EP2737963A1 - Procédé de calcul de déformation et système de laminage - Google Patents

Procédé de calcul de déformation et système de laminage Download PDF

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Publication number
EP2737963A1
EP2737963A1 EP12877083.1A EP12877083A EP2737963A1 EP 2737963 A1 EP2737963 A1 EP 2737963A1 EP 12877083 A EP12877083 A EP 12877083A EP 2737963 A1 EP2737963 A1 EP 2737963A1
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EP
European Patent Office
Prior art keywords
distortion
steel sheet
rolling
profile
rolled steel
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Granted
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EP12877083.1A
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German (de)
English (en)
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EP2737963A4 (fr
EP2737963B1 (fr
Inventor
Tooru Akashi
Shigeru Ogawa
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Nippon Steel Corp
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Nippon Steel and Sumitomo Metal Corp
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Publication of EP2737963A1 publication Critical patent/EP2737963A1/fr
Publication of EP2737963A4 publication Critical patent/EP2737963A4/fr
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B38/00—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product
    • B21B38/02—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product for measuring flatness or profile of strips
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21C—MANUFACTURE OF METAL SHEETS, WIRE, RODS, TUBES OR PROFILES, OTHERWISE THAN BY ROLLING; AUXILIARY OPERATIONS USED IN CONNECTION WITH METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL
    • B21C51/00—Measuring, gauging, indicating, counting, or marking devices specially adapted for use in the production or manipulation of material in accordance with subclasses B21B - B21F
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B2263/00—Shape of product
    • B21B2263/04—Flatness
    • B21B2263/06—Edge waves
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B2263/00—Shape of product
    • B21B2263/04—Flatness
    • B21B2263/08—Centre buckles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
    • B21B37/38—Control of flatness or profile during rolling of strip, sheets or plates using roll bending
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
    • B21B37/40—Control of flatness or profile during rolling of strip, sheets or plates using axial shifting of the rolls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B38/00—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product
    • B21B38/04—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product for measuring thickness, width, diameter or other transverse dimensions of the product
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B38/00—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product
    • B21B38/06—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product for measuring tension or compression

Definitions

  • This invention relates to a method of computing distortion and internal stress of flat-rolled steel and a rolling system.
  • the purpose of rolling a steel sheet is to obtain a steel plate or sheet of desired thickness, width and length (hereinafter sometimes called “desired values” or “target value”) from a pre-rolled steel by using a rolling mill to apply stress to a steel plate or sheet.
  • desired values or “target value”
  • target value desired thickness, width and length
  • the stress exerted on the flat steel by the rolling mill (hereinafter sometimes called “total stress”) is consumed 1) by distortion for achieving a predetermined size with the desired values, 2) by distortion that causes the different surface undulations as deviations from the desired values, and 3) as residual stress in the flat steel.
  • Patent Document 1 teaches a technique for ascertaining flat steel deformation due to strain, which uses a measuring device equipped with multiple optical rangefinders and associates measured steel thickness with position on the plane of the flat steel. Patent Document 1 additionally teaches a technique for inhibiting deformation of a rolled steel sheet by regulating roll position and roll force based on the flat steel deformation measured after rolling.
  • Patent Document 2 teaches a technique that utilizes measurement data obtained by continuously measuring the distortion of a rolled steel sheet in combination with a predicted profile model for measuring distortion to regulate work roll bending forces so as to sequentially correct profile defects of a steel sheet during rolling.
  • the predicted profile model is sequentially corrected based on the measured distortion taking into account a dead zone corresponding to a threshold value of the distortion appearing in an undulation on the surface of the rolled steel sheet.
  • Non-patent Document 1 describes a technology for analyzing the mechanisms of edge wave and center buckle occurrence by approximation using edge wave equations and center buckle buckling equations.
  • Non-patent Document 2 describes a technique for analyzing the buckling critical point that is the threshold value of the distortion appearing in an undulation on the surface of the rolled steel sheet.
  • Patent Document 3 teaches a technique for applying the buckling equations set out in Non-patent Document 1. Specifically, Patent Document 3 describes a technique for separating the difference between the total stress and the stress corresponding to the desired distortion of the steel sheet by the rolling into the stress component relieved by conversion into distortion appearing in an undulation after cooling and the stress component still remaining inside the steel sheet after the deformation. Patent Document 3 additionally sets out a technique based on the aforesaid for predicting the wave shape occurring when the steel sheet is cooled. In the techniques of Patent Document 3, the stress component relieved by conversion into distortion appearing in an undulation after cooling is obtained by subtracting the stress component still remaining inside the steel sheet after the deformation from the difference between the total stress and the stress corresponding to the desired distortion of the steel sheet by the rolling.
