JPH0464003B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a method capable of simultaneously measuring the straightness of an object to be measured, the straightness of a moving guide surface, and the amount of vertical wobbling during movement with high precision. 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 desired to make its measurement easier. Conventional methods for measuring straightness 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 negative effects from various noises, making them difficult to put to practical use in the field. Many problems remain. Therefore, as a new method for measuring straightness that can solve these problems, two displacement detectors are moved along the object to be measured, and the values measured by these displacement detectors are used to sequentially calculate the straightness and displacement of the object to be measured. A method of simultaneously measuring the straightness of the moving guide surface of the detector has been reported. As shown in Figure 1, which shows the principle, this is because the distance between the detector mount 3 (using a knife mount, for example) that moves along the measurement object 1 on the guide surface 2 and the measurement object 1 is Two displacement detectors A and B that measure In this method, the measured values of the two displacement detectors A and B are obtained for every l, and the straightness of the object to be measured 1 and the straightness of the guide surface 2 are separately calculated from these measured values. In other words, the measurement target 1 at the measurement start position
and the straightness of the guide surface 2 are Y ₀ and X ₀ respectively,
Let the straightness at the Kth measurement position be Y _K and
If X _K , then the straightness curves of the measuring object 1 and the guide surface 2 are obtained, which are shown as Y and X in FIG. 1, respectively. Here, the measured values at displacement detectors A and B are D _KA ,
Assuming D _KB (K=0, 1, 2,...), the following equations (1)(2)
holds true. D _KA −Y _K −X _K = D _0A ...(1) D _KB −Y _K+1 −X _K = D _0B −Y ₁ −X ₀ ...(2) In this equation (1), K→K+1 By substituting and transforming equations (1) and (2), the following equations (3) and (4) are obtained. D _K+1A −D _0A ＝Y _K+1 ＋X _K+1 ……(3) D _KB −D _0B ＝Y _K+1 ＋X _K −Y ₁ −X ₀ ……(4) And, equation (3) Subtracting equation (4) from, D _K+1A −D _0A −D _KB +D _0B = Y _K+1 +X _K+1 −Y _K+1 −X _K +Y ₁ +X _0Therefore , rearranging gives the following equation ( 5) is obtained. _{X K + 1 = _ _ _ _ _ _} , the following equation (6) is obtained. X _K+1 =X _K +D _K+1 −D _KB −X ₀ ...(6) Also, the following equation can be obtained from equation (3). Y _K+1 =X _K+1 +D _K+1A −D _0A ...(7) Therefore, from equations (6) and (7), K=0,
Using the measured values D _KA , D _KB at points 1, 2, . In this method, the straightness of the detector mount 3 is determined by the ups and downs (changes in straightness) of the detector mount 3 as it moves along the guide surface 2. Even if the entire stand 3 floats up and down as it is, there is no risk of adversely affecting the measured values, but in general, the detector mounting stand 3 often sways vertically (pitting) in the front-rear direction, and this causes measurement problems. This results in errors, making it impossible to perform highly accurate measurements. Based on this knowledge, the present invention aims to provide a straightness measuring method that eliminates measurement errors caused by vertical wobbling due to movement and allows more accurate measurement. 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 D _0A , D _0B , respectively.
D _0C , the detector mount or the object to be measured is moved every interval l to obtain the measured value of the detector each time, and the measured values at the Kth measurement position are respectively D _KA , D _KB , Let D _KC be the measured values at the K+i-th position sequentially as D _K+iA , D _K+iB , D _K+iC , and the guide surface straightness error at the measurement start position be X ₀ ,
Let the straightness error of the measuring object at the first position be _X1 , the straightness error of the object to be measured at the first position be _Y1 , that at the second position be _Y2 , and the straightness of the guide surface at the K+2nd position. _{degree X K + 2 as _ _ _ _ _ _ 1} - Y ₂ , and the values of X _{K+2 calculated} for K = 0, 1, 2,... _Y1 , _Y2
Estimate and calculate the straightness of the guide surface by correcting it by _{the numerical} value related to Calculate each by Y _K+2 = −X _K+2 +D _K+2A −D _0A θ _K+2 = −X _K+2 −Y _K+3 +D _K+2B −D _0A +X ₀ /l. It is characterized by Hereinafter, one embodiment of the straightness measuring method of the present invention will be described in detail based on the principle diagram shown in FIG. A detector mount 3 that moves along a guide surface 2 provided along the measurement object 1 is provided, and the detector mount 3 is equipped with three displacement detectors A for measuring the distance to the measurement object 1. , B, and C are installed at equal intervals l in the direction of movement of the detector mount 3. 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. Let D _KA , D _KB , and D _KC (K=0, 1, 2, . . . ) respectively.
