A vibration signal-based gear wear area monitoring method under variable speed conditions

Abstract

This invention belongs to the field of gear health status assessment technology and discloses a method for monitoring gear wear area under variable speed conditions based on vibration signals. The method includes the following steps: acquiring gear vibration signals; calculating the time-frequency distribution signal of the vibration signals based on multiple synchronous extraction and transformation; extracting phase information from the time-frequency distribution signal and then obtaining the angular domain signal through angular domain resampling; segmenting and aligning the angular domain signal according to the gear's fault cycle to obtain deterministic components related to gear wear; optimizing the deterministic components using a Savitzky-Golay filter and then calculating the order spectrum and comprehensive step energy ratio; repeatedly acquiring gear vibration signals and calculating the cumulative comprehensive energy ratio index. This invention uses the cumulative comprehensive energy ratio index to evaluate or monitor gear wear area, thereby quantifying the severity of wear. This invention can accurately quantify and evaluate gear wear area under variable speed conditions, achieving precise monitoring and assessment of gear wear.

Description

Technical Field

[0001] This invention relates to a method for monitoring gear wear area under variable speed conditions based on vibration signals, belonging to the field of gear health status assessment technology. Background Technology

[0002] Gears are key components for power transmission in high-end equipment such as aircraft engines and high-speed trains, and their health directly affects the safety and reliability of the system. Due to friction and load, tooth surface wear is inevitable, which not only impairs equipment performance and reduces operating efficiency but also leads to decreased operational reliability. Therefore, it is necessary to assess the severity of tooth surface wear to improve the operational reliability of the equipment.

[0003] Existing methods for monitoring gear wear primarily rely on acoustic emission signals, encoder signals, temperature signals, oil analysis, and vibration signals. Among these, vibration-based monitoring technology is the most widely used due to its stable and efficient characteristic response capabilities. Although vibration-based monitoring technology can achieve real-time monitoring of gear wear, it still has some limitations. Under variable speed conditions, current technologies often struggle to establish a direct and intuitive connection with the physical state of the gears, lacking sufficient interpretability for the actual degree of gear wear, resulting in relatively abstract monitoring results. Summary of the Invention

[0004] To address the technical problem of the inability to accurately and quantitatively assess the severity of gear wear in existing technologies, this invention proposes a gear wear area monitoring method based on vibration signals, so as to achieve accurate and quantitative assessment of the severity of gear wear under variable speed conditions.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for monitoring gear wear area based on vibration signals, comprising the following steps:

[0006] Step 1: Collect the vibration signal of the gear, and calculate the time-frequency distribution signal of the vibration signal based on multiple synchronous extraction and transformation;

[0007] Step 2: Extract the time-frequency ridge from the time-frequency distribution signal using the penalty optimization algorithm and calculate the instantaneous frequency. Then, perform an integral operation on the instantaneous frequency to obtain the phase information. Finally, obtain a stable angular domain signal through angular domain resampling.

[0008] Step 3: Segment and align the angular domain signal according to the gear failure cycle, and represent the deterministic components related to gear wear in the form of a synchronization matrix;

[0009] Step 4: Use the minimum mean square error between the estimated value of the deterministic component within the window and the original data as the estimation error of the filter, and find an optimal polynomial coefficient through the Savitzky-Golay filter.

[0010] Step 5: Evaluate and optimize the fitting process based on the generalized unbiased mean square error estimation, and adaptively obtain the optimal polynomial order and window width of the Savitzky-Golay filter;

[0011] Step 6: Perform Fourier transform on the deterministic components optimized by the Savitzky-Golay filter to obtain the order spectrum, and calculate the overall step energy ratio from the order spectrum;

[0012] Step 7: Repeatedly collect the vibration signal of the gear and calculate the comprehensive step energy ratio. Calculate the cumulative comprehensive energy ratio index by using the comprehensive step energy ratio at multiple continuous measurement times. Use the cumulative comprehensive energy ratio index to evaluate or monitor the wear area of ​​the gear, thereby quantitatively assessing the severity of wear.

