Metal strip shape detection device, rolling mill, and detection method

Abstract

Even when vibrations are occurring in the metal strip, the change in the strip's elongation distribution can be evaluated with high accuracy. [Solution] In the acquired image, the reflected light region is divided into j sections in the plate width direction, and in each divided section, the upstreammost position of the upstream boundary line of the reflected light region and the downstreammost position of the downstream boundary line are determined. For each acquired image, the difference in position data between the upstreammost boundary line and the downstreammost boundary line is calculated for each divided section and used as information corresponding to the maximum rolling direction length of the reflected light region in the k-th image. This is associated with the position of the center of the divided section i in the plate width direction, and when the value indicating the position in the plate width direction is taken as a variable x, the position in the plate width direction within the plate width range of the region in the image is normalized to the range -1≦x≦1. The value of the information is used as an index corresponding to the rolled plate elongation distribution in the plate width direction obtained from the k-th image, and its coefficient is obtained by applying it to a Chebyshev polynomial. The coefficient C1' of the first-order term is transmitted as the detection result signal of the rolled plate elongation distribution of the first-order component in the plate width direction of the k-th image.

Description

[Technical Field]

[0001] The present invention relates to a metal strip shape detection device, a rolling mill, and a detection method. [Background technology]

[0002] Patent Document 1 describes a defect detection device and defect detection method that can easily determine defects in the surface shape of a metal strip without using a special light source such as a rod, comprising: a roll with a rotating shaft extending in the width direction of the rolled steel sheet and lifting the rolled steel sheet upward; a camera that captures an image including the lifted area of ​​the rolled steel sheet lifted upward by the roll; and a control device that determines defects in the surface shape of the metal strip based on the image captured by the camera.

[0003] Patent Document 2 describes a metal strip shape determination device, rolling mill, and determination method that are less susceptible to the effects of slight disturbances and suddenly occurring small obstacles compared to conventional devices, comprising a camera set up to capture an image that includes a region in which a strip-shaped reflected light transverses the width direction of the rolled metal strip is reflected, and an image processing computer that determines the shape of the metal strip based on the image captured by the camera. The image processing computer divides the region in the image into multiple sections in the width direction of the metal strip, and transmits information as a signal corresponding to the distribution of elongation in the width direction of the metal strip in the rolling direction, based on index information representing the size related to each divided area. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Patent No. 6808888 [Patent Document 2] Patent No. 7130350 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] Numerous techniques have been known to detect the quality of the shape of a metal strip rolled by a rolling mill, such as whether or not there is any elongation, based on long linear or rod-shaped reflected light in the width direction of the metal strip.

[0006] The detection method is based on the fact that when some stretching occurs and the plate shape changes, the shape of the reflected light, which was linear or rod-shaped, becomes irregular, and some of it moves or displaces.

[0007] However, linear or rod-shaped lighting has the drawback that the area of ​​reflected light in the rolling direction at each position in the width direction of the plate surface is narrow, making it highly susceptible to the effects of even slight disturbances, such as small obstacles, and prone to false detections.

[0008] The inventors of the present invention have discovered that by detecting changes in the band-shaped reflected light region projected onto the surface of a metal strip near the curved portion of a strip lifted by a tension control looper installed between the rolling mill stands of a rolling mill line, using general lighting as disclosed in Patent Document 1, the influence of external disturbances can be reduced. As a technique that makes better use of the characteristics of the band-shaped reflected light region, they conceived the technique disclosed in Patent Document 2.

[0009] In the technology described in Patent Document 2, the length and area of ​​a band-shaped reflected light region projected onto the surface of a metal strip near the curved portion of the strip, which is lifted by a tension control looper installed between the rolling mill stands of a rolling line, are applied to a Chebyshev polynomial to determine the coefficients of the Chebyshev polynomial and to make a determination about the strip elongation distribution in the strip width direction.

[0010] In actual rolling operations, the metal strip may vibrate in the looper section, and the position, length in the rolling direction, and area of ​​the reflected light region projected onto the surface of the rolling metal strip are constantly fluctuating. This phenomenon can be observed where the reflected light region does not remain stably in the same position.

[0011] As a result of the present inventors' diligent studies on the technology described in Patent Document 2 mentioned above, it became clear that there are cases where the technology described in Patent Document 2 cannot cope with such fluctuations in the reflected light region.

[0012] The present invention provides a metal strip shape detection device, a rolling mill, and a detection method that can evaluate changes in the elongation distribution of a metal strip with high accuracy, even when vibrations are occurring in the metal strip. [Means for solving the problem]

[0013] The present invention includes multiple means for solving the above problems, but to give one example, a rolled metal strip shape detection device comprising: a camera installed in a rolling mill to capture an image that includes a range in which a strip-shaped area transverse in the width direction of the metal strip, called a reflected light area, can be confirmed on the surface of a metal strip lifted by a looper, and an image processing unit that detects the shape of the metal strip based on the image captured by the camera, wherein the image processing unit processes the acquired images in the order 1, 2, 3, ..., k,...and numbering is performed, and in the (k)th image, the reflected light region is divided into j sections in the plate width direction, and within each section (i) (i=1~j), the upstream position Pumin(k)i among the pixel positions constituting the upstream boundary of the reflected light region is determined in the rolling direction of the pixel coordinates, and the downstream position Pdmax(k)i among the pixel positions constituting the downstream boundary of the reflected light region is determined, and for each of the F images obtained from two or more image numbers (k-F+1) to image number (k), the data indicating the most upstream position from Pumin(k-F+1)i to Pumin(k)i is extracted as the first position data, and this is reset as Pure_min(k)i for the (k)th image, and the data indicating the most downstream position from Pdmax(k-F+1)i to Pdmax(k)i is extracted as the first position data The data is extracted as 2 position data and reset as Pdre_max(k)i as the data for the (k)-th image. The difference in the position data in the rolling direction [Pdre_max(k)i - Pure_min(k)i] is calculated for each of the divided areas (i). [Pdre_max(k)i - Pure_min(k)i] is taken as information D(k)i corresponding to the maximum rolling direction length of the reflected light region of the (k)-th image, and the value of the information D(k)i is set for each of the divided areas (i). Corresponding to the central position in the width direction of the plate, and with the value indicating the position in the width direction of the plate being the variable (x), the position in the width direction of the plate within the plate width range of the reflected light region in the image is normalized to the range -1≦x≦1, and the value of the j pieces of information D(k)i is used as an index corresponding to the rolled plate elongation distribution in the width direction of the plate obtained from the (k)th image, the notation for the position in the width direction of the plate is changed to (x), and D(k)i=E(xi), where E(x) = C0'+C1'×x+C2'×(2x, 2 -1) + C4' × (8x 4 -8x 2+1) (However, -1 ≤ x ≤ 1), apply it to the Chebyshev polynomial, and obtain the coefficients (C0’, C1’, C2’, C4’) of the Chebyshev polynomial from E(xi) having j values of x (xi). Then, transmit the coefficient (C1’) of its first-order term as a detection result signal of the rolling sheet elongation distribution of the first-order component in the sheet width direction of the (k)-th image. Here, xi is what represents the center position in the sheet width direction of the divided area (i) obtained by dividing the reflected light region into j parts in the sheet width direction in terms of (x). Note that F, i, j, and k are integers.

