JP2016151508A - Measurement method of dynamic imbalance of rotor, and measurement device thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a measurement method and a measurement device, capable of accurately and simply measuring dynamic imbalance of a measured object with a multiple component force detector, by a simpler and smaller device than conventional ones, without generating a measurement error resulting from abnormal vibration.SOLUTION: In a method for measuring dynamic imbalance of a measured body (rotor) with a multiple component force detector on the basis of two-plane balancing, imbalance amounts mr, mrin two-plane balancing of the rotor and phase angles φ, φthereof are measured, on the basis of a predetermined calculation process, by a measurement value ω of an angular speed in exciting the rotor in a reciprocatively rotatable manner, and four component force detection values (F, F, M, M) from the multiple component force detector.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a method for measuring a dynamic imbalance of an object to be measured in an electrical or mechanical part with various rotational movements, an artificial satellite, a car body of an automobile, and the like, and a measuring apparatus therefor.

  Electrical or mechanical parts with rotational movement, artificial satellites, car bodies, etc., for example, rotors of various electric motors, disk drive mechanisms of OA equipment, video or audio equipment, rotating parts of automobiles (brake discs, clutch plates) In a supercharger rotor, etc.) and automobile bodies, it is necessary to correctly measure the dynamic imbalance.

  As is well known, the dynamic imbalance measurement and its correction method are generally not installed with an unbalance detection sensor provided on the bearing unit, which is installed on a balance corrector (or field balancer) and rotated by an external drive. The size of the balance and its phase angle are detected. Then, the unbalance amount corresponding to the output of the unbalance detection sensor is corrected on two sides by cutting the outer periphery of the rotating body or adding a weight. This method is referred to as “two-surface balancing”, and can be corrected with high accuracy (see Patent Document 1).

  By the way, it has been pointed out that an error may occur due to abnormal vibration of a rotating body or a measurement system during measurement as a problem of the method for measuring and correcting the dynamic imbalance (see Patent Document 2). ). Regarding the above problems, paragraphs [0007] to [0009] of Patent Document 2 describe as follows.

That is, “the correction of unbalance by the conventional field balancer does not take into account that the natural frequency exists in the support system of the rotating body, and rotates the rotation at an appropriate number of rotations, and the magnitude and phase of the unbalanced vibration. When the rotating body is operated at a rotational frequency synchronized with the natural frequency, the vibration is not stabilized and the phase is not determined and measurement is impossible.
In addition, “Because the support rigidity of the rotating body is not taken into account, the vibration changes depending on the number of rotations, and it is necessary to repeat the measurement through trial and error until the imbalance is corrected. ”
Furthermore, “the detected vibrations may include abnormal vibrations other than imbalance, but in measurement, vibration components synchronized with the rotational speed are extracted, so it is caused by other than imbalance. For example, vibrations caused by abnormalities in the support system, etc. cannot be detected. is there.

  In order to solve the above problems, Patent Document 2 proposes the following solution. That is, “the stationary rotating body 10 is vibrated to detect vibration, and the frequency of the vibration waveform is analyzed to obtain the natural frequency of the support system, and the vibration force is input to the rotating body 10. A transfer function whose response is vibration is obtained, the rotating body 10 rotating at a test speed avoiding the natural frequency is vibrated to detect the vibration, the frequency analysis of the vibration signal is performed, and the transfer function is used for rotation. The body unbalance amount is calculated, the reference position of the rotating body rotating at the test rotational speed is detected, the detection signal is compared with the vibration signal, and the phase difference is calculated to obtain the unbalance position. Is described.

  However, even in the case of the improved conventional measuring method and apparatus as described above, there is a problem that the measuring apparatus is complicated and large-sized, the problem is that the measurement accuracy is still low, and the vibration meter is further calibrated. There was a problem that it was necessary to carry out frequently.

  The following Patent Document 3 relates to a known technique of a multi-component force detector used in the present invention, and is described with reference to the description of the present invention described later.

