JPH08117826A - Method for estimating plate crown and shape of rolling stock - Google Patents

Abstract

PURPOSE: To estimate a plate crown with high precision, which satisfactiorily coincides with a result obtained by a strict calculation in a short time without damaging the universal applicability of a divided model online even under a severe condition where a rolling load is high and a roll diameter is small. CONSTITUTION: In a process calculating the deflexion quantity of the roll of a rolling mill, simplifying a calculation so that the accuracy of the strict calculation is not damaged to estimate and determine online the operation quantity of a device controlling the plate crown and the shape of a rolling stock, the deflexion quantity of each roll is obtained, considering a linear load distribution between the rolls of the rolling mill as a straight line distribution. At the same time, a higher-order linear load between the rolls, canceling out the unadaptable parts of the deflexion of the rolls coming into contact with each other, is obtained. Consequently, when correcting the unadaptability of the deflexion, a distribution in the roll shaft direction of a spring constant between the rolls, is considered.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting the plate crown / shape of a rolled material that can be applied online.

[0002]

2. Description of the Related Art Demands for sheet thickness accuracy of rolled material in the sheet width direction are becoming stricter year by year, and it is important to improve the accuracy of a sheet crown prediction model.

In general, the plate crown of a rolled material is predicted by a simulation called a split model (shhoet et al .: JISI).
206-11 (1968), 1088). This division model calculates the plate crown by obtaining the amount of deflection and the amount of flatness of the roll from the rolling load when the rolled material is deformed based on the elastic deformation theory. Here, the rolling load is
It is obtained from rolling conditions such as deformation resistance of rolled material, roll diameter, plate thickness, plate width, and tension.

By the way, the division model used conventionally has a long calculation time because it requires an exact calculation which requires a convergence calculation, and cannot be used as an online model. Therefore, as the online model, a model in which the relationship between the strip crown and the rolling conditions is statistically processed based on the actual rolling result or the calculation result by the division model is used.

However, when the statistically processed model is applied under different rolling conditions, it is necessary to create a new model or review the coefficient of the model each time the rolling conditions change.

As a method for solving this problem, for example,
On page 49 (Kitahama et al.) Of the 37th Solid Plastic Working Joint Lecture (1986), a proposal for an online prediction model that simplifies and shortens the calculation time without compromising the physical meaning and versatility of the split model Has been done. In the prediction model according to the new proposal, the roll axial distribution of the contact pressure between the contacting rolls is used as the linear distribution, and the amount of deflection of each roll is calculated. The method of approximating the contact pressure distribution between the rolls caused by the non-conforming deflection by a high-order equation is adopted as the elastic deformation between the rolls.

[0007]

With the simple model according to the above method, it is possible to obtain a calculation result in a short time, which is in good agreement with the result obtained when the exact calculation is performed, while reducing the inconveniences so far. became. However, in this simple model, various assumptions are made to reduce the calculation time; for example, the assumption that the contact spring constant between the work roll and the backup roll is constant is provided.
Especially under severe rolling conditions in which the rolling load is increased and the roll diameter is reduced in order to improve the efficiency of rolling, there is a problem that a large error occurs in the calculation results between the exact calculation and the simplified model. The purpose of the present invention is to increase the rolling load online and to reduce the roll diameter even under severe rolling conditions.
We are proposing a method to accurately grasp the crown and shape of rolled material.

[0008]

SUMMARY OF THE INVENTION The present invention is a rolling mill which simplifies and predicts the operation amount of a device for controlling the plate crown and shape of a rolled material on-line so as not to impair the accuracy of strict calculation. In the process of calculating the amount of roll deflection of the rolling mill, by independently calculating the rolling conditions, roll profile, etc., in order to determine the operation amount of the device that controls the plate crown and shape of the rolled material online, In the method of predicting the amount of deflection of the rolls, the linear pressure distribution between the rolls of the rolling mill is used as the linear distribution to obtain the amount of deflection of each roll, and the higher order of offsetting the nonconformity of the deflection of the contacting rolls When correcting the incongruity of the roll deflection by obtaining the roll-to-roll linear pressure, it is calculated considering the roll axial distribution of the roll-to-roll spring constant. It is a method for predicting the crown shape. In this method, the spring constant between rolls is preferably expressed as a function of the linear pressure between rolls in the roll axial direction.

