CN103076174A - Bearing fault and fault degree diagnostic method on basis of phase-locked amplification algorithm - Google Patents

Abstract

The invention discloses a bearing fault and fault degree diagnostic method on the basis of a phase-locked amplification algorithm. According to the invention, due to the advantages of stable center frequency, narrow transmission band, high quality factor and the like of a phase-locked amplifier, a phase-locked amplification principle is applied to diagnosis on a bearing fault and a fault degree by utilizing the phase-locked amplifier. A reference signal on the basis of the bearing fault signal characteristics is established and the phase-locked amplification principle is utilized to remain and amplify information related to the fault and reduce noise signals which are not related to fault ingredients by multiplication and integral operation, so that rapid separation of signal noise and positioning on the fault are implemented. Meanwhile, a reference signal added with fault degree parameters is established and diagnosis on the bearing fault degree is implemented by combining a kurtosis value.

Description

A kind of bearing fault and fault degree diagnostic method based on phase-locked interpolator arithmetic

Technical field

The present invention relates to a kind of bearing fault and fault degree diagnostic method, particularly a kind of bearing fault and fault degree diagnostic method based on phase-locked interpolator arithmetic.

Background technology

The serviceability of industry kinematic train directly affects the work efficiency of whole production line.Bearing is as the important component part of industrial kinematic train, and its effect is very crucial.The inner topmost part of bearing comprises rolling bearing and gear, moves under high speed, the fully loaded transportation condition because these two kinds of parts are everlasting, and rate of breakdown is higher, will cause serious casualties and economic loss in case break down.Therefore bearing is carried out condition monitoring and fault diagnosis to guaranteeing production safety, prevent major accident, important in inhibiting reduces production costs.

At present, adopting the vibration signal processing technology based on high-speed computer is the main flow of bearing failure diagnosis technology.The key of bearing failure diagnosis is how to extract fault signature from the fault vibration signal.But because the environmental facies of the operation of the actual centre bearer of engineering are worked as badly, its vibration signal is very complicated, contains much noise and labile factor, is a kind of typical non-stationary signal, and when particularly early defect appearred in bearing inside, the signal fault feature was very faint.And the equipment to diagnosing malfunction in engineering reality often only possesses some simple signal analysis abilities, for the obvious situation of fault certain effect is arranged still, feeble signal or the larger signal of signal to noise ratio (S/N ratio) often be can not get effectively analysis result, analytical effect to fault degree also has much room for improvement, and has affected the efficient of signal analysis.

Therefore how adopting effective analysis tool and algorithm, the fault of bearing and fault degree are analyzed and diagnosed, extract fault signature and realize fault progression status monitoring and diagnosis, is a large difficult point of bearing being carried out fault detection and diagnosis.

Lock-in amplifier is owing to have CFS center frequency stabilization, and passband is narrow, and the quality factor advantages of higher is having good performance aspect feeble signal amplification and the noise separation.

Yet current phaselock technique great majority are applied to the amplification of sine, cosine signal, and the contrast signal kind of its input is also very single.By to the analysis and modeling of bearing fault signal as can be known, the bearing fault signal has the feature of periodic signal and can utilize the principle of phase locking unit to carry out the signal processing, from its mathematic(al) representation, can find out, as long as seek based on the contrast signal of bearing fault characteristics and process accordingly, can realize theoretically the amplification of fault-signal and noise signal to zero.

Therefore the principle design algorithm that utilizes lock-in amplifier based on bearing fault and the fault degree diagnostic method of phase-locked interpolator arithmetic described herein causes the state of the bearing fault of significant impact to study mainly for meeting to production.After the feature of fully having analyzed the bearing fault signal, determine the input signal of lock-in amplifier, after multiplying and integral operation, relevant with fault information is stayed and amplify, those and the incoherent noise signal of trouble unit are extremely zero, realize the quick separation of noise and the location of fault.In input signal, add simultaneously the fault degree parameter, realized the diagnosis of bearing fault degree.

Summary of the invention

Above-mentioned technical matters in bearing failure diagnosis and the fault degree diagnosis the invention provides a kind of bearing fault based on phase-locked interpolator arithmetic and fault degree diagnostic method.

The technical scheme that the present invention solves the problems of the technologies described above comprises sets up the input reference signal model, carries out phase-locked amplification and calculates, and calculates fault degree.

Because the bearing fault characteristics signal also has periodic characteristics, therefore can consider to select suitable reference signal to utilize phase-locking and amplification principle to weaken noise signal in the bearing burst, amplify and extract wherein fault characteristic signals.