JP-A-11-32464 JP 2003-194653 A Japanese Patent No. 2690626

  The present invention has been made in view of the above-described problems of the prior art, and an object of the present invention is that a measurement error caused by abnormal vibration of an object to be measured (rotating body) or a measurement system being measured. To provide a measurement method and a measurement apparatus that can solve the problems that occur and that can easily and dynamically measure the dynamic imbalance of an object to be measured using a multi-component force detector with a simpler and smaller apparatus than in the past. It is in.

In order to solve the above-described problems, the present invention employs the following method. That is, a method for measuring the dynamic imbalance of an object to be measured (rotating body) using a multi-component force detector based on two-plane balancing, and measuring the angular velocity when the rotating body is reciprocally rotated. value omega, maybe 4 component force value detected by the force detector _{(F x, F y, M} x, M y) by a, based on a predetermined algorithm, unbalance amount in two planes balancing of rotating bodies m ₁ r ₁ and m ₂ r ₂ and their phase angles φ ₁ and φ ₂ are measured.

The above F _x, F _y and M _x, M _y, respectively, X, Y, X and Z orthogonal coordinate system, the Y-axis direction force and X, a moment around the Y axis, m _1, m ₂ is an unbalanced mass at each position of the two-plane balancing, and r ₁ and r ₂ are rotation radii of the unbalanced mass, respectively. The predetermined calculation procedure will be described in detail in the section of the embodiment of the present invention.

Further, as the configuration and function of the multi-component force detector, for example, the one disclosed in Patent Document 3 can be used. Considering an arbitrary point of an object on which various external forces are acting, the external force includes forces F _x , F _y , F _z in each axis direction of the X, Y, Z orthogonal coordinate system and a moment M _x around each axis. , M _y, can be decomposed into six independent component force component composed of M _z, such 6 component force may be measured by decomposing each component force component above maybe force detector. Also, as described in Patent Document 3, a bridge circuit is formed for only the required 4 or 3 component forces among the 6 component forces, and only the 4 or 3 component forces are generated. Can be measured.

In the present invention described below, X, Y axis acts in the direction the force F _x, F _y and moments M _x acting on these axes, it is sufficient only to measure 4 component of the M _y.

  Further, as a measuring apparatus for solving the above-mentioned problems, a table for mounting an object to be measured, a multi-component force detector connected to the table in a vertical direction, the table and the multi-component force detector are simultaneously used. A motor for rotational excitation, an angular velocity measuring device for measuring the rotational angular velocity of the rotational excitation, and a predetermined component force measurement value of the multi-component force detector and the rotational angular velocity are determined based on a predetermined arithmetic expression. And an arithmetic and control unit that outputs a balance amount and a phase angle thereof.

  Further, as a preferred embodiment of the measuring device, the rotational angular velocity is obtained by measuring a rotational angle of rotational excitation with an encoder and inputting the measured value of the rotational angle into the arithmetic control device. Suppose that

  According to the present invention, there is no measurement error caused by abnormal vibration of the measurement object (rotating body) or measurement system being measured, and the multi-force detector can be obtained by a simpler and smaller apparatus as compared with the prior art. Thus, it is possible to provide a measuring method and a measuring apparatus capable of accurately and easily measuring the dynamic imbalance of an object to be measured.

The conceptual explanatory drawing of the method of measuring a dynamic imbalance by continuous constant-speed rotation similarly to the past using a multi-component force detector. The block diagram which shows schematic structure of the measuring apparatus of this invention. Explanatory drawing of the inertia force at the time of the rotational excitation of the dynamic imbalance amount (unbalance mass m) in connection with the measuring method of this invention.

