JPH06102036A - Method for detecting warp of plate in lateral and longitudinal direction - Google Patents

Abstract

PURPOSE:To obtain a method for detecting warp, in lateral and longitudinal directions, of a plate under nonrestrained state in production line. CONSTITUTION:Residual moments Mx0, My0 in longitudinal and lateral directions of a plate to be inspected are determined by the method of least squares based on lateral shape, tensile force, predetermined thickness, width, and material constant of the plate such that the difference from the lateral shape (w) calculated according to formula (1) is minimized and then warps Ll, Lc in the longitudinal and lateral directions are calculated according to formulas (2), (3). w(y)=Mx0.wx(y)+My0.wy(y)...(1) Ll=Mx0.10<2>/4D...(2) Lc= My0.b<2>/4D...(3) This method allows highly accurate on-line detection of the warp of band member and produces a highly accurate band steel when it is fed back to actual operation.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention determines the shape in the width direction and the plate length direction of a processed plate material in the state of a non-tensioned and unconstrained cut plate when processing a steel strip such as rolling and straightening a steel plate. ,
It relates to a detection method for in-line evaluation.

[0002]

2. Description of the Related Art In the field of materials to be inspected, such as steel plates for cans, it is necessary to remove the shape, especially warpage, from the viewpoint of securing the passing plate and ensuring coatability.

In the conventional rolling and shape correction of a steel sheet, a method for detecting the warp in the sheet width direction is as shown in the front view of FIG. 3A and the side view of FIG. Or at the end of operation under certain operating conditions,
There is a method of cutting a steel plate to a predetermined length and measuring the warp in the plate width direction.

As shown in FIG. 3B, this is a method of measuring a warp L which is a distance between the steel plate 1 and the support 2 when vertically suspended. At present, in general, the warp in the plate width direction is managed by this method, and the operating condition is changed so that the warp amount L satisfies the allowable range.

However, in such an inspection method, since the inspection is performed outside the line after the operation is completed, only the accuracy of the warpage processing is extracted, and if the inspection shows that the warpage is out of the allowable range, the operation is restarted based on that. There is no choice but to adjust the conditions again, so it is necessary to dispose of all the steel sheets up to that point as defective products, or to re-pass them to the line having a shape correcting function.

On the other hand, as a method of inspecting the warp in the line, as shown in FIG. 4, a rod-shaped light source 3 such as a fluorescent lamp is installed vertically to the side of the line, and the bending of the projected image on the steel plate 1 is visually inspected. There is a way to do it.

[0007]

Since this method is a visual judgment by the inspector, there is a large variation among the inspectors and not only a qualitative judgment but also a risk of overlooking the warp. Further, in the normal tension application state and the state in which the test material is constrained by the roll, the warp is difficult to be manifested, so it is necessary to judge a fine warp, and there are various drawbacks such as requiring skill to judge the warp. is there.

Further, Japanese Patent Laid-Open No. 1-2023142 discloses a method of arranging a plurality of displacement gauges 4 in the plate width direction as shown in FIG. 5 and calculating a warp between each of them and each point in the plate width direction and a laser. There is a method of irradiating light on a steel plate vertically in the plate width direction, capturing a bright line of a laser beam on the steel plate from a low angle with a camera, and calculating a warp by image processing.

Further, as shown in FIG. 6, a laser projector 6 is installed so that it can be obliquely illuminated in the plate width direction at a low angle, the reflected light is projected on a screen 7, and an image is obtained from an image obtained by an image pickup device 8. A method of calculating warpage by processing has been proposed, but in these cases, the shape in the width direction detected is the shape in the state where the steel plate is tensioned and the steel plate is constrained by rolls, so the change in tension The detection shape changes due to

In these cases, since the steel plate is strongly restrained in the plate longitudinal direction, the warp in the plate longitudinal direction appears as a warp in the plate width direction. Therefore, even if the warp in the width direction is the same in the cut plate state, that is, in the no-tension or unconstrained state, if the warp in the longitudinal direction is different, the detection and detection shape will change and not only sufficient accuracy will not be obtained, but also the plate longitudinal direction. Since the direction warp and the plate width direction warp cannot be discriminated from each other, there is a drawback that proper shape correction cannot be performed.

The present invention solves the above-mentioned drawbacks of the prior art by detecting the warp in the plate width direction of the material to be inspected in the line, and based on this shape, tension-free and unconstrained based on the tension value. Provided is a method for detecting a warp of a steel plate suitable for actual operation, in which the warp in the plate longitudinal direction and the warp in the plate width direction in a warped plate state are calculated, and the results can be immediately fed back to the operating conditions.

