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25СЕКЦИЯ 1. СУДОВОЖДЕНИЕ, СУДОСТРОЕНИЕ И СУДОРЕМОНТ
УДК 621.43.041.6
R.A. Varbanets
Odessa National Maritime University, Ukraine, Odessa, 65029;
IMES GmbH, Germany, Kaufbeuren, 87600 e-mail: roman. [email protected]
VIBRO-ACOUSTIC DIAGNOSTICS OF TURBOCHARGER
The proposed method is based on solving a system of complex equations. The article considers the method for diagnosing a turbocharger, based on the spectral analysis of vibroacoustic signals of a compressor. A method for eliminating the "DFT leakage effect" in the discrete spectrum is offered.
Key words: turbocharger diagnostics, leakage effect, spectral analysis, compressor blade frequency.
Turbocharger diagnostics. Turbochargers are an integral part of most modern marine diesel engines. Modern turbochargers provide a high value of charge air pressure (nk up to 6 at ST27-Serie and nk up to 10 at K2B serie) and highly efficient operation of marine diesel engines with low emissions of carbon oxides and soot [1, 2].
High efficiency of MAN ME and MAN MC diesel engines (with a real specific effective flow rate of 160-170 g/kWh) is provided by the high charge air pressure, in particular. When the efficiency of the turbocharger decreases, the efficiency of the diesel engine drops abruptly, the level of emission of carbon oxides and soot increases.
During operation of marine diesel engines, the exhaust manifolds become clogged with products of incomplete combustion. As a result, the throughput of the exhaust manifolds and the nature of the internal flow of gases before the blades of the turbocharger impeller may vary. In this case, the appearance of pulsations is possible which leads to rotor oscillation. The increased level of rotor oscillation creates additional loads on the turbocharger bearings and reduces their life. In the event of microdefects in the bearings of the turbocharger, the vibration level of the rotor increases even further that may lead to a severe accident.
Constant operational monitoring of the vibration level of the turbocharger rotor can prevent an emergency situation [3].
The experiments on diesel engines in laboratory and in sea conditions have revealed that the turbo-charger compressor blades generate oscillations which are always present in the overall vibration spectrum, regardless of the technical condition of the turbocharger. The spectral analysis of the turbocharger vibration has shown that the compressor blades generate a vibroacoustic signal with a frequency equal to the speed of the turbocharger rotor multiplied by the number of air blades [3, 4]
ub = nb x RPMtur / 60,
where ub - blade frequency of the turbocharger compressor, Hz; nb - the number of compressor air blades, RPMtur - the speed of the turbocharger rotor min1.
To determine the blade frequency of the turbocharger compressor and the subsequent calculation of the turbocharger speed, the amplitude spectrum of vibroacoustic signals was used. The recording was made on the opposite side of the compressor air filter (see Fig. 1) using a broadband industrial microphone with a frequency bandwidth of 10 Hz - 20 kHz.
In the case of recording vibration of the turbocharger of diesel engine 6L80MCE with the turbocharger VTR 564-31 (20 compressor blades), the expected blade frequency of the compressor was calculated on the basis of the turbocharger rotor speed rating at the nominal conditions:
ub = 20 blades x 9000 rpm / 60 = 3 kHz.
Due to the fact that the operating mode of the diesel engine was at a lower load, the expected speed of the turbocharger rotor shall be less than the nominal one. Thus, the value of the blade frequency calculated for the nominal conditions can be used as the upper limit for determining the actual operational value.
Fig. 1. Recording the vibration of turbocharger using the broadband microphone
Fig. 2 shows the vibration spectrum of the turbocharger VTR 564-31 recorded at a load close to the nominal one. It can be seen from Fig. 2 that the harmonic closest to 3 kHz has a frequency of 2 948 Hz. The nearest harmonic on the left has a frequency of 1 474 Hz and is a subharmonic with a frequency equal to half of the blade frequency ub /2. This leftmost subharmonic in the spectrum can be considered as the left boundary when determining of the harmonic corresponding to the blade frequency of the tur-bocharger compressor.
30 50 100 200 300 5D0 1000 2K 3< 5K 10000 Иг
Fig. 2. Vibroacoustic spectrum of turbocharger VTR 564-31
Thus, according to the blade frequency of the VTR 564-31 turbocharger compressor determined in the spectrum in the operational conditions, we calculate the speed of the turbocharger rotor:
RPMtur = 60 x ub / nb, RPMtur = 60 x 2948 Hz / 20 = 8844 RPM.
The regular tachometer of the turbocharger showed a rotation speed of 8 800 RPM, which in comparison with the value determined by the spectrum gives a relative error of 0,5%.
