JPH0573168B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a method for precisely balancing a rotating body of a grindstone or the like of a precision surface grinder.

2. Description of the Related Art In general, it is necessary to correct unbalance in a rotating body. For example, unbalance of the grinding wheel of a grinding machine or the axle of a vehicle will adversely affect machining accuracy in the former case, and will adversely affect running performance in the latter case.
This is because it adversely affects running performance, especially at high speeds. Therefore, conventional methods for balancing the rotating body include a method in which the rotating body is removed from the machine and the gravity is balanced statically, and a method using an auto balancer. However, the former method requires stopping the machine and removing the rotating body, which is troublesome and only allows for rough balancing. or,
The latter is large and requires high machine costs.

As a balancing technique that enables precise balancing to be performed at low cost and without stopping the machine, the present applicant has proposed, for example, the techniques disclosed in Japanese Patent Application Laid-open Nos. 186370-1986 and 220840-1984. proposed by. These are dynamic balancer systems that use trial weights for unbalance correction, and here, we will take an example of the latter publication and explain its balancing method. First, an apparatus for carrying out this method will be explained with reference to FIGS. 3 and 4. A rotating body 1, such as a grindstone for a grinding machine, is fixed to a rotating shaft 3 via a mounting flange 2. This mounting flange 2 is formed with an annular groove 4 having a constant radius r, and two unbalance correction weights 5 having the same mass are mounted in this groove 4.
6 is movably and removably attached. For example, a signal emitted from a vibration meter (such as a non-contact displacement meter or an acceleration pick-up) 7 for detecting the vibration of the bearing part 13 of the rotating shaft 3 is sent to an amplifier 8, and a signal that does not match the rotational speed of the rotating shaft 3 is transmitted. The data is inputted to a microcomputer 11 through a filter 9 and an A/D converter 10, etc., and is configured so that balancing work can be performed interactively with the operator via a display 12.

Therefore, the following steps are performed.

First, the vibration amplitude _A1 is measured when the rotating body 1 is rotated without an unbalance correction weight attached to the rotating body 1.

Vibration amplitude when the rotating body 1 is rotated with one unbalance correction weight 5 or 6 attached to an arbitrary point on a fixed radius r from the center of the rotating body 1
Measure B ₁ . Here, the position where this unbalance correction weight 5 or 6 is attached is defined as a reference position.

Unbalance correction weight 5 or 6 attached with
Vibration amplitude when rotating body 1 is rotated with
Measure C ₁ in the same way.

Similarly, unbalance correction weight 5 or 6
Measure the vibration amplitude D ₁ with the device installed at a position shifted by 3π/2.

Then, let the amplitude due to the centrifugal force of the unbalance correction weight 5 or 6 be W ₁ , and the unbalance phase angle of the position where the vibration amplitude A ₁ occurs with respect to the reference position be φ ₁
Then, the two unbalance correction weights 5 and 6 are positioned at the following angles α ₁ and β ₁ , respectively α ₁ =π+φ ₁ + [cos ^-1 {A ₁ /2√ ₁ ² +
₁ ² −2 ₁ ² ) 2}] β ₁ = π + φ ₁ − [cos ^-1 {A ₁ /2√( ₁ ²
+ ₁ ² −2 ₁ ² )2}].

Here, in order to calculate these angles α ₁ and β ₁ , it is necessary to find the unbalanced phase φ ₁ , and this phase φ ₁ is found as follows based on FIG. That is, according to FIG. 5, A ₁ ² = B ₁ ² + W ₁ ² −2B ₁・W ₁・cosγ ₁ C ₁ ² =B ₁ ² +4W ₁ ² −4B ₁・W ₁・cosγ _1Thus , Since the amplitude W ₁ satisfies W ₁ ≧0, W ₁ =√( ₁ ² + ₁ ² −2 ₁ ² )2 (1). Therefore, the unbalanced phase φ ₁ is obtained from C ₁ ² = A ₁ ² + W ₁ ² −2A ₁・W ₁・cosφ ₁ , φ ₁ = cos ⁻¹ {(A ₁ ² + W ₁ ² −C ₁ ² ) /2A ₁・W ₁ }
...(2) is obtained as follows.

