Time Synchronous Average Based Acoustic Emission Signal Analysis on Gear Fault Detection

7/22/2019 Time Synchronous Average Based Acoustic Emission Signal Analysis on Gear Fault Detection

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Time Synchronous Average Based Acoustic Emission

Signal Analysis on Gear Fault Detection

Yongzhi Qu, Junda Zhu, David He

Department of Mechanical andIndustrial Engineering

University of Illinois at Chicago

Chicago, IL USA

[email protected]

Bin Qiu

Guangxi College of Water Resourcesand Electric Power

99 Changgang Road, Nanning,

Guangxi, China

Eric Bechhoefer

NRG SystemsHinesburg, VT USA

[email protected]

Abstract Acoustic emission (AE) has been studied as a

potential information source for machine fault diagnosis for a

long time. However, AE sensors have not yet been applied widely

in real applications. Firstly, in comparison with other sensors

such as vibration, AE sensors require much higher sampling rate.

The characteristic frequency of AE signals generally falls into the

range of 100 kHz to several MHz, which requires a sampling

system with at least 5MHz sampling rate. Secondly, the storageand computational burden for large volume of AE data is

tremendous. Thirdly, AE signal generally contains certain non-

stationary behaviors which make traditional frequency analysis

ineffective. In this paper, a frequency reduction technique and a

modified time synchronous average (TSA) based signal

processing method are proposed to identify gear fault using AE

signals. Heterodyne technique commonly used in communication

is employed to preprocess the AE signals before sampling. By

heterodyning, the AE signal frequency is down shifted from

several hundred kHz to below 50 kHz. Then a low sampling rate

comparable to that of vibration sensors could be applied to

sample the AE signals. After that, a modified tachometer less

TSA method is adopted to further analyze the AE signal feature.

Instead of performing TSA on the raw signals, the time

synchronous averaging of the first order harmonic signal isobtained and analyzed. With the presented method, no

tachometer or real time phase reference signal is required. The

TSA reference signal is directly obtained from AE signals. By

examining the smoothness of obtained wave form, a noticeable

discontinuity or irregularity could be easily observed for gear

fault diagnosis. AE data collected from seeded fault tests on a

gearbox are used to validate the proposed method. The analysis

results of the tests have shown that the proposed method could

reliably and accurately detect the tooth fault.

Keywords - time synchronous average; tach-less; heterodyne;

acoustic emission;

I. INTRODUCTIONCurrently, vibration is the most widely used tool in

diagnosis of machine fault, like bearings, gears, etc. Commonvibration sensors include accelerometer, displacement andvelocity sensors. Various time and frequency domain analysistechniques have been applied to vibration signal analysis.However, vibration signal have some drawbacks when it cometo the incipient of the machine fault. Some early sign of faultin rotation machines might not show in vibration signal butwould be caught by AE sensors [1]. If these faults could be

caught in an early stage, significant maintenance cost could besaved. Hence, acoustic emission technique began to attractresearchers attention to machine health monitoring and faultdiagnosis.

Acoustic Emission (AE) is commonly defined as transientelastic waves within a material, caused by the release of

localized stress energy. It is produced by the sudden internalstress redistribution of material because of the changes in theinternal structure of the material. Possible causes of thesechanges are crack initiation and growth, crack opening andclosure, or pitting in various monolithic materials (gear,bearing material) or composite materials (concrete, fiberglass).Thus the ability to detect AE can be used to give diagnosticsindications of component health.

In comparison with vibration analysis, AE has thefollowing advantages [2]: 1) insensitive to structural resonanceand unaffected by typical mechanical background noises; 2)more sensitive to activities of faults; 3) provide good trendingparameters; and 4) localization of measurements to themachine being monitored, i.e., AE signals are sensitive to thelocation of the faults. Challenge of using AE sensor include:The output signal from AE sensor are generally highfrequency, even as high as several MHz. Thus very highsampling frequency is required, 5M-10MHz. Other challengesinclude the high data volume, complicated feature of AEsignal, which make the data processing highly difficult.

