CN114757071A - Method for predicting vibration pitch diameter number of blade disc based on vibration parameter period - Google Patents

Method for predicting vibration pitch diameter number of blade disc based on vibration parameter period Download PDF

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CN114757071A
CN114757071A CN202210375473.4A CN202210375473A CN114757071A CN 114757071 A CN114757071 A CN 114757071A CN 202210375473 A CN202210375473 A CN 202210375473A CN 114757071 A CN114757071 A CN 114757071A
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blade
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张荻
傅柏生
谢永慧
朱光亚
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Xian Jiaotong University
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Abstract

The invention discloses a method for predicting the vibration pitch diameter number of a blade disc based on a vibration parameter period, which comprises the following steps: obtaining a vibration signal of the rotating blade by a test method; preprocessing and denoising the obtained experimental data; then reconstructing the signal data; and identifying the pitch diameter number of the reconstructed signal. When pitch diameter number identification is carried out on the reconstructed signal, a vibration response curve of the whole circle of non-harmonious blades is obtained, and the resonant frequency period number W is extracted from the curve result1The number of cycles W of the resonance amplitude2And the mean value W of the vibration amplitude period number of the resonance interval3(ii) a Determining the range of pitch diameter number to be traversed from 0 to NbAnd/2, calculating the residual error e between the actual value and the predicted value of the three periodskThe mean square error value MSE is calculated by a weighting method, and the minimum mean square error of the nodal diameter number is traversedDetermining the initial value ND of pitch diameter0(ii) a When spatial wave aliasing is considered, the number of nodal diameters is calculated from the number of leaves. The invention can be suitable for a larger detuning state and provides a new effective idea for obtaining the modal shape pitch diameter number of the blade.

Description

Method for predicting vibration pitch diameter number of blade disc based on vibration parameter period
Technical Field
The invention belongs to the field of vibration analysis of turbine machinery blades, and particularly relates to a method for predicting the number of vibration pitch diameters of a blade disc based on a vibration parameter period.
Background
Along with the development trend of high power and changeable operating mode in the turbomachinery field, the operating mode of blade and rim plate is more and more abominable at the operation in-process of turbomachinery, often faces the condition of variable rotational speed and variable air intake situation, and then makes the blade wheel system to turbomachinery have higher vibration security requirement. Under the premise, the vibration condition of the blade disc needs to be detected, so that the working condition of the blade disc is predicted and monitored, and the normal operation of equipment is guaranteed.
In a general method for acquiring the vibration pitch diameter number of the blade disc, the problems that the blade vibration data is difficult to acquire, the signal data is seriously undersampled, the accurate prediction of the pitch diameter number of the blade disc is difficult under the influence of the non-harmonious blade disc structure and the deviation of a measurement system and the like exist. Therefore, a method for predicting the number of vibration pitch diameters of the blade disc is needed, which can overcome the structure and test system deviation and is suitable for a large detuning state so as to judge the vibration safety of the turbine machinery.
Disclosure of Invention
The invention aims to meet the high-speed, real-time and comprehensive detection requirements of turbomachinery, improve the working performance of a rotating blade measurement system and provide a method for predicting the vibration pitch diameter number of a blade disc based on a vibration parameter period.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a method for predicting blade disc vibration pitch diameter number based on vibration parameter period includes obtaining vibration response curve of whole circle of non-harmonious blade when pitch diameter number identification is carried out on reconstructed signal, extracting resonant frequency period number W from curve result1And the number W of resonant amplitude cycles2And vibration amplitude of resonance regionMean value of cycles W3(ii) a Then, determining the range of pitch diameter numbers 0-N to be traversedbAnd/2, calculating the residual error e between the actual value and the predicted value of the three periodskCalculating Mean Square Error (MSE) by a weighting method, and determining an initial value (ND) of the nodal diameter number by traversing the minimum mean square error of the nodal diameter number0(ii) a When spatial wave aliasing is considered, the number of nodal diameters is calculated from the number of leaves.
