Method and apparatus for measuring cross sectional dimensions of sectional steel

Cross sectional dimensions of an intermediate product of sectional steel are measured in the course of rolling, by simultaneously, horizontally reciprocating, in the direction transverse to a conveyance line of the sectional steel, two laser range finders which are disposed vertically opposite to each other. The method and apparatus are capable of determining, precisely and automatically, a sectional shape of the H-beam in an on-line manner, thereby improving product quality and yield.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method and apparatus for measuring the 
cross sectional dimensions of an intermediate product during the formation 
of sectional steel in a rolling line for rolling sectional steel such as 
H-beam, I-beam or channels, all of which include a pair of flanges and a 
web connecting the flanges. 
2. Description of the Related Art 
Conventionally, the cross sectional dimensions of sectional steel, 
particularly H-beam, are mainly manually measured using calipers or a dial 
gauge because of a variety of shapes. This measurement has the faults that 
reproducibility is low due to differences among operators, and that much 
time is required. 
In order to remove the faults, various techniques have been developed for 
automatically measuring the cross sectional dimensions of sectional steel. 
An example of generally known techniques is a .gamma.-ray penetration 
system in which radiation is applied to a flange portion and a web portion 
of H-beam, and the amount of penetrating radiation is measured to 
determine the thickness from the amount of attenuation. Another example is 
a spontaneous light emission system in which the light energy 
spontaneously emitted from a hot rolled steel material is received by a 
light receiving device to detect the edges of both ends of a flange, and 
the width of the flange is determined from the distance between the edges. 
Yet another example is a backlight auxiliary light source system in which 
a mirror is placed between a flange and a web inside the flanges, the 
light emitted from a light source is applied to the mirror and reflected 
by the mirror so as to generate a light flux perpendicular to the flanges, 
and the light transmitted is detected by a light receiving device. 
However, the above conventional automatic measurement systems have various 
problems. 
The .gamma.-ray penetration system has the defect that only the flange 
thickness and web thickness can be measured, and necessary items such as 
the web height, the leg length and center deviation cannot be measured, 
and the drawback of relatively high cost of equipment. 
The spontaneous light emission system is limited to a flange width meter, 
and produces error in detecting the edges due to the effect of temperature 
drops at both flange ends, and it is thus not possible to make sufficient 
use of the system. 
Unlike the spontaneous light emission system, the backlight auxiliary light 
source system produces no error due to the effect of the temperature 
drops. However, this system has the problem that the mirror must be placed 
close by the H-beam, as well as problems with respect to the complicated 
apparatus, reliability, maintainability, etc. Although the measurement 
principle of the apparatus can be applied only to measurement of the 
flange width, combination with another meter such as a laser range finder 
permits measurement of the other items. However, this system has a 
relatively high cost. 
Other methods and apparatus for measuring dimensions of sectional steel are 
disclosed in Japanese Patent Laid-Open Nos. 2-254304 (referred to herein 
as "Cited Reference 1" hereinafter), 4-157304 (referred to herein as 
"Cited Reference 2" hereinafter), and 7-27518 (referred to herein as 
"Cited Reference 3" hereinafter). 
Cited reference 1 discloses a measurement apparatus comprising stage 
mechanisms disposed above and below sectional steel so as to move in 
horizontal and vertical directions, a plurality of one-dimensional laser 
range finders provided on the stage mechanisms, and a data processing 
device for computing the sectional shape of the sectional steel from the 
detected values of the laser range finders. 
Cited Reference 2 discloses a method in which a pair of two-dimensional 
range finders and a pair of one-dimensional range finders are arranged 
opposite to each other in the widthwise direction of flanges of H-beam so 
as to face a flange and a web, respectively, for measuring the vertical 
distances to the opposite flange by the two-dimensional range finders, and 
the vertical distances to the opposite web by the one-dimensional range 
finders. The deviation of the web, flange width and web thickness are 
computed simultaneously. Cited Reference 3 discloses an apparatus 
comprising a two-dimensional range finder provided on U-shaped support 
frames which cover the right and left halves of H-beam and which can be 
moved in the transverse direction, for measuring the flange width by 
applying a widthwise slit laser beam to the outside of a flange, and a 
two-dimensional range finder for measuring a distance by applying a slit 
laser beam to the upper and lower sides of the flange, the inside of the 
flange and the upper and lower sides of the web at a predetermined angle 
perpendicular to the direction of conveyance, so that a sectional shape is 
determined by using a processor for processing the distance data obtained 
by detection by each of the laser range finders. 
