JPH062289B2 - Sheet rolling crown prediction method - Google Patents

Description

Detailed Description of the Invention [Industrial applications]

The present invention relates to a method of predicting a crown in strip rolling.

[Prior art]

Generally, in plate rolling, it is necessary to accurately control the plate crown in order to improve product quality and yield. Recently, rolling mills with extremely high crown controllability have appeared, such as HC mills. By the way, in order to set up the reduction distribution, bender force, intermediate roll shift amount, etc. from the target plate crown, it is necessary to accurately predict the plate crown. Conventional prediction of plate crown is based on the division model proposed by Shohet, Shiozaki, etc. (eg, the 26th (1975) Plastic Working Union Lecture Lecture Proceedings, pp. 49-52). Kono "Refer to the roll-deflection method for left-right asymmetric rolling". However, in this split model, the rolling pressure is
Since the elementary theory such as the Sims equation is used, the rolling pressure is a function of the rolling reduction only. For this reason, it is not possible to consider a rapid rolling pressure change due to the widthwise metal flow in the vicinity of the plate edge and a change in roll eccentricity due to this. For the same reason, the influence of the entrance side plate crown on the exit side plate crown can hardly be considered. Therefore, in the conventional plate crown prediction formula based on the split model,
The amount of strip crown due to the final rolling pass was overestimated, and the influence of the entry side strip crown on the exit side strip crown was a function of strip width (for example, pp. 9-12 of the Proc. Shiozaki et al., "Computer control of optimum roll bending force (first edition) mathematical model and configuration"). That is, the conventional crown prediction formula is expressed, for example, in the form of the following formula, and the entrance side plate crown influence rate K _i (W) representing the influence of the entrance side plate crown on the exit side plate crown is a function of the plate width W. I'm running. CRP _i = CRC _i + K _i (W) · CRP _i−1 ...
(1) K _i (W) = b ₁ + b ₂ ln (b ₃ / W ² ) ... (2) where CRP _i is the predicted plate crown of the i-th pass, CRC
_i is a calculated plate crown of the _i- th pass calculated by the conventional division model, CRP _i-1 is a plate crown on the output side of the i-th-1 path, that is, the i-th pass input side (predicted value or measured value, but i
= 1 (first pass for finishing), CRP _i-1 = 0), b ₁ is a constant, b ₂ is a negative constant, and b ₃ is a positive constant. The equation (1) substantially corresponds to the equation (1) described on page 10 of the Shiozaki et al. That is, the equation (1) of Shiozaki et al. Considers the influence of the entrance side plate crown H _{c on} the terms of the regression coefficients A ₉ and A ₁₀ , but at that time,
As the variable that affects the effect of H _c , the plate width B is simply included in the term of A ₁₀ . In addition, (1) of Shiozaki et al.
The formula shows the roll bending force to be exact,
In the model calculation, the roll bending force and the crown due to the deformation of the rolling mill have a replica relationship and can be regarded as equivalent. As is clear from the above equation (2), the entrance side plate crown influence rate K _i (W) is a function of the plate width W, and when the plate width W is narrow, the entrance side plate crown influence rate K _i (W). Is small, and conversely when the width W is wide, the entrance side plate crown influence rate K
_i (W) becomes large.

[Problems to be Solved by the Invention]