The invention is further improved in that the method comprises the following steps:
1) obtaining a vibration signal of the rotating blade by a test method;
2) carrying out data preprocessing on the obtained blade vibration signal, and denoising test data so as to improve the blade vibration signal obtaining precision;
3) based on a compressed sensing principle, performing signal reconstruction on the blade tip timing signal;
4) and identifying and predicting the number of vibration nodal diameters of the reconstructed signal.
The invention has the further improvement that in the step 1), No. 1-4 eddy current displacement sensors are respectively arranged at the corresponding preset positions of the test bracket to be used as blade tip timing sensors; a No. 0 eddy current displacement sensor is arranged to be aligned with the position of a rotating shaft key to serve as a rotating speed sensor, the blades are excited by using a high-speed airflow nozzle, and the rotating speed and the accelerating time of the blades are controlled by using a PLC (programmable logic controller).
The further improvement of the invention is that the specific implementation method of the step 1) comprises the following steps:
1-1) installing an eddy current displacement sensor: respectively installing No. 1-4 eddy current displacement sensors to corresponding preset positions of a test support to be used as blade tip timing sensors; installing a No. 0 eddy current displacement sensor to align to the position of a rotating shaft key to serve as a rotating speed sensor; a direct current power supply is adopted to supply power to the sensor, and a signal is output to a data acquisition unit for setting and debugging;
1-2) installing a test blade and a wheel disc: marking the blade number, and fixing the position of the wheel disc by using a locknut; adjusting the position height of the sensor, and calibrating; setting a rotating speed signal through a PLC and writing the rotating speed signal into a motor driver, wherein the rotating speed signal comprises a rotating speed value and acceleration time of each stage;
1-3) applying exciting force and collecting signals: starting an air compressor and a pressure stabilizing tank device, adjusting a valve until the air pressure is stable, and applying airflow excitation under preset pressure to the blade; blade tip timing method or strain gauge method is adopted to collect blade vibration signals under the working condition of constant speed or variable rotating speed, and multiple groups of data are collected for next signal processing;
1-4) repeating the steps 1-2) and 1-3), and acquiring blade vibration signals under different blade conditions and rotating speeds.
In a further improvement of the present invention, in step 2), the denoised signal WT (α, τ) is an inner product of the signal u (t) and the wavelet function Ψ (α, τ):
Figure BDA0003590560230000031
in the formula: WT (α, τ) -denoised signal; α -stretch factor; τ — translation factor; Ψ*-conjugation of Ψ.
The further improvement of the invention is that in the step 3), the blade vibration signal obtained by measurement is reconstructed by using a compressed sensing principle, so that the identification precision is ensured, and the measurement frequency range of the sensor is expanded, so that the measurement of the sensor can break through the limit of the Nyquist sampling theorem.
