- Email: [email protected]
Outer race defect width measurement in taper roller bearing using discrete wavelet transform of vibration signal
Measurement 46 (2013) 537–545
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Outer race defect width measurement in taper roller bearing using discrete wavelet transform of vibration signal Rajesh Kumar ⇑, Manpreet Singh Precision Metrology Laboratory, Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, Longowal 148 106, India
a r t i c l e
i n f o
Article history: Received 2 May 2012 Received in revised form 29 June 2012 Accepted 27 August 2012 Available online 7 September 2012 Keywords: Discrete wavelet transform Decomposition Symlet Vibration Bearing defect
a b s t r a c t Rolling element bearing is one of the important components in rotary machines. Although a significant quantum of work has been done on bearing defect monitoring, estimation of defect size in bearing elements is still a challenge. In this paper, a technique based on decomposition using Symlet wavelet is proposed for measuring outer race defect width of taper roller bearing. Experiments were carried out on a customized test setup. Seeded defects of different size were introduced separately in the form of an axial groove on the outer race of taper roller bearings using laser engraving technique. It is not only difficult but ambiguous to detect the entry point in the groove defect by making use of the signal. The ambiguity gets reduced by using Symlet5 wavelet due to its linear phase nature which maintains sharpness in the signal even when there is a sudden change in signal. The proposed technique has been successfully implemented for measuring defect width over a range of 0.5776–1.9614 mm. The resulting measure of defect width has been also verified using image analysis. Maximum deviation in result has been found to be 4.06% for the defect width of 1.1820 mm at no load which was found further reduced to 1.02% with increase in load. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Bearing defect is one of the causes of breakdown in rotating equipments. Different techniques based on the principle for measuring vibration, acoustic, thermal condition and wear analysis are used for detection of the bearing defects. Techniques based on vibration and acoustic emission are developing at a faster pace for monitoring rolling element bearings due to their non-invasive nature and their high reactivity to incipient faults [1,2]. In general, the diagnosis capability of the techniques is proportional to their complexity [3]. When bearings are installed as part of a complex mechanical system, the measured signal is often heavily clouded with various noises resulting from the compound effect of interferences caused by other machine elements and the background noise present in
⇑ Corresponding author. Tel.: +91 1672 253300; fax: +91 1672 280057. E-mail address: [email protected] (R. Kumar). 0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2012.08.012
the measuring device [4]. The defect position can be identified by time–frequency analysis of the vibration or acoustic emission signal. Junsheng et al. [5] constructed an impulse response wavelet by using continuous wavelet transform to extract the feature of vibration signals. They proposed two methods, namely, the scale-wavelet power spectrum comparison and the auto-correlation analysis of time-wavelet power spectrum for detecting the faults of roller bearing and identifying the fault patterns. Yan and Gao [6] presented a signal processing algorithm based on multi-scale enveloping spectrogram for vibration signal analysis. This technique was evaluated for localized structural defects and experimentally found successful. Patil et al. [7] developed an analytical model to predict the effect of a localized defect on the ball bearing vibrations by considering the contact between the ball and the races as non linear springs. For deep groove ball bearing they obtained numerical results by using the model which yielded both the frequency and the acceleration of vibration components of the bearing for simulating the defect.
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R. Kumar, M. Singh / Measurement 46 (2013) 537–545
Fig. 1. Test rig for bearing defect identification. Inset shows the enlarged view at different angle for mounting of accelerometer at the bearing housing.
The analytical mode has its own drawback in meeting real-time scenario. To overcome this, the envelop analysis – the most popular signal processing method for bearing is proposed. In this method the vibration signal is first passed through a band-pass filter to obtain a high signal-to-noise ratio (SNR) signal, and then Hilbert transform is used to obtain the envelope [8]. Patel et al. [9] proposed a method for detection of local defects on races of deep groove ball bearing in presence of external vibration using envelope analysis and Duffing oscillators but could not attempt for measurement of defect size. Kumar et al. [10] investigated Analytical Wavelet Transform (AWT) based acoustic emission technique for identifying not only the presence but also the severity of the defect in the inner race of radial ball bearing. A comparison of wavelet decomposition-based de-noising method and wavelet filter-based de-noising method was made by Qiu et al. [11] for signals from mechanical defects. The finding of the comparison reveals that the wavelet filter based de-noising method is more suitable to detect a weak signature. The wavelet decomposition de-noising method achieved satisfactory results on smooth signal detection. Al-Ghamd and Mba [12] made an attempt to determine the bearing outer race defect width directly from the raw signal. The relationship between the defect size and acoustic emission of burst size was a significant finding but had not dealt with vibration signal in detail. Sawalhi and Randall [13] attempted to measure the seeded defect width by using two different approaches. In first approach pre-whitening of signal is done and then octave band wavelet analysis is carried out to allow selection of the best band (or scale) for balancing the two pulses with similar frequency content. In the second approach, separate treatment is applied to the step and the impulse responses, so that they may be equally represented in the signal. They emphasized the theory that the rolling element could strike at the end of a spall, as the ball moved half way through it and that impact could get reflected in the signal. The impact in the signal might be due to contact of the ball with the spall base. The peak of impulse in signal would have emerged
Fig. 2. Photograph of a taper roller bearing.