Effect of the Invention

[0014] According to the present invention, even when vibration occurs in the metal strip, the change in the sheet elongation distribution during rolling can be evaluated with high accuracy. Problems, configurations, and effects other than those described above will be clarified by the description of the following embodiments.

Brief Description of the Drawings

[0015] [Figure 1] A diagram showing an example of the outline of a rolling facility equipped with a sheet shape detection device for a metal strip according to an embodiment of the present invention. [Figure 2] A diagram showing an example of a state where the reflected light of illumination is reflected in a substantially rectangular band shape in the sheet width direction on the surface of the metal strip at the looper section between stands during operation in the rolling facility. [Figure 3] A diagram showing an example of a state where the reflected light of illumination is reflected in an irregular band shape in the sheet width direction on the surface of the metal strip at the looper section between stands during operation in the rolling facility. [Figure 4] A diagram showing the definition of the leveling amount (Gd - Gw) in the case of (Gd = Gw). [Figure 5] A diagram showing the definition of the leveling amount (Gd - Gw) in the case of (Gd > Gw). [Figure 6] A diagram showing an example of the relationship between the first-order component (C1’) of the Chebyshev coefficient and the leveling amount using the “index A” obtained by the prior art. [Figure 7] A diagram showing an example of the relationship between the first-order component (C1’) of the Chebyshev coefficient and the leveling amount using the “index B” obtained by the present invention. [Figure 8] In the plate shape detection device for a metal strip in an embodiment, a diagram showing an example when the maximum length D(k)i in the rolling direction of the reflected light region is obtained by considering the variation of the boundary line between the upstream side and the downstream side of the reflected light region from the (k)-th image. [Figure 9] A diagram showing an example of a method for equally dividing the plate width direction in the plate shape detection device for a metal strip in an embodiment. [Figure 10] A diagram showing an example of a method for unevenly dividing the plate width direction in the plate shape detection device for a metal strip in an embodiment. [Figure 11] A flowchart for detecting the plate shape in the plate shape detection device for a metal strip in an embodiment. [Figure 12] A diagram showing an example of a display screen of a monitor showing the 0th, 1st, 2nd, and 4th components of x of the Chebyshev polynomial in the plate shape detection device for a metal strip in an embodiment.

Embodiments for Carrying Out the Invention

[0016] Examples of the plate shape detection device for a metal strip, the rolling mill, and the detection method of the present invention will be described with reference to FIGS. 1 to 12. In the drawings used in this specification, the same or corresponding components are denoted by the same or similar reference numerals, and repeated descriptions of these components may be omitted.

[0017] First, the overall configuration of the rolling equipment including the plate shape detection device for a metal strip will be described with reference to FIGS. 1 to 3. FIG. 1 is a schematic diagram showing the configuration of the plate shape detection device for a metal strip in this embodiment and the rolling equipment equipped with the same. FIGS. 2 and 3 are diagrams showing an example of a state in which the reflected light of illumination appears in a band shape on the surface of the metal strip at the looper part between stands during operation in the rolling equipment.

[0018] The rolling equipment 100 for rolling the metal strip 1 shown in FIG. 1 includes an F1 stand 10, an F2 stand 20, an F3 stand 30, an F4 stand 40, an F5 stand 50, cameras 61, 62, 63, 64, loopers 71, 72, 73, and 74 for tension control, an image processing computer 80, a database 81, a control device 82, a monitor 85, etc.

[0019] These F1 stand 10, F2 stand 20, F3 stand 30, F4 stand 40, F5 stand 50, cameras 61, 62, 63, 64, image processing computer 80, database 81, control device 82, and monitor 85 are connected by a communication line 90.

[0020] Of these, cameras 61, 62, 63, and 64, loopers 71, 72, 73, and 74, an image processing computer 80, and a database 81 constitute the metal strip plate shape detection device of the present invention.

[0021] Furthermore, the rolling mill 100 is not limited to the configuration with five rolling stands as shown in Figure 1; it is sufficient to have at least two stands.

[0022] Each of the F1 stand 10, F2 stand 20, F3 stand 30, F4 stand 40, and F5 stand 50 is equipped with an upper work roll and a lower work roll, an upper backup roll that supports the upper and lower work rolls by contacting them, a lower backup roll, and pressure cylinders 11, 21, 31, 41, 51 and load sensors 12, 22, 32, 42, 52 located above the upper backup roll. Furthermore, a six-stage configuration is possible by adding intermediate rolls between each work roll and each backup roll.

[0023] The looper 71 is a tension control roll installed between the F1 stand 10 and the F2 stand 20. The looper 71 is positioned so that the rotating shaft extends in the width direction of the metal strip 1 so that the moving metal strip 1 rests on the roll, and is installed to lift and hold the metal strip 1 upwards. The looper 71 could be biased upwards by a spring, or lifted by a hydraulic cylinder or motor drive, for example.

[0024] Similarly, a tension control looper 72 is installed between the F2 stand 20 and the F3 stand 30, a tension control looper 73 is installed between the F3 stand 30 and the F4 stand 40, and a tension control looper 74 is installed between the F4 stand 40 and the F5 stand 50.

[0025] Camera 61 is positioned to capture an image of the surface of the metal strip 1, which has been rolled and lifted and curved by the looper 71, including an area where a band of illumination light, called the reflected light area 2, is visible as reflected light that transverses the width direction of the metal strip. Preferably, when the metal strip 1 is viewed from above, camera 61 can be positioned on the outside of the metal strip 1 in the width direction. The image data captured by camera 61 is transmitted to the image processing computer 80 via the communication line 90.