An embodiment of the present invention will be described below with reference to FIGS.
(1) Description of a conventional measurement method by continuous constant speed rotation using a multi-component force detector FIG. 1 relates to the measurement method of the present invention described later. Prior to the description, FIG. It is a figure which illustrates the method conceptually considering the case where a dynamic imbalance is measured using a multi-component force detector based on two-plane balancing of a rotating body by constant speed rotation. FIG. 1A is a schematic side view in which an object to be measured (specimen) 1 as a rotating body and a multi-component force detector 2 are combined, and FIG. 1B shows FIG. 1A viewed from above. FIG. 2 is a diagram conceptually illustrating a phase angle of an unbalanced mass, an inertial force, and the like in a rotating state of the specimen 1.

  In FIG. 1 (a), the specimen 1 is placed on a table (not shown) and rotates continuously at a constant speed together with a multi-component force detector 2 coupled below the table. Therefore, the multi-force detector 2 is connected to a motor for rotating the table (not shown) and a measuring device for measuring the rotational angular velocity ω. For example, a commercially available encoder can be used to measure the rotational angular velocity ω.

In FIG. 1A, P ₁ and P ₂ indicate the positions of the unbalanced masses in the two-plane balancing, and Z ₁ and Z ₂ are reference points in the Z-axis direction of the unbalanced masses, respectively. The distance from the point O (the reference position of the top surface of the force detector 2) is shown.

In FIG. 1B, m _i is the unbalanced mass at each point P _i (P ₁ , P ₂ ), r _i is the rotational radius of the unbalanced mass at each point, and φ _i is The phase angle at the point. Further, _Myi is a moment acting around the Y coordinate axis of the multi-component force detector 2 due to the influence of each point, and M _xi is a moment acting around the X-coordinate axis of the multi-component force detector 2 due to the influence of each point.

The imbalance in the two correction surfaces of the specimen 1 in FIG.
At point P ₁ , m ₁ r ₁ (kg-m), phase angle φ ₁ (deg)
At point P ₂ , m ₂ r ₂ (kg-m), phase angle φ ₂ (deg)
Assuming that the component force (force F and moment M) acting on the force detector 2 is the influence component force (F _x1 , F _y1 , M _x1 , My ₁ ) due to the unbalanced mass at point P ₁ (1-1) to (1-4).

F _x1 = m ₁ r ₁ ω ² cos φ ₁ (1-1)
F _y1 = m ₁ r ₁ ω ² sinφ ₁ (1-2)
M _x1 = −F _y1 · Z ₁ (1-3)
M _y1 = F _x1・ Z ₁・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (1-4)
In addition, influence components (F _x2 , F _y2 , M _x2 , M _y2 ) due to the unbalanced mass at point P ₂ are as shown in the following equations (2-1) to (2-4).

F _x2 = m ₂ r ₂ ω ² cosφ ₂ (2)
F _y2 = m ₂ r ₂ ω ² sinφ ₂ (2)
M _x2 = −F _y2 · Z ₂ (2-3)
M _y2 = F _x2・ Z ₂・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ （2-4）
Accordingly, the component forces (force F and moment M) acting on the multi-component force detector 2 are as shown in equations (3-1) to (3-4). That is,
F _x = F _x1 + F _x2 = (m ₁ r ₁ cos φ ₁ + m ₂ r ₂ cos φ ₂ ) ω ² .. (3-1)
F _y = F _y1 + F _y2 = (m ₁ r ₁ sinφ ₁ + m ₂ r ₂ sinφ ₂ ) ω ² .. (3-2)
M _x = M _x1 + M _x2 = − (F _y1 · Z ₁ + F _y2 · Z ₂ ) (3-3)
_{M y = M y1 + M y2} = (F x1 · Z 1 + F x2 · Z 2) ······ (3-4)
Based on the preceding equations of (3-1) and (3-2) above and the equations of the following equations of (3-3) and (3-4), (3-1) to (3-4) The simultaneous equations can be rewritten as the following equations (4-1) to (4-4).

