proposed the use of kurtosis for bearing defect detection. ..... [3] Randall, R. B., Applications of spectral kurtosis in machine diagnostics and prognostics, Key.
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Defect size estimation in rolling element bearings using vibration time waveform Mehdi Behzad1, Ahmad AlandiHallaj1, Abbas Rohani Bastami1, David Mba2 ,Babak Eftekharnejad 2, B.Charnley 2 1: School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran 2: School of Engineering, Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK
Abstract In this paper a new approach to determine the defect size of rolling element bearings is proposed. This approach is based on the statistical characteristics of the vibrations signals generated by rolling element bearings. Although some traditional statistical parameters such as RMS and kurtosis have some diagnostic capabilities, these parameters are not suitable for quantifying the defect size. The proposed new model was validated experimentally for both inner and outer race defects and it is concluded that the newly proposed model can determine the defect length of rolling bearings.
Key words: level crossing – rolling bearing – vibrations – defect size – linear correlation – time signal
Introduction Rolling element bearings are essential to almost all rotating machinery and as such monitoring these elements is essential. Although vibration diagnostics of roller bearings have been investigated in several studies, accurate determination of the defect size on the outer and inner rings has continually been one of the challenging issues in this domain.
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INSIGHT, Journal of British Institute of Non-Destructive Testing, Vol 51(8), 426-430, 2009
Vibration analyses for rolling bearing diagnosis are typically undertaken in the time domain, frequency domain, and/or in the time-frequency domain. Analysis in time domain is the simplest approach that is used to calculate the statistical features of the vibration time signals. Alfredson and Mathew [1] evaluated the capabilities of the time domain analyses to diagnose the rolling element bearing faults.
Use of statistical features such as peak value and the broad-band, or filtered, root-mean-square (RMS) level is one of the diagnostic techniques for determination of the intensity of faults in the rolling element bearings. In addition it is widely established that Kurtosis can also identify defects in bearings. This factor is a measure of impulsiveness of a signal and recognizes the defects that generate a set of impulses in the vibration signals. Dyer and Stewart [2] first proposed the use of kurtosis for bearing defect detection. For an undamaged bearing with Gaussian distribution, the kurtosis value is close to 3. A value greater than 3 is judged by itself to be an indication of impending failure and no prior history is required. However, one disadvantage is that the kurtosis value comes down to the level of an undamaged bearing (i.e., 3) when the damage is well advanced. Randall [3] used this parameter to determine the rolling bearing defects. Martin and Honarvar [4] also used statistical moments for initial detection of bearing defects whilst Kiral and Karagulle [5] employed time and frequency domain analysis for damage detection.
Some studies have concentrated on the life prediction and determination of the defect size of rolling element bearings. Marble and Morton [6] undertook a comprehensive experimental study of bearing spall progression and a physics-based model was developed for bearing prognostics. The model computed the spall growth trajectory and time to failure based on
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operating conditions, and used diagnostic feedback to self-adjust and reduce the prediction uncertainty. The experimental data demonstrated that spall propagation can be predicted with high confidence. Barkov and Barkova [7] provided approaches for condition assessment and lifetime prediction of rolling bearings by considering some matters such as origin and characteristics of flaw induced rolling element bearing vibration, methods to extract and identify the characteristics of specific bearing defects, and comparative standards to assess condition and predict residual lifetime. Williams et al. [8] tested new undamaged ball and roller bearings through to failure. Traditional vibration metrics such as: root mean square, peak value, kurtosis and crest factor were recorded through the test duration from accelerometers and acoustic emission sensors and lifetime prediction of rolling element bearings was performed. Al-Dossary et al.[9] and Al-Ghamdi [10] found a correlation between defect size and specific AE parameters. They ascertained the relationship between the duration of AE transient bursts associated with seeded defects to the actual geometric size of the defect. By this approach the geometric size of outer race defects were determined from the AE waveform. The application of Acoustic Emission technology to bearing diagnosis, and its associated difficulties in implementation, have been discussed [11-14]. On such diffculty in the application of AE to determining the defect size is attenuation and as such the AE receiving sensor must be as close to the defect source as possible. This has practical limitations in its operation useage.