[0026] Furthermore, camera 62 is positioned to capture an image of the surface of the metal strip 1, which has been rolled and lifted by the looper 72, including an area where a band of illumination light, transverse in the width direction of the sheet, called the reflected light region 2, is visible reflected on the surface of the metal strip 1. Camera 63 is positioned to capture an image of the surface of the metal strip 1, which has been rolled and lifted by the looper 73, including an area where a band of illumination light, transverse in the width direction of the sheet, called the reflected light region 2, is visible reflected on the surface of the metal strip 1. Camera 64 is positioned to capture an image of the surface of the metal strip 1, which has been rolled and lifted by the looper 74, including an area where a band of illumination light, transverse in the width direction of the sheet, called the reflected light region 2, is visible reflected on the surface of the metal strip 1. The image data captured by cameras 62, 63, and 64 is transmitted to the image processing computer 80 via the communication line 90.

[0027] Cameras 62, 63, and 64, like camera 61, are preferably installed on the outside of the metal strip 1 in the width direction when the metal strip 1 is viewed from above.

[0028] These cameras 61, 62, 63, and 64 perform a shooting step in which they capture an image that includes a region where a band-shaped reflected light transverses the width direction of the rolled metal strip 1 is visible.

[0029] Further lighting can be provided to illuminate the lifted shooting area of ​​the metal strip 1, which is lifted upward by the roll and is primarily photographed by cameras 61, 62, 63, and 64. This lighting can be general lighting that is appropriately placed on the ceiling of the rolling mill where the rolling equipment 100 is installed, and no special new lighting equipment is required in this invention, however, dedicated lighting may be provided.

[0030] The image processing computer 80 is a device that performs various processes (including image processing steps) to detect the shape of the metal strip 1 based on images captured by cameras 61, 62, 63, and 64. Preferably, the image processing computer 80 is the main entity that performs the image processing steps.

[0031] For example, using image processing, an image including the lifted region, which is the curved vicinity of the metal strip 1 that has been rolled and lifted by loopers 71, 72, 73, and 74 as shown in Figure 2 or Figure 3, is identified as the reflected light region 2, which is the range including the upstream and downstream boundaries of the area where the brightness of the reflected light from the surface of the metal strip 1 shown in the image is greater than a specific brightness value.

[0032] Here, the reflected light region 2, which shows a band of reflected light transverse in the width direction of the metal strip 1, is flat on the surface of the metal strip 1, the shape is good, and the steepness is similar and small in the width direction. As shown in Figure 2, the difference in the distribution of the length in the rolling direction of the reflected light region 2 at each position in the width direction is small. Therefore, the boundary lines of the reflected light region 2 due to illumination, with the upstream boundary line 2A and the downstream boundary line 2B, are generally uniform and nearly parallel in the width direction. When the reflected light region 2 is evenly divided into multiple areas in the width direction, the parameters such as the area value of each area and the average length in the rolling direction are generally uniform in all areas.

[0033] In contrast, if there are differences in elongation in the rolling direction depending on the position in the width direction of the sheet (e.g., elongation at the edges, elongation in the middle), the metal strip will not be flat, the sheet shape will be poor, and the area of ​​reflected light on the sheet surface will differ due to the different degrees of steepness in the width direction. As shown in Figure 3, the boundary lines of the reflected light region 2 due to illumination will be wavy on either the upstream boundary line 2A or the downstream boundary line 2B, or both, and the distance between the upstream boundary line 2A and the downstream boundary line 2B of the reflected light region 2 will be non-uniform in the width direction. Therefore, when the reflected light region 2 is evenly divided into multiple areas in the width direction, the area value of each area, the average length in the rolling direction, and other parameters will be non-uniform in each area.

[0034] In the aforementioned Patent Document 1, curve fitting is performed using the Chebyshev polynomial (1) below, using the widthwise distribution of the reflected light region 2 projected onto the surface of the metal strip 1 near the curved portion of the metal strip 1 lifted by loopers 71, 72, 73, and 74 as an indicator of the sheet elongation distribution due to rolling.

[0035] E(x) = C0' + C1' × x + C2' × (2x 2 -1) + C4' × (8x 4 -8x 2 +1) (where -1 ≤ x ≤ 1) ··· (1) In the Chebyshev polynomial, for example, as an index of the sheet elongation distribution in the width direction due to rolling, E(x) is assumed to represent the length in the rolling direction of the reflected light region 2 on the surface of the metal strip 1 at loopers 71, 72, 73, and 74, as well as the magnitude corresponding to the sheet elongation due to rolling. C0', C1', C2', and C4' represent the values ​​of the coefficients when the Chebyshev polynomial, which is assumed to represent the magnitude corresponding to the sheet elongation distribution in the width direction, is separated into its 0th, 1st, 2nd, and 4th order components of x. x represents the normalized position in the width direction of the sheet; for example, x=-1 represents the sheet width end position on the drive side (DS), and x=1 represents the sheet width end position on the work side (WS). In other words, in this case, if the coefficient of the linear component of x in the Chebyshev polynomial (C1') is positive, it indicates that the plate elongation is large on the working side (WS). Also, if the coefficient of the quadratic component of x (C2') is positive, it indicates that the elongation at the edges of the plate width is greater than at the center of the plate width. Furthermore, if the coefficient of the quartic component of x (C4') is negative, it indicates that the quarter elongation in the plate width direction is large.

[0036] The definition of leveling amount is shown below.

[0037] As shown in Figures 4 and 5, the leveling amount is defined as the value obtained by subtracting the distance between the upper and lower work roll axes at the work side (WS) position from the distance between the upper and lower work roll axes Gd at the drive side (DS) position of the reduction cylinder (WS).

[0038] When changing the leveling amount, the plate thickness at the center of the plate width should not be changed. Therefore, as shown in Figure 5, when the leveling amount increases compared to the state shown in Figure 4, the plate thickness on the drive side (DS) becomes thicker, the plate thickness on the work side (WS) becomes thinner, and the plate elongation on the work side (WS) increases. The value of the first-order component of the Chebyshev coefficient (C1') obtained by this method indicates that if it is a positive value, the plate elongation on the work side (WS) is large, and if it is a negative value, the plate elongation on the drive side (DS) is large.

[0039] The reflected light region 2 is divided into a specific number of sections in the plate width direction. For example, the length of the reflected light region 2 in the rolling direction, which is used as an indicator of the plate elongation distribution in the plate width direction, is averaged within each section. This averaged value is then assumed to represent the magnitude corresponding to the plate elongation distribution in the plate width direction, and is set as the Chebyshev polynomial E(x). The E(x) obtained here is called "Indicator A," and its Chebyshev coefficient is the one obtained by conventional technology.