[0013] In step 1, the calculation formula for the time-frequency distribution signal of each vibration signal based on multiple synchronous extraction transformation is as follows:

[0014]

[0015] Among them, Tm C (t,ω) represents the time-frequency distribution signal obtained based on multiple synchronous extraction and transformation, C is the number of compression iterations, and S... STFT (t,ω) represents the time-frequency distribution based on the short-time Fourier transform, δ is the Dirac function, and represents the synchronous extraction transform operator; t and ω represent the time and frequency components in the time-frequency distribution, respectively. This is an estimate of the instantaneous frequency based on multiple synchronous extraction transformation.

[0016] In step 1, the estimated value of the instantaneous frequency The calculation formula is:

[0017]

[0018]

[0019] Where Round(·) is the rounding operation. This represents the frequency components after C compression iterations. Indicates instantaneous phase The first derivative, Indicates instantaneous phase The second derivative of .

[0020] In step 2, the calculation formula for extracting the time-frequency ridge from the time-frequency distribution signal using the penalty optimization algorithm is as follows:

[0021]

[0022] Where E(φ(t)) is the time-frequency ridge of the signal, φ(t) represents the estimated instantaneous frequency in the time-frequency distribution, TFR(t,φ(t)) is the estimated value of the time-frequency coefficient, and λ and β are two parameters for adjusting the regularization level.

[0023] In step 4, the formula for calculating the estimation error of the filter is:

[0024]

[0025] Where ε represents the filter estimation error, c p The coefficients are the polynomial coefficients, m p Let d represent the expansion term of the polynomial, p represent the order of the polynomial, and d represent the expansion term of the polynomial. m and x m These are the estimated values ​​and the original data for the deterministic components, respectively, where M is the window width.

[0026] In step 5, the formula for calculating the generalized unbiased mean square error is:

[0027]

[0028] In the formula, h is the filter coefficient matrix, x is the resampled angular domain signal, S is the length of the resampled angular domain signal, and h s,s This represents the element in the s-th row and s-th column of the filter coefficient matrix. Let V be the variance of the signal.

[0029] The formula for calculating the variance of a signal is:

[0030]

[0031] Where E{·} denotes the expectation, x s It is a discretized angular domain signal.

[0032] In step 6, the formula for calculating the overall bandgap energy ratio is:

[0033]

[0034] In the formula, COER is the combined band energy ratio, Z is the meshing harmonic number, and A z,l Let A be the amplitude of the l-th sideband at the z-th meshing harmonic. z It is the amplitude of the z-th harmonic component.

[0035] In step 7, the formula for the cumulative comprehensive energy ratio index is:

[0036]

[0037] In the formula, CCER represents the cumulative comprehensive energy ratio, t is the measurement time, COER(t) represents the comprehensive step energy ratio corresponding to the vibration signal at measurement time t, η is the correction factor, CER is the comprehensive energy ratio, and RMS is the total energy ratio. d (t) represents the root mean square value of the deterministic component of the vibration signal at measurement time t.

[0038] In step 7, the root mean square (RMS) value of the deterministic component. d The formula for calculating (t) is:

[0039]

[0040] Where, d m This represents the deterministic component optimized by the Savitzky-Golay filter, where S is the length of the angular domain signal after angular domain resampling.

[0041] Compared with the prior art, the present invention has the following technical effects:

[0042] This invention proposes a method for monitoring gear wear area based on vibration signals. First, the instantaneous frequency of the vibration signal is estimated using synchronous extraction transform within a multiple compression framework, and then resampled in the angular domain. Second, an adaptive synchronous fitting technique is developed based on the minimum mean square error of the generalized unbiased estimation to extract vibration components related to gear wear. Then, an index called the cumulative comprehensive energy ratio is constructed based on the dynamic characteristics of gear wear to monitor the wear area of ​​the gear, thereby quantitatively assessing the severity of wear. This invention can achieve a quantitative assessment of the severity of gear wear, and experiments have demonstrated a high degree of consistency between the assessment results of this invention and experimental results. Attached Figure Description

[0043] Figure 1 A schematic flowchart of a method for monitoring gear wear area under variable speed conditions based on vibration signals, provided in an embodiment of the present invention;

[0044] Figure 2 This refers to the time-frequency distribution after multiple synchronization extraction transformation in the embodiments of the present invention;