For calculation of the remaining useful life of rolling element bearings, an estimate of the defect size would be desirable. Given the limitation in applying the AE technology a simple, robust and reliable method for estimation of defect size with vibration analysis is explored. A new statistical parameter for determination of dimensions of the defect area on inner and outer
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races of rolling element bearings has been developed which is based on comparing the number of times the vibration signal exceeds a pre-set threshold amplitude level of the vibration acceleration signal.. Experimental tests validated the usefulness of this parameter for estimating the size of defect area on inner and outer rings.
Experimental Test Set-up An experimental test-rig was used to investigate the bearing defect size of inner and outer races of rolling element bearings as shown in Fig. 1. The test bearing is 1206 self-aligning ball bearing and type 22311EK spherical roller bearing was used as support bearing. The rated radial load for the test bearing is 14 kN.
The radial load was provided by four screws and the value of applied force is displayed by a digital load cell. The shaft is driven by a 3-phase electromotor with a speed controller. A piezoelectric accelerometer is attached to the housing of test bearing to acquire the vibration signals. The rotational speed of the shaft drive was constant at 1500 rev/min. The system is lubricated by oil with viscosity of 20 mm2/s at 64 oC.
The data acquisition system consisted of a measuring amplifier, A/D card; all vibration measurements passed thorough a high-pass and low-pass filter at 10 Hz and 10 kHz, respectively. A sampling rate of 20kHz was employed and a schematic of test rig and data acquisition system is shown in Fig. 2.
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It should be noted that the outer race defects were not simulated but occurred naturally due to the excessive load applied (larger than the dynamic load rating),dimension of which are detailed in table 1.Table 2 presents defect dimension on the inner race which were artificially seeded . During the tests, inspection of inner and outer rings for measurement of the size of defect area was performed. The test was interrupted every 400,000 cycles to measure the defect size. Some sample defects in the bearing elements are shown in Fig. 3.
Each bearing element has a characteristic rotational frequency. With a defect on a particular bearing element, an increase in vibration energy at this element’s rotational frequency may occur. These characteristic defect frequencies can be calculated from kinematic considerations; i.e., the geometry of the bearing and its rotational speed [15]. For a bearing with a stationary outer race, these frequencies are given by the following expressions: • Ball Pass Frequency Outer race (BPFO) f BPFO (Hz ) = n f r æç1 - BD cos b ö÷ 2
è
PD
(1)
ø
• Ball Pass Frequency Inner race (BPFI) f BPFI (Hz ) = n f r æç1 + BD cos b ö÷ 2
è
PD
(2)
ø
where fr is the shaft rotation frequency in Hz, BD is the diameter of the rolling element, PD is the pitch diameter, n is the number of rolling elements and b is the contact angle. For normal speeds, these defect frequencies lie in the low-frequency range and are usually less than 500 Hz. Moreover it has been observed that, in case of a defect on a moving element such as the inner race or a rolling element, the spectrum has sidebands about the components at characteristic defect frequencies [16-19]. With regard to the geometry of test bearing and
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rotational speed of shaft, values of 205.3 and 144.7 Hz were calculated for ball pass frequencies of inner and outer rings, respectively. Fig. 4 shows a vibration spectrum of defective test bearing with an inner race defect. The inner race defect frequency in this spectrum is at 205.1 Hz. Since inner race is a moving element, there are sidebands around this frequency. The sidebands are normally centered at the inner race defect frequency, and its harmonics, plus and minus integer multiples of the frequency of shaft rotation, i.e., 25 Hz. Fig. 5 also illustrates the vibration spectrum of defective bearing with a defect on the outer race. The observed peak at 144.5 Hz was related to the outer race defect. Harmonics of this frequency are also noted in fig 5.
