CN105426644B - Modal damping recognition methods, device and system - Google Patents
Modal damping recognition methods, device and system Download PDFInfo
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Abstract
The invention discloses a kind of modal damping recognition methods, device and system, the modal damping recognition methods is comprising steps of obtain the amplitude-frequency data and phase frequency data of rotor;According to the amplitude-frequency data of acquisition, amplitude frequency curve is drawn, determines critical speed point;According to the phase frequency data of acquisition, phase frequency curve is drawn and be fitted, obtains the phase frequency curve equation of fitting;According to the phase frequency curve equation of fitting, the tangent slope in the phase frequency curve of fitting at critical speed point is calculated;And according to calculated slope, damping ratios are obtained.Modal damping recognition methods proposed by the present invention conveniently and accurately determines critical speed from amplitude frequency curve;Identify damping ratios at reciprocal relation using tangent slope of the phase frequency curve at critical speed point and damping ratio, thus it is convenient, fast, accurately acquire damping ratios.
Description
Technical field
The present invention relates to aero-engine fields, particularly, are related to a kind of modal damping recognition methods and device.In addition,
The invention further relates to a kind of systems including above-mentioned modal damping identification device.
Background technique
Vibrate three elements frequency, amplitude and damping measurement in, damping accurately identifies difficulty maximum, damping to vibration and
The control of noise has highly important effect.Firstly, damping can inhibit the vibration and noise of rotor-support-foundation system.Due to damping
Vibration isolation effect, enables rotor to pass through critical speed, generated large amplitude when to avoiding passing through critical speed, and caused
Turn, stator touches mill.Secondly, using Finite element arithmetic rotor-support-foundation system dynamic characteristics when, it is necessary to input the damping of rotor-support-foundation system
Coefficient.Again, in common concern without in test mass dynamic balancing, it is also necessary to measure the damped coefficient of rotor-support-foundation system.
Damping is one of important motivity characteristic of structure, is influence rotor dynamic response amplitude and structural stability important
Parameter.Compared with the quality of structure and rigidity, the damping acquisition of information of structure is relatively difficult.This is because the complicated mechanism of damping
It has difficulties with experiment measurement.In the prior art, damping recognition methods is divided into time domain method and frequency domain method.
(1) time domain method (free Attenuation Method)
Single-mode system is most basic vibrational system, can disclose many fundamental characteristics of vibrational system.Multiple degrees of freedom
Linear system can usually regard the linear superposition of multiple single-mode system characteristics as.
The oscillatory differential equation that single-degree-of-freedom has damping system is
In formula (1), x,WithRespectively displacement, velocity and acceleration.Under normal circumstances, dampingratioζ < < 1, therefore should
The receptance function of system can be expressed as
In formula (2), t is time parameter,To there is a damped natural frequency, A andRespectively amplitude and
Initial phase.
By initial displacement x0And initial velocityAmplitude and initial phase can be obtained:
For small damping system (ζ < 0.1), have
In formula, n is damped cycle, usually takes damped cycle when amplitude attenuation half either 1/e to be calculated, such as schemes
Shown in 1.
(2) frequency domain method (half-power bandwidth method)
Frequency domain method solves damping ratio by half-power bandwidth (- 3dB), as shown in Figure 2.Viscous damping system frequency response function
Basic representation is
Polar coordinates (complex exponential) form of frequency response function is
Wherein, frequency ratio
From the prior art from the point of view of disclosed data, time domain method and frequency domain method both have respective shortcomings and limitations.
