CN103018043A - Fault diagnosis method of variable-speed bearing - Google Patents

Abstract

The invention discloses a fault diagnosis method of a variable-speed bearing, which comprises the following steps of: sampling the vibration signals of the bearing at equal time intervals through an acceleration sensor by a data acquisition module controlled by a fault diagnosis module to obtain a vibration signal sequence x(n); carrying out wavelet transformation on the acquired vibration signal sequence x(n) by adopting a plurality of Morlet wavelets as the wavelet basis functions of the wavelet transformation to obtain wavelet coefficient wt(m,n); carrying out modular operation on the wavelet coefficient wt(m,n) to acquire the envelope ewt(m,n)=||wt(m,n)|| of the wavelet coefficient wt(m,n); transforming the wavelet envelope coefficient at each size from an equal time interval sampling result to an equal angle sampling result; carrying out Fourier transformation on the wavelet envelope sequences ewt(m,t) at various sizes, which are subjected to equal angle sampling, to obtain the frequency spectra eswt (m,f)=FFT(ewt(m,t)) of the wavelet envelope sequences ewt(m,t); and making eswt(m,f) into a three-dimensional image.

Description

The variable speed Method for Bearing Fault Diagnosis

Technical field

The present invention relates to a kind of variable speed Method for Bearing Fault Diagnosis.

Background technology

Modern industry to the demand of good quality low cost product and to security in the production run and successional emphasize so that the maintenance policy center of gravity of plant equipment from initial correction maintenance, preventive maintenance shifts the maintenance that develops into present state-based.In order to implement the maintenance policy of state-based, need to carry out real-time detection, diagnosis and prediction to the health status of plant equipment, thereby corresponding plant equipment health monitoring becomes one of most active research emphasis of current industrial circle and academia, wherein as the rotating machinery of one of main equipment types, its critical component bearing becomes main research object owing to using all the more widely in the fields such as sustainable energy generation, processing and manufacturing.At present, Wavelet Transformation Algorithm is widely used in the middle of the fault diagnosis of bearing.Yet Wavelet Transformation Algorithm does not take full advantage of some important frequency domain characters of containing in the signal as a kind of time-frequency domain method, and therefore there is deviation in the diagnosis for failure-frequency; In addition, existing fault diagnosis algorithm General Requirements equipment invariablenes turning speed or near constant, and be not suitable for the fault diagnosis of variable speed condition lower bearing.For above-mentioned two problems, current do not have a disclosed solution.

Summary of the invention

The object of the invention is to propose a kind of variable speed Method for Bearing Fault Diagnosis, this method for diagnosing faults combines small wave converting method, envelope extraction method and frequency domain spectra analytical approach, when signal is carried out Time-Frequency Analysis, also effectively extracted and contained frequency domain character important in signal, can extract by more effective fault signature to bearing; Adopted and calculated the signal that rank comparison-tracking method is converted to the signal of constant duration sampling equiangular sampling, can eliminate rotation speed change to the impact of algorithm, under the condition of variable speed, can effectively diagnose bearing fault.

To achieve these goals, technical scheme of the present invention is as follows: the variable speed Method for Bearing Fault Diagnosis comprises acceleration transducer, speed probe, data acquisition module, fault diagnosis module, display module;

Data acquisition module is made of data collecting card or AD sample devices, and fault diagnosis module is made of computing machine or microprocessor;

The data input pin of acceleration transducer and speed probe data output end connection data acquisition module, the data of data acquisition module are input to fault diagnosis module, and fault diagnosis module links to each other with display module; Concrete diagnostic method comprises following step:

(1) fault diagnosis module control data acquisition module carries out the constant duration sampling by acceleration transducer to bearing vibration signal, obtains vibration signal sequence x (n), n=1, and 2 ..., N, n represent constant duration sampling time point, N is signal length;

