CN103076174B - A kind of bearing fault based on lock-in amplify algorithm and fault degree diagnostic method - Google Patents

Abstract

The invention discloses a kind of bearing fault based on lock-in amplify algorithm and fault degree diagnostic method.The present invention utilizes lock-in amplifier owing to having CFS center frequency stabilization, and passband is narrow, and phase-locking and amplification principle is applied to the diagnosis of bearing fault and fault degree by quality factor advantages of higher.The contrast signal established based on bearing fault signal characteristic utilizes phase-locking and amplification principle, after multiplying and integral operation, relevant to fault that information stays and amplifies, those and the incoherent noise signal of trouble unit are cut down, realizes the quick separating of noise and the location of fault.Establish a kind of reference signal adding fault degree parameter simultaneously, achieve the diagnosis of bearing fault degree in conjunction with kurtosis index.<!--1-->

Description

A kind of bearing fault based on lock-in amplify algorithm and fault degree diagnostic method

Technical field

The present invention relates to a kind of bearing fault and fault degree diagnostic method, particularly a kind of bearing fault based on lock-in amplify algorithm and fault degree diagnostic method.

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 topmost part of Bearing inner comprises rolling bearing and gear, and because these two kinds of parts are everlasting at a high speed, are run under fully loaded transportation condition, rate of breakdown is higher, will cause serious casualties and economic loss once break down.Therefore carry out condition monitoring and fault diagnosis to guaranteeing production safety to bearing, prevention major accident, reduces production cost important in inhibiting.

At present, the vibration signal processing technology based on high-speed computer is adopted to be the main flow of bearing failure diagnosis technology.The key of bearing failure diagnosis how from fault vibration signal, to extract fault signature.But because the environment facies of the operation of the actual centre bearer of engineering are when severe, its vibration signal is very complicated, containing much noise and labile factor, be a kind of typical non-stationary signal, when particularly early defect appears in Bearing inner, signal fault feature is very faint.And in engineering reality, some simple signal analysis abilities are often only possessed to the equipment of diagnosing malfunction, still certain effect is had for the obvious situation of fault, analysis result effectively often be can not get to feeble signal or the larger signal of signal to noise ratio (S/N ratio), the analytical effect of fault degree is also had much room for improvement, have impact on the efficiency of signal analysis.

Therefore how to adopt effective analysis tool and algorithm, analyze the fault of bearing and fault degree and diagnose, extracting fault signature and realize fault progression status monitoring and diagnosis, is a large difficult point of bearing being carried out to fault detection and diagnosis.

Lock-in amplifier is owing to having CFS center frequency stabilization, and passband is narrow, and quality factor advantages of higher is amplified in feeble signal and had good performance in SNR estimation and compensation.

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

Therefore the bearing fault based on lock-in amplify algorithm described herein and fault degree diagnostic method utilize the principle design algorithm of lock-in amplifier, mainly for the state of the bearing fault of significant impact being caused to study to production.After the feature fully analyzing bearing fault signal, determine the input signal of lock-in amplifier, after multiplying and integral operation, relevant to fault that information stays and amplifies, by those and the incoherent noise signal to zero of trouble unit, realize the quick separating of noise and the location of fault.Add fault degree parameter in the input signal simultaneously, achieve the diagnosis of bearing fault degree.

Summary of the invention

In order to the above-mentioned technical matters in bearing failure diagnosis and fault degree diagnosis, the invention provides a kind of bearing fault based on lock-in amplify algorithm and fault degree diagnostic method.

The technical scheme that the present invention solves the problems of the technologies described above comprises sets up input reference signal model, carries out lock-in amplify calculating, calculates fault degree.

Because bearing fault characteristics signal also has periodic feature, therefore can consider that the suitable reference signal of selection utilizes the noise signal in phase-locking and amplification principle weakening bearing burst, amplify and extract fault characteristic signals wherein.

