A torsional vibration measurement method based on time-frequency ridge extraction and numerical integration

Abstract

The application discloses a torsional vibration measurement method based on time-frequency ridge extraction and numerical integration, and relates to the technical field of rotating machinery torsional vibration signal extraction. The method can more accurately and effectively extract the torsional vibration signal of the required analysis rotating shaft under the condition of no key phase or no installation of a special torsional vibration tester, and can be used for subsequent signal analysis and processing of torsional vibration. The method comprises the following steps: collecting the vibration acceleration signal of the outer casing of the rotating machinery by using a vibration acceleration sensor, and performing pretreatment such as downsampling and then performing time-frequency analysis. The high-resolution time-frequency spectrum is obtained by using a high-resolution time-frequency analysis method, the rotating frequency information of the required analysis rotating shaft in the time-frequency distribution is extracted, and the rotating frequency information is converted into an angular velocity signal. Based on the physical characteristics of the torsional vibration, the angular velocity signal is subjected to numerical integration, and is subjected to detrending processing and smoothing operation to finally obtain the torsional vibration signal.

Description

Technical Field

[0001] This invention relates to the field of torsional vibration signal conversion and extraction technology for rotating machinery, and specifically to a torsional vibration measurement method based on time-frequency ridge extraction and numerical integration. Background Technology

[0002] To ensure the safe and stable operation of rotating machinery, monitoring and diagnosing its condition is crucial. Vibration, as one of the key indicators for health monitoring of rotating machinery rotor systems, has always received considerable attention. In practical applications, dampers are typically installed to increase lateral damping, thereby quickly suppressing and attenuating the hazards caused by lateral vibration. However, torsional vibration of the shaft system is a special form of unit vibration. Due to the low torsional damping in the rotor system, torsional resonance is difficult to dampen once excited. The essence of shaft torsional vibration is that during unit operation, the elastic shaft exhibits instantaneous angular velocities of different magnitudes and phases across its cross-sections along the axial direction, resulting in reciprocating torsion in the direction of rotation, generating torsional impacts or alternating stresses. Severe torsional vibration can lead to irreversible damage or failures, such as coupling fatigue damage, shaft cracking, and fan blade failure, seriously threatening the safe operation of rotating machinery.

[0003] Currently, specialized instruments such as strain gauge telemetry systems, rotary shaft encoders / gear teeth, and laser vibrometers can achieve real-time monitoring of torsional vibration. The principle of torsional testing is mainly to monitor the torsional stress or instantaneous angular velocity of the shaft. With the refinement of sensor design and manufacturing levels and the iterative improvement of corresponding algorithms, torsional vibration testing has achieved high accuracy. However, for some complex rotating machinery, since torsional vibration monitoring was not considered in the entire design phase, there is a lack of conditions for installing specialized torsional vibration monitoring instruments. In addition, most rotating machinery can only install vibration sensors on the surface of the casing or housing to sense the signal that the rotor system's vibration response reaches the casing after being transmitted through a complex path. Therefore, it is necessary to conduct in-depth research and propose digital signal processing methods suitable for demodulation and reconstruction of casing vibration signals, extracting the signal component containing only rotor torsional vibration information from the casing vibration signal containing multiple vibration response information, so as to achieve the extraction and analysis of torsional signals.

[0004] Time-frequency reconstruction is a method suitable for extracting multiple vibration components from rotating machinery. Early time-frequency analysis methods, such as wavelet transform and short-time Fourier transform, were mainly applicable to analyzing linear, stationary vibration signals. However, due to the influence of Heisenberg uncertainty, their time-frequency analysis results suffered from low time-frequency resolution and energy divergence, making it impossible to accurately extract multiple vibration components. Synchronous compression transform, as a time-frequency post-processing method, effectively improves the convergence of the time-frequency spectrum, thereby improving the accuracy of time-frequency reconstruction and showing great application potential in the extraction of torsional vibrations. Summary of the Invention

[0005] In view of this, the present invention provides a torsional vibration measurement method based on time-frequency ridge extraction and numerical integration. This method, under keyless conditions, utilizes the chassis vibration signal and employs a high-resolution time-frequency analysis method to successfully extract the rotational frequency information of the shaft. Since the physical vibration parameters characterizing torsional vibration are angular displacement (or angle), angular velocity, and angular acceleration, torsional vibration signals can be obtained by performing corresponding numerical integration operations based on the shaft's rotational frequency information. This method allows for additional torsional vibration monitoring of the machine without installing dedicated torsional vibration testing equipment such as gearboxes or encoders, and significantly utilizes the measurement information from the chassis vibration sensor, providing a convenient method for torsional vibration monitoring.