By analyzing bearing fault characteristics as can be known, bearing fault signal v _s(t) can be expressed as

$v_s\left(t\right)=\underset{t=0}{\overset{\max \left(t\right)}{\mathrm{\&Sigma;}}}{k}_1{e}^{-p_1\mathrm{<figure-callout\; id="2"\; label="t\; cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">t</figure-callout>}}\cos 2\mathrm{\&pi;}{f}_1\mathrm{t\&delta;}(t-n{T}_0)$ （n=0,1,2…）

That is:

$v_s\left(t\right)=k_1{e}^{-p_1\mathrm{<figure-callout\; id="2"\; label="t\; cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">t</figure-callout>}}\cos 2\mathrm{\&pi;}{f}_{1}t+k_1{e}^{-p_1(t-T_0)}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-T_0)+$ $k_1{e}^{-p_1(t-2T_0)}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-2T_0)+...+k_1{e}^{-p_1(t-n{T}_0)}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-n{T}_0)$

k ₁For the bearing fault signal amplitude can directly be measured, p wherein ₁For the damping coefficient of bearing fault signal shock response can be according to bearing parameter measurements and calculations, f ₁Corresponding to the damped natural frequency of measured bearing be each impact of bearing fault signal frequency can the corresponding frequency of spectrum peak position directly obtains T in the bearing fault signal spectrum figure resonant belt by reading ₀For the bearing fault characteristics cycle can calculate by bearing parameter, all t are the time and can directly measure in the literary composition, all δ are the impulse function identifier in the literary composition, to be the maximum occurrences of time t be that the length of measured signal s (t) can directly be measured to all max (t) in the literary composition, in the literary composition all e be exponential function represent the symbol, all n are bearing rotary week number in the literary composition, represent with nonnegative integer.

Measured signal can be expressed as:

s(t)=v _s(t)+n(t)

Wherein n (t) is random noise, v _s(t) be the bearing fault signal

According to phase-locking and amplification principle, if select the signal close with tested composition and choose suitable frequency and can amplify and de-noising measured signal.Traditional lock-in amplifier is all selected sinusoidal signal and is adjusted cosine composition in the suitable frequency abstraction analyzed signal.For the bearing fault signal, its most basic effective constituent is the impact-attenuating signal, therefore can select the impact-attenuating signal as reference signal extraction and amplify effective trouble unit.

Establishing reference signal at this is:

$y\left(t\right)=k_2{e}^{-p_{2}t}\sin 2\mathrm{\&pi;}{f}_{2}t$

Wherein y (t) is reference signal, k ₂For the reference signal amplitude can be set as arbitrarily number greater than 1, the larger enlargement factor of value is larger, p ₂Can get the arbitrary value value for the damping coefficient of reference signal shock response in 1000-1200, the larger kurtosis of value is larger, f ₂For the measured bearing damped natural frequency that dopes is that reference signal frequency needs according to f ₁Value be defined as equaling f ₁Value.

Measured signal and contrast signal then through the output signal of multiplier are:

v(t)=s(t)+y(t)

Therefore signal v (t) can be expressed as through the output signal V of integrator again:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right)y(t+u)\mathrm{du}$

Following formula is phase-locked amplification expression formula, and wherein u is the initial position of reference signal, and max (t) is that the length of measured signal s (t) can directly be measured for the maximum occurrences of time t.

Following formula launches to be expressed as:

$V=k_1{k}_2{e}^{-t(p_1+p_2)}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{1}t\sin 2\mathrm{\&pi;}{f}_{2}t++k_1{k}_2{e}^{-t(p_1+p_2)+T_0{p}_1}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-T_0)\sin 2\mathrm{\&pi;}{f}_{2}t+$ $...+k_1{k}_2{e}^{-t(p_1+p_2)+n{T}_0{p}_1}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-n{T}_0)\sin 2\mathrm{\&pi;}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">f</figure-callout>}}_2+{\&Integral;}_0^{\max \left(t\right)}\left[k_{2}n\left(t\right)\sin 2\mathrm{\&pi;}{f}_2(t+u)\right]\mathrm{du}$

Order

$V_s=k_1{k}_2{e}^{-t(p_1+p_2)}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{1}t\sin 2\mathrm{\&pi;}{f}_{2}t++k_1{k}_2{e}^{-t(p_1+p_2)+T_0{p}_1}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-T_0)\sin 2\mathrm{\&pi;}{f}_{2}t+$ $...+k_1{k}_2{e}^{-t(p_1+p_2)+n{T}_0{p}_1}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_1(t-n{T}_0)\sin 2\mathrm{\&pi;}{f}_{2}t$

$V_n={\&Integral;}_0^{\max \left(t\right)}\left[k_{2}n\left(t\right)\sin 2\mathrm{\&pi;}{f}_2(t+u)\right]\mathrm{du}$

Then V can be expressed as:

V=V _s+V _n

It is the addition of fault-signal item and noise signal item.V wherein _sBe integration fault-signal item later, V _nBe integration noise signal item later.

Wherein

$V_s=k_1{k}_2{e}^{-t(p_1+p_2)}\left\{\right[\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}(f_1+f_2)t+\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}(f_1-f_2)t]+$

$e^{-T_0{p}_1}[\cos (2\mathrm{\&pi;}(f_1+f_2)t-T_0)+\cos (2\mathrm{\&pi;}(f_1-f_2)t-T_0)]+...+$ $e^{-{\mathrm{nT}}_0{p}_1}[\cos (2\mathrm{\&pi;}(f_1+f_2)t-n{T}_0)+\cos (2\mathrm{\&pi;}(f_1-f_2)t-{\mathrm{nT}}_0)]\}$

Because f among the reference signal y (t) ₂For the measured bearing damped natural frequency that dopes is that reference signal frequency needs according to f ₁Value be defined as equaling f ₁Value, i.e. f ₁=f ₂, so noise item V _nGet zero, i.e. V _n=0 V=V _s, so the signal V of integrator output equals:

$V=\underset{t=0}{\overset{\max \left(t\right)}{\mathrm{\&Sigma;}}}k{e}^{-(p_1+p_2)\mathrm{<figure-callout\; id="2"\; label="t\; cos"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">t</figure-callout>}}\cos 2\mathrm{\&pi;}(f_1+f_2)\mathrm{t\&delta;}(t-n{T}_0)$ （n=0,1,2…）

Compare with measured signal s (t), dispelled noise contribution, and amplified the amplification of trouble unit.Namely realized the function of the amplification of denoising and fault-signal, wherein K is enlargement factor K=k ₁k ₂

Above-mentioned multiply each other and the process of integration is that phase-locked amplification process can be expressed as:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right)y(t+u)\mathrm{du}$

Be the sequence of impacts signal of a string not Noise, and fault signature has obtained K and has doubly amplified.Hence one can see that, when obtaining reference signal according to y (t) expression formula, the frequency values f in the reference signal ₂The centre frequency of analyzed signal s (t) resonant frequency is f ₂=f ₁The time, can to utilize phase-locking and amplification principle be phase-locked amplification expression formula amplifies and carries out effective de-noising to each failure impact signal of bearing.

In order to diagnose the bearing fault size, can utilize bearing fault signal accurate model as the reference signal, introduced fault size parameter d in the model _xAt first need calculate the linear velocity of rolling body motion and the pulse width that different faults causes in order to obtain this model

Bearing roller linear velocity s:

S=πdf _r

Pulse width p _x:

$p_x=\frac{d_x}{s}$

The pulse x (t) that can obtain thus the defective generation can be expressed as:

$x\left(t\right)=\left\{\begin{array}{cc}1& u<t<u+p_x\\ 0& \end{array}\right.$

The reference signal that the impact that is produced by defective namely contains the fault degree parameter can be expressed as:

φ′ _imp(p ₂,u,f ₂,dx,d,fr)=conv(x(t),φ _imp(p ₂,u,f ₂))

φ wherein _Imp(p ₂, u, f ₂) for its expression formula of decaying exponential function be:

${\mathrm{\&phi;}}_{\mathrm{imp}}({\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,u,f_2)=e^{-p_2(t+u)}\sin 2\mathrm{\&pi;}{f}_2(t+u)$

Be φ ' _Imp(p ₂, u, f ₂, dx, d, fr) and can be expressed as φ _Imp(p ₂, u, f ₂) with the convolution of x (t), (conv is the convolution algorithm symbol).

Wherein d is that the bearing path can be determined f according to bearing designation _rFrequently can record by the sensor of special measurement rotating speed for turning.d _xFor fault diameter (unit: mm), p ₂Can get the arbitrary value value for the damping coefficient of reference signal shock response in 1000-1200, the larger kurtosis of value is larger, f ₂For the measured bearing damped natural frequency that dopes is that reference signal frequency needs according to f ₁Value be defined as equaling f ₁Value.

Parameter p in the model ₂, u, f ₂Value is identical with the value of using y (t) as with reference to signal the time.Make d in the model _xSpan is [0.5, max (d _x)], get a value every 0.5, get altogether

Individual d _xValue, wherein max (d _x) be maximum fault diameter, this

Individual amount is correspondence 1,2 from small to large,,

This

Individual integer as the fault level label, is NO with letter representation.I.e. 0.5 corresponding numeral 1,1 corresponding numeral 2,, 5 corresponding numerals 10,, max (d _x) corresponding numeral

Be 0.5 each standards change d of 0.5 that increases according to initial value _xValue, d of every variation _xValue is utilized the phase-locked simplification expression formula of putting that signal is carried out single treatment, and is asked for the kurtosis index after the processing, and the record kurtosis is with d _xChange curve.

Kurtosis ks can be expressed as:

$\mathrm{ks}=\frac{\mathrm{mean}\left({\left|V\right|}^4\right)}{{\left[\mathrm{mean}\left({\left|V\right|}^2\right)\right]}^2}-2$

Wherein V is the analyzed signal after phase-locked amplification is processed, and mean is mean value.

What try to achieve Choose three maximum kurtosis values among the individual kurtosis, record their corresponding integer fault level labels, multiply by corresponding failure grade label with kurtosis value after sum obtain the fault degree eigenwert divided by three kurtosis sums.

Technique effect of the present invention is: utilize lock-in amplifier owing to have CFS center frequency stabilization, passband is narrow, and the quality factor advantages of higher is applied to phase-locking and amplification principle the diagnosis of bearing fault and fault degree.The contrast signal of having set up based on bearing fault characteristics utilizes phase-locking and amplification principle, after multiplying and integral operation, relevant with fault information is stayed and amplify, those and the incoherent noise signal of trouble unit to zero, are realized the quick separation of noise and the location of fault.Set up simultaneously a kind of reference signal that adds the fault degree parameter, realized the diagnosis of bearing fault degree in conjunction with the kurtosis index.

Description of drawings

The invention will be further described below in conjunction with the drawings and specific embodiments.

Fig. 1 is the chief component figure based on phase-locked interpolator arithmetic bearing failure diagnosis of the present invention.

Fig. 2 is of the present invention based on phase-locked interpolator arithmetic bearing failure diagnosis process flow diagram.

Fig. 3 is the emulation time domain waveform of housing washer fault.

Result after Fig. 4 processes through phase-locked interpolator arithmetic.

Fig. 5 is the process flow diagram of diagnosing based on phase-locked interpolator arithmetic bearing fault degree among the present invention.

Fig. 6 utilizes fault degree and the fault degree eigenwert graph of a relation that obtains based on phase-locked interpolator arithmetic bearing fault degree diagnosis among the present invention.

Embodiment

Fig. 1 is the chief component figure based on phase-locked interpolator arithmetic bearing failure diagnosis of the present invention.Formed by bearing failure diagnosis and bearing fault degree diagnosis two parts based on phase-locked interpolator arithmetic bearing failure diagnosis

Fig. 2 is the process flow diagram based on phase-locked interpolator arithmetic bearing failure diagnosis of the present invention.Below in conjunction with process flow diagram to being elaborated based on phase-locked interpolator arithmetic Method for Bearing Fault Diagnosis.

(1) utilize the acceleration vibration transducer that the vibration signal in the bearing operational process is measured, obtain vibration acceleration signal as signal s to be analyzed (t), sampling length is decided to be 2 integer power, sets sample frequency according to bearing rotating speed and model;

(2) set up reference signal

$y\left(t\right)=k_2{e}^{-p_2\mathrm{<figure-callout\; id="2"\; label="t\; sin"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">t</figure-callout>}}\sin 2\mathrm{\&pi;}{f}_{2}t$

P wherein ₂Be the vibration damping coefficient, according to the p as can be known of the reasoning in the summary of the invention ₂Value do not affect amplification effect, any value in theory is for so that the larger p of the kurtosis of phase-locked amplified signal ₂Can be taken as the arbitrary value among the 1000-1200, the larger kurtosis of value is larger.f ₂For being reference signal frequency for the measured bearing damped natural frequency that dopes, can from the frequency spectrum of analyzed signal, read, namely get in the frequency spectrum resonant belt the corresponding frequency values in spectrum peak and namely get f ₂=f ₁k ₂The value that is taken as greater than 1 is the reference signal amplitude, as long as can obtain amplification effect, k ₂The larger enlargement factor of value larger, amplification effect is more obvious.

(3) utilize the phase-locked amplification expression formula after simplifying to carry out phase-locked amplification calculating, expression formula is:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right)y(t+u)\mathrm{du}$

Wherein u is the initial position of reference signal, and max (t) can directly measure for the maximum occurrences of time t is the length of measured signal s (t).

Fig. 3 is the emulation time domain waveform of the housing washer fault of adding noise.Signal length is 8192 points, and the Signal-to-Noise SNR that dyes after making an uproar is-9.87dB.As can be seen from the figure, the impact composition that dyes the rear signal of making an uproar has been submerged substantially.

Fig. 4 is the result after Fig. 3 signal is processed through phase-locked interpolator arithmetic, and as seen from the figure, fault signature composition has after treatment obtained amplification, and noise contribution has obtained inhibition.

Fig. 5 is the process flow diagram based on phase-locked interpolator arithmetic bearing fault degree diagnosis of the present invention.Below in conjunction with process flow diagram to being elaborated based on phase-locked interpolator arithmetic bearing fault degree diagnostic method.

