Blade operation damping extraction method

Abstract

A blade operation damping extraction method comprises the following steps: extracting a dynamic strain signal of a blade at a constant rotating speed, performing correlation calculation to obtain an autocorrelation function, and only retaining a non-negative delay part; intercepting a head attenuation section and a part of constant-amplitude vibration section in the reserved autocorrelation function; performing narrowband inverted filtering on the intercepted function, and establishing a Hankel matrix according to the filtered frequency component; singular value decomposition is carried out on the Hankel matrix, reconstruction of a system matrix in a state-space equation is carried out to obtain a target matrix, eigenvalue decomposition is carried out on the target matrix to obtain discrete time eigenvalues, and the inherent frequency and the damping ratio are obtained through calculation according to the discrete time eigenvalues. According to the method, random signals can be converted into deterministic signals, modal response extraction of a single frequency component is realized, and the damping ratio extraction precision is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the field of aero-engines, and particularly relates to a method for extracting blade operating damping. Background Art

[0002] The modal damping characteristics of aero-engine blades directly affect the vibration amplitude of the engine blades under working conditions. The rotational speed of aero-engines covers a relatively large range, and the excited blade modes are numerous and complex. Therefore, obtaining the blade modal damping under the operating state of the engine has important guiding significance for the optimization of the structural blade profile. The static test in the conventional damping test cannot reflect the actual vibration characteristics of the blade in the rotating state under real working conditions; while the modal damping test for obtaining the blade operating state, such as the special up-rotation or down-rotation test, analyzes the damping ratio through the half-power bandwidth of the resonance spectrum, which is costly and has insufficient accuracy due to the influence of the blade transient response process, and it is also impossible to track the damping transformation under different working conditions. Therefore, providing a method for extracting blade operating damping has high practical value for optimizing the structural blade profile of the engine. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for extracting blade operating damping, which can improve the extraction accuracy of the damping of aero-engine blades during operation.

[0004] According to an embodiment of the present invention, there is provided a method for extracting blade operating damping, which includes the following steps: providing a blade to be analyzed and the concerned modal frequency of the blade to be analyzed, and collecting the dynamic strain signal of the blade to be analyzed at a constant rotational speed; performing a correlation function calculation on the dynamic strain signal, calculating the autocorrelation function of the dynamic strain signal, and retaining the part with non-negative delay in the autocorrelation function as a first object function; intercepting the head attenuation section and a part of the constant amplitude vibration section in the first object function as a second object function; performing narrowband inverse filtering on the second object function, and constructing a Hankel matrix based on the filtered frequency components to obtain an object matrix H; performing singular value decomposition on the object matrix H for denoising and order determination; reconstructing the system matrix in the state space equation based on the object matrix to obtain a target matrix A; performing eigenvalue decomposition on the target matrix to obtain discrete-time eigenvalues, and obtaining the natural frequency and damping ratio of the blade to be analyzed according to the discrete-time eigenvalues.

[0005] This method utilizes the attenuation characteristics of signals: the correlation function of the random response presents a vibration attenuation signal, which is related to the vibration mode of the blade; the correlation function of the periodic response remains a periodic signal with an unchanged amplitude. Through correlation operations, the random signal can be converted into a deterministic signal, enabling the correlation function to be used as a characteristic signal for extracting the vibration characteristic parameters of the blade. At the same time, this method adopts inverse filtering to transfer the signal distortion caused by filtering inversion to the tail of the signal, extracting the modal response of a single frequency component, creating conditions for the accurate extraction of the modal damping ratio. Further, this paper repeatedly proposes a state system construction method for damping parameter identification. By constructing the Hankel matrix and performing singular value decomposition, noise and other frequency components can be filtered out, thereby improving the extraction accuracy of the damping ratio.

[0006] Further, in some embodiments, the sampling frequency of the dynamic strain signal of the blade to be analyzed under a constant rotational speed is greater than twice the concerned modal frequency. Based on the Nyquist sampling theorem, the sampling frequency should be greater than twice the concerned modal frequency.

[0007] Further, in some embodiments, the sampling time of the dynamic strain signal of the blade to be analyzed under a constant rotational speed is not less than 120 s.

[0008] Further, in some embodiments, the truncation duration of the constant amplitude vibration segment in the second objective function is 2 s - 5 s.

[0009] Further, in some embodiments, the method for constructing the Hankel matrix based on the filtered frequency components is as follows:

[0010]

[0011] where F(·) is the inverse filtering, is the second objective function, m and k are positive integers, and n ≥ (2m + 2).

