JP2011240353A - Method for predicting rolling load of foil rolling, method for predicting shape of the foil rolling, and method for determining pass schedule for the foil rolling - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a model for improving the accuracy of predicting rolling load for rolling under light pressure.SOLUTION: In a model for predicting rolling load using the Hitchcock squamous transformation and the Hill function, a correction term F(r) to be multiplied by rolling load P in the Hitchcock squamous transformation and a correction term G(r) to be added to the Hill function are introduced. The correction terms F(r) and G(r) are determined so that the value of a friction coefficient when a foil plate material is rolled is constant without depending on a reduction rate (r), and so that the value of an influence coefficient with respect to a change in the reduction rate (r) is equal to an actual value.

Description

  The present invention accurately predicts a rolling load during foil rolling when rolling a foil material using a cluster type multi-stage rolling mill (hereinafter referred to as a multi-stage mill) such as a 12-stage type or a 20-stage type. The present invention relates to a method for predicting the shape of foil rolling using the method, and a method for determining a pass schedule for foil rolling.

  Rolling of foil material is performed by winding and unwinding alternately with two winding reels, passing through an ultra-thin metal plate so as to go back and forth between rolling mills, and repeatedly reducing the thickness of this ultra-thin metal plate Is done by reducing For example, a multi-stage mill is used as such a foil material rolling device. A multi-stage mill is a rolling mill having a cluster roll for cold-rolling hard materials such as stainless steel. In a multi-stage mill, a small-diameter work roll is used for the purpose of giving a strong reduction to a hard material.

  Prediction of rolling load in conventional cold rolling, including such multi-stage mills, is based on rolling load formulas (Hill's formula) and roll flatness based on rolling parameters such as the thickness of the inlet and outlet sides of each rolling stand. The rolling load is calculated by combining the equations (Hitchcock's equation), and the correction factor obtained by the ratio between the calculated value and the actual value is multiplied by the calculated rolling load obtained as the set value for the next rolling. It was. Furthermore, by learning this correction coefficient for each coil or steel type, the influence of fluctuations in the friction coefficient over time and the estimation error of deformation resistance is reduced, and the prediction accuracy of the rolling load is also increased. Yes.

  By the way, in foil rolling, as the plate thickness decreases, the rolling load increases, but the reduction amount decreases. For this reason, it becomes difficult to reduce, and it is necessary to increase the number of passes in order to roll to the target plate thickness. In addition, since it is not known how much the rolling can be reduced unless the rolling is actually performed, there is a difficulty in designing a rolling pass schedule. Furthermore, there is a problem that the flatness under such light pressure is different from the actual machine and the simulation, and flatness control is very difficult in foil rolling that requires very high flatness.

Under such a light rolling condition of foil rolling, it is known as a field result that a phenomenon in which the accuracy of the predicted rolling load is extremely reduced is recognized when the rolling load is calculated by the conventional method described above. .
The cause of this phenomenon is considered to be that rolling is performed in a region where the conventional sheet rolling theory does not hold because the sheet thickness of the material to be rolled is extremely thin and the friction coefficient is large and the rolling load is high. Actually, it is said that the approximate accuracy of Hill's equation is reduced except when the rolling reduction is in the range of 10 to 60%. Also in the hitchcock equation, under the rolling conditions where the plate thickness is thin and the friction coefficient is large, the roll after deformation The assumption that the surface shape is arcuate is no longer valid. For this reason, it has been found that, especially under rolling conditions where the rolling reduction is about 5% or less, the approximation accuracy of Hill's equation decreases, and in particular, the accuracy decreases as the plate thickness decreases.

  In Patent Document 1, in view of the deterioration of the approximation accuracy described above, a correction coefficient is introduced into the roll flat type of the rolling load model in order to improve the rolling load prediction accuracy for the final pass of the tandem rolling mill using a dull roll. It is disclosed that the load accuracy is improved by doing so.

JP 2006-55881 A

  However, by adopting the method disclosed in Patent Document 1, it can be expected that the rolling load prediction accuracy can be improved, but it has become clear from the results that it is difficult to improve the accuracy to the extent that it can be applied to the actual site. In addition, even if the rolling load is calculated using the method disclosed in Patent Document 1, it has also become clear that it is insufficient for improving the prediction accuracy of the rolling shape and calculating the rolling pass schedule.

