Vibration signature analysis of distributed defects in ball bearing using wavelet decomposition technique

Abstract

The analysis of vibration signals acquired from a ball bearing with an extended type of distributed defects is carried out using wavelet decomposition technique. The influence of artificially generated defect and its location on outer and inner race of the ball bearing is observed using vibration data acquired from bearing housing. The comparison of diagnostic information from fast Fourier transform and time frequency decomposition method is made for inner and outer race of ball bearing with single as well as multiple extended defects. To decompose vibration signal acquired from bearing, db04 wavelet technique was implemented. It is observed that impulses appear with a time period corresponding to characteristic defect frequencies. The results observed from wavelet decomposition technique and fast Fourier transform reveal that the characteristic defect frequency is quite consistent even with change in location of defect. The extended type of distributed defects in the ball bearings can also be effectively diagnosed with the help of wavelet decomposition technique and fast Fourier transform.

Keywords

Ball bearing distributed defect vibration signal analysis wavelet decomposition technique

Introduction

Bearings play a key role in the functioning of rotating machinery and widely used in a variety of industries such as sugar industry, construction, mining, paper mills, railway, and renewable energy. Bearing failure is one of the prime causes of halt in rotating machinery, resulting in expensive systems downtime. Therefore, the fault detection of rolling element bearing has been the subject of extensive research prepared by Howard.¹ The low speed, high load rotor bearing system often shows the unpredictable dynamic response during running condition. In sugar industries, the deep groove ball bearings used in crane applications for carrying sugar bags and canes are subjected to fatigue spalling. In such type of bearing, the inception of micro-scale subsurface fatigue cracks originates below highly stressed rolling region. These micro-structural discontinuities generate micro-plastic deformation in the area of maximum stresses.² Due to the uninterrupted and cyclic loading during bearing operation, such type of fatigue crack continues to extent along the periphery of rolling surface. The damage and failure of such type of bearings leads to increase in the machinery breakdown consequently costing the significant economical losses.

Bearing defects may be categorized as local, distributed faults. Local defects include spalling, cracks on rolling surfaces due to fatigue. The distributed defects include surface roughness, waviness, ring misalignment, and eccentric balls caused by manufacturing errors and working conditions.³ A review of the existing knowledge is applied to the vibration response of rolling element bearings having single and multiple localized defects^4,5 and distributed type waviness fault⁶ is obtained through experimental work. Whenever a local defect on bearing element interacts with its mating element, the periodic impacts are generated at a characteristic defect frequency. Various techniques have been adopted such as high-frequency resonance technique, localized current method, sound measurement technique, and acoustic emission technique for bearing fault detection.^7,8,9 Vibration-based detection techniques for monitoring the health of bearings have been widely used in both time and frequency domains.

Theoretically, the characteristic defect frequencies observed in the fast Fourier transform (FFT) spectra should be present corresponding to bearing defect. But, Nikolaou and Antoniadis¹⁰ and Elia et al.¹¹ have noticed that many times these frequency components are not present in the spectra because of impulses generated by a defect that are shrouded by structural resonance and noise. It has also been concluded that such ringing modes of bearing and its supporting structure cannot be predicted because they depend on operating condition and extent of defect. Yan and Gao¹² have examined that the stationary signals have time-invariant statistic properties resulting in periodic vibration, whereas non-stationary signals are transient in nature, generated due to sudden breakage of races. It has also been noticed by Tyagi¹³ that the impact generated by bearing faults distributes its energy in a wide frequency range since they are difficult to be identified by envelope detection in the low-frequency range due to their low-energy interference. In addition to this, it has been concluded that short-time Fourier transform and Wigner Ville are incompatible for feature extraction. However, wavelet analysis illustrates multi-resolution; both time and frequency can be considered suitable to detect the bearing faults.^14,15 Hence, wavelet transform has been considered as an attempt for diagnosis of non-stationary signal.

