CN112380671A - General amplitude demodulation method for gear fault vibration modulation signal - Google Patents
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Abstract
The invention discloses a general amplitude demodulation method for a gear fault vibration modulation signal. The method comprises the following steps: collecting a vibration acceleration signal when the gearbox fails; performing band-pass filtering to obtain a fault modulation signal which takes the meshing frequency as the center and takes the frequency conversion and the frequency multiplication of the fault gear as side frequency bands; discrete spectrum correction is carried out on the fault modulation signal, and accurate meshing frequency and accurate fault gear frequency conversion are obtained; carrying out square demodulation on the modulation signal, determining the order of amplitude modulation according to a square demodulation spectrum, and constructing a target mathematical model of the amplitude modulation; establishing a target function with the Hilbert envelope of the fault modulation signal equal to the Hilbert envelope of the target mathematical model; and solving amplitude modulation parameters by using a least square optimization algorithm based on confidence domain reflection to obtain an accurate amplitude modulation signal. The invention can realize the quantitative solution of the amplitude modulation parameter of the amplitude modulation signal under the condition of under-modulation and over-modulation of the amplitude, and has high solution precision and good noise immunity.
Description
Technical Field
The invention belongs to the field of fault diagnosis and signal processing of rotary machines, and particularly relates to a general amplitude demodulation method for a gear fault vibration modulation signal.
Background
The gear has high transmission efficiency and large bearing capacity, and is widely applied to a plurality of fields such as automobiles, ships, aviation and the like. However, the general gear mechanism has a severe working environment and is easy to break down, the service life of the equipment is influenced if the gear mechanism is in a severe working environment, and serious property loss and casualties are caused if the gear mechanism is in a severe working environment, so that the gear mechanism has important significance in correct fault diagnosis of the gear box. A large number of researches show that when a gear breaks down, the meshing vibration signal of the gear is obviously modulated, so that accurate amplitude demodulation is an important basis and precondition for accurate fault diagnosis of the gearbox.
The commonly used amplitude demodulation methods include Hilbert transform envelope (Zhengxiaxi, Dingkang, Jiangliang, Hilbert transform demodulation analysis, localization research applied in fault diagnosis [ J ] Shantou university bulletin (Nature science edition), 1999(02):3-5.), generalized detection filter demodulation, square demodulation (Dingkang, Jiangliang. demodulation analysis, three localization research applied in fault diagnosis of mechanical equipment [ J ] Houtou university bulletin (Nature science edition), 2000(01):1-12.) and energy operator demodulation (Marben, Hu, Menyangmen, Song, and Wao.) rolling bearing composite fault diagnosis based on multi-wavelet packet-energy operator demodulation [ J ] noise vibration control, 2018,38(04):154, 158.) and the like, and all use the frequency domain characteristics of extracting amplitude modulation as main characteristics, quantitative amplitude demodulation cannot be achieved, i.e., only the location of the gear failure can be diagnosed, and the degree of the gear failure cannot be diagnosed. The existing new amplitude modulation and frequency modulation signal separation method (X.Yang, K.Ding, G.He, Accurate separation of amplitude-modulation and phase-modulation signal and bits application to frequency fault diagnosis, J Sound Vib,452 (2019)) based on the relationship between the frequency modulation signal and the Bessel function of the first kind can realize the quantitative demodulation of the amplitude modulation signal which is under-modulated, but when the signal is over-modulated, the solving error of the amplitude modulation parameter is very large, so that the signal-to-noise ratio of the frequency modulation component in the residual signal is extremely poor, and finally the extraction of the frequency modulation component is invalid.
Disclosure of Invention
The invention aims to provide a general amplitude demodulation method for a gear fault vibration modulation signal aiming at the defects of the prior art. The Hilbert transform demodulation and amplitude modulation are combined with a nonlinear least square optimization algorithm based on signal domain reflection, quantitative solving of modulation signal amplitude modulation parameters can be achieved under the conditions of under-modulation and over-modulation of the amplitude, solving accuracy is high, and noise resistance is good.
The purpose of the invention is realized by at least one of the following technical solutions.
A general amplitude demodulation method for a gear fault vibration modulation signal comprises the following steps:
s1, collecting a vibration acceleration signal x (t) at a bearing end cover measuring point when the gearbox fails;
s2, performing band-pass filtering near a certain order of meshing frequency of the gear to obtain a fault modulation signal x taking the meshing frequency as the center and the frequency conversion and frequency multiplication of the fault gear as side bandsm(t)；
S3, performing discrete spectrum correction on the fault modulation signal to obtain accurate meshing frequency and accurate fault gear frequency conversion;
s4, demodulating the square of the modulation signal, determining the order of amplitude modulation according to the square demodulation spectrum, and constructing a target mathematical model y (t) of the amplitude modulation;
s5, establishing a target function with the Hilbert envelope of the fault modulation signal equal to that of the target mathematical model;
and S6, solving amplitude modulation parameters by using a least square optimization algorithm based on confidence domain reflection to obtain an accurate amplitude modulation signal.
