JP2007178296A - Rotating body measuring method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a rotating body measuring device 20 and a method without emergence of a higher order k not permitting correct calculation even when the higher order k is taken into consideration, thereby correctly obtaining the profile r (θ) of a rotating body and rotational deflection quantities x(θ), y(θ). <P>SOLUTION: A plurality of sets of angular arrangement of detectors in which magnification coefficients α<SB>1k</SB>, β<SB>1k</SB>emerging at denominators in expressions 22 and 23 are made uniform, are selected, using four or more detectors. The magnifications H<SB>1k</SB>, H<SB>2k</SB>(hence magnification coefficients α<SB>1k</SB>, β<SB>1k</SB>and so forth), are selected so that the parts in which the denominators of the expressions 22 and 23 become zero, are complemented among the plurality of sets. Using the complementary magnification coefficients α<SB>1k</SB>, β<SB>1k</SB>(hence A<SB>ak</SB>, B<SB>ak</SB>and so forth), the profile r (θ) and the rotational deflection quantities x (θ), y (θ) are obtained. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

The present invention relates to a rotating body measuring method and apparatus for measuring characteristics including the shape of a rotating body (hereinafter referred to as “rotating body measuring method and the like”), and in particular, the shape and rotation of a rotating shaft in an information device such as a hard disk or an optical disk. The present invention relates to a rotating body measuring method and the like for measuring the amount of shake without contact.

  In recent years, with the advancement and miniaturization of information devices such as hard disks and optical discs, the rotational accuracy required for bearings has been increasing, and at the same time, there has been a demand for higher accuracy in the measurement of rotational shaft runout. It is high. In particular, in a rotating body, not only the accuracy of a single displacement detector (hereinafter abbreviated as “detector”) but also a demand for detecting a higher order of a Fourier component during rotation has come out. For example, in a hard disk, frequency components up to the 20th order have become a problem.

  Conventionally, run-out measurement (hereinafter referred to as “rotational run-out measurement”) of a rotating shaft or a rotary body (hereinafter referred to as “rotating body” unless otherwise required) is measured in a non-contact manner. As a method, a three-point method has been studied in which three calibrated detectors are used at the same time to obtain the shape and rotational runout of the rotating body (see Non-Patent Document 1). In the three-point method, the arrangement (angle) of the three detectors and the weight of the detection data are carefully selected, and the weighted addition value of the detection data is obtained, so that it does not depend on the rotational shake (the eccentric amount of the rotating body). This is a method utilizing the feature that the shape of the rotating body can be detected. The rotational shake component is obtained based on the obtained shape of the rotating body. The three-point method is said to be able to determine the shape or rotational shake of the rotating body with very high accuracy when the shape of the rotating body or the behavior of the rotational shake is simple and the order of the Fourier series is low.

Next, the principle of the three-point method will be described. FIG. 5 shows the arrangement of the rotating body and the detector for explaining the principle of the three-point method. 5, reference numeral 10 is the rotating body 1, 2 and 3 the detector (probe), O is the origin of the xy coordinates, Oc is the center position of the rotator, theta is the angle of rotation of the rotating body 10, phi ₁ is detected The arrangement angle of the detector 1, φ ₂ is the arrangement angle of the detector 2, and φ ₃ is the arrangement angle of the detector 3. As shown in FIG. 5, it is assumed that the center position Oc of the rotating body is eccentric, and the eccentricity is (x (θ), y (θ)).

  When the shape of the rotator 10 is represented by r (θ), Fourier series expansion is performed and the components are displayed for each order, the following equation (1) is obtained.

    r (θ) = r0 + Σ (Akcos (kθ) + Bksin (kθ)) (1)

  In equation (1), r0 is the average radius of the rotating body, k is the order of the Fourier series, Ak and Bk are the shape Fourier coefficients representing the shape, and addition (Σ) is k = 1 to N (target Fourier series) Up to the highest order of the component). The average radius r0 can be considered to be 0 because it is considered to be a constant value when the shape r (θ) is obtained. When the detected displacement at each detector i (i = 1 to 3) is represented by di (θ), the following equation (2) is obtained.

    di (θ) = r (θ + φi) + x (θ) cosφi + y (θ) sinφi (2)

In order to obtain the shape r (θ), w _i (i = 1 to 3) is used as a weight, and the weighted addition dr (θ) is represented by the following equation (3).

dr (θ) = w ₁ r (θ + φ ₁ ) + w ₂ r (θ + φ ₂ ) + w ₃ r (θ + φ ₃ )
+ X (θ) (w ₁ cos φ ₁ + w ₂ cos φ ₂ + w ₃ cos φ ₃ )
+ Y (θ) (w ₁ sin φ ₁ + w ₂ sin φ ₂ + w ₃ sin φ ₃ ) (3)

When the weight w _i and the arrangement angle φ _i are expressed by the following equation (4) in the equation (3), the weighted addition dr (θ) does not depend on the eccentric amounts x (θ) and y (θ). Can be obtained.

w ₁ cos φ ₁ + w ₂ cos φ ₂ + w ₃ cos φ ₃ = 0
w ₁ sin φ ₁ + w ₂ sin φ ₂ + w ₃ sin φ ₃ = 0 (4)

Since generality is not lost even if w ₁ = 0 and φ ₁ = 0 in the equation (4), there is also a report examined by this method. When the equation (4) is established, the weighted addition dr (θ) does not depend on the eccentric amounts x (θ) and y (θ). From (3) and (1),

dr (θ) = w ₁ r (θ + φ ₁ ) + w ₂ r (θ + φ ₂ ) + w ₃ r (θ + φ ₃ )
= W ₁ Σ {Akcos (k (θ + φ ₁ )) + Bksin (k (θ + φ ₁ ))}
+ W ₂ Σ {Akcos (k (θ + φ ₂ )) + Bksin (k (θ + φ ₂ ))}
+ W ₃ Σ {Akcos (k (θ + φ ₃ )) + Bksin (k (θ + φ ₃ ))}
(5)

  By transforming equation (5) and setting αk and βk as the following equation (6), equation (5) can be expressed as equation (7). Since αk and βk represent the magnification for each order, they are called magnification factors.

w ₁ cos (kφ ₁ ) + w ₂ cos (kφ ₂ ) + w ₃ cos (kφ ₃ ): = αk
w ₁ sin (kφ ₁ ) + w ₂ sin (kφ ₂ ) + w ₃ sin (kφ ₃ ): = βk (6)
dr (θ) = Σ {(Akαk−Bkβk) cos (kθ)
+ (Bkαk + Akβk) sin (kθ)}
= Σ {Fkcos (kθ) + Gksin (kθ)} (7)

  Accordingly, the Fourier coefficients Fk and Gk of the weighted addition values dr (θ) of the three detectors i (i = 1 to 3) are obtained, and Ak and Bk are obtained from the magnification coefficients αk and βk by the following equation (8). Can do.