Model Development Based on Level Crossing Rate (LCR) Using kurtosis, a defect can be determined in initial stages. After a defect development on bearing rings, passing of each rolling element over the defect may generate impulses in the vibration signals, and so kurtosis value increases. Fig. 6 shows the variation of this parameter versus running cycle of a bearing. Observations of kurtosis indicated the test bearings became faulty at nearly 6.1 million cycles. As shown in fig.6, although this parameter facilitates the initial detection of defect, it offers no information on the defect size..
A method to estimate the defect size is based on RMS value of vibrations. In this instance, one can correlate the defect size on bearing rings and the RMS level of vibrations. Fig. 7 illustrates variation of the defect length on outer race of the test bearing versus the RMS level of the vibration acceleration. Parameter R2 stands for the correlation coefficient between the defect length on the outer race and the RMS level in this figure. When this coefficient tends to
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1, the defect length can be estimated with a linear correlation. Clearly a correlation between increasing defect size and r.m.s is evident as to be expected.
An increase in defect length on the inner and outer bearing rings will result in an increase in vibration impulses. For the investigation reported in this paper the defect on the bearing varied with length and depth over time whilst the defect width remained relatively constant. Fig. 8 shows the acceleration time signals of a defective bearing with an inner race defect at different running cycles. As shown in figure 8, the number of transient vibration peaks increases with increasing defect size.
Given the impulsive nature of the vibration signals associated with the defective bearing, and noting that the overall vibration levels also increased with increasing defect size, a ‘level crossing’ technique was developed. This type of analysis is similar to the count technique employed for Acoustic Emission analysis, and, this is the first known attempt at employing the count technique to analysis vibration signatures.
Level crossing is a statistical feature of a signal which counts the number of crossings of a specific level for that signal. This factor is related to the distribution of the peaks in a given period of time [20]. Fig. 9 shows a close-up view of the vibration time signal of a bearing with inner race defect during one shaft rotation. Different threshold levels have been plotted and the crossings of time signal with these levels are shown and presented in table 1. It is observed that the number of level crossings decreases for higher levels.
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In this study one second periods are used as samples of the time signal and the number of level crossings of these samples was used as a measure for estimation of defect length growth. Table 1 shows the rate of level crossings for various levels of the vibration acceleration associated with different defect length on inner race of the test bearing. The results presented in table 1 shows that growth of the defect length increases the number of peak crossings for a specific level. Fig. 10 shows the variation of the defect length versus the number of peak crossings for defect lengths less than 6 mm. As shown in figure 11, a linear correlation with defect length was noted, especially for the defects which have lengths less than 6 mm. This means that for a specific level value, the number of peak crossing increases linearly with increasing the defect length of inner race. Fig. 10 also gives the correlation coefficient of each level. This figure clearly shows levels of 30, 40, and 50 m/sec2 exhibit more linear trends than levels of 70 and 80 m/sec2. The correlation coefficients which are close to 1 indicate suitable levels for a better estimate of defect size. Therefore, it is necessary to specify a suitable level for reliable estimation of the defect size on the bearing rings. Since the width of defect area on the inner race is approximately constant and equal to 3 mm, this pattern can be used for defects with areas less than 18 mm2. Fig. 11 shows the variation of defect length on outer race versus the number of level crossings of levels of 10 to 80 m/sec2. As this figure shows, there is a linear correlation between the number of crossings and the length of defect for outer race defect. Level of 5 m/sec2 shows the best linear behavior between the level crossing rate and the defect length. However, all of these levels can be used to obtain a linear estimation in order to determine the approximate area of defects. The width of defect area on the outer race is relatively constant and equal to 2 mm; therefore, this model can be used for defects which have areas less than 28 mm2.