Further, step S1 specifically includes the following steps:
s1.1, establishing a three-dimensional space coordinate system according to a right-hand rule: the X axis is parallel to the axial direction of the axis where the gear is located, and the positive direction points to the motor side; the Z axis is vertical to the ground, and the positive direction is vertical upwards; the positive direction of the Y axis is determined by a right-hand rule;
s1.2, installing a sensor: 4 three-way piezoelectric acceleration sensors are respectively arranged above 4 end covers of the input shaft bearing and the output shaft bearing and are used for measuring vibration acceleration data in XYZ three directions; correctly connecting the sensor, the data acquisition system and the computer;
s1.3, setting data acquisition parameters: the total sampling time length T is set to 10s, and the sampling frequency is set to fsThen the corresponding sampling time interval Δ t is 1/fsThe number of sampling points N ═ fsAnd T, recording the acquired time domain vibration acceleration signal as x (T).
Further, in step S2, in order to reduce the influence of noise and the transfer function of the resonance region as much as possible, a certain order of meshing frequency without coupling with the formants is selected, and band-pass filtering is performed to ensure that the pass band of the filter can cover the effective modulation side bands on both sides of the order of meshing frequency.
After filtering, obtaining a fault modulation signal which takes the meshing frequency as the center and takes the frequency conversion and the frequency multiplication of the fault gear as side frequency bands and is marked as xm(t)：
Wherein A iskIs the k-th order meshing frequency amplitude; f. ofmIs the meshing frequency; thetakIs the engagement frequency phase of the k order; i is a modulation order; i is the maximum modulation order; b iskiThe amplitude of the ith order modulation signal around the k order meshing frequency; f. ofnRotating the frequency of the failed gear;
the phase of the i-th order modulated signal around the k-th order meshing frequency.
Further, step S3 includes the steps of:
s3.1, modulating the filtered fault signal xm(t) adding a Hanning window, determining spectral line numbers corresponding to the maximum amplitude point and the second maximum amplitude point near the theoretical meshing frequency in the frequency spectrum by using a peak search algorithm, and respectively recording the spectral line numbers as km、lm(ii) a Similarly, determining the spectral line numbers corresponding to the maximum amplitude point and the second maximum amplitude point near the theoretical modulation edge frequency at two sides of the meshing frequency, and respectively recording the spectral line numbers as km±i、lm±iI denotes the modulation order;
s3.2, obtaining accurate meshing frequency f by using ratio correction methodmcAnd accurate fault gear frequency fnc：
f＝(k-Δf)fs/N；
Wherein, Δ f is the frequency error after window length normalization; v is a function of Δ f; w is a frequency spectrum mode function of the fault modulation signal after a Hanning window is added; k is a spectral line number corresponding to the maximum value; l is the number of the spectral line corresponding to the next largest value; f is the corrected real frequency; f. ofsIs the sampling frequency; and N is the number of sampling points.
Further, step S4 includes the steps of:
s4.1, modulating signal x for faultm(t) is squared and the expression for the low frequency modulated part is:
wherein A iskIs the k-th order meshing frequency amplitude; i is a modulation order; i is the maximum modulation order; b iski、Bkm、BknThe amplitudes of the ith order, the mth order and the nth order modulation signals near the kth order meshing frequency respectively; f. ofnRotating the frequency of the failed gear;
the phases of the ith, mth and nth order modulation signals near the kth order meshing frequency respectively; when the maximum modulation order of the signal is I, the maximum modulation order of the square of the signal is 2I;
s4.2, for xm(t) low-pass filtering the squared signal to ensure that the cut-off frequency of the low-pass filter is greater than the highest-order frequency multiplication of the fault gear frequency conversion occurring in the low-frequency region of the frequency spectrum, and performing Fourier transform to obtain a square demodulation spectrum of the fault gear frequency conversion; from the highest modulation order o actually present in the squared demodulated spectrummaxDetermining the amplitude modulation order of the target mathematical model as I ═ o max2; the target mathematical model y (t) of the amplitude modulation is thus obtained:
wherein A is the meshing frequency amplitude to be solved; f. ofmcIs the corrected meshing frequency; theta is the meshing frequency phase; i is a modulation order; o max2 is the maximum modulation order; b isiThe amplitude of the ith order modulation signal to be solved; f. ofncRotating frequency for the corrected fault gear;
the phase of the i-th order modulated signal to be solved.
Further, step S5 includes the steps of:
s5.1, constructing fault modulation signal x by using Hilbert transformmEnvelope H (t) of (t):
wherein j is an imaginary unit;
a hilbert transform pair that modulates a signal for a fault; z (t) is an analytic signal obtained by performing Hilbert transform on the fault modulation signal;
s5.2, similarly, constructing an envelope h (t) of the target mathematical model y (t):
wherein j is an imaginary unit;
a Hilbert transform pair for the target mathematical model; w (t) is an analytic signal obtained by performing Hilbert transform on a target mathematical model;
s5.3, establishing an optimized objective function with the envelope of the fault modulation signal equal to the envelope of the target mathematical model:
min(||h(t)-H(t)||2)；
wherein | · | purple sweet2Represents a two-norm; h (t) is the envelope of the target mathematical model to be solved; h (t) is the envelope of the known fault modulation signal.
