Method and system for detecting modulation sideband frequency of gears in complex transmission systems

Abstract

The present invention provides a method and system for detecting the modulation sideband frequency of gears in a complex transmission system. The method comprises: a vibration sensor, a multi-channel data acquisition device, a computer, and data analysis software installed on the computer. The vibration sensor is used to sense the vibration of the integrated transmission device and convert it into an electrical signal for input. The vibration sensor is connected to the multi-channel data acquisition device, which converts the electrical signal into a digital signal and performs anti-aliasing filtering. Data transmission and communication with the computer are achieved via a network cable. The data analysis software installed on the computer is used to detect the modulation sideband frequency of the gears in the integrated transmission device and provide the detection results of the gear modulation sideband frequency. The detection results of the present invention are not affected by amplitude distortion caused by speed changes, are insensitive to speed changes, and can effectively avoid interference with the detection results caused by non-Gaussian noise and resonant frequency.

Description

Technical Field

[0001] The present invention relates to the technical field of complex transmission system fault diagnosis and signal detection, and in particular to a method and system for detecting the frequency of gear modulation sidebands in a complex transmission system. Background Art

[0002] Currently, there are few patents specifically for gear modulation sideband frequency detection. Most patents are based on fault diagnosis based on the amplitude of the modulation sideband frequency. The detection and extraction of gear modulation sideband frequency in their implementation plans are mainly based on frequency demodulation and signal decomposition, and are mostly suitable for rotating mechanical equipment with relatively simple structures, such as "A General Amplitude Demodulation Method for Gear Fault Vibration Modulation Signals".

[0003] Gear transmissions, with their precise ratios, high efficiency, compact structure, and long life, are the most widely used mechanical transmission method in modern equipment, particularly in the automotive, marine, and aerospace sectors. Complex transmission systems generally refer to mechanical, electrical, and hydraulic hybrid synchronous shifting systems that enable integrated control of steering, gear shifting, and speed change. They are core components of specialized vehicles and primarily comprise a large number of parallel-axis gear transmissions or planetary gear transmissions. Due to the harsh operating conditions of complex transmission systems, gear failures are prone to occur, leading to degradation or even failure of the entire system.

[0004] A large number of studies have shown that when a gear fails, fault-induced pulses will be introduced into its vibration signal, resulting in obvious modulation phenomena at the meshing frequency and its higher harmonic components in the frequency domain. Therefore, accurately detecting the gear modulation sideband frequency is an important basis and prerequisite for realizing gear fault detection.

[0005] Patent document CN110044610A (application number: CN201910413369.8) discloses a gear fault diagnosis method, including the following steps: S1, fix the acceleration sensor in the detection area of ​​the gearbox, and use the acceleration sensor to collect the acceleration vibration signal of the gearbox; S2, integrate the acceleration vibration signal to obtain a speed frequency domain signal; S3, according to the speed and number of teeth of the gear in the gearbox, respectively obtain the 1X, 2X, 3X meshing frequency and the corresponding speed sideband of the gear; S4, according to the speed frequency domain signal, respectively obtain the amplitude of the meshing frequency and the amplitude of the speed sideband of the gear at 1X, 2X, and 3X meshing frequencies; S5, respectively judge whether the meshing frequency and speed sideband of the gear at 1X, 2X, and 3X meshing frequencies are normal, and finally judge whether the gear is faulty.

[0006] Currently, the main techniques for processing gear modulation sideband frequencies are demodulation and noise reduction. Demodulation techniques utilize Hilbert transform envelopes, generalized detection filters, and energy operators to extract the frequency domain characteristics of the amplitude modulation. However, these techniques cannot quantitatively demodulate the modulation sideband frequencies, effectively diagnosing only the location of a gear fault, not the severity. Noise reduction techniques primarily convert the vibration signal into a corresponding Hankel matrix based on the calculated value of the gear modulation sideband frequency. Signal processing methods such as singular value decomposition, empirical mode decomposition, and variational mode decomposition are then used to remove perceived interfering frequency components, resulting in a denoised reconstructed signal that makes the gear modulation sideband frequencies more prominent and clear in the spectrum. However, due to the complex structure of complex transmission systems, numerous modulation sidebands, and even complex modulation, exist near the meshing frequency. The detection results obtained by these techniques either miss a significant number of detections or treat the actual modulation sidebands as noise, thus failing to meet practical engineering requirements.