For example time domain method applies in general to single-mode system, can be used for two degree freedom system after improving.But its is affected by noise
It is larger, it cannot be the superposition of multiple frequencies by the response averagely removing the influence of noise, and obtaining.It is identified using frequency domain method
When mechanical structure damps, the ratio between sample frequency, frequency resolution, sampling number, sample frequency and signal frequency, analysis data
Length, the position of spectral line, the size of tested damping and closeness and the frequency leakage of signal frequency etc. damping can be surveyed
Accuracy of measurement and stability have an impact.Since half-power bandwidth method is to calculate attenuation coefficient by the amplitude variations of rotating machinery
To obtain damping ratios.When the rotation speed change of rotor, support stiffness can also change.However, rotating machinery shakes
The variation of width is the comprehensive function of many factors such as damping, self-deformation and stiffness variation as a result, damping is therein one
A principal element.Therefore, the influence to amplitude of these other factors is also just at the source of damping measurement error.Especially work as resistance
When Buddhist nun's very little, influence of the other factors to amplitude is opposite more to be protruded, and the error of measurement will be bigger.Simultaneously in small damping
In the case of, the Δ ω (ω of frequency domain methodb-ωa) precision be difficult to improve, will also result in measurement error increase.Therefore, when small damping
Frequency domain method measurement accuracy can be lower.In addition, being gained knowledge according to rotor dynamic, it is known that rotor-support-foundation system amplitude with revolving speed variation with turn
The acceleration of subsystem is related.In the case where not can guarantee acceleration is constant value, the variation of amplitude is not also just true at one
It is quantitative.Therefore, frequency domain method determines that the stability of damping ratio also will be poor by amplitude variations.
Therefore, how easy, quick and accurately identify modal damping, it is a urgent problem to be solved.
Summary of the invention
The present invention provides a kind of modal damping recognition methods, device and system, thus easy, quick and accurately identify
Modal damping.
The technical solution adopted by the invention is as follows:
According to an aspect of the present invention, a kind of modal damping recognition methods is provided, comprising steps of
Obtain the amplitude-frequency data and phase frequency data of rotor;
According to the amplitude-frequency data of acquisition, amplitude frequency curve is drawn, determines critical speed point;
According to the phase frequency data of acquisition, phase frequency curve is drawn and be fitted, obtains the phase frequency curve equation of fitting;
According to the phase frequency curve equation of fitting, the tangent line in the phase frequency curve of fitting at critical speed point is calculated
Slope;And according to calculated slope, damping ratios are obtained.
Further, the step of obtaining the amplitude-frequency data and phase frequency data of rotor include:
Using the vibratory response of vibration-testing sensor measurement rotor, amplitude-frequency data and phase frequency data are obtained.
Further, include: using the step of vibratory response of vibration-testing sensor measurement rotor-support-foundation system
Using the rotor bow of eddy current displacement sensor measurement rotor, using the vibration of acceleration transducer measurement rotor
Acceleration, using the revolving speed of photoelectric sensor measurement rotor.
Further, at critical speed point,WhereinFor frequency ratio,ω is rotation angular frequency,
ωnFor undamped natural frequency,K is stiffness coefficient, and m is the quality of rotor.
Further, the tangent slope in the phase frequency curve of fitting at critical speed point is obtained by following equation:
Wherein,For phase angle,It is phase angle to the first derivative of frequency ratio.
Further, damping ratios are obtained by following equation:
ζn=1/K
According to another aspect of the present invention, a kind of modal damping identification device is additionally provided, comprising:
Data acquisition module, for obtaining the amplitude-frequency data and phase frequency data of rotor;
Determining module draws amplitude frequency curve, determines critical speed point for the amplitude-frequency data according to acquisition;
Equation obtains module and draws and be fitted phase frequency curve for the phase frequency data according to acquisition, obtains the phase frequency of fitting
Curvilinear equation;
Damping ratio obtains module and calculates in the phase frequency curve of fitting for the phase frequency curve equation according to fitting
Tangent slope at critical speed point;And according to calculated slope, damping ratios are obtained.
Further, data acquisition module is also used to the vibratory response using vibration-testing sensor measurement rotor, obtains
Amplitude-frequency data and phase frequency data.
