JP4706061B2 - Roundness measurement method - Google Patents

Description

  The present invention relates to a roundness measurement method capable of accurately measuring roundness from measurement data with a small number of steps by enhancing the analysis method in measuring roundness of measuring the roundness of an object. .

  FIG. 1 shows an overview of a conventional roundness measuring machine, and FIG. 2 shows a schematic diagram of a roundness measuring system in this roundness measuring machine. A multi-step method is widely used for analysis of roundness measurement. 1 and 2 show the case of a glass sphere as a measuring instrument. When measuring the roundness, place the glass sphere on the mounting table of the roundness measuring machine and use a detector such as a stylus attached to the rotation mechanism of the upper measurement unit to trace the radius of the glass sphere while tracing it. One measurement data is acquired by detecting unevenness in the direction and scanning once. However, with this measurement alone, not only the spherical shape component but also the addition of the rotation error component of the detector (stylus) is observed.

 Therefore, in the multi-step method, the measuring instrument is rotated at different angles using the rotary table on the stage shown in FIG. 2, and the measurement starting position of the measuring instrument is shifted relative to the measurement starting position of the detector. Acquire measurement data with the angle phase changed. FIG. 3 schematically shows the relationship between the rotation start position of the stylus and the angular position of the measuring instrument. There is a method that can simultaneously obtain the rotation error component of the roundness detector and the shape component of the measuring object (glass sphere, etc.) by performing analysis from these measurement data with different angular phases. Realized.

In the following, the conventional multi-step method in roundness measurement will be described using mathematical expressions and graphs, and the problems will be presented.
(About the multi-step method in roundness measurement)
Let Z (θ) be the rotation error component of the detector of the roundness measuring machine, and G (θ) be the shape component of the measuring object. FIG. 4 shows the rotational error component Z (θ) of the detector and the shape component G (θ) of the measuring instrument when ideally obtained.

A relative phase angle obtained by shifting the measurement start position of the measurement object with respect to the measurement start position of the detector is defined as φ _i . In the multi-step method, the angle phase φ _i is set to an angle obtained by dividing one round of 360 degrees into equal angles. If the number of steps is m, the angle phase φ _i can be expressed by the following equation.
(1)

Since the measurement data is detected as a combination of the rotation error component Z (θ) of the detector of the roundness measuring machine and the shape component G (θ) of the measuring object detected by the detector, the measurement data T (θ _j , φ _i ) can be expressed by the following equation.
(2)
Here, j represents the number of measurement points measured by the detector in one rotation scan, and N represents the total number of measurement points. (Example: When N = 2000, each measurement pitch angle is 360 ° / 2000.) FIG. 5 shows an example of measurement data of the multi-step method at m = 5.

It is assumed that Z (θ) and G (θ) can be expressed by Fourier series as shown in equations (3) and (4), respectively, with one round of the sample circumference as a reference cycle.
(3)
(4)
However, when the experimental data has already removed the eccentric component, the sum is not n = 1 but n = 2.

Here, an average of m pieces of measurement data T (θ _j , φ _i ) obtained by changing the relative angular phase using the equation (2) and changing φ _i to i = 1, 2,. The value μ (θ _j ) is calculated.
(5)

The second term in the last line on the right side of equation (5) is 0 when n ≠ km, and only the term n = km remains. However, the integer k = 1, 2, 3,..., N / m. Therefore, the following equation is obtained from equation (5).
(6)

The second term G ^(m) (θ) on the right-hand side of the above equation corresponds to a curve represented by the sum of Fourier components that are integral multiples of the number of steps m among the Fourier components of the shape component G (θ _j ) of the measuring instrument. is doing. Accordingly, the average value μ (θ _j ) indicates that Z (θ) is mixed with G ^(m) (θ) and cannot be removed. In the analysis method of the conventional multi-step method, the average value μ (θ _j ) is used as the final analysis result of the rotational error component Z (θ _j ) of the detector of the roundness measuring machine, and the shape component G of the measuring object that cannot be removed. An inadequate approximate value that includes a Fourier component G ^(m) (θ) that is an integral multiple of ^{m of} (θ) is employed.