[0040] In a situation where the leveling amount of the rolling mill is intentionally changed during actual hot rolling, and it is clearly expected that the first-order component (C1'), which is a coefficient of the Chebyshev polynomial, will change, Figure 6 shows the relationship between the first-order component (C1') of the Chebyshev coefficient and the leveling amount, when index A obtained by the conventional index extraction method is applied.

[0041] As shown in Figure 6, it can be confirmed that there is almost no correlation between the change in the leveling amount and the first-order component of the Chebyshev coefficient (C1') obtained by index A.

[0042] Therefore, it was hypothesized that there would be cases where the actual plate shape change could not be measured using the extraction method, which averages the length in the rolling direction in each divided area of ​​the reflected light region 2 and uses that as index A. Thus, the inventors considered that there might be room for improvement in the index selection method.

[0043] At the positions of loopers 71, 72, 73, and 74, vibrations of the metal strip 1 were observed. It was hypothesized that averaging the fluctuation data such as the position, rolling direction length, and area of ​​the reflected light region 2 projected onto the surface of the rolled metal strip would smooth out the resulting Chebyshev coefficient, making it impossible to clearly obtain the correlation between the change in leveling amount and the first-order component of the Chebyshev coefficient (C1') to which index A was applied.

[0044] In other words, the vibration of the metal strip 1 is affected by the elongation of the strip due to rolling, and we hypothesized that by extracting this effect, the elongation distribution due to rolling could be reflected in the Chebyshev coefficient. As a result of diligent research, we devised the following new method for extracting an index. This new index obtained in this invention will be called "Index B".

[0045] Similarly to the previous example, in a situation where the leveling amount of the rolling mill is intentionally changed during actual hot rolling, and it is clearly expected that the linear component (C1'), which is a coefficient of the Chebyshev polynomial, will change, Figure 7 shows the relationship between the linear component (C1') of the Chebyshev coefficient obtained in this embodiment and the leveling amount.

[0046] As shown in Figure 7, it can be confirmed that there is a certain degree of correlation between the change in the leveling amount and the change in the first-order component of the Chebyshev coefficient (C1') obtained by the processing of this embodiment described above. In other words, it is considered that the method for extracting index B was able to extract the effect of sheet elongation due to rolling.

[0047] Therefore, when applying the distribution of the maximum length in the rolling direction of the reflected light region 2 projected onto the surface of the metal strip 1 near the curved portion of the metal strip 1 lifted by loopers 71, 72, 73, and 74 installed between the rolling mill stands of the rolling line to the Chebyshev polynomial, and determining the distribution of sheet elongation due to rolling in the sheet width direction, it is preferable to use index B obtained by the processing of this embodiment. The method for extracting index B will be described below.

[0048] In this embodiment, the image processing computer 80 performs the following two analysis processes on each acquired image. The first analysis process performed by the image processing computer 80 is to number the acquired images 1, 2, 3, ..., k, ... in the order they are acquired, and for the (k)th image, it determines the rolling direction position Pumin(k)i of the pixel that is the most upstream in the rolling direction among the pixels constituting the upstream boundary line 2A of the reflected light region 2 within each divided region (i) (i=1~j) obtained by dividing the reflected light region 2 into j sections in the plate width direction. Similarly, it determines the rolling direction position Pdmax(k)i of the pixel that is the most downstream in the rolling direction among the pixels constituting the downstream boundary line 2B of the reflected light region 2. This data is stored in the database 81.

[0049] The second analysis process performed by the image processing computer 80 involves extracting the first position data, which represents the upstream position in the rolling direction within the divided area (i), from among the F data points from Pumin(k-F+1)i to Pumin(k)i stored in the database 81, for each of the F images from image number (k-F+1) to image number (k). This first position data is designated as Pure_min(k)i and used as the data for the (k)th image. Additionally, the second position data, which represents the downstream position in the rolling direction within the divided area (i), is extracted from among the F data points from Pdmax(k-F+1)i to Pdmax(k)i, and used as the data for the (k)th image. These are then stored in the database 81.

[0050] The difference in position data in the rolling direction [Pdre_max(k)i - Pure_min(k)i] is calculated for each divided area (i), and the j obtained [Pdre_max(k)i - Pure_min(k)i] values ​​are expressed as D(k)i, which is the index B (maximum length in the rolling direction of reflected light region 2) corresponding to the elongation of the rolled sheet in the (k)th image, and when the value indicating the position in the sheet width direction is taken as the variable (x), D(k)i corresponding to the position x normalized to the range -1 ≤ x ≤ 1 within the sheet width range is defined as E(xi) of the (k)th image. Note that xi is the center position in the sheet width direction of the divided area (i) expressed in (x) notation. The image processing computer 80 applies the central position xi in the plate width direction and the value of E(xi) (E(xi)=D(k)i) of each divided region (i) of the (k)-th image to the Chebyshev polynomial of equation (1) for each divided region (i), and using the least squares method, it obtains the coefficients of the Chebyshev polynomial (C0', C1', C2', C4') from the equation of the approximation curve, and transmits the linear coefficient (C1') as the detection result signal of the rolled plate elongation distribution of the linear component in the plate width direction.

[0051] As shown in Figure 8, the maximum length D(k)i of the reflected light region 2 in the rolling direction is obtained by matching the value of [Pdre_max(k)i - Pure_min(k)i] obtained in each divided region (i) to the central position of each divided region (i) in the plate width direction.

[0052] Preferably, the image processing computer 80 can further transmit, in addition to the first-order coefficient (C1'), one or more coefficients from among the second-order coefficient (C2') or the fourth-order coefficient (C4') as detection result signals of the rolled sheet elongation distribution of the second-order or fourth-order components in the sheet width direction.

[0053] Database 81 also functions as a recording medium containing various parameters used when operating the rolling mill 100.

[0054] In this embodiment, the database 81 can store first position data Pure_min(k)i(i=1~j) and second position data Pdre_max(k)i(i=1~j) in the rolling direction for each of the F images acquired consecutively from the (k-F+1)th image to the (k)th image, and for each of the regions (i) obtained by dividing the reflected light region 2 projected onto the surface of the metal strip into j sections in the width direction of the strip.