[0012]

DISCLOSURE OF THE INVENTION According to the present invention, a shape in the plate width direction obtained from a means for detecting a displacement of a material to be tested, which is passed from a reference plate passing position, in a plate width direction and a material to be tested. Based on the tension obtained from the means for detecting the tension and the thickness, width, and material constants of the test material obtained in advance, the deviation from the plate width direction shape w calculated by the following equation (1) should be minimized. The longitudinal residual moment Mx0 and the transverse residual moment M
y0 is obtained by the least squares method, and then the following (2) and (3)
A plate width direction warp and plate length direction warp detection method is characterized in that a plate length direction warp Ll and a plate width direction warp Lc in a cut plate state are calculated based on an equation.

[0013]

## EQU00004 ## w (y) = Mx0.wx (y) + My0.wy (y) ... (1)

[0014]

[Formula 5] Ll = Mx0 · 10 ² / 4D ... (2)

[0015]

[Formula 6] Lc = My0 · b ² / 4D ………… (3)

However, W: shape function in the width direction of the plate y: position in the width direction of the plate Mx0: residual moment in the plate longitudinal direction My0: residual moment in the plate width wx (y): residual moment in the plate longitudinal direction at the position y Displacement amount per unit moment wy (y): Displacement amount per unit moment that appears due to residual moment in strip width direction at position y in width direction 10: Cut plate length b: Strip width of test material D: Material constant and target Bending stiffness determined by inspection thickness

The contents of the present invention will be specifically described below.

The warp of the metal steel strip in the cut plate state occurs when the residual stress in the steel strip is released and the moments in each direction are balanced. However, the steel strip in the line is in a state where tension is applied and the steel strip is constrained by rolls,
Due to the tension and the stress generated by the restraint, the balance of the moment is different from that of the cut plate state, and thus the warped shape generated is also different from that of the cut plate state. Therefore, a method for obtaining the plate shape in the tension applied state and the state where the steel strip is restrained by the roll will be described.

First, the coordinate system has the plate longitudinal direction as the x-axis, the plate width direction as the y-axis, and the plate normal direction as the z-axis, and the coordinate origin is the midpoint between the roll restraint points and the plate width at the reference plate passing position. And Let w be the displacement in the z direction due to warpage, and w is sufficiently small, so the relationship between displacement and strain is given by the following equation (4).

[0020]

[Equation 7]

Since the thickness of the steel strip is sufficiently thin and the stress and strain in the plate direction can be ignored, from the relational expression of stress and strain, (5) a,
Equations (5) b and (5) c are established.

[0022]

[Equation 8]

[0023]

[Equation 9]

[0024]

[Equation 10]

However,

Therefore, each moment is (5) a, (5)
b, (5) c are integrated in the plate thickness direction to obtain (6) a to (6) c.
It can be expressed by the following formula.

[0027]

[Equation 11]

[0028]

[Equation 12]

[0029]

[Equation 13]

However, Mx: moment in the longitudinal direction of the plate,
MxO: Residual moment in plate longitudinal direction, My: Moment in plate width direction, MyO: Residual moment in plate width direction, Mxy, Myx: Torsional moment,

Next, considering a minute element on the steel strip, and letting the shearing forces acting on the xy plane of this minute element be Qx and Qy, from the balance of the moment around the x axis in this minute element as shown in FIG. The following expression (7) is obtained.

[0032]

[Equation 14]

Similarly, from the balance of the moment about the y-axis,
The following expression (8) is obtained.

[0034]

[Equation 15]

The equation (9) is obtained from the balance of the forces in the z direction acting on the minute elements.

[0036]

[Equation 16]

Here, f is the influence of the tension generated on this minute element due to the displacement w, and can be expressed by the following equation assuming that the tension is constant at all positions.

[0038]

[Equation 17] However, T: Unit tension

The above (6) a, (6) b, (6) c,
By substituting the equations (7), (8), and (10) into the equation (9), the following partial differential equation regarding the steel strip shape is obtained.

[0040]

[Equation 18]

[0041]

[Equation 19]

By solving this partial differential equation under desired boundary conditions, it is possible to represent all steel strip shapes that appear due to residual stress under tension.

In order to obtain the shape of the steel strip in the roll restrained state, the partial differential equation (11) is solved by solving the strip condition under the boundary conditions of the steel strip edge being the free end and the roll restraining being the simple supporting end. , The desired plate shape function w (x, y) is obtained. Specifically, if this boundary condition is expressed by a mathematical expression, (12) a to (1
2) It becomes like d.