Further, step S6 includes the following steps:
s6.1, determining boundary constraint of optimization parameters: value range of meshing frequency amplitude A
Wherein A is0Demodulating the amplitude value at the zero frequency position in the spectrum for the square of the fault signal; the lower limit of the amplitude of the modulated signal of each order is set to 0, taking into account that the sum of the amplitudes of the modulated signal of each order is strictly less than 1 when under-modulation occurs, i.e. the amplitude of each order is set to be equal to
Considering that the ratio delta of the fault modulation side frequency amplitude to the meshing frequency amplitude in the overmodulation experiment signal is generally less than 2, the requirement can be completely met when the amplitude upper limit is amplified to 6; the phase range of each order modulation signal is set to [0, 2 pi ]]；
S6.2, determining an initial value of the optimization parameter: amplitude B of each order modulation signaliInitial values are all set to 0.1, phase
Are all set as 1;
s6.3, setting an optimized cut-off condition: trust Domain reflection Algorithm default functional tolerance is 1 × 10-6Setting the maximum iteration times to be 800 times, setting the maximum iteration times of an equation to be 100 × equation unknowns, and exiting iteration when one of the conditions is met;
and S6.4, solving the objective function by using a least square optimization algorithm based on the confidence domain reflection to obtain the amplitude parameter and the phase parameter of each order of modulation signal, thereby realizing the quantitative demodulation of the amplitude modulation signal.
Compared with the prior art, the invention has the following advantages and effects:
(1) compared with the traditional amplitude demodulation method, the Hilbert demodulation and demodulation technology combining the least square optimization algorithm based on trust and reflection can extract the frequency domain characteristics of amplitude modulation and further realize the quantization parameter calculation of amplitude modulation signals.
(2) Compared with the existing square amplitude demodulation and the new amplitude modulation and frequency modulation signal separation method based on the frequency modulation signal and the Bessel function relation of the first class, the method can realize accurate solution of the amplitude parameter under the condition of overmodulation, and has stronger universality.
(3) Compared with the existing square amplitude demodulation and the new amplitude modulation and frequency modulation signal separation method based on the frequency modulation signal and Bessel function relation of the first class, the optimization objective function constructed by the method is simple and easy to obtain, heavy square demodulation mathematical formula derivation is not needed, the equivalent solving precision is ensured, and the algorithm has smaller calculated amount and shorter time consumption.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments will be briefly described below. The drawings constitute a part of this application and are intended as non-limiting examples embodying the inventive concept and not as limiting in any way.
FIG. 1 is a flow chart of a generalized amplitude demodulation method for gear failure vibration signals in an embodiment of the method of the present invention.
FIG. 2 is a block flow diagram of the method of the present invention.
Fig. 3 is a time-frequency diagram of a given noise-free under-modulated fault vibration simulation signal in embodiment 1 of the present invention.
Fig. 4 is a time domain graph comparing a matched amplitude modulated signal and an original under-modulated amplitude modulated signal in embodiment 1 of the present invention.
Fig. 5 is a frequency domain plot comparing a matched amplitude modulated signal with an original under-modulated amplitude modulated signal in embodiment 1 of the present invention.
FIG. 6 is a time-frequency plot of a given noise-free overmodulation fault vibration simulation signal in accordance with example 2 of the present invention.
Fig. 7 is a time domain graph comparing the envelope of the matched signal with the envelope of the original signal in embodiment 2 of the present invention.
Fig. 8 is a frequency domain graph comparing the envelope of the matched signal with the envelope of the original signal in embodiment 2 of the present invention.
Detailed Description
In order to make the objects, 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 with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1: amplitude demodulation of simulated under-modulated fault vibration signals under different degrees of noise
When the gearbox has stable faults such as shaft misalignment or uniform wear, the vibration signal of the gearbox can show the characteristic of amplitude modulation, and the fault vibration simulation signal x (t) is shown as the following formula:
wherein A ismIs the mth order meshing frequency amplitude; f. ofmIs the meshing frequency; thetamIs the mth order meshing frequency phase; i is a modulation order; i is the maximum modulation order; b ismiThe amplitude of the ith order modulation signal on both sides of the mth order meshing frequency; f. ofnRotating the frequency of the failed gear;
the phase of the ith order modulated signal is opposite to the mth order meshing frequency.
