CN101587017A - Gear fault diagnosis method based on part mean decomposition cycle frequency spectrum - Google Patents

Abstract

The invention discloses a gear fault diagnosis method based on local mean decomposition cycle frequency spectrum. The local mean value decomposition method decomposes the vibration signal into the sum of several single-component AM-FM signals, and obtains the instantaneous frequency of each component, and obtains the variation of the instantaneous frequency of each component with time, which is very suitable for dealing with multi-component AM-FM Signal. When a gear fails, its vibration signal is usually a multi-component AM-FM signal. Using the local mean decomposition method, the instantaneous frequency of the gear vibration signal changes with time, and the frequency spectrum of the instantaneous frequency is further analyzed to obtain the cyclic frequency spectrum. Status and faults are identified.

Description

A kind of gear failure diagnosing method based on local mean value Decomposition Cycle frequency spectrum

Technical field

The present invention relates to a kind of gear failure diagnosing method based on local mean value Decomposition Cycle frequency spectrum.

Background technology

When gear case breaks down, its vibration signal mostly is multicomponent AM signal, therefore demodulation analysis becomes a kind of signal processing method commonly used of Gear Fault Diagnosis, extracts modulation signal from vibration signal, analyzes degree and position that its intensity and the frequency just can be judged part injury.Yet great majority all focus on the extraction AM information, and the research aspect phase modulation (PM) is less relatively.At present, in gear failure diagnosing method based on demodulation analysis, because the method that can adopt Hilbert (Hilbert) conversion to extract the gear distress signal envelope obtains modulation intelligence, Hilbert transform simultaneously has fast algorithm again, therefore Hilbert transform is the most frequently used gear distress vibration signal demodulation method, but it only is suitable for handling the simple component signal.And all be multicomponent AM signal for most gear distress vibration signal, for this class signal, traditional method is by bandpass filtering it to be resolved into the AM signal of simple component, carries out demodulation then to extract frequency and amplitude information.But, in the gear distress vibration signal of reality, the size of what and carrier frequency of carrier frequency composition is difficult to definite, the selection of centre frequency just has very big subjectivity when therefore signal being carried out bandpass filtering, bring demodulating error like this, can not extract the feature of gear distress vibration signal effectively.In fact, the key of many components AM signal being carried out demodulation is to find a kind of effective signal decomposition method, multicomponent AM signal decomposition can be had the simple component AM signal sum of physical significance for several instantaneous frequencys.Multicomponent AM signal has non-stationary characteristic, and in present non-stationary signal decomposition method, have wavelet-decomposing method and empirical modal commonly used decompose (Empirical Mode Decomposition is called for short EMD) method.Though wavelet transformation has variable time-frequency window, the decomposition scale of wavelet transformation is only relevant with the signals sampling rate, and irrelevant with signal itself, it is not a kind of adaptive signal processing method in essence.Empirical mode decomposition method is a kind of adaptive signal processing method, can be decomposed into intrinsic modal components (the Intrinsic Mode Function that several instantaneous frequencys have physical significance with many component signals are adaptive, be called for short IMF) the component sum, further adopt Hilbert transform to obtain the instantaneous frequency and the instantaneous amplitude of each intrinsic modal components, thereby realize demodulation sophisticated signal.But also there are some problems in empirical mode decomposition method, obscure and the end effect problem as envelope algorithm, mode in the empirical mode decomposition method, also have when calculating instantaneous frequency after utilizing Hilbert transform to form analytic signal to produce unaccountable negative frequency, these problems need further be researched and solved.

Summary of the invention

In order to solve the above-mentioned technical matters that existing gear distress vibration signal diagnosis exists, the invention provides a kind of gear failure diagnosing method based on local mean value Decomposition Cycle frequency spectrum.