However, when D ₁ ² ≦A ₁ ² + W ₁ ² , φ ₁ = |φ ₁ |,
When D ₁ ² >A ₁ ² +W ₁ ² , φ ₁ =−|φ ₁ |.

In this way, the unbalanced phase φ ₁ can be calculated.

Problems to be Solved by the Invention However, in actual measurements of vibration amplitudes, it is difficult to measure them without errors. In some cases, such coronation errors may impose various mathematically unreasonable conditions, but
This tends to occur because the unbalanced phase φ ₁ becomes a dead zone near the reference position or a position (π) that differs by 180 degrees. This point will be explained below.

Now, let us consider, for example, a case where the unbalanced phase is at a position far from the reference position or π, for example, φ ₁ =45°.
Here, assuming that the amplitude A ₁ = 3 μm and W ₁ = 5 μm, B ₁ = √ ₁ ² + ₁ ² −2 ₁・₁ (180° − 45°) ≒
7.431μm C ₁ = √ ₁ ² + ₁ ² −2 ₁・₁ 45°≒3.576μm. The values of these amplitudes A ₁ , B ₁ , and C ₁ are
By substituting into equations (1) and (2), the amplitude W ₁ and the unbalanced phase φ ₁ can be determined. but,
Since the values of amplitudes A ₁ , B ₁ , and C ₁ are measured values, they always include errors. So, for example, if the value of amplitude A ₁ is 1%
Consider the case where the value becomes smaller by That is, this is the case where A ₁ =2.97 μm B ₁ =7.431 μm C ₁ =3.576 μm. Substituting these into equations (1) and (2) to find the amplitude W ₁ and unbalanced phase φ ₁ , W ₁ =√( ₁ ² + ₁ ² −2 ₁ ² )2≒5.018 μm φ ₁ = cos ^-1 {(A ₁ ² + W ₁ ² − C ₁ ² )/2A ₁・W ₁ }=44.6°. In other words, even if the measured value of amplitude A ₁ decreases by 1%, the phase φ ₁ will change with an error of about 0.4%.
can be found.

However, consider a case where the unbalanced phase φ ₁ is at a reference position or a position close to π, for example, φ ₁ =5°.
Here, assuming that the amplitude A ₁ = 3 μm and W ₁ = 5 μm, B ₁ = √ ₁ ² + ₁ ² −2 ₁・₁ (180° − 5°)
≒7.993μm C ₁ =√ ₁ ² + ₁ ² −2 ₁・₁ 5゜≒2.028μm. The values of these amplitudes A ₁ , B ₁ , and C ₁ are
By substituting into equations (1) and (2), the amplitude W ₁ and the unbalanced phase φ ₁ can be determined. but,
Since the values of amplitudes A ₁ , B ₁ , and C ₁ are measured values, they always include errors. Therefore, in this case as well, as in the case described above, a case is considered in which the value of the amplitude A ₁ is reduced by 1%, for example, and the calculation is performed. In other words, A ₁ =2.97 μm B ₁ =7.993 μm C ₁ =2.028 μm. Substituting these into equations (1) and (2) to find the amplitude W ₁ and unbalanced phase φ ₁ , W ₁ =√( ₁ ² + ₁ ² −2 ₁ ² )2≒5.018μm This amplitude W When calculating formula (2) including the value of ₁ , (A ₁ ² + W ₁ ² − C ₁ ² )/2A ₁・W ₁ )≒1.003＞1
Considering that cos×≦1, equation (2) becomes impossible to calculate, and the unbalanced phase φ ₁ cannot be determined.

In this way, the unbalanced phase changes to the reference position or π
When it is close to the position, calculation is likely to be impossible, and even if calculation is possible, the error will be large. for example,
Considering the case where the value of the amplitude A ₁ increases by 1% in the previous example, in the case of an unbalanced phase far from the reference position as in the former case, the error in the phase φ ₁ becomes
While the error in the unbalanced phase φ 1 was only 0.02°, in the latter case near the reference position, the error in the unbalanced phase φ ₁ was as large as 3.14°.

For this reason, in the conventional method as shown in the publication, such a position where calculation is impossible is called a dead zone, and when the unbalanced phase φ ₁ is in such a dead zone, it should be used as a reference. The position must be shifted 90 degrees and the measurement taken again.
In other words, it is not enough to do it once and requires trial and error.

