JP2000225407A - Method for correcting predicting model of roll profile - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a correcting method for a predicting model of roll wear and predicting model of the thermal expansion of a roll by which a roll profile can be predicted with high accuracy. SOLUTION: In this correcting method, the error of the predicted value of the roll crown is determined by subtracting the predicted value of the roll crown from the measured value of the roll crown and the inclination of a straight line to the number of rolling whose deviation to the error of the predicted value of the roll crown after a prescribed number of rolling is small is determined. By taking the straight line which has that inclination and is passed through the origin as the relationship with the error of the predicted value of worn roll crown to the number of the polling, the correction factor of the predicting model of the roll wear is determined. Next, by subtracting the error of the predicted value of worn roll crown from the error of the predicted value of roll crown, the error of the predicted value of the thermal crown of the roll is determined and the correction factor of the predicting model of the thermal expansion of the roll is determined.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a roll profile prediction model used when rolling a sheet material.

[0002]

2. Description of the Related Art The requirements for plate thickness accuracy in the plate width direction of plate materials are becoming more stringent year by year. Therefore, after accurately predicting or actually measuring the roll profile of a roll (work roll) for rolling a sheet material, a sheet crown such as a roll bender or a roll cross or a roll shift is obtained in order to obtain a target sheet crown. The control actuator is being set.

A roll profile prediction model used for predicting the sheet crown is composed of a prediction model of a roll wear amount in a barrel direction of a roll and a prediction model of a roll thermal expansion amount. In order to improve the prediction accuracy, various coefficients, physical property values, and the like used in those models have been adjusted to match the actually measured values.

On the other hand, as an apparatus installed on a rolling stand to measure the profile of a roll, an ultrasonic wave is propagated in water while moving a nozzle for spraying water toward the roll in the barrel direction of the roll. 2. Description of the Related Art A roll profile measuring device for measuring a gap between a roll and a nozzle with high accuracy has been developed.

[0005]

However, a model for predicting the amount of roll wear is based on factors such as, for example, pressure elongation, rolling load, roll diameter, and roll material, and their influence coefficients are determined based on actual results. However, there are many factors that affect the roll wear amount, and there is an interaction between the factors, so that the prediction error was large with respect to the actually measured roll wear amount. The roll thermal expansion prediction model is, for example, to determine the axial and radial temperature distribution of the roll, from the determined temperature distribution in the cross section of the roll, assuming a plane stress field or plane strain field, the roll of the roll This is to calculate the amount of thermal expansion. Then, in order to obtain the roll temperature distribution, considering the heat input in the area in contact with the rolled material and the heat removal in the non-contact area, solving the heat conduction model of the roll by the difference, To calculate the distribution,
Since it is difficult to actually match the temperature dependence of the physical properties of the roll and the boundary conditions such as the range of each area and the heat transfer coefficient, the prediction error is large with respect to the actually measured roll thermal expansion. Was.

[0006] On the other hand, the roll profile measuring device installed in the rolling stand has a complicated mechanism, so that the roll profile cannot be measured in some cases due to failure or maintenance. For this reason, there was a problem that the roll profile actual measurement value was not always obtained for each rolled material. Therefore, an object of the present invention is to provide a roll profile prediction model including a roll wear amount prediction model and a roll thermal expansion amount prediction model that can accurately predict a roll profile even for a rolled material for which a measured roll profile measurement value cannot be obtained. An object of the present invention is to provide a method for modifying a model.

[0007]

That is, the present invention provides a roll profile prediction model comprising a roll wear prediction model and a roll thermal expansion prediction model for a work roll by using the measured roll profile of the work roll. In the method of correcting the roll profile prediction model to be corrected, actual measured values of the roll crown are obtained for a plurality of rolled materials after a predetermined number of rolls from the start of rolling in the rolling cycle, and the roll wear amount prediction model and the roll thermal expansion amount are obtained. Based on the prediction model, a roll wear crown prediction value, a roll thermal crown prediction value and a roll crown prediction value are calculated from the start of rolling of the rolled material, and the roll crown prediction is determined from the measured roll crown value. Subtract the error to estimate the roll crown error. Therefore, after the end of the rolling of the rolling cycle, based on the relationship between the number of rolls from the start of rolling and the error of the roll crown predicted value, the deviation of the error of the roll crown predicted value after a predetermined number of rolls. Is smaller, the slope of the straight line with respect to the number of rolls is determined, and a straight line passing through the origin having the slope is defined as a relationship with the error of the roll wear crown predicted value with respect to the number of rolls, based on the error of the roll wear crown predicted value. Then, a correction coefficient of the roll wear amount prediction model is obtained, the roll wear amount prediction model is corrected using the correction coefficient, and then, the error of the roll wear crown prediction value is calculated from the error of the roll crown prediction value. Then, an error in the predicted value of the roll thermal crown is obtained, and based on the error of the predicted value of the roll thermal crown, the error in the roll thermal crown is calculated. Obtains a correction coefficient of Le thermal expansion amount prediction Dell, a correction method of a roll profile prediction model, characterized by modifying the rolls of thermal expansion amount prediction model by using the correction coefficient.

