CN113865871A - Rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment - Google Patents

Rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment Download PDF

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CN113865871A
CN113865871A CN202111293442.6A CN202111293442A CN113865871A CN 113865871 A CN113865871 A CN 113865871A CN 202111293442 A CN202111293442 A CN 202111293442A CN 113865871 A CN113865871 A CN 113865871A
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fault
signal
bearing
frequency
wavelet
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栾孝驰
沙云东
柳贡民
徐石
赵奉同
赵宇
陈兴武
温帅方
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Shenyang Aerospace University
AECC Shenyang Liming Aero Engine Co Ltd
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Abstract

The invention discloses a rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment, which relates to the field of rolling bearing fault diagnosis, is suitable for bearing fault diagnosis under simple and complex transmission paths, and decomposes vibration signals of a normal bearing and a fault bearing by adopting a wavelet packet analysis method; screening effective Node components based on the maximum kurtosis value index principle and performing signal reconstruction; performing Hilbert envelope demodulation analysis on the reconstructed signal; diagnosing frequency multiplication energy judgment based on fault characteristics; the diagnosis problem related to the judgment of the fault characteristic frequency multiplication energy of the rolling bearing is solved, and a method guidance is provided for the fault diagnosis and the state monitoring of the bearing under the nondisseparated state of the aircraft engine.

Description

Rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment
Technical Field
The invention relates to the field of fault diagnosis of rolling bearings, in particular to a fault diagnosis method of a rolling bearing based on fault characteristic frequency multiplication energy judgment.
Background
The rolling bearing is one of the most commonly used parts in various rotary machines, is an important component of the rotary machine, plays an important role in bearing load and transmitting load, the operating state of the rolling bearing is directly related to the working state and the operating safety of the whole rotary machine system, at present, the damage fault of the bearing in the fault of the rotary machine accounts for about thirty percent, the bearing defect is known as one of the main reasons of the fault of the rotary machine, the fault diagnosis and the state monitoring of the bearing are important contents of the fault diagnosis technology of mechanical equipment, statistics shows that during 2005 to 2018 years, serious faults of an engine caused by medium bearing damage are accumulated after a certain type of new machine is installed in China and are up to dozens of times, the serious flight accidents or airplane forced landing due to medium bearing damage occur for a plurality of times of aerial parking and two-grade serious flight accidents or airplane forced landing, the direct economic loss reaches dozens of RMB, and the bearing fault diagnosis methods are many, the method mainly comprises vibration detection, acoustic emission detection, temperature detection, lubricant detection, clearance detection and the like, wherein the vibration detection can detect the peeling, cracks, abrasion and burning of the bearing and is suitable for early detection and online detection, so that a vibration diagnosis method is generally applied, and the fault diagnosis of the bearing of the aeroengine mainly identifies the fault of the bearing from the aspect of vibration signal detection and analysis;
the method is characterized in that a foreign and domestic student aims at the characteristics that a rolling bearing fault vibration signal has pulse property, non-stationarity, nonlinearity and strong background noise, and the foreign and domestic student provides signal processing methods such as short-time Fourier transform, wavelet transform, Empirical Mode Decomposition (EMD), Stochastic Resonance (SR), integrated empirical mode decomposition (EEMD), sample entropy, a support vector machine, a neural network, a genetic algorithm, Wavelet Packet Decomposition (WPD) and the like for extracting the fault characteristic of the bearing, but different analysis methods have respective application ranges, but the invention of the diagnosis method for judging the fault characteristic frequency doubling energy of the rolling bearing is not involved;