(1) utilize the acceleration vibration transducer that the vibration signal in the bearing operational process is measured, obtain vibration acceleration signal as signal s to be analyzed (t), sampling length is decided to be 2 integer power, sets sample frequency (use based on the signal that collects in the phase-locked interpolator arithmetic bearing failure diagnosis and get final product) here according to bearing rotating speed and model;

(2) set up the reference signal that adds the fault size parameter, concrete grammar is as described below:

At first need calculate the linear velocity of rolling body motion and the pulse width that different faults causes in order to obtain this model

Bearing roller linear velocity s:

S=πdf _r

Pulse width p _x:

$p_x=\frac{d_x}{s}$

The pulse x (t) that can obtain thus the defective generation can be expressed as:

$x\left(t\right)=\left\{\begin{array}{cc}1& u<t<u+{\mathrm{<figure-callout\; id="0"\; label="p\; x"\; filenames="HDA00002698054100021.png,HDA00002698054100031.png"\; state="\{\{state\}\}">p</figure-callout>}}_x\\ 0& \end{array}\right.$

The reference signal that the impact that is produced by defective namely contains the fault degree parameter can be expressed as:

φ′ _imp(p ₂,u,f ₂,dx,d,fr)=conv(x(t),φ _imp(p ₂,u,f ₂))

φ wherein _Imp(p ₂, u, f ₂) for its expression formula of decaying exponential function be:

${\mathrm{\&phi;}}_{\mathrm{imp}}({\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,u,f_2)=e^{-p_2(t+u)}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00002698054100013.png,HDA00002698054100021.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{f}_2(t+u)$

Be φ ' _Imp(p ₂, u, f ₂, dx, d, fr) and can be expressed as φ _Imp(p ₂, u, f ₂) with the convolution of x (t), (conv is the convolution algorithm symbol).

Wherein d is that the bearing path can be determined f according to bearing designation _rFrequently can record by the sensor of special measurement rotating speed for turning.d _x(unit: mm), u is the initial position of reference signal, p for fault diameter ₂Can get the arbitrary value value for the damping coefficient of reference signal shock response in 1000-1200, the larger kurtosis of value is larger, f ₂For the measured bearing damped natural frequency that dopes is that reference signal frequency needs according to f ₁Value be defined as equaling f ₁Value.

Parameter p in the model ₂, u, f ₂Value is identical with the value of using y (t) as with reference to signal the time.

(3) utilize phase-locked interpolator arithmetic that analyzed signal is processed, detailed process is:

Make d in the model _xSpan is [0.5, max (d _x)], get a value every 0.5, get altogether

Individual d _xValue, wherein max (d _x) be maximum fault diameter, this

Individual amount is correspondence 1,2 from small to large,,

This

Individual integer as the fault level label, is NO with letter representation.I.e. 0.5 corresponding numeral 1,1 corresponding numeral 2,, 5 corresponding numerals 10,, max (d _x) corresponding numeral

Be 0.5 each standards change d of 0.5 that increases according to initial value _xValue, d of every variation _xValue, utilize the phase-locked simplification expression formula of putting that signal is carried out single treatment namely:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right){\mathrm{\&phi;}}_{\mathrm{imp}}^{\&prime;}(t+u)\mathrm{du}$

The kurtosis index of signal V after every processing is once got and processed, the record kurtosis is with d _xChanging value.

Kurtosis ks can be expressed as:

$\mathrm{ks}=\frac{\mathrm{mean}\left({\left|V\right|}^4\right)}{{\left[\mathrm{mean}\left({\left|V\right|}^2\right)\right]}^2}-2$

Wherein V is the analyzed signal after phase-locked amplification is processed, and mean is mean value.

(4) calculate fault degree eigenwert A:

What try to achieve

Choose three maximum kurtosis values among the individual kurtosis

,

, , record their corresponding integer fault level label NO (max ₁(d _x)), NO (max ₂(d _x)), NO (max ₃(d _x)) (maximum kurtosis value

Corresponding fault level label is NO (max ₁(d _x)), second largest kurtosis value

Corresponding fault level label is NO (max ₂(d _x)), the third-largest kurtosis value

Corresponding fault level label is NO (max ₃(d _x))).Sum obtains the fault degree eigenwert divided by three kurtosis sums after multiply by corresponding failure grade label with kurtosis value, can be expressed as:

$A=\frac{{\mathrm{ks}}_{{\max }_1\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_1\left(d_x\right)\right)+{\mathrm{ks}}_{{\max }_2\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_2\left(d_x\right)\right)+{\mathrm{ks}}_{{\max }_3\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_3\left(d_x\right)\right)}{{\mathrm{ks}}_{{\max }_1\left(\mathrm{dx}\right)}+{\mathrm{ks}}_{{\max }_2\left(\mathrm{dx}\right)}+{\mathrm{ks}}_{{\max }_3\left(\mathrm{dx}\right)}}$ The A value is larger when fault is larger, therefore can estimate according to A the fault size of measured bearing.

Fault degree and fault degree eigenwert graph of a relation that Fig. 6 obtains for test, wherein horizontal ordinate is fault degree value d _x, ordinate is the fault degree eigenwert A that tries to achieve.Along with the increase of fault, the fault degree eigenwert A that tries to achieve increases gradually, has proved the validity of method as seen from the figure.