The technical scheme that the present invention solves the problems of the technologies described above may further comprise the steps:

1) utilizes acceleration transducer that gear case is measured, obtain vibration acceleration signal;

2) adopt part mean decomposition method that the gear vibration acceleration signal is decomposed, decompose and obtain envelope signal and pure FM signal, envelope signal and pure FM signal can be obtained mutually at convenience the AM signal of a simple component, utilize pure FM signal to calculate its instantaneous frequency, be circulated to the AM signal and the instantaneous frequency thereof that obtain all simple components;

3) each instantaneous frequency is carried out spectrum analysis, obtain cycle frequency spectrum α _m=FFT[f _m(t)], FFT represents fast fourier transform in the formula;

4) from the cycle frequency spectrum, analyze whether contain gear gyro frequency f _sAnd frequency multiplication, if having, then fault has taken place in gear.

Above-mentioned gear failure diagnosing method based on local mean value Decomposition Cycle frequency spectrum, described step 2) it is as follows to adopt part mean decomposition method that the gear vibration acceleration signal is carried out decomposition step in:

1) finds out all Local Extremum n of gear vibration acceleration signal x (t) _i, obtain the mean value of all adjacent Local Extremum, the mean point that all are adjacent couples together with straight line, carries out smoothing processing with moving average method then and obtains the local mean value function m ₁₁(t);

2) calculate adjacent Local Extremum envelope estimated value, with all adjacent two envelope estimated value a _iConnect with straight line, adopt the running mean method to carry out smoothing processing then, obtain envelope estimation function a ₁₁(t);

3) from original signal x (t), deduct the local mean value function m ₁₁(t), obtain removing the h of low frequency signal ₁₁(t);

4) use h ₁₁(t) divided by envelope estimation function a ₁₁(t), obtain s ₁₁(t);

5) if satisfy 1-Δ≤a _1n(t)≤and the 1+ Δ, Δ is the variable less than 1, forwards step 6) to; Otherwise use s _1n(t) replace x (t), repeating step 1) to 4);

6) step 1) to 4) all envelope estimation functions of producing in the iterative process multiply each other and obtain envelope signal a ₁(t);

7) with envelope signal a ₁(t) and pure FM signal s _1n(t) multiply each other and obtain the 1st product function component PF of original signal ₁(t);

8) with the 1st PF component PF ₁(t) from original signal x (t), separate, obtain a new signal u ₁(t), with u ₁(t) replace x (t), repeating step 1 as raw data) to 7), circulation k time is up to u _kBe till the monotonic quantity, original x (t) is decomposed into k PF component and a monotonic quantity u _kSum.

Technique effect of the present invention is: the present invention adopts part mean decomposition method that the gear vibration acceleration signal is decomposed, adaptively many component signals of a complexity are decomposed into the AM signal of the simple component of several instantaneous frequencys, and obtain the instantaneous frequency of each component, instantaneous frequency is carried out spectrum analysis obtain the cycle frequency spectrum, just can analyze its main frequency composition, thereby fault diagnosis is accurately carried out in the failure judgement position.

The present invention is further illustrated below in conjunction with the drawings and specific embodiments.

Description of drawings

Fig. 1 is a part mean decomposition method process flow diagram of the present invention.

Fig. 2 is a process flow diagram of the present invention.

Fig. 3 is broken teeth gear vibration time domain plethysmographic signal figure.

Fig. 4 is broken teeth gear local mean value decomposition result figure.

Fig. 5 is the cycle frequency figure of the PF component of broken teeth gear vibration signal.

Fig. 6 is normal gear vibration signal time domain waveform figure.

Fig. 7 is the cycle frequency figure of the PF component of normal gear vibration signal.

Embodiment

At first need utilize acceleration transducer that gear case is measured in the Gear Fault Diagnosis process, obtain vibration acceleration signal x (t), again vibration acceleration signal be decomposed, extract eigenwert.The present invention utilizes part mean decomposition method that vibration acceleration signal is decomposed, and its idiographic flow is seen Fig. 1.

Below in conjunction with process flow diagram the gear failure diagnosing method principle based on local mean value Decomposition Cycle frequency is elaborated.Concrete steps are as follows:

1) piezoelectric acceleration transducer is installed on the gear box casing, gathers gear case vibration acceleration signal x (t).

