CN113533529B - Method for extracting natural frequency difference between blades by single or uniformly distributed blade end timing sensor - Google Patents

Method for extracting natural frequency difference between blades by single or uniformly distributed blade end timing sensor Download PDF

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CN113533529B
CN113533529B CN202110708302.4A CN202110708302A CN113533529B CN 113533529 B CN113533529 B CN 113533529B CN 202110708302 A CN202110708302 A CN 202110708302A CN 113533529 B CN113533529 B CN 113533529B
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blade
frequency
data
blades
displacement
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CN113533529A (en
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杨志勃
曹佳辉
陈雪峰
王增坤
杨来浩
田绍华
李浩琪
李文博
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Xian Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/12—Analysing solids by measuring frequency or resonance of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms

Abstract

The invention discloses a method for extracting a difference value of natural frequencies among blades by a single or uniformly distributed blade end timing sensor, wherein in the method, the actual reaching time of a rotating blade is obtained by the single or uniformly distributed blade end timing sensor, and the difference between the theoretical reaching time and the actual reaching time is converted into displacement data of a blade end according to the rotating speed and the length of the rotating blade; selecting displacement data of blade ends of two rotating blades with the same rotating speed and the same blade length; intercepting the displacement data and respectively carrying out discrete Fourier transform, wherein the sampling frequency is approximate to the average rotating speed so as to obtain frequency spectrum data; and respectively extracting corresponding frequency remainders after the natural frequencies of the two blades are mixed and overlapped from the frequency spectrum data, and obtaining the natural frequency difference between the two blades by taking the difference of the two frequency remainders.

Description

Method for extracting natural frequency difference between blades by single or uniformly distributed blade end timing sensor
Technical Field
The invention belongs to the field of non-contact nondestructive testing of blades, and particularly relates to a method for extracting a natural frequency difference value between blades by a single or uniformly distributed blade end timing sensor.
Background
The rotor blade is a key part of large equipment such as a gas turbine, an aeroengine and the like, usually rotates at a high speed under the conditions of high temperature and high pressure, bears the action of cyclic alternating load and dynamic load such as centrifugal force, aerodynamic force and the like, has very complex working state and structural behavior, and is easy to generate vibration. Statistics show that the blade damage accident accounts for about one third of the total structure fault of the gas turbine, so that fault detection on the rotor blade is necessary. However, the conventional contact type blade vibration measurement and detection method, such as a strain gauge measurement method, needs to be stopped and is difficult to monitor the vibration conditions of all blades, the blades are in a working state for a long time, if the detection is only carried out in the stopped state, the use of equipment is delayed, the equipment cannot be monitored in the working process, and potential safety hazards remain, so that a more reasonable monitoring method is needed. Leaf-end Timing techniques (Blade Tip Timing,
BTT) is a method for measuring the vibration of a rotating blade on line in a non-contact manner, a blade end timing sensor is embedded into a static casing near the blade to realize the non-contact type vibration on-line measurement, but the blade end timing sampling rate is related to the rotating speed and the number of sensors, and the blade end timing data has a serious undersampling characteristic due to the fact that the installation position of the sensors is limited in practical situations. In actual use, a plurality of leaf end timing sensors are often selected to weaken aliasing influence caused by undersampling, but the plurality of leaf end timing sensors are installed in a practical limited space to cause great trouble, and the measurement cost is also increased. On one hand, the algorithms all involve a large amount of operations and cannot realize online real-time detection and diagnosis, and on the other hand, the algorithms directly identify parameters such as the natural frequency of a single blade and the like, so that large errors exist. Therefore, it is important to improve the leaf-end timing measurement method and the modal parameter identification method.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for extracting the difference value of the natural frequency between the blades by a single or uniformly distributed blade end timing sensor.
