Novel method for rollingassessmentA tachometaveraged envelope featur

David Siegel a,n, Hassan Al-Atat a

John Snyder b, Jay Lee a

a Center for Intelligent Maintenance Systems, Universityb Techsolve Inc, 6705 Steger Drive, Cincinnati, OH 4523

a r t i c l e i n f o

Article history:

Received 7 December 2010

om a

signal

with

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outer

Contents lists available at SciVerse ScienceDirect

journal homepage: www.elsevier.com/locate/ymssp

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing 29 (2012) 3623760888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ymssp.2012.01.003n Corresponding author. Tel.: 1 513 290 8163.E-mail address: siegeldn@mail.uc.edu (D. Siegel).race of the rolling element bearing. Future work looks to further investigate this

proposed technique for data collected during a run to failure test in order to consider itsindication that can determine the health of rolling element bearings. Data fr

bearing test-rig is used to facilitate the comparison and evaluation of the

processing methods. Vibration data was collected from the test-rig for bearings

different levels of degradation. The calculated vibration features from the tachom

less synchronously averaged envelope (TLSAE) technique are compared to the

feature extraction techniques; with the synchronous average method providing a

bearing vibration features that can distinguish all three levels of damage on thetachometer signal that is representative of the impact due to a bearing defect. This

synthesized tachometer signal is combined with the high frequency envelope method

to perform synchronous averaging on the envelope signal, resulting in a defect

synchronous envelope spectrum in which the frequency content is in terms of the

fault frequency orders. The proposed method is further compared and evaluated with

other existing methods, in particular to the traditional Fourier Transform technique, the

bearing envelope analysis technique, and the empirical mode decomposition signal

processing methods on the basis of whether each method provides an enhanced level ofReceived in revised form

17 December 2011

Accepted 8 January 2012Available online 27 January 2012

Keywords:

Synchronous averaging

Hilbert transform

Envelope analysis

Bearing health assessmentelement bearing healther-less synchronouslye extraction technique

, Vishwesh Shauche a, Linxia Liao a,

of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072, United States

7-3097, United States

a b s t r a c t

The assessment and diagnosis of bearing health using vibration data has been a research

topic of interest for many years and includes developments in an assortment of signal

processing methods and classication algorithms. This paper investigates detecting

bearing degradation at different levels of damage, in that estimating the bearing health

at the various stages of degradation is important for predicting failure as well as making

maintenance decisions. The proposed technique does not require a measure of the

rotational shaft speed or bearing cage speed, which makes it very suitable in certain

applications in which it is very difcult or not cost effective to measure the rotational

speed. To effectively estimate the bearing health state, a novel tachometer-less

synchronously averaged envelope (TLSAE) signal processing and feature extraction

technique for rolling element bearing is proposed. The Tachometer-Less Synchronous

Averaged Envelope (TLSAE) method consists of rst using a narrow band pass lter

around a calculated bearing fault frequency of interest and using the derivative of the

phase of the Hilbert Transform of this narrow band signal to generate a synthesized

bearing using vibration data is presentethe proposed method. In Section 3, theexperimental test-rig used for the data col

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 363ection 2, a review of existing signal processing techniques for rolling elementd. The described methods will be later used to compare the results withdetailed description of the proposed method is presented. In Section 4, thelection and testing of the rolling element bearing is presented. In Section 5, theapplicable for detecting early or more advanced stages of bearing degradation.The paper is organized as follows: In Smerits for early detection of incipient bearing damage and whether it provides a

consistent monotonic trend from spall initiation to bearing failure.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Bearing diagnostics has been a topic of research interest for over 20 years, which has fostered many developments inimproved methods for signal processing, as well as improvements in algorithms for anomaly detection, classication andfailure prediction [1]. Considering that rolling element bearings are one of the key components for rotating machinerysuch as machine tools, motors, gearboxes, turbo-machinery, among others; the research interest in developingimprovement methods for bearing health monitoring and prognostics is warranted by the prevalent use of bearings andthe impact bearing failure has on the logistics and maintenance cost and downtime for these various applications [2].Previous evaluation studies on signal processing and feature extraction techniques for bearing health assessment haveeither limited the study to a comparison between two techniques; or evaluated each method with a bearing with only onelevel of damage. As mentioned in Qiu et al. [3], the bearing degradation stage can be divided into different stages; at theearly degradation stage an envelope demodulation technique might allow for easier detection of characteristic peaks in thevibration spectrum that are correlated with bearing outer and inner race damage. Limiting the study to bearings with onlyone level of damage does not allow for an understanding of which techniques provide the most robust features based onthe level of degradation and damage in the bearing.