[0045] Figure 3 This refers to the order spectrum based on adaptive synchronous fitting in the embodiments of the present invention;

[0046] Figure 4 This describes the evolution process of the gear wear surface morphology in the embodiments of the present invention;

[0047] Figure 5This illustrates the effect of the cumulative comprehensive energy ratio index on the monitoring of the wear area ratio under different rotational speeds in the embodiments of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] This invention provides a method for monitoring gear wear area under variable speed conditions based on vibration signals. First, multiple synchronous extraction and transformation are used to resample non-stationary vibration signals under different speed conditions in the angular domain to eliminate the influence of speed changes. Then, adaptive local synchronous fitting is used to extract vibration components related to gear wear. Next, an index called the cumulative comprehensive energy ratio is constructed based on the dynamic characteristics of gear wear to monitor the gear wear area and thus intuitively assess the degree of gear wear. This assessment method can eliminate the influence of speed changes on the assessment results and improve the assessment accuracy.

[0050] like Figure 1 As shown, the gear wear area monitoring method based on vibration signals under variable speed conditions in this embodiment specifically includes the following steps:

[0051] Step 1: Collect vibration signals from the gear, and calculate the time-frequency distribution of each vibration signal based on multiple synchronous extraction and transformation, such as... Figure 2 As shown.

[0052] In step 1, vibration signals under different rotational speeds were collected. Then, the time-frequency distribution of each vibration signal was calculated based on multiple synchronous extraction and transformation. The calculation formula is as follows:

[0053]

[0054] Among them, Tm C (t,ω) represents the time-frequency distribution signal obtained based on multiple synchronous extraction and transformation, C is the number of compression iterations, and S... STFT (t,ω) represents the time-frequency distribution based on the short-time Fourier transform, δ is the Dirac function, and represents the synchronous extraction transform operator; t and ω represent the time and frequency components in the time-frequency distribution, respectively. This is an estimate of the instantaneous frequency based on multiple synchronous extraction transformation.

[0055] In formula (1), the estimated value of instantaneous frequency The calculation formula is:

[0056]

[0057]

[0058] Where Round(·) is the rounding operation. This represents the frequency components after C compression iterations. Indicates instantaneous phase The first derivative, Indicates instantaneous phase The second derivative of .

[0059] Step 2: Use the penalty optimization algorithm to extract the time-frequency ridge from the time-frequency distribution signal and calculate the instantaneous frequency. Then, perform an integral operation on the instantaneous frequency to obtain the phase information. Finally, obtain a stable angular domain signal through angular domain resampling.

[0060] In step 2, the calculation formula for extracting the time-frequency ridge from the time-frequency distribution signal using the penalty optimization algorithm is as follows:

[0061]

[0062] Where E(φ(t)) is the time-frequency ridge of the signal, and φ(t) represents the estimated instantaneous frequency in the time-frequency distribution. φ′(t) and φ″(t) 2 Let represent the first and second derivatives of φ(t), respectively; TFR(t,φ(t)) is the estimated value of the time-frequency coefficient; and λ and β are two parameters for adjusting the regularization level.

[0063] Phase information is typically represented by angles, reflecting the position of the signal's periodic changes relative to a reference signal. After obtaining the phase information through integration, angular domain resampling of the keyless phase signal is achieved through interpolation, converting the time interval into an angle increment. This transforms the original non-stationary time-domain signal into a stationary angular-domain signal.

[0064] Step 3: Segment and align the angular domain signal according to the gear failure cycle to obtain the deterministic components related to gear wear, and represent the deterministic components related to gear wear in the form of a synchronization matrix.