  • the waveform after cooling is predicted by comparing the stress component obtained by the subtraction and the distortion computed from the steepness.
  • the difference between the total stress and the stress corresponding to the desired distortion of the steel sheet by the rolling is treated as a known value estimated from the temperature distribution and the like.
  • Patent Document 2 does not offer a method for calculating a dead zone corresponding to a threshold value of the distortion appearing in an undulation on the surface of the rolled steel sheet.
  • the control by the technique of Patent Document 2 is likely to be complicated because the subject of the control is the rate of crown variation, which is nonlinear.
  • Patent Document 3 is to separate the difference between the total stress and the stress corresponding to the desired distortion of the steel sheet by the rolling into the stress component relieved by conversion into distortion appearing in an undulation and the stress component still remaining inside the steel sheet after the deformation.
  • it provides no description or suggestion whatsoever regarding a method by which the difference between the total stress and the stress corresponding to the desired distortion of the steel sheet by the rolling can be calculated based on the stress component relieved by conversion into distortion appearing in an undulation and the stress component still remaining inside the steel sheet after the deformation.
  • an object of the present invention is to provide a computation method for computing difference between distortion corresponding to total stress and distortion for achieving predetermined size with desired values based on difference between distortion appearing in an undulation on a steel sheet surface as deviations from the desired values of the rolled steel sheet and distortion corresponding to internal stress of the rolled steel sheet, and also to provide a rolling system.
  • Second and third distortions are defined as follows.
  • first distortion The difference between distortion which should correspond to the stress applied to a steel sheet from a rolling mill and distortion for achieving predetermined size with a desired value is called first distortion.
  • Distortion appearing in an undulation on a surface of a rolled steel sheet that constitutes deviation from a desired value of the rolled steel sheet is called second distortion.
  • Distortion corresponding to internal stress of a rolled steel sheet is called third distortion.
  • the gist of the present invention is as set out below.
  • the present invention can compute first distortion indicating difference between distortion corresponding to stress applied to the steel sheet from a rolling mill and distortion for achieving predetermined size with the desired value.
  • the present invention can improve steel sheet yield when the tensile strength of the rolled steel sheet is small.
  • it can improve the yield of the portion (sometimes called the "head") rolled between the start of rolling and the occurrence of coiling tensile strength.
  • the present invention can improve the yield of the portion (sometimes called the "tail”) rolled just before the completion of rolling when tensile strength is low.
  • a rolling system according to the present invention which is equipped with a power supply selector circuit, is explained below with reference to FIGs. 1 to 12 .
  • a first embodiment of the rolling system is explained with reference to FIGs. 1 to 8 .
  • FIG. 1 is a circuit block diagram of an example of a rolling system according to a first embodiment.
  • the rolling system designated by reference symbol 1, has a distortion processing unit 10, a hot tandem rolling mill 20 (hereinafter sometimes called simply "rolling mill 20") for rolling a steel sheet 101 in the direction of arrow A.
  • the rolling system 1 additionally includes a profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33 for detecting the profile, thickness, width and tensile strength of the rolled steel sheet 101.
  • the distortion processing unit 10 has an arithmetic unit 11, a memory unit 12, and an I/O unit 13.
  • the hot tandem rolling mill 20 has multiple stands 21 for sequentially rolling the steel sheet 101, multiple conveyor rollers 22 for conveying the steel sheet 101, and a rolling control unit 23 for regulating the roll positions and roll pressures of the individual stands 21.
  • the arithmetic unit 11 is equipped with a CPU (Central Processing Unit) and a DSP (digital signal processor). Utilizing programs stored in the memory unit 12, the arithmetic unit 11 processes data received from the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33 to compute first distortion ⁇ 1 indicating the difference between distortion corresponding to total stress and distortion for achieving predetermined size with desired values.
  • a CPU Central Processing Unit
  • DSP digital signal processor
  • the memory unit 12 has a nonvolatile memory for storing various programs and a volatile memory for temporarily storing data.
  • the memory unit 12 stores programs executed by the arithmetic unit 11 and an OS and other basic software required for executing the programs.
  • the memory unit 12 also stores detection data received from the profilometer 30, thickness meter 31, width meter 32, and tensile strength meter 33.
  • the I/O unit 13 converts detection data transmitted from the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33 into data processable by the arithmetic unit 11.