Other past studies have focused on timefrequency representations and have compared the use of the continuouswavelet transform to other timefrequency methods. The timefrequency information that is provided by performingthe wavelet transform of the bearing vibration allows for detecting the impacts due to either outer race or inner racedamage, the visual information and calculated time difference between the impacts provide diagnostic information toclassify whether the bearing is in a healthy or degraded condition [4]. Peng et al. [5] compared the continuouswavelet transform to the empirical mode decomposition Hilbert Huang Transform timefrequency method, and concludedthat the Hilbert Huang Transform provides better time and frequency resolution compared to the wavelet transform. TheHilbert Huang Transform and empirical mode decomposition technique developed by Huang et al. [6] has been used as aneffective signal processing technique for non-stationary phenomena including machine diagnostics and structural healthmonitoring applications. The use of features extracted from the intrinsic mode functions (IMF) such as the energy level foreach mode can also be used to determine the health of the mechanical components and systems; the use of this techniquewas demonstrated for vibration signals from a helicopter health and usage monitoring system and provided indicators thatcould clearly classify the degraded transmission system from the healthy system [7]. In Wu and Qu [8], investigation of theIMFs is used to provide root cause analysis for the higher than normal compression vibration; the abnormal pipe excitingcan be seen by the noticeable amplitude modulation revealed by the time domain signal of one of the IMFs.

The use of synchronous averaging using a tachometer signal and accelerometer have been successfully used forgear health assessment and diagnosis since the gear mesh frequencies and other indicators are synchronous withthe shaft order; the synchronous average provides an enhancement in the signal to noise ratio since the random noiseis reduced during the averaging [9] Applying synchronous averaging for rolling element bearings is a challenge dueto the bearing fault frequencies being non-synchronous with the shaft speed. For the rolling element bearing application,the previous use of synchronous averaging required a tachometer signal based on the rotational speed of the bearing cage;however, this was done in a laboratory setting and in most application it is not feasible to have a tachometersignal that can measure the rotational speed of the cage [10]. In a previous evaluation study of signal processingtechniques for rolling element bearings [27], it was noted that the bearing envelope analysis method showed the bestresults for early detection and this prompted an improved method that captured some of the fundamental principles of theenvelope analysis method. In this particular study, a signal processing technique is developed for rolling element bearingdiagnosis that performs synchronous averaging based on a novel method that estimates the bearing fault frequency andgenerates a synthesized pulse train that is representative of the bearing fault frequency impact. The synchronousaveraging is applied using this synthesized tachometer signal for the envelope spectrum; the features extracted from thisparticular signal consist of the peak information at the bearing fault frequencies. This particular method is valid for smalluctuations in rotational speed and does not require a tachometer signal for the shaft or for the bearing cage. Featuresextracted using traditional signal processing and feature extraction methods such as statistical based features such as rootmean square, kurtosis, as well as frequency domain features such as the magnitude at bearing characteristic frequencies,as well as the energy of the decomposed signals from the empirical mode decomposition were used as a way to evaluatedand compare each of the signal processing methods. By conducting this study, the advantages of each signal processingmethod at the three levels of bearing degradation tested can be used to form a knowledge base of which technique is most

results from each signal processing method including the new proposed synchronous averaging envelope method arepresented and discussed.

2. Existing signal processing methods for bearing health assessment and fault diagnosis

2.1. Time domain and Fourier transform based feature extraction

Overall vibration levels as well as statistical based indicators are the features extracted from the time domain vibrationsignal that have been used in previous bearing diagnostic techniques; there is a level of correlation between the magnitudeof these time domain features and the level of degradation for the rolling element bearing. The root mean square ofthe vibration signal is one of the common time domain features used in bearing health monitoring and is shown in Eq. (1).A common statistical feature extracted from the time domain signal is the statistical standardized fourth moment knownas kurtosis, the equation used to calculate the kurtosis feature is provided in Eq. (2) [11]:

RMS

1

N

XNi 1

xi2vuut 1

Kurtosis 1N

XNi 1

xix4s4

2

An example time domain vibration signal at 1500 rpm is provided in Fig. 1; note that there is a difference in the overallvibration magnitude for the health new bearing when compared with the vibration level for the bearings with differentlevels of scratch damage. Features such as RMS should be able to capture this difference in the time domain signal for thebearings with outer race damage compared to the new healthy bearing; however, an overall increase in vibration level fora mechanical system that consists of gears, bearings and shafts could be due to shaft unbalance or misalignment or achipped gear tooth and not necessarily due to bearing degradation. Vibration indicators such as RMS that are onlyindicative of overall level in the vibration can only provide an indication on the overall health status of the system butprovide limited root cause and diagnosis information that can determine that the bearing degradation is the cause for theincrease in vibration.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376364Fig. 1. Time domain vibration signal: (a) time signal for new bearing 1, (b) time signal for bearing with level 1 scratch damage, (c) time signal for bearingwith level 2 scratch damage, (d) time signal for bearing with level 3 scratch damage.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 365For traditional frequency domain bearing health assessment methods, the bearing fault frequencies are key features

