JP2005297025A - Predicting method and controlling method of chattering in tandem rolling equipment - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To predict occurrence of chattering in tandem rolling equipment and to control the tandem rolling equipment on the basis of that prediction. <P>SOLUTION: In the tandem rolling equipment 1 in which a rolled stock 5 is continuously rolled with a plurality of rolling mills F(i), a self-excited vibration model of the rolling mill F(i) taking the vertical vibration of work rolls 3, 3 provided in each rolling mill F(i) and the tension vibration which is propagated in the interior of the rolled stock 5 during rolling into consideration is created and whether chattering in the rolling mill F(i) is caused or not is determined by using the self-excited vibration model. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a chattering prediction method in a tandem rolling apparatus and a control method for controlling the tandem rolling apparatus so that chattering does not occur using the chattering prediction method.

Conventionally, in a tandem rolling mill, when the rolling speed is increased, self-excited vibration occurs in the final rolling mill and the upstream rolling mill, and this trouble causes rolling trouble such as defective plate thickness and rolling material breakage. It is known to occur. This phenomenon is called chattering (self-excited vibration of a rolling mill), and has been particularly noticeable in cold sheet rolling. The vibration frequency of chattering is about 100 Hz to 700 Hz, and shows a value close to the natural frequency of the rolling mill.
It is known that the chattering phenomenon is related to rolling conditions such as the rolling mill's natural frequency, rolling lubrication state, rolling material tension and rolling speed. When this happened, chattering was avoided by reducing the rolling speed as an on-site response. However, other problems such as a reduction in productivity have occurred due to a reduction in rolling speed.

As a technique for avoiding such a chattering phenomenon, for example, there are Patent Documents 1 to 3 and Non-Patent Document 1.
In Patent Document 1, in cold rolling with a tandem rolling device, the lubricating oil film thickness is calculated on a work roll during high-speed rolling, and chattering occurs when the lubricating oil film thickness exceeds a set lower limit. In view of this, a technique for supplying lubricating oil so as not to exceed the lower limit is disclosed.
In Patent Document 2, in cold rolling by a tandem rolling device, a target range of a friction coefficient of a final rolling mill is set based on a friction coefficient of an upstream rolling mill adjacent to the final rolling mill, and the target range is set as follows. A technique for changing the lubrication conditions of the final rolling mill or the upstream rolling mill so as to satisfy the requirements is disclosed.

Patent Document 3 discloses that in cold rolling using a tandem rolling device, if the advance rate becomes negative, chattering is likely to occur, so that the reduction rate distribution, tension, and rolling are performed so that the advance rate of each rolling mill does not become negative. Techniques for controlling speed are disclosed.
On the other hand, Non-Patent Document 1 describes that a self-excited vibration model (chattering generation model) is constructed in consideration of the chattering generation mechanism. In this self-excited vibration model, in addition to the vertical vibration of the work roll of the rolling mill, horizontal vibration greatly contributes to chattering, and the chattering generation mechanism is modeled.
JP 09-239430 (pages 3 to 9, FIG. 1) JP 2000-94024 A (2nd to 7th pages, FIGS. 1 and 2) Japanese Laid-Open Patent Publication No. 03-151107 (first page to third page, FIG. 4) Ishino et al., “Vibration analysis of rolling mill chattering”, Transactions of the Japan Society of Mechanical Engineers (C), Japan Society of Mechanical Engineers, November 2003, Volume 69, No. 687, PP135-142.

However, Patent Documents 1 to 3 all deal with chattering prevention using the estimation formula obtained from the actual data, and after clarifying the mechanism of chattering occurrence, the preventive measures are taken. I have not taken it. Therefore, it is not a technique that can cope with chattering under different conditions.
Further, although the self-excited vibration model described in Non-Patent Document 1 is constructed after logically considering the mechanism of chattering occurrence, the tension acting on the rolling material is assumed to be constant, and a single rolling mill is used. It is focused on chattering that occurs. Accordingly, it is difficult to say that the self-excited vibration model reflects the behavior of vibrations in the entire tandem rolling apparatus, because the rolling mills affect each other to generate and increase vibrations.

