JPS5965710A - Measurement for center line profile of belt-shaped matter - Google Patents

Abstract

PURPOSE:To measure a center line profile of a belt-shaped matter, by calculating a shift distance between a straight line connecting the center positions measured at two areas and the center position measured at an area. CONSTITUTION:It is supposed that a center line l1 is equal to an n-order curved line which is shown by the following equation. That is, f(x)=Cnxn+Cn-1xn-1+...+ C1x+0 (x: lengthwise direction of a belt-shaped matter 20 and Cn, Cn-1...C1, C0: coefficients). It is understood that a shift distance DL is shown by an (n-2)- order equation containing coefficients C2-Cn by calculating an DL=f2(x3)-f(x3). Therefore a sufficient units of distances DL are repetitively measured with the line l1 to perform the regression of (n-2)-order. Thus a regression coefficient is obtained, and therefore coefficients C2-Cn are obtained. While the coefficients C0 and C1 are obtained by solving 2-dimensional simple simultaneous equations after measuring simultaneously the position of the line l1 of the matter 20 at three points and defining the measured value as A[(X1e, f(x1e)] and B[x2e, f(x2e)] at two points among those three measured points.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for measuring the centerline profile of a strip-shaped object, and in particular, 19-Length of a strip-shaped object such as a steel plate or a hot-rolled steel plate=J
This invention relates to a method for measuring the centerline profile of a strip-shaped object, which is suitable for use in measuring the bending of a strip-shaped object on a manufacturing line of the strip-shaped object.

Generally, on a manufacturing line for belt-shaped objects, it is important to know the degree of bending of the belt-shaped object in the longitudinal direction and the positional relationship of the belt-shaped object on the manufacturing line. For example, in the rolling process of thick steel plates (hereinafter referred to as thick plates), in order to improve the yield, it is important to measure the bending of the thick plates and appropriately control the entire rolling mill.

For such purposes, traditionally, plank tunes! Camber distance measurement is often used to control traffic conditions. As shown in Figure 1, this camber means the ratio of the straight line distance F connecting both ends of the buried board lO to the maximum distance G of the edges in the longitudinal direction, and is measured to camber G'. By this, plank 1
It is possible to grasp the extent to which the bend of 0 is possible, but this is limited to the case where the plank 10 has a simple bend.
In the case of a shape like the following curve, it becomes difficult to grasp the track 9 using only the camber G, and it becomes impossible to control the single bend sufficiently.

Therefore, a method of determining the centerline profile of a thick plate has been proposed. The problem with soil for determining the centerline profile of a plank is that the plank moves in a direction perpendicular to the longitudinal direction of the plank (hereinafter referred to as lateral digging) or rotates once on the production line. Therefore, it is not possible to obtain an accurate centerline profile by simply measuring all the side edge positions (referred to as edge positions) of a thick plate using an optical method or the like.

Therefore, conventionally, three detectors are installed at arbitrary intervals in the longitudinal direction of the plate to measure the edge position of the plate.
The lth detector measures the edge position at a specific point on the side edge of the plank. Then, when the plank advances by L in the longitudinal direction, the side measured by the first detector Measure the edge position at a specific point on the edge using the second detector, and find out how much the edge position shifts while the plate advances by L? Bomei. Furthermore,
2. Similarly, determine the amount of deviation of the plate edge position between the blind and third sparrow detectors. Repeat this measurement at every sampling interval to detect the horizontal deflection or rotation of the plate. There are ways to correct it. However, this method: (1) cannot determine the centerline profile of the plank between the detector installation intervals;

In order to compensate for the shortcomings of (2)-(1), the detector installation interval L
If it is shortened, it has the disadvantage that the calculated A difference increases, and as a result, the centerline profile of the thick plate
': I couldn't ask Bo III.

The present invention (d) was designed to eliminate the drawbacks of the conventional technology.
It is an object of the present invention to provide a method for measuring the centerline profile of a strip-shaped object, which can accurately determine the centerline profile of the strip-shaped object to n-th fineness without being affected by the shadow of tj runout.

