CN100516828C - Method for quantitatively identifying rolling bearing damage - Google Patents

Abstract

The present invention discloses a method for quantitatively identifying rolling bearing damage. Said method includes the following steps: making rolling bearing vibration signal undergo the process of second generation small wave packet decomposition; then respectively reconstructing decomposed signal of every frequency band; utilizing Hilbert conversion and demodulation to analyze every frequency band signal to obtain envelope spectrum correspondent to frequency band signal; calculating decibel value of envelope spectrum magnitude correspondent to rolling bearing failure characteristic frequency in every frequency band, extracting maximum value of decibel value correspondent to failure characteristic frequency in every frequency band, then quantitatively identifying rolling bearing early damage condition.

Description

A kind of method of quantitatively identifying rolling bearing damage

Technical field

The invention belongs to plant equipment incipient fault prognosis field, be specifically related to the quantitative identification method of rolling bearing earlier damage.

Background technology

Rolling bearing is the mechanical component that are most widely used in the rotating machinery, also is one of the most flimsy element.Rolling bearing may be owing to a variety of causes causes damage in operation process, as assembles improper, insufficient lubrication, moisture and foreign matter intrusion, corrosion and overload etc. and all may cause the rolling bearing premature damage.Even install, under the lubricated and all normal situation of working service, through running after a while, cisco unity malfunction fatigue flake and wearing and tearing also can appear and in rolling bearing.Therefore, rolling bearing fault is quantitatively discerned, accurately judged the order of severity of its damage, the prevention major accident takes place, and is an important research direction of fault diagnostic field.

At present, the common method of the quantitative identification of rolling bearing damage is the resonance and demodulation analytical technology.But resonance demodulation technique is difficult to extract the failure message feature that lies in each modulation band of vibration signal comprehensively.Resonance demodulation technique has certain effect for rolling bearing major injury in late period Fault Identification, but it is not suitable for discerning the earlier damage fault of rolling bearing.

When local damage faults such as the working surface of inner ring, outer ring, rolling body and four kinds of elements of retainer of rolling bearing occurs as spot corrosion, peels off, scratch, the vibration signal that damage causes presents the shape of oscillatory extinction, in order effectively to extract its fault signature, the wavelet basis function shape of selecting for use should be mated this shock oscillation waveform that damage of the bearing causes, can in conversion, obtain bigger wavelet coefficient, outstanding effectively fault signature.

Second generation wavelet packet is to propose on the basis of second generation wavelet transformation, and it decomposes the high frequency detail signal that each layer of second generation wavelet transformation do not have to decompose again, and improves frequency resolution, in the hope of extracting the frequecy characteristic of signal better.The scaling function of second generation wavelet packet and wavelet function are symmetrical, the tight supports, have the oscillatory extinction shape, and the vibration signal waveforms when local damage occurring to rolling bearing is similar, select for use it as basis function with coupling bearing vibration signal fault feature.

Summary of the invention

The object of the present invention is to provide a kind of quantitative identification method of rolling bearing damage.It is by the decomposition and reconstruction of second generation wavelet packet, the multi-carrier signal that is coupled is decomposed into a plurality of single-carrier signal, then each band signal is carried out envelope demodulation respectively, calculate the decibel value of the corresponding envelope spectrum amplitude of fault characteristic frequency in each frequency band, choose the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band, realize the rolling bearing earlier damage is quantitatively discerned.This recognition methods computational accuracy height, fast operation, simple and reliable, improved rolling bearing earlier damage recognition efficiency and accuracy.

Technical scheme of the present invention is to solve like this: the present invention carries out according to the following steps:

1) the bearing vibration signal is carried out second generation WAVELET PACKET DECOMPOSITION and reconstruct, make the multicarrier vibration signal that is coupled decompose and be a plurality of single carrier vibration signals;

2) utilize the Hilbert conversion to carry out envelope demodulation to each frequency band vibration signal, calculate the decibel value of the corresponding envelope spectrum amplitude of fault characteristic frequency in each frequency band, choose the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band, realize the rolling bearing earlier damage is quantitatively discerned.

