JPH0444928B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method that can be put to practical use and can simultaneously measure the straightness of an object to be measured, the straightness of a moving guide surface, and the amount of pitching during movement.

In recent years, with the increasing demand for higher precision in machine tools, the straightness control of guide surfaces (sliding surfaces) has become one of the important issues, and it is hoped that it will be easier to measure. . Conventional straightness measurement methods include using a reference bar such as Straight Edge, a piano wire as a reference straight line, or using an autocollimator. Methods using systems have also been developed.

However, all of these methods require a considerable amount of preparation and skill for measurement work, are inefficient, and are susceptible to adverse effects from various noises. Problems remain.

As a new method for measuring straightness that can solve these problems, three displacement detectors are moved along the object to be measured, and the straightness and displacement of the object to be measured are sequentially detected from the measured values by these displacement detectors. The present inventors have reported a method for simultaneously measuring the straightness of the moving guide surface of a device (Patent Application No. 57-167561).
``Straightness Measuring Method'') The previously filed ``Straightness Measuring Method'' (Patent Application 167561/1982) is based on a guide surface provided along the object 1 to be measured, as shown in Figure 1, which shows its principle. 2, and three displacement detectors A, B, and C are installed on this detector mount 3 to measure the distance to the object 1. Install them at equal intervals l in the direction. Then, while moving the detector mounting base 3 in the direction of the arrow in the figure, the distance from the surface of the object to be measured 1 is measured every movement distance l equal to the distance l between the displacement detectors A, B, and C, and the value is calculated. D _KA , D _KB , D _KC (K=
0, 1, 2,...). At this time, the straightness of the measuring object ₁ , the straightness of the guide surface 2, and the pitching of the detector mount ₃ are determined by using _the representative points for each distance l, respectively. , 2, ...).

Note that the pitching of the detector mount 3 is based on the displacement detector A.

Here, as shown in Fig. 1, the straightness error of the guide surface 2 at the measurement start position is X ₀ , that at the first position is X ₁ , and the straightness error of the measurement object 1 at the first position is Let Y ₁ and the second position be Y ₂ , and let the measurement values of each displacement detector A, B, and C at the measurement start position be D _0A , D _0B , and D _0C , and the measurement value at the K-th measurement position. D _KA ,
D _KB , D _KC , the measured value at the K+i-th position is D _K+iA ,
Assuming D _K+iB and D _K+iC , the following equations (1), (2), and (3) are established from the same figure.

D _KA −Y _K −X _K =D _0A …(1) D _KB −Y _K+1 −X _K −l・θ _K =D _0B −Y ₁ −X ₀ …(2) D _KC −Y _{K +2} −X _K −2l·θ _K =D _0C −Y ₂ −X ₀ (3) Furthermore, by transforming equations (2) and (3), the following equation (4) is obtained.

2D _KB −2・D _0B −D _KC +D _0C =X _K +2Y _K+1 −Y _K+2 −
2Y ₁ +Y ₂ −X ₀ ...(4) Also, in equation (1), K→K+1, K→K+2
By substituting Y _K+1 and Y _K+2 obtained by , into equation (4), the following equation (5) is obtained.

X _K+2 =2・X _K+1 −X _K −2D _K+1A +D _K+2A +2D _KB −D _KC +
D _0A −2・D _0B +D _0C +X ₀ +2Y ₁ −Y ₂ ...(5) Furthermore, it was calculated from equations (2), (5), and
The following equations (6) and (7) are obtained using Y _K+2 .

Y _K+2 = −X _K+2 +D _K+2A −D _0A …(6) θ _K+2 = −X _K+2 −Y _K+3 +D _K+2B −D _0B +Y ₁ +X ₀ /
l...(7) That is, using the measured values D _KA , D _KB , and D _KC of the displacement detectors A, B, and C at the positions of K = 0, 1, 2,..., the above equation (5), From equations (6) and (7), the straightness curve Y of the measuring object 1, the straightness curve X of the guide surface 2,
And the pitching θ of the detector mount 3 can be calculated.

In this way, according to the present method, not only the ups and downs (change in straightness) of the detector mount 3 when it moves along the guide surface, but also the longitudinal sway (pitching) in the front and rear direction can be prevented. This makes it possible to perform highly accurate measurements that take into account the effects of

In this example, the case where the object to be measured 1 is stationary and the detector mount 3 is moved has been explained, but conversely, the above-mentioned (( Equations 5), 6) and 7 can be applied.

Next, we will explain the specific calculation method.
As can be seen from equations (5), (6), and (7), _{Y K}
is calculated, and pitching θ _K is obtained from these values. Therefore, a specific application method of this equation (5) will be explained.

In equation (5), X ₀ is the straightness error at the measurement start position, and D _0A , D _0B , and D _0C are all displacement measurement values at the measurement start position. Therefore, if the initial setting values of each displacement detector A, B, and C are set to 0, then
It can be assumed that X ₀ =D _0A =D _0B =D _0C =0.

Under this assumption, for K=0, 1, 2, . . . , n, X _K+2 is as follows.

