Comparison of vibration and acoustic measurements for detection of bearing defects

Comparison of vibration and acoustic measurements for detection of bearing defects C. Freitas 1, J. Cuenca 1, P. Morais 1, A. Ompusunggu 2, M. Sarrazin 1, K. Janssens 1 1 Siemens Industry Software NV Interleuvenlaan 68, B-3001, Leuven, Belgium e-mail: carina.freitas@siemens.com 2 Flanders Make vzw Celestijnenlaan 300 C, B-3001, Heverlee, Belgium Abstract The breakdown of rotating machineries is often linked to the failure of rolling bearings. Thus, several methods have been developed to identify the signature of bearing faults and it was proved for medium to high speed regimes that it is possible to detect a fault through vibration signals. Although the available literature on acoustic measurements for fault detection is very limited, these can be useful to identify damage and have the advantage of using non-contact sensors. This paper aims at comparing the results obtained with vibration and acoustic signals under medium rotational speed. The selected techniques for this comparison belong to the semi-automated processing proposed by Randall and co-authors based on envelope analysis. This work includes a comparative analysis of the benefits of applying the different methods for obtaining key statistical features in the time domain to characterize a fault. The techniques of interest are cepstral editing method and minimum entropy deconvolution. 1 Introduction Rolling bearings are an important component in rotating machinery and are widely used in industry. Due to this fact, recent studies have been performed aiming at identifying key techniques to enhance and detect bearing faults. The most well-established monitoring technique is vibration analysis for medium to high speed regimes [1,2]. Some authors [3-5] noticed that acoustic condition monitoring, on the other hand, has received very limited attention. This could be related with the fact that the acoustic environment in industrial environments is generally complex and therefore measurements are prone to be contaminated by background noise. In the last years, sophisticated signal processing techniques have made it possible to extract useful information from contaminated signals. The acoustic measurements can be done at a distance from the machine avoiding a safety risk and eliminating the need for high temperature vibration sensors [3-5]. For local tooth damage, the authors in [4] measured in a back-to-back experimental gearbox test-rig acoustic and vibration signals and verified that vibration damage detection technologies can earlier detect this type of defect than acoustic sensors. In [5] acoustic measurements were carried out in order to detect a defect in rolling-element bearings using a two microphone sound-intensity technique for a speed range of 100 to 1500 rpm. It was observed that the detectability of an outer race defect was much better than for an inner race or ball defect. The authors also performed sound-pressure measurements and verified that the sound-intensity method presented better results. The authors also concluded that the defect detectability in races and balls, decreases with increasing load and for an outer race fault the detectability increases with speed. In order to improve the detection of bearing faults, an alternative approach was proposed in Ref. [2], by using indicators which are not sensitive to these operational conditions but to the change in health of the gearbox for vibration signals. In such study the authors defended the importance of pre-processing the signals before performing the feature extraction. The goal of the pre-processing is to filter out noise and