The invention is further improved in that when the blade vibration signals are reconstructed based on the compressed sensing principle, the periodic vibration of the multi-mode blade is formed by superposition of K simple harmonic vibration signals, namely
Figure BDA0003590560230000032
In the formula: y-oscillatory displacement, fi-the frequency of the ith harmonic; a. thei-cosine coefficients of the ith harmonic; b isi-the sine coefficient of the ith harmonic;
considering vibration displacement in discrete signal real space RMIn (b), the displacement dispersion signal is expressed as:
y＝[y1,y2，...yj,...yN] (3)
Figure BDA0003590560230000041
compressed sensing model of tip timing signal
Let z ∈ RQTo down-sample the resulting signal, consider the general down-sampling process:
z＝Φy (5)
Figure BDA0003590560230000042
in the formula:
Figure BDA0003590560230000043
-measuring the matrix;
Figure BDA0003590560230000044
-a unit row vector of length N;
phi is a sub-matrix of the identity matrix,
Figure BDA0003590560230000045
for determining whether to extract the corresponding element in y, i.e. the row vector in the identity matrix, in the sampling process:
Figure BDA0003590560230000046
when Q is<<N and
Figure BDA0003590560230000047
the selection of the leaf blade has random or non-uniformity, namely, the observation value z is randomly and non-uniformly obtained in a small amount from the original signal y, the leaf blade has the sampling characteristic under a compressed sensing frame, and the sparse expression of the leaf blade vibration displacement signal is substituted into the sparse expression to obtain the sparse expression of the leaf blade tip timing signal under the compressed sensing
z＝ΦΨs＝Θs (8)
In the formula: Ψ -sparse dictionary of sine-cosine transforms; Θ — the perceptual matrix; the measurement matrix phi is determined by the arrangement position of the blade tip timing sensor;
according to the compressed sensing principle, the reconstruction of the tip timing signal is changed into the optimization problem for constraint:
Figure BDA0003590560230000048
in the formula, L0Is 10Norm, namely counting the number of nonzero elements in s; employing l in the optimization objective1Norm to approximate l0Norm, which is to convert the combinatorial optimization problem into a convex optimization problem to complete the solution of the reconstruction signal, and indirectly reconstruct the signal by using a sparse greedy algorithm, that is, a target signal with the most sparsity is reconstructed based on a linear measurement-based tip timing signal z, that is:
Figure BDA0003590560230000051
In the formula:
Figure BDA0003590560230000052
-an index set; si-the ith element in the sparse vector s; thetai-column i of the perception matrix θ; the sparse approximation method is adopted to approximate the blade tip timing signal by gradually selecting the column vector of the perception matrix, so that the index set is gradually determined.
A further development of the invention is that, in step 4), N is assumedbNumber of blades, WexpFor the desired spatial wavenumber, WsTwo cases occur when the number of cycles of the space curve is obtained for the blade sampling:
when W isexp≤NbAt/2, the space wave can be identified as having WexpPeriodic curve, in this case Ws＝WexpAnd no aliasing occurs;
when W isexp>N b2, the number of blades is not sufficient to correctly disperse the particles with WexpPeriodic spatial curve, in which case the blade amplitude spatial wave appears aliased, the observed spatial wave having several periods W satisfying the following relationships：
Figure BDA0003590560230000053
The mode shape nodal diameter ND and the period number W are determined by aliasing of the space wavesIn a relationship of
Figure BDA0003590560230000054
Assuming that the number of resonance frequency cycles, the number of resonance amplitude cycles and the mean value of the number of amplitude cycles in the resonance range are W1、W2、W3Determining the range of the pitch diameter number ND to be considered according to the number Nb of the blades, taking the range as 0-Nb/2, traversing all values of the pitch diameter number ND, and calculating the predicted period number W expAnd the k-th vibration parameter period W obtained by actual measurementkSubtracting to obtain a residual ekThe formula is as follows:
ek＝Wexp-Wk,k＝0,1,2 (13)
then, the degree of deviation of the fitting value from the actual measurement value is compared according to the mean square error of the residual error, and the calculation formula is as follows:
Figure BDA0003590560230000061
under an ideal condition, the mean square error MSE of the residual error corresponding to the real pitch diameter number is 0, but because the system measurement error and the structural deviation can not be completely eliminated in practice, when the traversed pitch diameter number ND is equal to the actual blade modal shape pitch diameter number, the mean square error MSE of the residual error is also difficult to be reduced to 0, and the minimum value is obtained; therefore, when the obtained mean square error MSE is minimum, the corresponding pitch diameter number is the target parameter value ND0。
Compared with the prior art, the invention has at least the following beneficial technical effects:
according to the method for predicting the leaf disc pitch diameter number based on the vibration parameter period, the resonance frequency period number, the resonance amplitude period number and the vibration amplitude period number of the resonance interval are considered, the initial value of the pitch diameter number is determined by traversing the minimum mean square error of the pitch diameter number, and the leaf disc pitch diameter number can be more accurately identified; according to the method, when space wave aliasing is considered, the nodal diameter number is calculated according to the number of the blades, and compared with the traditional identification method, the nodal diameter number can be accurately identified when the space wave aliasing occurs; the invention considers the actual structure and the deviation condition of the test system, and can still more accurately obtain the vibration pitch diameter number of the blade under the condition of larger detuning.