Described the bearing vibration signal is carried out second generation WAVELET PACKET DECOMPOSITION and reconstruct, may further comprise the steps:

1) with a burst X={x _n, n ∈ Z}, wherein x _nBe n sample in the sequence X, Z is the positive integer set, is divided into two sub-sequence X _eAnd X _o

X _e＝{x _2k，k∈Z}

X _o＝{x _2k+1，k∈Z}

K is subsequence X _eAnd X _oIn the sample sequence number;

2), calculate each band signal that second generation wavelet packet l layer decomposes by following various

X _l1＝X _(l-1)1o-S(X _(l-1)1e)

X _l2＝X _(l-1)1e+G(X _l1)

…

$X_{l(2^l-1)}=X_{(l-1)2^{l-1}o}-S\left(X_{(l-1)2^{l-1}e}\right)$

$X_{{l2}^l}=X_{(l-1)2^{l-1}e}+G\left(X_{l(2^l-1)}\right)$

Wherein, S and G are second generation wavelet packet operator, and S obtains by following formula

WS＝[1，0，0，...，0] ^T

[W] _i，j＝[2j-N-1] ^i-1 i＝1，2，...，N；j＝1，2，...，N.

If $Q=\{Q_k,-N-\tilde{N}+2\≤k\≤N+\tilde{N}-2\},$ The relation of Q and S, G is represented with following formula

$Q_{(2l-1)}=\left\{\begin{array}{cc}1-\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{S}_m{G}_{(l-m+1)}& l=(N+\tilde{N})/2\\ \underset{m=1}{\overset{N}{\mathrm{\Σ}}}{S}_m{G}_{(l-m+1)}& l\≠(N+\tilde{N})/2\end{array}\right.$

Q _(2l+N-2)＝G _l $l=\mathrm{1,2},...,\tilde{N}$

When l gets other value, Q _2l=0;

Construct one

The dimension matrix

Its element representation is as follows

${\left[\tilde{W}\right]}_{m,n}=n^m$

Wherein $n=-N-\tilde{N}+2,-N-\tilde{N}+3,...,N+\tilde{N}-3,N+\tilde{N}-2,$ $m=\mathrm{0,1},...,\tilde{N}-1;$

G obtains by following formula

$\tilde{W}Q=0$

N and Be respectively the number of operator S and G coefficient;

3) second generation wavelet package reconstruction process is to treat that the reconstruct band signal keeps, and with other band signal zero setting, then according to following various being reconstructed;

$X_{(l-1)2^{l-1}e}=X_{{l2}^l}-G\left(X_{l(2^l-1)}\right)$

$X_{(l-1)2^{l-1}o}=X_{l(2^l-1)}+S\left(X_{(l-1)2^{l-1}e}\right)$

$X_{(l-1)2^{l-1}}\left(2k\right)=X_{(l-1)2^{l-1}e}\left(k\right),k\∈Z$

$X_{(l-1)2^{l-1}}(2k+1)=X_{(l-1)2^{l-1}o}\left(k\right),k\∈Z$

…

X _(l-1)1e＝X _l2-G(X _l1)

X _(l-1)1o＝X _l1+S(X _(l-1)1e)

X _(l-1)1(2k)＝X _(l-1)1e(k) k∈Z

X _(l-1)1(2k+1)＝X _(l-1)1o(k) k∈Z

The decibel value of the corresponding envelope spectrum amplitude of fault characteristic frequency in each frequency band of said calculating is chosen the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band, realizes the rolling bearing earlier damage is quantitatively discerned, and may further comprise the steps:

1) each band signal that reconstruct is obtained utilizes the Hilbert conversion to obtain its signal envelope, then signal envelope is carried out fast fourier transform, obtains the envelope spectrum of each frequency band reconstruction signal;

2) utilize following formula to calculate the decibel value of the corresponding envelope spectrum amplitude of rolling bearing inner ring, outer ring, rolling body and retainer fault characteristic frequency

$B=20\log \frac{2000\×\mathrm{SV}}{N\×D^{0.6}}$

In the formula, B represents decibel value dB, and N represents the rotating speed of axle, and unit is r/min; D represents the internal diameter of rolling bearing, and unit is m; SV represents the acceleration impact value, and unit is m/s ²Choose the maximal value of the corresponding decibel value of rolling bearing inner ring in each frequency band, outer ring, rolling body and retainer fault characteristic frequency respectively, and the earlier damage degree of rolling bearing inner ring, outer ring, rolling body and retainer is made quantitative identification according to the maximal value of decibel value.