Fig. 2. Frequency domain vibration signal: (a) frequency domain signal for new bearing 1, (b) frequency domain signal for bearing with level 1 scratchdamage, (c) frequency domain signal for bearing with level 2 scratch damage, (d) frequency domain signal for bearing with level 3 scratch damage.that are extracted from the frequency spectrum, since these particular peaks are associated with damage in a particularlocation of a rolling element bearing [12]. The particular equations used to calculate the bearing fault frequencies as wellas the bearings that were tested are provided in Section 4, example plots are shown in this section to illustrate the generalapproach of using the traditional FFT method. The frequency domain representation of the vibration signal for 1500 rpm isshown in Fig. 2; there is a clear difference in the frequency domain signal for the bearings with scratch damage andthe normal baseline bearing. These particular bearings have increasing levels of scratch damage on the outer race and thefrequency corresponding to outer race damage (BPFO) is at approximately 206 Hz. Note that this particular peak in thefrequency domain is clearly higher for the bearing with the second and third level of scratch damage; however the peak isactually lower in magnitude for the bearing with level 1 scratch damage when compared to the normal bearing. Thisprovides motivation for using other processing methods for detecting incipient levels of bearing damage.

2.2. Empirical mode decomposition frequency extraction method

The empirical mode decomposition (EMD) technique decomposes the time signal into a set of intrinsic mode functions(IMFs). This decomposition method was rst developed by Huang et al. [6] and recent interest has seen its application in awide variety of signal processing applications. With regard to machine condition monitoring, this method has been usedfor timefrequency visualization of rotating machinery defects [5]. In particular, some studies have indicated that thefeatures from the decomposed signals can be used to differentiate between a healthy and degraded bearing condition[7,13]. Due to the recent interest in EMD, the study compares the EMD method to the other bearing signal processing andfeature extraction methods. The interested reader is referred to [6] for a complete description on the decompositionprocess and how it can be used for timefrequency visualization.

Although a recently popular technique, there are several considerations or attempts made to improve the decomposi-tion process. Noise assisted techniques or improved spline tting techniques have been proposed to improve the empiricalmode decomposition method [14,15]. However, one major concern with the empirical mode decomposition is its limitedfrequency resolution and its inability to separate closely space harmonics [16]. In particular, a theoretical study conductedby Feldman [17] indicated that closely spaced harmonics with a frequency ratio less than 2/3 could not be separated byEMD regardless of the amplitude ratio. This limited frequency resolution makes it quite unsuitable for diagnosis ofmechanical systems; however, this study still compares the extracted features from the decomposed signal with vibrationindicators that are indicative of overall machine health.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376366The EMD technique was applied to the bearing vibration signals collected from the test-rig and the rst 7 intrinsicmode functions are shown for the rst normal bearing that was tested in Fig. 3. In this particular case, the signal consistedof 12 intrinsic mode functions and notice that the rst few IMFs are much higher in energy level than each successive IMF.The results of the EMD decomposition are shown for the bearing with the smallest scratch damage in Fig. 4. From visual

Fig. 3. Intrinsic mode functions (17) from normal bearing 1 vibration signal.

Fig. 4. Intrinsic mode functions (17) from bearing with scratch level 1 vibration signal.

Fig. 5. Comparing RMS ratio values for each IMF number for a bearing with scratch damage compared to normal bearings.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 367observation it is hard to distinguish the IMFs from the scratched bearing from the normal bearing; however, extractingfeatures from the IMF signals might provide insight on the condition of the bearing.

In prior work [7], the energy level at each intrinsic mode function provided a useful set of features for classifying thehealth condition of a rotorcraft transmission system; the RMS value for each IMF was extracted in this study after the EMDdecomposition. For each IMF, an RMS value was calculated for all 6 bearings, a ratio between the RMS values for eachbearing was compared to the RMS value for the baseline value from normal bearing 1. Fig. 5 shows the ratio between theRMS values for the bearings with outer race damage and the three normal bearings; IMFs 1-4 and IMFs 8-9 show a muchlarger value in RMS value for the bearings with outer race damage when compared with the normal bearings.2.3. Bearing envelope analysis feature extraction method

The underlying principle in the bearing envelope analysis feature extraction method is that a defect in the bearing inneror outer race creates an impact that excites the high frequency modes of the system. This creates an amplitude modulationphenomenon at the high frequency modes that are excited by the bearing impact; the modulated signal is the bearingcharacteristic frequency which could be the BPFO or BPFI frequency depending on the location of the bearing damage.For a very complete tutorial on bearing diagnostics, including the bearing envelope analysis method, the interested readeris referred to [18]. In this manuscript, selected aspects are reviewed for clarity and also to lead into the proposedsynchronous average method which aims to enhance the envelope method.

