JPH06277728A - Method for controlling and setting plate crown - Google Patents

Abstract

PURPOSE:To control a plate crown with high accuracy by separating an error caused by a roll profile from an error caused by a widening deformation property of a rolled stock in estimating the plate crown at places near a plate edge. CONSTITUTION:The plate crown of a preceding material after rolling is measured at >=2 positions different in distance from the plate edges, the plate crown corresponding to the measured position is calculated by the rolling condition of the preceding material through an estimation model for the plate crown and an estimation error caused by the roll profile at a position small in distance from the plate edge is calculated based on a difference between a measured value at a position large in distance from the plate edge and a calculated value. The difference at the position small in distance from the plate edge is calculated by adding the estimation error caused by the widening deformation property of the rolled stock to the estimation error of the roll profile and the model is corrected by these estimation errors to determine a controlled variable of the crown controlling mechanism of the following material.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for controlling and setting a strip crown in strip rolling.

[0002]

2. Description of the Related Art In order to control a strip crown of a rolled material as desired, a model capable of estimating the strip crown from a given rolling condition with practical accuracy is required. This model can be roughly classified as follows, focusing on the physical phenomenon that forms the plate crown. (1) Calculation model of elastic deformation of rolls (2) Calculation model of width expansion deformation characteristics of rolled material (3) Calculation model of roll profile Among these, (1) is the well-known "division model" or elastic finite element method The calculation technology used is established, and an online model based on these calculation results is also created.
It has been confirmed that it can be estimated with practical accuracy.

Regarding (2), a model was conventionally made based on the results of rolling experiments, and in recent years, an analysis using the rigid-plastic finite element method has been made. The change in the stress state on the roll bite entry / exit side due to the deformation cannot be sufficiently expressed by the rigid-plastic finite element method.
It is well known as the feedback effect of tension that the plate crown greatly changes depending on the stress state on the entrance and exit sides of the roll bite. Therefore, there is no online model that can estimate the change of the plate crown due to the difference in the width expansion deformation characteristics of the rolled material with practical accuracy.

Regarding (3), although an online model for estimating the wear and thermal expansion of the roll has been created and put into practical use, how the roll cooling water is applied in actual rolling, or variations in wear characteristics of individual rolls, etc. However, it is the fact that it is inevitable to allow some variation because it is a variable factor that is difficult to express in the model. For the above reasons, when performing plate crown control, there is a limit in accuracy in controlling the crown control mechanism using only the plate crown estimation model. To solve this problem, Japanese Patent Publication No. 63-2584
In No. 5, it is assumed that the error between the measured value of the plate crown of the preceding material and the calculated value obtained by the plate crown estimation model is due to the estimation error of the roll profile, and the error is calculated and learned to perform the setting calculation of the next material. Is proposed.

[0005]

However, the plate crown is an index for managing the plate thickness deviation in the plate width direction, and its evaluation, that is, the measurement of the plate crown is generally performed at the plate width end within 50 mm from the plate width end. It is done in a close position.
In the vicinity of the strip width edge, the width expansion deformation characteristics of the rolled material change rapidly. As described above, a model capable of estimating the width-spreading deformation characteristics of rolled material with sufficient accuracy has not yet been established. Therefore, the error of the model when the plate crown is estimated at the position close to the plate width end in this way has a large ratio due to the estimation error of the width spreading deformation characteristic of the rolled material. Therefore, in the method of learning the estimation error of the plate crown as the estimation error of the roll profile, there is a problem that the error of the roll profile estimated as the learning term varies depending on the error of the width-widening deformation characteristic of the rolled material.

The present invention has been made in view of the above problems, and when estimating a plate crown at a position close to the plate width end by a plate crown estimation model, an error caused by a roll profile and a widening deformation characteristic of a rolled material are considered. The purpose of this study is to realize the highly accurate plate crown control by separately estimating the errors caused by the estimation and correcting the model with these estimation errors.

[0007]

SUMMARY OF THE INVENTION The present invention is a plate crown control setting method for determining a control amount of a crown control mechanism for obtaining a target plate crown by using a plate crown estimation model. The crown is measured at two or more positions with different distances from the strip width end, and each strip crown corresponding to the measurement position is calculated by an estimation model using the rolling conditions of the preceding material, and the strip crown is measured. Of the difference between the calculated value and the calculated value, the difference at the position where the distance from the plate width end is large is caused by the estimated error A of the roll profile, the estimated error A is calculated, and the position where the distance from the plate width end is small is calculated. It is assumed that the difference in the above is due to the sum of the roll profile estimation error B calculated at the position calculated based on the estimation error A and the width widening deformation characteristic estimation error C of the rolled material. It calculates an error C, these estimation error B, and those that modify the strip crown estimation model by C as a constituent of the invention to determine the control amount of crown control mechanism follows material.