[0006] To achieve the above objectives, the technical solution of the present invention provides a torsional vibration measurement method based on time-frequency ridge extraction and numerical integration, comprising the following steps:

[0007] S1. Use a vibration acceleration sensor to collect vibration signals of the outer casing or outer housing to be analyzed;

[0008] S2. After downsampling to the required analysis range, the vibration acceleration signal is analyzed using a high-resolution time-frequency analysis method to obtain a high-resolution time spectrum.

[0009] S3. Extract the rotational frequency information of the shaft to be analyzed from the time-frequency distribution and convert it into an angular velocity signal;

[0010] S4. Based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated;

[0011] S5. Detrend and smooth the numerical integration results to obtain the torsional vibration signal;

[0012] S6. Perform spectrum analysis on the obtained torsional vibration signal to analyze the accuracy of the extraction method.

[0013] Further, in S1, the vibration signal of the outer casing or housing to be analyzed is collected using a vibration acceleration sensor, including the following steps: mounting the vibration acceleration sensor onto the outer casing of the rotating machinery using magnetic attraction or a bracket, and setting the sampling frequency f of the original signal. s At least higher than the frequency to be analyzed. max A multiple of 2.56.

[0014] Furthermore, the raw signal to be analyzed acquired by the vibration acceleration sensor is downsampled. Specifically, the raw signal to be analyzed and evaluated acquired by the vibration acceleration sensor is downsampled according to the required analysis frequency, reducing the subsequent computational load while retaining the required analysis frequency band. The portion of the downsampled signal to be analyzed is then extracted as the vibration acceleration signal required for time-frequency analysis.

[0015] Furthermore, in S2, a high-resolution time-frequency analysis method is used to perform time-frequency analysis on the vibration acceleration signal, specifically as follows:

[0016] Using the downsampled acceleration vibration signal as the signal to be analyzed, a short-time Fourier transform is first employed for time-frequency analysis. A Gaussian window is selected as the window function, and its length parameter is set to hlength, extending the one-dimensional time-series signal to a two-dimensional time-frequency space, resulting in a time-frequency spectrum with relatively low resolution. Post-processing is then performed based on this time-frequency spectrum, using a second-order synchronous compression transform to improve the time-frequency resolution, and instantaneous frequency operators are calculated. Group delay operator Frequency modulation estimation operator Finally, the second-order instantaneous frequency operator ω2(t,ω)=ω0(t,ω)+c0(t,ω)[t-t0(t,ω)] is calculated, where t represents time, ω represents frequency, G(t,ω) represents the short-time Fourier transform time spectrum, and i represents the imaginary unit. The ambiguous time-frequency energy is redistributed to the intermediate frequency estimate in the second-order instantaneous frequency direction, ultimately obtaining the high-resolution time spectrum. The second-order synchronous compression transform algorithm can be expressed as: In the formula, η represents the frequency position of the redistribution, and δ represents the Dirac distribution sign.

[0017] Furthermore, in S3, the rotation frequency information of the required analysis axis in the time-frequency distribution is extracted. Specifically, the penalty function method is used to calculate the ridge approximation value of the rotation frequency of the required analysis axis in the high-resolution time-frequency spectrum. The algorithm first determines the time-frequency ridge value at the initial moment through the maximum amplitude of the time-frequency, and then searches forward and backward. The output results include the time-frequency coefficient of the ridge index and the energy of the returned ridge.

[0018] Furthermore, based on the physical relationship between rotational speed and angular velocity, and since the physical vibration parameters characterizing torsional vibration are angular displacement (or angle), angular velocity, and angular acceleration, the extracted rotational frequency information is converted into an angular velocity signal.

[0019] Furthermore, in S4, based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated. Specifically, the angular velocity signal sequence is input, and the extracted angular velocity signal is numerically integrated at discrete points using the cumulative trapezoidal numerical integration method, thereby obtaining the numerical integration result of the angular velocity signal.