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FIG. 1 is a flow chart of the analysis of the vibration pitch diameter of the blade disc according to the present invention;
fig. 2 shows the mean square error corresponding to the number of traversal nodes.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be 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 disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
The invention provides a method for predicting the vibration pitch diameter number of a blade disc based on a vibration parameter period, which comprises the following steps:
1) the method comprises the following steps of obtaining a vibration signal of the rotating blade through a test method, wherein the monitoring and testing process of the vibration state of the rotating blade comprises the following steps:
1-1) installing an eddy current displacement sensor: respectively installing No. 1-4 eddy current displacement sensors to corresponding preset positions of a test support to be used as blade tip timing sensors; installing a No. 0 eddy current displacement sensor to align to the position of a rotating shaft key to serve as a rotating speed sensor; a direct current power supply is adopted to supply power to the sensor, and a signal is output to a data acquisition unit for setting and debugging;
1-2) installing a test blade and a wheel disc: marking the blade number, and fixing the position of the wheel disc by using a locknut; adjusting the position height of the sensor, and calibrating; setting a rotating speed signal through a PLC and writing the rotating speed signal into a motor driver, wherein the rotating speed signal comprises a rotating speed value and acceleration time of each stage;
1-3) applying exciting force and collecting signals: starting an air compressor and a pressure stabilizing tank device, adjusting a valve until the air pressure is stable, and applying airflow excitation under preset pressure to the blade; blade tip timing method or strain gauge method is adopted to collect blade vibration signals under the working condition of constant speed or variable rotating speed, and multiple groups of data are collected for next signal processing;
1-4) repeating the steps 1-2) and 1-3), and acquiring blade vibration signals under different blade conditions and rotating speeds.
2) And preprocessing and denoising the obtained signal, wherein the denoising method adopts a wavelet denoising algorithm.
The basic idea of wavelet denoising is to decompose a signal into a series of wavelets by scaling and transforming a mother wavelet, and reconstruct the processed wavelet coefficient by using wavelet inverse transformation to obtain a denoised signal. The wavelet transform of signal u (t) is the inner product of the signal with wavelet function Ψ (α, τ):
Figure BDA0003590560230000081
in the formula: WT (α, τ) — a denoised signal after wavelet transform; α -stretch factor; τ — translation factor; Ψ *-conjugation of Ψ.
3) Reconstructing a blade vibration signal based on a compressed sensing principle:
for a multi-modal blade periodic vibration, it can be considered to be a superposition of K simple harmonic vibration signals, i.e.
Figure BDA0003590560230000082
In the formula: y-oscillatory displacement, fi-the frequency of the ith harmonic; a. thei-cosine coefficients of the ith harmonic; b isi-the sine coefficient of the ith harmonic.
Considering vibration displacement in discrete signal real space RMThen the displacement dispersion signal can be expressed as:
y＝[y1,y2，...yj,...yN] (3)
Figure BDA0003590560230000083
compressed sensing model of tip timing signal
Let z ∈ RQTo down-sample the resulting signal, consider the general down-sampling process:
z＝Φy (5)
Figure BDA0003590560230000084
in the formula:
Figure BDA0003590560230000085
-a measurement matrix;
Figure BDA0003590560230000086
-a unit row vector of length N.
Phi is a sub-matrix of the identity matrix,
Figure BDA0003590560230000087
for determining whether to extract the corresponding element in y, i.e. the row vector in the identity matrix, in the sampling process:
Figure BDA0003590560230000088
particularly when Q is<<N and
Figure BDA0003590560230000089
the selection of the leaf blade has random or non-uniformity, namely, the observation value z is randomly and non-uniformly obtained in a small amount from the original signal y, the leaf blade has the sampling characteristic under a compressed sensing frame, and the sparse expression of the leaf blade vibration displacement signal is substituted into the sparse expression to obtain the sparse expression of the leaf blade tip timing signal under the compressed sensing
z＝ΦΨs＝Θs (8)
In the formula: Ψ -sparse dictionary of sine-cosine transforms; Θ — the perception matrix. The measurement matrix Φ is determined by the placement of the tip timing sensors.