Known by analyzing bearing fault characteristics, bearing fault signal v _st () can be expressed as

$v_s\left(t\right)=\underset{t=0}{\overset{\max \left(t\right)}{\mathrm{\&Sigma;}}}{k}_1{e}^{-p_{1}t}\cos 2\mathrm{\&pi;}{f}_1\mathrm{t\&delta;}(t-n{T}_0)$ （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 bearing fault signal amplitude can directly be measured, wherein p ₁for the damping coefficient of bearing fault signal shock response can according to bearing parameter measurements and calculations, f ₁the frequency can passed through in reading bearing fault signal spectrum figure resonant belt corresponding to spectrum peak position corresponding to damped natural frequency and each frequency of impacting of bearing fault signal of measured bearing directly obtain, T ₀for the bearing fault characteristics cycle can be calculated by bearing parameter, in literary composition, all t are the time and can directly measure, in literary composition, all δ are impulse function identifier, in literary composition, the length of maximum occurrences and measured signal s (t) that all max (t) are time t can directly be measured, in literary composition, all e are exponential function and represent symbol, in literary composition, all n are bearing rotary week number, represent by nonnegative integer.

Measured signal can be expressed as:

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

Wherein n (t) is random noise, v _st () is bearing fault signal

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

This set reference signal as:

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

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

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

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

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

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

Above formula is lock-in amplify expression formula, and wherein u is the initial position of reference signal, and the maximum occurrences that max (t) is time t and the length of measured signal s (t) can directly be measured.

Above formula launches to be expressed as:

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

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 can be expressed as:

V=V _s+V _n

I.e. being added of fault-signal item and noise signal item.Wherein V _sfor the fault-signal item after integration, V _nfor the noise signal item after integration.

Wherein

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

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

Due to f in reference signal y (t) ₂for the measured bearing damped natural frequency that dopes and reference signal frequency need according to f ₁value be defined as equaling f ₁value, i.e. f ₁=f ₂, therefore noise item V _nobtain zero, i.e. V _n=0 V=V _s, the signal V that therefore integrator exports equals:

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

Compared with measured signal s (t), dispel noise contribution, and be exaggerated the amplification of trouble unit.Namely achieve the function of the amplification of denoising and fault-signal, wherein K is enlargement factor K=k ₁k ₂

Above-mentionedly to be multiplied and the process of integration and lock-in amplify process can be expressed as:

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

The i.e. sequence of impacts signal of a string not Noise, and fault signature obtains K doubly amplifies.It can thus be appreciated that, when obtaining reference signal according to y (t) expression formula, the frequency values f in reference signal ₂the centre frequency of analyzed signal s (t) resonant frequency and f ₂=f ₁time, phase-locking and amplification principle and lock-in amplify expression formula each failure impact signal to bearing can be utilized to amplify and carry out effective de-noising.

In order to bearing fault size can be diagnosed, bearing fault signal accurate model can be utilized as with reference to signal, in model, introduce fault size parameter d _x.First need to calculate to obtain this model the pulse width that the linear velocity of rolling body motion and different faults cause

Bearing roller linear velocity s:

S=πdf _r

Pulse width p _x:

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

Pulse x (t) that can obtain defect generation thus 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 of the impact produced by defect namely containing 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))

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

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

I.e. 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 convolution algorithm symbol).

Wherein d is that bearing path can be determined according to bearing designation, f _rfrequently can be recorded by the special sensor measuring rotating speed for turning.D _xfor fault diameter (unit: mm), p ₂for the damping coefficient of reference signal shock response can get arbitrary value value in 1000-1200, the larger kurtosis of value is larger, f ₂for the measured bearing damped natural frequency that dopes and reference signal frequency need according to f ₁value be defined as equaling f ₁value.

Parameter p in model ₂, u, f ₂value and use y (t) are as identical with reference to value during signal.Make d in 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 fault level label, is NO with letter representation.The i.e. corresponding numeral 2 of 0.5 corresponding numeral 1,1,5 corresponding numerals 10, max (d _x) corresponding numeral .

According to the standards change d that initial value is 0.5 each increase by 0.5 _xvalue, often changes a d _xvalue, utilizes phase-locked simplified expression of putting to carry out single treatment to signal, and asks for the kurtosis index after process, and 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 lock-in amplify process, and mean is mean value.