  Accordingly, in view of the above problems, the present invention provides a chattering prediction method using such a model after constructing a self-excited vibration model considering the entire tandem rolling mill, and using the chattering prediction method, It is an object of the present invention to provide a control method for controlling a tandem rolling apparatus so as to prevent the occurrence of the above.

In order to achieve the above object, the present invention takes the following technical means.
As a result of observing and studying the occurrence of chattering in detail, the applicant of the present application, as shown in FIG. 1, in a tandem rolling mill, when self-excited vibration occurs in a certain rolling mill, the tension that propagates through the rolled material It was clarified that chattering occurred in the tandem rolling mill as a whole. That is, the inventors have reached the view that chattering is due to two important factors: vertical vibration of the work roll in each rolling mill and tension vibration in the rolled material that propagates the vertical vibration to the adjacent rolling mill.

Therefore, the inventor of the present application provided the technical means for solving the problem in the chattering prediction method of the tandem rolling apparatus, in each rolling mill, in a tandem rolling apparatus that continuously rolls the rolled material with a plurality of rolling mills. Create a self-excited vibration model of the rolling mill that takes into account the vertical vibration of the work roll and the tension vibration that propagates inside the rolled material during rolling. Using this self-excited vibration model, chattering occurs in the rolling mill. Presence or absence is predicted.
According to this technical means, it is possible to predict the occurrence of chattering under various conditions by using the self-excited vibration model.

In constructing the self-excited vibration model, first, the applicant of the present application is concerned with the vertical vibration of the work roll, and the vertical direction due to the vibration due to the fluctuation of the rolling load and the viscosity of the fluid existing in the rolling mill. And vibrations in the vertical direction due to the rigidity of the entire rolling mill were considered.
Furthermore, when the work roll of a certain rolling mill starts to vibrate up and down and the roll gap becomes narrower, the passage resistance of the roll gap becomes larger, and the transfer speed of the rolled material becomes slower, resulting in the tension in the rolled material. Will decrease. On the contrary, when the roll gap is widened, the transfer speed of the rolled material is increased, and as a result, the tension in the rolled material is increased. From the consideration of such a phenomenon, it has been considered that the vertical vibration of the work roll causes the tension vibration of the rolled material, which affects the adjacent rolling mill, and that the vibration affects the entire tandem rolling mill.

In view of the above, the applicant of the present application uses the self-excited vibration model as a work piece in which at least one of fluctuations in rolling load, fluid viscosity in the rolling mill, and elasticity of the entire rolling mill contribute to the vertical vibration of the work roll. The roll motion equation and the tension vibration equation in which the change in the transfer speed of the rolled sheet between adjacent rolling mills generates tension vibration are set for each rolling mill, and the vertical vibration and tension vibration of the work roll are Assuming that they occur at the same frequency, a characteristic equation is derived from the work roll equation of motion and tension vibration equation, and this characteristic equation is used.
In solving the work roll equation of motion and tension vibration equation in each rolling mill, the characteristic equation is derived assuming that both have vibration solutions of the same frequency. Under the condition of propagating to the machine, it is unlikely that the vertical and vertical vibrations of the work roll are different in frequency, and the assumption of the same frequency vibration is reasonable.

Based on the assumption, a characteristic equation can be derived using a mathematical method, and a self-excited vibration model can be constructed using the characteristic equation.
When predicting the occurrence of chattering from the characteristic equation, it is preferable to determine that chattering occurs when the real part of the complex solution of the characteristic equation is positive.
This assumes that a vibration solution is assumed as a solution of the characteristic equation, and if the solution is a complex number, the vibration diverges by looking at the sign of the real part of the complex solution (becomes self-excited vibration) This is because it is already mathematically obvious.

