A time domain synchronous averaging method based on correlation theory

Abstract

This invention relates to a time-domain synchronous averaging method based on correlation theory, comprising the following steps: calculating the average rotational speed of the gear shaft using the maximum spectral energy method; obtaining the most stable periodic gear meshing vibration harmonics through bandpass filtering; performing iterative correlation analysis on the most stable periodic gear meshing vibration harmonics to estimate the starting sequence; and using the starting sequence to segment, spline fit interpolate, and synchronously average the vibration signal to obtain the time-domain synchronous average signal. This invention introduces correlation theory twice to ensure the accuracy of the final time-domain synchronous averaging result. The bandpass filtering step selects a filter bandwidth including first-order sidebands, and since gears are usually subject to frequency modulation when faulty, this method is more robust to fault data analysis and has good application and promotion value.

Description

Technical Field

[0001] This invention relates to the field of wind turbine gearbox fault diagnosis technology, and in particular to a time-domain synchronous averaging method based on correlation theory. Background Technology

[0002] Wind energy is a renewable and clean energy source, and vigorously developing wind power generation is of great significance for ensuring energy security, protecting the ecological environment, and achieving sustainable development. To obtain better wind resources, wind turbines are typically installed in harsh natural conditions such as high mountains, plateaus, coastlines, and nearshore areas. This makes wind turbines prone to failure and significantly increases operation and maintenance costs. Therefore, condition-based intelligent operation and maintenance is crucial for the development of wind power. As the main transmission mechanism of a wind turbine, the gearbox is inevitably susceptible to fatigue damage, and downtime and repair costs caused by gearbox failures are relatively high. Only by timely fault detection can predictive maintenance be carried out, thereby reducing downtime and repair costs.

[0003] Time-domain synchronous averaging is a signal processing method used for fault diagnosis of rotating machinery. It can extract periodic vibration components related to the shaft under study from vibration signals. Particularly in gearbox fault diagnosis, time-domain synchronous averaging can retain the meshing vibration components (coherent components) of the gear under study while weakening the vibration components of other meshing gears (incoherent components), and also reducing noise. Classical time-domain synchronous averaging methods require a speed sensor or optical encoder to record the time points corresponding to each revolution of the gear shaft. These time points constitute a speed time series. Then, based on the speed time series, the vibration signal is segmented, spline-fitted, interpolated, and synchronously averaged to obtain the time-domain synchronous average signal. However, sometimes, due to cost and installation considerations, a speed sensor or optical encoder is not installed. In such cases, a method based solely on the gearbox vibration signal for time-domain synchronous averaging is needed.

[0004] Current time-domain synchronous averaging methods without rotational speed mostly rely on instantaneous angular velocity theory, which calculates instantaneous angular velocity or phase angle based on gear meshing vibration harmonics. Instantaneous angular velocity theory includes phase demodulation and time-frequency analysis. Phase demodulation involves performing a Hilbert transform on the gear meshing harmonics and then calculating the phase angle. However, the rotational speed estimated by current instantaneous angular velocity theory often exhibits local fluctuations, especially at the two ends where fluctuations may be significant. These speed fluctuations can cause mismatches or positional deviations between the signals to be synchronously averaged in the time domain. This not only fails to eliminate interference signals but also introduces additional errors. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a time-domain synchronous averaging method based on correlation theory.

[0006] This invention is achieved through the following technical solution:

[0007] A time-domain synchronous averaging method based on correlation theory includes the following steps: S1. Calculate the average rotational speed of the gear shaft according to the maximum spectral energy method; S2. Obtain the most stable periodic gear meshing vibration harmonics through bandpass filtering; S3. Perform iterative correlation analysis on the most stable periodic gear meshing vibration harmonics to estimate the starting point sequence; S4. Based on the starting point sequence, the vibration signal can be segmented, spline fitted, interpolated, and synchronously averaged to obtain the time-domain synchronous average signal.

[0008] According to the above technical solution, preferably, step S1 includes: performing a Fourier transform on the vibration signal of the wind turbine gearbox to obtain a spectrum; calculating the spectral energy of each assumed average rotational speed in the spectrum; the assumed rotational speed corresponding to the maximum spectral energy is the estimated average rotational speed of the gear shaft.