Because the present invention has quantitatively adopted second generation method of wavelet packet in the identification at rolling bearing damage, the second generation WAVELET PACKET DECOMPOSITION reconfiguration technique that proposes, the bearing vibration signal is carried out a plurality of band decomposition, make the rolling bearing multicarrier vibration signal that is coupled decompose and be a plurality of single carrier vibration signals;

1) utilize the Hilbert conversion to carry out envelope demodulation to each the decomposition frequency band vibration signal that obtains, calculate the decibel value of the corresponding envelope spectrum amplitude of fault characteristic frequency in each frequency band, choose the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band respectively, and the earlier damage degree of rolling bearing inner ring, outer ring, rolling body and retainer is made quantitative identification according to the maximal value of decibel value;

2) the rolling bearing fault feature can be effectively mated in the present invention, for the identification of rolling bearing earlier damage provides effective practical new technology, has improved rolling bearing earlier damage accuracy of identification;

3) the present invention constructs in time domain fully, and the computing real-time is good, and is simple, is convenient to use in the engineering practice.

Description of drawings

Fig. 1 is second generation wavelet packet scaling function of the present invention and wavelet function figure;

Fig. 1 (a) is second generation wavelet packet scaling function figure;

Fig. 1 (b) is wavelet function figure;

Fig. 2 is simulate signal of the present invention and envelope spectrum decibel value figure thereof;

Fig. 2 (a) is the time domain waveform figure of simulate signal;

Fig. 2 (b) is for directly carrying out the Hilbert envelope demodulation to simulate signal, the simulate signal envelope spectrum decibel value figure that obtains;

Fig. 3 is a simulate signal second generation WAVELET PACKET DECOMPOSITION restructuring graph of the present invention;

Fig. 4 is the decomposed and reconstituted envelope spectrum decibel value of simulate signal of the present invention figure;

Fig. 5 is measured signal of the present invention and envelope spectrum decibel value figure thereof;

Fig. 5 (a) is the bearing vibration time domain plethysmographic signal;

The envelope spectrum decibel value figure that Fig. 5 (b) obtains for the direct demodulation of bearing vibration signal;

Fig. 6 is a measured signal second generation WAVELET PACKET DECOMPOSITION restructuring graph of the present invention;

Fig. 7 is the decomposed and reconstituted envelope spectrum decibel value of measured signal of the present invention figure.

Embodiment

Accompanying drawing is specific embodiments of the invention.

Below in conjunction with accompanying drawing content of the present invention is described in further detail:

Shown in Fig. 1 (a) and (b), the scaling function of second generation wavelet packet and wavelet function are symmetry and tight the support, have the oscillatory extinction shape, the shock oscillation waveform similarity that occurs when with rolling bearing the damage fault taking place.Horizontal ordinate represents that between the Support, ordinate is represented amplitude among the figure.

Shown in Fig. 2 (a) and (b), directly simulate signal is carried out the Hilbert envelope demodulation, demodulation result then has than mistake with actual value.Horizontal ordinate express time among Fig. 2 (a), unit is s; Ordinate is represented vibration amplitude, and unit is m/s ²Horizontal ordinate is represented frequency among Fig. 2 (b), and unit is Hz; Ordinate is represented vibration amplitude, and unit is dB.