The invention aims to realize the purpose through the following technical scheme, and the method for extracting the difference value of the natural frequency between the blades by using the timing sensor at the single or uniformly distributed blade end comprises the following steps:
in the first step, a single blade end timing sensor or uniformly distributed blade end timing sensors are used for acquiring the actual reaching time of a rotating blade, and the difference between the theoretical reaching time and the actual reaching time is converted into displacement data of a blade end according to the rotating speed of the rotating blade and the length of the blade;
in the second step, the displacement data of the blade ends of two rotating blades with the same rotating speed and the same blade length are selected;
in the third step, intercepting the displacement data and respectively carrying out discrete Fourier transform, wherein the sampling frequency is approximate to the average rotating speed so as to obtain frequency spectrum data;
and in the fourth step, frequency remainders corresponding to the two blades after the natural frequencies are mixed and overlapped are respectively extracted from the frequency spectrum data, and the two frequency remainders are subjected to difference to obtain the natural frequency difference between the two blades.
In the method, in the first step, a single blade end timing sensor receives the reaching time t of each blade and the reaching time t is determined according to the rotating speed f of the blade r And the blade length R converts the difference between the theoretical arrival time and the actual arrival time into blade end displacement, and the expression is as follows:
Figure BDA0003130781270000021
wherein t is i，j Indicating the actual arrival time of the ith vane at the jth turn,
Figure BDA0003130781270000022
which represents the theoretical time of arrival of the signal,
Figure BDA0003130781270000023
wherein theta is i Indicating the angle, alpha, of the ith blade with respect to the mounting position of the rotation speed sensor k Indicates the angle of the kth sensor based on the mounting position of the rotation speed sensor, n is the rotation speed, and x (t) i，j ) Indicating the ith vane in the jth turn t i，j A shift in time.
The displacement data obtained by uniformly distributing the blade end timing sensors is actually obtained by fusing the displacement data respectively obtained by a plurality of single sensors according to the sequence that the blades pass through the sensors.
x(n p ·k+c i )＝x i (k) i＝1，2，…，n p
Wherein x (-) is data displacement data after multi-sensor fusion, k represents the number of turns, x i (k) The displacement value calculated when the blade passes the i-th sensor at the k-th turn is indicated, and the specific calculation method is described at the single sensor above. j denotes for the vane one revolution in the initial position, the i-th sensor is its c-th i And a passing sensor.
In the method, the rotation process of the blades is a predetermined acceleration process, a predetermined deceleration process or a predetermined uniform speed process, and the rotation process is stimulated by gas injection simulation gas with circumferentially uniformly distributed gas nozzles.
In the method, for the acceleration or deceleration process, the displacement data of the displacement sequence number interval near one displacement formant in the two blade displacements is selected, and the same displacement sequence number interval is selected in the other blade displacementDisplacement data of (2), sampling frequency f s Approximately equal to the average rotational speed of the motor,
Figure BDA0003130781270000031
the interception can be arbitrary: e.g. two displacement vectors L of length M 1 ，L 2 Selecting an index range [ Nl, N2 ]]I.e. intercept L 1 ，L 2 Index range of [ N1, N2 ]]The data in (c). But L 1 ，L 2 The displacement of two blades measured in the same experiment needs to be satisfied, and in addition, the required specifications are [ N1, N2 ]]The range is arbitrarily determined, and if it is measured data for the case of shifting, it is not preferable that the range is excessively long. The latter patent is how to intercept data to achieve better effect.
In the third step, the method carries out discrete Fourier transform on the two sections of intercepted discrete displacement data to obtain frequency spectrum data,
Figure BDA0003130781270000032
where x (n) is the sampled signal, i is an imaginary symbol,
Figure BDA0003130781270000033
n is the length of the acquired signal, the number of elements in X, N is an iteration number, and the data traverse from 0 to N-1, namely all elements in X are taken, k is an integer from 0 to N-1, and X (k)) represents the kth data after discrete Fourier transform.
In the fourth step, because the sampling frequency is equal to the rotating speed frequency, the aliasing condition of the rotating frequency and the frequency doubling is analyzed, the original signal sequence is subjected to discrete Fourier transform to obtain an undersampled frequency spectrum, the frequency appears near 0 frequency in the undersampled frequency spectrum, after the rotating speed frequency component is eliminated, the frequency in the undersampled frequency spectrum after the blade vibration frequency is mixed and overlapped is extracted, and the component with the highest amplitude value in the undersampled frequency spectrum is extracted to be called as a frequency remainder f sub Natural frequency difference
Figure BDA0003130781270000041
Figure BDA0003130781270000042
Referring to the frequency remainders of blade 2 and blade 1, respectively.
