CN108871543A - The anharmonic Fourier's analysis method of blade asynchronous vibration frequency under constant speed - Google Patents
The anharmonic Fourier's analysis method of blade asynchronous vibration frequency under constant speed Download PDFInfo
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- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
- G01H1/003—Measuring characteristics of vibrations in solids by using direct conduction to the detector of rotating machines
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
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Abstract
The invention belongs to machinery impeller vane the field of test technology, and to finally obtain correct vibration frequency value, the anharmonic Fourier's analysis method of blade asynchronous vibration frequency under constant speed of the present invention, steps are as follows：Step 1：Seek folding frequency and phase value；Step 2：Calculate phase difference；Step 3：Frequency multiplication integer traversal；Step 4：Blade asynchronous vibration frequencies omega is obtained by error analysis；Step 5：Step 2 is repeated to step 4, is obtained based on phasei' blade asynchronous vibration the frequencies omega calculated '；Further：Probable value ω and ω ' calculating to blade asynchronous vibration frequency estimation, obtains ωn、ωn' and corresponding HJ, iValue；If for i=0,1 ... N, Ri(ωn)>Ri(ωn') set up, then blade asynchronous vibration frequency values are ω, and otherwise blade asynchronous vibration frequency values are ω '.Present invention is mainly applied to machinery impeller vanes to test occasion.
Description
Technical field
The invention belongs to machinery impeller vane the field of test technology, especially a kind of blade asynchronous vibration frequency analysis side
Method.
Background technique
Aero-engine, combustion gas turbine are aircraft, large ship etc. " hearts ", and movable vane piece is done work first as core
Part, the monitoring of monitoring running state, especially vibration parameters have aero-engine, the safe and efficient operation of combustion gas turbine
Important meaning.When engine operation, the load acted on turbine rotor blade mainly has, blade sole mass under high-speed rotation
The centrifugal load of generation, aerodynamic loading of the fluid matasomatism on blade, high temperature are unevenly distributed caused temperature loading, various vibrations
Dynamic loading etc. [1].It is uneven that the structures such as support plate, stator blade in casing lead to air flow method, so that exciting force is generated, when this swashs
Power and the rotor speed frequency of shaking at integral multiple relation and numerically close to movable vane piece order frequency when, movable vane piece just synchronizes
Resonance.Other than synchro-resonance, in some cases, for example when compressor flutter, surge or rotating stall, blade can be sent out
Raw asynchronous vibration.Movable vane piece is under oscillating load, it may occur that fatigue is cracked and is even broken off, causes entirely to rotate
Machinery stops transport [2].
Blade health status on-line monitoring system can be rotating machinery daily maintenance, and improve rotating machinery operational efficiency
It submits necessary information.Traditional contact blade state monitoring technology is restricted in practical engineering applications.Such as patch strain
Piece method, this method is using limited in the monitoring of high temperature gas turbine machine, and furthermore this method needs telemetry system, somewhat expensive,
Installation is complicated, and foil gauge is pasted in movable vane piece, can impact [3] to the power performance of blade itself.Based on blade tip
The blade state monitoring method of timing belongs to non-contact measurement, and opposite to contact measurement method, this method installation is simple, can one
Secondary property measures the vaned vibration parameters of whole grade institute, with the obvious advantage.
Blade vibration parameter monitoring based on Tip-Timing principle belongs to lack sampling monitoring method, and difficult point is based on owing to adopt
How sample data are reconstructed blade vibration information.The oscillatory type difference occurred according to blade is calculated using corresponding reconstruct
Method.The Tip-Timing identification algorithm of common measurement synchronous vibration has：Single parameter method [4], two parameter method [5], autoregressive method
[6], the blade synchronization vibration parameters identification algorithm [7] based on random angle removes the blade synchronization vibration parameters identification algorithm of OPR
[8] etc..The Tip-Timing identification algorithm of common measurement asynchronous vibration has：Prony Power estimation method, sensor are evenly distributed with method, difference frequency
Method, " 5+2 " distribution [9], blade asynchronous vibration Identification of parameter [7] under constant speed, speed change motivate lower blade asynchronous vibration ginseng
Number identification algorithm [10] etc..