the method is based on vibration signal analysis and processing, and adopts wavelet packet decomposition and reconstruction, kurtosis value index, frequency spectrum analysis and envelope demodulation as preprocessing modes to provide a bearing fault diagnosis method based on characteristic difference of characteristic frequency doubling energy percentages of a fault bearing and a normal bearing; and then, bearing fault tests of the complex transmission path are carried out, and whether the method is suitable for bearing fault diagnosis under the complex transmission path is verified. The method provided by the invention is suitable for bearing fault diagnosis under simple and complex transmission paths, and provides certain method guidance for bearing fault diagnosis and state monitoring under the condition that an aircraft engine is not decomposed.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment, which is suitable for bearing fault diagnosis under simple and complex transmission paths, and is divided into the following steps for bearing fault diagnosis and state monitoring under the condition that an aircraft engine is not decomposed:
step 1: decomposing vibration signals of a normal bearing and a fault bearing by adopting a wavelet packet analysis method;
wavelet basis function psi (t) epsilon L2(R) Fourier transform thereof
Figure BDA0003335754810000021
If ψ (t) satisfies the permission condition:
Figure BDA0003335754810000022
the wavelet sequence psi is obtained after translation and expansion are carried out according to two parameters of expansion factor a and translation factor bb,a(t)}：
Figure BDA0003335754810000023
Defining function f (t) E L2The Continuous Wavelet Transform (CWT) of (R) is:
Figure BDA0003335754810000024
wherein > represents inner product operation; represents a conjugate operation;
and performing inverse transformation on the wavelet transformation result, and recovering and reconstructing the original function:
Figure BDA0003335754810000025
parameter psi with continuity in wavelet transformr,s(t) carrying out discretization value processing, wherein a0Discrete in power series to a value greater than 1, b0Taking a uniform discrete number greater than 0, define:
Figure BDA0003335754810000026
function f (t) ε L2The Discrete Wavelet Transform (DWT) of (R) is:
Figure BDA0003335754810000027
wherein r is a frequency range index; s is a time step change index;
the wavelet packet transformation formula is:
Figure BDA0003335754810000028
wherein,
Figure BDA0003335754810000031
representing a scale function; ψ (t) represents a wavelet basis function; h iskAnd gkRespectively representing a low-pass filter and a high-pass filter of length 2N; k is a translation parameter, and k belongs to Z;
the wavelet packet decomposition algorithm formula is as follows:
Figure BDA0003335754810000032
wherein,
Figure BDA0003335754810000033
and
Figure BDA0003335754810000034
different wavelet coefficients; j is a scale parameter, j belongs to Z+(ii) a k. n is a translation parameter, k and n belong to Z, and Z is an integer; m is a frequency parameter, m is equal to {2 ∈j-1,2j-2,…,0}；hn-2kA low-pass filter for wavelet packet decomposition; gn-2kA high-pass filter in wavelet packet decomposition;
the wavelet packet reconstruction algorithm formula is as follows:
Figure BDA0003335754810000035
wherein,
Figure BDA0003335754810000036
and
Figure BDA0003335754810000037
the wavelet packet coefficients after wavelet packet reconstruction are wavelet packet coefficients after wavelet packet reconstruction; h isk-2nA low pass filter for wavelet packet reconstruction; gk-2nA high pass filter for wavelet packet reconstruction;
step 2: screening effective Node components based on the maximum kurtosis value index principle and performing signal reconstruction;
the node components obtained by processing the original vibration signals by the wavelet packet decomposition method are removed and reserved according to the kurtosis value, the effect of screening the node components is achieved, a new signal is reconstructed and formed, and the calculation formula of the kurtosis value K is as follows:
Figure BDA0003335754810000038
wherein E is desired; y represents the vibration signal amplitude; u represents the mean value of the vibration signal amplitude y; α represents the standard deviation of the fault signal;
and step 3: performing Hilbert envelope demodulation analysis on the reconstructed signal;
envelope detection processing is carried out on a high-frequency vibration signal with a high signal-to-noise ratio to obtain an envelope waveform, then Hilbert transformation is adopted to realize envelope elimination and fault information extraction on the signal, Hilbert transformation of the signal is reconstructed, the signal is enabled to generate 90-degree phase shift, the original signal is used as a real part, the Hilbert transformation is used as an imaginary part to form an analytic signal, a module is obtained to obtain an envelope of the signal, low-pass filtering is carried out on the envelope signal, fast Fourier transformation is carried out to obtain an envelope spectrum, and the Hilbert transformation is defined as:
Figure BDA0003335754810000039
wherein, x (t) is an original time domain signal;
Figure BDA00033357548100000310
a Hilbert transform for signal x (t);
Figure BDA00033357548100000311
a convolution is performed for x (t), the impulse response of this convolution is
Figure BDA00033357548100000312
And 4, step 4: diagnosing frequency multiplication energy judgment based on fault characteristics;
when the normal bearing is in the normal operation process, the bearing cannot resonate; when a bearing has a local damage fault, the periodic pulse excitation generated in the operation process can cause high-frequency impact vibration of the bearing, the vibration signal of the fault bearing is subjected to resonance demodulation processing, a low-frequency fault characteristic frequency doubling signal related to the fault of the bearing is demodulated from a high-frequency modulation signal, a characteristic peak value exists at the fault characteristic frequency and the frequency doubling position in the obtained envelope spectrum, the energy at the fault characteristic frequency doubling position occupies the greatest proportion in the total energy of the whole envelope spectrum, and a percentage formula of the fault characteristic energy in the total energy of the envelope spectrum is defined as:
Figure BDA0003335754810000041
wherein,
Figure BDA0003335754810000042
representing the energy sum at the frequency multiplication of the fault characteristic;
Figure BDA0003335754810000043
represents the sum of the energies at each frequency in the entire envelope spectrum; y isiRepresenting the peak at which the fault signature doubles;
Figure BDA0003335754810000044
representing the energy at the frequency multiplication of the fault characteristic; i represents the ith frequency multiplication of the fault characteristic; y isjA peak representing the j point in the envelope spectrogram;
Figure BDA0003335754810000045
representing the energy at the j-th point in the envelope spectrogram.
Advantageous technical effects
The invention provides a vibration method for vibrating a fault of a rolling bearing, which is suitable for bearing fault diagnosis under simple and complex transmission paths and provides method guidance for bearing fault diagnosis and state monitoring under the condition that an aircraft engine is not decomposed.
Drawings
Fig. 1 is a flow chart of implementing a rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment according to an embodiment of the present invention;
FIG. 2 is a time domain diagram of an original vibration signal provided by an embodiment of the present invention;
fig. 3 is a diagram of 8 time-domain components after decomposition of a bearing wavelet packet according to an embodiment of the present invention;
fig. 4 is a frequency domain waveform diagram of node components of 8 wavelet packets after wavelet packet decomposition according to an embodiment of the present invention;
fig. 5 is a kurtosis value distribution diagram of 8 node components after wavelet packet decomposition according to an embodiment of the present invention;
FIG. 6 is a time domain diagram of a reconstructed signal according to an embodiment of the present invention;
FIG. 7 is an envelope spectrum of reconstructed signals of a failed bearing and a normal bearing under a simple transmission path according to an embodiment of the present invention;
fig. 8 is an envelope spectrum of reconstructed signals of a failed bearing and a normal bearing under a complex transmission path according to an embodiment of the present invention;
FIG. 9 is a graph of the ratio of the characteristic energy of a failed bearing to the characteristic energy of a normal bearing in a simple transmission path provided by an embodiment of the invention;
fig. 10 is a characteristic energy ratio diagram of a failed bearing and a normal bearing under a complex transmission path provided by the embodiment of the invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments;
in the embodiment, the effectiveness of the method is verified by using typical test data of the deep groove ball bearing under the simple transmission path of the university of Kaiser storage and typical test data of the main shaft bearing of the aeroengine under the complex transmission path based on the simulation case;
the invention provides a rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment, which is suitable for bearing fault diagnosis under simple and complex transmission paths as shown in figure 1, and is divided into the following steps for solving the bearing fault diagnosis and state monitoring under the nondisseparated state of an aircraft engine:
step 1: decomposing vibration signals of a normal bearing and a fault bearing by adopting a wavelet packet analysis method;