The method can extract the inherent frequency difference between different blades from the seriously undersampled data only by a single-blade-end timing sensor or uniformly distributed blade-end timing sensors without additional signal reconstruction and more blade-end timing sensors, has quick and stable operation, is simple and feasible, and can realize the real-time health monitoring of the rotating blades.
The above description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly apparent, and to make the implementation of the content of the description possible for those skilled in the art, and to make the above and other objects, features and advantages of the present invention more obvious, the following description is given by way of example of the specific embodiments of the present invention.
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Various additional advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is an experimental diagram of a blade end timing sensor measuring displacement of a rotating blade end;
FIG. 2 is a displacement diagram of displacement data of No. 1 blade captured during single-blade-end timing sensor after mean value removal;
FIG. 3 is a displacement diagram of No. 5 blade displacement data with the mean value removed, captured during single-blade-end timing sensor;
FIG. 4 is a DFT analysis amplitude-frequency diagram of a No. 1 blade undersampled signal during single-blade-end timing of a sensor;
FIG. 5 is a DFT analysis amplitude-frequency diagram of No. 5 blade undersampled signals at a single-blade-end timing sensor;
FIG. 6 is a displacement diagram of No. 1 blade displacement data after mean value removal intercepted when blade end timing sensors are uniformly distributed;
FIG. 7 is a displacement diagram of No. 5 blade displacement data after mean value removal intercepted when blade tip timing sensors are uniformly distributed in 2;
FIG. 8 is a DFT analysis amplitude-frequency diagram of No. 1 blade undersampled signals when 2 blade tip timing sensors are uniformly distributed;
FIG. 9 is a DFT analysis amplitude-frequency diagram of No. 5 blade undersampled signals when 2 blade tip timing sensors are uniformly distributed.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 9. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the present invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the convenience of understanding the embodiments of the present invention, the following detailed description will be given by way of example with reference to the accompanying drawings, and the drawings are not intended to limit the embodiments of the present invention.
The method for extracting the natural frequency difference between the blades by the single or uniformly distributed blade end timing sensor comprises the following steps,
the method for extracting the natural frequency difference between the blades comprises the following steps:
(1) The method comprises the steps of acquiring the reaching time of a rotating blade by using 1 blade end timing sensor or uniformly distributed blade end timing sensors, and converting the difference between the theoretical reaching time and the actual reaching time into blade end displacement according to the rotating speed and the length of the blade.
In the exemplary embodiment, the signals collected by the single-blade-end timing sensor and the signals collected by the 2 uniformly-distributed blade-end timing sensors are analyzed respectively, specifically, the single-fiber-type blade-end timing sensor and the 2 uniformly-distributed fiber-type blade-end timing sensor are fixed on a casing, the initial rotating speed is set to be 60Hz, the rotating speed acceleration is 0.5Hz/s, the rotating speed variation range is 60Hz-100Hz-60Hz, and the 100Hz constant speed period is 20s. The blade disc is an integral aluminum alloy blade disc with 8 blades, the radius of the blade disc is R =68mm, the thickness d =1mm, and the width w =20mm. 4 nozzles are uniformly distributed on a casing, high-pressure gas of 0.5Mpa is sprayed, the reaching time of the rotating blade is respectively obtained by utilizing a single blade end timing sensor and 2 uniformly distributed blade end timing sensors, and the theoretical reaching time difference and the actual reaching time difference are converted into blade end displacement according to the rotating speed and the blade length.
(2) Two pieces of displacement data of two blades to be analyzed at approximately the same rotational speed are selected. If the selected data is slow speed-up or slow speed-down data, the length of the intercepted data is not suitable to be too long so as to meet the requirement of approximate constant sampling frequency.
In the exemplary embodiment, specifically, the displacement data of the blade 1 and the blade 5 are selected, and the range of the intercepted data position serial number is [4719, 4959 ] for the displacement data collected by the single-blade-end timing sensor]The corresponding rotating speed variation range is as follows: 84.66 Hz-85.59 HzApproximate sampling frequency
Figure BDA0003130781270000061
The displacement graphs after the mean value of the displacement data intercepted by the blades No. 1 and No. 5 are shown in FIGS. 2 and 3. For the displacement data collected by the timing sensor with 2 uniformly distributed blade ends, the intercepted position serial number range is [9611, 9851 ]]The corresponding rotating speed variation range is as follows: 84.95 Hz-85.54 Hz, approximate sampling frequency
Figure BDA0003130781270000062
The displacement graphs after the mean value of the displacement data intercepted by the blades No. 1 and No. 5 are shown in FIGS. 6 and 7.
