JPH0236307A - Warp measuring method for beltlike body - Google Patents

Abstract

PURPOSE:To accurately find respective (n) coefficients of a function Y=F(x) of degree (n) and to accurately measure the warp of the beltlike body by setting the warp of the beltlike body nearby both ends, i.e. the distance from a measurement point to a reference straight line to '0'. CONSTITUTION:Distance sensors 2, 3, and 4 are arranged successively on the reference straight line parallel to the lengthwise direction of the beltlike body 1 and every time the beltlike body 1 is conveyed by a proper distance, the distance from the straight line to one side end part or center line of the beltlike body 1 is measured at three points and those distances are substituted in a polynomial of degree (n) to find the curvature. Here, the deviation distance between the straight light connecting two of the three measurement points and the remaining measurement point is found at N lengthwise positions, thereby finding coefficients from the degree (n) to the degree '0' of the polynomial of degree (n) according to N expressions showing the relation between the lengthwise position and two expressions wherein the deviation distance from the reference straight line is '0' nearby the tip end and tail end of the beltlike body 1. Consequently, the respective coefficients of the function Y=F(x) of degree (n) are found by single-time regressive arithmetic.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a method for measuring the bending state of a belt-shaped body such as a steel plate. n of the longitudinal position of the strip
This paper relates to a method for measuring bending as a degree polynomial.

[Conventional technology]

If a steel plate that has been rolled to a specified width is bent on the rolling line, it may not be possible to cut out a steel plate of the specified width and length, so it is important to know the degree of bending in the steel plate (strip) on the rolling line. be.

As a method for measuring the bending of a formed product such as a steel plate, as shown in FIG. Each time the strip 11 is conveyed an appropriate distance, each width is 12.13.
．． There is a known method of detecting the center position measurement value of 14 and measuring the bending of the strip 11 based on the detected value.
(Japanese Unexamined Patent Publication No. 59-65710).

This method will be explained below. The strip 11 is conveyed in its longitudinal direction as the table rolls 16, 16, etc. are rotated by the action of a drive system (not shown), and the center position of the strip 11 can be measured in the conveying direction. Three width gauges 12.13.14 are fixed in parallel, separated by a distance L2 between width gauges 12.13 and 12 width gauges 12.14. 11 center lines! ~
It is designed to measure the separation distance between reference lines.

FIG. 8 is a schematic diagram showing the relationship between distance measurement points, distance measurement values, and center line l for explaining the measurement principle of the prior art.
- In the figure, A, B, and C are distance measurement points on the strip 11 facing the distance sensors 12, 13, and 14, respectively.

However, the straight line connecting the measurement origin positions defined by the width gauges 12, 13, and 14 is defined as the X axis, and the direction opposite to the conveyance direction of the strip is defined as the positive direction. Also, perpendicular to the above X axis,
The direction from the reference line toward the strip is defined as the Y-axis stop direction, and the origin is defined as the measurement origin position of the measurement point first measured by the width gauge 12.

The curve Y=F(X) in the figure is a curve assumed to be the center line p of the strip 11, and is expressed by an n-th degree polynomial shown in equation (1) below.

A straight line Y passing through two distance measurement points A and B on the curve F(x)
= C (Xl and curve Y = F (X-Xc with Xl
Find the distance M (jl) at J. (However, each distance measurement point A, B.

The transport direction position coordinates of C are respectively X aj+ X bj+
Let it be X cj. ) Straight line Y = G (The formula for Xl is Y = G (Xl Therefore +F(X□) L+ L through M(jl-G (XcJ) -F (XcJ)-
F (XcJ) ... (2)
Here is the measured distance from the reference line at width meter 12, 13, and 14! ! ij+I! bj+'! cj, then F (X, J)=ff, ,, F (X
bj) −pbJ, F (XCJ) = 7! , so the above equation (2) becomes.

Therefore, by obtaining a large number of equations such as the above equation (4) from the above equations (i), (2+, (31) and at each conveyance timing of the strip 11, and solving these many simultaneous equations, Y = F. Each coefficient of fXl (C7゜CM-1
+..., C0) and measure the bending of the strip 11.

[Problem to be solved by the invention]

However, in this method, the coefficient CI of the first-order term and the constant term C8 are eliminated on the left side of the above equation (4) (see the calculation formula below).

==0 <x*=+Lz　))CI L.

+ CI Xaj+ Co ) (Cn X'
2J+ Cn-+ X: So=0 +-+ CI Only. and coefficients C,,C.

When calculating, two sets of values obtained at the same transport timing among the values obtained by combining a large number of transport direction position coordinates and distance 11J constant value, and the coefficient value of the calculated quadratic or higher term are used. and C+, C as unknowns.