In the present invention, when determining the center line profile of a strip-shaped object, -C, the total distance between the reference line parallel to the longitudinal direction of the strip-shaped object and the center position of the strip-shaped object, and
l i, and find the passing distance between the straight line connecting the center positions measured by the two radials M and the center position 1 measured by the remaining one M [, repeat at the longitudinal direction row position of the strip-like object, and find. The relationship between the deviation distance and the position of the belt-shaped object in the pitcher direction is calculated by regression calculation! 1n-2nd degree polynomial, each coefficient of the n-2nd degree polynomial, any two sets of data from the data used in the previous 6 regression calculations, and the centerline profile of the band-shaped object as the tnth degree polynomial. Each coefficient kik of the previous Nt n-th degree polynomial is calculated using the relation sound established between each coefficient in the case of approximation, and the center line profile of the strip-shaped object is approximated as an n-th degree polynomial. This is what I achieved.
An extension line of a straight line measured at M and connecting Guhi center position 1α,
This is the deviation distance from the center position measured for the remaining one piece M.

Alternatively, the above-mentioned slipping distance τ is the deviation distance between the center position measured at the two ends M, which connects all the center positions, and the center position measured at the center position M.

The present invention will be explained in detail below.

First, as shown in FIGS. 2 and 3, the center of the strip-shaped object 20! By determining the distance 11i [, D L '', Hjii1 between the extension of the straight line 12 where the two touching points A-B of l + - h and the center position C raised by the remaining one M are determined. , a case in which the center line of the strip-shaped object 20 is determined will be explained as an example.

In the second section, it is assumed that the center line 11 is an nth-order curved edge expressed by the following equation.

f (x)=Cn xn+ Cn-I X +-1-
C1x+Co ・・・・・・−・−・・・・・・
・(1) C':, -Q -X is -'itr g +)
Longitudinal position of 74 bodies 20, crt, Cn-1-・””
c, −”O is a coefficient.

On the other hand, the straight line B2 traces the two points A and B'i on the center line ll, so the two points A-B0) coordinates r, A(x+-
), B(x2, f (X2) ) is a linear equation. Therefore, the coordinates of point c-p (point on direct expansion 12) are:

B, C(X3-f(x3)), D(X3, f
2(x3)), the deviation distance is expressed as V as linear.

D'L=f2(X3) -f (X3) Here, as shown in Figure 2, x2-xI= L2-one in one stone (
f(x and f(X+)l+f(xl) -f(x3)...
-...(4)2 Furthermore, F21(X)=f(X2) f(xl)-Ft3
(x)=f(x+) When linked with f(xs), the above (1
), F 21 (x) and F+5(x) are respectively expressed as follows.

F2+(x)=Cn(x2rL-xl")+Cn-+(
x2 Xi )+ --F13(x)-Cn (x
,"-x3)+Cn-1(Xl"-'-X,n-4)
+ −...”””+C2()5”x3”)+C,(
x,
The result is as shown in the h-station linear equation.

From this equation (7), it can be seen that the deviation distance DL becomes a +(n-2) order equation. Further, among the coefficients Q to Cn of equation (1) represented by the center line 11, −C3 to Cn are included in equation (7). Therefore, with respect to the center line 11 of the strip-shaped object 20, a sufficient number of deviation distance shadows DLt are repeatedly measured, and the (n-2) regression is performed to obtain the 11 regression coefficient. If all the comparisons are made with each coefficient when expanded, then the center line of the strip-shaped object 20 is assumed to be l+k n-dimensional equation.

This means that 11 has not arrived at C2~ from the second to the nth order.

