CN105466550A - Inhomogeneous undersampled blade end timing vibration signal reconstruction method and device - Google Patents

Abstract

The invention provides an inhomogeneous undersampled blade end timing vibration signal reconstruction method and device, and the method comprises the following steps: 1), obtaining inhomogeneous blade end displacement sampling data through employing a blade end timing vibration measurement system; 2), determining the vibration characteristics and frequency band range of a high-speed blade; 3), achieving the interpolation reconstruction of a blade vibration signal based on a periodic inhomogeneous sampling principle. The method causes no deviation and aliasing during signal reconstruction.

Description

Non-uniform under-sampling leaf end timing vibration signal reconstruction method and device

Technical Field

The invention relates to the technical field of blade vibration signal online monitoring, in particular to a non-uniform under-sampling blade end timing vibration signal reconstruction method and a device thereof.

Background

High cycle fatigue is a common failure of high speed blades of rotating machinery such as gas turbines, aircraft engines and the like, and often occurs in the operation process of equipment, and causes cracks, fractures and even disastrous accidents of the blades. Blade vibration is a direct cause of high cycle fatigue. Especially, when the vibration frequency reaches synchronous vibration of integral multiple of the rotation speed cycle, the induced synchronous resonance can continuously increase the vibration amplitude and the borne stress of the blade, and huge irreversible damage is caused to the blade. Therefore, the vibration generated by the rotating blade is monitored on line, the stress distribution which has potential harm to the blade can be effectively avoided, and the method has important significance for ensuring the safe and stable operation of the rotating machine.

Since the 60's of the 20 th century, non-contact tip timing measurement methods have been widely used in online monitoring of blade vibration. Compared with the traditional strain gauge contact measurement method, the method has the outstanding advantages of simple structure, convenience in installation, high sensitivity, capability of simultaneously measuring the vibration conditions of all the blades and the like. Non-contact tip timing measurements record the time a blade passes over a sensor by a set of tip timing sensors mounted circumferentially on the casing. When the blade does not vibrate, the reference time of the blade reaching the sensor is only related to the rotating speed, the radius of the blade and the installation included angle of the sensor; when the blade vibrates, the actual time of the blade reaching the sensor is advanced or lagged behind the reference time, so that a time difference is generated. The time difference signal sequence is processed to obtain a vibration displacement sequence of the blade end of the rotating blade, so that various vibration characteristics of the blade can be estimated.

The method adopts a leaf end timing measurement method to carry out vibration monitoring, and undersampling is an important technical problem which needs to be solved. The sampling frequency of the timing measurement of the blade end depends on the rotating speed and the number of the sensors, and is limited by factors such as sensor installation cost, space and the like in actual working conditions, and the number of the timing sensors of the blade end is generally small, so that the sampling frequency of the timing sensors of the blade end is generally far lower than the natural frequency of a high-speed blade. Therefore, the sampling process does not satisfy the nyquist sampling theorem, so that the obtained sampling signals are mixed up and cannot truly reflect the vibration behavior of the blade, and the signals must be reconstructed to obtain accurate blade vibration characteristics.

Currently, research on a reconstruction algorithm of a leaf-end timing signal mainly focuses on reconstructing an asynchronous vibration signal by using a uniform sampling method, for example, CN201310460647.8 discloses an aliasing-free reconstruction method of a high-speed leaf-under-sampled leaf-end vibration signal. However, blade synchronous vibration is more disruptive during operation of the apparatus, and uniform sampling is not conducive to monitoring blade synchronous vibration. When the synchronous vibration of the blade occurs, a plurality of sensors uniformly installed in the casing sample, and there is a possibility of sampling: a plurality of sensors acquire the same displacement point on the blade vibration waveform in a plurality of periods, so that the sampled data redundancy is caused, and the data analysis difficulty is increased sharply.

Disclosure of Invention

The invention aims to provide a non-uniform under-sampling blade end timing vibration signal reconstruction method and a device thereof, and solves the technical problem that only a method for reconstructing a signal aiming at a blade vibration signal obtained by uniform sampling exists in the prior art.

The invention provides undersamplingThe method for reconstructing the timing vibration signal of the blade end comprises the following steps of S100: acquiring vibration characteristic parameters and vibration displacement of the blade, and acquiring a blade end timing signal time sequence of the vibration displacement after the blade rotates for N circles; step S200: constructing a non-uniform sampling model of the timing vibration signals of the blade ends, wherein the model comprises the sum of the timing signals of the blade ends uniformly sampled in multiple paths and the vibration signals r (t) of the blades, and accordingly sampling by adopting the model to obtain the timing signals of the uniformly sampled blade ends; step S300: an interpolation function S is constructed for each path of evenly sampled leaf end timing signals_i(t), obtaining a reconstruction formula of the leaf end timing vibration signal in a frequency domain, carrying out inverse Fourier transform on the reconstruction formula to obtain a time domain reconstruction formula of the leaf end timing vibration signal, and reconstructing a leaf end timing signal time sequence according to time domain reconstruction; the rotational frequency of the blades is constant.