In order to test the noise resistance of the method, the fault vibration signal is demodulated under three working conditions of no noise, Gaussian white noise with the added signal-to-noise ratio of 10db and Gaussian white noise with the added signal-to-noise ratio of 2 db. As shown in fig. 1 and fig. 2, the present embodiment is implemented by the following specific steps:
in step S1, a fault vibration simulation signal is established according to the above formula, and the simulation parameters are set as follows: number of teeth z of input shaft of gear box1Set as 24, the number of output shaft gear teeth z2Set to 56. When the theoretical set rotating speed n is 900rpm, the gear rotating frequency fnN/60-15 Hz, meshing frequency fm＝fnz1The actual output speed of the motor in the experiment is considered to have an error, the given speed 906rpm is given, the actual rotation frequency of the gear is 15.1Hz, and the actual meshing frequency is 362.4 Hz. Given sampling frequency fs2048Hz, total sampling time T is set to 1s, and the number of sampling points N is set to fs·T＝2048。
The order of the given meshing frequency is 1 order, the maximum order of the fault modulation frequency is 2 orders, and other corresponding parameter settings are shown in table 1.
Table 1 simulation signal parameter setting table
In the case of no noise, the time-frequency diagram of the under-modulated fault vibration simulation signal is shown in fig. 3.
In step S2, the upper limit frequency f of the band-pass filter is seth420Hz, lower limit frequency fl300Hz and the filter half order M300. Performing band-pass filtering near the meshing frequency to obtain a fault signal which is centered on the meshing frequency and contains a two-step gear frequency conversion modulation sideband and is marked as xm(t)；
Step S3 specifically includes the following steps:
s3.1, adding Hanning window to the filtered fault modulation signal, and determining f in the frequency spectrum by utilizing a peak search algorithmm、fm+fn、fm+2fn、fm-fn、fm-2fnThe spectral line numbers of the maximum amplitude point and the second maximum amplitude point are 362/363, 377/378, 393/392, 347/348 and 332/331 respectively.
S3.2, obtaining real gear meshing frequency f by using ratio correction methodmc362.4Hz true failure gear frequency fnc＝15.1Hz。
Step S4 specifically includes the following steps:
and S4.1, setting the cut-off frequency of the low-pass filter to be 100Hz, and setting the half-order number M of the filter to be 300. And (3) performing low-pass filtering after squaring the fault modulation simulation signal, and performing discrete Fourier transform, wherein the highest order of frequency conversion of the frequency spectrum is 4 orders, so that the modulation order of the target mathematical model is determined to be 4/2-2 orders.
S4.2, providing a target mathematical model y (t) of second-order amplitude modulation:
wherein A is the meshing frequency amplitude to be solved; f. ofmcIs the corrected meshing frequency; theta mesh frequency phase; b is1、B2Respectively 1 st order and 1 st order to be solvedThe amplitude of the order-2 modulation signal; f. ofncRotating frequency for the corrected fault gear;
the phases of the 1 st order modulation signal and the 2 nd order modulation signal to be solved are respectively.
Step S5 specifically includes the following steps:
s5.1, constructing fault modulation signal x by using Hilbert transformmEnvelope H (t) of (t):
wherein j is an imaginary unit;
a hilbert transform pair that modulates a signal for a fault; z (t) is an analysis signal obtained by subjecting the fault modulation signal to hilbert transform.
S5.2, similarly, constructing an envelope h (t) of the target mathematical model y (t):
wherein j is an imaginary unit;
a Hilbert transform pair for the target mathematical model; w (t) is an analysis signal obtained by subjecting the target mathematical model to hilbert transform.
S5.3, taking the minimum sum of the squares of the errors of the target mathematical model envelope and the fault modulation signal envelope as an optimization objective function:
min(||h(t)-H(t)||2)
wherein | · | purple sweet2Represents a two-norm; h (t) is the envelope of the target mathematical model to be solved; h (t) is the envelope of the known fault modulation signal.
Step S6 specifically includes the following steps:
s6.1, determining the amplitude parameter of the meshing frequency to be [0, 3.06], the boundary constraint of other amplitude parameters to be [0, 6], and the boundary constraint of the phase parameter to be [0, 2 pi ], as shown in Table 2.
TABLE 2 Parametric boundary constraints
S6.2, determining that the initial value of the amplitude parameter is set to be 0.1, and the initial value of the phase parameter is set to be 1, as shown in Table 3.
TABLE 3 initial value of parameter solution
S6.3, setting a cutoff condition of iterative optimization: trust Domain reflection Algorithm default functional tolerance is 1 × 10-6And setting the maximum iteration number as 800, setting the maximum iteration number of the equation as 100 x 5 as 500, and exiting the iteration when one of the conditions is met.
S6.4, solving the objective function by using a least square optimization algorithm based on the confidence domain reflection, wherein the amplitude and phase parameters and the error thereof obtained under the noise-free condition are shown in a table 4. It can be seen that the algorithm of the invention has no error basically in the solving results of the amplitude and the phase when no noise exists, and has high precision. The time domain graph of the matched amplitude-modulated signal compared with the original amplitude-modulated signal is shown in fig. 4, and the frequency domain graph is shown in fig. 5.
