Method for calculating the reliability of turn insulation of induction motor windings during the running-in period
Abstract Generated abstract
This paper addresses early failures of induction motor windings, emphasizing turn insulation as a principal weak element during the 800 to 1200 hour run-in period. It presents a calculation procedure that combines motor design parameters, slot geometry, winding data, impregnation properties, and test results for insulated wire before and after coil insertion to estimate defect probabilities and breakdown voltage distributions. The method derives probabilities of breakdown for adjacent conductor pairs with and without pre-impregnation damage, then uses these values to obtain a lower estimate of turn insulation reliability during run-in. The authors state that the procedure can also be used to evaluate measures intended to improve winding reliability in motors of 0.6 to 100 kW.
Full Text
METHOD FOR CALCULATING THE RELIABILITY OF TURN INSULATION IN INDUCTION-MOTOR WINDINGS DURING THE RUN-IN PERIOD
A. S. Gitman, O. P. Muravlev, Yu. P. Pokholkov,
E. K. Strelbitskii
(Presented by the scientific seminar of the departments of electrical machines
and general electrical engineering)
The proportion of failures of induction motors due to various kinds of winding damage reaches 70–80 percent, and the least reliable element in operation is the turn insulation [1].
As a result of observations of motors in operation, it has been established that squirrel-cage induction motors have a run-in period of 800–1200 hours, during which winding failure occurs in 10–16 percent of the motors. Without elimination of failures during the run-in period, efforts to increase service life are largely neutralized, since windings fail because of hidden defects much earlier than the time determined by thermal aging. In this connection, by assignment of the Main Directorate of Electrical Machine Building of the Ministry of Electrical Engineering Industry, at the Department of Electrical Machines of TPI a method was developed for calculating the reliability of turn insulation of induction-motor windings for the run-in period.
The initial data for the calculation are the following: diameters of the bare and insulated wire \(d_{\mathrm{g}}/d_{\mathrm{ins}}\), number of conductors in a slot \(S_{\mathrm{p}}\), electric strength of the impregnating compound at a temperature corresponding to the insulation class \(E_{\mathrm{p}}\), phase voltage with allowance for commutation overvoltages \(u_{\mathrm{cf}}\), slot fill factor \(K_{\mathrm{z}}\), perimeter of the free slot area \(\Pi\), number of stator slots \(z\), mean length of the stator winding \(l_w\), and number of coils (sections) in a phase \(n_{\mathrm{k}}\). In addition, the results of tests of insulated wire in a coil are required, in the as-delivered condition and after laying the winding into the slots [2].
The calculation of the reliability of turn insulation is carried out in the following sequence.
The number of elementary sections on a wire of length \(l = 125\) mm is
\[ n = \frac{l}{d_{\mathrm{ins}}}. \tag{1} \]
The theoretical maximum possible diameter of the wire that can be laid in the slot is
\[ d_{\mathrm{ins\,max}} = 1.075 d_{\mathrm{ins}} \sqrt{\frac{1}{K_{\mathrm{z}}}}, \tag{2} \]
where
\[ K_{\mathrm{z}} = \frac{d_{\mathrm{ins}}^{2} S_{\mathrm{p}}}{Q_{\mathrm{p}}}; \]
\(Q_{\mathrm{p}}\) is the free slot area, \(\mathrm{mm}^2\).
The number of conductors located in the outer layer of the slot,
\[ S_{\text{p\,out}}=\frac{\Pi}{d_{\text{ins max}}}. \tag{3} \]
The number of conductors located in the inner layers,
\[ S_{\text{p\,in}}=S_{\text{p}}-S_{\text{p\,out}}. \tag{4} \]
The number of pairs of adjacent conductors of length \(l=125\) mm
\[ N=(2S_{\text{p\,out}}+3S_{\text{p\,in}}-3)\cdot \frac{l_w}{2l}\cdot z. \tag{5} \]
The probability of the event consisting in the fact that a section of wire of length \(l\) has not received a single defect is
\[ p(0)= \frac{\displaystyle \sum_{u=4.5\ \text{kV}}^{\infty} w_{\text{p}}} {\displaystyle \sum_{u=4.5\ \text{kV}}^{\infty} w_{\text{n}}}, \tag{6} \]
where
\(w_{\text{p}}\) is the sum of the frequencies of damaged specimens having a breakdown voltage above 4.5 kV;
\(w_{\text{n}}\) is the sum of the frequencies of undamaged specimens having a breakdown voltage above 4.5 kV.