What try to achieve choose three maximum kurtosis values among individual kurtosis, record the integer fault level label corresponding to them, after being multiplied by corresponding failure grade label with kurtosis value, sum obtains fault degree eigenwert divided by three kurtosis sums.

Technique effect of the present invention is: utilize lock-in amplifier owing to having CFS center frequency stabilization, passband is narrow, and phase-locking and amplification principle is applied to the diagnosis of bearing fault and fault degree by quality factor advantages of higher.The contrast signal established based on bearing fault characteristics utilizes phase-locking and amplification principle, after multiplying and integral operation, relevant to fault that information stays and amplifies, by those and the incoherent noise signal to zero of trouble unit, realize the quick separating of noise and the location of fault.Establish a kind of reference signal adding fault degree parameter simultaneously, achieve the diagnosis of bearing fault degree in conjunction with kurtosis index.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

Fig. 1 is the chief component figure based on lock-in amplify algorithm bearing failure diagnosis of the present invention.

Fig. 2 is of the present invention based on lock-in amplify algorithm bearing failure diagnosis process flow diagram.

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

The result of Fig. 4 after lock-in amplify algorithm process.

Fig. 5 is the process flow diagram based on the diagnosis of lock-in amplify algorithm bearing fault degree in the present invention.

Fig. 6 utilizes in the present invention to diagnose based on lock-in amplify algorithm bearing fault degree the fault degree and fault degree eigenwert graph of a relation that obtain.

Embodiment

Fig. 1 is the chief component figure based on lock-in amplify algorithm bearing failure diagnosis of the present invention.Two parts are diagnosed to form based on lock-in amplify algorithm bearing failure diagnosis by bearing failure diagnosis and bearing fault degree

Fig. 2 is the process flow diagram based on lock-in amplify algorithm bearing failure diagnosis of the present invention.Be described in detail to based on lock-in amplify algorithm Method for Bearing Fault Diagnosis below in conjunction with process flow diagram.

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

(2) reference signal is set up

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

Wherein p ₂for vibration damping coefficient, according to the known p of the reasoning in summary of the invention ₂value do not affect amplification effect, in theory can value arbitrarily, in order to make the larger p of kurtosis of signal after lock-in amplify ₂can be taken as the arbitrary value in 1000-1200, the larger kurtosis of value is larger.F ₂for the measured bearing damped natural frequency for doping and reference signal frequency, can read from the frequency spectrum of analyzed signal, namely getting the frequency values composed corresponding to peak in frequency spectrum resonant belt and namely getting f ₂=f ₁.K ₂for reference signal amplitude, as long as be taken as the value being greater than 1 can be amplified effect, k ₂the larger enlargement factor of value larger, amplification effect is more obvious.

(3) utilize the lock-in amplify expression formula after simplifying to carry out lock-in amplify 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 the maximum occurrences of max (t) for time t and the length of measured signal s (t) can directly be measured.

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

Fig. 4 is the result of Fig. 3 signal after lock-in amplify algorithm process, and as seen from the figure, fault signature composition after treatment obtains amplification, and noise contribution obtains suppression.

Fig. 5 is the process flow diagram based on the diagnosis of lock-in amplify algorithm bearing fault degree of the present invention.Be described in detail to based on lock-in amplify algorithm bearing fault degree diagnostic method below in conjunction with process flow diagram.

(1) acceleration vibration transducer is utilized to measure the vibration signal in bearing operational process, obtain vibration acceleration signal as signal s (t) to be analyzed, sampling length is decided to be the integer power of 2, according to bearing rotating speed and model setting sample frequency (using the signal based on collecting in lock-in amplify algorithm bearing failure diagnosis here);

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

First need to calculate to obtain this model the pulse width that the linear velocity of rolling body motion and different faults cause

Bearing roller linear velocity s:

S=πdf _r

Pulse width p _x:

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

Pulse x (t) that can obtain defect generation thus 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 of the impact produced by defect namely containing 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))

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

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

I.e. 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 convolution algorithm symbol).

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

Parameter p in model ₂, u, f ₂value and use y (t) are as identical with reference to value during signal.

(3) utilize lock-in amplify algorithm to process analyzed signal, detailed process is:

Make d in 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 fault level label, is NO with letter representation.The i.e. corresponding numeral 2 of 0.5 corresponding numeral 1,1,5 corresponding numerals 10, max (d _x) corresponding numeral .

According to the standards change d that initial value is 0.5 each increase by 0.5 _xvalue, often changes a d _xvalue, utilizes phase-locked simplified expression of putting to carry out single treatment namely to signal:

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

Often process the kurtosis index of once getting the rear signal V of process, 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 lock-in amplify process, and mean is mean value.

(4) fault degree eigenwert A is calculated:

What try to achieve three maximum kurtosis values are chosen among individual kurtosis , , , record the integer fault level label NO (max corresponding to them 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))).After being multiplied by corresponding failure grade label with kurtosis value, sum obtains fault degree eigenwert divided by three kurtosis sums, can be expressed as:

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

Fig. 6 tests the fault degree and fault degree eigenwert graph of a relation that obtain, and wherein horizontal ordinate is fault degree value d _x, ordinate is the fault degree eigenwert A tried to achieve.As seen from the figure along with the increase of fault, the fault degree eigenwert A tried to achieve increases gradually, demonstrates the validity of method.

Claims (3)

1., based on bearing fault and the fault degree diagnostic method of lock-in amplify algorithm, comprise the following steps:

(1) bearing vibration signal is gathered as measured signal;

(2) reference signal is set up;

(3) lock-in amplify algorithm is utilized to carry out fault signature extraction and denoising;

(4) reference signal containing fault degree parameter is set up;

(5) lock-in amplify algorithm is utilized to process analyzed signal;

(6) calculating fault features value;

Reference signal method for building up y (t) in 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 ₂for amplitude, wherein p ₂for the damping coefficient of reference signal shock response, in 1000-1200, get arbitrary value value, f ₂corresponding to the damped natural frequency of system;

Utilize lock-in amplify algorithm to carry out fault signature extraction and denoising in described step (3), process prescription is by the principle according to lock-in amplify:

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

v(t)＝s(t)y(t)

The wherein measured signal that collects for described step (1) of s (t), with equation expression is:

s(t)＝v _s(t)+n(t)

Wherein n (t) is random noise, v _st () is expressed as bearing fault signal:

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

F ₁corresponding to the damped natural frequency of measured bearing

That is:

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

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

Measured signal is expressed as:

s(t)＝v _s(t)+n(t)

Wherein n (t) is random noise, v _st () is bearing fault signal;

According to phase-locking and amplification principle, for bearing fault signal, its most basic effective constituent is impact-attenuating signal, therefore selects impact-attenuating signal as reference signal extraction and amplifies effective trouble unit;

This set reference signal as:

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

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

Measured signal and contrast signal 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:

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

Above formula is lock-in amplify expression formula, and wherein u is the initial position of reference signal, and the maximum occurrences that max (t) is time t and the length of measured signal s (t) are directly measured;

Above formula launches to be expressed as:

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

Above formula launches to be expressed as:

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

Order

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

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

Then V is expressed as:

V＝V _s+V _n

I.e. being added of fault-signal item and noise signal item; Wherein V _sfor the fault-signal item after integration, V _nfor the noise signal item after integration;

Wherein

$\begin{array}{c}{V}_s=k_1{k}_2{e}^{-t(p_1+p_2)}\left\{\right[\cos 2\mathrm{\&pi;}(f_1+f_2)t+\cos 2\mathrm{\&pi;}(f_1-f_2)t]+\\ e^{-T_0{p}_1}[\cos (2\mathrm{\&pi;}(f_1+f_2)t-T_0)+\cos (2\mathrm{\&pi;}(f_1-f_2)t-T_0)]+...+\\ e^{-n{T}_n{p}_1}[\cos (2\mathrm{\&pi;}(f_1+f_2)t-n{T}_0)+\cos (2\mathrm{\&pi;}(f_1-f_2)t-n{T}_0)]\}\end{array}$