[0008]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A case where the method of the present invention is applied to a fourth stand of a hot rolling mill composed of seven stands will be described below in detail with reference to the drawings. Predictive model of roll wear amount used in the present invention, the four factors of the roll diameter D and the roll material M _{ro ll} and rolling of the rolled material per length L and the rolling load P as a variable, its cause relationship based on actual Is determined, and the wear amount of the roll at the position x in the barrel direction of the roll is determined. For example, the wear amount WEAR can be obtained by a functional expression represented by the following expression (1).

WEAR = g (L, P, D, M _roll , x) --- (1) Further, the roll thermal expansion amount prediction model used in the present invention is as follows.
The temperature distribution in the barrel direction x and the radial direction of the roll is determined, and the amount of thermal expansion of the roll in the barrel direction x of the roll is calculated from the determined temperature distribution in the cross section of the roll. For example, in the roll wear amount prediction model used in the present invention, FIG. 2 shows a roll wear amount prediction result when a rolled material having a sheet width shown in FIG. 1 (a rolling cycle including 100 rolled materials) is rolled. Show.

The roll wear amount WEAR shown in FIG. 2 is obtained by determining the influence coefficients a _L , a _P , a _D , and a _M of the following equation (2) as a linear relationship among the above four factors based on actual results. This is obtained by integrating the roll elongation caused by the roll length L and the rolling load P for each rolled material up to the i-th rolled material. WEAR (x, i) = Σ (a L × L + a P × P + a D × D + a M × M roll) × b (x) - (2) , although the scope outside the plate width range: b (x) = 0 Within the range of the sheet width: b (x) ≧ 1 Normally, as the number of rolls increases, the rolls within the range of the sheet width of the rolled material wear and the diameter of the rolls decreases, but hot tandem rolling is performed. In the front stand of the machine, black scale is formed and may hardly be reduced or may be unevenly worn in the roll barrel direction. Therefore, when the wear of the roll is not uniform, it is preferable to change the weight coefficient b (x) in the barrel direction of the roll to match the actual value.

In predicting the roll wear amount, the interaction of the above factors may be considered, and the factors such as the temperature of the rolled material, the rolled material, and the amount of lubricating oil may be added. FIG. 3 shows the calculation results of the roll thermal expansion amount in the roll barrel direction x obtained for the rolling cycle shown in FIG. The roll thermal expansion amount THER shown in FIG. 3 was divided into a heat input region in contact with the rolled material and a non-contact cooling region, and a roll heat distribution model was solved to calculate the temperature distribution of the roll. Things.

Here, the axial and radial directions of the roll
The temperature distribution determines the heat input and heat removal during one rotation of the roll.
Thermally averaged, heat input and cooling simultaneously at each rolling pitch
Rolling time to be performed and cooling time to perform only cooling
I asked. Heat input q at this time _RIs q_R= Α_R(θ₁−
θ), heat removal q_cIs q_c= Α_c(θ−θ₀Given by
You. Where α_RIs the heat transfer coefficient in the board road, α_cIs a board road
Heat transfer coefficient outside, θ₁Is the steady roll temperature (rolling continues
Temperature at the time of₀Is the ambient temperature, θ is the roll surface temperature
Degrees. In order to obtain the temperature distribution of the roll,
Divided into heat input area, water cooling area, and air cooling area during one rotation of
You may ask for it.

In order to calculate the thermal expansion amount THER (x, i) of the roll in the barrel direction x of the ith roll of the rolled material from the temperature distribution θ in the cross section of the roll, a plane strain field is assumed, It was obtained using the following equation (3).