Ak = (αkFk + βkGk) / (αk ² + βk ² )
Bk = (− βkFk + αkGk) / (αk ² + βk ² ) (8)

  Using the Ak and Bk in the equation (8), the shape r (θ) of the rotating body can be obtained by the equation (1). Here, it should be noted that the expression (8) has the scaling factors αk and βk in the denominator. When the shape r (θ) is obtained, the eccentric amounts x (θ) and y (θ) are obtained by the following equation (9).

x (θ) = {− (d ₂ (θ) −r (θ + φ ₂ )) sin φ ₁
+ (D ₁ (θ) −r (θ + φ ₁ )) sin φ ₂ } / sin (φ ₁ −φ ₂ )
y (θ) = {(d ₂ (θ) −r (θ + φ ₂ )) cos φ ₁
− (D ₁ (θ) −r (θ + φ ₁ )) cos φ ₂ } / sin (φ ₁ −φ ₂ )
(9)

  The eccentric amounts x (θ) and y (θ) of the rotating body 10 appear as primary rotational shakes during rotation. This rotational shake includes the rotational shake of the rotating body 10 itself and the mounting error of the rotating body 10, but the two cannot be separated. Furthermore, if the frequency components of the eccentric amounts x (θ) and y (θ) of the rotator 10 are expressed by Ck, Dk, Nk, and Mk, it is possible to obtain the following (10) rotational vibration frequency components. .

x (θ) = Σ {Ckcos (kθ) + Dksin (kθ)}
y (θ) = Σ {Nkcos (kθ) + Mksin (kθ)} (10)

The above is the principle of the three-point method. Next, the process flow of the three-point method will be described using a flowchart. FIG. 6 is a flowchart showing the process flow of the three-point method. As shown in FIG. 6, the weights w _i (i = 1 to 3) are obtained so that the primary component (eccentric amount) of the rotational shake of the rotating body 10 becomes zero (step S30). In accordance with the weights w _i (i = 1 to 3) obtained in step S30, a magnification coefficient αk obtained by adding the Fourier components for each angle φ _i (i = 1 to 3) of each detector i (i = 1 to 3), βk is obtained (step S32). In accordance with the weights w _i (i = 1 to 3) obtained in step S30, the weighted addition dr (θ) of the detector i (i = 1 to 3) output is obtained (step S34). Fourier coefficients Fk and Gk of the weighted addition dr (θ) obtained in step S34 are obtained (step S36). Shape Fourier coefficients Ak and Bk which are Fourier components of the shape are obtained from the Fourier coefficients Fk and Gk obtained in step S36 and the magnification coefficients αk and βk obtained in step S32 (step S38). The shape r (θ) of the rotating body 10 is obtained from the shape Fourier coefficients Ak and Bk obtained in step S38 (step S40). The rotational shake amounts x (θ) and y (θ) of the rotating body 10 are calculated from the shape r (θ) of the rotating body 10 obtained in step S40 and the output of each detector i (i = 1 to 3). (Step S42).

Eki Okuyama, Hajime Moritoki, “A Consideration on Measuring Roundness Shape and Measuring Rotational Accuracy of Shaft by Three-Point Method”, Journal of Precision Engineering, Vol.65, No.9, 1999.

In the above-described three-point method, αk ² + βk ² is included in the denominator of equation (8), so that there is a possibility that 0% may occur. In equation (8), the magnification Hk is defined as equation (11).

Hk = √ (αk ² + βk ² ) (11)

  Since the magnification Hk is selected so that the formula (6) is established, there is a possibility that it becomes 0 when considering higher order Fourier series. That is, in the conventional three-point method, the magnification Hk is 0 or a very small value, and therefore, when a higher order is considered, an order that cannot be calculated correctly appears. For this reason, there has been a problem that the shape r (θ) of the rotating body 10 and thus the rotational shake amounts x (θ) and y (θ) cannot be obtained correctly.

In order to clarify the problems described above, actual rotational shake measurement will be described. FIGS. 7A and 7B show a measuring apparatus 40 used for actual rotational shake measurement. 7A is a plan view of the detector device 20, and FIG. 7B is a cross-sectional view taken along the line XX ′. In FIGS. 7A and 7B, the portions denoted by the same reference numerals as those in FIG. 7A and 7B, reference numeral 12 denotes a rotating body (0.5 ″ true sphere), and an arrangement angle φ _i (i = 1 to 3) of each detector i (i = 1 to 3). Are φ ₁ = 0 °, φ ₂ = 120 °, and φ ₃ = −135 °.

  FIG. 8 is a graph showing an output waveform of each detector i (i = 1 to 3) and a waveform dr (θ) obtained by adding the outputs of three detectors i (i = 1 to 3). In FIG. 8, the horizontal axis represents the rotation angle θ (°), the left vertical axis represents the measured displacement (μm), and the right vertical axis represents the added displacement (μm). The output of each detector i (i = 1 to 3) is suppressed to 1.4 μm or less in width, although there is a magnification shift between the detectors. On the other hand, the waveform dr (θ) obtained by adding the outputs of the three detectors i (i = 1 to 3) has a value of less than 80 nm in width, and the primary component (component depending on the eccentricity) is canceled. I understand that.

  FIG. 9 is a diagram in which the shape of the rotating body 12 is obtained from the added waveform dr (θ). As shown in FIG. 9, the roundness error (roundness error: thick line in FIG. 9) of the obtained true sphere (steel ball) 12 is a small value of 40 nm or less, and rotational motion error: FIG. ) Is 80 nm or less.

  FIG. 10 is a graph showing the frequency component of rotational shake. In FIG. 10, the horizontal axis represents the order k of the Fourier series, and the vertical axis represents the amplitude (μm), which is shown in the order of the detector i (i = 1 to 3) for each order. In FIG. 10, frequency components are expanded as Fourier series and expressed as amplitude values of the respective components. As shown in FIG. 10, it can be seen that the third-order component is remarkable and gradually decreases with the third-order peak.

FIG. 11 is a graph plotting the magnification Hk with respect to the main measurement (arrangement angle φ ₁ = 0 °, φ ₂ = 120 °, φ ₃ = −135 °). In FIG. 11, the horizontal axis represents the order k of the Fourier series, and the vertical axis represents the magnification Hk (au). As described above, when the magnification Hk becomes 0 or becomes too small, there is a problem that an error of a Fourier series coefficient to be obtained becomes large. As shown in FIG. 11, the magnification Hk is 0 at the orders k = 1, 23, and 25. The primary order is 0 because the weights w _i (i = 1 to 3) are calculated so as to satisfy the expression (4).

  FIG. 12 is a graph showing the change in the magnification Hk by calculating the order k of the Fourier series as a continuous variable without taking it as an integer. In FIG. 12, the horizontal axis represents the Fourier series order k, and the vertical axis represents the magnification Hk (au). As shown in FIG. 12, it can be seen that there is a node at the order k = 12, and the amplitude value changes greatly in the vicinity. Furthermore, as shown in FIG. 12, the magnification Hk is 0 at orders k = 23 and 25.

13, the arrangement angle phi ₁ = 0 °, phi ₂ = 110 °, phi ₃ = -135 °, the case of changing only phi _2, is a graph showing the variation of magnification Hk (continuous). In FIG. 13, the horizontal axis represents the Fourier series order k, and the vertical axis represents the magnification Hk (au). As shown in FIG. 13, nodes appear at orders k = 8 and 22, and unlike FIG. 11, the change in amplitude value is large at order k = 14. On the other hand, in the order k = 23 and 25 where the magnification Hk was 0 in the case of FIG. 12 (φ ₂ = 120 °), the magnification Hk is not 0.

