- Email: [email protected]
Condition monitoring of a single-stage gearbox with artificially induced gear cracks utilizing on-line vibration and acoustic emission measurements
Applied Acoustics 70 (2009) 1148–1159
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Condition monitoring of a single-stage gearbox with artificially induced gear cracks utilizing on-line vibration and acoustic emission measurements T.H. Loutas, G. Sotiriades, I. Kalaitzoglou, V. Kostopoulos * Department of Mechanical Engineering and Aeronautics, University of Patras, Patras GR-26500, Greece
a r t i c l e
i n f o
Article history: Received 7 October 2008 Received in revised form 15 April 2009 Accepted 16 April 2009 Available online 17 May 2009 Keywords: Advanced signal processing Acoustic emission Vibration Condition monitoring Gearbox
a b s t r a c t The condition monitoring of a lab-scale, single stage, gearbox using different non-destructive inspection methodologies and the processing of the acquired waveforms with advanced signal processing techniques is the aim of the present work. Acoustic emission (AE) and vibration measurements were utilized for this purpose. The experimental setup and the instrumentation of each monitoring methodology are presented in detail. Emphasis is given on the signal processing of the acquired vibration and acoustic emission signals in order to extract conventional as well as novel parameters–features of potential diagnostic value from the monitored waveforms. Innovative wavelet-based parameters–features are proposed utilizing the discrete wavelet transform. The evolution of selected parameters/features versus test time is provided, evaluated and the parameters with the most interesting diagnostic behaviour are highlighted. The differences in the parameters evolution of each NDT technique are discussed and the superiority of AE over vibration recordings for the early diagnosis of natural wear in gear systems is concluded. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In gearboxes and power drive trains in general, gear damage detection is often very critical and can lead to increased safety in aviation and in industry as well. Thus the interest for their periodic non-destructive inspection and/or on-line health monitoring is growing and effective diagnostic techniques and methodologies are the objective of extensive research efforts over the last 50 years. Few research teams have published experimental data coming from long-term testing to see the effect of natural gear pitting mostly upon vibration recordings. Dempsey et al. [1–4] and Decker with Lewicki [5] have conducted some excellent experimental work at GRC/NASA and published interesting results from extensive gear testing at a special test-rig utilizing vibration and oil debris measurements. With the clear goal to improve the performance of the current helicopter gearbox health monitoring systems, they have tested gears at high shaft speed for multi-hour periods (up to 250 h) and correlated special features (based on higher order moments) extracted form the vibration recordings with the Fe debris mass accumulated during the tests. They have integrated their results in a fuzzy logic based health monitoring system with satisfactory performance. Researchers in the field have focused mainly on advanced signal processing techniques applied on vibration recordings coming mainly from artificial gear defects in short tests rather than inducing gear pitting damage in multi-hour testing. * Corresponding author. E-mail address: [email protected] (V. Kostopoulos). 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.04.007
The publications in the field of condition monitoring via vibrations are quite versatile. Selecting a few and focusing on advanced signal processing techniques the works of Wang and McFadden [6,7] must be mentioned, that utilized time-frequency analysis techniques and showed that the spectrogram has advantages over Wigner–Ville distribution for the analysis of vibration signals for the early detection of damage in gears. The same authors have also employed the wavelet transform [8,9] to analyze the local features of vibration signals and showed that unlike the time-frequency distribution, which incorporates a constant time and frequency resolution, the wavelet transform can accommodate simultaneously both the large and small scales in a signal, enabling the detection of both distributed and local faults. Baydar and Ball [10,11] have proposed the instantaneous power spectrum and have shown that it is capable in detecting local tooth faults in standard industrial helical gearboxes. The propagation of local faults was identified by monitoring variations in the features of the power spectrum distribution. The same authors have also applied the Wigner–Ville distribution [12] as well as the wavelet transform [13] on vibration and acoustic signals for the same purpose. The interest for applications of acoustic emission (AE) for condition monitoring in rotating machinery is relatively new and has grown significantly over the last decade. AE in rotating machinery is defined as elastic waves generated by the interaction of two media in motion, i.e. a pair of gears. Sources of AE in rotating machinery include asperities contact, cyclic fatigue, friction, material loss, cavitations, leakage, etc. AE technique has drawn
1149
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
attention as it offers some advantages over classical vibration monitoring. First of all, as AE is a non-directional technique, one AE sensor is sufficient in contrast to vibration monitoring which may require information from three axes. Since AE is produced at microscopic level it is highly sensitive and offers opportunities for identifying defects at an earlier stage when compared to other condition monitoring techniques. As AE mainly detects high-frequency elastic waves, it is not affected by structural resonances and typical mechanical background noise (under 20 kHz). Tandon and Mata [14] applied AE to spur gears in a gearbox test-rig. They simulated pits of constant depth but variable size and AE parameters such as energy, amplitude and counts were monitored during the test. AE was proved superior over vibration data on early detection of small defects in gears. Singh et al. [15] also applied AE technique in condition monitoring of test-rig gearboxes, while vibration methods was also used for comparative purposes by placing accelerometers on the gearbox casing. They also concluded that AE provided early damage detection over vibration monitoring. Toutountzakis et al. [16] investigated the influence of oil temperature and of the oil film thickness on AE activity and on AE signals captured during continuous running of a back-to-back gearbox test-rig. It was observed that the AE RMS varied with time as the gear box reached a stabilized temperature and the variation in AE activity RMS could be as much as 33%.
Tan and Mba [17] discussed in more detail the oil temperature effect on AE and concluded that the source of AE mechanism that produced the gear mesh bursts was from asperities contact. Toutountzakis and Mba [18] presented some interesting observations on AE activity due to misalignment and natural pitting and concluded that the AE technique is applicable for monitoring gear damage. Finally a comparative study [19] between AE and vibrations was conducted to show the diagnostic and prognostic capabilities of each technique in several multi-day tests in a singlestage gearbox. The present work reports the results concluded by long term (50 h) experiments to a defected gear system, with a transverse cut of 25% of root thickness to simulate the tooth crack. Different parameters, resulted by the analysis of the recording signals (both coming from vibration monitoring and AE) are presented and their diagnostic value is discussed in the direction of being used
Table 1 Conventional parameters calculated from the acquired waveforms. Time domain parameters PN xðnÞ p1 ¼ n¼1 N rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN ðxðnÞp1 Þ2 n¼1 p2 ¼ N1 PN pffiffiffiffiffiffiffiffi2 jxðnÞj n¼1 p3 ¼ N rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N
p4 ¼
Frequency domain parameters PK
p12 ¼
p13 ¼ p14 ¼
ðxðnÞÞ2 N
p15 ¼
n¼1
k¼1
sðkÞ
K
PK
ðsðkÞp12 Þ2 ðK1Þ
k¼1
PK
ðsðkÞp12 Þ3 pffiffiffiffiffiffi 3 K ð p13 Þ
k¼1
PK k¼1
ðsðkÞp12 Þ4 2
PK Kp13 fk sðkÞ p16 ¼ Pk¼1 K
p5 ¼ max jxðnÞj
k¼1
p6 ¼ p7 ¼
PN n¼1
PN
ðxðnÞp1 Þ3
p17 ¼
ðN1Þp32
n¼1
p8 ¼ p9 ¼
p5 p3
k¼1
ðxðnÞp1 Þ4
k¼1
f sðkÞ
k¼1 k
PK 2 f sðkÞ k¼1 k ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p20 ¼ qP P K
k¼1
n¼1
p11 ¼ 1 PNp5 N
n¼1
sðkÞ
jxðnÞj
jxðnÞj
17
Wavelet type
Number of levels
Time synchronous averaging (only for vibration signals)
K
f 4 sðkÞ k¼1 k
p21 ¼ pp17 16 PK ðfk p Þ3 sðkÞ p22 ¼ k¼1 Kp3 16 17 PK ðfk p Þ4 sðkÞ p23 ¼ k¼1 Kp4 16 17 PK ðfk p16 Þ1=2 sðkÞ ffi p24 ¼ k¼1 K pffiffiffiffiffi p
Fig. 1. Test bench setup.
Vibration and AE signals
sðkÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PK 4 f sðkÞ p19 ¼ PKk¼1 k2
p10 ¼ 1 PNp4 N
ðfk p16 Þ sðkÞ K
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PK 2 fk sðkÞ Pk¼1 p18 ¼ K
ðN1Þp42
p5 p4
sðkÞ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi PK 2
Discrete Wavelet transform – n levels of decomposition
Energy content determination for each level
Plot of energy levels vs defect types
Fig. 2. Flow chart of the DWT-based methodology.
1150
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
for the development of a condition monitoring system. Furthermore, a systematic comparison of the different diagnostic parameters is provided, in order to assess which are the most robust and reliable ones for the condition monitoring of gearboxes and drive trains. The paper closes with the conclusions drawn from this study.
