CN113065089A - Method for calculating amplification ratio of resonance amplitude of underwater equipment - Google Patents
Method for calculating amplification ratio of resonance amplitude of underwater equipment Download PDFInfo
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- CN113065089A CN113065089A CN202110371803.8A CN202110371803A CN113065089A CN 113065089 A CN113065089 A CN 113065089A CN 202110371803 A CN202110371803 A CN 202110371803A CN 113065089 A CN113065089 A CN 113065089A
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Abstract
The invention discloses a method for calculating the amplification ratio of the resonance amplitude of an underwater device, which comprises the following steps: calculating the underwater resonance frequency ratio w of the equipment on the basis of respectively measuring the free vibration frequency of the equipment in the air and the waterrw(ii) a Let the resonant frequency ratio wrResonance frequency ratio w of device in waterrwAccording to damping ratio xi to resonant frequency ratio wrThe expression of the variation curve of (1) calculates the damping ratio xi of the vibration of the equipment in waterw(ii) a Make damping ratio xi ═ damping ratio xi that the equipment vibrates in waterwAmplification ratio a according to resonance amplituderExpression calculation equipment resonance amplitude amplification ratio a in water along with damping ratio xi change curverw. The method for calculating the amplification ratio of the resonance amplitude of the underwater equipment is based on a single-degree-of-freedom linear forced vibration equation, has the advantages of clear scientific principle, simple and clear steps and strong operability, the estimated resonance amplitude ratio is not lower than the actual resonance amplitude ratio, the deviation is lower than 10 percent, and the application of the estimated result is safe and effective.
Description
Technical Field
The invention relates to the technical field of fluid machinery, mechanical vibration and resonance, in particular to a method for calculating the amplification ratio of the resonance amplitude of underwater operation equipment.
Background
Vibration is common in nature, daily life, and industrial and agricultural production, and refers to the reciprocating motion of an object near a balance position. Resonance is a special state of vibration, which refers to a situation that a physical system vibrates with a larger amplitude than other frequencies at a specific frequency, and is a phenomenon that the amplitude of the system is significantly increased when the excitation frequency of the system is equal to or close to the natural frequency of the system.
In the atmospheric environment, the damping is very small, the resonance power is huge, and great damage of eyes and heart is often caused. Karman vortex resonance caused a newly built Takema suspension bridge of 4 months in Washington, USA to generate severe torsional vibration in a strong wind with a wind speed of only 19m/s (21 m/s for nine-grade wind and 35m/s for twelve-grade wind), the amplitude of the vibration is close to 9m, the bridge deck inclines to about 45 degrees, and the suspenders are pulled apart one by one, so that steel beams on the bridge deck are broken and collapsed. Similarly, the karman vortex 'vortex-induced vibration' generated by the atmospheric streaming suspension bridge upright column causes the 11-seat bridge to resonate, and the damage is serious. The vibration problem is faced when vehicles, ships, aviation, power machines, machining equipment and all rotating machines are operated.
However, neither in air nor in water, the amplitude of the resonance of the device is known to be at all large. At present, the amplification effect of resonance on forced vibration amplitude under the damping condition is lack of research, so that the amplification factor of the amplitude of the resonance of the equipment in water is lack of understanding, and therefore, scientific basis cannot be found as guidance when economic, reasonable and sufficient anti-resonance measures are prepared.
Disclosure of Invention
The invention aims to provide a method for calculating the amplification ratio of the resonance amplitude of an underwater device, which is used for solving the problem that scientific basis cannot be found as guidance when economic, reasonable and sufficient anti-resonance measures are formulated at present.
The invention provides a method for calculating the amplification ratio of the resonance amplitude of an underwater device, which comprises the following steps:
step S1: acquiring the resonant frequency ratio w of the equipment in waterrw；
Step S2: let the resonant frequency ratio wrThe ratio w of the resonance frequency of the device in waterrwAccording to damping ratio xi to resonant frequency ratio wrThe expression of the variation curve of (1) calculates the damping ratio xi of the vibration of the equipment in waterw；
Step S3: make damping ratio xi ═ damping ratio xi that the equipment vibrates in waterwAmplification ratio a according to resonance amplituderExpression calculation equipment resonance amplitude amplification ratio a in water along with damping ratio xi change curverw。
Further, in the step S1, the apparatus has a resonant frequency ratio w in waterrwThe calculation expression of (a) is:
wrw＝ωfw/ωfa(formula 2)
In the formula, ωfaFor the frequency, ω, of the free vibration of the apparatus in airfwIs the frequency at which the device is free to vibrate in the water.