X ₂ =2X ₁ -0-2・D _1A +D _2A +0-0+2Y ₁ -
Y ₂ X ₃ =2X ₂ −X ₁ −2・D _2A +D _3A +2・D _1B −D _1C
+2Y ₁ −Y ₂ 〓 〓 X _o+2 =2X _o+1 −X _o −2・D _o+1A ＋D _o+2A +2・D
_oB −D _oC +2Y _{1 −Y} 2However, X ₁ , Y ₁ , and Y ₂ are values that cannot be obtained from the recurrence formulas (5) and (6), so in order to obtain the straightness curve To do this, it is necessary to estimate these values or remove their influence in some way.

Therefore, in equation (5), X ₁ = α, 2Y ₁ −Y ₂ =
If β is set, the following equation (8) holds true.

X _K = K・α+K(K−1)/2・β +C _K (K=2, 3,…) …(8) X _K : Straightness error at Kth position (true value) C _K : Straightness error at the Kth position (calculated value) Also, this C _K is the value obtained from the measured values D _KA , D _KB , and D _KC by equation (5) assuming α = β = 0. It is.

Here, if we consider the straightness error as ``the deviation from the virtual straight line that minimizes the root mean square value of the error at each measurement point,'' then we can calculate the straightness error using equation (8) above. It can be obtained using the following steps.

() Calculate C _K for K=2, 3, 4,..., n.

() Find α and β that minimize the root mean square value of X _K shown in equation (8).

These α and β can be relatively easily determined using the following equations (9) and (10) using the least squares method.

α=δ ₁ (γ ₄ −2γ ₃ +γ ₂ )−(δ ₂ −δ ₁ )
(γ ₃ −γ ₂ )/(γ ₃ −γ ₂ ) ² −γ ₂ (γ ₄ −2γ ₃ +γ ₂ )
...(9) β=2・(δ ₂ − δ ₁ )・γ ₂ −2δ ₁ (γ ₃ − γ ₂ )
/(γ ₃ −γ ₂ ) ² −γ ₂ (γ ₄ −2γ ₃ +γ ₂ )……(10) However, γ ₂ = _o 〓 ^K=2 K ² , γ ₃ = _o 〓 ^K=2 K ³ , γ ₄ = _o 〓 ^K=2 K ₄ , δ ₁ = _o 〓 ^K=2 (K・C _K ), δ ₂ = _o 〓 ^K=2 (K ²・C _K ) () (9) and (10) Calculate X _{K using equation (8) from α and β obtained using equations and C K obtained} using ().

This X _K becomes the straightness error as the deviation from the virtual straight line that minimizes the root mean square value of the error in each measurement.

On the other hand, the straightness curve of the object to be measured 1 can be found by substituting X _K into equation (6), and
The pitching of can be found by substituting Y _K and X _K (7) into the equation.

As can be seen from the above explanation, the method explained based on FIG. Due to the limitations of the method, there is a drawback that only values (straightness errors) can be determined at discrete points for each distance l. In other words, in order to grasp the detailed straightness shape of the measurement object 1 or the guide surface 2, the mounting interval l of the three displacement detectors A, B, and C should be made small, and measurements and calculations should be performed in small steps. There is a need. However, in order to reduce the mounting interval l, there are restrictions from the dimensions of the detector, the dimensions of the detector mounting base 3, etc., and it is difficult to make l sufficiently small.

SUMMARY OF THE INVENTION An object of the present invention is to provide a straightness measuring method that eliminates the above-mentioned drawbacks and makes it possible to grasp straightness in detail. The configuration of the present invention that achieves this object is such that one of the detector mount and the object to be measured moves along a guide surface, and the detector mount includes three sensors for measuring the distance to the object to be measured. Detectors are installed at equal intervals l in the movement direction, and the measured values of the three detectors at the measurement start position are respectively
D _0A , D _0B , D _0C , the detector mounting base or the object to be measured is moved every interval l to obtain the measured value of the detector each time, and the measured value at the Kth measurement position and D The deviations from _0A , D _0B , and D _OC are respectively D _KA , D _KB , and D _KC , the guide surface straightness error at the measurement start position is X ₀ , and that at the first position is X ₁ , 1
The straightness error of the measured object at the th position is Y ₁ ,
The value at the second position is defined as Y ₂ , and the straightness error of the guide surface at the measurement start position X ₀ is taken as the reference K + the straightness error of the guide surface at the second position X _K+2 is X _K+2 = 2・_K+1 −X _K-2・D _K+1A ＋D _K+2A +2・D _KB −D _K
Calculate by _C +2・Y ₁ −Y ₂ and calculate the value of X _K+2 calculated for K=0, 1, 2,... so that the root mean square value of the straightness error is minimized. Obtained X ₁ and Y ₁ , Y ₂
The straightness of the guide surface is estimated and calculated by correcting it by the numerical value related to , and the straightness of _the measurement target at this position is calculated _. Y _{K +2 =} −X _K+2 +D _K+2A θ K ₊₂ = −X _K+2 −Y _K+3 +D _K+2B In the method of measuring straightness calculated by D KA , D KB , D _KA , D KB , D KA , D _KB , Obtain N data groups consisting of D _KC (K = 0, 1, 2...), and from each data group, determine N groups of guide surface straightness X _K and straightness Y _K of the object to be measured, These N sets of straightness shapes X _K ,
It is characterized by grasping the overall detailed straightness shape from _YK .