According to the compressed sensing principle, the reconstruction of the tip timing signal is changed into the optimization problem for constraint:
Figure BDA0003590560230000091
in the formula, L0Is 10Norm, i.e. the number of non-zero elements in statistics s, obviously, equation (8) is a combinatorial optimization problem, i.e. NP problem. Employing l in the optimization objective1Norm to approximate l0Norm, which can transform the combinatorial optimization problem into a convex optimization problem to complete the solution of the reconstruction signal, and indirectly reconstruct the signal using a greedy algorithm of sparse approximation, that is, reconstructing the most sparse target signal based on the linear measurement of the tip timing signal z, that is:
Figure BDA0003590560230000092
in the formula:
Figure BDA0003590560230000093
-an index set; si-the ith element in the sparse vector s; theta.theta.i-column i of the perception matrix theta. The sparse approximation method can be adopted by gradually selecting the column vector of the perception matrixThe tip timing signal is approximated to determine the index set step by step.
4) And (3) identifying the pitch diameter number of the reconstructed signal:
the flow of the method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period is shown in fig. 1. Firstly, obtaining a vibration response curve of a whole circle of non-harmonious blades, and extracting the number W of resonant frequency cycles from the curve result1The number of cycles W of the resonance amplitude2And the mean value W of the vibration amplitude period number of the resonance interval 3(ii) a Then, determining the range of pitch diameter numbers 0-N to be traversedbAnd/2, calculating the residual error e between the actual value and the predicted value of the three periodskCalculating Mean Square Error (MSE) by a weighting method, and determining an initial value (ND) of the nodal diameter number by traversing the minimum mean square error of the nodal diameter number0。
When spatial wave aliasing is considered, the number of nodal diameters is calculated from the number of leaves. Specifically, assume NbNumber of blades, WexpFor the desired spatial wavenumber, WsTwo cases occur when the number of cycles of the space curve is obtained for the blade sampling:
when W isexp≤NbAt/2, the space wave can be well recognized as having WexpA periodic curve. In this case, Ws＝WexpAnd no aliasing occurs;
when W isexp>N b2, the number of blades is not sufficient to correctly disperse the particles with WexpA spatial profile of the period. In this case, aliasing occurs in the blade amplitude spatial wave, and the observed spatial wave has several periods W satisfying the following relationships：
Figure BDA0003590560230000101
The mode shape nodal diameter ND and the period number W are determined by aliasing of the space wavesIn a relationship of
Figure BDA0003590560230000102
Assuming that the number of resonance frequency cycles, the number of resonance amplitude cycles and the mean value of the number of amplitude cycles in the resonance range are W1、W2、W3Determining the range of the pitch diameter number ND to be considered according to the number Nb of the blades, generally taking the range as 0-Nb/2, traversing all values of the pitch diameter number ND, and calculating the predicted period number W expAnd the k-th vibration parameter period W obtained by actual measurementkSubtracting to obtain a residual error ekThe formula is as follows:
ek＝Wexp-Wk,k＝0,1,2 (13)
then, the degree of deviation of the fitting value from the actual measurement value is compared according to the mean square error of the residual error, and the calculation formula is as follows:
Figure BDA0003590560230000103
ideally, the mean square error MSE of the residual error corresponding to the true pitch diameter number is 0, but because the system measurement error and the structural deviation cannot be completely eliminated in practice, when the traversed pitch diameter number ND is equal to the actual blade mode vibration mode pitch diameter number, the mean square error MSE of the residual error is also difficult to be reduced to 0, and the minimum value is obtained. Therefore, when the obtained mean square error MSE is minimum, the corresponding nodal diameter number is considered to be the target parameter value ND0。
