CN110779723A - Hall signal-based precise fault diagnosis method for variable-speed working condition motor bearing - Google Patents
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Abstract
The invention discloses a variable speed working condition motor bearing accurate fault diagnosis method based on Hall signals, which comprises the following steps: 1) carrying out polynomial fitting on a motor rotating speed signal acquired by a Hall sensor to obtain a roughly estimated rotating speed function; 2) optimizing the polynomial coefficient of the rotating speed function obtained in the first step in a certain range, carrying out equal-angle sampling on the fault signal by using the rotating speed function determined by the polynomial during optimizing, and taking the frequency spectrum kurtosis of the obtained equal-angle sampling signal as an optimization index; 3) carrying out equal-angle sampling on the fault signal by the optimal estimated rotating speed function obtained in the step 2), and obtaining a diagnosis conclusion through envelope spectrum analysis. The method is suitable for variable-speed fault diagnosis of the bearing of the motor which is provided with the Hall sensor or is inconvenient to install the encoder but can be provided with the Hall sensor, has better noise resistance compared with the traditional method, and can realize accurate fault diagnosis without additionally installing the encoder.
Description
Technical Field
The invention is applied to the technical field of accurate fault diagnosis of a motor bearing under a variable-speed working condition, and particularly relates to an accurate fault diagnosis method of the motor bearing under the variable-speed working condition based on a Hall signal.
Background
The fault signals (such as vibration, sound and the like) of the motor bearing contain rich running state information of the bearing, and the motor bearing can be effectively monitored healthily and diagnosed with faults through a signal processing means. Frequency spectrum analysis is one of the common means for fault diagnosis, but the frequency spectrum of the bearing fault signal of the motor under the variable-speed working condition can generate a frequency aliasing phenomenon, so that the accuracy of the diagnosis result is reduced. The main technical means for solving the problem at present is to perform equal-angle resampling on a fault signal, and the premise of the equal-angle resampling is to obtain an accurate rotating speed signal of a motor, the current rotating speed signal obtaining means includes two major types, one type is to directly measure the accurate rotating speed through a speed measuring sensor represented by an encoder, and the other type is to calculate the rotating speed in a non-encoder mode, for example, the rotating speed is calculated through measurement of armature current of the motor closely related to the rotating speed, the method needs to install an external current sensor, and the calculation amount is large, and the noise-resistant capability needs to be improved.
The Hall sensor is also one of the important means for measuring the speed of the motor, has the characteristics of low cost and convenient installation and debugging, and particularly has obvious advantages under the condition that the measurement space is limited or the sensor is inconvenient to install. However, the angular resolution of the hall sensor is poor, the motor shaft can only obtain a plurality of rotating speed pulses after rotating for one circle, and the rotating speed measurement precision provided by the motor shaft under the variable speed working condition is far from the requirement of precise fault diagnosis. Aiming at the motor products which are provided with Hall sensors or are inconvenient to be provided with encoders, the invention realizes the accurate estimation of the rotating speed by the technical means of index feedback optimization based on the inaccurate rotating speed of the Hall sensors, realizes the accurate resampling of fault signals and improves the accuracy of frequency spectrum analysis. The method is based on the idea that the spectral kurtosis value of a signal obtained by performing equal-angle sampling on a fault signal under a variable-speed working condition by using an accurate speed signal is the largest, and the method for accurately diagnosing the fault of the motor bearing under the variable-speed working condition based on the Hall signal is provided, the detailed steps of the method are provided, and the validity of the method is verified by a simulation case. Compared with the traditional method, the method has better noise resistance, and can realize accurate fault diagnosis without additionally installing an encoder. The method is suitable for the variable-speed fault diagnosis of the bearing of the motor which is provided with the Hall sensor or is inconvenient to install the encoder but can be provided with the Hall sensor.
Disclosure of Invention
The invention aims to provide a variable-speed working condition motor bearing accurate fault diagnosis method based on Hall signals, which can accurately estimate the rotating speed based on inaccurate rotating speed signals obtained by a Hall sensor, realize accurate equal-angle sampling of bearing fault signals and further improve the accuracy of fault diagnosis.