[0014]

(Equation 1)

Here, β: coefficient of linear expansion, R: roll radius, r: radial coordinate The roll profile predicted value is the sum of the above equations (2) and (3), and the result is used as the roll profile measuring device. FIG. 4 shows the measured values of the roll profile together with the actual measured values. The roll profile prediction value has less unevenness than the roll profile measurement value because the wear within the sheet width is assumed to be uniform.

Here, the actual measurement of the roll profile used in the present invention may be performed during the rolling of the rolled material, or may be performed during the rolling interval. When the roll profile is measured during rolling, the amount of elastic deformation of the roll due to the rolling load is corrected. Roll profile measuring device
While moving the nozzle which sprays water toward the roll in the barrel direction of the roll, ultrasonic waves are propagated in the water to measure the distance between the roll and the nozzle. However, a roll profile measuring device in which a plurality of nozzles are fixed in the barrel direction of the roll may be used. Although the roll profile measuring device having this nozzle fixed does not need to move the nozzle in the roll barrel direction, it is necessary to arrange many nozzles in the roll barrel direction in order to measure the roll profile with high accuracy. .

Next, a roll crown actual measurement value is obtained based on the roll profile actual measurement value measured by the roll profile measuring device, and a roll crown prediction value is obtained based on the roll profile prediction value. From the roll crown predicted value,
An error of the roll crown prediction value, which is the deviation, is obtained.
The measured roll crown value _{fr, meas} and the predicted roll crown value _{fr , cal} are values obtained by subtracting the value at the end of the roll barrel from the value at the center of the roll barrel (value per diameter). _{fr, meas} is obtained _{by the following equation} (4), and the roll crown predicted value _{fr, cal} is obtained by the following equation (5). Further, the error f _{r, err} of the predicted roll crown value is obtained by the following equation (6) by subtracting the predicted roll crown value _{fr , cal} from the actual measured roll crown value _{fr, meas} .

_{Fr, meas} = D _{cent, meas} −D _{edge, meas} −−− (4) _{fr , cal} = D _{cent, cal} −D _{edge, cal} −−− (5) _{fr, err} = _{fr , meas} −fr _{, cal} −−− (6) where D _{cent, meas is the} measured value of the roll crown at the center of the roll barrel D _{edge, meas is the} measured value of the roll crown at the end of the roll barrel D _{cent, cal is the} roll barrel Roll _edge predicted value at the center D _{edge, cal} : Roll crown predicted value at the end of the roll barrel For the rolling cycle shown in FIG. 1 above, the actual measured roll crown values _{fr, meas} and roll crown predicted values _{fr , cal} based on the number of rolls. 5 is shown in FIG. FIG. 6 shows the change in the error f _{r, err} of the roll crown prediction value with the number of rolls.
Shown in

The error of the roll crown predicted value shown in FIG.
Is positive at the beginning of the rolling cycle,
Negative in the range of 80-100 rolls in the latter half of the rolling cycle
Value. The present invention is based on the error of the roll crown prediction value.
The number of rolls after the 80th roll where x is a negative value x
(80-100th roll)
Error f _{r, err}And the number of rolls x
Through the origin with that slope
A straight line was drawn as shown in FIG.
Measurement error f_{w, err}For the number of rolls x
It is the one who was involved.

[0020] That is, the solid line inclination α with respect to the number of rolled x shown in FIG. 6, (- 0.00117) is because, error f _w of the roll wear crown predicted _value, for _err, rolled number x
Is expressed by the following equation (7). fw _{, err} = (-0.00117) .x ------ (7) By the way, the roll wear crown predicted value fw _{, cal} and the roll thermal crown predicted value ft _{, cal} are the roll wear amount predicted value and the roll thermal expansion. The predicted amount was calculated by subtracting the value at the end of the roll barrel (per roll) from the value at the center of the roll barrel (per roll diameter).

The roll wear crown predicted value f
_{w, cal} and roll thermal crown predicted value f
The behaviors of _{t and cal} are different as shown in FIG. That is, the roll thermal crown predicted value f _{t, cal}
Increases sharply at the beginning of the rolling cycle, and becomes almost constant in the latter half of the rolling cycle. In addition, the roll wear crown predicted value _{fw, cal} decreases almost in proportion to the number of rolls. Due to this difference in growth behavior, the number of rolls
The gradient of the straight line with respect to the number of rolls x is determined to reduce the deviation from the error fr _{r, err} of the estimated roll crown value of the 80th and subsequent rolls. Rolling number x for _{w and err}
The reason for the relationship is that there is the following relationship. That is, most of the change in the prediction error in the latter half of the rolling cycle is caused by the change in the prediction error of the wear crown.