TABLE 4 noiseless solution results and errors
In order to test the solving accuracy of the method under different degrees of noise, the steps are repeated under the conditions of signal-to-noise ratios of 10db and 2db, and the amplitude, phase parameters and errors are obtained as shown in table 5.
TABLE 5 solving results and errors for different SNR plus noise
From the table, it can be found that as the signal-to-noise ratio decreases, the matching accuracy of the amplitude and the phase also decreases, but the total error can be basically controlled within 10%, and the variation of the matching error of each parameter has certain randomness because the added noise is white gaussian noise. When white noise with a signal-to-noise ratio of 2db is added, the maximum frequency error is 19%.
Example 2: amplitude demodulation of simulated overmodulation fault vibration signal (method comparison)
When the gearbox has stable faults such as shaft misalignment or uniform wear, the vibration signal of the gearbox can show the characteristic of amplitude modulation, and the fault vibration simulation signal x (t) is shown as the following formula:
wherein A ismIs the mth order meshing frequency amplitude; f. ofmIs the meshing frequency; thetamIs the mth order meshing frequency phase; i is a modulation order; i is the maximum modulation order; b ismiThe amplitude of the ith order modulation signal; f. ofnRotating the frequency of the failed gear;
the phase of the i-th order modulation signal.
The implementation effect of the method of the present invention and the existing method (method two) for accurately separating amplitude modulated signals based on square demodulation are compared to give an amplitude overmodulation signal to illustrate the superiority of the method in separating the overmodulation signal. The embodiment is realized by the following specific steps:
in step S1, a fault vibration simulation signal is established according to the above formula, and the simulation parameters are set as follows: number of teeth z of input shaft of gear box1Set as 24, the number of output shaft gear teeth z2Set to 56. When the theoretical set rotating speed n is 900rpm, the gear rotating frequency fnN/60-15 Hz, meshing frequency fm＝fnz1The actual output speed of the motor in the experiment is considered to have an error, the given speed 906rpm is given, the actual rotation frequency of the gear is 15.1Hz, and the actual meshing frequency is 362.4 Hz. Given sampling frequency fs2048Hz, total sampling time T is set to 1s, and the number of sampling points N is set to fs·T＝2048。
The order of the given meshing frequency is 1 order, the maximum order of the fault modulation frequency is 2 orders, and other corresponding parameter settings are shown in table 6.
Table 6 simulation signal parameter setting table
The time-frequency diagram of the overmodulation fault vibration simulation signal is shown in fig. 6.
In step S2, the upper limit frequency f of the band-pass filter is seth420Hz, lower limit frequency fl300Hz and the filter half order M300. Performing band-pass filtering near the meshing frequency to obtain a fault signal which is centered on the meshing frequency and contains a two-step gear frequency conversion modulation sideband and is marked as xm(t)；
In step S3:
s31, adding Hanning window to the filtered fault modulation signal, and determining f in frequency spectrum by using peak search algorithmm、fm+fn、fm+2fn、fm-fn、fm-2fnThe spectral line numbers of the maximum amplitude point and the second maximum amplitude point are 362/363, 377/378, 393/392, 347/348 and 332/331 respectively.
S32, use ofObtaining true gear meshing frequency f by ratio correction methodmc362.4Hz true failure gear frequency fnc＝15.1Hz。
In step S4:
and S41, setting the cut-off frequency of the low-pass filter to be 100Hz, and setting the half-order number M of the filter to be 300. And (3) performing low-pass filtering after squaring the fault modulation simulation signal, and performing discrete Fourier transform, wherein the highest order of frequency conversion of the frequency spectrum is 4 orders, so that the modulation order of the target mathematical model is determined to be 4/2-2 orders.
S42, a target mathematical model y (t) of second-order amplitude modulation is given:
wherein A is the meshing frequency amplitude to be solved; f. ofmcIs the corrected meshing frequency; theta mesh frequency phase; b is1、B2The amplitudes of the 1 st order modulation signal and the 2 nd order modulation signal to be solved are respectively; f. ofncRotating frequency for the corrected fault gear;
the phases of the 1 st order modulation signal and the 2 nd order modulation signal to be solved are respectively.
In step S5:
s51, constructing fault modulation signal x by using Hilbert transformmEnvelope H (t) of (t):
wherein j is an imaginary unit;
a hilbert transform pair that modulates a signal for a fault; z (t) is a pairAnd the fault modulation signal is subjected to Hilbert conversion to obtain an analysis signal.
S52, similarly, constructing an envelope h (t) of the target mathematical model y (t):
wherein j is an imaginary unit;
a Hilbert transform pair for the target mathematical model; w (t) is an analysis signal obtained by subjecting the target mathematical model to hilbert transform.
S53, taking the minimum sum of the squares of the errors of the target mathematical model envelope and the fault modulation signal envelope as an optimization objective function:
min(||h(t)-H(t)||2)
wherein | · | purple sweet2Represents a two-norm; h (t) is the envelope of the target mathematical model to be solved; h (t) is the envelope of the known fault modulation signal.