Document [7] can refer to for the theory deduction of blade asynchronous vibration Identification of parameter under constant speed.Due to the present invention
On the basis of the analysis method of proposition is the blade asynchronous vibration Identification of parameter under constant speed, to blade asynchronous vibration frequency into
The secondary identification of row, it is therefore necessary to blade asynchronous vibration Identification of parameter calculating process under constant speed be sketched, and illustrated
Defect existing for the current algorithm.Assuming that rotor speed be Ω, using more Tip timing sensors (number is followed successively by 0,1,
2 ... N) blade asynchronous vibration is monitored.
Step 1：Seek folding frequency and phase value
Full phase is carried out to 2n-1 data of the vibration signal interception same time period of every Tip timing sensor monitoring
Position Fourier analysis obtains spectrum analysis as a result, finding out the corresponding frequency of peak value spectral line in [- Ω/2,0] and [0, Ω/2] range
Point | Δ f |, then find out the corresponding phase value of this peak valueWithWherein i=0,1,2 ... N indicate corresponding sensor number.
Step 2：Calculate phase difference
The phase value obtained according to previous stepWithHere with phaseFor.According toEach sensor is calculated with respect to 0
The measured phase difference of number sensorAnd it is regular to [0,360 °).Respective phase difference should be written as：
M-vibration frequency multiplication integer part
ai- Tip timing sensor setting angle
Assuming that correctly m value is m*, measured phase difference size isIt is expressed as a vector：
Step 3：Frequency multiplication integer traversal
The m value that traversal is chosen is mk, phase difference is calculated according to (1) formulaAnd it is regular to [0,360 °), indicated with vector
For：
Step 4：, blade asynchronous vibration frequencies omega is obtained by error analysis.
Survey phase delta Ф*With traversal phase delta ФkIt compares, acquires error Ek,
With error EkRoot-mean-square value SE indicate phase difference traversal estimated value deviate actual measured value size：
Theoretically, work as mk=m*When, SE=0.Consider the presence of error, it is corresponding to can use obvious the smallest SE in traversal range
Frequency multiplication mkAs actual m*.To pick out the frequency of blade asynchronous vibration：
ω=mkΩ+△ f or ω=mkΩ-△f (6)
Due to there is " ± " symbol in formula (1), to mkIt is traversed, need to be calculated respectively by "+" and "-", jointly relatively SE
Size, so that it is determined that a mkCorresponding "+" or "-" oeprator in value and formula (1).
Step 5：Step 2 is repeated to step 4, is obtained based on phaseThe blade asynchronous vibration frequencies omega of calculating '.
Blade asynchronous vibration Identification of parameter under the constant speed known to above-mentioned narration, can calculate two possible asynchronous vibrations
Dynamic frequency value ω and ω ', but the indeed vibrations frequency of blade can not be further judged in ω and ω '.It is different for blade
Deficiency existing for vibration parameters identification algorithm is walked, document [11] forms different using the more different sensors of setting angle difference
Calculating group calculates vibration frequency of blade according to step 1 to step 4 respectively, sentences by comparing whether multiple groups calculated result is identical
Whether the calculated vibration frequency of blade that breaks is correct.This kind of method needs to increase Tip timing sensor quantity, in Practical Project
It is restricted in.Document [10] is directed to variable speed situation, is carried out using the data that two-way Tip timing sensor monitors slotting
Value is made by improving sample frequencyWithBe worth it is identical, further according to above-mentioned steps 1 to step 4 process calculate, obtain
Unique blade asynchronous vibration frequency values.But interpolation is carried out to blade tip timing data under speed change, so that sample frequency is no longer kept
It is constant, the accuracy of calculated result is impacted.
