Condition Based Monitoring and Diagnosis of Rotating Electrical Machines Bearings Using FFT and Wavelet Analysis

Transcription

1 350 Condition Based Monitoring and Diagnosis of Rotating Electrical Machines Bearings Using FFT and Wavelet Analysis Ioan COZORICI, Ioan VĂDAN and Horia BALAN Abstract: Condition Based Monitoring of rotating electrical machines is usually based on vibration signal analysis. In the presence of a mechanical or electrical failure, vibration signals contain periodic pulses with a characteristic frequency corresponding to a certain fault. However, due to higher noise levels present in industrial applications, feature extraction of vibration signals requires the use of appropriate techniques. This paper describes the use of Fast Fourier Transform (FFT) and Wavelet Analysis (WA) as a technique to detect bearing faults of rotating electrical machines. Keywords: wavelet, FFT, bearing, vibration analysis. 1. INTRODUCTION Rotating machinery is widely used in today s industry. Condition based monitoring and diagnosis is a process that can be used to detect early electrical and mechanical faults, leading to a significant reduction of maintenance costs. In the literature are described various methods for monitoring electrical machinery [1]. In this paper we turn our attention to monitoring and diagnosis methods based on vibration signal analysis. The literature describes several methods for monitoring faults using time domain analysis [2, 3], frequency domain analysis [4] and time-frequency analysis [18]. The outcome of rotating electrical machines vibration analysis, depends largely on the vibration signal processing techniques used. Using an appropriate signal processing technique, it is possible to detect variations of vibration signals caused by defective components. Classical vibration signals analysis was generally based on spectrum analysis using FFT, which. is suitable for stationary signal processing, but provides a poor representation of signals in time domain and thus is unsuitable for nonstationary signals analysis. The above mentioned problems could be resolved by using WA [5]. Wavelet functions are composed of a family of basic functions that are able to represent a signal in time (or space) and frequency (or scale). The Manuscript received November 12, This paper was supported by the project "Doctoral studies in engineering sciences for developing the knowledge based society-sidoc contract no POSDRU/88/1.5/S/60078, project co-funded from European Social Fund through Sectorial Operational Program Human Resources main advantage of using wavelet transform is the ability to perform local analysis of a signal. In this paper a comparison between FFT and WA will be made in order to illustrate the usefulness of WA in the detection and diagnosis of rotating electrical machines faults. Some of the most common faults of electric machines are bearing faults. Bearings vibration can lead to malfunction, resulting in downtime of the whole system operation and significant economic losses [6]. Lately WT techniques were used to analyze nonstationary vibration signals generated by the rolling elements of bearings [7, 8]. In [9] the author used WT for identifying faults on the bearing outer race. In another study [10] the authors studied the bandwidth properties of the bearing vibration and applied WT to identify the bearing faults. These studies have shown that time-frequency analysis of vibration signals provides a wide range of information regarding bearing components. In addition to well-established bearing monitoring techniques of induction motors [13], in [11] the authors present a method for fault diagnosis of induction generators by using wavelet packet decomposition of the stator current. This method can be successfully used to identify faults in the rotor and stator as shown in [12] where the study was carried on a motor on two working situations, in good condition and with a provoked rotor fault. Given the nonstationary nature of the current the use of WT offered a better resolution under variable load. Therefore, WA is a powerful alternative for nonstationary signal analysis whose spectral features vary over time and is also suitable for vibration signals analysis of whose components of short duration and 2012 Mediamira Science Publisher. All rights reserved.

2 Volume 53, Number 4, high frequency are located close together in time, and those whose components of long duration are located closely in frequency domain [14]. 2. FAST FOURIER TRANSFORM (FFT) The Fast Fourier Transform is a computerized mathematical algorithm used for transforming vibration signals from the time domain (time waveform) into the frequency domain. Fourier amplitude spectrum A(f) corresponding to the signal frequency f(t) can be obtained as [10]: (1) By means of this analysis, a correlation of variations in the vibration signal and different faults of the equipment can be achieved [22]. Fourier transform, considers all systems as being linear and because of that all frequency spectrum is allocated to the linear part, thus neglecting the nonlinearities of any kind. FFT is helpful in diagnosing faults associated with unbalance, misalignment, eccentric components and damaged bearings, shafts, gears or motor electrical faults [23],[26]. There are some cases where it is not advisable to use spectral analysis for the analysis of vibration signals, as in the case of very low frequency signals acquired from shafts with low rotational speed. any analytical expression, have a finite duration and the mean value is always zero (4). By the means of computed wavelet coefficients we can reconstruct the original x (t) signal. (5) Since the wavelet coefficients appreciate the similarity between signal x (t) and wavelet function, the main problem of applying CWT consists of the appropriate selection of mother wavelet function. In [18], the author suggests using Morlet wavelet function to detect periodic pulses corresponding to bearing faults. The author shows that by using Morlet wavelet function is achieved a high level of correlation between x(t) and. CWT has a very high precision, but in practice is preferred the use of DWT due to its reduced computing time. To implement the DWT, one could use discrete filter banks to compute discrete wavelet coefficients Figure 2. Low pass filters remove high-frequency fluctuations from the signal and their outputs provide an approximation of the signal. High pass filters preserve high-frequency fluctuations of the signal and. their outputs provide detail information about the signal. The outputs of low pass filters and high pass filters define the approximation coefficients and detail coefficients, respectively. 3. WAVELET TRANSFORM Study and analysis of wavelets has grown exponentially in the field of mathematics and engineering research, with some undeniable advantages to Fourier analysis [15]. Wavelet function is defined as [17]: (2) where a is the scale parameter and b is the translation parameter. There are two types of wavelet transform: continuous wavelet transform (CWT) and discrete wavelet transform (DWT). Mathematically, the CWT calculates the inner products of a continuous signal x(t) with a set of continuous wavelets according to the following equation: (3) Decomposition of ψ (t) must be quick enough to ensure analysis in time / space and frequency. Also, wavelet function must satisfy the following condition [16]: (4) where is the Fourier transform of ψ(t) and is a constant that depends on the chosen wavelet function. Unlike the sine functions, wavelet functions are a class of asymmetric functions that are not described by Total number of decomposition levels can be calculated with the following equation: (6) where N n is the number of levels, and f S is the sampling frequency. 4. CASE STUDY Fig. 1. Wavelet decomposition tree [24]. Beside the use in rotating electric machines bearings are widely used in industrial applications. An unexpected failure of a bearing can cause significant economic losses. It is therefore very important that bearing faults to be detected in early stages of development. In the presence of mechanical or electrical failures, vibration signals contain periodic pulses with a characteristic frequency corresponding to a certain type of fault [21].