Further onIn the step S2, the damping ratio ξ is dependent on the resonance frequency ratio wrThe expression of the variation curve of (a) is:
in the formula, wrWhen let w be the ratio of resonance frequenciesrThe ratio w of the resonance frequency of the device in waterrwThe damping ratio xi obtained in the time is the damping ratio xi of the equipment vibrating in the waterw。
Further, in the step S3, the resonance amplitude amplifying ratio arThe expression of the change curve along with the damping ratio xi is as follows:
in the formula, wrIs the resonance frequency ratio, xi is the damping ratio, when let wrThe ratio w of the resonance frequency of the device in waterrwAnd damping ratio xi is equal to damping ratio xi of equipment vibrating in waterwAmplification ratio a of resonance amplitude obtainedrI.e. the amplification ratio a of the resonance amplitude of the equipment in waterrw。
Compared with the prior art, the invention has the beneficial effects that:
the invention discloses a method for calculating the amplification ratio of the resonance amplitude of an underwater device, which comprises the steps of firstly measuring the frequency omega of the free vibration of the device in air and water respectivelyfaAnd ωfwAssuming the free vibration frequency ω of the device in airfaIs the natural frequency omega of the device0On the basis of the frequency omega of the free vibration of the equipment in waterfwWith natural frequency omega0The ratio of the resonant frequency w of the device in waterrw(ii) a Damping ratio xi and resonant frequency ratio w in resonancerThe damping ratio xi and the resonant frequency ratio w are obtained by adopting a scattered point fitting moderChanging polynomial of the ratio w of the resonant frequencies in waterrwSubstituting the polynomial to calculate and obtain the damping of the vibration of the equipment in the waterRatio xiw(ii) a Damping ratio xi of equipment vibrating in waterwAnd the resonant frequency ratio w of the device in waterrwSubstituted resonance amplitude amplification ratio arAccording to damping ratio xi and resonance frequency ratio wrIn the expression of the change curve, the amplification ratio a of the resonance amplitude of the equipment in water is calculatedrwTo estimate the amplification factor of the amplitude value to the laser amplitude value when the water resonates, so as to determine the harmfulness of the resonance. The method for calculating the amplification ratio of the resonance amplitude of the underwater equipment is based on a single-degree-of-freedom linear forced vibration equation, has the advantages of clear scientific principle, simple and clear steps and strong operability, the estimated resonance amplitude ratio is not lower than the actual resonance amplitude ratio, the deviation is lower than 10 percent, and the application of the estimated result is safe and effective.
Detailed Description
The invention discloses a method for calculating the amplification ratio of the resonance amplitude of an underwater device, which comprises the steps of measuring the free vibration frequency of the device in water and air, applying the one-to-one correspondence relationship between the amplification ratio of the amplitude of a resonance working condition point, the damping ratio and the resonance frequency ratio found by people on the basis of assuming that the free vibration frequency in the air is the inherent frequency of the device, reversely solving the damping ratio in water by utilizing the actually measured free vibration frequency ratio in water, further obtaining the amplification ratio of the resonance amplitude of the device in water to confirm the resonance hazard size of the device, and further clarifying the resonance intensity of the device when the device runs in water so as to carry out prejudgment and analysis on the resonance hazard. It should be noted that, in this method embodiment, the free vibration frequency in the air is assumed to be the system natural frequency, which has a certain effect on the estimated underwater resonance amplitude ratio, but since this assumption makes the estimated value slightly larger than the actual value (about 0.2% larger), it is safe and has a very small effect on the estimation accuracy.
It should be noted that, the method for calculating the amplification ratio of the resonance amplitude of the underwater device disclosed by the present invention is not limited to be applied to water, and can also be applied to other liquids, and all the methods are used for replacing other liquids with "water".