Fig. 3. A typical outer race groove defect of width 0.5776 mm.
when the ball might have come out from the spall after touching the exit corner of the spall. So there is possibility of error in measurement of defect width using the above
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
539
Fig. 4. A typical raw signal of 0.1 s duration for defect free bearing.
Fig. 5. A typical raw signal of 0.1 s duration for bearing having outer race defect of width 0.5776 mm.
method implemented by Sawalhi and Randall [13]. Clearly there appears a room for improvement in the methods suggested for identifying defect size in ball bearing system as locating exact position of commencement and end of the defect by vibration signal is still a challenge. The current work is carried out to estimate defect width in outer race of taper roller bearing using Symlet based wavelet decomposition. Extracting desired information from the signal is difficult especially when there is a mismatch between direction of defect and the roller-outer race line contact while passing over the defect. The acceleration signals resulting from the entry of the rolling element into the defect and that from its exit are of different nature. The Symlet wavelet is a near symmetri-
cal/linear phase filter, which makes it easier to deal with the small discontinuity present in the signal without any major loss of information which helps in properly locating the point of commencement and exit of roller from the groove defect. 2. Feature extraction in vibration signal The wavelet technique provides a time-scale information in the signal, and it can efficiently detect the transients [14]. The Continuous Wavelet Transform (CWT) is used in time–frequency analysis that decomposes a signal in both time domain and frequency domain simultaneously. The CWT can be defined as
540
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
Fig. 6. Decomposition graph up to 4th level using Symlet 5th order wavelet: (a) for the signal shown in Fig. 5 and (b) enlarged decomposition graph for the signal marked in Fig. 6a.
1 CWTða; bÞ ¼ pffiffiffi a
Z
1
1
XðtÞw
tb dt a
ð1Þ
where a represents the scale parameter, b represents the translation parameter, w represents the ‘mother’ wavelet and w⁄ is the complex conjugate of w. The CWT and its
computation may consume significant amount of time and resources, depending upon the resolution required. The Discrete Wavelet Transform (DWT), which is based on sub band coding is found to yield a fast computation of wavelet transform. Also, the CWT has the drawback of redundancy and impracticability with digital computers
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
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for a given N and have the same number of vanishing moments as the dbN family. They have the perfect reconstruction and cancellation capability that allows them to be used in both the CWT and the DWT. The Daubechies wavelet modified to construct the Symlet wavelet [16] involves reusing the mother wavelet function m0 introduced in the dbN, considering the jm0 ðxÞj2 as a function W of Z = eix. The use of Symlet based decomposition properly locates the point of commencement and exit of roller in the groove defect. The size of defect present on bearing race can be calculated with the knowledge of vibration burst duration Dt which is estimated using Symlet based decomposition, fundamental train frequency (FTF) and average outer race inner diameter (tapered one) DOI of the bearing. The outer race defect width Lod is [13]
Lod ¼ p Dt DOI FTF
ð4Þ
For the bearing NBC 30205 at inner race rpm 2050, the FTF is 14.316. Putting the given geometric parameter and value of FTF for the bearing, Eq. (4) is simplified as Fig. 7. A typical burst obtained after Symlet decomposition and the corresponding roller positions over an outer race defect width of 0.5766 mm size.
Lod ¼ 1993:61 Dt mm ðwhere Dt is in secondsÞ
ð5Þ
3. Experiment and result as it takes continuous values of parameters (a, b) [15]. Therefore, the scale and shift parameters are evaluated on a discrete grid of time-scale plane leading to a discrete set of continuous basis functions [16]. The DWT is a discrete form of the CWT. It adopts the dyadic scale and translation to reduce computation time. The DWT can be defined as
1 DWTða; bÞ ¼ pffiffiffiffi 2j
Z
1
1
XðtÞw
t 2j k 2j
! dt
ð2Þ
where 2j and 2jk represent the scale parameter and the translation parameter respectively. In this j and k are integers. The functions and scales are represented as an approximations value. The curves of scale functions can be modified by the scale parameter, which is the inverse ratio to frequency. The DWT analysis is made by passing the signal through a series of filters. These filters include both high-pass filters and low-pass filters. The high-pass filters examine the high frequency bands [i.e. Details (Dj)]. On the other hand, the low-pass filter analyzes the low frequency band [Approximations (Aj)]. The original signal X(t) can be defined as [15]
XðtÞ ¼ Aj þ
X
Dj
ð3Þ
j6j
where Aj and Dj represent the approximation and the detail signals of the jth level. Symlet wavelets are more symmetrical than the Daubechies wavelets. The Symlets have also nearly linear phase which makes them easier to deal with small discontinuity present in the signal without major loss of information [17]. They become more regular with larger N (‘‘SymN’’). They have the same compact support as the Daubechies
Experiments were performed on a customized test rig shown in Fig. 1. The shaft in the test rig is supported by two self aligned taper roller bearings (Make: NBC, Bearing number: 30205). The shaft is driven by an alternating current motor of 0.75 kW capacity (Make: Crompton, frequency 50 Hz, current 4.2 amp and speed 1440 rpm) with the help of V-belt and step pulley arrangement. This arrangement provides option of three different speeds of 1050 rpm, 2050 rpm and 3080 rpm approximately to the test rig shaft. During each experiment speed of the shaft is measured using an optical tachometer with digital display. The condition of the bearing mounted towards loading arrangement side as shown in Fig. 1 is monitored using a PCB make uni-axial accelerometer having sensitivity 1000 mV/g. Bearing under test is placed at this position only. The accelerometer is placed right above the bearing casing perpendicular to the axis of the rotation of the shaft in such a way so that it can acquire vertical acceleration. A personal computer based data acquisition system (Make: National Instrument, Model: SCXI-1000 having 4 channel input) is used to acquire the vibration data obtained from accelerometer. A program has been developed in Labview environment to acquire and display the signal along with its Fourier Transform. There is provision to record/store the signal in the hard disk of computer for further processing and analysis. The defect width has been analyzed using wavelet decomposition approach in Matlab environment. In the present study investigations have been made on four sets of the said bearing (NBC 30205 as shown in Fig. 2) each having different defect width 0.5776 mm,1.1820 mm, 1.7266 mm and 1.9614 mm on the outer race (OR). The defects have been generated using laser engraving technique. A typical defect of size 0.5776 mm is shown in Fig. 3. In this paper, results at the shaft speed of 2050 rpm are presented.