Means for solving the problem: Two unbalance correction weights having the same mass are freely installed at arbitrary positions on a constant rotation radius of a rotating body, and vibrations of the rotation axis of the rotating body are detected. Equipped with a vibration meter, A = vibration amplitude due to the unbalance amount of the rotating shaft without the unbalance correction weight attached, φ = phase from the reference position of the position that produces vibration amplitude A, B = unbalance correction weight 1 to any reference position
Vibration amplitude of the rotating shaft due to the centrifugal force of the rotating body when the unit is attached, C = 2π/
The vibration amplitude of the rotating shaft due to the centrifugal force of the rotating body when the weight is moved by 3 and installed, D = 4π/
The vibration amplitude of the rotating shaft due to the centrifugal force of the rotating body when it is mounted after being moved by 3, W = the amplitude due to the centrifugal force of the weight for unbalance correction, 2S = A + B + W, When the above phase angle φ is C≧ When D, φ=π−2tan ^-1 √(−)(−)(−
), and when C<D, φ=-{π-2tan ^-1 √(-)(-)(
-)}, and the two unbalance correction weights are positioned at the following angles α and β with respect to the reference position, α=π+φ+[cos ^-1 {A/2√( ² + ₂ −2 ₂ )
2}] β=π+φ− [cos ^-1 {A/2√( ² + ² −2 ² )
2}].

Effect When the unbalanced phase is near the initially arbitrarily set reference position, it is a dead zone, so
The phase cannot be calculated as is. However, various amplitude measurements using the unbalance correction weight as a test weight are performed at the reference position, the 2π/3 position, and the 4π/3 position.
The measurements are performed at positions formed by dividing the circumference into three equal parts, and each measurement data can be treated equivalently.
As a result, even if there is an unbalanced phase in the dead zone, for example, the unbalanced phase can be calculated with less error by recalculating using the measurement position that is not the initial reference position as the reference value. Based on this, the angles α and β at which the two unbalance correction weights should be attached are determined.

Embodiment An embodiment of the present invention will be described based on FIGS. 1 and 2. This example is basically a dynamic balancer method in which a measuring device as shown in Figs. 3 and 4 is used and a test weight is used for balancing. The major difference from the publication is that the mounting position of the unbalance correcting weight 5 or 6 is devised after the unbalance correcting weight 5 or 6 is attached to an arbitrary reference position and the amplitude is measured. That is, to explain in order: First, the vibration amplitude A when the rotating body 1 is rotated without the unbalance correction weight attached to the rotating body 1 is measured.

Vibration amplitude B when the rotating body 1 is rotated with one unbalance correction weight 5 or 6 attached to an arbitrary point on a fixed radius r from the center of the rotating body 1
Measure. Here, the position where this unbalance correction weight 5 or 6 is attached is defined as a reference position.

Unbalance correction weight 5 or 6 attached with
The vibration amplitude C when the rotating body 1 is rotated is similarly measured with the rotating body 1 mounted at a position shifted by 2π/3, that is, 120° from the reference position.

Similarly, unbalance correction weight 5 or 6
Further, the vibration amplitude D is measured with the sensor mounted at a position shifted by 2π/3, that is, 240° from the reference position.

Then, when the amplitude due to the centrifugal force of the unbalance correction weights 5 or 6 is W, and the unbalance phase angle of the position where the vibration amplitude A occurs with respect to the reference position is φ, the two unbalance correction weights 5 and 6 The positions of the following angles α and β, respectively α=π+φ+[cos ^-1 {A/2√( ² + ² −2 ² )
2}] β=π+φ− [cos ^-1 {A/2√( ² + ² + 2 ² )
2}].

Here, the unbalanced phase φ with respect to the reference position is determined as follows based on FIG. Note that it is assumed here that the phase φ satisfies 0≦φ≦π.
First, according to FIG. 1, the following equations are derived.