[0007] Existing demodulation technologies are often limited to demodulating a single modulation frequency and are incapable of handling the multi-frequency or even compound modulation commonly found in complex transmission systems. This results in significant omissions in the detection of gear modulation sideband frequencies. Existing noise reduction technologies are significantly affected by non-Gaussian noise and resonant frequencies, making it easy to misidentify small-amplitude modulation sidebands as noise. Summary of the Invention

[0008] In view of the defects in the prior art, the purpose of the present invention is to provide a method and system for detecting the modulation sideband frequency of gears in a complex transmission system.

[0009] The method for detecting the frequency of gear modulation sidebands in a complex transmission system provided by the present invention includes:

[0010] Step 1: Make the complex transmission system run in the preset gear and load conditions, and when the engine speed is f s When the vibration signal is collected by a three-axis acceleration sensor, it is pre-processed by removing the mean and trend items to obtain a discrete vibration signal.

[0011] Step 2: Perform short-time Fourier transform on the discrete vibration signal to obtain the time-frequency distribution of the vibration signal and extract the corresponding frequency component f s The trend of the signal component changing with time is obtained as a discrete time series Then, generalized polynomial frequency modulation time-frequency transformation is performed to re-extract the time-varying trend of the signal components of the corresponding frequency components to obtain the discrete time series

[0012] Step 3: Numerical integration is used to obtain the angle of rotation of the input bevel gear shaft of the complex transmission system in the angular domain. By resampling θ(t) at equal intervals, the resampled vibration signal s is obtained. o (t i ), perform fast Fourier transform on the vibration signal to obtain the spectrum of the resampled signal;

[0013] Step 4: Based on the transmission relationship of the complex transmission system, calculate the engine speed f s When all the shafts rotate at a frequency f shaft and the meshing frequency f of all gear pairs m ;

[0014] Step 5: Define the spectrum concentration index ζ(f k ), for S BF (f k ), k=1,2,...,K, is calculated as follows:

[0015]

[0016] Calculate S BF (f k ),k=1,2,...,K spectral concentration index ζ(f k ) of the mean ∑ζ(f k ) / K as the threshold, and extract the f that exceeds the threshold k Constructing spectrum centrality detection sequence;

[0017] Step 6: All frequency values ​​f contained in the spectrum concentration detection sequence k with mf shaft ,m=1,2,…,M compare one by one and judge the meshing frequency Is there a rotating shaft with a rotation frequency f nearby? shaft The mth modulation sideband frequency component.

[0018] Preferably, the step 2 comprises:

[0019] Define the generalized polynomial kernel function Among them, {c1,...,c n} represents the coefficient of the generalized polynomial kernel function, L is the order of the kernel function defined arbitrarily, L>1 and L∈N * ; Using the generalized polynomial kernel function κ p Fitting discrete time series When the mean square error is minimized, the coefficients of the kernel function {c1,...,c n} specific value, and then the original discrete vibration signal s(t i ), i=1,2,…,N, and the generalized polynomial frequency modulation time-frequency transform is as follows:

[0020]

[0021] Where j is the imaginary unit, h(τ-t) is the window function, and t i represents the sampling time; ω represents the frequency independent variable; τ represents the time independent variable; N represents the total number of sampling points of the discrete vibration signal;

[0022] In the obtained time-frequency distribution, the corresponding frequency component f s The time-frequency energy concentration of the signal component is greatly improved, and the corresponding frequency component f is extracted from GMTF(t,ω) again. s The trend of the signal component changing with time is obtained as a discrete time series at this time It is the speed change trend component.

[0023] Preferably, the spectrum S of the resampled signal o (f k ) is:

[0024]

[0025] Among them, k and i are serial numbers.

[0026] Preferably, step 4 includes:

[0027] Set the maximum value of the shaft rotation frequency to f smax , the meshing frequency of the gear pair whose modulation sideband frequency is to be detected is The frequency range is Hz signal is band-pass filtered to obtain the filtered signal S F (t i ), where M represents the maximum modulation order considered, and then S F (t i ) Calculate the square envelope spectrum S BF (f k ), the expression is:

[0028]

[0029] in, Indicates S F (t i ) is used to obtain the analytical signal of the filtered signal.