[0012] Further, in some embodiments, the method for denoising and determining the order of the object matrix H is as follows:

[0013] Perform singular value decomposition on H: H(0) = USV T , where U and V are unitary orthogonal matrices respectively, and S is a singular value matrix with non-negative diagonal elements;

[0014] Perform singular value truncation:

[0015]

[0016] where, is a 2m × 2m singular value matrix, m is a positive integer corresponding to the number of intercepted modes, and the singular values are located on the diagonal elements, The singular values in Σ are the first 2m non - zero singular values in S. By retaining the singular values of the effective order, the filtering of noise and other frequency components is achieved. Usually, m takes the value of 1 or 2.

[0017] Further, in some embodiments, the target matrix where and are the singular vectors corresponding to the first 2m non - zero singular values.

[0018] Further, in some embodiments, the calculation method of the discrete - time eigenvalues is to perform eigenvalue decomposition on the target matrix A, A = PΛP -1 , where P is the eigenvector matrix and Λ is a diagonal matrix, and the diagonal elements of Λ are the discrete - time eigenvalues z i .

[0019] Further, in some embodiments, the calculation method of calculating the natural frequency and damping ratio of the blade to be analyzed through the discrete - time eigenvalues is: calculate the continuous - system eigenvalue λ i =ln(z i )fs, where fs is the sampling frequency; the natural frequency f i of the blade to be analyzed =|ln(λ i )|fs / 2π; the damping ratio ζ i of the blade to be analyzed =|Re(ln(λ i )| / |ln(λ i )|.

[0020] Further, in some embodiments, the concerned modal frequencies of the blade to be analyzed are the natural frequencies and / or damping ratios of at least the first three modes of the blade to be analyzed. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flowchart for extracting the running damping of a blade in an embodiment;

[0022] Figure 2a is the time history of a blade in an operating state in an embodiment;

[0023] Figure 2b is the spectrum of a blade in an operating state in an embodiment;

[0024] Figure 3 is the autocorrelation function of the response of a blade in an embodiment;

[0025] Figure 4a is the frequency - domain response of modal component 1 in an embodiment;

[0026] Figure 4b is the time - domain response of modal component 1 in an embodiment;

[0027] Figure 5a is the frequency-domain response of modal component 2 in an embodiment;

[0028] Figure 5b is the time-domain response of modal component 2 in an embodiment;

[0029] Figure 6a is the frequency-domain response of modal component 3 in an embodiment;

[0030] Figure 6b is the time-domain response of modal component 3 in an embodiment.

[0031] The purpose of the above-mentioned drawings is to illustrate the present invention in detail so that those skilled in the art can understand the technical concept of the present invention, rather than to limit the present invention. Detailed implementation manners

[0032] The following further elaborates on the present invention through specific embodiments in conjunction with the drawings.

[0033] When referring to "embodiment" in this article, it means that the specific features, structures or characteristics described in connection with the embodiment may be included in at least one embodiment of this article. The phrase appearing in various positions in the specification does not necessarily refer to the same embodiment, nor is it limited to mutually exclusive independent or alternative embodiments. Those skilled in the art should be able to understand that the embodiments in this article can be combined with other embodiments without structural conflicts. In the description of this article, the meaning of "a plurality of" is at least two.

[0034] Under the engine operating condition, the damping of the blade includes static damping and starting damping. The static damping is related to the blade material and configuration, while the aerodynamic damping is related to the relative speed, temperature and pressure. Affected by temperature changes, aerodynamic loads and centrifugal forces, the vibration modal damping characteristics obtained by the blade in the static state cannot replace its modal damping characteristics under actual operation. In addition, when the blade is in operation, it is affected by random turbulent loads, rotor unbalance loads, etc. The noise has a significant impact on the measurement signal, with many and dense harmonic components, making it difficult to extract the damping characteristics and with poor accuracy.

[0035] To solve the above problems, an embodiment of the present invention provides a method for extracting the running damping of a blade, as Figure 1 shown, the method includes the following steps:

[0036] Step 1: Provide the blade to be analyzed, as well as the concerned modes and mode frequencies of the blade to be analyzed. In the preferred embodiment, the concerned modes are the first three modes of the blade to be analyzed, and the natural frequencies are 63.18 Hz, 326.06 Hz, and 796.01 Hz respectively. At a constant rotational speed of 3360 rpm, continuously collect data for 120 s at a sampling frequency fs = 5000 Hz to obtain the time history of the blade operating state as shown in Figure 2a shown, and the spectrum is as shown in Figure 2b shown.

[0037] Step 2: Perform relevant calculations on the collected signal, calculate the autocorrelation function of the dynamic strain signal, and only retain the autocorrelation function with non - negative delay as the first objective function, where x(m) is the discrete digital signal, N is the signal length, m and k are positive integers, and n≥(2m + 2).