B ² =A ² +W ² −2A・W・cosγ ...(3) C ² =A ² +W ² −2A・W・cosη ...(4) D ² =A ² +W ² −2A・W・cosλ ... …(5) φ+γ=π …(6) (2π/3)−φ+η=π …(7) φ+λ+(2π/3)=π …(8) Therefore, each angle is φ=π−γ ...(9) η=(4π/3)−γ ...(10) λ=γ−(2π/3) ...(11) Therefore, equation (10) is changed to equation (4), and equation (11) Substituting each into equation (5), C ² = A ² + W ² −2A・W・cos(−1/2cosγ−√3/2
sinγ)……(12) D ² =A ² +W ² −2A・W・cos(−1/2cosγ+√3/2
sinγ)...(13). Therefore, by performing the calculation of equation (12) + equation (13), cosγ=(C ² −D ² −2A ² −2W ² )/2A·W (14). Substituting this equation (14) into equation (3), W=√( ² + ² − ² −3 ² )3 ……(15). Also, if A+B+W=2S, tan(γ/2)=√(-)(-)(-
), γ=2tan ^-1 √(-)(-)(-). Therefore, the unbalanced phase φ is φ=π−2tan ⁻¹ √(−)(−)(−
)...(16) becomes. In addition, if −π<φ<0, the unbalanced phase φ is φ=−{π−2tan ^-1 √(−)(−)(
−)}……(16)′.

In this manner, according to this embodiment, the amplitude W can be calculated using equation (15), and the unbalanced phase φ can be calculated using equation (16) or (16)'. However, if left as is, this embodiment will still have a dead zone in the vicinity of the arbitrarily determined reference position. However, in this embodiment, the unbalance correction weight 5 or 6 is at the reference position (0°),
Measurement is carried out by sequentially installing the rotating body 1 in three equal parts in the circumferential direction at 120° and 240°.For example, the 120° position or the 240° position is changed to the reference position. It is easy to recalculate by
This can be dealt with without re-measurement. This point will be explained using a specific example similar to that described in the conventional example.

Now, let us consider, for example, a case where the unbalanced phase is close to the reference position, for example, φ=5°. Here, assuming that the amplitude A = 3 μm and W = 5 μm, B = √ ² + ² −2・(180° − 5°) ≒ 7.9
93μm C=√ ² + ² −2・{180゜−(120゜−5
゜）｝≒4.618μm D=√ ² + ² −2・(60゜−5゜)≒4.09
It becomes 8μm. In this case as well, the amplitude W and the phase φ are calculated assuming that the value of the amplitude A is reduced by 1% due to a measurement error. That is, A=2.97 μm, B=7.993 μm, C=4.618 μm, and D=4.098 μm. Substituting these into equation (15) to find the amplitude W, W = √ ( ² + ² + ² − 3 ² ) 3≒5.018μ Based on this result, calculate the internal term of the square root of equation (16). Then, (S-A)(S-W)/S(S-B)≒-749.472
<0, and the square root of equation (16) cannot be opened.

However, in this case, if the 120° position is considered as the reference position and the calculation is recalculated, the values of A, B, C, and D can be considered as the following values.
That is, A=2.97μm B=4.618μm C=4.098μm D=7.993μm. Then, by substituting these values into equation (15) and finding W, we get: W=√( ² + ² + ² −3 ² )3≒5.018μm Also, since C<D, from Figure 1, The balance phase φ is −π<φ<0. Therefore, (16)′
Determining the phase φ from the formula, φ=−{π−2tan ^-1 √(−)(−)(
−)}≒−115.17°. Here, since the calculation is performed with the reference position shifted by 120°, the original unbalanced phase φ with respect to the initially set reference position is φ=120°−115.17°=4.83°.

Therefore, even if the value of the measured amplitude A decreases by 1%, the unbalanced phase φ in the dead zone can be determined with an error of 0.17° without remeasuring. In addition, in the case of the conventional method, the unbalance correction weight is attached at a position 3π/2 from the reference position and the amplitude D ₁ is measured because the unbalance phase φ ₁ is 0≦φ ₁ <π or not. −π＜ _φ1 ＜
This is to determine whether the amplitude D is 0 or not, and in this embodiment as well, the fourth measurement of the amplitude D determines whether the unbalance φ ₁ is 0≦φ<π or −π<φ ₁ <0. This is for the purpose of making this determination. However, in this implementation, this amplitude D is data that is treated equally like the other amplitudes B and C, and is highly reliable from the point of view of effective use of data. Become. Furthermore, according to this embodiment, even when the unbalanced phase is not near the reference position (that is, when it can be detected even with the conventional method), it can be detected not only at the reference position of 0° but also at 120° and Reliability can be further improved by performing calculations based on 240° and comparing the results.

