CC BY
47
Section 13. Transport
Ziyoda Mukhamedova, Ph D., Tashkent Institute of Engineers of Railway Transport Tashkent, Uzbekistan E-mail: muxamedovaz@list.ru
DIAGNOSTICS OF ASYNCHRONOUS ELECTRIC MOTORS ON THE BASIS OF SPECTRAL ANALYSIS OF AMPLITUDE-MODULATED STATOR CURRENT
Abstract: Continuous diagnostics of asynchronous electric motors is described in the article by spectral analysis of amplitude-modulated current of the stator, due to the faults of its elements and units. Keywords: electric motor; asynchronous; amplitude, diagnostic, method, amplitude.
Introduction
A study of current trend in development of methods for diagnosing electrical equipment has recently shown that the methods based on the analysis of electrical parameters of operating equipment, for example, by measuring the current of the stator of asynchronous motor (AM), are the most preferred ones. Improvement of the circuitry and application of microprocessor technologies broadens the possibilities of practical implementation of spectral analysis and algorithms based on the theory of optimal filtration to obtain more accurate results on technical condition of AM [1; 2; 3; 4; 5; 7; 8].
Previous studies concentrated on various methods of the diagnostics and maintenance of asynchronous electric motor with use of mathematical modelling. The research conducted by Cunkas and Akkaya [9] covered the comparison of three different induction motors with the same motor of other type. The first motor was designed optimally with three-phase squirrel-cage system. The method of modelling for optimization was genetic modelling with focus on three dimensions: torque, cost and efficiency. Moreover, study by a group of experts and researchers as Kolpakhchyan, Shaikh-iev, Kochin [10] covered the identification of asynchronous traction motor characteristics of a locomotive. Their study found certain limitation of the rotation of the traction motor given the different power input, like inverter type.
In the study of Liudvinavicius and Lingaitis [11], authors analyzed different aspects of the operation of asynchronous motor including the frequency regimes, speed regulation and factors affecting the stable operation of the motor. The authors suggested to use so called method of
vector control in the design of a locomotive including algorithmic control. Likewise, American Public Transport Association recommended various practical methods for maintenance and evaluation of the work of electric motors of locomotives with special focus on issues as manufacturer recommended maintenance intervals, operating space, information about past performance and usage, analysis of failures and testing in near to real-life conditions [12].
Unfortunately, in available sources, the studies on operating frequency range of the analyzer and the harmonic components of current stator are not carried out, as well as the measurement range in decibels, and, most importantly, the mathematical processing of the level of individual harmonics in real time, taking into account that the periodic deterministic useful signal of static analysis characterizing the malfunction of AM elements, is additively mixed in practice with stationary white noise with a minimum signal-to-noise ratio; and the structure and parameters of smoothed out, optimal or predictive filter synthesized on a computer are not defined.
In this paper, an attempt is made to eliminate these shortcomings. The presence in the spectrum of AM stator current of characteristic frequencies of a certain magnitude indicates the presence of faults to its electrical or mechanical units and other actuators connected with it.
Methods
Measuring shunts and Hall sensors are used as a current sensor. The most preferable for measurement of AM stator current, in our opinion, is the magneto-optical sensor, the sensor manufactured by Airak, the measured range of which is 0.003-30 kA in current, the frequency band is 5-5000
Hz. From the sensor output, the reproduced curve through AC amplifier is fed to a frequency harmonics analyzer, for example, of 2031 type (manufactured by Bruel Kjaev); its operation is based on a fast Fourier transform in real time at frequencies up to 2 kHz [6]. The duration of the current recording must be within the time required for spectral analysis at a frequency of no less than 0.01-0.03 Hz.
In the aspect of spectral analysis of AM continuous diagnostics, the problem consists in finding the law and distribution of the output quantity (the current consumed according to the known law of distribution of the input quantity) and the a priori target data, or, in terms of statistics, the passage of stationary or non-stationary random signals through a linear circuit.