[0020] Furthermore, in S5, the numerical integration results are detrended and smoothed to obtain the torsional vibration signal. Specifically, the numerical integration results of the input angular velocity signal are subjected to a polynomial trend removal operation, removing the best-fit line from the sequence data of the integration results. This eliminates the influence of the offset generated during numerical integration on subsequent calculations. Removing the trend from the numerical integration results allows the analysis to focus on the fluctuations in the data trend itself. Finally, a moving average method is used for smoothing to make the extracted torsional vibration signal smooth.

[0021] Furthermore, in S6, the obtained torsional vibration signal is subjected to spectral analysis to analyze the accuracy of the extraction method. Specifically, a fast Fourier transform is performed on the extracted torsional vibration time-domain signal to obtain its spectrum, and it is determined whether its frequency components are consistent with the theoretical values, thus determining the accuracy of the method used. Similarly, envelope spectrum analysis is performed on the extracted torsional vibration time-domain signal to determine whether its frequency components are consistent with the theoretical values, thereby verifying the accuracy of the method used.

[0022] Beneficial effects:

[0023] 1. This invention provides a torsional vibration measurement method based on time-frequency ridge extraction and numerical integration. It utilizes a vibration acceleration sensor to collect vibration acceleration signals from the outer casing of rotating machinery. After preprocessing such as downsampling, the signals are used for time-frequency analysis. A high-resolution time-frequency spectrum is obtained using high-resolution time-frequency analysis methods. The rotational frequency information of the shaft to be analyzed is extracted from the time-frequency distribution and converted into an angular velocity signal. Based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated, and detrending and smoothing operations are performed to finally obtain the torsional vibration signal. This invention completes the time-frequency analysis, ridge extraction, signal conversion, and numerical integration of the shaft to be analyzed, successfully extracting the torsional vibration signal of the shaft to be analyzed from the casing vibration signal containing multiple vibration response information. This signal can be used for feature extraction and analysis of rotor torsional vibration signals, thereby guiding the fault diagnosis of rotor systems.

[0024] 2. This invention provides a method for extracting torsional vibration signals based on the vibration signals of the outer casing of rotating machinery. It can accurately extract the torsional vibration signals of the required shaft. This method can perform additional torsional vibration monitoring on the machine without installing a dedicated torsional vibration tester such as a gear disk or encoder. It can serve the field monitoring of rotor torsional vibration under conditions without a key phase or without the installation of a dedicated torsional vibration tester. It solves the problem of difficult extraction of rotor torsional vibration under conditions without a key phase or without the installation of a dedicated torsional vibration tester in engineering applications, and provides a simple and convenient method for torsional vibration monitoring. Attached Figure Description

[0025] Figure 1A schematic diagram of the torsional vibration measurement method based on time-frequency ridge line extraction and numerical integration provided by the present invention;

[0026] Figure 2 This is a time-domain waveform diagram of the vibration of the outer casing of the rotating machinery in an embodiment of the present invention;

[0027] Figure 3 This is a time-frequency distribution map obtained using a high-resolution time-frequency analysis method in an embodiment of the present invention;

[0028] Figure 4 These are the frequency conversion signal and angular velocity signal extracted in the embodiments of the present invention;

[0029] Figure 5 The results of numerical integration, detrending, and smoothing of the torsional vibration signal are presented in the embodiments of the present invention.

[0030] Figure 6 The results are the spectral and envelope spectra of the torsional vibration signal in this embodiment of the invention. Detailed Implementation

[0031] The present invention will now be described in detail with reference to the accompanying drawings and examples.

[0032] This invention provides a torsional vibration measurement method based on time-frequency ridge extraction and numerical integration, the process of which is shown in the attached figure. Figure 1 As shown, it includes:

[0033] S1. Use a vibration acceleration sensor to collect vibration signals of the outer casing or outer housing to be analyzed;

[0034] S2. After downsampling to the required analysis range, the vibration acceleration signal is analyzed using a high-resolution time-frequency analysis method to obtain a high-resolution time spectrum.