In step S6:
s61, determining the amplitude parameter of the meshing frequency as [0, 2.97], the boundary constraint of other amplitude parameters as [0, 6], and the boundary constraint of the phase parameter as [0, 2 pi ], as shown in Table 7.
TABLE 7 parametric boundary constraints
S62, setting the initial value of the amplitude parameter to 0.1, and setting the initial value of the phase parameter to 1, as shown in table 8.
TABLE 8 initial value of parameter solution
S63, setting a cutoff condition of iterative optimization: trust Domain reflection Algorithm default functional tolerance is 1 × 10-6And setting the maximum iteration number as 800, setting the maximum iteration number of the equation as 100 x 5 as 500, and exiting the iteration when one of the conditions is met.
S64, solving the objective function by using the method to obtain amplitude and phase parameters and errors thereof; meanwhile, amplitude and phase parameters and errors thereof are obtained by solving the existing amplitude modulation signal accurate separation method (method II) based on square demodulation and are listed in a table 9 in a unified way. The time domain graph and the frequency domain graph comparing the envelope of the matched signal with the envelope of the original signal are respectively shown in fig. 7 and fig. 8.
TABLE 9 comparison of results
It can be seen from the above table that the error of the amplitude and phase parameters is below 0.2% when the overmodulation is solved by the algorithm, and basically, no error exists, and the accuracy is very high. The error of the comparison method is basically over 10 percent, and the maximum error reaches 17.85 percent when no noise influence exists. The superiority of the method of the invention can be obviously seen by comparing the above.
In summary, the general amplitude demodulation method for the gear fault vibration modulation signal provided by the invention has the following advantages:
(1) compared with the traditional amplitude demodulation method, the demodulation technology combining Hilbert demodulation and amplitude modulation with the least square optimization algorithm based on trust and reflection, which is provided by the invention, can not only extract the frequency domain characteristics of amplitude modulation, but also further realize the quantization parameter calculation of amplitude modulation signals.
(2) The optimization objective function constructed by the method is simple and easy to obtain, heavy square demodulation mathematical formula derivation is not needed, zero-error solution of amplitude modulation parameters can be basically realized under the noise-free condition, quite high solution precision can be ensured under the condition of low signal-to-noise ratio, and the algorithm has small calculation amount and short time consumption.
(3) Compared with the existing square amplitude demodulation and the new amplitude modulation and frequency modulation signal separation method based on the frequency modulation signal and the Bessel function relation of the first class, the method can realize accurate solution of the amplitude parameter under the condition of overmodulation, and has stronger superiority and universality.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution of the present invention and the inventive concept within the scope of the present invention disclosed by the present invention.
Claims (7)
1. A general amplitude demodulation method for a gear fault vibration modulation signal is characterized by comprising the following steps:
s1, collecting a vibration acceleration signal x (t) at a bearing end cover measuring point when the gearbox fails;
s2, performing band-pass filtering near a certain order of meshing frequency of the gear to obtain a fault modulation signal x taking the meshing frequency as the center and the frequency conversion and frequency multiplication of the fault gear as side bandsm(t)；
S3, performing discrete spectrum correction on the fault modulation signal to obtain accurate meshing frequency and accurate fault gear frequency conversion;
s4, demodulating the square of the modulation signal, determining the order of amplitude modulation according to the square demodulation spectrum, and constructing a target mathematical model y (t) of the amplitude modulation;
s5, establishing a target function with the Hilbert envelope of the fault modulation signal equal to that of the target mathematical model;
and S6, solving amplitude modulation parameters by using a least square optimization algorithm based on confidence domain reflection to obtain an accurate amplitude modulation signal.
2. The method for demodulating the general amplitude of the gear fault vibration modulation signal according to claim 1, wherein the step S1 specifically comprises the steps of:
s1.1, establishing a three-dimensional space coordinate system according to a right-hand rule: the X axis is parallel to the axial direction of the axis where the gear is located, and the positive direction points to the motor side; the Z axis is vertical to the ground, and the positive direction is vertical upwards; the positive direction of the Y axis is determined by a right-hand rule;
s1.2, installing a sensor: 4 three-way piezoelectric acceleration sensors are respectively arranged above 4 end covers of the input shaft bearing and the output shaft bearing and are used for measuring vibration acceleration data in XYZ three directions; correctly connecting the sensor, the data acquisition system and the computer;
s1.3, setting data acquisition parameters: the total sampling time length T is set to 10s, and the sampling frequency is set to fsThen the corresponding sampling time interval Δ t is 1/fsThe number of sampling points N ═ fsAnd T, recording the acquired time domain vibration acceleration signal as x (T).