Earlier research had paid attention toward vibration signature analysis for detection of local defects in the bearing; however, fewer efforts have been taken for the detection of extended raceway defects. In the present experimentation work, the diagnosis has been carried out on inner and outer race of ball bearing with single as well as multiple extended defects. Time and frequency domain signals of healthy and defective bearings have been analyzed and compared with wavelet analysis.

Characterization of fault

Earlier studies have been carried out in the fault diagnosis of ball bearing vibration generated due to local defect. Fatigue is the major mode of failure in rolling element bearing.¹⁶ In addition to this, Singh and Howard¹⁷ have noticed that localized defects are frequently developed in the bearing raceway during its operation and reported that during running condition of bearing, entry and exit edge of local defect wears, which tends to spread the size of the defect. Moreover, Behzad et al.¹⁸ have noticed that when a defect grows in the bearing, the roughness of the contacting surface grows locally, and stochastic excitation becomes stronger in defective areas. However, there is necessity to access effective diagnosis tool for feature extraction of such type of defect.

It has been observed that, because of variable loading, such type of local defects tends to grow along the path of a point of contact between the ball and raceway, considered as extended raceway defect. In this work, it is termed as a distributed type of defect. The existing distributed type of defect on the raceway has been characterized as an enlarged localized defect, whose length is less than spacing between two balls. It can also be categorized as defect smaller than the waviness.

Data acquisition

To characterize the vibration response obtained from faulty bearing and to monitor its condition, the experimental test rig was designed. Figure 1 shows the experimental test rig. In the present experimental investigation, electro discharge machining was used to artificially create extended distributed fault on the inner and outer race of the ball bearing as shown in Figures 2 and 3. The special purpose bearings DFM-85 are used as test bearing normally used in four wheeler engines. It was mounted in bearing housing on the shaft and loaded by turn buckle in radial direction.

Figure 1.

Experimental test rig.

Figure 2.

Defect on outer ring.

Figure 3.

Defect on inner ring.

The vibrations of bearing were recorded using piezoelectric accelerometer with DEWOSOFT FFT analyzer. Vibration signals were acquired at different speeds up to 1200 r/min of the system for both healthy and defective bearings. The signals are sampled at 5000 Hz with 2048 samples. The parameters of DFM-85 bearing are as follows: number of balls, 7; diameter of balls, 17.463 mm; pitch diameter, 57.5 mm; and contact angle, 0°. The vibration signal was acquired for the analysis of four test bearings at different speeds. Description of fault is indicated in Table 1 and fault location of respective bearing numbers (BN) as shown in Figure 4(b–g).

Table 1.

Fault description in the ball bearings.

BN	Location of defect	Defect size
a.	Healthy bearing	No defect
b.	Outer race track (45°)	Defect amplitude Ra = 4.6 µm, defect width = 15°
c.	Inner race track (45°)	Defect amplitude Ra = 4.6 µm, defect width = 15°
d.	Two defects on outer race track (45°–45°apart)	Defect amplitude Ra = 4.6 µm, defect width = 15°
e.	Two defects on inner race track (45°–45°apart)	Defect amplitude Ra = 4.6 µm, defect width = 15°
f.	Three defects on outer race track (90°apart)	Defect amplitude Ra = 4.6 µm, defect width = 15°
g.	Three defects on inner race track (90°apart)	Defect amplitude Ra = 4.6 µm, defect width = 15°

BN: bearing number.

Figure 4.

Fault location of respective bearing numbers (BN) (b–g).

Results

The defect present in the bearing element tends to increase vibration energy at defect frequency. The characteristic defect frequencies of inner and outer race are calculated²⁰ as follows

fo = \frac{z \times fs}{2} [1 - \frac{d}{D} \cos α]

(1)

fi = \frac{z \times fs}{2} [1 + \frac{d}{D} \cos α]

(2)

where f_s is the rotational frequency of shaft, z is number of ball, d is the ball diameter, α is contact angle which is zero for ball bearing, and D is the pitch diameter of bearing. Figures 5 –11 show the vibration spectrum (FFT) of healthy as well as defective bearings. In all the spectra, peak at 900 r/min running speed under 100 N radial load is present. At this speed, the theoretical characteristic defect frequencies of outer and inner race are found around 36.55 and 68.44 Hz, respectively.

Figure 5.

Experimental frequency spectrum of healthy bearing at 900 r/min.

Figure 6.

Experimental frequency spectrum of bearing with outer race defect at 900 r/min.

Figure 7.

Experimental frequency spectrum of inner race defective bearing at 900 r/min.

Figure 8.

Experimental frequency spectrum of bearing with two outer race defects at 900 r/min.

Figure 9.

Experimental frequency spectrum of bearing with two inner race defects at 900 r/min.

Figure 10.

Experimental frequency spectrum of bearing with three outer race defects at 900 r/min.

Figure 11.

Experimental frequency spectrum of bearing with three inner race defects at 900 r/min.

In the case of inner race defective bearing, the vibration signal acquired from FFT shows the peaks around 73.8 Hz characteristic of defect frequency of inner race which are nearby theoretical defect frequency (68.44 Hz) as shown in Figures 7, 9, and 11. Moreover, in case of inner race defective bearing, multiples of running frequency components is present in the spectrum. But the characteristic inner race defect frequency shows deviation in the vibration spectrum. However, this may lead to movable inner race defect or around five times the running frequency of the bearings. In addition to this, impulses components are quite weak in the vibration signal, may be because of inner race defects have more transfer elements while transmitting the impulses to outer race.

In the case of outer race defective bearing, the vibration signal acquired from FFT shows the peaks around 36.6 Hz characteristic of defect frequency of outer race, which are approximately close to the theoretical defect frequency. In addition to this, in case of outer race defective bearing the multiples (2fo to 6fo) of outer race characteristic defect frequencies are present in the frequency spectrum. Moreover, same trend was observed in frequency spectrum of bearing outer race with two and three defects. Hence, FFT method can diagnose single and multiple extended outer race defects and shows the defect frequency in the spectrum which resembles with theoretical frequencies.

Discrete wavelet transform

Wavelet provides time scale statistics of the signal assisting the feature extraction that varies in time. For analyzing transient and non-stationary signal, wavelet can be used as a diagnosis tool. It has been proposed by Kankar et al.¹⁵ and Randall and Antoni¹⁹ that the effectiveness of signal processing techniques is to handle large quantity of data and provide a timely and accurate assessment of bearing condition. To get more information and identify the faults in the bearing, wavelet-based feature extraction methodology is used. The Continuous wavelet transform (CWT) of f(t) is a time scale method of signal processing which is the sum over all the time of signal multiplied by the scaled shifted versions of wavelet function ψ(t). Mathematically

CWT (a, b) = \frac{1}{\sqrt a} \int_{- \infty}^{\infty} f (t) \times φ (\frac{t - b}{a}) dt

(3)

where ψ(t) is the mother wavelet. The parameter “a” represents the scale index. The parameter “b” indicates the time shifting. The discrete wavelet transform (DWT) is derived from discretization of CWT (“a,” “b”) and dyadic is the most common discretization, given by

DWT (j, k) = \frac{1}{\sqrt 2^{j}} \int_{- \infty}^{\infty} f (t) x φ (\frac{t - 2^{j} k}{2^{j}}) dt

(4)

where “a” and “b” are replaced by 2j and 2jk. Sampling indicates the minimum number of coefficients sampled from continuous wavelet transform to ensure that all information should be present in original signal which can be retained by wavelet coefficients. The original signal (t) comprises two complementary filters and emerges as low frequency (approximations (A’s)) and high frequency (details D’s).The decomposition process is further iterated with consecutive approximations, so as to break signal into many lower resolution components. According to Nyquist’s rule, the maximum frequency of vibration signals of all the bearings has considered to be 2.5 kHz because of sampling frequency 5 kHz. The vibration signals are then decomposed up to four levels using Daubechies-4 mother (Db4) wavelet. The frequency bandwidth of approximation and detailed coefficients of wavelet decompositions are as shown in Figures 12 –18.

Figure 12.

Original time signal and wavelet decomposition of healthy bearing.

Figure 13.

Original time signal and wavelet decomposition of bearing with outer race defect.

Figure 14.

Original time signal and wavelet decomposition of bearing with inner race defect.

Figure 15.

Original time signal and wavelet decomposition of bearing with two outer race defects.

Figure 16.

Original time signal and wavelet decomposition of bearing with two inner race defects.

Figure 17.

Original time signal and wavelet decomposition of bearing with three outer race defects.

Figure 18.

Original time signal and wavelet decomposition of bearing with three inner race defects.

Figure 12 shows acceleration response of time signal with 500 ms of healthy bearing and corresponding detail and approximate coefficients obtained by DWT up to four levels. The time signal of outer race, inner race defect bearings, and its four-level decomposition into an approximation and detail coefficient are shown in Figures 13 –18. All the observations are plotted at 900 r/min under 100 N radial load.

The periodic impulses due to outer race defects appear at an equal interval of time, which corresponds to outer race defect frequency in the remaining levels. From Figure 13, it is observed that outer race defect bearing shows the periodic impulses at a time of 27.1 ms in 1, 2, and 3 level decomposition which corresponds to the outer race defect frequency of bearing.

However, in the case of inner race defect as shown in Figure 14, periodic impulses are not visible in the time domain as well as in the low-level decomposition throughout its time signal because of their high-frequency nature. For inner race defect bearing, these impulses appear with an impact time of 15.2 ms at a higher level of decomposition in the signal. The corresponding frequency at this impulse time is 65.78 Hz. Even if the obtained defect frequency is close to theoretical frequency, the deviation in interval of impact time was observed throughout the time signal spectrum. Decomposition of signal received from bearing with inner race defect is not consistent at every decomposition level.

Figures 15 and 16 depict the decomposition of outer and inner race multiple defective bearing with two defects (bearing no. (d) and (e)). It is observed that the amplitudes of vibration from bearing with two defects are at the higher end as compared with vibration amplitude of single defect in the bearing. It is also noticed that, for outer race with two defects, impulses are consistently spaced at a time period of 27.1 ms (BPFO = 36.55 Hz) in the wavelet decomposition. The impulses observed in the decomposition correspond to ball pass frequency of outer race of bearing. In the case of inner race with two defects bearing as shown in Figure 16, the impulses are spaced at 15.2 ms, observed in D2 level of decomposition. However, lack of consistency in impulses was noticed in remaining decomposition levels.

Figures 17 and 18 depict the decomposition of inner and outer race multiple defective bearing with three defects (bearing no. (f) and (g)). In the case of bearing with multiple defects, significant rise in amplitude of vibration was observed as compared with bearing with single defect. It is also noticed that, for outer race multiple defects, impulses are still spaced at a time period of 27.1 ms having ball frequency of outer race (BPFO = 36.55 Hz) in the wavelet decomposition. These impulses are sensitive in wavelet decompositions which are equally spaced according to BPFO. However, in the case of multiple inner race defects bearing as shown in Figure 18, the impulses are not clear in the time signal as well as its decomposition levels. This may be because of resonance generated due to a movable defect in the ball bearing as the results defect on its inner race.

Discussion

Wavelet transform provides a multi-resolution analysis in the sense that it gives the information about faulty bearing frequency along with instant of time of fault existence in the spectrum. Tables 2 and 3 show impact time and corresponding dominating frequency at different speeds for all BNs as mentioned in Table 1. It has been observed that there are dominating components of frequency for outer race defective bearings observed at BPFO (fo). The dominating frequencies through wavelet analysis have been compared and show good agreement with theoretical frequencies as well as defect frequency obtained through FFT. But, there is some discrepancy in defect frequencies of inner race defective bearing while compared with theoretical ball pass inner race frequency. The results in Table 2 also illustrate the percentage frequency error between the theoretical frequency and defect frequency obtained from wavelet decomposition at different speeds. The results in case of outer race defect bearing depict that the close agreement between theoretical BPFO and decomposed frequency is found to be less than 2.5%.

Table 2.

Impact time and percentage frequency error of outer race defective bearing.

	BPFO	Single defect		Two defects		Three defects
Speed in r/min	Theoretical frequency	Impact time (ms)	% Frequency error	Impact time (ms)	% Frequency error	Impact time (ms)	% Frequency error
300	12.18	82.4 (12.13 Hz)	0.363219	80.03 (12.495 Hz)	2.523427	83.1 (12.03 Hz)	1.201196
600	24.37	40.8 (24.51 Hz)	0.570384	40.8 (24.51 Hz)	0.570384	41.55 (24.08 Hz)	1.241737
900	36.55	27.06 (36.95 Hz)	1.095713	27.43 (36.46 Hz)	0.256663	27.1 (36.9 Hz)	0.958602
1200	48.74	20.8 (48.077 Hz)	1.379206	20.4 (49.01 Hz)	0.570404	20.3 (49.2 Hz)	1.069109

Table 3.

Impact time and percentage frequency error of inner race defective bearing.

	BPFI	Single defect		Two defects		Three defects
Speed in r/min	Theoretical frequency	Impact time (ms)	% Frequency error	Impact time (ms)	% Frequency error	Impact time (ms)	% Frequency error
300	22.81	46.7 (21.41 Hz)	6.1232	45 (22.22 Hz)	2.576843	39.2 (25.5)	10.5490
600	45.63	21.95 (45.56 Hz)	0.157601	22.8 (43.85 Hz)	3.9000	21.9 (45.66 Hz)	0.657
900	68.44	15.2 (65.78 Hz)	3.872774	15.2 (65.78 Hz)	3.872774	14.9 (67.6 Hz)	1.937326
1200	91.25	11.2 (89.29 Hz)	2.152642	11.1 (90.09)	1.271134	11 (90.9 Hz)	0.373599

However, percentage frequency error in inner race defective bearing is shown at higher end as compared with outer race defect bearing. The vibrations generated in the bearing with inner race defect shows variation in spectrum due to variation in load. However, applied radial load modulates the periodic excitations produced by inner race defect. In this instance, strong fault signatures are observed when defect is in the load region; however, weaker signature is acquired while the defect is outside the load region.

As a result, impulses show randomness effect in their spacing. In addition to this, impulses are only clear in high-frequency signal wavelet decomposition, but not in low-frequency signal coefficients. The spectrum observed due to inner race fault shows the presence of inner race defect as indicated in Table 3 with 10% deviation. Hence, the impulses can be extracted from time signals of faulty bearing using DWT and FFT.

Conclusion

The vibration responses have been measured experimentally based on typical bearing assembly. Multiple faults have been artificially generated on inner, outer ring of bearing and frequency response is measured through FFT and compared with time frequency decomposition. The diagnosis of bearing with outer ring defect has been successfully demonstrated with the help of FFT and wavelet transform, whereas discrepancy in feature extraction was witnessed for inner ring defective bearing. Significant rise in amplitude of vibration is observed for bearing with multiple defects as compared with single defect in the bearing.

FFT and wavelet transform methods have shown their potential application in feature extraction of outer ring defective bearing whose impulses are consistently spaced with a time corresponding to BPFO. The same trend was observed in the case of bearing with multiple outer ring defects. However, deviation in impulse time spacing is observed from bearing with single and multiple inner ring defects. Feature extracted at higher level of decomposition have shown impulses corresponding to ball pass frequency of inner race (BPFI) to certain extent.

The characteristic defect frequency of bearing is consistent even with change in location of defect. Moreover, the characteristic frequencies of bearing with outer race defect depict that the close agreement between theoretical BPFO and decomposed frequency is within 2.5%. The spectrum observed due to inner race fault shows the presence of inner race defect within 3 with 10% deviation. The scope of this work is limited to measurement of frequency response at outer and inner ring defects in bearing.

Footnotes

Acknowledgements

The authors are thankful to the research and development department of Delux Bearings Pvt Ltd, Sanaswadi, Pune (India), for making availability of bearings and the test facility for the present investigation.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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