[0065] In step 3, the deterministic component related to gear wear is a periodic signal. According to Fourier series theory, any periodic signal can be decomposed into the sum of multiple harmonic components, which can be expressed as:

[0066]

[0067] In the formula, d(n) represents the deterministic component related to gear wear, and n is the index of the discretized signal.k (n) represents the envelope signal of the k-th harmonic component. This is the corresponding harmonic exponent term, where N is the gear failure period. According to the Weirstrass approximation theorem, d k (n) can be obtained through the P-order polynomial function n p To approximate, that is:

[0068]

[0069] in, Let represent the weighting coefficients of the complex envelope under each order of polynomial. Substituting equation (6) into (5), we have:

[0070]

[0071] Therefore, the polynomial coefficients corresponding to the complex envelope of polynomials of each order can be expressed as:

[0072]

[0073] Because the vibration signal of gear wear failure exhibits significant periodicity, it can be segmented and aligned according to the gear's failure cycle. Stacking the data from each cycle forms a matrix representation indexed by the failure cycle. Each column of this matrix corresponds to a complete failure cycle, thus the deterministic components can be represented in the form of a synchronization matrix as follows:

[0074]

[0075]

[0076] In the formula, d(m) represents the deterministic component after segment alignment, and m represents the q-th period. One sampling point.

[0077] Step 4: Use the minimum mean square error between the estimated value of the deterministic component within the window and the original data as the estimation error of the filter, and find an optimal polynomial coefficient through the Savitzky-Golay filter.

[0078] In step 4, the formula for calculating the estimation error of the filter is:

[0079]

[0080] Where ε represents the filter estimation error, d m and x m These are the estimated values ​​of the deterministic components and the original data, respectively, where M is the window width and c is the value of the original data. p The coefficients are the polynomial coefficients, m p Let p represent the expansion term of the polynomial, and p represent the order of the polynomial.

[0081] In this embodiment, the minimum mean square error between the estimated value of the deterministic component within the window and the original data is used as the estimation error of the filter. By using the Savitzky-Golay filter to find an optimal polynomial coefficient, the minimum mean square error between the estimated value of the deterministic component within the window and the original data can be minimized.

[0082] Step 5: Evaluate and optimize the fitting process based on the generalized unbiased mean square error estimation, and adaptively obtain the optimal polynomial order and window width of the Savitzky-Golay filter.

[0083] Specifically, in step 5, a point-by-point search method is used to determine the optimal combination of the Savitzky-Golay filter's polynomial order and window width. First, for a fixed order, the window width is gradually increased, and the corresponding generalized unbiased mean square error is calculated. After completion, the process is repeated for the next order. Finally, the combination with the smallest generalized unbiased mean square error among all combinations is selected as the optimal parameters for the current time step.

[0084] In step 5, the formula for calculating the generalized unbiased mean square error is:

[0085]

[0086] In the formula, h is the filter coefficient matrix, x is the resampled angular domain signal, S is the length of the resampled angular domain signal, and h s,s This represents the element in the s-th row and s-th column of the filter coefficient matrix. Let V be the variance of the signal. The formula for calculating the variance of a signal is:

[0087]

[0088] Where E{·} denotes the expectation, x s It is a discretized angular domain signal.

[0089] Step 6: Perform Fourier transform on the deterministic components optimized by the Savitzky-Golay filter to obtain the order spectrum, and calculate the overall step energy ratio using the order spectrum.

[0090] In step 6, after obtaining the deterministic components related to gear wear through adaptive synchronous fitting, Fourier transform is performed on them to obtain the order spectrum, and the comprehensive step energy ratio is calculated for significant meshing harmonics.

[0091] In step 6, the order spectrum of the deterministic component is as follows: Figure 3 As shown. Based on the amplitude of the gear wear characteristic order, the comprehensive step energy ratio is calculated. The calculation formula is:

[0092]

[0093] In the formula, COER is the combined band energy ratio, Z is the meshing harmonic number, and OER is the total energy of the band. z It is the step-band energy ratio at the z-th meshing harmonic, J0(B r Let A be a zero-order Bessel function. z,l Let A be the amplitude of the l-th sideband at the z-th meshing harmonic. z This is the amplitude of the z-th meshing harmonic component. Typically, only some meshing harmonics and their sidebands contain fault information. Therefore, this embodiment selects significant meshing harmonics for analysis based on the amplitude relationship between the meshing harmonics and the fundamental meshing order. Specifically, in this embodiment, when calculating only the comprehensive step-band energy ratio, only those satisfying condition A are considered. z / zA1>1×10 -2 The meshing harmonics z.