As described above, as further clarified by actual rotational shake measurement, the conventional three-point method includes αk ² + βk ^{2 in} the denominator of equation (8). There was a problem. Since the magnification Hk is selected so that the formula (6) is established, there is a possibility that it becomes 0 when considering higher order Fourier series. That is, in the conventional three-point method, the magnification Hk is 0 or a very small value, and therefore, when a higher order is considered, an order that cannot be calculated correctly appears. For this reason, there has been a problem that the shape r (θ) of the rotating body 10 and thus the rotational shake amounts x (θ) and y (θ) cannot be obtained correctly.

  Accordingly, an object of the present invention is to solve the above-described problem. Even when a higher order is considered, an order that cannot be calculated correctly does not appear, and the shape r ( It is an object of the present invention to provide a rotating body measuring method and the like that can correctly obtain θ) and, in turn, rotational shake amounts x (θ) and y (θ).

  A rotating body measuring apparatus according to the present invention is a rotating body measuring apparatus for measuring characteristics including the shape of a rotating body, and includes at least four detectors arranged toward a measurement center on a rotating circumference of the rotating body. And a processing unit connected to the detector group, and an arrangement angle of a first set of detectors including three of the detector groups is a Fourier series of the shape of the rotating body A first set of magnifications used for component calculation is set to an angle according to a predetermined condition, and a second set of detectors in which at least one different from the first set in the detector group is one set. The arrangement angle is set to an angle in accordance with a complementary condition in which the second set of magnifications used when calculating the Fourier series component of the shape of the rotating body is supplemented with the first set of magnifications. The characteristic including the shape of the rotating body is calculated based on the output and a predetermined multipoint method. To.

  Here, in the rotating body measuring apparatus according to the present invention, an m-th set (m ≧ 2), in which three sets are included in the detector group, is set, and the m-th set is the first to m−1. The arrangement angle of the m-th detector is different from that of the set, and the m-th set magnification used when calculating the Fourier series component of the shape of the rotating body is the first to m-1th set. Each angle can be set to an angle according to a complementing condition for complementing.

  Here, in the rotating body measuring apparatus of the present invention, the shape of the rotating body is represented by a Fourier series according to the rotation angle, and the detected displacement that is the output of the displacement detector is the eccentric amount of the rotating body and the arrangement angle of the displacement detector. A weight calculation processing means for obtaining a weight when calculating the weighted addition of the detected displacement of each detector for each group so that the eccentricity amount is 0 A magnification coefficient calculation processing means for obtaining a magnification coefficient by adding a Fourier component for each arrangement angle of each displacement detector using the weight obtained by the weight calculation processing means for each set; and the magnification coefficient for each set. Selection processing means for obtaining a magnification based on the magnification coefficient obtained by the calculation processing means, comparing the magnitudes of the magnifications of each set for each order of the Fourier series, and selecting a larger set for each order; and for each set The weight calculation process Weighted addition processing means for obtaining weighted addition of detection displacement of each detector using the weight obtained by the stage, and Fourier coefficient calculation processing means for obtaining Fourier coefficient of weighted addition obtained by the weighted addition processing means for each set And, for each set, the shape Fourier coefficient for obtaining the Fourier coefficient of the shape of the rotating body using the magnification coefficient obtained by the magnification coefficient calculation processing means and the weighted addition Fourier coefficient obtained by the Fourier coefficient calculation processing means. About the Fourier coefficient of the shape of the rotating body for each set obtained by the calculation processing means and the shape Fourier coefficient calculating processing means, the Fourier coefficient of the shape of the rotating body of the set selected for each order by the selection processing means And a positive shape Fourier coefficient calculation processing means for calculating the positive shape for each order as a Fourier coefficient of the shape of the positive rotating body; Based on the Fourier coefficients of the shape of the positive rotating body obtained by the coefficient calculation processing means can comprise a shape calculation processing means for calculating the shape of the rotating body.

  Here, in the rotating body measuring apparatus according to the present invention, the processing unit is configured to rotate the rotating body of the rotating body based on the shape obtained by the shape calculation processing means and the weighted addition for each set obtained by the weighted addition processing means. A rotational shake amount calculating means for obtaining the amount can be further provided.

  Here, in the rotating body measuring apparatus according to the present invention, the predetermined condition is an arrangement angle in a case where the maximum value in the order of the Fourier series in the first set of magnifications for a plurality of arrangement angles is a minimum. Can be.

  Here, in the rotating body measuring apparatus according to the present invention, the complementary condition may be an arrangement angle in a case where the magnification of each set is an approximately uniform value greater than or equal to a predetermined value.

  Here, in the rotating body measuring apparatus of the present invention, when the number of detectors is four, the arrangement angles of the displacement detectors can be 0 °, 110 °, 120 °, and −135 °, respectively.

  The rotating body measuring method of the present invention is a rotating body measuring method for measuring characteristics including the shape of the rotating body, and is provided with at least four detectors arranged on the rotating circumference of the rotating body toward the measurement center. Group and a processing unit connected to the detector group, and the arrangement angle of the first set of detectors including three of the detector groups as a set is the shape of the rotating body. The first set of magnifications used for calculating the Fourier series component of the second set is set to an angle in accordance with a predetermined condition, and a second set of three sets, at least one of which is different from the first set in the detector group. The arrangement angle of the detector is set to an angle according to a complementary condition in which the second set of magnifications used when calculating the Fourier series component of the shape of the rotating body is supplemented with the first set of magnifications, and the processing unit The characteristics including the shape of the rotating body are calculated based on the output of the vessel group and a predetermined multipoint method. I am characterized in.

  Here, in the rotating body measuring method according to the present invention, an m-th group (m ≧ 2) is set in which three sets are included in the detector group, and the m-th group is the first to m−1. The arrangement angle of the m-th detector is different from that of the set, and the m-th set magnification used when calculating the Fourier series component of the shape of the rotating body is the first to m-1th set. Each angle can be set to an angle according to a complementing condition for complementing.

  Here, in the rotating body measuring method of the present invention, the shape of the rotating body is represented by a Fourier series based on the rotation angle, and the detected displacement that is the output of the displacement detector is the eccentric amount of the rotating body and the arrangement angle of the displacement detector. A weight calculation processing step which is expressed based on the shape of the rotating body, and the processing unit obtains a weight when calculating the weighted addition of the detection displacement of each detector for each group so that the eccentricity becomes zero; A magnification factor calculation processing step for obtaining a magnification factor by adding a Fourier component for each arrangement angle of each displacement detector using the weight obtained by the weight calculation processing step for each group; and the magnification factor for each group A magnification step based on the magnification coefficient obtained in the calculation processing step is obtained, a comparison processing step is performed for each order of the Fourier series, the magnitude of each pair is compared, and a larger pair is selected for each order; A weighted addition processing step for obtaining a weighted addition of the detected displacement of each detector using the weight obtained by the weight calculating step, and a Fourier for obtaining a Fourier coefficient of the weighted addition obtained by the weighted addition processing step for each set. Using the coefficient calculation processing step, and for each set, the magnification coefficient obtained by the magnification coefficient calculation processing step and the weighted addition Fourier coefficient obtained by the Fourier coefficient calculation processing step, the Fourier coefficient of the shape of the rotating body is calculated. About the shape Fourier coefficient calculation processing step to be obtained, and the Fourier coefficient of the shape of the rotator for each set obtained by the shape Fourier coefficient calculation processing step, the pair of rotators selected for each order by the selection processing step The Fourier coefficient of the shape is obtained as the Fourier coefficient of the shape of the positive rotating body for each order. And a shape calculation processing step for obtaining the shape of the rotating body based on the Fourier coefficient of the shape of the positive rotating body obtained by the positive shape Fourier coefficient calculation processing step. .