Until now, only limited techniques have been successfullyapplied to AE signal analysis. Traditionally, only the timedomain features, like peak, total energy, standard deviation,median, AE counts, root mean square (RMS) voltage andduration have been extracted in condition monitoring [3][4].However, these are all related to the absolute energy levels ofthe measured signal. As the absolute energy could vary from

one machine to another, or vary in different locations on thesame machine, so these kinds of standard could be inaccurate.Consequently, these parameters are not ideal for fault detectionpurpose. Stochastic model based analysis methods wereproposed in [5]. In these methods, the feature of multiple AEburst must be extracted first, and then statistical model andclustering criteria are employed to do classification. Inevitablyfor these methods, large volume of data needs to be processedand baseline criteria need to be established, which make themodel less attractive. Gao et al. propose a wavelet transform


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based method to analysis AE signal, which could act as asupplement redundant method for vibration test [6]. He and Lideveloped a data mining based method to classify the conditionindicators derived from different AE data to detect fault [7].Later, Li and He introduced an EMD-based AE featurequantification method [8]. In their work, successful detectionof gear fault is achieved on AE data sampled at as low as 500kHz. Artificial neural networks (ANN) have also been adoptedfor AE signal classification [9].

For all of these methods, there are some common shortcomings. First, the AE signals are sample at several MHz,which make it difficult to process. Second, nearly all of thesepapers view the AE signal as separate energy burst, but not aconsecutive wave form just like any vibration signal. Ingeneral, the time domain features extracted from the AE signalare transient time based. These features are then comparedwith other healthy case reference. They do not give anyinterpretation of the overall AE signal dynamics along timeaxis. Take gear fault diagnosis as an example. When a smallportion of the gear is damaged or only one tooth has a crack onit, most of energy related AE burst are normal or near normal,only these burst signal generated when the faulty tooth is

meshing may have certain abnormal time domain feature. Soby statistical analysis in the above reviewed papers, the faultyAE features are not enhanced but weakened, which makesthese method have an even more hard time to conclude a fault.A more sound and efficient AE signal processing technique isrequired. Consider that one actually pre-knows someinformation about the testing object, for example, the structureof a gear box, the approximate rotation speed of the shaft, etc.In this paper, the authors aim to develop a method which couldutilize these kinds of useful information.

For vibration signal analysis, methods of interpretation ofvibration signals could be classified in three categories: timedomain analysis, frequency domain analysis and time-

frequency domain analysis. In time domain analysis, besidesthe features of the waveform itself such as mean, peak, peak topeak, crest factor, root mean square, kurtosis, etc., a moreadvanced time domain analysis, time synchronous averaging(TSA), is becoming very popular in processing the vibrationsignal [10-12]. The idea of TSA is to use the ensemble averageof the raw signal over a number of revolution in order to get anenhance signal of interest with less noise from other source.For a function x(t), digitized at a sampling interval nT,resulting in sampling in samples x(nT). Denoting the averagedperiod by mT, TSA is given as [13]:

=1

!!!

!!!

(1)

More details about TSA could be found in [14].

The successful application of TSA on vibration signalanalysis provides the possibility of using it to process AEsignal. In order to apply TSA to AE signal analysis, twoproblems must be addressed. The first problem is to reduce theamount of sampled data while not losing useful information.The second problem is to demodulate the AE signal to recoverthe machine rotation related frequency. AE signal is modulatedby the internal frequency response of the AE sensor itself. In

order to obtain clean data which only reflects the useful signalof interest, a signal demodulation and frequency reducedtechnique need to be developed.

The remainder of the paper is organized as follow. Section2 illustrates in details about the methodology. In Section 3, thesetup of the experiments for the validation of the methodologyis explained. Section 4 discusses the experiment results andillustrates how a fault is identified. Finally, Section 5

concludes the paper.

II. THE METHODOLOGYA. The Heterodyne Technique

First, take a brief look at current AE signal processingsteps. The diagram of a commonly taken procedure of AEsignal processing is given in Fig. 1.