Based on these mathematical knowledge, it is possible to know the occurrence of chattering by focusing only on the real part of the complex solution of the characteristic equation.
On the other hand, the technical means for solving the problem in the optimum control method of the tandem rolling apparatus calculates the rolling control amount in each rolling mill that can prevent chattering using the self-excited vibration model. Each rolling mill is controlled based on this.
According to this technical means, in a tandem rolling machine under various conditions, it is possible to theoretically prevent chattering from occurring using a self-excited vibration model.

Preferably, the rolling control amount in each rolling mill is calculated so that the real part of the complex solution of the self-excited vibration model is negative, and each rolling mill is controlled based on this.
According to this, it is possible to control the tandem rolling apparatus by paying attention only to the real part of the complex solution of the characteristic equation.
More preferably, the real part of the complex solution of the self-excited vibration model is changed by a rolling control amount, and when this variation value is positive, the rolling control amount of each rolling mill is reduced so that the variation value decreases. When the variation value is negative, the rolling control amount of each rolling mill may be changed so that the variation value increases.

This makes it possible to control the tandem rolling apparatus more easily and in real time using the idea of the variational method used in the optimal control theory.
In addition, the said rolling control amount is good in a rolling material tension | tensile_strength and board thickness.

  According to the present invention, the chattering occurrence of the tandem rolling mill can be accurately predicted by the self-excited vibration model considering the entire tandem rolling mill, and chattering does not occur using the self-excited vibration model. The tandem rolling device can be controlled.

Hereinafter, a chattering prediction method and a control method of a tandem rolling apparatus according to the present invention will be described by exemplifying a tandem rolling apparatus that performs cold rolling of a thin plate.
2 and 3 schematically show a tandem rolling apparatus 1 for cold sheet rolling.
Each rolling mill F (i) provided in the tandem rolling mill 1 has a pair of work rolls 3 and 3 and a pair of backup rolls 4 and 4 for backing them up. The rolled material 5 is transferred while being rolled from the downstream side (i-1 side) to the upstream side (i + 1 side).
Each rolling mill F (i) is provided with an entry side thickness meter 6 for measuring the thickness of the rolled material 5 on the entry side and an exit side thickness meter 7 for measuring the exit side plate thickness. A side tension meter 8 and an output side tension meter 9 for measuring the output side tension are also provided. In addition, a plate speedometer 10 that measures the speed (sheet speed) of the rolled material on the delivery side and a rolling load meter 11 that measures the rolling load are also provided.

Further, the rolling control amount of the rolling mill F (i) measured by each of the measuring meters 6, 7, 8, 9, 10, and 11 is input, and the rolling control amount that does not cause chattering is calculated according to the control method described later. And the control means 12 which controls the rolling mill F (i) with the rolling control amount is provided.
In this tandem rolling apparatus 1, the chattering prediction method and its control method in the said apparatus 1 are implemented, and the prediction method and control method are demonstrated below.
First, a self-excited vibration model used to determine whether chattering occurs in the tandem rolling device 1 will be described.
[Self-excited vibration model]
As a result of observing and studying the occurrence of chattering in detail, the applicant of the present application, as shown in FIG. 1, when a self-excited vibration (A in the figure) occurs in a certain rolling mill F (i), these are rolled materials. 5 is propagated to adjacent rolling mills F (i + 1) and F (i-1) as tension vibrations propagating through 5 (B in the figure), and finally it becomes clear that chattering occurs in the tandem rolling device 1 as a whole. did. From this, as a cause of chattering, the vertical vibrations of the work rolls 3 and 3 in each rolling mill F (i) and the rolling that propagates the vertical vibrations to the adjacent rolling mills F (i + 1) and F (i-1). We reached the view that two things, tension vibration in the material 5, are important.