[0009] According to the above technical solution, preferably, step S1 further includes: filtering the vibration signal of the fan gearbox collected at low speed based on frequency domain indicators.

[0010] According to the above technical solution, preferably, step S2 includes: based on the average rotational speed of the gear shaft and the number of gear teeth, locating the first 5 harmonic frequencies of the high-speed gear meshing vibration; using the first 5 harmonic frequencies as the center frequency and the rotational frequency as the bandwidth, calculating the maximum amplitude near each harmonic frequency, and using the amplitude as the basis for judging the magnitude of the harmonic energy; selecting the harmonic frequency with higher energy, and performing bandpass filtering with a multiple of the rotational frequency as the bandwidth to obtain high-energy vibration harmonics; finally, selecting the vibration harmonic with the largest peak value ratio R as the most periodic and stable gear meshing vibration harmonic.

[0011] According to the above technical solution, preferably, in step S3, the accuracy of the starting sequence is determined based on the rotational speed continuity index.

[0012] According to the above technical solution, preferably, the rotational speed continuity index is:

[0013] I rsc =max([|s3+s1-2s2|,|s4+s2-2d3|,,|s i+2 +s i -2s i+1 |,])

[0014] According to the above technical solution, preferably, step S4 includes: taking the vibration signal between the first starting point and the second starting point in the starting point sequence as the standard vibration signal x. s ; for the standard vibration signal x s Spline fitting and interpolation are performed to obtain the standard interpolated signal x. s’; Shift the i-th starting point in the starting point sequence forward by a i The (i+1)th starting point is shifted a step to the right. i At point i, the i-th matching signal x is generated. m,i ; for the matching signal x m,i Perform spline fitting and interpolation to obtain the matched interpolated signal x. m,i’ ; for each of the said matching interpolation signals x m,i’ With standard interpolated signal x s’ Perform motion correlation matching and extract each of the matching interpolation signals x. m,i’ With standard interpolated signal x s’ The region with the highest correlation; the standard interpolated signal x s’ The time-domain synchronous average signal is obtained by averaging with all the regions with the highest correlation.

[0015] The beneficial effects of this invention are:

[0016] This invention can calculate the average rotational speed of the gear shaft based on the vibration signal collected from the gearbox. The starting sequence calculated based on correlation theory corresponds to the rotational period of the gear shaft. The rotational speed fluctuation, i.e., the real-time rotational speed, can be calculated from the starting sequence and the sampling frequency. A rotational speed continuity index is proposed to ensure the estimation accuracy of the starting sequence. Correlation theory is introduced twice to ensure the accuracy of the final time-domain synchronous averaging result. In the bandpass filtering step, a filter bandwidth including the first-order sideband is selected. Since gears are usually subject to frequency modulation when they fail, the invention has higher robustness for fault data analysis. Attached Figure Description

[0017] Figure 1 This is the time-domain synchronous averaging method based on correlation theory in Embodiment 1 of the present invention.

[0018] Figure 2 This is the composition of the high-speed axial radial vibration signal spectrum in Embodiment 1 of the present invention.

[0019] Figure 3 This is the maximum spectral energy method in Embodiment 1 of the present invention.

[0020] Figure 4 This refers to the harmonic frequency region of gear meshing vibration in Embodiment 1 of the present invention.

[0021] Figure 5 It is the gear meshing harmonics and their peak sequence in Embodiment 1 of the present invention.

[0022] Figure 6 This is the second starting point estimated in Embodiment 1 of the present invention.

[0023] Figure 7 This is the third starting point estimated in Embodiment 1 of the present invention.

[0024] Figure 8 This is the synchronous averaging process in Embodiment 1 of the present invention.

[0025] Figure 9 This refers to the motion-related matching in Embodiment 1 of the present invention.

[0026] Figure 10 It is the high-speed shaft gear of the gearbox in Embodiment 2 of the present invention.

[0027] Figure 11 These are the vibration waveforms and spectra in Embodiment 2 of the present invention.

[0028] Figure 12 It is the spectral energy in Embodiment 2 of the present invention.

[0029] Figure 13 It is the gear meshing harmonic in Embodiment 2 of the present invention.

[0030] Figure 14 This refers to the rotational speed fluctuation in Embodiment 2 of the present invention.