For a whole circle of blades, the problem that the pitch diameter number is not accurately predicted due to aliasing of the number of space periods also exists, when the number of the blades is not enough to reasonably disperse a space curve with larger period numbers, aliasing occurs to space curve points, for example, 2 ND and 4 th order excitation is performed, the period numbers are the same at the moment, but the vibration types respectively belong to 2-pitch diameter vibration types and 4-pitch diameter vibration types, the relation between the general pitch diameter number and the space wave period number is approximate to a continuous triangular wave shape, and whether the period numbers are aliased or not can be estimated through the front and back resonance point period numbers or other methods, so that the actual pitch diameter number ND is obtained; in addition, when the cycle number is 2, it is necessary to pay attention to whether the pitch diameter number ND is N b/2, because when ND ═ NbActual cycles at/2 result WsDeviation from the predicted cycle number due to structural and measurement variationsIt is also understood that the number of cycles is equal to the number of leaves, but the peak points of the actual curves are not equal. Therefore, the determination result is corrected by the cycle number of at least two consecutive resonance points in the obtained whole-circle blade vibration data, and the final pitch diameter number result ND is obtained.
The accuracy of the proposed method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period is verified by adopting a numerical analysis method.
And establishing a finite element vibration analysis model of the rotating blade disc. Assuming that the blade density is ρm＝ρt(1+dmξ) in which d ismξ denotes the relative tuning value ρtIs disturbed by a random normal distribution sequence xi with a standard deviation of 0.01 and a detuning degree dmAnd (4) forming. The detuning degree d is calculatedm0.01 lower blade disc vibration response result. And carrying out non-quantitative processing on the vibration response result by taking the resonance amplitude of the blade during tuning as a standard.
And traversing each pitch diameter, and analyzing to obtain a corresponding mean square error. Fig. 2 shows the mean square error curves of the respective working conditions during the pitch path traversal, and it can be seen that the error results of the front and rear pitch path portions are completely symmetrical due to the aliasing of the cycle number. And selecting the pitch diameter corresponding to the minimum mean square error as an initial value, and further judging whether the cycle number is aliasing or not and whether the cycle number is the maximum pitch diameter number or not, thereby obtaining the actual pitch diameter number ND. The result shows that the modal shape nodal diameter number can be effectively identified, and the nodal diameter number is completely and accurately predicted. The reason why the mean square error of the mode shape of the 6-pitch diameter mode corresponding to the working condition 5 is large is that the periodicity deviates from an expected value when the maximum pitch diameter number is reached, but the maximum pitch diameter number can be identified through aliasing judgment of the periodicity of the front and rear resonance points.
TABLE 1 results of testing cycle number and prediction of pitch diameter for each pitch diameter test of leaf disk
Figure BDA0003590560230000121
The above contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention should not be limited thereby, and any modification made on the basis of the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims (8)

1. A method for predicting blade disc vibration pitch diameter number based on vibration parameter period is characterized in that when pitch diameter number identification is carried out on a reconstructed signal, firstly, a whole circle of non-harmonious blade vibration response curve is obtained, and resonance frequency period number W is extracted from a curve result1And the number W of resonant amplitude cycles2And the mean value W of the vibration amplitude period number of the resonance interval3(ii) a Then, determining the range of pitch diameter numbers 0-N needing to be traversedbAnd/2, calculating a residual error e between the actual value and the predicted value of the three periodskCalculating the mean square error value MSE by a weighting method, and determining the initial value ND of the nodal diameter number by traversing the minimum mean square error of the nodal diameter number0(ii) a When spatial wave aliasing is considered, the number of nodal diameters is calculated from the number of leaves.