Further, the vibration characteristic parameter of the blade includes an estimated value of a natural frequency of the bladeVibration bandwidth B and vibration mode; further comprising step S110: determining the frequency band of the blade, the frequency band being the signal frequency band [ f₀-B₀/2,f₀+B₀/2]Wherein: f. of₀Is a center frequency, B₀Is the bandwidth; the leaf-end timing vibration signal belongs to a frequency band,

further, the leaf-end timing vibration signal non-uniform undersampling model is formula (2):

$x\left(t\right)=r\left(t\right)\underset{i=1}{\overset{I-1}{\Σ}}\underset{n=1}{\overset{N-1}{\Σ}}\mathrm{\δ}(t-\frac{n}{f_r}-\frac{{\mathrm{\α}}_i}{2{\mathrm{\πf}}_r})---\left(2\right)$

where r (t) is the true blade vibration signal, and x (t) is the displacement sampling data of the blade tip, which is the dirichlet function.

Further, the reconstruction formula of the leaf-end timing vibration signal in the frequency domain is formula (3):

$R_1\left(f\right)=\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_i\left(f\right)\underset{n=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}R(f-{\mathrm{nf}}_r)e^{-{\mathrm{jn\α}}_i}---\left(3\right)$

wherein R (f) is the power spectrum of r (t), S_i(f) Is S_i(t) power spectrum, R₁(f) To reconstruct the power spectrum of the tip-timed vibration signal, α_iFor the mounting angle of the ith leaf-end timing sensor, j is according to B₀/f_rDividing the original leaf-end timing signal frequency band into the jth sub-band of the plurality of sub-bands, f_rIs the rotational frequency of the blade.

Further, step S300 includes the following steps: step S310: calculating a replica signal index in the sub-band due to undersampling;

step S320: with R₁(f) R (f), resulting in a system of equations for cancellation of the replica signal:

$\{\begin{array}{c}\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_{i,j}\left(f\right)=1\\ \underset{i=0}{\overset{I-1}{\Σ}}{S}_{i,j}\left(f\right)e^{-{\mathrm{jn\α}}_i}=0,\∀n\∈Z,n\≠0\end{array}---\left(4\right)$

wherein Z is an integer field, S_i,j(f) Is S_i(f) Solving formula (4) to obtain S at the jth component in the given sub-band_i(f) (ii) a Step S330: will S_i(f) Substituting the formula (3) into a formula (3), and constructing a reconstruction formula of the leaf end timing vibration signal in a frequency domain; b is₀/f_rLess than the number I of tip timing sensors.

Further, the vibratory displacement of the blade is obtained according to equation (1):

$x\left(t_{i,n}^k\right)=R\[({\mathrm{\α}}_i-{\mathrm{\θ}}_k)+2\mathrm{\π}n-2{\mathrm{\πf}}_r{t}_{i,n}^k\]---\left(1\right);$ wherein:showing the vibration displacement of the kth blade through the ith blade end timing sensor in the nth rotating speed period,representing the actual arrival time of the kth blade past the ith tip timing sensor during the nth speed cycle, α_iRepresenting the mounting angle, theta, of the ith blade-end timing sensor_kDenotes the kth

The position of each blade, R represents the distance from the blade end of the blade to the central axis of rotation, f_rIs the rotational frequency of the blade.

In another aspect of the inventionThe device for the method for reconstructing the timing vibration signal of the undersampled leaf end comprises the following steps: a signal acquisition module: the system comprises a blade end timing signal time sequence acquisition module, a vibration characteristic parameter acquisition module, a vibration displacement acquisition module and a control module, wherein the blade end timing signal time sequence acquisition module is used for acquiring a vibration characteristic parameter and a vibration displacement of a blade and acquiring a blade end timing signal time sequence of the vibration displacement after the blade rotates for N circles; constructing a sampling module: the method is used for constructing a non-uniform sampling model of the timing vibration signals of the blade end, the model comprises the sum of the timing signals of the blade end and the blade vibration signals r (t) of multiple paths of uniform sampling, and accordingly the uniform sampling blade end timing signals are obtained after sampling is carried out by adopting the model; a reconstruction module: for constructing interpolation function S for each path of uniformly sampled leaf-end timing signals_i(t), obtaining a reconstruction formula of the leaf end timing vibration signal in a frequency domain, carrying out inverse Fourier transform on the reconstruction formula to obtain a time domain reconstruction formula of the leaf end timing vibration signal, and reconstructing a leaf end timing signal time sequence according to time domain reconstruction; the rotational frequency of the blades is constant.