F _x = F _x1 + F _x2 (4-1)
F _y = F _y1 + F _y2 (4-2)
M _x = −F _y1 · Z ₁ −F _y2 · Z ₂ ... (4-3)
_{M y = F x1 · Z 1} + F x2 · Z 2 ··············· (4-4)
In the above (4-1) to (4-4) _{below, F x, F y, M} x, M y, Z 1, Z 2 are known. Therefore, in order to calculate the unknown using a matrix, the equations (4-1) to (4-4) are arranged as (4-1) ′ to (4-4) ′ as follows.

F _x1 + F _x2 = F _x (4-1) '
_{F y1 + F y2 = F y} ··· (4-2) '
−F _y1 · Z ₁ −F _y2 · Z ₂ = M _x (4-3) ′
_{F x1 · Z 1 + F x2} · Z 2 = M y ··· (4-4) '
Based on the left side of the above (4-1) ′ to (4-4) ′, the matrix A is represented by the following [Equation 1].

Based on the matrix A and its inverse matrix A ⁻ , the following [Equation 2] holds.

According to the right-hand side of the above Expression 2, a known amount based on the _{(F x, F y, M} x, M y, Z 1, Z 2), (F x1, F x2, F y1, F y2) Can be calculated.

Here, with respect to the equations (1-1) to (1-2) and (2-1) to (2-2), (F _x1 , F _y1 , F _x2 , F _y2 ) are changed to X1, Y1 respectively. , X2, Y2 are rewritten into the following equations (5-1) to (5-4). That is,
F _x1 = m ₁ r ₁ ω ² cos φ ₁ = m ₁ X ₁ ω ² (5-1)
F _y1 = m ₁ r ₁ ω ² sinφ ₁ = m ₁ Y ₁ ω ² (5-2)
F _x2 = m ₂ r ₂ ω ² cosφ ₂ = m ₂ X ₂ ω ² (5-3)
F _y2 = m ₂ r ₂ ω ² sinφ ₂ = m ₂ Y ₂ ω ² (5-4)
Based on the above equations (5-1) to (5-4) and [Equation 2], unbalanced phase angles φ ₁ and φ ₂ and unbalanced amounts m ₁ r _{1 at} points P ₁ and P ₂ to be measured. m ₂ r ₂ can be calculated by the following equations (6-1) and (6-2) and equations (7-1) and (7-2).

tan φ ₁ = m ₁ Y ₁ / m ₁ X ₁ = F _y1 / F _x1 (6-1)
tanφ ₂ = m ₂ Y ₂ / m ₂ X ₂ = F _y2 / F _x2 (6-2)
m ₁ r ₁ = (F _x1 ² + F _y1 ² ) ^1/2 / ω ² ... (7-1)
m ₂ r ₂ = (F _x2 ² + F _y2 ² ) ^1/2 / ω ² (7-2)
(2) Description of measurement method by reciprocal excitation according to the present invention using a multi-component force detector Next, a measurement method by reciprocal excitation according to the present invention will be described. At first glance, the configuration of the measuring apparatus is the same as that described above, but in the case of the present invention, reciprocal excitation, for example, the specimen 1 is moved along the Z axis in FIG. By rotating around 90 ° and −90 °, measurement is performed using a multi-force detector, and accordingly, the calculation formulas are naturally different.

  The point that dynamic imbalance can be measured with a simpler and smaller apparatus compared to the conventional measurement method such as Patent Document 2 is the same as the method using the continuous constant speed rotation using the multi-component detector. However, the feature of the present invention is that the reciprocating vibration does not cause a measurement error due to an abnormal vibration of the measured object (rotating body) or the measurement system during measurement, and can be measured accurately and easily. It is.

  Below, the embodiment of this invention is explained in full detail based on FIGS.

  1 (a) and 1 (b) are substantially common in the embodiment of the present invention, except that the specimen 1 and the multi-component force detector 2 are not shown in the table rotation excitation motor. And a measuring instrument (for example, an encoder) for measuring the rotational angular velocity ω of the rotational excitation.