PROCEEDINGS OF ISMA2016 INCLUDING USD2016 normalize operational variability. It has been shown that root mean square (RMS) and peak amplitude values are good indicators for gearbox health monitoring. However, it was pointed out that RMS is only suitable for intermediate/high speed. Several studies have been performed in order to identify the features that better detect bearing faults. In [6], the author studied statistical parameters such as RMS, crest factor, skewness and kurtosis for a test rig operating from 500 to 3500 rpm for vibration and acoustic signals. The study led to identifying certain trends per rotational speed range for kurtosis, and kurtosis versus crest factor. Four different bearing conditions (healthy, inner and outer race fault and ball defect) were analysed. The author concluded that the statistical parameters were rotational speed dependent. In [7] a study was performed to verify the variations of statistical moments to identify damage at a much earlier stage. An important step introduced in this analysis was the removal of unwanted noise using digital filtering. Four bearing conditions (healthy, inner and outer race fault and ball defect) were analysed by means of kurtosis and skewness and five test speeds between 1000 and 3000 rpm were selected. The presence of a rolling element line defect was identified using both sound and vibration signals. The authors in [1,8] defended the need of applying signal pre-processing in order to enhance the bearing fault signature in the vibration signals. A vibration signal collected from the bearing housing is composed of different components that might mask the bearing fault signature. The authors confirmed that this procedure was successfully applied to the majority of the cases and it could be as well applicable for low speed. The first step is the removal of unwanted deterministic components, and then it is important to recover the impulsiveness of the signal at the source by removing the transfer path between the sensor and the location where the fault occurred. After this pre-processing, the final step is the application of the traditional envelope analysis. Recent work by the authors [9] studied the effect of cepstral editing and minimum entropy deconvolution on the detectability of outer and inner race bearing faults on a variety of statistical features of vibration signals. The goal of this work is to combine the procedure developed in [8] with the application of statistical features [6,7] in the time domain for outer race faults in medium speed regime and to comparatively examine its applicability to vibration and acoustic signals. 2 Method 2.1 Vibration Signature of Bearing Faults Vibration signals generated by bearing faults are impulsive, at least at the source. However, the vibration signal measured at the bearing housing is the result of a combination of different types of signals originating from gears, transmission path and measurement noise. Shaft- and gear-related signals are deterministic and dominant, thus representing one of the most important masking components. The other source that needs to be taken into account is the transmission path from the source to the sensor which can in turn yield a decrease in the impulsivity of the signal. This paper intends to study the benefits of different signal pre-processing techniques, namely cepstral editing and minimum entropy deconvolution (MED) for bearing fault identification in different speed and load regimes, following the schematic diagram of Figure 1. Figure 1: Schematic representation of the procedures under analysis

MONITORING AND DIAGNOSTICS OF ROTATING MACHINERY 2.2 Deterministic Components Removal Different techniques are available in literature, which allow the removal of the deterministic components (linear prediction, adaptive noise cancellation, self-adaptive noise cancellation, discrete/random separation, time synchronous averaging, cepstral editing procedure) [10,11]. The method investigated in this paper is the cepstral editing procedure (CEP) due to the efficiency and ease of interpretation and implementation. It has been shown in literature that CEP enhances the bearing-fault-related signals more significantly than other techniques [10,11]. It allows the removal of selected discrete frequency components, including sidebands. The cepstrum is commonly defined as the inverse Fourier Transform of the logarithmic spectrum of a signal x(t), which can be written as C(τ) = I 1 {ln(x(f))}, (1) X(f) = I{x(t)} = A(f)e jφ (f), (2) where X(f) is the frequency spectrum of x(t), I 1 the inverse Fourier Transform and τ is the quefrency. If the phase is retained, the complex cepstrum, C c, has logarithmic amplitude as real part and phase as imaginary part. If the phase is disregarded, the real cepstrum C r is obtained: C c (τ) = I 1 {ln(a(f)) + jφ(f)}, (3) C r (τ) = I 1 {ln( A(f))}, (4) Figure 2 shows the procedure used to remove the deterministic components. The main advantage of cepstral editing for the present application is that the unwanted deterministic components are removed in a subtractive manner. Figure 2: Schematic representation of the cepstral method to remove deterministic components [10] 2.3 Transmission Path Removal Minimum entropy deconvolution (MED) is an existing method allowing the removal of the effect of the transmission path from the source (the fault) to the receiver (the sensor). This technique is a type of adaptative filtering that searches for an optimum set of filter coefficients that recover the output signal (or inverse filter) with the maximum value of kurtosis [12]. As referred by Randall [1], this method permits to reconstruct the shape of the original impulses at the source position. By minimizing the entropy, the kurtosis of the inverse filter output is maximized. Figure 3 illustrates the concept behind the MED. The forcing signal e(n) passes through the structural filter h

PROCEEDINGS OF ISMA2016 INCLUDING USD2016 whose output is mixed with noise u(n) and gives the measured output x(n). The inverse filter f produces the output y(n) which has to be as close to the original input e(n) which is unknown but should be as impulsive as possible. Figure 3: Inverse filtering (deconvolution) process for MED The filter f is modelled as a FIR filter with L coefficients. f has to invert the system h. L y(n) = f(l)x(n 1) l=1 The objective function to be maximized is the kurtosis of the output signal y(n) through the filter f. The maximum is found through the coeficients of the filter f by making the derivative of the following objective function equal to zero: (5) O k (f) = N 1 n=0 y4 (n) [ N 1 n=0 y 2 (n)] (6) 2 that is, O k (f) f = 0 (7) 2.4 Envelope Analysis and Frequency Domain Feature Extraction Over years, the envelope technique has been used to identify bearing faults. In this technique, the signal is band-pass filtered in a high frequency range and then the band-pass filtered is demodulated to form the envelope signal. Subsequently, the envelope spectrum is estimated from the envelope signal wherein the diagnostic information is present [1]. For the case where the signal includes other impulsive signals, it is not easy to identify the frequency band in which the fault impulses are amplified by the structural resonances and for this reason in this paper the envelope was applied to the whole signal. In Figure 4 the different steps for obtaining the fault frequencies are presented.