The main objective of the above-described conventional measurement 
techniques is to measure a section of a final product of H-beam after 
final rolling by a mill. In this case, a flange portion and a web portion 
are at right angles to each other in a section of the H-beam. In a section 
of an intermediate product in the course of rolling, on the other hand, 
e.g., a section of the H-beam which are passed through a break-down mill 
before a universal mill, a flange 1f has a taper at an angle .alpha. with 
respect to the web 1w, as shown in FIG. 13. Such a section of an 
intermediate product can not be measured accurately by the measurement 
apparatus disclosed in Cited References 1, 2 and 3. 
Furthermore, because each of the conventional techniques uses many laser 
range finders (8 finders in embodiments of Cited References 1 and 2, and 6 
finders in Cited Reference 3), the apparatus becomes extremely expensive 
and the frequency of accidents might be increased. 
SUMMARY OF THE INVENTION 
The present invention has been developed to solve the above problems of the 
conventional techniques, and an object to the present invention is to 
provide a method and apparatus which are capable of measuring cross 
sectional dimensions of an intermediate product during the formation of 
sectional steel with high precision, even when the section thereof is not 
a rectangular shape. 
In accordance with one aspect of the present invention, there is provided a 
method of measuring cross sectional dimensions of an intermediate product 
of sectional steel in the course of rolling by simultaneously 
reciprocating horizontally, in the direction transverse to the conveyance 
direction of the sectional steel, two laser range finders which are 
disposed opposite to each other in the vertical direction of the sectional 
steel. The method comprises the steps of irradiating, in forward 
traveling, the sectional steel with laser beams at predetermined angles 
from the laser range finders to measure the positions of the laser range 
finders, the distances to the sectional steel and the irradiation angles; 
irradiation, in backward running, the sectional steel with the laser beams 
at angles different from the angles in forward traveling to measure the 
positions of the laser range finders, the distances to the sectional steel 
and the irradiation angles; selecting measurement data at the same 
position on the sectional steel from the obtained measurement data to 
output space coordinates of a section of the sectional steel so that the 
selected measurement data agree with each other; and computing data of a 
shape from the space coordinates. 
In accordance with another aspect of the present invention, there is 
provided an apparatus for measuring cross sectional dimensions of an 
intermediate product of sectional steel during the course of rolling, 
comprising an upper laser range finder tiltably provided above the 
sectional steel, which is passed through a gate-like frame installed to 
surround a conveyance line of the sectional steel, for measuring the 
distance to the sectional steel; upper laser beam irradiation angle 
detecting means for detecting the angle of irradiation of the laser beam 
from the upper laser range finder; upper laser range finder moving means 
containing the upper laser range finder and the upper laser beam 
irradiation angle detecting means so as to be horizontally movable; upper 
laser range finder position detecting means for detecting the position to 
which the upper laser range finder is moved; a lower laser range finder 
tiltably provided below the sectional steel opposite to the upper laser 
range finder, for measuring the distance to the sectional steel; lower 
laser beam irradiation angle detecting means for detecting the irradiation 
angle of laser beam from the lower laser range finder; lower laser range 
finder moving means containing the lower laser range finder and the lower 
laser beam irradiation angle detecting means so as to be horizontally 
movable; lower laser range finder position detecting means for detecting 
the position to which the lower laser range finder is moved; and a 
sectional shape computing device for determining a sectional shape profile 
of the sectional steel from the space coordinates thereof, which are 
obtained by phase matching between the measurements of the position of the 
upper laser range finder, the distance to the sectional steel and the 
irradiation angle and the measurements of the position of the lower laser 
range finder, the distance to the sectional steel and the irradiation 
angle during traveling of the upper laser range finder moving means and 
the lower laser range finder moving means, to compute the cross sectional 
dimensions of the sectional steel from the sectional shape profile. 
In the method and apparatus for measuring cross sectional dimensions of an 
intermediate product of sectional steel as a measurement object in the 
course of rolling in accordance with the present invention, the positions 
of the two laser range finders, which are disposed above and below the 
sectional steel, the distances to the sectional steel and irradiation 
angles of the laser beams are measured by horizontally reciprocating the 
two laser range finders in the direction crossing the conveyance line for 
the sectional steel, and cross sectional dimensions of the sectional steel 
are obtained from the sectional shape profile which is determined by phase 
matching of the measurements. It is thus possible to automatically 
determine the sectional shape of the sectional steel with high precision 
in an on-line manner.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Embodiment 1! 
