JP5257559B1 - Strain calculation method and rolling system - Google Patents

Abstract

A step of detecting the shape of the steel plate 101 rolled by the rolling device 20, and a second strain ε indicating a distortion appearing as an uneven shape on the plate surface that is a deviation from the target value of the rolled steel plate from the detected shape. _From the step of calculating ₂ , the correlation between the threshold value of the third strain ε ₃ indicating the strain corresponding to the internal stress of the rolled steel sheet and the shape of the rolled steel sheet, and the detected shape A step of determining a third strain ε ₃ , wherein the correlation is a boundary condition determined by the detected shape, a plate thickness of the rolled steel plate, a plate width of the rolled steel plate, and the rolled By adding the step calculated by buckling analysis from the tension of the steel sheet and the distribution shape of the third strain, the second strain ε ₂ and the third strain ε ₃ , the strain corresponding to the total stress, and the target 1 showing the difference from the distortion of the steel sheet due to rolling Distortion calculation method characterized by comprising the steps of: calculating a viewing epsilon _1.

Description

The present invention relates to a calculation method and a rolling system for calculating strain and internal stress of a rolled steel sheet.
The purpose of rolling steel sheets is to obtain a steel sheet having a predetermined size (hereinafter also referred to as a target value) by applying stress to the steel sheet with a rolling device with respect to the steel material before rolling. . However, it is not easy to obtain a steel plate according to the target value, and various irregularities such as ear waves or medium waves are likely to occur on the surface of the rolled steel plate. The stress applied to the steel sheet from the rolling machine (hereinafter also referred to as total stress) is as follows: 1) generation of strain to obtain a predetermined size as a target value, and 2) various stresses on the plate surface that are offset from the target value. And 3) generation of residual stress in the steel sheet.
In order to perform rolling that does not cause unevenness on the plate surface, it is necessary to grasp and control all the relations between these strains and stresses. In particular, it is important to grasp and control the difference between the strain corresponding to the total stress and the strain for obtaining a predetermined size. However, a method for accurately grasping this difference has not yet been realized.

  In order to grasp the distortion in rolling, the shape of the steel sheet before and after rolling must be measured. Several techniques for measuring the shape of a rolled steel sheet are known. For example, in Patent Document 1, the thickness of a steel plate measured using a measuring device having a plurality of optical distance meters is associated with the position on the plate plane of the steel plate to grasp the deformation of the steel plate due to distortion. The technology to do is described. Furthermore, Patent Document 1 describes a technique for suppressing deformation of a rolled steel sheet by adjusting a rolling position and a rolling force based on the deformation of the steel sheet measured after rolling.

  In addition, a technique for suppressing the occurrence of a shape defect of a steel sheet due to rolling using a shape prediction model for predicting the distortion of the rolled steel sheet and measurement data obtained by measuring the distortion of the rolled steel sheet is known. In Patent Document 2, a work roll bending force is used to sequentially correct a defective shape of a steel plate during rolling from measurement data obtained by continuously measuring the strain of a rolled steel plate and a predicted shape model for predicting the strain. The technique to adjust is described. Here, the predicted shape model is sequentially corrected based on the measured strain in consideration of a dead zone corresponding to the threshold value of the strain appearing as the uneven shape on the surface of the rolled steel sheet.

  On the other hand, a technique for analyzing a generation mechanism of a shape defect of a thin plate such as an ear wave (Edge Wages) and a medium wave (Center Wages) is known. Non-Patent Document 1 describes a technique for approximately analyzing the generation mechanism of an ear wave and a medium wave using an ear wave buckling equation and a medium wave buckling equation, respectively. Non-Patent Document 2 describes a technique for analyzing a buckling critical point, which is a threshold value of strain appearing as an uneven shape on the surface of a rolled steel sheet.

  Patent Document 3 describes a technique applying the buckling equation described in Non-Patent Document 1. Specifically, in Patent Document 3, the difference between the total stress and the stress corresponding to the distortion of the steel sheet due to the target rolling is converted into a distortion that appears as an uneven shape after cooling, and a stress component that is released, A technique for separating stress components remaining in a steel plate even after deformation is described. Furthermore, Patent Document 3 describes a technique for predicting a corrugated shape generated when a steel sheet is cooled based on such a technique. In the technique described in Patent Document 3, the stress component that is converted into strain that appears as an uneven shape after cooling and released is deformed from the difference between the total stress and the stress corresponding to the strain of the steel sheet due to the target rolling. It is obtained by subtracting the stress component remaining in the steel plate afterwards. Next, the wave shape after cooling is predicted by comparing the stress component obtained by subtraction with the strain calculated from the steepness. Here, the difference between the total stress and the stress corresponding to the distortion of the steel sheet due to the target rolling is treated as a known value estimated from the temperature distribution or the like.

JP-A-5-237546 Japanese Patent Laid-Open No. 9-295022 Patent No. 4262142

"Analytical research on the generation mechanism of ear waves and middle elongation (Buckling Analysis of Edge Wabes and Middle Waves of Cold Rolled Sheet)" Journal of Japan Society for Technology of Plasticity: Plasticity and Processing, Vol. 28, No. 312 (1987-1) p58 -66 “Development of prediction model and prevention method of buckling of TMCP steel plate” CAMP-ISIJ Vol.8 (1995) -1210

  However, in the control in the technique described in Patent Document 1, although the distortion that appears as the uneven shape on the surface of the rolled steel sheet is considered, the internal stress of the steel sheet is not considered. For this reason, when the stress at the time of rolling changes by some disturbance, there exists a possibility that an internal stress may appear as an uneven | corrugated shape on the plate surface of a steel plate.

  Moreover, in the technique described in Patent Document 2, there is no description of a method for calculating a dead zone corresponding to a threshold value of distortion appearing as an uneven shape on the surface of a rolled steel sheet. Furthermore, since the control target of the technique described in Patent Document 2 is a non-linear crown change rate, the control may be complicated.

