JPH0810814A - Method for calculating contact region between rolls of rolling mill - Google Patents

Abstract

PURPOSE:To exactly recognize a contact region between rolls at the time of rolling with high accuracy by assuming the contact region between rolls at the time of rolling, calculating only flattening amounts at end points in the axial direction of the contact region, checking only whether this value is positive or negative and repeatedly correcting the assumption of the contact region between rolls. CONSTITUTION:The contact region between rolls is assumed and the flattening amounts at both end points of the contact region are calculated using a flattening amount predicting formula modeled based on this contact length. Next, by judging whether the assumed contact length is longer or shorter than the true contact length, the assumption of contact length is corrected in accordance with the positive or negative of the flattening amounts at these two points. To be concrete, in the case (b) that the assumed contact length lBW is shorter than the true value, that is, in the case of delta (0)>0, delta(lBW)>0, recalculation is executed by making the assumed contact length lBW larger. Conversely, in the case (c) that the assumed contact length lBW is longer than the true value, that is, in the case of delta(0)<0, delta(lBW)<0, the recalculation is executed by making the contact length lBW smaller. By such a procedure, the contact length is converged at the true value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calculating a contact area between rolls during rolling at high speed.

[0002]

2. Description of the Related Art In recent years, a plate crown and a plate shape have been very important in view of needs for higher dimensional accuracy and higher quality of products in hot rolling. Therefore, accurate control of the crown and shape of a rolling mill such as a steel plate in continuous rolling is important not only for maintaining the product of the rolled material but also for avoiding troubles during rolling. For this reason, a roll bending device or a variable crown roll is provided in each stand of the continuous rolling mill, and the operation amount of these is adjusted in each stand to control the crown and shape to target values.

On the other hand, in order to cancel the bending of the roll due to the rolling load, an initial crown roll is attached to increase the thickness accuracy of the rolled product in the plate width direction. If the rolling conditions such as change, it is necessary to replace it with another crown roll, so it is necessary to have a roll with multiple types of initial crowns. This leads to a decrease in the operating rate, and because the roll crown changes significantly due to roll wear and thermal expansion accompanying the progress of rolling work, etc., the thickness distribution in the plate width direction of the plate material can be conventionally changed without replacing the roll. A means of controlling is desired.

[0004]

Therefore, accurate determination of the contact area between rolls due to rolling load is indispensable data for predicting roll profile and plate thickness prediction by mill stretch. As a method of accurately grasping the range, a method of calculating is proposed. As the calculation of the contact area between rolls, conventionally, assuming the contact area between rolls, the roll is divided into a number of meshes, and simultaneous equations of stress and displacement are established for each division to determine the contact conditions in the contact area. A method is used in which the lower surface of the upper roll and the upper surface of the lower roll are checked for coincidence, and if they are not correct, the contact area is repeatedly corrected until they coincide. This way, even if you only want to know the contact area,
It is necessary to obtain stresses and displacements of all meshes at the same time, and in general, a large amount of calculation time is consumed due to the small improvement margin of accuracy for each convergence calculation, and the final accuracy is more than the divided mesh width. There is a problem that cannot be improved. In addition, a method of expressing the contact length between rolls by a direct regression equation under rolling conditions such as plate thickness and rolling load is also used, but it is significantly predicted when the roll profile changes irregularly due to expansion and wear. There is a drawback that the accuracy is reduced.

[0005]

As a result of intensive development, the inventors of the present invention should solve the above problems. As a result, assuming a contact area between rolls at the time of rolling, the flatness at the axial end point of the contact area is assumed. It is extremely simple to calculate only the amount, check only the positive and negative of this value, and correct the assumption of the contact area between rolls.
Moreover, it is to provide a calculation method for highly accurately predicting arbitrary conditions such as rolling mill settings, roll material, and profile. The gist of the present invention is to assume the contact area between rolls during rolling, calculate only the flatness amount at the axial end point of the contact area, and judge the positive / negative of the flatness amount to assume the contact area. It is a method for calculating the contact area between rolls of a rolling mill, which is characterized in that the correction is repeated in sequence to converge to an appropriate contact length.