As shown in the block diagram of FIG. 2, the measuring device of the present invention is configured to rotate the rotation based on the detected values of the multi-force detector 2, the table rotation excitation motor 4, and the rotation angle ψ of the rotation excitation. The encoder 5 for measuring the rotational angular velocity ω of vibration, the predetermined component force measurement value of the multi-component force detector 2 and the output value ψ of the encoder are input, and the unbalance amount m ₁ based on a predetermined arithmetic expression. and an arithmetic and control unit 20 that outputs r ₁ and m ₂ r ₂ and phase angles φ ₁ and φ ₂ .

FIG. 3 is an explanatory diagram of the inertial force during the rotational excitation of the dynamic unbalance amount (unbalance mass) related to the measurement method of the present invention, and the component force by the unbalance mass m in FIG. 1 (b). Is shown in detail. In FIG. 3, r is the rotational radius of the unbalanced mass at each point, φ is its phase angle, F _t is the tangential force due to the unbalanced mass m, and F _tx and F _ty are their X and Y axes. is the direction of the component force, F _n is a force in the normal direction due to unbalance mass m, F _nx and F _ny is its X-axis and Y-axis direction component force.

Here, also in the embodiment of the present invention, the dynamic imbalance (unbalance) in the two correction surfaces of the specimen 1 in FIG.
At point P ₁ , m ₁ r ₁ (kg-m), phase angle φ ₁ (deg)
At point P ₂ , m ₂ r ₂ (kg-m), phase angle φ ₂ (deg)
And Then, the rotation angle of the specimen 1 and the force detector 2, that is, the unbalance mass m is ψ, the angular velocity is ω = dψ / dt, and the angular acceleration is (dω / dt) = d ² ψ / dt ² .

Maybe regard component force acting on the force detector 2 (the force F and moment M), impact component force due to unbalance the mass of P ₁ point (tangential and normal force) becomes the following equation.

F _tx1 = −m ₁ r ₁ (dω / dt) sinφ ₁ = −m ₁ Y ₁ (dω / dt) (8-1)
F _ty1 = m ₁ r ₁ (dω / dt) cosφ ₁ = m ₁ X ₁ (dω / dt) (8-2)
F _nx1 = m ₁ r ₁ ω ² cosφ ₁ = m ₁ X ₁ ω ² (8-3)
_{F ny1 = m 1 r 1 ω} 2 sinφ 1 = m 1 Y 1 ω 2 ··············· (8-4)
Accordingly, the component forces in the X-axis and Y-axis directions are expressed by the following equations (9-1) and (9-2), respectively.

F _x1 = F _tx1 + F _nx1 = −m ₁ Y ₁ (dω / dt) + m ₁ X ₁ ω ² ... (9-1)
F _y1 = F _ty1 + F _ny1 = m ₁ X ₁ (dω / dt) + m ₁ Y ₁ ω ² (9-2)
Here, when the above equations (9-1) and (9-2) are integrated twice, the following equations (10-1) and (10-2) are obtained.

∬F _x1 dt ² = −m ₁ Y ₁ ψ + m ₁ X ₁ ∬ω ² dt ² (10-1)
∬F _y1 dt ² = m ₁ X ₁ ψ + m ₁ Y ₁ ∬ω ² dt ² (10-2)
In the above formulas (10-1) and (10-2), assuming that the integration interval is one period of rotational excitation, for example, + 90 ° and −90 ° reciprocating rotational excitation, (10-1) and (10 Since the first term on the right side of the expression -2) is zero, the following expressions (11-1) and (11-2) are obtained in this case.

∬F _x1 dt ² = m ₁ X ₁ ∬ω ² dt ² (11-1)
∬F _y1 dt ² = m ₁ Y ₁ ∬ω ² dt ² (11-2)
Further, regarding the influence component force (force in the tangential direction and normal direction) due to the unbalanced mass at point P ₂ , the following formulas (12-1) and (12-2) are established as in the case of point P _1. .