One embodiment of the present invention relating to H-beam is described in 
detail below with reference to the drawings. 
FIG. 12 is a drawing illustrating the arrangement in a line for producing 
H-beam by using a breakdown mill BD, a rough universal mill UR and a 
finish universal mill UF. An intermediate product of the H-beam, which was 
rolled by the breakdown mill BD, is stocked in a skid 61 where the cross 
sectional dimensions of the sectional steel are measured by a cross 
sectional dimension measuring device 60, and then sent into the rough 
universal mill UR. 
FIG. 1 is a schematic diagram showing the construction of the cross 
sectional dimension measuring device 60 for measuring an intermediate 
product of H-beam in accordance with one embodiment of the present 
invention. 
In FIG. 1, reference numeral 1 denotes an intermediate product of H-beam as 
a measurement object which is conveyed by a conveyance roller 2. Reference 
numeral 3 denotes a gate-like frame comprising support members 3a and 3b 
which are erectly provided on a floor 4 so as to hold the conveyance 
roller 2 therebetween, and a support member 3c placed between the support 
members 3a and 3b. 
Reference numeral 10 denotes an upper laser range finder contained in an 
upper laser range finder moving device 11 that is suspended by wheels 6 
which can be moved on a rail 5 provided on the lower side of the support 
member 3c in parallel relation therewith. The signal output from the upper 
laser range finder 10 is input to a range signal processor 12. Irradiation 
angle adjusting device 13 adjusts the irradiation angle of the upper laser 
range finder 10. Reference numeral 14 denotes an upper laser beam 
irradiation angle detector, a signal output therefrom being input to an 
irradiation angle signal processor 15. Reference numeral 16 denotes a 
driving device for moving the upper laser range finder moving device 11. 
Reference numeral 17 denotes an upper laser range finder position detector 
for detecting the position to which the upper laser range finder is moved, 
a position signal output from the upper laser range finder position 
detector 17 being input to a position signal processor 18. A purging 
device 19 is provided on the upper laser range finder 10 so as to ensure 
an optical path for a laser beam. 
Reference numeral 20 denotes a lower laser range finder contained in a 
lower laser range finder moving device 21 supported by wheels 8 which can 
be moved on a rail 7 provided on the floor 4 between the support members 
3a and 3b. A signal output from the lower laser range finder 20 is input 
to a range signal processor 22. Reference numeral 23 denotes an 
irradiation angle adjusting device for adjusting the irradiation angle of 
the lower laser range finder 20. Reference numeral 24 denotes a lower 
laser beam irradiation angle detector, a signal output therefrom being 
input to an irradiation angle signal processor 25. Reference numeral 26 
denotes a driving device for moving the lower laser range finder moving 
device 21. Reference numeral 27 denotes a lower laser range finder 
position detector for detecting the position to which the lower range 
finder 20 travels, a position signal being input to a position signal 
processor 28. 
Reference numeral 30 denotes a sectional shape computing device which 
computes a sectional shape profile by computing and synthesizing space 
coordinates of the measurement distances on the basis of the signal output 
from the range signal processor 12, the irradiation angle signal processor 
15, and the position signal processor 18 on the side of the upper laser 
range finder 10, and the signal output from the range signal processor 22, 
the irradiation angle signal processor 25, and the position signal 
processor 28 on the side of the lower laser range finder 20. Sectional 
shape computing device 30 also output an irradiation angle adjustment 
signal and a traveling command signal to the irradiation angle adjusting 
devices 13 and 23 and the driving devices 16 and 26, respectively. 
The operation of the upper and lower laser range finders 10 and 20 is 
described on the basis of a triangulation system laser range finder as an 
example. As shown in FIG. 2, laser beam LB is applied to a measurement 
object 42 from a laser oscillator 41, and the light reflected by a 
measurement surface 42a of the measurement object 42 is converged by a 
converging lens 43 to form an image at position x on a light receiving 
device 44 such as an image sensor. A range computing device 45 determines 
position X on the measurement object 42 from image formation position x by 
using the relations between the image formation positions a and b, and the 
measurement positions A and B, which were previously determined. As shown 
in FIG. 3, an energy intensity distribution of received light is produced 
on the light receiving device 44. Generally, center N.sub.0 between 
intersections N.sub.1 and N.sub.2 of the threshold level and the 
distribution curve is determined as image formation position x. In this 
way, the triangulation system laser range finder is able to measure the 
distance L.sub.x to position X where laser beam LB is reflected. 