2) find out all Local Extremum n of gear vibration acceleration signal x (t) _i, obtain the mean value of all adjacent Local Extremum:

$m_i=\frac{n_i+n_{i+1}}{2}---\left(1\right)$

The mean point m that all are adjacent _iCouple together with straight line, carry out smoothing processing with moving average method then and obtain the local mean value function m ₁₁(t).

3) obtain the envelope estimated value

$a_i=\frac{|n_i-n_{i+1}|}{2}---\left(2\right)$

With all adjacent two envelope estimated value a _iConnect with straight line, adopt the running mean method to carry out smoothing processing then, obtain envelope estimation function a ₁₁(t).

4) with the local mean value function m ₁₁(t) from original signal x (t), separate, promptly removed a low-frequency component, obtain

h ₁₁(t)＝x(t)-m ₁₁(t) (3)

5) use h ₁₁(t) divided by envelope estimation function a ₁₁(t) with to h ₁₁(t) carry out demodulation, obtain

s ₁₁(t)＝h ₁₁(t)/a ₁₁(t) (4)

To s ₁₁(t) repeat above-mentioned steps and just can obtain s ₁₁(t) envelope estimation function a ₁₂(t), if a ₁₂(t) be not equal to 1, s is described ₁₁(t) not a pure FM signal, need repeat above-mentioned iterative process n time, until s _1n(t) being a pure FM signal, also is s _1n(t) envelope estimation function a _{1 (n+1)}(t)=1, so, have

$\left\{\begin{array}{c}{h}_{11}\left(t\right)=x\left(t\right)-m_{11}\left(t\right)\\ h_{12}=s_{11}\left(t\right)-m_{12}\left(t\right)\\ .\\ .\\ .\\ h_{1n}\left(t\right)=s_{1(n-1)}\left(t\right)-m_{1n}\left(t\right)\end{array}\right.---\left(5\right)$

In the formula,

$\left\{\begin{array}{c}{s}_{11}\left(t\right)=h_{11}\left(t\right)/a_{11}\left(t\right)\\ s_{12}\left(t\right)=h_{12}\left(t\right)/a_{12}\left(t\right)\\ .\\ .\\ .\\ s_{1n}\left(t\right)=h_{1n}\left(t\right)/a_{1n}\left(t\right)\end{array}\right.---\left(6\right)$

The condition that iteration stops is

$\underset{n\→\∞}{\lim }{a}_{1n}\left(t\right)=1---\left(7\right)$

In the practical application,, can set variation Δ=10 not influencing under the prerequisite of decomposing effect ^-4, use

1-Δ≤a _1n(t)≤1+Δ (8)

Condition as the iteration termination.

5) can obtain envelope signal (instantaneous amplitude function) to all envelope estimation functions that produce in the iterative process mutually at convenience

$a_1\left(t\right)=a_{11}\left(t\right)a_{12}\left(t\right)...a_{1n}\left(t\right)=\underset{q=1}{\overset{n}{\mathrm{\Π}}}{a}_{1q}\left(t\right)---\left(9\right)$

6) with envelope signal a ₁(t) and pure FM signal s _1n(t) can obtain mutually the 1st PF (product function is called for short PF, below all the represent the product function) component of original signal at convenience by PF

PF ₁(t)＝a ₁(t)s _1n(t) (10)

It has comprised frequency content the highest in the original signal, is the AM signal of a simple component, and its instantaneous amplitude is exactly envelope signal a ₁(t), its instantaneous frequency f ₁(t) then can be by pure FM signal s _1n(t) obtain, promptly

$f_1\left(t\right)=\frac{1}{2\mathrm{\π}}\frac{d\left[\arccos \left(s_{1n}\left(t\right)\right)\right]}{\mathrm{dt}}---\left(11\right)$

7) with the 1st PF component PF ₁(t) from original signal x (t), separate, obtain a new signal u ₁(t), with u ₁(t) repeat above step as raw data, circulation k time is up to u _kTill being a monotonic quantity.