FIG. 6 shows the rotation error component of the roundness measuring machine obtained by analyzing the equation (6) from the experimental data with the number of steps m = 5 as shown in FIG. Compared with the rotational error component Z (θ) of the true detector shown in FIG. 4, the value is slightly different because G ^(m) (θ) is mixed.

Next, an analysis procedure for obtaining the shape component G (θ) of the measuring instrument in the multi-step method will be described. Subtract (6) from (2) to obtain (7).
(7)

That is, as shown in FIG. 7, this 'T (θ _j , φ _i ) -μ (θ _j )' is G (θ _j -φ _i ) in which the shape component G (θ) of the measuring object differs by the angular phase φ _i. This is the value obtained by subtracting G ^(m) (θ) from. In the analysis method of the conventional multi-step method, φ ₀ = 0 in the first term on the left side of Equation (7) is used.
(8)
In many cases. This corresponds to one (R line) in FIG. The value of T (θ _j , 0) −μ (θ _j ) is obtained as an approximate value of the shape component G (θ) of the measuring instrument. However, in this case, the value is insufficient in the sense that only the Fourier component of G ^(m) (θ) is insufficient.

FIG. 8 shows the shape components of the measuring instrument obtained by analyzing the equation (8) from the experimental data of the number of steps m = 5. Compared to the shape component G (θ) of the true measuring instrument shown in FIG. 4, the value is slightly different because G ^(m) (θ) is subtracted.

The following Non-Patent Document 1 introduces data analysis technology related to shape measurement. Introduces a method to separate the systematic error (motion error) component and shape component of the measurement device included in the measurement data. Non-Patent Document 2 shown below introduces data analysis technology related to roundness, shows a multi-step method and a reversal method (inversion method), and introduces the effects thereof. Non-Patent Document 3 below considers each condition when applying the multi-step method, such as the number of steps and the number of measurement data points when measuring roundness. Further, in Non-Patent Document 4, in order to explain that the multi-step method cannot remove a Fourier component corresponding to an integral multiple of the number of steps, each Fourier component is obtained from experimental data having different numbers of steps and is compared. The results are introduced.
DJWhitehouse, “Some theoretical aspects of error separation techniques in surface metrology”, J.Phys.E: Sci.Instrum, 9, 531-536 (1976) DGChetwynd, “Hight-precision measurement of small balls”, J.Phys.E: Sci.Instrum, 20, 1179-1187 (1987) Cao Linxiang, “The measuring accuracy of the multistep method in the error separation technique”, J.Phys.E: Sci.Instrum, 22, 903-906 (1989) Cao Linxiang etal, “Full-harmonic error separation technique”, Meas. Sci. Technol., 3, 1129-1132 (1992)

As described above, in the conventional roundness measurement analysis method, the rotational error component Z (θ) of the detector is evaluated by equation (6), and the shape component G (θ) of the measuring object is evaluated by equation (8). is doing. In addition, as described above, this multi-step analysis method includes the term G ^(m) (θ), so that the component on the detector side and the component on the measurement object side cannot be separated sufficiently or are not Only complete component evaluation is possible. Furthermore, there is a problem that the equation (8) largely depends on the specific measurement data among the m pieces of analysis data defined by the equation (7), that is, the measurement data obtained under the condition of i = 0. is there. Therefore, the present invention proposes a method capable of strictly separating components by improving the analysis method of the conventional multi-step method.

Therefore, the present invention proposes the following method in order to solve the problems of the conventional roundness measurement method.
1. In the equation (8), calculation is performed using specific measurement data among m measurement data. We propose a method that can obtain highly reliable measurement results by processing m measurement data equally.
2. A method is proposed that can be separated so that the solution of the shape component Z (θ) on the measuring instrument side expressed by the equation (6) does not include the Fourier component G ^(m) (θ).
3. In the case of an m-step experiment, a Fourier component corresponding to an integer multiple of m cannot be obtained. When the number of steps is small, a low-order Fourier component cannot be obtained, and the error increases with respect to the true value. In order to solve this problem, a method is proposed in which this is combined with measurement data having a different number of steps to obtain a higher order Fourier component than an integer multiple of m.