  • the detection data received by the I/O unit 13 is stored in the memory unit 12.
  • the I/O unit 13 sends the data processed by the arithmetic unit 11 to the rolling control unit 23.
  • each of the stands 21 has a pair of upper and lower work rolls and a pair of backup rolls arranged to sandwich the work rolls.
  • the stands 21 can have any number of rolls and, for example, can be two-high, four-high or six-high.
  • each stand 21 comprises profile control actuators (not illustrated). The profile control actuators operate in accordance with control signals received from the rolling control unit 23 to apply predetermined rolling loads to the steel sheet 101 and impart various contours to the steel sheet 101 by bender, work roll shift, pair cross and other rolling.
  • the profilometer 30 comprises multiple point-like light sources and an image pickup device. It detects the profile of the rolled steel sheet 101 by imaging light sequentially projected from the multiple point-like light sources onto upper surface of the steel sheet 101 in the rolling direction and vertically.
  • the thickness meter 31 is an X-ray thickness meter that detects the thickness of the steel sheet 101.
  • the width meter 32 is a spot-type laser beam distance meter that detects the width of the steel sheet 101.
  • the tensile strength meter 33 includes two detectors arranged at a predetermined spacing. It detects the tensile strength of the steel sheet 101 by using the two detectors to detect detection holes formed in the steel sheet 101.
  • FIG. 2 is a function block diagram of the arithmetic unit 11 of the distortion processing unit 10.
  • the arithmetic unit 11 has a profile data analyzing unit 51, a second-distortion arithmetic unit 52, a boundary condition determination unit 53, a third-distortion arithmetic unit 54, and a first-distortion arithmetic unit 55.
  • the arithmetic unit 11 executes the programs stored in the memory unit 12 to perform the processing by these constituent elements 51 to 255.
  • the profile data analyzing unit 51 analyzes the profile of the steel sheet 101 detected by the profilometer 30 to determine the wavelength 2L of the rolling-direction component of an undulation appearing periodically on the steel sheet 101 and the height direction displacement at every detection site on the surface of the steel sheet 101.
  • FIG. 3(a) illustrates an analysis image 300 obtained by plotting an example of data analyzed by the profile data analyzing unit 51 from the profile of the steel sheet 101 detected by the profilometer 30.
  • the analysis image 300 has an x coordinate axis, a y coordinate axis and a z coordinate axis.
  • the x coordinate axis corresponds to the rolling direction at the width-direction central region of the steel sheet 101.
  • the y coordinate axis corresponds to the width direction of the steel sheet 101.
  • the z coordinate axis corresponds to the height direction of the steel sheet 101.
  • the sine-wave shaped cross-section of the analysis image 300 corresponds to a section of a width-direction edge region of the steel sheet 101.
  • the analysis image 300 has a sine-wave-shaped cross-section at the width-direction edge region.
  • a sine-wave-shaped cross-section is formed along the x coordinate axis corresponding to the width-direction central region of the steel sheet 101, with no formation of an undulation at the width-direction edge region of the steel sheet 101.
  • the second-distortion arithmetic unit 52 computes from data analyzed by the profile data analyzing unit 51 second distortion ⁇ 2 appearing in an undulation on a surface of the steel sheet that constitutes deviation from a desired value of the rolled steel sheet.
  • the second-distortion arithmetic unit 52 sequentially computes distortion ⁇ j , at j th width positions in accordance with Mathematical (1) to (3).
  • dx ij is the distance between adjacent detection sites in the x-axis direction and dz ij is the distance in the z-axis direction between detection sites corresponding to dx ij .
  • L is the half-wavelength of the rolling-direction component of an undulation appearing periodically on the steel sheet 101 and ⁇ j is a value including the z-direction height of the width-direction central region of the steel sheet 101 and the value of the second distortion ⁇ 2 of the j th site in the width direction.
  • FIG. 3(b) is a diagram illustrating a relationship between second distortion ⁇ 2 computed using Mathematical (1) to (3) and width-direction position of a steel sheet 101.
  • the boundary condition determination unit 53 determines from data analyzed by the profile data analyzing unit 51 whether the distortion appearing in an undulation on the surface of the rolled steel sheet 101 is edge wave, center buckle, or quarter wave.
  • FIG. 4 is a diagram illustrating the determination processing flow of the boundary condition determination unit 53.
  • step S101 the boundary condition determination unit 53 compares the height of a width-direction quarter region of the steel sheet 101 with the heights of the width-direction central region and edge region of the steel sheet 101.