By the way, in the rolling for repeating the rolling for several passes to finish the product sheet thickness, the entrance side plate crown of a certain pass is the exit side plate crown of the preceding pass. Hot tandem rolling (F _{1 to} F ₇
In the case of 7-stand tandem rolling), there is a crown meter only on the exit side of the seventh stand F _7, and there is no crown measuring means between the stands. Further, what is important as a product is the F ₇ exit crown, and it is important to predict what will be the final F ₇ exit crown as a result of rolling in each pass. It is well known that there is a gap between the crown expected in the split model and the crown actually measured, and the cause is the crown made in the upstream pass due to the problem of metal flow in the width direction. It was presumed that it could not be corrected. At this time, it is considered that the influence of each pass entrance crown on the exit side, that is, the easiness of the metal flow in the width direction is caused by the plate width, and the prediction formula as shown in the formula (1) is prepared. It was By the way, the crown CRC _i expected from the split model
Is known to be approximately proportional to the rolling load. Furthermore, K of the conventional prediction model expressed by the equation (1)
_{Since i} (W) is a fairly small value, if this model is correct, it is expected that its crown will be substantially similar to the rolling load fluctuation of F ₇ . However, it cannot be said that the rolling heat crown grows up to about 5 rollings, but it is estimated that the F ₇ load and the crown are similar to each other after the 5th rolling. And rolling load of the seventh stand F ₇ in the 9 as shown in FIG, Hotsutotandemu rolled using a finishing mill consisting of HC mill 7 stands F ₁ to F _7, the seventh stand F ₇
FIG. 10 shows an example of the relationship between the plate crown on the delivery side, that is, the finished plate crown, and FIG. 11 shows an example of the relationship between the rolling load of the fifth stand F ₅ and the finished plate crown. K _i (W) of the conventional prediction model represented by the equation (1) is
Since this value is quite small, if the model is correct, after the fifth rolling, in which the influence of the heat crown growth of the roll is eliminated, the finished plate crown may be similar to the rolling load fluctuation of the final 7th stand F _7. is expected. However, in reality, as is clear from FIG. 10, after the tenth rolling, the rolling load of the seventh stand F ₇ and the finished plate crown are not similar to each other, and when compared with the rolling loads of other stands. As is clear from FIG. 11, the rolling load of the fifth stand F ₅ and the finished plate crown show a relatively similar behavior, and it is clear that the influence of the fifth stand F ₅ is very strong. It was By the way, if the conventional prediction model expressed by the equation (1) is also correct from the viewpoint of tendency, the influence of the crown formed in the upstream path such as the fifth stand F ₅ largely affects the material. It is when the plate width is expanded that it is difficult for the crown to change due to the metal flow in the width direction. FIG. 12 shows the relationship between the plate width and the finished plate crown in this cycle. As is clear from FIG. 12, after the 10th rolling in which the influence of the heat crown growth is eliminated and the influence of the previous pass (fifth stand F ₅ ) is strong, contrary to the prediction from the model, the strip width is It is becoming narrower, which is inconsistent with the tendency of the entrance side plate crown influence rate K _i (W) in the above-mentioned formula (2). Thus, a phenomenon that is qualitatively contradictory to what is predicted with the conventional model has been actually observed,
It is clear that the conventional plate crown prediction formula cannot accurately predict the plate crown.

[Object of the Invention]

The present invention has been made to solve the above conventional problems, and an object of the present invention is to provide a method of predicting a sheet rolling crown that can accurately predict a sheet crown.

[Means for confronting problems]

The present invention relates to a method for predicting the crown of strip rolling, as shown in the outline of FIG. 1, a procedure for obtaining a single stand output side plate crown prediction calculation value CRC _i based on a split model and an input side plate crown CRP _i-1. To obtain the plate crown transfer rate α _i (h), which represents the rate of change of the output side plate crown with respect to the change of the roll crown, as a function of the input side plate thickness h, and the output side plate crown with respect to the change of the input side plate crown. Incoming side plate crown influence rate β
_i (h) is also obtained as a function of the entrance side plate thickness h, and the following equation CRP _i = α _i (h) CRC _i + β _i (h) CRP _i-1 ...
According to (3), the above object is achieved by including the procedure for obtaining the i-th pass exit plate crown predicted value CRP _i .

[Action]