Example 1
Embodiment 1 provides a method for calculating an amplification ratio of a resonance amplitude of an underwater device, the method comprising the steps of:
step S1: measuring respectively the frequency omega of the free vibration of the device in waterfwAnd the frequency omega of the free vibration of the equipment in the airfaCalculating the resonant frequency ratio w of the device in waterrw；
Wherein the frequency of free vibration of the equipment in vacuum is the natural frequency omega of the equipment0The resonant frequency of the device in water is omegarwThe ratio w of the resonant frequency of the device in waterrwThe calculation expression of (a) is:
wrw＝ωrw/ω0(formula 1)
In the formula, ωrwFor the resonant frequency, omega, of the apparatus in water0The frequency at which the device is free to vibrate in a vacuum, also known as the natural frequency of the device;
wherein the natural frequency omega of the device0Frequency omega of free vibration of equipment in airfaResonant frequency of the device in water omegarwFrequency omega of free vibration of equipment in waterfwAlso called the natural frequency of the device in water, equation 1 can be evolved as:
wrw＝ωfw/ωfa(formula 2)
Step S2: calculating damping ratio xi of vibration of equipment in waterwThe calculation expression is as follows:
in the formula, wrWhen let w be the ratio of resonance frequenciesrThe ratio w of the resonance frequency of the device in waterrwThe damping ratio xi obtained in the time is the damping ratio xi of the equipment vibrating in the waterw。
Step S3: calculating the amplification ratio a of the resonance amplitude of the equipment in waterrwThe calculation expression is as follows:
in the formula, wrIs the resonance frequency ratio, xi is the damping ratio, when let wrThe ratio w of the resonance frequency of the device in waterrwAnd damping ratio xi is equal to damping ratio xi of equipment vibrating in waterwAmplification ratio a of resonance amplitude obtainedrI.e. the amplification ratio a of the resonance amplitude of the equipment in waterrw。
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (4)
1. A method for calculating the amplification ratio of the resonance amplitude of an underwater device is characterized by comprising the following steps:
step S1: acquiring the resonant frequency ratio w of the equipment in waterrw；
Step S2: let the resonant frequency ratio wrThe ratio w of the resonance frequency of the device in waterrwAccording to damping ratio xi to resonant frequency ratio wrThe expression of the variation curve of (1) calculates the damping ratio xi of the vibration of the equipment in waterw；
Step S3: make damping ratio xi ═ damping ratio xi that the equipment vibrates in waterwAmplification ratio a according to resonance amplituderExpression calculation equipment resonance amplitude amplification ratio a in water along with damping ratio xi change curverw。
2. The method of calculating the amplification ratio of resonance amplitude of an underwater apparatus according to claim 1,
in the step S1, the device has a resonant frequency ratio w in waterrwThe calculation expression of (a) is:
wrw＝ωfw/ωfa(formula 2)
In the formula, ωfaFor the equipment in the airFrequency of medium free vibration, omegafwIs the frequency at which the device is free to vibrate in the water.
3. The method of calculating the amplification ratio of resonance amplitude of an underwater apparatus according to claim 2,
in the step S2, the damping ratio xi follows the resonance frequency ratio wrThe expression of the variation curve of (a) is:
in the formula, wrWhen let w be the ratio of resonance frequenciesrThe ratio w of the resonance frequency of the device in waterrwThe damping ratio xi obtained in the time is the damping ratio xi of the equipment vibrating in the waterw。
4. The method of calculating the amplification ratio of resonance amplitude of an underwater apparatus according to claim 3,
in the step S3, the resonance amplitude magnification ratio arThe expression of the change curve along with the damping ratio xi is as follows:
in the formula, wrIs the resonance frequency ratio, xi is the damping ratio, when let wrThe ratio w of the resonance frequency of the device in waterrwAnd damping ratio xi is equal to damping ratio xi of equipment vibrating in waterwAmplification ratio a of resonance amplitude obtainedrI.e. the amplification ratio a of the resonance amplitude of the equipment in waterrw。
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20120299442A1 (en) * | 2010-02-04 | 2012-11-29 | Konica Minolta Advanced Layers, Inc. | Drive device |
| CN103592530A (en) * | 2013-09-27 | 2014-02-19 | 华北电力大学（保定） | Method for discriminating type of low frequency oscillation mechanism based on envelope fitting |
| CN107121497A (en) * | 2017-06-02 | 2017-09-01 | 东莞理工学院 | The ultrasonic guided wave detecting method of accidental resonance characteristic based on Duffing systems |
| CN112052596A (en) * | 2020-09-11 | 2020-12-08 | 苏州科技大学 | Simulation method of resonance mode in servo mechanical system |
| CN112504597A (en) * | 2020-11-10 | 2021-03-16 | 北京强度环境研究所 | Method for acquiring damping ratio from phase information |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20120299442A1 (en) * | 2010-02-04 | 2012-11-29 | Konica Minolta Advanced Layers, Inc. | Drive device |
| CN103592530A (en) * | 2013-09-27 | 2014-02-19 | 华北电力大学（保定） | Method for discriminating type of low frequency oscillation mechanism based on envelope fitting |
| CN107121497A (en) * | 2017-06-02 | 2017-09-01 | 东莞理工学院 | The ultrasonic guided wave detecting method of accidental resonance characteristic based on Duffing systems |
| CN112052596A (en) * | 2020-09-11 | 2020-12-08 | 苏州科技大学 | Simulation method of resonance mode in servo mechanical system |
| CN112504597A (en) * | 2020-11-10 | 2021-03-16 | 北京强度环境研究所 | Method for acquiring damping ratio from phase information |
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