[0008]

[Function] Among the roll profile estimation error and the roll width widening deformation characteristic estimation error, which are the two major factors of the plate crown estimation error, the width widening deformation characteristic of the rolled material largely changes at the plate width end, Since the estimation error A of the roll profile is dominant in the estimation error of the plate crown in the portion excluding the end portion of the plate width, the estimation error A is easily calculated. On the other hand, to the estimation error of the sheet crown at the portion including the sheet width end portion, the estimation error C of the roll widening deformation characteristic of the rolled material is added to the estimation error B of the roll profile at the position. At this time, the former estimation error B is easily calculated from the estimation error A according to the roll profile. Therefore, the latter estimation error C
Can also be calculated. Therefore, according to the method of the present invention, since the error of the plate crown estimation model is learned based on the characteristics of the physical phenomenon, the plate crown estimation error can be reduced,
The plate crown control accuracy can be greatly improved.

[0009]

EXAMPLES Prior to the description of the examples, first, a plate crown estimation model used for plate crown control will be briefly described. Various types of plate crown estimation models have been introduced and it is not necessary to specify them, but the model introduced on page 143 of the Proceedings of the 33rd Joint Conference on Plastic Workings is used here.

Parameters representative of elastic deformation of the roll and
Is formed when the rolling pressure distribution in the strip width direction is uniform.
Plate crown C_h* (Hereinafter referred to as the two-dimensional crown)
It is expressed by the following formula. C_hi* = A_pi・ P_i+ A_Fi・ F_i+ A_Ri・ C_Ri (1) where P is rolling load, F is roll bending force, and C
_RIs the roll crown corresponding to the plate crown definition point
The initial mechanical crown and roll wear profile.
And calculated from thermal profile synthesis
It a_P, A_F, A _RIs roll size, roll shift amount, etc.
Model coefficient determined by the mill specifications and the strip width of the rolled material,
The subscript i is the stand number.

In actual rolling, the rolling pressure distribution in the strip width direction is not uniform because of the widening deformation of the strip and the entry side strip crown (plate crown in the front stand).
The plate crown C _h is expressed by the following equation by modifying the equation (1). C _hi = (1−η _i ) C _hi * + η _i (h _i / h _i-1 ) C _hi-1 (2) where h is the plate width central plate thickness and η is the crown genetic coefficient. Yes, and is expressed by the following equation.

[0012]

[Equation 1]

Here, l _d is a contact arc length, ξ is a parameter which is called a shape change coefficient and which represents a width-widening deformation characteristic of the rolled material, and K is a geometrical contact area between the roll and the rolled material and a coordinate in the plate width direction. The function A is a function of the strength of the rolled material and the coordinate in the plate width direction. In order to simplify the description, the value obtained by dividing the plate crown by the plate width center plate thickness (called a ratio crown) is used to express the formula (2) as follows.

C _i = (1−η _i ) C _i * + η _i C _i-1 (4) where C _i * is the value obtained by dividing the two-dimensional crown by the center plate thickness on the exit side, and C _{i -1} is a value obtained by dividing the entry side plate crown by the entry side plate width center plate thickness. Embodiments in which the present invention is applied to plate crown control in a hot strip mill will be described below with reference to the drawings. In this embodiment, the number of stands of the mill is 7, and each stand is equipped with a roll bending device as a crown control mechanism. The roll bending force output from the roll bending device is controlled by a plate crown control device in which a program that realizes the operation of the flowchart described below is incorporated.

FIG. 1 shows an overall flow chart of plate crown control in a hot strip mill to which the present invention is applied.
Regarding the setting calculation of the control amount, detailed description is omitted because it is well known, but the rolling load of each stand calculated by the strip thickness control system together with the rolling command information such as the steel type of the rolled material, size, target strip crown, etc. And the entrance / exit side plate thickness is input to the control device (steps A1 and A2). Next, the target plate crown on each exit side of the finishing mill is determined so that the target plate crown is satisfied and the flatness between the stands of the finishing mill is minimized (step A3). Finally, using the roll wear profile and the thermal profile, which are separately calculated from the rolling history data of the rolled rolls after recomposition, the roll crown corresponding to the plate crown defining point is calculated (step A4), and the plate crown estimation model is used. , Crown control mechanism that realizes the target plate crown on the exit side of each finishing mill, here, the control amount of the roll bending force is determined. The plate crown estimation model is sequentially corrected after rolling the preceding material by the following learning calculation.