(2) adopt plural Morlet small echo as the wavelet basis function of wavelet transformation, described plural Morlet wavelet basis function shown in formula (1), f wherein _b, f _cBandwidth and centre frequency for wavelet basis function;

According to formula (2) the vibration signal x (n) that collects is carried out continuous wavelet transform;

$\mathrm{\&psi;}\left(t\right)=\frac{1}{\sqrt{\mathrm{\&pi;}{f}_{\mathrm{<figure-callout\; id="2"\; label="b\; e\; j"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">b</figure-callout>}}}}{e}^j{2\mathrm{\&pi;}{f}_{c}t}^{}{e}^{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}^2/f_b}---\left(1\right)$

$\mathrm{wt}(m,n)={\&Integral;}_{-\&infin;}^{+\&infin;}x\left(t\right)\frac{1}{\sqrt{m}}{\mathrm{\&psi;}}^{*}\left(\frac{t-n}{m}\right)\mathrm{dt}---\left(2\right)$

Obtain wavelet coefficient wt (m, n), m=1,2 ... M, n=1,2 ..., N, wherein m is the scale parameter after the wavelet decomposition, and M is out to out, and n is time parameter;

(3) to wavelet coefficient wt (m, n) delivery, obtain its envelope ewt (m, n)=|| wt (m, n) ||;

(4) with the result of the Based on Wavelet Envelope coefficient under each yardstick from the results conversion of constant duration sampling to equiangular sampling;

(5) the Based on Wavelet Envelope sequence ewt (m, t) for each yardstick behind the equiangular sampling carries out Fourier transform, obtains its frequency spectrum eswt (m, f)=FFT (ewt (m, t));

(6) with eswt (m, f) make three-dimensional picture, be presented on the display module, its coordinate is respectively: yardstick m, f is compared on rank, amplitude eswt (m, f), in the middle of figure, find out the corresponding rank of point that peak place appears in amplitude and compare f, these rank than f and the rotation rank ratio of bearing, in theory bearing rotary kinetoplast fault rank ratio, in theory bearing outer ring fault rank ratio, bearing inner race fault rank ratio is compared in theory, if the corresponding rank of high peak dot only equal the rotation rank ratio of bearing than f, fault diagnosis module judges that there is not fault in bearing;

If there are the corresponding rank of high peak dot to equal theoretical fault rank ratio than f ', fault diagnosis module judges that namely there is fault in bearing and judges abort situation according to the theoretical fault rank ratio that equates with it.

Described step (4) specific implementation step is as follows:

4.1) when turning over respectively angle 0,2 π, 4 π, axle writes down corresponding time point t ₀, t _{2 π}, t _{4 π}, utilize formula (3):

$\left(\begin{array}{c}0\\ 2\mathrm{\&pi;}\\ 4\mathrm{\&pi;}\end{array}\right)=\left(\begin{array}{ccc}1& t_0& {{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}^2\\ 1& {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{2\mathrm{\&pi;}}& {{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{2\mathrm{\&pi;}}}^2\\ 1& t_{4\mathrm{\&pi;}}& {t_{4\mathrm{\&pi;}}}^2\end{array}\right)\left(\begin{array}{c}{b}_0\\ b_1\\ b_2\end{array}\right)---\left(3\right)$

Obtain the system features parameter b ₀, b ₁, b ₂

4.2) be the Based on Wavelet Envelope coefficient sequence ewt (k of k to yardstick, n), set constant angle θ, speed probe sends pulse signal and sends into fault diagnosis module by data acquisition module when axle turns over the θ angle, and fault diagnosis module utilizes time t and axle to turn over the relational expression of angle θ:

$t=\frac{1}{2b_2}[\sqrt{4b_2(\mathrm{\&theta;}-b_0)+{b_1}^2}-b_1]---\left(4\right)$

Obtain corresponding time t ₁, use Lagrange's interpolation formula, shown in formula (5), utilize among the Based on Wavelet Envelope coefficient sequence ewt (k, n) existing point to determine ewt (k, t ₁);