It is generally considered that the plate crown in plate rolling is a transfer of elastic deformation due to rolling load on the rolling roll. From this point, it is considered qualitatively that the rolling load and the plate crown have a substantially proportional relationship when a positive crown control operation such as an intermediate roll shift is not performed. On the other hand, considering the principle of constant volume during plastic deformation of the material, if the material is rolled and, as a result, only extends in the longitudinal direction, the plate crown on the rolling out side is the plate thickness of the rolling in side plate crown in and out. It is a value that is multiplied by the ratio (also called constant entry / exit crown pulling rate). On the contrary, when the plate crown changes from the above expected value, the material causes widthwise metal flow (width expansion, width contraction) by the amount of change (correctly, shape change of material (ear extension, belly). Elongation), but there is also some, but it is generally small compared to the value due to the amount of crown change that is the subject here, so it is ignored). Therefore, in the region where the metal flow in the width direction of the material is easily generated (the plate width is narrow and the plate thickness is thick), the rolling load and the plate crown have a substantially proportional relationship. However, in the region where the metal flow in the width direction is unlikely to occur (the plate width is wide and the plate pressure is thin), there is almost no change from the expected value at a constant crown ratio regardless of the rolling load. In this case, when viewed microscopically, the metal flow in the width direction is unlikely to occur, so the apparent deformation resistance of the material has a distribution in the width direction, which causes the flat deformation of the rolling roll to change in the width direction. The plate crown is close to the expected value when the crown ratio is constant (see FIGS. 2 and 3). However, such a micro analysis can be understood by using the rigid-plastic finite element method, and only the conventional split motel could predict only the crown proportional to the rolling load. The present invention has been made on the basis of the results of the analysis made by the inventors using a rigid-plastic finite element method that allows for consideration of metal flow during rolling. That is, as a result of the analysis, it was found that the crown shape was remarkably different depending on the plate thickness due to the difference in the metal flow in the width direction, and the plate crown measured by the crown control point was different. Furthermore,
From the same difference in metal flow in the width direction, it was found that the influence rate of the entrance side plate crown on the exit side plate crown also changes depending on the plate thickness. From the above, the plate crown transfer rate α which is a function of the plate thickness
By introducing _i (h) and the entrance side plate crown influence rate β _i (h), it is possible to improve the crown prediction accuracy. Here, the plate crown transfer rate is a rate at which hard-side factors such as a roll crown, an intermediate roll shift amount, and a roll bender are transferred to the exit side plate crown. Hereinafter, the present invention will be described in detail with reference to the drawings. In Fig. 2, plastic analysis of rolled material is carried out by the rigid-plastic finite element method (for example, Shibuya et al., "Rigid-plastic finite element method" on pages 147 to 150 of Proceedings of the 33rd (1982) Plastic Working Union Conference). Edge drop phenomenon analysis "),
It was obtained by calculating the roll surface flat deformation based on the resulting rolling load distribution, calculating the rolling load distribution again with this roll surface flat deformation as the input condition, and repeating until the roll surface flat deformation converged. The distribution of rolling pressure is shown. This FIG. 2 shows the result in one pass for each thickness with respect to the finished plate thickness t. The roll diameter in the experiment was 640 mm, the rolling reduction was 30%, and the friction coefficient was 0.3. . As it is clear from FIG. 2, (thickness 4t in FIG. 2, in the case of 2t) accordance connexion plate thickness t is thinner, after rolling pressure Q _p at the plate end portion is once, was higher summer, sharply lower It is connected. This is because the widthwise metal flow at the plate end differs depending on the plate thickness t. That is, as the plate thickness of the rolled material becomes thinner, widthwise metal flow is less likely to occur, and the plate crown of the rolled material is less likely to change from the constant crown ratio condition than the constant volume condition. Microscopically, if you pay attention to a certain point in the width direction, it cannot flow in the width direction, and since it can extend only in the same direction as the circumference in the longitudinal direction, it is strongly confined in both the longitudinal and width directions. Then, the rolling pressure increases, and the roll is pushed up until the volume becomes constant. As a result, as shown in FIG. 2, the rolling pressure temporarily rises at the plate end. However, as the width direction metal flow is generated further closer to the plate end, the constraint on the deformation of the material is rapidly relaxed, and as a result, the rolling pressure at the plate end is sharply reduced. When the strip thickness changes, the distance from the strip end in the region where the widthwise metal flow occurs changes. Therefore, as shown in FIG. 2, the rolling pressure distribution changes depending on the strip thickness. FIG. 3 shows the plate thickness deviation (plate crown) in the case of FIG. 2 calculated with the entrance side plate crown being zero. From the difference in rolling pressure distribution, it can be seen that the shape of the plate crown varies depending on the plate thickness