FAULT DIAGNOSIS ON BEARINGS IN SYNCHRONOUS MACHINE BY PROCESSING VIBRO- ACOUSTIC SIGNALS USING HIGHER ORDER SPECTRAL

1. Department of Electrical Engineering, Instituto Tecnológico de Mexicali, Mexicali, Baja California, México. 2. Imperial Valley College, Calexico California, U.S.A. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

This work presents a methodology for detecting faults in synchronous generator bearings using vibration signals recorded by acceleration transducers (piezoelectric accelerometers) and acoustic transducers (omnidirectional microphones). The advantage of using the spectra of higher-order ( ) in the diagnosis of faults in rotating electric machines bearings is analyzed. A comparison for two special cases of ( ) was made: spectral density of power ( ) and biespectrum ( ). Vibration signals of bearings without fail and with an artificially induced failure were analyzed. The artificial fault consisted of a crack produced on a bearing cage. This procedure allowed to determine that the shows much more clearly the frequencies generated by the defective bearing.

…………………………………………………………………………………………………….... Introduction:-
Synchronous generators produce about 99% of the electricity consumed all over the world (Medrano et al., 2015a). Because of this great importance in the global electricity generation it is necessary to prevent the occurrence of failures which could possibly cause unwanted problems. Such generators are generally exposed to a large number of faults and are the most expensive equipment of the power system placing them in a critical position Suarez (1998). Failure of bearings is one of the most common problems in synchronous generators, approximately 40% of faults in rotating electrical machines (Sin et al., 2003), (Medrano et al., 2013), (Medrano et al., 2014), (Medrano et al., 2016).
The conventional way of analysis and fault diagnosis of bearings is based on recording vibration signals from accelerometers that play an important role in predictive maintenance of electrical machines. Vibration signals caused by a bearing may contain spectral components that are related to the bearing geometry, the number of rolling elements, the rotation speed, the location of the fault and the type of load applied.
Thus, a window of opportunity of having a different but equally reliable methodology arises by using another type of signal which is not invasive neither expensive. This allows us to propose a diagnosis system based on the acoustic emission of machines using microphones and sensors. This technique detects internal acoustic changes caused by phenomena such as the emergence and growth of cracks, detachment of small pieces of material, metal deformation, among others, and it is based on that part of the energy released is transmitted outside as sound waves. These acoustic waves can be recorded by means of transducers (microphones) installed in the vicinity of the generator. At the same time, these transducers convert the waves of sound into electrical signals that can then be processed and analyzed for obtaining a diagnosis.

ISSN: 2320-5407
Int. J. Adv. Res. 5(4), 1210-1225 1211 The information provided from vibration signals through acceleration or acoustic transducers in the frequency domain can be processed and analyzed to determine possible abnormal conditions in the bearings of synchronous generators. Earlier detection of bearing failures analyzing vibration signals requires the use of appropriate techniques of signal processing that involves higher-order spectra analysis ( ).
Causes of bearing failure:-Among the most commonly identified causes of failure on bearings are: adequate lubrication, 36%; improper operation (excessive dynamic loads on the bearing, imbalance and misalignment), 34%; contamination (including moisture), 14%; and about 16% due to defects from other factors such as transportation/storage problems or inadequate bearing installation (Medrano et al. 2016). In most cases, failures do not appear suddenly bu gradually making possible their detection before a catastrophe occurs.
Vibration Analysis:-Under normal operating conditions, bearings would fail due to wear or fatigue of the material, and when such a failure appears vibrations and acoustic emission levels in a synchronous generator increase too. These bearings fault frequencies are a function of geometry of the bearings and driving speed (Stack et al., 2004), Palomino (2011), Wowk (1991). Each one of the components of a bearing has a particular fault frequency that might be identified depending on the element failed and it should be defined by at least one of four characteristic frequencies when occurring in: the outer race , ball pass frequency of the outer race), the inside track ( , ball pass frequency of the inner race), the rolling elements ( , ball spin frequency), the cage ( , fundamental train of frequency). (1) where is the pitch diameter ( ), is the diameter of balls ( ), is the contact angle between the balls and tracks (°), is the rotation speed ( ), and is the number of rolling elements. Failure frequencies are reference points when analyzing the spectrum obtained from the vibration signals of bearing, because if there is a problem, the spectrum provides information to determine the location, the cause, and how critical the problem could it be Suarez (1998).
Theoretical framework:-If analyze an infinite-length signal composed of a sinusoid , The second-order cumulant is defined as: (8) where is the mathematical expectation operator in random variables, either of a data set or a function related with the data between the square brackets. The can then be rewritten as: (9) where is the time delay variable, is the frequency variable.
The frequency spectrum can be represented as: (11) where is the Fourier transform signal, is the conjugate of the function, and is the amplitude function. The power density method has limitations such as loss of signal phase, inability to detect non-stationary signals, and cannot be detected when two signal frequencies are equal or very similar that could be overlapped. Because of this some limitations could result in detecting and diagnose a failure in the machine.