With reference to shown in Figure 3, simulate signal is carried out three layers of second generation WAVELET PACKET DECOMPOSITION and reconstruct, obtain the reconstruction signal of eight frequency bands.Among the figure, X31, X32 ..., X38 represent respectively first frequency band of the 3rd layer, second frequency band ..., the reconstruction signal of the 8th frequency band.Horizontal ordinate express time among the figure, unit are s; Ordinate is represented vibration amplitude, and unit is m/s ²

With reference to shown in Figure 4, the decibel value of the 3rd and the 7th band modulation source frequency correspondence is bigger, and its carrier wave center is just in frequency band corresponding.With the method that the present invention proposes, recognition result and actual value are very approaching.Horizontal ordinate is represented frequency among the figure, and unit is Hz; Ordinate is represented vibration amplitude, and unit is dB.

Shown in Fig. 5 (a) and (b), directly housing washer damage vibration signal is carried out the Hilbert envelope demodulation, the decibel value of the rolling bearing retainer that obtains, rolling body, outer ring and inner ring fault characteristic frequency correspondence does not all reach alarming value.Horizontal ordinate express time among Fig. 5 (a), unit is s; Ordinate is represented vibration amplitude, and unit is m/s ²Horizontal ordinate is represented frequency among Fig. 5 (b), and unit is Hz; Ordinate is represented vibration amplitude, and unit is dB.

With reference to shown in Figure 6, the bearing vibration signal is carried out three layers of second generation WAVELET PACKET DECOMPOSITION and reconstruct, obtain the reconstruction signal of eight frequency bands.Horizontal ordinate express time among the figure, unit are s; Ordinate is represented vibration amplitude, and unit is m/s ²

With reference to shown in Figure 7, extract the decibel value of rolling bearing retainer in each frequency band, rolling body, outer ring and inner ring fault characteristic frequency correspondence, the decibel value of the outer ring fault characteristic frequency correspondence of rolling bearing exceeds alarming value in the 6th frequency band, matches with housing washer damage fault.Horizontal ordinate is represented frequency among the figure, and unit is Hz; Ordinate is represented vibration amplitude, and unit is dB.

The present invention implements according to the following steps:

(1) baroque bearing vibration signal is carried out second generation WAVELET PACKET DECOMPOSITION and reconstruct, make the multicarrier vibration signal that is coupled decompose and be a plurality of single carrier vibration signals;

(2) each the decomposition frequency band vibration signal that obtains is carried out the Hilbert envelope demodulation, calculate the decibel value of fault characteristic frequency correspondence in each frequency band, choose the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band, rolling bearing damage is quantitatively discerned.

The decomposition of second generation wavelet packet and restructuring procedure specifically may further comprise the steps:

(1) with a burst X={x _n, n ∈ Z}, wherein Z is the positive integer set, is divided into two sub-sequence X _eAnd X _o

X _e＝{x _2k，k∈Z}

X _o＝{x _2k+1，k∈Z} (1)

(2), calculate each band signal that second generation wavelet packet l layer decomposes by following various

X _l1＝X _(l-1)1o-S(X _(l-1)1e)

X _l2＝X _(l-1)1e+G(X _l1)

…(2)

$X_{l(2^l-1)}=X_{(l-1)2^{l-1}o}-S\left(X_{(l-1)2^{l-1}e}\right)$

$X_{{l2}^l}=X_{(l-1)2^{l-1}e}+G\left(X_{l(2^l-1)}\right)$

Wherein, S and G are second generation wavelet packet operator.S obtains by following formula

WS＝[1，0，0，...，0] ^T (3)

[W] _i，j＝[2j-N-1] ^i-1 i＝1，2，...，N；j＝1，2，...，N.

If $Q=\{Q_k,-N-\tilde{N}+2\≤k\≤N+\tilde{N}-2\}.$ The relation of Q and S, G is represented with following formula

$Q_{(2l-1)}=\left\{\begin{array}{cc}1-\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{S}_m{G}_{(l-m+1)}& l=(N+\tilde{N})/2\\ \underset{m=1}{\overset{N}{\mathrm{\Σ}}}{S}_m{G}_{(l-m+1)}& l\≠(N+\tilde{N})/2\end{array}\right.---\left(4\right)$

Q _(2l+N-2)＝G _l $l=\mathrm{1,2},...,\tilde{N}$

When l gets other value, Q _2l=0.