wavelet basis function psi (t) epsilon L2(R) Fourier transform thereof
Figure BDA0003335754810000051
If ψ (t) satisfies the permission condition:
Figure BDA0003335754810000052
the wavelet sequence psi is obtained after translation and expansion are carried out according to two parameters of expansion factor a and translation factor bb,a(t)}：
Figure BDA0003335754810000053
Defining function f (t) E L2The Continuous Wavelet Transform (CWT) of (R) is:
Figure BDA0003335754810000054
wherein > represents inner product operation; represents a conjugate operation;
and performing inverse transformation on the wavelet transformation result, and recovering and reconstructing the original function:
Figure BDA0003335754810000055
parameter psi with continuity in wavelet transformr,s(t) carrying out discretization value processing, wherein a0Discrete in power series to a value greater than 1, b0Taking a uniform discrete number greater than 0, define:
Figure BDA0003335754810000056
function f (t) ε L2The Discrete Wavelet Transform (DWT) of (R) is:
Figure BDA0003335754810000057
wherein r is a frequency range index; s is a time step change index;
the wavelet packet transformation formula is:
Figure BDA0003335754810000061
in the formula,
Figure BDA0003335754810000062
representing a scale function; ψ (t) represents a wavelet basis function; h iskAnd gkRespectively representing a low-pass filter and a high-pass filter of length 2N; k is a translation parameter, and k belongs to Z;
the wavelet packet decomposition algorithm formula is as follows:
Figure BDA0003335754810000063
wherein,
Figure BDA0003335754810000064
and
Figure BDA0003335754810000065
different wavelet coefficients; j is a scale parameter, j belongs to Z+(ii) a k. n is a translation parameter, k and n belong to Z, and Z is an integer; m is a frequency parameter, m is equal to {2 ∈j-1,2j-2,…,0}；hn-2kA low-pass filter for wavelet packet decomposition; gn-2kA high-pass filter in wavelet packet decomposition;
the wavelet packet reconstruction algorithm formula is as follows:
Figure BDA0003335754810000066
wherein,
Figure BDA0003335754810000067
and
Figure BDA0003335754810000068
the wavelet packet coefficients after wavelet packet reconstruction are wavelet packet coefficients after wavelet packet reconstruction; h isk-2nA low pass filter for wavelet packet reconstruction; gk-2nA high pass filter for wavelet packet reconstruction;
in the embodiment, wavelet packet decomposition is adopted, and a wavelet packet analysis method is adopted to carry out n-layer decomposition on the bearing fault vibration signal to obtain 2nWavelet packet node component time domain signals; in the embodiment, the outer ring fault vibration signal (rotating speed 1730r/min) of the deep groove ball bearing under the simple transmission path of the university of Kaiser storage is decomposed by 3 layers of wavelet packets to obtain 8 wavelet packet node component time domain signals of the outer ring fault vibration signal, wherein the original vibration time domain signal is shown in figure 2, and the time domain signal after the wavelet packet decomposition is shown in figure 3;
fast FFT, on obtained 2nFast FFT is carried out on the wavelet packet node component time domain signal to obtain 2nWavelet packet node component frequency domain signals; in this embodiment, 8 wavelet packet node component frequency domain signals of the outer ring fault vibration signal are obtained, as shown in fig. 4
Step 2: effective Node components are screened out based on the maximum kurtosis value index principle and signal reconstruction is carried out
The node components obtained by processing the original vibration signals by the wavelet packet decomposition method are removed and reserved according to the kurtosis value, the effect of screening the node components is achieved, a new signal is reconstructed and formed, and the calculation formula of the kurtosis value K is as follows:
Figure BDA0003335754810000069
wherein E is desired; y represents the vibration signal amplitude; u represents the mean value of the vibration signal amplitude y; α represents the standard deviation of the fault signal;
in this embodiment, the kurtosis value index is calculated, calculation 2nThe kurtosis values of the node components are sorted from big to small; in this embodiment, a histogram of kurtosis values of 8 node components of an outer ring fault vibration signal is obtained as shown in fig. 5, and the kurtosis values are sorted from large to small as shown in table 1:
TABLE 1
Sorting 1 2 3 4 5 6 7 8
Node number 3 7 8 6 5 4 2 1
Kurtosis value 13.65 12.34 10.71 10.5 9.76 7.05 3.52 3.42
Reconstructing a time domain signal, namely reconstructing n (n is less than or equal to 4) time domain components with the maximum kurtosis value to obtain a reconstructed time domain signal; in this embodiment, the 4 time domain components with the largest kurtosis value are reconstructed to obtain an outer ring fault reconstruction time domain signal, as shown in fig. 6;