  Here, in the rotating body measuring method according to the present invention, the processing unit may rotate the rotating body of the rotating body based on the shape obtained by the shape calculating process step and the weighted addition for each set obtained by the weighted adding process step. A rotational shake amount calculation step for obtaining the amount can be further provided.

  Here, in the rotating body measuring method of the present invention, the predetermined condition is an arrangement angle in a case where the maximum value in the order of the Fourier series in the first set of magnifications for a plurality of arrangement angles is a minimum. Can be.

  Here, in the rotating body measuring method of the present invention, the complementary condition may be an arrangement angle in the case of a magnification at which each set of magnifications is an approximately uniform value equal to or greater than a predetermined value.

  Here, in the rotating body measuring method of the present invention, when the number of detectors is four, the arrangement angles of the displacement detectors can be 0 °, 110 °, 120 °, and −135 °, respectively.

  According to the rotating body measuring method and the like of the present invention, in the conventional three-point method, the limit of the number of detectors of three is removed, and four or more detectors are used. A plurality of sets of detector angular arrangements with uniform magnification coefficients are selected (predetermined conditions). Secondly, a magnification (as a result, a magnification factor) is selected so that a portion where the denominator of the same equation is 0 is complemented between a plurality of sets (complementation condition). Thirdly, the shape and the rotational shake amount are obtained by using the complementary magnification coefficient and the like (resulting Fourier coefficient). Therefore, the variation in error when calculating the shape and the like is small, and the rotating body measuring method of the present invention can be applied even when the order is high. For this reason, even when a higher order is considered, there is provided an apparatus and method for measuring a rotating body capable of correctly obtaining the shape of the rotating body and thus the amount of rotational run-out without causing an order that cannot be calculated correctly. There is an effect that can be.

  First, the principle of the rotating body measuring method (predetermined multipoint method) of the present invention will be described, and then each embodiment will be described in detail with reference to the drawings.

Principle of the rotating body measuring method of the present invention.

FIG. 1 shows the arrangement of a rotating body and detectors for explaining the principle of the rotating body measuring method and the like of the present invention. In FIG. 1, portions denoted by the same reference numerals as those used in the background art in FIG. In FIG. 1, reference numeral 4 is a detector (probe), and φ ₄ is an arrangement angle of the detector 4. The rotating body 10 has many shafts made of metal, and the detector i (i = 1 to 4) uses a capacitance type (displacement) detector, but an optical detector may be used. . All of the four detectors 1 to 4 are set so as to pass through the measurement center O (0, 0). Four detectors 1 to 4 are sequentially attached to the arrangement angles of φ ₁ , φ ₂ , φ ₃ , and φ ₄ , and the rotating body 10 is installed at substantially the center thereof. As shown in FIG. 1, the rotation angle of the rotating body 10 is θ, and the center position Oc of the rotating body is eccentric (x (θ), y (θ)), that is, the amount of eccentricity is (x (θ), y (θ)). With the arrangement angle shown in FIG. 1, the first set is detector 1 (φ ₁ ), detector 2 (φ ₂ ), detector 3 (φ ₃ ), and the second set is detector 1 (φ ₁ ), It is assumed that detector 4 (φ ₄ ) and detector 3 (φ ₃ ).

First, how to attach weights and the like will be briefly described. The symbols and terms are in accordance with the principle of the three-point method described in the background art. The weights (coefficients) of the first set are w ₁₁ , w ₁₂ , and w _13, and the weights of the second set are w ₂₁ , w ₂₄ , and w ₂₃ . The first set of magnification coefficients are α _1k and β _1k, and the second set of magnification coefficients are α _2k and β _2k . The magnification of the first set is H _k1 , and the magnification of the second set is H _k2 . The first set of shapes Fourier coefficients _A1K, and _{B 1k,} the second set of shapes Fourier coefficients _{A 2k,} and _{B 2k.} The output signals from the detectors 1 to 4 are d1, d2, d3, and d4. The sum of the first set of signal outputs d1, d2, and d3 is designated as dr1, and the sum of the second set of signal outputs d1, d4, and d3 is designated as dr2. The shape obtained from dr1 and its order components are rr1 and rr1k, and the shape obtained from dr2 and its order components are rr2 and rr2k.

  When the shape of the rotator 10 is represented by r (θ) and expanded by Fourier series and displayed with components for each order, the following equation (1) is obtained as in the case of the three-point method.

    r (θ) = r0 + Σ (Akcos (kθ) + Bksin (kθ)) (1)

  In equation (1), r0 is the average radius of the rotating body, k is the order of the Fourier series, Ak and Bk are the shape Fourier coefficients representing the shape, and addition (Σ) is k = 1 to N (target Fourier series) Up to the highest order of the component). The average radius r0 can be considered to be 0 because it is considered to be a constant value when the shape r (θ) is obtained. When the detected displacement at each detector i (i = 1 to 4) is represented by di (θ), the following equation (2) is obtained as in the case of the three-point method.

    di (θ) = r (θ + φi) + x (θ) cosφi + y (θ) sinφi (2)

In order to obtain the shape r (θ), w _i (i = 1 to 4) is used as a weight, and weighted additions dr1 (θ) and dr2 (θ) are taken as in the following equations (12) and (13). .

dr1 (θ) = w ₁₁ r (θ + φ ₁ ) + w ₁₂ r (θ + φ ₂ ) + w ₁₃ r (θ + φ ₃ )
+ X (θ) (w ₁₁ cos φ ₁ + w ₁₂ cos φ ₂ + w ₁₃ cos φ ₃ )
+ Y (θ) (w ₁₁ sin φ ₁ + w ₁₂ sin φ ₂ + w ₁₃ sin φ ₃ )
(12)
dr2 (θ) = w ₂₁ r (θ + φ ₁ ) + w ₂₄ r (θ + φ ₂ ) + w ₂₃ r (θ + φ ₃ )
+ X (θ) (w ₂₁ cos φ ₁ + w ₂₄ cos φ ₂ + w ₂₃ cos φ ₃ )
+ Y (θ) (w ₂₁ sinφ ₁ + w ₂₄ sinφ ₂ + w ₂₃ sinφ ₃ )
(13)

In equation (11), when the weight w _ij and the arrangement angle φ _i (i = 1 to 4) are taken as in the following equations (14) and (15), the eccentric amounts x (θ) and y (θ The weighted additions dr1 (θ) and dr2 (θ) can be obtained without depending on.