In order to solve the above-described problems, the roundness measurement method according to the present invention makes one rotation by scanning a single rotation while detecting the radial unevenness of the surface of the measuring instrument by bringing the detector into contact with the surface of the measuring instrument. The roundness measurement data of the measuring instrument surface is acquired, and the measurement start position of the measurement instrument with respect to the measurement start position of the detector is shifted by an angular phase obtained by dividing the circumference 360 degrees into equal angles and divided into m pieces. Analysis of obtaining m measurement data by measuring the roundness of the surface of the measuring instrument a plurality of times at equal intervals, and obtaining the rotation error component of the detector of the roundness measuring machine from the m measurement data. in the roundness measuring method of performing the data of the difference between the average value and the m of each measurement data, said staggered m pieces of each measurement data only each of the angular phase, do to adjust the origin position, take the average of these And by, and performs analysis using all measured data.

Also, other roundness measuring method according to the present invention comprises contacting a detector relative to the surface of the measuring vessels, one measurement by one revolution scanning while detecting the radial irregularities of the surface of the measuring vessels Obtain roundness measurement data on the surface of the object, shift the measurement start position of the measurement object relative to the measurement start position of the detector by an angular phase obtained by dividing 360 degrees around the circumference into equal angles , and equidistant on the circumference a plurality m of times the get the m pieces of measurement data obtained by the roundness measuring measurement vessels the surface of the roundness measuring method for analyzing for determining the shape component of the measurement vessels by said m measurement data, the each measured data angle different phases returns the angle phase by phase, by matching the position of the origin of the shape component of the measurement vessels, performs phase operation to shifting the phase of the rotation error components of the detector, the phase The value obtained by work alternative to the m pieces of the measurement data and performs analysis.

Also, other roundness measuring method according to the present invention comprises contacting a detector relative to the surface of the measuring vessels, one measurement by one revolution scanning while detecting the radial irregularities of the surface of the measuring vessels Obtain the roundness measurement data on the surface of the object, shift the measurement start position of the measurement object with respect to the measurement start position of the detector by an angle phase divided into m at 360 ° round , and equidistant on the circumference M measurement data is obtained by measuring the roundness of the surface of the measuring instrument a plurality of m times, and the measurement starting position of the measuring instrument with respect to the measurement starting position of the detector is n pieces at an equal angle of 360 ° in a circle ( n measurement data are obtained by measuring the roundness of the surface of the measuring instrument a plurality of n times at equal intervals on the circumference by shifting the angular phase divided by n ≠ m). Find the difference data of the average values, and calculate the roundness solution. The sum of Fourier components of integer multiples of m when performing analysis, and the Fourier of the multiples of n when analyzing roundness by obtaining data of the difference between each of the n measurement data and the average value thereof Using the sum data of the components, the shortage of each data is extracted and complemented with each other.

The present invention makes it possible to measure the roundness with high accuracy by measuring with a small number of steps, thereby enabling a reduction in measurement time and high accuracy even in places where long-term environmental conditions are not stable. The purpose of enabling measurement / evaluation of the surface of the measuring object is to make one rotation scan by making the detector contact with the surface of the measuring object and scanning for one rotation while detecting the unevenness of the radius of the measuring object surface. The roundness measurement data is acquired, the measurement start position of the measurement object is shifted with respect to the measurement start position of the detector, and m rounds of the measurement object surface are measured m times at equal intervals on the circumference. The measurement data is obtained, and the measurement start position of the measurement object is shifted from the measurement start position of the detector, and n is obtained by measuring the roundness of the measurement object surface a plurality of n (n ≠ m) at equal intervals on the circumference. Acquired measurement data, When the difference between each measured value and its average value is obtained and roundness is analyzed, the shape component of the measuring instrument or the rotation error component of the detector of the roundness measuring instrument is an integer multiple of m. The sum of ingredients cannot be obtained. The sum of Fourier components of an integer multiple of n cannot be obtained from the result of analyzing the roundness by obtaining data of the difference between the n measurement data and the average value thereof. Since the sum is included, this is extracted and the difference between the m measurement data and the average value is obtained, and the result of the roundness analysis is complemented.
(The invention's effect)