In other words, in the tandem rolling device 1 that continuously rolls the rolled material 5 with a plurality of rolling mills F (i), the vertical vibrations of the work rolls 3, 3 provided in each rolling mill F (i), and rolling A self-excited vibration model of the rolling mill was created in consideration of the tension vibration propagating through the inside of the rolled material 5 inside.
FIG. 4 shows a process of deriving a self-excited vibration model based on this idea.
First, the equation of motion of the work roll 3 in each rolling mill F (i) and the tension vibration equation between the adjacent rolling mills F (i) and F (i + 1) are set. By combining these dynamic equations with a static equation indicating fluctuations in rolling load and the like, an equation indicating the rolling state of the entire tandem rolling device 1 is derived.

In the expression indicating the rolling state, the vibration solution is assumed to be Δx = exp (ωt), Δσ = exp (ωt), and ω is a complex number, and a characteristic equation is derived (for the characteristic equation, see, for example, “Oedo Ogawa , Introduction to Applied Mathematics, 1980, Baifukan, etc.). The characteristic equation derived in this way is a self-excited vibration model.
Hereinafter, the derivation of the self-excited vibration model will be described in detail.
First, the variables used in the model are as follows. In addition, the variable has shown the thing regarding the i-th rolling mill F (i) (i stand).

・ Input tension: σ ⁽ⁱ⁾ _in
・ Exit tension: σ ⁽ⁱ⁾ _out
・ Entry side thickness: h ⁽ⁱ⁾ _in
-Outboard thickness: h ⁽ⁱ⁾ _out
・ Entry side plate speed: V ⁽ⁱ⁾ _in
-Outboard plate speed: V ⁽ⁱ⁾ _out
・ Work roll speed: Vr _(i)
・ Work roll flat deformation coefficient: K ⁽ⁱ⁾
-Apparent mass of the rolling mill F (i) (mass coefficient of the mill): m ⁽ⁱ⁾
・ Damping coefficient for work rolls and backup rolls: λ ⁽ⁱ⁾
・ Mill constant of rolling mill F (i): M ⁽ⁱ⁾
-Sheet width of rolled material: W
・ Distance between adjacent stands: L
・ Sonic velocity: Vs
・ Tension transmission delay to the next stand: τ ₀ = L / Vs = 1.0 × 10 ⁻⁴
・ Thickness transmission delay to the next stand: τ ₁ = L / V ⁽ⁱ⁾ _out = 1.0 × 10 ^{−2 to} 5.0 × 10 ⁻³

Next, consider a static equation.

  First, the static equation of the load variation ΔP is expressed by Equation (1).

  When the displacement of the upper work roll 3 is Δx, the static equation of the displacement of the work rolls 3 and 3 is expressed by Expression (2).

  The fluctuation Δfs of the advance rate fs in the rolling mill F (i) is expressed by Expression (3).

Next, consider the equation of motion of the work roll 3 provided in the rolling mill F (i) as a dynamic equation.
The work roll equation of motion is considered that at least one of the fluctuation of the rolling load, the viscosity of the fluid existing in the rolling mill, and the elasticity of the entire rolling mill F (i) contributes to the vertical vibration of the work roll 3. As shown.
That is, as a cause of the vertical vibration of the work roll 3, first, the fluctuation of the rolling load P ⁽ⁱ⁾ can be considered. In addition, the elasticity of the whole rolling mill F (i) represented by the mill constant M ⁽ⁱ⁾ is considered to be involved.

Further, the viscosity of the fluid existing in the rolling mill F (i) is expressed as an apparent damping coefficient λ ⁽ⁱ⁾ of the work roll 3 and contributes to the vertical vibration of the work roll 3.
The work roll 3 and the backup roll 4 in the rolling mill F (i) are supported by the main body of the rolling mill with a bearing structure, and there is an oil film (fluid) for lubrication in the bearing structure, and the viscosity of this oil film Or vertical fluid vibration caused by Further, when each of the work roll 3 and the backup roll 4 is supported by a fluid cylinder or the like, vertical vibration due to the viscosity of the fluid in the fluid cylinder may occur. These vibrations are reflected in the work roll equation of motion via the damping coefficient λ ⁽ⁱ⁾ .