w ₁₁ cos φ ₁ + w ₁₂ cos φ ₂ + w ₁₃ cos φ ₃ = 0
w ₁₁ sin φ ₁ + w ₁₂ sin φ ₂ + w ₁₃ sin φ ₃ = 0 (14)
w ₂₁ cosφ ₁ + w ₂₄ cosφ ₄ + w ₂₃ cosφ ₃ = 0
w ₂₁ sinφ ₁ + w ₂₄ sinφ ₄ + w ₂₃ sinφ ₃ = 0 (15)

  When the expressions (14) and (15) are established, the weighted additions dr1 (θ) and dr2 (θ) do not depend on the eccentric amounts x (θ) and y (θ). From Equation (12), Equation (13) and Equation (1),

dr1 (θ) = w ₁₁ r (θ + φ ₁ ) + w ₁₂ r (θ + φ ₂ ) + w ₁₃ r (θ + φ ₃ )
= W ₁₁ Σ {Akcos (k (θ + φ ₁ )) + Bksin (k (θ + φ ₁ ))}
+ W ₁₂ Σ {Akcos (k (θ + φ ₂ )) + Bksin (k (θ + φ ₂ ))}
+ W ₁₃ Σ {Akcos (k (θ + φ ₃ )) + Bksin (k (θ + φ ₃ ))}
(16)
dr2 (θ) = w ₂₁ r (θ + φ ₁ ) + w ₂₄ r (θ + φ ₄ ) + w ₂₃ r (θ + φ ₃ )
= W ₂₁ Σ {Akcos (k (θ + φ ₁ )) + Bksin (k (θ + φ ₁ ))}
+ W ₂₄ Σ {Akcos (k (θ + φ ₄ )) + Bksin (k (θ + φ ₄ ))}
+ W ₂₃ Σ {Akcos (k (θ + φ ₃ )) + Bksin (k (θ + φ ₃ ))}
(17)

If the equations (16) and (17) are modified and the magnification coefficients α _1k , β _1k , α _2k , and β _2k are set as in the following equations (18) and (19), the equation (16) becomes Like equation (20), equation (17) can be expressed as equation (21).

w ₁₁ cos (kφ ₁ ) + w ₁₂ cos (kφ ₂ ) + w ₁₃ cos (kφ ₃ ): = α _1k
w ₁₁ sin (kφ ₁ ) + w ₁₂ sin (kφ ₂ ) + w ₁₃ sin (kφ ₃ ): = β _1k
(18)
w ₂₁ cos (kφ ₁ ) + w ₂₄ cos (kφ ₄ ) + w ₂₃ cos (kφ ₃ ): = α _2k
w ₂₁ sin (kφ ₁ ) + w ₂₄ sin (kφ ₄ ) + w ₂₃ sin (kφ ₃ ): = β _2k
(19)
dr1 (θ) = Σ {(A _1k α _1k −B _1k β _1k ) cos (kθ)
+ (B _1k α _1k + A _1k β _1k ) sin (kθ)}
= Σ {F _1k cos (kθ) + G _1k sin (kθ)} (20)
dr2 (θ) = Σ {(A _2k α _2k −B _2k β _2k ) cos (kθ)
+ (B _2k α _2k + A _2k β _2k ) sin (kθ)}
= Σ {F _2k cos (kθ) + G _2k sin (kθ)} (21)

Accordingly, the Fourier coefficients F _1k and G _1k of the weighted addition values dr1 (θ) of the four detectors i (i = 1 to 4) are obtained, and the magnification coefficients α _1k and β _{1k are converted} into A _1k and B _1k as follows ( 22). Similarly, for the second set, A _2k and B _2k can be obtained by the following equation (23).

A _1k = (α _1k F _1k + β _1k G _1k ) / (α _1k ² + β _1k ² )
B _1k = (− β _1k F _1k + α _1k G _1k ) / (α _1k ² + β _1k ² ) (22)
A _2k = (α _2k F _2k + β _2k G _2k ) / (α _2k ² + β _2k ² )
B _2k = (− β _2k F _2k + α _2k G _2k ) / (α _2k ² + β _2k ² ) (23)

In the expressions (22) and (23), the sum of squares of α _1k and β _1k and the sum of squares of α _2k and β _2k are included. Here, the magnifications H1k and H2k are defined as the following expressions (24) and (25).

H _1k = √ (α _1k ² + β _1k ² ) (24)
H _2k = √ (α _2k ² + β _2k ² ) (25)

Since H _1k and H _2k have values for each order k, the magnitudes of each order k are compared, and the larger set is adopted as the coefficient of the order k. That is, for each order k, it is determined whether (A _1k , B _1k ) or (A _2k , B _2k ) is taken. The Fourier coefficient determined for each order k is set as (A _ak , B _ak ), and using this, the shape r (θ) of the rotating body can be obtained by equation (1). When the shape r (θ) is obtained, the eccentricity amounts x (θ) and y (θ) are obtained by the following equation (9) as in the three-point method.

x (θ) = {− (d ₂ (θ) −r (θ + φ ₂ )) sin φ ₁
+ (D ₁ (θ) −r (θ + φ ₁ )) sin φ ₂ } / sin (φ ₁ −φ ₂ )
y (θ) = {(d ₂ (θ) −r (θ + φ ₂ )) cos φ ₁
− (D ₁ (θ) −r (θ + φ ₁ )) cos φ ₂ } / sin (φ ₁ −φ ₂ )
(9)

  The eccentric amounts x (θ) and y (θ) of the rotating body 10 appear as primary rotational shakes during rotation. This rotational shake includes the rotational shake of the rotating body 10 itself and the mounting error of the rotating body 10, but the two cannot be separated. Further, if the frequency components of the eccentric amounts x (θ) and y (θ) of the rotating body 10 are expressed by Ck, Dk, Nk, and Mk, the frequency component of the rotational shake is expressed by the equation (10) as in the three-point method. It is possible to ask. The above is the principle of the rotating body measuring method of the present invention.

x (θ) = Σ {Ckcos (kθ) + Dksin (kθ)}
y (θ) = Σ {Nkcos (kθ) + Mksin (kθ)} (10)

Hereinafter, an embodiment of the present invention will be described. 2A and 2B show a rotating body measuring apparatus 20 in Embodiment 1 of the present invention. 2A is a plan view of the rotating body detector device 20, and FIG. 2B is a cross-sectional view taken along line XX ′. 2 (A) and 2 (B), the same reference numerals as those in FIG. 2 (A) and 2 (B), reference numeral 12 denotes a rotating body (0.5 ″ sphere), and an arrangement angle φ _i (i = 1 to 4) of each detector i (i = 1 to 4). Are preferably φ ₁ = 0 °, φ ₂ = 120 °, φ ₃ = −135 °, φ ₄ = 110 °, and each set is an example described in the above principle (the first set is the detector 1). (Φ ₁ ), detector 2 (φ ₂ ), detector 3 (φ ₃ ), and the second set is detector 1 (φ ₁ ), detector 4 (φ ₄ ), detector 3 (φ ₃ )) Will be described.

