/(M+Q)=M
It is. The roll gap change amount ΔS is a composite amount of the roll gap change component ΔSc due to control and the roll eccentric component ΔSe, which is a superposition of the eccentric components of each rolling roll. ΔS = ΔSc − ΔSe ...(2) The amount of change in rolling load ΔP is determined from the value of the signal obtained by removing the DC component from the output of the load cell 6, and the roll gap change component due to control ΔSc
can be detected from the control output to the roll gap adjustment means 7. Therefore, of the rolling load change ΔP, the component ΔPe due to roll eccentricity can be determined from equations (1) and (2) as follows. ΔPe=-(MQ/M+Q) ΔSe = ΔP+(MQ/M+Q) ΔSc (3) The above processing is performed in the signal processing routine []. [] Estimation calculation of eccentricity parameter For simplicity, if we ignore the harmonic components of each roll's eccentricity and approximate each roll's eccentricity with a sine wave of the roll's fundamental frequency θi, the roll gap change ΔSe due to roll eccentricity is The eccentricity of each roll can be expressed by the following equation. ΔSe= ₄ 〓 ⁱ⁼¹ Ai・sin(θi+φi)...(4) However, i...Roll number Ai...Eccentricity amplitude of each roll φi...Eccentricity phase of each roll θi...Rotation angle of each roll Above In equation (4), the rotation angle θi of each roll is
It is known from the output of each pulse generator 8 to 11, and can also be determined by continuously measuring the angular velocity ωi of each roll and integrating it over time. Now, the load change due to roll eccentricity obtained in synchronization with the k-th sampling pulse is ΔPe
(k), and the rotation angle of each roll is θi(k), (4)
From the formula, ΔPe(k) = (MQ/M+Q) ΔSe+n(k) = (MQ/M+Q) ₄ 〓 ⁱ⁼¹ Ai・sin(θi(k)+φi) +n(k) = (MQ/M+Q) ₄ 〓 ⁱ⁼¹ [Ai・cosφi・sinθi(k) +Ai・sinθφi・cosi(k)] +n(k) ...(6) Here, n(k) is observation noise (measurement error) when measuring ΔPe(k). Now, the rotation angle θi(k) of each roll is a known quantity.
vector a→(k) whose vector components are the sine and cosine of
A vector x whose component is represented by a function of φi→
(hereinafter referred to as eccentric vector) is defined as follows. Using the vectors defined in equations (7) and (8) above, equation (6) can be expressed as follows. ΔPe(k)=a→ ^T (k)・x→+n(k) ...(9) This equation (9) is the inner product of the known vector a→ and the unknown eccentricity vector x→, and the rolling due to roll eccentricity is This means that the load component ΔPe(k) is expressed, in other words, it is expressed as a linear function of the component xi of the eccentric vector x→. Therefore, the eccentricity vector x in equation (9) above →
A sequential identification rule can be applied to estimate . Now, the estimated value x→ of the eccentricity vector x→ based on the measurement results synchronized with the k-th sampling pulse
(k) can be determined by the following equation according to the sequential form identification rule. However, the vector g(k) is called the gain vector, is given by Further, B(k) is a covariance matrix representing estimation accuracy, and is given by the following equation. Note that x→(0) can be appropriately given as the initial value of the estimated value, and the covariance matrix B(0) can be appropriately given as the initial value of the covariance matrix of the estimated value. Furthermore, the parameters λ ₀ , λ ₁ , and λ ₂ are parameters for adjusting the estimation function, [λ ₀ =λ ₁ =λ ₂ =1]
Then, the estimation is by the sequential least squares method,
[λ ₁ = 1, λ ₀ = 1/λ ₂ = σe ² (σe ² is the observation noise n(
k)
power)], then it is estimated by Kalman filter. Also [λ ₂ = 1, λ ₀ = λ ₁ = γ (0.995<γ<1)]
If set as , the estimation is performed using the weighted least squares method, and it is possible to speed up the tracking speed for changes in the eccentric state due to thermal expansion of the roll or the like. By the above calculation, each component xi of the eccentric vector x→
Once the estimated value of is obtained, the eccentricity amplitude Ai of each roll,
The eccentric phase φi can be determined as follows. Ai = √ ² _2i-1 + ² _2i ... (13) φi = tan ^-1 (x _2i / x _2i-1 ) ... (14) In the above manner, the eccentricity parameter is estimated for each roll. It turns out. Such estimation calculation is performed in the eccentricity parameter estimation calculation routine []. [] Estimation accuracy/model discrimination This discrimination utilizes the properties of the above covariance matrix B(k) to determine the accuracy of estimation and the validity of the model used for estimation. The sum trB of the diagonal components of the above covariance matrix B(k)