  • step S102 the boundary condition determination unit 53 determines that the peak height of the width-direction quarter region of the steel sheet 101 is higher.
  • step S103 the boundary condition determination unit 53 determines that the peak height of the width-direction quarter region of the steel sheet 101 is lower, processing goes to step S103.
  • the boundary condition determination unit 53 determines in step S101 that the height of the width-direction quarter region of the steel sheet 101 is higher, the boundary condition determination unit 53 determines in step S102 that the profile of the distortion appearing in an undulation on the surface of the steel sheet 101 is quarter wave.
  • the boundary condition determination unit 53 determines in step S101 that the height of the width-direction quarter region of the steel sheet 101 is lower, the boundary condition determination unit 53 compares the heights of the width-direction central region and edge region of the steel sheet 101.
  • the boundary condition determination unit 53 determines in step S103 that the height of the width-direction central region of the steel sheet 101 is higher, the boundary condition determination unit 53 determines in step S104 that the profile of the distortion appearing in an undulation on the surface of the steel sheet 101 is center buckle.
  • the boundary condition determination unit 53 determines in step S103 that the height of the width-direction central region of the steel sheet 101 is lower, the boundary condition determination unit 53 determines in step S105 that the profile of the distortion appearing in an undulation on the surface of the steel sheet 101 is edge wave.
  • FIG. 5 is a set of diagrams schematically illustrating boundary conditions determined by the undulation of the steel sheet 101.
  • FIG. 5(a) illustrates a boundary condition in the case where the profile of distortion appearing in an undulation on the surface of the steel sheet is edge wave.
  • FIG. 5(b) illustrates a boundary condition in the case where the profile of distortion appearing in an undulation on the surface of the steel sheet is center buckle.
  • FIG. 5(c) illustrates a boundary condition in the case where the profile of distortion appearing in an undulation on the surface of the steel sheet is quarter wave.
  • the distortion profile appearing in an undulation on the surface of the steel sheet 101 illustrated in FIG. 5(a) is edge wave.
  • the boundary condition of the steel sheet 101 in FIG. 5(a) is a condition wherein width-direction displacement and height-direction displacement are restrained at the central region and unrestrained at the edge region of the width-direction section (hereinafter sometimes called the "C-section").
  • the distortion profile appearing in an undulation on the surface of the steel sheet 101 illustrated in FIG. 5(b) is center buckle.
  • the boundary condition of the steel sheet 101 in FIG. 5(b) is a condition wherein rotation around the rolling direction is constrained at the central region and height-direction displacement is constrained at the edge region of the C-section.
  • the distortion profile appearing in an undulation on the surface of the steel sheet 101 illustrated in FIG. 5(c) is quarter wave.
  • the boundary condition of the steel sheet 101 in FIG. 5(c) is a condition wherein width-direction displacement and height-direction displacement are restrained at both the central region and edge region of the C-section.
  • the third-distortion arithmetic unit 54 computes third distortion ⁇ 3 indicating distortion corresponding internal stress of the rolled steel sheet 101.
  • the third-distortion arithmetic unit 54 performs buckling analysis using buckling equations to compute the third distortion ⁇ 3 from the thickness, width and tensile strength of the rolled steel sheet 101, the boundary condition determined by the boundary condition determination unit 53, and the wavelength of the rolling-direction component of the undulation appearing periodically on the steel sheet 101.
  • the third-distortion arithmetic unit 54 solves the buckling equations indicated in Mathematical (4) to (11) for each predetermined width-direction position.
  • the third-distortion arithmetic unit 54 determines threshold values (criteria) of the third distortion ⁇ 3 of the rolled steel sheet 101 from the solutions obtained.
  • the threshold value of the third distortion ⁇ 3 determined by the third-distortion arithmetic unit 54 is a value indicating that the steel sheet 101 experiences second distortion when distortion equal to or greater than this value remains in the steel sheet 101. It is assumed here that second distortion occurs in the rolled steel sheet 101 in the case where distortion equal to or greater than the third distortion ⁇ 3 threshold value value remains in the rolled steel sheet 101. In other words, it is assumed that a steel sheet 101 in which second distortion occurred has residual internal distortion corresponding to at least the threshold value of the third distortion ⁇ 3 .
  • w indicates the height-direction displacement of the undulation
  • subscript 1 indicates displacement increment after buckling
  • b is half the length of the width of the rolled steel sheet 101
  • h is the thickness of the rolled steel sheet 101
  • ⁇ f is the tensile strength of the rolled steel sheet 101.