∬F _x2 dt ² = m ₂ X ₂ ∬ω ² dt ² (12-1)
∬F _y2 dt ² = m ₂ Y ₂ ∬ω ² dt ² (12-2)
Next, for point P ₁ , moments acting by tangential and normal forces are as shown in the following formulas (13-1), (13-2), (13-3), and (13-4). is there. In the following equation, for example, the suffix 1 in M _txz1 indicates 1 of the P ₁ point, Z indicates rotational excitation about the Z axis, and tx indicates the X axis by the tangential force F _t . Indicates moment that occurs in the direction. The same applies to other suffixes.

M _txz1 = −Z ₁ F _ty1 = −m ₁ X ₁ Z ₁ (dω / dt) (13-1)
M _tyz1 = −Z ₁ F _tx1 = m ₁ Y ₁ Z ₁ (dω / dt) (13-2)
M _nxz1 = −Z ₁ F _ny1 = −m ₁ Y ₁ Z ₁ ω ² _... (13-3)
M _nyz1 = Z ₁ F _nx1 = m ₁ X ₁ Z ₁ ω ² (13-4)
Therefore, the following equation holds.

M _x1 = M _xz1 = M _txz1 + M _nxz1 = −m ₁ X ₁ Z ₁ (dω / dt) −m ₁ Y ₁ Z ₁ ω ²
... (14-1)
M _y1 = M _yz1 = −M _tyz1 + M _nyz1 = −m ₁ Y ₁ Z ₁ (dω / dt) + m ₁ X ₁ Z ₁ ω ²
... (14-2)
Regarding the above formulas (14-1) and (14-2), when integrating twice in one cycle integration interval,
Similarly to the expressions (11-1) and (11-2), the first term on the right side is set to zero, and the following expressions (15-1) and (15-2) are obtained.

∬M _x1 dt ² = −m ₁ Y ₁ Z ₁ ∬ω ² dt ² (15-1)
∬M _y1 dt ² = m ₁ X ₁ Z ₁ ∬ω ² dt ² (15-2)
Similarly, the following formulas (16-1) and (16-2) are obtained for the P ₂ point.

∬M _x2 dt ² = −m ₂ Y ₂ Z ₂ ∬ω ² dt ² (16-1)
∬M _y2 dt ² = m ₂ X ₂ Z ₂ ∬ω ² dt ² (16-2)
Here, (11-1), (11-2), (12-1), (12-2) and (15-1), (15-2), (16-1), (16-2) ) In order to rearrange the formulas, it will be rewritten as That is,
∬M _x1 dt ² / ∬ω ² dt ² → M _x1 , ∬M _y1 dt ² / ∬ω ² dt ² → M _y1 .. (17-1)
∬M _x2 dt ² / ∬ω ² dt ² → M _x2 , ∬M _y2 dt ² / ∬ω ² dt ² → M _y2 (17-2)
∬F _x1 dt ² / ∬ω ² dt ² → F _x1 , ∬F _y1 dt ² / ∬ω ² dt ² → F _y1 (17-3)
∬F _x2 dt ² / ∬ω ² dt ² → F _x2 , ∬F _y2 dt ² / ∬ω ² dt ² → F _y2 (17-4)
m ₁ X ₁ → mX ₁ , m ₁ Y ₁ → mY ₁ , m ₂ X ₂ → mX ₂ , m ₂ Y ₂ → mY ₂ (17-5)
Then, (11-1) and (11-2) become the following (11) ′, and (12-1), (12-2), (15-1), (15-2) The expressions (16-1) and (16-2) are the following expressions (12) ′, (15) ′, and (16) ′, respectively.

F _x1 = mX ₁ , F _y1 = mY ₁ (11) ′
F _x2 = mX ₂ , F _y2 = mY ₂ (12) '
M _x1 = −mY ₁ Z ₁ , My ₁ = mX ₁ Z ₁ (15) ′
_{M x2 = -mY 2 Z 2,} M y2 = mX 2 Z 2 ············· (16) '
Further, the following expression is obtained from the expressions (11) ′, (12) ′, (15) ′ and (16) ′.