It is necessary to take into account the industrial accuracy class of the standard tachometer (division scale of 200 RPM).
Spectral analysis of a vibroacoustic signal recorded at a frequency of 44,1 kHz makes it possible to analyze harmonics in steps of less than 1 Hz at a recorded signal frequency up to 20 kHz [5]. The blade frequency of the turbocharger compressor is significantly lower. Thus, as a result of the spec-
tral analysis of the vibroacoustic signal of the turbocharger compressor, an error in determining the frequency less than 1 RPM can be reasonably obtained. Such accuracy is much higher than the accuracy of the standard tachometers, which makes it possible to use the blade frequency of the turbocharger compressor in accurate calculations of the main rotational speed of the turbocharger and the subsequent estimation of the diesel engine power.
After determining the compressor blade frequency and the main speed of the turbocharger (RPMtur), we can analyze the harmonic amplitude at the main speed of the rotor:
uturbocharger ub / nb
In the case shown in Fig. 2
Uturbocharger = 2948 Hz / 20 = 147,4 Hz.
We eliminate the "leakage effect" for the harmonic at the fundamental frequency u of the turbocharger, using the algorithm described in paragraph 4, solving the system of equations (1). After recovering the amplitude of the uturbocharger, we analyze it.
Obviously, if there is a significant increase in the amplitude A of the harmonic at the main speed of the turbocharger rotor, this demonstrates an increased vibration of the rotor. Fig. 2 shows a slight increase in the amplitude of the fundamental harmonic A, which characterizes the permissible vibration level of the turbocharger rotor.
Preliminary experiments on MAN MC diesel engines have shown that an increase in the amplitude of the harmonic at the main frequency uturbocharger in 2-3 times regarding the average level of the amplitude spectrum characterizes the dangerous vibration level of the turbocharger rotor. The average level of the harmonic amplitudes was estimated in the frequency range
[u turbocharger 50 Hz .. uturbocharger + 50 Hz] .
To better quantify the limits of vibration level of the turbocharger rotor, further research is required. It may be noted that the spectrum analysis of vibroacoustic signals of the turbocharger compressor can be made quickly under operating conditions.
Eliminating the "leakage effect" of discrete spectrum. In the process of analyzing the discrete spectrum of vibroacoustic signals in order to estimate their frequency and amplitude characteristics, it is necessary to solve the problem of eliminating the effect of "leakage". This effect is a consequence of the finiteness of the analyzed temporal realization and its discrete representation. The effect of "leakage" or outflow of power from the spectral peaks into the adjacent spectral lines is considered to be one of the main DFT errors [4, 5].
As an example, Fig. 3 shows the amplitude spectra of the same sinusoidal signal with an integer (a) and a non-integer (b) number of samples per one signal period. Let the frequency of a signal be represented by y = M/ T, where T is the period of the signal; M = n + o, where n is an integer and 0 < o < 1, then the maximum distortions of the amplitude, frequency and phase of the central harmonica and leakage of power into the neighbouring ones will be observed at o = 0,5 See [5].
a) a = 0
b) a ф 0
Fig. 3. DFT leakage effect
Thus, when analyzing the parameters of the original spectrum signal, i. e. the central harmonic, the resulting amplitude, frequency and phase will be distorted in the case of a non-integer number of signal
samples per its period. In practice, for discrete recording of signals, an ADC with a selected and fixed sampling rate is used. It is understandable that the number of samples per period will never be an integer and the value of o will change from 0 to 1 depending on the natural frequency of the measured signal, and the accuracy of estimating the signal parameters along the central harmonic will change.
The most common solution for leakage effect reduction is based on window transform methods. The essence of the method is simple: to reduce the number of discontinuities at the edges in order to reduce leakage it is necessary to reduce the amplitude of the signal near the edges. This scaling is carried out during the implementation of the multiplication by the window with the special form
SW = S *W (j),
where W(j) is stands for Window functions (see Table).
As a result of applying window functions, the spectrum of the original signal is changed and its RMS decreases by RMS Coeff times, as shown in Table. The decrease in RMS when using the Hanning window is 0,707 / 0,433 = 1,633. Thus, the dependence of the amplitude, frequency and phase of the fundamental harmonic in the spectrum from the value of o decreases. This means that the fundamental harmonic swj can be used to approximate the signal parameters with a certain constant error, which can be taken into account.