The technical scheme adopted by the invention is as follows: a method for accurately diagnosing faults of a motor bearing under variable speed working conditions based on Hall signals is characterized in that if collected fault signals of the motor bearing are X (t), and rotating speed signals obtained by a Hall sensor are n (t), the processing steps are as follows:
step 1: carrying out polynomial fitting on the rotating speed signal n (t) obtained by the Hall sensor to obtain a roughly estimated rotating speed function: y (t) ═ a
0+a
1*t+a
2*t
2+…a
n*t
nWherein (a)
0，a
1，a
2,…,a
n) Is a polynomial coefficient;
step 2: for the polynomial coefficient (a) obtained in step 2
0，a
1，a
2,…,a
n) Initializing to set parameter range and step length to obtain initialized parameter set U (a)
0，a
1，a
2,…,a
n)；
And step 3: parameter set U (a)
0，a
1，a
2,…,a
n) A set of parameters (a)
0m，a
1m，a
2m,…,a
nm) Performing equal-angle cubic spline interpolation resampling on the signal X (t) to obtain a signal sig1
m；
And 4, step 4: resampling to obtain signal sig1
mCarrying out band-pass filtering processing in a resonance frequency band to obtain a signal sig
m；
And 5: for the signal sig obtained in step 4
mPerforming fast Fourier transform to obtain Y
mAnd calculate Y
mKurtosis of (1);
step 6: repeating steps 3, 4 and 5 until the parameter set U (a) is calculated
0，a
1，a
2,…,a
n) The kurtosis values corresponding to all the parameter combinations in the process;
and 7: selecting a parameter combination (a) corresponding to the maximum value in the kurtosis values obtained in the step 6
0kumax,a
1kumax,a
2kukmax,…,a
nkumax) Constructing an optimal rotating speed function y (t) by using polynomial coefficients as the optimal estimated rotating speed function
_best＝a
0kumax+a
1kumax*t+a
2kumax*t
2+…+a
nkumax*t
nAccording to the optimal rotation speed function y (t)
_bestPerforming equal-angle cubic spline interpolation resampling on the fault signal X (t) to obtain an equal-angle sampling signal R _ sig;
and 8: and (4) carrying out envelope spectrum analysis on the equiangular sampling signal R _ sig obtained in the step (7) to obtain a diagnosis conclusion.
Further, in the step 1, when polynomial fitting is performed on the rotating speed signal n (t) obtained by the hall sensor, the fitting criterion is a least square method; and (3) gradually increasing the highest order of fitting from 1 order upwards, and meeting the fitting requirement when the determination coefficient R-square of fitting data and original data is more than 0.97, so as to obtain the expression of the fitting speed curve expression y (t). The mathematical calculation formula for determining the coefficient R-square is as follows:
the SSR is the sum of squares of differences between fitted data and an original data mean value, and a calculation formula is as follows:
SST is the sum of the squares of the differences between the raw data and the mean of the raw data, and the calculation formula is as follows:
wherein the content of the first and second substances,
the mean value of the raw data is calculated as follows:
wherein m is the number of signal points acquired by the Hall sensor, w
iIs weight, here taken as 1, y'
iIs fitting data, y
iIs the original data of the image data,
is the mean of the raw data. The value range of the coefficient R-square is determined to be between 0 and 1, the closer to 1, the better the data fitting is, and the stronger the interpretation capability of the variable on the fitting result is.
Further, in step 2, the parameter set U (a)
0，a
1，a
2,…,a
n) Is defined as:
wherein A is
0、A
1、A
2、…、A
nIs the lower limit of the parameter range, Δ a
0、Δa
1、Δa
2、…、Δa
nIs a set interval step, A'
0、A′
1、A′
2、…、A′
nIs the upper limit of the parameter range.