2. Experimental setup Fig. 1 shows the experimental setup used for the gears testing. The test-rig consists of two gears made from 045M15 steel with a module of 3 mm, pressure angle 20°, which have 53 and 25 teeth with 7 mm face width. The axes of the gears are supported by two ball bearings each. The entire system is settled in an oil basin in order to ensure proper lubrication. The gear box is powered by a motor and consumes its power on a generator. Their characteristics are as follows: – 1 stage gearbox with two gears (25 and 53 teeth); – 3-phase 5 hp motor (220 V, 9 A, 50 Hz, 1400 rpm) controlled by inverter; – single phase generator with continuous power consumption control (load fluctuation), 4.2 KVA, 3000 rpm, 50 Hz; – the oil pump is of the wet type without oil recirculation; – the shafts are ball bearing supported. Two non-destructive techniques have been employed to monitor the gearbox during operation, namely vibration and acoustic emission. Two Bruel & Kjaer accelerometers were used for the vibration monitoring both mounted upon the gearbox case, one in each side-axis. The sampling frequency used was 50 kHz and signals of 1 s duration were recorded. Additionally three wide band
Fig. 3. Tooth crack.
(a)
(b)
3rd transition (tooth break)
1.0
0.8
ED1
0.6 1st transition
2nd transition
0.4
700%
p6 parameter
0.8
0.4 350%
1100%
1500%
0.0 0
25
0.0
300 350 400 450 500 550 600 650 # of recordings
0
(d)
1.0
0.8
0.6
0.6
0.4 0.2
450%
25
400
450 500 550 # of recordings
600
650
1.0
0.8
p13 parameter
p7 parameter
0.6
0.2
0.2
(c)
1.0
0.4
300%
0.2 90%
2800%
0.0 0
25
400
450
500
550
# of recordings
600
650
0.0 0
25
400
450
500
550
# of recordings
Fig. 4. Parameters evolution during the test for vibration ch1 (a) ED1, (b) p6, (c) p7 and (d) p13.
600
650
1151
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
acoustic emission sensors manufactured by Physical Acoustics Corporation (PAC) with a frequency response range of 100–800 kHz recorded continuous AE signals of 100 ms duration at a sampling rate of 2 MHz. Fig. 1 shows the positions of all the sensors. One AE sensor is mounted on the output shaft (AE channel 1), the second is placed upon one of the bearings of the same shaft (AE channel 3) and the third (AE channel 2) is in friction contact with the input rotating gear. A special innovative device was designed in-house and discussed elsewhere [20] in order to mount the AE sensor upon a rotating component without the expensive/ demanding solution of the slip-ring generally used in literature. The recordings of all the above data coming from accelerometers and AE sensors are realized by a National Instruments NI6070 1MS/SEC FIREWIRE data acquisition device and assisted by special software developed in-house, in Labview programming environment. Finally, the temperature of the oil bath within the gearbox is measured via a thermocouple. 3. Signal processing methodologies Significant effort was dedicated to the signal processing of the vibration and AE waveforms acquired during the tests. The goal set a priori was to calculate a number of parameters–features extracted by the signals and check their behavior during the tests
(a)
in order to identify the most promising ones that may be used for damage detection and condition monitoring of the gear system. In the literature, very few research groups have been involved in long term gear testing and they have mainly used higher order moments and their combinations to form diagnostic parameters [1–5] with interesting behavior during the tests. In this work, apart from parameters usually found in the literature, we have introduced some more advanced signal processing techniques such as the discrete wavelet transform and extracted innovative wavelet-based parameters from the signals. In total more than 40 parameters are checked for their diagnostic ability. Those capable of monitoring the damage are identified and compared. 3.1. Conventional parameters In Table 1 conventional parameters from the time and frequency domain that were calculated, are shown. Where x(n) is a signal series for n = 1, 2, . . . , N, N is the number of signal samples and s(k) is the Fourier transform for k = 1, 2, . . . , K, K is the number of spectrum lines, fk is the frequency value of the kth spectrum line. Parameter p1 is the mean of the signal, p2 is its root mean square, p5 is obviously the absolute maximum of the signal, p4 the standard deviation, p6 and p7 the third and fourth moments whilst p8–p11 result as a combination of previous parameters all calculated by the
(b)
0.014
0.0020
0.012 0.0015
0.006 25%
p6 parameter
0.008 ED1
1st transition
1st transition
0.010
0.0010
0.0005 2200%
0.004 0.0000
0.002 0.000 0
50
100
150
200
250
300
350
0
400
50
100
200
250
300
350
400
# of recordings
# of recordings
(c)
150
(d)
0.00015
0.10 1st transition
p13 parameter
p7 parameter
0.00010
0.00005
0.08
0.06
122%
0.04
0.00000 0
50
100
150
200
250
300
350
400
0
50
# of recordings Fig. 5. A magnification of Fig. 2 over the first 420 recordings.
100
150
200
250
# of recordings
300
350
400
1152
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
signal in time domain. Correspondingly, p12–p24 are extracted in the frequency domain. These parameters are typical parameters in the time and in the frequency domain that can be extracted from any signal. 3.2. Discrete wavelet transform based parameters The wavelet transform was utilized to develop new parameters and check their behavior during the tests. The major advantage of wavelets is their inherent ability to perform local analysis with varying precision. Wavelet transform treats low frequencies with low resolution and high frequencies with high resolution [21]. Wavelets stem from the iteration of filters and filter banks (with rescaling) so they are inherently orthogonal or biorthogonal. In contrast to the Fourier analysis, which consists of breaking up a signal into sine waves of various frequencies, wavelet analysis breaks up the signal into shifted and scaled versions of the original (or mother) wavelet. The inverse discrete wavelet transform can be expressed as:
f ðtÞ ¼ c
XX j
DWðj; kÞwj;k ðtÞ
ð1Þ
k
where c is a constant depending only on w. Eq. (1) is the backbone of the present work and the whole philosophy of using wavelets for analysis of transient and non-stationary signals, as it states that a given time series signal can be decomposed by the discrete
1.0
(b) 1.0
0.8
0.8
0.6
0.6 ED2
ED1
(a)
0.4
0.2
0.0
0.0
25
400
450 500 550 # of recordings
600
650
1.0
(d) 1.0
0.8
0.8
0.6
0.6
p23 parameter
p12 parameter
0.4
0.2
0
(c)
wavelet transform into its wavelet levels, where the summation of these levels represent the original input signal. The decomposed wavelet levels are channeled in such a way that each level corresponds to a certain frequency range of the acquired signal. The DWT-based methodology used in this work was introduced and described elsewhere [21,22]. Fig. 2 schematically summarizes the complete procedure. It comprises the Discrete Wavelet Transform (DWT) of the time synchronous averaged acquired vibration signals and AE signals in 10 levels of decomposition using the ‘db10’ wavelet. As far as the type of wavelet for the discrete transform is concerned ‘db10’ was a good compromise of smooth function, without sharp edges as in the case of ‘db’ wavelets of lower order. The family of Daubechies wavelets was chosen because it consists of biorthogonal, compactly supported wavelets, satisfactorily regular though not symmetrical. Other wavelets having similar properties to the Daubechies family, such as symlets or coiflets were also tried with minor impact upon the results. The decomposed wavelet levels are split in a way that each level corresponds to a certain frequency range. After the 10-level decomposition the energy of each level (10 details and one approximation) is calculated. Thus eleven parameters namely ED1–ED10 (for the details) and Ea10 (for the approximation) were resulted. Additionally the sub-band wavelet entropy (SWE) is calculated. SWE is defined in terms of the relative wavelet energy of the wavelet coefficients. The energy at each resolution level j is defined in
0.4 0.2
0
25
400
450 500 550 # of recordings
600
650
0
25
400
450 500 550 # of recordings
600
650
0.4 0.2 0.0
0.0 0
25
400
450 500 550 # of recordings
600
650
Fig. 6. Parameters evolution during the test for vibration ch2 (a) ED1, (b) ED2, (c) p12 and (d) p23.
1153
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
(1). The total energy of the wavelet coefficients will then be given by:
Etotal ¼
X
Ej
ð2Þ
j
Then; the normalized values are expressed as :
pj ¼ Ej =Etotal : ð3Þ
and the SWE at resolution j is defined as :
Hj ¼ pj log pj ð4Þ
Eleven more parameters HD1–HD10 and HA1 are then calculated.
ducted on the same configuration yielding similar parameter behaviours. Recordings every 5 min were acquired and a total of 650 recordings (54 h of test duration) were resulted until the termination of the test, that is about 2 h after the tooth was cut-off the gear. This type of test was preferred in order to have the opportunity to monitor both damage modes i.e. the natural gear wear as well as the crack propagation, though the latter is dominant between the two as seen by the minimum wear in the gear faces after the tests. From the recorded vibration and AE waveforms the whole set of parameters–features – as described in Section 3 – are calculated utilizing in-house algorithms developed in Matlab environment. In the following sections the behaviour of the best – from a diagnostic point of view – parameters is analytically presented.