Blade asynchronous vibration frequency estimation algorithm under constant speed there are aiming at the problem that, in the present invention, be firstly introduced non-tune
With Fourier analysis [12], the ω and ω ' that blade asynchronous vibration frequency estimation under constant speed is gone out by anharmonic Fourier analysis
Secondary identification is carried out, finally obtains the indeed vibrations frequency of blade.
[1] Yan Xiaojun, the Nie Jing rising sun turbo blade fatigue [M] Science Press, 2014.
[2] Krause C, Giersch T, Stelldinger M, et al.Asynchronous Response
Analysis of Non-Contact Vibration Measurements on Compressor Rotor Blades
[C]//ASME Turbo Expo 2017：Turbomachinery Technical Conference and
Exposition.2017：V07BT35A004.
[3] Neri P, Peeters B.Non-Harmonic Fourier Analysis for bladed wheels
Damage detection [J] .Journal ofSound&Vibration, 2015,356：181-194.
[4] I.Y.Zablotsky and Yu.A.Korostelev, Measurement of resonance
vibrations of turbine blades with the ELURA device[J]
.Energomashinostroneniye1970(2)：36-39.
[5]Heath S.ANew Technique for Identifying Synchronous Resonances
Using Tip-Timing[C]//1999：219-225.
[6] Gallegogarrido J, Dimitriadis G, Carrington I B, et al.A Class of
Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies
Undergoing Simultaneous Resonances-Part II：Experimental Validation[J]
.International Journal of Rotating Machinery, 2007,2007 (4)：981-1077.
[7] apparatus for rotating vane vibration detection and parameter identification technique [D] University Of Tianjin of the Ou Yangtao based on Tip-Timing,
2011
[8] Guo H, Duan F, Zhang J.Blade resonance parameter identification
based on tip-timing method without the once-per revolution sensor[J]
.Mechanical Systems&Signal Processing, 2016, s 66-67：625-639.
[9] Zhang Yugui, Duan Fajie, local records are strong, leaf good reputation, the frequency identification technology of the small river rotating vane asynchronous vibration of stone
[J] vibration and impact, 2007 (12)：106-108+174-175.
[10] Yue Lin, Li Haihong, Wang Deyou, Wang Lei, Hu Wei speed change motivate lower blade asynchronous vibration parameter identification method
The Jiangsu [P]：CN104697623A, 2015-06-10.
[11] Guo Hao days Tip-Timing principle blade oscillation measurements and the fatigue crack discrimination method research Tianjin [D] are big
It learns, 2015.
[12]Yoshimutsu Hirata.Non-harmonic Fourier analysis available for
detecting very low-frequency components[J].Journal of Sound and
Vibration.2005(287)：611-613.
Summary of the invention
In order to overcome the deficiencies of the prior art, the present invention is directed to introduce anharmonic Fourier analysis, to blade under current constant speed
All possible outcomes of asynchronous vibration frequency estimation carry out secondary identification, finally obtain correct vibration frequency value.For this purpose, this hair
Bright to adopt the technical scheme that, the anharmonic Fourier's analysis method of blade asynchronous vibration frequency under constant speed, steps are as follows：
Rotor speed is Ω, and being followed successively by 0,1,2 using number ..., N branch Tip timing sensor carries out blade asynchronous vibration
Monitoring：
Step 1：Seek folding frequency and phase value
Full phase is carried out to 2n-1 data of the vibration signal interception same time period of every Tip timing sensor monitoring
Position Fourier analysis obtains spectrum analysis as a result, finding out the corresponding frequency of peak value spectral line in [- Ω/2,0] and [0, Ω/2] range
Point | Δ f |, then find out the corresponding phase value of this peak valueWithWherein i=0,1,2 ... N indicate corresponding sensor serial number；
Step 2：Calculate phase difference
The phase value obtained according to previous stepWithHere with phaseFor.According toEach sensor is calculated with respect to 0
The measured phase difference of number sensorAnd it is regular to [0,360 °), respective phase difference should be written as：
M- vibrates frequency multiplication integer part
ai- Tip timing sensor setting angle
Assuming that correctly m value is m*, measured phase difference size isIt is expressed as a vector：
Step 3：Frequency multiplication integer traversal
The m value that traversal is chosen is mk, phase difference is calculated according to (1) formulaAnd it is regular to [0,360 °), indicated with vector
For：
Step 4：, blade asynchronous vibration frequencies omega is obtained by error analysis.