and step 3: performing Hilbert envelope demodulation analysis on the reconstructed signal;
envelope detection processing is carried out on a high-frequency vibration signal with a high signal-to-noise ratio to obtain an envelope waveform, then Hilbert transformation is adopted to realize envelope elimination of the signal to extract fault information, Hilbert transformation of the signal is reconstructed, the signal generates 90-degree phase shift, the original signal is used as a real part, the Hilbert transformation is used as an imaginary part to form an analytic signal, a module is obtained to obtain the envelope of the signal, low-pass filtering is carried out on the envelope signal, and fast Fourier transformation is carried out to obtain an envelope spectrum;
the Hilbert transform is defined as:
Figure BDA0003335754810000071
wherein, x (t) is an original time domain signal;
Figure BDA0003335754810000072
a Hilbert transform for signal x (t);
Figure BDA0003335754810000073
a convolution is performed for x (t), the impulse response of this convolution is
Figure BDA0003335754810000074
In this embodiment: analyzing an envelope spectrum, and carrying out envelope demodulation on the reconstructed time domain signal to obtain a frequency domain signal; in this embodiment, the outer ring fault reconstructs a time domain signal envelope spectrum, as shown in fig. 7 (a);
repeating the steps 1-2, and then carrying out envelope spectrum analysis to obtain a normal deep groove ball bearing vibration signal envelope spectrum (rotating speed 1730r/min) under a simple transmission path of the university of Kaiser-Sichu, as shown in FIG. 7(b), and obtaining an aeroengine spindle bearing rolling element fault and a normal bearing vibration signal envelope spectrum (rotating speeds are 1140r/min) under a complex transmission path based on a simulation casing, as shown in FIG. 8(a) and FIG. 8(b), respectively;
and 4, step 4: diagnosing frequency multiplication energy judgment based on fault characteristics;
when a normal bearing is in a normal operation process, the bearing cannot resonate, when the bearing has a local damage fault, the bearing is caused to vibrate by high-frequency impact by periodic pulse excitation generated in the operation process, a vibration signal of the fault bearing is subjected to resonance demodulation processing, a low-frequency fault characteristic frequency doubling signal related to the fault of the bearing is demodulated from a high-frequency modulation signal, characteristic peaks exist in the fault characteristic frequency and the frequency doubling position of the fault characteristic frequency doubling position in an obtained envelope spectrum, the energy at the fault characteristic frequency doubling position occupies the largest proportion in the total energy of the whole envelope spectrum, and the energy at the fault characteristic frequency doubling position and a percentage formula occupying the total energy of the envelope spectrum are defined as:
Figure BDA0003335754810000081
wherein,
Figure BDA0003335754810000082
representing the energy sum at the frequency multiplication of the fault characteristic;
Figure BDA0003335754810000083
represents the sum of the energies at each frequency in the entire envelope spectrum; y isiMultiple of representative fault characteristicsA peak at frequency;
Figure BDA0003335754810000084
representing the energy at the frequency multiplication of the fault characteristic; i represents the ith frequency multiplication of the fault characteristic; y isjA peak representing the j point in the envelope spectrogram;
Figure BDA0003335754810000085
representing the energy of the j point in the envelope spectrogram;
in the embodiment, fault characteristic energy is calculated, and the proportion of the fault characteristic energy of the normal bearing and the fault bearing in the whole spectrum energy is calculated respectively; in the embodiment, a fault characteristic energy proportion pie chart of an outer ring fault deep groove ball bearing and a fault characteristic energy proportion pie chart of a normal deep groove ball bearing under a simple transmission path of the university of Kaisyi, USA are provided and respectively shown in figures 9(a) and 9(b), and a spindle bearing characteristic energy proportion pie chart of a rolling element fault aeroengine and a normal deep spindle bearing under a complex transmission path based on a simulation case are provided and respectively shown in figures 10(a) and 10 (b);
and (4) fault diagnosis, namely performing statistical analysis on the difference of the characteristic energy ratios of the fault bearing and the normal bearing to diagnose the bearing fault.