It is known that (k) satisfies the following relationship. trB(k)∝E [‖x→(k)−x→(k) ^‖2 ]
...(15) However, E(f) represents the expected value of f. In other words, trB(k) corresponds to the accuracy (dispersion) of the estimated value x→(k) of the eccentric vector x→, and thereby the current estimation accuracy can be confirmed. In addition, in general, the number of samples of rolling load (k)
As trB(k) increases, trB(k) decreases, so
By setting an appropriate tolerance for this trB(k) in advance, it is possible to determine the number of samples that will fall below the tolerance.For example, in offline eccentricity parameter estimation performed in a kiss-roll state, samples that fall below the tolerance can be determined. By terminating sampling when the number of samples is reached, offline measurements can be performed in a short time and without waste. On the other hand, the sum of diagonal components of the above covariance matrix B(k)
There may be cases where trB(k) does not converge below the tolerance. This can occur, for example, if there are two or more rolls with exactly the same radius. That is, in this case, since the eccentricity caused by these rolls having the same diameter has exactly the same frequency, it is impossible to separate and measure these eccentricity parameters from the rolling load signal. In fact, if trB(k) does not converge to a small value, at the time of estimation in the kiss-roll state, the model is changed to a reduced model that approximates one roll eccentricity by combining the eccentricities of rolls with the same diameter. The above determination process is actually performed in the following order before starting rolling of the material. First, in step ()-1, when the sampling number k reaches a preset number K, trB(K) is compared with a preset model judgment threshold ε ₁ , and trB(K)>ε When it is ₁ , it is assumed that there is no convergence and the model is switched to a synthetic model (described in detail below). When trB(K)≦ε ₁ , estimation is continued using the initially set initial model. In addition, in step ()-2, for each estimation calculation, trB(k) is compared with a preset threshold value ε ₂ (ε ₂ < ε ₁ ) for determining accuracy, and it is determined whether the threshold value ε ₂ has been reached. If not, the estimation calculation is continued using the same process as in [] and [], and the estimated values are sequentially updated. When trB(k) falls below the threshold value ε ₂ , it is determined that the accuracy of the estimated value is sufficient, and the off-line estimation calculation in the kiss-roll state is terminated. [] Eccentricity parameter calculation using a composite model For example, if the roll diameters of work rolls 1 and 2 are exactly the same, the eccentricity of these two work rolls is combined and replaced with the eccentricity of one roll. In other words, after replacing the sum of the eccentricities of the two rolls with one eccentricity A ₁₂ sin (θ ₁ +φ ₁₂ ),
The composite eccentricity parameter is calculated in the same manner as above. [] Determination of eccentricity parameters Before the start of rolling operation, the off-line estimated values obtained by the above processes [] to [] are stored in a predetermined address of the computer as eccentricity parameters of each roll. <Online Eccentricity Control> Next, an example of an online eccentricity control method will be described. If the roll eccentricity state does not change during rolling, the roll opening degree can be controlled to compensate for the roll eccentricity by feed forward using eccentricity parameters determined off-line. In this case, roll eccentricity changes due to thermal expansion of the roll, etc., so online correction is required. As mentioned at the beginning, online control using this estimation method has the characteristics of rapid response and scalability to multi-frequency components, but here we will discuss a control method based on the conventional control method. explain. A^ ₁ off ~ A^ ₄ off, with estimates of the amplitude and phase of the roll eccentricity estimated and memorized offline.
Assuming that φ^ ₁ off ~ φ^ ₄ off, the roll gap variation due to roll eccentricity at each time point k estimated from this is ΔSe → off (k) = ₄ 〓 ⁱ⁼¹ Ai → off sin (θi (k) +φ^ioff) ...(16) It can be estimated. On the other hand, online estimation is performed using, for example, the standard back-up roll 3 as a model for roll eccentricity.