3. The method for demodulating the general amplitude of the gear fault vibration modulation signal according to claim 1, wherein in step S2, in order to minimize the influence of noise and the transfer function of the resonance region, a certain order of meshing frequency without coupling with the formant is selected and band-pass filtering is performed to ensure that the pass band of the filter can cover the effective modulation side bands on both sides of the order of meshing frequency;
after filtering, obtaining a fault modulation signal which takes the meshing frequency as the center and takes the frequency conversion and the frequency multiplication of the fault gear as side frequency bands and is marked as xm(t)：
Wherein A iskIs the k-th order meshing frequency amplitude; f. ofmIs the meshing frequency; thetakIs the engagement frequency phase of the k order; i is a modulation order; i is the maximum modulation order; b iskiThe amplitude of the ith order modulation signal around the k order meshing frequency; f. ofnRotating the frequency of the failed gear;
is the k-th orderThe phase of the i-th order modulated signal around the meshing frequency.
4. The method for demodulating the general amplitude of a gear failure vibration modulation signal as claimed in claim 1, wherein the step S3 comprises the steps of:
s3.1, modulating the filtered fault signal xm(t) adding a Hanning window, determining spectral line numbers corresponding to the maximum amplitude point and the second maximum amplitude point near the theoretical meshing frequency in the frequency spectrum by using a peak search algorithm, and respectively recording the spectral line numbers as km、lm(ii) a Similarly, determining the spectral line numbers corresponding to the maximum amplitude point and the second maximum amplitude point near the theoretical modulation edge frequency at two sides of the meshing frequency, and respectively recording the spectral line numbers as km±i、lm±iI denotes the modulation order;
s3.2, obtaining accurate meshing frequency f by using ratio correction methodmcAnd accurate fault gear frequency fnc：
f＝(k-Δf)fs/N；
Wherein, Δ f is the frequency error after window length normalization; v is a function of Δ f; w is a frequency spectrum mode function of the fault modulation signal after a Hanning window is added; k is a spectral line number corresponding to the maximum value; l is the number of the spectral line corresponding to the next largest value; f is the corrected real frequency; f. ofsIs the sampling frequency; and N is the number of sampling points.
5. The method for demodulating the general amplitude of a gear failure vibration modulation signal as claimed in claim 1, wherein the step S4 comprises the steps of:
s4.1, modulating signal x for faultm(t) is squared and the expression for the low frequency modulated part is:
wherein A iskIs the k-th order meshing frequency amplitude; i is a modulation order; i is the maximum modulation order; b iski、Bkm、BknThe amplitudes of the ith order, the mth order and the nth order modulation signals near the kth order meshing frequency respectively; f. ofnRotating the frequency of the failed gear;
the phases of the ith, mth and nth order modulation signals near the kth order meshing frequency respectively; when the maximum modulation order of the signal is I, the maximum modulation order of the square of the signal is 2I;
s4.2, for xm(t) low-pass filtering the squared signal to ensure that the cut-off frequency of the low-pass filter is greater than the highest-order frequency multiplication of the fault gear frequency conversion occurring in the low-frequency region of the frequency spectrum, and performing Fourier transform to obtain a square demodulation spectrum of the fault gear frequency conversion; from the highest modulation order o actually present in the squared demodulated spectrummaxDetermining the amplitude modulation order of the target mathematical model as I ═ omax2; the target mathematical model y (t) of the amplitude modulation is thus obtained:
wherein A is the meshing frequency amplitude to be solved; f. ofmcIs the corrected meshing frequency; theta is the meshing frequency phase; i is a modulation order; omax2 is the maximum modulation order; b isiThe amplitude of the ith order modulation signal to be solved; f. ofncRotating frequency for the corrected fault gear;
the phase of the i-th order modulated signal to be solved.
6. The method for demodulating the general amplitude of a gear failure vibration modulation signal as claimed in claim 1, wherein the step S5 comprises the steps of:
s5.1, constructing by using Hilbert transformFault modulated signal xmEnvelope H (t) of (t):
wherein j is an imaginary unit;
a hilbert transform pair that modulates a signal for a fault; z (t) is an analytic signal obtained by performing Hilbert transform on the fault modulation signal;
s5.2, similarly, constructing an envelope h (t) of the target mathematical model y (t):
wherein j is an imaginary unit;
a Hilbert transform pair for the target mathematical model; w (t) is an analytic signal obtained by performing Hilbert transform on a target mathematical model;
s5.3, establishing an optimized objective function with the envelope of the fault modulation signal equal to the envelope of the target mathematical model:
min(||h(t)-H(t)||2)；
wherein | · | purple sweet2Represents a two-norm; h (t) is the envelope of the target mathematical model to be solved; h (t) is the envelope of the known fault modulation signal.