At this time, the measurement target 1 is
, the straightness of the guide surface 2 and the pitching of the detector mount 3 are respectively Y _K , X _K and θ _K (K=0,
1, 2,...). Note that the pitching of the detector mount 3 is based on the displacement detector A. Here, as shown in Fig. 2, 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 Y ₁ , that of the second position
Y ₂ , each displacement detector A at the measurement start position,
Let the measured values of B and C be D _0A , D _0B , D _0C and K
The measured values at the th measurement position are 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 (8), (9), and (10) hold true from the same figure. D _KA −Y _K −X _K =D _0A …(8) D _KB −Y _K+1 −X _K −l・θ _K =D _0B −Y ₁ −X ₀ …(9) D _KC −Y _{K +2} −X _K −2l・θ _K = D _0C −Y ₂ −X ₀ ...(10) Then, by multiplying equation (9) by 2 and subtracting equation (10), the following equation (11) is obtained. It will be done. 2D _KB −2D _0B −D _KC +D _0C =X _K +2Y _K+1 −Y _K+2 −2Y ₁ +Y ₂ −X ₀ ...(11) Also, in equation (8), K→K+1, K→K+2
By doing so, the following equation is obtained. D _K+1A −Y _K+1 −X _K+1 ＝D _0A D _K+2A −Y _K+2 −X _K+2 ＝D _0AIf we organize this, Y _K+1 ＝D _K+1A −X _K+1 ＝D _0A Y _K+2 ＝D _K+2A −X _K+2 ＝D _0A ……(11)′ This formula (11)′ is converted to Y _K+1 and Y _K+2 by (11) _{When substituted into _ _ _ _ _ _ _ _ _ ＋ Y 2 −X 0If we rearrange this , we get : _ _ _} ...(12) Also, from equation (11)′, Y _K+2 = −X _K+2 +D _K+2A −D _0A ...(13) In equation (9), substitute K→K+2 and get D _0B =
By using the relationship D _0A +Y ₁ , the following equation can be obtained. D _K+2B −Y _K+3 −X _K+2 −lθ _K+2 = (D _0A +Y ₁ )−Y ₁ −X ₀ By rearranging this, the following equation (14) is obtained. θ _K+2 = −X _K+2 −Y _K+3 +D _K+2B −D _0A +X ₀ /l ...(14) That is, displacement detector A at the positions of K=0, 1, 2, ... , B, C using the measured values D _KA , D _KB , and D _KC , the straightness curve Y of the measurement object 1 and the guide surface 2 are sequentially calculated from the above equations (12), (13), and (14). straightness curve
And the pitching θ of the detector mount 3 can be calculated. According to this 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 addition, in this embodiment, the case where the object to be measured 1 is stationary and the detector mounting base 3 is moved has been explained.