A ow chart for the bearing envelope analysis method is illustrated in Fig. 6. It consist of rst identifying a highfrequency resonant peak, choosing an appropriate band pass lter, using the Hilbert Transform and taking the magnitudeof the analytical signal to obtain the envelope; and lastly taking the Fourier Transform of the envelope signal andextracting the peak information at the bearing fault frequencies.

Perhaps the most important aspect regarding bearing envelope analysis is the selection of a suitable band-pass lterprior to performing the demodulation. In earlier work, the use of modal testing for nding the structural resonances of thesystem or comparing spectrums of a known good and faulted condition were used for selecting the demodulation location[18]. Modal testing would provide a set of potential natural frequencies to consider; however, it is unlikely to know whichvibration mode would be excited by the localized bearing fault a priori. Although effective, spectral comparison wouldrequire historical data in which a particular fault has occurred, this again would restrict this method if historical data is notavailable.

More recently, the use of spectral kurtosis has been demonstrated to be an effective technique for selecting the mostsuitable demodulation band for performing bearing envelope analysis and does not require historical data for guiding theselection of the demodulation band. For a more complete discussion on spectral kurtosis and the kurtogram, the interestedreader is referred to [1921]; however, a brief review is provided in order to highlight the overall concept and how it canbe applied to bearing condition monitoring. Kurtosis as a vibration condition indicator has been used in machine condition

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376368monitoring for quite some time [22]; the physical nature of localized gear or bearing faults would produce impulses andimpacts that would be characterized by higher kurtosis values. As opposed to a global calculation across the entirefrequency spectrum, the spectral kurtosis can be used to provide an indication of which frequency band contains themaximum level of impulsiveness. This technique can serve two uses for the vibration based condition monitoring; theselection of the optimum band-pass lter for envelope analysis, and for machine surveillance [20]. In this study, it was

Fig. 6. Bearing envelope analysis feature extraction method ow diagram.used for both facets, but this section focuses discusses how it can be used for selecting the demodulation band. Thecalculation procedure consists of rst performing a short time Fourier Transform (STFT) on the measured accelerometervibration signal. The STFT result can be denoted as H(t,f); the average value of the fourth power of H(t,f) divided by themean square value of H(t,f) gives the kurtosis value as a function of frequency:

Kf /H4t,f S

/H2t,f S22 3

The kurtogram was calculated using the code available at [23], in which the short time Fourier Transform and theclassical kurtosis calculation were selected. The results of performing the kurtogram calculation on are provided in Fig. 7.The results show a signicantly high kurtosis value at approximately 1800 Hz; this result can be used to guide the band-pass lter center frequency and bandwidth. The chosen band-pass lter based on the kurtogram results is a Chebyshevband pass lter of order 9; a center frequency of 1875 Hz and the band-pass frequency range is chosen at 18757840 Hz toinclude some of the higher harmonics of the bearing fault frequencies. This band-pass lter was used for both the proposedsynchronous average envelope spectrum method as well as the conventional envelope spectrum. Section 3 presentsthe synchronous average method along with plots of the envelope spectrum from both methods for direct comparison.Section 5 also provides a comparison of both methods with tabular and graphic results of the extracted vibration features.

3. Novel method using synchronous averaging signal processing technique for rolling element bearings

The advantages of using synchronous averaging for gear or shaft related fault diagnosis is well established; however,amending that approach for non-synchronous vibration frequencies such as the bearing fault frequencies remainsa challenge. Ideally, a measurement of the rotational speed of the cage could provide a method for performing thesynchronous averaging for bearings but this is not always practical in a real application [10]. The particular approachadopted here is shown as a ow chart in Fig. 8, and in more detail in Fig. 9, in which each signal processing step is shownwith a respective plot.

The rst initial step is to band pass lter around a calculated bearing fault frequency of interest; the band pass lterlimits should be chosen in a very narrow band. In this study, the method was applied to a mechanical system in which the

0.180.160.140.120.100.080.060.040.02

010 2 3 4 5 6 7 8 9 10

Fig. 8. Flow chart for tachometer-less synchronously averaged envelope spectrum (TLSAE) method for rolling element bearings.

