JPH0151761B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention is designed to reduce waviness, which is a continuously changing geometric shape change (which can also be thought of as a small angular change) of a grinding surface, such as a rolling roll surface. This invention relates to an optical crack measurement method for measuring grinding cracks using an optical lever.

To detect chatter from changes in the angle of reflection of the light reflected from the surface, the surface to be measured is moved while shining light of a small cross-sectional area almost perpendicularly onto the surface to be measured, such as a ground surface. The one shown in Publication No. 1307 has been proposed. This detection device has a first
As shown in the figure, light from a suitable linear light source 1 is passed through an aperture 2 and focused by a condenser lens 3, the image of this linear light source 1 is reduced and formed at the position of a pinhole 5, and this image is passed through the condenser lens. 6
It is designed to be connected to the surface to be measured 11 by. However, immediately after the condenser lens 6, there is a slit plate 7 having, for example, a substantially rectangular slit 7a as shown enlarged in FIG.
It is placed at the focal point position of the objective lens 9 with its longitudinal direction perpendicular to the grinding direction (vertical direction in FIGS. 1 and 2). 4 is a water tank for removing thermal noise of light; 10 is a cylindrical lens for more effectively reflecting the amount of light flux into the surface to be measured 11; 8 and 20 are semi-transparent mirrors that reflect the incident light flux at observation window 23; This is to confirm the position of the linear light source 1, detect the amount of incident light by directing the incident light beam onto the photoelectric element 22 using the condenser lens 21, and maintain the amount of light from the linear light source 1 at a predetermined value by a controller (not shown).

The reflected light from the surface 11 to be measured is directed downward in FIG. The end is cut off, passes through a reflecting mirror 13, is focused by a condenser lens 14, and is focused by a semi-transparent mirror 15.
The reflected light, which is directed downward in FIG.
The photoelectric elements 18 and 19 are arranged so as to correspond to the photoelectric elements 18 and 19, respectively. The ridgeline at the tip of the prism 17 is arranged in a direction perpendicular to the grinding direction, and this ridgeline divides the reflected light into two equal parts in FIG. 1 when the reflected light is vertically reflected from the surface to be measured 11. is placed in a position to do so. The position where this reflected light is divided into two, ie, the position of the ridgeline at the tip of the prism 17, is called a reference position.

Therefore, if the irradiation point on the surface to be measured 11 is perpendicular to the incident light as described above, the photoelectric element 1
8 and 19 each receive the same amount of reflected light, but
If the irradiation point on the surface to be measured 11 is tilted, the reflected light will be tilted, and the amount of reflected light hitting the photoelectric elements 18 and 19 will change. The geometric waviness of the surface to be measured 11 is detected from this change.

FIG. 3 is a diagram illustrating the principle of the apparatus shown in FIG. 1 by shortening its optical path, and the same parts as in FIG. 1 are denoted by the same reference numerals. In addition, in the figure, a light with a width of 2h is projected onto the surface to be measured 11 in the measurement direction (horizontal direction in the figure), and the light is projected at a distance l from the surface to be measured 11 (however, the change due to waviness is ignored). The reflected light is received by photoelectric elements 18 and 19 placed adjacent to each other. As is clear from this figure, the amount of light received by each of the photoelectric elements 18 and 19 can be determined by determining at which position the reflected light that hits the boundary between the photoelectric elements 18 and 19, that is, the reference position mentioned above, is incident. In Figure 3, (x
+q) It can be known as the ratio α:β of the incident light divided into two at the position.

Now, let the curve of the geometric waviness of the surface to be measured 11 be y=f(ξ), and the angles formed between this curve and the ξ axis (axis parallel to the measurement direction) at the x and (x+q) positions are θ and θ, respectively. When φ is assumed, the following equation approximately holds true.

tanφtanθ+qd ² y/dx ² ………(1) Since q2l tanφ, substituting this into equation (1) to find q yields q2l/1−2ld ² y/dx ²・tanθ, and tanθ=dy /dx, so q2l/1−2ld ² y/dx ²・dy/dx ………(2) As is clear from equation (2), the basic formula for q is dy/dx, and the differential of the above curve It is almost proportional to the value.
However, in formula (2), 2l is the magnification, and 1/1-2ld ² y/dx ² is the measurement accuracy.