  Moreover, in the technique described in Patent Document 3, the difference between the total stress and the stress corresponding to the distortion of the steel sheet due to the target rolling is converted into a distortion that appears as a concavo-convex shape and released, and the deformation After that, it is separated into stress components remaining in the steel plate. However, based on the stress component that is converted into strain that appears as uneven shapes and released, and the stress component that remains in the steel plate even after deformation, the total stress and the stress corresponding to the target steel plate strain due to rolling There is no description or suggestion of how to calculate the difference between. In view of the above problems, the present invention is based on the distortion that appears as an uneven shape on the plate surface, which is a deviation from the target value of the rolled steel plate, and the strain corresponding to the internal stress of the rolled steel plate. An object of the present invention is to provide a calculation method and a rolling system for calculating a difference between a strain corresponding to a stress and a strain for obtaining a predetermined size as a target value.

The first, second and third distortions are defined as follows.
The difference between the strain that should correspond to the stress applied to the steel plate from the rolling mill and the strain that is used to obtain a predetermined size that is the target value is called the first strain. The distortion that appears as an uneven shape on the plate surface, which is a deviation from the target value of the rolled steel sheet, is called a second distortion. Furthermore, the strain corresponding to the internal stress of the rolled steel sheet is called third strain.
The gist of the present invention is as follows.
(1) detecting a shape of a steel sheet rolled by a rolling device;
From the detected shape, calculating a second strain appearing as an uneven shape on the plate surface that is a deviation from the target value of the rolled steel plate;
The correlation between the threshold value of the third strain indicating the strain corresponding to the internal stress of the rolled steel sheet and the wavelength of the rolling direction component of the detected shape, and the wavelength of the rolling direction component of the detected shape Determining the third strain from the correlation conditions determined by the detected shape, the plate thickness of the rolled steel plate, the plate width of the rolled steel plate, and the rolled steel plate Calculated by buckling analysis from the tension and the third strain distribution shape,
By adding the second strain and the third strain, the first strain indicating the difference between the strain corresponding to the stress applied to the steel plate from the rolling device and the strain for obtaining a predetermined size as the target value is obtained. A step of calculating;
A distortion calculation method characterized by comprising:
(2) The distribution shape of the third strain is such that the width direction component is a linear straight line having one end at the center of the steel plate and the other end at the end of the steel plate, a monotonically increasing curve, and a monotonically decreasing curve, the center of the steel plate Any one selected from a mountain shape that monotonously increases from the vicinity of the end of the steel plate and monotonously decreases from the vicinity of the end of the steel plate, and a valley shape that monotonously decreases from the center of the steel plate and monotonously increases from the vicinity of the end of the steel plate. The distortion calculation method of (1) calculated as a shape.
(3) The distortion calculation method according to any one of (1) and (2), wherein the correlation is calculated by a buckling equation.
(4) The correlation is obtained by FEM and stored as a table indicating the correspondence between the wavelength of the rolling direction component of the detected shape and the third strain threshold (1) or (2 ) Any one of the distortion calculation methods.
(5) The method further includes a step of transmitting a signal indicating the calculated first strain to the rolling device, and the rolling device controls the rolled steel sheet to have a desired shape based on the calculated first strain. The distortion calculation method according to any one of (1) to (4).
(6) The distortion calculation method according to (5), further including a step of detecting that an ear wave or a medium wave is formed over at least a half wavelength.
(7) The distortion calculation method according to (5), wherein the calculation device is controlled so that the first distortion becomes zero.
(8) a rolling device for rolling a steel sheet;
A shape meter for detecting the shape of a steel sheet rolled by a rolling device;
From the detected shape, a second distortion indicating a distortion appearing as an uneven shape on the plate surface, which is a deviation from the target value of the rolled steel plate, is calculated,
The third strain is determined from the correlation between the threshold value of the third strain indicating the strain corresponding to the internal stress of the rolled steel plate and the shape of the rolled steel plate and the detected shape. The correlation is determined by the boundary condition determined by the detected shape, the thickness of the rolled steel sheet, the width of the rolled steel sheet, the tension of the rolled steel sheet, and the third strain distribution shape. And is calculated by buckling analysis from
By adding the second strain and the third strain, the first strain indicating the difference between the strain corresponding to the stress applied to the steel plate from the rolling device and the strain for obtaining a predetermined size as the target value is obtained. Operate,
A strain calculation device that transmits a signal indicating the calculated first strain to the rolling device,
The rolling system is controlled such that the first strain is set to a desired value based on the calculated first strain.

  According to this invention, the 2nd distortion which shows the distortion which appears as the uneven | corrugated shape on the plate | board surface which is a shift | offset | difference from the target value of the rolled steel plate, and the 3rd distortion which is a distortion corresponding to the internal stress of the rolled steel plate. Based on the above, it is possible to calculate the first strain indicating the difference between the strain corresponding to the stress applied to the steel sheet from the rolling device and the strain for obtaining a predetermined size as the target value.

  Moreover, according to this invention, it becomes possible to improve the yield of a steel plate when the tension | tensile_strength of the rolled steel plate is small. For example, in hot rolling, it is possible to improve the yield of a portion (also referred to as a rolling top portion) that is rolled between the start of rolling and the occurrence of winding tension. In hot rolling, it is also possible to improve the yield of a portion (also referred to as a rolling bottom portion) that is rolled while the winding tension just before the end of rolling is reduced.