Claims (6)

1. bearing fault and fault degree diagnostic method based on a phase-locked interpolator arithmetic may further comprise the steps:

(1) gathers bearing vibration signal as measured signal;

(2) set up reference signal;

(3) utilizing phase-locked interpolator arithmetic to carry out fault signature extracts and denoising;

(4) set up the reference signal that contains the fault degree parameter;

(5) utilize phase-locked interpolator arithmetic that analyzed signal is processed;

(6) calculating fault features value.

2. bearing fault and fault degree diagnostic method based on phase-locked interpolator arithmetic according to claim 1, the reference signal method for building up y (t) in the described step (2) is as follows:

$y\left(t\right)=k_2{e}^{-p_{2}t}\sin 2\mathrm{\&pi;}{f}_{2}t$

Wherein y (t) is reference signal, k ₂Be amplitude, wherein p ₂Be the damping vibration attenuation characteristic of shock response, f ₂Damped natural frequency corresponding to system.

3. bearing fault and fault degree diagnostic method based on phase-locked interpolator arithmetic according to claim 1 utilize phase-locked interpolator arithmetic to carry out fault signature and extract and denoising in the described step (3), according to the principle device process prescription of phase-locked amplification be:

Measured signal and reference signal then through the output signal v of multiplier (t) are:

v(t)=s(t)y(t)

Wherein s (t) is the bearing fault based on phase-locked interpolator arithmetic according to claim 1 and fault degree diagnostic method, and the measured signal that described step (1) collects with equation expression is:

s(t)=v _s(t)+n(t)

Wherein n (t) is random noise, v _s(t) for the bearing fault signal indication be:

$v_s\left(t\right)=\underset{t=0}{\overset{\max \left(t\right)}{\mathrm{\&Sigma;}}}{k}_1{e}^{-p_{1}t}\cos 2\mathrm{\&pi;}{f}_1\mathrm{t\&delta;}(t-n{T}_0)$ ，n=0,1,2…；

That is:

$v_s\left(t\right)=k_1{e}^{-p_{1}t}\cos 2\mathrm{\&pi;}{f}_{1}t+k_1{e}^{-p_1(t-T_0)}\cos 2\mathrm{\&pi;}{f}_1(t-T_0)+$ $k_1{e}^{-p_1(t-2T_0)}\cos 2\mathrm{\&pi;}{f}_1(t-2T_0)+...+k_1{e}^{-p_1(t-n{T}_0)}\cos 2\mathrm{\&pi;}{f}_1(t-n{T}_0)$

k ₁For the bearing fault signal amplitude is directly measured, p wherein ₁For the damping coefficient of bearing fault signal shock response according to bearing parameter measurements and calculations, f ₁Be that the corresponding frequency of spectrum peak position directly obtains T in the bearing fault signal spectrum figure resonant belt by reading for the frequency of each impact of bearing fault signal corresponding to the damped natural frequency of measured bearing ₀For the bearing fault characteristics cycle calculates by bearing parameter, all t directly measure the time in the literary composition, all δ are the impulse function identifier in the literary composition, to be the maximum occurrences of time t be that the length of measured signal s (t) is directly measured to all max (t) in the literary composition, in the literary composition all e be exponential function represent the symbol, all n are bearing rotary week number in the literary composition, represent with nonnegative integer;

Measured signal is expressed as:

s(t)=v _s(t)+n(t)

Wherein n (t) is random noise, v _s(t) be the bearing fault signal;

According to phase-locking and amplification principle, if select the signal close with tested composition and choose suitable frequency and namely measured signal is amplified and de-noising; Traditional lock-in amplifier is all selected sinusoidal signal and is adjusted cosine composition in the suitable frequency abstraction analyzed signal; For the bearing fault signal, its most basic effective constituent is the impact-attenuating signal, therefore selects the impact-attenuating signal as reference signal extraction and amplifies effective trouble unit;

Establishing reference signal at this is:

$y\left(t\right)=k_2{e}^{-p_{2}t}\sin 2\mathrm{\&pi;}{f}_{2}t$

Wherein y (t) is reference signal, k ₂For the reference signal amplitude is set as arbitrarily number greater than 1, the larger enlargement factor of value is larger, p ₂Get the arbitrary value value for the damping coefficient of reference signal shock response in 1000-1200, the larger kurtosis of value is larger, f ₂For the measured bearing damped natural frequency that dopes is that reference signal frequency is defined as equaling f ₁Value;

Measured signal and contrast signal then through the output signal of multiplier are:

v(t)=s(t)y(t)

Therefore signal v (t) is expressed as through the output signal V of integrator again:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right)y(t+u)\mathrm{du}$

Following formula is phase-locked amplification expression formula, and wherein u is the initial position of reference signal, and max (t) is that the length of measured signal s (t) is directly measured for the maximum occurrences of time t;