[0044]

(My) _{y =} ± _{b / 2} = 0 at ∀x (12) a

[0045]

[Equation 21]

[0046]

[Equation 22] w (± l / 2, y) = 0 at ∀y (12) c

[0047]

(Mx) _{x =} ± _{l / 2} = 0 at ∀y (12) d

Where b: width of steel strip, l: distance between restraint points of rolls for restraining steel strip

The partial differential equation of the equation (11) is given by (12) a-
(12) The steel strip shape function w under the tension applied state and the roll restrained state solved under the boundary condition of the equation (d) is expressed by the following equation (13).

[0050]

[Mathematical formula-see original document] w (x, y) = Mx0.wx (x, y) + My0.wy (x, y) ... (13)

Here, wx is a shape function that represents the displacement per unit moment that appears due to the residual moment in the plate longitudinal direction, and wy is a shape function that represents the displacement per unit moment that appears due to the residual moment in the plate width direction.
4) a to (14) f.

[0052]

[Equation 25]

[0053]

[Equation 26]

However, in the equations (12) a and (12) b, n = 1, 3, 5, ..., ∞

[0055]

[Equation 27]

[0056]

[Equation 28]

[0057]

[Equation 29]

[0058]

[Equation 30]

[0059]

If the position for detecting the shape in the plate width direction in the line is l ', then equation (13) can be rewritten as equation (1).

[0061]

## EQU00003 ## w (y) = Mx0.wx (y) + My0.wy (y) ... (1)

However, w (y) = w (l ', y),
wx (y) = wx (l ′, y), wy (y) = wy
(L ', y)

As shown in the equation (1), the steel strip shape has a residual moment in each of the plate longitudinal direction and the strip width direction, and a moment in each direction determined by the tension and the thickness, width, and material constants of the steel strip which are known in advance. It can be expressed by a linear combination with the dependent shape function in the plate width direction.

Therefore, if the plate width direction shape in the line is detected and the obtained z direction displacement amount at each plate width direction position y and the actual tension or tension fluctuation at the time of detection are negligible, the setting is made. Wx (y), wy calculated from tension
(Y) is compared, and residual moments Mx0, My are set so as to minimize the total deviation between the respective points detected by a mathematical method such as the least square method and the plate width direction shape function w represented by the equation (1).
0 can be calculated separately.

It is known that the steel strip shape w0 in the cut plate state can be obtained from this residual moment by the following equation.

[0066]

[Number 32] w0 (x, y) = ( Mx0 / D) · x 2 + (My0 / D) · y 2 ... (15)

From this, the warp amount s in the longitudinal direction of the plate which is a control value
The amount of warp l and the amount of warp sc in the plate width direction are expressed by the above equations (2) and (3).

[0068]

[Expression 33] Ll = Mx0 · 10 ² / 4D (2)

[0069]

[Equation 33] Lc = My0 · b ² / 4D (3) where l0: cut plate length

As described above, since the warp amount in the plate longitudinal direction and the warp amount in the plate width direction can be accurately obtained in the passing plate, Ll, Lc or Mx0, My0 can be fed back or feed forward during the actual operation. In addition to being able to manufacture products with good plate shape, it is also possible to control and guarantee the full-length quality of products.

Although wx and wy shown in the equation (1) are infinite series functions, sufficient accuracy can be obtained even if n is cut off at about 5. In addition, since the function itself becomes quite complicated, wx and wy are higher-order functions, such as a quartic function and a 6th-order function, when the tension at the time of passing the steel strip, the thickness, width, and material constant of the steel strip are known in advance. It is possible to shorten the calculation time at the time of detection by approximating with, for example.

As a result of applying the present invention to the actual line operation, when the conventional in-line shape detecting method is used, the occurrence of the warp disagreement can be made zero even if the warp disagreement occurs in the cutting plate inspection. did it.

[0073]

Embodiments of the present invention will now be described in detail with reference to the drawings.

FIG. 1 shows an embodiment of the present invention. 1 is a material to be inspected, 5 and 5a are deflector rolls, 10 is a width direction shape detector, 11 is a tension detector, 12 is a shape calculator, 13
Indicates a display device.