Further, data acquisition module is also used to adopt using the rotor bow of eddy current displacement sensor measurement rotor
With the vibration acceleration of acceleration transducer measurement rotor, the revolving speed of rotor is measured using photoelectric sensor.
According to another aspect of the present invention, a kind of modal damping identifying system is additionally provided, including above-mentioned modal damping
Identification device.
The invention has the following advantages:
1, critical speed is conveniently and accurately determined from amplitude frequency curve.
2, the tangent slope K and dampingratioζ using phase frequency curve at critical speed pointnMode is identified at reciprocal relation
Damping ratio.From the variation relation of phase and revolving speedIt can be seen that phaseOnly dampingratioζnWith frequency ratioFunction the accuracy of identification of modal damping can be improved due to the influence of not no other factors.
Other than objects, features and advantages described above, there are also other objects, features and advantages by the present invention.
Below with reference to figure, the present invention is described in further detail.
Detailed description of the invention
The attached drawing constituted part of this application is used to provide further understanding of the present invention, schematic reality of the invention
It applies example and its explanation is used to explain the present invention, do not constitute improper limitations of the present invention.In the accompanying drawings:
Fig. 1 is signal when amplitude attenuation half being taken to calculate damping ratio as damped cycle in prior art time domain method
Figure;
Fig. 2 is schematic diagram when calculating damping ratio in prior art frequency domain method by half-power bandwidth;
Fig. 3 is scheme of installation of the rotor on exerciser;
Fig. 4 is the process intention that example is preferably applied in modal damping recognition methods of the present invention;
Fig. 5 is the amplitude frequency diagram in modal damping recognition methods of the present invention;
Fig. 6 is the phase frequency figure in modal damping recognition methods of the present invention;
Fig. 7 is the resulting phase frequency data of different approximating methods and original phase frequency in modal damping recognition methods of the present invention
According to comparison diagram;
Fig. 8 is the phase frequency data and original phase frequency data pair of the exponential function fitting in modal damping recognition methods of the present invention
Than the tangent line figure at figure and critical speed point;
Fig. 9 is tangent line schematic diagram of the phase-fitting curve at critical speed point in modal damping recognition methods of the present invention;
Figure 10 is the functional block diagram of modal damping identification device preferred embodiment of the present invention.
Specific embodiment
It should be noted that in the absence of conflict, the features in the embodiments and the embodiments of the present application can phase
Mutually combination.The present invention will be described in detail below with reference to the accompanying drawings and embodiments.
Referring to Fig. 3, Fig. 3 is that rotor is mounted on the scheme of installation on exerciser, wherein is mounted on the rotor of the exerciser
System includes rear support 1, the turbine disk 2, transmission shaft 3, balance boss 4;Preceding support 5;Output shaft 6;High speed speed increaser 7 and vacuum tank
8.Rotor-support-foundation system Dynamic Characteristics Test carries out on the exerciser.Entire exerciser is made of speed end and low speed end, speed end
It is driven respectively by the direct current generator of a 400kW with low speed end.There are respective acceleration system, supporting system in speed end and low speed end
(driving motor overloads in order to prevent, provides safety guard plate with vacuum system;It will be evacuated, use in vacuum tank 8 in test
Come the windage effect of blade when eliminating rotor rotation).When test direct current generator by two-stage speed increaser 7 power from transmission shaft 3
Input terminal input, pass through output shaft 6 drive rotor rotation.
Further, referring to fig. 4, the preferred embodiment of the present invention provides a kind of modal damping recognition methods, comprising steps of
Step 100, the amplitude-frequency data and phase frequency data for obtaining rotor.