$\mathrm{ewt}(k,t)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Pi;}}}(j-t)}{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Pi;}}}(j-i)}\mathrm{ewt}(k,i)---\left(5\right)$

4.3) axle is rotated further the θ degree, when this moment, axle corotation over-angle was 2 θ, recycling formula (4) was obtained corresponding time t ₂, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₂);

4.4) axle continues to rotate the θ degree again, this moment, axle corotation over-angle was 3 θ, tried to achieve corresponding time t according to formula (4) ₃, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₃);

4.5) if t ₃＜n repeating step 4.2), 4.3), 4.4), until t _nDuring 〉=n, having obtained one is the Based on Wavelet Envelope coefficient sequence ewt (k, t) of k based on equal angles θ sampling scale, t=t ₁, t ₂..., t _n

4.6) utilize step 4.2), 4.3), 4.4) and 4.5) process the Based on Wavelet Envelope coefficient sequence of each yardstick, finally obtain a series of Based on Wavelet Envelope coefficient sequence ewt (m, t) based on equal angles θ sampling, m=1,2 ... M, t=t ₁, t ₂..., t _n, above-mentioned ewt (m, t) is write as matrix form and can be expressed as:

$\left[\begin{array}{cccc}\mathrm{ewt}(1,t_1)& \mathrm{ewt}(1,t_2)& ...& \mathrm{ewt}(1,t_n)\\ \mathrm{ewt}(2,t_1)& \mathrm{ewt}(2,t_2)& ...& \mathrm{ewt}(2,t_n)\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ \mathrm{ewt}(M,t_1)& \mathrm{ewt}(M,t_2)& ...& \mathrm{ewt}(M,t_n)\end{array}\right].$

Compared with prior art, beneficial effect of the present invention is as follows: 1) the technical program combines small wave converting method, envelope extraction method and frequency domain spectra analytical approach, when signal is carried out Time-Frequency Analysis, also effectively extracted and contained frequency domain character important in signal, can extract by more effective fault signature to bearing; 2) the technical program has adopted and has calculated the signal that rank comparison-tracking method is converted to the signal of constant duration sampling equiangular sampling, can eliminate rotation speed change to the impact of algorithm, can effectively diagnose bearing fault under the condition of variable speed.

Description of drawings

Fig. 1 is the theory diagram of variable speed Method for Bearing Fault Diagnosis of the present invention;

Fig. 2 is Method for Bearing Fault Diagnosis process flow diagram of the present invention;

Fig. 3 is constant duration sampling of the present invention and equiangular sampling schematic diagram;

Fig. 4 is actual measurement bearing rotating speed and vibration signal;

Fig. 5 is the diagnostic result schematic diagram of the present invention's combined failure bearing under the variable speed condition.

Embodiment

Below in conjunction with accompanying drawing the present invention is described in further detail.

The variable speed Method for Bearing Fault Diagnosis comprises acceleration transducer, speed probe, data acquisition module, fault diagnosis module, display module;

Data acquisition module is made of data collecting card or AD sample devices, and fault diagnosis module is made of computing machine or microprocessor;

The data input pin of acceleration transducer and speed probe data output end connection data acquisition module, the data of data acquisition module are input to fault diagnosis module, and fault diagnosis module links to each other with display module; Concrete diagnostic method comprises following step:

(1) fault diagnosis module control data acquisition module carries out the constant duration sampling by acceleration transducer to bearing vibration signal, obtains vibration signal sequence x (n), n=1, and 2 ..., N, n represent constant duration sampling time point, N is signal length;

(2) adopt plural Morlet small echo as the wavelet basis function of wavelet transformation, described plural Morlet wavelet basis function shown in formula (1), f wherein _b, f _cBandwidth and centre frequency for wavelet basis function;

According to formula (2) the vibration signal x (n) that collects is carried out continuous wavelet transform;