On the other hand, the coefficient Co%C1 is determined by the following method. That is, as shown in the fRa diagram, in order to obtain one deviation distance DL', the position of the center line 11 of the strip-shaped object 20 is measured at three points at the same time. Among these measured values, measured value 2 at two points A (X, e-f(x+e)) -B (Xy
a, f(x2e)), the following two equations of 5th order are obtained.

f(x,6)=C1x,(r-)On-1xl"-'to-+C2x,."+C,x1gtenc.・(8)f
(x2e)=Cn X2 enl(h-1x22”-1
+ HHH+C2x2e 2+ CI X2e + C
o・-(9) In this formula (8) and formula (9), 102~
Since cn is known, equations (8)-(9) become as follows.

x+eCH 10. =s, ・・・・・・・・・・・・
・(!0)XvC,+C6=S2 ・・・・・・・
... (11) Here, S+""f(x+e) CllX1e Cn-lX
1e"-'"' C3x, 6"""" (12)S
2”f(X2e) CllX26 Ch-tx,,
+++ E2x26” (13).

Therefore, by solving the two-dimensional simultaneous equation of (LO)-(11), the coefficient Co-C1 can be found. Next, the 41st Nu! Shown in 1"<, even, shape,) 20
Center of ffMel upper nol:f#,reft 2 points A-C
'11it Nil LMk13. ! :, deviation distance from center position B measured by one central piece F5i M'< 1iil
l', i:y: The centerline profile of the strip-shaped object 20 by ? As shown in FIG. Assume.

On the other hand, city i1. lJ! 13, two points A- on the center line ll
Since it is a straight line passing through Ct, the coordinates of the two points A and C are A(X
If I−f(x, )) and C(x3, f(x3)), it is expressed by the following equation.

On the coordinates of point B-E (point on straight line 13).

respectively, B(X2- f(X2)-E(x2- f3
(X2)), the deviation distance M is expressed as the following equation.

M= f3(X2)-f(x2) Here, as shown in Figure 4, X3-XI"L, + x
2-Xl-L2, equation (15) becomes as follows.

Furthermore, F3+ (xl)=f (X3)−f(x,),
If we set F+z(x)=f(xl)-f(X2),
From the above equation (1), -F31 (X) and F12 (X) are respectively as follows.

Fa+ (x) = Cn (X311-xln)+C
n-1(x3n-x,, n-1) + -”+C2(
x3”-x I 2) +C1(x3-xl)F12(
X)-Cn(XInX2n)-+-c,-1(x, n
-'X2"-') +""""'+C2(XI
"x2") + C, (xIX2) this (17) - (18
) is substituted into the above-mentioned equation (16), the deviation distance M is finally as shown in the following equation.

From this formula (19), the deviation distance M is also (n-2)
It can be seen that the following formula is obtained. Of the coefficients Co'''-Cn of equation (1) given to the center MAAi+, c2 to cn are (
19) Included in Eq. Using a hammer, a sufficient number of deviation distances Mi are repeatedly measured about the center line 111 of the strip-shaped object 2o.

(n-2) Next L 1 almost) Bij 5 times 5 broomstick calculation - Comparison with each coefficient when formula (19) is fully expanded and 7 is completed. The coefficients 02 to C11 from the second order to the nth order are found when assuming that the equation is the n-th order equation.

On the other hand, the coefficient Cn-C1 is calculated in the same way as when calculating the center line freon from the sliding distance L)L.

It can be obtained by solving the two-dimensional simultaneous equations of equations (10) and (11) above.

In addition, the relationship between the front bB demarcation IJ distance L1 and L2 and the length d of the 2° diameter object is, for example), ==ffl-1,2
:'! -tona2'4 55 N) Regeyoi. This relationship is based on the band-shaped object 2
If the centerline profile of 0 is sharpened, it will tremble somewhat, but it is usually fully applicable to the centerline profile of a slab observed during the process.

As mentioned above, the main departure] is the passing distance 1) L or l1-1
By measuring M, it is determined as a polynomial of the center line flow field It k n rL of the strip-shaped object 20. In the present invention, the deviation distance I#lit D L M does not change even if the strip-shaped object 20 is translated in the y-axis direction.