The procedure for measuring the dimensions of each portion of the section 
using the cross sectional dimension measuring apparatus of the present 
invention, constructed as described above, is described with reference to 
FIGS. 4A-4D. 
Step 1; As shown in FIG. 4A, it is assumed that a measurement distance when 
the upper laser range finder 10 has traveled in the direction shown by 
arrow F (referred to as "forward traveling" hereinafter) for distance X 
from measurement position P.sub.1, as detected by the upper laser range 
finder position detector 17, under irradiation of a laser beam at an angle 
.theta..sub.1, is L.sub.1, and the measurement distance when the lower 
laser range finder 20 has traveled in the direction shown by arrow F for 
distance X from measurement position P.sub.2, as detected by the lower 
laser range finder position detector 27, under irradiation with a laser 
beam at an angle .theta..sub.2, is L.sub.2. It is also assumed that the 
distance between the upper and lower range finders 10 and 20 is Y. Thus, 
measurement data of the portions which are measured by the upper and lower 
laser range finders 10 and 20 are represented by x-y space coordinates 
(x.sub.1, y.sub.1) and (x.sub.2, y.sub.2), respectively. These coordinates 
are determined according to the following equations (6) to (9): 
EQU x.sub.1 =X-L.sub.1 sin .theta..sub.1 -P.sub.1 (6) 
EQU y.sub.1 =Y-L.sub.1 cos .theta..sub.1 (7) 
EQU x.sub.2 =X-L.sub.2 sin .theta..sub.2 -P.sub.2 (8) 
EQU y.sub.2 L.sub.2 cos .theta..sub.2 (9) 
Step 2; as shown in FIG. 4B, the direction of measurement by the upper and 
lower range finders 10 and 20 is reversed, and the irradiation angles 
.theta..sub.1 and .theta..sub.2 are changed to .theta..sub.3 and 
.theta..sub.4, respectively, (.theta..sub.3 .noteq..theta..sub.1 and 
.theta..sub.4 .noteq..theta..sub.2). It is assumed that measurement 
distances when the upper and lower range finders 10 and 20 have traveled 
in the direction opposite to direction F (referred to as "backward 
traveling" hereinafter) to positions where the distances measured by the 
upper and lower laser range finder position detectors 17 and 27 are 
P.sub.3 and P.sub.4, respectively, are L.sub.3 and L.sub.4. Thus, 
measurement data of the portions which are respectively measured by the 
upper and lower laser range finders 10 and 20 are represented by x-y space 
coordinates (x.sub.3, y.sub.3) and (x.sub.4, y.sub.4). These coordinates 
are determined according to the following equations (10) to (13): 
EQU x.sub.3 =X+L.sub.3 sin .theta..sub.3 -P.sub.3 (10) 
EQU y.sub.3 =Y-L.sub.3 cos .theta..sub.3 (11) 
EQU x.sub.4 =X+L.sub.4 sin .theta..sub.4 -P.sub.4 (12) 
EQU y.sub.4 =L.sub.4 cos .theta..sub.4 (13) 
Step 3; as shown in FIG. 4C, phase matching is performed so that the 
measurement data of the same position on the measurement object in forward 
traveling agrees with the data in backward traveling. Space coordinates as 
shown in FIG. 4D are determined to obtain a sectional shape profile. 
The profiles obtained by the loci of space coordinates (x.sub.1, y.sub.1), 
(x.sub.2, y.sub.2), (x.sub.3, y.sub.3) and (x.sub.4, y.sub.4) are 
summarized in FIGS. 5A to 5D. 
Description will now be made of the procedure for determining a sectional 
profile by synthesizing the loci of the space coordinates (x.sub.2, 
y.sub.2), (x.sub.3, y.sub.3) and (x.sub.4, y.sub.4) shown in FIGS. 5B, 5C, 
and 5D, respectively, on the basis of the locus of the coordinates 
(x.sub.1, y.sub.1) shown in FIG. 5A. 
Specifically, correction amounts .DELTA.x.sub.2, .DELTA.y.sub.2, 
.DELTA.x.sub.3, .DELTA.y.sub.3, .DELTA.x.sub.4 and .DELTA.y.sub.4 of the 
loci of the space coordinates (x.sub.2, y.sub.2), (x.sub.3, y.sub.3) and 
(x.sub.4, y.sub.4) are first determined, and the space coordinates are 
converted to the following equations (14), (15), and (16). 