Further, the signal acquisition module further comprises a frequency band determination module for determining the frequency band of the blade, the frequency band being the signal frequency band [ f ]₀-B₀/2,f₀+B₀/2]Wherein: f. of₀Is a center frequency, B₀Is the bandwidth; the leaf-end timing vibration signal belongs to a frequency band, $f_0={\stackrel{\‾}{f}}_N.$

further, the reconstruction module further comprises: a replica signal index module: for calculating an index of the replica signal in the sub-band due to undersampling;

a replica signal cancellation module: for using R as₁(f) R (f), resulting in a system of equations for cancellation of the replica signal:

$\{\begin{array}{c}\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_{i,j}\left(f\right)=1\\ \underset{i=0}{\overset{I-1}{\Σ}}{S}_{i,j}\left(f\right)e^{-{\mathrm{jn\α}}_i}=0,\∀n\∈Z,n\≠0\end{array}---\left(4\right)$

wherein Z is an integer field, S_i,j(f) Is S_i(f) Solving formula (4) to obtain S at the jth component in the given sub-band_i(f) (ii) a A reconstruction formula generation module: for mixing S_i(f) Substituting the formula (3) into a formula (3), and constructing a reconstruction formula of the leaf end timing vibration signal in a frequency domain.

The invention has the technical effects that:

the under-sampling blade end timing vibration signal reconstruction method provided by the invention can realize reconstruction of the blade vibration signal obtained by non-uniform sampling, avoid data redundancy and improve the accuracy of blade vibration analysis and fault monitoring.

2. The method provided by the invention is simple in calculation process and easy to realize.

3. The method provided by the invention has the advantages of no deviation and no aliasing of the reconstructed signal.

4. The method provided by the invention can be used for signal reconstruction aiming at uniform or non-uniform leaf end sampling.

5. The method provided by the invention provides real and reliable high-speed blade vibration characteristics.

6. The under-sampling leaf-end timing vibration signal reconstruction device provided by the invention has the advantages of simple calculation process, easiness in realization, and no deviation and aliasing of the reconstructed signal.

Drawings

FIG. 1 is a schematic flow chart diagram of a preferred embodiment of a method for reconstructing a timing vibration signal of an under-sampled leaf tip provided by the present invention;

FIG. 2 is a schematic diagram of non-uniform sampling interpolation reconstruction in a preferred embodiment of the method for reconstructing a timing vibration signal at an under-sampled leaf-end provided by the present invention;

FIG. 3 is a schematic structural diagram of an apparatus for providing a method for reconstructing a timing vibration signal of an under-sampled leaf-end according to the present invention;

FIG. 4 is a schematic structural diagram of a leaf-end timing signal acquisition device used in a preferred embodiment of the under-sampling leaf-end timing vibration signal reconstruction method provided by the present invention;

FIG. 5 is a schematic diagram of a frequency spectrum of any one uniform sampling in leaf-end non-uniform sampling according to a preferred embodiment of a reconstruction method of an under-sampled leaf-end timing vibration signal provided by the present invention;

FIG. 6 is a schematic diagram of four-path high-speed pulse signals output by an optical fiber sensor in a preferred embodiment of the method for reconstructing the under-sampled leaf-end timing vibration signal provided by the invention;

FIG. 7 is a schematic diagram of a blade vibration frequency spectrum obtained by reconstructing a blade vibration signal according to a preferred embodiment of the method for reconstructing a timing vibration signal of an undersampled blade tip provided by the present invention.

Illustration of the drawings:

110. a first fiber optic leaf end timing sensor; 120. a second fiber optic leaf end timing sensor; 130. a third fiber optic leaf end timing sensor; 210. a rotational speed synchronization sensor; 310. a leaf disc; 410. a high-speed pulse collector; 510. collecting cards; 610. and (4) a computer.

Detailed Description

The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention.

The reconstruction method provided by the invention is particularly suitable for reconstructing signals such as vibration displacement of the high-speed blade.

Referring to fig. 1, the method for reconstructing the timing vibration signal of the under-sampled leaf end comprises the following steps:

step S100: acquiring vibration characteristic parameters and vibration displacement of the blade, and acquiring a blade end timing signal time sequence of the vibration displacement after the blade rotates for N circles;

step S200: constructing a non-uniform sampling model of the timing vibration signals of the blade ends, wherein the model comprises the sum of the timing signals of the blade ends uniformly sampled in multiple paths and the vibration signals r (t) of the blades, and accordingly sampling by adopting the model to obtain the timing signals of the uniformly sampled blade ends;

step S300: an interpolation function S is constructed for each path of evenly sampled leaf end timing signals_i(t), obtaining a reconstruction formula of the leaf end timing vibration signal in a frequency domain, carrying out inverse Fourier transform on the reconstruction formula to obtain a time domain reconstruction formula of the leaf end timing vibration signal, and reconstructing a leaf end timing signal time sequence according to time domain reconstruction; the rotational frequency of the blades is constant. Referring to fig. 1 and 2, the method provided by the invention converts the non-uniformly sampled blade end vibration signal r (t) into a uniformly sampled signal through a sampling model, and performs interpolation reconstruction on the uniformly sampled signal to obtain a reconstruction formula capable of reconstructing the non-uniformly sampled blade end vibration signal.