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Fig. 8. Decomposition graph up to 4th level using Symlet 5th order wavelet for the outer race defect of width 1.1820 mm.
When tested with the defect free bearing, the amplitude of the raw signal is obtained in the range of 1 to +1 mV as shown in Fig. 4. While dealing with the defective bearing it has been observed that amplitude of the burst in the raw signal has increased and is appearing in the range of 7 to +10 mV. A typical raw signal of the bearing having defect width of 0.5776 mm at 2 kg external load is shown in Fig. 5. The acceleration signals resulting from the entry of the rolling element into the defect and that from its exit are of different nature in terms of amplitude and probably in frequency as it appears from the raw signal. The wavelet decomposition analyzes the signal at different frequency bands with different resolution. The decomposition graph up to 4th level has been drawn by using Symlet 5th order mother wavelet for the case having defect width 0.5776 mm in the outer race and is shown in Fig. 6. Out of the three bursts appearing in Fig. 6b, one of the bursts of relevant time duration obtained using the symlet decomposition at 4th level is marked and put just above the bearing defect geometry to explain the phenomena of roller-outer race interaction while passing over the defect and is shown in Fig. 7. Three points in the signal namely GC1, GC2 and P shown in the Fig. 7 represent groove corner 1, groove corner 2 of the defect and maximum de-stressing point respectively. When the roller enters the defect groove passing GC1, point of the roller on the tangent parallel to the groove surface comes in air due to which signal appears to be de-stressed. Three different positions of the roller with respect to points GC1, P and GC2 at a cross section are shown as a circle having centers at c1, c2 and c3 respectively. Spotting GC1 from raw signal is very difficult because there is no distinct variation in amplitude but by using
decomposition graph de-stressing level in the signal gets enhanced. The de-stressing value (point GC1 to point P) has been calculated in percentage of the range for each individual burst (appropriate bursts selected for measuring defect width) in the 4th level decomposition graph obtained through Symlet5 and raw signal graph. The average value of de-stressing in the decomposition graph is 49.27% where as that in raw signal graph is 8.12%. This may arise due to the fact that the Symlet wavelet actually spots the GC1 by modulating the signal in such a way that amplitude due to de-stressing gets enhanced. The roller comes out from the groove defect when it comes in contact with GC2. This is generally a re-stressing event having highest amplitude. After this, the signal starts stabilizing as its amplitude progressively decreases due to damping action of elastic elements of the bearing. The variation in signal shown in Fig. 7 does not indicate any intermediate peak between the points GC1 and GC2 which implies that the roller is not touching the groove base. Data points are calculated between the points GC1 and GC2 marked on the signal to obtain the time taken by roller to pass the groove defect. In the similar manner signals were acquired for other defect sizes. The symlet wavelet decomposition of the signal for the outer race defect widths 1.1820 mm, 1.7266 mm and 1.9614 mm at 2 kg load are shown in Figs. 8–10 respectively. Encircled portion of the burst in Fig. 10 is superimposed on defect geometry diagram and is shown in Fig. 11. To explain the case of maximum defect size, three vertical lines have been drawn from the points GC1, GB1 and GC2. At point GB1, the roller strikes the groove base with high impact which results in re-stressing and high impulse in signal. After this event the roller
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
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Fig. 9. Decomposition graph up to 4th level using Symlet 5th order wavelet for the outer race defect of width 1. 7266 mm.