0

3

3.6

4

4.6

5

5.6

6

6.6

7

stft-kurt.2 - Kmax = 8.8 @ Nw = 27, fc = 1796.875 Hz

FREQUENCY (Hz)0

8

7

6

5

4

3

2

1

01000 2000 3000 4000 5000

Fig. 7. Kurtogram plot using STFT method and classical kurtosis calculation: result is from a vibration signal collected on the experimental test-rig.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 369

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 3623763703.5

3

2.5

2

1.5

1

0.5

0

0.25

0.2

0.15

0.1

0.05

x10-3

0.3

0.2

0.1

0

0.18

0.16

0.14

0.12

0.1

0.08bearing shaft speed was kept at a nominal xed speed; further investigation is being considered to investigate thelimitations of this method with regard to speed uctuations.

In this case study, the limits were chosen to be 5 Hz plus or minus the calculated bearing fault frequency. The next stepperforms the Hilbert Transform on the ltered signal, the Hilbert Transform is shown in Eq. (4) and is dened as a timedomain convolution between 1/(pt) and the original signal x(t):

yt 1p PZ 11

xttt dt 4

The original signal, x(t), and the Hilbert Transform of the signal, y(t), form the analytical signal which is provided inEq. (5); there is a corresponding envelope and phase of this analytical signal which are shown in Eqs. (6) and (7) [24]. Thephase information of this narrow band signal is a key aspect and allows for the calculation of the instantaneous frequencywhich is used for generating the synchronized tachometer signal:

zt xt jyt 5

at xt2yt21=2 6

ct arctanyt=xt 7There are a few methods for calculating the instantaneous frequency; in this current work the derivative of the

unwrapped phase signal is used. Calculating the instantaneous frequency of this signal provides an estimation of thebearing fault frequency pulses as a function of time. The concept of instantaneous frequency is not well dened ifthe signal contains several frequency components [25] but in this particular instance a narrow band pass lter is used prior

TACH SIGNAL

100050052.59552.5952.58552.5852.57552.56552.56 0

-0.1

-0.2

-0.3

0.06

0.04

0.02

0

0.22

0.2

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

1500

0 1 2 3 4 5 6 7 8 9 10

2000 250052.57

Fig. 9. Step by step diagram of tachometer-less synchronously averaged envelope spectrum (TLSAE) method for rolling element bearings.

to performing the Hilbert Transform and the instantaneous frequency calculation. From the estimated frequencyinformation, a synthesized tachometer signal can be generated from this information; a more detail explanation of thisparticular technique that generates a synthesized tachometer pulse train is provided in [26].

Fig. 9 provides a visual ow chart of the proposed processing method as well as intermediate results of the variousprocessing steps. The instantaneous frequency calculation and synthesized tachometer signal are processed in parallelwith the conventional demodulation step used in bearing envelope analysis. The processed result of the instantaneousfrequency is shown in Fig. 9; there are minor uctuations in the bearing fault frequency impact even though the motor inthe bearing test-rig is set to run at a constant rotational speed.

Since this method is performing the synchronous averaging for the envelope spectrum, a portion of the previouslydescribed high frequency envelope method is used to calculate the envelope signal. The tachometer signal along with theenvelope signal allows the synchronous averaging to be performed. The nal output is a defect synchronous envelopespectrum in which the frequency content is in terms of the fault frequency orders.

In this particular example, 18 averages were used when performing the synchronous averaging, which results in anorder resolution of 0.1. Two comparative plots are shown to illustrate the improved signal to noise ratio and enhancedestimation of the bearing fault frequency peak information. The example shown in Fig. 10 compares the traditionalenvelope spectrum to the defect synchronous envelope spectrum using the proposed TLSAE method. This particularbearing had the smallest level of induced damage on the outer race of the ones that were tested; both the envelopespectrum and defect synchronous envelope spectrum clearly show a noticeable peak at the BPFO, but there is much lessnoise associated with the synchronous average envelope spectrum.

A plot of the envelope spectrum and defect synchronous envelope spectrum is shown in Fig. 11 for vibration data collectedfor a bearing that had the second largest level of induced outer race damage. In this example, both processing methods candetect a clearly observable peak related to an outer race fault as well as its harmonics. The reduction in noise, however, is thepotential advantage offered by the TLSAE method. In both example plots, the BPFO peaks and harmonics were easier to visuallyobserve due to the reduction in random noise. In many automated bearing condition monitoring systems, features such asbearing fault frequency peak information are extracted from the envelope signal. The extracted features from both theconventional envelope processing method and the TLSAE method are compared and discussed in Section 5.

AG

NIT

UD

E (G

) 0.03

0.025

0.02

0.015

0.03

0.025

0.02

0.015AG

NIT

UD

E (G

)

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 371VIB

RAT

ION

M

FREQUENCY (Hz)

0.01

0.005

0

0.01

0.005

00 1 2 3 4 5 6 7 8 9 10

ORDER IN TERMS OF BPFO

VIB

RAT

ION

M

0 500 1000 1500 2000 2500

Fig. 10. Comparing synchronous average to traditional envelope spectrum for bearing with smallest level of outer race damage: (a) envelope spectrumand (b) defect-synchronous envelope spectrum.