4. Test procedure and results 4.1. Vibration results The experimental setup was analytically described in Section 2 of the present work. Many tests were conducted in order to calibrate the multi-sensor configuration and assure the repeatability of the recordings and the proper operation with minimum noise of acquisition cards, amplifiers, pre-amplifiers as well as the various cables and connections. Results – in terms of various parameters evolution during the test – from a representative test on a gear system with a transverse cut of 25% of root thickness to simulate the tooth crack (Fig. 3) will be presented and detailed in this study. Two more tests were con-
(a)
From a total set of about 50 parameters, about 12 of them seem to have a clear diagnostic potential. For the vibration recordings, parameters p4, p6, p7, p12, p13, p17, p21, p24, ED1, ED2 and ED3 proved capable of attending the damage accumulation upon the gears and have shown an almost monotonic behaviour during the tests. It is reminded here that p4, p6 and p7 parameters come from the time domain, parameters p12, p13, p17, p21 and p24 come from the frequency domain whereas ED1, ED2 and ED3 are the wavelet-based ones. Fig. 4 depicts the evolution of four se-
(b) 0.10 0.06 1st transition
oil temeperature effect
0.08
0.06 ED2
ED1
0.04
0.04
0.02 0.02
0.00
0.00
0
(c)
50
100
150 200 250 300 # of recordings
350
400
0
50
100
0
50
100
150 200 250 # of recordings
300
350
400
(d) 0.04
0.50 0.45
p23 parameter
p12 parameter
0.03
0.40 0.35 0.30
0.02
0.01
0.25 0.00
0.20 0
50
100
150 200 250 300 # of recordings
350
400
Fig. 7. A magnification of Fig. 4 over the first 420 recordings.
150 200 250 300 # of recordings
350
400
1154
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
lected parameters for ch1 during the test namely ED1, p6, p7 and p13. All parameters shown are normalized in the (0–1) range. At first sight it seems that no important changes take place until approximately the 420th recording (35 h). To assist the more accurate observation of the parameters evolution during this stage of the test, a magnification was drawn in the diagrams of Fig. 5. In Fig. 5a–c a transition in the region near 325th recording (27 h), in the middle of the test, is observed. The size of this first (of the three transitions observed throughout the test) transition depends on the parameter one is looking at and in the case of p6 parameter reaches 2200%. Prior to this point no significant variation of the parameters are observed. This transition is not evident in Fig. 5d though. A 2nd transition is identified at the region of the 530th recording (44 h) according to Fig. 4a–d. The percentage rise reaches 2800% for parameter p7. A 3rd transition – related to the tooth cut-off – takes place at about the 625th recording (52 h) as all the graphs in Fig. 4 clearly show. Parameter ED1 sees an increase of 700%. These transitions are important and possess diagnostic value as they can be used to define and characterize critical stages of the gears damage accumulation and evolution. Results from the processing of the vibration signals from ch2 are depicted in Fig. 6. The 3rd transition at approximately the
(a)
625th recording (52 h) is quite clear whereas the 2nd is not clear in any of the selected parameters. Looking at Fig. 7 the location of the 1st transition is not very clear as well, at least not as evident as in the case of vibration ch1, rendering ch2 less interesting diagnostically. Parameter ED1 presented in Fig. 6a suggests the 1st transition at the neighbourhood of the 325th recording (27 h). In spite of the uncertainty and the significant fluctuations, the above parameters are monotonically increased, which is very useful from a diagnostic point of view. The area at the very beginning of the test highlighted in Fig. 7b seems to have non-consistent parameter values behaviour, a phenomenon that is attributed to the oil temperature effect upon the recordings. In the beginning of the test it normally takes few hours until the lubricant reaches a steady temperature. While the oil temperature changes, so does the oil film thickness between the asperity contacts of the gears affecting the vibration as well as the AE recordings. This is a statement not only valid for the parameter ED2 of Fig. 7b. This behaviour in the beginning of the tests is observed more or less in almost every parameter presented in the paper. In ch3, a behaviour similar to that of vibration ch1 is observed. The 2nd and 3rd transitions are clearly defined in the graphs given in Fig. 8. The 1st transition is not as clear as in Fig. 4 graphs but still can be marked at least in Fig. 9a and b.
(b) 1.0
1.0
0.8
3rd transition (tooth break)
0.6
2nd transition 0.4
440%
0.2
ED2 parameter
ED1 parameter
0.8
25
400
450
0.4 320% 0.2 700%
600%
0.0
0.0 0
0.6
500
550
600
0
650
25
400
# of recordings
(c)
600
650
600
650
(d) 1.0
1.0
0.8 p12 parameter
0.8 p7 parameter
450 500 550 # of recordings
0.6 0.4 0.2
25
400
450
500
130%
0.0
1500% 0
0.4 0.2
690%
0.0
110%
0.6
550
# of recordings
600
650
0
25
400
450 500 550 # of recordings
Fig. 8. Parameters evolution during the test for vibration ch3 (a) ED1, (b) ED2, (c) p7 and (d) p12.
1155
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
0.015
(a)
(b) 0.08 1st transition
1st transition
ED2 parameter
ED1 parameter
0.06
0.010
0.005
0.04
0.02
0.000
0.00
0
(c)
50
100
150 200 250 300 # of recordings
350
400
0
50
100
150 200 250 300 # of recordings
0
50
100
150 200 250 300 # of recordings
350
400
(d) 0.20
0.0008
0.0006
p12 parameter
p7 parameter
0.15
0.0004
0.10
0.0002
0.0000
0.05 0
50
100
150 200 250 300 # of recordings
350
400
350
400
Fig. 9. A magnification of Fig. 6 over the first 420 recordings.
Table 2 Parameter percentage changes for vibration channels 1 and 3. Channel
Parameter
1st transition (%)
2nd transition (%)
3rd transition (%)
1
ED1 p6 p7 p13
25 2200 122 –
1500 1100 2800 90
700 350 450 300
3
ED1 ED2 p7 p12
– – – –
600 700 1500 130
440 320 690 110
Table 2 summarizes the percentage changes of the various parameters shown in vibration channel 3. Channel 2 is not included as the least interesting from the three. The 1st transition in some cases is not clear and no value is given. 4.2. AE results For the acoustic emission recordings, parameters p4, p6, p7, p12, p13, p17, p21, p24, ED3, ED4 and ED5 proved capable of attending the damage accumulation upon the gears and have shown an inter-
esting monotonic behaviour during the tests. Parameters p4, p6 and p7 are calculated in the time domain, p12, p13, p17, p21 and p24 in the frequency domain and parameters ED3, ED4, ED5 are the wavelet-based ones. AE in total has a very interesting behaviour in this test (Fig. 10). Unlike the results from vibration recordings in the previous section, even from the early beginning it has a seemingly linear increasing behaviour and it seems capable of diagnosing even the initial stages of crack propagation. A closer look at the first 400 recordings reveals a bilinear behaviour more evident in parameters ED3 and ED5 (see Fig. 11). It is reminded that the dominant damage mode involved in this test is the crack propagation and much less the natural wear. This change in the slope could be associated with changes in the crack propagation rate. Parameter ED5 has a diagnostic advantage since its slope changes close to the 150th (12.5 h) recording much earlier than the 250th recording (21 h) of parameter ED3. An important transition around the 625th recording (52 h) warns with respect to the oncoming tooth failure. In acoustic emission ch2, interesting diagnostically behaviours are acquired as Fig. 12 shows. More than two different slopes can be identified as Fig. 13 suggests for parameters ED3 and ED4. In any case, as in AE ch1, an important transition around the 625th recording (52 h) warns with respect to the oncoming tooth failure.
1156
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
1.0
(b) 1.0
0.8
0.8
0.6 90%
transition (tooth break)
ED5 parameter
ED3 parameter
(a)
0.4 300%
0.2
0.6 130%
0.4
0.2 1700%
0.0
0.0 0
100
200
300 400 # of recordings
500
600
(c) 1.0
0
100
200
300 400 # of recordings
500
600
(d) 1.0
0.9
0.9 0.8
45%
0.7
p12 parameter
p4 parameter
0.8
0.6 0.5
60%
30% 0.7 0.6
50%
0.4 0.5
0.3 0.4
0.2 0
100
200
300 400 # of recordings
500
0
600
100
200
300 400 # of recordings
500
600
Fig. 10. Parameters evolution during the test for AE ch1 (a) ED3, (b) ED5, (c) p4 and (d) p12.
(b) 0.25
(a) 0.25
0.20 ED5 parameter
ED3 parameter
0.20
0.15
0.10
0.15
0.10
0.05
0.05
0.00 0
50
100
150 200 250 300 # of recordings
350
400
0
50
100
150 200 250 300 # of recordings
350
400
Fig. 11. A magnification of ED 3 and ED 5 over the first 420 recordings – AE ch1.