Fig. 10. Decomposition graph up to 4th level using Symlet 5th order wavelet for the outer race defect of width 1.9614 mm.
remains in contact with the groove base for some time and during this period impulses due to the rough surface of groove are observed. When the roller comes in contact with the point GC2 it again generates high amplitude in the signal and beyond this (i.e. after GC2) progressive decrease in amplitude of signal is observed due to elastic
damping of bearing element. Three different positions of the roller with respect to the points GC1, GB1 and GC2 at a cross section are shown as a circle having centers at c1, c2 and c3 respectively. The roller may spin or slide during the operation of the bearing. Change in signal takes place when it slides. Also
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the shaft is not loaded. It may be due to the clearance between the cage and the roller which results into improper stressing and de-stressing while crossing over the groove edges. The difference between the two values appears reducing at loaded condition of shaft/bearing. 4. Conclusion
Fig. 11. A typical burst obtained after Symlet decomposition and the corresponding roller positions over an outer race defect width of 1.9614 mm size.
varying clearance between cage and roller changes the signal when the roller enters and exits from the groove defect. In the bearing under investigation there are 17 rollers. There is variation in data points for each roller crossing over the defect. Average data points for 17 successive bursts are calculated for estimating the time taken by roller to pass over the groove defect. The average of data points so calculated is converted into time duration to cross over from GC1 to GC2 taking into account the sampling frequency. Further using Eq. (5) which has been simplified for the specified bearing at the speed 2050 rpm (i.e. FTF = 14.316) the defect width is calculated. The defect width is also evaluated using image analysis. The values of defect width under different loading conditions have been measured by making use of signal processing as well as image processing. The details are presented in Table 1. It has been observed that the variation in data points between bursts is more at low defect widths when shaft is not loaded. The maximum difference in result has been obtained to be 4.06% for defect width of 1.1820 mm when
A technique based on decomposition using Symlet wavelet has been proposed for measuring outer race defect width of bearing. Experimental measurement and subsequent analysis reveal that decomposition of vibration signal by using Symlet 5th order mother wavelet is suitable for measuring outer race defect width of taper roller bearing. Sharp and high amplitude impulses are obtained when roller crosses over the entry and exit of the defect. When the roller remains in contact with the groove base between entry and exit, the impulses due to roughness of the groove surface are observed. The defect evaluation technique using decomposition extracts roller entry and exit components of signal from the groove defect in good time resolution. The difficulty in detecting the commencement/entry point of the defect in the signal is reduced by using Symlet5 which improves the sharpness of the signal. The proposed technique has been successfully implemented for measuring defect width over a range of 0.5776 mm to 1.9614 mm. The defect width has been also verified using image analysis. The maximum deviation in the two values of defect width obtained using aforementioned two different approaches at no load is 4.06% for defect width of 1.1820 mm. At intermediate load of 2 kg deviation has reduced to 1.02% for the same defect width. References [1] N. Tandon, A. Choudhury, A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings, Tribology International 32 (1999) 469–480. [2] M. Elforjani, D. Mba, Accelerated natural fault diagnosis in slow speed bearings with acoustic emission, Engineering Fracture Mechanics 77 (2010) 112–127. [3] J. Antoni, Cyclic spectral analysis in practice, Mechanical Systems and Signal Processing 21 (2007) 597–630. [4] I.S. Bozchalooi, M. Liang, A joint resonance frequency estimation and in-band noise reduction method for enhancing the detectability of
Table 1 Outer race groove defect width measurement using image processing and signal decomposition by Symlet5 at different loading conditions. Case
Loading condition
Average data points calculated Measured defect width Defect width measured % Deviation in result from from signal processing from the data points (mm) using image processing (mm) the image processing
OR defect-1 Without load 20.706 2 kg load 19.882 4 kg load 20.353
0.5900 0.5664 0.5798
0.5776
+3.70 1.93 +0.38
OR defect-2 Without load 40.674 2 kg load 41.059 4 kg load 42.059
1.1340 1.1700 1.1984
1.1820
4.06 1.02 +1.39
OR defect-3 Without load 59.706 2 kg load 60.941 4 kg load 60.882
1.7007 1.7358 1.7342
1.7266
1.50 +0.53 +0.44
OR defect-4 Without load 70.059 2 kg load 68.882 4 kg load 68.765
1.9956 1.9621 1.9587
1.9614
+1.74 +0.04 0.14
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
[5]
[6]
[7]
[8]
[9]
[10]
[11]
bearing fault signals, Mechanical Systems and Signal Processing 22 (2008) 915–933. C. Junsheng, Y. Dejie, Y. Yu, Application of an impulse response wavelet to fault diagnosis of rolling bearings, Mechanical Systems and Signal Processing 21 (2007) 920–929. R. Yan, R.X. Gao, Multi-scale enveloping spectrogram for vibration analysis in bearing defect diagnosis, Tribology International 42 (2009) 293–302. M.S. Patil, J. Mathew, P.K. Rajendrakumar, S. Desai, A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing, International Journal of Mechanical Sciences 52 (9) (2010) 1193–1201. W. He, Z. Jiang, K. Feng, Bearing fault detection based on optimal wavelet filter and sparse code shrinkage, Measurement 42 (2009) 1092–1102. V.N. Patel, N. Tandon, R.K. Pandey, Defect detection in deep groove ball bearing in presence of external vibration using envelope analysis and Duffing oscillator, Measurement 45 (5) (2012) 960–970. R. Kumar, D.P. Jena, M. Bains, Identification of inner race defect in radial ball bearing using acoustic emission and wavelet analysis, in: Proceedings of ISMA 2010 including USD 2010 Leuven (Belgium), 2010, pp. 2883–2891. H. Qiu, J. Lee, J. Lin, G. Yu, Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics, Journal of Sound and Vibration 289 (2006) 1066–1090.