Following formula launches to be expressed as:

$V=k_1{k}_2{e}^{-t(p_1+p_2)}\cos 2\mathrm{\&pi;}{f}_{1}t\sin 2\mathrm{\&pi;}{f}_{2}t++k_1{k}_2{e}^{-t(p_1+p_2)+T_0{p}_1}\cos 2\mathrm{\&pi;}{f}_1(t-T_0)\sin 2\mathrm{\&pi;}{f}_{2}t+$ $...+k_1{k}_2{e}^{-t(p_1+p_2)+n{T}_0{p}_1}\cos 2\mathrm{\&pi;}{f}_1(t-n{T}_0)\sin 2\mathrm{\&pi;}{f}_2+{\&Integral;}_0^{\max \left(t\right)}\left[k_{2}n\left(t\right)\sin 2\mathrm{\&pi;}{f}_2(t+u)\right]\mathrm{du}$

Following formula launches to be expressed as:

$V=k_1{k}_2{e}^{-t(p_1+p_2)}\cos 2\mathrm{\&pi;}{f}_{1}t\sin 2\mathrm{\&pi;}{f}_{2}t++k_1{k}_2{e}^{-t(p_1+p_2)+T_0{p}_1}\cos 2\mathrm{\&pi;}{f}_1(t-T_0)\sin 2\mathrm{\&pi;}{f}_{2}t+$ $...+k_1{k}_2{e}^{-t(p_1+p_2)+n{T}_0{p}_1}\cos 2\mathrm{\&pi;}{f}_1(t-n{T}_0)\sin 2\mathrm{\&pi;}{f}_{2}t+{\&Integral;}_0^{\max \left(t\right)}\left[k_{2}n\left(t\right)\sin 2\mathrm{\&pi;}{f}_2(t+u)\right]\mathrm{du}$

Order

$V_s=k_1{k}_2{e}^{-t(p_1+p_2)}\cos 2\mathrm{\&pi;}{f}_{1}t\sin 2\mathrm{\&pi;}{f}_{2}t++k_1{k}_2{e}^{-t(p_1+p_2)+T_0{p}_1}\cos 2\mathrm{\&pi;}{f}_1(t-T_0)\sin 2\mathrm{\&pi;}{f}_{2}t+$ $...+k_1{k}_2{e}^{-t(p_1+p_2)+n{T}_0{p}_1}\cos 2\mathrm{\&pi;}{f}_1(t-n{T}_0)\sin 2\mathrm{\&pi;}{f}_{2}t$

$V_n={\&Integral;}_0^{\max \left(t\right)}\left[k_{2}n\left(t\right)\sin 2\mathrm{\&pi;}{f}_2(t+u)\right]\mathrm{du}$

Then V is expressed as:

V=V _s+V _n

It is the addition of fault-signal item and noise signal item; V wherein _sBe integration fault-signal item later, V _nBe integration noise signal item later;

Wherein

$V_s=k_1{k}_2{e}^{-t(p_1+p_2)}\left\{\right[\cos 2\mathrm{\&pi;}(f_1+f_2)t+\cos 2\mathrm{\&pi;}(f_1-f_2)t]+$

$e^{-T_0{p}_1}[\cos (2\mathrm{\&pi;}(f_1+f_2)t-T_0)+\cos (2\mathrm{\&pi;}(f_1-f_2)t-T_0)]+...+$ $e^{-{\mathrm{nT}}_0{p}_1}[\cos (2\mathrm{\&pi;}(f_1+f_2)t-n{T}_0)+\cos (2\mathrm{\&pi;}(f_1-f_2)t-{\mathrm{nT}}_0)]\}$

Work as f ₁=f ₂The time, noise item is zero, i.e. V=V _s, so the signal of integrator output:

$V=\underset{t=0}{\overset{\max \left(t\right)}{\mathrm{\&Sigma;}}}{\mathrm{Ke}}^{-(p_1+p_2)t}\cos 2\mathrm{\&pi;}(f_1+f_2)\mathrm{t\&delta;}(t-n{T}_0)$ ，n=0,1,2…；

Compare with measured signal s (t), dispelled noise contribution, and amplified the amplification of trouble unit; Namely realized the function of the amplification of denoising and fault-signal, wherein K is enlargement factor K=k ₁k ₂

Above-mentioned multiply each other and the process of integration is that phase-locked amplification process is expressed as:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right)y(t+u)\mathrm{du}$

Be the sequence of impacts signal of a string not Noise, and fault signature has obtained K and has doubly amplified; Know thus, when obtaining reference signal according to y (t) expression formula, the frequency values f in the reference signal ₂The centre frequency of analyzed signal s (t) resonant frequency is f ₂=f ₁The time, namely to utilize phase-locking and amplification principle be phase-locked amplification expression formula amplifies and carries out effective de-noising to each failure impact signal of bearing.