Further, in step 3, the cubic spline interpolation resampling step is:
step 3-1: suppose that the signal x (t) has a length N and a sampling rate f
sThen its sampling time sequence is t
s(n)＝0,1/f
s,…,(N-1)/f
sFor parameter U (a)
0，a
1，a
2,…,a
n) And calculating a sampling point sequence:
wherein f is
sIs the sampling frequency of the fault signal, N is the length of the signal acquired, y (t)
s(n)) is a rotation speed coefficient of (a)
m、b
m、c
m、d
m…) in time series t
s(n) the value of the rotation speed, the time sequence being a synchronous time sequence of the signal x (t);
step 3-2: calculating a resampling sequence: resampling sequence theta
2(n) is the sequence used for interpolation, the value of which is θ
2The calculation formula of (n) is:
wherein min (y)) is the number of (a)
0，a
1，a
2,…,a
n) Corresponding to a minimum value of y (t);
step 3-3: using theta
2(n) pairs of [ theta ]
1(n), X (t) } to obtain the correction signal sig1 by carrying out cubic spline interpolation resampling treatment
m。
Further, in step 5, the obtained sig is processed
mPerforming fast Fourier transform to obtain Y
mThen, Y is calculated according to the following formula
mThe kurtosis of (2):
Ku
m＝S
m 4
wherein N is the length of the collected signal, Ku
mIs Y
mThe kurtosis of (c).
Further, in step 7, the optimal bearing rotation speed parameter is used to perform cubic spline interpolation sampling on x (t), where the cubic spline interpolation sampling method is the same as that in step 3.
Compared with the prior art, the invention has the advantages that:
(1) the invention only needs the Hall sensor to measure the speed, and has lower hardware cost and higher reliability compared with the existing encoder speed measuring scheme.
(2) Compared with the current velocity measurement technology, the method has more advantages in noise resistance and cost.
(3) The motor with the Hall sensor does not need to additionally replace the high-precision speed measuring sensor.
(4) The method has obvious advantages under the condition that the measuring space is limited or the sensor is inconvenient to install.
Drawings
FIG. 1 is a flow chart of a method for accurately diagnosing faults of a motor bearing under variable speed conditions based on Hall signals according to the invention;
FIG. 2 is a time domain diagram, a spectrogram and an envelope spectrogram of signal X (t);
FIG. 3 is a speed point fitting curve obtained by an actual rotating speed curve and a Hall sensor;
FIG. 4 is a diagram of an equiangular sampling result of a motor bearing fault signal under a Hall signal;
FIG. 5 is a graph of kurtosis values as a function of number of seeks;
fig. 6 is a time domain diagram, a frequency spectrum diagram and an envelope spectrum diagram of the equiangular sampling signal R _ sig obtained by performing equiangular cubic spline interpolation resampling on x (t) according to the optimal rotating speed estimation function.
Detailed Description
The invention is described in further detail below with reference to the figures and experimental data from simulations.
Selecting a periodic impact signal as a single-point fault simulation signal of a motor bearing, wherein the expression is as follows:
where mod denotes a residue function for generating periodic impulses, A denotes the amplitude of the signal, f
mRepresenting the centre of the resonance frequency of the bearing, f
0The failure frequency of the bearing is shown, and d is 500, which is the attenuation speed of the signal. In the simulation case, the four parameters are respectively taken as follows: a is 1, f
m＝1500Hz，f
0150Hz and 500 d. The angular rotation speed of the bearing is as follows: y0(t) 425 t
3-680*t
2The fault signal collected under +260 x t +59 (unit is rad/s) is x (t), the rotating speed signal n (t) collected by the Hall sensor is fitted into y (t), and the sampling frequency of the signal is 10 KHz. The signal x (t) is added with white gaussian noise with a signal-to-noise ratio of-5 dB to obtain a signal x (t), and a time domain waveform, a spectrogram and an envelope spectrogram of the signal x (t) are shown in fig. 2. It is also difficult to identify the failure frequency of 150Hz from the envelope spectrogram. The following treatment is carried out by using the method provided by the invention, and the specific steps are as follows:
step 1: and carrying out polynomial fitting on the rotating speed signals n (t) obtained by the Hall sensor, adopting a least square method criterion for the fitting of the n (t), and when the highest fitting term number is 3, determining a coefficient R-square equal to 1 and larger than 0.97 by using the sum of the coefficients and the variance, so as to meet the fitting requirement. Obtaining a roughly estimated rotation speed function: y (t) ═ 58.49+262.28 t + (-684.59) t
2+428.99*t
3FIG. 3 is a comparison of a fitted rotation speed curve and an actual rotation speed curve, FIG. 4 is a diagram of equal-angle sampling results of motor bearing fault signals under Hall signals, and it can be seen from the diagram that Hall sensors are directly appliedThe frequency spectrum obtained by performing equal-angle sampling on the obtained speed function is not sharp, and 1.6Hz deviation exists in fault frequency identification in the envelope spectrum.