Survey phase delta Ф*With traversal phase delta ФkIt compares, acquires error Ek,
With error EkRoot-mean-square value SE indicate phase difference traversal estimated value deviate actual measured value size：
The presence for considering error takes the corresponding frequency multiplication m of obvious the smallest SE in traversal rangekAs actual m*.To distinguish
Know the frequency of blade asynchronous vibration out：
ω=mkΩ+△ f or ω=mkΩ-△f (6)
Due to there is " ± " symbol in formula (1), to mkIt is traversed, need to be calculated respectively by "+" and "-", jointly relatively SE
Size, so that it is determined that a mkCorresponding "+" or "-" oeprator in value and formula (1)；
Step 5：Step 2 is repeated to step 4, is obtained based on phaseThe blade asynchronous vibration frequencies omega of calculating '；
Further：The probable value ω and ω ' of blade asynchronous vibration frequency estimation is calculated according to formula (7), obtains ωn
And ωn', wherein [x] indicates that Ω is speed-frequency to x round numbers part：
Further：Anharmonic Fourier analysis expression such as formula (8) is shown, wherein Hj,i(ω) indicates analyzed letter
Number yj,iMiddle frequency is the amplitude for the sensor monitoring that ω number is i, by ω obtained in the previous stepnAnd ωn' bring formula (8) into respectively,
Obtain corresponding HJ, iValue；
Wherein, ω-analysis frequency；
I-sensor number；
J-sequence of data points；
npData point sum；
F- sample frequency；
yJ, iAnalyzed signal.
Every Tip timing sensor (is calculated according to formula (8) respectively, successively obtains HJ, 0(ωn), HJ, 0(ωn'),
HJ, 1(ωn), HJ, 1(ωn') ..., HJ, N(ωn), HJ, N(ωn′)；
Further：The corresponding R of every Tip timing sensor is calculated according to formula (9)i(ωn) and Ri(ωn′)
Wherein i representative sensor is numbered；
Further：Compare Ri(ωn) and Ri(ωn') size of value.
If for i=0,1 ... N, Ri(ωn) > Ri(ωn') set up, then blade asynchronous vibration frequency values are ω.Otherwise leaf
Piece asynchronous vibration frequency values are ω '.
The features of the present invention and beneficial effect are：
It, can to all of blade asynchronous vibration Identification of parameter calculating under constant speed by introducing anharmonic Fourier analysis
Can result carry out secondary identification, finally obtain correct vibration frequency value, overcome blade asynchronous vibration parameter identification under constant speed
The deficiency of algorithm can promote in engineering practice the innovatory algorithm, be aero-engine, the large rotating machineries such as gas turbine
Health status monitoring, fault diagnosis, condition maintenarnce management etc. provide technical support.
Detailed description of the invention：
Fig. 1 is blade asynchronous vibration Identification of parameter process, and wherein serial number 1 is blade asynchronous vibration algorithm stream under constant speed
Journey, serial number 2 are the anharmonic analysis method process of blade asynchronous vibration frequency under constant speed proposed by the present invention.
Fig. 2 is the blade vibration mathematical model (bibliography based on G.Dimitridis：Dimitriadis G,
Carrington I B, Wright J R, et al.Blade-tip Timing Measurement of Synchronous
Vibrations of Rotating Bladed Assemblies[J].Mechanical Systems&Signal
Processing, 2002,16 (4)：599-622.), it is displaced using the blade asynchronous vibration of 4 Tip timing sensor monitorings imitative
True data.Wherein vibration displacement is the numerical value for adding 10% white noise after normalizing.
Fig. 3 is to be analyzed using the data that 4 Tip timing sensors of all phase Fourier transform pairs monitor, and obtains phase
The folding frequency and phase result answered.