[0031] Figure 15 This is a comparison between the standard interpolated signal and the last region with the highest correlation in Embodiment 2 of the present invention.

[0032] Figure 16 It is the time-domain synchronous average signal in Embodiment 2 of the present invention. Detailed Implementation

[0033] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0034] Example 1: As Figure 1 As shown, the present invention includes the following steps:

[0035] S1. Average speed estimation: The average speed of the gear shaft is calculated based on the maximum spectral energy method;

[0036] S2. Bandpass filtering: The most stable periodic gear meshing vibration harmonics are obtained through bandpass filtering;

[0037] S3. Starting point sequence estimation: Perform iterative correlation analysis on the most stable periodic gear meshing vibration harmonics to estimate the starting point sequence;

[0038] S4. Synchronous averaging: Based on the starting point sequence, the vibration signal can be segmented, spline fitted, interpolated, and synchronously averaged to obtain a time-domain synchronous average signal.

[0039] Based on the above steps, specifically:

[0040] S1 - Average Speed ​​Estimation:

[0041] The vibration signal of the wind turbine gearbox mainly consists of gear meshing vibration, and the gear meshing frequency f m With the average rotational speed v of the gear shaft s Satisfying a fixed relationship:

[0042] f m =v s / 60*n t

[0043] Where n t The gear has the number of teeth, and the average speed of the gear shaft can be calculated from the gear meshing frequency.

[0044] Most wind turbine gearboxes contain multiple speed-increasing stages. The vibration signals collected from the gearboxes have the following characteristics: 1) The energy of the vibration signal generated by the meshing of the high-speed stage gears is higher than that of the low-speed stage; 2) The vibration signal usually contains the first three harmonics of the gear meshing vibration, and some vibration signals contain higher-order harmonics; 3) The vibration signal also contains the vibration component generated by the rotation of the gear shaft; 4) Due to the fluctuation of the wind turbine speed, the harmonics of gear meshing vibration exist in the form of spectral peaks in the spectrum; 5) The height order of the spectral peaks of the gear meshing vibration harmonics is not fixed, but the height of the spectral peak of the first harmonic of gear meshing vibration will not be low.

[0045] A 2MW wind turbine gearbox consists of a single-stage planetary gear train and a two-stage parallel gear train. The spectrum of the vibration signal collected radially from the high-speed shaft of the gearbox is as follows: Figure 2 As shown, the high-speed shaft rotational vibration, low-speed shaft gear meshing vibration harmonics and high-speed shaft gear meshing vibration harmonics can be clearly seen.

[0046] Based on the aforementioned objective laws, the Maximum Spectral Energy (MSE) method is developed to calculate the average rotational speed of the gear shaft. First, a Fourier transform is performed on the vibration signal to obtain its spectrum. Second, the spectral energy of each assumed average rotational speed is calculated from the spectrum. Finally, the assumed rotational speed corresponding to the maximum spectral energy is the estimated average rotational speed of the gear shaft. The flowchart of the Maximum Spectral Energy method is as follows: Figure 3 As shown.

[0047] The formula for calculating spectral energy is as follows:

[0048]

[0049]

[0050]

[0051]

[0052] in and These represent the energy regions corresponding to the first three harmonic frequencies of the meshing vibration of the i-th pair of gears. and For the corresponding spectral line index; A k is the amplitude of spectral line k; l controls the spectral range for regional energy calculation, which is half the number of narrowband spectral lines at the meshing frequency of the i-th pair of gears. Its value is sufficient to satisfy most gear meshing frequencies. Due to the fluctuation of gear shaft speed, the region width increases linearly. Let w be the rotational frequency amplitude of the j-th gear shaft. Considering that the energy in the region corresponding to the first-order frequency of gear meshing vibration is usually very high, it should be given a higher weight, i.e., w should be a number greater than 1, such as 1.2 to 1.6. When assuming the average speed is close to the actual average speed, the region corresponding to the first three harmonic frequencies of gear meshing vibration is as follows: Figure 4 As shown.