F _x1 + F _x2 = mX ₁ + mX ₂ = F _x '(18-1)
_{F y1 + F y2 = mY 1} + mY 2 = F y '············· (18-2)
M _x1 + M _x2 = −mY ₁ Z ₁ −mY ₂ Z ₂ = M _x ′ (18-3)
_{M y1 + M y2 = mX 1} Z 1 + mX 2 Z 2 = M y '·········· (18-4)
In the above formulas (18-1) to (18-4), F _x ′, F _y ′, M _x ′, and M _y ′ are known values as will be described later, and Z ₁ and Z ₂ are known. is there. Therefore, in order to calculate the unknowns using a matrix, equations (18-1) to (18-4) are arranged as (18-1) ′ to (18-4) ′ as follows. At that time, to make it easier to understand, rewrite as follows. That is,
When rewritten as mX ₁ → X ₁ , mX ₂ → X ₂ , mY ₁ → Y ₁ , mY ₂ → Y ₂ ,
_{X 1 + X 2 = F x} '··· (18-1)'
Y ₁ + Y ₂ = F _y ′ (18-2) ′
-Y ₁ · Z ₁ -Y ₂ · Z ₂ = M _x '(18-3)'
X ₁ · Z ₁ + X ₂ · Z ₂ = M _y ′ (18-4) ′
Based on the left side of the above (18-1) ′ to (18-4) ′, the matrix B is represented by the following [Equation 3].

Based on the matrix B and its inverse matrix B ⁻ , the following [Equation 4] holds.

According to the right side of the Equation 4], a known or known based on the _{(F x ', F y'} , M x ', M y', Z 1, Z 2), (X 1, X 2 , Y ₁ , Y ₂ ) can be calculated.

And the rewriting which reverses the said rewriting is performed. That is,
X ₁ = mX ₁ = m ₁ X ₁ , Y ₁ = mY ₁ = m ₁ Y ₁
X ₂ = mX ₂ = m ₂ X ₂ , Y ₂ = mY ₂ = m ₂ Y ₂
And rewriting (18-1) to (18-4) to reverse the rewriting of (17-1) to (17-4), the following (19-1) to (19 -4) Equation is obtained.

F _x1 + F _x2 → ∬F _x1 dt ² / ∬ω ² dt ² + ∬F _x2 dt ² / ∬ω ² dt ² =
∬ (F _x1 + F _x2 ) dt ² / ∬ω ² dt ² = ∬F _x dt ² / ∬ω ² dt ² = F _x ′ · (19-1)
Similarly,
F _y1 + F _y2 → ∬F _y dt ² / ∬ω ² dt ² = F _y ′ (19-2)
M _x1 + M _x2 → ∬M _x dt ² / ∬ω ² dt ² = M _x ′ (19-3)
_{M y1 + M y2 → ∬M y} dt 2 / ∬ω 2 dt 2 = M y '············ (19-4)
Based on the above equations (19-1) to (19-4), F _x ′, F _y ′, M _x ′, and M _y ′ are measured values F _x , F _y , M _x , can be calculated by M _y and measurements of the rotational angular velocity omega, based on the Equation _{4], (X 1, X} 2, Y 1, Y 2) can be calculated.

And, similar to the equations (6-1) and (6-2),
tanφ ₁ = m ₁ Y ₁ / m ₁ X ₁ = Y ₁ / X ₁
tanφ ₂ = m ₂ Y ₂ / m ₂ X ₂ = Y ₂ / X ₂
Since it is, the P _1, the phase angle phi ₁ and phi ₂ of the unbalance amount of P ₂ points is obtained by the following equation.