Therefore, by integrating the above-mentioned q, it is possible to obtain the above-mentioned curve, that is, the geometric waviness of the surface to be measured 11, and this q can be determined by the above-mentioned relationship α:β, that is, the relationship between the amount of light received by the photoelectric elements 18 and 19. Therefore, by calculating q from the detection values of these photoelectric elements 18 and 19 and integrating it, the geometric waviness can be found.

Note that q can be determined as (α-h) or (h-β) from only the amount of light received from either one of the photoelectric elements 18 or 19, but in order to improve measurement accuracy, both photoelectric elements 18 and 19 It is preferable to calculate it from the difference in the amount of light received. This relationship can be found as follows.

2h=α+β ………(3) Now t=α−β ………(4) From equation (4), β=α−t, so if we substitute this into equation (3) and rearrange it, we get , α−h=t/2=q……(5) Also, from equation (4), α=β+t, so this can be expressed as (3)
Substituting into the equation and rearranging, h-β=t/2=q (6), and q can be found as 1/2 of the difference t in the light receiving range.

However, the above explanation does not apply to the surface to be measured 11.
This is true when there is no unevenness in gloss and the reflectance is always constant.In actual ground surfaces, there are many unevenness in gloss apart from geometric undulations, so as mentioned above, the photoelectric elements 18 and 19 Correct geometric waviness cannot be determined by integrating based on detected values.

The present invention provides an optical chatter measuring method that takes into consideration the unevenness of gloss and determines correct geometric waviness.

Hereinafter, the present invention will be explained in detail using FIG. 4, which shows the glossiness V=H(ξ) of the surface to be measured 11, which is drawn in correspondence with FIGS. 3 and 3 described above. As shown in FIG. 4, if uneven gloss exists on the surface to be measured 11 shown in FIG.
Vα and the amount of light received by the other photoelectric element 19, Vβ, are as follows (7):
It is expressed by equation (8).

Vα＝∫ ^(x+q) _(xh) H(ξ)dξ ………(7) Vβ＝∫ ^(x+h) _(x+q) H(ξ)dξ ………(8) That is, the third Of the incident light shown in the figure, light in the range indicated by α is reflected by the surface to be measured 11 and the photoelectric element 1
The amount of light that enters the photoelectric element 19 is the area Vα shown by the hatched area on the upper right in FIG. The area indicated by the diagonal line on the lower right in Figure 4
It becomes Vβ.

Therefore, the glossiness V=H(ξ) is the output of the photoelectric element 16 shown in FIG.
It is obtained from the sum U of the outputs of 8 and 19 as described later, and in the above equations (7) and (8), Vα, Vβ, and h are known values, so the equation (7) or (8) x to be found from
The value of q at the position can be known.

As is clear from Figure 4, this q is obtained by adding the glossiness, so by integrating q(ξ) obtained at each x position in the ξ-axis direction, the unevenness of gloss can be determined. Even if the surface to be measured 11 has a geometric waviness, it is possible to accurately determine the geometric waviness.

Incidentally, the above Vα and Vβ may be taken out directly from the respective photoelectric elements 18 and 19, but as in the case described above, the difference T and the sum of Vα and Vβ (since it is the amount of total reflection light, the output of the photoelectric element 16 is also taken out). It is preferable to find it from U). Since these are related by the following equations (9) and (10), they can be obtained from the same equations as equations (11) and (12).

T=Vα−Vβ……(9) U=Vα+Vβ……(10) Vα=U+T/2……(11) Vβ=U−T/2……(12) Therefore, the above glossiness V=H(ξ) is given by shining light onto a flat surface of a block gauge, for example, which has no uneven gloss or geometric undulations, and when the amount of total reflected light at this time is U and the width of the light is 2h, then 2hV= U......(13) Since the following relationship holds true, it can be found by multiplying the amount of total reflected light U by 1/2h.

In addition, when uneven gloss exists, by multiplying the total reflected light amount U at that time by 1/2h, the average glossiness within the 2h width range where the light is irradiated can be determined. If the width of the light is wide in this way, the glossiness will be leveled out, and it will be necessary to correct it by multiplying by a correction coefficient, etc., and accurate glossiness cannot be obtained. Narrower is better. However, the photoelectric elements 18, 19
The width of the light for detecting the inclination of the surface to be measured 11 must be such that even if the reflected light is tilted due to this inclination, the reflected light always hits the photoelectric elements 18 and 19. If the precision of the surface to be measured 11 is poor, it may not be possible to narrow it down very much, so detection may be performed in synchronization using separate optical systems. However, since the present invention generally targets the measurement of geometric waviness such as the surface of a rolling roll, which is extremely slight and cannot be measured by mechanical measurement, it is not practical to use a separate optical system. No problem.

