JPS5973108A - Method for setting rolling schedule of rolling mill - Google Patents

Abstract

PURPOSE:To obtain a setting method applicable for an operation where a formation of rolling units is changed in a wide range, by determining the sheet thickness at the outlet side of each pass basing on a calculating equation for obtaining a deviation of sheet thickness at the outlet side, constituted of a deviation of sheet thickness in the width direction at the time when a distribution of rolling load in the width direction is uniform and said deviation at the inlet side of a mill, in case of obtaining a prescribed sheet thickness by plural number of times of rollings. CONSTITUTION:A model equation of mechanical sheet crown (a sheet thickness distribution in the width direction, expressed by a sign C, which is realized when a load distribution in the width direction is uniform) of a four high mill equipped with a bending device and an euqation of rolling load are combined. Thus the crown C for an optional rolling schedule is calculated. A sheet crown Ch at the outlet side of the mill is estimated by a prescribed equation formed by using the crown C, a crown CH at the inlet side, a draft, a correction factor of sheet crown, and a modified-crown-genetic factor. Further, a sheet shape is estimated by a prescribed equation where an elongation-strain difference is obtained from a shape changing factor, the crowns Ch, CH, and the sheet thicknesses at the inlet and outlet sides. Inversely, the crowns C, Ch and the sheet shape are controlled by changing the rolling schedule.

Description

[Detailed Description of the Invention] The present invention relates to a setting method for determining the exit side plate thickness of each pass, that is, the pressure F schedule, in rolling a metal plate to increase the predetermined plate thickness by rolling multiple times. It is.

Multiple rolling literally means that the rolled material is rolled multiple times, and when rolling is performed multiple times using a reverse type rolling mill, rolling is performed continuously using multiple rolling mills until t7. It includes cases where the above is the case, and cases where these are combined.

The conventional method for determining a rolling schedule is generally to distribute the power and load required for rolling according to the capacity of each rolling mill, and does not take into account the crown or shape of the rolled plate.

Regarding this, in recent years, a technology has been developed that involves changing the reduction schedule between the first half and the second half of a rolling unit in order to minimize fluctuations in the plate crown during rolling performed using a set of work rolls, especially in hot rolling. has also been put into practical use, but even in this case, a change pattern in the rolling reduction schedule is only given in advance in order to deal with the plate crown change expected in advance at a specific rolling position 41, and this does not affect the plate crown shape. Since the optimal rolling schedule is not calculated by taking into account the factors involved in calculating the settings for each rolled material, it is difficult to apply it to operations where the organization of rolling units changes significantly, which has been the trend in recent years. It has the disadvantage of being difficult.

The present invention was made with the aim of solving the following problems with the conventional method, and its first gist is:
In the rolling process of obtaining a rolled plate of a predetermined thickness from a rolled original plate by rolling multiple times, the thickness deviation in the width direction is realized when the load distribution in the width direction between the rolled plate and the work roll is uniform; Determining the outlet side plate thickness of each pass through a formula for calculating the widthwise plate thickness deviation of the rolled plate on the rolling machine outlet side, which is configured as a linear combination of the widthwise plate thickness deviations of the rolled plate on the rolling machine input side,
The second gist is that in step 1 of rolling to obtain a rolled plate of a predetermined thickness by rolling multiple times from an original rolled plate, the widthwise load between the rolled plate and the working rolls is uniform. In such a case, the thickness distribution calculated using a model equation without showing the relationship between the thickness distribution in the width direction realized in the case of rolling conditions and the rolling conditions is the closest to the thickness distribution of the rolled original plate in terms of thickness. To,
The third point is to determine the exit plate thickness for each pass.
Relationship between the widthwise load distribution and rolling conditions achieved when the widthwise load distribution between the rolled plate and the work rolls is uniform in the rolling process of obtaining a rolled plate of a predetermined thickness from an original plate by rolling multiple times At each pass, the exit side plate is adjusted so that the plate thickness distribution calculated using the model formula showing Determine the thickness.

The applicant filed the "Rolling Control Method" on October 20, 1981.
I filed a patent application for the name. The invention of this patent application is related to rolling shape control, and in this invention, the width direction plate thickness distribution that is realized when the width direction load distribution between the rolled plate and the work roll is uniform is expressed. The plate crown was defined as a mechanical plate crown, and it was proved that the rolling mill outlet plate crown CI+ is basically expressed by the mechanical plate crown and the inlet plate crown C+ as shown in the following equation.

ch=ζ・c+'i (1-r) CH--(1) where r is the reduction rate, ζ is the plate crown correction coefficient, M is the modified crown hereditary coefficient, and the relationship between 1 and 1 is as follows: holds true.

ζ = 1 - In case - - - - - (2) Furthermore, if the mechanical plate crown is given the rolling load, contact arc length, and plate width, it is independent of the deformation characteristics of other rolled materials. In addition, we clarified that estimation can be performed with high accuracy using a relatively simple model equation, and invented a rational and highly versatile method for controlling the crown shape during rolling using equation (1) and the mechanical plate crown model equation.

In addition to that invention, the present invention has invented a method for finding the optimal rolling schedule for the crown and shape of a rolled plate by introducing the mechanical plate crown and the above relational expression into the setting calculation for reducing the rolling schedule. This is what I did.

” As explained in the specification of the patent application No. 1,
The feature of the basic constitutive equation (1) is that it separates the concept of a mechanical plate crown, which is determined with high precision regardless of the deformation characteristics of the rolled material, and the concept of the modified crown genetic coefficient, which depends on the deformation characteristics of the rolled material. be.

Therefore, even when carved into steel types with greatly different deformation characteristics,
If you have a modified crown genetic coefficient corresponding to each steel type, you can similarly estimate the plate crown and shape with high accuracy. Regarding the plate shape, as explained in the specification of the patent application No. 1, the elongation strain difference of 4 stones is 8ε=ξ ((Ch/h) (CH/T-1
) )---(3) It can be estimated by the following. Note that ξ is a shape change coefficient, and 11 and l-( are the exit side and entrance side plate thicknesses, respectively.

Further, the present invention relates to a method for determining a rolling schedule that takes into account the crown and shape, but among the factors related to the crown and shape, the main factors that change when the rolling schedule is changed are the plate thickness and rolling load. The contact arc length also changes, but the amount of change is relatively small, and although the contact arc length has an effect on the work roll flatness of the mechanical plate crown, it does not affect this and the effect is even smaller. , seems to be negligible compared to changes in plate thickness and rolling load. 4 with roll bending equipment
The mechanical plate crown model equation of the corrugated rolling mill can be expressed by the following equation, as explained in the specification of the invention above.

C=Cp-F'-1-OF"F+Go-(4
) However, P is the rolling load, F is the roll pending force, and CP, CF, and Co are determined by conditions such as sheet width and mill dimension, and are constants that hardly change with changes in the rolling F schedule. It can be considered as such. However, CO includes the influence term of roll crown, and in addition to the initial crown, it is necessary to consider the effects of wear and thermal expansion, so it is necessary to always use the current estimated value of roll crown. . In addition, if the roll profile can be directly measured at JL, that value may be used. Therefore, by combining the formula (4) and the formula for calculating the rolling load, the mechanical plate crown for any rolling schedule can be HIWed, and by formula (1), the plate crown, (3
) can be used to estimate the plate shape. In other words, by changing the reduction schedule, the mechanical plate crown, plate crown, and plate shape can be controlled.

Hereinafter, for convenience, the present invention will be explained in detail by dividing the cases into cold rolling and hot rolling.

Generally, the width expansion is very small in cold rolling (3)
The shape change coefficient ξ in the equation is very close to 1, and when the crown ratio is changed, the strain difference appears as an elongation strain difference in the plate shape, and in order to return the plate shape to its original state, the crown ratio must also be changed. The crown ratio must be returned to its value, and the crown ratio cannot be changed after all. Therefore, in cold rolling, the goal is to always perform rolling with a flat shape, that is, rolling with a constant crown ratio, even when rolling is performed several times.

By the way, performing crown ratio constant rolling means that the rolling reduction distribution in the width direction becomes uniform, so for general materials whose deformation resistance distribution in the width direction is almost uniform, the distribution of rolling load in the width direction also becomes uniform. It becomes uniform. This is the only condition that defines a mechanical plate crown, and the exit plate crown will match the mechanical plate crown.

Therefore, in order to perform rolling with a constant crown ratio, the value obtained by dividing the mechanical plate crown by the exit side plate thickness (hereinafter referred to as the mechanical plate crown ratio) may be made to match the input side plate crown ratio. This means (1),
This can also be confirmed using equation (2). That is, (
Substituting i; = c H・H/ h into equation 1) and further substituting equation (2) yields d; = (1m) CHII/h+
'M・CH・I− [/ h Therefore, Ch/ l+ = C
It can be seen that H/+(--(5) holds true, and that rolling with a constant crown ratio actually holds true.The relationship in equation (5) should hold even if the reverse is true for the rolled original sheet. The crown ratio is the target value for all passes. To put the following into general terms, the plate thickness distribution represented by the mechanical plate crown is similar in terms of plate thickness to the plate thickness distribution of the rolled original plate. Shape flat rolling can be realized by making the shape as follows.

Next, a method for bringing the mechanical plate crown closer to the target value by adjusting the reduction schedule will be explained in detail. When it comes to adjusting the rolling schedule, the original plate thickness and finished plate thickness are fixed, and the equipment capacity of the rolling mill for each pass is also limited, so it is necessary to select the best one within a certain limited tolerance range. There is no guarantee that you will be able to completely achieve your target value. The devices that can compensate for this deviation from the target value are roll bending devices, variable crown rolls, work roll shift 1, roll cross, intermediate roll shift of 6-high rolling mills, and rolling mills with sleeves placed on reinforcing rolls. This is the so-called crown shape control end, such as the sleeve shift function. Therefore, one practical method is to leave as much margin as possible at these crown shape control ends, first adjust the roll reduction schedule to get it as close as possible to the target value, and then adjust the roll reduction schedule using the crown shape control ends after the roll reduction schedule is determined. One possible method is to compensate for the difference from the target value. This method will be explained in more detail below.

In a four-high rolling mill with a roll bending device,
In order to leave some margin in the roll pending force, if we fix it at a certain intermediate value Fo between the maximum value (-(increase MAX, ) and the minimum value (defrease MAX)) (4)
From the formula (e=cp-P+cF jFo+Go=Cp' P+C
F.

−−−−−−(6) Therefore, CP yCF
Since O can be regarded as a constant, the mechanical plate crown C can be expressed by a linear expression of the rolling load P. Also in other types of rolling mills, by fixing the value of the crown shape control end, the (l process) can be expressed in the form of equation (6).

On the other hand, the target value C1(i
Pass N01) is given by the following equation, where the plate crown of the rolled original plate is CHo, the plate thickness is Ho, and the i-pass exit side plate thickness is hi.

d;1==CHo-hi/Ha --------(7
) Therefore, when considering N-pass rolling, it is sufficient to find the one that minimizes the number of evaluation intervals J in the following equation within the range of permissible rolling reduction schedules.

J=Σg], 1cj-ifm---(8) 1: However, σ/1 is the predicted mechanical plate crown obtained by substituting the predicted load obtained by bar calculation for each pass into equation (6). value, and gi is the weighting coefficient for each stand (always gi≧
0), and usually gl "g2"...= g N ---
--It seems that (9) is sufficient, but adjustments such as increasing the weight of paths near the final path may be made depending on the operating conditions. In formula (8), as a general expression, the absolute value of the difference between the predicted value and the target value is raised to the rn power, but the optimum value may also be selected according to each operating state. The general tendency is that the larger m is, the more the shape will be distorted in a certain path! flt can be avoided.

By the way, the search range for the reduction schedule can be limited to the range shown in Figure 1 (hereinafter referred to as the schedule cone) by taking into account the limits of equipment capacity, but this still limits the range of possible reduction schedules. There are countless combinations.

Since it is very difficult to find the optimal value (the one that minimizes J) from these countless combinations, we discretize the range of plate thicknesses that can be taken on the exit side of each pass as shown in Figure 1, and create a finite number of The optimum value may be found from among the combinations of the search points of each path.

Even with this method, calculating the evaluation function J for all combinations of search points may take too long a calculation time for online subtraction. In such cases, Kado and Suzuki proposed ``Pass schedule optimization theory and rolling operation evaluation function J (m property and processing, V
ol, 9. No. 88 (1968) 315-323
), you can use dynamic programming techniques. The details of this method are omitted here as they are detailed in the article 1, but it is an effective method in that it can significantly reduce the number of calculations.

Next, the case of hot rolling will be explained. In hot rolling, unlike cold rolling, the crown ratio of the finished product does not need to match the crown ratio of the original sheet.

In other words, since there is a metal flow in the width direction of the rolled material, it is possible to make plate crowns according to the target even after the prerequisite that the product shape is flat. Therefore, in the case of hot rolling, in addition to the condition of a flat shape, there is also a target value for the plate crown, so the concept of the target value for the mechanical plate crown is significantly different from that in the case of cold rolling.

Even in hot rolling, as can be seen from equation (3), rolling with equal crown ratio results in a flange shape of 1-, which is still the most desirable rolling from the viewpoint of the plate shape. However, this generally does not allow the target plate crown to be achieved, so some degree of shape disturbance must be allowed for intermediate passes. However, if the irregularity of the shape is concentrated on a specific rolling pass at this time, there is a high possibility that a rolling accident will occur, so the change from the crown ratio of the original sheet to the target crown ratio is It is desirable to allocate it so that it is minimized. As a method for implementing this, the following may be considered, for example.

For N-pass rolling, the plate crown of the rolled original plate is CHo,
The plate thickness is Ha, the i-pass outlet plate thickness is hi, the i-pass outlet plate crown is Ci, and the target value of the N-pass outlet plate crown is CN.
, i/() When the ideal value of the exit side plate crown is Ci, the ideal value of the mechanical plate crown of the i pass is Cj, and the shape change coefficient of the i pass is Ci, the disturbance in the shape of each pass is minimized. is equivalent to making the shape of each path equal, so from equation (3), C1((to t / b t ) (CHo/I(
o))=ξ2 [(C2/h2) (Ct/f(i
)) = CN-1('(CN-1/ h N-1) -
(Self N-2/h N-2)) -" ----(10) should hold.Also, the N-pass exit shape is naturally aimed at something close to flat, For more general handling, if we assume that there is a target value ΔFN, then CN[(CN/hN)-CCN-1/b N-+ ))
= Δ”iN−−−−−−(II) holds.Here, we allowed the shape change from 1 pass to N-1 pass, but for operational reasons, we avoided shape change at a specific stand. Alternatively, each term in equation 1o) may be weighted. Here, (Ci/l+j,)-(
Ci-+ / hj-1) = A Ci-(12)
Then, the formula (10) is C1ΔC,=ξ2ΔC2=... =CN-1ΔCN+ However, (self1/h1)-(CHO/Ho)=
Because of ΔC1.

ΔCi=ΔG+(C1/Ci) (+ =2....
, N-1)---(13) Also, from equation (12), ΔC1+ΔC2+...ΔCN+=(gox-+ /
h N-1) - (CH'o/Ho) ----------(14) (4) Substituting equations (11) and (13) into equation ξ+ ('X' 1/ξi) ΔCj=Cx/hN1=
+ -ΔEN/ξN −CHo/Ho −−(15) Therefore, ΔC1= ((CN/hN)−(Δ?N/ΔN)(
CHo/ Ho)) / [C1 (vo11/ξ1)]1
:1 ----(1,6) By substituting equation (16) into equation (13), ΔC2+
..., ΔCN'l is determined, and by substituting these into equation (12) and solving sequentially, the ideal plate crown schedule d1 + C2g ...
CN-1 is found. Once Gl is determined, the ideal value correction j of the mechanical plate crown can be calculated by H1 from the following equation, which is obtained by reversing equation (1).

Silk j = [go j −';i”i (1−r j,) to i−
1) /ζj, --(17) However, 10,000 j, ζi, ri
are the modified crown genetic coefficient, plate crown correction coefficient, and rolling reduction rate of the i-pass, respectively, and C1-1 in the case of i=1 means CHo.

Since the above has been explained based on the formula, an explanation will be added about the tendency of the ideal value of the plate crown of each pass obtained as a result of the calculation. The value of the shape change coefficient was calculated by Nakataka et al.
Research on lip crown/shape control method (5th report)
” 30th Plastic Processing Union Lecture, No. 102 (19
According to the experiment of 79) ), it can be arranged as shown in Figure 2. It can be seen from FIG. 2 that as the rolling progresses, the plate thickness decreases and the shape change coefficient ξ increases. Therefore, determining the ideal temporary crown for each pass so that the relational expression (1o) holds true means that if there is a difference between the target plate crown ratio and the plate crown ratio of the original plate, the difference is large in the first half pass. The crown ratio is changed, and in the latter half of the pass, the crown ratio change is made smaller, and the crown ratio change roughly shown in FIG. 3 is selected as an ideal value.

The method after finding the ideal value of the mechanical plate crown using equation (17) is exactly the same as in the case of cold rolling. Since the mechanical plate crown model formula does not change in any way between cold rolling and hot rolling, by fixing the crown shape control end to a certain value, the mechanical plate crown can be expressed in the form of equation (6). . Then, the evaluation function J may be set in the form of equation (8), and a reduction schedule that minimizes J may be selected. This specific method is also exactly the same as the case of cold rolling, so the explanation will be omitted.

Note that although we have classified hot rolling and cold rolling here, this classification covers the most common type of steel sheet rolling, and includes materials with relatively low deformation resistance such as aluminum, copper, or buttons. When a relatively thick plate is cold rolled, the metal flow in the width direction is relatively large, so
It is also possible to control the plate crown as in the case of hot rolling described in -1-. Of course, it cannot be considered that the contribution is ξ-1 in the case of cold rolling of steel sheets, so as in the case of hot rolling, the reduction schedule should be set with a target sheet crown within a range very close to the original sheet crown ratio. It is possible to decide.

However, if the plate crown definition point is set near the plate edge and the plate Jv is relatively thick, the edge drop will occupy a fairly large proportion of the plate crown, so the basic formula for determining the crown shape ( The inventors' research has revealed that although the accuracy of equations 1) and (3) decreases if they are left as they are, the following modifications can be made.

CI+-ξ・a; + η(1-r)CH1Bh
-(18) However, 〇 is the mechanical plate crown corresponding to the so-called body crown, which is obtained by removing the term related to edge drop among the work roll flatness from the mechanical plate crown model formula, and cH is the edge drop from the entry side plate crown CH. is the body crown on the entrance side after subtracting , and old 1 is the contribution term of edge drop.

In this case, the plate shape must also be considered as a change in the ratio of the body crown as shown in the following equation.

ΔE=ξ [(your h/h)-(your own h/h)-ΔεB--
--(19) Note that ΔεB is a term that represents the effect of the widthwise metal flow near the plate end of the rolled material on the plate shape, and in normal plate rolling, its influence is very small compared to other terms.

As explained above, even when the edge drop occupies a fairly large proportion, the basic formula is slightly modified t=c
It is clear that the present invention can be applied to this case as well.

The explanation so far has only dealt with how to find the optimal rolling schedule for the crown shape, but
In many cases, there are operational target values not only for the crown shape but also for the distribution of rolling power, distribution of rolling load, etc. In such a case, an evaluation function is created to quantify the deviation from these target values, and the reduction schedule can be calculated using the sum of these and the evaluation function of the round shape as expressed by equation (8) as the true evaluation function. For example, it is possible to find a reduction schedule that takes into account factors other than crown shape. Also, if you multiply the weighting coefficients before calculating the sum of the evaluation functions in l), you can adjust the reduction schedule based on different viewpoints according to operational requirements by adjusting the weighting coefficient values. You can ask for it.

By applying the tr of the present invention, it becomes possible to find the optimal rolling schedule to achieve the target board crown and shape for each rolled material, even in a rolling mill with a small crown shape control capacity. , it can handle operations where the organization of rolling units changes significantly.
Furthermore, it becomes possible to realize a crown and shape of the finished product with a more rounded shape.

[Brief explanation of the drawing]

Figure 1 is a graph that does not show the range of possible rolling reduction schedule given by taking into consideration the equipment capacity of the rolling mill.
Figure 3 shows the trend of the ideal value of the crown ratio in each rolling pass from the original plate crown ratio to the target crown ratio during hot rolling. The graph is not shown. Patent Applicant: Nippon Steel Corporation” Mine Continuation “0 Original (Spontaneous) October 1981 611 1. Indication of the Case 1984 Patent Application No. 184131 2
, Title of the invention Rolling mill rolling schedule setting method 3, Relationship with the case of the person making the amendment Patent applicant address 2-6-3 Otemachi, Chiyoda-ku, Tokyo Name (665) Nippon Steel Corporation Representative Shotake 1) Yutaka 4, Agent 103 Phone: 03-864-60
52 Address: 2-27-6-5 Higashi Nihonbashi, Chuo-ku, Tokyo, Subject of amendment: Scope of Claims in the Specification, Column 2, Detailed Description of the Invention, 6, Contents of Amendment (1) Patent Claims in the Specification Correct the entire text of the range column as follows. [2. Claims (1) In the rolling process of obtaining a rolled plate of a predetermined thickness from a rolled original plate by rolling multiple times, when the load distribution in the width direction between the rolled plate and the work rolls is uniform; Through a reduction formula that calculates the thickness deviation in the width direction of the rolled plate on the exit side of the rolling mill, which is a linear combination of the realized thickness deviation in the width direction and the thickness deviation in the width direction of the rolled plate on the input side of the rolling mill. , a method for setting a rolling schedule for a rolling mill, characterized by determining the plate thickness at the exit side of each pass. (2) In the rolling process of obtaining a rolled plate of a predetermined thickness from a rolled original plate by rolling multiple times, the thickness distribution in the width direction is achieved when the load distribution in the width direction between the rolled plate and the work rolls is uniform. The plate thickness at the exit side of each pass is determined so that the plate thickness distribution calculated by H1 using a model formula showing the relationship between A model equation showing the relationship between the widthwise plate thickness distribution and rolling conditions that is realized when the widthwise load distribution between the rolling plate and the work roll is uniform in the rolling process that obtains the rolling reduction of a rolling mill characterized by The plate thickness at the exit side of each pass is determined so that the plate thickness distribution calculated using Features: How to set the rolling mill rolling schedule. (2) Correct the two lines on the following page of the specification that are incorrect. (3) Correct Figure 3 as per the attached appendix. 7. Attachment V catalog drawings...1 page, Figure 3, pass N. 471

Claims (3)

[Claims] (1) In the rolling process of obtaining a rolled plate of a predetermined thickness from a rolled original plate by rolling multiple times, the widthwise plate thickness achieved when the widthwise load distribution between the rolled plate and the work rolls is uniform. The thickness at the exit side of each pass is determined through a subtraction formula that calculates the deviation in the width direction of the rolled plate on the exit side of the rolling mill, which is a linear combination of the deviation and the thickness deviation in the width direction of the rolled plate on the exit side of the rolling mill. A rolling mill rolling schedule setting method characterized by determining. (2) In the rolling process of obtaining a rolled plate of a predetermined thickness from a rolled original plate by rolling multiple times, the thickness distribution in the width direction is achieved when the load distribution in the width direction between the rolled plate and the work rolls is uniform. Using a model formula showing the relationship between and rolling conditions, iI
A rolling mill rolling schedule setting method, characterized in that the plate thickness at the exit side of each pass is determined so that the calculated plate thickness distribution is closest to the plate thickness distribution of the original plate to be rolled. (3) In the rolling process of obtaining a rolled plate of a predetermined thickness from a rolled original plate by rolling multiple times, the widthwise thickness distribution is achieved when the widthwise load distribution between the rolled plate and the work rolls is uniform. Using a model formula showing the relationship between rolling conditions, gi
The plate thickness at the exit side of the pass is determined so that the plate thickness distribution to be rl is closest to the ideal value for achieving the target plate thickness distribution and plate shape of the finished product from the plate thickness distribution of the rolled original plate. How to set the rolling reduction Lj joule of a rolling mill.