International Journal on Mechanical Engineering and Robotics (IJMER)
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Early Detection of Abnormal Vibrations on High-Power Diesel Generator
1Metaga Jeremi SOGOBA, 2Said GUEDIRA, 3Badie DIOURTE
1Registered for a PhD at Higher Institute of Education and Applied Research (ISFRA) of Bamako in Mali (West Africa).
2Professor of Higher Education, is the Scientific Director of the Laboratory of Vibration Analysis in Higher National School of Mines of Rabat (ENSMR) in Morocco.
3Professor of higher Education, Specialty: Instrumentation and Measurements Industrial Data Processing, General Inspector of National Education in Mali.
Abstract - This study deals with early detection of abnormal vibration on high-power diesel generator. The generating sets under the study are manufactured by Wartsila, with a nominal capacity of 14 733 KVA each.
They are operated by the electricity generation company of Mali (West Africa).
A diesel power unit consists basically of a diesel engine and an alternator. The diesel component is the source of strong shocks due to explosion in cylinders during power strokes.
The shocks produce high vibrations that tend to drown out vibrations caused by defects. The study seeks to detect abnormal vibrations regardless of the constraints relating to strong vibration energy in explosion shocks. For these constraints, traditional methods for signal processing in frequency domain prove inadequate. Indeed, we processed the signals measured on the generating sets in a cyclostationary context by introducing the cepstrum.
The findings obtained are relevant. The spectrum analysis of the signals measured helped us diagnose correctly a radial misalignment defect in elastic coupling between the diesel engine and alternator on the diesel generating set n°2 (G2), in spite of strong vibration energy caused by explosion shocks in cylinders.
Key Words: abnormal vibration, cepstrum, cyclostationarity, Diesel generator.
I. INTRODUCTION
The study reported here originated from a visual examination of abnormal vibration on the diesel generating set n°2 at the power plant of Balingué BID in Mali (West Africa), by the technical staff in charge of running the generating sets. Balingué BID power plant is one of 45 MW operated by the generation company of Mali (EDM S.A). We have been conducting investigations on set n°4 certified as sound, and set n°2 showing signs of abnormal vibrations. The diagnosis is based on the analysis of vibration signals measured with an accelerometer placed on the generating sets according to standard measurement points (figure 3.1).
As the signals produced by the diesel generating sets are cyclostationary, we introduce the notion of cyclostationarity.
An engine cycle corresponds to 2 crankshaft rotation turns and comprises successive events in each cylinder:
injection, explosion, closing and opening of admission and exhaust valves. Each event means a vibration signal of impulsive type. Since the signals are of impulsive type, cyclostationary, processing in frequency domain proves inadequate for diagnosis. To alleviate in part this limitation, we process the signals measured in cepstrum domain.
II. CYCLOSTATIONARITY
The first studies on cyclostationary-type signals date back to the 1950s. In telecommunication, cyclostationarity attracted increased interest in particular from the 1980s. However, its application in mechanics started only recently. Diesel generating sets produce cyclostationary signals.
2.1 Cyclostationary random process
A random process is strictly cyclostationary, with period T if its probability density is periodic to period T:
Px t = Px(t + nT) ∀(t,n) ∈ ℝ × ℤ (2.1) Period T is called cyclic period. A random process can present several cyclic periods; in this case, we refer to polycyclostationarity.
In practice, estimating statistical descriptors (moments and cumulants) allows to determine probability density.
2.2 Cyclostationarity of order n
A random process is cyclostationary of order n with T cyclic period, if its moment of order n μx n exists, and is periodic to period T = [T,…, T]
μx n ( t ) = μx n ( t + T ) (2.2)
2.2.1 Frequency domain
The passing into frequency domain is accomplished either through the breakdown in serials Fourier with relation to the temporal variable t or by Fourier transform with relation to the delay variable τ. Then two different quantities are differentiated based on representation space (see figure 2.1) [1], [6], [7]:
- Cyclic autocorrelation Cx∝ τ : Cx(t, τ) = α=kCx∝ τ
T ej2πα t ∀ k ∈ ℤ (2.3) - Spectral density of cyclic power or spectral correlation Sx∝(f) :
Sx∝(f) = Cx∝ τ e−j2πfτdτ (2.4) - Wigner-Ville Spectrum :
Wx(t, f) = Cx(t, τ) e−j2πfτdτ (2.5) The Figure 2.2 shows an example of cyclostationary process of order 2. It is a process that corresponds to the total of a periodic deterministic process and a residual process. These cyclostationary signals present hidden periodicities [2]: they are not periodic in the strict meaning, but some of their statistical properties are periodic. On the whole, cyclostationarity mathematical modelling is based upon the theory of statistics of higher order (moments and cumulants).