Conversely, the above equations (12), (13), and (14) can also be applied when the detector mount 3 is stationary and the measurement object 1 is moving. Next, a specific calculation method will be explained. the above
As can be seen from equations (12), (13), and (14), Y _K is calculated using X _K (K = 2, 3, 4...) obtained from equation (12), and their values are The pitching θ _K can be found from Therefore, a specific application method of this equation (12) will be explained. In equation (12), 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,
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 _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} expressed by equation (12) These values cannot be obtained from the recurrence formula of equation (13), and in order to obtain the straightness curve X, these values must be estimated in some way, or their influence needs to be removed. Therefore, in equation (12), X ₁ = α, 2Y ₁ −Y ₂ =
If β is set, the following equation (15) holds true. X _K = K・α+K(K−1)/2・β +C _K (K=2, 3,…) …(15) X _K : Straightness error at Kth position (true value) C _K : Straightness error at the K-th position (calculated value) In addition, this C _K is obtained from the measured values D _KA , D _KB , D _KC by equation (12) assuming α = β = 0. This is the value. 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 (15) above. It can be obtained using the following steps. () Find C _K for K=2, 3, 4,..., n. () Find α that minimizes the root mean square value of X _K shown in equation (15). These α and β can be relatively easily determined by the following equations (16) and (17) using the least squares method. α=δ, (γ ₄ −2γ ₂ +γ ₂ )−(δ ₂ −δ ₁ )(γ ₃ −γ ₂
)/(γ ₃ −γ ₂ ) ² −γ ₂ (γ ₄ −2γ ₃ +γ ₂ )……(16) 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 )……(17) 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 ) () Obtained using equations (16) and (17) Calculate X _K from α, β, and C _K obtained in () using equation (15). 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 at each measurement point. On the other hand, the straightness curve of measurement object 1 is X _K (13)
The pitching of the detector mount 3 can be determined by substituting Y _K and X _K into Equation (14). Next, a more specific explanation will be given using the model data shown in FIG. The values shown in FIG. 3 are for measurement positions K=0, 1,
2. Straightness and pitching amount in... The polarity is as shown in the figure, and regarding rotation, the direction in which the measured value of the displacement detector C in FIG. 2 increases is defined as positive. From this model data, D _KA , D _KB , and D _KC are obtained, and the result of calculating C _K and K=2 from K=
Table 1 shows the calculated values of α, β, X _K , Y _K , and θ _K obtained from the above formula for the measurement points up to 9. At the same time, the data _of The values are shown in Table 1 as the data values of Y _K and the data values of θ _K. In addition, the values in parentheses are K = 2 ~
K=9

[ _{Table ]} Although it is outside the _{range of} The value calculated using that. Further, the results shown in Table 1 are illustrated in FIG. As is clear from the figure, errors that are thought to be caused by the nature of the model data and the selection of subbans (K = 2 to K = 9) occur, but the overall trends are in good agreement, and the regression line The graphs in the figure appear to be slightly rotated due to an error in understanding the slope, but by rotating one of the graphs, the whole matches well. In addition, the above-mentioned error can be made sufficiently small by lengthening the selection span.
This method is very effective when applied to actual equipment. Furthermore, when compared with the conventional case in which the effect of pitching is not taken into consideration, which is indicated by the white circle (-○-) in FIG. 4, it can be seen that highly accurate measurement values with extremely small errors can be obtained. As described above in detail along with the embodiments, according to the present invention, the straightness of the object to be measured, the straightness of the movement guide surface, and the amount of vertical wobbling during movement can be simultaneously measured with high precision. In addition, 3
It can be easily applied to actual equipment by simply installing several detectors, and the measurement work is simple and does not require any skill.

[Brief explanation of the drawing]

Figure 1 is a principle diagram of the conventional straightness measuring method, Figure 2 is a principle diagram of the straightness measuring method of the present invention, and Figures 3 and 4 are explanatory diagrams of model data to which the method of the present invention is applied. and an explanatory diagram of the results. 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 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 is respectively Let D _KA , D _KB , D _KC be the measured values at the K+i-th position sequentially as D _K+iA , D _K+iB ,
D _K+iC , and the guide surface straightness error at the measurement start position is X ₀ , that at the first position is X ₁ , the straightness error of the object to be measured at the first position is Y ₁ , and the second position is Let the straightness of the guide surface at the K+2 position be _Y2 , and the straightness of the guide surface at the K+2nd position is X _{K +2} = 2・X _K+1 −X _K −2・D _K+1A +D _{K +2A} +2・D _KB −D _KC +D _0A −2・D _0B +D _0C +X ₀ +2Y ₁ −Y ₂ , and the value of X _K+2 calculated for K=0, 1, 2,... , X ₁ and Y ₁ , Y ₂ calculated to minimize the root mean square value of the straightness error
Estimate and calculate the straightness of the guide surface by correcting it by _{the numerical} value related to Calculate each by Y _K+2 = −X _K+2 +D _K+2A −D _0A θ _K+2 = −X _K+2 −Y _K+3 +D _K+2B −D _0A +X ₀ /l. A straightness measurement method characterized by: