JPH1038029A - Dick shape structure with vibration damping function - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce the amplitude of a disc shape structure when a resonance occurs and also improve a stability when an unsatable vibration comes into problem by installing plural piezoelectric elements on the outer periphery part of one side or both sides of the disc shape structure equally and connecting an electric resistance to both electrodes of the piezoelectric element. SOLUTION: A disc shape structure with a restraint function is provided with a disc body 1 like an elastic disc and plural piezoelectric elements 2 installed on the outer periphery part of one side or both sides. A closed circuit is formed by connecting an electric resistance 4 by a lead wire 3 on the positive electrode and negative electrode of each piezoelectric element 2. The piezoelectric element 2 is formed in a film shape and installed by sticking or vapor deposition or burying in to the disc body 1. In this piezoelectric element 2, the optimum number of the piezoelectric element 2 is existed per a problematic vibration mode. The electric resistance 4 is a surface packaging type resistance and formed by the metal film resistance like an oxidized metal film resistance and the resistance value of the electric resistance 4 is decided so as to enlarge the damping of a problematic vibration mode.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

TECHNICAL FIELD The present invention relates to a compressor, a pump,
The present invention relates to a disk-shaped structure with a vibration control function used for a centrifuge, a magnetic disk device, and the like.

[0002]

2. Description of the Related Art In a rotating machine having a disk-shaped rotating body such as a compressor, a pump, and a centrifugal separator, resonance occurs when its natural frequency matches the rotating speed of the rotating body or an integral multiple of the rotating speed. Sometimes. Therefore, at the design stage, both are designed so that they do not match. In addition, since an elastic disk such as a magnetic disk used in a magnetic disk device has a small attenuation, the problem of unstable vibration restricts the reduction in weight and speed for improving the performance of the device.

[0003]

However, in the above-described conventional rotary machine, the operating speed may be variable, and resonance may not be avoided. In addition, an elastic disk such as a magnetic disk has a problem of unstable vibration due to a small attenuation as described above, and therefore, there is a problem that reduction in weight and speed of the device is limited. The present invention has been made in view of the above circumstances, and by adding damping, the amplitude of a disk-shaped structure when resonance occurs is reduced, and stability is improved even when unstable vibration becomes a problem. An object of the present invention is to provide a disk-shaped structure with a vibration damping function that can be improved.

[0004]

In order to achieve the above-mentioned object, the present invention provides a disk-shaped structure having a plurality of piezoelectric elements provided on one or both outer peripheral portions thereof in a circumferentially equidistant manner. And electrical resistances connected to both electrodes.

When the number of piezoelectric elements is twice as large as the node diameter mode of interest, the damping effect is greatest. The resistance value of the connected resistor is determined so that the damping ratio of the vibration mode in question becomes maximum.

In the disk-shaped structure with the vibration damping function configured as described above, the vibration energy is converted into electric energy by the piezoelectric element, and further converted into heat energy by the resistance and dissipated. Therefore, the damping of the system increases,
The amplitude is reduced.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a disk-shaped structure with a vibration damping function according to the present invention will be described below with reference to FIGS. FIG. 1 is a plan view showing a disk-shaped structure with a vibration damping function, and FIG. 2 is a cross-sectional view showing a disk-shaped structure with a vibration damping function. As shown in FIGS. 1 and 2, the disk-shaped structure with a vibration damping function includes a disk 1 such as an elastic disk, and a plurality of disks 1 provided on an outer peripheral portion of one or both surfaces of the disk 1. Piezoelectric element 2
And The plurality of piezoelectric elements 2 are arranged at equal intervals around the circumference.

An electrical resistor 4 is connected to a positive electrode and a negative electrode of each piezoelectric element 2 by a lead wire 3 to form a closed circuit. The piezoelectric element 2 is formed in a thin film shape, and is provided on the disc body 1 by sticking, vapor deposition, or embedding.
The piezoelectric element 2 has an optimal number of piezoelectric elements for each vibration mode in which there is a problem. Specifically, the number is preferably twice the number of node diameters in the node diameter mode in which attenuation is desired to be increased. For example,
In the case of the 4-node diameter mode, it is preferable to provide 4 × 2 = 8.
Further, it is preferable that the piezoelectric element 2 is mounted at a position where the disk 1 has a large distortion. FIG.
2 shows an example in which a shaft for holding the disc 1 is provided at the center, and the piezoelectric element 2 is provided on one surface of the disc 1.

The electric resistance 4 is a surface mount type resistance,
It consists of metal film resistors such as metal oxide film resistors. The resistance value of the electric resistance 4 is determined so that the damping of the vibration mode in question becomes large.

FIG. 3 shows an example in which the same number of piezoelectric elements are provided in the same phase on both surfaces of the disc body 1. That is, the same number and the same number of the piezoelectric elements 2 are provided on both surfaces of the disc 1. When the same number of piezoelectric elements are provided in the same phase on both sides of the disk, the effect is almost twice as large as that of the case of one side.

FIG. 4 shows an example in which the same number of piezoelectric elements are provided at different phases on both surfaces of the disc 1. That is, when the same number and the same phase of the piezoelectric elements are provided on both surfaces of the disc body,
The magnitude of the attenuation may change depending on the position of the excitation point. If this is not desirable, the piezoelectric elements are provided on both sides of the disc with different phases. When the piezoelectric elements are provided on both sides of the disk, different numbers are provided on the front and back sides so that the attenuation of two different modes is increased. For example, when it is desired to increase the attenuation in the three-node diameter mode and the six-node diameter mode, the piezoelectric element is placed on the surface at 3 × 2 = 6.
And 6 × 2 = 12 on the back surface.

FIG. 5 shows an example in which a piezoelectric element is provided on a disk 1 such as a magnetic disk. FIG. 5 (a) is a plan view and FIG.
(B) is a sectional view. That is, like a magnetic disk,
When it is difficult to change the thickness t of the disc body 1 depending on the location by providing the piezoelectric element, the substrate at the position where the piezoelectric element 2 and the resistor 4 are to be vapor-deposited is shaved by a necessary thickness.

[0013]

Next, specific embodiments of the present invention will be described.
In this embodiment, an elastic disk will be described as an example of the disk body. FIG. 6 shows a conceptual diagram of the system taken up in this embodiment. The material of the elastic disk is an aluminum alloy, and the piezoelectric element is an arc-shaped piezoelectric ceramic polarized in the thickness (z) direction. Table 1 Piezoelectric material Elastic disk material Density (kg / m ³ ) 7600 2600 Young's modulus (GPa) 64 67 Piezoelectric constant (C / m ² ) -13.35 Dielectric constant (A ² s ² / Nm ² ) 1985ε ₀ ε ₀ = 8.9 × 10 ⁻¹² (A ² s ² / Nm ² )

Twelve arc-shaped piezoelectric elements were stuck to the outer periphery of the disk at equal intervals with a conductive adhesive, and both electrodes of all the piezoelectric elements were connected to an electric resistor having the same resistance value. The disk is fixed at a radius r ₀ from the center. Let r _{2 be} the outer radius of the disk and h be the thickness. The inside radius of the piezoelectric element stuck thereon is r ₁ , the thickness is H, and the angle of the arc is θ ₀ . The external resistance connected to the piezoelectric element is represented by R. The experiment was performed with changing the external resistance.
Table 2 shows these values. Table 2 r ₀ (mm) 25 r ₁ (mm) 140 r ₂ (mm) 150 h (mm) 2 H (mm) 0.5 θ ₀ (rad) 28 × (2π / 180) R (kΩ) 0, 7.5, 15, 30, 45, 60, 75

The vicinity of the fixed portion of the disk was hit using an impulse hammer, and the vibration was measured with an overcurrent type non-contact displacement meter. The result was input to an FFT (Fast Fourier Transformer) to obtain a transfer function. As examples, the transfer functions obtained when the short circuit (R = 0) and R = 15 (kΩ) obtained by the experiment are shown in FIGS. 7 and 8, respectively. Table 3 shows the experimental results of the natural frequency of each mode at the time of short circuit (R = 0) and the analysis results by the finite element method. Table 3 Experiment Finite element method Frequency (Hz) Frequency (Hz) Mode 83.4 86.0 (0,1) 94.4 97.3 (1, 0) 123.1 121.2 (0, 2) 260.0 255.0 (0,3) 458.1 449.6 (0,4) −615.6 (2,0) 649.0 661.6 (1,1) 705.9 694.7 (0,5) 822.5 823.7 (1, 2)

The (m, n) mode means a mode in which the number of node circles is m and the number of node diameters is n. When the eigenvalue analysis was performed by the finite element method, the piezoelectric effect of the piezoelectric element was ignored. FIG. 9 shows the vibration modes of (0,3), (0,4), and (0,5) modes obtained by the analysis. From the comparison between FIG. 7 and FIG. 8, (0, 3),
The damping effect in the (0,4) and (0,5) modes is clear. In this experiment, even if the resistance value was changed, the change in the natural frequency was within 1%.