2. The method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period according to claim 1, characterized by comprising the following steps:
1) Obtaining a vibration signal of the rotating blade by a test method;
2) carrying out data preprocessing on the obtained blade vibration signals, and denoising test data to improve the blade vibration signal obtaining precision;
3) based on a compressed sensing principle, performing signal reconstruction on the blade tip timing signal;
4) and identifying and predicting the number of vibration nodal diameters of the reconstructed signal.
3. The method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period is characterized in that in the step 1), No. 1-4 eddy current displacement sensors are respectively installed at corresponding preset positions of a test bracket to serve as blade tip timing sensors; a No. 0 eddy current displacement sensor is arranged to be aligned with the position of a rotating shaft key to serve as a rotating speed sensor, the blades are excited by using a high-speed airflow nozzle, and the rotating speed and the accelerating time of the blades are controlled by using a PLC (programmable logic controller).
4. The method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period according to claim 3, wherein the specific implementation method of the step 1) is as follows:
1-1) installing an eddy current displacement sensor: respectively installing No. 1-4 eddy current displacement sensors at preset positions corresponding to the test support to serve as tip timing sensors; installing a No. 0 eddy current displacement sensor to align to the position of a rotating shaft key to serve as a rotating speed sensor; a direct current power supply is adopted to supply power to the sensor, and a signal is output to a data acquisition unit for setting and debugging;
1-2) installing a test blade and a wheel disc: marking the blade number, and fixing the position of the wheel disc by using a locknut; adjusting the position height of the sensor, and calibrating; setting a rotating speed signal through a PLC and writing the rotating speed signal into a motor driver, wherein the rotating speed signal comprises a rotating speed value and acceleration time of each stage;
1-3) applying exciting force and collecting signals: starting an air compressor and a pressure stabilizing tank device, adjusting a valve until the air pressure is stable, and applying airflow excitation under preset pressure to the blade; blade tip timing method or strain gauge method is adopted to collect blade vibration signals under the working condition of constant speed or variable rotating speed, and multiple groups of data are collected for next signal processing;
1-4) repeating the steps 1-2) and 1-3), and acquiring blade vibration signals under different blade conditions and rotating speeds.
5. The method for predicting the blade disc vibration nodal diameter number based on the vibration parameter period as claimed in claim 2, wherein in step 2), the denoised signal WT (α, τ) is an inner product of the signal u (t) and the wavelet function Ψ (α, τ):
Figure FDA0003590560220000021
in the formula: WT (α, τ) -denoised signal; α -stretch factor; τ — translation factor; Ψ*-conjugation of Ψ.
6. The method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period is characterized in that in the step 3), the blade vibration signals obtained through measurement are reconstructed by using a compressed sensing principle, the identification precision is ensured, and meanwhile, the measurement frequency range of the sensor is expanded, so that the measurement of the sensor can break through the limit of the Nyquist sampling theorem.
7. The method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period as claimed in claim 6, wherein when the blade vibration signal is reconstructed based on the compressed sensing principle, the periodic vibration of the multi-mode blade is obtained by the superposition of K simple harmonic vibration signals
Figure FDA0003590560220000031
In the formula: y-oscillatory displacement, fi-the frequency of the ith order harmonic; a. thei-the cosine coefficient of the ith order harmonic; bi-the sine coefficient of the ith order harmonic;
considering vibration displacement in discrete signal real space RMIn (b), the displacement dispersion signal is expressed as:
y＝[y1,y2，…yj,...yN] (3)
Figure FDA0003590560220000032
compressed sensing model of tip timing signal
Let z ∈ RQTo down-sample the resulting signal, consider the general down-sampling process:
z=Φy (5)
Figure FDA0003590560220000033
in the formula:
Figure FDA0003590560220000034
-a measurement matrix;
Figure FDA0003590560220000035
-a unit row vector of length N;
phi is a sub-matrix of the identity matrix,
Figure FDA0003590560220000036