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[12] A.M. Al-Ghamd, D. Mba, A comparative experimental study on the use of acoustic emission and vibration analysis for bearing defect identification and estimation of defect size, Mechanical Systems and Signal Processing 20 (7) (2006) 1537–1571. [13] N. Sawalhi, R.B. Randall, Vibration response of spalled rolling element bearings: observations, simulations and signal processing techniques to track the spall size, Mechanical Systems and Signal Processing 25 (2011) 846–870. [14] S. Prabhakar, A.R. Mohanty, A.S. Sekhar, Application of discrete wavelet transform for detection of ball bearing race faults, Tribology International 35 (2002) 793–800. [15] Wu. Jian-Da, H. Chuang-Chin, Fault gear identification using vibration signal with discrete wavelet transform technique and fuzzy–logic inference, Expert Systems with Applications 36 (2009) 3785–3794. [16] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Transactions on Information Theory 36 (5) (1990) 961–1005. [17] R. Kumar, I.P. Singh, C. Shakher, Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform, Optics and Lasers in Engineering 41 (1) (2004) 81–93.
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Outer race defect width measurement in taper roller bearing using discrete wavelet transform of vibration signal Rajesh Kumar ⇑, Manpreet Singh Precision Metrology Laboratory, Department of Mechanical Engineering, Sant Longowal Institute of Engineering and Technology, Longowal 148 106, India
a r t i c l e
i n f o
Article history: Received 2 May 2012 Received in revised form 29 June 2012 Accepted 27 August 2012 Available online 7 September 2012 Keywords: Discrete wavelet transform Decomposition Symlet Vibration Bearing defect
a b s t r a c t Rolling element bearing is one of the important components in rotary machines. Although a significant quantum of work has been done on bearing defect monitoring, estimation of defect size in bearing elements is still a challenge. In this paper, a technique based on decomposition using Symlet wavelet is proposed for measuring outer race defect width of taper roller bearing. Experiments were carried out on a customized test setup. Seeded defects of different size were introduced separately in the form of an axial groove on the outer race of taper roller bearings using laser engraving technique. It is not only difficult but ambiguous to detect the entry point in the groove defect by making use of the signal. The ambiguity gets reduced by using Symlet5 wavelet due to its linear phase nature which maintains sharpness in the signal even when there is a sudden change in signal. The proposed technique has been successfully implemented for measuring defect width over a range of 0.5776–1.9614 mm. The resulting measure of defect width has been also verified using image analysis. Maximum deviation in result has been found to be 4.06% for the defect width of 1.1820 mm at no load which was found further reduced to 1.02% with increase in load. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Bearing defect is one of the causes of breakdown in rotating equipments. Different techniques based on the principle for measuring vibration, acoustic, thermal condition and wear analysis are used for detection of the bearing defects. Techniques based on vibration and acoustic emission are developing at a faster pace for monitoring rolling element bearings due to their non-invasive nature and their high reactivity to incipient faults [1,2]. In general, the diagnosis capability of the techniques is proportional to their complexity [3]. When bearings are installed as part of a complex mechanical system, the measured signal is often heavily clouded with various noises resulting from the compound effect of interferences caused by other machine elements and the background noise present in
⇑ Corresponding author. Tel.: +91 1672 253300; fax: +91 1672 280057. E-mail address: [email protected] (R. Kumar). 0263-2241/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2012.08.012
the measuring device [4]. The defect position can be identified by time–frequency analysis of the vibration or acoustic emission signal. Junsheng et al. [5] constructed an impulse response wavelet by using continuous wavelet transform to extract the feature of vibration signals. They proposed two methods, namely, the scale-wavelet power spectrum comparison and the auto-correlation analysis of time-wavelet power spectrum for detecting the faults of roller bearing and identifying the fault patterns. Yan and Gao [6] presented a signal processing algorithm based on multi-scale enveloping spectrogram for vibration signal analysis. This technique was evaluated for localized structural defects and experimentally found successful. Patil et al. [7] developed an analytical model to predict the effect of a localized defect on the ball bearing vibrations by considering the contact between the ball and the races as non linear springs. For deep groove ball bearing they obtained numerical results by using the model which yielded both the frequency and the acceleration of vibration components of the bearing for simulating the defect.
538
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
Fig. 1. Test rig for bearing defect identification. Inset shows the enlarged view at different angle for mounting of accelerometer at the bearing housing.