[0009]

[Function] The error from the exact calculation that occurs when rolling is performed under severe conditions where the rolling load is large and the roll diameter is small is
This is because it is assumed that the inter-roll spring constant is constant in the roll axial direction in the simplified model. Therefore, in the present invention, by correcting the incompatibility of the deflection between the rolls in contact, when predicting and determining the operation amount of the device for controlling the plate crown and shape of the rolled material, in consideration of the inter-roll spring constant I decided to do it.

The prediction model in the present invention is a method for calculating a roll deflection amount of a rolling mill which is simplified so as not to impair the accuracy of the strict calculation of the conventional general-purpose split model. Deflection deformation of the roll,
It is separated into four by rolling load, linear pressure between rolls, work roll bender and roll profile under no load,
Furthermore, regarding the no-load roll profile, it is divided into three categories: initial, wear, and thermal profile. It is possible to independently calculate the work roll deflection due to these influences and superimpose the respective deformations.

In the following, considering the distribution in the axial direction of the spring constant between the work rolls and the backup rolls in the four-high rolling mill, the contact pressure distribution between the rolls caused by the incompatibility of the deflection between the rolls is a quartic expression. The correction of the nonconforming deflection will be described.

Now, consider contact conditions at five points (a) to (e) in the figure in a coordinate system as shown in FIG. Here, it is possible to expand the equation that is left-right asymmetric, but here, only the symmetric term is used. That is, the deflection V _{W0 of the} work roll and the deflection V _{bO of the} backup roll are approximated by a quartic equation as shown in the following equations (1) and (2). V _W0 = C ₄ ^w x ⁴ + C ₂ ^w x ² (1) V _b0 = C ₄ ^b x ⁴ + C ₂ ^b x ² (2) Note that the work roll fourth-order approximation coefficients C ₂ ^w and C ₄ ^w Is as follows. ^{_{C 2 w = (64V Wq -4V}} We) / 3L 2 ... (3) C 4 w = (64V We -256 V Wq) / 3L 4 ... (4) Here, the work roll end deflection V _We, Quarter The deflection V _Wq of the portion can be easily obtained from the elastic theory of beam deflection by making the contact pressure distribution between rolls a linear distribution, and the fourth-order approximation coefficient C ₂ ^b , C of the backup roll can be obtained.
₄ ^b may also be obtained in the same manner.

Next, the corrected linear pressure distribution P associated with the nonconforming deflection
_{When hX} is approximated by a quartic equation as shown in equation (5), the deflections V _W and V _B of the work roll and the backup roll due to the corrected linear pressure distribution are expressed by equations (6) and (7), respectively. P _hX = α ₄ x ⁴ + α ₂ x ² + α ₀ (5) Then, since the total sum of the corrected linear pressures becomes ₀ , α ₀ = −
It becomes 1/5 (α ₄ L ₂ ² ) −1/3 (α ₂ L ₂ ² ).

[0014]

[Equation 1]

[0015]

[Equation 2]

The distribution of the corrected linear pressure is calculated from the following equation (8) by using the spring constant for the difference δ _X between the work roll and the backup roll at each position in the roll axial direction and the difference in the flatness between the work roll and the backup roll. It will be multiplied.

(Equation 3)

[0017] can be obtained above (8) x in l _2, l simultaneous equations _2/2 by substituting each of (9).

[Equation 4]

Here,

(Equation 5)

From the above equation (9), α ₂ and α ₄ are obtained,
The final deflection amount of the work roll can be obtained by calculating the deflection of the work roll due to the corrected linear pressure from the equation (6) and adding the linear pressure distribution to the deflection obtained as the linear distribution. Incidentally, the roll between the spring constant _{K 0, Kl 2/2,} Kl 2 in the axial direction position _{X = 0, l 2/2} , l 2 , according to Feppuru can be calculated by the following equation (10) .