In the conventional technique, the rotation error component and the measuring instrument included in the detector of the roundness measuring machine are evaluated in a state where the Fourier component corresponding to an integral multiple of the number of steps cannot be removed. Since this component can be removed by the present invention, the roundness measuring instrument and the measuring instrument can be evaluated with high accuracy.
Further, in the prior art, in order to perform an analysis without missing even higher-order Fourier components, it is necessary to increase the number of steps accordingly. However, since this requires a long measurement time, it is a serious problem in roundness measurement in which the measurement environment such as temperature is required to be stable. By using the “phase combination method” of the present invention, a result equivalent to that of an experiment with a high number of steps can be derived from experimental data with a small number of steps, so that highly accurate evaluation can be performed in a short time.

In order to solve the above-mentioned problem 1 of the present invention, the present invention proposes the following method. That is, as described above, the value T (θ _j , 0) −μ (θ _j ) obtained by the above equation (8) is the left side T (θ _j , φ of equation (7) in the conventional analysis method as described above. _{Since i} ) −μ (θ _j ) is set to φ ₀ = 0, one of m measurements is performed with an excessively weighted calculation.

However, since the equation (7) is only shifted by the angle phase φ _i defined in the equation (1), if this value is phase-shifted, the first term G (θ on the right side of the equation (7) _j −φ _i ) can be unified with G (θ _j ).
(9)

That is, the analysis using all the measurement data can be performed by averaging the m analysis values of the expression (7) by the angle phase φ _i and adjusting the origin position. The analysis data is g _m (θ _j ). g _m (θ _j ) is simply expressed by the following equation.
(10)

This operation will be described using an m = 5 step experiment as an example.
FIG. 9 is a diagram showing FIG. 7 individually.
Since the measurement data of each step expressed by the equation (7) is out of phase by the angle phase φ _i , the phase is shifted back to match the origin of G (θ _j ). FIG. 10 shows the operation. A value obtained by averaging these is indicated by a thick black line in FIG. In the conventional analysis method, only the uppermost data in FIG. 9 is used, so that the first measurement data is excessively weighted.
However, the method according to the present invention can obtain more reliable results with higher statistics by using all measurement data equally.

Next, a technique for solving the problem 2 of the present invention will be described.
In the equation (2), as shown in FIG. 5, the rotation error component Z (θ) of the detector of the roundness measuring machine has the same origin position, but the shape component G (θ) of the measuring object is different from each other. The phase is shifted by the angle phase φ _{i of the} step. Therefore, first previously, angular phase phi _i are different measurement data T (θ _j, φ _i) returns only the phase angle the phase phi _i, to match the original position of the measurement vessels shaped component G (theta), The phase of the rotation error component Z (θ) of the detector is shifted. If the phase manipulated value is T ′ (θ _j , φ _i ),
From the formula (2), T ′ (θ _j , φ _i ) is represented by the formula (11).
(11)
FIG. 12 shows an example in which the phase of T (θ _j , φ _i ) is shifted by the angle phase φ _i based on the above method.

This is because the origin position of the shape component G (θ) of the measuring object is the same, and thereafter, equivalent calculations are performed by exchanging Z (θ) and G (θ) in equations (7) and (8). Thus, the equation (12) corresponding to the equation (10) can be obtained.
(12)
As described above, the rotation error component Z (θ) of the detector and the shape component G (θ) of the measuring instrument can be separated without including each other.

Next, a technique for solving the problem 3 of the present invention will be described.
This g _m (θ _j ) does not include the sum G ^{( m)} (θ _j ) of higher-order Fourier components that are integral multiples of m with respect to G (θ _j ) to be obtained. Therefore, an experiment with a different number of steps (here, n times) is newly performed by the phase difference method, and a result obtained by performing similar processing from these data is defined as g _n (θ _j ). This is analysis data that does not include an nth-order higher-order Fourier component.

