JP2005308703A - Offset error calibration method for detector - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To realize an accurate offset error calibration method simple in a calibration procedure and capable of using an inexpensive test piece, in straightness measurement using a 2- or 3-point method. <P>SOLUTION: A surface shape of the test piece is measured by rotating a detector attaching table having two angle detectors or three displacement detectors, or the test piece. Outputs from the two or three detectors are computed in this constitution, and an offset error is calculated accurately in each of the detectors, using the fact that a shape on a circumference is brought into a periodic function. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for measuring the surface of an object to be measured, and more particularly to a detector calibration method in a 2-3 point method for measuring the straightness of the surface of the object to be measured.

  FIG. 1 is a diagram for explaining an outline of a three-point straightness measurement method that is generally performed. That is, the guide surface 5 of the detector mounting base 3 and the object to be measured 7 are installed so as to be substantially parallel to the reference shaft 1, and the detector mounting base 3 moves smoothly along the guide surface 5. The detector mounting base 3 is configured with three displacement detectors 9. The displacement detector 9 includes displacement detectors A, B, and C. The longitudinal axes of the detectors are parallel to each other at equal intervals, and the gap to the surface 11 of the object to be measured can be measured. Installed.

  When measuring straightness, the three displacement detectors A, B, and C are first calibrated. The state at the time of calibration is shown in FIG. The detector mounting base 3 is detachable. Here, the detector mounting base 3 is fixed on the lower mounting base 13, and the standard test piece 17 is fixed to the upper mounting base 15 so as to face the three displacement detectors 9. The upper installation table 15 or the lower installation table 13 is configured to be movable in a direction perpendicular to the longitudinal axis of the detector. In this state, the relative position of the upper installation table 15 and the lower installation table 13 is set in the direction of the arrow 19. When the outputs of the three displacement detectors 9 are measured while changing, for example, a result as shown in FIG. 3 is obtained. The relative position of the upper installation table 15 and the lower installation table 13 is measured by a length calibrated in advance such as a laser length measuring device. The measured quantity represents the horizontal axis, and the output of each displacement detector A, B, C represents the vertical axis. Each output is taken into, for example, a DSP (Digital Signal Processor) and linearized and the gradient (= sensitivity) is made uniform as shown in FIG.

と表す。次に各オフセットを

となるように調整する。この調整は標準試験片１７の表面形状が平らであるとの前提で行われるが、標準試験片１７の表面形状が湾曲等しているとこの調整が不確かなものとなる。Here, linearization and sensor output at each output in which the gradient (= sensitivity) is aligned; μ _A (z) μ _B (z) μ _C (z)
Sensor offset; s _A s _B s _C
Where A is a proportional constant and z is the output of a calibrated length measuring instrument.

It expresses. Then each offset

Adjust so that This adjustment is performed on the assumption that the surface shape of the standard test piece 17 is flat. However, if the surface shape of the standard test piece 17 is curved or the like, this adjustment is uncertain.

ここで、ｓ_Ｅをオフセット誤差と呼ぶ。Therefore, assuming that there is always an adjustment error, the relationship between each offset is expressed in the following form.

Here, s _E is called an offset error.

と表すことができる．
従って、各変位センサの出力は、

となる．The straightness measurement algorithm is derived as follows.
Surface shape of object to be measured; f (x)
Guide surface shape; g (x)
Pitching error of the mount; _e p (x)
Sensor interval; h / 2
1, as shown in FIG. 1, the guide surface 5 and the object 7 to be measured are arranged substantially parallel to the x axis which is the reference axis 1, and the detector mounting base 3 is scanned along the x axis. Since the measurement is performed, the outputs of the three displacement detectors 9 can be considered as a function of x.
It is assumed that the detector mounting base 3 travels along the guide surface 5 with two wheels, and the two wheels coincide with the mounting positions of the displacement detectors A and C. At this time, the pitching error of the detector mount 3 is

It can be expressed as.
Therefore, the output of each displacement sensor is

It becomes.