FIG. 2 shows a flowchart of the learning calculation which is the aim of the method of the present invention. In the learning calculation, the preceding material is rolled by the plate profilometer on the exit side of the finishing mill final stand (7th stand). The subsequent plate crown is measured at two or more positions with different distances from the plate width edge (step B
Together with 1), the plate crown corresponding to each measurement position is calculated by the plate crown estimation model based on the actual rolling conditions of the preceding material. In the present embodiment, the plate crown is measured at two points at a position at a distance of 75 mm from the plate width end as a position with a large distance from the plate width end and at a position of 25 mm from the plate width end as a position with a small distance from the plate width end. did.

First, the plate crown measured at the exit side of the finishing mill at the position of 75 mm from the plate width end and the plate crown calculated by the plate crown estimation model are converted into ratio crowns, respectively, C ^A _fI. , C ^C _fI , the ratio crown error ΔC _fI to be learned at the position 75 mm from the plate width end is calculated from the following equation (step B
2).

[0018] _{^{ΔC fI = C A fI -C C}} fI (5) where the subscript I indicates that the value of the position of 75mm from the strip width end. As described above, the widening deformation of the rolled material does not change much at the position 75 mm from the plate width end,
_{Replace the} ratio crown error ΔC _fI to be learned with the roll crown estimation error. Here, it is assumed that the error tendency of the roll profile calculation model is the same at each stand, and the roll crown calculation error ΔC _{RI, that} is, the roll crown correction amount at each stand is constant at each stand. (1)
From equations (4) and (4), the roll crown calculation error in the i-stand ΔC _RI , the ratio crown estimation error Δ
C _iI is expressed by the following equation.

ΔC _iI = (a _Ri / h _i ) (1-η _iI ) ΔC _RI + η _iI ΔC _{(i-1) I} (6) At the entrance side of the first stand with respect to the plate crown on the exit side of the finishing mill final stand Since the influence of the rough bar crown is small, when ΔC ₀₁ = 0 and equation (6) is successively calculated from the first stand, ΔC _fI is represented by the following equation. _{ΔC fI = (α 7 + η} 7I (α 6 + η 6I (α 5 + η 5I (α 4 + η 4I (α 3 + η 3I (α 2 + η 2I α I)))))) ΔC RI (7) Here, α _i = (a _Ri / h _i ) (1-η _iI ).

ΔC _RI is obtained from the equations (5) and (7) (step B3). Next, the plate crown and the plate crown estimation model measured on the exit side of the finishing mill final stand at a position 25 mm from the plate width end. those terms of the calculated strip crown ratio crown by, respectively C ^a _fo, when the C ^C _fo, the ratio crown error Δ to be learned at the position of 25mm from the strip width end
C _fo is given by the following equation.

ΔC _fo = C ^A _fo −C ^C _fo (8) Here, the subscript O indicates a value at a position of 25 mm from the plate width end. In the calculation of C ^C _fo by the plate crown estimation model, ΔC _RI obtained from the formulas (5) and (7) is the roll crown corresponding to the position 75 mm from the plate width end, so the roll profile is a quadratic curve. Assuming that, the correction amount ΔC _RO of the roll crown corresponding to the position 25 mm from the plate width end is obtained by the following formula (step B4)

[0022]

[Equation 2]

Here, B is the plate width. This ΔC_ROFor
And the plate width edge estimated by the roll profile calculation model
Roll crown C at a position of 25 mm from_ROFix
Position of 25 mm from the plate width edge using equations (1) and (4)
At C^C _fOTo calculate. This C^C _fOIs a roll profile
Error is corrected and the remaining error is as described above.
Due to the estimation error of the width spread deformation characteristics of rolled material
Therefore, the ratio crown error ΔC to be learned_fOThe crown
Replace with the estimation error of the genetic coefficient η.