4. bearing fault and fault degree diagnostic method based on phase-locked interpolator arithmetic according to claim 1 are set up the reference signal that contains the fault degree parameter and are comprised the steps: in the described step (4)

In order to diagnose the bearing fault size, utilize bearing fault signal accurate model as the reference signal, introduced fault size parameter d in the model _xAt first need calculate the linear velocity of rolling body motion and the pulse width that different faults causes in order to obtain this model

Bearing roller linear velocity s:

S=πdf _r

Pulse width p _x:

$p_x=\frac{d_x}{s}$

The pulse x (t) that obtains thus the defective generation is expressed as:

$x\left(t\right)=\left\{\begin{array}{cc}1& u<t<u+p_x\\ 0& \end{array}\right.$

The reference signal that the impact that is produced by defective namely contains the fault degree parameter is expressed as:

Φ′ _imp(p ₂,u,f ₂,dx,d,fr)=conv(x(t),φ _imp(p ₂,u,f ₂))

φ wherein _Imp(p ₂, u, f ₂) for its expression formula of decaying exponential function be:

${\mathrm{\&phi;}}_{\mathrm{imp}}(p_2,u,f_2)=e^{-p_2(t+u)}\sin 2\mathrm{\&pi;}{f}_2(t+u)$

Be Φ ' _Imp(p ₂, u, f ₂, dx, d, fr) and be expressed as φ _Imp(p ₂, u, f ₂) with the convolution of x (t), conv is the convolution algorithm symbol;

Wherein d is that the bearing path is determined f according to bearing designation _rFor the sensor that turns frequently by special measurement rotating speed records; d _xBe fault diameter, unit: mm, u are the initial position of reference signal, get the arbitrary value value for the damping coefficient of reference signal shock response in 1000-1200, and the larger kurtosis of value is larger, f ₂For the measured bearing damped natural frequency that dopes is that reference signal frequency needs according to f ₁Value be defined as equaling f ₁Value.

5. bearing fault and fault degree diagnostic method based on phase-locked interpolator arithmetic according to claim 1, utilize phase-locked interpolator arithmetic that analyzed signal is processed in the described step (5) and be described as:

Make d in the model _xSpan is [0.5, max (d _x)], get a value every 0.5, get altogether

Individual d _xValue, wherein max (d _x) be maximum fault diameter, this

Individual amount is correspondence 1,2 from small to large,, 1- This

Individual integer as the fault level label, is NO with letter representation; I.e. 0.5 corresponding numeral 1,1 corresponding numeral 2,, 5 corresponding numerals 10,, max (d _x) corresponding numeral

Be 0.5 each standards change d of 0.5 that increases according to initial value _xValue, d of every variation _xValue, utilize the phase-locked simplification expression formula of putting that signal is carried out single treatment namely:

$V={\&Integral;}_0^{\max \left(t\right)}s\left(t\right){\mathrm{\&phi;}}_{\mathrm{imp}}^{\&prime;}(t+u)\mathrm{du}$

The kurtosis index of signal V after every processing is once got and processed, the record kurtosis is with d _xChanging value;

Kurtosis ks is expressed as:

$\mathrm{ks}=\frac{\mathrm{mean}\left({\left|V\right|}^4\right)}{{\left[\mathrm{mean}\left({\left|V\right|}^2\right)\right]}^2}-2$

Wherein V is the analyzed signal after phase-locked amplification is processed, || be absolute value sign, mean is mean value.

6. the process prescription that calculates fault eigenvalue in bearing fault and the fault degree diagnostic method based on phase-locked interpolator arithmetic according to claim 1, described step (6) is:

What try to achieve

Choose three maximum kurtosis values among the individual kurtosis

,

,

, record their corresponding integer fault level label NO (max ₁(d _x)), NO (max ₂(d _x)), NO (max ₃(d _x)), maximum kurtosis value Corresponding fault level label is NO (max ₁(d _x)), second largest kurtosis value

Corresponding fault level label is NO (max ₂(d _x)), the third-largest kurtosis value

Corresponding fault level label is NO (max ₃(d _x))); Sum obtains the fault degree eigenwert divided by three kurtosis sums after multiply by corresponding failure grade label with kurtosis value, is expressed as:

$A=\frac{{\mathrm{ks}}_{{\max }_1\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_1\left(d_x\right)\right)+{\mathrm{ks}}_{{\max }_2\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_2\left(d_x\right)\right)+{\mathrm{ks}}_{{\max }_3\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_3\left(d_x\right)\right)}{{\mathrm{ks}}_{{\max }_1\left(\mathrm{dx}\right)}+{\mathrm{ks}}_{{\max }_2\left(\mathrm{dx}\right)}+{\mathrm{ks}}_{{\max }_3\left(\mathrm{dx}\right)}}$ The A value is larger when fault is larger, estimates the fault size of measured bearing according to A.

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