Table
Window functions and RMS coefficient used to reduce the effect of "leakage"
Hemming window RMS Coeff = 1,414 ( 2m Л w(n) = 0,53836 - 0,46164 cos 1 - 1 ^ N -1)
Hanning window RMS Coeff = 1,633 w(n) = 0,5 (1 - cos (-^jj
Kaiser window RMS Coeff = 1,61 /„ (ßV1 -(^ )2) ra( n) = , , VM
Blackman-Harris window RMS Coeff = 1,585 та(и) = 0,42 - 0,5 cos(2nn / (N -1)) + 0,8cos(4nn / (N -1))
More precisely, we can eliminate the "leakage" effect by a numerical method based on the processing of the complex DFT results. In [5], a suggestion was made that the frequency m, the phase 9, and the amplitude A of the original signal from the values of two maximum harmonics in the spectrum Xk, X+1 should be specified. For this it is proposed to solve numerically the system of complex equations. To do so, the system of complex equations is proposed to be solved numerically:
f|E(m, ft / E(m,ft+J = |Xt / Xk+1\\
[Arg(E(m,ft) = Arg(Xk) J,
where the parameters of the k-th harmonic are specified as:
xk = Rek+jImk;
X, = NAkej4k,
Ak = ^Re2k + Im2k ,
4 = arctg(^) = Arg(Xk). Rek
The harmonic coefficients can be represented in the form Xk = (Ak / 2)E(m, ft, where E(m, ft is a complex function independent of the amplitude, but dependent on the frequency and phase:
27!j(m-k) _ 1 j(m+k) _ 1 Em 40k = ej 2j, (m_k) + e --
27t/ (m-k) -27tj(m+k) '
" -1 e N -1
The system of equations (1) must be solved in the case where the harmonics to the left and right of the central one are not equal to zero (in practice it is more than a given small value S):
xk_, >S, X,+, >5 .
If Xk_x = 0, Xk+l = 0, then the leakage effect is absent and the frequency, amplitude and phase of the central harmonica correspond to parameters of the measured initial signal See Fig. 4.
When solving the system (1) for the situation of strong leakage effects (a ~ 0,5 See Fig. 4), only five full iterations were required to provide a specified error of less than 0,5% in frequency and phase. For a sinusoidal signal, the amplitude and frequency are recovered to the value specified in the original signal with accuracy to 5 decimal places. In this case, the amplitude of the central harmonic in the spectrum after the DFT before the recovery procedure was with an error of 35% (!) See Fig. 4, c [3, 4].
Fig. 4. DFT leakage effect eliminating [3, 4]
An error in estimating the frequency of the original signal with respect to the frequency of the central harmonic can also be significant. It depends on the frequency of the ADC and the frequency of the original signal. As the frequency of the ADC increases, the error in estimating the frequency will decrease.
The solution of the system (1) is not associated with additional memory as is the case for the fast Fourier transform (FFT). Despite the iterative numerical solution for system (1), such procedure only very slightly increases the overall computation time, and make it possible to obtain not only the spectrum of the signal, but also the restored value of the fundamental frequency, amplitude and phase of the measured signal, when it is close to sinusoidal.
The solution of system (1) is not connected with allocating additional memory for storing volumetric data sets and computed coefficients, as in case of fast Fourier transform (FFT). In this regard, the algorithm can be programmed on a modern DSP controller which implements the FFT.
Despite the iterative numerical solution (1), such a recovery procedure increases the total calculation time very slightly and it allows recovery of not only the signal spectrum, but also the restored value of the fundamental frequency and amplitude and phase of the measured signal, if it is close to sinusoidal.
This method was investigated in case of noise in the original signal (with a white noise of 5% and 10% of the amplitude of the sinusoid). Fig. 4 shows the solution of the system (1) for a sinusoid with an amplitude of 0,8 and for the cases a) 6 = 0,1, b) 6 = 0,3 c) 6 = 0,5 and c) 6 = 0. The central green line in each Fig. 4, a-d is the main harmonic of a sinusoid with amplitude of 0,8 with the restored amplitude, frequency and phase, being a result of solving the system of equations (1).
For all the cases, not more than 5 complete iterations were required to ensure a given accuracy. As a result of the solution of the system (1), the phase and frequency of the signal with the addition of white noise to 10%, are restored to the initial value with an error of not more than 0,5%.
Conclusions. The methods of vibrodiagnostics of marine diesel engines with turbocharging considered in the article can be helpful for practical use. The "leakage effect" method improves the reliability of diagnostic findings. A vibroacoustic method for determining the speed of a turbocharger rotor and estimating the level of the oscillation amplitude at the main rotational speed can be used as a basis for the express diagnostics of the turbocharger under operating conditions.
Literature
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4. Varbanets R.A. The "leakage" elimination methods analysis of the spectrum in the diagnosis system of marine diesel engines turbo system / R.A. Varbanets, Y.N. Kucherenko, A.I. Golovanov, N. Alexandrovskaya // Artificial intelligence. - 2013. - № 4 (62). - P. 289-295.
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