AE results of diagnostic parameters coming from ch3 (Fig. 14) seems to have an almost linear behaviour again, with not significant slope changes during the test, thus making ch3 behaviour the least interesting among the three AE channels. Still the critical transition at around the 625th recording (52 h) is clearly shown.
Table 3 summarizes the percentage changes of the various parameters presented in all three AE channels. The first refers to the change observed from the test start until the transition and the second refers to the change measured at the neighbourhood of the transition.
1157
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
1.0
(b) 1.0
0.8
0.8 ED4 parameter
ED3 parameter
(a)
0.6
0.4
35%
0.6
0.4
80%
100% 0.2
290%
0.2
0.0
0.0
0
100
200
300 400 # of recordings
500
600
(c) 1.0
0
100
200
300 400 # of recordings
500
600
(d) 1.0
0.8
p13 parameter
p6 parameter
0.8 0.6 0.4 400%
0.6
60%
0.4
150%
0.2
0.2 0.0
3500% 0
100
200
300 400 # of recordings
0.0 500
600
0
100
200
300 400 # of recordings
500
600
Fig. 12. Parameters evolution during the test for AE ch2. (a) ED3, (b) ED5, (c) p6 and (d) p13.
(a)
(b) 0.40
0.30 0.30 ED4 parameter
ED3 parameter
0.35
oil temperature effect
0.25 0.20 0.15 0.10
0.25 0.20 0.15 0.10
0.05
0.05
0.00
0.00
0
50 100 150 200 250 300 350 400 450 500 # of recordings
0
50 100 150 200 250 300 350 400 450 500 # of recordings
Fig. 13. A magnification over the first 500 recordings for (a) ED3 and (b) ED4 – AE ch2.
After analysing and commenting on the behaviour of carefully selected parameters in the previous, in Fig. 15 an example of the
behaviour of non-useful –diagnostically- parameters extracted by the analysis of AE monitored signals is depicted.
1158
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
(a)
(b)
1.0
1.0
0.9 ED8 parameter
ED5 parameter
0.9
0.8
980% 0.10
870%
0.10
350%
0.05
25%
0.05
0.8
0.00 0
(c)
100
200
300 400 # of recordings
500
600
1.0
0
(d)
200
300 400 # of recordings
500
600
1.0
0.8 p13 parameter
0.8 p4 parameter
100
51% 0.6 55%
0.6 130% 0.4 170%
0.4 0.2
0.0
0.2 0
100
200
300 400 # of recordings
500
600
0
100
200
300 400 # of recordings
500
600
Fig. 14. Parameters evolution during the test for AE ch3. (a) ED5, (b) ED8, (c) p4 and (d) p13.
Table 3 Parameter percentage changes for AE channels 1–3. Channel
Parameter
Start until transition (%)
Transition (%)
1
ED3 ED5 p4 p12 ED3 ED4 p6 p13 ED5 ED8 p4 p13
300 1700 60 50 100 290 3500 150 25 350 55 170
90 130 45 30 35 80 400 60 980 870 51 130
2
3
5. Conclusions The health monitoring of rotating machinery and power drive trains is of utmost importance in various industrial applications in industry and in rotorcraft aviation. A single-stage gearbox was utilized in order to study the development of damage in artificially induced cracks in the gears. Multi-hour tests were conducted and numerous recordings were acquired using acoustic emission and vibration monitoring. The main goal of the study was to extract a set of parameters–features and check their diagnostic behaviour
searching for the most potential and appropriate for future health monitoring schemes. A large number of parameters are proposed. Among them, conventional time domain based parameters, frequency domain based and a set of innovative parameters based on the discrete wavelet transform. Detailed results on the diagnostic behaviour and potentiality of the most interesting of the above parameters/features – novel and conventional – were analytically presented and discussed. Transitions in the parameter values were highlighted suggesting critical changes in the operation of the gearbox. Very interesting behaviour of selected parameters was observed for both monitoring techniques. The oil temperature effect upon vibration and AE recordings was clearly identified in the beginning of the tests rendering it an important factor that should be taken into account in health monitoring of rotating structures. Several features extracted from the recorded vibration and AE waveforms revealed their variation as the oil temperature was rising up to the operational temperature. Acoustic emission technique seems superior in the early stages of the test and up to the middle being more capable of giving significant indications and differentiations to the monitored parameters, something that was not observed for the vibration monitoring. A regionally linear behaviour of AE parameters was observed and the gradients changes were associated with changes in the crack propagation rate. A superiority of the AE technique
1159
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
(b) 1.0
(a) 1.0
0.8 ED8 parameter
p8 parameter
0.9 0.8 0.7 0.6
0.6
0.4
0.2
0.5 0.0
0.4 0
100
200
300 400 # of recordings
500
600
0
100
200
300 400 # of recordings
500
600
Fig. 15. Non-interesting parameters evolution during the test for (a) p8 from AE ch1 and (b) ED8 from vibration ch2.
over vibration monitoring regarding the monitoring of early crack propagation, is thus concluded. Acknowledgements A big part of this research work was conducted in the framework of FP6-European Project ADHER ‘Automated Diagnosis for Helicopter Engines and Rotating Parts’ Project. References [1] Dempsey PJ. Integrating oil debris and vibration measurements for intelligent machine health monitoring. Technical report, NASA/TM-2003-211307. [2] Dempsey PJ. A comparison of vibration and oil debris gear damage detection methods applied to pitting damage. Technical report, NASA/TM-2000-210371. [3] Dempsey PJ, Mosher M, Huff Edward M. Threshold assessment of gear diagnostic tools on flight and test rig data. Technical report, NASA/TM-2003212220. [4] Dempsey PJ, Afjeh AA. Integrating oil debris and vibration gear damage detection technologies using fuzzy logic. Technical report, NASA/TM-2002211126. [5] Decker Y, Lewicki D. Spiral bevel pinion crack detection in a helicopter gearbox. Technical report, NASA/TM-2003-212327. [6] Wang WJ, McFadden PD. Early detection of gear failure by vibration analysis – I. Calculation of the time-frequency distribution. Mech Syst Signal Process 1993;7(3):193–203. [7] Wang WJ, McFadden PD. Early detection of gear failure by vibration analysis – II. Interpretation of the time–frequency distribution using image processing techniques. Mech Syst Signal Process 1993;7(3):205–15. [8] Wang WJ, McFadden PD. Application of orthogonal wavelets to early gear damage detection. Mech Syst Signal Process 1995;9(5):497–507. [9] Wang WJ, McFadden PD. Application of wavelets to gearbox vibration signals for fault detection. J Sound Vib 1996;192(5):927–39.