3 352 In most cases acquired vibration signals from piezoelectric accelerometers have complex and nonstationary character. Most of the techniques used for bearing monitoring use vibration analysis, but there are some techniques using acoustic monitoring [19] or motor current signal analysis [20]. A careful analysis of a rolling bearing elements shows that there are four predominant frequencies generated by bearings: BPFO Bearing Outer Race Frequency BPFI Bearing Inner Race Frequency BSF Ball Spin Frequency FTF Fundamental Train Frequency. These frequencies and multiples of these frequencies show up as spikes on a vibration analysis spectrum when bearings begin to fail (Table 1) and they are determined using the shaft rotational speed and the dimensions of the bearing elements. A vast majority of bearing failures are associated with the bearing inner and outer race. Since the characteristic fault frequencies have a certain periodicity in the vibration spectrum, these frequencies can provide good information on fault location. Table 1. Bearing fault frequencies.[25] Fault Equation Significance Fig. 3. Bearing with outer race fault. acquisition board. Signals were processed using a virtual instrument developed in the LabView. In the experiment we used a 6203 ball bearing type Z. The fault on the bearing outer race was simulated by drilling two holes with diameter of 4 mm each (Fig. 4). BPFO BPFI BSF [ ] FTF n = nr. de bile fr= rev./s (rel) Fig. 4. Acquired vibration signals: a) good bearing; b) faulty bearing. For an effective diagnosis of bearing faults is very important to isolate the characteristic fault frequencies of the original signal from the other insignificant components. Acquired vibration signals are shown in Figure 5. In this paper a comparison is made between WT and FFT as failure detection techniques with a focus on diagnosis of bearings for rotating electrical machines. To exemplify these diagnostic techniques using FFT and WT, we analyzed the vibration signals of a 0.37 kw motor in two situations: with the bearings in good condition and with a provoked fault on the bearing outer race. Fig. 2. Vibration measuring setup. In figure 3 is presented the setup used for signals acquisition. The setup consists of a KD 45 piezoelectric accelerometer, a charge amplifier, the NI 6100 Fig. 5. Spectral analysis of vibration signal of good bearing (a) and faulty bearing (b). As we can see in figure 6 it is very hard to identify and differentiate the fault frequencies, just by analyzing the frequency spectrum, due to the amount of noise present in vibration signal. In order to remove the noise from vibration signal a wavelet thresholding technique was applied which removes or keeps some of the wavelet coefficients. Using the DWT with symlet of order N = 2, these

4 Volume 53, Number 4, Fig. 6. Denoised signals and their corresponding scalogram of good bearing (a) and the faulty one (b). signals were decomposed on 4 levels. Elimination of noise was achieved using hard thresholding technique that produces very large oscillations near the discontinuity points. By using wavelet analysis all irrelevant noise was successfully removed from the input without using additional filters. The CWT was applied for the signal reconstruction and for scalogram plot. In Figure 6 are presented the results after applying the DWT. In scalogram (b) corresponding to vibration signal of the faulty bearing, can be observed that in addition to bearing fundamental frequency there are highly emphasized the outer race fault frequencies of the bearing, which are not present in scalogram (a) corresponding to vibration signal of the good bearing. 5. CONCLUSIONS This paper described the use of Wavelet analysis and detection of different technical faults occurring in bearings of rotating electrical machines. This method proves to be reliable in fault diagnosis and it provides a good resolution for identifying of bearing faults. ACKNOWLEDGMENT This paper was supported by the project "Doctoral studies in engineering sciences for developing the knowledge based society-sidoc contract no POSDRU/88/1.5/S/60078, project co-funded from European Social Fund through Sectorial Operational Program Human Resources REFERENCES 1. 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5 Drd. ing. Ioan COZORICI Prof. dr. ing. Ioan VĂDAN Prof. dr. ing. Horia BALAN Technical University of Cluj-Napoca Department of Energetics and Management Faculty of Electrical Engineering