The analytical mode has its own drawback in meeting real-time scenario. To overcome this, the envelop analysis – the most popular signal processing method for bearing is proposed. In this method the vibration signal is first passed through a band-pass filter to obtain a high signal-to-noise ratio (SNR) signal, and then Hilbert transform is used to obtain the envelope [8]. Patel et al. [9] proposed a method for detection of local defects on races of deep groove ball bearing in presence of external vibration using envelope analysis and Duffing oscillators but could not attempt for measurement of defect size. Kumar et al. [10] investigated Analytical Wavelet Transform (AWT) based acoustic emission technique for identifying not only the presence but also the severity of the defect in the inner race of radial ball bearing. A comparison of wavelet decomposition-based de-noising method and wavelet filter-based de-noising method was made by Qiu et al. [11] for signals from mechanical defects. The finding of the comparison reveals that the wavelet filter based de-noising method is more suitable to detect a weak signature. The wavelet decomposition de-noising method achieved satisfactory results on smooth signal detection. Al-Ghamd and Mba [12] made an attempt to determine the bearing outer race defect width directly from the raw signal. The relationship between the defect size and acoustic emission of burst size was a significant finding but had not dealt with vibration signal in detail. Sawalhi and Randall [13] attempted to measure the seeded defect width by using two different approaches. In first approach pre-whitening of signal is done and then octave band wavelet analysis is carried out to allow selection of the best band (or scale) for balancing the two pulses with similar frequency content. In the second approach, separate treatment is applied to the step and the impulse responses, so that they may be equally represented in the signal. They emphasized the theory that the rolling element could strike at the end of a spall, as the ball moved half way through it and that impact could get reflected in the signal. The impact in the signal might be due to contact of the ball with the spall base. The peak of impulse in signal would have emerged
Fig. 2. Photograph of a taper roller bearing.
Fig. 3. A typical outer race groove defect of width 0.5776 mm.
when the ball might have come out from the spall after touching the exit corner of the spall. So there is possibility of error in measurement of defect width using the above
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
539
Fig. 4. A typical raw signal of 0.1 s duration for defect free bearing.
Fig. 5. A typical raw signal of 0.1 s duration for bearing having outer race defect of width 0.5776 mm.
method implemented by Sawalhi and Randall [13]. Clearly there appears a room for improvement in the methods suggested for identifying defect size in ball bearing system as locating exact position of commencement and end of the defect by vibration signal is still a challenge. The current work is carried out to estimate defect width in outer race of taper roller bearing using Symlet based wavelet decomposition. Extracting desired information from the signal is difficult especially when there is a mismatch between direction of defect and the roller-outer race line contact while passing over the defect. The acceleration signals resulting from the entry of the rolling element into the defect and that from its exit are of different nature. The Symlet wavelet is a near symmetri-
cal/linear phase filter, which makes it easier to deal with the small discontinuity present in the signal without any major loss of information which helps in properly locating the point of commencement and exit of roller from the groove defect. 2. Feature extraction in vibration signal The wavelet technique provides a time-scale information in the signal, and it can efficiently detect the transients [14]. The Continuous Wavelet Transform (CWT) is used in time–frequency analysis that decomposes a signal in both time domain and frequency domain simultaneously. The CWT can be defined as
540
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
Fig. 6. Decomposition graph up to 4th level using Symlet 5th order wavelet: (a) for the signal shown in Fig. 5 and (b) enlarged decomposition graph for the signal marked in Fig. 6a.
1 CWTða; bÞ ¼ pffiffiffi a
Z
1
1
XðtÞw
tb dt a
ð1Þ
where a represents the scale parameter, b represents the translation parameter, w represents the ‘mother’ wavelet and w⁄ is the complex conjugate of w. The CWT and its
computation may consume significant amount of time and resources, depending upon the resolution required. The Discrete Wavelet Transform (DWT), which is based on sub band coding is found to yield a fast computation of wavelet transform. Also, the CWT has the drawback of redundancy and impracticability with digital computers
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541
for a given N and have the same number of vanishing moments as the dbN family. They have the perfect reconstruction and cancellation capability that allows them to be used in both the CWT and the DWT. The Daubechies wavelet modified to construct the Symlet wavelet [16] involves reusing the mother wavelet function m0 introduced in the dbN, considering the jm0 ðxÞj2 as a function W of Z = eix. The use of Symlet based decomposition properly locates the point of commencement and exit of roller in the groove defect. The size of defect present on bearing race can be calculated with the knowledge of vibration burst duration Dt which is estimated using Symlet based decomposition, fundamental train frequency (FTF) and average outer race inner diameter (tapered one) DOI of the bearing. The outer race defect width Lod is [13]
Lod ¼ p Dt DOI FTF
ð4Þ
For the bearing NBC 30205 at inner race rpm 2050, the FTF is 14.316. Putting the given geometric parameter and value of FTF for the bearing, Eq. (4) is simplified as Fig. 7. A typical burst obtained after Symlet decomposition and the corresponding roller positions over an outer race defect width of 0.5766 mm size.