Vibration-testing sensor is installed, the vibratory response of rotor-support-foundation system is measured at the balance boss of rotor-support-foundation system, therefrom
A group rotor transient response data is tested out, to obtain amplitude-frequency and phase frequency data.The vibration-testing sensor is current vortex displacement
Sensor, acceleration transducer and photoelectric sensor, vibratory response includes rotor bow, vibration acceleration and revolving speed, in rotor
During Dynamic Characteristics Test, the vibration acceleration and rotor speed of measurement rotor bow, two support of supporting rotor.Rotor bow
(wherein 3 sensor measurement vertical vibrations and 1 sensor measurement horizontal vibration) is measured by 4 eddy current displacement sensors,
The vibration acceleration of two support of supporting rotor measures (wherein 2 sensor measurement vertical vibrations and 2 by 4 acceleration transducers
A sensor measurement horizontal vibration), the revolving speed of rotor is measured by 1 photoelectric sensor.
Step 200, the amplitude-frequency data according to acquisition draw amplitude frequency curve, determine critical speed point.
Rotor-support-foundation system draws amplitude frequency curve, as shown in figure 5, by the amplitude frequency curve figure in Fig. 5 according to the amplitude-frequency data of acquisition
In, the critical speed point of rotor, i.e. peak point are obtained, is determinedPosition, whereinFor frequency ratio,ω is
Rotate angular frequency, ωnFor undamped natural frequency,K is stiffness coefficient, and m is the quality of rotor.
Forced vibration of the toughness damping system when the external world is actuated to simple harmonic quantity power is considered, if harmonic excitation power is
F=F0sinωt (10)
Then single-degree-of-freedom have damping system sine excitation power effect under differential equation of motion be
Wherein, m is quality, and c is damped coefficient, and k is stiffness coefficient, and t is time, F0For amplitude of exciting force, ω is rotation
Angular frequency, x are the displacement that quality m leaves equilbrium position.
Formula (11) both sides are obtained divided by m simultaneously
Wherein,For the undamped natural frequency of system,For n-th order damping ratios.
Its solution is
Wherein
For frequency ratio.
In formula (15), phase angle is askedTo frequency ratioFirst derivative
At critical speed point, have
Step 300, the phase frequency data according to acquisition, draw and are fitted phase frequency curve, obtain the phase frequency curve equation of fitting.
Rotor-support-foundation system is according to the phase frequency data of acquisition, as shown in fig. 6, drawing phase frequency curve.And it is fitted phase frequency curve, such as scheme
Shown in 7, approximating method can be divided into fitting of a polynomial, power function fitting and exponential function fitting etc..In Fig. 7, by comparing hair
The fitting precision of existing exponential function is some higher.
Step 400, the phase frequency curve equation according to fitting calculate in the phase frequency curve of fitting at critical speed point
Tangent slope;And according to calculated slope, damping ratios are obtained.
Rotor-support-foundation system is according to the phase frequency curve equation of fitting, and as shown in Figure 8 and Figure 9, work is fitted at critical speed point
Phase frequency curveThe tangent line at place, acquires tangent slope K, and inverse 1/K is required damping ratios ζn。
The modal damping recognition methods that the present embodiment proposes conveniently and accurately determines critical speed from amplitude frequency curve;
Utilize tangent slope K and dampingratioζ of the phase frequency curve at critical speed pointnDamping ratios ζ is identified at reciprocal relationn, from
And it is convenient, fast, accurately acquire damping ratios.
Preferably, as shown in Figure 10, the present invention also provides a kind of modal damping identification devices, comprising:
Data acquisition module 10, for obtaining the amplitude-frequency data and phase frequency data of rotor;
Determining module 20 draws amplitude frequency curve, determines critical speed point for the amplitude-frequency data according to acquisition;
Equation obtains module 30 and draws and be fitted phase frequency curve for the phase frequency data according to acquisition, obtains the phase of fitting
Frequency curvilinear equation;
Damping ratio obtains module 40 and calculates the phase frequency curve of fitting for the phase frequency curve equation according to fitting
Tangent slope at middle critical speed point;And according to calculated slope, damping ratios are obtained.