となり、次に

と近似する。ただし、ｆ′（ｘ）のダッシュはｘに関する１階微分を表す。
式（８）と式（９）の差を計算し、式（１０）と式（１１）を代入すれば、

を得る。ここで

とおき、更に

と近似すれば、結局

を得る。ここでｆ″（ｘ）の２つのダッシュはｘに関する２階微分を表す。If formula (5) -formula (6) and formula (6) -formula (7) are calculated,

And then

And approximate. However, the dash of f ′ (x) represents the first derivative with respect to x.
If the difference between Equation (8) and Equation (9) is calculated and Equation (10) and Equation (11) are substituted,

Get. here

And more

And eventually

Get. Here, two dashes of f ″ (x) represent a second derivative with respect to x.

を得る。
Ｍ（ｘ）は測定される数値列であるので、これを２階数値積分することにより、オフセット誤差ｓ_Ｅ＝０の場合、被測定物７の表面形状ｆ（ｘ）が求められることになる。ただし、ここで、係数Ｃ_１とＣ_０は求められていないが、形状には直接関係しないので、敢えて求める必要がない。If equation (15) is integrated twice,

Get.
Since M (x) is a numerical sequence to be measured, the surface shape f (x) of the DUT 7 is obtained by integrating the second-order numerical value when the offset error s _E = 0. . However, here, although not the coefficient C ₁ and C ₀ is obtained, since the shape is not directly related, there is no need to seek dare.

However, if there is an offset error, a parabolic error 2s _E (x / h) ² is added to the shape.
For example, if x / h = 20,
Since 2 (x / h) ² = 800, the error s _E is multiplied by 800, and a slight error is greatly enlarged.

Therefore it becomes important to the offset error s _E to zero, or knowing its magnitude precisely without zero. That is, if an error is subtracted from the resulting shape, an accurate shape can be obtained. Therefore, in the present invention, accurately knowing the value is expressed as calibrating the offset error.

  Now, a calibration method using a set of standard test pieces corresponding to surface irregularities has been proposed as a conventional method for calibrating offset errors (see Patent Document 1). A set of standard test pieces to which the shape irregularities correspond is usually processed by a slicing method, but the processing time becomes long, so that it becomes very expensive. In addition, accurate calibration requires calibration at the corresponding points on the concave and convex surfaces, and the corresponding points must be accurately positioned at the detection points of the detector to be calibrated, but this is difficult. . Moreover, although it is necessary to calibrate every measurement for accurate measurement, the measurement of the concave surface and the convex surface twice and complicated procedures are required.

JP 2003-254747 A

  It is an object to realize a calibration method that requires a simple calibration procedure and requires an accurate offset error, and a method for calibrating the offset error characterized in that the test piece used therein is inexpensive.

  The test piece used in the present invention has a disk shape, and a detector mounting base having three detectors is rotated to measure the surface shape of the disk. The outputs of the three detectors obtained with this configuration are calculated, and the offset error is accurately calculated by utilizing the fact that the shape on the circumference of the disk becomes a periodic function.

  The algorithm for obtaining the shape is roughly the same as the conventional one. In the conventional example, the change was made on a straight line, but this idea is applied to the circumference of the disk.

  FIG. 5 is a configuration example of the calibration apparatus. The disc 101 is coupled with a drive motor 103 and a shaft 105 and rotates around a rotation shaft 107. A detector mounting base 3 is fixed to the disk 101, and three displacement detectors 9 are fixed thereto. In addition, the DUT 7 that is a test piece is installed almost in parallel with the disk 101, and the surface shape (lower surface in the figure) can be measured by the three displacement detectors 9. The drive motor 103 and the DUT 7 are fixed to a base (not shown) serving as a reference and do not move. The drive motor 103 is controlled to rotate the disk 101 at a constant speed.

  As shown in FIG. 6, the detector mounting base 3 is fixed to the disk 101, and the three displacement detectors A, B, and C detect the undulation on the surface of the object 7 to be measured. The detector is installed so that the longitudinal axis of each detector is substantially orthogonal to the surface of the disk 101. In this figure, the device under test 7 is omitted.

  FIG. 7 is a schematic view of the disk 101 shown in FIG. 6 as viewed from above. As shown here, the three displacement detectors A, B, and C are arranged at an angle α on the circumference of the radius r centering on the rotation center 111 of the disk 101.