The method specifically comprises the following steps:

the blade end timing measurement system in the step (1) comprises a series of blade end timing sensors arranged on a casing of an engine shell along the circumferential direction, a rotating speed synchronization sensor, high-speed pulse regulation and acquisition equipment and a computer. The tip timing sensors of the present invention include, but are not limited to, fiber optic or capacitive tip timing sensors.

The non-uniform sampling in the step (1) means that the blade end timing sensors of the measuring system are installed on an engine shell casing at unequal intervals along the circumferential direction, so that the continuous sampling intervals of the blade end timing data are non-uniform. It is emphasized that the present invention is not only applicable to non-uniform sampling, but also to uniformly sampled blade-end timing signal reconstruction for high-speed blades.

Step (1), the blade end displacement sampling data is related to the arrival time of the blade passing through a blade end timing sensor, and the method comprises the following substeps:

and (1-1) determining the time for the blade to reach the blade end sensor. When each blade on the blade disc passes through each blade end timing sensor and the synchronous reference sensor, a pulse is generated, and the time of each blade passing through each blade end timing sensor can be calculated by using a pulse counting method.

And (1) calculating the displacement data of the leaf end. The number of timing sensors at the blade end is recorded as I, the number of blades is recorded as K, and the rotation frequency of the blades is recorded as f_rThen, each blade rotates one circle to generate I actual arrival times, and the ith vibration displacement of the blade end of the blade in the nth rotation period can be obtained according to the I actual arrival times, and the expression is

$x\left(t_{i,n}^k\right)=R\[({\mathrm{\α}}_i-{\mathrm{\θ}}_k)+2\mathrm{\π}n-2{\mathrm{\πf}}_r{t}_{i,n}^k\]---\left(1\right)$

Wherein,representing the vibrational displacement of the kth blade through the ith sensor during the nth speed cycle,representing the actual arrival time of the kth blade past the ith sensor during the nth speed cycle, α_iIndicates the ith sensor mounting angle, theta_kDenotes the kth vane position, R denotes the distance of the vane tip from the center axis of rotation, f_rThe blade rotation frequency is adopted, further, after N circles of rotation, a time sequence of a timing signal at the blade end of each blade can be acquired, the length of the time sequence is N × I, the time sequence is an undersampled blade end timing signal, and the sampling frequency of a single sensor is f assuming that the blade rotation frequency is constant_s＝f_r；

Step (2) vibration characteristics of the high speed blade include, but are not limited to, natural frequency f_NThe vibration bandwidth B and the vibration mode thereof.

Step (2) frequency band is central frequency f₀Bandwidth B₀Signal band of (f)₀-B₀/2,f₀+B₀/2]It must be ensured that the true vibration signal lies within this frequency band, i.e. satisfies $\[f_N-B/2,f_N+B/2\]\⊆\[f_0-B_0/2,f_0+B_0/2\].$ Blade natural frequency estimationThe method can be carried out in one of three ways of dynamic model, finite element model or modal experiment test, so that the central frequency can be taken $f_0={\stackrel{\‾}{f}}_N.$

The interpolation reconstruction method based on the periodic non-uniform sampling theorem in the step (3) comprises the following substeps:

step (3-1) constructing a mathematical model of leaf end timing non-uniform sampling:

$x\left(t\right)=r\left(t\right)\underset{i=1}{\overset{I-1}{\Σ}}\underset{n=1}{\overset{N-1}{\Σ}}\mathrm{\δ}(t-\frac{n}{f_r}-\frac{{\mathrm{\α}}_i}{2{\mathrm{\πf}}_r})---\left(2\right)$

where r (t) is the true blade vibration signal, and x (t) is the displacement sampling data of the blade tip, which is the dirichlet function. The true blade vibration signal is here represented by a continuous function. In equation (2), the time series of tip displacement recorded by each sensor is uniform sampling with the rotation speed as the period, so that the non-uniform sampling can be decomposed into the sum of multiple paths of uniform sampling.