Fig. 4 is frequency multiplication integer traversing result.
Fig. 5 is Ri(ωn) and Ri(ωn') comparing result.
Specific embodiment
Blade asynchronous vibration Identification of parameter can only calculate two possible asynchronous vibration frequency values under constant speed, and nothing
Method makes further judgement to calculated two vibration frequency of blade again.For deficiency existing for the algorithm, the present invention is main
Solve the problems, such as be：Anharmonic Fourier analysis is introduced, to the probable value ω of blade asynchronous vibration frequency estimation under current constant speed
With the secondary identification of ω ' carry out, the indeed vibrations frequency of blade is finally obtained.
The invention is realized in this way：
Further：The probable value ω and ω ' of blade asynchronous vibration frequency estimation is calculated according to formula (7), obtains ωn
And ωn', wherein [x] indicates that Ω is speed-frequency to x round numbers part.
Further：Shown in anharmonic Fourier analysis expression such as formula (8).Wherein Hi(ω) indicates analyzed signal
The amplitude of i-th of data point when frequency is ω in y.By ω obtained in the previous stepnAnd ωn' bring formula (8) into respectively, it obtains corresponding
HiValue.
Wherein, ω-analysis frequency；
I- sensor number；
J- sequence of data points；
npData point sum；
F- sample frequency；
yJ, iAnalyzed signal.
Every Tip timing sensor (number is followed successively by 0,1,2 ... N) is calculated according to formula (8) respectively, can successively be obtained
To HJ, 0(ωn), HJ, 0(ωn'), HJ, 1(ωn), HJ, 1(ωn') ..., HJ, N(ωn), HJ, N(ωn′)。
Further：The corresponding R of every Tip timing sensor is calculated according to formula (9)i(ωn) and Ri(ωn′)。
Wherein i representative sensor is numbered.
Further：Compare Ri(ωn) and Ri(ωn') size of value.
If for i=0,1 ... N, Ri(ωn) > Ri(ωn') set up, then blade asynchronous vibration frequency values are ω.Otherwise leaf
Piece asynchronous vibration frequency values are ω '.
The present invention will be further described with example with reference to the accompanying drawing.
In conjunction with the blade vibration mathematical model (bibliography of G.Dimitridis：Dimitriadis G, Carrington
I B, Wright J R, et al.Blade-tip Timing Measurement of Synchronous Vibrations
Of Rotating Bladed Assemblies [J] .Mechanical Systems&Signal Processing, 2002,16
(4)：599-622.), asynchronous vibration emulation is carried out to 4 blade vibration systems, by emulation data to constant speed proposed by the present invention
Lower blade asynchronous vibration parameter identification innovatory algorithm is verified.4 Tip timing sensor gathering simulation numbers are used when emulation
According to, 4 Tip timing sensor established angles set gradually for：0 °, 18.4 °, 119.5 °, 238.9 °.Assuming that 4 blades are ideal
Blade, resonant frequency 143.2Hz.Blade rotational speed is 1080r/min, when emulation a length of 12s, to the displacement data after emulation into
Row normalized, and add 10% white noise.The asynchronous vibration frequency of emulation is set as 5.3, then knows the simulation process middle period
The asynchronous vibration frequency of piece is：
ω*=5.3 × 1080/60=95.4Hz.
The first step：Seek folding frequency and phase value
For the Tip-Timing data of every Tip timing sensor monitoring, 128 points in emulation data are taken, using complete
Phase Fourier methods calculate folding frequency and corresponding phase value, as a result as shown in Figure 3.Folding frequency and corresponding phase value
Specific value is as shown in the table,
Table 1
Second step：Calculate phase difference
The phase value obtained according to previous stepWithCalculate measured phase difference of each sensor with respect to No. 0 sensor
And it is regular to [0,360 °), calculated result is as shown in table 2,
Table 2
Third step：Integer frequency traversal
Selecting the frequency multiplication of m to traverse range is 0-30.SE value is calculated with "-" and "-" respectively according to formula (5) and is normalized
Processing, traversing result are as shown in Figure 4.Specific evaluation is as shown in Table 3 and Table 4, and wherein table 3 is corresponding phaseCalculating knot
Fruit, table 4 are corresponding phaseCalculated result, wherein minimum value SE has carried out overstriking and underscore in the table.Corresponding phaseSE minimum value be 0.1012, corresponding m value be 13, corresponding symbol be "-".Corresponding phaseSE minimum value be
0.0043, corresponding m value is 5, and corresponding symbol is "+".