Statistics of third order ( ):-
The BIS is a particular case of higher-order spectra and by definition is a two-dimensional Fourier transform of the third order cumulants (Gomez and Paredes, 2005), (Toledo et al., 2001), (Nikias and Mendel, 1990), Rivola (2000), (McCormick and Nandi, 1999), Mendel (1991), (Swami et al., 1998), (Brillinger and Murray, 1967). One of the main reasons for the use of is that provides information about the amplitude and phase of the signals.
If is a stochastic signal with zero mean, the BIS is defined as: It can be seen that the bispectrum is a function of two independent variable frequencies ( and ). The reflects the interaction between , and . The third-order cumulant is defined as: (13) The can then be rewritten as: (14) Similar to , the BIS satisfies the following relationship: (15) where is a constant of proportionality, the scale is: (16) and the phase is: (17) This result indicates that the has magnitude and phase, which does not happen with the . The has the advantage that being a three-dimensional representation, frequencies can be displayed graphically and making possible to detect coupling between similar frequencies.
Experimental Methodology:- Figure 1 shows the steps followed for detecting faults in bearings based on vibration analysis (continuous frames), and the steps followed to evaluate the with acoustic transducers (dotted boxes).

Tests and Results:-
First of all, experimental tests were performed in a non-failed new machine and data were collected. After that, a crack was induced in the cage of a bearing . Tests were carried out in a test lab as shown in figure 2 (a), the characteristics of the engine generator system are:  single phase induction motor,  ,  ,  , , , , synchronous generator , . Acceleration transducers (piezoelectric accelerometers, Analog Device ) and acoustic transducers (omnidirectional microphones, Panasonic ) were used for vibration analysis.  1 3-axes accelerometer (Analog Device ) 10 2 Omnidirectional microphone (Panasonic ) Bearing failure frequencies :-When deterioration occurs on a single component of the bearing then a peak at a particular frequency appears and its value depends on the geometry of the bearing and its rotation speed. Palomino . In Table 2, the values of the vibration frequencies for the bearing elements are listed. Vibration and acoustic bearing signals were acquired by means of a data acquisition card , taking a representative sample of 6000 points recording the sample after five minutes operation once the machine was running stable. Figures 3 and 4 show the results obtained for the horizontal signal ( axis) and vertical ( axis) of the generator piezoelectric accelerometer. In each case, the signals are plotted as amplitude vs. frequency for (a) without failure and (b) with failure (crack in the bearing). The effect of signal overlapping when analysis is used is quite explained in (Ypma et al., 1997). In this work the analysis was performed for a frequency of which is about times the frequency of rotation of the shaft.

Analysis of the signal in the frequency domain (accelerometers and microphones):-
In figure 3 (a), with the accelerometer, the vibration signal amplitude of the component without failure is and while with failure is ( figure 3 (b)). In figure 4 (a) the amplitude of the component without failure is while with failure is ( figure 4 (b)).

ISSN: 2320-5407
Int. J. Adv. Res. 5(4), 1210-1225 1219 For the microphone, the acoustic signal amplitude of the component without failure is whilst with failure is ( figure 5(a) and (b)). For y axis the amplitude without failure was whilst with failure was ( figure 6 (a) and (b)).
When the fault is severe there appear sidebands around the important frequencies of rotation of the machine. In figures 3, 4, 5 and 6, frequency peaks of , , and were analyzed. It was observed that these frequencies are closely related as multiples of 30 Hz which is the theoretical frequency of shaft rotation. Figures 7 and 8 show the results obtained for the signal in the and axis from piezoelectric accelerometers. In each case, the signals are plotted in amplitude of the for (a) without failure and (b) with failure (crack in the bearing). In figures 7 and 8, when an accelerometer was used for both and axes the components of the vibration signal without failure and with failure exhibit couplings at 30 Hz that represents the theoretical frequency of shaft rotation.