[10] Baydar N, Ball A. Detection of gear deterioration under varying load conditions by using the instantaneous power spectrum. Mech Syst Signal Process 2000;14(6):907–21. [11] Baydar N, Chen Q, Ball A, Kruger U. Detection of incipient tooth defect in helical gears using multivariate statistics. Mech Syst Signal Process 2001;15(2):303–21. [12] Baydar N, Ball A. A comparative study of acoustic and vibration signals in detection of gear failures using Wigner–Ville distribution. Mech Syst Signal Process 2001;15(6):1091–107. [13] Baydar N, Ball A. Detection of gear failures via vibration and acoustic signal using wavelet transform. Mech Syst Signal Process 2003;17(4):787–804. [14] Tandon N, Mata S. Detection of defects in gears by acoustic emission measurements. J Acoust Emiss 1999;17(1-2):23–7. [15] Singh A, Houser DR, Vijayakar S. Early detection of gear pitting. In: Power transmission and gearing conference, ASME, DE, vol. 88; 1996. p. 673–8. [16] Toutountzakis T, Tan CK, Mba D. Application of acoustic emission to seeded gear fault detection. NDT&E Int 2004;37:1–10. [17] Tan CK, Mba D. Identification of the acoustic emission source during a comparative study on diagnosis of a spur gearbox. Tribol Int 2005;38:469–80. [18] Toutountzakis T, Mba D. Observations of acoustic emission activity during gear defect diagnosis. NDT&E Int 2003;36:471–7. [19] Tan CK, Irving P, Mba D. A comparative experimental study on the diagnostic and prognostic capabilities of acoustics emission, vibration and spectrometric oil analysis for spur gears. Mech Syst Signal Process 2007;21(1):208–33. [20] Loutas TH, Kalaitzoglou J, Sotiriades G, Kostopoulos V. A novel approach for continuous acoustic emission monitoring on rotating machinery without the use of slip-ring. J Vib Acoust 2008;130(6). [21] Kostopoulos V, Loutas T, Derdas C, Douzinas E. Wavelet analysis of head acceleration response under Dirac excitation for early oedema detection. Trans ASME J Biomech Eng 2008;130(2). [22] Loutas TH, Kostopoulos V. Health monitoring of carbon/carbon woven reinforced composites. Damage assessment by using advanced signal processing techniques. Part II: acousto-ultrasonics monitoring. Compos Sci Technol 2009;69(2):273–83.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Condition monitoring of a single-stage gearbox with artificially induced gear cracks utilizing on-line vibration and acoustic emission measurements T.H. Loutas, G. Sotiriades, I. Kalaitzoglou, V. Kostopoulos * Department of Mechanical Engineering and Aeronautics, University of Patras, Patras GR-26500, Greece
a r t i c l e
i n f o
Article history: Received 7 October 2008 Received in revised form 15 April 2009 Accepted 16 April 2009 Available online 17 May 2009 Keywords: Advanced signal processing Acoustic emission Vibration Condition monitoring Gearbox
a b s t r a c t The condition monitoring of a lab-scale, single stage, gearbox using different non-destructive inspection methodologies and the processing of the acquired waveforms with advanced signal processing techniques is the aim of the present work. Acoustic emission (AE) and vibration measurements were utilized for this purpose. The experimental setup and the instrumentation of each monitoring methodology are presented in detail. Emphasis is given on the signal processing of the acquired vibration and acoustic emission signals in order to extract conventional as well as novel parameters–features of potential diagnostic value from the monitored waveforms. Innovative wavelet-based parameters–features are proposed utilizing the discrete wavelet transform. The evolution of selected parameters/features versus test time is provided, evaluated and the parameters with the most interesting diagnostic behaviour are highlighted. The differences in the parameters evolution of each NDT technique are discussed and the superiority of AE over vibration recordings for the early diagnosis of natural wear in gear systems is concluded. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In gearboxes and power drive trains in general, gear damage detection is often very critical and can lead to increased safety in aviation and in industry as well. Thus the interest for their periodic non-destructive inspection and/or on-line health monitoring is growing and effective diagnostic techniques and methodologies are the objective of extensive research efforts over the last 50 years. Few research teams have published experimental data coming from long-term testing to see the effect of natural gear pitting mostly upon vibration recordings. Dempsey et al. [1–4] and Decker with Lewicki [5] have conducted some excellent experimental work at GRC/NASA and published interesting results from extensive gear testing at a special test-rig utilizing vibration and oil debris measurements. With the clear goal to improve the performance of the current helicopter gearbox health monitoring systems, they have tested gears at high shaft speed for multi-hour periods (up to 250 h) and correlated special features (based on higher order moments) extracted form the vibration recordings with the Fe debris mass accumulated during the tests. They have integrated their results in a fuzzy logic based health monitoring system with satisfactory performance. Researchers in the field have focused mainly on advanced signal processing techniques applied on vibration recordings coming mainly from artificial gear defects in short tests rather than inducing gear pitting damage in multi-hour testing. * Corresponding author. E-mail address: [email protected] (V. Kostopoulos). 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.04.007
The publications in the field of condition monitoring via vibrations are quite versatile. Selecting a few and focusing on advanced signal processing techniques the works of Wang and McFadden [6,7] must be mentioned, that utilized time-frequency analysis techniques and showed that the spectrogram has advantages over Wigner–Ville distribution for the analysis of vibration signals for the early detection of damage in gears. The same authors have also employed the wavelet transform [8,9] to analyze the local features of vibration signals and showed that unlike the time-frequency distribution, which incorporates a constant time and frequency resolution, the wavelet transform can accommodate simultaneously both the large and small scales in a signal, enabling the detection of both distributed and local faults. Baydar and Ball [10,11] have proposed the instantaneous power spectrum and have shown that it is capable in detecting local tooth faults in standard industrial helical gearboxes. The propagation of local faults was identified by monitoring variations in the features of the power spectrum distribution. The same authors have also applied the Wigner–Ville distribution [12] as well as the wavelet transform [13] on vibration and acoustic signals for the same purpose. The interest for applications of acoustic emission (AE) for condition monitoring in rotating machinery is relatively new and has grown significantly over the last decade. AE in rotating machinery is defined as elastic waves generated by the interaction of two media in motion, i.e. a pair of gears. Sources of AE in rotating machinery include asperities contact, cyclic fatigue, friction, material loss, cavitations, leakage, etc. AE technique has drawn
1149
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
attention as it offers some advantages over classical vibration monitoring. First of all, as AE is a non-directional technique, one AE sensor is sufficient in contrast to vibration monitoring which may require information from three axes. Since AE is produced at microscopic level it is highly sensitive and offers opportunities for identifying defects at an earlier stage when compared to other condition monitoring techniques. As AE mainly detects high-frequency elastic waves, it is not affected by structural resonances and typical mechanical background noise (under 20 kHz). Tandon and Mata [14] applied AE to spur gears in a gearbox test-rig. They simulated pits of constant depth but variable size and AE parameters such as energy, amplitude and counts were monitored during the test. AE was proved superior over vibration data on early detection of small defects in gears. Singh et al. [15] also applied AE technique in condition monitoring of test-rig gearboxes, while vibration methods was also used for comparative purposes by placing accelerometers on the gearbox casing. They also concluded that AE provided early damage detection over vibration monitoring. Toutountzakis et al. [16] investigated the influence of oil temperature and of the oil film thickness on AE activity and on AE signals captured during continuous running of a back-to-back gearbox test-rig. It was observed that the AE RMS varied with time as the gear box reached a stabilized temperature and the variation in AE activity RMS could be as much as 33%.
Tan and Mba [17] discussed in more detail the oil temperature effect on AE and concluded that the source of AE mechanism that produced the gear mesh bursts was from asperities contact. Toutountzakis and Mba [18] presented some interesting observations on AE activity due to misalignment and natural pitting and concluded that the AE technique is applicable for monitoring gear damage. Finally a comparative study [19] between AE and vibrations was conducted to show the diagnostic and prognostic capabilities of each technique in several multi-day tests in a singlestage gearbox. The present work reports the results concluded by long term (50 h) experiments to a defected gear system, with a transverse cut of 25% of root thickness to simulate the tooth crack. Different parameters, resulted by the analysis of the recording signals (both coming from vibration monitoring and AE) are presented and their diagnostic value is discussed in the direction of being used
Table 1 Conventional parameters calculated from the acquired waveforms. Time domain parameters PN xðnÞ p1 ¼ n¼1 N rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN ðxðnÞp1 Þ2 n¼1 p2 ¼ N1 PN pffiffiffiffiffiffiffiffi2 jxðnÞj n¼1 p3 ¼ N rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N
p4 ¼
Frequency domain parameters PK
p12 ¼
p13 ¼ p14 ¼
ðxðnÞÞ2 N
p15 ¼
n¼1
k¼1
sðkÞ
K
PK
ðsðkÞp12 Þ2 ðK1Þ
k¼1
PK
ðsðkÞp12 Þ3 pffiffiffiffiffiffi 3 K ð p13 Þ
k¼1
PK k¼1
ðsðkÞp12 Þ4 2
PK Kp13 fk sðkÞ p16 ¼ Pk¼1 K
p5 ¼ max jxðnÞj
k¼1
p6 ¼ p7 ¼
PN n¼1
PN
ðxðnÞp1 Þ3
p17 ¼
ðN1Þp32
n¼1
p8 ¼ p9 ¼
p5 p3
k¼1
ðxðnÞp1 Þ4
k¼1
f sðkÞ
k¼1 k
PK 2 f sðkÞ k¼1 k ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p20 ¼ qP P K
k¼1
n¼1
p11 ¼ 1 PNp5 N
n¼1
sðkÞ
jxðnÞj
jxðnÞj
17
Wavelet type
Number of levels
Time synchronous averaging (only for vibration signals)
K
f 4 sðkÞ k¼1 k
p21 ¼ pp17 16 PK ðfk p Þ3 sðkÞ p22 ¼ k¼1 Kp3 16 17 PK ðfk p Þ4 sðkÞ p23 ¼ k¼1 Kp4 16 17 PK ðfk p16 Þ1=2 sðkÞ ffi p24 ¼ k¼1 K pffiffiffiffiffi p
Fig. 1. Test bench setup.
Vibration and AE signals
sðkÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PK 4 f sðkÞ p19 ¼ PKk¼1 k2
p10 ¼ 1 PNp4 N
ðfk p16 Þ sðkÞ K
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PK 2 fk sðkÞ Pk¼1 p18 ¼ K
ðN1Þp42
p5 p4
sðkÞ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi PK 2
Discrete Wavelet transform – n levels of decomposition
Energy content determination for each level
Plot of energy levels vs defect types
Fig. 2. Flow chart of the DWT-based methodology.
1150
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
for the development of a condition monitoring system. Furthermore, a systematic comparison of the different diagnostic parameters is provided, in order to assess which are the most robust and reliable ones for the condition monitoring of gearboxes and drive trains. The paper closes with the conclusions drawn from this study.