[0022] Then, as shown in FIG. 8, the roll wear crown predicted value f ^A _w of the _{modified, ca l} is roll wear crown predicted value f _w before _{modification, cal} and error f roll wear crown predicted value Since it is the sum of _{w and err} , it is expressed by the following equation (8). f ^A _{w, cal} = _{f w, cal + f w,} err = f w, cal + (- 0.00117) · x --- (8) Therefore, the roll wear crown predict the corrected value f ^A _{w, err}
Is integrated with respect to the number of rolls x, and the value is divided by the value obtained by integrating the roll wear crown predicted value _{fw, cal} before correction with respect to the number of rolls x, and the quotient is used as a correction coefficient of the roll wear amount prediction model. Since the correction coefficient of the roll wear prediction model shown in FIG. 8 was 1.8, the roll wear prediction model WEA (Equation (2)) was multiplied by the correction coefficient 1.8 to obtain the corrected roll wear prediction model. And

Next, an error of the roll thermal expansion prediction model will be described. The error f _{t, err} of the roll thermal crown prediction value is a value obtained by subtracting the roll wear crown prediction value from the roll crown prediction value, and the roll crown prediction error f
_{It is obtained} by subtracting the error f _{w, err} of the predicted value of the roll wear crown from _{r, err} . That is, it is represented by the following equation (9).

F_{t, err}= F_{r, err}−f_{w, err} −−−− (9) Then, as shown in FIG.
Le crown predicted value f^A _{t, cal}Is the roll therma before correction
Le crown predicted value f_{t, cal}And roll thermal crown
Measurement error f_{t, err}Is the sum of
Is done. f^A _{t, cal}= F_{t, cal}+ F_{t, err} −−−− (10) Therefore, the corrected roll thermal crown predicted value f^A
_{t, cal}Is integrated with respect to the rolling number x, and the value is
Roll thermal crown predicted value f_{t, cal}To the number of rolls x
Divide by the integrated value and estimate the quotient of the roll thermal expansion.
The Dell correction factor. The amount of roll thermal expansion shown in FIG.
The correction factor of the measurement model was 1.7,
Multiply the correction amount prediction model THE (Equation (3)) by a correction coefficient of 1.7.
Then, a corrected roll thermal expansion prediction model was obtained.

In the same manner as described above, in the rolling cycle shown in FIG. 1, the corrected roll wear amount prediction model for the fifth, sixth, and seventh stands provided with the roll profile measuring device and the corrected The roll thermal expansion prediction model is obtained. Then, in the next rolling cycle, using the rolling conditions of each rolled material, based on the corrected roll wear amount prediction model and the corrected roll thermal expansion amount prediction model for the fourth to seventh stands, the roll wear is estimated. The predicted value of the amount of roll and the predicted value of the amount of thermal expansion of the roll were determined, and the predicted value of the amount of roll wear and the predicted value of the amount of thermal expansion of the roll were added to calculate the predicted value of the roll profile. Then, using the roll profile prediction value, the plate crown is predicted (predicted by a plate crown prediction model composed of a roll profile prediction model, a roll deformation model of a rolling mill, and a deformation characteristic model of a rolled material). At the same time, the sheet material was rolled by setting the bender force of the roll bending device. At that time, the sheet crown was measured on the exit side of the seventh stand.

FIG. 10 shows the relationship between the predicted value and the actually measured value of the sheet crown when rolling is performed using the present invention. Further, FIG. 11 shows the roll profile predicted values of the fourth stand predicted using the present invention, together with the roll profile actual measured values. On the other hand, as a conventional example, in the same rolling cycle as the invention example, the sheet width, the sheet thickness, the steel type, the rolling temperature and the rolling schedule, using the rolling conditions of each rolled material, the roll wear amount predicted value and the roll thermal expansion amount The predicted values are respectively predicted by a roll wear amount prediction model WEAR (formula (2)) and a roll thermal expansion amount prediction model THER (formula (3)), and the roll wear amount predicted value and the roll thermal expansion predicted value are added. The roll was rolled assuming that the roll profile was the predicted value, and the other conditions were the same as those of the invention, and the strip crown was measured on the exit side of the seventh stand.