[0030] Preferably, step 6 includes:

[0031] If the following criteria are met, it is proved that the meshing frequency There is a shaft rotation frequency f nearby shaft The mth-order modulation sideband frequency component:

[0032] The complex transmission system gear modulation sideband frequency detection system provided by the present invention includes:

[0033] Module M1: Make the complex transmission system run in the preset gear and loading conditions, and when the engine speed is f s When the vibration signal is collected by a three-axis acceleration sensor, it is pre-processed by removing the mean and trend items to obtain a discrete vibration signal.

[0034] Module M2: Perform short-time Fourier transform on the discrete vibration signal to obtain the time-frequency distribution of the vibration signal and extract the corresponding frequency component f s The trend of the signal component changing with time is obtained as a discrete time series Then, generalized polynomial frequency modulation time-frequency transformation is performed to re-extract the time-varying trend of the signal components of the corresponding frequency components to obtain the discrete time series

[0035] Module M3: Numerical integration is used to obtain the angle of rotation of the input bevel gear shaft of the complex transmission system in the angular domain. By resampling θ(t) at equal intervals, the resampled vibration signal s is obtained. o (t i ), perform fast Fourier transform on the vibration signal to obtain the spectrum of the resampled signal;

[0036] Module M4: Based on the transmission relationship of the complex transmission system, calculate the engine speed f s When all the shafts rotate at a frequency f shaft and the meshing frequency f of all gear pairs m ;

[0037] Module M5: Define the spectrum concentration index ζ(f k ), for S BF (f k ), k=1,2,…,K, is calculated as follows:

[0038]

[0039] Calculate S BF (f k ),k=1,2,...,K spectral concentration index ζ(f k ) of the mean ∑ζ(f k ) / K as the threshold, and extract the f that exceeds the threshold k Constructing spectrum centrality detection sequence;

[0040] Module M6: All frequency values ​​f contained in the spectrum concentration detection sequence k with mf shaft,m=1,2,...,M compare one by one to determine the meshing frequency Is there a rotating shaft with a rotation frequency f nearby? shaft The mth modulation sideband frequency component.

[0041] Preferably, the module M2 includes:

[0042] Define the generalized polynomial kernel function Among them, {c1,…,c n} represents the coefficient of the generalized polynomial kernel function, L is the order of the kernel function defined arbitrarily, L>1 and L∈N * ; Using the generalized polynomial kernel function κ p Fitting discrete time series When the mean square error is minimized, the coefficients of the kernel function {c1,...,c n} specific value, and then the original discrete vibration signal s(t i ), i=1,2,...,N, and the generalized polynomial frequency modulation time-frequency transform is as follows:

[0043]

[0044] Where j is the imaginary unit, h(τ-t) is the window function, and t i represents the sampling time; ω represents the frequency independent variable; τ represents the time independent variable; N represents the total number of sampling points of the discrete vibration signal;

[0045] In the obtained time-frequency distribution, the corresponding frequency component f s The time-frequency energy concentration of the signal component is greatly improved, and the corresponding frequency component f is extracted from GMTF(t,ω) again. s The trend of the signal component changing with time is obtained as a discrete time series at this time It is the speed change trend component.

[0046] Preferably, the spectrum S of the resampled signal o (f k ) is:

[0047]

[0048] Among them, k and i are serial numbers.

[0049] Preferably, the module M4 includes:

[0050] Set the maximum value of the shaft rotation frequency to f smax , the meshing frequency of the gear pair whose modulation sideband frequency is to be detected is The frequency range is Hz signal is band-pass filtered to obtain the filtered signal S F (t i ), where M represents the maximum modulation order considered, and then S F (t i ) Calculate the square envelope spectrum S BF (f k ), the expression is:

[0051]

[0052] in, Indicates S F (t i ) is used to obtain the analytical signal of the filtered signal.

[0053] Preferably, the module M6 includes:

[0054] If the following criteria are met, it is proved that the meshing frequency There is a shaft rotation frequency f nearby shaft The mth modulation sideband frequency component:

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] The present invention can realize accurate detection of gear modulation sideband frequency under multi-frequency modulation or even compound modulation in complex transmission systems; the detection results of the present invention are not affected by amplitude distortion caused by speed conversion, are insensitive to speed changes, and can effectively avoid interference of non-Gaussian noise and resonant frequency on the detection results. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0058] Figure 1 This is a flow chart of the method for detecting the frequency of gear modulation sidebands in a complex transmission system according to the present invention;