t. In Fig. 3, the region where the plate thickness does not change is the region that can be calculated assuming that the crown ratio is constant (there is no metal flow in the width direction). Can be seen as a region where changes occur. In the conventional split model, since the sheet crown is obtained by using the primary logic for the rolling pressure generated between the rolling material and the roll, the rolling load is determined in the region where the crown ratio is constant and the widthwise metal flow generation region is due to these constant volume constraints. Can not be taken into account and the rolling pressure distribution becomes relatively uniform in the width direction, and the plate crown has a shape similar to that in the case where the plate pressure is thick in FIG. As is more apparent from FIG. 3, since the plate crown shape is different depending on the plate thickness t, when the plate crown is managed at the place entering from the plate end, the plate crown amount changes depending on the plate thickness t. That is, when the deformation of the rolling mill is considered, it can be easily estimated that the total amount is proportional to the rolling load as long as it is an elastic body. However, when a micro load distribution in the width direction is calculated and analyzed, the deformation amount distribution (crown shape) in the width direction is considerably different depending on the plate thickness due to the difference in the load distribution. Therefore, as shown in FIG. 4, the crown amount ED at the plate edge (= the total amount of deformation of the rolling mill is considered to be transferred) is proportional to the rolling load. This FIG. 4 (plate edge) and FIG. 5 (50 mm inside from the plate edge) are for the finished plate thickness t
It shows the relationship between rolling load and strip crown in one pass at each thickness. On the other hand, as shown in FIG. 5, the crown amount (ED50) at a point which is inserted to some extent from the plate edge is not simply proportional to the rolling load. This is because the distance from the plate edge in the region where the widthwise metal flow occurs changes depending on the plate thickness. Therefore,
It becomes proportional to the rolling load with the plate thickness as a parameter. In FIG. 5, as the plate thickness becomes thinner, the measuring plate crown also becomes smaller. By the way, the crown control in actual rolling is performed, but in the case of a strip, it is difficult to measure the plate edge, and therefore it is managed at a point (generally about 25 mm) from the plate edge. Therefore, it is estimated that the crown measured as the control point has the characteristics as shown in FIG. The characteristics as shown in FIG. 5 are caused by the change in the crown distribution due to the difference in the metal flow in the width direction of the material depending on the plate thickness. However, in the conventional strip crown analysis using the split model, the solution based on the two-dimensional elementary theory is used to calculate the rolling pressure, so that the crown is simply proportional to the rolling load as shown in Fig. 4. It exhibits the characteristics as described above. As described above, in order to correct the difference between the estimated crown obtained by the split motel and the crown at the management point due to the difference in the width direction metal flow generation region, in the present invention, the plate crown is set at a point entering from the plate end to the inside. In the case of control, the plate crown transfer rate α _i (h), which represents the rate of change of the exit side plate crown with respect to the change, is used. The plate crown transfer rate α _i (h) represents how much the plate crown calculated by the division model is actually transferred when the three-dimensional deformation of the material including the plate end is taken into consideration. Specifically, the plate crown transfer rate α _i (h), which is a function of the entrance side plate thickness h, is used to express the predicted plate crown CRP _i of the i-th pass by the following equation. CRP _i = α _i (h) · CRC _i (4) Here, CRC _i is a conventional calculation plate crown based on a division model. Similarly, as the plate thickness becomes thinner, widthwise metal flow becomes less likely to occur, and it becomes difficult to change the crown from the constant crown ratio condition, but what shows the ratio to follow this constant crown ratio condition is: If defined as the entrance side plate crown influence rate β _i (h) that represents the rate of change of the exit side plate crown with respect to the entrance side plate crown change, this can also be expressed as a function of the entrance side plate thickness h, and as a result, the exit side plate crown prediction of the i-th pass. The value CRP _i can be expressed by the equation (3). FIG. 6 shows a plate crown transfer rate α _i (h) and an entrance side plate crown influence rate β when the roll diameter is 640 mm and the plate width is 1000 mm, calculated by the same method as in FIG. 2 using the rigid-plastic finite element method. An example of calculation of _i (h) is shown. Where α _i (h)
Is a calculation of the ratio of the change amount of the output side plate crown to the change amount of the roll crown by using two types of roll crowns when the entrance side plate crown is zero.
Further, β _i (h) is a value obtained by calculating the ratio of the change amount of the outgoing side plate crown to the change amount of the incoming side plate crown by using two types of incoming side plate crowns, with the roll crown being zero. In FIG. 6, Ch is a delivery side plate crown, Ch '
Is the output side plate crown when rolled with a roll having a reference plate crown (in the case of FIG. 6, the output side plate crown when using a roll with zero crown), CH is the input side plate crown,
CH 'is a reference plate crown (in the case of FIG. 6, CH' =
0) and Cr are roll crowns (= D) shown in FIG.
c-De) and Cr 'are reference roll crowns (Cr' = 0 in the case of FIG. 6).