FIG. 12 shows the relationship between the predicted value and the actually measured value of the sheet crown when rolled using the method of the conventional example. By comparing FIG. 10 and FIG. 12, it can be seen that the predicted value of the plate crown matches the actually measured value and the required plate crown is obtained by using the method of the present invention. this is,
As shown in FIG. 11, the accuracy of the roll profile prediction value predicted by using the method of the present invention is improved, and becomes closer to the actually measured value.

[0028]

According to the present invention, the roll wear amount prediction model and the roll thermal expansion amount prediction model are corrected using the actually measured values of the roll profile, thereby providing a highly accurate roll wear amount prediction model and roll thermal expansion amount. Since the roll profile prediction model including the quantity prediction model can be obtained, the roll profile can be predicted with high accuracy even when the actual roll profile measurement value cannot be obtained for each rolled material.

Further, by using the corrected roll wear amount prediction model and the roll thermal expansion amount prediction model, the roll profile can be predicted with high accuracy, and the prediction accuracy of the strip crown of the rolled material is improved.

[Brief description of the drawings]

FIG. 1 is a characteristic diagram showing a change in a sheet width of a rolled material with respect to the number of rolls.

FIG. 2 is a characteristic diagram showing a change in a predicted roll wear amount in a roll barrel direction.

FIG. 3 is a characteristic diagram showing a change in a predicted value of a roll thermal expansion amount in a roll barrel direction.

FIG. 4 is a characteristic diagram showing a change in a roll profile predicted value in a roll barrel direction.

FIG. 5 is a characteristic diagram showing changes in a predicted roll crown value and a measured roll crown value with respect to the number of rolls.

FIG. 6 is a characteristic diagram showing a change in an error of a roll crown prediction value with respect to the number of rolls.

FIG. 7 is a characteristic diagram showing changes in a roll thermal crown predicted value, a roll wear crown predicted value, and a roll crown predicted value with respect to the number of rolls.

FIG. 8 shows estimated values of roll wear crown with respect to the number of rolls,
It is a characteristic diagram which shows the error of the roll wear crown prediction value, and the change of the roll wear crown prediction value after correction.

FIG. 9 is a characteristic diagram showing changes in roll thermal crown predicted values, corrected roll thermal crown predicted values, errors in roll crown predicted values, and errors in roll wear crown predicted values with respect to the number of rolls.

FIG. 10 is a characteristic diagram showing a relationship between a predicted sheet crown value and an actual measured sheet crown value predicted by a model modified using the method of the present invention.

FIG. 11 is a characteristic diagram in which a roll profile predicted value predicted by a model corrected using the method of the present invention is compared with a measured roll profile value.

FIG. 12 is a characteristic diagram showing a relationship between a predicted sheet crown value and a measured sheet crown value predicted without correcting a model using a conventional method.

Claims (1)

[Claims] 1. A method for correcting a roll profile prediction model, comprising: correcting a roll profile prediction model comprising a roll wear amount prediction model and a roll thermal expansion amount prediction model for a work roll by using a measured roll profile value of a work roll. For a plurality of rolled materials after a predetermined number of rolling after starting the rolling of the rolling cycle, a roll crown actual measurement value is determined, and based on the roll wear amount prediction model and the roll thermal expansion amount prediction model, From the start of rolling, the roll wear crown predicted value, the roll thermal crown predicted value and the roll crown predicted value are obtained, and the roll crown predicted value is subtracted from the roll crown measured value to obtain the roll crown predicted value. Find the error, after the end of the rolling of the rolling cycle Based on the relationship between the number of rolls since the start of rolling and the error of the roll crown prediction value,
The inclination of the straight line with respect to the number of rolls having a small deviation with respect to the error of the roll crown predicted value after the predetermined number of rolls is determined, and a straight line passing through the origin having the slope is defined as the roll wear crown predicted value with respect to the number of rolls. With the relationship with the error, based on the error of the roll wear crown prediction value, determine a correction coefficient of the roll wear amount prediction model, and using the correction coefficient to correct the roll wear amount prediction model, and then, The error in the roll thermal crown prediction value is obtained by subtracting the error in the roll wear crown prediction value from the error in the roll crown prediction value, and based on the error in the roll thermal crown prediction value, Determining a correction coefficient, and correcting the roll thermal expansion prediction model using the correction coefficient. Method of correcting feel prediction model.