[0094] Step 7: Repeatedly collect the vibration signal of the gear and calculate the comprehensive step energy ratio. Calculate the cumulative comprehensive energy ratio index by using the comprehensive step energy ratio at multiple continuous measurement times. Use the cumulative comprehensive energy ratio index to evaluate or monitor the wear area of ​​the gear, thereby quantitatively assessing the severity of wear.

[0095] In this embodiment, the cumulative comprehensive energy ratio index is calculated based on the comprehensive step energy ratio at multiple continuous measurement times. The cumulative comprehensive energy ratio index is used to evaluate or monitor the wear area of ​​the gear, thereby quantifying the severity of wear.

[0096] In step 7, the formula for the cumulative comprehensive energy ratio index is:

[0097]

[0098] In the formula, CCER represents the cumulative comprehensive energy ratio, t is the measurement time, η is the correction factor, and CER represents the comprehensive energy ratio. T represents the number of vibration signal segments measured, taking into account the gear damage size S. def The relationship between vibration characteristics and the following is: RMS0 is the reference standard for the measured signal, and RMS is the root mean square value of the measured signal. Therefore, the formula for calculating the Comprehensive Energy Ratio (CER) is:

[0099] CER = COER(t) × RMS d (t); (16)

[0100] Where COER(t) represents the comprehensive step energy ratio of the vibration signal at measurement time t, and RMS d (t) represents the root mean square value of the deterministic component of the vibration signal at measurement time t, and its calculation formula is:

[0101]

[0102] Where, d m This represents the deterministic component optimized by the Savitzky-Golay filter, where S is the length of the angular domain signal after angular domain resampling.

[0103] Substituting equation (16) into equation (15), the final formula for calculating the cumulative comprehensive energy ratio is:

[0104]

[0105] In the formula, CCER represents the cumulative comprehensive energy ratio, t is the measurement time, COER(t) represents the comprehensive step energy ratio corresponding to the vibration signal at measurement time t, η is the correction factor, CER is the comprehensive energy ratio, and RMS is the total energy ratio. d (t) represents the root mean square value of the deterministic component of the vibration signal at measurement time t.

[0106] like Figure 4 The figure shows the variation law of gear wear morphology characteristics obtained in this embodiment.

[0107] like Figure 5 The figure shows a schematic diagram of the cumulative comprehensive energy ratio (CCER) calculated after processing vibration signals collected under different rotational speeds in an embodiment of the present invention. The figure also compares the monitoring results of the wear area percentage of a single tooth and the wear area percentage of all teeth. Experiments have confirmed that in this embodiment of the present invention, the CCER corresponding to vibration signals collected under different rotational speeds has good consistency. Furthermore, the CCER of this invention shows the same trend as the change in gear wear area. Therefore, this invention can accurately quantify and evaluate gear wear area under variable rotational speed conditions.

[0108] In summary, this invention provides a method for monitoring gear wear area under varying speed conditions based on vibration signals. First, by performing two rounding operations and extracting key coefficients of the time-frequency distribution, the concentration of time-frequency energy and the resolution of instantaneous frequencies can be improved, alleviating the frequency ambiguity problem caused by speed changes. Then, by optimizing the key parameters of the Savitzky-Golay filter based on the generalized unbiased mean square error, deterministic components related to gear wear can be adaptively extracted. Finally, the constructed cumulative comprehensive energy ratio index, combined with the relationship between the vibration characteristics and morphological features of gear wear, achieves more accurate gear wear monitoring and evaluation.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for monitoring gear wear area under variable speed conditions based on vibration signals, characterized in that, Includes the following steps: Step 1: Collect the vibration signal of the gear, and calculate the time-frequency distribution signal of the vibration signal based on multiple synchronous extraction and transformation; Step 2: Extract the time-frequency ridge from the time-frequency distribution signal using the penalty optimization algorithm and calculate the instantaneous frequency. Then, perform an integral operation on the instantaneous frequency to obtain the phase information. Finally, obtain a stable angular domain signal through angular domain resampling. Step 3: Segment and align the angular domain signal according to the gear failure cycle, and represent the deterministic components related to gear wear in the form of a synchronization matrix; Step 4: Use the minimum mean square error between the estimated value of the deterministic component within the window and the original data as the estimation error of the filter, and find an optimal polynomial coefficient through the Savitzky-Golay filter. Step 5: Evaluate and optimize the fitting process based on the generalized unbiased mean square error estimation, and adaptively obtain the optimal polynomial order and window width of the Savitzky-Golay filter; Step 6: Perform Fourier transform on the deterministic components optimized by the Savitzky-Golay filter to obtain the order spectrum, and calculate the overall step energy ratio from the order spectrum; Step 7: Repeatedly collect the vibration signal of the gear and calculate the comprehensive step energy ratio. Calculate the cumulative comprehensive energy ratio index by using the comprehensive step energy ratio at multiple continuous measurement times. Use the cumulative comprehensive energy ratio index to evaluate or monitor the wear area of ​​the gear, thereby quantitatively assessing the severity of wear. In step 6, the formula for calculating the overall bandgap energy ratio is: ； In the formula, COER is the overall band energy ratio. Z It is the meshing harmonic number. A z,l For the first z The first harmonic at the meshing harmonic l The amplitude of each sideband, A z It is the first z The amplitude of each harmonic component; In step 7, the formula for the cumulative comprehensive energy ratio index is: ； In the formula, CCER represents the cumulative comprehensive energy ratio. t For measuring time, express t The overall step energy ratio corresponding to the vibration signal at the measurement moment. η The correction factor is CER, which stands for Overall Energy Ratio. express t The root mean square value of the deterministic component corresponding to the vibration signal at the measurement time.