As a method of correcting the crown genetic coefficient η,
Although various methods are conceivable, it is assumed here that the error tendency of the crown genetic coefficient η is the same at each stand, and the product of the same correction coefficient β at each stand represents the correct crown genetic coefficient. Using the corrected crown genetic coefficient, equation (4) is expressed as follows. C _i = (1−βη _i ) C _i * + βη _i C _i-1 (10) The formula (10) is calculated sequentially from the first stand to the final stand, and the ratio crown is measured on the exit side of the finishing mill. The following expression is obtained from the condition of being equal to C ^A _fO .

[0025] _{^{C A fO = (1-βη}} 7O) C 7O + βη 7O (1-βη 6O) C 6O + β 2 η 6O η 7O (1-βη 5O) C 5O + β 3 η 5O η 6O η 7O (1- ^{_{βη 4O) C 4O + β 4}} η 4O η 5O η 6O η 7O (1-βη 3O) C 3O + β 5 η 3O η 4O η 5O η 6O η 7O (1-βη 2O) C 2O + β 6 η 2O η 3O η _{4O η 5O η 6O η 7O (} 1-βη 1O) C 1O + β 7 η 1O η 2O η 3O η 4O η 5O η 6O η 7O C 0O (11) here, eta _iO from plate width end in i stand It is a crown genetic coefficient at a position of 25 mm. Similarly, the value obtained by sequentially calculating the equation (4) from the first stand to the final stand is the calculated value C ^C _fO of the plate crown estimation model, and thus the following equation is obtained.

[0026] _{^{C C fO = (1-η}} 7O) C 7O + η 7O (1-η 6O) C 6O + η 6O η 7O (1-η 5O) C 5O + η 5O η 6O η 7O (1-η 4O) C _{4O + η 4O η 5O η 6O} η 7O (1-η 3O) C 3O + η 3O η 4O η 5O η 6O η 7O (1-η 2O) C 2O + η 2O η 3O η 4O η 5O η 6O η 7O (1- _{η 1O) C 1O + η 1O} η 2O η 3O η 4O η 5O η 6O η 7O C 0O (12) (11) formula (12) by substituting expression (8) below, the plate width end 25mm of The ratio crown error ΔC _fO to be learned at the position is given by the following equation (step B5).

The _{ΔC fo = (1-β)} η 7O (C 7O -C 6O) + (1-β 2) η 6O η 7O (C 6O -C 5O) + (1-β 3) η 5O η 6O η _{7O (C 5O -C 4O) +} (1-β 4) η 4O η 5O η 6O η 7O (C 4O -C 3O) + (1-β 5) η 3O η 4O η 5O η 6O η 7O (C 3O _{-C 2O) + (1-β} 6) η 2O η 3O η 4O η 5O η 6O η 7O (C 2O -C 1O) + (1-β 7) η 1O η 2O η 3O η 4O η 5O η 6O η Although _{7O (C 1O -C 0O) (} 13) (13) formula is higher equations for beta, for beta is a value in a narrow range close to the nature 1 easily by repeating the calculation of the Newton's method Can be solved (step 6). Note that the rough bar ratio crown C _{0O in} the seventh term of the equation (13) is not usually measured. The crown genetic coefficient η is a value in the range of 0 to 1 and has a smaller value in the former stand, so that the absolute value of each term in the equation (13) becomes smaller as the latter term. The seventh term has a value that is two orders of magnitude smaller than the terms in the first half, so it was ignored here in the calculation.

As described above, the error of the plate crown in the rolling of the preceding material can be learned by separating it into the error of the roll crown and the error of the crown genetic coefficient as the width-spreading deformation characteristic of the rolled material. Next, a method of reflecting the learning result on the estimation of the plate crown of the next material will be described. In the learning calculation, the plate crowns at two positions of 25 mm and 75 mm from the plate width end were used, but the plate crown to be controlled in the setting calculation is usually at one point. In this embodiment, it is 25 from the plate width end.
The plate crown is controlled at the position of mm.

First, ΔC _RO obtained by the equation (9) is added to the roll crown C _Ri at the position 25 mm from the plate width end in each stand calculated by the roll profile calculation model, and the equation (1) is used to calculate Calculate the dimensional crown. When the plate width of the preceding material is different from that of the following material, the contact width between the rolled material and the roll changes. Therefore, assuming that the roll crown is a quadratic curve, ΔC _RO is corrected by the following equation. In the following equation, the subscript j represents the next material and j-1 represents the preceding material. It should be noted that this correction calculation may be executed when reading the correction coefficient β described later.