As shown in FIG. 1 and FIGS. 2A and 2B, the rotating body measuring device 20 that measures various characteristics (rotational shake amount and the like) including the shape r (θ) of the rotating body 12 includes the rotating body 12. And at least four detector groups i (i = 1 to 4) arranged toward the measurement center O on the rotation circumference of the sensor, and the processing unit 30 connected to the detector group i (i = 1 to 4). And. The function of the processing unit 30 will be described later. The arrangement angle (φ ₁ , φ ₂ , φ ₃ ) of a first set of three detectors i (i = 1 to 4) in the detector group i is a shape r (θ of the rotating body 12 The first set of magnifications H _1k used when calculating the Fourier series component of) is set to an angle according to a predetermined condition. As a predetermined condition, a first set of magnifications H _1k is obtained for a desired arrangement angle, and a magnification H _1k that is the maximum value in the order k of the Fourier series is selected. This operation is repeated for other desired arrangement angles, and the arrangement angle when the maximum magnification H _1k is the minimum is the arrangement angle (φ ₁ , φ ₂ , φ ₃ ) of the first set of detectors. That is, the predetermined condition is a condition for setting the arrangement angle in the case of a magnification at which the maximum value in the order k of the Fourier series in the first set of magnifications H _1k for a plurality of desired arrangement angles is the minimum. On the other hand, in the detector group i (i = 1 to 4), the arrangement angle (φ ₁ , φ ₄ , φ) of the second set of detectors, each of which includes at least one set different from the first set. ₃ ) is set to an angle according to a complementary condition in which the second set of magnifications H _2k used when calculating the Fourier series component of the shape r (θ) of the rotating body 12 is supplemented with the first set of magnifications H _1k . The complementary condition is a condition for setting the arrangement angle when the magnifications H _1k and H _{2k of} each set are approximately uniform values equal to or larger than a predetermined value. For example, there is a condition for the arrangement angle when H _2k is complemented so as to increase when the magnification H _1k of each order k obtained in the first set becomes smaller. An approximately uniform value means that the magnification H _1k and H _1k are compared and the larger one is taken, and the magnification should be determined so that all of them are substantially uniform. For example, 0.7 is preferable as the predetermined value, but the value is not limited to this value, and any value that does not become too small may be used. Based on the output of the detector group i (i = 1 to 4) and a predetermined multipoint method (for example, the principle of the method for measuring a rotating body of the present invention described above), the processing unit 30 forms the shape r ( A characteristic (rotational shake amount) including θ) is calculated.

  Next, functions of the processing unit 30 will be described. FIG. 3 is a functional block diagram showing functions of the processing unit 30. As described above, the shape r (θ) of the rotating body 12 is represented by a Fourier series based on the rotation angle θ, and the detected displacement di (θ) that is the output of the (displacement) detector i (i = 1 to 4) is This is expressed based on the eccentric amounts x (θ) and y (θ) of the rotating body 12 and the shape of the rotating body 12 at the arrangement angle of the (displacement) detector i (i = 1 to 4). As shown in FIG. 3, the processing unit 30 includes a weight calculation processing unit (weight calculation processing unit) 31, a magnification factor calculation processing unit (magnification coefficient calculation processing unit) 32, a selection processing unit (selection processing unit) 33, weighting. Addition processing section (weighted addition processing means) 34, Fourier coefficient calculation processing section (Fourier coefficient calculation processing means) 35, shape Fourier coefficient calculation processing section (shape Fourier coefficient calculation processing means) 36, positive shape Fourier coefficient calculation processing section (positive A shape Fourier coefficient calculation processing means) 37 and a shape calculation processing section (shape calculation processing means) 38. The above functions of the processing unit 30 are preferably realized as a computer program, and the computer program constitutes the present invention. The computer program can be supplied to the computer CPU in the form of a recording medium such as a CD-ROM or DVD, and a recording medium such as a CD-ROM on which the computer program is recorded also constitutes the present invention. Become.

The weight calculation processing unit 31 calculates the weight w ₁₁ when obtaining the weighted addition dr1 (θ) of the detection displacement di (θ) at each detector (formula (12), formula (13)) for each set. Etc. are calculated so that the eccentric amounts x (θ) and y (θ) are 0 (formulas (14) and (15)).

The magnification coefficient calculation processing unit 32 uses the weights w ₁₁ , w ₁₂ , w _{13, and the} like obtained by the weight calculation processing unit 31 for each group, for each (displacement) detector i (i = 1 to 4). Magnification coefficients α _1k , β _{1k and the} like obtained by adding the Fourier components for each arrangement angle are obtained (Equations (18) and (19)).

The selection processing unit 33 _obtains the magnifications H _1k and H _2k based on the magnification factors α _1k and β _1k obtained by the magnification factor calculation processing unit 32 for each set, and the magnification of each set for each order k of the Fourier series. The magnitudes of H _1k and H _2k are compared, and the larger set is selected for each order k.

The weighted addition processing unit 34 detects the detected displacement di (θ) of each detector i (i = 1 to 4) using the weights w ₁₁ , w ₁₂ , w _{13 and the} like obtained by the weight calculation processing unit 31 for each group. ) Weighted addition dr1 (θ) and the like (Equations (16) and (17))). For example (16) weight _w 11 of the first in _Expressions, w _{12, w 13} uses the weights _{w 11, w 12, w 13} that Motoma' the weight calculation unit 31. For r (θ + φ ₁ ), the detector output (μm) of the detector 1 at the angle θ + φ ₁ is used. The same applies to r (θ + φ ₂ ) and r (θ + φ ₃ ). As a result, the weighted addition dr1 (θ) at the angle θ (0 to 360 °) is obtained.

The Fourier coefficient calculation processing unit 35 obtains Fourier coefficients F _1k , G _{1k and the} like such as weighted addition dr1 (θ) obtained by the weighted addition process 34 for each group (Equations (20) and (21)). .

The shape Fourier coefficient calculation processing unit 36 uses, for each group, the magnification coefficients α _1k and β _1k obtained by the magnification coefficient calculation processing unit 32 and the weighted addition Fourier coefficients F _1k and G obtained by the Fourier coefficient calculation processing unit 35. _{Using 1k} and the like, Fourier coefficients A _1k and B _{1k and the} like of the shape of the rotating body 12 are obtained (equations (22) and (23)).

The regular shape Fourier coefficient calculation processing unit 37 uses the selection processing unit 33 for each order k for the Fourier coefficients A _1k , B _1k, etc. of the shape of the rotating body 12 for each set obtained by the shape Fourier coefficient calculation processing unit 36. The Fourier coefficient of the shape of the rotating body 12 of the selected pair is obtained as the Fourier coefficients A _ak and B _ak of the shape of the positive rotating body 12 for each order k.

The shape calculation processing unit 38 obtains the shape r (θ) of the rotating body 12 based on the Fourier coefficients A _ak and B _ak of the shape of the positive rotating body 12 obtained by the regular shape Fourier coefficient calculation processing unit 37 ((1 )formula).

  The processing unit 30 further includes a rotational shake amount calculation unit (rotational shake amount calculation means) 39 in order to measure not only the shape r (θ) of the rotating body 12 but also other characteristics such as the rotational shake amount. . The rotational shake amount calculation unit 39 rotates the rotating body 12 based on the shape r (θ) obtained by the shape calculation processing unit 38 and the weighted addition d1 (θ) for each set obtained by the weighted addition processing unit 34. The shake amount (eccentric amount, x (θ) and y (θ)) is obtained (Equation (9)).