[0055] Here, regarding the method of dividing the reflected light region 2, each divided region (i) (i=1~j) divided into j sections in the plate width direction may be equally divided into j sections as shown in Figure 9, or each of the j sections may be unequally divided into arbitrary widths as shown in Figure 10.

[0056] Returning to Figure 1, the control device 82 is a device that controls the operation of each piece of equipment within the rolling mill 100. In this embodiment, it is a device that performs various controls in accordance with the detection of the plate shape of the metal strip 1 by the image processing computer 80.

[0057] These image processing computers 80, databases 81, and control devices 82 can be composed of computers having monitors 85 such as liquid crystal displays, input devices, storage devices, CPUs, memory, etc., and may be composed of a single computer, or each may be composed of separate computers; there are no particular limitations.

[0058] The operation of each device is controlled by the image processing computer 80 and the control device 82 based on various programs stored in the memory. The control processes performed by the image processing computer 80 and the control device 82 may be combined into a single program, each part may be divided into multiple programs, or a combination of these. Furthermore, some or all of the programs may be implemented in dedicated hardware or may be modularized.

[0059] The monitor 85 is a display device such as a screen or an audio device such as an alarm. For example, when the image processing computer 80 detects that there is a problem with the board shape, it is a device that informs the operator about the necessary corrective actions. Therefore, a screen is often used as such a monitor 85.

[0060] Here, the image processing computer 80 mentioned above includes a display signal unit, which transmits signals related to the content to be displayed on the monitor 85 to the control device 82 and the monitor 85.

[0061] During operation, the operator can visually check the state of the board shape by looking at the display screen of monitor 85, each stand itself, and the spaces between the stands.

[0062] Furthermore, the system is not limited to a configuration in which the operator is notified of a problem with the plate shape and the control device 82 automatically performs an operation to correct the problem with the plate shape. It can also be configured to simply display the problem on the monitor 85, or to omit the display on the monitor 85 and have only the control device 82 automatically perform an operation to correct the problem with the plate shape.

[0063] Next, the flow of the plate shape detection device and detection method for the rolled metal strip 1 in the present invention will be explained using Figures 11 and 12.

[0064] The method for calculating the index of the present invention is shown in Figure 11 as a flowchart.

[0065] As shown in Figure 11, before or during rolling, the image processing computer 80 sets the number of images F (for example, F=20) for determining the maximum rolling direction length of the reflected light region 2 (step S201), and also sets the image number k (step S202). Here, the initial value of the image number is k=1.

[0066] Subsequently, the image processing computer 80 acquires a surface image (image number k) of the metal strip 1 near the curved portion of the metal strip 1 that has been lifted by the loopers 71, 72, 73, and 74, which were captured by the cameras 61, 62, 63, and 64 (step S203). Here, the acquired images are numbered 1, 2, 3, ..., k, ... in the order they were acquired.

[0067] Next, the image processing computer 80 processes the images (image number k) captured by cameras 61, 62, 63, and 64 to extract the reflected light region 2 on the surface of the metal strip 1 near the curved portion of the metal strip 1 (step S204).

[0068] For example, the image processing computer 80 performs binarization on all pixels (image pixels) in the selected rolled surface image range from the images captured by cameras 61, 62, 63, and 64 to determine an appropriate brightness threshold. This determines the pixel coordinates that constitute the upstream boundary line 2A and the downstream boundary line 2B visible in the plate width direction on the upstream and downstream sides of the reflected light region 2 projected on the surface of the metal strip, thereby identifying the reflected light region 2. The details of this process can be based on known methods.

[0069] Next, the image processing computer 80 divides the reflected light region 2 extracted from the image (k) captured by cameras 61, 62, 63, and 64 into j sections in the plate width direction (for example, j=7) (step S205).

[0070] Next, the image processing computer 80 selects, within the range of each divided area (i) (i = 1 to j) of the reflected light area 2 extracted from the image (k) taken by the cameras 61, 62, 63, 64, the pixel with the most upstream rolling direction position among the positions of the pixels constituting the upstream boundary line 2A of the reflected light area 2, and preferably stores the rolling direction pixel position as "Pumin(k)i" in the database 81 (step S206). At the same time, the pixel with the most downstream rolling direction position among the positions of the pixels constituting the downstream boundary line 2B of the reflected light area 2 is selected, and the rolling direction pixel position is stored as "Pdmax(k)i" in the database 81 (step S207). These steps S206 and S207 can be in any order, can be processed in parallel, or step S207 can be processed prior to step S206.

[0071] Furthermore, the image processing computer 80 determines whether the image number k < F (step S208). When it is determined that the image number k < F, the process proceeds to step S209, where the image number k is updated (k = k + 1) (step S209), and the process proceeds to step S203, waiting for the processing of a predetermined number of images. In contrast, when it is determined in step S208 that the image number k ≧ F, the process proceeds to step S210.

[0072] Next, for each divided area (i) of the reflected light area 2, the image processing computer 80 compares "Pumin(k)i" stored in step S206 among the images with image numbers from (k - F + 1) to k, and re-extracts the pixel position indicating the most upstream position and preferably stores it as "Pure_min(k)i" in the database 81 (step S210). At the same time, "Pdmax(k)i" stored in step S207 is compared among the images with image numbers from (k - F + 1) to k, and the pixel position indicating the most downstream position is re-extracted and stored as "Pdre_max(k)i" in the database 81 (step S211).

[0073] Here, we assume that the rolling direction position of the pixel coordinates in the image increases as you move from the upstream side to the downstream side. Therefore, in the divided area (i), the upstreammost position within the upstream boundary line is denoted as "Pure_min(k)i", and the downstreammost position within the downstream boundary line is denoted as "Pdre_max(k)i".

[0074] Specifically, in Table 1 below (an example of resetting the first position data (Pure_min(k)i) and the second position data (Pdre_max(k)i), and an example of extracting index B), if the number of images is f, the database 81 stores the upstream and downstream data for each image when the reflected light region 2 is divided into j areas, targeting the (k-f+1)th image to the (k)th consecutive image. In each area, the first and second position data are reset from the f images, and the first position data is subtracted from the second position data to get D(k)i = [Pdre_max(k)i] - [Pure_min(k)i]. In this invention, this value D(k)i is used as index B for the kth image. Note that the representation of Pure_min(k)i and Pdre_max(k)i in the table is an example. In Table 1, the bolded Pumin represents the data point at the upstream position among the Pumin values ​​of f images from the (k-f+1)th image to the (k)th image, and the bolded Pdmax represents the data point at the downstream position among the Pdmax values ​​of f images from the (k-f+1)th image to the (k)th image.