[0059] Figure 2 Schematic diagram of the rotation speed variation trend component fitted from the time-frequency distribution in an embodiment of the present invention;

[0060] Figure 3 Schematic diagram of the spectrum of the resampled vibration signal and the third-order modulation bandpass filtering range of the front transmission input bevel gear meshing frequency in an embodiment of the present invention;

[0061] Figure 4 Schematic diagram of the detection results of the modulation sideband frequency of the front transmission input bevel gear in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0063] Example:

[0064] The present invention proposes a spectrum concentration index that performs peak detection on the bandpass filtered square envelope spectrum of the M-order modulation of the meshing frequency and its higher harmonic components, achieving accurate detection of gear modulation sideband frequencies under multi-frequency modulation or even composite modulation conditions. The present invention proposes a generalized polynomial frequency modulation time-frequency transform to fit the speed variation trend under the service conditions of a complex transmission system, and then uses angular domain resampling to remove the amplitude distortion caused by speed variation, effectively suppressing the interference of non-Gaussian noise and resonant frequency on the detection results. A complex transmission system gear modulation sideband frequency detection system includes a vibration sensor, a multi-channel data acquisition device, a computer, and data analysis software installed on the computer. The vibration sensor is used to sense the vibration of the complex transmission system and convert it into an electrical signal input. The vibration sensor is connected to the multi-channel data acquisition device, which converts the electrical signal into a digital signal and performs anti-aliasing filtering. Data transmission and communication are achieved with the computer via a network cable. The data analysis software installed on the computer is used to implement a complex transmission system gear modulation sideband frequency detection method and provide the gear modulation sideband frequency detection results.

[0065] The present invention proposes a method for detecting the frequency of gear modulation sidebands in complex transmission systems. Figure 1 As shown, the following steps are included:

[0066] Step 1: Run the complex transmission system in forward 4th gear and 50% load condition. When the engine speed is 1700RPM (the frequency is 28.33Hz), use the three-axis acceleration sensor to collect the vibration signal for 10 seconds. After preprocessing by removing the mean and trend items, the discrete vibration signal s(t i ),i=1,2,...,N, where t i Indicates a sampling moment.

[0067] Step 2, for s(t i ), i=1,2,...,N, perform short-time Fourier transform to obtain the time-frequency distribution of the vibration signal, and extract the corresponding frequency component f s The trend of the signal component changing with time is obtained as a discrete time series Define the generalized polynomial kernel function Among them, {c1,...,c n} represents the coefficient of the generalized polynomial kernel function, L(L>1 and L∈N * ) is the order of the kernel function defined arbitrarily. Using the generalized polynomial kernel function κ p Fitting discrete time series When the mean square error is minimized, the coefficients of the kernel function {c1,...,c n} specific value. Further analysis of the original discrete vibration signal s(t i ), i=1,2,...,N, and the generalized polynomial frequency modulation time-frequency transform is as follows:

[0068]

[0069] Where j is the imaginary unit and h(τ-t) is the window function. Then in the obtained time-frequency distribution, the corresponding frequency component f s The time-frequency energy concentration of the signal components is greatly improved.

[0070] Step 3: Re-extract the corresponding frequency component f from GMTF(t,ω) s The trend of the signal component changing with time is obtained as a discrete time series at this time This is the speed change trend component, such as Figure 2 As shown in the figure, for this embodiment, it can be seen that the engine speed is not actually stable at 1700RPM, but is always in a fluctuating state. Numerical integration is used to obtain the angle of rotation of the input bevel gear shaft of the complex transmission system in the angular domain. By resampling θ(t) at equal intervals, the resampled vibration signal s is obtained. o (t i ),i=1,2,...,N, then in s o (t i ), the amplitude distortion caused by the speed change is effectively eliminated, and the influence of the non-Gaussian noise and resonance frequency of the signal is also suppressed. o (t i ), i=1,2,…,N perform fast Fourier transform and obtain the spectrum S of the resampled signal o (f k ),like Figure 3 As shown:

[0071]

[0072] Step 4: Based on the transmission relationship of the complex transmission system, the engine speed f s =28.33Hz, the maximum value of the shaft rotation frequency f smaxThe gear modulation sideband frequency is 61 Hz. The front transmission input bevel gear is used as an example to detect the gear modulation sideband frequency. For this embodiment, the meshing frequency of the front transmission input bevel gear is The maximum modulation order considered is M=3, so the signal with a frequency range of [1488.5, 1854.5] Hz is band-pass filtered to obtain the filtered signal S F (t i ), the meshing frequency and filtering range are also marked on Figure 3 middle.