Analysis of the signal (accelerometers and microphones):-
In figures 9 and 10, from the microphone signals, on both the and axes it is observed acoustic couplings without failure signal frequency it represents the theoretical frequency of shaft rotation. And with failure has coupling to frequency representing the frequency of failure of the bearing cage.
When the fault is in the bearing cage the frequencies of failure, decrease or disappear due to the occurrence of many components at random frequencies that prevent the formation of sidebands around the frequency of failure, 1223 presenting an increase in background noise (Medrano et al. 2015b). This prevents to make a diagnosis for failure in the bearing cage through the use of accelerometers, but allows the use of microphones in detecting these.

Discussion and Analysis:-
Results of graphic signals with respect to the frequency ( ):a. Frequency peaks that occur in the of the accelerometer signals in the and axes for the condition without failure are related to the theoretical frequency of shaft rotation (approximately ). b. The peaks that occur in the of the accelerometer signals in the and axes for the condition with failure are related to the theoretical frequency of shaft rotation (approximately ), the theoretical frequency of failure for the bearing cage (approximately ) is masked by other frequencies of operation of the machine which makes it complicated to make a diagnostic resolution with this type of graph. c. The peaks that occur in the of acoustic signals in the and axes for the condition without failure, is less regarding the condition with failure, the frequency peaks related to the theoretical frequency of shaft rotation (approximately ). d. The peaks that occur in the of acoustic signals in the and axes for the condition with failure is related to the theoretical frequency of shaft rotation (approximately ), the theoretical frequency of failure for the bearing cage (approximately ) is masked by other frequencies of operation of the machine which makes it complicated to make a diagnostic resolution with this type of graph.

Results of graphic signals bispectrum (
):a. The couplings presented in the accelerometer signals in the and axes for the condition without failure are related to the theoretical frequency of shaft rotation (approximately ). b. The couplings presented in the accelerometer signals in the and axes for the faulted condition is related to the theoretical frequency of shaft rotation (approximately ) couplings caused by the defect frequency (approximately ) is attenuated or not displayed due to the appearance of many components of random frequencies, making it difficult to identify couplings caused by the defect often as many couplings are of small amplitude and are masked by other frequencies of operation of the machine making it complicated to make a diagnostic resolution with this type of graph. c. Couplings often presented in the of acoustic signals in the and axes for without failure condition are lower with respect to the condition with failure. Appearing frequency peaks related to the theoretical frequency of shaft rotation (approximately ). d. The couplings presented in the of acoustic signals in the and y axes for the condition with failure are related to the theoretical frequency of failure for the bearing cage (approximately ) is present in a clear and obvious way. e. With obtained in both axes (for faulty condition) spaced by the frequency of failure for the bearing cage peaks are observed. So the obtained through acoustic signals in horizontal axis ( ) and vertical ( ) allows this type of methodology is appropriate for the detection of this type of bearing failure.

Conclusions:-
An acquisition system which consisted of triaxial piezoelectric accelerometers, omnidirectional microphones in the and axes are used for the experimental phase. An analysis of the results it can be deduced that: 1. Piezoelectric accelerometers detect no significant differences for conditions without failure and failure so it is concluded that this type of transducers are not a viable alternative for fault detection analysis of vibration signals. 2. Omnidirectional microphones are capable of detecting a fault in the bearing cage of a synchronous generator in both the direction and in the direction and from the acoustic signals emitted by it. 3. The increased width of the sound level is a parameter that allowed detect bearing damage, while the number of separated peaks failure frequency allowed to determine the location of damage in the cage.
Leading to the conclusion that the use of omnidirectional microphones is a viable option for the detection of bearing failures in a synchronous generator, performing the analysis of the signals through the , which allows monitoring the evolution of the spectrum signals which can be detected any abnormal signs or changes that could indicate a possible failure ahead.

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Scientific innovation:-A methodology that uses signal processing technique for analyzing acoustic signals of synchronous generators, which can identify early failures in their bearings and establish accurate and reliable diagnosis less invasive than those obtained by the methods used so far.