(3) Respectively carrying out discrete Fourier transform on the two sections of intercepted data, wherein the sampling frequency is approximate to the average rotating speed, and obtaining frequency spectrum data;
in the present exemplary example, the calculation formula of the discrete fourier transform is:
Figure BDA0003130781270000063
where x (n) is the sampled signal, i is an imaginary symbol,
Figure BDA0003130781270000064
n is the length of the collected signal, the number of elements in X is N is an iteration number, and the data traverse from 0 to N-1 is performed, namely all elements in X are taken, k is an integer from 0 to N-1, and X (k) represents the kth data after discrete Fourier transform.
(4) And extracting corresponding frequency remainders after the natural frequencies of the two blades are overlapped from the frequency spectrum data, and obtaining the natural frequency difference between the 2 blades by subtracting the two frequency remainders.
In the present exemplary embodiment, the following steps are specifically included:
a) Analyzing the frequency spectrum data, drawing a magnitude-frequency curve,
b) The rotating speed frequency component is eliminated, because the signal contains the vibration frequency component of the blade, the rotating frequency and the frequency multiplication thereof,because the sampling frequency is equal to the rotating frequency, the aliasing condition of the rotating frequency and the frequency multiplication thereof is analyzed, the frequency appears near 0 frequency in the undersampled frequency spectrum, after the rotating speed frequency component is eliminated, the frequency in the undersampled frequency spectrum after the blade vibration frequency is mixed and overlapped is extracted, and the frequency is called as the frequency remainder f sub 。
Figure BDA0003130781270000071
For the satisfaction of
Figure BDA0003130781270000072
Two blades of the condition, Δ f = Δ f, can also be directly obtained sub 。
[ application example ]
In the embodiment, signals acquired by the single-blade-end timing sensor and signals acquired by the 2 uniformly-distributed blade-end timing sensors are respectively analyzed, and the method provided by the invention is used for extracting the natural frequency difference between the blades so as to explain the method used in the single-blade-end timing sensor acquisition mode and the uniformly-distributed blade-end timing sensor acquisition mode.
As shown in a blade end timing test bed in figure 1, a single optical fiber type blade end timing sensor and 2 uniformly distributed optical fiber blade end timing sensors are fixed on a casing, the initial rotating speed is set to be 60Hz, the rotating speed acceleration is 0.5Hz/s, the rotating speed variation range is 60Hz-100Hz-60Hz, and the 100Hz constant speed section time is 20s. The blade disc is an integral aluminum alloy blade disc with 8 blades, the radius of the blade disc is R =68mm, the thickness d =1mm, and the width w =20mm. 4 nozzles are uniformly distributed on a casing, high-pressure gas of 0.5Mpa is sprayed, the reaching time of the rotating blade is obtained by utilizing a single blade end timing sensor and 2 blade end timing sensors uniformly distributed, and the difference between the theoretical reaching time and the actual reaching time is converted into blade end displacement according to the rotating speed and the length of the blade.
Specifically, the displacement data of the blade 1 and the blade 5 are selected, and the range of the serial number of the data position intercepted by the displacement data acquired by the timing sensor at the single blade end is [4719, 4959 ]]Corresponding speed variation rangeThe circumference is as follows: 84.66Hz to 85.59Hz, approximate sampling frequency
Figure BDA0003130781270000073
The schematic diagrams of the mean values of the displacement data of blade numbers 1 and 5 are shown in fig. 2 and 3. The position sequence number range of the displacement data collected by the timing sensor of the 2 uniformly distributed blade ends is [9611, 9851 ]]The corresponding rotating speed variation range is as follows: 84.95 Hz-85.54 Hz, approximate sampling frequency
Figure BDA0003130781270000074
The schematic diagrams of the mean values of the displacement data taken from blade nos. 1 and 5 are shown in fig. 6 and 7. And (3) respectively carrying out discrete Fourier transform on the two sections of intercepted data, wherein the sampling frequency is approximate to the average rotating speed, and obtaining amplitude-frequency graphs of the sections intercepted by the blades 1 and 5, wherein the amplitude-frequency graphs of the displacement data of the blades 1 and 5 obtained by the timing sensor at the single blade end are respectively shown in fig. 4 and 5, and the amplitude-frequency graphs of the displacement data of the blades 1 and 5 obtained by uniformly distributing the timing sensors at the blade end 2 are respectively shown in fig. 8 and 9.