The data acquisition module 10 of rotor-support-foundation system is measured at the balance boss of rotor-support-foundation system by vibration-testing sensor
The vibratory response of rotor-support-foundation system therefrom tests out a group rotor transient response data, to obtain amplitude-frequency and phase frequency data.The vibration
Test sensor is eddy current displacement sensor, acceleration transducer and photoelectric sensor, and vibratory response includes rotor bow, vibration
Dynamic acceleration and revolving speed, during rotor dynamic behavior test, the vibration of measurement rotor bow, two support of supporting rotor accelerates
Degree and rotor speed.Rotor bow is measured (wherein 3 sensor measurement vertical vibrations and 1 by 4 eddy current displacement sensors
Sensor measurement horizontal vibration), the vibration acceleration of two support of supporting rotor measures (wherein 2 biographies by 4 acceleration transducers
Sensor measures vertical vibration and 2 sensor measurement horizontal vibrations), the revolving speed of rotor is measured by 1 photoelectric sensor.
The determining module 20 of rotor-support-foundation system draws amplitude frequency curve, as shown in figure 5, by Fig. 5 according to the amplitude-frequency data of acquisition
Amplitude frequency curve figure in, obtain the critical speed point of rotor, i.e. peak point, determinePosition, whereinFor frequency ratio,ω is rotation angular frequency, ωnFor undamped natural frequency,K is stiffness coefficient, and m is the matter of rotor
Amount.
The equation of rotor-support-foundation system obtains module 30 according to the phase frequency data of acquisition, as shown in fig. 6, drawing phase frequency curve.And
It is fitted phase frequency curve, as shown in fig. 7, approximating method can be divided into fitting of a polynomial, power function fitting and exponential function fitting etc..?
It is some higher by comparing the fitting precision for finding exponential function in Fig. 7.
The damping ratio of rotor-support-foundation system obtains module 40 and is being faced as shown in Figure 8 and Figure 9 according to the phase frequency curve equation of fitting
Make the phase frequency curve being fitted at boundary's revolving speed pointThe tangent line at place, acquires tangent slope K, and inverse 1/K is required
Damping ratios ζn。
The modal damping identification device that the present embodiment proposes, it is more convenient and accurately determine critical turn from amplitude frequency curve
Speed;Utilize tangent slope K and dampingratioζ of the phase frequency curve at critical speed pointnDamping ratios are identified at reciprocal relation
ζn, thus it is convenient, fast, accurately acquire damping ratios.
The present embodiment additionally provides a kind of modal damping identifying system, including above-mentioned modal damping identification device, herein
It repeats no more.
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field
For art personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair
Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (3)
1. a kind of modal damping recognition methods, which is characterized in that comprising steps of
Obtain rotor amplitude-frequency data and phase frequency data, it is described obtain rotor amplitude-frequency data and phase frequency data the step of include:
Vibration-testing sensor is installed, the vibratory response of rotor-support-foundation system is measured at the balance boss of rotor-support-foundation system, is therefrom tested
A group rotor transient response data out, to obtain amplitude-frequency and phase frequency data, the vibration-testing sensor is current vortex displacement biography
Sensor, acceleration transducer and photoelectric sensor, vibratory response include rotor bow, vibration acceleration and revolving speed, are moved in rotor
During force characteristic test, the vibration acceleration and rotor speed of measurement rotor bow, two support of supporting rotor;Rotor bow by
4 eddy current displacement sensor measurements, wherein 3 sensor measurement vertical vibrations, 1 sensor measurement horizontal vibration;Bearing
The vibration acceleration of two support of rotor is measured by 4 acceleration transducers, wherein 2 sensor measurement vertical vibrations, 2 sensings
Device measures horizontal vibration;The revolving speed of rotor is measured by 1 photoelectric sensor;
According to the amplitude-frequency data of acquisition, amplitude frequency curve is drawn, determines critical speed point;
According to the phase frequency data of acquisition, phase frequency curve is drawn and be fitted, obtains the phase frequency curve equation of fitting;
According to the phase frequency curve equation of fitting, cutting at the point of critical speed described in the phase frequency curve of fitting is calculated
The slope of line;And according to the calculated slope, damping ratios are obtained;
At the critical speed point,WhereinFor frequency ratio,ω is rotation angular frequency, ωnFor undamped
Natural frequency,K is stiffness coefficient, and m is the quality of rotor;
Tangent slope at critical speed point described in the phase frequency curve of fitting is obtained by following equation:
Wherein, K is the tangent slope at critical speed point,For phase angle,It is led for single order of the phase angle to frequency ratio
Number,
The damping ratios are obtained by following equation:
ζn=1/K
Wherein, ζnFor damping ratios, K is the tangent slope at critical speed point.