It is a circuit block diagram of an example of a rolling system. It is a functional block diagram of a calculating part. (A) is a figure which shows the analysis image which plotted and displayed an example of the data which the shape data analysis part analyzed, (b) is a figure which shows the relationship between a 2nd distortion and the width direction position of a steel plate. is there. It is a figure which shows the determination processing flow of a boundary condition determination part. (A) is a figure which shows roughly the boundary conditions in case the shape of the distortion which appears as the uneven | corrugated shape on the plate surface of a steel plate is an ear wave, (b) appears as the uneven | corrugated shape on the plate surface of a steel plate. It is a figure which shows roughly the boundary condition in case the shape of distortion is a medium wave, (c) is the boundary condition in case the shape of distortion which appears as the uneven | corrugated shape on the plate | board surface of a steel plate is a quarter wave roughly FIG. (A) is a figure which shows the displacement of the rolling direction component of the uneven | corrugated shape of a steel plate, (b) is the correlation between the average value of plastic strain distribution, and the half wavelength of the rolling direction component of the uneven shape of a steel plate. Is a diagram showing the distribution of the third strain of the width direction component used when calculating, and (c) is between the average value of the plastic strain distribution and the half wavelength of the rolling direction component of the uneven shape of the steel sheet It is a figure which shows a correlation, (d) is a figure which shows distribution of the calculated 3rd distortion. (A) is a figure which shows the distribution from the width direction center part of the 2nd distortion steel plate to the width direction edge part, (b) is the distribution from the width direction center part of the 3rd distortion steel plate to the width direction edge part. (C) is a figure which shows distribution from the width direction center part of the 1st distortion steel plate which added the 2nd distortion and the 3rd distortion to the width direction edge part. It is a figure which shows an example of the calculation flow which calculates 1st distortion. It is a circuit block diagram of the other example of a rolling system. It is a figure which shows the other example of the calculation flow which calculates 1st distortion. It is a circuit block diagram of the other example of a rolling system. It is a figure which shows the other example of distribution of 3rd distortion.

  Hereinafter, with reference to FIGS. 1-12, the rolling system which has a power supply selection circuit which concerns on this invention is demonstrated. First, with reference to FIGS. 1-8, 1st Embodiment of a rolling system is described.

  FIG. 1 is a circuit block diagram of a rolling system 1 according to the first embodiment.

  The rolling system 1 includes a strain calculation device 10 and a hot tandem rolling device 20 (hereinafter also simply referred to as a rolling device 20) that rolls the steel plate 101 in the direction of arrow A. Furthermore, the rolling system 1 includes a shape meter 30, a plate thickness meter 31, a plate width meter 32, and a tension meter 33 that detect the shape, thickness, width, and tension of the rolled steel plate 101.

  The distortion calculation device 10 includes a calculation unit 11, a storage unit 12, and an I / O unit 13. The hot tandem rolling device 20 includes a plurality of stages 21 for sequentially rolling the steel plates 101, a plurality of sheet passing rolls 22 for conveying the steel plates 101, and a rolling for adjusting the reduction position and the reduction force of the plurality of stages 21. And a control device 23.

The calculation unit 11 includes a CPU (Central Processing Unit) and a DSP (digital signal processor). The calculation unit 11 is based on a calculation program stored in the storage unit 12 with detection data received from the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33, and distortion corresponding to the total stress, A first strain ε ₁ indicating a difference from a strain for obtaining a predetermined size as a target value is calculated.

  The storage unit 12 includes a non-volatile memory for storing various programs and a volatile memory for temporarily storing data. The storage unit 12 stores a calculation program executed by the calculation unit 11 and basic software such as an OS necessary for executing the calculation program. The storage unit 12 stores detection data received from the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33.

  The I / O unit 13 converts the detection data transmitted from the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33 into data that can be processed by the calculation unit 11. The detection data received by the I / O unit 13 is stored in the storage unit 12. The I / O unit 13 transmits the data processed by the calculation unit 11 to the rolling control unit 23.

  Each of the multi-stage stands 21 has a pair of upper and lower work rolls and a pair of reinforcing rolls arranged so as to sandwich the work roll. The number of stages of the stand 21 may be any number, but may be two stages, four stages, and six stages. Each of the plurality of stages 21 has a shape control actuator (not shown). The shape control actuator applies a predetermined rolling load to the steel plate 101 based on a control signal transmitted from the rolling control unit 23 and gives the steel plate 101 various shapes such as a bender, a work roll shift, and a pair cloth.

  The shape meter 30 has a plurality of point light sources and an imaging device, and images the light from the plurality of point light sources sequentially irradiated on the upper surface of the steel plate 101 in a direction perpendicular to the rolling direction of the steel plate 101. The shape of the rolled steel plate 101 is detected.

  The plate thickness meter 31 is an X-ray thickness meter and detects the plate thickness of the steel plate 101.

  The plate width meter 32 is a spot type laser lightwave distance meter, and detects the plate width of the steel plate 101.

  The tensiometer 33 has two detectors arranged at a predetermined interval, and detects the tension of the steel plate 101 by detecting the detection holes formed in the steel plate 101 by the two detectors.

  FIG. 2 is a functional block diagram of the calculation unit 11 of the distortion calculation apparatus 10.

  The calculation unit 11 includes a shape data analysis unit 51, a second distortion calculation unit 52, a boundary condition determination unit 53, a third distortion calculation unit 54, and a first distortion calculation unit 55. Processing by these components 51 to 255 is performed by the calculation unit 11 executing the calculation program stored in the storage unit 12.

  From the shape of the steel plate 101 detected by the shape meter 30, the shape data analyzing unit 51 has a wavelength 2L of the rolling direction component of the uneven shape periodically appearing on the steel plate 101 and the height direction of each detection point on the plane of the steel plate 101. Analyzes the displacement of.

  FIG. 3A is a diagram showing an analysis image 300 in which an example of data analyzed by the shape data analysis unit 51 from the shape of the steel plate 101 detected by the shape meter 30 is plotted and displayed.

