Novel method for rolling element bearing health assessment—A tachometer-less synchronously averaged envelope feature extraction technique David Siegel a,n , Hassan Al-Atat a , Vishwesh Shauche a , Linxia Liao a , John Snyder b , Jay Lee a a Center for Intelligent Maintenance Systems, University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072, United States b Techsolve Inc, 6705 Steger Drive, Cincinnati, OH 45237-3097, United States article info Article history: Received 7 December 2010 Received in revised form 17 December 2011 Accepted 8 January 2012 Available online 27 January 2012 Keywords: Synchronous averaging Hilbert transform Envelope analysis Bearing health assessment abstract 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 classification 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 difficult 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 first using a narrow band pass filter 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 tachometer 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 of indication that can determine the health of rolling element bearings. Data from a bearing test-rig is used to facilitate the comparison and evaluation of the signal processing methods. Vibration data was collected from the test-rig for bearings with different levels of degradation. The calculated vibration features from the tachometer- less synchronously averaged envelope (TLSAE) technique are compared to the other feature extraction techniques; with the synchronous average method providing a set of bearing vibration features that can distinguish all three levels of damage on the outer 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 its Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2012.01.003 n Corresponding author. Tel.: þ1 513 290 8163. E-mail address: [email protected] (D. Siegel). Mechanical Systems and Signal Processing 29 (2012) 362–376
Transcript
Contents lists available at SciVerse ScienceDirect
Mechanical Systems and Signal Processing
Mechanical Systems and Signal Processing 29 (2012) 362–376
0888-32
doi:10.1
n Corr
E-m
journal homepage: www.elsevier.com/locate/ymssp
Novel method for rolling element bearing healthassessment—A tachometer-less synchronouslyaveraged envelope feature extraction technique
David Siegel a,n, Hassan Al-Atat a, Vishwesh Shauche a, Linxia Liao a,John Snyder b, Jay Lee a
a Center for Intelligent Maintenance Systems, University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072, United Statesb Techsolve Inc, 6705 Steger Drive, Cincinnati, OH 45237-3097, United States
a r t i c l e i n f o
Article history:
Received 7 December 2010
Received in revised form
17 December 2011
Accepted 8 January 2012Available online 27 January 2012
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376 363
merits 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, classification 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 time–frequency representations and have compared the use of the continuouswavelet transform to other time–frequency methods. The time–frequency 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 time–frequency 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 smallfluctuations 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 mostapplicable for detecting early or more advanced stages of bearing degradation.
The paper is organized as follows: In Section 2, a review of existing signal processing techniques for rolling elementbearing using vibration data is presented. The described methods will be later used to compare the results withthe proposed method. In Section 3, the detailed description of the proposed method is presented. In Section 4, theexperimental test-rig used for the data collection and testing of the rolling element bearing is presented. In Section 5, the
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376364
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]:
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.
Fig. 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 bearing
with level 2 scratch damage, (d) time signal for bearing with level 3 scratch damage.
Fig. 2. Frequency domain vibration signal: (a) frequency domain signal for new bearing 1, (b) frequency domain signal for bearing with level 1 scratch
damage, (c) frequency domain signal for bearing with level 2 scratch damage, (d) frequency domain signal for bearing with level 3 scratch damage.
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376 365
For traditional frequency domain bearing health assessment methods, the bearing fault frequencies are key featuresthat 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 first 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 time–frequency 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 time–frequency 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 fitting 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.
Fig. 3. Intrinsic mode functions (1–7) from normal bearing 1 vibration signal.
Fig. 4. Intrinsic mode functions (1–7) from bearing with scratch level 1 vibration signal.
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376366
The EMD technique was applied to the bearing vibration signals collected from the test-rig and the first 7 intrinsicmode functions are shown for the first normal bearing that was tested in Fig. 3. In this particular case, the signal consistedof 12 intrinsic mode functions and notice that the first 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. 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) 362–376 367
observation 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.
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 flow chart for the bearing envelope analysis method is illustrated in Fig. 6. It consist of first identifying a highfrequency resonant peak, choosing an appropriate band pass filter, 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 filterprior to performing the demodulation. In earlier work, the use of modal testing for finding 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 [19–21]; 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) 362–376368
monitoring 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 filter for envelope analysis, and for machine surveillance [20]. In this study, it wasused for both facets, but this section focuses discusses how it can be used for selecting the demodulation band. Thecalculation procedure consists of first 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:
Kðf Þ ¼/H4ðt,f ÞS
/H2ðt,f ÞS2
�2 ð3Þ
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 significantly high kurtosis value at approximately 1800 Hz; this result can be used to guide the band-pass filter center frequency and bandwidth. The chosen band-pass filter based on the kurtogram results is a Chebyshevband pass filter 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 filter 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 flow chart in Fig. 8, and in more detail in Fig. 9, in which each signal processing step is shownwith a respective plot.