for determining whether to extract the corresponding element in y, i.e. the row vector in the identity matrix, in the sampling process:
Figure FDA0003590560220000037
when Q is<<N and
Figure FDA0003590560220000038
the selection of the leaf blade has random or non-uniformity, namely, the observation value z is randomly and non-uniformly obtained in a small amount from the original signal y, the leaf blade has the sampling characteristic under a compressed sensing frame, and the sparse expression of the leaf blade vibration displacement signal is substituted into the sparse expression to obtain the sparse expression of the leaf blade tip timing signal under the compressed sensing
z=ΦΨs＝Θs (8)
In the formula: Ψ -sparse dictionary of sine-cosine transforms; Θ — the perceptual matrix; the measurement matrix phi is determined by the arrangement position of the blade tip timing sensor;
according to the compressed sensing principle, the reconstruction of the tip timing signal is changed into the optimization problem for constraint:
Figure FDA0003590560220000041
in the formula, L0Is 10Norm, namely counting the number of nonzero elements in s; employing l in the optimization objective1Norm to approximate l0Norm, which is to convert the combinatorial optimization problem into a convex optimization problem to complete the solution of the reconstruction signal, and indirectly reconstruct the signal by using a sparse greedy algorithm, that is, a target signal with the most sparsity is reconstructed based on a linear measurement-based tip timing signal z, that is:
Figure FDA0003590560220000042
in the formula:
Figure FDA0003590560220000043
-an index set; si-the ith element in the sparse vector s; thetai-column i of the perception matrix θ; the sparse approximation method is adopted to approximate the blade tip timing signal by gradually selecting the column vector of the perception matrix, so that the index set is gradually determined.
8. The method for predicting the vibration pitch diameter number of the blade disc based on the vibration parameter period as claimed in claim 2, wherein in the step 4), N is assumedbNumber of blades, WexpFor the desired spatial wavenumber, WsTwo cases occur when the number of cycles of the space curve is obtained for the blade sampling:
When Wexp≤NbAt/2, the space wave can be identified as having WexpPeriodic curve, in this case Ws＝WexpAnd no aliasing occurs;
when W isexp>Nb2, the number of blades is not sufficient to correctly disperse the particles with WexpPeriodic spatial curve, in which case the blade amplitude spatial wave appears aliased, the observed spatial wave having several periods W satisfying the following relationships：
Figure FDA0003590560220000044
The mode shape nodal diameter ND and the period number W are determined by aliasing of the space wavesIn a relationship of
Figure FDA0003590560220000045
Assuming that the number of resonance frequency cycles, the number of resonance amplitude cycles and the mean value of the number of amplitude cycles in the resonance range are W1、W2、W3Determining the range of the pitch diameter number ND to be considered according to the number Nb of the blades, taking the range as 0-Nb/2, traversing all values of the pitch diameter number ND, and calculating the predicted period number WexpAnd the k-th vibration parameter period W obtained by actual measurementkSubtracting to obtain a residual ekThe formula is as follows:
ek＝Wexp-Wk,k＝0,1,2 (13)
then, the degree of deviation of the fitting value from the actual measurement value is compared according to the mean square error of the residual error, and the calculation formula is as follows:
Figure FDA0003590560220000051
under an ideal condition, the mean square error MSE of the residual error corresponding to the real pitch diameter number is 0, but because the system measurement error and the structural deviation can not be completely eliminated in practice, when the traversed pitch diameter number ND is equal to the actual blade modal shape pitch diameter number, the mean square error MSE of the residual error is also difficult to be reduced to 0, and the minimum value is obtained; therefore, when the mean square error MSE is the minimum, the corresponding pitch diameter is the target parameter value ND 0。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115640649A (en) * 2022-11-09 2023-01-24 中国航发沈阳发动机研究所 Blisk and active detuning vibration reduction design method thereof

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115640649A (en) * 2022-11-09 2023-01-24 中国航发沈阳发动机研究所 Blisk and active detuning vibration reduction design method thereof
CN115640649B (en) * 2022-11-09 2023-10-20 中国航发沈阳发动机研究所 Blisk and active detuning vibration reduction design method thereof

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