Cx(t, τ)
Fourier transform serial Fourier 𝛕 ↔ 𝐟 𝐭 ↔ 𝛂 Wx(t, f) Cx∝ τ
serial Fourier Fourier transform 𝐭 ↔ 𝛂 𝛕 ↔ 𝐟 Sx∝(f)
Figure 2.1: Representation spaces of a cyclostationary process of order 2
Figure 1.2: Cyclostationary process in order 2
2.2.2 Cepstrum domain
The cepstrum was introduced by Bogert for detecting echoes. The cepstrum efficiency in vibration analysis of mechanical systems has been demonstrated by R.B.
Randall in 1975, and in recent years in 2004 [3], [4].
Given 𝐒 (t) the cepstrum of a signal S(t), by definition:
S (t) = TF−1[Ln TF(s t ) ] (2.6) It is a representation of the Fourrier transform of the spectrum; it equals two times the Fourier transform of the timing reference signal. The image obtained is a curve based on time quefrency measured in seconds.
The cepstrum is to the spectrum what the spectrum represents for signal temporal representation.
Simply, a cepstrum is defined as the spectrum of the logarithm to the spectrum. The variable defining periodicities in pseudo-time domain represented by the cepstrum is termed quefrency followed by its rhamonics.
[5]
III. IMPLEMENTATION
The Figure 3.1 is the graph representing standard measurement points [8]. The measurements have been performed by placing the accelerometer on these points.
3.1 Experimental conditions
Measurements are performed on the generating set working at full capacity. The measurement points are on both sides of the set:
Side A: left side back to the alternator Side B: right side back to the alternator
We select measurement points in accordance with IS/ISO 8528-9. We have 3 measurement points on the turbochargers: support bearing TC, support bearing TBR and support bearing CAC. On the diesel component we have 4 measurement points: support bearing 1, support bearing 2, support bearing 3, and support bearing 4.
Similarly, 4 measurement points are located on the alternator: support bearing 5, support bearing 6, support bearing 7, and support bearing 8.
On each measurement point, measurements are performed in three positions: Axial (AX),
Radial vertical (RV), and Radial horizontal (RH) For each measurement point, the following parameters are measured:
- Overall acceleration level expressed in m/s2 rms;
- Overall velocity level expressed in mm/s rms;
- Peak extract to rotation frequency:10Hz;
- Peak extract to harmonics H2:20Hz and H3:30Hz.
Remark: In diesel generating sets, explosion frequency is an important parameter to determine, for the main source of vibrations is at this frequency. It is determined
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cylinders in the diesel engine. Explosion frequency is given by the formula:
Fexplo = number of explo .per cycle
number of turns per cycle (3.1) f0 = turn1 (3.2) Fexplo = number of explo .per cycle
2 f0 (3.3)
With f0 : diesel engine rotation frequency.
With regards to the generating sets of Balingué BID on which we are conducting our study, explosions in the 18 cylinders occur 2 by 2, that is to say 9 explosions by cycle. In a cycle, the crankshaft makes 2 turns. The Formula 3.3 gives: Fexplo = 45 Hz.
Figure 2.1: Standard measurement point configuration on a diesel generator
3.2 Findings Presentation and Analysis
The velocity on alternators front bearings of G2 and G4 are summarized in Table 1. These indicators lead us during the investigations on spectra. We carry out a spectrum analysis in frequency field and spectrum range.
3.2.1 Frequency Domain Analysis
We process the signals measured through the FFT method (Fast Fourier Transform). It is a simple and robust method for processing pure-frequency signals.
The Figures 3.2 and 3.3 show that frequency content of significant amplitude signals concentrates on a frequency band ranging from 0 to 250 hz, corresponding to the first 25 harmonics. These findings are in line with
the studies by Williams. According to Williams, 1996 [9], for a diesel generating set, the frequencies ranging from 0 to 250 Hz only represent significant amplitudes.
We note that in frequency domain the spectra measured on the 2 generating sets are identical. These spectra are all characterized by a dominant frequency which is 45 Hz, corresponding to the technically calculated explosion frequency. For the generating set G2, the spectrum is borne out at C1 = 45 Hz. For the generating set G4, we notice the same situation yet again.
Frequency domain analysis shows that spectra are borne out by explosion frequency at 45 Hz. Yet, this frequency is not a default frequency; it determines the functioning of the diesel engine.
Item Measurement Point Velocity (mm/s) Threshold (mm/s)
G2 Alternator front bearing Side A radial horizontal direction 18.4 20 G4 Alternator front bearing Side A radial horizontal direc-tion 14.5 20
Tableau 1: Velocity on alternators front bearings.
G2: diesel generating set n°2 G4: diesel generating set n°4
Figure 3.2: spectrum G2
Figure 3.3: Spectrum G4
Figure 3.4: Spectra G2 and G4 3.2.2 Cepstrum domain analysis
By definition, a cepstrum is a representation of two-time transform of Fourier to the reference temporal signal.
The image obtained is a curve based on time (quefrency) measured in seconds. The Figures 3.5 and 3.6 show the separation, through cepstra, of components due to exciting forces, from those caused by the structural response. The first peak characterizes transfer function, while the harmonics characterize excitation spectrum.
Contrary to pure-frequency spectra where we cannot see any variations between the generating set n°4, which is
abnormal vibrations, we observe that the cepstrum describes the vibration condition of the generating set.
The Figure 3.6 shows that the energy of components caused by excitation forces on G4 declines relative to time, thus characterizing the stability of this generating set. On the other hand, on the generating set G2
( figure 3.5), we can see a rebound in peaks. This reflects the presence of abnormal vibration. We observe mechanical shocks in radial direction. This confirms the findings made by the technical staff in charge of running the generating
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sets. Superposing the cesptra on the same graph (figure 3.7) shows that the two generating sets have different vibration
condition, while the superposition of spectra (figure 3.4) forms the impression of the same vibration condition.
We also note that the vibration velocity on G2 stands at 12.5 mm/s on the bearing of the drive end of the diesel engine just before the coupling; and after the coupling, it goes up to 18.4 mm/s, against a threshold of 20 mm/s.
The source of shocks on G2 is, therefore, in the elastic coupling where there are three clearance adjustments to be tuned up:
- Axial clearance adjustment;
- Radial clearance adjustment;
- Angle clearance adjustment.
It is a coupling with 4 fingers that are arranged 90° to each other. The Table 2 shows the coupling characteristics.
Elastic coupling (4x90)
Axial clearance Radial clearance Backlash 0.5 – 1 mm 0.1 – 0.15 mm 0.54 – 1.52 mm
Table 2: Characteristics of the coupling Since the mechanical shocks on G2 are in radial direction, we can say that the defect observed is a misadjustment of the radial clearance in the elastic coupling, traced back to the generator installation, or a physical wear of the coupling’s fingers. This radial clearance resulted in misalignment causing mechanical shocks in radial direction. These shocks are impulsive, thus of lesser energy than explosion shocks. The spectrum of explosion shocks, therefore, muffles the spectrum of mechanical shocks.
Figure 3.5: Cepstrum G2
Figure 3.6: Cepstrum G4
Figure3.7: Cepstra G2 and G4 (0 – 3.2 s)
IV. CONCLUSIONS
In pure frequency domain, the spectrum of the sound generating set is identical to the spectrum of the faulty set. Strong energy frequency corresponds to explosion frequency in cylinders. In a traditional analysis, this frequency should be considered as a default frequency.
But on the contrary, it is normal frequency as for the functioning of the diesel engine there must be necessarily explosions in cylinders. Then, an analysis in frequency domain proves inadequate for diagnosing diesel power generators. The explosion shock spectrum muffles the mechanical shock spectrum. Indeed, we processed the signals with the cepstrum, which is an appropriate tool for diagnosing diesel generating sets.
The cepstrum helps differentiate defects that give complex spectral images resulting from several simultaneous amplitude modulations. From the cepstrum analysis, we saw that generating set n°4 and generating set n°2 do not have the same vibration behaviours. The difference brought about by G2 relative to G4 is due to a default in the coupling (physical wear of the fingers in the coupling).
BIBLIOGRAPHY
[1] Genossar, 1992 Genossar, M. (1992). Spectral characterization of nonstationary processes.
Thèse de doctorat, Dept. of Electrical Engineering, Standford University.
[2] J. Max et J.L. Lacoume, Méthodes et techniques de traitement du signal et applications aux mesures physiques, 5ième édition, Masson, 1996.
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Mech.E), volume 1, pages 169{174, Londres.
[4] El Badaoui, M., Guillet, F., et Danière, J. (2004).
New applications of the real cepstrum to gear signals, including definition of a robust fault indicator. Mechanical Systems and Signal Processing, 18(5) :1031 - 1046.
[5] cf. Doc. MT 9 285
[6] P. FLANDRIN, B . EscuDIE, Principe et Mise en Œuvre de l'Analyse Temps-Fréquence par Transformation de Wigner- Ville, Traitement du Signal, 1985, vol. 2, n'2, pp . 143-151 .
[7] P. FLANDRIN, Représentations Temps- Fréquence des Signaux Non Stationnaires, Thèse de Doctorat d'Etat ès Sciences Physiques, INPG, Grenoble, 1987.
[8] norme IS/ISO 9528-9
[9] Williams, J. (1996). An overview of misfiring cylinder engine diagnostic techniques based on crankshaft angular velocity measurements. SAE paper n°960039.