EQU (x.sub.2, y.sub.2)=(x.sub.2 .DELTA.x.sub.2, y.sub.2 +.DELTA.y.sub.2)(14) 
EQU (x.sub.3, y.sub.3)=(x.sub.3 .DELTA.x.sub.3, y.sub.3 +.DELTA.y.sub.3)(15) 
EQU (x.sub.4, y.sub.4)=(x.sub.4 .DELTA.x.sub.4, y.sub.4 +.DELTA.y.sub.4)(16) 
(i) Correction amounts .DELTA.x.sub.2 and .DELTA.y.sub.2 are determined 
according of the following procedure. 
(1) Data of measurement at the same position are selected from space 
coordinates (x.sub.1, y.sub.1) and (x.sub.2, y.sub.2). Namely, n values 
are extracted from each of the higher-value sides of x.sub.1 and x.sub.2 
to obtain coordinates (x.sub.1, y.sub.1).sub.1, (x.sub.1, y.sub.1).sub.2, 
. . . (x.sub.1, y.sub.1).sub.n and (x.sub.2, y.sub.2).sub.1, (x.sub.2, 
y.sub.2).sub.2, . . . (x.sub.2, y.sub.2).sub.n. 
(2) Assuming that when coordinates (x.sub.1, y.sub.1).sub.i (wherein i=1 to 
n) have maximum x.sub.1 value, set i=j. 
(3) Coordinates x.sub.1, y.sub.1).sub.i where i=1 to j and coordinates 
(x.sub., y.sub.1).sub.i where i-j to n are approximated to straight lines 
by the following equations (17) and (18), respectively: 
EQU y=a.sub.1 x+b.sub.1 (17) 
EQU y=a.sub.2 x+b.sub.2 (18) 
(4) The intersection of the two lines shown by equations (17) and (18) is 
represented by (x.sub.1, y.sub.1)*. 
(5) Coordinates (x.sub.2, y.sub.2).sub.i where i=1 to n, are determined 
according in the same manners as Steps (2) to (4) to obtain (x.sub.2, 
y.sub.2)*. 
(6) Correction amounts .DELTA.x.sub.2 and .DELTA.y.sub.2 are determined 
according the following equations (19) and (20), respectively: 
EQU .DELTA.x.sub.2 =x.sub.1 *-x.sub.2 * (19) 
EQU .DELTA.y.sub.2 =y.sub.1 *-y.sub.2 * (20) 
(ii) Correction amounts .DELTA.x.sub.3 and .DELTA.y.sub.3 are determined 
according to the following procedure. 
(1) Measurement data at the same position are selected from space 
coordinates (x.sub.1, y.sub.1) and (x.sub.3, y.sub.3). Namely, n values 
are extracted from each of the higher-value sides of y.sub.1 and y.sub.2 
to obtain coordinates (x.sub.1, y.sub.1).sub.1, (x.sub.1, y.sub.1).sub.2, 
. . . (x.sub.1, y.sub.1).sub.n and (x.sub.3, y.sub.3).sub.1, (x.sub.3, 
y.sub.3).sub.2, . . . (x.sub.3, y.sub.3).sub.n. The n value is determined 
by the sampling interval and the flange thickness. 
(2) The centers of gravity of coordinates (x.sub.1, y.sub.1) and (x.sub.3, 
y.sub.3) are obtained and represented by (x.sub.1, y.sub.1)* and (x.sub.3, 
y.sub.3)*, respectively. 
(3) Correction amounts .DELTA.x.sub.3 and .DELTA.y.sub.3 are determined 
according to the following equations (21) and (22), respectively: 
EQU .DELTA.x.sub.3 =x.sub.1 *-x.sub.3 * (21) 
EQU .DELTA.y.sub.3 =y.sub.1 *-y.sub.3 * (22) 
(iii) Correction amounts .DELTA.x.sub.4 and .DELTA.y.sub.4 are determined 
according to the following procedure. 
(1) Measurement data at the same position are selected from space 
coordinates (x.sub.2, y.sub.2) and (x.sub.4, y.sub.4). Namely, n values 
are extracted from each of the lower-value sides of y.sub.2 and y.sub.4 to 
obtain coordinates (x.sub.2, y.sub.2).sub.1, (x.sub.2, y.sub.2).sub.2, . . 