FIG. 10 shows the relationship between the resistance value and the attenuation ratio obtained from the experiment. In the figure, the horizontal axis represents the resistance value R, and the vertical axis represents the attenuation ratio ζ. However, the (0,1) mode is not shown because the obtained attenuation ratio has a large variation. It is considered that the reason is that this mode is greatly affected by the fixed condition of the inner circumference of the disk. From FIG. 10, the following can be seen for the mode in which only the nodal diameter exists.
In the (0, 2) mode, the damping effect was not so large, but the effect tended to increase as the number of node diameters increased. Also,
In a mode having a larger number of node diameters than the (0, 3) mode, there is a resistance value at which a maximum attenuation effect is obtained for each mode, and as the number of node diameters increases, the optimum resistance value decreases. Therefore, the ratio between the energy consumed by the resistance and the vibration energy is maximized. In modes with knots, the damping ratio is almost independent of resistance. This is considered to be because the piezoelectric element used this time has a small width in the radial direction.

The structural relationship of the arc-shaped piezoelectric material polarized in the thickness (z) direction can be obtained by using a cylindrical coordinate system (r, θ, z) (see FIG. 6).

(Equation 1) Given by However, in the present embodiment, the radial deformation of the piezoelectric element was ignored, assuming that the radial width of the piezoelectric element was sufficiently smaller than the outer diameter of the disk. Here, T.theta and Sθ is strain the circumference (theta) direction of the stress, D _z and E _z is the thickness (z)
Direction electric displacement (electric flux density) and electric field strength, C ₁₁ ^E is the Young's modulus in the circumferential (θ) direction when short-circuited, and e ₃₁ is the electric field in the thickness (z) direction and the circumferential (θ) direction. The piezoelectric constant that expresses the relationship with the strain, ε ₃₃ ^S is the thickness without strain (z)
Is the dielectric constant of the direction. Between the strain Sθ and the deflection displacement w of the center line of the disk, and between the electric field E _z and the electric potential φ inside the piezoelectric element, respectively.

(Equation 2) There is a relationship. Assuming that the electric potential of the electrode of the piezoelectric element in contact with the disk is 0, the internal electric potential is

(Equation 3) Given by Here, v is a voltage generated between both electrodes of the piezoelectric element when the disk vibrates, that is, a voltage applied to the resistor R. From equations (2) and (3),

(Equation 4) Can be obtained. Assuming that a total of K piezoelectric elements are attached, the current ik flowing in the _k- th circuit is given by the following equation.

(Equation 5)

Here, the superscript represents the derivative with respect to time t. Θ _k1 and θ _k2 represent circumferential coordinates of both ends of the arc of the k-th piezoelectric element. Where θ _k2 −θ _k1 = θ
It is ₀ . Assuming that the system is in harmonic oscillation,

(Equation 6) Then, equation (5) becomes

(Equation 7) Becomes Here, the overlined w and the overlined φ represent the deflection displacement and the amplitude of the electric potential, respectively. On the other hand, between the current i _k When the voltage generated between the electrodes of k-th piezoelectric elements and v _k,

(Equation 8) There is a relationship. Substituting this into Equation (7) and using the relationship of Equation (4),

(Equation 9) Is obtained. This equation gives the deflection w of the disk and the resistance R
_Represents the relationship with the voltage v _k applied to the.

Next, in the forced oscillation when the frequency of the excitation force is equal to the natural frequency omega _n of n-th order mode of the system, approximately during the deflection of the disk displacement and eigenvectors,

(Equation 10) Holds. Here, X _n is the eigenvector of the n-th mode of displacement, and α _n is the corresponding mode coordinate. here,
When λ = jω _n and Expression (10) is used, the voltage v _kn corresponding to the n-th mode of the k-th piezoelectric element is

[Equation 11] Becomes However,

(Equation 12) It is. Mode coordinates,

(Equation 13) Then, equation (11) can be transformed as follows.

[Equation 14] Energy J _kn consumed by k-th resistor over one period of the _oscillation, when the conjugate of v _kn and v ^* _kn,

(Equation 15) Becomes Therefore, vibration energy J _n dissipated during one cycle of vibration in all K sheets of the piezoelectric element,

(Equation 16) Becomes

[0021] The ratio of the maximum kinetic energy T _n dissipation is energy and system in resistance and beta _n in n-th order mode, mode mass when assumed to be normalized,

[Equation 17] Becomes Here, c _n and ζ _n represent the equivalent viscosity coefficient and damping ratio of the n-th mode, respectively. If β _n is known, the damping ratio corresponding to the n-th mode of the system can be obtained by the following equation (17).

(Equation 18) In the present embodiment, the eigenvector X _n is obtained by the finite element method. However, when obtaining the eigenvector, the piezoelectric effect of the piezoelectric element was ignored. In this analysis, the articulation mode cannot be analyzed because the distortion in the radial direction is ignored. Formula (1
From 5), it can be seen that a large damping effect can be obtained when the following terms are large.