  On the other hand, the tension vibration equation is such that the change in the transfer speed of the rolled sheet between the adjacent rolling mills F (i) generates tension vibration, and is represented by equation (5).

  Since the tension vibration propagates through the rolled material 5 at a longitudinal wave speed and a sonic speed, a time delay occurs in the propagation of the vibration by that speed. This delay is expressed by equation (6). In addition, the rolled material 5 itself is delayed with respect to the next stand (dead time) as shown by the equation (7).

  By substituting equation (1) into equation (4), equation (8) is obtained.

  By substituting equation (2) into equation (8), equation (9) can be obtained.

  Since the relationship of Expression (9) is established in each rolling mill F (i), the entire tandem rolling device 1 is expressed by Expression (10).

  On the other hand, when Expression (2) is substituted into Expression (7), Expression (11) is obtained.

  Substituting equation (11) into equation (10) leads to equation (12).

  Substituting equation (6) into equation (12) derived in this way yields equation (13).

  Further, when Expression (2), Expression (6), and Expression (11) are substituted into Expression (5), Expression (14) is obtained.

Expressions (13) and (14) are simultaneous equations of Δx and Δσ _out and can be expressed as follows.

  In solving the simultaneous partial differential equation (formula (15)), it is assumed that the vertical and vertical vibrations of the work rolls 3 and 3 are generated at the same frequency as shown in the formula (16).

Work roll up-and-down vibration generated in a certain rolling mill F (i) propagates through the rolling material 5 as tension vibration and propagates vibration to the adjacent rolling mills F (i + 1) and F (i-1). However, it is very unlikely that the vertical vibration and the tension vibration of the work rolls 3 and 3 are different under this situation, and the assumption that both have the same frequency is reasonable.
Considering the determinant (determinant) of equation (15) under the solution of equation (16), equation (17) is obtained.

  When equation (17) is solved, equation (18) is obtained. When the calculation is further advanced, equation (19) can be derived. This is a characteristic equation of the simultaneous partial differential equation (Formula (15)).

  Expression (20) can be derived by moving the second item of Expression (19) to the right side and proceeding the calculation after squaring both sides.

  Formula (21) is arranged so that Formula (20) is easy to understand. This is a self-excited vibration model of the tandem rolling device 1.

In the partial differential calculation with respect to the rolling load P and the advanced rate fs, P and fs are calculated from an appropriately set load model and advanced rate model. These load models and advanced rate models include a friction coefficient μ, which can be calculated by identification.
[Chattering prediction method using self-excited vibration model]
The result of simulating the occurrence of chattering using this self-excited vibration model is shown in FIGS.

The self-excited vibration model (formula (21)) is a quartic equation, and has a clear solution with ω = 0, one real solution, and two complex solutions. The real part of the complex solution is a damping term. When the value is positive, divergence, that is, self-excited vibration is generated, and when it is negative, damping, that is, vibration damping. The imaginary part of the complex number is a vibration term and determines the frequency of self-excited vibration.
Since it is generally difficult to obtain the solution of Equation (21) analytically, in this embodiment, the real part and the imaginary part of the complex solution are obtained by numerical analysis using a computer or the like. Yes. The computer may be a process computer (process computer) or a workstation provided as the control means 12 of the tandem rolling apparatus 1, and is a workstation installed in a laboratory or the like independent of the tandem rolling apparatus 1. There may be.