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

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

Compared with measured signal s (t), dispel noise contribution, and be exaggerated the amplification of trouble unit; Namely achieve the function of the amplification of denoising and fault-signal, wherein K is enlargement factor K=k ₁k ₂

Above-mentionedly to be multiplied and the process of integration and lock-in amplify procedural representation are:

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

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

In described step (4), the reference signal set up containing fault degree parameter comprises the steps:

In order to bearing fault size can be diagnosed, utilize bearing fault signal accurate model as with reference to signal, in model, introduce fault size parameter d _x; First need to calculate to obtain this model the pulse width that the linear velocity of rolling body motion and different faults cause

Bearing roller linear velocity s:

s＝πdf _r

Pulse width p _x:

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

Pulse x (t) obtaining defect generation is thus expressed as:

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

The reference signal of the impact produced by defect namely containing fault degree parameter represents:

φ' _imp(p ₂,u,f ₂,dx,d,fr)＝conv(x(t),φ _imp(p ₂,u,f ₂))

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

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

I.e. 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 convolution algorithm symbol;

Wherein d is that bearing path is determined according to bearing designation, f _rfrequently recorded by the special sensor measuring rotating speed for turning; d _xfor fault diameter, unit: mm, u are the initial position of reference signal, p ₂for the damping coefficient of reference signal shock response gets arbitrary value value in 1000-1200, the larger kurtosis of value is larger, f ₂for the measured bearing damped natural frequency that dopes and reference signal frequency need according to f ₁value be defined as equaling f ₁value, f ₁corresponding to the damped natural frequency of measured bearing.

2. the bearing fault based on lock-in amplify algorithm according to claim 1 and fault degree diagnostic method, utilizes lock-in amplify algorithm to carry out process to analyzed signal and is described as in described step (5):

Make d in bearing fault signal accurate 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 fault level label, is NO with letter representation; The i.e. corresponding numeral 2 of 0.5 corresponding numeral 1,1,5 corresponding numerals 10, max (d _x) corresponding numeral

According to the standards change d that initial value is 0.5 each increase by 0.5 _xvalue, often changes a d _xvalue, utilizes phase-locked simplified expression of putting to carry out single treatment namely to signal:

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

Often process the kurtosis index of once getting the rear signal V of process, record kurtosis is with d _xchanging value;

Kurtosis ks is expressed as:

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

Wherein V is the analyzed signal after lock-in amplify process, || be absolute value sign, mean is mean value, d _xfor fault diameter, u is reference signal initial position, and s (t) is measured signal, φ ' _imp(t+u) be described φ ' _impt () has carried out the displacement of u.

3. the bearing fault based on lock-in amplify algorithm according to claim 2 and fault degree diagnostic method, the process prescription calculating fault eigenvalue in described step (6) is:

What try to achieve three maximum kurtosis values are chosen among individual kurtosis d _xfor fault diameter, record the integer fault level label NO (max corresponding to them 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))); After being multiplied by corresponding failure grade label with kurtosis value, sum obtains fault degree eigenwert divided by three kurtosis sums, is expressed as:

$A=\frac{{\mathrm{ks}}_{{\max }_1\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_1\left(d_x\right)\right)+{\mathrm{ks}}_{{\max }_2\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_2\left(d_x\right)\right)+{\mathrm{ks}}_{{\max }_3\left(\mathrm{dx}\right)}*\mathrm{NO}\left({\max }_3\left(d_x\right)\right)}{{\mathrm{ks}}_{{\max }_1\left(\mathrm{dx}\right)}+{\mathrm{ks}}_{{\max }_2\left(\mathrm{dx}\right)}+{\mathrm{ks}}_{{\max }_3\left(\mathrm{dx}\right)}}$

When fault is larger, A value is larger, estimates the fault size of measured bearing according to A.