0.180.160.140.12

0.10.080.060.040.02

0

FREQUENCY (Hz)

0.180.160.140.12

0.10.080.060.040.02

0

ORDER IN TERMS OF BPFO

VIB

RAT

ION

MA

GN

ITU

DE

(G)

VIB

RAT

ION

MA

GN

ITU

DE

(G)

BPFO (207 Hz)

2X BPFO (415 Hz)

10500 25002000150010000 2 3 4 5 6 7 8 9 10

Fig. 11. Comparing synchronous average to traditional envelope spectrum for bearing with second level of induced outer race damage: (a) envelopespectrum and (b) defect-synchronous envelope spectrum.

These two examples shown in Figs. 10 and 11 illustrate the effective use of this proposed TLSAE method for bearingdiagnosis; however, there are a few considerations for using this method. This method would require a synchronousaverage spectrum to be calculated for each bearing fault frequency. In this case study, only outer race damage wasinduced, so the examples presented are for the bearing fault frequency outer race (BPFO). Another aspect to consider isthat the experimental testing was conducted at a nominally xed rotational speed. Further investigation is needed toevaluate this proposed method and determine its tolerance for speed uctuations. Also, the bearing impulses typicallyhave some random percentage of slip on the order of 12% [18]; the inuence this has on the TLSAE method is also plannedfor further investigation. Considering that the processing method worked well for this experimental case study in whichthere was some amount of random slip, there appears to be promise that warrants further study. A simulation study thatallows the random slip to be controlled and the proposed method to be evaluated for different amounts of random slipwould provide some further guidance and limitations for this processing method.

4. Experimental bearing test-rig conguration

A bearing test-rig was used to evaluate the signal processing and feature extraction methods for bearing health assessment.The test-rig shown in Fig. 12 consists of a 1 horsepower motor used as the prime mover to drive a shaft coupled with a bearinghousing; an ac drive is used for speed control and to test the bearing at speeds of 1500, 2400 and 3600 rpm. A single axisaccelerometer is placed on the outer surface of the bearing housing to measure the vibration signal for the testing of thebearing. For data acquisition, a sampling rate of 10 kHz is used with a block size of 10,000 data points is used; 30 blocks of dataare taken for each bearing that is tested at each of the three speeds. In order to compare the results from the different signalprocessing methods, 6 bearings are tested; 3 new bearings and 3 bearings with increasing levels of induced scratch damage.Note that the induced damage is on the outer race for the 3 bearings with scratch damage.

The 6 bearings were of the same type, and for a particular bearing geometry the bearing characteristic frequencies that areassociated with a particular bearing defect such as damage in the outer race can be calculated. The bearing characteristic faultfrequency equations [11] are provided in Eqs. (8)(12) and the calculated quantities are listed in Table 1. For the equations

BEARING HOUSING AC MOTOR (1HP)

Bearing characteristic frequencies.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376372Inner race rotational speed oi (rpm) 1500Outer race rotational speed oo (rpm) 0Bearing pitch diameter Dp (mm) 86

Rolling element diameter Db (mm) 11.906

Contact angle y (deg) 15Number of rotating elements N 19

Order

Outer race defect (BPFO) 8.230

Inner race defect ( BPFI) 10.770

Ball spin frequency (BSF) 3.547

Cage defect frequency (FTF) 0.433

Rolling element defect frequency 7.094SINGLE AXIS ACCELEROMETER VARIABLE FREQUENCY DRIVE

Fig. 12. Bearing test-rig.

Table 1

listed, the bearing geometry parameters consist of the ball diameter (Db), the pitch diameter (Dp), the number of rollingelements (N) and the contact angle (y), which are used to calculate the bearing fault frequencies that are seen in the vibrationspectrum. For extracting features in the frequency domain as well as the envelope method, the peak information at the bearingfault frequencies are key indicators for assessing the health of the rolling element bearing:

BPFO N2

$ 1 Db

Dp

cos y

8

BPFI N2

$ 1 Db

Dp

cos y

9

BSF Dp2D

$ 1 Db

D

2cos2 y

" #10

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 373b p

FTF $2

h i1 Db

Dp

cos y

11

Rolling Element Defect 2 BSF 12

5. Comparative analysis of health assessment results

5.1. Comparison of features for overall machine health

Certain vibration indicators can only provide an indication of the overall machine health state; this particular sectionprovides a comparison between the processing method and features that are only suitable for this task. Time domainstatistics, features from the empirical mode decomposition (EMD), as well as statistic or overall energy levels from theband-pass ltered signal suggested by the kurtogram, are a set of indicators that are indicative of the overall machinehealth status of the mechanical system but cannot provide detailed diagnosis information. In this case study, the bearingswere either in the normal healthy condition or had a known level of induced damage; the features can be evaluated basedon the known degradation level and their associated value for the three normal cases and the three levels of induceddamage. Table 2 provides a tabular list of the overall health vibration indicators that were considered in this study. Notethat the features shown in this table are divided by the feature value for the rst normal bearing; showing the results as aratio allows for a quick insight on how much greater in magnitude each feature is for the bearings with damage comparedto a baseline condition. The RMS feature shows an increasing level that corresponds with increasing level of induceddamage on the outer race of the bearing; however the RMS value for the smallest level of scratch damage is only two timesgreater than normal while the energy of the decomposed levels using the empirical mode decomposition method havefeatures that are 46 times greater than normal for the smallest level of damage.

The energy in the ltered signal is monotonic with the induced outer race damage; this suggest that the kurtogramprovides an effective way of selecting the band pass lter and that there is a considerable difference in this vibrationmagnitude in this frequency band between a healthy bearing and one with damage on the outer race. The energy of theltered signal provides signicantly more separation between the second and third levels of induced damage compared tothe time statistics or EMD features. The kurtosis features from both the time signal and the ltered signal were notmonotonic with the outer race damage level or provided much separation between a healthy and degraded bearing.

5.2. Comparison of features for bearing diagnosis

A list of the features that were extracted in the frequency domain using the traditional FFT, the envelope spectrum, and thetachometer-less synchronously averaged envelope (TLSAE) method are provided in Table 3. Note that the convention used for

Table 2Comparison of potential machine surveillance indicators for assessing bearing condition.

Normal

bearing 1

Normal

bearing 2

Normal

bearing 3

Scratch level 1

bearing

Scratch level 2

bearing

Scratch level 3

bearing

RMS 1.00 1.22 1.08 2.68 7.40 14.72

Kurtosis 1.00 1.45 0.88 0.75 0.58 0.62

IMF1 RMS 1.00 2.89 2.42 6.07 17.66 10.28

IMF2 RMS 1.00 1.98 1.65 4.35 12.66 10.59

IMF3 RMS 1.00 2.92 1.98 4.36 14.08 16.34

IMF4 RMS 1.00 3.00 1.97 3.77 17.67 13.03

Kurtosis of ltered signal 1.00 1.23 0.74 0.68 0.56 0.65

Energy of ltered signal 1.00 5.34 1.16 7.32 144.03 175.70

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376374Table 3Comparison of potential bearing diagnostics features for assessing bearing condition; subscript e denotes features extracted using the envelope method

while new indicates features extracted under the proposed TLSAE method.

Normal

bearing 1

Normal

bearing 2

Normal

bearing 3

Scratch

level 1 bearing

Scratch level

2 bearing

Scratch level

3 bearing

BPFO FFT 1.00 0.36 0.85 0.46 5.21 3.74

BPFOe 1.00 1.74 0.58 5.19 26.27 50.50

2XBPFOe 1.00 2.58 1.06 2.66 9.99 86.93

3XBPFOe 1.00 1.58 0.94 3.51 60.06 93.23

4XBPFOe 1.00 1.43 1.05 2.35 8.59 57.54

5XBPFOe 1.00 1.43 1.05 11.60 38.38 57.54

New BPFO 1.00 1.84 0.34 6.13 32.31 56.56

New 2XBPFO 1.00 1.33 0.39 9.76 30.02 74.98

New 3XBPFO 1.00 1.65 0.46 5.47 21.61 92.16

New 4XBPFO 1.00 1.28 0.50 4.88 6.16 54.50

New 5XBPFO 1.00 1.43 0.50 4.47 8.82 75.58presenting the results is to show the feature values as a ratio compared to the rst normal bearing. The rst row is the BPFOfeature from the FFT, while rows 26 are the peak values of the BPFO and its harmonics from the envelope spectrum, while rows711 are the peak values of the BPFO and its harmonics from the synchronous average envelope spectrum. The BPFO featureextracted from the Fourier Transform of the original signal is approximately 5 times larger for a bearing with scratch level 2damage compared to a normal bearing. At the early stages, for the bearing with scratch level 1 damage, the BPFO magnitude isactually less compared to a normal bearing. The traditional frequency domain features such as BPFO did not provide anindication of early bearing degradation; this shows the limitation of using the traditional FFT for bearing fault diagnosis.