[0053] To protect the wind turbine, it will adjust its pitch or stop when the wind speed is too high. This means the average rotational speed of the gear shaft will not be very high, so the maximum rotational speed is conservatively set to v. max That is, the gear shaft speed will not exceed v. max When the fan operates at low speed, the vibration signal collected from the gearbox is distorted and cannot accurately reflect faults. Therefore, it is necessary to remove the vibration signal collected at low speed. This example proposes a frequency domain index, frequency kurtosis K. F This is used to filter low-speed data, and its formula is as follows:

[0054]

[0055]

[0056] Where f k A k F represents the frequency and amplitude of spectral line k in the spectrum, respectively. C The centroid frequency of the frequency spectrum. When the average rotational speed of the gear shaft is below a certain range, the frequency kurtosis K... F The frequency kurtosis will exceed a certain threshold, so it can be used as a screening criterion to eliminate vibration signals collected at low speeds. Of course, some data needs to be analyzed beforehand to determine the threshold value. Similarly, the minimum speed is conservatively set to v. min That is, the average rotational speed corresponding to the vibration signals retained after frequency kurtosis filtering is greater than v. min Therefore, the maximum spectral energy method has a range for estimating the average rotational speed.

[0057] S2-Bandpass Filter:

[0058] The purpose of bandpass filtering is to obtain the most stable periodic gear meshing vibration harmonics. Bandpass filtering includes four main steps: 1) Based on the previously calculated average rotational speed and number of gear teeth, locate the frequencies of the first 5 harmonics of high-speed gear meshing vibration; 2) Using the first 5 harmonic frequencies as the center frequency and the rotational frequency as the bandwidth, calculate the maximum amplitude near each harmonic frequency, and use the amplitude as the basis for judging the harmonic energy; 3) Select the harmonic frequencies with higher energy. Without loss of generality, 10 times the average amplitude of the spectrum can be used as the selection criterion. Then, bandpass filtering is performed with the rotational frequency multiple as the bandwidth to obtain high-energy vibration harmonics. In order to include the first-order sideband of the gear meshing frequency, the 2.5 harmonic of the rotational frequency is selected as the filtering bandwidth; 4) Finally, select the vibration harmonic with the largest peak-to-peak ratio R as the most stable periodic gear meshing vibration harmonic.

[0059] The peak-to-peak ratio is defined as follows:

[0060]

[0061] Where x n,p The peak sequence of the nth order meshing vibration harmonics, such as Figure 5 As shown, μ and σ are the mean and standard deviation, respectively, and Φ -1 Let α be the inverse function of the Gaussian probability density function, and α be the confidence level, which is usually taken as 0.05.

[0062] S3 - Starting point sequence estimation:

[0063] The vibration signal consists of a large number of discrete data points. The first point corresponds to a certain axial angle position of the gear shaft, which is taken as the first starting point s1 = 1. When the gear shaft rotates to the same axial angle position again, the corresponding vibration signal point is the second starting point s2. All the starting points constitute the starting point sequence. With the starting point sequence, the vibration signal can be segmented, spline fitted, interpolated, and synchronously averaged to obtain the synchronously averaged signal. This step involves iterative correlation analysis on the most stable periodic gear meshing vibration harmonics obtained above to estimate the starting point sequence. From the s-th harmonic of the vibration... i Starting from point 1, N points are selected forward as the correlation analysis scale. The scale is defined as follows:

[0064] r i =[x n (s i ),x n (si+1),…,x n (s i +N-1)]

[0065] Here, N represents the signal value corresponding to two rotations of the gear. This avoids local anomalies caused by an excessively short scale, while also preventing errors due to an excessively long scale. The scale is moved point by point, r. i , and harmonics xn Conduct correlation analysis

[0066]

[0067] x i,j =[x n (s i +j),x n (s i +j+1),…,x n (s i +j+N-1)]j≥0

[0068] Wherein, each correlation result ρ i,j Each corresponds to a harmonic point s i +j, the nth t *The n points form the next starting point s i+1 , where n t Let n be the number of teeth and n be the harmonic order. The starting point sequence is obtained using mathematical induction. The calculation of the second and third starting points is illustrated below. Figure 6 and Figure 7 As shown.