  The present invention has been made to solve the above-described problems, and its purpose is to improve the prediction accuracy of the rolling load in rolling under light reduction (particularly, a reduction rate of 10% or less), and The present invention provides a foil rolling rolling load prediction method, a foil rolling shape prediction method, and a foil rolling pass schedule determination method capable of predicting a plate shape with high accuracy and designing a pass schedule.

In order to achieve the above object, the present invention takes the following technical means.
That is, the rolling load prediction method of the foil rolling according to an aspect of the present invention is a rolling load model having correction terms F (r) and G (r) depending on the reduction ratio r when the foil sheet material is lightly reduced ( The rolling load is predicted using equations (1) to (5).

  According to this rolling load prediction method, the formula for calculating the work roll radius R is corrected by multiplying the rolling load p per unit width by the correction term F (r), and calculating the rolling force function Q. Thus, correction is made by directly adding and subtracting the correction term G (r). As a result, the estimated friction coefficient becomes constant and the influence coefficient agrees with the actual value and the calculated value, so that a rolling load prediction model preferable for foil rolling under light pressure can be proposed.

Preferably, the value of the coefficient of friction at the time of rolling the foil sheet material is constant without depending on the rolling reduction, and the correction term F ( r) and G (r) are determined, and the rolling load is predicted using the rolling load model having the determined correction terms F (r) and G (r).
Preferably, the correction terms F (r) and G (r) can be expressed by the following equations.

The foil rolling shape prediction method according to another aspect of the present invention is characterized in that the outlet side shape prediction of the foil sheet material is performed using a foil rolling rolling load prediction method.
According to this shape prediction method, it is possible to improve the shape prediction accuracy of the foil material on the outlet side after rolling in rolling under light reduction (particularly, a reduction rate of 10% or less).
A foil rolling pass schedule determination method according to still another aspect of the present invention is characterized in that the foil rolling material pass schedule is determined using a foil rolling rolling load prediction method.

  According to this pass schedule determination method, the rolling shape can be predicted with high accuracy in the design stage, the optimum pass schedule can be designed, and rational rolling can be performed to improve productivity.

  According to the present invention, in rolling under light reduction (especially a reduction rate of 10% or less), it is possible to improve the prediction accuracy of the rolling load, predict the plate shape with high accuracy, and design the pass schedule. It becomes possible.

It is a figure which shows schematic structure of the multistage mill to which the rolling load prediction method of foil rolling which concerns on embodiment of this invention is applied. It is a figure explaining the mechanism of foil rolling of the multistage mill of FIG. (A) is the figure which showed the relationship between a reduction ratio and an estimated friction coefficient, (b) is the figure which showed the relationship between a reduction ratio and an influence coefficient. It is the figure which put together the actual value which shows the relationship between tension change and rolling load, (a) is a reduction rate of 12%, (b) is a reduction rate of 6%, (c) is a reduction rate. When 4%, (d) is when the rolling reduction is 1.2%. It is a figure which shows the correction | amendment term in a rolling load model. (A) is the figure which showed the relationship between a reduction ratio and the estimated friction coefficient after correction | amendment, (b) is the figure which showed the relationship between a reduction ratio and the influence coefficient after correction | amendment. It is a flowchart which shows the prediction method of the outgoing side board shape of foil rolling. (A) is a figure which shows the prediction result of the exit side plate shape by a conventional model, (b) is a figure which shows the prediction result of the exit side plate shape by a new model.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
First, an outline of a 12-stage cluster type multi-stage rolling mill (multi-stage mill) to which the rolling load prediction method for foil rolling according to the embodiment of the present invention is applied will be described.
FIG. 1 is a schematic view of a multi-stage mill 1 for rolling a metal foil such as stainless steel (hereinafter, foil material). The multi-stage mill 1 has a pair of work rolls 4, 4, a plurality of intermediate rolls 5 and a backup roll 6, and is disposed between two winding reels 2, 3.

That is, these two winding reels 2 and 3 are alternately wound and unwound and the foil material 7 is passed through the multi-stage mill 1 so that the reduction of the ultrathin metal plate is repeated. The foil material 7 is rolled while reducing the thickness.
Between the multi-stage mill 1 and each of the winding reels 2, 3, a thickness gauge (not shown) that measures the thickness of the foil material 7 in order from the upstream side to the downstream side in the sheet passing direction of the foil material 7. Or a deflector roll 8 for making the pass line of the foil material 7 constant.
[Prediction of rolling load]
Here, it is considered that when the foil material 7 is lightly reduced using the multi-stage mill 1 described above, the rolling situation is simulated using a conventional rolling load prediction model.