φ ₁ = tan ^-1 Y ₁ / X ₁ (20-1)
φ ₂ = tan ^-1 Y ₂ / X ₂ (20-2)
Furthermore, the P _1, P unbalance amount at _two points m ₁ r ₁ and m ₂ r ₂ is determined by the following equation.

m ₁ r ₁ = m ₁ X ₁ / cosφ ₁ (21-1)
m ₂ r ₂ = m ₂ X ₂ / cosφ ₂ (21-2)
As described above, the object to be measured and the measured value ω of angular speeds at the time of the (rotor) and vibration reciprocally rotated pressurized, maybe 4 component force value detected by the force detector _{(F x, F y, M} x, M y) Thus, according to the method of measuring the unbalance amounts m ₁ r ₁ and m ₂ r ₂ and the phase angles φ ₁ and φ ₂ in the two-plane balancing of the rotating body based on a predetermined arithmetic expression, Measurement errors due to vibration do not occur, and accurate and simple measurement can be performed with a simple and small device.

  1: object to be measured (specimen), 2: multi-component detector, 4: motor for table rotation excitation, 5: encoder, 20: arithmetic control device.

Claims (3)

This is a method for measuring the dynamic imbalance of an object to be measured (rotating body) using a multi-component force detector based on two-plane balancing, and a measured value ω of angular velocity when the rotating body is reciprocally rotated. If, perhaps 4 component force value detected by the force detector _{(F x, F y, M} x, M y) and by, on the basis of the calculation procedure of the following unbalance amount m ₁ r in two planes balancing of rotating bodies ₁ and m ₂ r ₂ and their phase angles φ ₁ and φ ₂ are measured.
The above F _x, F _y and M _x, M _y, respectively, X, Y, X and Z orthogonal coordinate system, the Y-axis direction force and X, a moment around the Y axis, m _1, m ₂ is an unbalanced mass at each position of the two-plane balancing, and r ₁ and r ₂ are rotation radii of the unbalanced mass, respectively.
here,
∬F _x dt ² / ∬ω ² dt ² = F _x ′, ∬F _y dt ² / ∬ω ² dt ² = F _y ′
^{_{∬M x dt 2 / ∬ω 2 dt}} 2 = M x ', ∬M y dt 2 / ∬ω 2 dt 2 = M y'
And the above-mentioned two-time integration ∬ is the integration in one cycle of the integration section in the reciprocating rotational excitation.
Based on the above F _x ′, F _y ′, M _x ′, and M _y ′, (X ₁ , X ₂ , Y ₁ , Y ₂ ) is calculated by the following [Equation 5]. In [Expression 5] below, B ⁻ is an inverse matrix of the matrix B, and the matrix B is expressed by [Expression 6] below.
In the above [Equation 6], Z ₁ and Z ₂ are known amounts indicating the distance from the predetermined reference point in the Z-axis direction of each unbalance amount.
Based on the calculated values (X ₁ , X ₂ , Y ₁ , Y ₂ ) of [Equation 5], the phase angles φ ₁ , φ ₂ and the unbalance amounts m ₁ r ₁ , m ₂ r ₂ are obtained as follows.
φ ₁ = tan ⁻¹ Y ₁ / X ₁ , φ ₂ = tan ⁻¹ Y ₂ / X ₂
m ₁ r ₁ = m ₁ X ₁ / cosφ ₁ , m ₂ r ₂ = m ₂ X ₂ / cos φ ₂   A dynamic unbalance measuring apparatus for a rotating body for carrying out the method of claim 1, a table for mounting an object to be measured, a multiple force detector connected to the table in a vertical direction, A motor for simultaneously rotating and exciting the table and the component force detector, an angular velocity measuring unit for measuring the rotational angular velocity of the rotational excitation, a predetermined component force measurement value of the component force detector and the rotational angular velocity And a calculation control device that outputs an unbalance amount and a phase angle based on a predetermined calculation formula.   3. The measuring apparatus according to claim 2, wherein the rotational angular velocity is obtained by measuring a rotational angle of rotational excitation with an encoder and inputting a measured value of the rotational angle into the arithmetic control device. A measuring device characterized by that.