The first initial step is to band pass filter around a calculated bearing fault frequency of interest; the band pass filterlimits 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.
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) 362–376 369
3.5
3
2.5
2
1.5
1
0.5
0
0.25
0.2
0.15
0.1
0.05
x10-3
TACH SIGNAL
100050052.59552.5952.58552.5852.57552.56552.56 0
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
0.18
0.16
0.14
0.12
0.1
0.08
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.
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376370
bearing shaft speed was kept at a nominal fixed speed; further investigation is being considered to investigate thelimitations of this method with regard to speed fluctuations.
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 filtered signal, the Hilbert Transform is shown in Eq. (4) and is defined as a timedomain convolution between 1/(pt) and the original signal x(t):
yðtÞ ¼1
p P
Z 1�1
xðtÞt�t dt ð4Þ
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:
zðtÞ ¼ xðtÞþ jyðtÞ ð5Þ
aðtÞ ¼ ½ðxðtÞÞ2þðyðtÞÞ2�1=2 ð6Þ
cðtÞ ¼ arctanðyðtÞ=xðtÞÞ ð7Þ
There are a few methods for calculating the instantaneous frequency; in this current work the derivative of theunwrapped 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 defined ifthe signal contains several frequency components [25] but in this particular instance a narrow band pass filter is used prior
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376 371
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 flow 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 fluctuations 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 final 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.
VIB
RAT
ION
MA
GN
ITU
DE
(G)
FREQUENCY (Hz)
0.03
0.025
0.02
0.015
0.01
0.005
0
0.03
0.025
0.02
0.015
0.01
0.005
00 1 2 3 4 5 6 7 8 9 10
ORDER IN TERMS OF BPFO
VIB
RAT
ION
MA
GN
ITU
DE
(G)
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 spectrum
and (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) envelope
spectrum and (b) defect-synchronous envelope spectrum.
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376372
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 fixed rotational speed. Further investigation is needed toevaluate this proposed method and determine its tolerance for speed fluctuations. Also, the bearing impulses typicallyhave some random percentage of slip on the order of 1–2% [18]; the influence 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 configuration
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
SINGLE AXIS ACCELEROMETER
AC MOTOR (1HP)
VARIABLE FREQUENCY DRIVE
Fig. 12. Bearing test-rig.
Table 1Bearing characteristic frequencies.
Inner race rotational speed oi (rpm) 1500
Outer race rotational speed oo (rpm) 0
Bearing pitch diameter Dp (mm) 86
Rolling element diameter Db (mm) 11.906
Contact angle y (deg) 15
Number 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 7.094
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376 373
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:
BPFO¼N
2
� �ð$Þ 1�
Db
Dp
� �cos y
� �ð8Þ
BPFI¼N
2
� �ð$Þ 1þ
Db
Dp
� �cos y
� �ð9Þ
BSF ¼Dp
2Db
� �ð$Þ 1�
Db
Dp
� �2
cos2 y
" #ð10Þ
FTF ¼$2
h i1�
Db
Dp
� �cos y
� �ð11Þ
Rolling Element Defect¼ 2� BSF ð12Þ
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 filtered 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 first 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 4–6 times greater than normal for the smallest level of damage.
The energy in the filtered signal is monotonic with the induced outer race damage; this suggest that the kurtogramprovides an effective way of selecting the band pass filter 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 thefiltered signal provides significantly 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 filtered 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 filtered signal 1.00 1.23 0.74 0.68 0.56 0.65
Energy of filtered signal 1.00 5.34 1.16 7.32 144.03 175.70
Table 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.
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) 362–376374
presenting the results is to show the feature values as a ratio compared to the first normal bearing. The first row is the BPFOfeature from the FFT, while rows 2–6 are the peak values of the BPFO and its harmonics from the envelope spectrum, while rows7–11 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
Fig. 14. Comparing results from 2X 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) 362–376 375
in 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 amore consistent feature value with less variation for the bearing with the largest level of outer race damage. The results inFig. 14 which plot the first 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 classification and trending algorithms for diagnosing and predicting bearing failure. Also,some of the features, in particular the first 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 filtered 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 first harmonic of the outer race ball pass frequency when comparing the TLSAE
D. Siegel et al. / Mechanical Systems and Signal Processing 29 (2012) 362–376376
and envelope method. Less variation in the calculated features provides a better input for classification 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 speedfluctuations 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(SMPI) under award number (COES000102). The authors also appreciate TechSolve Inc. for supporting and guiding thisresearch project and providing the experimental test-bed.
References
[1] A.K.S. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mech. Syst. SignalProcess. 20 (7) (2006) 1483–1510.