  The analysis image 300 has an x coordinate, ay coordinate, and a z coordinate. The x coordinate is a coordinate corresponding to the rolling direction in the central portion of the steel plate 101 in the width direction. The y coordinate is a coordinate corresponding to the width direction of the steel plate 101. The z coordinate is a coordinate corresponding to the height direction of the steel plate 101.

  The cross section of the sine wave shape of the analysis image 300 corresponds to the cross section of the end of the steel plate 101 in the width direction. Since the distortion shape appearing as the uneven shape of the steel plate 101 is an ear wave, the analysis image 300 has a sinusoidal cross section at the end in the width direction. In addition, when the shape of the distortion appearing as the uneven shape of the steel plate 101 is a medium wave, the uneven shape does not occur at the end portion in the width direction of the steel plate 101, and the x coordinate corresponding to the center portion in the width direction of the steel plate 101. A sinusoidal cross-section is formed.

The second distortion calculating section 52, based on the data form the data analysis unit 51 analyzes, calculates a second distortion epsilon ₂ appearing as irregularities on the plate surface is a deviation from the target value of the rolled steel sheet. First, the second distortion calculator 52 sequentially calculates the distortion ε _j ′ whose width position is the jth, based on the equations (1) to (3).

Here, dx _ij is a distance between detection points adjacent to each other in the x-axis direction, and dz _ij is a distance in the z-axis direction between detection points corresponding to dx _ij . L is the half-wavelength of the rolling direction component of the concavo-convex shape that periodically appears on the steel plate 101, and ε _j is the height in the z direction at the center of the width direction of the steel plate 101 and the second strain at the jth point from the width direction. a value and a epsilon ₂ values. In the equation (3), ε _{(j = 1)} is the height in the z direction at the center in the width direction. The strain ε ′ _j calculated by Expression (3) corresponds to the value of the second strain ε ₂ at the j-th point from the width direction.

FIG. 3B is a diagram showing a relationship between the calculated second strain ε ₂ and the position in the width direction of the steel plate 101 based on the equations (1) to (3).

  Based on the data analyzed by the shape data analysis unit 51, the boundary condition determination unit 53 is any one of an ear wave, a medium wave, and a quarter wave as a distortion shape that appears as an uneven shape on the plate surface of the steel plate 101. Determine whether.

  FIG. 4 is a diagram illustrating a determination process flow of the boundary condition determination unit 53.

  First, in step S <b> 101, the boundary condition determination unit 53 compares the height of the quarter portion in the width direction of the steel plate 101 with the height of the center portion and the end portion in the width direction of the steel plate 101. If the boundary condition determination unit 53 determines that the peak height of the quarter portion in the width direction of the steel plate 101 is high, the process proceeds to step S102. On the other hand, if the boundary condition determination unit 53 determines that the peak height of the quarter portion in the width direction of the steel plate 101 is low, the process proceeds to step S103.

  In step S101, when the boundary condition determination unit 53 determines that the height of the quarter portion in the width direction of the steel plate 101 is high, the boundary condition determination unit 53 appears as an uneven shape on the plate surface of the steel plate 101 in step S102. The shape of the distortion is determined to be a quarter wave.

  In step S101, when the boundary condition determination unit 53 determines that the height of the quarter portion in the width direction of the steel plate 101 is low, in step S103, the boundary condition determination unit 53 determines the height of the central portion in the width direction of the steel plate 101. Compare the height of the end.

  In step S103, when the boundary condition determination unit 53 determines that the height of the central portion in the width direction of the steel plate 101 is high, the boundary condition determination unit 53 appears as an uneven shape on the plate surface of the steel plate 101 in step S104. It is determined that the shape of the distortion is a medium wave.

  In step S103, when the boundary condition determination unit 53 determines that the height of the central portion in the width direction of the steel plate 101 is low, the boundary condition determination unit 53 appears as an uneven shape on the plate surface of the steel plate 101 in step S105. It is determined that the shape of the distortion is an ear wave.

  FIG. 5 is a diagram schematically showing boundary conditions determined by the uneven shape of the steel plate 101. FIG. 5A shows a boundary condition when the shape of distortion appearing as an uneven shape on the plate surface of the steel plate is an ear wave. FIG.5 (b) shows the boundary conditions in case the shape of the distortion which appears as an uneven | corrugated shape on the plate surface of a steel plate is a medium wave. FIG.5 (c) shows the boundary conditions in case the shape of the distortion which appears as an uneven | corrugated shape on the plate surface of a steel plate is a quarter wave.

  The boundary condition when the shape of the distortion appearing as the uneven shape on the plate surface of the steel plate 101 shown in FIG. 5A is an ear wave is the width direction at the center of the cross section in the width direction (hereinafter also referred to as C cross section). And the displacement in the height direction are constrained and the end portion is unconstrained.

  The boundary condition in the case where the shape of the distortion appearing as the uneven shape on the plate surface of the steel plate 101 shown in FIG. 5B is a medium wave is that the rotation around the rolling direction is constrained at the center of the C cross section, and the end portion Is a condition for restraining displacement in the height direction.

  In the case where the shape of the distortion appearing as the uneven shape on the plate surface of the steel plate 101 shown in FIG. 5C is a quarter wave, the boundary conditions are the displacement and the height in the width direction at both the center and the end of the C cross section. This is a condition for restraining the displacement in the direction.

The third strain calculation unit 54 calculates a third strain ε ₃ indicating a strain corresponding to the internal stress of the rolled steel plate 101. The third strain ε ₃ is the thickness, width, tension of the rolled steel plate 101, boundary conditions determined by the determination of the boundary condition determination unit 53, and the rolling direction component of the uneven shape that appears periodically on the steel plate 101. Based on the wavelength, it is calculated by buckling analysis using a buckling equation.