7. The method for demodulating the general amplitude of the gear fault vibration modulation signal according to any one of claims 1 to 6, wherein the step S6 comprises the following steps:
s6.1, determining boundary constraint of optimization parameters: value range of meshing frequency amplitude A
Wherein A is0Demodulating the amplitude value at the zero frequency position in the spectrum for the square of the fault signal; the lower limit of the amplitude of each order modulation signal is set to 0, the upper limit of the amplitude is set to 6, and the phase range of each order modulation signal is set to 0, 2 pi]；
S6.2, determining an initial value of the optimization parameter: amplitude B of each order modulation signaliInitial values are all set to 0.1, phase
Are all set as 1;
s6.3, setting an optimized cut-off condition: trust Domain reflection Algorithm default functional tolerance is 1 × 10-6Setting the maximum iteration times to be 800 times, setting the maximum iteration times of an equation to be 100 × equation unknowns, and exiting iteration when one of the conditions is met;
and S6.4, solving the objective function by using a least square optimization algorithm based on the confidence domain reflection to obtain the amplitude parameter and the phase parameter of each order of modulation signal, thereby realizing the quantitative demodulation of the amplitude modulation signal.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114593908A (en) * | 2022-03-01 | 2022-06-07 | 西人马(深圳)科技有限责任公司 | Gear fault analysis method and device |
| CN115022128A (en) * | 2022-04-27 | 2022-09-06 | 湖南开放大学(湖南网络工程职业学院、湖南省干部教育培训网络学院) | Parity block FFT-based CSK modulation efficient demodulation algorithm |
| CN115077690A (en) * | 2022-06-27 | 2022-09-20 | 重庆长安汽车股份有限公司 | Method for evaluating periodic pulsation noise of internal combustion engine |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101644623A (en) * | 2009-06-19 | 2010-02-10 | 湖南大学 | Gear fault diagnosis method based on multiscale morphological analysis |
| US20140172326A1 (en) * | 2012-12-17 | 2014-06-19 | General Electric Company | Fault detection system and associated method |
| CN104006962A (en) * | 2014-05-08 | 2014-08-27 | 昆明理工大学 | Gear fault feature extraction method and system |
| US20180059135A1 (en) * | 2015-10-14 | 2018-03-01 | Green Power Monitoring Systems, LLC | System and method for generation of a tachometer signal and reduction of jitter |
| CN109323858A (en) * | 2018-09-21 | 2019-02-12 | 华南理工大学 | A kind of gear distress vibration amplitude-modulation frequency-modulation signal is precisely separating method |
-
2020
- 2020-10-14 CN CN202011094791.0A patent/CN112380671B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101644623A (en) * | 2009-06-19 | 2010-02-10 | 湖南大学 | Gear fault diagnosis method based on multiscale morphological analysis |
| US20140172326A1 (en) * | 2012-12-17 | 2014-06-19 | General Electric Company | Fault detection system and associated method |
| CN104006962A (en) * | 2014-05-08 | 2014-08-27 | 昆明理工大学 | Gear fault feature extraction method and system |
| US20180059135A1 (en) * | 2015-10-14 | 2018-03-01 | Green Power Monitoring Systems, LLC | System and method for generation of a tachometer signal and reduction of jitter |
| CN109323858A (en) * | 2018-09-21 | 2019-02-12 | 华南理工大学 | A kind of gear distress vibration amplitude-modulation frequency-modulation signal is precisely separating method |
Non-Patent Citations (4)
| Title |
|---|
| CHUNGUANG ZHANG ET AL: "Fault Diagnosis for Rolling Bearings Using Optimized Variational Mode Decomposition and Resonance Demodulation", ENTROPY, vol. 22, no. 739, 3 July 2020 (2020-07-03), pages 1 - 15 * |
| YUANBO XU ET AL: "Application of high-order differential energy operator in bearing fault diagnosis", IOP CONF. SERIES: JOURNAL OF PHYSICS: CONF. SERIES, vol. 1303, 31 December 2019 (2019-12-31), pages 1 - 11 * |
| 丁康 等: "解调分析在机械设备故障诊断中应用的三个局限性研究", 汕头大学学报(自然科学版), vol. 15, no. 1, 31 December 2000 (2000-12-31), pages 1 - 12 * |
| 夏均忠;刘远宏;李树珉;冷永刚;苏涛;: "应用Hilbert变换和ZFFT提取变速器齿轮故障特征", 振动与冲击, vol. 32, no. 6, 31 December 2013 (2013-12-31), pages 63 - 66 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114593908A (en) * | 2022-03-01 | 2022-06-07 | 西人马(深圳)科技有限责任公司 | Gear fault analysis method and device |
| CN115022128A (en) * | 2022-04-27 | 2022-09-06 | 湖南开放大学(湖南网络工程职业学院、湖南省干部教育培训网络学院) | Parity block FFT-based CSK modulation efficient demodulation algorithm |
| CN115022128B (en) * | 2022-04-27 | 2024-03-15 | 湖南开放大学(湖南网络工程职业学院、湖南省干部教育培训网络学院) | CSK modulation high-efficiency demodulation algorithm based on parity block FFT |
| CN115077690A (en) * | 2022-06-27 | 2022-09-20 | 重庆长安汽车股份有限公司 | Method for evaluating periodic pulsation noise of internal combustion engine |
| CN115077690B (en) * | 2022-06-27 | 2024-04-19 | 重庆长安汽车股份有限公司 | Method for evaluating periodic pulsation noise of internal combustion engine |
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