【Example】

Embodiments of the present invention will be described in detail below with reference to the drawings. In the present embodiment, the plate crown transfer rate α _i (h)
And, the entrance side plate crown influence rate β _i (h) is assumed to be a quadratic expression from FIG. 6 described above, and this is simplified and set as the following expression. α _i (h) = − a ₁ (h _i −a ₂ ) ² + a ₃ ...
_{(5) β i (h)} = a 4 (h i -a 5) 2 + a 6 ··· (6) _where, a 1 ~a ₆ are constants. Then, using the supra (3) according to the present invention, the prediction plate modified to fit the coefficients actual operation in the crown CRP _i, first predicts the plate crown CRP ₁ out of the first stand F _1,
By sequentially predicting the outgoing side plate crown CRP _i of the stand on the downstream side based on the predicted value, the final seventh
When the plate crown CRP ₇ on the exit side of the stand F ₇ was predicted, the prediction results shown in FIG. 8 were obtained. The difference between this predicted value and the actual measured value shown in FIG.
The accuracy was improved up to σ = 11 μm. On the other hand, when the same operation is performed using the above-mentioned equation (1) which is the conventional method, the difference between the predicted value and the actually measured value is the standard deviation 1σ = 14.
Only accuracy of about μm could be obtained. Note in the above described embodiment, the first first predicts the plate crown CRP ₁ out of the stand F _1, convex how to continue to predict the plate crown CRP _i out sequentially downstream of the stand on the basis of the predicted value However, the application method of the present invention is not limited to this. For example, it is also possible to measure the entrance side plate crown CRP _i-1 as the rolling progresses and use the measured value for the calculation of the above equation (3). . In this case, higher prediction accuracy can be obtained.

【The invention's effect】

As described above, according to the present invention, it is possible to accurately predict the plate crown. Therefore, there is an excellent effect that the crown control can be performed with higher accuracy than the conventional one.

[Brief description of drawings]

FIG. 1 is a flow chart showing the gist of the method for predicting the crown of sheet rolling according to the present invention, and FIG. 2 is a diagram showing an example of rolling load distribution for each sheet thickness for explaining the principle of the present invention. Similarly, FIG. 3 is a diagram showing an example of the plate crown shape for each plate thickness, FIG. 4 is a diagram showing an example of the relationship between the plate crown and rolling load at the plate end, and FIG. Similarly, a diagram showing an example of the relationship between the plate crown and the rolling load within 50 mm from the plate edge, and FIG. 6 similarly show the plate thickness and the plate crown transfer rate α _i (h) and the entrance side plate crown influence rate β _i ( h) is a diagram showing an example of the relationship, FIG. 7 is a diagram for explaining the roll crown, and FIG. 8 is a relationship between the predicted plate crown and the actually measured plate crown in the embodiment in which the present invention is adopted. 9 is a schematic front view showing the structure of a 7-stand finishing mill, FIG. The figure is a diagram showing an example of the relationship between the actually measured plate crown and the seventh stand rolling load, FIG. 11 is a diagram showing the example of the relationship between the actually measured plate crown and the fifth stand rolling load, and FIG. It is a diagram showing an example of the relationship between the plate crown and the plate width.

Claims (1)

[Claims] 1. A procedure for obtaining a single stand outgoing side plate crown prediction calculation value CRC _i based on a division model, a step for obtaining an incoming side plate crown CRP _i-1, and a rate of change of the outgoing side plate crown with respect to a change in roll crown. The procedure for obtaining the plate crown transfer rate α _i (h) represented as a function of the entrance side plate thickness h and the entrance side plate crown influence rate β _i (h) representing the rate of change of the exit side plate crown with respect to the change of the entrance side plate crown are also the same. A procedure for obtaining as a function of the entrance side plate thickness h, and a procedure for obtaining the exit side plate crown predicted value CRP _i of the i-th path by the following equation: CRP _i = α _i (h) CRC _i + β _i (h) CRP _i-1 A method for predicting a crown for strip rolling, comprising: