COLD ROLLING METHOD, METHOD OF PRODUCING STEEL SHEET, COLD ROLLING LINE, AND STEEL SHEET PRODUCTION LINE

Abstract

Provided are a cold rolling method, a method of producing a steel sheet, a cold rolling line, and a steel sheet production line that can suppress the occurrence of fracture. The cold rolling method includes: a process of calculating a leveling target value for a cold mill (10) that carries out cold rolling on rolled material, the calculation being based on an index of an asymmetric component of an elongation difference rate distribution of the rolled material after cold rolling at delivery of the cold mill; and a process of executing leveling control of the cold mill. The index of the asymmetric component of the elongation difference rate distribution is calculated based on a correlation between the elongation difference rate distribution and an odd function, where the odd function is obtained by multiplying a first-order power function by an absolute value power function that is greater than zero-order.

Claims

1. A method of cold rolling, the method comprising: a process of calculating a leveling target value for a cold mill that carries out cold rolling on rolled material, the calculation being based on an index of an asymmetric component of an elongation difference rate distribution of the rolled material after cold rolling at delivery of the cold mill; and a process of executing leveling control of the cold mill based on the leveling target value, wherein the index of the asymmetric component of the elongation difference rate distribution is calculated based on a correlation between the elongation difference rate distribution and an odd function, where the odd function is obtained by multiplying a first-order power function by an absolute value power function that is greater than zero-order.

2. The cold rolling method according to claim 1, wherein the odd function is a third-order power function.

3. The cold rolling method according to claim 1, wherein the cold mill comprises a plurality of stands, and the leveling control based on third-order or higher-order correlation is executed for all stands of the plurality of stands except the last stand.

4. The cold rolling method according to claim 1, wherein, in the index of the asymmetric component, the leveling target value is calculated so that the shape difference between an OP side and a DR side of the rolled material is 20 I-units or less.

5. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 1.

6. A cold rolling line comprising: a cold mill that carries out cold rolling on rolled material; and a controller that calculates a leveling target value of the cold mill based on an index of an asymmetric component of an elongation difference rate distribution of the rolled material after cold rolling at delivery of the cold mill, and executes leveling control of the cold mill based on the leveling target value, wherein the index of the asymmetric component of the elongation difference rate distribution is calculated based on a correlation between the elongation difference rate distribution and an odd function, where the odd function is obtained by multiplying a first-order power function by an absolute value power function that is greater than zero-order.

7. The cold rolling line according to claim 6, wherein the odd function is a third-order power function.

8. The cold rolling line according to claim 6, wherein the cold mill comprises a plurality of stands, and the leveling control based on third-order or higher-order correlation is executed for all stands of the plurality of stands except the last stand.

9. The cold rolling line according to claim 6, wherein, in the index of the asymmetric component, the leveling target value is calculated so that the shape difference between an OP side and a DR side of the rolled material is 20 I-units or less.

10. A steel sheet production line comprising the cold rolling line according to claim 6, wherein the cold rolling line cold rolls a steel sheet as the rolled material.

11. The cold rolling method according to claim 2, wherein the cold mill comprises a plurality of stands, and the leveling control based on third-order or higher-order correlation is executed for all stands of the plurality of stands except the last stand.

12. The cold rolling method according to claim 2, wherein, in the index of the asymmetric component, the leveling target value is calculated so that the shape difference between an OP side and a DR side of the rolled material is 20 I-units or less.

13. The cold rolling method according to claim 3, wherein, in the index of the asymmetric component, the leveling target value is calculated so that the shape difference between an OP side and a DR side of the rolled material is 20 I-units or less.

14. The cold rolling method according to claim 11, wherein, in the index of the asymmetric component, the leveling target value is calculated so that the shape difference between an OP side and a DR side of the rolled material is 20 I-units or less.

15. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 2.

16. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 3.

17. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 11.

18. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 4.

19. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 12.

20. A method of producing a steel sheet, comprising a cold rolling process of cold rolling a steel sheet as the rolled material by the cold rolling method according to claim 13.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In the accompanying drawings:

[0035] FIG. 1 is a schematic diagram illustrating an example configuration of a cold rolling line that carries out a cold rolling method according to an embodiment of the present disclosure;

[0036] FIG. 2 is a diagram illustrating an example of elongation difference rate distribution of delivery shape;

[0037] FIG. 3 is a block diagram of leveling control;

[0038] FIG. 4 is a graph illustrating changes in shape 1;

[0039] FIG. 5 is a graph illustrating changes in leveling control output;

[0040] FIG. 6 is a diagram illustrating std-1 leveling change amounts;

[0041] FIG. 7 is a diagram illustrating elongation difference rate distribution at std-1 delivery;

[0042] FIG. 8 is a diagram illustrating std-1 leveling change amounts; and

[0043] FIG. 9 is a diagram illustrating a relationship between error frequency and leveling update amount.

DETAILED DESCRIPTION

[0044] A cold rolling method, a method of producing a steel sheet, a cold rolling line, and a steel sheet production line according to an embodiment of the present disclosure are described below with reference to the drawings. In each drawing, identical or equivalent parts are marked with the same reference sign. In description of the present embodiment, description of identical or equivalent parts is omitted or simplified as appropriate.

[0045] FIG. 1 illustrates an example configuration of a cold rolling line that carries out the cold rolling method according to the present embodiment. According to the present embodiment, the cold rolling line is part of a steel sheet production line and cold rolls steel material (a steel sheet) that is rolled material. In other words, the cold rolling method according to the present embodiment is used as a cold rolling process to cold roll the rolled material in the method of producing a steel sheet.

[0046] In FIG. 1, the right hand side is the upstream side in the conveyance direction of the rolled material, and the left hand side is the downstream side in the conveyance direction of the rolled material. The continuous cold mill (cold mill 10) illustrated in FIG. 1 is a machine that applies cold rolling to target material and comprises N stands (std-1 to std-N). Nis an integer greater than or equal to 1, for example 5. That is, the cold mill 10 includes a plurality of stands. On the delivery side (downstream side) of each stand is disposed a shape meter 30 (30-1 to 30-N in FIG. 1). The shape meter 30 is a load meter divided in the transverse direction. The load meter measures normal force received from the steel sheet and calculates elongation difference rate distribution in the transverse direction from the normal force. FIG. 2 illustrates an example of the elongation difference rate distribution of delivery shape. The elongation difference rate distribution is illustrated in I-units, with positive values representing elongation and negative values representing tension. The elongation difference rate is defined as the difference between the length along the steel sheet curve surface of a certain rolling direction section and average value of same in the transverse direction, divided by the difference of the average value. I-units are the elongation difference rate multiplied by 10.sup.5. Further, in the horizontal axis of FIG. 2, the left side is the operator (OP) side and the right side is the drive (DR) side.

[0047] Further, at each stand is disposed a controller 20 (20-1 to 20-N in FIG. 1) that controls the cold mill 10. According to the present embodiment, the controller 20 inputs the elongation difference rate distribution from the shape meter 30 and outputs target values for leveling and bender load. Hereinafter, control over the leveling of the cold mill 10 is referred to as leveling control.

[0048] FIG. 3 is a block diagram of leveling control. Arrows in FIG. 3 indicate data flow. Further, i corresponds to one of 1 to N in FIG. 1. That is, the leveling control according to the present embodiment is carried out in all of the plurality of stands (std-1 to std-N).

[0049] As an overview, the controller 20-i calculates a leveling target value of the cold mill 10 (std-i) based on an index of an asymmetric component of the elongation difference rate distribution of the rolled material after cold rolling at delivery of the cold mill 10 (std-i). The controller 20-i then executes leveling control of the cold mill 10 (std-i) based on the leveling target value. The details of processing calculating the leveling target value are described below. Hereafter, descriptions of processing that does not depend on the order of the stands does not use suffixes such as i, N, and the like. For example, the controller 20-i is denoted simply as controller 20.

[0050] First, the controller 20 inputs the elongation difference rate distribution from the shape meter 30 and evaluates with an evaluation function J indicated in the following Expression (1).

[00001]$\left[\mathrm{Math}.1\right]$$\begin{array}{cc}J\left(b,l\right)={}_{-1}^1{\left(e_b{\mathrm{bx}}^2+e_l\mathrm{lx}-k\left(x\right)\right)}^2\mathrm{dx}& \mathrm{Expression}\left(1\right)\end{array}$

[0051] The controller 20 searches for and finds a leveling update amount (l) and a bender update amount (b) such that the evaluation function J is minimized. Here x is the normalized transverse direction position. e.sub.b is a bender influence coefficient. e.sub.1 is a leveling influence coefficient. k is shape deviation (difference between delivery shape and target shape). As illustrated in FIG. 3, the controller 20 integrates the leveling update amount (PI control) to calculate the leveling target value. The controller 20 then executes leveling control of the cold mill 10 based on the leveling target value. The purpose of the leveling control is to calculate a leveling target value that makes the delivery shape in FIG. 2 bilaterally symmetrical.

[0052] From Expression (1), the leveling update amount and bender update amount can be obtained analytically. The leveling update amount (l) is calculated by the following Expression (2). Further, the bender update amount (Ab) is calculated by the following Expression (3).

[00002]$\left[\mathrm{Math}.2\right]$$\begin{array}{cc}l=\frac{{}_{-1}^{1}k\left(x\right)\mathrm{xdx}}{e_l{}_{-1}^1{x}^2\mathrm{dx}}& \mathrm{Expression}\left(2\right)\end{array}$$\begin{array}{cc}b=\frac{{}_{-1}^{1}k\left(x\right)x^2\mathrm{dx}}{e_b{}_{-1}^1{x}^4\mathrm{dx}}& \mathrm{Expression}\left(3\right)\end{array}$

[0053] The numerator on the right-hand side of Expression (2) is the correlation of k and x, which are functions. Correlation is a metric of similarity; the greater the correlation, the more similar the functions are to each other. In this example, the function x is a first-order power function, so is referred to as a first-order correlation of shape deviation k. The leveling update amount is a first-order correlation of the shape deviation k and is a metric of an asymmetric component recognized by the control. The asymmetric component and symmetric component of shape are controlled independently, and the first-order correlation of the delivery shape is used as an index of asymmetry. Expression (1) is a standard leveling control law, that is, a conventional method.

[0054] Here, an example of leveling control failure is described. FIG. 4 is a graph of shape 1, with time on the horizontal axis and shape 1 on the vertical axis. One tick on the horizontal axis is 10 seconds. Further, the units for the shape 1 of the vertical axis are I-units. The shape 1 is the difference between the OP side and the DR side obtained based on an approximated function, obtained by approximating the elongation difference rate distribution with a sixth-order polynomial function using the least squares method. In other words, the shape 1 is the difference in shape between the OP side and the DR side of the rolled material.

[0055] Here, as a failure example, it is assumed that the shape 1 of std-1 (the most upstream stand) does not reach zero and a fracture occurs between std-1 and std-2 (the second stand from the upstream side). When such a failure occurs, the leveling control output is, for example, as illustrated in FIG. 5. The vertical axis of leveling in FIG. 5 means the leveling change amount output from the controller 20, which corresponds to the leveling target value. The unit is m. The horizontal axis in FIG. 5 is the same as in FIG. 4. In the example in FIG. 5, the delivery shape of std-1 is OP elongation, and therefore the leveling control output must move in the DR closing direction. However, the leveling control output of std-1 is moving in a DR-closing manner, but movement is slow and does not fully correct the asymmetry of the delivery shape. Here, OP elongation refers to the state in which the rolled material is elongated on the OP side. DR elongation means the same for the DR side. Further, DR closing refers to narrowing the work roll gap on the DR side, resulting in OP elongation. OP closing means the same for the OP side. Here, in FIG. 4 and FIG. 5, std-3 is the third stand from the upstream side and std-4 is the fourth stand from the upstream side.

[0056] FIG. 6 illustrates the leveling change amount of std-1 in this failure example. Search in FIG. 6 indicates the leveling update amount of std-1 expressed in Expression (2). Further, Output in FIG. 6 indicates the leveling control output of std-1. The leveling update amount is somewhat biased to OP elongation, but does not indicate OP elongation as clearly as shape 1.

[0057] Further, FIG. 7 illustrates the elongation difference rate distribution of the delivery side of std-1 in this failure example. The vertical and horizontal axes are the same as in FIG. 2. Although clearly recognizable as OP elongation to a human observer, the leveling update amount represented by the first-order correlation in Expression (2) does not result in OP elongation even for the elongation difference rate distribution illustrated in FIG. 7, resulting in almost no elongation. Here, the time to fracture is illustrated at the top of each graph.

[0058] Here, it is known that the shape 1 calculated by the difference between the OP side and the DR side of the elongation difference rate approximation curve is relatively close to the asymmetry recognized by a human observer. Further, the distribution shape in FIG. 7 illustrates that the information at the transverse direction ends needs to be emphasized.

[0059] Based on the above considerations, the following evaluation function J in Expression (4) is used. In this case, the leveling update amount (l) is calculated by the following Expression (5), where the numerator on the right-hand side can be a third-order correlation.

[00003]$\left[\mathrm{Math}.3\right]$$\begin{array}{cc}J\left(b,l\right)={}_{-1}^1{\left(e_b{\mathrm{bx}}^2+e_l{\mathrm{lx}}^3-k\left(x\right)\right)}^2\mathrm{dx}& \mathrm{Expression}\left(4\right)\end{array}$$\begin{array}{cc}l=\frac{{}_{-1}^{1}k\left(x\right)x^3\mathrm{dx}}{e_l{}_{-1}^1{x}^6\mathrm{dx}}& \mathrm{Expression}\left(5\right)\end{array}$

[0060] FIG. 8 illustrates the leveling change amount of std-1 when the leveling update amount is a third-order correlation. As in FIG. 6, Search indicates the leveling update amount for std-1, and Output indicates the leveling control output for std-1. FIG. 8 illustrates that the leveling update amount is OP elongation and is improved. Further, the leveling control output is in the DR closing direction.

[0061] Here, according to the embodiment described above, third-order correlation was assumed by multiplying the elongation difference rate distribution by a third-order power function as an odd function, but may be a higher-order correlation other than third-order. In general, the evaluation function J can be expressed as the following Expression (6). In this case, the leveling update amount (l) is calculated by the following Expression (7), where the numerator of the right-hand side can be a p-order correlation. p is a real number greater than or equal to 1. However, when p is 1, this corresponds to a conventional method.

[00004]$\left[\mathrm{Math}.4\right]$$\begin{array}{cc}J\left(b,l\right)={}_{-1}^1{\left(e_b{\mathrm{bx}}^2+e_l\mathrm{lx}{.Math.x.Math.}^{p-1}-k\left(x\right)\right)}^2\mathrm{dx}& \mathrm{Expression}\left(6\right)\end{array}$$\begin{array}{cc}l=\frac{{}_{-1}^{1}k\left(x\right)x{.Math.x.Math.}^{p-1}\mathrm{dx}}{e_l{}_{-1}^1{x}^2{.Math.x.Math.}^{2\left(p-1\right)}\mathrm{dx}}& \mathrm{Expression}\left(7\right)\end{array}$

[0062] That is, the odd function can be obtained by multiplying a first-order power function by an absolute value power function that is greater than zero-order to obtain a p-order correlation. Using higher-order correlations can bring the shape closer to 1 (that is, closer to the asymmetry observed by humans), but would be more susceptible to errors in the shape meter 30. Here, in Expression (7), when the shape deviation k is a measurement error model sin (x), the error impact on the leveling update amount can be expressed as the following Expression (8).

[00005]$\left[\mathrm{Math}.5\right]$$\begin{array}{cc}l=\frac{{}_{-1}^1\sin \left(x\right)x{.Math.x.Math.}^{p-1}\mathrm{dx}}{{}_{-1}^1{x}^2{.Math.x.Math.}^{2\left(p-1\right)}\mathrm{dx}}& \mathrm{Expression}\left(8\right)\end{array}$

[0063] Here, the leveling influence coefficient (e.sub.1) is set to 1 and is the frequency of the modeled error. The larger the value of , the shorter the wavelength and the higher the error frequency. Expression (8) can be transformed into the following Expression (9) by considering the leveling update amount as a function of . Here, F is a hypergeometric function.

[Math. 6]

[00006]$\begin{array}{cc}l\left(\right)=F\left(\frac{p}{2}+1,\frac{3}{2};\frac{p}{2}+2;-\frac{{}^2}{4}\right)& \mathrm{Expression}\left(9\right)\end{array}$

[0064] FIG. 9 illustrates a relationship between the error frequency () and the leveling update amount (l). The horizontal axis in FIG. 9 is the error frequency (no units). It can be seen in FIG. 9 that the larger the order, the higher the susceptibility to high-frequency error.

[0065] Leveling control based on third-order correlation is applied to at least the most upstream stand, preferably to four upstream stands other than the last stand, and leveling control based on first-order correlation is applied to the last stand. For the last stand (the most downstream stand), first-order correlation is preferable because the shape must be created for the downstream line. That is, leveling control based on third-order or higher order correlation is executed for all stands except the last stand. Further, third-order or higher order correlation may be applied only to steel grades that are prone to fracture, for example, those containing at least 1.5% silicon.

Examples

[0066] By using the leveling control with the evaluation function J of Expression (4), the shape 1 of std-1 to std-4 can be suppressed to 20 I-units or less. As indicated in Table 1 below, the fracture rate was decreased for the Examples using higher-order correlation. Here, the fracture rate was calculated for approximately 1000 coils for the Comparative Example and each of the Examples. The columns std-1 to std-5 indicate the order of correlation, or p-order, in Expression (7), which calculates the leveling update amount (l). Further, the failure ratio was calculated as shape defective coils/total coils.

TABLE-US-00001 TABLE 1 Failure ratio of std-5 Fracture delivery No. std-1 std-2 std-3 std-4 std-5 rate shape Remarks 1 1st-order 1st-order 1st-order 1st-order 1st-order 2.00% 1.00% Comparative Example 2 3rd-order 3rd-order 3rd-order 3rd-order 1st-order 0.40% 1.00% Example 3 5th-order 5th-order 5th-order 5th-order 1st-order 1.20% 1.00% Example 4 7th order 7th order 7th order 7th order 1st-order 1.50% 1.00% Example 5 3rd-order 3rd-order 3rd-order 3rd-order 3rd-order 0.40% 1.50% Example

[0067] Although embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that a person skilled in the art may make variations and modifications based on the present disclosure. Therefore, it should be noted that such variations and modifications are included within the scope of the present disclosure.

REFERENCE SIGNS LIST

[0068] 10 cold mill [0069] 20 controller [0070] 30 shape meter