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Estimation of the defect size Taking into the considerations the result of this research, the levels of 30, 40, and 50 m/sec2 can be selected as the best levels to determine the defects on the inner race of rolling bearings. Given that the test results are particular to the test bearing the authors have attempted to explore an automatic threshold setting which may be applied to any bearing. As such threshold levels determined in terms of the standard deviation of vibrations was employed. Since the standard deviation of vibrations for a healthy bearing in the test operating conditions is 15 m/sec2, it can be concluded that the levels between 2so and 3.5so are the best levels to estimate the defect size on inner race where so denotes the standard deviation of vibrations for a healthy bearing. For the outer race defects, the levels of 5, 10, and 20 m/sec2 are the best levels to determine the defect length. It should be noted that other levels may also be used to estimate the size of defect area with quite acceptable reliability. Similarly, the levels between 0.3so and 1.5so are considered as the best levels to estimate the defect size on outer race of rolling bearings. The results of experimental tests show that for outer race defects, a wide range of values can be considered as the acceptable levels which can estimate the defect size with a high reliability, but for inner race defects, only a limited range of values can be used to estimate the defect size with a good estimation.
Having determined the location of defect through characteristic defect frequencies, a level should be selected to estimate the defect size. Employing a correlation between the defect size and the rate of level crossing, the approximate defect length can be calculated. For example, if the level of 5 m/sec2 is selected to estimate the outer race defect size, the following equation can be used to calculate the defect length
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L = 0.009 LCR a =5 - 72.45
(3)
where LCR a =5 is the level crossing rate (Number/second) at 5 m/sec2 and L denotes the defect length on outer race in terms of millimeter.The equation was dervived from an empirical fit to data at 5 m/sec2 see figure 11. To consider other levels for defect size estimation, other linear relations can be extracted from experimental data to use as a new formula to determine the defect size.
Having developed a model to determine the defect size on both inner and outer races, the next test was performed to evaluate the effectiveness of this model. A new test was run which was inspected every 100,000 cycles and the defect length on outer race was measured. The results of this test are shown in Table. 1. The estimated values for defect length were obtained based on the LCR values and considering the level of 5 m/sec2 as the threshold level; this threshold level is within the range 0.3so and 1.5 so. As this table shows, the estimated defect lengths are in a good agreement with measured values of defect sizes. These results show that the new approach can approximate the length of defect with a reliable estimation.
Conclusion In this paper, the rate of level crossing of vibration time signals was used as an approach in order to determine the defect size of rolling element bearings for the first time. To estimate the defect length on the inner and outer rings, threshold levels have been specified and the rate of crossings was employed to estimate the defect length on both inner and outer races of
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rolling element bearings. Experimental results showed that this parameter has an acceptable linear correlation with the defect length on the rolling bearing rings.
References [1] Alfredson, R. J., Mathew, J., Time domain methods for monitoring the condition of rolling element bearings, Transactions of the Institution of Engineers, Australia. Mechanical engineering ME 10 (2), 1985, pp. 102-107. [2] Dyer D, Stewart RM. Detection of rolling element bearing damage by statistical vibration analysis. Trans ASME, J Mech Design 1978;100(2):229–35. [3] Randall, R. B., Applications of spectral kurtosis in machine diagnostics and prognostics, Key Engineering Materials, v 293-294, 2005, pp. 21-30. [4] Martin, H.R., Honarvar, F., Application of statistical moments to bearing failure detection, Applied Acoustics 44 (1), 1995, pp. 67-77. [5] Kiral, Z., Karagülle, H., Simulation and analysis of vibration signals generated by rolling element bearing with defects, Tribology International 36 (9), 2003, pp. 667-678. [6] Marble, S., Morton, B. P., Predicting the remaining life of propulsion system bearings, IEEE Aerospace Conference Proceedings 2006, art. no. 1656121. [7] Barkov, A., Barkova, N., Condition assessment and life prediction of rolling element bearings, S V Sound and Vibration, v 29, n 9, Sep, 1995, pp. 27-31. [8] Williams, T., Ribadeneira, X., Billington, S., Kurfess, T., Rolling element bearing diagnostics in run-to-failure lifetime testing, Mechanical Systems and Signal Processing, v 15, n 5, Sept. 2001, 979-93. [9] Al-Dossary, S., Hamzah, R.I.R., Mba, D., Observations of changes in acoustic emission waveform for varying seeded defect size in a rolling element bearing, Applied Acoustics, DOI: 10.1016/j.apacoust.2008.01.005.