The model consists of a sine wave with a frequency of , and As and φs
We use a simplified model that only requires estimating Parameter estimation is performed in the same way as in the process of , in FIG. 1 using data for one rotation of the reference roll. The obtained estimated value is used for feedforward control of the amount of roll eccentricity during the next revolution. In other words, if the obtained estimated values are A^on and φ^on, then the estimated value of roll gap fluctuation due to roll eccentricity at time k during the next rotation is ΔSe→on
(k) is ΔSe→on(k)=A^on・sin(θ(k)+φ^on)
...(17) becomes. As mentioned earlier, an online method is essential to deal with changes in roll eccentricity over time. However, when trying to use the above-mentioned simplified model as an online method, it is necessary to use the estimation results from a strict model obtained offline to express the beat phenomenon caused by the superposition of the frequency components of each roll. I need to make up for it. Therefore, in general, control is performed using the weighted average of the estimated values of eccentricity obtained from both, ΔSe→(k)=α・ΔSe→off(k) +(1−α)・ΔSe→on(k)...( 18) However, 0≦α≦1 is used. In order to cancel ΔSe→(k), feedforward control is performed so that the roll opening degree ΔSe(k) at time k becomes ΔSc(k)=ΔSe→(k) (19). <Results of implementation> Next, results of implementation according to the method of the present invention will be described. The eccentric amplitude Ai, eccentric phase φi, and roll radius Ri of each roll used in this experiment were as shown in the table, and the rolling speed was 300 (m/min). Ninety pulses were emitted from the pulse generator 10 for each rotation of the upper back-up roll, and the rolling load was measured approximately every 10 msec using these pulses as sampling timing. Note that the power of observation noise was assumed to be 2 (ton ² ). FIG. 2 shows the rolling load change ΔPe due to eccentricity. Based on this rolling load change ΔPe, λ ₀ = 2, λ ₁ =
1. Eccentricity parameters were successively estimated using a Kalman filter with λ ₂ =0.5.

[Table] FIG. 3 shows the eccentricity amplitude of each roll obtained by estimation calculation, and FIG. 4 shows the eccentricity phase of each roll. As is clear from a comparison with the table above, it can be seen that the estimated values converge to the true values in a very short period of time. Also, from Figure 5, trB, which is related to estimation accuracy,
It can be seen that (k) also quickly reaches a value of 10 ^-5 or less. Furthermore, in Figures 6 and 7, in equation (18), α = 0 (that is, when only the simplified model is used)
and the rolling load fluctuation ΔPe when α=1 (based only on off-line estimation using a strict model). In the simplified model, as shown in Fig. 6, the influence of roll eccentricity is not sufficiently removed, whereas in the case of Fig. 7, the roll eccentricity is The influence of has been almost eliminated. In the above embodiments, harmonic components of roll eccentricity have been ignored for the sake of simplicity, but as is clear from the estimation principle according to the present invention, this type of harmonic components can be easily incorporated into the estimation calculation. Further, in the above embodiment, a four-high rolling mill has been described, but the number of stages is not limited, and it goes without saying that the eccentricity parameter of each roll in a multi-high rolling mill can be determined. Furthermore, online control of roll eccentricity is not limited to the above-mentioned simplified model, but can be performed online using a strict model to perform calculations for estimating eccentricity parameters according to the method of the present invention, and based on the obtained eccentricity parameters. Needless to say, eccentricity control can be performed by

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing a roll eccentricity measuring system according to the present invention, FIGS. 2 to 7 are graphs showing calculation results according to the estimation method according to the present invention, and FIG. Fig. 3 and Fig. 4 show the convergence state of the roll eccentricity amplitude and eccentricity phase obtained by the estimation method, respectively, and Fig. 5 shows the change in trB representing the estimation accuracy. 6 and 7 respectively show the case where the roll eccentricity control is performed using only the simplified model and the case where it is performed using only the off-line estimated value of the exact model.

Claims (1)

[Claims] 1. Detect variations in rolling load due to eccentricity of rolling rolls, linearly expand the variations into vector components represented by eccentric amplitude and eccentric phase of each rolling roll, and calculate these vector components at predetermined timings. A method for measuring the eccentricity state of a rolling roll, characterized in that the eccentricity amplitude and eccentricity phase of each rolling roll are calculated by sequentially estimating the eccentricity amplitude and eccentricity phase of each rolling roll using a sequential form identification rule.