2. Experimental setup Fig. 1 shows the experimental setup used for the gears testing. The test-rig consists of two gears made from 045M15 steel with a module of 3 mm, pressure angle 20°, which have 53 and 25 teeth with 7 mm face width. The axes of the gears are supported by two ball bearings each. The entire system is settled in an oil basin in order to ensure proper lubrication. The gear box is powered by a motor and consumes its power on a generator. Their characteristics are as follows: – 1 stage gearbox with two gears (25 and 53 teeth); – 3-phase 5 hp motor (220 V, 9 A, 50 Hz, 1400 rpm) controlled by inverter; – single phase generator with continuous power consumption control (load fluctuation), 4.2 KVA, 3000 rpm, 50 Hz; – the oil pump is of the wet type without oil recirculation; – the shafts are ball bearing supported. Two non-destructive techniques have been employed to monitor the gearbox during operation, namely vibration and acoustic emission. Two Bruel & Kjaer accelerometers were used for the vibration monitoring both mounted upon the gearbox case, one in each side-axis. The sampling frequency used was 50 kHz and signals of 1 s duration were recorded. Additionally three wide band
Fig. 3. Tooth crack.
(a)
(b)
3rd transition (tooth break)
1.0
0.8
ED1
0.6 1st transition
2nd transition
0.4
700%
p6 parameter
0.8
0.4 350%
1100%
1500%
0.0 0
25
0.0
300 350 400 450 500 550 600 650 # of recordings
0
(d)
1.0
0.8
0.6
0.6
0.4 0.2
450%
25
400
450 500 550 # of recordings
600
650
1.0
0.8
p13 parameter
p7 parameter
0.6
0.2
0.2
(c)
1.0
0.4
300%
0.2 90%
2800%
0.0 0
25
400
450
500
550
# of recordings
600
650
0.0 0
25
400
450
500
550
# of recordings
Fig. 4. Parameters evolution during the test for vibration ch1 (a) ED1, (b) p6, (c) p7 and (d) p13.
600
650
1151
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
acoustic emission sensors manufactured by Physical Acoustics Corporation (PAC) with a frequency response range of 100–800 kHz recorded continuous AE signals of 100 ms duration at a sampling rate of 2 MHz. Fig. 1 shows the positions of all the sensors. One AE sensor is mounted on the output shaft (AE channel 1), the second is placed upon one of the bearings of the same shaft (AE channel 3) and the third (AE channel 2) is in friction contact with the input rotating gear. A special innovative device was designed in-house and discussed elsewhere [20] in order to mount the AE sensor upon a rotating component without the expensive/ demanding solution of the slip-ring generally used in literature. The recordings of all the above data coming from accelerometers and AE sensors are realized by a National Instruments NI6070 1MS/SEC FIREWIRE data acquisition device and assisted by special software developed in-house, in Labview programming environment. Finally, the temperature of the oil bath within the gearbox is measured via a thermocouple. 3. Signal processing methodologies Significant effort was dedicated to the signal processing of the vibration and AE waveforms acquired during the tests. The goal set a priori was to calculate a number of parameters–features extracted by the signals and check their behavior during the tests
(a)
in order to identify the most promising ones that may be used for damage detection and condition monitoring of the gear system. In the literature, very few research groups have been involved in long term gear testing and they have mainly used higher order moments and their combinations to form diagnostic parameters [1–5] with interesting behavior during the tests. In this work, apart from parameters usually found in the literature, we have introduced some more advanced signal processing techniques such as the discrete wavelet transform and extracted innovative wavelet-based parameters from the signals. In total more than 40 parameters are checked for their diagnostic ability. Those capable of monitoring the damage are identified and compared. 3.1. Conventional parameters In Table 1 conventional parameters from the time and frequency domain that were calculated, are shown. Where x(n) is a signal series for n = 1, 2, . . . , N, N is the number of signal samples and s(k) is the Fourier transform for k = 1, 2, . . . , K, K is the number of spectrum lines, fk is the frequency value of the kth spectrum line. Parameter p1 is the mean of the signal, p2 is its root mean square, p5 is obviously the absolute maximum of the signal, p4 the standard deviation, p6 and p7 the third and fourth moments whilst p8–p11 result as a combination of previous parameters all calculated by the
(b)
0.014
0.0020
0.012 0.0015
0.006 25%
p6 parameter
0.008 ED1
1st transition
1st transition
0.010
0.0010
0.0005 2200%
0.004 0.0000
0.002 0.000 0
50
100
150
200
250
300
350
0
400
50
100
200
250
300
350
400
# of recordings
# of recordings
(c)
150
(d)
0.00015
0.10 1st transition
p13 parameter
p7 parameter
0.00010
0.00005
0.08
0.06
122%
0.04
0.00000 0
50
100
150
200
250
300
350
400
0
50
# of recordings Fig. 5. A magnification of Fig. 2 over the first 420 recordings.
100
150
200
250
# of recordings
300
350
400
1152
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
signal in time domain. Correspondingly, p12–p24 are extracted in the frequency domain. These parameters are typical parameters in the time and in the frequency domain that can be extracted from any signal. 3.2. Discrete wavelet transform based parameters The wavelet transform was utilized to develop new parameters and check their behavior during the tests. The major advantage of wavelets is their inherent ability to perform local analysis with varying precision. Wavelet transform treats low frequencies with low resolution and high frequencies with high resolution [21]. Wavelets stem from the iteration of filters and filter banks (with rescaling) so they are inherently orthogonal or biorthogonal. In contrast to the Fourier analysis, which consists of breaking up a signal into sine waves of various frequencies, wavelet analysis breaks up the signal into shifted and scaled versions of the original (or mother) wavelet. The inverse discrete wavelet transform can be expressed as:
f ðtÞ ¼ c
XX j
DWðj; kÞwj;k ðtÞ
ð1Þ
k
where c is a constant depending only on w. Eq. (1) is the backbone of the present work and the whole philosophy of using wavelets for analysis of transient and non-stationary signals, as it states that a given time series signal can be decomposed by the discrete
1.0
(b) 1.0
0.8
0.8
0.6
0.6 ED2
ED1
(a)
0.4
0.2
0.0
0.0
25
400
450 500 550 # of recordings
600
650
1.0
(d) 1.0
0.8
0.8
0.6
0.6
p23 parameter
p12 parameter
0.4
0.2
0
(c)
wavelet transform into its wavelet levels, where the summation of these levels represent the original input signal. The decomposed wavelet levels are channeled in such a way that each level corresponds to a certain frequency range of the acquired signal. The DWT-based methodology used in this work was introduced and described elsewhere [21,22]. Fig. 2 schematically summarizes the complete procedure. It comprises the Discrete Wavelet Transform (DWT) of the time synchronous averaged acquired vibration signals and AE signals in 10 levels of decomposition using the ‘db10’ wavelet. As far as the type of wavelet for the discrete transform is concerned ‘db10’ was a good compromise of smooth function, without sharp edges as in the case of ‘db’ wavelets of lower order. The family of Daubechies wavelets was chosen because it consists of biorthogonal, compactly supported wavelets, satisfactorily regular though not symmetrical. Other wavelets having similar properties to the Daubechies family, such as symlets or coiflets were also tried with minor impact upon the results. The decomposed wavelet levels are split in a way that each level corresponds to a certain frequency range. After the 10-level decomposition the energy of each level (10 details and one approximation) is calculated. Thus eleven parameters namely ED1–ED10 (for the details) and Ea10 (for the approximation) were resulted. Additionally the sub-band wavelet entropy (SWE) is calculated. SWE is defined in terms of the relative wavelet energy of the wavelet coefficients. The energy at each resolution level j is defined in
0.4 0.2
0
25
400
450 500 550 # of recordings
600
650
0
25
400
450 500 550 # of recordings
600
650
0.4 0.2 0.0
0.0 0
25
400
450 500 550 # of recordings
600
650
Fig. 6. Parameters evolution during the test for vibration ch2 (a) ED1, (b) ED2, (c) p12 and (d) p23.
1153
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
(1). The total energy of the wavelet coefficients will then be given by:
Etotal ¼
X
Ej
ð2Þ
j
Then; the normalized values are expressed as :
pj ¼ Ej =Etotal : ð3Þ
and the SWE at resolution j is defined as :
Hj ¼ pj log pj ð4Þ
Eleven more parameters HD1–HD10 and HA1 are then calculated.
ducted on the same configuration yielding similar parameter behaviours. Recordings every 5 min were acquired and a total of 650 recordings (54 h of test duration) were resulted until the termination of the test, that is about 2 h after the tooth was cut-off the gear. This type of test was preferred in order to have the opportunity to monitor both damage modes i.e. the natural gear wear as well as the crack propagation, though the latter is dominant between the two as seen by the minimum wear in the gear faces after the tests. From the recorded vibration and AE waveforms the whole set of parameters–features – as described in Section 3 – are calculated utilizing in-house algorithms developed in Matlab environment. In the following sections the behaviour of the best – from a diagnostic point of view – parameters is analytically presented.