[0073] Step 5, then S F (t i ) Calculate the square envelope spectrum S BF (f k ):

[0074]

[0075] in, Indicates S F (t i ) is used to obtain the analytical signal of the filtered signal.

[0076] Define the spectrum concentration index ζ(f k ), for S BF (f k ),k=1,2,...,K, can be calculated as follows:

[0077]

[0078] Calculate S BF (f k ),k=1,2,…,K spectral concentration index ζ(f k ) of the mean ∑ζ(f k ) / K as the threshold, and extract the f that exceeds the threshold k Construct a spectrum centrality detection sequence.

[0079] Step 6: All frequency values ​​f contained in the spectrum concentration detection sequence k with mf shaft ,m=1,2,3 are compared one by one, such as Figure 4 As shown, the vertical dotted line represents the rotation frequency component mf of all shafts shaft ,m=1,2,3, the circles mark the frequency values ​​f contained in the spectrum centrality detection sequence k The results that meet the following criteria:

[0080]

[0081] Thus, the final detection result can be obtained, that is, the modulation sideband frequency of the front transmission input bevel gear includes the fundamental frequency and double frequency of the rotation frequency of shaft 1, and the rotation frequencies of shafts 2 and 3.

[0082] In step 1, in addition to using a three-axis acceleration sensor, a single-axis acceleration sensor, or other vibration sensors such as a displacement sensor may also be used.

[0083] The complex transmission system gear modulation sideband frequency detection system provided by the present invention includes: module M1: making the complex transmission system run in a preset gear and loading condition, when the engine speed is f s When the vibration signal is collected by the three-axis acceleration sensor, the discrete vibration signal is obtained after the mean and trend removal preprocessing; Module M2: Perform short-time Fourier transform on the discrete vibration signal to obtain the time-frequency distribution of the vibration signal and extract the corresponding frequency component f s The trend of the signal component changing with time is obtained as a discrete time series Then, generalized polynomial frequency modulation time-frequency transformation is performed to re-extract the time-varying trend of the signal components of the corresponding frequency components to obtain the discrete time series Module M3: Numerical integration is used to obtain the angle of rotation of the input bevel gear shaft of the complex transmission system in the angular domain. By resampling θ(t) at equal intervals, the resampled vibration signal s is obtained. o (t i ), perform fast Fourier transform on the vibration signal to obtain the spectrum of the resampled signal; Module M4: Calculate the frequency of the engine at f according to the transmission relationship of the complex transmission system s When all the shafts rotate at a frequency f shaft and the meshing frequency f of all gear pairs m Module M5: Define the spectrum concentration index ζ(f k ), for S BF (f k ), k=1,2,…,K, is calculated as follows: Calculate S BF (f k ),k=1,2,…,K spectral concentration index ζ(f k ) of the mean ∑ζ(f k ) / K as the threshold, and extract the f that exceeds the threshold k Construct a spectrum concentration detection sequence; Module M6: Construct all frequency values ​​f contained in the spectrum concentration detection sequence k with mf shaft ,m=1,2,...,M compare one by one to determine the meshing frequency Is there a rotating shaft with a rotation frequency f nearby? shaftThe mth modulation sideband frequency component.

[0084] The module M2 includes: defining a generalized polynomial kernel function Among them, {c1,...,c n} represents the coefficient of the generalized polynomial kernel function, L is the order of the kernel function defined arbitrarily, L>1 and L∈N * ; Using the generalized polynomial kernel function κ p Fitting discrete time series When the mean square error is minimized, the coefficients of the kernel function {c1,...,c n} specific value, and then the original discrete vibration signal s(t i ), i=1,2,...,N, and the generalized polynomial frequency modulation time-frequency transform is as follows: Where j is the imaginary unit, h(τ-t) is the window function, and t i represents the sampling time; ω represents the frequency independent variable; τ represents the time independent variable; N represents the total number of sampling points of the discrete vibration signal; in the obtained time-frequency distribution, the corresponding frequency component f s The time-frequency energy concentration of the signal component is greatly improved, and the corresponding frequency component f is extracted from GMTF(t,ω) again. s The trend of the signal component changing with time is obtained as a discrete time series at this time This is the speed change trend component. The spectrum S of the resampled signal o (f k ) is: Among them, k and i are serial numbers.