MONITORING AND DIAGNOSTICS OF ROTATING MACHINERY Figure 4: Signal Processing applied to obtain the enhanced fault frequencies The amplitude demodulation was done through the Hilbert Transform (h(t)) which is the convolution of the input signal x(t)with the impulse response 1/πt [13]: h(t) = H{x(t)} = 1 π x(τ) dτ, (8) t τ The autocorrelation function is applied in this paper to find the periodicity in a noisy signal. The autocorrelation (R x (t)) of a signal x(t) is the cross correlation of x(t) with itself, at lag τ [13]: R x (t) = x ( τ) x(τ) = x(t + τ)x (t)dt, (9) In the frequency domain it is possible to identify the bearing fault signatures that appear at specific frequencies using the envelope analysis [1]. These bearings fault characteristic frequencies are expressed in the following formulae: nf s d BPFO 1 cos, (10) 2 D nf s d BPFI 1 cos, (11) 2 D f s d FTF 1 cos, (12) 2 D f sd BSF 1 2d d D 2 cos, (13) where f s is the shaft speed, the n is the number of rolling elements within the bearing, d is the mean diameter of the rolling element, D is the pitch diameter and θ is the contact angle of the load from the radial plane. BPFO stands for ball pass frequency outer corresponding to an outer race fault, BPFI stands for ball pass frequency inner corresponding to an inner race fault, BSF stands for ball (roller) spin frequency and FTF stands for fundamental train frequency corresponding to a cage fault.

PROCEEDINGS OF ISMA2016 INCLUDING USD2016 For the feature extraction analysis will be considered the three first harmonics of the outer race fault: NMH-1: Normalized Magnitude of 1 st harmonic NMH-2: Normalized Magnitude of 2 nd harmonic NMH-3: Normalized Magnitude of 3 rd harmonic NMH_1 = y(1 x BPFO) (14) NMH_2 = y(2 x BPFO) (15) NMH_3 = y(3 x BPFO) (16) 2.5 Time Domain Feature Extraction For this paper seven statistical features [14] are considered. These are applied to the vibration and acoustic signals in the time domain and are detailed as follows: Variance: a measure of the spread of a signal from its mean. Variance = 1 n n 1 (x k x ) 2 k=1 (17) Kurtosis: a measure of the peakedness of the vibration signal. s corresponds to the standard deviation. Peak to Peak: the range between the maximum and minimum amplitude value in the signal. Kurtosis = n k=1 (x i x ) 4 (18) (n 1)s 4 Peak_to_Peak = max(x) min (x) (19) Crest Factor: the ratio of the peak value to the RMS value. It gives the shape of the waveform. Root Mean Square: the square root of the arithmetic mean of the squares of the original signal. Crest Factor = Peak value RMS n RMS = 1 n x k 2 k=1 (20) (21) 75 th percentile: x 0.75 is the value below which 75% of the time data falls. Log energy entropy [15]: log energy entropy in the signal. 0.75 = P(x x 0.75 ) (22) n Ent log = log ( x 2 k ) (23) k=1 3 Experimental Setup: Machine Fault Simulator SpectraQuest The measurements for medium speed regime were performed in a fault machine simulator from SpectraQuest (Figure 5). The machine is driven by a 3 HP Marathon Electric Three Phase AC motor controlled by a Delta VFD-S Inverter. Two different bearing conditions were measured (healthy and outer race fault) for a speed range between 780 and 2340 rpm with an interval of 120 rpm. A 5 kg mass was added to enhance the fault. The bearings under analysis were ER-16K. The accelerometer PCB 365A01