First, in the numerical calculation, the apparent mass (mill mass coefficient) m ^{(i) of} the rolling mill obtained as the dynamic characteristics of each rolling mill F (i), the apparent elastic coefficient (damping coefficient) λ ^{(i ) of} the work roll 3 ⁾ , It is necessary to determine the mill constant M ⁽ⁱ⁾ of the rolling mill F (i). These parameters can be determined by a forced vibration experiment on the rolling mill F (i). In the present embodiment, each parameter is determined so as to coincide with the chattering frequency (about 100 Hz).
Specifically, the measured values of the rolling speed, rolling load, plate thickness, etc. of the rolled material (rolled material coil) in which chattering has occurred and the chattering frequency are measured, and these values are used to increase the rolling speed. Then, m ⁽ⁱ⁾ and λ ⁽ⁱ⁾ were determined so that the speed at which the real part of the complex solution of the self-excited vibration model is positive and the occurrence of chattering coincide. As described above, it is clear from the numerous experiments conducted by the applicants of the present application that chattering in other rolled materials can be predicted based on m ⁽ⁱ⁾ and λ ⁽ⁱ⁾ determined for a specific rolled material.

In FIG. 5, the horizontal axis represents the rolling speed and the vertical axis represents the friction coefficient. From the calculation result of the self-excited vibration model, it was found that the shaded area is the divergence region (chattering generation region) and the white portion is the attenuation region. That is, the divergence region is a region where the real part of the complex solution of Equation (21) is plus, and the attenuation region is a minus region.
In the calculation, the rolling conditions other than the rolling speed and the coefficient of friction, that is, the sheet thickness, the rolling reduction, the sheet tension, and the like are those when the rolling mill F (i) is operated at the maximum rolling speed.
As can be seen from FIG. 5, the divergence regions where chattering is considered to occur are present on the high friction coefficient side and the low friction coefficient side.

In actual rolling, as the rolling speed increases, the film thickness of the oil introduced into the roll bite increases and the lubricity improves. This is the reason why the friction coefficient decreases with the rolling speed in the rolling results in the figure.
In addition, since the friction coefficient decreases with the rolling speed, the high speed region is starting to reach the divergent region, which is consistent with the current operational performance where chattering occurs due to excessive lubrication. Therefore, it can be seen from this figure that chattering can be prevented by increasing the friction coefficient.
In addition, although it is applied to the upper limit side of the friction coefficient on the low speed side, no chattering is observed in actual operation. This requires some disturbance (trigger supplied from outside at the same frequency as the self-excited vibration) as a self-excited vibration mechanism, and the frequency due to the rotation of the rolling mill F (i) is not sufficiently high in the low-speed part. For this reason, it is presumed that the disturbance cannot be realized.

If the self-excited vibration model is used in this way, it is possible to predict the existence of upper and lower friction coefficients regarding chattering occurrence, which is a past finding. In addition, it can be explained that the influence of the friction coefficient is large in the occurrence of chattering in this way, and it can be seen that the self-excited vibration model accurately simulates the chattering occurrence situation.
Therefore, FIG. 6 shows the result of calculation of the stability region based on the exit side tension and the friction coefficient using this self-excited vibration model. In this figure, the horizontal axis is the exit tension of the rolling mill F (i), and the vertical axis is the friction coefficient.

As is clear from FIG. 6, it can be seen that the actual result of occurrence of chattering (x mark in the figure) is in the divergence region in the simulation result. Conversely, it can also be seen that the case where chattering did not occur in the rolling record (marked with ● in the figure) is in the attenuation region.
From these results, it can be seen that the limit of chattering can be sufficiently predicted by this self-excited vibration model. It can be seen that the rolling state can be shifted to the attenuation region by changing the exit tension, and chattering can be prevented.
Furthermore, from this simulation result, it is clear that there are two patterns, a case where chattering can be prevented on the low tension side and a case where chattering can be prevented on the high tension side.
[Control method using self-excited vibration model (1)]
Next, a method for performing control so that chattering does not occur in the tandem rolling device 1 using the above-described self-excited vibration model will be described.

