Logic Circuit for Automatic Assessment of the Magnitude of Casting Defects in the Rotor of an Induction Motor
Abstract Generated abstract
This paper addresses automatic evaluation of casting defects in squirrel-cage rotors of induction motors, using the fluctuation of short-circuit current during slow rotor rotation as an indirect quality criterion. The authors relate the percentage current fluctuation to the percentage change in active rotor resistance caused by defective bars, present a calculation formula for one or more defects, and compare it with experimental PZR test results. On this basis they propose a logic circuit that quantizes the output voltage of a rotor defect detection installation into levels, counts the resulting pulses, and displays the corresponding estimated PZR percentage. The circuit is described as simple and reliable, with potential use for rejecting defective rotors immediately after casting.
Full Text
LOGIC CIRCUIT FOR AUTOMATIC ASSESSMENT OF THE SIZE OF CASTING DEFECTS IN THE ROTOR OF AN ASYNCHRONOUS MOTOR
A. I. ZAITSEV, V. I. MIKHALEV, L. V. PERFIL'EV, M. P. TABINSKII
(Recommended by the scientific seminar of the Electromechanical Faculty)
At present there is no clear criterion for determining the permissible magnitude of casting defects in the winding of a squirrel-cage rotor. To assess the quality of a manufactured rotor, in addition to visual inspection of the cast cage, motor-building plants test the assembled motor for the so-called PZR (rotor filling completeness), by which is meant the ratio of the short-circuit current fluctuation to its maximum value during slow rotation of the rotor, expressed as a percentage,
\[ \left(\frac{I_{\max}-I_{\min}}{I_{\max}}\cdot 100\right). \]
According to this criterion, one can indirectly judge the presence of casting defects in the rotor, since fluctuations of the short-circuit current are caused mainly by asymmetry of the rotor winding (magnetic asymmetry in a cylindrical rotor is unlikely). Electric-motor plants permit rotor defects for which the current fluctuations when testing the motor for PZR are not more than 5%.
In [1] an installation is described for determining casting defects in the rotors of asynchronous motors before mechanical machining of the rotor. The output quantity of the installation is a voltage proportional to the casting defect. Since a certain number of defects in the rotor is permissible, the authors have proposed a logic circuit for automatic conversion of the readings of the installation into the magnitude of the short-circuit-current fluctuation when testing the motor for PZR, which will be obtained if the tested rotor is machined and installed in an asynchronous motor.
Experimentally, it is possible to reveal a direct relationship between definite rotor defects and short-circuit-current fluctuations. For this purpose, a defect is deliberately created in the winding of a known good rotor, after which the motor is tested for PZR. It has been established that the percentage fluctuation of the short-circuit current in absolute value is approximately equal to the percentage change in the active resistance of the rotor, if the rotor is regarded as a parallel connection of \(N_2\) active resistances, where \(N_2\) is equal to the number of rotor slots.
If the active resistance of a bar is denoted by \(R\), the number of bars forming the rotor winding by \(N_2\), and the coefficient showing by how many times the resistance \(R_c\) has changed as a result of a casting defect by \(\delta\) \((\delta = 1 \div \infty)\), then the change in the resistance of the parallel connection of the bars, expressed as a percentage, can be calculated by the formula
\[ \Delta R\%=\frac{R_2-R_1}{R_1}\cdot 100= \left( \frac{N_2}{N_2-K+\frac{1}{\delta_1}+\frac{1}{\delta_2}+\ldots+\frac{1}{\delta_K}} -1 \right)\cdot 100. \tag{1} \]
where
\[ R_1=\frac{R_c}{N_2}, \]
\[ \frac{1}{R_2}=\frac{1}{R_c}+\frac{1}{R_c}+\frac{1}{R_c}+\ldots+ \frac{1}{R_c\cdot\delta_1}+\frac{1}{R_c\cdot\delta_2}+\ldots+ \frac{1}{R_c\cdot\delta_K}. \]
\(K\) is the number of defective bars.
Example 1: The rotor has a winding consisting of \(N_2=46\) bars. A casting defect increases the resistance of one bar twofold \((\delta_1=2,\ K=1)\).
\[ \Delta R= \left( \frac{N_2}{N_2-k+\frac{1}{\delta_1}}-1 \right)\cdot 100 = \left( \frac{46}{46-1+\frac{1}{2}}-1 \right)\cdot 100 \approx 1.1\%. \]
Example 2: In the rotor winding, with \(N_2=46\), one bar has broken \((\delta_1 \simeq =\infty,\ K=1)\).
\[ \Delta R= \left( \frac{46}{46-1+\frac{1}{\infty}}-1 \right)\cdot 100 \approx 2.2\%. \]
The same value of the ratio of the short-circuit current fluctuation to the maximum current was obtained when the motor was tested on the PZR.