で表す。FIG. 8 is a diagram for explaining the coordinate system. The disk 101 is assumed to rotate in the clockwise direction indicated by an arrow 109. The rotation angle is θ, and the displacement x on the circumference of the radius r where the detector is arranged is as follows:

Represented by

が成立する。上の３式はそれぞれ式（５）、式（６）式（７）と一致するので、式（８）から式（１６）までそのまま成立する。Consider an algorithm similar to that described above. In the straightness measurement illustrated in FIG. 1, the detector mount 3 moves in a straight line, but the detector mount 3 moves while being supported by a rotating shaft. Here, the output of each of the three detectors can be expressed as follows.
f (x) is the vertical movement e _P (x) is the slope h of the disc 101 of the surface shape g (x) is a disk 101 of the object 7 along a circumference of radius r 3 pieces shown in FIG. 8 If we consider the interval of the displacement detector 9 of

Is established. Since the above three expressions coincide with Expression (5), Expression (6), and Expression (7), Expressions (8) to (16) hold as they are.

  FIG. 9 is a diagram illustrating an output example of the displacement detectors A, B, and C. When the detector mount 3 rotates once, that is, when the rotation angle θ changes by 2π, x on the circumference of the radius r changes by L (= 2πr).

が得られる。なお式（１９）は式（１６）の再掲である。Therefore, when the numerical sequence M (x) defined by the equation (13) is cut out by one rotation and integrated as shown in FIG.

Is obtained. Equation (19) is a reprint of Equation (16).

の性質がある。この性質を利用して未知数Ｃ_１、Ｃ_０を決める。Now, the surface shape f (x) of the disk returns to its original state once the disk rotates once.

There is a nature of. Using this property, the unknowns C ₁ and C ₀ are determined.

ｘ＝Ｌのとき、

である。In equation (18),
When x = 0

When x = L

It is.

るので、オフセット誤差ｓ_Ｅは正確に計算され、これで校正作業は完了となる。When equation (23) -equation (22) is calculated,

Therefore, the offset error s _E is accurately calculated, and the calibration operation is completed.

ｘ＝Ｌのとき、

であるから、式（２６）−式（２５）を計算すれば

を得る。
式（２７）よりＣ_１が求められ、式（１９）に代入すれば、試料の形状ｆ（ｘ）が決定する。Furthermore, when x = 0 in equation (19),

When x = L

Therefore, if equation (26) -equation (25) is calculated,

Get.
If C ₁ is obtained from the equation (27) and substituted into the equation (19), the shape f (x) of the sample is determined.

  In the above description, three displacement detectors are used, but an angle detector may be used. In this case, two angle detectors are sufficient. FIG. 11 is a diagram for explaining the outline of the straightness measurement method of the two-point method using an angle detector. As in FIG. 1, the guide surface 5 of the detector mounting base 3 and the object to be measured 7 are installed so as to be substantially parallel to the reference shaft 1, and the detector mounting base 3 is smooth along the guide surface 5. The detector mounting base 3 is provided with two angle detectors 119. The angle detector 119 includes angle detectors D and E, and is installed so that the surface angle of the surface 11 of the object to be measured can be measured.

となる．
式（２８）−式（２９）を計算し、式（１４）で表される関係および

を用いると

となり、結局、式（１５）と同様な２階の微分方程式が得られ、本発明に従えば、式（２４）と同様にして

が得られ、２つの角度検出器のオフセット誤差（ａｓ_Ｄ−ａｓ_Ｅ）が求められることになる。here,
Sensor output: aμ _D (x) aμ _E (x)
Sensor offset as _D as _E
To obtain the relationship between the surface shape and sensor output. However, the unit of the sensor offset here is an angle.

It becomes.
Formula (28) -Formula (29) is calculated, and the relationship represented by Formula (14) and

With

Eventually, a second-order differential equation similar to equation (15) is obtained, and according to the present invention, as in equation (24)

Is obtained, and the offset error (as _D −as _E ) of the two angle detectors is obtained.

  In the above description, the disk used to determine the offset error in the present invention is expressed as an object to be measured or a test piece and is not called a standard test piece. The standard test piece generally refers to a highly accurate test piece that is priced, and if the detector outputs a continuous data as described in the embodiment of the present invention, the processing accuracy of the disk is particularly problematic. Because it does not. Of course, it doesn't have to be priced.