The 3rd distortion calculating part 54 calculates | requires the solution of the buckling equation shown by Formula (4)-(11) for every predetermined | prescribed width direction position. The third strain calculation unit 54 determines a threshold value (criteria) of the third strain ε ₃ of the rolled steel plate 101 from the obtained solution. The threshold value of the third strain ε ₃ determined by the third strain calculation unit 54 is a value indicating that the second strain is generated in the steel plate 101 when a strain equal to or greater than this value remains in the steel plate 101. Here, when a strain equal to or greater than the threshold value of the third strain ε ₃ remains in the rolled steel plate 101, the second strain is generated in the rolled steel plate 101. That is, it is assumed that at least a strain corresponding to the threshold value of the third strain ε ₃ remains inside the steel plate 101 in which the second strain is generated.

The third strain calculation unit 54 obtains a solution of the buckling equation of the strain ε _x ^* by obtaining a solution satisfying F = 0 in Equation (4) as described in Non-Patent Document 1.

で表され、塑性歪分布ε_x ^*の平均値を示す。また、ｂは圧延された鋼板１０１の板幅の半分の長さであり、ｈは圧延された鋼板１０１の板厚であり、σ_fは圧延された鋼板１０１の張力である。また、Ｅはヤング率を示し、νはポアソン比を示す。また、Ｄは、

である。さらに、圧延された鋼板１０１の凹凸形状の高さ方向の変位の幅方向成分ｗ（ｙ）は、式（７）に示すように、幅方向の中央部を原点とする３次関数とする。

Here, w represents the displacement in the height direction of the concavo-convex shape, the subscript 1 represents the minute displacement increment after buckling, and ε _m ^* is

And represents the average value of the plastic strain distribution ε _x ^* . Further, b is half the width of the rolled steel plate 101, h is the thickness of the rolled steel plate 101, and σ _f is the tension of the rolled steel plate 101. E represents Young's modulus and ν represents Poisson's ratio. D is

It is. Furthermore, the width direction component w (y) of the displacement in the height direction of the concavo-convex shape of the rolled steel sheet 101 is a cubic function with the center in the width direction as the origin, as shown in Equation (7).

  On the other hand, the rolling direction component of the displacement in the height direction of the uneven shape of the rolled steel sheet 101 is a sine curve having a wavelength of 2L. When finding the solution of the buckling equation, the wavelength 2L is given as a variable within a predetermined range.

FIG. 6A shows the rolling direction component of the uneven shape of the steel plate 101. From this, the displacement of the concavo-convex shape of the steel plate 101 is as shown in Expression (8).

Further, as shown in FIG. 6B and Equation (9), the width direction component of the third strain distribution is a non-dimensional quadratic curve having the center in the width direction as the origin. And

  Further, when equation (3) is integrated by a half wavelength L and simplified, equation (10) is derived.

Further, in order to obtain a solution by discretizing Equation (10), Equation (10) is discretized as shown in Equation (11).

Here, the right side is obtained by integrating each element. By developing equation (11) to the determinant, as a general eigenvalue of the entire discretized element half wavelength L in the rolling direction component of plastic strain distribution epsilon _x ^* Average value epsilon _m ^* and irregular shape of the steel plate 101 of The correlation between can be derived. When the solution of Expression (11) is obtained, the boundary condition determined by the boundary condition determination unit 53 based on the determination is applied.

FIG. 6C shows a correlation between the average value ε _m ^* of the plastic strain distribution ε _x ^* calculated by the equation (11) and the half-wavelength L of the rolling direction component of the uneven shape of the steel plate 101. It is. As shown in FIG. 6 (c), the average value ε _m ^* of the plastic strain distribution ε _x ^* initially decreased rapidly when the half-wavelength L value of the rolling direction component of the uneven shape of the steel plate 101 was increased. Later, it gradually decreases, takes a flat minimum, and then gradually increases.

The third strain calculation unit 54 performs rolling of the uneven shape of the steel plate 101 from the correlation between the average value ε _m ^* of the plastic strain distribution ε _x ^* and the half wavelength L of the rolling direction component of the uneven shape of the steel plate 101. The distortion ε _ms corresponding to the half wavelength L of the directional component is determined. Here, as the half-wavelength L of the rolling direction component of the uneven shape of the steel plate 101, a value analyzed by the shape data analysis unit 51 from the shape of the steel plate 101 detected by the shape meter 30 is used.

Next, the third strain calculation unit 54 associates the calculated strain ε _ms with the distribution of the third strain of the width direction component indicated by the dimensionless quadratic curve, thereby rolling the rolled steel plate 101. The third distortion threshold is determined. The threshold value of the third strain ε ₃ is obtained by setting the strain ε _ms calculated by the third strain calculation unit 54 as the value of the third strain end of the width direction component indicated by the non-dimensional quadratic curve. Is determined.

FIG. 6D is a diagram illustrating a relationship between the threshold value of the third strain ε ₃ determined by the third strain calculation unit 54 and the position in the width direction of the steel plate 101. The strain ε _ms is a third strain at the end of the steel plate 101 in the width direction.

The first distortion calculation unit 55 adds the second distortion ε ₂ calculated by the second distortion calculation unit 52 and the third distortion ε ₃ calculated by the third distortion calculation unit 54 to add the first distortion ε ₁ . Calculate.

FIG. 7A is a diagram showing a distribution of the second strain ε ₂ from the center portion in the width direction to the end portion in the width direction of the steel plate 101. FIG. 7B is a diagram showing a distribution of the third strain ε ₃ from the center portion in the width direction to the end portion in the width direction of the steel plate 101. FIG. 7C is a diagram showing a distribution of the first strain ε ₁ obtained by adding the second strain ε ₂ and the third strain ε ₃ from the center in the width direction to the end in the width direction of the steel sheet 101.

Next, the calculation flow of the first strain ε ₁ by the strain calculation device 10 will be described.