  The rolling load prediction model used is as follows.

In FIG. 2, the enlarged view of the rolling part in the multistage mill 1 is shown. As shown in this figure, the foil material 7 sandwiched between the work rolls 4 and 4 is rolled from a thickness h ₁ to a thickness h ₀ in a rolling pass. l is the contact length of the work roll 4, R is the radius of the work roll 4 after flat deformation, Δh is the reduction amount (h ₁ −h ₀ ), φ ₁ is the contact angle, and the reduction rate r is Δh / h Represented by ₁ .
The results calculated using equations (8) to (12) are shown in FIG.

FIG. 3A shows the change of the friction coefficient μ with the transition of the rolling reduction ratio r. This friction coefficient μ is a calculated value and is also called an estimated friction coefficient. The graph shown in FIG. 3B shows the change in the influence coefficient (the rolling load differentiated by the tension) with the change in rolling reduction, where ◯ is the calculated value and ● is the actual value.
As shown in FIG. 3A, the friction coefficient μ becomes significantly larger as the rolling reduction ratio r becomes smaller, particularly in the light rolling area (r <0.1). It has been found that the friction coefficient μ is originally a constant value (about 0.1 in FIG. 3A) regardless of the rolling reduction r. That is, it is assumed that the friction coefficient μ is excessive in the region where the rolling reduction r is small.

On the other hand, the impact coefficient was compared between the actual value and the calculated value.
As a result, as shown in FIG. 3 (b), the actually matched actual value and the calculated value do not match in the light reduction region where the reduction rate r <0.1.
In addition, the actual value in FIG.3 (b) collects the actual data of many foil rolling like FIG.4 (a)-FIG.4 (d), and calculated | required the inclination of each graph as an influence coefficient.

The actual rolling rolling data shown in Fig. 4 is for rolling reduction r = 12% (normal rolling) to rolling reduction r = 1% (light reduction). The thickness of the inlet and outlet plates is AGC (Auto Gap Control). Thickness control was performed by moving the inlet and outlet tensions independently, and the load change with respect to the tension change was obtained by changing the rolling reduction ratio r.
FIG. 4A shows a change in load with respect to a change in tension when the rolling reduction ratio r = 12%. FIG. 4B shows a change in load with respect to a change in tension when the rolling reduction ratio r = 6%. FIG. 4C shows the load change with respect to the tension change when the rolling reduction ratio r = 2%. FIG. 4D shows a load change with respect to a tension change when the rolling reduction ratio r = 1%. In addition, the tension shown in FIGS. 4A to 4D indicates a deviation of the sum of the entry side and exit side tensions. As shown in these figures, regardless of the rolling reduction ratio r, the distribution of the inlet side / outer side tension with respect to the load is substantially equal.

In order to avoid the situation where “the friction coefficient and the influence coefficient do not coincide with the actual values” as described above, the inventors of the present application have reached the following idea.
First, in the Hitchcock equation shown in equations (10) and (11), the contact length l is an arc deformation assuming that the rolling load distribution applied from the work roll 4 to the foil material 7 is a parabolic shape. It is assumed that However, an FEM analysis of the state of rolling deformation at the time of light reduction revealed that roll deformation that cannot be expressed by arc deformation has occurred at the time of light reduction.

For this reason, in order to make the friction coefficient μ constant regardless of the rolling reduction r and to make the influence coefficient coincide with the actual value and the calculated value, it is considered that a correction term that affects the rolling load p is effective. It came. More specifically, focusing on (C · P / Δh) in equation (11), it was found that the term multiplied by the rolling load P is preferably the correction term F (r).
Next, the influence coefficient is a value obtained by partially differentiating the rolling load with the tension, and as apparent when the equation (8) is partially differentiated with the tension σ, the rolling force function Q and the contact length l of the work roll 4 are Is a function of In view of this, in order to make the influence coefficient coincide with the actual value and the calculated value, it is necessary to correct the contact length l and the rolling force function Q.

However, since the contact length l is a function of the radius R of the work roll 4 after the flat deformation from the equation (10), the correction of the contact length l corrects the radius R of the work roll 4, that is, the equation (11). Has already been realized.
Therefore, the reduction force function Q is corrected. The correction term G (r) of the rolling force function Q is directly added to the equation (12).

  The rolling load prediction formula according to the present invention in which the above correction term is incorporated is as shown in Formula (1) to Formula (5).

Specific expressions of the correction terms F (r) and G (r) are obtained as follows.
First, in FIG. 3A, even if the rolling reduction r becomes variable, the friction coefficient μ takes a substantially constant value (for example, μ = 0.1), and in FIG. Even if r changes, the numerical values of the correction terms F (r) and G (r) are determined so that the calculated value of the influence coefficient matches the actual value.

  Specifically, the situation at the time of rolling with a reduction ratio r = 12% was simulated using the equations (1) to (5), and “the friction coefficient μ is substantially constant” and “the influence coefficient of The numerical values of F (r) and G (r) such that the calculated value and the actual value match are obtained. Similarly, rolling with a reduction ratio r = 6%, a reduction ratio r = 2%, and a reduction ratio r = 1% is simulated, and F (r) and G (r) at each reduction ratio r are obtained. A convergence calculation method may be used for these calculations.

The ● graph in FIG. 5 is a plot of the obtained values of F (r), and F (r) is determined as shown in Equation (6) by a regression equation based on these points.
The circled graph in FIG. 5 is a plot of the obtained G (r) value, and G (r) is determined as shown in Equation (7) by a regression equation based on these points.

FIG. 6 shows the result of simulating foil rolling using Expressions (1) to (7) (sometimes referred to as a new model).
As shown in the “corrected graph” in FIG. 6A, the friction coefficient μ is substantially constant regardless of the rolling reduction r. As for the influence coefficient, as shown in FIG. 6B, even if the rolling reduction r changes, the calculated value by the new model and the actual value are substantially the same.

As a result, the new model can reliably reproduce the rolling situation even under light pressure of the foil material, and can accurately predict the rolling load and the like.
[Prediction of exit plate shape]
Next, a method for predicting the shape of the exit side plate of the foil rolling using the new model to which the above-described equations (1) to (7) are applied will be described.

FIG. 7 is a flowchart showing the foil rolling shape prediction method. The predicted shape is the shape of the exit side plate of the rolled material.
First, in step S10, the load distribution p (x) of the rolled material immediately below the work roll 4, the roll gap S (x), and the tension distribution σ (x) in the sheet width direction are assumed.
In step S20, the contact surface pressure q (x) between the rolls is calculated from the balance of forces between the work rolls 4 and the backup rolls 6 and the roll surface matching conditions.

In step S30, the amount of deflection of each roll (work roll 4 or backup roll 6) from the load distribution p (x) of the rolled material and the contact surface pressure q (x) between the rolls, that is, p (x) · q (x). Is calculated.
In step S40, the surface displacement of the work roll 4 is calculated from the calculated deflection amount.
In step S50, a plate thickness distribution and a tension distribution σ (x) are calculated based on the obtained surface displacement of the work roll 4.

In step S60, the rolling load distribution p (x) is calculated using the new model (formulas (1) to (7)) based on the reduction amount Δh obtained from the plate thickness distribution, the tension distribution σ (x), and the like. Ask for.
Steps S20 to S50 as described above are repeatedly calculated until, for example, the calculated value converges.
In step S50, the rolling reduction ratio ε (x) in the sheet width direction is calculated from the inlet and outlet side plate thicknesses, and this rolling reduction ratio ε (x), that is, the elongation ratio ε (x) is defined as the outlet plate shape. Further, after calculating the deviation Δε (x) of the rolling reduction ε (x), the tension distribution σ (x) is calculated by σ (x) = σ (x) + Ε · (1-ξ) · Δε (x) To do. Here, ξ is a shape change coefficient.

The result calculated in this way will be described with reference to FIG.
FIG. 8A shows a shape prediction result using a conventional model (formula (8) to formula (12)), and FIG. 8B shows a new model (formula (1) to formula (7)). It is the shape prediction result used. In each figure, the rolling is performed at a rolling reduction r = 1%, and the vertical axis represents the flatness after rolling.
It can be seen that when the new model is used, the friction coefficient is almost constant regardless of the rolling reduction r, and the prediction accuracy of the plate shape is improved even in the light rolling region.
[Determination of rolling pass schedule]
In rolling the foil material 7 with a small rolling reduction r, it is very preferable to calculate the pass schedule using the above-described rolling load prediction method, that is, a new model. Hereinafter, a method for determining the path schedule will be described.