  In the above description, the three displacement detectors 9 are arranged on the coaxial circumference with respect to the center of rotation, but may be arranged on a substantially coaxial circumference. If not on the coaxial circumference, as can be seen from FIG. 8, the three displacement detectors do not measure the exact same location, so the relationships of equations (5)-(7) do not hold. However, in general, the shape of the waviness on the surface changes at a larger pitch than the size of the detection surface of the detector, so that it can be approximated with considerable accuracy. More specifically, FIG. 12 shows the AA cross section shown in FIG. 7, but as can be seen, the shape of the swell changes greatly compared to the size of the detection surface of the detector. Even if it is displaced in the left-right direction by about one device (the state in which the displacement detector C is displaced to the right is indicated by a dotted line), there is no significant change in the magnitude of the output. On the other hand, the degree of approximation can be increased by using a detection surface having a sufficiently small size as compared with the undulating pitch assumed. In this figure, the surface 11 of the object to be measured is over-expressed for explanation.

  In the above description, it is expressed that the arrangement on the substantially coaxial circumference is sufficient, but naturally the case of a linear arrangement is included. In the case of the linear arrangement, the radius of rotation of the detection portion may be determined in consideration of the size of the detection surface of the detector used there and the size of the swell to be measured or the test piece. The linear arrangement has an advantage that it can be applied to the straightness measurement described in the conventional example immediately after calibrating according to the present invention.

  In the above description, the case where the detector moves is described. However, the detector may be fixed and the non-measurement object may move. This is apparent from the fact that it is based on the relative motion of the detector and the object to be measured.

  In addition, although it is expressed that the offset error is calculated by calculating based on the data obtained by one rotation, it is more accurate to calculate the offset error by averaging the data obtained by a plurality of rotations. I can do it. However, there is a disadvantage that the processing time becomes long.

  In addition, the disk in the present invention is controlled to rotate at a constant speed by a drive motor, but this is because a higher reproducibility is generally obtained for each rotation of the disk. Reproducibility is easy to realize during continuous rotation, but rotation that repeats start and stop may be used as long as reproducibility can be realized.

  In the above description, the test piece or the object to be measured is a disk. However, it is only necessary that the shape on the circumference can be measured by rotating, so the shape is not limited to the disk. Any shape such as can be used.

The invention's effect

    As described above, according to the present invention, a rotating test piece or a measured object is used to calibrate on a closed curve that repeats the surface shape in one rotation. It can be obtained with high accuracy. In addition, the disk used there does not require a so-called standard test piece, and there is an effect that is possible with a disk obtained by ordinary processing.

Diagram for explaining the outline of straightness measurement method Diagram showing how the displacement detector is calibrated Output example during calibration of displacement detector Output example of displacement detector after adjustment Front view showing a configuration example of the present invention The perspective view which shows the structural example of this invention Schematic diagram showing the arrangement of displacement detectors Illustration for explaining the coordinate system Output example of displacement detector Diagram for explaining numerical integration Explanatory drawing when measuring with two angle detectors Relationship between detector size and surface waviness

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Reference axis | shaft 3 Detector mounting base 5 Guide surface 7 Measured object 9 Displacement detector 9 'Displacement detector 11 Surface of measured object 13 Lower installation base 15 Upper installation base 17 Standard test piece 19 Arrow 101 Disk 103 Drive Motor 105 Shaft 107 Rotating shaft 109 Arrow 111 Rotation center 119 Angle detector

Claims (3)

Either the detector mounting base or the object to be measured is moved along the guide surface, the geometric relationship between the detector mounting base and the object to be measured is measured, and the object to be measured is obtained from the obtained data string. In the straightness measurement method to find the straightness of the surface of
Rotating either one of the detector mount and the object to be measured substantially parallel to the surface of the object to be measured, and measuring the geometric relationship between the detector mount and the surface of the object to be measured A plurality of detectors are installed at a predetermined interval along a rotation axis of the rotational motion and substantially on the same circumference, and the detector detector mounting base or the object to be measured is rotated and moved for each predetermined movement amount. The geometric relationship between the detector mounting base and the surface of the object to be measured is simultaneously measured by the detector, and the calculation of the plurality of detectors is performed by calculation from a data string obtained during at least one rotation. A method for calibrating an offset error of a detector, characterized by calibrating the offset error A method for calibrating an offset error of a detector, wherein the plurality of detectors according to claim 1 are three displacement detectors. A method for calibrating an offset error of a detector, wherein the plurality of detectors according to claim 1 are two angle detectors.

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