The data A (Xt
e-f(x+e))-B(x2e-f(x2e))
Since k ears B are included, data A (Xte −f (x
The positional relationship between the strip-shaped object 20 and the production line at the time of measuring te)) and B(Xze-f(X2e)) can also be clarified. Therefore, it is also possible to continuously change the control amount for one bend over the longitudinal direction of the strip-shaped object 20.

However, according to the present invention, an error does not occur due to lateral vibration of the belt-shaped object 20, but if the belt-shaped object 20 rotates, an error occurs, and the extent to which the error increases due to rotation is as follows.

It will be as shown by the solid line H or broken line in FIG.

However, the rotation of the belt-shaped object 201, for example, a thick plate, is approximately 2501 klK for a plate length of 64 on at most.
That is, -〇=ta, n' (250/40000)=0
．． It is about 36°. Therefore, even if such a rotation occurs during centerline and profile measurement, when calculating the centerline profile from the deviation distance DL, the difference between the actual centerline profile and the calculated centerline profile will be very small. Since it is O, it does not have a big influence as a whole. Furthermore, even if one thick plate is rotated by 15 degrees, the error will be 8 to 1.
It only increases by about 4 fights. In the process of ￥,
Such a large rotation can never occur, and even if it were to occur, its impact I# would be slight.

On the other hand, I am disappointed in the method of determining the center line profile from the deviation distance M (-1:, from Fig. 5, the rotation angle θ =
0. ．． It is clear that almost no error occurs for a rotation of about 36°. Also, even for a rotation of -5 degrees, the increase in error is within 2 degrees, and its influence is extremely small. In this way, the present invention is also almost unaffected by the rotation of the strip-shaped object 20.

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the method for measuring the centerline profile of a strip-shaped object according to the present invention will be described in detail below with reference to the drawings.

Figure 6 d + This is a schematic diagram of an apparatus for measuring the entire center line profile from the deviation distance DL or M in a plate rolling mill.

It was installed at the rear of the mill. Width meter 22- that can measure the center position
24-26 to measure the position of the center line 11 of the plank IO. The origin of the position measurement of the center line Itl is in the -y axis direction.
Line center m J −x il! ll+ direction is thick plate J
Return to the vicinity of the tail end 10b of O. In general, the tip 10a and the vicinity of the O/tail end 10b of the thick plate 1O during rolling are cropped, so the position measurement of the center line 1 of the thick plate 10 1. This is inappropriate as a fake place. Therefore, on the line center line J, an infrared detection type tip detector 28 and a tail edge detector 30 are installed at positions 1 m apart from the total width 22.26, and the tip detector 28 is located at the tip of the thick plate lO. 10 a'
<At the moment of detection, the position measurement of the center line 1 starts completely, and the moment the tail end detector 30 detects the tail A#10 k)', H of the thick plate lO, the position measurement of the center line 11 is finished. I try to do that. In the meantime, a pulse generator (not shown) installed on the goop roller 32 is used to set the entire sampling length in units of 0.1 m, making it possible to perform repeated measurements.

Below - first - the operation will be explained for all cases of the first embodiment in which the center line profile is determined from the deviation distance DL.

As shown in FIG.
The position measurement result of the center line 11 of O.

A (-f (x+k) to x+), B (-f (X
2k> ), C(xak, f(Xak) ), (where k = l % m-yl is the number of one package measured), then by substituting these data into equation (3) above and subtracting, we get , m
The displacement distance DL is determined. By the way, in the case of thick plate lO, it has been found that the profile of the center line e1 can be accurately approximated by the 6th order equation, so in this example, Q, (Xl
−DLk) (k = 1~m), and the sixth order −2
Next = 4th time. At this time,
The regression coefficient 'fKi~Ko (
D L = = 4 Xl ' +Ks Xl '' + K2
If X12+ is 1xl+Ko), then the number of the 6th order expression % expression % expressing the center line profile of the -thick plate lO can be found as 1st order.