. (x.sub.2, y.sub.1).sub.n, and (x.sub.4, y.sub.4).sub.1, (x.sub.4, 
y.sub.4).sub.2, . . . (x.sub.4, y.sub.4).sub.n. The n value is determined 
by the sampling interval and the flange thickness. 
(2) The centers of gravity of coordinates (x.sub.2, y.sub.2) and (x.sub.4, 
y.sub.4) are obtained and represented by (x.sub.2, y.sub.2)* and (x.sub.4, 
y.sub.4)*, respectively. 
(3) Correction amounts .DELTA.x.sub.4 and .DELTA.x.sub.4 are determined 
according to the following equations (23) and (24), respectively: 
EQU .DELTA.x.sub.4 =x.sub.2 *-x.sub.4 *+.DELTA.x.sub.2 (23) 
EQU .DELTA.y.sub.4 =y.sub.2 *-y.sub.4 *+.DELTA.y.sub.2 (24) 
Step 4; By such a division method as shown in FIG. 6 using the sectional 
profile obtained in Step 3, the sectional areas A.sub.f1, A.sub.f2, 
A.sub.f3 and A.sub.f4 of the respective flange legs are determined from 
the lengths b.sub.U1, b.sub.L1, b.sub.U2 and b.sub.L2 of the four legs of 
the flanges and the thicknesses T.sub.f1, T.sub.f2, T.sub.f3 and T.sub.f4 
thereof, and the sectional area A.sub.W of the web is determined from the 
web thickness T.sub.W and the web height H.sub.W. 
The sectional areas and lengths of the legs, the flange width and the 
center deviation are determined according to the following procedure. 
(1) The averages x.sub.AV and y.sub.AV of x and y are obtained by averaging 
all data of the space coordinates (x.sub.1, y.sub.1), (x.sub.2, y.sub.2), 
(x.sub.3, y.sub.3) and (x.sub.4, y.sub.4) and used as the origins of the x 
and y axes. 
(2) The coordinates are rewritten to the equation (25) below, and data are 
converted into the spaces of the first to fourth quadrants of x-y axes: 
##EQU1## 
(3) In each of the quadrants, data are rearranged in the order of 
increasing x value. 
(4) The web surface and the inner surface of a flange area approximated to 
straight lines to determine the intersection of the two straight lines. 
(5) The sectional area A.sub.f of a leg is determined according to the 
following equation (26). 
EQU A.sub.f =.SIGMA..vertline.y.vertline..times..vertline..DELTA.x.vertline.(26 
) 
wherein .DELTA.x is a difference between adjacent data values. 
(6) The lengths b.sub.U1, b.sub.L1, b.sub.U2 and b.sub.L2 of the legs are 
determined from the maximum value in each quadrant (the minimum value in 
the second and third quadrants) and the intersection obtained in Step (4). 
The flange widths W.sub.1 and W.sub.2 are determined from the difference 
between the maximum and minimum values. 
Center deviations S.sub.1 and S.sub.2 are obtained by the following 
equations (27) and (28): 
EQU S.sub.1 =(b.sub.U1 +b.sub.L1)/2 (27) 
EQU S.sub.2 =(b.sub.U2 +b.sub.L2)/2 (28) 
Embodiment 2! 
In some cases, when the coordinates axes are deviated because the 
irradiation angles of the upper and lower laser range finders 10 and 20 in 
forward traveling area different from those in backward traveling, in some 
cases, measurement data at the same position on the measurement object are 
different. Means for correcting the deviations of the axes is described 
with reference to a second embodiment. 
FIG. 7 shows the construction of the second embodiment of the present 
invention. This embodiment is different from the first embodiment shown in 
FIG. 1 in the point that a correction point piece 50 is mounted on a frame 
51 by the side of the H-beam 1 as the measurement object. Any object 
having known cross sectional dimensions may be used as the correction 
piece 50. For example, a prismatic piece having a square section and 
surfaces as reference surfaces parallel to the x axis and y axis, as shown 
in FIG. 8, is described. 