FIG. 7 is a flowchart showing the first embodiment of the control method.
First, in each rolling mill F (i), m ⁽ⁱ⁾ and λ ⁽ⁱ⁾ are obtained in advance from vibration characteristic experiments of the rolling mill F (i). (S1-1)
Next, the mill constant M ⁽ⁱ⁾ , the distance L between the stands, the Young's modulus E of the plate, and the flatness coefficient K of the work roll 3 are read. (S1-2)
Thereafter, cold sheet tandem rolling is started. (S1-3)
After starting rolling, the plate speed V ⁽ⁱ⁾ and the roll speed Vr are measured as the actual values of rolling to obtain the advanced rate fs. (S1-4)
Further, the friction coefficient μ is identified from the entry side plate thickness h _in , the exit side plate thickness h _out , the entry side tension σ _in , the exit side tension σ _out , and the roll radius R of each rolling mill F (i). (S1-5)
From this friction coefficient μ, entry side thickness h _in , exit side thickness h _out , entry side tension σ _in , exit side tension σ _out , deformation resistance to match the actual rolling load P ⁽ⁱ⁾ using the rolling load equation Find Kp. (S1-6)
Substituting the friction coefficient μ and the deformation resistance Kp thus determined for the appropriately set advanced rate model and rolling load model, and calculating the values of p, q, and r in Expression (21) by calculating numerically. . (S1-7, S1-8, S1-9)
Finally, the solution of Equation (21) is obtained from the values of p, q, r, and the sign of the real part of the complex solution is determined. If the real part is positive, chattering occurs, and the real part is If it is negative, it is stable (no chattering). (S1-10, S1-11)
When chattering occurs, the rolling control amount is controlled so that the value of the real part is negative. (S1-12)
The above processing is performed by the control means 12 shown in FIGS. 1 and 2, and the control means 12 is composed of a process controller connected to the rolling mill F (i) or a workstation attached to the process control. ing.

The control means 12 is inputted with output signals from the rolling load meter 11, the plate speed meter 10, the entry side tension meter 8, the exit side tension meter 9, the entry side plate thickness meter 6, and the exit side plate thickness meter 7. It has become. Based on these input values, the processing of S1-1 to S1-12 is performed in a process control or a workstation, and the rolling control amount calculated based on the calculation result is output. Specifically, the above processing is made a subroutine, and the real part of the complex solution is returned by sending the plate thicknesses h _in , h _out , tension σ _in , σ _out , roll speed Vr, plate speed V, and rolling load P ^(i). It is like that.
The real part value, which is an indicator of chattering, is displayed on the monitor screen of a computer or workstation, and the operator can check whether the rolling conditions have become unstable before chattering actually occurs. Judgment can be made. If there is a sign that the real part value is negative or negative, based on this, the rolling load and work roll gap are changed, and the looper system is controlled to control the input side tension σ _in and the output side. The tension σ _out may be changed.

The processing described above is performed in real time during rolling. In this control, actual values are desirable for the plate thickness and plate speed, but estimated values based on models such as mass flow plate thickness and gauge plate thickness may also be used.
[Optimum control method using self-excited vibration model (2)]
FIG. 8 is a flowchart showing a second embodiment of the optimum control method.
In this embodiment, S2-1 to S2-10 are substantially the same processing steps as those in the first embodiment and S1-1 to S1-10.

Subsequent steps, S2-11 to S2-14, are greatly different from those of the first embodiment, and the variation of the real part of the complex solution of the self-excited vibration model is obtained. Based on the variation value, the rolling mill F (I) is controlled.
Specifically, first, it is considered that the complex real part Q can be expressed as a function as shown in Expression (22).

Next, the concept of the variational method is introduced into equation (22), and when the value of Q increases (changes from minus to plus), Q is decreased and the rolling state is kept in the stable range. To do. As variables for changing Q, the input side plate thickness h _in , the output side plate thickness h _out , the input side tension σ _in , and the output side tension σ _out are selected, and equation (23) obtained by changing equation (22) is obtained. Think.