Table 3
Table 4
4th step：Obtain ω and ω '
According to formula (6) and previous step calculate as a result,
5th step：Calculate ωnAnd ωn′
According to formula (7) and previous step calculated result, obtain,
6th step：Calculate HJ, i(ω n) and HJ, i(ωn′)
The ω that previous step is calculated respectivelynAnd ωn' and emulation data bring into formula (8), calculate HJ, i(ω n) and HJ, i(ω
N '), due to HJ, i(ω n) and HJ, iThe data of (ω n ') are more, are not listed one by one herein.
7th step：Calculate Ri(ωn) and Ri(ωn′)
Previous step calculated result is brought into formula (9), R is calculatedi(ωn) and Ri(ωn') value as shown in table 5 and table 6.It will
It is as shown in Figure 5 that calculated result is drawn in line chart.
Table 5
Table 6
8th step：Compare Ri(ωn) and Ri(ωn') size
According to previous step calculated result, it is known that work as m=0, when 1,2,3, Ri(ωn) < Ri(ωn') set up.So blade
Vibration frequency is ω '=95.3438Hz.Identification Errors can be solved according to the following formula,
Then this Identification Errors Δ E=0.059% is obtained according to formula (11).Meet engine request, illustrates that this identification algorithm can
Row.For verification algorithm robustness, choosing simulation frequency respectively is 127.8Hz, 205.2Hz, 237.6Hz, and 266.4Hz is distinguished
Know, identification result and Identification Errors are as shown in table 7.Identification result is respectively less than 1%, meets requirement of engineering precision.
Table 7
Claims (1)
1. the anharmonic Fourier's analysis method of blade asynchronous vibration frequency under a kind of constant speed, characterized in that steps are as follows：
Rotor speed is Ω, and being followed successively by 0,1,2 using number ..., N branch Tip timing sensor supervises blade asynchronous vibration
It surveys：
Step 1：Seek folding frequency and phase value
All phase Fu is carried out to 2n-1 data of the vibration signal interception same time period of every Tip timing sensor monitoring
In leaf analysis obtain spectrum analysis as a result, finding out the corresponding Frequency point of peak value spectral line in [- Ω/2,0] and [0, Ω/2] range | Δ
F |, then find out the corresponding phase value of this peak valueWithWherein i=0,1,2 ... N indicate corresponding sensor serial number；
Step 2：Calculate phase difference
The phase value obtained according to previous stepWithHere with phaseFor, according toIt calculates each sensor and is passed with respect to No. 0
The measured phase difference of sensorAnd it is regular to [0,360 °), respective phase difference should be written as：
M-vibration frequency multiplication integer part
ai- Tip timing sensor setting angle
Assuming that correctly m value is m*, measured phase difference size isIt is expressed as a vector：
Step 3：Frequency multiplication integer traversal
The m value that traversal is chosen is mk, phase difference is calculated according to (1) formulaAnd it is regular to [0,360 °), be expressed as a vector：
Step 4：, blade asynchronous vibration frequencies omega is obtained by error analysis
Survey phase delta Ф*With traversal phase delta ФkIt compares, acquires error Ek,
With error EkRoot-mean-square value SE indicate phase difference traversal estimated value deviate actual measured value size：
The presence for considering error takes the corresponding frequency multiplication m of obvious the smallest SE in traversal rangekAs actual m*, to pick out
The frequency of blade asynchronous vibration：
ω=mkΩ+△ f or ω=mkΩ-△f (6)