  • E indicates Young's modulus and ⁇ indicates Poisson's ratio.
  • D Eh 3 / 12 ⁇ 1 - ⁇ 2
  • the width-direction component w (y) of the height-direction displacement of the undulation of the rolled steel sheet 101 is, as indicated by Mathematical 7, defined as a cubic function with origin at the width-direction central region.
  • w y a 1 + a 2 ⁇ y 1 + a 3 ⁇ y 2 + a 4 ⁇ y 3
  • the rolling-direction component of the height-direction displacement of the undulation of the rolled steel sheet 101 is defined as a sine curve of wavelength 2L.
  • wavelength 2L is given as a variable within a predetermined range.
  • the width-direction component of the third distortion distribution is defined as a non-dimensional quadratic curve with origin at the width-direction central region.
  • ⁇ x * y 1 / b 2 y 2 0 ⁇ y ⁇ b
  • Mathematical (10) is derived when Mathematical (3) is simplified by integration over half-wavelength L.
  • F L ⁇ 0 b ⁇ ⁇ w 1 h ⁇ ⁇ ⁇ f + Eh ⁇ ⁇ m * - ⁇ x * ⁇ w 1 ⁇ dy ⁇ ⁇ / L 2 + DL ⁇ 0 b [ ⁇ ⁇ w 1 ⁇ w 1 ⁇ ⁇ / L 4 + ⁇ ⁇ w 1 , yy ⁇ w 1 , yy + ⁇ ⁇ ⁇ w 1 ⁇ w 1 , yy + ⁇ ⁇ w 1 , yy ⁇ w 1 - / L 2 + 2 ⁇ 1 - ⁇ ⁇ ⁇ w 1 , y ⁇ w 1 , y ⁇ ⁇ / L 2 ] dy
  • Mathematical (10) is discretized as indicated by Mathematical (11).
  • the right side here is the result of integrating the elements.
  • the correlation between the average value ⁇ m * of the plastic strain distribution ⁇ x * and the half-wavelength L of the rolling-direction component of the undulation of the steel sheet 101 can be derived by developing Mathematical (11) into determinants to obtain generalized characteristic values of the discretized elements as a whole.
  • Mathematical (11) is solved, the boundary condition decided based on the determination of the boundary condition determination unit 53 is applied.
  • FIG. 6(c) is a diagram illustrating correlation between the average value ⁇ m * of the plastic strain distribution ⁇ x * computed by Mathematical (11) and the half-wavelength L of the rolling-direction component of the undulation of the steel sheet 101.
  • the average value ⁇ m * of the plastic strain distribution ⁇ x * first falls sharply, then declines slowly to assume a very small level value, and thereafter increases gradually.
  • the third-distortion arithmetic unit 54 determines distortion ⁇ mS corresponding to the half-wavelength L of the rolling-direction component of the undulation of the steel sheet 101.
  • the value of the half-wavelength L of the rolling-direction component of the undulation of the steel sheet 101 used here is the value the profile data analyzing unit 51 analyzes from the profile of the steel sheet 101 detected by the profilometer 30.
  • the third-distortion arithmetic unit 54 determines a threshold value of the third distortion of the rolled steel sheet 101 by associating the computed distortion ⁇ mS and the width-direction component of the third distortion distribution indicated by the non-dimensional quadratic curve.
  • the threshold value of the third distortion ⁇ 3 is determined by defining the distortion ⁇ mS computed by the third-distortion arithmetic unit 54 as the edge region value of the width-direction component of the third distortion indicated by the non-dimensional quadratic curve.
  • FIG. 6(d) is a diagram illustrating a relationship between the threshold value of the third distortion ⁇ 3 determined by the third-distortion arithmetic unit 54 and the width-direction position of the steel sheet 101.
  • the distortion ⁇ mS is the third distortion at the width-direction edge region.
  • the first-distortion arithmetic unit 55 computes the first distortion ⁇ 1 by adding the second distortion ⁇ 2 computed by the second-distortion arithmetic unit 52 to the third distortion ⁇ 3 computed by the third-distortion arithmetic unit 54.
  • FIG. 7(a) is a diagram illustrating a distribution of the second distortion ⁇ 2 from the width-direction central region to the width-direction edge region of the steel sheet 101.
  • FIG. 7(b) is a diagram illustrating a distribution of the third distortion ⁇ 3 from the width-direction central region to the width-direction edge region of the steel sheet 101.