Step (3-2) constructs corresponding interpolation function S for each path of uniform sampling_i(t), then the reconstruction formula of the blade vibration signal in the frequency domain is:

$R_1\left(f\right)=\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_i\left(f\right)\underset{n=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}R(f-{\mathrm{nf}}_r)e^{-{\mathrm{jn\α}}_i}---\left(3\right)$

wherein: r (f) is the power spectrum of r (t), S_i(f) Is S_i(t) power spectrum, R₁(f) To reconstruct the power spectrum of the vibration signal.

And (3-3) constructing an interpolation function equation set based on the periodic non-uniform sampling theorem by taking the elimination of signal confusion as a target. The method is characterized by comprising the following substeps:

step (3-3-1) according to B₀/f_rThe original vibration signal frequency band of the blade is divided into a plurality of sub-frequency bands.

And (3-3-2) calculating a replica signal index in the sub-band due to undersampling.

In the step (3-3-3), the sub-band division modes of the uniformly sampled signals are the same, but as shown in the formula (3), the sub-bands are different in α_iCorresponding to different phase offsets, so that the contribution of each path of uniform sampling to the non-uniform sampling is different. To eliminate aliased replica signals so that R₁(f) With r (f) as the target, the following equation set is established by simultaneous paths of uniform sampling interpolation functions in each subband.

$\{\begin{array}{c}\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_{i,j}\left(f\right)=1\\ \underset{i=0}{\overset{I-1}{\Σ}}{S}_{i,j}\left(f\right)e^{-{\mathrm{jn\α}}_i}=0,\∀n\∈Z,n\≠0\end{array}---\left(4\right)$

Where j is the jth sub-band, Z is the integer field, S_i,j(f) Is S_i(f) The jth component within a given sub-band.

Step (3-4) solving the interpolation function equation set (4) in the step (3-3) to obtain S_i,j(f) Thereby obtaining S_i(f) Then, the structure can be made according to the formula (3)Establishing a frequency domain reconstruction formula of the blade vibration signal, and performing inverse Fourier transform to obtain a time domain reconstruction formula of the blade vibration signal, wherein B₀/f_rMust be less than the number I of tip timing sensors.

Referring to fig. 3, another aspect of the present invention provides an apparatus for the above method, the apparatus comprising a signal acquisition module: the system comprises a blade end timing signal time sequence acquisition module, a vibration characteristic parameter acquisition module, a vibration displacement acquisition module and a control module, wherein the blade end timing signal time sequence acquisition module is used for acquiring a vibration characteristic parameter and a vibration displacement of a blade and acquiring a blade end timing signal time sequence of the vibration displacement after the blade rotates for N circles;

constructing a sampling module: the method is used for constructing a non-uniform sampling model of the timing vibration signals of the blade end, the model comprises the sum of the timing signals of the blade end and the blade vibration signals r (t) of multiple paths of uniform sampling, and accordingly the uniform sampling blade end timing signals are obtained after sampling is carried out by adopting the model;

a reconstruction module: for constructing interpolation function S for each path of uniformly sampled leaf-end timing signals_i(t), obtaining a reconstruction formula of the leaf end timing vibration signal in a frequency domain, carrying out inverse Fourier transform on the reconstruction formula to obtain a time domain reconstruction formula of the leaf end timing vibration signal, and reconstructing a leaf end timing signal time sequence according to time domain reconstruction; the rotational frequency of the blades is constant. Through the device, the obtained blade vibration signals can be reconstructed, and the copied signals caused by non-uniform sampling are eliminated through reconstruction, so that the accuracy of the signals is improved.

Preferably, the signal acquisition module further comprises a frequency band determination module for determining a frequency band of the blade, the frequency band being a signal frequency band [ f ]₀-B₀/2,f₀+B₀/2]Wherein: f. of₀Is a center frequency, B₀Is the bandwidth; the leaf-end timing vibration signal belongs to a frequency band,by limiting the frequency band of the obtained blade vibration signal, the occurrence of problems such as aliasing of the sampled vibration signal can be reduced.

Preferably, the reconstruction module further comprises:

a replica signal index module: for calculating an index of the replica signal in the sub-band due to undersampling;

a replica signal cancellation module: for using R as₁(f) R (f), resulting in a system of equations for cancellation of the replica signal:

$\{\begin{array}{c}\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_{i,j}\left(f\right)=1\\ \underset{i=0}{\overset{I-1}{\Σ}}{S}_{i,j}\left(f\right)e^{-{\mathrm{jn\α}}_i}=0,\∀n\∈Z,n\≠0\end{array}---\left(4\right)$

wherein Z is an integer field, S_i,j(f) Is S_i(f) Solving formula (4) to obtain S at the jth component in the given sub-band_i(f)；

A reconstruction formula generation module: for mixing S_i(f) Substituting the formula (3) into a formula (3), and constructing a reconstruction formula of the leaf end timing vibration signal in a frequency domain. The module can effectively remove the confusion of the complex signals to the signals by the obtained reconstruction formula. The accuracy of the reconstructed signal is improved.

The specific embodiment is as follows:

the following describes a method for reconstructing a high-speed under-sampled leaf-end timing signal of a leaf according to the present invention with reference to a specific embodiment. Get B₀＝f_rAt this time, at least two sensors are needed to reconstruct the non-uniformly sampled signal, where I is 2.

(1) And acquiring non-uniform leaf end displacement sampling data by using a leaf end timing vibration measurement system.

Referring to fig. 4, a leaf-end timing signal acquisition device in the present embodiment is shown. The device is disposed on a casing (not shown) of the blisk 310. The center of the circle of the blade disc 310 is used as the center on the blade disc 310, the blade disc is equally divided into 16 parts, and 16 blades are arranged according to the number 1-16. The monitoring head of the fiber-optic leaf-end timing sensor is disposed opposite the periphery of the blisk 310. The rotational speed synchronous sensor 210 is arranged on the blade disc 310, and the detection head is arranged right opposite to the root of the blade. To detect various parameters during rotation of the blisk 310. The fiber-optic blade-end timing sensors include a first fiber-optic blade-end timing sensor 110, a second fiber-optic blade-end timing sensor 120, and a third fiber-optic blade-end timing sensor 130 that are spaced apart. The first fiber-optic blade-end timing sensor 110, the second fiber-optic blade-end timing sensor 120, and the third fiber-optic blade-end timing sensor 130 are embedded in the ring support 710 at regular intervals, wherein any 2 sensors vibration displacement sampling constitutes non-uniform sampling. The rotating speed synchronization sensor 210, the first optical fiber blade end timing sensor 110, the second optical fiber blade end timing sensor 120 and the third optical fiber blade end timing sensor 130 respectively transmit collected signals to the high-speed pulse collecting circuit 410. The high-speed pulse acquisition circuit 410 is in signal electrical connection with the acquisition card 510, and the acquisition card 510 is in signal electrical connection with the computer 61.

The structural parameters of blisk 310 are listed in table 1. The rotating speed of the blade disc 310 is 5000 rpm, the under-sampled blade end timing signal of each blade can be obtained by using the formula (1) when the blade disc 310 rotates, and the blade end timing sampling frequency of the optical fiber blade end timing sensor and the rotating speed synchronous sensor 210 is f_r＝83.3Hz。

TABLE 1 leaf disc structure parameter table

Parameter(s)	Structural parameters
		Leaf disc structure material	No. 45 steel
Number of blades	16
		Blade length	45mm
Width of blade	20mm
		Thickness of blade	2mm
Distance of blade end to center of rotation	95mm

(2) Determining frequency band range of high speed blade vibration characteristics

In this embodiment, a finite element modeling and simulation method is adopted to obtain an estimated value of the first-order natural frequency of each bladeAbout 827.5Hz, so the center frequency is taken as f₀827 Hz; further, select B₀＝f_r83.3 Hz. The signal band of the signal to be reconstructed is then [743.7,910.3 ]]Hz。

(3) Interpolation reconstruction of blade vibration signal based on period non-uniform sampling theorem

In this embodiment, the first fiber-optic-blade-end timing sensor 110 and the second fiber-optic-blade-end timing sensor 120 are used to perform non-uniform interpolation reconstruction, and at this time, B is calculated according to equations (3) and (4)₀＝f_rWhen 83.3Hz, the reconstruction formula of the following formula (5) can be obtained:

$r_1\left(t\right)=\underset{n=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}r\left(\frac{n}{B_0}\right)S(t-\frac{n}{B_0})+r(\frac{n}{B_0}+\frac{{\mathrm{\α}}_1}{2{\mathrm{\πB}}_0})S(-t+\frac{n}{B_0}+\frac{{\mathrm{\α}}_1}{2{\mathrm{\πB}}_0})---\left(5\right)$

where S (-) is the interpolation function:

wherein f is_L＝f₀-B₀/2，

Based on the periodic non-uniform sampling theorem, as shown in fig. 2, an interpolation function is first created for each path of uniformly sampled signals recorded by the sensors. Because B₀＝f_rAs shown in fig. 5, each path of original signal interval of the uniform sampling signal is divided into 2 sub-bands, each sub-band establishes an interpolation function equation set, and an interpolation function S (-) is solved; the undersampled leaf end timing signals collected by the first optical fiber leaf end timing sensor 110 and the second optical fiber leaf end timing sensor 120 respectively correspond to the time sequenceAndthus, the original leaf-end timing signal obtained by undersampling can be reconstructed according to the formula (5).

The effect of the method of the present invention is further demonstrated by the following experiments.