The results of several experiments are given in Table 1.
Table 1
| Motor type | Number of rotor bars | Nature of defect | Nature of defect | Nature of defect | (by formula 1) | PZR % |
|---|---|---|---|---|---|---|
| Motor type | Number of rotor bars | \(K\) | \(\delta_1\) | \(\delta_2\) | (by formula 1) | PZR % |
| KO-12—6 | 46 | 1 | 2 | — | 1.1 | 1 |
| KO-12—6 | 46 | 1 | \(\infty\) | — | 2.2 | 2.2 |
| KO-12—6 | 46 | 2 | \(\infty\) | \(\infty\) | 4.5 | 5 |
| A 42.4 | 26 | 1 | 2 | — | 1.8 | 2 |
| A 42/4 | 26 | 1 | \(\infty\) | — | 4 | 4.95 |
| A 42/4 | 26 | 2 | \(\infty\) | \(\infty\) | 8.3 | 13 |
Fig. 1.
In the oscillograms (Fig. 1) the waveform of the output voltage in the device for detecting casting defects in rotors is recorded when the following defects are present in the rotor: an increase in the resistance of a bar as a result of narrowing by a factor of two (a), the breakage of one bar (b), and the breakage of two bars located side by side. As can be seen from the oscillogram in Fig. 1, the output voltage consists of double triangular pulses with a front duration of \(0.1\) sec., with an amplitude proportional to the rotor defect.
To construct the logic circuit for automatic recalculation of the signals present in the output voltage of the installation, as a result of testing the motor on the PZR, the output voltage is classified by magnitude into 4 levels, with two pulses in each level. The pulses of the individual levels are assigned a rank expressed in percent. The sum of the ranks of one level is equal to the percent PZR corresponding to a particular type of casting defect (Table 2).
Table 2
| Output-voltage level | Voltage magnitude | No. of PZR | $\delta$ | Rank of one pulse |
|---|---|---|---|---|
| 1 | 10 | 1 | 2 | 0.5 |
| 2 | 20 | 2 | $\infty$ | 1 |
| 3 | 30 | 3 | $\delta_1 = 2;\ \delta_2 = \infty$ | 1.5 |
| 4 | 40 | 4 | $\delta_1 = \delta_2 = \infty$ | 2 |
The functional diagram for automatic recalculation of the signals of the installation output voltage into percent PZR is shown in Fig. 2. The circuit consists of an input device VU, a counting circuit SS, and an indicator unit IU.
Fig. 2.
The VU is intended for converting linearly increasing signals with a rise-front duration on the order of 0.1 s and an amplitude of up to 40 V into a number of pulses with a quantization interval of 10 V/pulse.
To implement such a device, static flip-flops with separate inputs \((T_1 \div T_4)\) are used; their triggering level is adjusted from 10 to 40 V in accordance with the levels of the incoming signals. When, for example, a 40 V signal appears, four flip-flops, set respectively to 10, 20, 30, and 40 V, are actuated sequentially in time; in this case, 4 pulses are generated. With a 20 V signal, 2 flip-flops \((T_1\) and \(T_2)\) are actuated—2 pulses are generated, etc. The output signals of the flip-flops are differentiated and combined according to an OR circuit.
The pulses formed in the BU enter the counting circuit SS, consisting of a binary pulse counter (flip-flops \(T_5 \div T_8\)) and a binary-decimal decoder, which provides information on defects in the rotor winding in accordance with the adopted scale.
This information passes to the indicator unit IU, consisting of amplifiers \(U_1 \div U_7\), from whose outputs the signals are applied to the cathodes of the digital indicator IN-1, lighting the digit corresponding to the percentage of the PZR.
Conclusions
The proposed circuit for automatic assessment of the size of casting defects in the rotor of an asynchronous motor is distinguished by simplicity and high reliability. It may find application at motor-building plants for rejecting rotors of asynchronous motors immediately after casting.
Literature
- A. I. Zaitsev, M. P. Tabinskii. Analysis and equivalent circuit of the rotor-inductor circuit of an installation for detecting casting defects in squirrel-cage rotors. Proceedings of the Tomsk Polytechnic Institute, 1966.