Measurement data of the position signals P.sub.1n and P.sub.2n obtained by 
the upper and lower laser range finder position detectors 17 and 27, and 
the angle signals .theta..sub.1n and .theta..sub.2n obtained by the upper 
and lower laser beam irradiation angle detectors 14 and 24, which are 
detected at the same time as the distance measurement by the upper and 
lower laser range finders 10 and 20, are represented by x-y space 
coordinates (x.sub.1n, y.sub.1n) and x.sub.2n, x.sub.2n) at each 
measurement point (refer to FIG. 9). The coordinates are determined by the 
following equations (29) to (32), assuming that the angle signals 
.theta..sub.1n and .theta..sub.2n are the same as the angle signal 
.theta..sub.1 and .theta..sub.2 of the H-beam 1: 
EQU x.sub.1n =P.sub.1n +L.sub.1n sin .theta..sub.1n (29) 
EQU y.sub.1n =L.sub.1n cos .theta..sub.1n +K.sub.n (30) 
EQU x.sub.2n =P.sub.2n +L.sub.2n sin .theta..sub.2n (31) 
EQU y.sub.2n =L.sub.2n cos .theta..sub.2n (32) 
where n is a number corresponding to the time-series sampling period in 
measurement, .theta..sub.n is a term for correcting the y axis of the 
upper laser range finder 10 on the basis of the lower laser range finder 
20. 
Measurement points on correction surfaces of the correction piece 50 
parallel to the x axis and y axis, which are fixed at absolute positions, 
are extracted based on the position signals P.sub.1n and P.sub.2n and the 
angle signals .theta..sub.1n and .theta..sub.2n refer to FIG. 10A). 
It is preferred to secure at least 10 measurement points per surface of the 
correction piece 50. Therefore, the length h of each of the sides parallel 
to the direction of forward movement and backward movement of the upper 
and lower laser range finders 10 and 20 is preferably determined according 
to the following equation (33): 
EQU h.gtoreq.10.times.V.sub.max /T.sub.min (33) 
wherein V.sub.max is the maximum moving speed of each of the laser range 
finders, and T.sub.min is the minimum time for data sampling. 
Since the measurement points on each of the surfaces of the correction 
piece 50 contain error due to the laser range finders and other machines 
in the x-y directions, and even profile cannot be obtained by connecting 
the measurement points. The y coordinates at the measurement points on a 
correction surface in parallel to the x-axis are averaged to determine 
deviation .DELTA.y.sub.0 from coordinate y.sub.0 of the reference y axis. 
The same processing is performed for a surface parallel to the y axis to 
determine deviation .DELTA.x.sub.0. 
These deviations .DELTA.y.sub.0 and .DELTA.y.sub.0 are calculated as 
.DELTA.y.sub.1 and .DELTA.y.sub.1 for each laser range finder or each 
measurement condition to correct measurement coordinates. The corrected 
measurement points are connected by a line in the order of sampling to 
form a profile. When the profiles for the laser range finders or 
measurement conditions are drawn in the same x-y coordinates, the profiles 
of the same measurement surface coincide with each other, thereby obtaining 
a sectional profile with high precision. 
If, in measurement of the correction piece 50, the coordinate axes of a 
surface profile measured while forward traveling deviate from the axes 
while backward traveling, each of the deviations .DELTA.x and .DELTA.y may 
be determined so as to correct the measurement coordinates, as shown in 
FIG. 10B. 
FIGS. 11A-11D show the measured profiles of the H-beam 1 and the correction 
piece 50 obtained by reciprocating the upper and lower laser range finders 
10 and 20. FIG. 11A shows profiles obtained by forward traveling of the 
upper laser range finder 10; FIG. 11B shows profiles obtained by forward 
traveling of the lower laser range finder 20; FIG. 11C shows profiles 
obtained by backward traveling of the upper laser range finder 10; and 
FIG. 11D shows profiles obtained by backward traveling of the lower laser 
range finder 20. 
Deviations .DELTA.x and .DELTA.y which indicate offset amounts in the x- 
and y-axis directions are determined from the measured profiles of the 
correction piece 50, and then used for correcting the space coordinates 
(x.sub.1, y.sub.1), (x.sub.2, x.sub.2), (x.sub.3, y.sub.3) and (x.sub.4, 
y.sub.4) in the first embodiment. A satisfactory sectional shape profile 
can then be synthesized. 
Thus, in summary, in the method and apparatus for measuring cross sectional 
dimensions of H-beam of the present invention, the cross sectional 
dimensions are measured while horizontally reciprocating two laser range 
finders which are disposed above and below the H-beam opposite to each 
other. It is thus possible to precisely automatically determine a 
sectional shape of the H-beam in an on-line manner, thereby significantly 
contributing to improvements in product quality and yield.