[0075] [Table 1]

[0076] For example, in the case shown in Table 1, the reflected light region 2 is divided into j regions in the plate width direction, and in the first region of the divided region i=1, the pixel in the rolling direction that is the most upstream of the pixels constituting the upstream boundary line 2A of the reflected light region 2 is selected, and this rolling direction position is designated as Pumin(k)1 in the k-th image. However, in the f images used as the evaluation target images, Pumin(1)1 is used in the (k-f+1)th image, Pumin(2)1 is used in the (k-f+2)th image, When the notation is changed to Pumin(3)1, ..., in the (k-f+3)th image, and Pumin(f)1 in the kth image, if the upstream position among the Pumin(1 / ... / f)1 of these f images is Pumin(1)1 in the (k-f+1)th image, then this upstream rolling direction position, Pumin(1)1, is reset and saved as "Pure_min(k)1" as the rolling direction position indicating the uppermost point at image number k.

[0077] Similarly, in the first region of the divided region i=1, the downstreammost pixel in the rolling direction is selected among the pixels that constitute the downstream boundary line 2B of the reflected light region 2, and this rolling direction position is designated as Pdmax(k)1 in the k-th image. However, when the notation is changed to Pdmax(1)1 in the (k-f+1)th image, Pdmax(2)1 in the (k-f+2)th image, Pdmax(3)1... in the (k-f+3)th image, and Pdmax(f)1 in the k-th image, if the downstreammost position among the Pdmax(1 / ... / f)1 of these f images is Pdmax(3)1 in the (k-f+3)th image, then this furthest downstream rolling direction position, Pdmax(3)1, is reset and saved as "Pdre_max(k)1" to represent the furthest downstream rolling direction position for image number k.

[0078] Similarly, in the second region of the divided region i=2, the upstream pixel in the rolling direction among the pixels constituting the upstream boundary line 2A of the reflected light region 2 is selected, and this rolling direction position is denoted as Pumin(k)2 in the k-th image. However, when the notation is changed for the f images used as the evaluation target, to Pumin(1)2 in the (k-f+1)th image, Pumin(2)2 in the (k-f+2)th image, Pumin(3)2 in the (k-f+3)th image, ..., and Pumin(f)2 in the k-th image, the upstream position among the Pumin(1 / ... / f)2 of these f images is the (k-f+1)th image If Pumin(1)2 is the position at the time of image number k, this upstream position Pumin(1)2 is reset and saved as "Pure_min(k)2" as the rolling direction position indicating the upstreammost point at image number k. Additionally, if the downstreammost rolling direction pixel position Pdmax(1 / ··· / f)2 among the pixel positions constituting the downstream boundary line 2B of the reflected light region 2 is Pdmax(2)2 in the (k-f+2)th image, this downstreammost position Pdmax(2)2 is reset and saved as "Pdre_max(k)2" as the rolling direction position indicating the downstreammost point at image number k.

[0079] These "Pure_min(k)i" and "Pdre_max(k)i" values ​​are reset for each division area from i=1 to i=j.

[0080] Next, the image processing computer 80 calculates the difference between the furthest downstream position "Pdre_max(k)i" re-extracted at the position of the downstream boundary line 2B in each divided area (i) of the reflected light region 2 at the time of the camera image (k) obtained in steps S210 and S211 above, and the furthest upstream position "Pure_min(k)i" re-extracted at the position of the upstream boundary line 2A, as the maximum rolling direction length of the reflected light region 2 "D(k)i=[Pdre_max(k)i]-[Pure_min(k)i]" (step S212).

[0081] Next, the image processing computer 80 re-expresses the center position in the plate width direction of each divided area (i) when the reflected light region 2 is divided in the plate width direction using the variable (x) of the plate width direction position in each divided area (i). The maximum rolling direction length "D(k)i" of the reflected light region 2 in each divided area (i) obtained at the time of the camera image (k) in step S212 is associated with the center position (xi) in the plate width direction of the divided area (i), and E(xi) = D(k)i is curve-fitted to the Chebyshev polynomial of equation (1), and the Chebyshev coefficients (C0', C1', C2', C4') obtained from the resulting approximation are calculated (step S213).

[0082] Next, the image processing computer 80 transmits the Chebyshev coefficients (C1', C2', C4') obtained in step S213 as detection result signals of the plate elongation distribution in the k-th image to, for example, the control device 82 or the monitor 85 (step S214).

[0083] Subsequently, the image processing computer 80 determines whether or not rolling is continuing (step S215). If it determines that rolling is continuing, it returns to step S209 and continues the plate shape detection process. If it determines that rolling is complete, it terminates the process.

[0084] In this embodiment, a cubic component is not used in the Chebyshev polynomial. This is because the rolling control mechanism of the rolling mill is not designed to handle sheet elongation correction for the cubic component. By omitting the calculation processing and handling means for the cubic component, it becomes easier to judge the condition of the rolled sheet shape and correct sheet elongation for the separated primary, quaternary, and quartic components.

[0085] The image processing computer 80 can output a control command signal to the control device 82 to correct the leveling, bending force, pair crossing angle, etc. based on the polynomial approximation result in the plate width direction obtained using the Chebyshev polynomial of equation (1). Furthermore, alternatively, or in addition, by outputting a display command signal for performing guidance display necessary for correcting the leveling, bending force, pair crossing angle, etc. to the monitor 85, the operator can be informed of correction information such as the leveling, bending force, pair crossing angle, etc.

[0086] Preferably, the image processing computer 80 outputs a signal to the monitor 85 to display the graphs of the 0th component [C0'], 1st component [C1'×x], 2nd component [C2'×(2x 2 -1)], and 4th component [C4'×(8x 4 -8x 2 +1)] of each component term of the function of each degree term vector (C0’, C1’, C2’, C4’) in the Chebyshev polynomial E(x) of the above-mentioned equation (1). The screen displayed on the monitor 85 becomes, for example, the screen as shown in FIG. 12.

[0087] FIG. 12 is a diagram showing an example of the display screen of the monitor 85. In FIG. 12, examples of the distribution displays of the 0th, 1st, 2nd, and 4th components of the Chebyshev polynomial are shown at the plate width direction positions (-1≦x≦1) within the plate width. The operator can perform an operation to correct, for example, the leveling, bending force, pair crossing angle (in the case of a pair crossing rolling mill), etc. by checking the display screen of the monitor 85 shown in this FIG. 12.