Lod ¼ 1993:61 Dt mm ðwhere Dt is in secondsÞ
ð5Þ
3. Experiment and result as it takes continuous values of parameters (a, b) [15]. Therefore, the scale and shift parameters are evaluated on a discrete grid of time-scale plane leading to a discrete set of continuous basis functions [16]. The DWT is a discrete form of the CWT. It adopts the dyadic scale and translation to reduce computation time. The DWT can be defined as
1 DWTða; bÞ ¼ pffiffiffiffi 2j
Z
1
1
XðtÞw
t 2j k 2j
! dt
ð2Þ
where 2j and 2jk represent the scale parameter and the translation parameter respectively. In this j and k are integers. The functions and scales are represented as an approximations value. The curves of scale functions can be modified by the scale parameter, which is the inverse ratio to frequency. The DWT analysis is made by passing the signal through a series of filters. These filters include both high-pass filters and low-pass filters. The high-pass filters examine the high frequency bands [i.e. Details (Dj)]. On the other hand, the low-pass filter analyzes the low frequency band [Approximations (Aj)]. The original signal X(t) can be defined as [15]
XðtÞ ¼ Aj þ
X
Dj
ð3Þ
j6j
where Aj and Dj represent the approximation and the detail signals of the jth level. Symlet wavelets are more symmetrical than the Daubechies wavelets. The Symlets have also nearly linear phase which makes them easier to deal with small discontinuity present in the signal without major loss of information [17]. They become more regular with larger N (‘‘SymN’’). They have the same compact support as the Daubechies
Experiments were performed on a customized test rig shown in Fig. 1. The shaft in the test rig is supported by two self aligned taper roller bearings (Make: NBC, Bearing number: 30205). The shaft is driven by an alternating current motor of 0.75 kW capacity (Make: Crompton, frequency 50 Hz, current 4.2 amp and speed 1440 rpm) with the help of V-belt and step pulley arrangement. This arrangement provides option of three different speeds of 1050 rpm, 2050 rpm and 3080 rpm approximately to the test rig shaft. During each experiment speed of the shaft is measured using an optical tachometer with digital display. The condition of the bearing mounted towards loading arrangement side as shown in Fig. 1 is monitored using a PCB make uni-axial accelerometer having sensitivity 1000 mV/g. Bearing under test is placed at this position only. The accelerometer is placed right above the bearing casing perpendicular to the axis of the rotation of the shaft in such a way so that it can acquire vertical acceleration. A personal computer based data acquisition system (Make: National Instrument, Model: SCXI-1000 having 4 channel input) is used to acquire the vibration data obtained from accelerometer. A program has been developed in Labview environment to acquire and display the signal along with its Fourier Transform. There is provision to record/store the signal in the hard disk of computer for further processing and analysis. The defect width has been analyzed using wavelet decomposition approach in Matlab environment. In the present study investigations have been made on four sets of the said bearing (NBC 30205 as shown in Fig. 2) each having different defect width 0.5776 mm,1.1820 mm, 1.7266 mm and 1.9614 mm on the outer race (OR). The defects have been generated using laser engraving technique. A typical defect of size 0.5776 mm is shown in Fig. 3. In this paper, results at the shaft speed of 2050 rpm are presented.
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Fig. 8. Decomposition graph up to 4th level using Symlet 5th order wavelet for the outer race defect of width 1.1820 mm.
When tested with the defect free bearing, the amplitude of the raw signal is obtained in the range of 1 to +1 mV as shown in Fig. 4. While dealing with the defective bearing it has been observed that amplitude of the burst in the raw signal has increased and is appearing in the range of 7 to +10 mV. A typical raw signal of the bearing having defect width of 0.5776 mm at 2 kg external load is shown in Fig. 5. The acceleration signals resulting from the entry of the rolling element into the defect and that from its exit are of different nature in terms of amplitude and probably in frequency as it appears from the raw signal. The wavelet decomposition analyzes the signal at different frequency bands with different resolution. The decomposition graph up to 4th level has been drawn by using Symlet 5th order mother wavelet for the case having defect width 0.5776 mm in the outer race and is shown in Fig. 6. Out of the three bursts appearing in Fig. 6b, one of the bursts of relevant time duration obtained using the symlet decomposition at 4th level is marked and put just above the bearing defect geometry to explain the phenomena of roller-outer race interaction while passing over the defect and is shown in Fig. 7. Three points in the signal namely GC1, GC2 and P shown in the Fig. 7 represent groove corner 1, groove corner 2 of the defect and maximum de-stressing point respectively. When the roller enters the defect groove passing GC1, point of the roller on the tangent parallel to the groove surface comes in air due to which signal appears to be de-stressed. Three different positions of the roller with respect to points GC1, P and GC2 at a cross section are shown as a circle having centers at c1, c2 and c3 respectively. Spotting GC1 from raw signal is very difficult because there is no distinct variation in amplitude but by using
decomposition graph de-stressing level in the signal gets enhanced. The de-stressing value (point GC1 to point P) has been calculated in percentage of the range for each individual burst (appropriate bursts selected for measuring defect width) in the 4th level decomposition graph obtained through Symlet5 and raw signal graph. The average value of de-stressing in the decomposition graph is 49.27% where as that in raw signal graph is 8.12%. This may arise due to the fact that the Symlet wavelet actually spots the GC1 by modulating the signal in such a way that amplitude due to de-stressing gets enhanced. The roller comes out from the groove defect when it comes in contact with GC2. This is generally a re-stressing event having highest amplitude. After this, the signal starts stabilizing as its amplitude progressively decreases due to damping action of elastic elements of the bearing. The variation in signal shown in Fig. 7 does not indicate any intermediate peak between the points GC1 and GC2 which implies that the roller is not touching the groove base. Data points are calculated between the points GC1 and GC2 marked on the signal to obtain the time taken by roller to pass the groove defect. In the similar manner signals were acquired for other defect sizes. The symlet wavelet decomposition of the signal for the outer race defect widths 1.1820 mm, 1.7266 mm and 1.9614 mm at 2 kg load are shown in Figs. 8–10 respectively. Encircled portion of the burst in Fig. 10 is superimposed on defect geometry diagram and is shown in Fig. 11. To explain the case of maximum defect size, three vertical lines have been drawn from the points GC1, GB1 and GC2. At point GB1, the roller strikes the groove base with high impact which results in re-stressing and high impulse in signal. After this event the roller
R. Kumar, M. Singh / Measurement 46 (2013) 537–545
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Fig. 9. Decomposition graph up to 4th level using Symlet 5th order wavelet for the outer race defect of width 1. 7266 mm.