$\mathrm{\&psi;}\left(t\right)=\frac{1}{\sqrt{\mathrm{\&pi;}{f}_{\mathrm{<figure-callout\; id="2"\; label="b\; e\; j"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">b</figure-callout>}}}}{e}^j{2\mathrm{\&pi;}{f}_{c}t}^{}{e}^{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}^2/f_b}---\left(1\right)$

$\mathrm{wt}(m,n)={\&Integral;}_{-\&infin;}^{+\&infin;}x\left(t\right)\frac{1}{\sqrt{m}}{\mathrm{\&psi;}}^{*}\left(\frac{t-n}{m}\right)\mathrm{dt}---\left(2\right)$

Obtain wavelet coefficient wt (m, n), m=1,2 ... M, n=1,2 ..., N, wherein m is the scale parameter after the wavelet decomposition, and M is out to out, and n is time parameter;

(3) to wavelet coefficient wt (m, n) delivery, obtain its envelope ewt (m, n)=|| wt (m, n) ||;

(4) with the result of the Based on Wavelet Envelope coefficient under each yardstick from the results conversion of constant duration sampling to equiangular sampling;

(5) the Based on Wavelet Envelope sequence ewt (m, t) for each yardstick behind the equiangular sampling carries out Fourier transform, obtains its frequency spectrum eswt (m, f)=FFT (ewt (m, t));

(6) with eswt (m, f) make three-dimensional picture, be presented on the display module, its coordinate is respectively: yardstick m, f is compared on rank, amplitude eswt (m, f), in the middle of figure, find out the corresponding rank of point that peak place appears in amplitude and compare f, these rank than f and the rotation rank ratio of bearing, in theory bearing rotary kinetoplast fault rank ratio, in theory bearing outer ring fault rank ratio, bearing inner race fault rank ratio is compared in theory, if the corresponding rank of high peak dot only equal the rotation rank ratio of bearing than f, fault diagnosis module judges that there is not fault in bearing;

If there are the corresponding rank of high peak dot to equal theoretical fault rank ratio than f ', fault diagnosis module judges that namely there is fault in bearing and judges abort situation according to the theoretical fault rank ratio that equates with it.

Described step (4) specific implementation step is as follows:

4.1) when turning over respectively angle 0,2 π, 4 π, axle writes down corresponding time point t ₀, t _{2 π}, t _{4 π}, utilize formula (3):

$\left(\begin{array}{c}0\\ 2\mathrm{\&pi;}\\ 4\mathrm{\&pi;}\end{array}\right)=\left(\begin{array}{ccc}1& t_0& {{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}^2\\ 1& {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{2\mathrm{\&pi;}}& {{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA00002418418700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{2\mathrm{\&pi;}}}^2\\ 1& t_{4\mathrm{\&pi;}}& {t_{4\mathrm{\&pi;}}}^2\end{array}\right)\left(\begin{array}{c}{b}_0\\ b_1\\ b_2\end{array}\right)---\left(3\right)$

Obtain the system features parameter b ₀, b ₁, b ₂

4.2) be the Based on Wavelet Envelope coefficient sequence ewt (k of k to yardstick, n), set constant angle θ, speed probe sends pulse signal and sends into fault diagnosis module by data acquisition module when axle turns over the θ angle, and fault diagnosis module utilizes time t and axle to turn over the relational expression of angle θ:

$t=\frac{1}{2b_2}[\sqrt{4b_2(\mathrm{\&theta;}-b_0)+{b_1}^2}-b_1]---\left(4\right)$

Obtain corresponding time t ₁, use Lagrange's interpolation formula, shown in formula (5), utilize among the Based on Wavelet Envelope coefficient sequence ewt (k, n) existing point to determine ewt (k, t ₁);

$\mathrm{ewt}(k,t)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Pi;}}}(j-t)}{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Pi;}}}(j-i)}\mathrm{ewt}(k,i)---\left(5\right)$