The quantities \(w_{\text{p}}\) and \(w_{\text{n}}\) are determined from the results of tests of specimens in the as-supplied condition and after insertion of the winding.
The mean number of defects of wire sections of length \(l\) is determined as the argument of the exponential function from the expression
\[ e^{-a}=p^{(0)}. \tag{7} \]
The probability of damage to an elementary segment during the process of inserting the winding is
\[ p=\frac{a}{n}. \tag{8} \]
The fraction of elementary segments along the length of wire \(\frac{l}{a}\) that are broken down by voltage up to \(u_{\text{br}}=z_1\) is
\[ q_{\text{el}}(z_1)=\frac{q(z_1)}{a}, \tag{9} \]
where
\(q(z_1)\) is the fraction of specimens broken down by voltage up to \(z_1\). It is determined from the table of results of tests of insulated wire after insertion of the winding.
The argument of the probability integral \(\alpha(z_1)\) for the value \(q_{\text{el}}(z_1)\) is found from table [3].
The fraction of elementary segments along the length of wire \(\frac{l}{a}\) that are broken down by voltage up to \(u_{\text{br}}=z_2\) is
\[ q_{\text{el}}(z_2)=\frac{q(z_2)}{a}, \tag{10} \]
where \(q(z_2)\) is the fraction of specimens broken down by voltage up to \(z_2\). It is determined from the table of results of tests of insulated wire after insertion of the winding.
The argument of the probability integral \(\alpha(z_2)\) for the value \(q_{\text{el}}(z_2)\) is found from table [3].
Note. It is recommended to take \(z_1=0.5\) kV and \(z_2=1.0\) kV, or \(z_1=0\) and \(z_2=0.5\) kV, with \(q(z_1)\) and \(q(z_2)\) being the average values for the slot and end-winding parts.
The root-mean-square deviation of the breakdown voltages, distributed according to the normal law, is
\[ \sigma=\frac{z_2-z_1}{a(z_2)-a(z_1)} . \tag{11} \]
The mean value of the breakdown voltages, distributed according to the normal law, is
\[ \overline{u}=z_1-a(z_1)\sigma . \tag{12} \]
The mean distance between conductors is
\[ x_{\mathrm{p}}=d_{\mathrm{izmax}}-d_{\mathrm{iz}} . \tag{13} \]
The parameter of the exponential law of distribution of breakdown voltages of insulation gaps is
\[ \lambda=\frac{1}{E_{\mathrm{p}}\cdot k_{\mathrm{p}}} . \tag{14} \]
The voltage falling on a coil (section) is
\[ u_k=\frac{u_{\mathrm{fk}}}{n_k} . \tag{15} \]
The probability of breakdown of a pair of conductors of length \(\dfrac{l}{a}\), which had damage before impregnation, is
\[ q'(u_k)=\frac{n}{a}\,p^2 \left[ F\left(-\frac{\overline{u}}{\sigma}\right) \right]^2 \lambda I_1, \tag{16} \]
where
\[ I_1=\int_{0}^{u_k} e^{-\lambda u} \left(1-\frac{u}{u_k}\right)^2\,du \]
—the integral is determined by a numerical method.
The probability of breakdown of a pair of conductors of length \(\dfrac{l}{a}\), which had no damage before impregnation, is
\[ q''(u_k)=\frac{n}{a}\,p^2 \exp\{\lambda(2\overline{u}-\lambda\sigma^2)\}\lambda I_2, \tag{17} \]
where
\[ I_2=\int_{0}^{u_k} e^{-\lambda u} F\left( \frac{u-2\overline{u}-2\lambda\sigma^2}{\sqrt{2}\,\sigma} \right) \left(1-\frac{u}{u_k}\right)^2\,du \]
—the integral is determined by a numerical method.
The lower estimate of the reliability of turn insulation during the run-in period is
\[ R_b=\left[1-q'(u_k)-q''(u_k)\right]^{Na}. \tag{18} \]
The method considered is being introduced at all enterprises of Glavelektromash of the Ministry of Electrical Engineering Industry of the USSR, which manufacture and develop motors with a power rating from 0.6 to 100 kW. It makes it possible to determine the reliability of turn insulation during the run-in period, and also to assess the effectiveness of measures for increasing reliability.
References
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E. K. Strelbitskii. Study of the reliability and quality of electrical machines. Dissertation, Tomsk, 1967.
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Yu. P. Pokholkov. The influence of winding-insulation operations and insulation quality on the reliability of windings of electrical machines. Dissertation, Tomsk, 1966.
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A. K. Mitropol’skii. Technique of Statistical Computations, Moscow, Fizmatgiz, 1961.