Fig. 10. Decomposition graph up to 4th level using Symlet 5th order wavelet for the outer race defect of width 1.9614 mm.
remains in contact with the groove base for some time and during this period impulses due to the rough surface of groove are observed. When the roller comes in contact with the point GC2 it again generates high amplitude in the signal and beyond this (i.e. after GC2) progressive decrease in amplitude of signal is observed due to elastic
damping of bearing element. Three different positions of the roller with respect to the points GC1, GB1 and GC2 at a cross section are shown as a circle having centers at c1, c2 and c3 respectively. The roller may spin or slide during the operation of the bearing. Change in signal takes place when it slides. Also
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the shaft is not loaded. It may be due to the clearance between the cage and the roller which results into improper stressing and de-stressing while crossing over the groove edges. The difference between the two values appears reducing at loaded condition of shaft/bearing. 4. Conclusion
Fig. 11. A typical burst obtained after Symlet decomposition and the corresponding roller positions over an outer race defect width of 1.9614 mm size.
varying clearance between cage and roller changes the signal when the roller enters and exits from the groove defect. In the bearing under investigation there are 17 rollers. There is variation in data points for each roller crossing over the defect. Average data points for 17 successive bursts are calculated for estimating the time taken by roller to pass over the groove defect. The average of data points so calculated is converted into time duration to cross over from GC1 to GC2 taking into account the sampling frequency. Further using Eq. (5) which has been simplified for the specified bearing at the speed 2050 rpm (i.e. FTF = 14.316) the defect width is calculated. The defect width is also evaluated using image analysis. The values of defect width under different loading conditions have been measured by making use of signal processing as well as image processing. The details are presented in Table 1. It has been observed that the variation in data points between bursts is more at low defect widths when shaft is not loaded. The maximum difference in result has been obtained to be 4.06% for defect width of 1.1820 mm when
A technique based on decomposition using Symlet wavelet has been proposed for measuring outer race defect width of bearing. Experimental measurement and subsequent analysis reveal that decomposition of vibration signal by using Symlet 5th order mother wavelet is suitable for measuring outer race defect width of taper roller bearing. Sharp and high amplitude impulses are obtained when roller crosses over the entry and exit of the defect. When the roller remains in contact with the groove base between entry and exit, the impulses due to roughness of the groove surface are observed. The defect evaluation technique using decomposition extracts roller entry and exit components of signal from the groove defect in good time resolution. The difficulty in detecting the commencement/entry point of the defect in the signal is reduced by using Symlet5 which improves the sharpness of the signal. The proposed technique has been successfully implemented for measuring defect width over a range of 0.5776 mm to 1.9614 mm. The defect width has been also verified using image analysis. The maximum deviation in the two values of defect width obtained using aforementioned two different approaches at no load is 4.06% for defect width of 1.1820 mm. At intermediate load of 2 kg deviation has reduced to 1.02% for the same defect width. References [1] N. Tandon, A. Choudhury, A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings, Tribology International 32 (1999) 469–480. [2] M. Elforjani, D. Mba, Accelerated natural fault diagnosis in slow speed bearings with acoustic emission, Engineering Fracture Mechanics 77 (2010) 112–127. [3] J. Antoni, Cyclic spectral analysis in practice, Mechanical Systems and Signal Processing 21 (2007) 597–630. [4] I.S. Bozchalooi, M. Liang, A joint resonance frequency estimation and in-band noise reduction method for enhancing the detectability of
Table 1 Outer race groove defect width measurement using image processing and signal decomposition by Symlet5 at different loading conditions. Case
Loading condition
Average data points calculated Measured defect width Defect width measured % Deviation in result from from signal processing from the data points (mm) using image processing (mm) the image processing
OR defect-1 Without load 20.706 2 kg load 19.882 4 kg load 20.353
0.5900 0.5664 0.5798
0.5776
+3.70 1.93 +0.38
OR defect-2 Without load 40.674 2 kg load 41.059 4 kg load 42.059
1.1340 1.1700 1.1984
1.1820
4.06 1.02 +1.39
OR defect-3 Without load 59.706 2 kg load 60.941 4 kg load 60.882
1.7007 1.7358 1.7342
1.7266
1.50 +0.53 +0.44
OR defect-4 Without load 70.059 2 kg load 68.882 4 kg load 68.765
1.9956 1.9621 1.9587
1.9614
+1.74 +0.04 0.14
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