MONITORING AND DIAGNOSTICS OF ROTATING MACHINERY was located on the top of the housing of the faulty bearing and a microphone GRAS 40 PH was located close by this bearing. Bearing ER-16K Rolling element 7.94 mm diameter Pitch diameter 39.32 mm Ball number 9 Contact angle 0 o Figure 5: Fault Machine Simulator SpectraQuest and bearing characteristics 4 Data Analysis and Discussion To understand the benefits of the different pre-processing techniques, vibration and acoustic signals were acquired and analyzed for different speed on the machine fault simulator of SpectraQuest (Figure 5). In order to obtain the faulty frequencies, the procedure introduced in the Section 2.4 was followed. In this paper is shown the spectrum for an outer race fault versus healthy case at 1260 rpm (Figure 6 and 7). In these figures the spectra of the autocorrelation of the envelope after removing the deterministic components and enhancing the impulsiveness for vibration and acoustic signals, are presented respectively. The magnitude of the envelope spectrum was normalized diving by the magnitude of the frequency at 0 Hz (DC component). Observing these figures, one can clearly identify the harmonics of the fault frequency for both vibration and acoustic sensors, being noticed that the vibration signal provides a cleaner spectrum. 0.02 0.018 Outer Race Fault Healthy 0.016 0.014 0.012 0.01 NMH-1 NMH-2 0.008 0.006 NMH-3 0.004 0.002 0 50 100 150 200 250 Frequency [Hz] Figure 6: Spectrum of the autocorrelation of the envelope for the vibration signal

Magnitude PROCEEDINGS OF ISMA2016 INCLUDING USD2016 0.02 NMH-1 NMH-2 Outer Race Fault Healthy NMH-3 0.015 0.01 0.005 0 50 100 150 200 250 Frequency [Hz] Figure 7: Spectrum of the autocorrelation of the envelope for the acoustic signal Figure 8 a) shows a representative case for the Kurtosis feature calculated in the healthy and outer race fault cases for the vibration signal. Focusing on the feature value in the healthy case, as expected, the Kurtosis level is much lower (~3) compared to the faulty case. Still it is possible to verify the benefits of the MED for this feature, due to a higher difference in the values when compared with the reference (healthy). Moreover, it is relevant to add that for this processing the tuning parameters for the cepstrum were a liftering band of 15% and for the MED a filter length of 200 samples. The stop criterion was chosen as a difference in Kurtosis of 0.5 between successive iterations. In Figure 8 b) it can be noticed that the Kurtosis does not provide satisfactory results for the acoustic signals. One of the reasons can be related with the fact that the faulty signal for this sensor is not very impulsive when in presence of a fault, as observed for the vibration signal. Figures 9 a) and b) allow to draw similar conclusions for the Crest Factor as draw before for the Kurtosis. a) b) Figure 8: Kurtosis for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Legend for figures 8 to 17:, without pre-processing for healthy case;, with application of edited cepstrum for healthy case;, with application of edited cepstrum and MED methods for healthy case;, without pre-processing for the faulty case; with application of edited cepstrum and MED methods for faulty case; with application of edited cepstrum and MED methods for faulty case

MONITORING AND DIAGNOSTICS OF ROTATING MACHINERY Figure 9: Crest Factor for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8 Figure 10 presents the calculated Variance feature for the outer race fault versus the healthy case for two different sensors a) accelerometer and b) microphone. For this feature it can be concluded there is no benefit of applying the MED method for vibration signal. There is already a clear distinction between the faulty and healthy feature value without any other extra processing. For this case, the application of the cepstral editing method did not provide any other extra advantage in further increasing the deviation of faulty from healthy results. Regarding the acoustic signals, Figure 10 b), as concluded already for the vibration signals, the application of the MED does not bring extra benefits while the cepstral editing method provides a clearer distinction between the faulty and healthy data while for higher speeds this difference tends to decrease. It was also verified for acoustic signals that it is already possible to have a good distinction of the faulty versus healthy data without any processing. All these conclusions are also valid for the other statistical features: Variance (Figure 10), Peak to Peak (Figure 11), RMS (Figure 12), Percentile 75 (Figure 13) and Entropy (Figure 14). Figure 10: Variance for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8