  • FIG. 7(c) is a diagram illustrating a distribution of the first distortion ⁇ 1 obtained by adding the second distortion ⁇ 2 to third distortion s 3 , from the width-direction central region to the width-direction edge region of the steel sheet 101.
  • FIG. 8 is a diagram illustrating the computation flow of the distortion processing unit 10 for computing the first distortion ⁇ 1 .
  • step S201 the distortion processing unit 10 reads detection data stored in the memory unit 12.
  • the data read by the distortion processing unit 10 are data detected by the profilometer 30, thickness meter 31, width meter 32, and tensile strength meter 33.
  • step 202 the profile data analyzing unit 51 analyzes the read detection data to determine the wavelength 2L of the rolling-direction component of the undulation appearing periodically on the steel sheet 101 and the height direction displacement at every detection site on the surface of the steel sheet 101.
  • step 203 the second-distortion arithmetic unit 52 computes from the data analyzed by the profile data analyzing unit 51 the second distortion ⁇ 2 appearing in an undulation on the surface of the steel sheet that constitutes deviation from a desired value of the rolled steel sheet.
  • the boundary condition determination unit 53 determines from the data analyzed by the profile data analyzing unit 51 whether the distortion appearing in an undulation on the surface of the rolled steel sheet 101 is edge wave, center buckle, or quarter wave.
  • the third-distortion arithmetic unit 54 computes the third distortion ⁇ 3 indicating distortion corresponding internal stress of the rolled steel sheet 101.
  • the third-distortion arithmetic unit 54 performs buckling analysis to compute the third distortion ⁇ 3 from the thickness, width and tensile strength of the rolled steel sheet 101, the boundary condition determined by the boundary condition determination unit 53, and the wavelength of the rolling-direction component of the undulation appearing periodically on the steel sheet 101.
  • step 206 the first-distortion arithmetic unit 55 computes the first distortion ⁇ 1 by adding the second distortion ⁇ 2 computed in step 203 to the third distortion ⁇ 3 computed in step 205.
  • the computation flow of the arithmetic unit 11 is explained in the foregoing.
  • the arithmetic unit 11 includes the profile data analyzing unit 51, second-distortion arithmetic unit 52, boundary condition determination unit 53, third-distortion arithmetic unit 54, and first-distortion arithmetic unit 55; it computes the first distortion ⁇ 1 from the second distortion ⁇ 2 appearing in an undulation on the surface of the rolled steel sheet and the third distortion ⁇ 3 computed by buckling equations.
  • the arithmetic unit 11 takes only the 1 st mode into consideration. This is because theoretically there is no need to consider the second and higher modes within the thickness and width ranges of the steel sheets to be rolled by the rolling system 1.
  • the hot tandem rolling mill 20 has the multiple stands 21 for sequentially rolling the steel sheet 101, multiple conveyor rollers 22 for conveying the steel sheet 101, and rolling control unit 23 for regulating the roll positions and roll pressures of the individual stands 21.
  • the rolling control unit 23 Based on the first distortion ⁇ 1 computed by the arithmetic unit 11, the rolling control unit 23, which is a sequencer, performs PID control to individually regulate the roll positions, roll forces and other rolling conditions of the multiple stands 21 so as to achieve the desired profile of the rolled steel sheet.
  • the rolling control unit 23 can control the roll positions, roll forces and other rolling conditions of the multiple stands 21 so as to make the first distortion of the rolled steel sheet zero.
  • the rolling control unit 23 can control the roll positions, roll forces and other rolling conditions of the multiple stands 21 so that edge waves having a steepness ⁇ of 1% are formed. If the first distortion computed based on the second distortion and third distortion is fed back to the rolling mill, it becomes possible to feedback-control the first distortion to a desired value. In addition, if the roll positions, roll forces and other rolling conditions of the multiple stands 21 are controlled to make the first distortion of the rolled steel sheet zero, strain relieved when the rolled steel sheet is cut becomes zero, so that the cut steel sheet maintains its flatness.
  • the profilometer 30, thickness meter 31, width meter 32, and tensile strength meter 33 respectively detect the profile and the like of the steel sheet 101 rolled by multiple stands 21 under respective regulated rolling conditions and send the detection data to the arithmetic unit 10.
  • the arithmetic unit 10 feedback-controls distortion of the steel sheet 101 by feeding back to the hot tandem rolling mill 20 the first distortion ⁇ 1 computed based on detection data detected by the profilometer 30, thickness meter 31, width meter 32, and tensile strength meter 33.
  • FIG. 9 is a circuit block diagram of a rolling system 2 in accordance with the second embodiment.
  • the rolling system 2 differs from the rolling system 1 illustrated in FIG. 1 in that the distortion processing unit 10 is connected to a host computing system 40 rather than to the thickness meter 31, width meter 32, and tensile strength meter 33.
  • the host computing system 40 comprises steel sheet profile tables 41 and third distortion computation tables 42.
  • Each steel sheet profile table 41 contains the identification number of a steel sheet rolled by the rolling mill 20, estimated thickness and width of the rolled steel sheet, and correspondence with estimated tensile strength of the rolled steel sheets.
  • Each third distortion computation table 42 contains a correlation between the average value ⁇ m * of plastic strain distribution ⁇ x * and the half-wavelength L of the rolling-direction component of the undulation of a steel sheet.
  • the arithmetic unit 11 generates the third distortion computation table 42 by applying the FEM (Finite Element Method) under given computation conditions to solve the buckling equations set out in Mathematical (4) to (11). Multiple tables are included for each computation condition.
  • the FEM computation conditions include, inter alia, the width, thickness, unit tensile strength, and distribution profile of the third distortion ⁇ 3 of the rolled steel sheet.
  • FIG. 10 is a diagram illustrating the computation flow for computing the first distortion ⁇ 1 in the rolling system 2.
  • steps S301 to S304 and S306 of the computation flow illustrated in FIG. 10 is the same as that performed in steps S201 to S204 and S206 of the computation flow illustrated in FIG. 8 .
  • the processing flow illustrated in FIG. 10 differs from the processing flow illustrated in FIG. 8 in the processing of step S305.
  • the arithmetic unit 11 does not compute the third distortion ⁇ 3 by solving the buckling equations set out in Mathematical (4) to (11) but instead determines the third distortion ⁇ 3 by referring to the steel sheet profile tables 41 and the third distortion computation tables 42.
  • FIG. 11 is a circuit block diagram of a rolling system 3 in accordance with the second embodiment.
  • the rolling system 3 differs from the rolling system 1 illustrated in FIG. 1 in being equipped with a reversible rolling mill 25 instead of the hot tandem rolling mill 20.
  • a steel sheet 103 is, as indicated by a left-right arrow C, reciprocally conveyed in the left and right directions of the reversible rolling mill 25 by the conveyor rollers 22.
  • the rolling system 3 is therefore equipped on one side with the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33 and additionally on the other side with a profilometer 35, thickness meter 36, width meter 37 and tensile strength meter 38.
  • the arithmetic unit 10 computes the first distortion ⁇ 1 based on the detection data of the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33, and also computes the first distortion ⁇ 1 based on the detection data of the profilometer 35, thickness meter 36, width meter 37 and tensile strength meter 38.
  • rolling systems 1 to 3 were explained regarding hot rolling, the rolling systems can also be applied in cold rolling.
  • the functional and structural features of the distortion processing unit 10 can be incorporated into the rolling control unit 23 of the rolling mill 20.
  • the functional and structural features of the distortion processing unit 10 can be incorporated into the rolling control unit 23, profilometer 30 or host computing system 40.
  • the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33 are installed only on the downstream side of the final stand 21, it is possible to install them on the downstream side of every multiple stand 21. Moreover, while the control signals from the rolling control unit 23 are sent to all of the multiple stands 21, it is possible to send them to only the final stand 21.
  • the profilometer 30 is installed only on the downstream side of the final stand 21, it can be installed on the downstream side of every multiple stand 21. Moreover, while the control signals from the rolling control unit 23 are sent to all of the multiple stands 21, it is possible to send them to only the final stand 21.
  • the profilometer 35, thickness meter 36, width meter 37 and tensile strength meter 38 are installed in addition to the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33, it is possible to install only the profilometer 30, thickness meter 31, width meter 32 and tensile strength meter 33 on one or the other side of the stand 21.
  • the second-distortion arithmetic unit 52 computes the second distortion ⁇ 2 by Mathematical (1) to (3), it can instead compute the second distortion ⁇ 2 using the following Mathematical (12) indicating steepness ⁇ .
  • the second-distortion arithmetic unit 52 can fit the width-direction component of the undulation to a quadratic curve based on these data.
  • the second-distortion arithmetic unit 52 can fit the width-direction component of the undulation to quadratic to quartic curves based on these data.