Construct one

The dimension matrix

Its element representation is as follows

${\left[\tilde{W}\right]}_{m,n}=n^m---\left(5\right)$

Wherein $n=-N-\tilde{N}+2,-N-\tilde{N}+3,...,N+\tilde{N}-3,N+\tilde{N}-2,$ $m=\mathrm{0,1},...,\tilde{N}-1.$

G obtains by following formula

$\tilde{W}Q=0---\left(6\right)$

N and

Be respectively the number of operator S and G coefficient.

(3) second generation wavelet package reconstruction process is that the frequency band signal is kept, and with other band signal zero setting, then according to following various being reconstructed.

$X_{(l-1)2^{l-1}e}=X_{{l2}^l}-G\left(X_{l(2^l-1)}\right)$

$X_{(l-1)2^{l-1}o}=X_{l(2^l-1)}+S\left(X_{(l-1)2^{l-1}e}\right)$

$X_{(l-1)2^{l-1}}\left(2k\right)=X_{(l-1)2^{l-1}e}\left(k\right),k\∈Z$

$X_{(l-1)2^{l-1}}(2k+1)=X_{(l-1)2^{l-1}o}\left(k\right),k\∈Z$

…?(7)

X _(l-1)1e＝X _l2-G(X _l1)

X _(l-1)1o＝X _l1+S(X _(l-1)1e)

X _(l-1)1(2k)＝X _(l-1)1e(k) k∈Z

X _(l-1)1(2k+1)＝X _(l-1)1o(k) k∈Z

Each the decomposition frequency band vibration signal that obtains is carried out the Hilbert envelope demodulation, calculate the decibel value of the corresponding envelope spectrum amplitude of fault characteristic frequency in each frequency band, choose the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band, rolling bearing damage is quantitatively discerned, specifically be may further comprise the steps:

(1) each band signal that reconstruct is obtained carries out the Hilbert envelope demodulation, then restituted signal is carried out fast fourier transform, obtains the envelope spectrum of each frequency band reconstruction signal.

(2), utilize following formula to calculate its decibel value with the envelope spectrum of each frequency band reconstruction signal

$B=20\log \frac{2000\×\mathrm{SV}}{N\×D^{0.6}}---\left(8\right)$

In the formula, B represents decibel value dB, and N represents the rotating speed of axle, and unit is r/min; D represents the internal diameter of rolling bearing, and unit is m; SV represents the acceleration impact value, and unit is m/s ²

(3) the fault characteristic frequency value of calculating rolling bearing retainer, rolling body, outer ring and inner ring.Extract the decibel value of each fault characteristic frequency corresponding envelope spectrum amplitude in each frequency band of second generation wavelet packet.

(4) choose the maximal value B of the corresponding decibel value of fault characteristic frequency in each frequency band _Max, the damage of rolling bearing is quantitatively discerned.

0≤B _Max＜21dB normal condition, the rolling bearing duty is good;

21≤B _Max≤ 35dB slight damage, rolling bearing has initial failure;

35＜B _Max≤ 60dB major injury, the existing obviously damage of rolling bearing.

Embodiment 1:

Construct the shock response simulate signal x (t) at two carrier wave centers of a modulation source, simulate rolling bearing and the outer ring fault takes place and have the response signal at a plurality of carrier waves center:

$x\left(t\right)=\underset{i=1}{\overset{42}{\mathrm{\Σ}}}(e^{-\mathrm{\ζ}2\mathrm{\π}{f}_1(t-i/f_{\mathrm{ou}})}\sin 2\mathrm{\π}{f}_1(t-i/f_{\mathrm{ou}})\sqrt{1-{\mathrm{\ζ}}^2}+e^{-\mathrm{\ζ}2\mathrm{\π}{f}_2(t-i/f_{\mathrm{ou}})}\sin 2\mathrm{\π}{f}_2(t-i/f_{\mathrm{ou}})\sqrt{1-{\mathrm{\ζ}}^2})---\left(9\right)$

The centre carrier frequency of x (t) is respectively f ₁=2000Hz, f ₂=5200Hz, damping ratio is ζ=0.02; f _Ou=64.819Hz.Sample frequency with 12800Hz is carried out discrete sampling to x (t), and sampling number is 8192.Fig. 2 (a) is the time domain waveform figure of simulate signal, and Fig. 2 (b) is for directly carrying out the Hilbert demodulation to simulate signal, the simulate signal envelope spectrum decibel value figure that obtains.