The present invention will be described in detail below with reference to the drawings. FIG. 1 is an explanatory view showing an influence on work roll bending caused by a rolling load. As shown in FIG. 1, a rolling mill provided with a quadruple roll includes a work roll 2 that rolls the plate material 1 and a backup roll 3 that contacts the work roll 2 and reinforces it. When rolling is performed in this configuration, the rolling load is applied to the upper and lower backup rolls 3, the work rolls 2 and the backup rolls 3 are in complete contact with each other, and a contact load distribution between rolls is generated, which is the roll gap that was present when there was no load. In the width direction affects the deflection of the work roll and the backup roll through the width distribution of the load acting on the contact surface between the work roll 2 and the backup roll 3.

FIG. 2 is an explanatory view showing the load distribution applied to the work roll and the backup roll and the flatness between the rolls. As shown in this figure, the roll-to-roll contact load distribution 4 generated on the backup roll causes roll axis deflection due to the load distribution 5 applied to the work roll. Reference numeral 6 is a backup roll lower surface profile when there is no flatness between rolls, 7 is a work roll upper surface profile when there is no flatness between rolls, 8 is a roll boundary profile when there is flatness between rolls, and 9 is a flatness amount between rolls Is.

FIG. 3 is a flow chart for explaining a method for obtaining the contact length between the work roll and the backup roll. As shown in Fig. 3, first, the contact area between rolls occurring in the work roll and the backup roll is estimated, and the flatness distribution is calculated according to the flat model between the work roll and the backup roll at the end points of the contact area between the rolls, and the calculated value is assumed. The difference between the contact length is determined according to the contact area conversion model between the work roll and the backup roll, and if the result of the determination is appropriate, it is used for the prediction of the plate shape by the mechanical crown model or the mill stretch model. If the result of the determination is improper, the contact area is estimated again, and the above-mentioned operation is repeated to converge it to an appropriate value.

FIG. 4 is a process diagram for the method for calculating the contact area between rolls according to the present invention. FIG. 4A shows a true contact state between the work roll 2 and the backup roll 3. In this state, a flat load distribution is generated between the work roll 2 and the backup roll 3 due to the contact load, and a roll bending state occurs. In this roll deformation state, the flatness amount must be 0 at both end points of the contact area between rolls unless there is a discontinuity such as a step in the roll profile. That is, δ (0) = 0 and δ (l _BW ) = 0.
It is considered to estimate the unknown contact length between rolls using this flatness characteristic.

First, assuming the contact area between rolls, the flatness amount at both end points of the contact area is calculated by using the flatness amount prediction formula modeled based on this contact length. Next, the contact length hypothesis is corrected by discriminating the length of the assumed contact length from the true contact length according to the positive or negative of the flatness amount at these two points. In particular,
When the assumed contact length l _BW is shorter than the true value, as shown in FIG. 4B, that is, when δ (0)> 0 and δ (l _BW )> 0, the assumed contact length l _BW is recalculated largely. On the contrary, when the assumed contact length l _BW is longer than the true value, FIG. 4C, that is, δ
When (0) <0 and δ (l _BW ) <0, the assumed contact length l
_{The BW} is reduced and it is converged to the true value by the procedure of recalculation.

FIG. 5 is a diagram showing a method for detecting a contact area between a work roll and a backup roll according to the present invention. As shown in the figure, the center of the mill center is 0, x is from the drive side (DS) to the working side (WS), and the center of the contact area center is 0 and z is on the working side (WS). Flatness δ between rolls at arbitrary point z in the axial direction
Find (z). That is, as a method of calculating the flatness amounts δ (0) and δ (l _BW ) at the end points in the axial direction of the contact area between the rolls, the zero point of roll deflection is set at both ends of the contact area.
The flatness amount δ can be simplified by the following formula.