4. Test procedure and results 4.1. Vibration results The experimental setup was analytically described in Section 2 of the present work. Many tests were conducted in order to calibrate the multi-sensor configuration and assure the repeatability of the recordings and the proper operation with minimum noise of acquisition cards, amplifiers, pre-amplifiers as well as the various cables and connections. Results – in terms of various parameters evolution during the test – from a representative test on a gear system with a transverse cut of 25% of root thickness to simulate the tooth crack (Fig. 3) will be presented and detailed in this study. Two more tests were con-
(a)
From a total set of about 50 parameters, about 12 of them seem to have a clear diagnostic potential. For the vibration recordings, parameters p4, p6, p7, p12, p13, p17, p21, p24, ED1, ED2 and ED3 proved capable of attending the damage accumulation upon the gears and have shown an almost monotonic behaviour during the tests. It is reminded here that p4, p6 and p7 parameters come from the time domain, parameters p12, p13, p17, p21 and p24 come from the frequency domain whereas ED1, ED2 and ED3 are the wavelet-based ones. Fig. 4 depicts the evolution of four se-
(b) 0.10 0.06 1st transition
oil temeperature effect
0.08
0.06 ED2
ED1
0.04
0.04
0.02 0.02
0.00
0.00
0
(c)
50
100
150 200 250 300 # of recordings
350
400
0
50
100
0
50
100
150 200 250 # of recordings
300
350
400
(d) 0.04
0.50 0.45
p23 parameter
p12 parameter
0.03
0.40 0.35 0.30
0.02
0.01
0.25 0.00
0.20 0
50
100
150 200 250 300 # of recordings
350
400
Fig. 7. A magnification of Fig. 4 over the first 420 recordings.
150 200 250 300 # of recordings
350
400
1154
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
lected parameters for ch1 during the test namely ED1, p6, p7 and p13. All parameters shown are normalized in the (0–1) range. At first sight it seems that no important changes take place until approximately the 420th recording (35 h). To assist the more accurate observation of the parameters evolution during this stage of the test, a magnification was drawn in the diagrams of Fig. 5. In Fig. 5a–c a transition in the region near 325th recording (27 h), in the middle of the test, is observed. The size of this first (of the three transitions observed throughout the test) transition depends on the parameter one is looking at and in the case of p6 parameter reaches 2200%. Prior to this point no significant variation of the parameters are observed. This transition is not evident in Fig. 5d though. A 2nd transition is identified at the region of the 530th recording (44 h) according to Fig. 4a–d. The percentage rise reaches 2800% for parameter p7. A 3rd transition – related to the tooth cut-off – takes place at about the 625th recording (52 h) as all the graphs in Fig. 4 clearly show. Parameter ED1 sees an increase of 700%. These transitions are important and possess diagnostic value as they can be used to define and characterize critical stages of the gears damage accumulation and evolution. Results from the processing of the vibration signals from ch2 are depicted in Fig. 6. The 3rd transition at approximately the
(a)
625th recording (52 h) is quite clear whereas the 2nd is not clear in any of the selected parameters. Looking at Fig. 7 the location of the 1st transition is not very clear as well, at least not as evident as in the case of vibration ch1, rendering ch2 less interesting diagnostically. Parameter ED1 presented in Fig. 6a suggests the 1st transition at the neighbourhood of the 325th recording (27 h). In spite of the uncertainty and the significant fluctuations, the above parameters are monotonically increased, which is very useful from a diagnostic point of view. The area at the very beginning of the test highlighted in Fig. 7b seems to have non-consistent parameter values behaviour, a phenomenon that is attributed to the oil temperature effect upon the recordings. In the beginning of the test it normally takes few hours until the lubricant reaches a steady temperature. While the oil temperature changes, so does the oil film thickness between the asperity contacts of the gears affecting the vibration as well as the AE recordings. This is a statement not only valid for the parameter ED2 of Fig. 7b. This behaviour in the beginning of the tests is observed more or less in almost every parameter presented in the paper. In ch3, a behaviour similar to that of vibration ch1 is observed. The 2nd and 3rd transitions are clearly defined in the graphs given in Fig. 8. The 1st transition is not as clear as in Fig. 4 graphs but still can be marked at least in Fig. 9a and b.
(b) 1.0
1.0
0.8
3rd transition (tooth break)
0.6
2nd transition 0.4
440%
0.2
ED2 parameter
ED1 parameter
0.8
25
400
450
0.4 320% 0.2 700%
600%
0.0
0.0 0
0.6
500
550
600
0
650
25
400
# of recordings
(c)
600
650
600
650
(d) 1.0
1.0
0.8 p12 parameter
0.8 p7 parameter
450 500 550 # of recordings
0.6 0.4 0.2
25
400
450
500
130%
0.0
1500% 0
0.4 0.2
690%
0.0
110%
0.6
550
# of recordings
600
650
0
25
400
450 500 550 # of recordings
Fig. 8. Parameters evolution during the test for vibration ch3 (a) ED1, (b) ED2, (c) p7 and (d) p12.
1155
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
0.015
(a)
(b) 0.08 1st transition
1st transition
ED2 parameter
ED1 parameter
0.06
0.010
0.005
0.04
0.02
0.000
0.00
0
(c)
50
100
150 200 250 300 # of recordings
350
400
0
50
100
150 200 250 300 # of recordings
0
50
100
150 200 250 300 # of recordings
350
400
(d) 0.20
0.0008
0.0006
p12 parameter
p7 parameter
0.15
0.0004
0.10
0.0002
0.0000
0.05 0
50
100
150 200 250 300 # of recordings
350
400
350
400
Fig. 9. A magnification of Fig. 6 over the first 420 recordings.
Table 2 Parameter percentage changes for vibration channels 1 and 3. Channel
Parameter
1st transition (%)
2nd transition (%)
3rd transition (%)
1
ED1 p6 p7 p13
25 2200 122 –
1500 1100 2800 90
700 350 450 300
3
ED1 ED2 p7 p12
– – – –
600 700 1500 130
440 320 690 110
Table 2 summarizes the percentage changes of the various parameters shown in vibration channel 3. Channel 2 is not included as the least interesting from the three. The 1st transition in some cases is not clear and no value is given. 4.2. AE results For the acoustic emission recordings, parameters p4, p6, p7, p12, p13, p17, p21, p24, ED3, ED4 and ED5 proved capable of attending the damage accumulation upon the gears and have shown an inter-
esting monotonic behaviour during the tests. Parameters p4, p6 and p7 are calculated in the time domain, p12, p13, p17, p21 and p24 in the frequency domain and parameters ED3, ED4, ED5 are the wavelet-based ones. AE in total has a very interesting behaviour in this test (Fig. 10). Unlike the results from vibration recordings in the previous section, even from the early beginning it has a seemingly linear increasing behaviour and it seems capable of diagnosing even the initial stages of crack propagation. A closer look at the first 400 recordings reveals a bilinear behaviour more evident in parameters ED3 and ED5 (see Fig. 11). It is reminded that the dominant damage mode involved in this test is the crack propagation and much less the natural wear. This change in the slope could be associated with changes in the crack propagation rate. Parameter ED5 has a diagnostic advantage since its slope changes close to the 150th (12.5 h) recording much earlier than the 250th recording (21 h) of parameter ED3. An important transition around the 625th recording (52 h) warns with respect to the oncoming tooth failure. In acoustic emission ch2, interesting diagnostically behaviours are acquired as Fig. 12 shows. More than two different slopes can be identified as Fig. 13 suggests for parameters ED3 and ED4. In any case, as in AE ch1, an important transition around the 625th recording (52 h) warns with respect to the oncoming tooth failure.
1156
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
1.0
(b) 1.0
0.8
0.8
0.6 90%
transition (tooth break)
ED5 parameter
ED3 parameter
(a)
0.4 300%
0.2
0.6 130%
0.4
0.2 1700%
0.0
0.0 0
100
200
300 400 # of recordings
500
600
(c) 1.0
0
100
200
300 400 # of recordings
500
600
(d) 1.0
0.9
0.9 0.8
45%
0.7
p12 parameter
p4 parameter
0.8
0.6 0.5
60%
30% 0.7 0.6
50%
0.4 0.5
0.3 0.4
0.2 0
100
200
300 400 # of recordings
500
0
600
100
200
300 400 # of recordings
500
600
Fig. 10. Parameters evolution during the test for AE ch1 (a) ED3, (b) ED5, (c) p4 and (d) p12.
(b) 0.25
(a) 0.25
0.20 ED5 parameter
ED3 parameter
0.20
0.15
0.10
0.15
0.10
0.05
0.05
0.00 0
50
100
150 200 250 300 # of recordings
350
400
0
50
100
150 200 250 300 # of recordings
350
400
Fig. 11. A magnification of ED 3 and ED 5 over the first 420 recordings – AE ch1.
AE results of diagnostic parameters coming from ch3 (Fig. 14) seems to have an almost linear behaviour again, with not significant slope changes during the test, thus making ch3 behaviour the least interesting among the three AE channels. Still the critical transition at around the 625th recording (52 h) is clearly shown.