[0035] S3. Extract the rotational frequency information of the shaft to be analyzed from the time-frequency distribution and convert it into an angular velocity signal;

[0036] S4. Based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated;

[0037] S5. Detrend and smooth the numerical integration results to obtain the torsional vibration signal;

[0038] S6. Perform spectrum analysis on the obtained torsional vibration signal to analyze the accuracy of the extraction method.

[0039] This invention utilizes a high-resolution time-frequency analysis method to perform time-frequency analysis on the vibration acceleration signal of the outer casing, obtaining a high-resolution time spectrum. Based on the time spectrum results, the rotational frequency information of the shaft to be analyzed is extracted from the time-frequency distribution and converted into an angular velocity signal. Based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated, and the time-domain signal of the torsional vibration signal is finally obtained through detrending processing and smoothing operations. This effectively realizes the extraction of the torsional vibration signal, which can be used for feature extraction and analysis of the torsional vibration signal, thereby guiding the fault diagnosis of the rotor system.

[0040] Example:

[0041] The data in this embodiment was obtained during field testing of an accessory gearbox, which has a total of ten shafts. A BK4519 accelerometer was used to measure the vibration acceleration signal of the outer casing of the accessory gearbox. The sensor was fixed to a designed bracket, which was bolted to the outer casing. During the test, the rotational speed was stabilized at 90% of its rated capacity. The rotational frequency information of each shaft is shown in the table below. Shaft 2 is the input shaft, with a rotational speed of 11984 rpm and a sampling frequency of 128000 Hz. During the test, the second-order torsional vibration frequency of shaft 2 at 90% load differed from the rotational frequency of shaft 4 by approximately 1.3 Hz, causing beat frequency fluctuations in the rotational frequency of shaft 4. In this case, the torsional vibration signal of shaft 4 was extracted.

[0042] Table 1. Rotational frequency information of each shaft in the gearbox (attached).

[0043]

[0044] A torsional vibration measurement method based on time-frequency ridge line extraction and numerical integration, the process of which is as follows: Figure 1 As shown, the specific steps are as follows:

[0045] S1. Mount the vibration acceleration sensor onto the outer casing of the rotating machinery using magnetic attraction or a bracket, and set the sampling frequency f of the original signal. s At least higher than the frequency f to be analyzed max The value is 2.56 times the value of the original signal to be analyzed and evaluated by the vibration acceleration sensor. The original signal is downsampled according to the required analysis frequency, which reduces the subsequent computational load while retaining the required analysis frequency band. The portion of the downsampled signal to be analyzed is then extracted as the vibration acceleration signal required for time-frequency analysis.

[0046] In this embodiment, the sampling frequency is 128000Hz. The maximum analysis frequency of the 4-axis rotation is approximately below 500Hz. Therefore, based on the maximum analysis frequency of the required axis, the sampling frequency is downsampled to 1000Hz, and a stable operating condition is selected for analysis. The time frame is 10 seconds, and the number of data points after downsampling is 10000.

[0047] S2. The downsampled acceleration vibration signal is used as the signal to be analyzed. First, a short-time Fourier transform is used for time-frequency analysis. A Gaussian window is selected as the window function, and the length parameter of the window function is set to hlength. This expands the one-dimensional time-series signal to a two-dimensional time-frequency space, obtaining a time spectrum with relatively low time-frequency resolution. Post-processing is then performed on this time spectrum to calculate the second-order instantaneous frequency operator to obtain accurate instantaneous frequency information. Finally, the obtained short-time Fourier transform time-frequency result is subjected to a second-order synchronous compression transform, and the ambiguous time-frequency energy is redistributed to the intermediate frequency estimate in the instantaneous frequency direction, ultimately obtaining a high-resolution time spectrum.

[0048] In this embodiment, the intercepted signal time length is 10s, and the number of sampling points obtained after downsampling is 10000. Therefore, a Gaussian window is selected as the window function for time-frequency analysis, and the window length parameter hlength is set to 2000. By using the second-order synchronous squeezing transform, a time-frequency distribution with better time-frequency aggregation is obtained.