C6= 4/15・Mo・・・・・・・・・・・・
... (20) C, = 3/10 M, -2MIC
6・・−=・(21) C4=to 2/6M0 5M+Cs
/3-5M2C1,/2 ・−・−・(22)C3==
ni1/3Mo 4HI C4/3-5 H2CV/3
-2M3Co -...' (23) C2-Ko/Mo
MIC3M2C4M3C5H4C11””””””(2
4) Here, MO=L, (L2-L, ) IA+ =L14-L2 H2=L12+ LIL2 +L2" H3: LI"+ LI2L2 +LI L2"10L2"
H4=I4'+ 143L2+L12L22+LI 1
4'+L2'.

Also, the coefficient C8-C is the last position measurement data CXun-f (X+ m)) - (xam-
Using f (X3m)) k, from the following formula, ``<.

C+-(St-83)/ (X+m xam) ・
+・・・・・・・−・= (25)Co”' (X
+m °S3 X3m°S1)/(x+m xam
)−°°°(26) Here, 5t=f(x+m)−C6x1m” Csxlrn5C
4XB11LC3X1m”-C2X1m”・・・・・・
・・・・・・ (27) 8s=f(xam)-C6X3m'Csx3m'-C
4xgLCaxp3-c2X3m"・・・・・・
(28).

FIG. 8 shows an example of the measurement results according to the first embodiment when Ll=23m, L2=12m, and sampling length 'i is set every 0.577L. The points plotted in FIG. 8(A) are the measured values of the grazing distance DL, and the solid line K shows the result of all the fourth-order regressions. or.

In Fig. 8(B), the solid line 1h shows the actual center line profile of the thick plate 10c'), and the broken line N shows 1
This figure shows the centerline profile obtained by the sixth-order approximation of this example. As is clear from Figure 8 (B),
The difference between the actual centerline profile 11 and the centerline profile N determined according to the present invention is about 25·ill at most, and the two agree well.

Next, Sure II! A second embodiment of the present invention will now be described in full detail, in which the centerline 7' profile is measured from a distance of 12 M.

In this second* embodiment as well, the same scissor cage as in the first embodiment is used, so a description of the device will be omitted and the operation will be explained with reference to the ninth embodiment. In Figure 9, width total 2
2.24.26 Position measurement result of center line JISl of plank io, p, (x, to, f(xsk)), B
(X2k = f(x2 to 3- C(x3 to f(xs
k)) - (where = 1 to m, where m is the number of measurements), by substituting these data into the above equation (15) and calculating, m deviation distances i to 1 are found. The misalignment distance M obtained in this way is 7, and as in the previous example, (-Mk to X+) (k=1- ・-
・, m) h, 6th order - 2nd order = 4th order regression was performed. At this time, 1 regression coefficient is 4~Ko (Ai =
K4 x 3x to 1'+, 2x to 3+ + X to l'+
l +Ko), the center line block 1- of the thick plate 10
The coefficient of the % formula % is 1 and the 5th order is 1, C 6 "" K4/ I 5 HO...
・・・・・・・・・・・・・・・・・・・・・ (29)
C5 2 3/10 HO 2HI C6 ・
・・・・・・・・・・・・・・・・・・・・・ (30)C
42i<2/sHo 5HIC73 5H2Ca/
'2 --- (31)C3=to1/3Hoa)(
, C4,/3 5H2C5/'32) izc6 −
(32) Cz=Ko/Ho n, C3) i2c4
M3C5-H4C6...--(33) Here.

)io:'[, zls L2) )it = LI + L2 1 (2 = LI" + LI L2 + Ln Ha = L1
"+L+" L2+ LI L22+L2'H4"
LI'+LIJL2+LI" L22+LI L23+
It is L2'.

On the other hand, the coefficient a C6-C is the last position measurement data (xlm-f(xtm)), (Xprn-f
(xyn))' is used to calculate d) from the above-mentioned equations (25) and (26) in the same way as in the first actual calculation.