Claims (7)

1. A rolling bearing fault diagnosis method based on fault characteristic frequency multiplication energy judgment is characterized in that: comprises the following steps:
step 1: decomposing vibration signals of a normal bearing and a fault bearing by adopting a wavelet packet analysis method;
step 2: screening effective Node components based on the maximum kurtosis value index principle and performing signal reconstruction;
and step 3: performing Hilbert envelope demodulation analysis on the reconstructed signal;
and 4, step 4: and diagnosing frequency multiplication energy judgment based on fault characteristics.
2. The rolling bearing fault diagnosis method based on fault feature frequency multiplication energy judgment of claim 1, characterized in that: the specific process of the step 1 is as follows:
wavelet basis function psi (t) epsilon L2(R) Fourier transform thereof
Figure FDA0003335754800000011
If ψ (t) satisfies the permission condition:
Figure FDA0003335754800000012
the wavelet sequence psi is obtained after translation and expansion are carried out according to two parameters of expansion factor a and translation factor bb,a(t)}：
Figure FDA0003335754800000013
Defining function f (t) E L2The Continuous Wavelet Transform (CWT) of (R) is:
Figure FDA0003335754800000014
wherein > represents inner product operation; represents a conjugate operation;
and performing inverse transformation on the wavelet transformation result, and recovering and reconstructing the original function:
Figure FDA0003335754800000015
parameter psi with continuity in wavelet transformr,s(t) carrying out discretization value processing, wherein a0Discrete in power series to a value greater than 1, b0Taking a uniform discrete number greater than 0, define:
Figure FDA0003335754800000016
function f (t) ε L2The Discrete Wavelet Transform (DWT) of (R) is:
Figure FDA0003335754800000017
wherein r is a frequency range index; s is a time step change index;
the wavelet packet transformation formula is:
Figure FDA0003335754800000021
wherein,
Figure FDA0003335754800000022
representing a scale function; ψ (t) represents a wavelet basis function; h iskAnd gkRespectively representing a low-pass filter and a high-pass filter of length 2N; k is a translation parameter, and k belongs to Z;
the wavelet packet decomposition algorithm formula is as follows:
Figure FDA0003335754800000023
wherein,
Figure FDA0003335754800000024
and
Figure FDA0003335754800000025
different wavelet coefficients; j is a scale parameter, j belongs to Z+(ii) a k. n is a translation parameter, k and n belong to Z, and Z is an integer; m is a frequency parameter, m is equal to {2 ∈j-1,2j-2,…,0}；hn-2kA low-pass filter for wavelet packet decomposition; gn-2kA high-pass filter in wavelet packet decomposition;
the wavelet packet reconstruction algorithm formula is as follows:
Figure FDA0003335754800000026
wherein,
Figure FDA0003335754800000027
and
Figure FDA0003335754800000028
the wavelet packet coefficients after wavelet packet reconstruction are wavelet packet coefficients after wavelet packet reconstruction; h isk-2nA low pass filter for wavelet packet reconstruction; gk-2nA high pass filter for wavelet packet reconstruction.