[0085] The module M4 includes: setting the maximum value of the shaft rotation frequency to f smax , the meshing frequency of the gear pair whose modulation sideband frequency is to be detected is The frequency range is Hz signal is band-pass filtered to obtain the filtered signal S F (t i ), where M represents the maximum modulation order considered, and then S F (t i ) Calculate the square envelope spectrum S BF (f k ), the expression is: in, Indicates S F (t i ) is used to obtain the analytical signal of the filtered signal.

[0086] The module M6 includes: if the following criteria are met, it is proved that the meshing frequency There is a shaft rotation frequency f nearby shaft The mth-order modulation sideband frequency component:

[0087] Those skilled in the art will appreciate that, in addition to implementing the system, device, and various modules provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like by logically programming the method steps. Therefore, the system, device, and various modules provided by the present invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; the modules for implementing various functions can also be considered both software programs for implementing the method and structures within the hardware component.

[0088] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for detecting the frequency of gear modulation sidebands in a complex transmission system, characterized in that: include: Step 1: Make the complex transmission system run in the preset gear and load conditions, and when the engine speed is f s When the vibration signal is collected by a three-axis acceleration sensor, it is pre-processed by removing the mean and trend items to obtain a discrete vibration signal. Step 2: Perform short-time Fourier transform on the discrete vibration signal to obtain the time-frequency distribution of the vibration signal and extract the corresponding frequency component f s The trend of the signal component changing with time is obtained as a discrete time series Then, generalized polynomial frequency modulation time-frequency transformation is performed to re-extract the time-varying trend of the signal components of the corresponding frequency components to obtain the discrete time series Step 3: Numerical integration is used to obtain the angle of rotation of the input bevel gear shaft of the complex transmission system in the angular domain. By resampling θ(t) at equal intervals, the resampled vibration signal s is obtained. o (t i ), perform fast Fourier transform on the vibration signal to obtain the spectrum of the resampled signal; Step 4: Based on the transmission relationship of the complex transmission system, calculate the engine speed f s When all the shafts rotate at a frequency f shaft and all gear pair meshing frequencies f m ; Step 5: Define the spectrum concentration index ζ(f k ), for the square envelope spectrum S BF (f k ), calculated as follows: Calculate S BF (f k ) Spectrum concentration index ζ(f k ) of the mean ∑ζ(f k ) / K as the threshold, and extract the f that exceeds the threshold k Constructing spectrum centrality detection sequence; Step 6: All frequency values ​​f contained in the spectrum concentration detection sequence k with mf shaft Compare one by one to determine the meshing frequency Is there a rotating shaft with a rotation frequency f nearby? shaft The mth-order modulated sideband frequency component, where m = 1, 2, ..., M.

2. The method for detecting the modulation sideband frequency of gears in a complex transmission system according to claim 1, characterized in that: The step 2 includes: Define the generalized polynomial kernel function Among them, {c1,...,c n } represents the coefficient of the generalized polynomial kernel function, L is the order of the kernel function defined arbitrarily, L>1 and L∈N * ; Using the generalized polynomial kernel function κ p Fitting discrete time series When the mean square error is minimized, the coefficients of the kernel function {c1,...,c n } specific value, and then the original discrete vibration signal s(t i ) Run the generalized polynomial frequency modulation time-frequency transform as follows: Where j is the imaginary unit, h(τ-t) is the window function, and t i represents the sampling time; ω represents the frequency independent variable; τ represents the time independent variable; N represents the total number of sampling points of the discrete vibration signal; In the obtained time-frequency distribution, the corresponding frequency component f s The time-frequency energy concentration of the signal component is greatly improved, and the corresponding frequency component f is extracted from GMTF(t,ω) again. s The trend of the signal component changing with time is obtained as a discrete time series at this time It is the speed change trend component.

3. The method for detecting the frequency of gear modulation sidebands in a complex transmission system according to claim 1, characterized in that: The spectrum S of the resampled signal o (f k ) is: Among them, k and i are serial numbers.

4. The method for detecting the frequency of gear modulation sidebands in a complex transmission system according to claim 1, characterized in that: The step 4 comprises: Set the maximum value of the shaft rotation frequency to f smax , the meshing frequency of the gear pair whose modulation sideband frequency is to be detected is The frequency range is The signal is band-pass filtered to obtain the filtered signal S F (t i ), where M represents the maximum modulation order considered, and then S F (t i ) Calculate the square envelope spectrum S BF (f k ), the expression is: in, Indicates S F (t i ) is used to obtain the analytical signal of the filtered signal.