[0069] In the starting sequence, the vibration signal between two adjacent starting points corresponds to one revolution of the gear shaft. The difference in signal quantity represents the fluctuation of the rotational speed, which in reality is always continuous. Therefore, the continuity of the rotational speed fluctuation can be used as a criterion for judging whether the calculated starting sequence is accurate. That is, if the rotational speed fluctuation obtained from the starting sequence is continuous rather than abrupt, then the estimated starting sequence is accurate. The rotational speed continuity index is as follows:

[0070] I rsc =max([|s3+s1-2s2|,|s4+s2-2s3|,,|s i+2 +s i -2s i+1 |,])

[0071] S4 - Synchronous Average:

[0072] The above analysis yielded the average rotational speed corresponding to the vibration signal, and the vibration signal points corresponding to each revolution of the gear shaft, i.e., the starting point sequence. From the starting point sequence and sampling frequency, the rotational speed fluctuation can be calculated. Therefore, time-domain synchronous averaging analysis of the vibration signal can be performed. The flowchart for synchronous averaging is as follows... Figure 8 As shown.

[0073] First, the vibration signal between the first and second starting points is taken as the standard vibration signal x. s As shown in the formula below, spline fitting and interpolation are performed on the standard signal to increase the signal quantity by m times to obtain the standard interpolated signal x. sTo ensure that the signal quantity of the standard interpolation signal is greater than the signal quantity between any two adjacent starting points, without loss of generality, m can be set to 2.

[0074] x s =[x(s1),x(s1+1),…,x(s2-1)]

[0075] Then move the i-th starting point forward by a. i The (i+1)th starting point is shifted a step to the right. i The i-th matching signal x is generated at point i. m,i As shown in the formula below. The reason for adding 'a' before and after is... i The point is to compensate for the small bias in the estimation of the starting sequence, usually a i The vibration signal quantity is less than that corresponding to a single tooth meshing. Similarly, spline fitting and interpolation are performed on the matched signal to increase the signal quantity to the theoretical m*c value. i The matched interpolated signal x is obtained by multiplying the two values. m,i ', where c i The calculation formula is as follows:

[0076] x m,i =[x(s i -a i ),…,x(s i ),x(s i +1),…,x(s i+1 ),…,x(s i+1 +a i )]i≥2

[0077]

[0078] Finally, each matched interpolated signal is compared with the standard interpolated signal using a moving correlation analysis, and the region x with the highest correlation between each matched interpolated signal and the standard interpolated signal is extracted. m,i ", indicating as Figure 9 As shown, the time-domain synchronous average signal is obtained by averaging the standard interpolated signal with all regions with the highest correlation.

[0079]

[0080] Example 2: The method is applied using a 2MW wind turbine gearbox as an example. The high-speed shaft gear of the gearbox has cracks, such as... Figure 10 As shown, the vibration signal and its spectrum collected from the high-speed shaft of the gearbox are as follows: Figure 11 As shown, modulation and sidebands are clearly visible.

[0081] This invention includes the following steps:

[0082] S1. Average speed estimation: The average speed of the gear shaft is calculated based on the maximum spectral energy method.

[0083] Specifically, the average rotational speed of the above vibration signal is estimated, and the spectral energy is as follows: Figure 12 As shown, despite the presence of many sidebands, it is still evident that the spectral energy reaches its maximum at 1695 rpm, and the gear meshing frequency calculated from the average speed is accurate.

[0084] S2. Bandpass filtering: The most stable periodic gear meshing vibration harmonics are obtained through bandpass filtering.

[0085] Specifically, by performing a bandpass filter on the aforementioned vibration signal with a bandwidth of 2.5 times the rotational frequency, the periodicity of the first harmonic of the gear meshing frequency becomes the most stable. The harmonics are as follows: Figure 13 As shown.

[0086] S3. Starting point sequence estimation: Perform iterative correlation analysis on the most stable periodic gear meshing vibration harmonics to estimate the starting point sequence.

[0087] Specifically, based on the aforementioned vibration signal harmonics, the starting point sequence is estimated, and the rotational speed fluctuation calculated from the starting point sequence and sampling frequency is examined, such as... Figure 14 As shown, smooth speed fluctuations indicate that the estimated starting sequence is accurate.

[0088] S4. Synchronous averaging: Based on the starting point sequence, the vibration signal can be segmented, spline fitted, interpolated, and synchronously averaged to obtain a time-domain synchronous average signal.

[0089] Specifically, examine the standard interpolated signal and the last region of highest correlation, such as... Figure 15 As shown, the two match well, indicating that the final accuracy of this method meets the requirements. The final time-domain synchronous average signal is as follows: Figure 16 As shown.