[0049] S3. The penalty function method is used to calculate the approximate value of the ridge line of the rotational frequency of the shaft to be analyzed in the high-resolution time-frequency spectrum. This algorithm first determines the initial time-frequency ridge line value through the maximum amplitude of the time-frequency signal, and then searches forward and backward. The output results include the time-frequency coefficient of the ridge line index and the energy of the returned ridge. Based on the physical relationship between rotational speed and angular velocity, and since the physical vibration parameters characterizing torsional vibration are angular displacement (or angle), angular velocity, and angular acceleration, the extracted rotational frequency information is converted into an angular velocity signal.

[0050] In this invention example, a penalty function method is used to calculate the approximate value of the ridge line of the rotational frequency of the axis to be analyzed in the time-frequency distribution. This algorithm first determines the initial time-frequency ridge line value through the maximum amplitude of the time-frequency wave, then searches forward or backward. The output includes a vector of ridge line indices and the energy of the returned ridge. The formula can be expressed as follows: In the formula, IF(n-1) represents the time-frequency ridge value determined at the previous moment, A[n,m] represents the high-resolution time-frequency spectrum, and w is the penalty factor. Based on the physical relationship between rotational speed and angular velocity, the extracted rotational frequency information is converted into an angular velocity signal.

[0051] S4. Input the angular velocity signal sequence, and use the cumulative trapezoidal numerical integration method to perform discrete point numerical integration on the extracted angular velocity signal to obtain the numerical integration result of the angular velocity signal.

[0052] In this invention, the extracted angular velocity signal is numerically integrated at discrete points using the cumulative trapezoidal numerical integration method. The main requirement is to perform cumulative integration with uniform spacing. For the same sequence a(n), the calculation process can be expressed as follows:

[0053] S5. Detrend and smooth the numerical integration results to obtain the torsional vibration signal.

[0054] In this invention, the numerical integration result of the input angular velocity signal is subjected to a polynomial trend removal operation. This removes the best-fit line from the sequence data of the integration result, thereby eliminating the influence of the offset generated during numerical integration on subsequent calculations. Removing the trend from the numerical integration result allows the analysis to focus on the fluctuations in the data trend itself. Finally, a smoothing process is performed using a moving average method to smooth the extracted torsional vibration signal. A smoothing window length of 2001 is selected in the moving average method.

[0055] S6. Perform spectrum analysis on the obtained torsional vibration signal to analyze the accuracy of the extraction method. Specifically, perform a fast Fourier transform on the extracted torsional vibration time-domain signal to obtain its spectrum and determine whether its frequency components are consistent with the theoretical values. This will determine the accuracy of the method used. Similarly, perform envelope spectrum analysis on the extracted torsional vibration time-domain signal to determine whether its frequency components are consistent with the theoretical values. This will determine the accuracy of the method used.

[0056] The time-domain waveform of the vibration acceleration signal of the outer casing of the accessory gearbox measured in this embodiment is as follows: Figure 2 As shown, the time-domain waveform is a truncated portion of the data used for analysis after downsampling. The time-frequency spectrum obtained using high-resolution time-frequency analysis in this example is as follows: Figure 3 As shown, Figure 3 The time-frequency distribution has better time-frequency clustering, which can be used for accurate extraction and separation of subsequent ridge lines. Figure 4 The present invention demonstrates the frequency conversion signal and angular velocity signal extracted in the embodiments of the present invention, showing that the present invention can effectively extract the frequency conversion trend over time under bondless conditions. Figure 5 It utilizes the integration results of numerical integration and the torsional vibration signal after detrending and smoothing operations. This signal can be used for feature extraction and analysis of torsional vibration, thereby guiding the fault diagnosis of the rotor system. Figure 6 These are the spectral and envelope spectrum results of the torsional vibration signal, used to verify the accuracy of the method.

[0057] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A torsional vibration measurement method based on time-frequency ridge line extraction and numerical integration, characterized in that, It includes the following steps: S 1. Use a vibration acceleration sensor to collect vibration signals from the outer casing or housing to be analyzed; S 2. After downsampling to the required analysis range, the vibration acceleration signal is analyzed using a high-resolution time-frequency analysis method to obtain a high-resolution time spectrum; S 3. Extract the rotational frequency information of the shaft to be analyzed from the time-frequency distribution and convert it into an angular velocity signal; S 4. Based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated; S 5. Detrend and smooth the numerical integration results to obtain the torsional vibration signal; S 6. Perform spectrum analysis on the obtained torsional vibration signal to analyze the accuracy of the extraction method; The S In step 3, the rotational frequency information of the shaft to be analyzed is extracted from the time-frequency distribution, specifically as follows: The penalty function method is used to calculate the approximate value of the ridge line of the rotation frequency of the required analysis shaft in the high-resolution time spectrum. The algorithm first determines the time-frequency ridge line value at the initial time by the maximum time-frequency amplitude, and then searches forward and backward. The output results include the time-frequency coefficient of the ridge line index and the energy of the returned ridge.