Figure 10 shows an example of the second embodiment where L1 = 23m - L2 = = 12rn and the sampling length is L5mvJ. Figure 10 (AJ
The points drawn by 10 are the 611j constant straight line with the -no-run distance M, and the solid line 0 indicates the result of performing the 4th-order im. Also, Figure 10! In (B) 2, 1 is the actual centerline profile of the thick plate LO on the east line, and the broken line P is the centerline profile obtained by the 6th approximation of the 5 actual examples. Figure 10 (B
), the igneous centerline profile 11
The difference between the center line profile and the center line profile obtained according to the present invention is
The two ministries are in good agreement, with 25 sections being the same.

2. In each of the above examples of firearms, the present invention is applied to the measurement of the central axis of one thick plate, but the scope of application of the present invention is not limited to this. First, the center line profile of other strip objects such as hot-rolled copper plates, etc.
Alternatively, it is clear that the present invention can be similarly applied to the curve 9 of bar-shaped objects such as shaped steel and steel bars.

As explained above, according to the present invention, what is the effect of lateral vibration of the belt-shaped object? Centerline profile of a band-shaped object without receiving? It is possible to obtain detailed information with high accuracy. Moreover, it has excellent effects such as being able to know the positional relationship of strip-like objects that are moved on one production line at the same time.

[Brief explanation of drawings]

Figure 1 shows 2. The bending of the board? 4(
11 Definition of camber that is defined The plan view shown in Figure 2 shows the extension of a straight line connecting the center positions suppressed at two adjacent places and the hand center position measured at the remaining one place. Diagrams for explaining the present invention in detail when measuring the center line profile of a strip-shaped object from the deviation distance DL. FIG. 75 MA I - The deviation distance from the center position measured at one point in the center [M], which is useful when measuring the entire center line profile of a strip-shaped object.Detailed explanation of the present invention The diagram for FIG. 5, 1, is also
Figure 1 shows the relationship between the [01 rotation angle and the measurement error state of a strip-shaped object. Fig. 17 is a perspective view showing the configuration of an example of the device, and Fig. 17 shows a state in which the centerline profile of a buried board is measured using the first example of the centerline profile of a band-shaped object according to the present invention.
μ? The plan views shown in FIGS. 8(A) and 8(B) are
r7 In the first embodiment, the plate longitudinal direction IU, the curl distance DL and the center +l! 1% of the relationships in the profile
Fig. 7i shows 1-diagram and Fig. 179 shows J.
Inside the board I
In the example. It is a line diagram shown in fl, l' of the relationship between the position in the direction of the plate, the deviation distance M, and the centerline profile. io...Thick plate, 20...Striped object-2124-26.
...Width total -32...Dipple roller. Figure 1 Rotation angle 6th F Return]

Claims (3)

[Claims] (1) When determining the center line profile/L of the strip-shaped object, measure the distance between the reference line parallel to the longitudinal direction of the strip-shaped object and the center position of the strip-shaped object at three points Rr in the longitudinal direction of the strip-shaped object,
Disparity distance 1iI11 between the straight line connecting the center positions measured at two of the points and the center position measured at the remaining one point.
The relationship between the displacement distance repeatedly determined at the longitudinal position of the strip-shaped object and the longitudinal position of the strip-shaped object is calculated by regression calculation.
9n-2nd degree polynomial, and each coefficient of the n2nd degree polynomial, any two sets of data used in @gji regression calculation, and the center line profile of the band-shaped object as an nth degree polynomial. Each coefficient of the n-th degree polynomial is determined using a related sound established between each coefficient of the approximated lifting platform, and the centerline profile of the strip-shaped object is approximated as an n-th degree polynomial. A method for measuring the centerline profile of a strip-shaped object. (2) The scope of claims where the front alignment distance is defined as the deviation distance between the extension of a straight line connecting the center positions measured at two adjacent locations and the center position 1 measured at one location on the left side. No. L
*Method for measuring the centerline profile of a strip-shaped object as described in K@6. (3) The deviation distance K is defined as the distance between a straight line connecting the center position A and the center position measured at two points on the inner edge and the center position measured at one point in the center. Method for measuring the centerline profile of a strip-shaped object as described in 8th Edition.