The problem is formulated as follows. A stationary random signal at t = to is fed to the input of a linear system with generalized complex transfer function K (jo>), its mathematical expectation and the correlation function B1(t) are assumed to be known; it is necessary to find the correlation function B2(t) and the mathematical expectation of random function at the circuit output [7; 8].
Let the mixture of uncorrelated periodic deterministic signal s(t), occurring as a result of damage to electrical or mechanical units of the AM and interference n(t), act on consumed current of the motor,
x (t) = s(t) + n(t) (1)
Consider an example where the signal s(t) occurs due to static or dynamic eccentricity of the rotor relative to the stator,
i.e. when the distance between the length of the stator bore and the rotor is not equal along the whole circumference and as a result the magnetic flux inside the air gap changes, resulting in a characteristic modulated in amplitude stator current: x(t) = s(1 + Mam sin(Qt))cos(©0t + Mm + y) + n(t), (2) where S - is an amplitude of the modulated signal; n - rotation speed of the rotor; Mm - modulation depth, Q = n/60 (r/s) -modulation frequency; ®0 - is an angular frequency of the motor power supply, f - an initial angle of shear; n(t) - a random function having the normal distribution law with mean value of m(t), variance o2n(t).
For the diagnostic analysis, it is necessary to find according to (2) the mathematical expectation m (t), the variance of the output process o2n(t) and to write the law of distribution of the spectral probability density Wx (t).
It is obvious that mlx(t) = mm(t) + s[1 + Mam sin0.t]cos(©ot)MmHt) + 9 (3)
a2x(t ) = a2n(t ) + Ds = a2n(t ).
(4)
Taking into account that the spectral function contains information about certain relations between the amplitudes and modes of oscillations of different frequencies and bearing in mind [7], we get
Wn(n) = PT- eXP V 2nan (t )
For the sum x(t) we obtain
[n - mln(t)]
2a2n(t )
(x ,t ) =-
I—--exP
V 2non (t)
Transforming expression (5) into a series and taking into account that the intensity of spectral components is determined by spectral density F(jw), calculated by the formula of
{x - [min (t ) + S(l + M am )sin(Qt )cos(©0t ) + M^Ht ) + ç]\
2<5n(t )
(5)
direct Fourier transform F(ja>)I Wx(x,t)e dt for each
J—co
term of the series, we obtain
Figure 1. Spectrum of AM current in the presence of an eccentricity
F (®) = a ea a
a
(af ) ( + Dv)
(n + Dçf+Ù2
-(1 - 2a] )x£-
(a] )n (n +1 + DÇ
(n +1 + Dçf+Ù2
+ af Z
(a] J (n + 2 + D)
(n + 2 + Dç) +Q2
(6)
where o] = o] Ma
M'f. ;
Dp=
N„ - i
is a
phase fluctuation; Mam, Mfm - are the depth of amplitude
and phase modulation, respectively; Q = (® , ®> 0-
a - is an independent random variable with zero mathematical expectation ma= 0 Da=o2.
The graphs of function F(u) using the parameters of AM traction of 1 TB262-OGA02 type are shown in (Fig. 1).
Experimental studies have been carried out on a three-phase asynchronous electric motor of 1TV262 type [2].
For example, if the rotor bars or the parts of the squirrel cage ring of tractive AM are damaged, the stator current will be modulated in amplitude with a slip frequency s. This modulation increases in the event of damage to the rotor. Obtained by the Fourier integral transform, the spectrum of the modulated stator current in amplitude with damage to a different number of rotor bars is shown in (Fig. 3), from which it can be seen that the rupture of the bars is accompanied by the appearance of side components with a double slip frequency in fundamental harmonic.