As an example, g (θ _j ) obtained from a 5-step experiment and a 9-step experiment and its Fourier component are shown in FIGS. As apparent from FIGS. 14 and 16, the multiple-order Fourier component of 5 is 0 in the 5-step experiment, and the multiple-order Fourier component of 9 is 0 in the 9-step experiment. However, since FIG. 14 includes a Fourier component (thick line) of a multiple of 9 in the 5-step experiment and FIG. 16 includes a Fourier component (thick line) of a multiple of 5 in the 9-step experiment. Can make up for each other. The only Fourier components that cannot be complemented are the Fourier components that are multiples of the least common multiple 45 of 5 and 9.

Here, we propose a method to compensate for this. This method is called “phase combination method” and is proposed as a method for improving the analysis method of roundness measurement.
(About “Phase Combination Method”)
Since g _n (θ _j ) includes m-order components, only high-order Fourier components that are integer multiples of m are extracted from this. In order to extract, g _n (θ _j ) is set as described in equation (6).

M pieces of phase-shifted data are created. When the average value μ _{n, m} (θ _j ) of these m pieces of data is expressed by the following equation.
(13)

The average value μ _{n, m} (θ _j ) is an operation for selectively extracting only the Fourier component of an integer multiple of m from g _n (θ _j ). Therefore, by simply adding this value to g _m (θ _j ), an analysis value g _mxn (θ _j ) supplemented with a Fourier component that is an integral multiple of m can be obtained. However, a Fourier component of an integer multiple of m × n cannot be obtained.
(14)
Thus, the same analysis result as the m × n shift experiment can be derived from the m shift experiment and the n shift experiment.

Five curves are produced by shifting the 9-step experiment (see the shape component (R line) of the measuring instrument in FIG. 15) by an angle when m = 5 in the equation (1). FIG. 17 shows five shifted curves. When these are averaged, an average value μ _9,5 (θ _j ) shown in FIG. 18 is obtained. The Fourier component of the average value μ _9,5 (θ _j ) has only a multiple Fourier component of 5 as shown in FIG. 19, and the Fourier component of a multiple of 5 is obtained from the Fourier component of the 9-step experiment shown in FIG. It can be seen that they are selectively extracted.

Therefore, as shown in FIG. 20, by adding this average value μ _9,5 (θ _j ) to g ₅ (θ _j ), as shown in FIG. 22, the combined curve g _m (θ _j ) + μ _{n, m} (θ _j ) = g _mxn (θ _j ) can obtain a curve having no missing components up to the 44th order of the Fourier component. That is, a result equivalent to the experimental result of the high step number (m × n steps) can be derived from the experimental data of the multi-step method performed at two different number of steps (for example, m step and n step). With this operation, Z _mxn (θ _j ) can be similarly obtained for the rotation error component of the detector. The result is shown in FIG.

  At present, more accurate evaluation of the rotational motion accuracy of the spindle of a magnetic storage device and the spindle of a machine tool that performs machining on the order of nm is required. Therefore, by using the present invention, it is possible to provide a rotation accuracy detection standard calibrated with high accuracy, and therefore it becomes possible to evaluate with higher accuracy.

  In addition, the present technology makes it possible to evaluate the rotation accuracy detection standard device with high accuracy by measurement with a reduced number of steps, so that the measurement time can be shortened. This eliminates the need to stabilize the measurement environment for a long time. Therefore, this technique enables high-precision measurement and evaluation even in a place that does not have such long-term stable conditions.