In order to compare the method of the present invention with the existing reconstruction method of the uniform undersampled leaf end timing signal, the experimental test apparatus shown in fig. 4 is adopted, and the signal pulses acquired by the first optical fiber leaf end timing sensor 110, the second optical fiber leaf end timing sensor 120, the third optical fiber leaf end timing sensor 130 and the rotational speed synchronization sensor 210 are transmitted to the high-speed pulse collector 410, so as to obtain four paths of high-speed pulse signals shown in fig. 6.

With the blade with the number of 1 as an object, the signals output by the first optical fiber blade end timing sensor 110 and the second optical fiber blade end timing sensor 120 are used for calculating to obtain an undersampled blade end timing signal according to the formula (1), and the method is used for reconstructing the undersampled blade end timing signal, so that the obtained frequency spectrum is the signal reconstruction result shown by the solid line in fig. 7.

Then, the output signals of the first optical fiber leaf end timing sensor 110, the second optical fiber leaf end timing sensor 120, and the third optical fiber leaf end timing sensor 130 are used to obtain a leaf end timing signal that is uniformly undersampled, and an existing reconstruction method (for example, the method disclosed in CN 201310460647.8) of the uniformly undersampled leaf end timing signal is used to reconstruct the signal of the leaf end timing signal, and the obtained frequency spectrum is shown by a dotted line in fig. 7. Comparing the solid and dashed lines in FIG. 7, it can be seen that both clearly distinguish the natural frequency of vibration of the blade as 833.5Hz, thus demonstrating the feasibility and effectiveness of the method of the present invention.

It will be clear to a person skilled in the art that the scope of the present invention is not limited to the examples discussed in the foregoing, but that several amendments and modifications thereof are possible without deviating from the scope of the present invention as defined in the attached claims. While the invention has been illustrated and described in detail in the drawings and the description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments.

Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the term "comprising" does not exclude other steps or elements, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims shall not be construed as limiting the scope of the invention.

Claims (9)

1. A non-uniform under-sampling leaf-end timing vibration signal reconstruction method is characterized by comprising the following steps:

step S100: acquiring vibration characteristic parameters and vibration displacement of the blade, and acquiring a blade end timing signal time sequence of the vibration displacement after the blade rotates for N circles;

step S200: constructing a non-uniform sampling model of the blade end timing vibration signals, wherein the model comprises the sum of a plurality of paths of uniformly sampled blade end timing signals and a blade vibration signal r (t), and accordingly sampling is carried out by adopting the model to obtain uniformly sampled blade end timing signals;

step S300: constructing an interpolation function S for each path of uniformly sampled leaf-end timing signals_i(t) obtaining a reconstruction formula of the leaf end timing vibration signal in a frequency domain, performing inverse Fourier transform on the reconstruction formula to obtain a time domain reconstruction formula of the leaf end timing vibration signal, and reconstructing the time sequence of the leaf end timing signal according to the time domain reconstruction;

the rotational frequency of the blades is constant;

the vibratory displacement is acquired by a first blade end timing sensor and a second blade end timing sensor mounted in the casing.

2. The method of claim 1, wherein the vibration characteristics of the blade comprise an estimate of the natural frequency of the bladeVibration bandwidth B and vibration mode;

further comprising step S110: determining a frequency band of the blade, the frequency band being a signal frequency band [ f ]₀-B₀/2,f₀+B₀/2]Wherein: f. of₀Is a center frequency, B₀Is the bandwidth; the tip timing vibration signal belongs to the frequency band,

3. the non-uniform under-sampling leaf-end timing vibration signal reconstruction method according to claim 2, wherein the leaf-end timing vibration signal non-uniform under-sampling model is formula (2):

$x\left(t\right)=r\left(t\right)\underset{i=1}{\overset{I-1}{\Σ}}\underset{n=0}{\overset{N-1}{\Σ}}\mathrm{\δ}(t-\frac{n}{f_r}-\frac{{\mathrm{\α}}_i}{2{\mathrm{\πf}}_r})---\left(2\right)$

where r (t) is the true blade vibration signal, and x (t) is the displacement sampling data of the blade tip, which is the dirichlet function.

4. The non-uniform under-sampling leaf-end timing vibration signal reconstruction method according to claim 3, wherein the reconstruction formula of the leaf-end timing vibration signal in the frequency domain is formula (3):

$R_1\left(f\right)=\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_i\left(f\right)\underset{n=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}R(f-{\mathrm{nf}}_r)e^{-{\mathrm{jn\α}}_i}---\left(3\right)$

wherein R (f) is the power spectrum of r (t), S_i(f) Is said S_i(t) power spectrum, R₁(f) To reconstruct the power spectrum of the tip-timed vibration signal, α_iFor the mounting angle of the ith leaf-end timing sensor, j is according to B₀/f_rDividing the original leaf-end timing signal frequency band into a jth sub-band, f, of a plurality of sub-bands_rIs the rotational frequency of the blade.