At first the simulate signal shown in the formula (9) is carried out three layers of second generation WAVELET PACKET DECOMPOSITION and reconstruct, obtain the reconstruction signal of eight frequency bands, the result as shown in Figure 3.Among the figure, X31, X32 ..., X38 represent respectively first frequency band of the 3rd layer, second frequency band ..., the reconstruction signal of the 8th frequency band.

Eight frequency band reconstruction signals that Fig. 3 is obtained carry out the Hilbert envelope demodulation respectively, ask for eight frequency band reconstruction signal envelope spectrums, use formula (8) to extract modulation source frequency f in each frequency band then _OuThe decibel value that (outer ring fault characteristic frequency) is corresponding, the result as shown in Figure 4.As seen from Figure 4, the 3rd and the 7th frequency band f _OuThe decibel value that (outer ring fault characteristic frequency) is corresponding is bigger, and its carrier wave center is just in frequency band corresponding.

This simulate signal is analyzed, and it is f that table 1 has provided the modulation source frequency _OuThe Hilbert demodulation recognition result of=64.819Hz and utilize the inventive method to carry out recognition result.By table 1 as seen, with the method that the present invention proposes, recognition result and actual value are very approaching, and the direct demodulation result of Hilbert then has than mistake with actual value.

Table 1f _OuThe quantitative recognition result of=64.819Hz simulate signal

Embodiment 2:

In order to verify the correctness of methods described herein, on the rolling bearing experiment table, be provided with housing washer earlier damage fault.The model of rolling bearing is 552732QT, and its parameter is as follows: internal diameter 160mm, external diameter 290mm, roller diameter 34mm, roller number 17.During test, it is 515r/min that the testing table axle changes frequently.

Sample frequency is made as 12800Hz, sampling number is 8192, the bearing vibration signal of Fig. 5 (a) for collecting from the rolling bearing testing table carries out the Hilbert envelope demodulation to the bearing vibration signal, and the decibel value that obtains its envelope spectrum is shown in Fig. 5 (b).

The bearing vibration signal is carried out three layers of second generation WAVELET PACKET DECOMPOSITION and reconstruct, obtain the reconstruction signal of eight frequency bands, the result as shown in Figure 6.Eight frequency band reconstruction signals that Fig. 6 is obtained carry out the Hilbert envelope demodulation respectively, ask for eight frequency band reconstruction signal envelope spectrums, use formula (8) to extract the decibel value of rolling bearing retainer in each frequency band, rolling body, outer ring and inner ring fault characteristic frequency correspondence then, the result as shown in Figure 7.As seen from Figure 7, the decibel value maximum of the outer ring fault characteristic frequency correspondence of rolling bearing in the 6th frequency band, be 22.806dB, there is outer ring earlier damage fault in the expression rolling bearing, and the corresponding decibel value of the outer ring fault characteristic frequency that directly utilizes Hilbert envelope demodulation analytical approach to obtain is 19.859dB.

Claims (1)

1. the method for a quantitatively identifying rolling bearing damage is characterized in that:

1) the bearing vibration signal is carried out second generation WAVELET PACKET DECOMPOSITION and reconstruct, make the multicarrier vibration signal that is coupled decompose and be a plurality of single carrier vibration signals; Described the bearing vibration signal is carried out second generation WAVELET PACKET DECOMPOSITION and reconstruct, may further comprise the steps:

A. with a burst X={x _n, n ∈ Z}, wherein x _nBe n sample in the sequence X, Z is the positive integer set, is divided into two sub-sequence X _eAnd X _o

X _e＝{x _2k，k∈Z}

X _o＝{x _2k+1，k∈Z}

K is subsequence X _eAnd X _oIn the sample sequence number;