Δ (z) = δ ₀ (z) + δ ₁ + δ _RND (z) When z = 0, δ (0) = δ ₀ + δ ₁ (0) + δ _RND (0) z = l _BW , δ (l _BW ) = δ ₀ + δ ₁ (l _BW ) + δ _RND (l _BW ) where δ (0): Flatness at 0 point between roll length axes δ (l _BW ): Roll length axis _Flatness at direction l _BW point δ ₀ : 0th-order equation component (roll deflection, average value of roll profile) δ ₁ : 1st-order equation component (roll deflection, roll profile and center of roll contact area width direction and mill center) 1st-order flat component corresponding to the moment of force generated by the difference) δ _RND : Difference between the original roll curve and the optimum quadratic approximation curve (deviation roll curve)

FIG. 6 is a diagram showing a processing flow according to the present invention. As shown in this figure, assuming the contact area for the entire contactable area, calculate the flatness amount of the contact point between rolls according to the flattening model between the work roll and the backup roll,
For the driving side (DS) and the working side (WS), the difference between the calculated value and the assumed contact length is appropriate. As the side (WS), first, (1) δ
When (D) ≧ 0 and δ (W) ≧ 0, (2) δ (D) <
When 0, δ (W) <0, (3) δ (D)> 0, δ
When (W) <0, (4) δ (D) <0, δ (W)> 0
It can be divided into four. In the case of the above (1), the new drive side and the new work side are set as both ends of the contactable area.

Next, in the case of (2), the new contact length is assumed, the new contact area is centered, the contact area is checked, new l _BW (contact length between work roll and backup roll), new x _BW (contact area). Center and mill center length), flatness calculation (DS /
WS), contact area correction direction determination, loop count updating, and convergence determination are performed, repeated as necessary, and the number of times of convergence calculation is repeated to obtain 1 _BW and x _BW .

Further, in the case of (3), a new contact length is assumed,
Convergence judgment is performed through each process of new l _BW and new x _BW flatness calculation (SW), judgment of contact area correction direction, update of loop count, repeated as necessary, and repeated convergence calculation results, After assuming the new contact area, find l _BW and x _BW . Also in the case of (4), the assumption of new contact length, new l _BW and new x _BW flatness amount calculation (SW), judgment of contact area correction direction,
Convergence judgment is performed after each process of updating the loop count, repeated as necessary, and the result of repeating the convergence calculation
After assuming the new contact area, calculate l _BW and x _BW .

As described above, when the flatness amount other than the end points of the contact area is not calculated and the bisection method is used as the convergence calculation method, it is 1
The accuracy is doubled in one convergence calculation (the error range is ½), and by increasing the number of convergence calculations, the final error is reduced to ½ the number of iterations, and the accuracy becomes better and better. Become.

[0017]

As described above, assuming the contact area between rolls during rolling according to the present invention, only the flatness amount at the axial end point of the contact area is calculated, and only the positive or negative of this value is checked to determine the roll interval. With the extremely simple and highly accurate calculation method that corrects the contact area assumption, the contact area between rolls during rolling can be accurately grasped with high accuracy, and roll profile prediction and plate thickness prediction by mill stretch can be performed. It is possible to achieve high precision and high quality of products in hot rolling, which is an excellent effect.

[Brief description of drawings]

FIG. 1 is an explanatory view showing an influence on work roll bending caused by a rolling load,

FIG. 2 is an explanatory view showing a load distribution applied to a work roll and a backup roll and flatness between rolls,

FIG. 3 is a flowchart for explaining a method for obtaining a contact length between a work roll and a backup roll,

FIG. 4 is a process chart for a roll contact area calculation method according to the present invention,

FIG. 5 is a diagram showing a method for detecting a contact area between a work roll and a backup roll according to the present invention.

FIG. 6 is a diagram showing a processing flow according to the present invention.

[Explanation of symbols] 1 plate material 2 work roll 3 backup roll 4 contact load distribution between rolls 5 load distribution applied to work rolls 6 backup roll lower surface profile when there is no flatness between rolls 7 work roll upper surface profile when there is no flatness between rolls 8 Roll boundary profile when there is flatness between rolls 9 Flatness between rolls

Continuation of front page (51) Int.Cl. ⁶ Identification number Office reference number FI technical display location 8315-4E B21B 37/00 116 F

Claims (1)

[Claims] 1. A roll contact area during rolling is assumed, only flatness at axial end points of the contact area is calculated, the positive or negative of the flatness is determined, and the assumption of the contact area is sequentially corrected. A method for calculating the contact area between rolls of a rolling mill, which is characterized by converging to an appropriate contact length.