5. The method for detecting the modulation sideband frequency of gears in a complex transmission system according to claim 1, characterized in that: The step 6 comprises: If the following criteria are met, it is proved that the meshing frequency There is a shaft rotation frequency f nearby shaft The mth-order modulation sideband frequency component:

6. A complex transmission system gear modulation sideband frequency detection system, characterized in that: include: Module M1: Make the complex transmission system run in the preset gear and loading conditions, and when the engine speed is f s When the vibration signal is collected by a three-axis acceleration sensor, it is pre-processed by removing the mean and trend items to obtain a discrete vibration signal. Module M2: Perform short-time Fourier transform on the discrete vibration signal to obtain the time-frequency distribution of the vibration signal and extract the corresponding frequency component f s The trend of the signal component changing with time is obtained as a discrete time series Then, generalized polynomial frequency modulation time-frequency transformation is performed to re-extract the time-varying trend of the signal components of the corresponding frequency components to obtain the discrete time series Module M3: Numerical integration is used to obtain the angle of rotation of the input bevel gear shaft of the complex transmission system in the angular domain. By resampling θ(t) at equal intervals, the resampled vibration signal s is obtained. o (t i ), perform fast Fourier transform on the vibration signal to obtain the spectrum of the resampled signal; Module M4: Based on the transmission relationship of the complex transmission system, calculate the engine speed f s When all the shafts rotate at a frequency f shaft and all gear pair meshing frequencies f m ; Module M5: Define the spectrum concentration index ζ(f k ), for the square envelope spectrum S BF (f k ), calculated as follows: Calculate S BF (f k ) Spectrum concentration index ζ(f k ) of the mean ∑ζ(f k ) / K as the threshold, and extract the f that exceeds the threshold k Constructing spectrum centrality detection sequence; Module M6: All frequency values ​​f contained in the spectrum concentration detection sequence k with mf shaft Compare one by one to determine the meshing frequency Is there a rotating shaft with a rotation frequency f nearby? shaft The mth-order modulated sideband frequency component, where m = 1, 2, ..., M.

7. The complex transmission system gear modulation sideband frequency detection system according to claim 6, characterized in that: The module M2 includes: Define the generalized polynomial kernel function Among them, {c1,...,c n } represents the coefficient of the generalized polynomial kernel function, L is the order of the kernel function defined arbitrarily, L>1 and L∈N * ; Using the generalized polynomial kernel function κ p Fitting discrete time series When the mean square error is minimized, the coefficients of the kernel function {c1,...,c n } specific value, and then the original discrete vibration signal s(t i ) Run the generalized polynomial frequency modulation time-frequency transform as follows: Where j is the imaginary unit, h(τ-t) is the window function, and t i represents the sampling time; ω represents the frequency independent variable; τ represents the time independent variable; N represents the total number of sampling points of the discrete vibration signal; In the obtained time-frequency distribution, the corresponding frequency component f s The time-frequency energy concentration of the signal component is greatly improved, and the corresponding frequency component f is extracted from GMTF(t,ω) again. s The trend of the signal component changing with time is obtained as a discrete time series at this time It is the speed change trend component.

8. The complex transmission system gear modulation sideband frequency detection system according to claim 6, characterized in that: The spectrum S of the resampled signal o (f k ) is: Among them, k and i are serial numbers.

9. The complex transmission system gear modulation sideband frequency detection system according to claim 6, characterized in that: The module M4 includes: Set the maximum value of the shaft rotation frequency to f smax , the meshing frequency of the gear pair whose modulation sideband frequency is to be detected is The frequency range is The signal is band-pass filtered to obtain the filtered signal S F (t i ), where M represents the maximum modulation order considered, and then S F (t i ) Calculate the square envelope spectrum S BF (f k ), the expression is: in, Indicates S F (t i ) is used to obtain the analytical signal of the filtered signal.

10. The complex transmission system gear modulation sideband frequency detection system according to claim 6, characterized in that: The module M6 includes: If the following criteria are met, it is proved that the meshing frequency There is a shaft rotation frequency f nearby shaft The mth-order modulation sideband frequency component:

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