In addition, the two unbalance correction weights 5 and 6 which are regulated including the phase φ of such unbalance.
The calculation of the angles α and β of the final mounting position can be performed in the same manner as in the case of Japanese Patent Application Laid-Open No. 60-220840. That is, the amplitude A without the unbalance correction weights 5 and 6 is proportional to the centrifugal force unbalance amount, so if this centrifugal force unbalance amount is F, then A=K・F (however, K is proportional to constant). Similarly, unbalance correction weight 5 or 6
One centrifugal force unbalance amount W is expressed by W=K·m·r·ω ² where m is the mass of each of the unbalance correction weights 5 and 6 and ω is the angular velocity of the rotating body 1. According to both of these formulas, F=(A/W)・m・r・ω ² . In order to correct such an unbalance, the mounting angle of the two unbalance correcting weights 5 and 6 should be determined so that the resultant force _F0 is the same magnitude as F and opposite in direction. good. The centrifugal force of unbalance correction weights 5 and 6 is m・r・ω ² respectively.
Therefore, from Fig. 2, we obtain cosθ=A/2W. Therefore, θ=cos ^-1 (A/2W), and this angle θ is the angle formed by the two weights 5 and 6 when the unbalance correction weights 5 and 6 are distributed with respect to the unbalance direction. shows.

Therefore, the unbalance correction weights 5 and 6 to be attached are α=π+φ+cos ⁻¹ (A/2W) and β=π+φ−cos ⁻¹ (A/2W) with respect to the reference position. The balancing work is completed by attaching the unbalance correction weights 5 and 6 based on the angles α and β displayed on the display 12.

Effects of the Invention As described above, the present invention sequentially attaches the unbalance correction weights to an arbitrary reference position, the 2π/3 position, and the 4π/3 position, measures the amplitude of each, and calculates the phase of the unbalance. Since the mounting angle is calculated based on the measurement position, even if an unbalanced phase exists in the dead zone near the arbitrarily determined reference position, the error can be reduced by simply recalculating using another measurement position as the reference position. This unbalanced phase can be calculated in the current state, and therefore, the balancing work can be performed without repeating trial and error.

[Brief explanation of the drawing]

FIG. 1 is a vector diagram showing an embodiment of the present invention, FIG. 2 is a vector diagram, FIG. 3 is a front view for explaining the content already proposed by the applicant, and FIG. 4 is a side view. FIG. 5 is a vector diagram. 1... Rotating body, 3... Rotating shaft, 5, 6... Unbalance correction weight, 7... Vibration meter.

Claims (1)

[Scope of Claims] 1. Two unbalance correction weights having the same mass are freely installed at any position on a constant radius of rotation of a rotating body, and a vibration detecting vibration of the rotation axis of the rotating body is provided. A = vibration amplitude due to the unbalance amount of the rotating shaft with no unbalance correction weight attached, φ = phase from the reference position of the position that produces vibration amplitude A, B = unbalance correction weight 1 at any reference position
Vibration amplitude of the rotating shaft due to the centrifugal force of the rotating body when the unit is attached, C = 2π/
The vibration amplitude of the rotating shaft due to the centrifugal force of the rotating body when the weight is moved by 3 and installed, D = 4π/
The vibration amplitude of the rotating shaft due to the centrifugal force of the rotating body when it is mounted after being moved by 3, W = amplitude due to the centrifugal force of the weight for unbalance correction, 2S = A + B + W, When the above phase angle φ is C≧ When D, φ=π−2tan ^-1 √(−)(−)
(-), and when C<D, φ=-{π-2tan ^-1 √(-)(-
)(-)}, and the two unbalance correction weights are positioned at the following angles α and β with respect to the reference position, α=π+φ+[cos ^-1 {A/2√( ² +
² −2 ² ) 2}] β=π+φ− [cos ^-1 {A/2√( ² +
^{2-2 2} )2}] Precision balancing method for a rotating body.