FIG. 8 is a diagram illustrating a calculation flow of the first distortion ε ₁ by the distortion calculation apparatus 10.

  First, in step S <b> 201, the distortion calculation device 10 reads detection data stored in the storage unit 12. The detection data read by the strain calculation device 10 is data detected by the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33.

  Next, in step S202, the shape data analysis unit 51, based on the read detection data, the wavelength 2L of the uneven shape rolling direction component that periodically appears on the steel plate 101, and the detection points on the plane of the steel plate 101, respectively. Analyze the displacement in the height direction.

Next, in step S203, the second strain calculation unit 52 shows the distortion that appears as the uneven shape on the plate surface, which is a deviation from the target value of the rolled steel plate, based on the data analyzed by the shape data analysis unit 51. The second distortion ε ₂ is calculated.

  Next, in step S204, the boundary condition determination unit 53 determines whether the shape of the distortion appearing as an uneven shape on the plate surface of the steel plate 101 is an ear wave, a medium wave, or a quarter based on the data analyzed by the shape data analysis unit 51. Determine which of the waves is.

Next, in step S <b> 205, the third strain calculation unit 54 calculates a third strain ε ₃ indicating a strain corresponding to the internal stress of the rolled steel plate 101. The third strain ε ₃ is the thickness, width, tension of the rolled steel plate 101, boundary conditions determined by the determination of the boundary condition determination unit 53, and the rolling direction component of the uneven shape that appears periodically on the steel plate 101. Based on the wavelength, it is calculated by buckling analysis.

In step S206, the first strain calculation unit 55 adds the second strain ε ₂ calculated in step S203 and the third strain ε ₃ calculated in step S205 to add the first strain ε. Calculate ₁

The calculation flow of the calculation unit 11 has been described above. The calculation unit 11 includes a shape data analysis unit 51, a second strain calculation unit 52, a boundary condition determination unit 53, a third strain calculation unit 54, and a first strain calculation unit 55, on the surface of the rolled steel sheet. The first strain ε ₁ is calculated based on the second strain ε ₂ that appears as an uneven shape and the third strain ε ₃ calculated from the buckling equation.

Note that the third distortion ε ₃ includes n-th order modes having different periods, but the calculation unit 11 considers only the first-order mode. This is because, in the range of the plate thickness and the plate width of the steel plate targeted by the rolling system 1, it is theoretically unnecessary to consider the second and higher modes.

  The hot tandem rolling device 20 includes a plurality of stages 21 for sequentially rolling the steel plates 101, a plurality of sheet passing rolls 22 for conveying the steel plates 101, and a rolling for adjusting the reduction position and the reduction force of the plurality of stages 21. And a control device 23.

The rolling control device 23 is a sequencer, and based on the first strain ε ₁ calculated by the calculation unit 11, the rolling positions of the multiple stages of the stands 21 are controlled by PID control so that the rolled steel sheet has a desired shape. And the rolling conditions such as rolling force are adjusted. For example, the rolling control device 23 can control the rolling conditions such as the rolling position and the rolling force of the multi-stage stand 21 so that the first strain of the rolled steel sheet is zero. In addition, the rolling control device 23 can control the rolling conditions such as the rolling position and the rolling force of the multi-stage stand 21 so that an ear wave having a steepness λ of 1% is formed. By feeding back the first strain calculated based on the second strain and the third strain to the rolling device, it is possible to perform feedback control so that the first strain becomes a desired value. Furthermore, the strain released when the rolled steel plate is cut by controlling the rolling conditions such as the rolling position and the rolling force of the multi-stage stand 21 so that the first strain of the rolled steel plate is zero. Therefore, the flatness of the steel sheet after cutting is maintained.

  The shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33 each detect the shape and the like of the steel plate 101 rolled by the multi-stage stand 21 in which the rolling conditions are adjusted, respectively, and calculate the calculation unit 10. Send detection data to.

The calculation unit 10 feeds back the first strain ε ₁ calculated based on the detection data detected by the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33 to the hot tandem rolling device 20. Thus, the distortion of the steel plate 101 is feedback controlled.

  The first embodiment of the rolling system has been described above.

  Next, a second embodiment of the rolling system will be described with reference to FIGS.

  FIG. 9 is a circuit block diagram of the rolling system 2 according to the second embodiment.

  The rolling system 2 is different from the rolling system 1 shown in FIG. 1 in that the strain calculation device 10 is connected to the host computer 40 instead of the plate thickness meter 31, the plate width meter 32, and the tension meter 33.

  The host computer 40 includes a steel plate shape table 41 and a third strain calculation table 42.

  The steel plate shape table 41 shows the correspondence between the identification number of the steel plate rolled by the rolling device 20, the estimated value of the thickness and width of the rolled steel plate, and the estimated value of the tension of the rolled steel plate. Including.

The third strain calculation table 42 includes a correlation between the average value ε _m ^* of the plastic strain distribution ε _x ^* and the half wavelength L of the rolling direction component of the uneven shape of the steel plate 101. In the third strain calculation table 42, the calculation unit 11 obtains the solution of the buckling equation described in the equations (4) to (11) by FEM (Finite Element Method) under given calculation conditions. And includes a plurality of tables for each calculation condition. The FEM calculation conditions include the thickness, width, unit tension, and distribution shape of the third strain ε ₃ of the rolled steel sheet.

FIG. 10 is a diagram illustrating a calculation flow of the first strain ε ₁ in the rolling system 2.

In steps S301 to S304 and S306 of the calculation flow shown in FIG. 10, the same processing as steps S201 to S204 and S206 of the calculation flow shown in FIG. 8 is executed. That is, the calculation flow shown in FIG. 10 is different from the calculation flow shown in FIG. Specifically, in the calculation flow shown in FIG. 10, the calculation unit 11 calculates the third strain ε ₃ by finding the solution of the buckling equation described in the equations (4) to (11), and calculates the steel plate shape. The third strain ε ₃ is determined with reference to the table 41 and the third strain calculation table 42.