Step 2: for the polynomial coefficient (a) obtained in step 2
0，a
1，a
2,a
3) Initializing, setting parameter range and step length, and obtaining an initialization parameter set as follows:
the lower parameter range limit is set to (49, 252, -694, 419); the step size of the interval is set to Δ a
0＝1、Δa
1＝1、Δa
2＝1、Δa
31 is ═ 1; the upper limit of the parameter range is set to (59, 272, -674, 439);
and step 3: parameter set U (a)
0，a
1，a
2,…,a
n) A set of parameters (a)
0m，a
1m，a
2m,…,a
nm) Performing equal-angle cubic spline interpolation resampling on the signal X (t) to obtain a signal sig1
m；
And 4, step 4: selecting a band-pass frequency band of the band-pass filter including the resonance frequency of the band-pass filter, wherein the selected filter is a Butterworth band-pass filter, the band-pass frequency band of the Butterworth band-pass filter is selected from a spectrogram to be 500Hz-2500Hz, and a signal sig is obtained after filtering
m；
And 5: for the signal sig obtained in step 4
mPerforming fast Fourier transform to obtain Y
mAnd calculate Y
mKurtosis of (1);
step 6: for parameter set U (a)
0，a
1，a
2,a
3) The kurtosis of all the parameter combinations in the steps 3, 4 and 5 is calculated in a traversal mode, 194481 kurtosis are obtained in total, the trend of the obtained 194481 kurtosis values along with the number of optimizing times is shown in figure 5, and the maximum kurtosis value is 482.4;
and 7: selecting the parameters {59,260, -680,425} when the kurtosis value obtained in the step 6 is the maximum of 482.4, and constructing an optimal rotating speed signal y (t)
_best＝59+260*t-680*t
2+425*t
3Performing equal-angle cubic spline interpolation resampling on the fault signal X (t) to obtain an equal-angle sampling signal R _ sig;
and 8: the result of performing envelope spectrum analysis on the equiangular sampling signal R _ sig obtained in step 7 is shown in fig. 6, it can be seen that there is a fault frequency at 150.5Hz, and there is only a 0.5Hz deviation from the theoretical value, and it can be seen by comparing fig. 4 that the spectral peaks in the resonance frequency band in the spectrogram are sharp and clear, and the number of visible spectral peaks is large. Illustrating the effectiveness of the method of the present invention.
The above-described embodiments are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.
Claims (6)
1. A method for accurately diagnosing faults of a motor bearing under variable speed working conditions based on Hall signals is characterized by comprising the following steps of:
step 1: carrying out polynomial fitting on the rotating speed signal n (t) obtained by the Hall sensor to obtain a roughly estimated rotating speed function: y (t) ═ a
0+a
1*t+a
2*t
2+…a
n*t
nWherein (a)
0，a
1，a
2,…,a
n) Is a polynomial coefficient;
step 2: for the polynomial coefficient (a) obtained in step 2
0，a
1，a
2,…,a
n) Initializing to set parameter range and step length to obtain initialized parameter set U (a)
0，a
1，a
2,…,a
n)；
And step 3: parameter set U (a)
0，a
1，a
2,…,a
n) A set of parameters (a)
0m，a
1m，a
2m,…,a
nm) Performing equal-angle cubic spline interpolation resampling on the signal X (t) to obtain a signal sig1
m；
And 4, step 4: for the signal obtained in step 3sig1
mCarrying out band-pass filtering in a bearing resonance frequency band to obtain a signal sig
m；
And 5: for the signal sig obtained in step 4
mPerforming fast Fourier transform to obtain Y
mAnd calculate Y
mKurtosis of (1);
step 6: repeating steps 3, 4 and 5 until the parameter set U (a) is calculated
0，a
1，a
2,…,a
n) The kurtosis values corresponding to all the parameter combinations in the process;
and 7: selecting a parameter combination (a) corresponding to the maximum value in the kurtosis values obtained in the step 6
0kumax,a
1kumax,a
2kumax,…,a
nkumax) Constructing an optimal rotating speed function y (t) by using polynomial coefficients as the optimal estimated rotating speed function
_best＝a
0kumax+a
1kumax*t+a
2kumax*t
2+…+a
nkumax*t
nAccording to the optimal rotation speed function y (t)
_bestPerforming equal-angle cubic spline interpolation resampling on the fault signal X (t) to obtain an equal-angle sampling signal R _ sig;
and 8: and (4) carrying out envelope spectrum analysis on the equiangular sampling signal R _ sig obtained in the step (7) to obtain a diagnosis conclusion.