Frequency, (Hz)
Figure 2. BP current spectrum in the presence of eccentricity
-2
§
I
-6
i l "1 i i i i
A / > : [/ : b) A V * //> x
"v' V/ ' i i i i V 1 \/ \ \ / \ , i\ \/ ^ 1
30
uo
50
60 70
Frequency. (Hz)
Figure 3. Current spectrum in case of damage to (a) four and (b) six rotor bars
n=0 n
n=0 n !
n=0 n
Because of the presence of noise and quantitative-qualitative characteristics in deterministic signal that determines the state of refuse unit of AM, the evaluation of its implementation does not coincide with the true implementation. Therefore, it is necessary to determine the parameters of the optimal filter by the criterion of the maximum signal-to-noise ratio at its output, from which one or another condition of AM can be identified. As an example, consider the case where the incoming signal has a component in the form of a random process n(t), which is a stationary Gaussian
white noise with a density spectrum Sn(&) = 9 . The complex frequency response of the filter that maximizes the signal-to-noise ratio at its output can be described in the following form [8]
K o( jw) = kI (jw)' ejT, (7)
where k - is a certain constant; I(j®)' - a function complex-conjugated with the spectrum I (j®), for example, of periodic input signal i(t) = Imsim(wt) at 0 " t" tu, to which any non-sinusoidal value can be equivalent; this value arises from the defect of any unit of the engine, its spectrum expressed in the form:
I(№)* = f i(t)e~-j№dt = K
J-w O
TT Im--COS- .<
K m 2 2 -j-
2 ( n 1 ( №
(8)
If the observation interval coincides with the pulse dura-tioni.e.T =tu , then
I —- cos—-r
K 0(j©) =
n } №
u V
1 - e
(9)
2 J 2
The structural scheme of above mentioned optimal filter is shown in (Fig. 4).
Figure 4. Structural diagram of the optimal filter
Define the signal at filter output, keeping in mind that its impulse response has the form [9]
h0(t) = KoS(T-1) = K0S(ru -1) (10)
Se* (t) = J0\(TS(t-t)dt= K0 Cstu-TS(t-t)dt (11)
tion
The maximum value of [S^t (t )]m found from the condi-
dS .. (t) m3X
exi = 0 is reached at t-Tu and is equal to
dt
[exit(t )]max = KoE, where E - is an energy of signal S(t). Variance at the output of the optimal filter is
Dexit =fjn (®)| K o( iffl)|2 dm
Hence the maximum signal-to-noise ratio is
[Sexit )]maI KE
(12)
a =
= ^2ËN0 (13)
Expressions (6, 7, 13) from a practical point ofview make it possible to more accurately determine the difference between the amplitudes of spectral components associated with technical state of AM units.
Current and voltage measurements and their spectral analysis must be carried out at regular intervals, depending on the results of preliminary experiment. Results of the analysis are compared and checked by the dynamics of fault development over time, and the residual engine life is determined.
The application of the proposed method will fully realize the technology of electric motors maintenance on the actual state; it will ensure a reduction in damage from emergency failures due to early detection of defects.
Malfunction diagnosis of electric motor is unambiguously carried out and related to the characteristic spectral components of the frequencies, for example, to dangerous motor overloading by a small difference in amplitude between the main, 3rd and 5th harmonics of the stator current; to bearing damage - at frequencies that are multiples of the rotor speed of rotation; to stalling of the rotor - a characteristic beating, i.e. amplitude modulated stator current with rotor speed; the presence of coil-winding short circuit in the stator - at fundamental harmonic of the stator current.
Conclusion
Described methods of diagnostics, processing and analysis of the results of AM technical condition on the basis of the analysis of spectral components of the stator current make it possible to increase the reliability of technical solution to maintain operational reliability by a combination of measured parameters and to study the evolution of technical condition and to reduce the probability of unreasonable withdrawal.
The use of magneto-optical sensors with broad dynamic range in amplitude and frequency for measuring the currents of high-power AM, and further processing on a computer, operating in real time and based on a fast Fourier transform makes it possible to apply powerful mathematical tools in processing measurement data.
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2
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