4.3) axle is rotated further the θ degree, when this moment, axle corotation over-angle was 2 θ, recycling formula (4) was obtained corresponding time t ₂, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₂);

4.4) axle continues to rotate the θ degree again, this moment, axle corotation over-angle was 3 θ, tried to achieve corresponding time t according to formula (4) ₃, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₃);

4.5) if t ₃＜n repeating step 4.2), 4.3), 4.4), until t _nDuring 〉=n, having obtained one is the Based on Wavelet Envelope coefficient sequence ewt (k, t) of k based on equal angles θ sampling scale, t=t ₁, t ₂..., t _n

4.6) utilize step 4.2), 4.3), 4.4) and 4.5) process the Based on Wavelet Envelope coefficient sequence of each yardstick, finally obtain a series of Based on Wavelet Envelope coefficient sequence ewt (m, t) based on equal angles θ sampling, m=1,2 ... M, t=t ₁, t ₂..., t _n, above-mentioned ewt (m, t) is write as matrix form and can be expressed as:

$\left[\begin{array}{cccc}\mathrm{ewt}(1,t_1)& \mathrm{ewt}(1,t_2)& ...& \mathrm{ewt}(1,t_n)\\ \mathrm{ewt}(2,t_1)& \mathrm{ewt}(2,t_2)& ...& \mathrm{ewt}(2,t_n)\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ \mathrm{ewt}(M,t_1)& \mathrm{ewt}(M,t_2)& ...& \mathrm{ewt}(M,t_n)\end{array}\right].$

Utilize the present invention that a bearing that has simultaneously the combined failures such as inner ring fault, outer ring fault, rotor fault is diagnosed under the variable speed condition.

Referring to Fig. 2, fault diagnosis module control data acquisition module carries out the constant duration sampling by acceleration transducer to vibration signal, obtains sequence x (n), n=1, and 2 ..., N,

Referring to Fig. 4, the vibration signal that collects is sent into fault diagnosis module by data acquisition module; Adopt plural Morlet small echo as the wavelet basis function of wavelet transformation, utilize formula (1) to carry out continuous wavelet transform to the vibration signal x (n) that collects, obtain a series of wavelet coefficient wt (m, n), m=1,2 ... M, n=1,2 ..., N, wherein m is the scale parameter after the wavelet decomposition, and n is time parameter; All wavelet coefficient wt (m, n) deliverys that then decomposition obtained, obtain its envelope ewt (m, n)=|| wt (m, n) ||;

Referring to Fig. 3: utilize and calculate rank comparison-tracking method with the result of the Based on Wavelet Envelope coefficient under each yardstick from the results conversion of constant duration t sampling to equal angles θ sampling.Concrete method carried out therewith is: write down corresponding time point t when axle turns over respectively angle 0,2 π, 4 π ₀, t _{2 π}, t _{4 π}, utilize formula (3) to obtain the system features parameter b ₀, b ₁, b ₂Be the Based on Wavelet Envelope coefficient sequence ewt (k of k to yardstick, n), the signal that utilizes speed probe to record, regulation constant angle θ, speed probe sends pulse signal and sends into fault diagnosis module by data acquisition module when axle turns over the θ angle, and the relational expression formula (4) that fault diagnosis module utilizes time t and axle to turn over angle θ is obtained corresponding time t ₁, use Lagrange's interpolation formula (5), utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₁); When turning over angle 2 θ for rotating machinery, recycling formula (4) is obtained corresponding time t ₂, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₂); Repeat above-mentioned steps, until t _nTill＞the n, having obtained one is the Based on Wavelet Envelope coefficient sequence ewt (k, t) of k based on equal angles θ sampling scale, t=t ₁, t ₂..., t _nUtilize said method to process the Based on Wavelet Envelope coefficient sequence of each yardstick, finally obtain a series of Based on Wavelet Envelope coefficient sequence ewt (m, t) based on equal angles θ sampling, m=1,2 ... M, t=t ₁, t ₂..., t _nBased on Wavelet Envelope sequence ewt (m, t) for each yardstick behind the equiangular sampling carries out Fourier transform, obtains its frequency spectrum, obtains eswt (m, f)=FFT (ewt (m, t)); Eswt (m, f) is made three-dimensional picture, be presented on the display module, its coordinate is respectively: yardstick m, and rank are than f, amplitude eswt (m, f),