2. The method for accurately diagnosing the fault of the variable-speed working condition motor bearing based on the Hall signal according to claim 1, wherein in the step 1:
(1) the fitting criterion for the rotating speed signal n (t) is a least square method;
(2) the polynomial order n is gradually increased from 1 order during fitting until the fitting requirement is met when the determination coefficient R-square of fitting data and original data is more than 0.97, and the expression of the fitting speed curve expression y (t) can be obtained:
the mathematical calculation formula for determining the coefficient R-square is as follows:
the SSR is the sum of squares of differences between fitted data and an original data mean value, and a calculation formula is as follows:
SST is the sum of the squares of the differences between the raw data and the mean of the raw data, and the calculation formula is as follows:
wherein the content of the first and second substances,
the mean value of the raw data is calculated as follows:
wherein m is the number of signal points acquired by the Hall sensor, w
iIs weight, here taken as 1, y'
iIs fitting data, y
iIs the original data of the image data,
is the mean of the raw data. The value range of the coefficient R-square is determined to be between 0 and 1, and the closer to 1, the better the data fitting is, and the stronger the interpretation capability of the variable on the fitting result is.
3. The method for accurately diagnosing the fault of the variable-speed working condition motor bearing based on the Hall signal according to claim 1, is characterized in that: in said step 2, the parameter set U (a)
0，a
1，a
2,…,a
n) Is defined as:
wherein A is
0、A
1、A
2、…、A
nAs a parameterLower limit of range, Δ a
0、Δa
1、Δa
2、…、Δa
nIs a set interval step, A'
0、A′
1、A′
2、…、A′
nIs the upper limit of the parameter range.
4. The method for accurately diagnosing the fault of the variable-speed working condition motor bearing based on the Hall signal according to claim 1, wherein in the step 3, the step of equal-angle cubic spline interpolation resampling comprises the following steps:
step 3-1: suppose that the length of signal X (t) is N and the sampling rate is f
sThen its sampling time sequence is t
s(n)＝0,1/f
s,…,(N-1)/f
sFor parameter (a)
0m，a
1m，a
2m,…,a
nm) And calculating a sampling point sequence:
wherein f is
sIs the sampling frequency of the fault signal, N is the length of the signal acquired, y (t)
s(n)) is a rotation speed coefficient of (a)
0m，a
1m，a
2m,…,a
nm) In a time series t
s(n) the value of the rotational speed, the time series being a synchronous time series of the signal x (t);
step 3-2: calculating a resampling sequence: resampling sequence theta
2(n) is the sequence used for interpolation, the value of which is θ
2The calculation formula of (n) is:
wherein min represents taking the minimum value;
step 3-3: using theta
2(n) pairs of [ theta ]
1(n), X (t) } to obtain the correction signal sig1 by carrying out cubic spline interpolation resampling treatment
m。
5. Hall signal based variable speed drive according to claim 1The method for accurately diagnosing the fault of the working condition motor bearing is characterized in that in the step 5, the obtained sig is subjected to signal processing
mPerforming fast Fourier transform to obtain Y
mThen, Y is calculated according to the following formula
mThe kurtosis of (2):
Ku
m＝S
m 4
wherein N is the length of the collected signal, Ku
mIs Y
mThe kurtosis of (c).
6. The method for accurately diagnosing the fault of the motor bearing under the variable speed working condition based on the Hall signal as claimed in claim 1, wherein in the step 7, the optimal bearing rotating speed parameter is used for carrying out equal-angle cubic spline interpolation resampling on X (t), wherein the equal-angle cubic spline interpolation resampling is the same as that in the step 3.
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| CN114123936A (en) * | 2022-01-29 | 2022-03-01 | 天津德科智控股份有限公司 | Method for detecting motor rotor angle signal fault for EPS (electric power steering) |
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