3. The rolling bearing fault diagnosis method based on fault feature frequency multiplication energy judgment of claim 1, characterized in that: the specific process of the step 2 is as follows:
and (3) processing the original vibration signal by a wavelet packet decomposition method to obtain a node component, and removing and reserving the node component according to the kurtosis value K, so that the effect of screening the node component is achieved, and a new signal is reconstructed and formed.
4. The rolling bearing fault diagnosis method based on fault feature frequency multiplication energy judgment of claim 3, characterized in that: the kurtosis value K is calculated according to the following formula:
Figure FDA0003335754800000029
wherein E is desired; y represents the vibration signal amplitude; u represents the mean value of the vibration signal amplitude y; alpha represents the standard deviation of the fault signal.
5. The rolling bearing fault diagnosis method based on fault feature frequency multiplication energy judgment of claim 1, characterized in that: the specific process of the step 3 is as follows:
envelope detection processing is carried out on the high-frequency vibration signal with the high signal-to-noise ratio to obtain an envelope waveform, then Hilbert transformation is adopted to realize envelope solving and fault information extraction on the signal, Hilbert transformation of the signal is reconstructed, and the signal generates 90-degree phase shift; the original signal is taken as a real part, Hilbert transform is carried out on the original signal to form an imaginary part to form an analytic signal, a module is calculated to obtain an envelope of the signal, the envelope signal is subjected to low-pass filtering, fast Fourier transform is carried out on the envelope signal to obtain an envelope spectrum, and Hilbert transform is defined as:
Figure FDA0003335754800000031
wherein, x (t) is an original time domain signal;
Figure FDA0003335754800000032
a Hilbert transform for signal x (t);
Figure FDA0003335754800000033
a convolution is performed for x (t), the impulse response of this convolution is
Figure FDA0003335754800000034
6. The rolling bearing fault diagnosis method based on fault feature frequency multiplication energy judgment of claim 1, characterized in that: the specific process of the step 4 is as follows:
when the normal bearing is in the normal operation process, the bearing cannot resonate; when the bearing has a local damage fault, the periodic pulse excitation generated in the operation process can cause high-frequency impact vibration of the bearing, the vibration signal of the fault bearing is subjected to resonance demodulation processing, the low-frequency fault characteristic frequency doubling signal related to the fault of the bearing is demodulated from the high-frequency modulation signal, the fault characteristic frequency and the frequency doubling position of the fault characteristic frequency in the obtained envelope spectrum have characteristic peak values, and the energy at the fault characteristic frequency doubling position and the total energy in the whole envelope spectrum have the highest proportion.
7. The rolling bearing fault diagnosis method based on fault feature frequency multiplication energy judgment of claim 6, characterized in that: the proportion percentage formula of the energy at the fault specific frequency and the total energy in the envelope spectrum is defined as follows:
Figure FDA0003335754800000035
wherein,
Figure FDA0003335754800000036
representing the energy sum at the frequency multiplication of the fault characteristic;
Figure FDA0003335754800000037
represents the sum of the energies at each frequency in the entire envelope spectrum; y isiRepresenting the peak at which the fault signature doubles;
Figure FDA0003335754800000038
representing the energy at the frequency multiplication of the fault characteristic; i represents the ith frequency multiplication of the fault characteristic; y isjA peak representing the j point in the envelope spectrogram;
Figure FDA0003335754800000039
representing the energy at the j-th point in the envelope spectrogram.
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Cited By (2)

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Publication number Priority date Publication date Assignee Title
CN116609060A (en) * 2023-04-13 2023-08-18 中国航发沈阳发动机研究所 Rolling bearing fault feature extraction method under complex path based on multi-parameter screening
CN116659860A (en) * 2022-10-24 2023-08-29 中国人民解放军93208部队 Novel method for monitoring main bearing fault evolution of aeroengine in service environment

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