Referring to Fig. 5, from figure, can find out, the rank ratio that several high peak dots are corresponding is f _RPM, f _BSF, f _BPFO, f _BSFFrequency multiplication 2*f _BSF, inner ring fault rank compare f _BPFI, and f _BPEIAnd f _RPMModulation f _BPFI+ f _RPM, by these rank ratios are compared with theoretical fault rank ratio, draw f _RPMEqual theoretical rank ratio, the f of rotating of bearing _BSFEqual theoretical rotor fault rank ratio, f _BPFOEqual fault rank, theoretical outer ring ratio, f _BPFIEqual theoretical inner ring fault rank and compare f _BPFITherefore fault diagnosis module is reached a conclusion, and this bearing exists rotor fault, outer ring fault and inner ring fault.

Claims (2)

1. the variable speed Method for Bearing Fault Diagnosis is characterized in that: comprise acceleration transducer, speed probe, data acquisition module, fault diagnosis module, display module;

Data acquisition module is made of data collecting card or AD sample devices, and fault diagnosis module is made of computing machine or microprocessor;

The data input pin of acceleration transducer and speed probe data output end connection data acquisition module, the data of data acquisition module are input to fault diagnosis module, and fault diagnosis module links to each other with display module; Concrete diagnostic method comprises following step:

(1) fault diagnosis module control data acquisition module carries out the constant duration sampling by acceleration transducer to bearing vibration signal, obtains vibration signal sequence x (n), n=1, and 2 ..., N, n represent constant duration sampling time point, N is signal length;

(2) adopt plural Morlet small echo as the wavelet basis function of wavelet transformation, described plural Morlet wavelet basis function shown in formula (1), f wherein _b, f _cBandwidth and centre frequency for wavelet basis function;

According to formula (2) the vibration signal x (n) that collects is carried out continuous wavelet transform;

$\mathrm{\&psi;}\left(t\right)=\frac{1}{\sqrt{\mathrm{\&pi;}{f}_b}}{e}^{j2\mathrm{\&pi;}{f}_{c}t}{e}^{-t^2/f_b}---\left(1\right)$

$\mathrm{wt}(m,n)={\&Integral;}_{-\&infin;}^{+\&infin;}x\left(t\right)\frac{1}{\sqrt{m}}{\mathrm{\&psi;}}^{*}\left(\frac{t-n}{m}\right)\mathrm{dt}---\left(2\right)$

Obtain wavelet coefficient wt (m, n), m=1,2 ... M, n=1,2 ..., N, wherein m is the scale parameter after the wavelet decomposition, and M is out to out, and n is time parameter;

(3) to wavelet coefficient wt (m, n) delivery, obtain its envelope ewt (m, n)=|| wt (m, n) ||;

(4) with the result of the Based on Wavelet Envelope coefficient under each yardstick from the results conversion of constant duration sampling to equiangular sampling;

(5) the Based on Wavelet Envelope sequence ewt (m, t) for each yardstick behind the equiangular sampling carries out Fourier transform, obtains its frequency spectrum eswt (m, f)=FFT (ewt (m, t));

(6) with eswt (m, f) make three-dimensional picture, be presented on the display module, its coordinate is respectively: yardstick m, f is compared on rank, amplitude eswt (m, f), in the middle of figure, find out the corresponding rank of point that peak place appears in amplitude and compare f, these rank than f and the rotation rank ratio of bearing, in theory bearing rotary kinetoplast fault rank ratio, in theory bearing outer ring fault rank ratio, bearing inner race fault rank ratio is compared in theory, if the corresponding rank of high peak dot only equal the rotation rank ratio of bearing than f, fault diagnosis module judges that there is not fault in bearing;

If there are the corresponding rank of high peak dot to equal theoretical fault rank ratio than f ', fault diagnosis module judges that namely there is fault in bearing and judges abort situation according to the theoretical fault rank ratio that equates with it.