Acoustic

emissionsensor

(100KHz-1MHz)

Pre-amplifier

Typically,20/40/60dBADconverter

Computer

post-processing

Figure 1. Traditional AE signal acquisition and preprocessing procedure

In a traditional AE signal processing procedure, all of the

data are collected and stored to computer without any advancedsignal processing. There are two disadvantages associated withthis procedure. First, it makes the data acquisition veryexpensive. Second, it will highly rely on the computer toprocess the huge volume of data.

When taking a further look at an AE signal, one will findthat the AE signal is virtually a carrier signal for the faultsignal. The information of interest is related to the load signal,not the high frequency AE carrier signal. In order to get theload signal, demodulation process is required before sampling.This demodulation process is similar to information retrieval inan amplitude/phase modulated radio frequency signal. Thecarrier signal of a medium wave is radio signal in several MHz,

while the information modulated onto that signal is audiosignal in kHz. The information is recovered by demodulatingthe radio signal. After demodulating the carrier using ananalog signal conditioning circuit, the acquisition system canthen be sampled at audio frequency (10s of kHz). The signalprocessing can then be performed at lower cost with embeddedmicrocontrollers instead of higher end computers.

The AE signal demodulator proposed in this paper wouldwork similarly to a radio frequency quadrature demodulator,effectively shifting the carrier frequency to baseband, followedby low pass filtering. The technique applied here is calledheterodyne, which could shift the frequency of the signals to anew frequency range. Mathematically, Heterodyning is basedon the trigonometric identity:

=1

2

1

2 + (2)

Further, for two signals with frequency f! and f! ,respectively, it could be written as

2 ! 2 ! =

1

2cos 2 ! !

1

2cos 2 ! + !

(3)


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Where, f!

is the carrier frequency of the modulated signal,f! is the demodulators reference input signal frequency. This

process could be explained with a simple example.

Let f! = 4Hz and f! = 5Hz, note y! = sin 2 4 t andy! = sin 2 5 t . Take their multiplication as Y= y!. y!.

Their plots are shown below in Fig. 2.

Then this multiplication signal could be low pass filtered.

The high frequency image at frequency (f!+ f

! ) will beremoved prior to sampling. This is shown in Fig. 3.

In order to successfully shift the signal to a new frequencyrange, two conditions must be satisfied: (1) Certain nonlinearoperations, typically multiplication, must be presented in theheterodyne devices. (2) The frequency components containedin two source signals must be different. Otherwise, only thehigh frequency signal is left after heterodyning.

A detailed discussion of the heterodyne technique appliedon the raw AE signal is given in the following. In general,amplitude modulation is the major modulation form for AEsignal. Although, frequency modulation and phase modulationcould present in the AE signal potentially, they are considered

trivial and will not be discussed here. The amplitudemodulation function is given in (4).

Amplitude modulation function:

!= (

!+)

! (4)

Where, U!

is the carrier signal amplitude, !

is the carriersignal frequency, m is the modulation coefficient. x is themodulated signal, note as

= ! (5)

If the modulated signal is not in a sinusoid form, it could bebreak down into the sum of sinusoid functions in the form ofFourier series.

Then, with heterodyne technique, the modulated signal withbe multiplied with a unit amplitude reference signal cos(

!t).

The result is given in the following.

!=

!+

!

!

= !+

1

2+1

2 2

!

(6)

Then substitute (5) in into Eq. (6),

!=

1

2!+1

2! +

1

2! 2

!

+1

4

![ 2

!+ + 2

!

(7)

Since U! does not contain any useful information relatedwith the modulated signal, it could be removed by detrend.From (7), it could be seen that only the modulated signal willbe preserved after low pass filtering, where the high frequencycomponents around 2

!will be removed. The diagram of the

proposed frequency down shifting system using heterodyningis shown in Fig. 4. By using the heterodyning technique, theAE data is transformed to the equivalent of vibration data.Two collected examples of faulty AE data and healthy AE dataare shown in Fig. 5.

Figure 2. The multiplication of two sinusoid signals

Figure 3. Extraction of the heterodyned signal by low pass filtering

B.AE Signal Processing Using Tach-less TSATSA is a very useful technique for analyzing vibration data.