B. by following various, calculate each band signal that second generation wavelet packet l layer decomposes

X _l1＝X _(l-1)1o-S(X _(l-1)1e)

X _l2＝X _(l-1)1e+G(X _l1)

…

$X_{l(2^l-1)}=X_{(l-1)2^{l-1}o}-S\left(X_{(l-1)2^{l-1}e}\right)$

$X_{l{2}^l}=X_{(l-1)2^{l-1}e}+G\left(X_{l(2^l-1)}\right)$

Wherein, S and G are second generation wavelet packet operator, and S obtains by following formula

WS＝[1，0，0，...，0] ^T

[W] _i，j＝[2j-N-1] ^i-1 i＝1，2，...，N；j＝1，2，...，N.

If $Q=\{Q_k,-N-\tilde{N}+2\≤k\≤N+\tilde{N}-2\},$ The relation of Q and S, G is represented with following formula

$Q_{(2l-1)}=\left\{\begin{array}{cc}1-\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{S}_m{G}_{(l-m+1)}& l=(N+\tilde{N})/2\\ \underset{m=1}{\overset{N}{\mathrm{\Σ}}}{S}_m{G}_{(l-m+1)}& l\≠(N+\tilde{N})/2\end{array}\right.$

Q _(2l+N-2)＝G _l l＝1，2，...，

When l gets other value, Q _2l=0;

Construct one

The dimension matrix

Its element representation is as follows

${\left[\tilde{W}\right]}_{m,n}=n^m$

Wherein $n=-N-\tilde{N}+2,-N-\tilde{N}+3,...,N+\tilde{N}-3,N+\tilde{N}-2,$ m＝0，1，...，

G obtains by following formula

$\tilde{W}Q=0$

N and Be respectively the number of operator S and G coefficient;

Second generation wavelet package reconstruction process is to treat that the reconstruct band signal keeps, and with other band signal zero setting, then according to following various being reconstructed;

$X_{(l-1)2^{l-1}e}=X_{l{2}^l}-G\left(X_{l(2^l-1)}\right)$

$X_{(l-1)2^{l-1}o}=X_{l(2^l-1)}+S\left(X_{(l-1)2^{l-1}e}\right)$

$X_{(l-1)2^{l-1}}\left(2k\right)=X_{(l-1)2^{l-1}e}\left(k\right),k\∈Z$

$X_{(l-1)2^{l-1}}(2k+1)=X_{(l-1)2^{l-1}o}\left(k\right),k\∈Z$

…

X _(l-1)1e＝X _l2-G(X _l1)

X _(l-1)1o＝X _l1+S(X _(l-1)1e)

X _(l-1)1(2k)＝X _(l-1)1e(k) k∈Z

X _(l-1)1(2k+1)＝X _(l-1)1o(k) k∈Z；

2) utilize the Hilbert conversion to carry out envelope demodulation to each frequency band vibration signal, calculate the decibel value of the corresponding envelope spectrum amplitude of fault characteristic frequency in each frequency band, choose the maximal value of the corresponding decibel value of fault characteristic frequency in each frequency band, according to maximal value the rolling bearing earlier damage is quantitatively discerned, be may further comprise the steps:

A. each band signal that reconstruct is obtained utilizes the Hilbert conversion to obtain its signal envelope, then signal envelope is carried out fast fourier transform, obtains the envelope spectrum of each frequency band reconstruction signal;

B. utilize following formula to calculate the decibel value of the corresponding envelope spectrum amplitude of rolling bearing inner ring, outer ring, rolling body and retainer fault characteristic frequency

$B=20\log \frac{2000\×\mathrm{SV}}{N\×D^{0.6}}$

In the formula, B represents decibel value dB, and N represents the rotating speed of axle, and unit is r/min; D represents the internal diameter of rolling bearing, and unit is m; SV represents the acceleration impact value, and unit is m/s ²Choose the maximal value of the corresponding decibel value of rolling bearing inner ring in each frequency band, outer ring, rolling body and retainer fault characteristic frequency respectively, and the earlier damage degree of rolling bearing inner ring, outer ring, rolling body and retainer is made quantitative identification according to the maximal value of decibel value.

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