The values of C+ and Co were obtained by substituting Y = F (X) and solving the resulting two equations.

In other words, in this method, the coefficients of quadratic and higher terms are obtained by regression calculation, so the accuracy is relatively good, but
. is determined based only on two sets of measurement data that are likely to contain errors. Therefore, the calculation accuracy of C+ and Co is extremely low, and as a result, there is a problem in that the bending measured using these coefficients lacks accuracy.

The present invention has been made in view of such circumstances, and it is possible to obtain each coefficient of Xi with high accuracy,
It is an object of the present invention to provide a method for measuring the bending of a band-like object, which can accurately measure the bending of the band-like object.

[Means to solve the problem]

According to the conventional method, for example, the center line as shown in FIG.
(where Q and R indicate the leading and trailing ends of the strip, respectively) are obtained.

By the way, the measurement result required in measuring the bending of a strip-shaped body may be the bending at the center when the bending at the leading and trailing ends is set to O. Therefore, in the present invention, as shown in FIG. 6, the curves at both ends are assumed to be O, and each coefficient of a zero-order function approximated as one end or center line of the strip is calculated.

The method for measuring the bending of a strip according to the present invention obtains a distance measurement value by measuring the distance from a reference straight line substantially parallel to the longitudinal direction of the strip to one end of the strip or the center line of the strip at three locations. , a method for measuring the bending of a strip in which the distance from the reference straight line to one end of the strip or the center line of the strip is determined as an n-th degree polynomial of the longitudinal position of the strip based on these distance measurement values. The deviation distance between the straight line connecting two of the distance measurement points and the remaining one distance measurement point is determined at N (≧rl-1) points in the longitudinal direction of the strip, and The n-th degree polynomial is calculated based on N equations showing the relationship between the position and this deviation distance, and two equations in which the deviation distance from the reference straight line near the leading edge and near the rear end of the strip is set to 0. It is characterized by finding the coefficients from the nth order to the zeroth order.

[Effect]

In the present invention, the bending (distance from the reference straight line to the distance measurement point) near the leading edge and the trailing edge of the strip is defined as O.

Then, the function Y = F fX) consisting of an n-dimensional polynomial
Each coefficient can be obtained by one regression calculation.

〔Example〕

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be specifically described below based on drawings showing embodiments thereof.

FIG. 1 is a schematic diagram showing the implementation state of the bending measuring method according to the present invention.

Three distance sensors 2, 3.4 are arranged in parallel on a reference straight line parallel to the longitudinal (conveyance) direction of the strip 1, and each distance sensor 2, 3. 4 is detected, and the bending of the strip 1 is measured based on the detected value.

The strip 1 is conveyed in the direction of the white arrow in the figure as the table rolls 6, 6, . Moreover, on one frame 5, in the extending direction of the frame 5, there is a distance L1.3 between the distance sensors 2.3. Three distance sensors 2.3 are separated by a distance L2 between the distance sensors 3 and 4.
．． 4 are fixedly arranged in parallel, and the distance sensors 2, 3.4 measure the distance between the side surface of the strip 1 and each distance sensor 2, 3.4. However, the distance between the distance sensors 24 is assumed to be LO (=LI +LZ).

Figure 2 shows distance measurement points and distance measurement values 9 in the method of the present invention.
It is a schematic diagram showing the relationship between curved shape curves, and in the figure A and B
, C are distance measuring points on the strip 1 facing the distance sensors 2, 3.4, respectively.

However, the straight line connecting the measurement origin positions defined by the distance sensors 2, 3.4 is defined as the X axis, and the direction opposite to the conveying direction of the strip is defined as the positive direction. Also, perpendicular to the above X axis,
The direction from the distance sensors 2, 3.4 toward the strip is defined as the Y-axis stop direction, and the origin is defined as the measurement origin position of the measurement point first measured by the distance sensor 2.

In the figure, the curve Y = F (Xi is a curve assumed as the curved shape of the strip I, and is expressed by the n-th order polynomial 2 shown in the following equation (5).

Find the distance M(j) (BD) at X = X bJ between the two distance measurement points A and C on the curve F (x+). (However, the transport direction position coordinates of each distance measurement point A, B, and C are respectively X aj + XbjX (J.) The equation of the straight line Y = G (X) is expressed as X Cj X aj.

pbj L.

L.

here XbJ=XaJ+L.

X cj = X aj + L.

Therefore, the first term and the second term on the left side of equation (8) become 1. Therefore, 10F (Xo) L+ F (XcJ) ” Lz F (X
a;)M(J)-F(XbJ)-c(Xb
j)...(6)

Here, the distance measurement values at distance sensors 2, 3.4 are (!
If llj+ I' bj+ 12 Cj, then F (X,,)= 1-;, F (XbJ)
= lb,, F (Xc, H) = pcJ, so the above equation (6) becomes.

Therefore, the above 15), +61. (From formula 71, L.

Since the distance from the measurement points at both ends of the strip to the reference straight line (X-axis) is 0, if the length of the strip is L, then F(0)=O F(L)=0, so (5) From the formula, Co”O...00) (91, Qω, 0υ When expressed as a matrix, X-C=Y
...Oz (Leave space below) ■ □ ■ L' bj bs Here, N is the number of distance measurements.

Therefore, if you solve for C in equation (2), Y = F
(Each coefficient of Xi (C-, C,,-+,"', C+,
Co) can be found.

When N=n-1, X becomes a square matrix, so C is uniquely determined as shown in equation 09 below.

C=X-'.Y...Q31 When N>n-1, it must be determined using the least squares method as shown in the aa formula below.

C-(X''-X)-'・Xl ・Y...θ0(
However, xT is the transposed matrix of easily requested.

Note that from the formula 00), co"O, so in the formula a, X
Xl (N+1 row, n column) by deleting the N+1st row and first column of C, and C by deleting the first row of C.

(row n, column 1) and deleted the N+1st row of Y
+(N+1 row, 1 column) to obtain each coefficient of Y=F(X), the same result as above is obtained.

By the way, when distances are measured using three distance sensors in the song vAm shown in FIG. 3 and the curve m1 obtained by translating this curve m0, the distances are B, D6-large. Therefore, bending can be accurately measured even if there is lateral wobbling. Curve m shown in FIG. , and a curve m2 formed by moving this curve mo in parallel and shaking the head, when the distance is measured using three distance sensors, if the swing angle is small, "屓 = meditate. Therefore, the swing is If the angle is small, C8-07 of m(,, m2 will be the same, so even if there is a slight swing, the bend can be measured accurately.

It goes without saying that a distance sensor may be arranged to directly measure the distance to the center line as in the conventional method.

In this embodiment, each coefficient is calculated based on the distance difference between the straight line passing through the distance measurement points A and C and the distance measurement point B, but this is not limited to this.
Of course, it may be determined based on the distance difference between the straight line passing through B (B, C) and the distance measurement point C (A).

In addition, in this example, three distance sensors are placed on the reference straight line, but if the distance to the reference straight line is to be determined, they can be placed at any position on the straight line that passes through each measurement point and is perpendicular to the reference straight line. May be placed.

Further, the two points at which the bending is zero need not be limited to the most extreme support and the rearmost end of the strip, but may be two points in the vicinity thereof.

〔Effect of the invention〕

As detailed above, the bending measuring method of the present invention sets the distance from the measurement point near both ends of the strip to the reference straight line as O, and calculates the n coefficients of xi at once. Since it can be determined only by regression calculation,
The calculation accuracy of those n coefficients becomes extremely high. As a result, in the present invention, the bending of the strip can be accurately measured.

[Brief explanation of the drawing]

Fig. 1 is a schematic diagram showing the implementation state of the method of the present invention, Fig. 2 is a schematic diagram showing the relationship between distance measurement points and distance measurement values 2 curved shape curves in the method of the present invention, and Figs. A schematic diagram for explaining the principle of the invention method, FIG. 7 is a schematic diagram showing the implementation state of the conventional method, and FIG. 8 is a schematic diagram showing the relationship between distance measurement points and distance measurement value 1 curve shape curve in the conventional method. It is. ■...Striped body 2.3.4...Distance sensor patent
applicant

Claims (1)

[Claims] 1. Obtain distance measurement values by measuring the distance from a reference straight line substantially parallel to the longitudinal direction of the strip to one end of the strip or the center line of the strip at three locations, and calculate these distances. In the method for measuring the bending of a strip, the distance from the reference straight line to one end of the strip or the center line of the strip is determined as an n-th order polynomial of the longitudinal position of the strip based on the measured value. Find the deviation distance between the straight line connecting the two distance measurement points and the remaining one distance measurement point at N (≧n-1) points in the longitudinal direction of the strip, and calculate the longitudinal position and this deviation. N equations showing the relationship with distance, and 2 where the deviation distance from the reference straight line near the leading edge and the trailing edge of the strip is set to 0.
A method for measuring curvature of a band-shaped body, characterized in that coefficients from the nth to the zeroth order of the nth-order polynomial are determined based on the equations in this book.