Firstly, analyzing the amplitude-frequency diagram of the data obtained by the single-blade end timing sensor, namely, fig. 4 and fig. 5, wherein the analysis of the amplitude-frequency diagram of the blade 1 shows that the blade 1 generates synchronous resonance in the intercepted data segment, the natural frequency is equal to the frequency multiplication of the rotating speed, and the natural frequency is overlapped with the components of the rotating speed after the rotating speed frequency is overlapped at the position of 0.35Hz near the 0 frequency, so the natural frequency is overlapped with the components of the rotating speed frequency after the rotating speed frequency is overlapped, and the components are positioned at the position of 0.35Hz near the 0 frequency, therefore, the single-blade end timing sensor can obtain the data
Figure BDA0003130781270000081
In this case, the frequency component includes the energy of the natural frequency component of the blade vibration and the energy of the frequency conversion and frequency doubling component thereof, so the amplitude is 0.68. Analyzing the amplitude-frequency diagram of the blade 5 shows that the data segment intercepted by the blade 5 generates asynchronous vibration, and the undersampled frequency spectrum contains the frequency components of the rotating frequency and the frequency multiplication thereof after mixing and overlapping and the frequency components of the natural frequency of the blade 5 after mixing and overlapping. According to the amplitude-frequency diagram of the blade 1, the frequency component of 0.35Hz is the frequency component after the rotation frequency and the frequency multiplication thereof are mixed and overlapped, and the amplitude is 0.33; the frequency component of 19.09Hz is the frequency of the blade 5 after the natural frequency is mixed and overlappedThe component with the amplitude of 0.34Hz and the sum of the amplitudes of 0.67 is closer to 0.68 of the blade 1, which shows that the analysis result is credible, so the analysis result is reliable
Figure BDA0003130781270000082
Then, the amplitude-frequency diagrams of data obtained by the 2 equispaced blade end timing sensors are analyzed, namely, the diagrams of fig. 8 and 9 are analyzed, wherein the frequency residue of the blade 1 can be known by analyzing the amplitude-frequency diagrams of the blade 1
Figure BDA0003130781270000083
Analyzing the amplitude-frequency diagram of the blade 5 can find out the frequency remainder of the blade 5
Figure BDA0003130781270000084
Through modal experiment analysis, it can be known that the first-order natural frequencies of No. 1 blade and No. 2 blade of this aluminum alloy bladed disk are respectively: 341Hz, 361Hz, the inherent frequency difference is 20Hz, the inherent frequency difference between the actual blades is not too large, and the sampling frequency of the selected data segment is f s =85.125Hz, it is clear to satisfy
Figure BDA0003130781270000085
So that the difference Δ f = Δ f between the frequencies of the blade 1 and the blade 5 can be obtained by the method for extracting the difference between the natural frequencies of the blades of the single-blade-end timing sensor with the frequency remainder proposed by the patent of the present invention sub Further, the frequency difference between the blade 1 and the blade 5 obtained by analyzing the data of the single-blade-end timing sensor can be calculated as
Figure BDA0003130781270000086
Δ f =18.74Hz is thus available. The frequency difference of the blade 1 and the blade 5 obtained by analyzing the data of the 2 uniformly distributed blade end timing sensors is
Figure BDA0003130781270000087
The inherent frequency differences of the blades 1 and 5 obtained with the single sensor arrangement and the 2 equispaced sensor arrangement are very close, differing by only 0.33Hz.
The natural frequency of the rotating blade is measured by using a strain gauge and an electricity leading slip ring, and the natural frequency difference of the blade 1 and the blade 5 is 19Hz.