Next, the processing flow (function of the processing unit 30) of the rotating body measuring method of the present invention will be described with reference to a flowchart. FIG. 4 is a flowchart showing the process flow of the rotating body measuring method of the present invention. As shown in FIG. 4, first, for each group, a weighted addition dr1 (θ) of detection displacement di (θ) at each detector (formula (12), formula (13))) is obtained. The weights w _{11 and the} like are obtained so that the eccentric amounts x (θ) and y (θ) are 0 (weight calculation processing step, step S10, formulas (14) and (15)).

For each group, using the weights w ₁₁ , w ₁₂ , w _{13, and the} like obtained in the weight calculation processing step (step S 10), Fourier for each arrangement angle of each (displacement) detector i (i = 1 to 4). Magnification coefficients α _1k , β _{1k and the} like obtained by adding the components are obtained (magnification coefficient calculation processing step, step S12 (formula (18), formula (19))).

The magnifications H _1k and H _2k based on the magnification factors α _1k and β _1k obtained by the magnification factor calculation processing step (step S12) are obtained for each group, and the magnification H _1k of each set is obtained for each order k of the Fourier series. Compare the magnitude with _H2k, and select the larger set for each order k (selection processing step, step S14).

For each group, the weighted addition of the detected displacement di (θ) of each detector i (i = 1 to 4) using the weights w ₁₁ , w ₁₂ , w _13, etc. obtained in the weight calculation processing step (step S 10). dr1 (θ) and the like are obtained (weighted addition processing step, step S16, equations (16) and (17)). For example (16) weight _w 11 of the first in _Expressions, w _{12, w 13} uses the weights _{w 11, w 12, w 13} that Motoma' the weight calculation unit 31. For r (θ + φ ₁ ), the detector output (μm) of the detector 1 at the angle θ + φ ₁ is used. The same applies to r (θ + φ ₂ ) and r (θ + φ ₃ ). As a result, the weighted addition dr1 (θ) at the angle θ (0 to 360 °) is obtained.

For each group, Fourier coefficients F _1k , G _{1k and the} like such as weighted addition dr1 (θ) obtained in the weighted addition processing step (step S16) are obtained (Fourier coefficient calculation processing step; step S18, equation (20), (20). 21) Formula)).

For each group, the magnification coefficients α _1k , β _{1k and the} like obtained in the magnification coefficient calculation processing step (step S18), the weighted addition Fourier coefficients F _1k and G _{1k and the} like obtained in the Fourier coefficient calculation processing step (step S18), _{Are used} to find the Fourier coefficients A _1k , B _1k, etc. of the shape of the rotating body 12 (shape Fourier coefficient calculation processing step, step S20 (formula (22), formula (23))).

For the Fourier coefficients A _1k , B _1k, etc. of the shape of the rotating body 12 for each set obtained in the shape Fourier coefficient calculation processing step (step S20), the set selected for each order k in the selection processing step (step S14). The Fourier coefficient of the shape of the rotating body 12 is obtained as the Fourier coefficients A _ak and B _ak of the shape of the positive rotating body 12 for each order k (positive shape Fourier coefficient calculation processing step, step S22).

Based on the Fourier coefficients A _ak and B _ak of the shape of the positive rotating body 12 obtained in the regular shape Fourier coefficient calculating process step (step S22), the shape r (θ) of the rotating body 12 is obtained (shape calculating process step. S24 (Formula (1)).

  The processing unit 30 further includes a rotational shake amount calculation step to measure not only the shape r (θ) of the rotating body 12 but also other characteristics such as the rotational shake amount. In the rotational shake amount calculation step, based on the shape r (θ) obtained in the shape calculation processing step (step S24), the weighted addition d1 (θ) for each set obtained in the weighted addition processing step (step S16), etc. A rotational shake amount (eccentric amount, x (θ) and y (θ)) of the rotating body 12 is obtained (step S26, equation (9)).

As described above, according to the first embodiment of the present invention, the rotating body measuring apparatus 20 includes at least four detector groups i (i = 1) arranged on the rotation circumference of the rotating body 12 toward the measurement center O. 4) and a processing unit 30 connected to the detector group i (i = 1 to 4). The arrangement angle (φ ₁ , φ ₂ , φ ₃ ) of a first set of three detectors i (i = 1 to 4) in the detector group i is a shape r (θ of the rotating body 12 The first set of magnifications H _1k used when calculating the Fourier series component of) is set to an angle according to a predetermined condition. As a predetermined condition, a first set of magnifications H _1k is obtained for a desired arrangement angle, and a magnification H _1k that is the maximum value in the order k of the Fourier series is selected. This operation is repeated for other desired arrangement angles, and the arrangement angle when the maximum magnification H _1k is the minimum is the arrangement angle (φ ₁ , φ ₂ , φ ₃ ) of the first set of detectors. On the other hand, in the detector group i (i = 1 to 4), the arrangement angle (φ ₁ , φ ₄ , φ) of the second set of detectors, each of which includes at least one set different from the first set. ₃ ) is set to an angle according to a complementary condition in which the second set of magnifications H _2k used when calculating the Fourier series component of the shape r (θ) of the rotating body 12 is supplemented with the first set of magnifications H _1k . The complementary condition is a condition for setting the arrangement angle when the magnifications H _1k and H _{2k of} each set are approximately uniform values equal to or larger than a predetermined value. Based on the output of the detector group i (i = 1 to 4) and a predetermined multipoint method (for example, the principle of the method for measuring a rotating body of the present invention described above), the processing unit 30 forms the shape r ( A characteristic (rotational shake amount) including θ) is calculated.

That is, according to the rotating body measuring method and the like of the present invention, in the conventional three-point method, the limit of the number of detectors of three is removed, and using four or more detectors, A plurality of sets of detector angular arrangements with uniform magnification factors α _1k , β _1k, etc. coming to the denominator of the equation (23) are selected (predetermined conditions). Secondly, magnifications H _1k , H _2k (resulting magnification factors α _1k , β _1k, etc.) so that the portions where the denominator of the equations (22) and (23) are 0 are complemented between a plurality of sets. Select (complementary condition). Thirdly, the shape r (θ) and the rotational shake amounts x (θ) and y (θ) are obtained using the complementary magnification factors α _1k , β _1k, etc. (resulting in A _ak , B _ak ). Therefore, the variation in error when calculating the shape r (θ) and the like is small, and the rotating body measuring method of the present invention can be applied even when the order k is high. For this reason, even when a high-order order k is considered, there is no occurrence of an order k that cannot be calculated correctly, and the shape r (θ) of the rotating body, and hence the rotational shake amounts x (θ) and y (θ). Thus, it is possible to provide the rotating body measuring apparatus 20 and the method capable of correctly obtaining the value.

  In Example 1, the structure which arranged the detector simultaneously was shown. In the second embodiment, by using one detector and a rotation mechanism (not shown), first, one output is detected at a certain angle (φ1), and then the position of the second detector (φ2 ) To detect the value there, then rotate to the third detector position (φ3), detect the value there and rotate to the fourth detector position (φ4) And detect the value there. As described above, the values of the positions of the four detectors are acquired by shifting the position and time of the detector, and each calculation process such as the rotating body measuring method of the present invention is applied to the acquired values. That's fine.