[2] A. Heng, S. Zhang, A.C.C Tan, J. Mathew, Rotating machinery prognostics: state of the art, challenges and opportunities, Mech. Syst. Signal Process.23 (3) (2008) 724–739.
[3] Qiu, H., Luo, H., Eklund, N., On-board aircraft engine bearing prognostics: enveloping or fft analysis?, in: Proceedings of the ASME 2009 InternationalDesign Engineering Technical Conferences & Computers Information in Engineering, 2009.
[4] Z.K. Peng, F.L. Chu, Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography, Mech.Syst. Signal Process. 18 (2) (2004) 199–221.
[5] Z.K. Peng, P.W. Tse, F.L. Chu, A comparison study of improved Hilbert-Huang transform and wavelet transform: application to fault diagnosis forrolling bearing, Mech. Syst. Signal Process. 19 (5) (2005) 974–988.
[6] Huang, N.E., Shen, Z., Long, S.R., Wu, M.L.C., Shih, H.H., Zheng, Q.N., Yen, N.C., Tung, C.C., Liu, H.H., The empirical mode decomposition and the Hilbertspectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Long Ser. A-Math. Phys. Eng. Sci. 454 (1998) 903–995.
[7] Khatri, H., Ranney, K., Tom, K., del Rosario, R., New features for diagnosis and prognosis of systems based on empirical mode decomposition, in:Proceedings of 2008 International Conference on Prognostics and Health Management, 2008.
[8] F. Wu, L. Qu, An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of largerotating machinery, J. Sound Vib. 314 (2008) 586–602.
[9] P. Vecer, M. Kreidl, R. Smid, Condition indicators for gearbox monitoring systems, Acta Polytech. 45 (6) (2005) 35–43.[10] P.D. McFadden, M.M. Toozhy, Application of synchronous averaging to vibration monitoring of rolling element bearings, Mech. Syst. Signal Process.
14 (6) (2000) 891–906.[11] Sawalhi, N., Diagnostics, prognostics and fault simulation for rolling element bearings, PhD Thesis, University of New South Wales, 2007.[12] B. Li, M. Chow, Y. Tipsuwan, J. Hung, Neural-network-based motor rolling bearing fault diagnosis, IEEE Trans. Ind. Electron. 47 (5) (2000) 1060–1069.[13] Q. Du, S. Yang, Application of the EMD method in the vibration analysis of ball bearings, Mech. Syst. Signal Process. 21 (6) (2007) 2634–2644.[14] Huang, N.E., Wu, Z., Ensemble empirical mode decomposition: a noise-assisted data analysis method, COLA Technical Report 193, Center for Ocean-
Land-Atmosphere Studies, 2005.[15] Q. Chen, N. Huang, S. Riemenschneider, Y. Xu, A B-spline approach for empirical mode decompositions, Adv. Comput. Math. 24 (2006) 171–195.[16] G. Rilling, P. Flandrin, One or two frequencies? The empirical mode decomposition answers, IEEE Trans. Signal Process. 56 (1) (2008) 85–95.[17] M. Feldman, Analytical basics of the EMD: two harmonics decomposition, Mech. Syst. Signal Process. 23 (7) (2009) 2059–2071.[18] R.B. Randall, J. Antoni, Rolling element bearing diagnostics–a tutorial, Mech. Syst. Signal Process. 25 (2) (2011) 485–520.[19] J. Antoni, The spectral kurtosis: a useful tool for characterizing nonstationary signals, Mech. Syst. Signal Process. 20 (2) (2006) 282–307.[20] J. Antoni, R.B. Randall, The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines, Mech. Syst. Signal
Process. 20 (2) (2006) 308–331.[21] J. Antoni, Fast computation of the kurtogram for the detection of transient faults, Mech. Syst. Signal Process. 21 (1) (2006) 108–124.[22] Dyer, D., Stewart, R.M., Detection of rolling element bearing damage by statistical vibration analysis, ASME Paper, 26-30 September, 1997.[23] Antoni, J., webpage; /http://www.utc.fr/_antoniS.[24] M. Feldman, Hilbert transform in vibration analysis, Mech. Syst. Signal Process. 25 (3) (2011) 735–802.[25] B. Boashas, Estimating and interpreting the instantaneous frequency of a signal-Part 1: Fundamentals, Proc. IEEE 80 (4) (1992) 520–539.[26] H. Luo, H. Qiu, G. Ghanime, M. Hirz, G. Van der Merwe, Synthesized synchronous sampling technique for differential bearing damage detection,
J. Eng. Gas Turbines Power 132 (7) (2010).[27] Siegel, D., Evaluation of health assessment techniques for rotating machinery, Master Thesis, University of Cincinnati, 2009.
