Reliability of Insulation of Random-Wound Windings of Asynchronous Motors
Abstract Generated abstract
The paper addresses reliability estimation for low-voltage induction motors with random-wound windings, focusing on winding insulation as the dominant source of electrical-machine failures. It argues that insulation reliability can be evaluated through theoretical probabilistic methods based on the density of through defects, the breakdown-voltage distribution of defective insulation, winding design parameters, and commutation overvoltage levels. A calculation procedure is outlined for turn insulation during the running-in period, using defect probabilities for elementary insulation sections, conductor spacing assumptions, and switching-frequency effects. Experimental comparison on 100 motors showed close agreement between calculated and observed reliability, suggesting that the approach can identify design, manufacturing, and operating factors that most affect winding reliability.
Full Text
RELIABILITY OF THE INSULATION OF RANDOM-WOUND WINDINGS OF INDUCTION MOTORS
Yu. P. Pokholkov
(Presented by the scientific seminar of the departments of electrical machines and general electrical engineering)
Modern industrial production is placing ever higher demands on the reliability of all elements of automation, including the reliability of electrical machines. At the same time, electrical-machine manufacturers are often required to give in advance an estimate of the reliability of the machines they produce.
Such an estimate can be obtained either in the course of accelerated tests or from calculation results using theoretical-probabilistic methods. In both cases, however, there are difficulties. Conducting accelerated tests of electrical machines requires special equipment and premises and is associated with large expenditures of time and material resources.
Mathematical calculations of reliability can be carried out without special material expenditures. For this, however, it is necessary to know the physical nature of the failure processes of an electrical machine.
In Soviet and foreign technical literature, the question of failures of electrical machines in operation has been treated fairly thoroughly [1, 2, 3, 4]. At present there is no doubt that the least reliable element of an electrical machine is the insulation of its windings. According to published data, from 70% to 90% of all failures occur because of insulation breakdown [1]. In this connection, the problem of machine reliability is the problem of the reliability of the insulation of their windings. The enormous number of types and sizes of electrical machines, the great variety of insulating materials, and the operating conditions of machines do not permit the creation of unified methods for reliability estimation and accelerated testing; however, for individual groups of machines with definite operating conditions, the creation of unified methods for reliability estimation is possible in principle. This paper sets forth certain features of estimating the reliability of the insulation of low-voltage electrical machines, in particular induction motors with random-wound windings.
The insulation of machine windings is, in principle, a nonrepairable element; therefore the reliability of winding insulation can be characterized by the probability of failure-free operation over a specified time.
When evaluating the longevity of winding insulation it is advisable to use the term “γ-percent life,” i.e., the time during which the probability of failure-free operation of the winding is not less than γ [5]. At present, when designing the insulation of windings of low-voltage electrical machines, high requirements are not imposed on the electric strength of the insulation. The main attention is given to mechanical streng—
ness and heat resistance of the insulation, which, on the one hand, is quite fair [2]. In low-voltage electrical machines, operating voltages and even pulses of commutation overvoltages are not dangerous for undamaged winding insulation. Usually breakdown of winding insulation occurs if there are through-damage defects in the insulation. For insulation consisting of two or more layers, a necessary condition for breakdown is the presence of through-defects in all layers on the same elementary area of the insulation.
Note. By the area of an elementary section we mean an area over the surface of which flashover can occur at a voltage equal to the maximum breakdown voltage of air over a thickness equal to the thickness of the insulation layer. The area of an elementary section of insulation depends on the moisture content and contamination of the windings.
The causes of defect formation in insulation may be roughly divided into two groups:
a) technological,
b) operational.
In the first case, defects such as punctures, cuts, abrasions, and cracks are formed in the insulation either during the manufacture of the insulating materials themselves or during the manufacture of machine windings [3]. The share of insulation with such defects is determined by the level of the technological processes for manufacturing materials and machines and by the production culture.
In the second case, the cause of defect formation is the operating conditions and the working conditions of the insulation of machine windings. As a result of temperature action, the insulation becomes brittle, and under the action of vibration defects of the type of through-cracks may appear in it.
The mechanism for detecting through-defects formed under the action of these and other causes is the same. If the winding is not moistened and not contaminated, insulation breakdown can occur under the action of pulses of commutation overvoltages, provided that the defects in all layers practically coincide. A moistened and contaminated winding may break down under the action of the operating voltage even when the defects in individual layers do not coincide, owing to flashover along the surface.
Thus, if it is assumed that the main cause of failures of windings of low-voltage electrical machines is the presence in the insulation of gross through-defects, the reliability of winding insulation can be evaluated on the basis of estimating the fraction of defective elementary sections of insulation, the parameters of the distribution of the breakdown voltage of defective places in the insulation, and the levels of commutation overvoltages.