Table 3 summarizes the percentage changes of the various parameters presented in all three AE channels. The first refers to the change observed from the test start until the transition and the second refers to the change measured at the neighbourhood of the transition.
1157
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
1.0
(b) 1.0
0.8
0.8 ED4 parameter
ED3 parameter
(a)
0.6
0.4
35%
0.6
0.4
80%
100% 0.2
290%
0.2
0.0
0.0
0
100
200
300 400 # of recordings
500
600
(c) 1.0
0
100
200
300 400 # of recordings
500
600
(d) 1.0
0.8
p13 parameter
p6 parameter
0.8 0.6 0.4 400%
0.6
60%
0.4
150%
0.2
0.2 0.0
3500% 0
100
200
300 400 # of recordings
0.0 500
600
0
100
200
300 400 # of recordings
500
600
Fig. 12. Parameters evolution during the test for AE ch2. (a) ED3, (b) ED5, (c) p6 and (d) p13.
(a)
(b) 0.40
0.30 0.30 ED4 parameter
ED3 parameter
0.35
oil temperature effect
0.25 0.20 0.15 0.10
0.25 0.20 0.15 0.10
0.05
0.05
0.00
0.00
0
50 100 150 200 250 300 350 400 450 500 # of recordings
0
50 100 150 200 250 300 350 400 450 500 # of recordings
Fig. 13. A magnification over the first 500 recordings for (a) ED3 and (b) ED4 – AE ch2.
After analysing and commenting on the behaviour of carefully selected parameters in the previous, in Fig. 15 an example of the
behaviour of non-useful –diagnostically- parameters extracted by the analysis of AE monitored signals is depicted.
1158
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
(a)
(b)
1.0
1.0
0.9 ED8 parameter
ED5 parameter
0.9
0.8
980% 0.10
870%
0.10
350%
0.05
25%
0.05
0.8
0.00 0
(c)
100
200
300 400 # of recordings
500
600
1.0
0
(d)
200
300 400 # of recordings
500
600
1.0
0.8 p13 parameter
0.8 p4 parameter
100
51% 0.6 55%
0.6 130% 0.4 170%
0.4 0.2
0.0
0.2 0
100
200
300 400 # of recordings
500
600
0
100
200
300 400 # of recordings
500
600
Fig. 14. Parameters evolution during the test for AE ch3. (a) ED5, (b) ED8, (c) p4 and (d) p13.
Table 3 Parameter percentage changes for AE channels 1–3. Channel
Parameter
Start until transition (%)
Transition (%)
1
ED3 ED5 p4 p12 ED3 ED4 p6 p13 ED5 ED8 p4 p13
300 1700 60 50 100 290 3500 150 25 350 55 170
90 130 45 30 35 80 400 60 980 870 51 130
2
3
5. Conclusions The health monitoring of rotating machinery and power drive trains is of utmost importance in various industrial applications in industry and in rotorcraft aviation. A single-stage gearbox was utilized in order to study the development of damage in artificially induced cracks in the gears. Multi-hour tests were conducted and numerous recordings were acquired using acoustic emission and vibration monitoring. The main goal of the study was to extract a set of parameters–features and check their diagnostic behaviour
searching for the most potential and appropriate for future health monitoring schemes. A large number of parameters are proposed. Among them, conventional time domain based parameters, frequency domain based and a set of innovative parameters based on the discrete wavelet transform. Detailed results on the diagnostic behaviour and potentiality of the most interesting of the above parameters/features – novel and conventional – were analytically presented and discussed. Transitions in the parameter values were highlighted suggesting critical changes in the operation of the gearbox. Very interesting behaviour of selected parameters was observed for both monitoring techniques. The oil temperature effect upon vibration and AE recordings was clearly identified in the beginning of the tests rendering it an important factor that should be taken into account in health monitoring of rotating structures. Several features extracted from the recorded vibration and AE waveforms revealed their variation as the oil temperature was rising up to the operational temperature. Acoustic emission technique seems superior in the early stages of the test and up to the middle being more capable of giving significant indications and differentiations to the monitored parameters, something that was not observed for the vibration monitoring. A regionally linear behaviour of AE parameters was observed and the gradients changes were associated with changes in the crack propagation rate. A superiority of the AE technique
1159
T.H. Loutas et al. / Applied Acoustics 70 (2009) 1148–1159
(b) 1.0
(a) 1.0
0.8 ED8 parameter
p8 parameter
0.9 0.8 0.7 0.6
0.6
0.4
0.2
0.5 0.0
0.4 0
100
200
300 400 # of recordings
500
600
0
100
200
300 400 # of recordings
500
600
Fig. 15. Non-interesting parameters evolution during the test for (a) p8 from AE ch1 and (b) ED8 from vibration ch2.
over vibration monitoring regarding the monitoring of early crack propagation, is thus concluded. Acknowledgements A big part of this research work was conducted in the framework of FP6-European Project ADHER ‘Automated Diagnosis for Helicopter Engines and Rotating Parts’ Project. References [1] Dempsey PJ. Integrating oil debris and vibration measurements for intelligent machine health monitoring. Technical report, NASA/TM-2003-211307. [2] Dempsey PJ. A comparison of vibration and oil debris gear damage detection methods applied to pitting damage. Technical report, NASA/TM-2000-210371. [3] Dempsey PJ, Mosher M, Huff Edward M. Threshold assessment of gear diagnostic tools on flight and test rig data. Technical report, NASA/TM-2003212220. [4] Dempsey PJ, Afjeh AA. Integrating oil debris and vibration gear damage detection technologies using fuzzy logic. Technical report, NASA/TM-2002211126. [5] Decker Y, Lewicki D. Spiral bevel pinion crack detection in a helicopter gearbox. Technical report, NASA/TM-2003-212327. [6] Wang WJ, McFadden PD. Early detection of gear failure by vibration analysis – I. Calculation of the time-frequency distribution. Mech Syst Signal Process 1993;7(3):193–203. [7] Wang WJ, McFadden PD. Early detection of gear failure by vibration analysis – II. Interpretation of the time–frequency distribution using image processing techniques. Mech Syst Signal Process 1993;7(3):205–15. [8] Wang WJ, McFadden PD. Application of orthogonal wavelets to early gear damage detection. Mech Syst Signal Process 1995;9(5):497–507. [9] Wang WJ, McFadden PD. Application of wavelets to gearbox vibration signals for fault detection. J Sound Vib 1996;192(5):927–39.
[10] Baydar N, Ball A. Detection of gear deterioration under varying load conditions by using the instantaneous power spectrum. Mech Syst Signal Process 2000;14(6):907–21. [11] Baydar N, Chen Q, Ball A, Kruger U. Detection of incipient tooth defect in helical gears using multivariate statistics. Mech Syst Signal Process 2001;15(2):303–21. [12] Baydar N, Ball A. A comparative study of acoustic and vibration signals in detection of gear failures using Wigner–Ville distribution. Mech Syst Signal Process 2001;15(6):1091–107. [13] Baydar N, Ball A. Detection of gear failures via vibration and acoustic signal using wavelet transform. Mech Syst Signal Process 2003;17(4):787–804. [14] Tandon N, Mata S. Detection of defects in gears by acoustic emission measurements. J Acoust Emiss 1999;17(1-2):23–7. [15] Singh A, Houser DR, Vijayakar S. Early detection of gear pitting. In: Power transmission and gearing conference, ASME, DE, vol. 88; 1996. p. 673–8. [16] Toutountzakis T, Tan CK, Mba D. Application of acoustic emission to seeded gear fault detection. NDT&E Int 2004;37:1–10. [17] Tan CK, Mba D. Identification of the acoustic emission source during a comparative study on diagnosis of a spur gearbox. Tribol Int 2005;38:469–80. [18] Toutountzakis T, Mba D. Observations of acoustic emission activity during gear defect diagnosis. NDT&E Int 2003;36:471–7. [19] Tan CK, Irving P, Mba D. A comparative experimental study on the diagnostic and prognostic capabilities of acoustics emission, vibration and spectrometric oil analysis for spur gears. Mech Syst Signal Process 2007;21(1):208–33. [20] Loutas TH, Kalaitzoglou J, Sotiriades G, Kostopoulos V. A novel approach for continuous acoustic emission monitoring on rotating machinery without the use of slip-ring. J Vib Acoust 2008;130(6). [21] Kostopoulos V, Loutas T, Derdas C, Douzinas E. Wavelet analysis of head acceleration response under Dirac excitation for early oedema detection. Trans ASME J Biomech Eng 2008;130(2). [22] Loutas TH, Kostopoulos V. Health monitoring of carbon/carbon woven reinforced composites. Damage assessment by using advanced signal processing techniques. Part II: acousto-ultrasonics monitoring. Compos Sci Technol 2009;69(2):273–83.