Due to there is " ± " symbol in formula (1), to mkIt is traversed, need to be calculated respectively by "+" and "-", common relatively SE's is big
It is small, so that it is determined that a mkCorresponding "+" or "-" oeprator in value and formula (1)；
Step 5：Step 2 is repeated to step 4, is obtained based on phaseThe blade asynchronous vibration frequencies omega of calculating '；
Further：The probable value ω and ω ' of blade asynchronous vibration frequency estimation is calculated according to formula (7), obtains ωnWith
ωn', wherein [x] indicates that Ω is speed-frequency to x round numbers part：
Further：Anharmonic Fourier analysis expression such as formula (8) is shown, wherein Hj,i(ω) indicates analyzed signal yj,i
Middle frequency is the amplitude for the sensor monitoring that ω number is i, by ω obtained in the previous stepnAnd ωn' bring formula (8) into respectively, it obtains
Corresponding Hj,iValue；
Hj,i(ω)=a (ω) Cj,i(ω)+b(ω)Sj,i(ω)
Cj,i(ω)=cos (2 π (j- (np+1)/2)ω/F)
Sj,i(ω)=sin (2 π (j- (np+1)/2)ω/F)
Wherein, ω-analysis frequency；
J-sequence of data points；
np- data point sum；
F-sample frequency；
yj,i- analyzed signal.
Every Tip timing sensor is calculated according to formula (8) respectively, successively obtains Hj,0(ωn), Hj,0(ωn'), Hj,1
(ωn), Hj,1(ωn') ..., Hj,N(ωn), Hj,N(ωn′)；
Further：The corresponding R of every Tip timing sensor is calculated according to formula (9)i(ωn) and Ri(ωn′)
Wherein i representative sensor is numbered；
Further：Compare Ri(ωn) and Ri(ωn') size of value；
If for i=0,1 ... N, Ri(ωn)>Ri(ωn') set up, then blade asynchronous vibration frequency values are ω, and otherwise blade is asynchronous
Vibration frequency value is ω '.
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| CN110530495A (en) * | 2019-09-10 | 2019-12-03 | 长沙理工大学 | A kind of cutting polarization monitoring method based on vibration analysis |
| CN110686764A (en) * | 2019-09-17 | 2020-01-14 | 天津大学 | Method for measuring asynchronous vibration frequency of constant-speed blade based on full-phase difference principle |
| CN111175033A (en) * | 2020-01-10 | 2020-05-19 | 中国人民解放军国防科技大学 | Method for reconstructing timing signal of synchronous vibration blade end under variable rotating speed |
| CN112903271A (en) * | 2021-01-22 | 2021-06-04 | 中国航发沈阳发动机研究所 | Non-contact asynchronous vibration parameter identification method for rotor blade |
| CN113404555A (en) * | 2021-05-18 | 2021-09-17 | 西安交通大学 | Blade natural frequency identification method based on multiple blade end timing sensors |
| CN114812794A (en) * | 2022-01-12 | 2022-07-29 | 天津大学 | Method for correcting blade tip timing parameter identification error caused by frequency sweep rate |
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| CN110686764A (en) * | 2019-09-17 | 2020-01-14 | 天津大学 | Method for measuring asynchronous vibration frequency of constant-speed blade based on full-phase difference principle |
| CN111175033A (en) * | 2020-01-10 | 2020-05-19 | 中国人民解放军国防科技大学 | Method for reconstructing timing signal of synchronous vibration blade end under variable rotating speed |
| CN111175033B (en) * | 2020-01-10 | 2021-08-13 | 中国人民解放军国防科技大学 | Method for reconstructing timing signal of synchronous vibration blade end under variable rotating speed |
| CN112903271A (en) * | 2021-01-22 | 2021-06-04 | 中国航发沈阳发动机研究所 | Non-contact asynchronous vibration parameter identification method for rotor blade |
| CN113404555A (en) * | 2021-05-18 | 2021-09-17 | 西安交通大学 | Blade natural frequency identification method based on multiple blade end timing sensors |
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