2. The method for monitoring the wear area of a gear under variable speed conditions based on a vibration signal according to claim 1, characterized in that, In step 1, the calculation formula for the time-frequency distribution signal of each vibration signal based on multiple synchronous extraction transformation is as follows: ； in, The time-frequency distribution signal is obtained based on multiple synchronous extraction and transformation. C To reduce the number of iterations, For time-frequency distribution based on short-time Fourier transform, δ Let be the Dirac function, representing the synchronous extraction transform operator; t and ω These represent the time and frequency components in the time-frequency distribution, respectively. This is an estimate of the instantaneous frequency based on multiple synchronous extraction transformation.

3. A method of monitoring the wear area of a gear under variable speed conditions based on a vibration signal according to claim 2, characterized in that, In the step 1, the estimated value of the instantaneous frequency The calculation formula is: ； ； Where Round(·) is the rounding operation. Indicates the process C Frequency components after the first compression iteration Indicates instantaneous phase The first derivative, Indicates instantaneous phase The second derivative of .

4. The method for monitoring the wear area of a gear under variable speed conditions based on a vibration signal according to claim 1, characterized in that, In step 2, the calculation formula for extracting the time-frequency ridge from the time-frequency distribution signal using the penalty optimization algorithm is as follows: ； where E is the time-frequency ridge of the signal, denotes the estimated instantaneous frequency in the time-frequency distribution, is the time-frequency coefficient estimate, λ and β are two parameters that adjust the level of regularization.​ 5. The method for monitoring the wear area of a gear under variable speed conditions based on a vibration signal according to claim 1, characterized in that, In step 4, the formula for calculating the estimation error of the filter is: ； wherein ε denotes the estimation error of the filter, c p are polynomial coefficients, denotes the expansion term of the polynomial, p denotes the polynomial order, d m and x m are the estimated value and the original data, respectively, of the deterministic component, M is the window width.

6. A method of monitoring the wear area of a gear under variable speed conditions based on a vibration signal according to claim 1, characterized in that, In step 5, the formula for calculating the generalized unbiased mean square error is: ； wherein h is the filter coefficient matrix, x is the resampled angular domain signal, S is the length of the resampled angular domain signal, denotes the element in the filter coefficient matrix in the s row and the s column, is the variance of the signal.

7. A method of monitoring the area of wear of a gear under variable speed conditions based on a vibration signal according to claim 6, characterized in that, The formula for calculating the variance of a signal is: ； wherein E {•} denotes taking the expectation, x s is a discretized angular domain signal.

8. The method for monitoring the wear area of a gear under variable speed conditions based on a vibration signal according to claim 1, characterized in that, The step 7, the root mean square value of the deterministic component The calculation formula is: wherein denotes the deterministic component optimized by a Savitzky-Golay filter, S is the length of the angular domain signal after angular domain resampling.

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