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[10] Al-Ghamd, A. M., Mba, D., A comprehensive experimental study on the use of Acoustic Emission and vibration analysis for beairng defect identification and estimation of defect size, Mechanical Systems and Signal Processing 20 (7), 2006, pp. 1537-1571. [11] Choudhury, A. Tandon, N., Application of acoustic emission technique for the detection of defects in rolling element bearings, Tribology International 33 (1), 2000, pp. 39-45. [12] Yoshioka, T., Fujiwara, T., Measurement of propagation initiation and propagation time of rolling contact fatigue crack by observation of acoustic emission and vibration. In: Dowson D et al, editor. Interface dynamics. Amsterdam: Elsevier, 1988. p.29–33. [13] Mba, D., Rao, R.B.K.N., Development of Acoustic Emission Technology for Condition Monitoring and Diagnosis of Rotating Machines; Bearings, Pumps, Gearboxes, Engines and Rotating Structures, Shock and Vibration digest 38(1), 2006, pp. 3-16. [14] Sikorska, J.Z., Mba, D., Challenges and obstacles in the application of acoustic emission to process machinery, Journal of Process Mechanical Engineering, Part E, IMechE 222 (1), 2008, pp. 1-19. [15] Tandon, N., Nakra, B. C., Vibration and acoustic monitoring techniques for the detection of defects in rolling element bearings-a review, Shock Vibr Digest 24(3), 1992, pp. 3–11. [16] Dyer, D., Bearing condition monitoring. In: Interim Report 1. Southampton (UK): Department of Mechanical Engineering, University of Southampton, 1973. [17] Igarashi, T., Hamada, H., Studies on the vibration and sound of defective rolling bearings (first report: vibration of ball bearings with one defect). Bull JSME 1982;25(204):994–1001. [18] Martins, LG., Gerges, SNY., Comparison between signal analysis for detecting incipient bearing damage. In: Proceedings of the International Condition Monitoring Conference, Swansea, UK, 10–13 April, 1984. p.191–204 [19] Tandon, N., Nakra, BC., Detection of defects in rolling element bearings by vibration monitoring. J Instn Engrs (India) — Mech Eng Div 1993;73:271–82. [20] Newland, D. E., An introduction to random vibrations, spectral and wavelet analysis, Longman Scientific & Technical, New York, 1993.