A specific calculation example for determining q from the above-mentioned equation (7) or (8) is shown below. As shown in Figure 4, x
Let the value of the glossiness V read at a 2h pitch of ±h centering on the position be Vi, V _i+1 , and to simplify the calculation, assume a straight line approximation between 2h, then the glossiness at the (x+q) position is V is expressed by the following formula.

V′=Vi+(V _i+1 −Vi)h+q/2h (14) Furthermore, the area Vα during measurement at the x position is expressed by the following formula.

Vα1/2(h+q)(Vi+V') (15) Substituting the above equation (14) into equation (15) and rearranging it, the following equation is obtained.

Aq ² +2Bq+CO……(16) A=V _i+1 −Vi B=h(Vi+V _i+1 ) C=(3Vi+V _i+1 )h ² −4hVα From this equation (16), a valid 1 is obtained. Finding the root q of q gives the following formula.

q−B+√B ² −AC/A ………(17) In this way, q at each x position, that is, q
(ξ) and integrate it, the surface to be measured 11
The geometric waviness y=f(ξ) is obtained.

As described above, according to the present invention, even if the surface to be measured has uneven gloss, the geometric undulations of the surface to be measured can be detected more accurately regardless of the unevenness of gloss.

[Brief explanation of drawings]

FIG. 1 is an explanatory diagram showing an optical system arrangement showing one example of an optical chatter measuring device applied to the present invention, and FIG.
The figure is an enlarged front view showing an example of a slit plate, Figure 3 is a principle diagram showing the shortened optical path of the optical chatter measuring device shown in Figure 1, and Figure 4 shows the glossiness of the surface to be measured and the photovoltaic It is a graph showing the relationship with the amount of light received by the element. 1...Line light source, 2...Aperture, 3, 6, 14, 2
1...Condenser lens, 4...Aquarium, 5...
Pinhole, 7... Slit plate, 7a... Slit, 8, 15, 20... Semi-transparent mirror, 9... Objective lens, 10... Cylindrical lens, 11... Surface to be measured,
12...Calibration device, 13...Reflector, 16,1
8, 19, 22...photoelectric element, 17...prism, 23...observation window.

[Claims]

1. When measuring the remaining length of a rolled sheet wound around a core tube, measure the outer circumference at each point at any two points separated by at least one rotation, and rotate the sheet at least two times around each point. Calculate the number of turns from an arbitrary point to the outer circumference of the core cylinder using the outer circumference length of the core cylinder, and calculate the outer circumference at any one point of the calculated roll sheet. Assuming a trapezoid in which the length and the outer circumference of the core tube are the lengths of two opposing parallel sides, and the calculated number of turns is a function of the height, and by finding the area of this trapezoid, A method for measuring the remaining length of a roll sheet, comprising calculating the remaining length of the roll sheet from an arbitrary point to the outer periphery of a core cylinder.

Claims (1)

[Scope of Claims] 1. The surface to be measured is moved in the measurement direction (ξ-axis) while applying light of a small cross-sectional area of a substantially rectangular shape almost perpendicularly to the surface to be measured, and the light is totally reflected from the surface to be measured. The amount of light U is detected to determine the glossiness V=H (ξ), and at the reference position of the optical system, the reflected light of the above-mentioned light or another light similarly applied to the surface to be measured is 2 times in the measurement direction.
Vα=∫ ^(x+q) _(xh) H(ξ)dξ or Vβ=∫ ^(x+h) _(x+q) H( ξ) An optical system characterized by determining the value of q at each x position in the ξ-axis direction from dξ, that is, q(ξ), and then integrating the q(ξ) to determine the geometric waviness of the surface to be measured. Chattering measurement method. However, in the above formula, h is 1/2 of the width in the measurement direction of the light that is divided into two, and q is the branch position on the surface to be measured of the reflected light that is divided into two at the reference position and the x
distance from location. 2. Set a reference position so as to divide the reflected light into two equal parts when the reflected light is reflected perpendicularly from the surface to be measured, detect the difference T between the amounts of reflected light divided into two at this reference position, and calculate this difference T and From the total reflected light amount U, Vα is calculated by the following formula.
or the chemical formula chatter measuring method according to claim 1, wherein Vβ is determined. Vα=U+T/2, Vβ=U-T/2