The reliability of winding insulation during the running-in period and normal operation can be calculated on the basis of estimating the level of defectiveness of the insulation, determined by the technology of manufacturing the materials and windings.
In this case, defectiveness may be taken as the probability of occurrence, in a batch, of such specimens whose breakdown voltage does not exceed the maximum breakdown voltage of air over a thickness equal to the insulation thickness, i.e., does not exceed the maximum breakdown voltage of insulation with through-damage,
\[ q=\frac{n_{\overline{U}_1+3\sigma_1}}{\displaystyle\sum_{i=1}^{m} n_i}, \tag{1} \]
where
\(q\) — defectiveness of the insulation;
\(n_{\overline U_1+3\sigma_1}\) — the number of specimens punctured by the voltage \(\overline U_1+3\sigma_1\);
\(\displaystyle \sum_{i=1}^{n} n_i\) — the sum of all tested specimens;
\(\overline U_1, \sigma_1\) — respectively, the mean value and the standard deviation of the breakdown voltage of insulation with through damage. These parameters are determined from the breakdown results for artificially damaged conductors.
The defectiveness value is estimated from the breakdown results for wire and insulating materials removed from the slots of a machine after laying the winding (before impregnation). Experimental data on the study of aging of enameled wires and a number of insulating materials under the action of temperature and vibrations occurring in electric machines under normal operating conditions show that during the running-in period and normal operation no appreciable increase in insulation defectiveness is observed. In time, this period amounts to about 5 thousand hours.
For longer operating times of the machine, the defectiveness value begins to increase, and the rate of its increase depends on the levels of the acting factors and on the duration of their action.
At present, methods for calculating the reliability and service life of random-wound induction motors have been developed at the Tomsk Polytechnic Institute [6, 7], in which an attempt has been made to take account of technological, design, and operating factors.
The initial data in calculations of reliability and service life are the insulation defectiveness value, the distributions of the breakdown voltages of defective insulation, the winding parameters, the operating mode, and the levels of switching overvoltages in the windings.
As an example, let us show how the reliability of turn insulation of random-wound windings of induction motors during the running-in period is estimated [6]. The defectiveness of the wire insulation is determined by formula (1). Let us proceed to the defectiveness of an elementary section of the insulation of a single wire.
The radius of the elementary insulation section \((\delta)\) is determined from the maximum breakdown voltage of the defective location and the electric strength of the air at the defect location, taking account of surface flashover \((\overline E_{\mathrm{B}})\):
\[ \delta = \frac{\overline U_1 + 3\sigma_1}{\overline E_{\mathrm{B}}} \tag{2} \]
We denote by \(n\) the number of elementary sections on the area of insulation characterized by defectiveness \(q\):
\[ n = \frac{d_{\text{ins}}\cdot l_{\text{spec}}\cdot k}{\delta^2}, \tag{3} \]
where
\(d_{\text{ins}}\) — diameter of the insulated wire;
\(l_{\text{spec}}\) — length of the tested wire specimen;
\(k\) — coefficient accounting for the area of insulation being tested.
Considering that through damage of a wire specimen is a rare event, we assume that the distribution of defects along the length of the wire obeys the Poisson law [8]:
\[ 1-q = l^{-a}, \tag{4} \]
where
\(a\) — the average number of insulation damages on the tested area of the wire specimen.
Then the probability of damage to an elementary section of insulation of a single wire specimen, \(P\), is determined as follows:
\[ P = \frac{a}{n}. \tag{5} \]
The probability of coincidence of defective elementary insulation sections in two adjacent conductors, according to the probability multiplication theorem, will be equal to \(P^2\). Breakdown between two closely touching conductors with coincident defects will occur with probability \((q')\)
\[ q' = P^2 \cdot F \left( \frac{U - \overline{U}_2}{\sigma_2} \right), \tag{6} \]
where
\[ F \left( \frac{U - \overline{U}_2}{\sigma_2} \right) \]
— the normal distribution function of the breakdown voltage of the insulation of a pair of closely touching conductors with coincident defects,
\(\overline{U}_2\) and \(\sigma_2\) — respectively, the mean value and the root-mean-square deviation of the breakdown voltage of a pair of damaged conductors with coincident defects (determined experimentally).