  • the width-direction distribution of the third distortion is defined to be a non-dimensional quadratic curve with origin at the width-direction central region. However, it can instead be defined as linear, cubic or quartic. Moreover, when the third-distortion arithmetic unit 54 solves the buckling equations, the width-direction distribution of the third distortion can be defined as a ridge pattern monotonically rising from the central region of the steel sheet and monotonically falling from near the edge region of the steel sheet. Furthermore, the width-direction distribution of the third distortion can be defined as a valley pattern monotonically falling from the central region of the steel sheet and monotonically rising from near the edge region of the steel sheet.
  • FIGs. 12(a) 12(e) show examples of directional distributions of the third distortion.
  • the profilometer 30 can have the ability to detect that an edge wave or center buckle has been formed over a length corresponding to the half-wavelength L. For example, if the profilometer 30 has the ability to detect the heights of the opposite width-direction edge regions and the central region, then when the heights become the same as the height of the end of the rolled head, it can detect that an edge wave or center buckle appearing on the surface of the rolled steel sheet has been formed over a half-wavelength L. When the profilometer 30 detects that an edge wave or center buckle has been formed from the end of the rolled head over at least the length of a half-wavelength L, it sends a half-wavelength detection signal to the distortion processing unit 10.
  • the distortion processing unit 10 Upon receiving the half-wavelength detection signal, the distortion processing unit 10 starts the processing of the first distortion ⁇ 1 computation flow illustrated in FIG. 8 . So if the profilometer 30 has the ability to detect that an edge wave or center buckle has been formed over a prescribed length such as a half-wavelength L, the processing of the first distortion ⁇ 1 computation flow can be initiated when an edge wave or center buckle of the prescribed length from the rolled head is detected. The processing of the first distortion ⁇ 1 computation flow can therefore be promptly commenced at a rolled head with relatively low tensile strength, thereby making it possible to enhance the flatness of the rolled steel sheet. Moreover, the flatness of the rolled steel sheet can also be improved at the rolled tail where tensile strength is low.
  • the steel sheet profile table 41 and third distortion computation table 42 are deployed in the host computing system 40, they can instead be stored in the memory unit 12 of the distortion processing unit 10.
  • the steel sheet profile table 41 and third distortion computation table 42 can be included in the rolling control unit 23 or the profilometer 30.
  • the distortion processing unit 10 can be configured to connect with the host computing system 40 instead of the thickness meter 31, width meter 32, and tensile strength meter 33.
  • a steel sheet was rolled in the hot tandem rolling system 1 illustrated in FIG. 1
  • a steel plate was rolled in the hot reversible rolling system 3 illustrated in FIG. 11 .
  • the profile accuracy of the hot-rolled steel sheet was 20% better than when using the conventional profilometer method.

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US10307806B2 (en) 2014-09-16 2019-06-04 Nippon Steel & Sumitomo Metal Corporation Rolling control method for metal strip, rolling control apparatus, and manufacturing method for rolled metal strip
US11281818B2 (en) 2019-02-28 2022-03-22 Ford Motor Company Method for evaluating an adhesive for a vehicular joint

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US11045922B2 (en) 2016-05-16 2021-06-29 Sintokogio, Ltd. Surface treatment processing method and surface treatment processing device
JP6607318B2 (ja) * 2016-07-26 2019-11-20 東芝三菱電機産業システム株式会社 エッジャの制御装置
CN112789123B (zh) * 2018-10-05 2024-03-22 纽科尔公司 使用单个厚度轮廓仪检测平整度缺陷
JP7151513B2 (ja) * 2019-01-29 2022-10-12 日本製鉄株式会社 ローラ矯正方法
CN111922267A (zh) * 2020-07-31 2020-11-13 安徽信息工程学院 一种轧钢控制系统和方法
CN113405485B (zh) * 2021-04-20 2022-10-04 北京机科国创轻量化科学研究院有限公司 一种基于塑性变形-空气动力学交叉理论的表面质量诊断方法

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US10307806B2 (en) 2014-09-16 2019-06-04 Nippon Steel & Sumitomo Metal Corporation Rolling control method for metal strip, rolling control apparatus, and manufacturing method for rolled metal strip
US11281818B2 (en) 2019-02-28 2022-03-22 Ford Motor Company Method for evaluating an adhesive for a vehicular joint

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EP2737963B1 (fr) 2016-05-18
CN103842107A (zh) 2014-06-04
KR101454147B1 (ko) 2014-10-22
JP5257559B1 (ja) 2013-08-07
JPWO2014054140A1 (ja) 2016-08-25
KR20140066752A (ko) 2014-06-02
CN103842107B (zh) 2015-09-30
WO2014054140A1 (fr) 2014-04-10

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