2. variable speed Method for Bearing Fault Diagnosis according to claim 1, it is characterized in that: described step (4) specific implementation step is as follows:

4.1) when turning over respectively angle 0,2 π, 4 π, axle writes down corresponding time point t ₀, t _{2 π}, t _{4 π}, utilize formula (3):

$\left(\begin{array}{c}0\\ 2\mathrm{\&pi;}\\ 4\mathrm{\&pi;}\end{array}\right)=\left(\begin{array}{ccc}1& t_0& {t_0}^2\\ 1& t_{2\mathrm{\&pi;}}& {t_{2\mathrm{\&pi;}}}^2\\ 1& t_{4\mathrm{\&pi;}}& {t_{4\mathrm{\&pi;}}}^2\end{array}\right)\left(\begin{array}{c}{b}_0\\ b_1\\ b_2\end{array}\right)---\left(3\right)$

Obtain the system features parameter b ₀, b ₁, b ₂

4.2) be the Based on Wavelet Envelope coefficient sequence ewt (k of k to yardstick, n), set constant angle θ, speed probe sends pulse signal and sends into fault diagnosis module by data acquisition module when axle turns over the θ angle, and fault diagnosis module utilizes time t and axle to turn over the relational expression of angle θ:

$t=\frac{1}{2b_2}[\sqrt{4b_2(\mathrm{\&theta;}-b_0)+{b_1}^2}-b_1]---\left(4\right)$

Obtain corresponding time t ₁, use Lagrange's interpolation formula, shown in formula (5), utilize among the Based on Wavelet Envelope coefficient sequence ewt (k, n) existing point to determine ewt (k, t ₁);

$\mathrm{ewt}(k,t)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\frac{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Pi;}}}(j-t)}{\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Pi;}}}(j-i)}\mathrm{ewt}(k,i)---\left(5\right)$

4.3) axle is rotated further the θ degree, when this moment, axle corotation over-angle was 2 θ, recycling formula (4) was obtained corresponding time t ₂, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₂);

4.4) axle continues to rotate the θ degree again, this moment, axle corotation over-angle was 3 θ, tried to achieve corresponding time t according to formula (4) ₃, use Lagrange's interpolation formula (5) to utilize the point among the existing Based on Wavelet Envelope coefficient sequence ewt (k, n) to determine ewt (k, t ₃);

4.5) if t ₃＜n repeating step 4.2), 4.3), 4.4), until t _nDuring 〉=n, having obtained one is the Based on Wavelet Envelope coefficient sequence ewt (k, t) of k based on equal angles θ sampling scale, t=t ₁, t ₂..., t _n

4.6) utilize step 4.2), 4.3), 4.4) and 4.5) process the Based on Wavelet Envelope coefficient sequence of each yardstick, finally obtain a series of Based on Wavelet Envelope coefficient sequence ewt (m, t) based on equal angles θ sampling, m=1,2 ... M, t=t ₁, t ₂..., t _n, above-mentioned ewt (m, t) is write as matrix form and can be expressed as:

$\left[\begin{array}{cccc}\mathrm{ewt}(1,t_1)& \mathrm{ewt}(1,t_2)& ...& \mathrm{ewt}(1,t_n)\\ \mathrm{ewt}(2,t_1)& \mathrm{ewt}(2,t_2)& ...& \mathrm{ewt}(2,t_n)\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ \mathrm{ewt}(M,t_1)& \mathrm{ewt}(M,t_2)& ...& \mathrm{ewt}(M,t_n)\end{array}\right].$

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