  The second embodiment of the rolling system has been described above.

  Next, a third embodiment of the rolling system will be described with reference to FIG.

  FIG. 11 is a circuit block diagram of the rolling system 3 according to the second embodiment.

The rolling system 3 is different from the rolling system 1 shown in FIG. 1 in that a hot reverse rolling device 25 is arranged instead of the hot tandem rolling device 20. As indicated by an arrow C, in the hot reverse rolling device 25, the steel plate 103 is transported by the sheet passing roll 22 so as to reciprocate in the left-right direction of the hot reverse 25. For this reason, in addition to the shape meter 30, plate thickness meter 31, plate width meter 32, and tension meter 33 arranged on one side, the rolling system 3 includes a shape meter 35, a plate thickness meter 36, a plate arranged on the other side. A width meter 37 and a tension meter 38 are further provided. The calculation unit 10 calculates the first strain ε ₁ based on the detection data of the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33, and the shape meter 35, plate thickness meter 36, plate width The first strain ε ₁ is calculated based on the detection data of the meter 37 and the tension meter 38.

  The third embodiment of the rolling system has been described above.

  Next, deformation of the rolling system will be described.

  In the rolling systems 1 to 3, hot rolling is described, but the rolling system can also be applied to cold rolling.

  In the rolling systems 1 to 3, the strain calculation device 10 is not included in the hot tandem rolling device 20 or the hot reverse 25 rolling device, but the function and configuration of the strain calculation device 10 are the rolling control device of the rolling device 20. 23 may be included. In the rolling system 2, the function and configuration of the strain calculation device 10 may be included in the rolling control device 23, the shape meter 30, or the host computer 40.

  In the rolling system 1, the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33 are arranged only on the outlet side of the last stage stand 21, but all the outlets of the multiple stage stands 21 are arranged. It may be arranged on the side. Further, the control signal from the rolling control device 23 is output to all of the several stages of the stands 21, but may be output only to the final stage of the stands 21.

  In the rolling system 2, the shape meter 30 is disposed only on the outlet side of the last stage stand 21, but may be disposed on the outlet side of all the multi-stage stands 21. Further, the control signal from the rolling control device 23 is output to all of the several stages of the stands 21, but may be output only to the final stage of the stands 21.

  The rolling system 3 further includes a shape meter 35, a plate thickness meter 36, a plate width meter 37, and a tension meter 38 in addition to the shape meter 30, the plate thickness meter 31, the plate width meter 32, and the tension meter 33. However, the thickness gauge 31, the width gauge 32, and the tension gauge 33 may be provided on any one of the stands 21.

Further, the second distortion calculation unit 52 calculates the second distortion ε ₂ based on the equations (1) to (3), but based on the equation (12) indicating the steepness λ below, Two strains ε ₂ may be calculated.

  Further, when the detection data transmitted from the shape meter 30 is only data corresponding to the central portion and both end portions in the width direction, the second distortion calculation unit 52 calculates the uneven width direction component based on these data. You may approximate a quadratic curve.

  In addition, the detection data transmitted from the shape meter 30 includes the center portion in the width direction, both end portions, and the work side (WS, work side) and drive side (DS, drive side) quarter portions (in the middle portion and the end portion). 2, the second distortion calculation unit 52 may approximate the widthwise component of the uneven shape to a quadratic to quartic curve based on these data.

Further, when the third strain calculation unit 54 obtains the solution of the buckling equation, the distribution of the third strain in the width direction is assumed to be a non-dimensional quadratic curve with the center in the width direction as the origin. However, it may be a linear line, a cubic curve, or a quartic curve. Further, when the third strain calculation unit 54 obtains the solution of the buckling equation, the distribution of the third strain in the width direction monotonously increases from the center of the steel plate and decreases monotonously from the vicinity of the end of the steel plate. It may be a mold shape. The distribution of the third strain in the width direction may be a valley shape that monotonously decreases from the center of the steel plate and monotonously increases from the vicinity of the end of the steel plate. Expressions (13) to (22) and FIGS. 12 (a) to 12 (e) illustrate the third strain distribution in the direction.

Further, the shape meter 30 may have a function of detecting that the ear wave or the medium wave is formed over a length corresponding to the half wavelength L. For example, the shape meter 30 has a function of detecting the heights of both end portions and the center portion in the rolling direction, so that when the height becomes the same as the tip end of the rolling top portion, the rolled steel plate It is detected that an ear wave or a medium wave appearing on the surface is formed over the half wavelength L. When the shape meter 30 detects that an ear wave or a medium wave is formed over the length of at least the half wavelength L from the tip of the rolling top portion, the shape meter 30 transmits a half wavelength detection signal to the distortion calculation device 10. The distortion calculation apparatus 10 that has received the half-wavelength detection signal starts processing of the calculation flow of the first distortion ε ₁ shown in FIG. The shape meter 30 has a function of detecting that an ear wave or a medium wave is formed over a predetermined length such as a half-wavelength L, so that an ear wave or a medium of a predetermined length from the rolling top portion. When a wave is detected, the processing flow of the first distortion ε ₁ can be started. Therefore, since the processing of the calculation flow of the first strain ε ₁ can be started at an early stage in the rolling top portion having a relatively low tension, the flatness of the rolled steel sheet can be improved. Moreover, the flatness of the rolled steel plate can also be improved at the rolling bottom portion where the tension is reduced.

  In the rolling system 2, the steel plate shape table 41 and the third strain calculation table 42 are arranged in the higher order calculation device 40, but may be stored in the storage unit 12 of the strain calculation device 10. Further, when the function and configuration of the strain calculation device 10 are included in the rolling control device 23 or the shape meter 30, the steel plate shape table 41 and the third strain calculation table 42 are included in the rolling control device 23 or the shape meter 30. Also good.