In the first embodiment, an example has been described in which at least four detector groups are used and two sets of three detector groups are taken from the detector groups. In the third embodiment, an m-th set (m ≧ 2) is set, in which at least three detector groups are included in at least four detector groups. Here, the m-th set is different from at least one of the first to m-1 sets, and the arrangement angle of the m-th set of detectors is the Fourier series component of the shape r (θ) of the rotating body 12. The m-th set of magnifications H _mk used at the time of calculation may be set to an angle according to a complementary condition that complements each of the first to m- _1th sets of magnifications H _ik (i = 1 to m). Thereafter, the rotating body measuring method of the present invention can be applied in the same manner as in the first embodiment. For example, in the selection processing unit 33, the magnifications H _1k , H _2k , _... Based on the magnification coefficients α _1k , β _1k, etc. obtained by the magnification coefficient calculation processing unit 32 for each group (1 to m groups). . . , H _mk, and for each order k of the Fourier series, each set of magnifications H _1k , H _2k,. . . , H _mk are compared, and the largest pair is selected for each order k.

  As an application example of the present invention, the present invention can be applied to a rotating body measuring apparatus and method for measuring the shape and rotational shake amount of a rotating shaft in an information device such as a hard disk or an optical disk in a non-contact manner.

It is a figure which shows arrangement | positioning of the rotary body and detector for demonstrating principles, such as the rotary body measuring method of this invention. It is a figure which shows the rotary body measuring apparatus 20 in Example 1 of invention. 3 is a functional block diagram illustrating functions of a processing unit 30. FIG. It is a flowchart which shows the flow of a process (function of the process part 30) of the rotary body measuring method of this invention. It is a figure which shows arrangement | positioning of the rotary body and detector for demonstrating the principle of a three-point method. It is a flowchart which shows the flow of a process of 3 point | piece method. It is a figure which shows the measuring apparatus 20 used for the actual rotational shake measurement. It is a graph which shows the waveform dr ((theta)) which added the output waveform of each detector i (i = 1-3), and the three detector i (i = 1-3) output. It is a figure which calculates | requires the shape of the rotary body 12 from the added waveform dr ((theta)). It is the graph which displayed the frequency component of rotational shake. This measurement (arrangement angle phi ₁ = 0 °, phi ₂ = 120 °, phi ₃ = -135 °) with respect to a graph plotting magnification Hk. It is a graph which shows the variation | change_quantity of the magnification Hk by calculating as a continuous variable instead of making the order k of a Fourier series into an integer. Arrangement angle phi ₁ = 0 °, phi ₂ = 110 °, phi ₃ = -135 °, the case of changing only phi _2, is a graph showing the variation of magnification Hk (continuous).

Explanation of symbols

1, 2, 3, 4 detector, 10, 12 rotator, 20 rotator measurement apparatus of the present invention, 30 processing unit, 31 weight calculation processing unit, 32 magnification factor calculation processing unit, 33 selection processing unit, 34 weighted addition A processing unit, a 35 Fourier coefficient calculation processing unit, a 36 shape Fourier coefficient calculation processing unit, a 37 regular shape Fourier coefficient calculation processing unit, a 38 shape calculation processing unit, a 39 rotational shake amount calculation processing unit, and a conventional rotating body measuring apparatus.

Claims (7)

A rotating body measuring method for measuring characteristics including a shape of a rotating body, comprising at least four detector groups arranged toward a measurement center on a rotation circumference of the rotating body, and connected to the detector groups And a processing unit
The arrangement angle of the first set of detectors, which is a set of three of the detector groups, is set to an angle in which the first set of magnifications used when calculating the Fourier series component of the shape of the rotating body is in accordance with a predetermined condition. And
An arrangement angle of a second set of detectors in which at least one of the detector groups is at least one different from the first set is the second set used when calculating the Fourier series component of the shape of the rotating body. Is set to an angle that complies with the complementary conditions that complement the first set of magnifications,
The processing unit calculates a characteristic including a shape of a rotating body based on an output of the detector group and a predetermined multipoint method.   2. The rotating body measurement method according to claim 1, wherein an m-th set (m ≧ 2) of three sets is set in the detector group, and the m-th set is the first to m−1th sets. And the arrangement angle of the m-th set of detectors is such that the m-th set magnification used when calculating the Fourier series component of the shape of the rotating body is the first to m-1th set. A rotating body measuring method, characterized in that the angle is set according to a complementary condition for complementing a magnification. 3. The method of measuring a rotating body according to claim 1, wherein the shape of the rotating body is represented by a Fourier series based on the rotation angle, and the detected displacement that is an output of the displacement detector is an eccentric amount of the rotating body and an arrangement angle of the displacement detector. And based on the shape of the rotating body in
The processing unit is
For each set, a weight calculation processing step for obtaining the weight when calculating the weighted addition of the detection displacement of each detector so that the amount of eccentricity becomes zero;
A magnification factor calculation processing step for obtaining a magnification factor by adding a Fourier component for each arrangement angle of each displacement detector using the weight obtained by the weight calculation processing step for each set;
Select the magnification based on the magnification coefficient obtained by the magnification coefficient calculation processing step for each group, compare the magnitude of each group for each order of the Fourier series, and select the larger group for each order Processing steps;
For each set, a weighted addition processing step for obtaining a weighted addition of detection displacement of each detector using the weight obtained by the weight calculation processing step;
For each set, a Fourier coefficient calculation processing step for obtaining a Fourier coefficient of weighted addition obtained by the weighted addition processing step;
Shape Fourier coefficient calculation processing for obtaining the Fourier coefficient of the shape of the rotating body using the magnification coefficient obtained in the magnification coefficient calculation processing step and the weighted addition Fourier coefficient obtained in the Fourier coefficient calculation processing step for each set Steps,
For the Fourier coefficient of the shape of the rotating body for each set obtained by the shape Fourier coefficient calculation processing step, the Fourier coefficient of the shape of the rotating body of the set selected for each order by the selection processing step is calculated for each order. A positive shape Fourier coefficient calculation processing step to obtain as a Fourier coefficient of the shape of the positive rotating body;
A rotating body measuring method comprising: executing a shape calculating process step for obtaining a shape of a rotating body based on a Fourier coefficient of the shape of the positive rotating body obtained by the positive shape Fourier coefficient calculating process step.   4. The rotating body measuring method according to claim 3, wherein the processing unit is configured to calculate a rotational shake amount of the rotating body based on the shape obtained by the shape calculating process step and the weighted addition for each set obtained by the weighted adding process step. A rotating body measuring method, further comprising: a rotational shake amount calculating step for obtaining.   5. The rotating body measurement method according to claim 1, wherein the predetermined condition is a magnification at which a maximum value in the order of the Fourier series in the first set of magnifications for a plurality of arrangement angles is a minimum. A rotating body measuring method, characterized in that the angle is an arrangement angle.   6. The rotating body measurement method according to claim 1, wherein the complementary condition is an arrangement angle in a case where a magnification of each set is an approximately uniform value equal to or greater than a predetermined value. A method for measuring a rotating body. 7. The rotating body measurement method according to claim 1, wherein when there are four detectors, the arrangement angles of the displacement detectors are 0 °, 110 °, 120 °, and −135 °, respectively. A method for measuring a rotating body.