[0038] Step 3: Intercept the second objective function in the first objective function. The autocorrelation function of the blade response is as shown in shown. The envelope head of this function shows a decaying trend, forming a decaying section 8; after the decaying section 8 is a constant - amplitude vibration section 9; intercept the decaying section and the 2s - 5s constant - amplitude vibration section as the second objective function. In the preferred embodiment, the intercepted duration of the constant - amplitude vibration section is 5 s. For the collected signal, the correlation function of the random response presents a vibration - decaying signal, which is related to the blade vibration mode; the correlation function of the periodic response is still a periodic signal with non - decaying amplitude. Therefore, the correlation operation realizes the conversion of the random signal into a deterministic signal, and the correlation function can be used as a characteristic signal for extracting blade vibration characteristic parameters. Figure 3

[0039] Step 4: Perform inverse filtering. Perform narrow - band inverse filtering on the second objective function to obtain where F(·) represents narrow - band inverse filtering. First, invert the intercepted second objective function, and then perform band - pass filtering using a Butterworth non - recursive impulse filter. The filter has the peak frequency as the center frequency, and the bandwidth covers the half - power frequency band of the peak. The center frequency of the inverse filtering corresponds to the center frequency of the modal peak, and the filtered frequency components are relatively single. After filtering, the first three main modes are obtained. The frequency - domain response of modal component 1 is as shown in Figure 4a shown, and the time - domain response of modal component 1 is as shown in Figure 4b shown; the frequency - domain response of modal component 2 is as shown in Figure 5a shown, and the time - domain response of modal component 2 is as shown in Figure 5b shown; the frequency - domain response of modal component 3 is as shown in Figure 6a shown, and the time - domain response of modal component 3 is as shown in Figure 6b ​​As shown in the figure. The inverse filtering transfers the signal distortion of the inverse filtering to the tail of the signal, extracts the modal response of a single frequency component, and creates conditions for the accurate extraction of the modal damping ratio.

[0040] The above steps are the preprocessing stage of the dynamic strain signal. The following is the damping ratio identification process.

[0041] Step 5: Construct the Hankel matrix. Taking the first-order mode as an example, establish the Hankel matrix of modal component 1. The number of columns of the matrix is taken as 6, that is, m is taken as 2, and the object matrix is obtained:

[0042]

[0043] Step 6: Perform singular value decomposition on the Hankel matrix H(0): H(0) = USV T , where U is a 494×6 numerical matrix, V is a 6×6 numerical matrix; S is a singular matrix, the diagonal elements are singular values, and the non-diagonal elements are 0. The singular value matrix S is:

[0044]

[0045] Intercept and determine the order of the S matrix. The order is 2, and a 4×4 matrix is obtained

[0046]

[0047] The above singular value truncation process can remove the influence of noise and other order modal residues on the signal within the bandwidth.

[0048] At the same time, take the first 4 columns of U and the first 4 columns of V to construct the system matrix, and obtain the target matrix

[0049]

[0050] Step 7: Perform eigenvalue decomposition and calculate to obtain the natural frequency and damping ratio. A = PΛP -1 , where P is the eigenvector matrix, Λ is the diagonal matrix, and the diagonal elements of Λ are the discrete-time eigenvalues z i .

[0051] Among them, the eigenvector matrix P is:

[0052]

[0053] The diagonal matrix Λ is:

[0054]

[0055] The diagonal elements of the matrix Λ are the conjugate eigenvalues z 1 、z 1 *, z 2 、z 2 *, which are 0.9958 ± 0.0790i and 1.0020 ± 0.0720i in this example, and are discrete-time eigenvalues. The eigenvalues λ of the continuous system i = ln(z i )fs. The natural frequency f of the blade to be analyzed i = |ln(λ i )|fs / 2π; the damping ratio ζ of the blade to be analyzed i = |Re(ln(λ i )| / |ln(λ i )|. Substituting the result of the eigenvalue decomposition of the target matrix A into the calculation, the natural frequencies are 57.22 Hz and 63.09 Hz, and the damping ratios are 6.29% and 1.23%. Since 57.22 Hz actually corresponds to the rotational speed peak, it is excluded. The determined first-order modal natural frequency is 63.09 Hz, and the damping ratio is 1.23%, corresponding to Figure 4a the peak frequency 10 shown in

[0056] Using the same method, the natural frequencies and damping ratios corresponding to the second-order and third-order modes can be calculated, and the results are shown in Table 1.