[0088] Among the coefficients of the Chebyshev polynomial of equation (1), since the coefficient (C1’) of the 1st component indicates the index of unilateral elongation, the leveling of the backup rolls 41 on the drive side (DS) and the work side (WS) on the upstream side of the corresponding camera 64, and / or the backup rolls 51 on the drive side (DS) and the work side (WS) on the downstream side is operated, and an operation command signal is output to the control device 82 to normalize the 1st component (within the target range).

[0089] The coefficient of the quadratic component (C2') of the Chebyshev polynomial coefficients in equation (1) indicates an indicator of edge elongation or mid-roll elongation. Therefore, one or more of the following operations are performed: an operation command signal is output to the control device 82 to operate the bending device of the work roll / intermediate roll of the F4 stand 40, which is the upstream rolling mill of the camera 64, and / or the F5 stand 50, which is the downstream rolling mill; to operate the pair cross angle in the case of a pair cross rolling mill; or, in the case of a work roll shift / intermediate roll shift rolling mill, to shift the work roll / intermediate roll in advance by predicting mid-roll elongation / edge elongation because it is difficult to shift during rolling, thereby normalizing the quadratic component (to within the target range).

[0090] The coefficient of the fourth-order component (C4') of the Chebyshev polynomial coefficients in equation (1) indicates an index of quarter elongation. Therefore, in order to correct quarter elongation, one or more of the following operations are performed: The bending operation of the work roll bending device of the F4 stand 40, which is the upstream rolling mill of the camera 64, and / or the F5 stand 50, which is the downstream rolling mill, is performed, and in the case of a pair cross mill, the pair cross angle is operated together with the bending operation or independently. In the case of a 6-stage intermediate roll shift rolling mill, the quarter elongation is predicted in advance and the intermediate rolls are shifted to the appropriate position. By outputting operation command signals to the control device 82 to perform the bending operation and pair cross angle operation, the fourth-order component indicating quarter elongation is normalized (to within the target range so that the target plate shape is achieved). Note that quarter elongation is more likely to occur when the roll diameter is small relative to the roll length, as the roll is more likely to bend in the region of the roll width end due to the bending operation, but it can be normalized by the above operations.

[0091] Next, the effects of this embodiment will be described.

[0092] In the metal strip 1 plate shape detection device in the rolling mill of the above-described embodiment, the image processing computer 80 numbers the acquired images as 1, 2, 3, ..., k, ... in the order they are acquired, and in the (k)th image, the reflected light region 2 is divided into j sections in the plate width direction, and in each divided section (i) (i=1~j), the upstream position Pumin(k)i of the pixels that constitute the upstream boundary position of the reflected light region 2 is determined with respect to the rolling direction of the pixel coordinates, and the downstream boundary position of the pixels that constitute the downstream boundary position of the reflected light region 2 is determined. Then, the furthest downstream position Pdmax(k)i is determined, and for each of the two or more obtained F images from image number (k-F+1) to image number (k), the data representing the furthest upstream position is extracted from the F data from Pumin(k-F+1)i to Pumin(k)i and set as the first position data, which is then reset as Pure_min(k)i for the (k)th image, and the furthest downstream position is extracted from the F data from Pdmax(k-F+1)i to Pdmax(k)i. The data indicating the side position is extracted as the second position data, and this is reset as Pdre_max(k)i as the data for the (k)-th image. The difference in position data in the rolling direction [Pdre_max(k)i - Pure_min(k)i] is calculated for each divided area (i), and [Pdre_max(k)i - Pure_min(k)i] is taken as information D(k)i corresponding to the maximum rolling direction length of the reflected light region of the (k)-th image, and is associated with the position of the center in the plate width direction of the divided area (i), and the plate width direction position When the value representing this is taken as the variable (x), the position in the width direction within the plate width range of the reflected light region 2 in the image is normalized to the range -1≦x≦1, and the value of the maximum rolling direction length D(k)i=[Pdre_max(k)i―Pure_min(k)i] of the reflected light region 2 is used as an index corresponding to the rolled plate elongation distribution in the width direction obtained from the (k)th image, and the notation for the position in the width direction is changed to (x), so D(k)i=E(xi). Equation (1) E(x) = C0'+C1'×x+C2'×(2x 2 -1) + C4' × (8x 4 -8x 2By applying the Chebyshev polynomial (+1) (where -1≦x≦1), the coefficients of the Chebyshev polynomial (C0', C1', C2', C4') are obtained from E(xi) with j values ​​of x (xi) by curve fitting, and the coefficient of the first term (C1') is transmitted as the detection result signal of the rolled sheet elongation distribution of the first component in the sheet width direction of the (k)-th image. Here, xi is the position of the center in the sheet width direction of the divided area (i) obtained by dividing the reflected light region 2 into j sections in the sheet width direction, expressed in (x) notation. Note that for the normalized sheet width direction position (x) in -1≦x≦1, for example, x=-1 indicates the end position of the sheet width on the drive side, x=0 indicates the center position of the sheet width, and x=1 indicates the end position of the sheet width on the work side. Also, F, i, j, and k are integers.

[0093] This makes it possible to evaluate changes in plate elongation distribution, which could not be addressed by the aforementioned Patent Document 1, with high accuracy.

[0094] Furthermore, the image processing computer 80 transmits one or more coefficients from among the first-order coefficient (C1'), second-order coefficient (C2'), or fourth-order coefficient (C4') as detection result signals of the rolled sheet elongation distribution of the first-order, second-order, or fourth-order components in the sheet width direction, thereby enabling it to respond to a wider range of sheet shape changes.