As a pass schedule of the rolled material, a rolling schedule is considered in which each rolling mill performs rolling under conditions (evaluation function) that increase the reduction ratio as much as possible under the constraint conditions that do not exceed the maximum rolling load. This pass schedule is obtained by the following procedure, for example.
(Procedure 1) In each of a plurality of rolling mills, a maximum rolling load (load resistance of the rolling mill) P _MAX is determined.

(Procedure 2) Determine the original plate thickness h _in and the product plate thickness h _{out in} the rolling mill.
(Procedure 3) The friction coefficient μ estimated from the radius R of the work roll 4 of the rolling mill and the past actual value is determined, and the reduction ratio r ⁽ⁱ⁾ of the ^i- th pass is assumed.
(Procedure 4) The outlet side plate thickness h _out ⁽ⁱ⁾ is obtained from the inlet side plate thickness h _in ⁽ⁱ⁾ of the i-th pass based on the rolling reduction ratio r ⁽ⁱ⁾ . When i = 1, it is assumed that h _in ⁽¹⁾ = h _in .

(Procedure 5) The deformation resistance K of the rolled material is obtained from h _in ⁽ⁱ⁾ and r ⁽ⁱ⁾ .
(Procedure 6) From the deformation resistance K and the input side plate thickness h _in ⁽ⁱ⁾ of the i-th pass, the input side tension σ _in and the output side tension σ _out are determined.
(Procedure 7) Friction coefficient μ, inlet side tension σ _in , outlet side tension σ _out , deformation resistance K, inlet side plate thickness h _in ⁽ⁱ⁾ , outlet side plate thickness h _out ⁽ⁱ ) Substituting into the expression (7)), the predicted rolling load P _cal for the i-th pass is obtained.

(Procedure 8) If P _cal ⁽ⁱ⁾ > P _MAX , the set rolling reduction ratio r ⁽ⁱ⁾ = r ⁽ⁱ⁾ + δr is returned to Procedure 4.
(Procedure 9) If P _cal ⁽ⁱ⁾ <P _MAX , return to Procedure 4 with the set rolling reduction ratio r ⁽ⁱ⁾ = r ⁽ⁱ⁾ · α. However, it is a predetermined value with α <1.0.
(Procedure 10) If the previous load calculation P _cal ^(i-1) > P _MAX and P _cal ⁽ⁱ⁾ <P _MAX , the reduction ratio r ⁽ⁱ⁾ of the i-th pass is set, and h _in ^{(i + 1 )} = H _out ⁽ⁱ⁾ and i = i + 1.

(Procedure 11) If h _out ⁽ⁱ⁾ > h _out , return to step 4.
(Procedure 12) If h _out ⁽ⁱ⁾ <h _out , the i path is the final path. In this case, the reduction ratio r ⁽ⁱ⁾ is (h _in ⁽ⁱ⁾ −h _out ) / h _in ⁽ⁱ⁾ .
If it does as mentioned above, the pass schedule of rolling of foil material 7 with a small rolling reduction r can be determined exactly.

  The embodiment disclosed this time should be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

1 Multistage Mill 2 Winding Reel 3 Winding Reel 4 Work Roll 5 Intermediate Roll 6 Backup Roll 7 Foil Material 8 Deflector Roll

Claims (5)

When the foil sheet material is lightly reduced, the rolling load is predicted using a rolling load model (equations (1) to (5)) having correction terms F (r) and G (r) depending on the reduction ratio r. A method for predicting a rolling load of foil rolling.
The correction term F (r), so that the value of the coefficient of friction when rolling the foil sheet material is constant without depending on the rolling reduction and the value of the influence coefficient with respect to the change in rolling reduction matches the actual value. G (r) is determined,
The rolling load prediction method for foil rolling according to claim 1, wherein the rolling load is predicted using the rolling load model having the determined correction terms F (r) and G (r). The rolling load prediction method for foil rolling according to claim 2, wherein the correction terms F (r) and G (r) can be expressed by the following equations.
  A method for predicting the shape of a rolled foil, wherein the shape of the exit side of the foil sheet material is predicted using the method for predicting the rolling load of the foil rolling according to any one of claims 1 to 3.   A foil rolling pass schedule determination method, wherein the foil rolling material pass schedule is determined using the foil rolling rolling load prediction method according to claim 1.