[0057] Order Natural frequency (Hz) Modal damping ratio (%) 1 63.09 1.23 2 326.35 1.15 3 795.50 0.41

[0058] Table 1 Natural Frequencies and Damping Ratios of the First Three Modes

[0059] Through the above method, the damping ratio of the blade during the operation of the aero-engine test can be accurately extracted, and the actual damping ratio and vibration natural frequency of each order mode of the blade can be extracted under the condition of constant rotational speed of the blade, so as to analyze the dynamic characteristics of the blade under the real operation condition, extract the damping ratio at different rotational speeds, and thus analyze the change of the aerodynamic damping of the blade with the engine rotational speed, providing guidance for the structural design and optimization of the engine blade. It can be understood that the above method is not limited to extracting the damping of the first three modes, and can also be used for the analysis of the natural frequency and / or damping ratio of modes above the third order.

[0060] The purpose of the above embodiments is to further elaborate the present invention in combination with the drawings, so that those skilled in the art can understand the technical concept of the present invention. Within the scope of the present invention disclosed, optimizing or equivalently replacing the method steps involved, and combining the implementation manners in different embodiments without conflict in structure and principle, all fall within the protection scope of the present invention.

Claims

1. A method for extracting blade operation damping, characterized in that, it includes the following steps: Provide the blade to be analyzed and the concerned modal frequency of the blade to be analyzed, and collect the dynamic strain signal of the blade to be analyzed at a constant rotational speed; Perform a correlation function calculation on the dynamic strain signal, calculate the autocorrelation function of the dynamic strain signal, and retain the part with non - negative delay in the autocorrelation function as the first object function; Intercept the head attenuation segment and part of the constant - amplitude vibration segment in the first object function as the second object function; Perform narrow - band inverse filtering on the second object function, and construct a Hankel matrix based on the filtered frequency components to obtain the object matrix H; Perform singular value decomposition on the object matrix H for denoising and order determination; Reconstruct the system matrix in the state - space equation based on the object matrix to obtain the target matrix A; Perform eigenvalue decomposition on the target matrix to obtain discrete - time eigenvalues, and obtain the natural frequency and damping ratio of the blade to be analyzed according to the discrete - time eigenvalues.

2. The method for extracting blade operation damping according to claim 1, characterized in that, The sampling frequency of the dynamic strain signal of the blade to be analyzed at a constant rotational speed is greater than 2 times the concerned modal frequency.

3. The method for extracting blade operation damping according to claim 1 or 2, characterized in that, The sampling time of the dynamic strain signal of the blade to be analyzed at a constant rotational speed is not less than 120 s.

4. The method for extracting blade operation damping according to claim 1 or 2, characterized in that, The interception duration of the constant - amplitude vibration segment in the second object function is 2 s - 5 s.

5. The method for extracting blade operation damping according to claim 1, characterized in that, The method for constructing a Hankel matrix based on the filtered frequency components is: wherein F(·) is an inverse filter, is the second object function, m and k are positive integers, and n ≥ (2m + 2).

6. The method for extracting blade operation damping according to claim 5, characterized in that, The method for denoising and order determination of the object matrix H is: Perform singular value decomposition on H: H(0) = USV T , where U and V are respectively unitary orthogonal matrices, and S is a singular value matrix with non-negative diagonal elements; Perform singular value truncation: Among them, is a 2m×2m singular value matrix, where m is a positive integer corresponding to the intercepted mode number, and the singular values are located at the diagonal elements. The singular values in are the first 2m non-zero singular values in S.

7. The method for extracting blade operation damping according to claim 6, characterized in that, The target matrix where and are the singular vectors corresponding to the first 2m non-zero singular values.

8. The method for extracting blade operation damping according to claim 7, characterized in that, The calculation method of the discrete-time eigenvalues is to perform eigenvalue decomposition on the target matrix A, A = PΛP -1 , where P is the eigenvector matrix, Λ is the diagonal matrix, and the diagonal elements of Λ are the discrete-time eigenvalues z i .

9. The method for extracting blade operation damping according to claim 8, characterized in that, The calculation method for calculating the natural frequency and damping ratio of the blade to be analyzed through the discrete - time eigenvalues is: Calculate the continuous system eigenvalue λ based on the discrete-time eigenvalue i = ln(z i ) fs, where fs is the sampling frequency; The natural frequency f of the blade to be analyzed i = |ln(λ i )| fs / 2π; The damping ratio ζ of the blade to be analyzed i = |Re(ln(λ i ))| / |ln(λ i ))|.

10. The method for extracting blade operation damping according to claim 1 or 2, characterized in that, The concerned modal frequency of the blade to be analyzed is the natural frequency and / or damping ratio of at least the first three - order modes of the blade to be analyzed.

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