ΔQ _{1 to} δQ ₄ in equation (23) are calculated numerically (S2-11), and δQ _(i) = max having the largest absolute value is selected. If the absolute value of δQ _(i) = max is a positive value, the rolling control amount is controlled so that δQ _(i) decreases. (S2-12, S2-13)
Conversely, if the absolute value of δQ _(i) = max is negative, the rolling control amount is controlled so that δQ _(i) increases. (S2-12, S2-14)
By doing so, the value of Q is kept at a substantially constant value, chattering does not occur, and a stable rolling state is maintained.

In addition, when the tandem rolling apparatus 1 is controlled by the method of the present embodiment, the thickness variation of the rolled material 5 occurs by changing the rolling control amount. At this time, the rolling mill F (i-1) or F (i + 1) at the front stage or the rear stage of the rolling mill F (i) whose rolling control amount is changed is appropriately controlled so that the final exit side plate thickness does not change. It is good to control. These plate thicknesses may be controlled by using existing technology as a plate thickness control function of a rolling mill.
The present invention is not limited to the above embodiment.
That is, the technique according to the present invention can be applied to a rolling apparatus that may generate chattering and that needs to control the occurrence. There is no problem even if the rolled material 5 is a thick plate or hot rolled.

It is a figure which shows the chattering generation | occurrence | production situation. It is the schematic of a tandem rolling apparatus. It is a figure which shows a control means. It is a flowchart which shows the derivation process of a self-excited vibration model. It is a simulation result of a self-excited vibration model. It is a simulation result of a self-excited vibration model. It is a flowchart which shows the control procedure of a tandem rolling apparatus. It is a flowchart which shows the control procedure of a tandem rolling apparatus.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Tandem rolling apparatus 3 Work roll 4 Backup roll 12 Control means F (i) Rolling mill (i-th)

Claims (7)

A tandem rolling device that continuously rolls rolled material with a plurality of rolling mills.
Create a self-excited vibration model of the rolling mill considering the vertical vibration of the work roll provided in each rolling mill and the tension vibration propagating inside the rolled material during rolling,
A chattering prediction method for a tandem rolling apparatus, wherein the presence or absence of chattering in a rolling mill is predicted using the self-excited vibration model. The self-excited vibration model includes a work roll equation of motion in which at least one of fluctuations in rolling load, viscosity of a fluid existing in the rolling mill, and elasticity of the entire rolling mill contributes to vertical vibration of the work roll, and between adjacent rolling mills. The tension vibration equation that the change in the transfer speed of the rolled plate generates tension vibration is set for each rolling mill,
The tandem rolling apparatus according to claim 1, wherein a characteristic equation is derived from the work roll equation of motion and the tension vibration equation, assuming that the vertical vibration and tension vibration of the work roll are generated at the same frequency. Chattering prediction method.   3. The chattering prediction method for a tandem rolling mill according to claim 2, wherein chattering is determined to occur when a real part of a complex solution of the characteristic equation is positive.   Using the self-excited vibration model according to any one of claims 1 to 3, a rolling control amount in each rolling mill that can prevent chattering is calculated, and each rolling mill is controlled based on the calculated amount. A control method for a tandem rolling apparatus.   The rolling control amount in each rolling mill is calculated so that the real part of the complex number solution of the self-excited vibration model becomes negative, and each rolling mill is controlled based on the calculated amount. Method for controlling the tandem rolling mill. The real part of the complex solution of the self-excited vibration model is changed by a rolling control amount.If this variation value is positive, the rolling control amount of each rolling mill is changed so that the variation value decreases,
The control method of a tandem rolling apparatus according to claim 4, wherein when the variation value is negative, the rolling control amount of each rolling mill is changed so that the variation value increases.   The control method for a tandem rolling apparatus according to any one of claims 4 to 6, wherein the rolling control amount is a rolling material tension and a plate thickness.