The BPFO and 2XBPFO taken from the envelope spectrum are a much more robust set of features for detecting bearingdegradation at the early stages. For example, the envelope BPFO feature for a bearing with scratch level 1 damage isapproximately 5 times larger compared to the normal baseline bearing and this particular feature increases with the levelof outer race damage. The tachometer-less synchronously averaged envelope (TLSAE) feature for 2XBPFO is more robustthen the envelope 2XBPFO feature for detecting damage at lower level. It is approximately 10 times larger for the bearingwith the smallest level of outer race scratch as opposed to the very marginal separation between a normal bearing and thesmallest level of outer race damage provided by the traditional envelope 2XBPFO feature.

Considering that the tabular results are showing the mean feature value, it is perhaps further illustrative to showgraphical plots of the calculated features to further examine whether the TLSAE processing method provides less variation

BPF

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Fig. 13. Comparing results from BPFO feature: (a) envelope spectrum and (b) tachometer-less synchronously averaged envelope (TLSAE) method.

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376 375in the calculate features and a more consistent health estimation when compared with the traditional envelope processingmethod. Fig. 13 shows the BPFO feature from the envelope processing method and the TLSAE processing method. Theresults show that both methods can clearly distinguish all levels of outer race damage; however, the TLSAE method has a

2X B

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Fig. 14. Comparing results from 2X BPFO feature: (a) envelope spectrum and (b) tachometer-less synchronously averaged envelope (TLSAE) method.more consistent feature value with less variation for the bearing with the largest level of outer race damage. The results inFig. 14 which plot the rst harmonic of the BPFO using both processing methods further show the merits of the proposedTLSAE method. The envelope method provides little if any separation between a normal bearing and one with a smallestlevel of outer race damage using the 2XBPFO feature; however, there is clear separation between these two conditionsusing the TLSAE method. Furthermore, there is considerable less variation and a more consistent 2XBPFO feature valueusing the synchronous average envelope method for the bearing with the largest outer race damage.

Both the proposed synchronous average and the traditional envelope spectrum are suitable signal processingtechniques for diagnosing and assessing the bearing condition. The synchronous average method did offer improvementin that the calculated feature values had less variation. A more consistent and accurate estimation of the bearing conditionwould provide better inputs for classication and trending algorithms for diagnosing and predicting bearing failure. Also,some of the features, in particular the rst harmonic of the BPFO, had much more separation and discrimination abilityusing the TLSAE technique when compared with the traditional bearing envelope analysis method.

6. Conclusions

The development of the tachometer-less synchronously averaged envelope (TLSAE) method and the comparison of thismethod to other baseline signal processing methods provided some valuable insight for detecting the different levels ofouter race bearing damage. With regard to features that are indicative of the overall health state, using the kurtogram andcalculating the energy of the ltered signal provide a robust indicator that could describe all levels of outer race damage.The RMS of the time signal was also monotonic with the bearing damage level but provided less discrimination between anormal bearing and one with the smallest level of scratch. Features from the empirical mode decomposition can onlybe used as an overall health indicator due to its limited frequency resolution; also many of the energy levels of thedecomposed signals were not necessarily monotonically increasing with outer race bearing damage.

The bearing fault features taken from the FFT of the time signal are not suitable for detecting the early levels of damage;however, the use of the envelope method or the TLSAE method provides a way for early detection of bearing degradationusing the magnitude at particular bearing fault frequencies. The TLSAE method offered some improvement whencompared with the envelope method; less variation in the calculated feature values and also in certain features moreseparation between the normal and smallest level of induced bearing damage. This increased level of discrimination wasclearly observed for the magnitude of the rst harmonic of the outer race ball pass frequency when comparing the TLSAE

and envelope method. Less variation in the calculated features provides a better input for classication or trendingalgorithms which highlight the potential merits of the TLSAE method. Future work plans to conduct a simulation study andadditional experimental testing to further understand the limitations of the TLSAE method with regard to speeductuations and periodic variability of the bearing impulses due to slippage. Run to failure testing is also considered forfuture work in order to evaluate whether this processing method provides a set of indicators that increase monotonicallyfrom spall initiation to bearing failure.

Acknowledgments

The authors gratefully acknowledge the funding provided by TechSolve Inc under Smart Machine Platform Initiative

D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362376376(SMPI) under award number (COES000102). The authors also appreciate TechSolve Inc. for supporting and guiding thisresearch project and providing the experimental test-bed.

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Novel method for rolling element bearing health assessment--A tachometer-less synchronously averaged envelope feature...IntroductionExisting signal processing methods for bearing health assessment and fault diagnosisTime domain and Fourier transform based feature extractionEmpirical mode decomposition frequency extraction methodBearing envelope analysis feature extraction method

Novel method using synchronous averaging signal processing technique for rolling element bearingsExperimental bearing test-rig configurationComparative analysis of health assessment resultsComparison of features for overall machine healthComparison of features for bearing diagnosis

ConclusionsAcknowledgmentsReferences