2. a kind of modal damping identification device characterized by comprising
Data acquisition module (10), for obtaining the amplitude-frequency data and phase frequency data of rotor;The data acquisition module of rotor-support-foundation system
(10) by vibration-testing sensor, the vibratory response of rotor-support-foundation system is measured at the balance boss of rotor-support-foundation system, is therefrom tested
A group rotor transient response data out, to obtain amplitude-frequency and phase frequency data;The vibration-testing sensor is current vortex displacement biography
Sensor, acceleration transducer and photoelectric sensor, vibratory response include rotor bow, vibration acceleration and revolving speed, are moved in rotor
During force characteristic test, the vibration acceleration and rotor speed of measurement rotor bow, two support of supporting rotor;Rotor bow by
4 eddy current displacement sensor measurements, wherein 3 sensor measurement vertical vibrations, 1 sensor measurement horizontal vibration;Bearing
The vibration acceleration of two support of rotor is measured by 4 acceleration transducers, wherein 2 sensor measurement vertical vibrations, 2 sensings
Device measures horizontal vibration;The revolving speed of rotor is measured by 1 photoelectric sensor;
Determining module (20) draws amplitude frequency curve, determines critical speed point for the amplitude-frequency data according to acquisition;
Equation obtains module (30) and draws and be fitted phase frequency curve for the phase frequency data according to acquisition, obtain fitting
Phase frequency curve equation;
Damping ratio obtains module (40), and for the phase frequency curve equation according to fitting, the phase frequency for calculating fitting is bent
Tangent slope at the point of critical speed described in line;And according to the calculated slope, damping ratios are obtained;
At the critical speed point,WhereinFor frequency ratio,ω is rotation angular frequency, ωnFor undamped
Natural frequency,K is stiffness coefficient, and m is the quality of rotor;
Tangent slope at critical speed point described in the phase frequency curve of fitting is obtained by following equation:
Wherein, K is the tangent slope at critical speed point,For phase angle,It is led for single order of the phase angle to frequency ratio
Number,
The damping ratios are obtained by following equation:
ζn=1/K
Wherein, ζnFor damping ratios, K is the tangent slope at critical speed point.
3. a kind of modal damping identifying system, which is characterized in that including modal damping identification device as claimed in claim 2.
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CN112504597B (en) * | 2020-11-10 | 2023-06-30 | 北京强度环境研究所 | Method for obtaining damping ratio from phase information |
CN113266538B (en) * | 2021-05-31 | 2022-03-22 | 明阳智慧能源集团股份公司 | Method and system for automatically identifying modal frequency of offshore wind power tower and transmission chain |
CN113375789B (en) * | 2021-06-09 | 2023-03-14 | 北京科技大学 | Structural damping ratio identification method based on free vibration |
WO2023115510A1 (en) * | 2021-12-24 | 2023-06-29 | 方兴 | Phase slope-based system damping ratio determining method |
CN115391744B (en) * | 2022-10-27 | 2022-12-27 | 中国航空工业集团公司北京长城计量测试技术研究所 | Load sensor dynamic model parameter identification method and device |
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