2. The method as described in claim 1, characterized in that, The S In step 1, the vibration signal of the outer casing or housing to be analyzed is collected using a vibration acceleration sensor, including the following steps: The vibration acceleration sensor is mounted to the outer casing of the rotating machinery using magnetic attraction or a bracket, and the sampling frequency of the original signal is set. At least higher than the frequency to be analyzed A multiple of 2.56; The raw signal to be analyzed, acquired by the vibration acceleration sensor, is downsampled, specifically as follows: The vibration acceleration sensor acquires the original signal to be analyzed and evaluated. The original signal is downsampled according to the required analysis frequency to reduce the subsequent calculation load while retaining the required analysis frequency band. The downsampled signal is then extracted to be analyzed as the vibration acceleration signal required for time-frequency analysis.

3. The method as described in claim 1 or 2, characterized in that, The S In section 2, a high-resolution time-frequency analysis method is used to perform time-frequency analysis on the vibration acceleration signal, specifically as follows: Using the downsampled acceleration vibration signal as the signal to be analyzed, a short-time Fourier transform is first performed for time-frequency analysis. A Gaussian window is selected as the window function, and the length parameter of the window function is set to... hlength The one-dimensional time-series signal is extended to a two-dimensional time-frequency space, resulting in a time-frequency spectrum with relatively low time-frequency resolution. Post-processing is then performed on this time spectrum, using a second-order synchronous compression transform to improve the time-frequency resolution, and instantaneous frequency operators are calculated. Group delay operator Frequency modulation estimation operator Finally, the second-order instantaneous frequency operator is calculated. In the formula Indicates time, Indicates frequency, Represents the spectrum during short-time Fourier transform. The imaginary unit is used to redistribute the fuzzy time-frequency energy to the intermediate frequency estimate in the second-order instantaneous frequency direction, ultimately obtaining a high-resolution time spectrum. The second-order synchronous compression transform algorithm is expressed as follows: In the formula Indicates the frequency position of the redistribution. This represents the Dirac distribution symbol.

4. The method as described in claim 3, characterized in that, Based on the physical relationship between rotational speed and angular velocity, and since the physical vibration parameters characterizing torsional vibration are angular displacement, angular velocity, and angular acceleration, the extracted rotational frequency information is converted into an angular velocity signal.

5. The method as described in claim 4, characterized in that, The S In section 4, based on the physical characteristics of torsional vibration, the angular velocity signal is numerically integrated, specifically as follows: Input an angular velocity signal sequence, and use the cumulative trapezoidal numerical integration method to perform discrete-point numerical integration on the extracted angular velocity signal, thereby obtaining the numerical integration result of the angular velocity signal.

6. The method as described in claim 5, characterized in that, The S In step 5, the numerical integration results are detrended and smoothed to obtain the torsional vibration signal, specifically as follows: The numerical integration result of the input angular velocity signal is subjected to a polynomial trend removal operation, which removes the best-fit line from the sequence data of the integration result, thereby eliminating the influence of the offset generated during numerical integration on subsequent calculations. Removing the trend from the numerical integration result allows the analysis to focus on the fluctuations of the data trend itself. Finally, the moving average method is used for smoothing to make the extracted torsional vibration signal smooth.

7. The method as described in claim 1, characterized in that, The S In step 6, the obtained torsional vibration signal is subjected to spectral analysis to analyze the accuracy of the extraction method. Specifically: Perform a Fast Fourier Transform on the extracted torsional vibration time-domain signal to obtain its spectrum, and determine whether its frequency components are consistent with the theoretical values ​​to determine the accuracy of the method used. Similarly, perform envelope spectrum analysis on the extracted torsional vibration time-domain signal to determine whether its frequency components are consistent with the theoretical values, in order to verify the accuracy of the method used.

Images