5. The non-uniform under-sampling leaf-end timing vibration signal reconstruction method according to claim 4, wherein the step S300 further comprises the steps of:

step S310: calculating a replica signal index in the sub-band due to undersampling;

step S320: with R₁(f) R (f), resulting in a system of equations for canceling the replica signal:

$\left\{\begin{array}{c}\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_{i,j}\left(f\right)=1\\ \underset{i=0}{\overset{I-1}{\Σ}}{S}_{i,j}\left(f\right)e^{-{\mathrm{jn\α}}_i}=0,\∀n\∈Z,n\≠0\end{array}\right.---\left(4\right)$

wherein Z is an integer field, S_i,j(f) Is S_i(f) Solving formula (4) to obtain S at the jth component in the given sub-band_i(f)；

Step S330: will S_i(f) Substituting the formula (3) into a formula (3), and constructing a reconstruction formula of the leaf end timing vibration signal in a frequency domain;

B₀/f_rless than the number I of tip timing sensors.

6. The non-uniform under-sampling blade-end timing vibration signal reconstruction method according to any one of claims 1 to 5, wherein the vibration displacement of the blade is obtained according to formula (1):

$x\left(t_{i,n}^k\right)=R\[({\mathrm{\α}}_i-{\mathrm{\θ}}_k)+2\mathrm{\π}n-2{\mathrm{\πf}}_r{t}_{i,n}^k\]---\left(1\right);$

wherein:showing the vibration displacement of the kth blade through the ith blade end timing sensor in the nth rotating speed period,representing the actual arrival time of the kth blade past the ith tip timing sensor during the nth speed cycle, α_iRepresenting the mounting angle, theta, of the ith blade-end timing sensor_kDenotes the position of the kth blade, R denotes the distance of the blade tip from the center axis of rotation, f_rIs the rotational frequency of the blade.

7. An apparatus for a non-uniform under-sampling leaf-end timing vibration signal reconstruction method according to any one of claims 1 to 6, comprising:

a signal acquisition module: the system comprises a blade end timing signal time sequence acquisition module, a vibration characteristic parameter acquisition module, a vibration displacement acquisition module and a control module, wherein the blade end timing signal time sequence acquisition module is used for acquiring a vibration characteristic parameter and a vibration displacement of a blade and acquiring a blade end timing signal time sequence of the vibration displacement after the blade rotates for N circles;

constructing a sampling module: the model is used for constructing the non-uniform sampling model of the blade end timing vibration signals, the model comprises the sum of a plurality of paths of uniformly sampled blade end timing signals and a blade vibration signal r (t), and accordingly the uniformly sampled blade end timing signals are obtained after sampling is carried out by the model;

a reconstruction module: for constructing interpolation function S for each path of uniformly sampled leaf-end timing signals_i(t) obtaining a reconstruction formula of the leaf end timing vibration signal in a frequency domain, performing inverse Fourier transform on the reconstruction formula to obtain a time domain reconstruction formula of the leaf end timing vibration signal, and reconstructing the time sequence of the leaf end timing signal according to the time domain reconstruction;

the rotational frequency of the blades is constant.

8. The compound of claim 7, whereinThe device for reconstructing the timing vibration signal of the uniform undersampled blade end is characterized in that the signal acquisition module further comprises a frequency band determination module for determining the frequency band of the blade, wherein the frequency band is a signal frequency band [ f ]₀-B₀/2,f₀+B₀/2]Wherein: f. of₀Is a center frequency, B₀Is the bandwidth; the tip timing vibration signal belongs to the frequency band,

9. the non-uniform under-sampled leaf-tip timing vibration signal reconstruction apparatus of claim 8, wherein the reconstruction module further comprises:

a replica signal index module: for calculating a replica signal index in the sub-band due to undersampling;

a replica signal cancellation module: for using R as₁(f) R (f), resulting in a system of equations for canceling the replica signal:

$\left\{\begin{array}{c}\underset{i=0}{\overset{I-1}{\Σ}}{f}_r{S}_{i,j}\left(f\right)=1\\ \underset{i=0}{\overset{I-1}{\Σ}}{S}_{i,j}\left(f\right)e^{-{\mathrm{jn\α}}_i}=0,\∀n\∈Z,n\≠0\end{array}\right.---\left(4\right)$

wherein Z is an integer field, S_i,j(f) Is S_i(f) Solving formula (4) to obtain S at the jth component in the given sub-band_i(f)；

A reconstruction formula generation module: for mixing S_i(f) Substituting the formula (3) into a formula (3), and constructing a reconstruction formula of the leaf end timing vibration signal in a frequency domain.