(Equation 6) Where π is the circular constant, D _W and D _B are the work roll and backup roll diameters respectively, ν ² _W and ν ² _B are the work roll and backup roll Poisson's ratios respectively, and P _X is the roll-to-roll linear pressure. . Further, since the roll-to-roll spring constant is a function of the linear pressure, the roll axial direction distribution may be assumed in advance, or it may be obtained by repeating the calculation once or twice.

[0020]

EXAMPLE FIG. 2 shows that the work rolls have different diameters.
700mm, 600mm, 500mm roll barrel length 2050mm, plate width 15
Under the conditions of 50 mm, rolling load 2000 tonf / m, rolling mill type pair cross mill, cross angle 1.05 deg, using the conventional method in which the spring constant between rolls is constant and the method of the present invention, the strip width distribution of rolling load is uniform. Plate crown that can be realized when
(Mechanical uranium) is calculated and compared with the calculation result of the split model, which is an exact calculation that cannot be applied online.However, in the method of the present invention, the split model and the calculation result are the same even when the roll diameter is small. It is clear that the accuracy is high.

Next, when the work roll diameter is in the former stage (F ₁ ~
F ₄₎ 700 mm, subsequent (F ₅ to F ₇₎ in the hot finishing mill consisting of 4-high mill 7 stand 600 mm, the sheet bar thickness 30mm mixed rolling cycle of stainless steel and general material
60 pieces are rolled, and the actual value of the plate crown at a position 25 mm from the plate edge of the rolled material and the prediction result by the method of the present invention are shown in comparison with FIG. At this time, the strip width of the rolled material was 785 to 1240 mm, and the finished strip thickness was 1.6 to 3.5 mm. As is clear from FIG. 3, it was confirmed that the plate crown of the rolled material can be accurately predicted online by using the method of the present invention.

[0022]

As described above, according to the present invention, even under severe rolling conditions where the rolling load is high and the roll diameter is small, the results obtained by exact calculation in a short time without impairing the versatility of the split model online. It is possible to make a highly accurate prediction of the plate crown that closely matches with.

[Brief description of drawings]

FIG. 1 is a diagram showing a coordinate system at the time of correcting a nonconforming deflection.

2 (a) and 2 (b) are diagrams showing a comparison between the calculation results obtained by the conventional method and the method of the present invention and the results obtained by the exact calculation using the division model.

FIG. 3 is a diagram showing a comparison between actual values and predicted values obtained according to the present invention.

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁶ Identification code Internal reference number FI Technical display location B21B 37/18 BBH 8315-4E B21B 37/00 116 Z 8315-4E 117 Z 8315-4E 37/08 Z 8315-4E BBH (72) Inventor Kunio Isobe 1 Kawasaki-cho, Chuo-ku, Chiba City, Chiba Prefecture, Kawasaki Steel Research Laboratories (72) Inventor Shohoku Kitahama 1 Kawasaki-cho, Chuo-ku, Chiba Prefecture Kawasaki Steel Steel Research Institute Co., Ltd.

Claims (2)

[Claims] 1. A roll deflection amount of a rolling mill is predicted by independently calculating rolling conditions, roll profile, etc. in order to determine online the operation amount of a device for controlling the strip crown and shape of a rolled material. In this method, the linear pressure distribution between the rolls of the rolling mill is used as the linear distribution to determine the amount of deflection of each roll, and the higher-order linear pressure between the rolls that cancels out the incompatibility of the deflection of the contacting rolls is determined. A method for predicting the strip crown and shape of a rolled material, which is characterized in that when the incongruity of the roll deflection is corrected, it is calculated in consideration of the roll axial distribution of the inter-roll spring constant. 2. The roll-to-roll spring constant is expressed as a function of roll-to-roll linear pressure in the roll axial direction.
The described method.