Tribology International 35 (2002) 793–800www.elsevier.com/locate/triboint

Application of discrete wavelet transform for detection of ballbearing race faults

S. Prabhakar, A.R. Mohanty, A.S Sekhar∗

Indian Institute of Technology, Department of Mechanical Engineering, Kharagpur 721 302, India

Abstract

Bearing race faults have been detected by using discrete wavelet transform (DWT). Vibration signals from ball bearings havingsingle and multiple point defects on inner race, outer race and the combination faults have been considered for analysis. Theimpulses in vibration signals due to bearing faults are prominent in wavelet decompositions. It is found that the impulses appearperiodically with a time period corresponding to characteristic defect frequencies. It has been shown that DWT can be used as aneffective tool for detecting single and multiple faults in the ball bearings. 2002 Published by Elsevier Science Ltd.

Keywords: Discrete wavelet transform; Bearing faults; Impulses

1. Introduction

Detection of rolling element-bearing faults has beengaining importance in recent years because of its detri-mental effect on the reliability of the machines. Bearingdefects can be classified as distributed or local. The dis-tributed defects are surface roughness, waviness, mis-aligned races, and off-size rolling elements. The localdefects include cracks, pits, and spalls on the rolling sur-faces. McFadden and Smith [1,2] have developed themodels for high-frequency vibration produced by a sin-gle and multiple point defects on the inner race of therolling element bearing under radial load.

Bearings frequently develop localized defects in theraceways, rollers, and cage. Periodic impacts are gener-ated when rollers pass upon these defects with the excep-tion of cage defects. The periodic impacts occur at ball-passing frequency (characteristic defect frequencies),which can be estimated from bearing geometry and rotat-ing speed. There are several methods to detect bearinglocal faults using vibration signals as given in an excel-lent review [3]. Theoretically, in Fast Fourier Transform(FFT) spectra, the characteristic defect frequenciesshould present corresponding to the bearing defect. But

∗ Tel.: +91-3222-82976; fax:+91-32222-755303.E-mail address: sekhar@mech.iitkgp.ernet.in (A.S. Sekhar).

0301-679X/02/$ - see front matter. 2002 Published by Elsevier Science Ltd.PII: S0301-679X(02 )00063-4

sometimes these frequency components are not presentin the spectra because the impulses generated by thedefects are masked by noise. To overcome this problem,signal processing techniques such as a processing tech-nique based on averaging technique [4], adaptive noisecanceling [5] and high-frequency resonance technique(HFRT) [6] have been developed to improve signal-to-noise ratio for more effective detection of bearing localdefects. Among these [4–6] signal-processing tech-niques, the high-frequency resonance technique is morepopular for bearing fault detection. However, it requiresmany computations and also several runs of impact teststo be performed to find the bearing resonance frequency.Hence, extra instruments such as impact hammers orvibration exciters and their controller are needed forHFRT.

Recently, the application of wavelets has emerged inthe context of damage detection, and an excellent reviewof this is given in [7]. Mori and et al. [8] have predictedthe spalling on the ball bearing by applying discretewavelet transform to vibration signals. Jing and Qu [9]have proposed a denoising method based on Morletwavelets for feature extraction and they have success-fully applied it to inner race fault detection of the rollerbearing. However, the previous works [8–10] dealt withthe detection of one fault in a bearing using wavelettransform. In the present study, the diagnosis of singleand multiple ball bearing race faults has been investi-gated using discrete wavelet transform.

794 S. Prabhakar et al. / Tribology International 35 (2002) 793–800

2. Discrete wavelet transform

Wavelets provide a time-scale information of a signal,enabling the extraction of features that vary in time. Thisproperty makes wavelets an ideal tool for analyzing sig-nals of a transient or non-stationary nature. The continu-ous wavelet transform (CWT) of f(t) is a time-scalemethod of signal processing that can be defined as thesum over all time of the signal multiplied by scaled,shifted versions of the wavelet function �(t). Mathemat-ically,

CWT (a,b) �1

��a���

��

f(t) �∗�t�ba � dt (1)

where �(t) denotes the mother wavelet. The parametera represents the scale index which is a reciprocal of fre-quency. The parameter b indicates the time shifting (ortranslation). The discrete wavelet transform (DWT) isderived from the discretization of CWT (a,b) and themost common discretization is dyadic, given by

DWT (j,k) �1

�2j ��

��

f(t) �∗�t�2jk2j � (2)

where a and b are replaced by 2j and 2jk. An efficientway to implement this scheme using filters wasdeveloped in 1989 by Mallat [11]. The original signal,f(t), passes through two complementary filters andemerges as low frequency [approximations (A’s)] andhigh frequency [details (D’s)] signals. The decompo-sition process can be iterated, with successive approxi-mations being decomposed in turn, so that a signal canbe broken down into many lower-resolution components.

3. Experimental measurements

In the present study, the faults were introduced in theinner race and outer race of the ball bearings by makinga scratch mark with an electric pulse, the bearing compo-nents were then assembled as different bearings at abearing manufacturer’s plant. All scratch marks are ofthe same size with 2 mm length, 500 µm width and 300µm depth. Table 1 shows the type of faults introduced.In the present investigation of the bearings, the balls andcage were not scratched.

The ball bearings were then tested one by one in aball bearing noise and vibration test facility. The testfacility, FAG vibration tester (MGG 11), measures thevibrations of the radial bearings with a bore diameter ofup to 100 mm. The instrument is preferably used fordeep grooves and angular contact bearings. The mechan-ical part is made up of the drive elements, the supportarbor for the bearing, and of the setting elements for the

Table 1Fault description in the ball bearings

Bearing Location of the defect Type of defectNumber

1 Good bearing No scratch mark2 Inner race (on the track) One scratch mark3 Outer race (on the track) One scratch mark4 Outer race (1800 apart on the Two scratch marks

track)5 Inner race (on the track) and One scratch mark on

Outer race (on the track) each race

pickup. For carrying through a measurement, the bearingmust only be pressed on the arbor with a pressure. Thevibration measurements on the bearings were done withan axial and radial load present as per AFBMA standards[12]. The inner race was rotated at 1800 rpm whereasthe outer race was held stationary. The bearing vibrationsignals were acquired by mounting a B&K 4399 acceler-ometer directly on the outer race and an FFT analyzerwith a sampling frequency of 25.6 kHz (�t = 0.039 ms).The signals were then analyzed using discrete wavelettransform.

4. Results and discussion

The time domain vibration signals of good and defec-tive bearings as given in Table 1 have been consideredfor analysis with the following data: bearing classi-fication = 6203 series deep groove ball bearings; balldiameter (Bd) = 6.747 mm; pitch diameter (Pd) = 28.7mm; number of balls (Nb) = 8 and the contact angle (α)= 0. The characteristic bearing defect frequencies ofinner and outer race are then calculated by using thefollowing formulae:

Ball Pass Inner Race (BPIR) �

Nb

2 �1 � �Bd

Pd�cosa� f

(3)

Ball Pass Outer Race (BPOR) �

Nb

2 �1��Bd

Pd�cosa� f

(4)

where f is the rotating frequency of the spindle (30 Hz).At a speed of 1800 rpm the characteristic bearing defectfrequencies of inner race and outer race are found to be148.2 Hz and 91.8 Hz.

Time signals of good and defective bearings as givenin Table 1 are shown in the Fig. 1. Overall RMS (rootmean square) and kurtosis values [3] of the time signalsin Fig. 1 have been found and are given in Table 2, sincethese values indicate the bearing condition whether it isa good or a defective bearing. As expected, the overall

795S. Prabhakar et al. / Tribology International 35 (2002) 793–800

Fig. 1. Time signals of the bearings rotating at a speed of 1800 RPM and their kurtosis values; (a) good (b) inner race defect (c) outer race defect(d) two defects on outer race (e) one defect on each race

RMS value is low for good bearings compared to defec-tive bearings and it can also be observed in Table 2 thatthe value is high for bearings with multiple faults com-pared to a single fault. The kurtosis values of the bearingalso show the same trend; kurtosis values increase as the

bearing defects are increase, i.e., (kurtosis)good �(kurtosis)single defect � (kurtosis)two defects. However, withthese values, one cannot pinpoint the location of thedefect in the bearing. For finding the location of thedefect, the frequency domain approach (FFT) and wave-

796 S. Prabhakar et al. / Tribology International 35 (2002) 793–800

Table 2Overall RMS and kurtosis values

Bearing Overall RMS value Kurtosis valueNumber

1 0.072 3.702 0.258 5.273 0.121 3.894 0.401 9.585 0.230 7.54

lets (DWT) can be used and are discussed in the follow-ing section.

When the ball passes over the localized defects,impulses are generated. The impulses are generatedperiodically according to bearing defect frequencies. Fig.2 shows the vibration spectra (FFT) of good as well as

Fig. 2. Vibration spectra of the bearings, rotating at a speed of 1800 RPM; (a) good (b) inner race defect (c) our race defect (d) two defects onouter race (e) one defect on each races

defective bearings with a frequency resolution of 1.25Hz. In all the spectra, a peak at running speed is present.In the case of an inner race defective bearing, multiplesof running frequency components are present [see Fig.2(b)]. But the characteristic inner race defect frequency(148.2 Hz) is not clear from the vibration spectrum. Apeak at 150 Hz is present, however, this may be due toan inner race defect or five times the running frequencyof the bearing. It can be seen from Fig. 2 (c&d) that thepeaks at the characteristic defect frequency of the outerrace (91.8 Hz) and its multiples (184 Hz, 275 Hz) arepresent in the frequency spectrum of the outer racedefect bearings. However, there are no clear symptomsof defects in case of bearing number 5 (one defect oneach race) vibration spectrum [see Fig. 2 (e)]. Hence,from the FFT plots, the outer race defects are clear inthe spectra but the inner race defects are not. This is

797S. Prabhakar et al. / Tribology International 35 (2002) 793–800

because the inner race defects have more transfer seg-ments when transmitting the impulse to the outer race;usually, the impulse components are rather weak in thevibration signal. These impulses can be extracted usingwavelet transforms.

The impulses may appear in the time signal of thedefect bearing or embedded in the time signals due tonoise. Since impulses are of high frequency in nature,these should appear in the high frequency range of wave-let decomposition or first few decompositions. Accord-ing to Nyquist’s rule, the maximum frequency of thevibration signals of all the bearings in Table 1 is 12.8kHz because the sampling frequency is 25.6 kHz. Thevibration signals are then decomposed up to four levelsusing Daubechies 4 mother wavelet. The frequencybandwidths of approximation and detail coefficients ofwavelet decompositions are shown in Fig. 3.

Fig. 4 shows the acceleration response of one revol-ution of the good bearing and the corresponding approxi-mation and detail coefficients (obtained by DWT) up tofour levels. The time signal and its four level decompo-sition into approximation and detail coefficients of innerrace defect bearing is shown in Fig. 5. The periodicimpulses due to inner race defects are not visible in timedomain as well as in level one decomposition. However,these impulses appear at an equal time interval of about6.75 ms, which corresponds to the inner race defect fre-

Fig. 3. Frequency bandwidth of wavelet decompositions.

quency (148.2 Hz) in the remaining levels. It is observedthat these impulses do not appear in the lower levelsbecause of their high frequency nature (results of levelsbelow four are not shown here). Similarly, the outer racedefect bearing shows the periodic impulses at a timeinterval of 10.9 ms in level two approximation coef-ficients (see Fig. 6). The time period of 10.9 ms corre-sponds to the outer race defect frequency of the bearing(91.8 Hz).

In case of multiple bearing defects (bearing numbers4 and 5), it is observed that the amplitudes of vibrationsare more as expected compared to the single defect bear-ings (see Figs. 7 and 8). It can be seen that the impulsesare still spaced at a time period of 10.9 ms (BPOR =91.8 Hz) in the wavelet decompositions as well as in thetime signals of bearing number 4 (see Fig. 7). But theimpulses are still more sensitive in wavelet decompo-sitions. The impulses in wavelet decompositions of bear-ing number 4 are equally spaced according to BPORbecause the two defects on the outer race tract are 180°apart and the number of balls is even [13]. A bearingwith combined faults such as the one on the inner racetrack and the other on the outer race track has been con-sidered in bearing number 5. Fig. 8 shows the time signaland the wavelet decompositions of multiple defects bear-ing (bearing number 5). In this case the impulses areclear only in wavelet decomposition but not in the time

798 S. Prabhakar et al. / Tribology International 35 (2002) 793–800

Fig. 4. Original time signal and the wavelet decompositions for onerevolution of the good bearing.

signal of the bearing. One set of impulses is observedat a time period corresponding to the inner race defectfrequency while the other set of impulses is observedat a time period corresponding to the outer race defectfrequency (see Fig. 8). These time periods are shown inlevel two-approximation coefficient plot. The amplitudesof impulses are high when the two impulses due to twodefects are occurring at the same time.

Fig. 5. Original time signal and the wavelet decompositions for onerevolution of the inner race defect bearing.

Hence, the impulses can be extracted from the timesignals of the faulty bearings using discrete wavelettransform. The spacing of the impulses obtained bywavelet decompositions of the time signals can be usedto detect bearing race faults. There are only a few papers[8–10] available on the application of wavelet transformfor fault detection in rolling element bearings. Sincewavelet transform is an emerging technique for fault

799S. Prabhakar et al. / Tribology International 35 (2002) 793–800

Fig. 6. Original time signal and the wavelet decompositions for onerevolution of the outer race defect bearing.

detection, its use needs to be stressed in the fault detec-tion of bearings, which are present in any machine. Andin this paper, it has been successfully demonstrated theapplication of DWT for multiple fault detection in ballbearings. Thus, DWT can be used as a condition moni-toring tool for detecting bearing race faults.

Fig. 7. Original time signal and wavelet decompositions for one rev-olution of the bearing with two defects on outer race.

5. Conclusions

The impulses due to bearing faults are clear in waveletdecompositions of the defect bearings. In case of singledefects and two defects on outer race at 180° apart, theimpulses appear periodically with a time period corre-sponding to characteristic defect frequencies. But, in thecase of two defects, one on the inner race and the otheron the outer race, one set of impulses is running at a

800 S. Prabhakar et al. / Tribology International 35 (2002) 793–800

Fig. 8. Original time signal and the wavelet decompositions for onerevolution of the bearing with one defect on inner race and other onouter race.

time period corresponding to the inner race defect fre-quency while the other set of impulses is running at atime period corresponding to the outer race defect fre-quency. Thus, DWT can be used as an effective tool fordetecting single and multiple faults in the ball bearings.

Acknowledgements

The authors are grateful to the R&D department ofTATA STEEL, Bearings Division, Kharagpur for pro-viding the test facility and bearings for the present inves-tigations.

References

[1] McFadden PD, Smith JD. Model for the vibration produced bya single point defect in a rolling element bearing. Journal ofSound and Vibration 1984;96(1):69–82.

[2] McFadden PD, Smith JD. The vibration produced by multiplepoint defects in a rolling element bearing. Journal of Sound andVibration 1985;98(2):263–73.

[3] Tandon N, Nakra BC. Vibration and Acoustic monitoring tech-niques for the detection of defects in rolling element bearings —a review. The shock and vibration digest 1992;24:3–11.

[4] Braun S, Datner B. Analysis of roller/ball bearing vibrations.ASME paper 77-WA/DE-5 1977;1–8.

[5] Chaturvedi GK, Thomas DW. Bearing fault detection usingAdaptive Noise Canceling. ASME paper 81-DET-7 1981;1–10.

[6] Prasad H, Ghosh M, Biswas S. Diagnostic monitoring of rollingelement bearings by High Frequency Resonance Technique.ASLE paper 84-LC-3c3 1984;1–9.

[7] Staszewski WJ. Structural and mechanical damage detectionusing wavelets. The Shock and Vibration Digest1998;30(6):457–72.

[8] Mori K, Kasashima N, Yoshioka T, Ueno Y. Prediction of spal-ling on a ball bearing by applying discrete wavelet transform tovibration signals. Wear 1996;195:162–8.

[9] Jing Lin, Qu Liangsheng. Feature extraction based on morletwavelet and its application for mechanical fault diagnosis. Journalof Sound and Vibration 2000;234(1):135–48.

[10] J. Li and M. Jun. Bearing localized defects detection throughwavelet decomposition of vibration. Proceedings of the winterannual meeting of the ASME, Anaheim, California, 1992.

[11] Mallat SG. A theory for multiresolution signal decomposition:the wavelet representation. IEEE Transaction on pattern analysisand machine intelligence 1989;11(7):674–93.

[12] AFBMA standard, American National Standard. Rolling bear-ings, Vibration and Noise. ANSI/AFBMA Std. 13-1970 (R 1977).

[13] Lipovszky Gy, Solyomvari K, Varga G. Vibration testing ofmachines and their maintenance. Amsterdam: Elsevier, 1990.