[0095] <Other> It should be noted that the present invention is not limited to the embodiments described above, and various modifications and applications are possible. The embodiments described above are explained in detail for the purpose of clearly illustrating the present invention, and are not necessarily limited to those having all the configurations described. [Explanation of symbols]

[0096] 1...Metal strip 2...Reflected light area 2A... Upstream boundary line of the reflected light region 2B... Downstream boundary line of the reflected light region 10…F1 Stand 11, 21, 31, 41, 51… Reducing cylinders 12, 22, 32, 42, 52… Load detectors 20…F2 Stand 30…F3 Stand 40…F4 Stand 50…F5 stand 61, 62, 63, 64… Camera 71, 72, 73, 74… Looper 80…Image processing computer (image processing unit) 81…Database 82...Control device 85... Monitor 90...communication line 100...Rolling equipment

Claims

1. In a rolling mill, a camera is installed to capture an image that includes the area in which a band-shaped region, called the reflected light region, which is transverse in the width direction of the sheet and reflects illumination light, can be observed on the surface of a metal strip lifted by a looper. A rolled metal strip shape detection device comprising: an image processing unit for detecting the shape of the metal strip based on the image captured by the camera, The aforementioned image processing unit, The images were numbered 1, 2, 3, ..., k, ... in the order they were acquired. In the (k)-th image, within each of the division areas (i) (i=1 to j) obtained by dividing the reflected light region into j sections in the plate width direction, Pumin(k)i is determined as the most upstream pixel position constituting the upstream boundary line of the reflected light region with respect to the rolling direction of the pixel coordinates, and Pdmax(k)i is determined as the most downstream pixel position constituting the downstream boundary line of the reflected light region. For each of the F images obtained, from image number (k-F+1) to image number (k), the data indicating the upstream position is extracted from the F data from Pumin(k-F+1)i to Pumin(k)i as the first position data, and this is reset as Pure_min(k)i as the data for the (k)th image. From the F data points from Pdmax(k-F+1)i to Pdmax(k)i, the data point indicating the furthest downstream position is extracted as the second position data, and this is reset as Pdre_max(k)i as the data for the (k)th image. The difference in the rolling direction position data [Pdre_max(k)i - Pure_min(k)i] is calculated for each divided area (i), and [Pdre_max(k)i - Pure_min(k)i] is taken as information D(k)i corresponding to the maximum rolling direction length of the reflected light region of the (k)-th image, and the value of the information D(k)i is assigned to the position of the center in the plate width direction of the divided area (i). When the value indicating the position in the width direction of the plate is taken as the variable (x), the position in the width direction of the plate within the plate width range of the reflected light region in the image is normalized to the range -1 ≤ x ≤ 1, and the value of the j pieces of information D(k)i is used as an index corresponding to the rolled plate elongation distribution in the width direction of the plate obtained from the (k)th image, the notation for the position in the width direction of the plate is changed to (x), and D(k)i = E(xi), consisting only of the 0th, 1st, 2nd, and 4th order terms of x. E(x) = C ０ '+C １ × x + C ２ '×(2x ２ -1) + C ４ '×(8x ４ -8x ２ Substituting this into the Chebyshev polynomial (+1) (where -1 ≤ x ≤ 1), we get E(xi) with j values ​​of x (xi), The coefficients (C ０ ’, C １ ’, C ２ ’, C ４ ’) of the Chebyshev polynomial are obtained, and the coefficient (C １ ’) of the first-order term is transmitted as a detection result signal of the rolling plate elongation distribution of the first-order component in the sheet width direction of the (k)-th image Here, xi represents the central position in the width direction of the divided region (i) obtained by dividing the reflected light region into j sections in the width direction of the plate, as denoted by (x). Note that F, i, j, and k are integers. A device for detecting the shape of metal strips.

2. In the metal strip shape detection device according to claim 1, The image processing unit determines the coefficient of the second term (C ２ ') or the coefficient of the fourth term (C ４ The system further transmits one or more of the aforementioned coefficients as a detection result signal of the rolled sheet elongation distribution of the second or fourth component in the sheet width direction. A device for detecting the shape of metal strips.

3. A metal strip plate shape detection device according to claim 1 or 2, In a rolling mill equipped with a control device, Based on the detection result signal, the control device transmits one or more operation signals related to the leveling amount of the rolling mill, the bending force, or the pair cross angle. Rolling mill.

4. In a rolling mill, the shooting step involves using a camera to capture an image of the surface of a metal strip lifted by a looper, including an area where a band-shaped illumination light, called the reflected light region, is reflected across the width of the strip. A method for detecting the shape of a rolled metal strip, comprising: an image processing step for detecting the shape of the metal strip based on the image captured in the aforementioned shooting step, In the aforementioned image processing step, The images were numbered 1, 2, 3, ..., k, ... in the order they were acquired. In the (k)-th image, within each of the division areas (i) (i=1 to j) obtained by dividing the reflected light region into j sections in the plate width direction, Pumin(k)i is determined as the most upstream pixel position constituting the upstream boundary line of the reflected light region with respect to the rolling direction of the pixel coordinates, and Pdmax(k)i is determined as the most downstream pixel position constituting the downstream boundary line of the reflected light region. For each of the F images obtained, from image number (k-F+1) to image number (k), the data indicating the upstream position is extracted from the F data from Pumin(k-F+1)i to Pumin(k)i as the first position data, and this is reset as Pure_min(k)i as the data for the (k)th image. From the F data points from Pdmax(k-F+1)i to Pdmax(k)i, the data point indicating the furthest downstream position is extracted as the second position data, and this is reset as Pdre_max(k)i as the data for the (k)th image. The difference in the rolling direction position data [Pdre_max(k)i - Pure_min(k)i] is calculated for each divided area (i), and [Pdre_max(k)i - Pure_min(k)i] is taken as information D(k)i corresponding to the maximum rolling direction length of the reflected light region of the (k)-th image, and the value of the information D(k)i is assigned to the position of the center in the plate width direction of the divided area (i). When the value indicating the position in the width direction of the plate is taken as the variable (x), the position in the width direction of the plate within the plate width range of the reflected light region in the image is normalized to the range -1 ≤ x ≤ 1, and the value of the j pieces of information D(k)i is used as an index corresponding to the rolled plate elongation distribution in the width direction of the plate obtained from the (k)th image, the notation for the position in the width direction of the plate is changed to (x), and D(k)i = E(xi), consisting only of the 0th, 1st, 2nd, and 4th order terms of x. E(x) = C ０ '+C １ × x + C ２ '×(2x ２ -1) + C ４ '×(8x ４ -8x ２ Substituting this into the Chebyshev polynomial (+1) (where -1 ≤ x ≤ 1), we get E(xi) with j values ​​of x (xi), The coefficient (C) of the Chebyshev polynomial. ０ ', C １ ', C ２ ', C ４ Find the coefficient of the linear term (C) １ The (k)-th image is transmitted as the detection result signal of the rolled sheet elongation distribution of the first component in the sheet width direction. Here, xi represents the central position in the width direction of the divided region (i) obtained by dividing the reflected light region into j sections in the width direction of the plate, as denoted by (x). Note that F, i, j, and k are integers. A method for detecting the shape of a metal strip.

Images