Basically, two types of TSA algorithm are available in theliterature, i.e., TSA with tachometer, and tachometer less TSA.For TSA with tachometer, a tachometer needs to record the

shaft speed and the real time angle. But in most applications,the installation of tachometer might be expensive or evenimpossible. For tachometer less TSA algorithm, although anangular reference signal is still required, it can be deriveddirectly from the tested signal, generally vibration signal, thusno external tachometer is required.

The feasibility of extracting a phase reference signaldirectly from the vibration signal by phase demodulation hasbeen studied in the following papers. Jong et al. proposed asynchronous phase averaging method which could transform aquasi-period signal into a period signal and then perform TSA[15]. They proposed to narrow band filtered out one of themeshing harmonic. The phase variation signal is then

calculated by Hilbert transform. Then a standard periodicsignal is obtained by non-uniform sampling of the originalsignal with reference to the phase variation signal. After that, auniformly sampled periodic signal could be reconstructed byinterpolation. Later, standard TSA is calculated and plotted.This was the first paper to show that the gear fault could beidentified by discontinuity and irregularity in enhanced TSAwaveform. Bonnardot et al. introduced another tachometer lessTSA method by angular resampling [11], and later this workwas enhanced by Combet and Gelman [12]. They processed


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There are several ways to calculate the instantaneousfrequency [17]. In this work, the derivative of the unwrappedphase signal is taken. The zero crossing time is then computedfrom the instantaneous frequency. A more detailed explanationof extract phase reference is provided in [11][17].

In order to extract a phase reference signal, it is needed tofirstly perform Hilbert transform on the narrow band filteredsignal and then construct the analytic signal and calculate the

instantaneous frequency. To determine the narrow band filterrange, the meshing frequency is needed. Although according tothe shaft speed, the meshing frequency could be calculated,however, a more accurate meshing frequency is obtained fromthe power spectrum density (PSD). The PSD corresponding tothe data shown in Fig.5 is given below in Fig. 6.

Figure 6. Power spectrum of faulty and healthy data after Heterodyne

According to [15], a periodic signal can be reconstructedfrom the original signal by non-uniform sampling and timesynchronous averaging. A similar procedure is followed in thiswork. However, raw AE signal can not be transformed intoperiodic signal because AE signal has a lot of complicatedfrequency components. Hence, instead of performing TSA onthe raw AE data, a narrow band filtering is proposed to filterout the meshing harmonics and the filtered AE data will beused to perform TSA. In this paper, a zero-phase filter with abandwidth of only 2Hz is designed. Then, through classic TSAtechnique, an enhanced periodic signal of a single meshingharmonic frequency could be calculated. The procedure of themodified TSA algorithm for processing AE data is givenbelow.

The Modified TSA Procedure is listed below:

Calculate the power spectrum density. Identify thebase meshing frequency and the harmonics frequency.

Construct the analytic signal based on the meshingfrequency and the raw AE data. Narrow band filterthe analytic signal and take the unwrapped version ofthe phase, and then the angular position of the shaftcould be extracted as proposed in [11].

Narrow band filter the original data. Notice thatzero-phase filtered is required in order to preventphase shifting of the signal.

Perform TSA algorithm on the filtered data. Inspect the wave form of TSA signal for any irregular

behavior to identify gear fault.

This modified TSA algorithm is performed on a zero-phasefiltered harmonic signal instead of on the original signal. Asshown in (10), the fault related modulation function ispreserved in the meshing harmonics after filtering. It enables

us to inspect a single harmonic to detect the hidden fault. ByTSA the irregular modulation effect will be enhanced andeasily observed.

The reason why the demodulated AE signal need to benarrow band filtered is explained as follows: The demodulationprocess could only demodulate the AE signal modulated on aspecific carrier frequency. The signal modulated on otherfrequency bands will be shifted down to a frequency band

around their base bands and will act as noise. In order toenhance the signal to noise ratio, the narrow band pass filter isproposed. Classic TSA is also tested without band pass filter,the fault feature is not revealed as expected, which then lead tothis improved TSA methods.