A straightness measuring method according to an embodiment of the present invention will be explained below with reference to FIG. FIG. 2a is a diagram showing the measuring method according to the present invention, and the same symbols as in FIG. 1 indicate the same items. Note that for simplicity, the guide surface 2 has been omitted. In FIG. 2a, a _i (i=0, 1, 2, . . . ) is a set of measurement object points on the measurement object 1, which are set at equal intervals l. b _i (i=0, 1, 2, . . . ) is another set of measurement target point sequences, which are similarly set at equal intervals l. The separation between a _i and b _i is set to l/2 as shown in the figure.

As shown in the figure, three displacement detectors A, B, and C are arranged on the detector mount 3 and are moved in the direction of the arrow in the figure to obtain measured values every 1/2 of the moving distance. By applying the method of Japanese Patent Application No. 57-167561 to a set of measurement data for the sequence of measurement points a _i (i = 0, 1, 2...), the measurement points a _i (i =2,
3, 4,...) can be found. Similarly, the measurement target point sequence b _i (i=0, 1, 2,...)
From one set of measurement data group for , the measurement target point b _i
The straightness error at (i=2, 3, 4...) can be found.

Thus, as shown in FIG. 2b, the detailed straightness shape of the measurement object 1 can be grasped from the straightness errors at these two sets of measurement object points. As a method for synthesizing straightness errors at two sets of measurement target points, for example, from the straightness error at measurement target point a _i ,
Include the straightness error at the positions corresponding to the start and end points of the measurement target point b _i (the first and last points for which the straightness error is calculated, e.g. b ₂ and b _o ), and calculate the straightness error of b _i . One possible method is to calculate the straightness error at point b _i by converting the straightness errors at the start point and end point to a certain value. In addition, in FIG. 2a, the case of two sets of measurement target point sequences a _i and b _i was explained, but
Similar measurement and calculation processing is also possible for N sets of measurement object point sequences a _i , b _i , c _i , . . . set with a separation of l/N. Of course, in this case, N sets of measurement data groups may be obtained for each moving distance l/N, and the method disclosed in Japanese Patent Application No. 57-167561 may be applied to the N sets of data groups.

As explained above, according to the present invention, it is possible to grasp the straightness shape of the object to be measured 1 in detail at a fine pitch.

[Brief explanation of drawings]

FIG. 1 is an explanatory diagram for explaining the conventional technology,
FIGS. 2a and 2b are explanatory diagrams for explaining an embodiment of the present invention. In the drawings, 1 is an object to be measured, 2 is a guide surface, 3 is a detector mounting base, and A, B, and C are displacement detectors.

Claims (1)

[Claims] 1. Either the detector mount or the object to be measured moves along a guide surface, and the detector mount is provided with three detectors for measuring the distance to the object to be measured. The three detectors are installed at equal intervals l in the movement direction, and the measured values of the three detectors at the measurement start position are measured.
D _0A , D _0B , D _0C , the detector mounting base or the object to be measured is moved every interval l to obtain the measured value of the detector each time, and the measured value at the Kth measurement position and D The deviations from _0A , D _0B , and D _0C are respectively D _KA , D _KB , and D _KC , the guide surface straightness error at the measurement start position is X ₀ , and that at the first position is X ₁ , 1
The straightness error of the measured object at the th position is Y ₁ ,
The value at the second position is defined as Y ₂ , and the straightness error of the guide surface at the measurement start position X K+2 with reference to the guide surface straightness error X ₀ at the second position is defined as X _{K+2 =} Calculated by 2・X _K+1 −X _K −2・D _K+1A +D _K+2A +2・D _KB −D _KC +2・Y ₁ −Y ₂ , and for K=0, 1, 2,... X 1 , _{Y 1} , Y ₂ calculated by calculating the calculated value of X _K+2 so that the root mean square value of the straightness error is minimized
The straightness of the guide surface X _K+2 (K=0, 1, 2,...) is estimated and calculated by correcting it by the numerical value related to the straightness of the object to be measured at this position.
Y _K+2 and longitudinal vibration amount θ _K+2 due to movement are respectively Y _K+2 = −X _K+2 +D _K+2A θ _K+2 = −X _K+2 −Y _K+3 +D _K In the method of measuring straightness calculated by _+2B /l, the measured value of the detector is obtained every distance l/N of movement of the detector mount or the object to be measured, and thereby D _KA , D Obtain N data groups consisting of _KB , D _KC (K = 0, 1, 2,...), and from each data group, calculate N groups of guideway straightness X _K and straightness Y _K of the object to be measured. Find the straightness shapes of these N sets X _K , Y _K
A straightness measurement method characterized by grasping the detailed straightness shape of the whole.