$\left\{\begin{array}{c}{u}_1\left(t\right)=x\left(t\right)-{\mathrm{PF}}_1\left(t\right)\\ u_2\left(t\right)=u_1\left(t\right)-{\mathrm{PF}}_2\left(t\right)\\ .\\ .\\ .\\ u_k\left(t\right)=u_{k-1}\left(t\right)-{\mathrm{PF}}_k\left(t\right)\end{array}\right.---\left(12\right)$

So far, original x (t) is decomposed into k PF component (the AM signal of simple component) and a monotonic quantity u _kSum, promptly

$x\left(t\right)=\underset{p=1}{\overset{k}{\mathrm{\Σ}}}{\mathrm{PF}}_p\left(t\right)+u_k\left(t\right)---\left(13\right)$

In the actual gear case system, when faults such as gear existence wearing and tearing, fatigue crack, the amplitude of vibration signal and phase place can change, and produce amplitude and phase modulation (PM), and its vibration signal can be expressed as:

$y\left(t\right)=\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{X}_m(1+d_m\left(t\right))\cos (2\mathrm{\πmz}{f}_{s}t+{\mathrm{\φ}}_m+b_m\left(t\right))---\left(14\right)$

In the formula, f _sBe the gear gyro frequency, z is the number of teeth of gear, φ _mBe the initial phase of m rank meshing frequency harmonic component, d _m(t) and b _m(t) be respectively the amplitude and the phase modulation function of m rank meshing frequency harmonic component, and when local fault appears in gear, rotate with the axis engagement weekly once owing to the fault tooth, so d _m(t) and b _m(t) be the periodic function of gyro frequency, further can be write formula (14) as following form

$y\left(t\right)=\underset{m=1}{\overset{N}{\mathrm{\Σ}}}{a}_m\left(t\right)\cos {\mathrm{\Φ}}_m\left(t\right)---\left(15\right)$

A in the formula _m(t)=X _m[1+d _m(t)], Φ _m(t)=2 π mzf _sT+ φ _m+ b _m(t).

The gear distress vibration signal is typical many components AM signal as can be seen from formula (15), contains several meshing frequency families, each a of meshing frequency family _m(t) cos Φ _m(t) be a simple component AM signal again, therefore can adopt the LMD method that the gear distress vibration signal is decomposed, each frequency family is separated, obtain several PF components, wherein each PF component represents of gear vibration signal with certain rank meshing frequency mf _zBe the frequency family at center, in the process of decomposing, can obtain the instantaneous frequency of each PF component by formula (11) $f_m\left(t\right)=\frac{1}{2\mathrm{\π}}{{\mathrm{\Φ}}^{\′}}_m\left(t\right)=\mathrm{mz}{f}_s+\frac{1}{2\mathrm{\π}}{b^{\′}}_m\left(t\right).$

8) to instantaneous frequency f _m(t) carry out spectrum analysis, obtain cycle frequency

α _m＝FFT[f _m(t)] (16)

In the formula, FFT represents Fast Fourier Transform (FFT).

9) from the cycle frequency spectrum, analyze whether contain gear gyro frequency f _sAnd frequency multiplication, if having, then fault has taken place in gear.

With reference to accompanying drawing 3, be broken teeth gear vibration time domain plethysmographic signal figure.With tooth of the artificial cutting of the driving gear on the gearbox fault testing table, simulation gear tooth breakage fault, the input shaft and the output shaft gear number of teeth are 37, modulus 2.5mm.Gather the gear case vibration acceleration signal, sample frequency is 1024Hz, and the sampling duration is 1 second, at 420rpm (f _s=7Hz) rotating speed is gathered down one group of broken teeth vibration signal and one group of normal gear vibration signal, and normal gear is identical with the broken teeth gear parameter.

Adopt part mean decomposition method that this vibration signal is decomposed, obtain 5 PF components and 1 surplus, as shown in Figure 4, preceding several PF components all have tangible AM feature.Because sample frequency is 1024Hz, so only to comprise 1 in the gear distress vibration signal be the frequency family at center with meshing frequency (259Hz), the 1st PF component of correspondence, and remaining PF component is noise signal.Instantaneous frequency to the 1st PF component is done the cycle frequency analysis, and the result also is the phase modulation frequency f of vibration signal in gyro frequency as shown in Figure 5 as can be seen from Figure _sThere is tangible spectral line in=7Hz place, and phase modulation function b is described _m(t) contain the cyclic component that changes with gyro frequency, can judge that local fault has taken place this gear.

Fig. 6 is the time domain waveform of the normal gear vibration acceleration signal of collection, and the gear gyro frequency is 7Hz, and sample frequency is 1024Hz.The cycle frequency of the instantaneous frequency of its 1st PF component as shown in Figure 7, as can be seen at f _s=7Hz and frequency multiplication place thereof do not have tangible peak value, and the instantaneous frequency of other PF component is carried out same analysis, all do not have tangible peak value at 7Hz and frequency multiplication place thereof, illustrate that this gear is normal gear, conforms to actual conditions.

Claims (3)

1. A gear fault diagnosis method based on local mean decomposition cyclic frequency spectrum, comprising the following steps: 1) Use the acceleration sensor to measure the gearbox to obtain the vibration acceleration signal; 2) The local mean value decomposition method is used to decompose the gear vibration acceleration signal, and the envelope signal and pure FM signal are obtained by decomposing, and a single-component AM-FM signal can be obtained by multiplying the envelope signal and pure FM signal. The signal calculates its instantaneous frequency, and loops until all single-component AM-FM signals and their instantaneous frequencies are obtained; 3) carry out frequency spectrum analysis to each instantaneous frequency, obtain cyclic frequency spectrum α _m =FFT[f _m (t)], FFT represents fast Fourier transform in the formula; 4) Analyze whether the gear rotation frequency f _s and its multiplier are contained in the cycle frequency spectrum, if so, the gear has failed. 2. According to the gear fault diagnosis method based on local mean decomposition cyclic frequency spectrum according to claim 1, the step of calculating instantaneous frequency f ₁ (t) by pure frequency modulation signal in said step 2) is: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\frac{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{\mathrm{<span\; class="notranslate">\; dt</span>}}$ s _1n (t) is a pure frequency modulation signal. 3. According to the gear fault diagnosis method based on local mean decomposition cyclic frequency spectrum according to claim 1, the steps of decomposing the gear vibration acceleration signal by adopting the local mean decomposition method in the step 2) are as follows: 1) Find all the local extremum points n _i of the gear vibration acceleration signal x(t), calculate the average value of all adjacent local extremum points, connect all adjacent average points with a straight line, and then use The moving average method is used for smoothing to obtain the local mean function m ₁₁ (t); 2) Calculate the envelope estimation value of the adjacent local extremum points, connect all the two adjacent envelope estimation values a _i with a straight line, and then use the moving average method for smoothing to obtain the envelope estimation function a ₁₁ (t) ; 3) Subtracting the local mean function m ₁₁ (t) from the original signal x(t) to obtain h ₁₁ (t) with the low-frequency signal removed; 4) Divide h ₁₁ (t) by the envelope estimation function a ₁₁ (t) to obtain s ₁₁ (t); 5) If 1-Δ≤a _1n (t)≤1+Δ is satisfied, and Δ is a variable less than 1, go to step 6); otherwise, replace x(t) with s _1n (t), repeat steps 1) to 4 ); 6) multiplying all the envelope estimation functions generated in the iterative process from steps 1) to 4) to obtain the envelope signal a ₁ (t); 7) Multiply the envelope signal a ₁ (t) and the pure frequency modulation signal s _1n (t) to obtain the first product function PF ₁ (t) of the original signal; 8) Separate the first PF component PF ₁ (t) from the original signal x(t) to obtain a new signal u ₁ (t), and use u ₁ (t) as the original data to replace x(t), Repeat steps 1) to 7) for k times until u _k is a monotone function, decompose the original x(t) into the sum of k PF components and a monotone function u _k .

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