III. EXPERIMENTAL TEST RIG CONFIGURATIONIn this section, the experiment to verify the proposed AE

signal processing method is presented. In Fig. 7, thedemodulation board (Analog devices - AD8339) and samplingdevices (NI-DAQ 6211) are shown. These devices wereprovided by NRG Systems, Inc. The demodulation boardperformed the multiplication of sensor signals and referencesignals. It is an analog device and much more affordable than a

high rate sampling board. It takes two inputs, one from the AEsensor, and another from function generator as reference signal.The basic principle of AD8339 could be explained by Gilbertcell mixers. In electronics, the Gilbert cell is commonly usedas an analog multiplier and frequency mixer. This circuitsoutput current is an accurate multiplication of the base currentsof both inputs. According to (3), it could convert the signal tobaseband and twice the carrier frequency. This demodulationboard could support up to 4 channels with analog inputs as highas 40MHz. These features make it well satisfy AE signaldemodulation requirement. The output of the demodulationboard goes to the sampling board and the high frequencycomponent is filtered out. NI-DAQ 6211 is a low frequencydata acquisition device, with a sample frequency up to 250kS/s.

Before data acquisition, one needs first to determine thefrequency of the reference signal for demodulation. Thepurpose is to down shift the AE signal frequency as low aspossible. In order to remove the carrier frequency, thereference signal frequency needs to be equal to or close to theAE carrier frequency. This is the most challenging part ofutilizing the heterodyne technique. Note that raw AE signal isa wide band signal with complicated modulation. The purposehere is to demodulate the component with highest amplitude.

Each AE sensor has its specific frequency response range,which further depends on the testing system they are mountedon. With reference to the AE sensor user manual, a coarserange of the sensor response frequency is given. In order to

identify a more accurate AE sensor response frequency, it isproposed to use a function generator with sweep function totest the system and record the output. With a wide range ofsweep frequency signal as the reference signal to demodulationboard, the demodulation result varies accordingly. Asmentioned before, the energy impact information is modulatedon high frequency carrier signals in a wide frequency band.When the strongest carrier signal is successfully demodulated,the highest amplitude will display in the output signal. Thismeans the demodulation frequency matches the strongest


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modulation frequency of the AE sensor. Otherwise, the energyrelated information will still dwell in high frequency end andtherefore would be lost after low pass filtering and sampling.With sweep frequency input, one can analyze the energy levelof the signal at different demodulation frequency. The AEsensor modulation frequency would be identified when thedemodulated AE signal have the largest energy level. By thismethod, a more accurate frequency range of the sensor outputcould be found. In the performed experiment, it was identified400kHz as the major AE carrier signal frequency. Thisfrequency is used as the demodulation reference frequency.

Figure 7. Demodulation device and data sampling board

The proposed method was then tested on a two stage splittorque gearbox. Compared with traditional gear box, the splittorque gear box has an intermediate stage which could split thetorque and change the transmission ratio between input andoutput shaft. The structure of the gear box is given in Fig. 8.Since this is speed reduction gear box, the input side and theoutput side have a 2.4 times reduction ratio.

For the faulty split torque gear box, at the output side, oneof the intermediate gears with 48 teeth had a 50% tooth loss onone of the teeth as shown in Fig.8. The location of the sensoron the gearbox is shown in Fig. 9. The AE sensor was locatedon the gear house close to the faulty gear. Note that this paperis primarily to evaluate the heterodyne technique and thefeasibility of time synchronous averaging on AE data, so arelatively large fault is created on the gear. Incipient fault likeinitial crack and tooth surface wear will be tested in the future.

Figure 8. Dynamic model of the experimental split torque gearbox

As for signal acquisition, Labview signal express softwarewas used. The data sampling rate of the acquisition could bemodified in setting options. Even if the data sample boardcould support up to 250kHz sampling rate, it was set to only100 kHz for the tests.