It is an outline figure of a roundness measuring machine. It is a schematic diagram of a roundness measuring machine system. It is a figure which shows the angle relationship of the detector (stylus) and measuring instrument in a multistep method. It is a figure which shows the example of a rotation error component and the shape component of a measuring device. It is a figure which shows the example of measurement data of a multistep method (m = 5). It is a figure which shows the example which calculated | required the rotation error component of the detector of a roundness measuring device from measurement data using (6) Formula. It is a figure which shows the example of 'T ((theta) _j , (phi) _i )-(mu) _j ) "data in case the number of steps m = 5. It is a figure which shows the example which calculated | required the shape component G ((theta)) of the measuring instrument from the experimental data of step number m = 5 using (8) Formula. It is a figure which shows a m = 5 step experiment example, It is explanatory drawing which shows the state from which the phase of the shape component measurement data by the phase angle position of each step calculated | required from (7) Formula has shifted | deviated by the angle phase (phi) _i . is there. It is a figure which shows the example which shifted the shape component by the angular position of each step. m = 5 Step experiments by the shape component T (θ _j, 0) is a diagram showing a -μ (θ _j) and the average value _{g m} (θ _j). It is a figure which shows the example which shifted the phase of measurement data T ((theta) _j , (phi) _i ) of 5 step experiment shown in FIG. 5 by angle phase (phi) _i . 5 is a diagram showing an example of z ₅ and g ₅ in experimental steps. It is a figure which shows the example of the Fourier component of the shape component of the measuring instrument in 5 step experiment. Is a diagram illustrating an example of z ₉ and g ₉ at 9 steps of the experiment. It is a figure which shows the example of the Fourier component of the shape component of the measuring instrument in 9 step experiment. Is a diagram illustrating an example of manufacturing an angle shifted to five curve when the m = 5 in the shape component g ₉ of the measuring vessels (1) at 9 steps of the experiment. It is a figure which shows the average of five curves of FIG. It is a figure which shows the average Fourier component of FIG. It is a figure which shows the example of the curve which has the Fourier component of the multiple of 5 extracted from the experimental result of 5 steps, and the experiment of 9 steps. It is a figure which shows the Fourier component of the shape component of the measuring instrument in experiment of 5 steps and 9 steps. It is a figure which shows the analysis result of the phase combination method of 5 steps and 9 steps.

Claims (3)

By bringing the detector into contact with the surface of the measuring object and scanning one revolution while detecting the radial unevenness on the surface of the measuring object, the roundness measurement data of the measuring object surface is acquired once.
The measurement start position of the measurement object with respect to the measurement start position of the detector is shifted by an angular phase obtained by dividing 360 degrees around the circumference into m at equal angles, and the true surface of the measurement object surface is measured a plurality of m times at equal intervals on the circumference. Acquire m measurement data by circularity measurement,
In the roundness measurement method for analyzing the rotation error component of the detector of the roundness measuring machine from the m measurement data,
The data of the difference between the average value and the m of each measurement data, said shifted by m-number of each of the angular phase of each measurement data, do to adjust the origin position, by taking the average of these, A roundness measurement method characterized by performing analysis using all measurement data. Contacting the detector relative to the surface of the measuring vessels, it obtains the roundness measurement data in the radial direction uneven detected while one revolution scanning one measurement vessels surface by the surface of the measuring vessels,
The measurement start position of the measurement object with respect to the measurement start position of the detector is shifted by an angular phase obtained by dividing m at 360 ° around the circumference, and a perfect circle on the surface of the measurement object at a plurality of m times at equal intervals on the circumference. Get m measurement data by degree measurement,
In the roundness measuring method for analyzing seeking the m measured data by the shape component of the measurement vessels,
Wherein the angular phase are different from each measurement data returns the angle phase by phase, by matching the position of the origin of the shape component of the measurement vessels, it performs phase operation to shifting the phase of the rotation error components of the detector,
A roundness measurement method characterized in that an analysis is performed by substituting the phase measurement value with the m pieces of measurement data. Contacting the detector relative to the surface of the measuring vessels, it obtains the roundness measurement data in the radial direction uneven detected while one revolution scanning one measurement vessels surface by the surface of the measuring vessels,
The measurement start position of the measurement object with respect to the measurement start position of the detector is shifted by an angular phase obtained by dividing the circumference 360 ° into m at equal angles, and a perfect circle on the surface of the measurement object a plurality of m times at equal intervals on the circumference. M measurement data is acquired by measuring the degree,
The measurement start position of the measurement object with respect to the measurement start position of the detector is shifted by an angular phase obtained by dividing 360 ° of a circle into n pieces (n ≠ m) at an equal angle , and a plurality of n times of the measurement start positions at equal intervals on the circumference. Acquire n measurement data by measuring the roundness of the measuring object surface,
The difference between the m measurement data and the average value is obtained, and the sum of Fourier components of an integer multiple of m when analyzing roundness, the n measurement data and the average Using the sum of Fourier components of integer multiples of n when obtaining the difference data and analyzing the roundness, the deficiency of each data is extracted and complemented with each other How to measure roundness.