As shown in FIG. 1, in this embodiment, the test material 1 to be passed is installed so that it can pass vertically between a pair of deflector rolls 5, 5a having parallel axes.
This is because the shape of the steel strip cannot be accurately detected due to the effect of deflection due to gravity in the horizontal threading state, and the effect of gravity can be made sufficiently small and negligible compared to normal tension by vertically threading.

Further, the test material 1 is passed through so as not to give an excessive tension, so that the shape of the steel strip becomes visible. The shape detector 10 is installed so as to detect the shape in the plate width direction at the substantially central portion between the deflector rolls 5 and 5a. The shape detector 10 may be a discrete displacement measuring method, but in order to improve the detection accuracy, it is preferable that the shape detector 10 be capable of detecting a continuous steel strip shape as shown in FIG.

Further, since the displacement from the reference plate passing position is required in principle, another displacement sensor is installed for the shape detector that cannot simultaneously detect the displacement from the reference plate passing position, and the detected shape value is corrected. There is a need to.

The shape calculator 12 is first expressed by the equations (14) a to (14) f from the tension value obtained from the tension detector 11, the thickness, width and material constant of the material to be tested in the strip. Shape function w that appears due to the moment in the plate longitudinal direction and the plate width direction
Calculate x and wy. When the tension is almost constant, the tension detector 4 is not necessary, and the calculation of wx and wy may be performed once just before the threading based on the set tension.

If the type of the target steel strip can be limited, the calculation time can be shortened by approximating with a quartic function or a hexagonal function. Based on these wx and wy, (1)
The residual moments Mx0 and My0 are obtained so as to minimize the deviation between the shape function in the plate width direction expressed by the equation and the shape in the plate width direction obtained from the shape detector 10. Further, the warp amounts Ll and Lc in the cut plate state are calculated by the equations (2) and (3), and the result is output to the display device 13 such as a CRT.

For example, if a shape correcting device such as a tension leveler is installed on the front surface of the present device, the leveler unit may be adjusted so that the warp amount in each direction becomes zero.

[0081]

As described above, according to the detection method of the present invention, the longitudinal warpage and the longitudinal warpage of the strip-shaped test material are accurately detected online, and feedback or feedforward to the actual operation is performed. It is possible to obtain a highly accurate steel strip.

[Brief description of drawings]

FIG. 1 is a schematic view showing an example of an apparatus suitable for carrying out the detection method of the present invention.

FIG. 2 is a schematic diagram of a moment and force acting on minute elements on a steel strip.

3A and 3B show a conventional method for measuring the warp of a steel strip, where FIG. 3A is a front view and FIG. 3B is a side view.

FIG. 4 is a perspective view showing an arrangement position of an illumination light source used in a warpage measuring method using another conventional rod-shaped light source.

FIG. 5 is a plan view showing an arrangement position of an instrument used in a warpage measuring method using a displacement gauge of another example of the related art, and a test material shows a cross section.

FIG. 6 is a perspective view showing a detection end portion used in another conventional warpage measuring method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Steel strip (material to be inspected) 2 Support 3 Bar light source 4 Displacement meter 5, 5a Deflector roll 6 Laser projector 7 Screen 8 Imager 9 Laser projected image position 10 Plate width direction shape detector 11 Tension detector 12 Shape calculator 13 Display

Claims (1)

[Claims] 1. A plate width direction shape obtained from a means for detecting a displacement of a material to be inspected being passed from a reference threading position in a plate width direction, and a means for detecting a tension of the material to be inspected. Based on the tension and the thickness, width, and material constants of the test material obtained in advance, the residual moment Mx0 and the width of the plate in the plate longitudinal direction are minimized so that the deviation from the shape w in the plate width direction calculated by the following equation 1 is minimized. The direction residual moment My0 is obtained by the least squares method, and then the plate longitudinal warp Ll and the plate width direction warp Lc in the cut plate state are calculated based on the following Equations 2 and 3, and Warp detection method in the longitudinal direction of the plate. [Formula 1] w (y) = Mx0 · wx (y) + My0 · wy (y) [Formula 2] Ll = Mx0 · 10 ² / 4D [Formula 3] Lc = My0 · b ² / 4D where: W: plate Width direction shape function y: Plate width direction position Mx0: Plate longitudinal direction residual moment My0: Plate width direction residual moment wx (y): Displacement amount per unit moment that appears due to plate longitudinal direction residual moment at width direction position y wy ( y): Displacement amount per unit moment that appears due to the residual moment in the sheet width direction at position y in the sheet width direction l0: Cutting plate length b: Sheet width of the test material D: Bending stiffness determined by the material constant and the thickness of the test material