Figure 9. AE sensor location on test rig

In order to verify the effectiveness of the proposed method,both healthy and faulty gear box were tested with input shaftspeeds: 10Hz, 20Hz, 30Hz, 40Hz, 50Hz, and 60Hz. In the

whole experiment process, the gear box has 0 loading. Withloadings the faulty gear feature will be enlarged due to largerimpact on each tooth, and therefore the faulty feature in AEcould be more easily detected. In this 0 load experimentalsetting, the identification of gear fault is more difficult thanloaded cases.

As mention above, this gear box has a total of 2.4 timespeed reduction ratio. In table 1, the output shaft frequencyand the interested shaft (faulty gear shaft) frequency are givenunder the tested speed.

TABLE 1. OUTPUT SHAFT SPEED CORRESPONDING TO INPUT SHAFT SPEED

Input shaft speed

(Hz)

10 20 30 40 50 60

Faulty gear shaftfrequency (Hz)

5.56 11.1 16.7 22.2 27.8 33.3

Output shaftspeed (Hz)

4.17 8.33 12.5 16.7 20.8 25

IV. THE RESULTSIn order to get a consistent result, the base band meshing

signal is chosen to do TSA for all of the following result. Butthe method works as well with the meshing harmonics. Resultsshow that all 10Hz-60Hz faulty TSA signals show an obviouswave form defect. While there is faulty feature involved, someof the teeth are not meshing normally. This will affect the wave

shape in some cycles as well the overall dynamic of the shaft.Therefore, the faulty signal will have some underdevelopedwave cycles. Now, the analysis results of the experiments onthe test-rig are presented in Fig. 10 through Fig. 15.

Each figure shows the result under one operation speed.Both the fault TSA result and the healthy TSA result are shownfor comparison.


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Figure 10. Faulty and healthy TSA at 10Hz input speed over one rev.

From Fig. 10 Fig. 15, it is easy to observe the abnormalmeshing behavior corresponding to the faulty tooth. Awaveform detect, in the form of undeveloped cycles or cyclesmissing, could be seen from all of the faulty TSA data.Intuitively, since there was a 50% tooth loss, the faulty toothwould not mesh normally as other health teeth on the gear.From the perspective of AE signal, the meshing impactcorresponding to that specifically cycle is corrupted. Thus,waveform defect will be presented. While in the health case,the wave form of the TSA signal is almost pure periodic witheach cycle fully developed.





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V. CONCLUSIONSIn this paper, a new methodology for gear fault diagnosis

suing AE sensors is presented. In comparison with existingAE signal processing techniques, this technique gives aninsight interpretation of the internal physical characteristics ofthe gearbox and AE signals. Previously, researchers treatedAE signals as separate energy bursts, focusing mainly on thecharacteristic within the burst, but ignored the time continuous

features, which is closely related to the faults in a gearbox. Bycomparison of the signal features along the time axis, abnormalbehavior occurred repeatedly in a rotating machine could beextracted and detected. Specifically, heterodyning technique isutilized to demodulate the AE sensor signals at the first stage.Using the heterodyning demodulator, the AE signal frequencycan be down shifted to below 50kHz with most of the highfrequency carrier signal removed. After that, a modified TSAbased approach can be used to process the AE data. In thepresented method, the TSA signals of the meshing harmonicsinstead of the raw signals are used. By inspecting the TSAsignal waveform defect, a tooth fault can be detected. Thepresented method could be utilized on most rotational machinefault diagnosis when AE sensor is used. The system cost

could be largely reduced in comparison with traditionalmethods. This paper has established a foundation that AEsignals could be sampled at a relatively low rate while notlosing any useful information significantly. It also makes thelow cost industrial application of AE based fault detectionfeasible in practice.

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[11] F. Bonnardot, M. El Badaoui, R.B. Randall, J. Daniere, and F. Guillet,Use of the acceleration signal of a gearbox in order to perform angularresampling (with limited speed fluctuation) , Mechanical Systems andSignal Processing, Vol. 19, No. 4, pp. 766 785, 2005.

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Time Synchronous Average Based Acoustic Emission Signal Analysis on Gear Fault Detection

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