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Test Bearing
Fig. 1. Experimental test set-up
RMS 12.6 Peak-to-Peak 96.3
Fig. 2. A schematic of test set-up and data acquisition system
(a)
(c)
(b)
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Fig. 3. Defect on (a) outer race, (b) inner race, and (c) ball
15000
X: 179.7 Y: 1.101e+004
fBPFI
Amplitude (m/s2)
10000
X: 254.9 Y: 5682 X: 279.3 Y: 4597
5000 X: 155.3 Y: 3328
0
50
100
150
X: 205.1 X: 229.5 Y: 2554 Y: 2655
200
250
300
350
400
Frequency (Hz)
Fig. 4. A typical vibration spectrum of rolling bearing with inner race defect 4
x 10
3ÍfBPFO
4
3.5
X: 579.1 Y: 4.396e+004
X: 434.6 Y: 3.184e+004
2ÍfBPFO
2.5
fBPFO
Amplitude (m/s2)
3
2
1.5 X: 144.5 Y: 9490
1
X: 290 Y: 7057
0.5
0
50
100
150
200
250
300
350
400
450
500
550
Frequency (Hz)
Fig. 5. A typical vibration spectrum of rolling bearing with outer race defect
14
600
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9
8
Kurtosis
7
6
5
4
3
2
0
1
2
3
4
5
6
7 6
x 10
Fig. 6. Kurtosis value greater than 3 is the symptom of impending failure
14 R2 = 0.89 12
Defect Length (mm)
Cycles
10 8 6 4 2 0 0
10
20
30
40
50
RMS level (m/s2)
Fig. 7. Variation of the defect length on outer race of the best bearing versus the RMS level of the vibration acceleration
15
800
800
600
600
400
400
Amplitude (m/s2)
Amplitude (m/s2)
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200 0 -200 -400 -600 0
0.2
0.4
-400
0.6
0.8
-800
1
0.2
0.4
Time (s)
(a)
(b)
800
800
600
600
400
400
200 0 -200 -400
-800
0
Time (s)
-600
0.6
0.8
1
0.6
0.8
1
200 0 -200 -400 -600
0
0.2
0.4
0.6
0.8
-800
1
0
0.2
0.4
Time (s)
Time (s)
(c)
(d)
Fig. 8. Vibration time signals of a faulty bearing with inner race defect (a) 1 million, (b) 2 million, (c) 3 million, and (d) 4 million cycles
150
100 90 80 70 60 50 40 30 20 10 0
Amplitude (m/s2)
0 -200
-600
Amplitude (m/s2)
Amplitude (m/s2)
-800
200
-50
-100
-150
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Time (sec)
Fig. 9
Vibration time signal of a bearing with inner race defect and its crossings with different levels
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Table 2. Rate of level crossings for various defect lengths on inner race Running Cycle (million cycle)
Defect Length (mm)
30 m/s2
1.0 2.0 2.4 3.0 3.4 4.0 4.4
0.7 1.7 1.9 4.4 6 11.5 17.3
2193 2332 2599 3515 3751 5795 5870
Rate of level crossings (number/second) 40 m/s2 50 m/s2 60 m/s2 70 m/s2 1331 1572 1704 2338 2590 4625 4696
859 1204 1280 1591 1833 3594 3702
609 992 1010 1162 1371 2792 2868
461 820 845 873 1013 2080 2194
80 m/s2 355 699 730 743 803 1562 1666
9 Level 10
8
2
R = 0.77 2 R = 0.89
7
Defect Length (mm)
Level 20
2
2
R = 0.64
R = 0.97
Level 30
6
R2 = 0.99
5
2
R = 0.97
R2 = 0.87
2
R = 0.86
Level 40
4
Level 50
3
Level 60
2
Level 70
1 Level 80
0 0
1000
2000
3000
4000
5000
6000
7000
8000
Rate of Crossings (number/second)
Fig. 10. Defect length on inner race versus the level crossing rate for defect lengths less than 6 mm
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14 Level 2 2
2 R = 0.85 R2 = 0.83 R = 0.85 R2 = 0.87 2 R = 0.84
12
2
R = 0.89
2
R = 0.92
2
2
R = 0.93 R = 0.95
Level 10
10
Defect Length (mm)
Level 5
Level 20
8
Level 30 Level 40
6 2
R = 0.89
4
Level 50 Level 60 Level 70
2
Level 80
0 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Rate of Crossings (number/second)
Fig. 11 . Defect length on outer race versus the level crossing rate for defect lengths less than 14 mm
Table 1. Estimation of defect length on outer race through LCR values Running Cycle (million cycle) 1.1 1.2 1.3 1.4 1.5 1.6
LCR (No./sec) 8129 8998 9026 9138 9189 9268
Estimated Defect Length (mm) 0.7 8.4 8.8 9.9 10.2 11
18
RMS (m/sec2) 21 31.3 32.8 39.7 40.4 43.2
Actual Defect Length (mm) 1 8.7 9.25 10.7 11.1 12.25