  Further, in the rolling system 3, as in the rolling system 2, a configuration is adopted in which the strain calculation device 10 is connected to the host computer 40 instead of the plate thickness meter 31, plate width meter 32, and tension meter 33. May be.

  Two examples, an example of rolling a thin steel plate in the hot tandem rolling device 1 shown in FIG. 1 and an example of rolling a thick steel plate in the hot reverse rolling device 3 shown in FIG.

In the hot tandem rolling apparatus 1, a steel plate having a plate thickness of 35 mm and a plate width of 1200 mm was rolled into a steel plate having a plate thickness of 3 mm and a plate width of 1200 mm. The tension at this time is 20 MPa. Further, the measurement data measured by the shape meter 30 was approximated by a quartic curve. Based on the calculated first strain ε ₁ , the bender force of the work roll bender of the final stage stand 21 by the control signal generated by the rolling control device 23 so that the first strain of the rolled steel sheet is zero. Was corrected in real time.

  As a result, the geometric mid ratio of the thin steel sheet was improved by 20% in the geometric mid ratio of the hot-rolled steel sheet as compared with the conventional shape measuring method.

In the hot reverse rolling apparatus 3, a steel plate having a plate thickness of 200 mm and a plate width of 2000 mm was rolled into a steel plate having a plate thickness of 15 mm and a plate width of 4000 mm. The tension at this time is 0 MPa. Further, the measurement data measured by the shape meter 30 was approximated by a quartic curve. Based on the calculated first strain ε ₁ , the bender force of the work roll bender after the next pass is determined by the control signal generated by the rolling control device 23 so that the first strain of the rolled steel sheet is zero. Corrected.

  As a result, the geometric mid ratio of the thick steel plate was improved by 15% in the reverse-rolled thick steel plate as compared with the conventional shape meter method.

  Although the embodiment has been described above, all examples and conditions described herein are described for the purpose of helping understanding of the concept of the invention applied to the invention and the technology. It is not intended to limit the scope of the invention, and the construction of such examples in the specification does not indicate the advantages and disadvantages of the invention. Although embodiments of the invention have been described in detail, it should be understood that various changes, substitutions and modifications can be made without departing from the spirit and scope of the invention.

1, 2, 3 Rolling system 10 Strain calculation device 20 Hot tandem rolling device 25 Hot reverse rolling device 30, 35 Shape meter

Claims (8)

Detecting the shape of the steel sheet rolled by the rolling device;
From the detected shape, calculating a second strain indicating a strain that appears as an uneven shape on the plate surface that is a deviation from the target value of the rolled steel plate;
The correlation between the third strain threshold value indicating the strain corresponding to the internal stress of the rolled steel sheet and the wavelength of the rolling direction component of the detected shape, and the shape determined from the detected shape Determining the third strain from the wavelength of the rolling direction component of the step, wherein the correlation is a boundary condition determined by the detected shape, a plate thickness of the rolled steel sheet, and rolled A step calculated by buckling analysis from the plate width of the steel plate, the tension of the rolled steel plate, and the distribution shape of the third strain;
By adding the second strain and the third strain, the first strain indicating the difference between the strain corresponding to the stress applied to the steel plate from the rolling device and the strain of the steel plate due to the target rolling is calculated. And steps to
A distortion calculation method characterized by comprising:   The distribution shape of the third strain is such that the width direction component is a linear straight line having one end at the center of the steel plate and the other end at the end of the steel plate, a monotonically increasing curve, and a monotonically decreasing curve. In any one shape selected from a mountain shape that increases and monotonously decreases from the vicinity of the edge of the steel plate, and a valley shape that decreases monotonously from the center of the steel plate and monotonously increases from the vicinity of the edge of the steel plate. The distortion calculation method according to claim 1, wherein the distortion calculation method is calculated as being.   The strain calculation method according to claim 1, wherein the correlation is calculated by a buckling equation.   The said correlation is calculated | required by FEM, and is memorize | stored as a table which shows the correspondence between the wavelength of the rolling direction component of the said detected shape, and the threshold value of the said 3rd distortion. Distortion calculation method. Further comprising the step of transmitting a signal indicating the calculated first strain to the rolling apparatus,
2. The strain calculation method according to claim 1, wherein the calculation device is controlled based on the calculated first strain so that the rolled steel sheet has a desired shape.   The distortion calculation method according to claim 5, further comprising a step of detecting that an ear wave or a medium wave is formed over at least a half wavelength.   The distortion calculation method according to claim 5, wherein the calculation device is controlled so that the first distortion becomes zero. A rolling device for rolling steel sheets;
A shape meter for detecting the shape of the steel sheet rolled by the rolling device;
From the detected shape, to calculate a second strain showing a strain that appears as an uneven shape on the plate surface that is a deviation from the target value of the rolled steel plate,
From the detected shape and the correlation between the third strain threshold value indicating the strain corresponding to the internal stress of the rolled steel sheet and the wavelength of the rolling direction component of the shape obtained from the detected shape Determining the third strain from the wavelength of the rolling direction component of the required shape, wherein the correlation is a boundary condition determined by the detected shape, and the thickness of the rolled steel sheet; Calculated by buckling analysis from the sheet width of the rolled steel sheet, the tension of the rolled steel sheet, and the distribution shape of the third strain,
By adding the second strain and the third strain, the first strain indicating the difference between the strain corresponding to the stress applied to the steel plate from the rolling device and the strain of the steel plate due to the target rolling is calculated. And
A strain computation device that transmits a signal indicating the computed first strain to the rolling device,
The rolling system is controlled to make a rolled steel plate into a desired shape based on the calculated first strain.

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