[Equation 19] In this term, when the order of the nodal diameter mode increases, tensile and compressive stresses are simultaneously present in one piezoelectric element, and the generated voltage is canceled. Conversely, if the order of the nodal diameter mode is too low, the distortion will be small and the damping effect will be small. Therefore, when the piezoelectric elements are stuck on the outer periphery of the disk at equal intervals as in the present embodiment, it can be seen that there is an optimal number of piezoelectric elements corresponding to each mode. By using this estimation method, a piezoelectric element can be designed so as to increase the attenuation ratio of a specific mode.

In the experiment, analysis was performed on the (0, 3), (0, 4), and (0, 5) modes in which the damping effect was large. The result is shown in FIG. For comparison, the experimental values of the corresponding modes are also shown. In the figure, the horizontal axis represents the resistance value R, and the vertical axis represents the attenuation ratio ζ. In the analysis so far, mechanical damping was neglected, but in FIG. 11, the damping ratio at the time of short circuit (R = 0) obtained from the experiment is considered by adding to the analysis result. From FIG. 11, the analysis and the experiment are in good agreement with each other for the (0, 3) and (0, 4) modes. (0,
5) The modes do not agree quantitatively, but the trends do. In the case of the (0,5) mode, the effect of damping when the resistor was connected was large, and the peak of the transfer function was small as shown in FIG. 8, so it is considered that the error of the experimental value was large.

As described above, the damping ratio was experimentally obtained by performing impulse excitation on the elastic disk to which the arc-shaped piezoelectric element was attached. As a result, it was found that there is an optimum resistance value for obtaining the maximum damping effect for each mode, and that the optimum resistance value decreases as the number of nodal diameters increases. Furthermore, the damping ratio of the nodal diameter mode was analytically estimated from the ratio between the energy dissipated in one cycle of vibration and the maximum kinetic energy when receiving a forced excitation force. Both showed the same tendency. The analysis shows that the optimal number of piezoelectric elements can be obtained for each node diameter mode. It was confirmed that the damping ratio can be increased by using the method proposed in the present invention as a method of damping the elastic disk.

[0024]

As described above, according to the present invention,
By adding attenuation, the amplitude of the disk-shaped structure when resonance occurs can be reduced. In addition, the stability of a disk-shaped structure in which unstable vibration is a problem can be improved.

[Brief description of the drawings]

FIG. 1 is a plan view showing a disk-shaped structure with a vibration damping function according to the present invention.

FIG. 2 is a sectional view showing a disk-shaped structure with a vibration damping function according to the present invention.

FIG. 3 is a diagram showing an example in which the same number of piezoelectric elements are provided in the same phase on both surfaces of a disk.

FIG. 4 is a diagram showing an example in which the same number of piezoelectric elements are provided at different phases on both surfaces of a disk.

5A and 5B are diagrams showing an example in which a piezoelectric element is provided on a disk such as a magnetic disk, wherein FIG. 5A is a plan view and FIG. 5B is a cross-sectional view.

6A and 6B are diagrams showing an example of a case where an elastic disk is used as a disc body, FIG. 6A is a plan view, and FIG. 6B is a cross-sectional view.

FIG. 7 is a graph showing a transfer function when R = 0.

FIG. 8 is a graph showing a transfer function when R = 15 kΩ.

FIG. 9 is a diagram showing a vibration mode of the elastic disk.

FIG. 10 is a graph showing a relationship between a resistance value and a damping ratio.

FIG. 11 is a graph showing a comparison between analysis and experiment.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Disc body 2 Piezoelectric element 3 Lead wire 4 Electric resistance

Claims (9)

[Claims] 1. A vibration damper characterized in that a plurality of piezoelectric elements are provided at equal circumferential positions on one or both outer peripheral portions of a disk-shaped structure, and electrical resistance is connected to both electrodes of the piezoelectric elements. Disc-shaped structure with functions. 2. The disk-shaped structure with a vibration-damping function according to claim 1, wherein the piezoelectric element is provided on the disk-shaped structure by sticking, vapor deposition, or embedding. 3. The disk-shaped structure with a vibration-damping function according to claim 1, wherein the piezoelectric element is a thin-film piezoelectric element. 4. The disk-shaped structure with a vibration damping function according to claim 1, wherein the piezoelectric element is a piezoelectric element deposited on a surface of the disk-shaped structure. 5. The disk-shaped structure with a vibration damping function according to claim 1, wherein the resistor is a surface-mounted resistor. 6. The disk-shaped structure with a vibration damping function according to claim 1, wherein the resistance is a metal film resistance. 7. The disk-shaped structure with a vibration damping function according to claim 6, wherein the resistor is a metal oxide film resistor. 8. The disk-shaped structure with a vibration damping function according to claim 1, wherein the number and the arrangement of the piezoelectric elements are determined so that the attenuation of the vibration mode is increased. 9. The disk-shaped structure with a vibration damping function according to claim 1, wherein the resistance value is determined so that attenuation of a vibration mode is increased.