PROCEEDINGS OF ISMA2016 INCLUDING USD2016 a) b) Figure 11: Peak to Peak for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8 Figure 12: RMS for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8 Figure 13: Percentile for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8

MONITORING AND DIAGNOSTICS OF ROTATING MACHINERY Figure 14: Entropy_Log for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8 The other important aspect to be noted from this investigation is the fact that the feature values calculated from time domain features are speed-dependent and the method of the static threshold will not provide satisfactory results and might lead to false alarms. Therefore, the threshold should be set as a function of the rotational speed. In Figure 15 a) shows the normalized magnitude of the first harmonic of the envelope spectra obtained from outer race fault and healthy cases. It can be concluded from the figure that there is no benefit of applying the MED method. However, it can be noticed that the use of the cepstral editing technique helps to enhance the fault when compared with the healthy case. For the data without any processing it is difficult to have a clear distinction between faulty and healthy cases. From the Figure 15 b), for the acoustic signals, the same conclusions can be achieved. For both sensors, the feature values seem to be speed independent and normally the threshold method should provide satisfactory results. The same conclusions can be drawn for the two other frequency features, Normalized Magnitude Harmonic 2 (NMH-2, Figure 16) and Normalized Magnitude Harmonic 3 (NMH-3, Figure 17). However, for acoustic signals for NMH-2 and NMH-3 for certain rotational speeds it is not possible to have the same separation between faulty and healthy as for the NMH-1. Figure 15: NMH-1 for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8

PROCEEDINGS OF ISMA2016 INCLUDING USD2016 Figure 16: NMH-2 for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8 Figure 17:NMH-3 for Outer Race Fault vs. healthy case for: a) vibration signal b) acoustic signal. Same Legend as Figure 8 Figure 18 provides the correlation matrix of the considered features for the outer race fault case for the accelerometer sensor. There are general observations that can be made; the parameters Variance, Percentile 75, Entropy_log, NMH2 and NMH-3 provide the higher correlations for the vibration sensor. With the application of the cepstral editing method and the MED, it can be observed that the number of highly correlated variables is reduced to four, leaving out the NMH-2. The use of this processing reduces the correlation coefficient between variables. In Figure 19 the correlation coefficients were calculated for the acoustic signals. The features with higher correlations are the Variance, Crest Factor, Percentile 75, Entropy and NMH-1, NMH-2 and NMH-3. After the processing the number of correlated variables were reduce to five, Variance, Crest Factor, Percentile 75, Entropy and NMH-3. The main difference between the two sensors is that for the microphone, the Crest Factor is highly correlated with the other features and this does not happen for the vibration signals. An aspect of interest for fault detection is the identification of patterns by using a minimum set of uncorrelated features. Based on the present results, it is worth noting that a set of correlated features provide redundant information for fault detection purposes. Thus, in that case the consideration of one feature should be enough to evaluate the trend with speed.

MONITORING AND DIAGNOSTICS OF ROTATING MACHINERY Figure 18: Correlation Coefficient of the features for Outer Race Fault for vibration signal left) without processing, middle) with cepstral editing, right) with cepstral editing and MED Figure 19: Correlation Coefficient of the features for Outer Race Fault for acoustic signal left) without processing, middle) with cepstral editing, right) with cepstral editing and MED 5 Conclusions This paper was intended to study the benefits of different signal pre-processing techniques, namely cepstral editing and minimum entropy deconvolution (MED) for bearing outer race fault identification in different speed regimes. This was performed by extracting several features from vibration and acoustic signals acquired on a bearing fault simulator setup for different speed regimes. It has been shown that the analysis tools proposed applies both vibration and acoustic measurements. For medium speed the benefit of the pre-processing techniques seem to be not substantial and the efficiency of their application may be related with the complexity of the machine. Only the Kurtosis and Crest Factor seemed to benefit from it for vibration signals. In case of the acoustic signals the MED did not provide any benefits but the cepstral editing method helped enhance the fault for all the features except for Kurtosis and Crest Factor. These last two features do not provide any interesting information to help the fault identification. It was as well verified that several features were correlating with each other, and it might be important to consider the application of feature selection algorithms for pattern recognition proposes. As final remark, the selection of the MED parameters needs to be done carefully in order to prevent false alarms in the fault detection.

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