[0030]

[Equation 3]

Next, a method of reflecting the learning result of the crown genetic coefficient on the next material will be described. Basically, (3)
25mm from the plate width edge in each stand calculated by the formula
The plate crown from the first stand is sequentially calculated by the formula (2) by using the product of the crown genetic coefficient η _iO at the position of β multiplied by β obtained by the formula (13). As mentioned above, the current calculation model of the crown genetic coefficient is based on the change tendency of the dimension of the rolled material and the ratio crown during rolling, that is, the change of the widening deformation characteristics of the rolled material due to the difference between the medium elongation rolling and the selvage rolling. Since β is not always expressed accurately, there is a tendency for β determined by learning calculation to depend on the strip thickness and strip crown.

Therefore, the plate thickness of the rolled product is 5 here.
Divide into 3 groups by division and plate crown, total 15 groups, store the calculated β in the column of the group to which the preceding material belongs in the table for each group (step B7),
The β of the group to which the next material belongs is selected from the values stored in this table (step B8), and the crown genetic coefficient of the next material is corrected (step B9). When storing β in the table, the well-known exponential smoothing method
The table value was rewritten by the following formula.

Β _k = γ β _k ^j + (1−γ) β _k ^j-1 (15) Here, the subscript k is the group number, j-1 is the previous table value, and j is the learning calculation this time. It is the obtained value.
γ is a weighting factor for rewriting the table value, and is set to 0.3 here. FIG. 3 shows the results of rolling using the hot strip mill of the above-mentioned embodiment, applying the learning calculation method of the present invention described in detail above. The figure also shows the sheet thickness and sheet width of the rolled product, the roll crown correction amount ΔC _RO obtained by learning calculation, and the correction coefficient β of the crown genetic coefficient. The actual value of the plate crown agrees very well with the plate crown calculated by the plate crown estimation model by correcting the plate crown target value, that is, the learning amount. In particular, even when the plate thickness of the product and the target plate crown greatly change, the deviation of the actual plate crown value from the target value is small, and it can be seen that the learning calculation method of the present invention accurately corrects the plate crown estimation model. That is, when the plate thickness of the product and the target plate crown greatly change, the correction coefficient β of the crown genetic coefficient changes, and the plate crown as the target is obtained by this correction effect. It should be noted that the roll crown correction amount ΔC _RO does not show a drastic change, which seems to reflect a physical phenomenon that the roll wear profile and the thermal profile change only gradually.

In the above embodiment, the control by the roll bending device has been described. However, even when a crown control device such as a roll cloth or a variable crown roll is used, learning calculation is performed in the same manner as in the present invention, and the rolling result is obtained. By correcting the plate crown estimation model on the basis of the obtained error, the plate crown can be controlled with high accuracy.

[0035]

According to the present invention, the plate crown of the preceding material is measured at two or more positions having different distances from the plate width end, and the error of the plate crown at the position close to the plate width end is caused by the roll profile. Calculation is performed separately from the error due to the width expansion deformation characteristics of the rolled material, and the plate crown estimation model is corrected based on these estimation errors. It is possible to reduce, and it is possible to precisely control the plate crown in plate rolling, especially in the hot rolling where the width expansion deformation of the rolled material at the edge of the plate width is large, and it is possible to significantly improve the quality and yield of rolled products. be able to.

[Brief description of drawings]

FIG. 1 is an overall flowchart of plate crown control according to an embodiment.

FIG. 2 is a flowchart showing learning calculation of a plate crown estimation model according to the embodiment.

FIG. 3 is a graph showing a plate crown control accuracy according to the embodiment.

Claims (1)

[Claims] 1. A plate crown control setting method for determining a control amount of a crown control mechanism for obtaining a target plate crown by using a plate crown estimation model, wherein a rolled plate crown of a preceding material is separated from a plate width end by a distance. Is measured at two or more different points, and the rolling conditions of the preceding material are used to calculate each plate crown corresponding to the measured position with an estimated model, and the difference between the measured value of the plate crown and the calculated value is calculated. Assuming that the difference at the position where the distance from the plate width end is large is due to the estimation error A of the roll profile, the estimation error A is calculated, and the difference at the position where the distance from the plate width end is small is the estimation error A. The estimation error C of the latter is calculated as being due to the sum of the estimation error B of the roll profile at the position calculated based on the above and the estimation error C of the width-widening deformation characteristic of the rolled material. Estimation error B, the strip crown control setting method characterized by modify the strip crown estimation model determines a control amount of crown control mechanism of the following material by C in.