In the slot of a machine with a random-wound winding, there are distances between conductors, the distribution of which may be considered to obey an exponential law with parameter \(\lambda\). The parameter \(\lambda\) is determined from the slot fill factor \((k_3)\), the average electric strength of the impregnating compound \((E_{\mathrm{p}})\), the average volume fraction of the impregnating compound in the interval between conductors \((\overline{V}_{\mathrm{p}})\), and the diameter of the uninsulated wire \((d_{\mathrm{neiz}})\)
\[ \lambda = \frac{1} {\left( 1.075 \sqrt{\frac{1}{k_3}} - d_{\mathrm{neiz}} \right) \cdot \overline{E}_{\mathrm{p}} \eta_{\mathrm{p}}} \tag{7} \]
Taking into account that the conductors in a random-wound winding are uniformly distributed, i.e., the probability of the occurrence of voltage \(U\) on an elementary section is equal to
\[ \int_0^{U_k} \left( 1 - \frac{U}{U_k} \right) dU, \]
we write the expression for estimating the probability of breakdown of an elementary section of a pair of conductors in a machine slot \((q_{\mathrm{el}})\)
\[ q_{\mathrm{el}} = P^2 \cdot \lambda \int_0^{U_k} e^{-\lambda U} F \left( \frac{U - \overline{U}_2}{\sigma_2} \right) \left( 1 - \frac{U}{U_k} \right) dU, \tag{8} \]
where
\(U_k\) — the voltage, taking into account switching overvoltages, falling on a single insulated coil of the phase.
The level of amplitudes of switching overvoltages falling on the winding with a probability close to 1 increases with an increase in the number of switchings \((\nu)\) and, consequently, with the operating time of the machine.
The dependence of the amplitudes of switching overvoltages on the phase of the motor winding \((U_\phi)\) on the number of switchings of the machine \((\nu)\) may be estimated by a formula obtained as a result of processing experimental data
\[ U_\phi = \frac{0.7 + \ln \nu}{2.25} \tag{9} \]
The quantity \(U_k\) depends on the number of separately insulated coils in a phase (\(n_k\)) and, consequently, on the type of machine winding
\[ U_k=\frac{U_\phi}{n_k}. \tag{10} \]
In this connection, expression (8) makes it possible to estimate the probability of breakdown of an elementary section of turn insulation over a definite interval of time during which \(v\) switchings-on of the machine have occurred. The latter circumstance also makes it possible to calculate the probability of failure-free operation of the turn insulation of the winding over a definite time, i.e., the reliability \((R_{\text{turn}})\)
\[ R_{\text{turn}}=(1-q)^N, \tag{11} \]
where
\(N\) — the number of elementary sections of turn insulation in the entire machine winding.
\[ N=n\left(S_{\text{nar}}+1.5S_{\text{vn}}-1.5\right)\frac{\overline{l}_w}{l_{\text{obr}}}\cdot z, \tag{12} \]
\(S_{\text{nar}}\) and \(S_{\text{vn}}\) — respectively, the number of conductors in the outer and inner layers of the winding in the slot;
\(\overline{l}_w\) — the average length of a winding turn;
\(z\) — the number of stator slots.
An experimental verification of the results of calculating the reliability of turn insulation, carried out on 100 AO2-32-4 motors, showed an insignificant discrepancy between the experimental and calculated data (calculation — \(R_{\text{turn}}=0.921\), experiment — \(R_{\text{turn}}=0.93\)).
Analysis of the calculation results makes it possible to find the main cause of winding unreliability: a high slot fill factor, low production standards, a small number of coils in a phase, a small wire diameter, a high switching frequency, a low level of inspection, etc. All this makes it possible, in each particular case, to outline ways to increase the reliability of machine windings.
Conclusions
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The reliability of electrical machines is determined primarily by the reliability of the insulation of their windings.
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The reliability of the winding insulation of low-voltage electrical machines should be evaluated on the basis of the number of through defects in the insulation and the level of commutation overvoltages.
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Theoretical-probabilistic methods for calculating the reliability of the insulation of machine windings make it possible to establish the relationship between reliability, the parameters of the machine winding, and its operating mode.
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Evaluation of the reliability of machine windings during the period when through defects appear in the insulation under the action of operating factors requires additional investigations of the operating conditions of machines, the operating conditions of insulation in machine windings, and the influence of these conditions on the rate of defect formation.
Literature
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E. K. Strelbitskii, O. P. Muravlev, Yu. P. Pokholkov. The effect of winding-insulation work on the breakdown voltage of turn and ground insulation of induction motors. Izv. VUZov, “Elektromekhanika”, 1966, No. 1.
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I. S. Johnson. Processes of breakdown of insulation electromotors “Electrical insulation materials and application” 5-th conf. Chicago. Ill. 1963.
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GOST 13377-67.
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E. K. Strelbitskii, Yu. P. Pokholkov, O. P. Muravlev, L. I. Shtuden, V. M. Fedorov. Method for calculating the reliability of random-wound windings of induction motors with ratings from 0.18 to 100 kW. TMTsNTI, Tomsk, 1969.
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E. K. Strelbitskii, Yu. P. Pokholkov, O. P. Muravlev, L. I. Shtuden, V. M. Fedorov. Method for calculating the service life of random-wound windings of induction motors with ratings from 0.18 to 100 kW. Tomsk, 1969.
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