The inherent frequency difference measured by using the method provided by the invention is 18.74Hz and 18.41Hz, is very close to 19Hz measured by experiments, and the difference is only within 1Hz, and the method does not involve complex operation, and only needs to carry out discrete Fourier transform analysis on 2 groups of small data, so that the operation is fast and stable, is simple and feasible, and can realize real-time health monitoring of the rotating blade.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications to the disclosed embodiments without departing from the scope of the invention as defined by the appended claims.

Claims (6)

1. A method for extracting a difference in natural frequency between blades by a single or uniformly distributed blade tip timing sensor, the method comprising the steps of:
in the first step (S1), a single blade end timing sensor or uniformly distributed blade end timing sensors are used for obtaining the actual reaching time of a rotating blade, and the difference between the theoretical reaching time and the actual reaching time is converted into displacement data of the blade end according to the rotating speed of the rotating blade and the length of the blade;
in the second step (S2), the displacement data of the blade ends of two rotating blades with the same rotating speed and the same blade length are selected;
in the third step (S3), intercepting the displacement data and respectively carrying out discrete Fourier transform, wherein the sampling frequency is approximate to the average rotating speed so as to obtain frequency spectrum data;
in the fourth step (S4), frequency remainders corresponding to the two blades after the natural frequencies are overlapped are respectively extracted from the spectrum data, and the two frequency remainders are subtracted to obtain the natural frequency difference between the two blades.
2. A method according to claim 1, wherein in a first step (S1) a single tip timing sensor collects the arrival time t for each blade and is dependent on the rotational speed f of the blade r And the blade length R converts the difference between the theoretical arrival time and the actual arrival time into blade end displacement, and the expression is as follows:
Figure FDA0003589306800000011
wherein t is i，j Indicating the actual arrival time of the ith vane at the jth turn,
Figure FDA0003589306800000012
which represents the theoretical time of arrival of the signal,
Figure FDA0003589306800000013
wherein theta is i Indicating the angle, alpha, of the ith blade with respect to the mounting position of the rotation speed sensor k Indicates the angle of the kth sensor based on the mounting position of the rotation speed sensor, n is the rotation speed, and x (t) i，j ) Indicating the ith vane in the jth turn t i，j The displacement of the moment.
3. The method of claim 2, wherein the rotation process of the blade is a predetermined acceleration process, a predetermined deceleration process or a predetermined uniform velocity process, and the gas excitation is simulated by using circumferentially distributed gas nozzles for injecting gas during the rotation process.
4. A method according to claim 3, wherein for the ramping up or down process, the displacement data for the displacement number interval near one of the two blade displacements is selected, the displacement data for the same displacement number interval is selected for the other blade displacement, and the sampling frequency f is selected s Approximately equal to the average rotational speed of the motor,
Figure FDA0003589306800000014
wherein n is p Indicating the number of sensors, N 1 And N 2 Respectively representing the intercepted data index, f ri Indicates the ith numberAccording to the rotation speed at the sampling moment.
5. The method according to claim 1, wherein in the third step (S3), the truncated two-segment discrete displacement data is subjected to discrete Fourier transform to obtain frequency spectrum data,
Figure FDA0003589306800000015
where x (n) is the sampled signal, i is the imaginary symbol,
Figure FDA0003589306800000021
n is the length of the acquired signal, the number of elements in X, N is an iteration number, and the data traverse from 0 to N-1, namely all the elements in X are taken, k is an integer from 0 to N-1, and X (k) represents the kth data after discrete Fourier transform.
6. The method as claimed in claim 5, wherein in the fourth step (S4), since the sampling frequency is equal to the rotation speed frequency, the aliasing of the rotation frequency and the frequency multiplication thereof is analyzed, and the original signal sequence is subjected to discrete Fourier transform to obtain an undersampled frequency spectrum, wherein the frequency appears near 0 frequency in the undersampled frequency spectrum, after the rotation speed frequency component is eliminated, the frequency in the undersampled frequency spectrum after the mixing and overlapping of the blade vibration frequency is extracted, and the component with the highest amplitude value in the undersampled frequency spectrum is extracted to be called a frequency remainder f sub Natural frequency difference
Figure FDA0003589306800000022
Figure FDA0003589306800000023
f 1 sub Referring to the frequency remainders of blade 2 and blade 1, respectively.
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