[0090] This invention can calculate the average rotational speed of the gear shaft based on the vibration signal collected from the gearbox. The starting sequence calculated based on correlation theory corresponds to the rotational period of the gear shaft. The rotational speed fluctuation, i.e., the real-time rotational speed, can be calculated from the starting sequence and the sampling frequency. A rotational speed continuity index is proposed to ensure the estimation accuracy of the starting sequence. Correlation theory is introduced twice to ensure the accuracy of the final time-domain synchronous averaging result. In the bandpass filtering step, a filter bandwidth including the first-order sideband is selected. Since gears are usually subject to frequency modulation when they fail, the invention has higher robustness for fault data analysis.

[0091] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A time-domain synchronous averaging method based on correlation theory, characterized in that, Includes the following steps: S1. Calculate the average rotational speed of the gear shaft using the maximum spectral energy method; S2. Obtain the most stable periodic gear meshing vibration harmonics through bandpass filtering; S3. Perform iterative correlation analysis on the most stable periodic gear meshing vibration harmonics to estimate the starting point sequence, which is the vibration signal point corresponding to each revolution of the gear shaft, i.e., the starting point sequence. S4. Based on the starting point sequence, the vibration signal can be segmented, spline fitted, interpolated, and synchronously averaged to obtain a time-domain synchronously averaged signal; Step S2 includes: based on the average rotational speed of the gear shaft and the number of gear teeth, locating the first 5 harmonic frequencies of the high-speed gear meshing vibration; using the first 5 harmonic frequencies as the center frequency and the rotational frequency as the bandwidth, calculating the maximum amplitude near each harmonic frequency, and using the amplitude as the basis for judging the magnitude of the harmonic energy; selecting the harmonic frequencies with higher energy, and performing bandpass filtering with a multiple of the rotational frequency as the bandwidth to obtain high-energy vibration harmonics; finally, selecting the vibration harmonic with the largest peak value ratio R as the most periodically stable gear meshing vibration harmonic; Step S4 includes: using the vibration signal between the first and second starting points in the starting point sequence as the standard vibration signal x. s ; for the standard vibration signal x s Spline fitting and interpolation are performed to obtain the standard interpolated signal x. s ， ; Shift the i-th starting point in the starting point sequence forward by a i The (i+1)th starting point is shifted a step to the right. i At point i, the i-th matching signal x is generated. m,i ; for the matching signal x m,i Perform spline fitting and interpolation to obtain the matched interpolated signal x. m,i ， ; for each of the said matching interpolation signals x m,i ， With standard interpolated signal x s ， Perform motion correlation matching and extract each of the matching interpolation signals x. m,i ， With standard interpolated signal x s ， The region with the highest correlation; the standard interpolated signal x s ， The time-domain synchronous average signal is obtained by averaging with all the regions with the highest correlation.

2. The time-domain synchronous averaging method based on correlation theory according to claim 1, characterized in that, Step S1 includes: performing a Fourier transform on the vibration signal of the wind turbine gearbox to obtain a spectrum; calculating the spectral energy of each assumed average rotational speed in the spectrum; the assumed rotational speed corresponding to the maximum spectral energy is the estimated average rotational speed of the gear shaft.

3. The time-domain synchronous averaging method based on correlation theory according to claim 1 or 2, characterized in that, Step S1 also includes: filtering the vibration signal of the fan gearbox collected at low speed based on frequency domain indicators.

4. The time-domain synchronous averaging method based on correlation theory according to claim 1, characterized in that, In step S3, the accuracy of the starting sequence is determined based on the rotational speed continuity index.

5. The time-domain synchronous averaging method based on correlation theory according to claim 4, characterized in that, The rotational speed continuity index is: , The vibration signal consists of a large number of discrete data points. The first point corresponds to a certain axial angle position of the gear shaft, which is taken as the first starting point. The vibration signal point corresponding to when the gear shaft rotates to the same shaft angle position again is the second starting point. All the starting points constitute the starting point sequence; the vibration signal between two adjacent starting points in the starting point sequence corresponds to one revolution of the gear shaft, and the difference in signal quantity represents the fluctuation of the rotational speed.

Images