A New Method for Detecting Casting Defects in the Squirrel Cage of an Induction Motor Rotor Before Machining

M. P. Tabinskii, A. I. Zaitsev

(Presented by the scientific and technical seminar of the Department of Electrification of Industrial Enterprises, Electromechanical Faculty)

At present, at electric-motor plants, the quality of rotor casting is not checked during the course of the technological process; therefore, casting defects in the squirrel cage are detected only in the assembled machine during acceptance testing. In many cases, motors with poor-quality rotors pass through acceptance tests unnoticed. As a result, our industry suffers losses both because of the direct expenditure of labor on manufacturing poor-quality motor rotors and because of the premature failure of electric motors that have passed inspection.

The reason for this is the absence of a simple and reliable, and at the same time productive, method for checking the quality of rotor casting [1]. Therefore, the search for a rational method of inspecting the casting of unmachined rotors continues.

The method described below, based on comparing the mechanical characteristics of motors with normal and defective rotors, is fundamentally new.

It is known that the mechanical characteristics of an induction motor depend on the parameters of the stator and rotor windings. Casting defects in the squirrel cage cause a certain change in the motor parameters: cavities in a bar increase the active resistance, practically without changing the leakage resistance, while the breakage of one bar is accompanied by an increase in the active resistance of the rotor and an increase in the leakage resistance [2].

Experimental studies carried out in the laboratory of the Department of Electrification of Industrial Enterprises of the Tomsk Polytechnic Institute revealed the possibility of recognizing squirrel-cage defects from differences in the mechanical characteristics of motors with sound and faulty rotors [3]. For this purpose, a laboratory installation was constructed for the rotors of EMU-5A and EMU-12A electric motors. The installation consists of a multiphase stator with an internal diameter 10 mm larger than that of the rotor being tested, a cantilever shaft for centering the tested rotor in the stator bore, and a source of unbalanced voltage supplied to the stator of the induction motor.

With a large air gap and unsaturated steel, the m.m.f. of the stator phase winding has the form of a trapezoid. For convenience of analysis, pro—

...occurring in the machine, let us decompose the m.m.f. curve into harmonics; moreover, harmonics of the fifth and higher orders may be neglected because of their smallness.

According to [4], the resultant m.m.f. of a symmetrical three-phase winding, with a symmetrical system of voltages applied to the stator phases, is a forward-traveling wave along the stator circumference with amplitude equal to

\[ F_1 = \frac{3}{2} F_{\phi 1}, \tag{1} \]

where \(F_{\phi 1}\) is the amplitude of the fundamental harmonic of the phase winding. All m.m.f. harmonics that are multiples of three vanish. It is easy to show that, with an asymmetrical system of voltages applied to the stator phases, the amplitude of the resultant m.m.f. of the fundamental harmonic will already be considerably smaller, since, in addition to the forward-traveling wave, a backward-traveling wave will appear, and a forward-traveling wave of the m.m.f. third harmonic will also appear\(^1\).

\[ \begin{aligned} F_2 ={}& \kappa_1 F_{\phi 1}\sin\left(\omega t - \frac{\pi}{\tau}x\right) + \kappa_2 F_{\phi 1}\sin\left(\omega t + \frac{\pi}{\tau}x\right) +{}\\ &+ \kappa_3 F_{\phi 3}\sin\left(\omega t - \frac{3\pi}{\tau}x\right), \end{aligned} \tag{2} \]

where \(F_{\phi 3}\) is the amplitude of the m.m.f. of the third harmonic;
\(\kappa_1, \kappa_2, \kappa_3\) are coefficients;
\(x\) is the spatial coordinate;
\(\tau\) is the pole pitch.

Equation (2) makes it possible to represent the machine as a set of three independent elementary motors of different powers with rigidly connected shafts, with numbers of pole pairs \(p = 2\) and \(p = 6\), there being two four-pole machines (Fig. 1).

The resultant mechanical characteristic of such a machine with a symmetrical rotor is shown in Fig. 2.

Let us consider the phenomena that arise in the machine in the presence of a blowhole, which causes an increase in the active resistance of a bar, leading to a certain asymmetry of the rotor currents. This asymmetry of the currents arises in each of the three elementary motors.

Fig. 1.

The asymmetrical system of rotor currents can be decomposed into symmetrical components of positive and negative sequence. Under these conditions [5], two rotating magnetic fields arise in each motor. The first is produced by the m.m.f. of the stator currents and by the positive-sequence rotor currents; the second, by the m.m.f. of the negative-sequence rotor currents and by stator currents of frequency \(f = (1 - 2s)f_1\), induced in the stator windings by the flux of the negative-sequence rotor—

\(^1\) For simplicity of reasoning, we do not take into account the backward-traveling m.m.f. wave of the third harmonic, since its maximum influence lies in the region of negative speeds.

of phase. Accordingly, in each elementary motor there will exist two torques: \(M_i'\) and \(M_i''\) (Fig. 3). The resulting mechanical characteristic of the machine is obtained by adding the individual mechanical characteristics of the elementary motors.

Fig. 2.

As can be seen from a comparison of Figs. 2 and 3, the mechanical characteristics of a machine with a normal rotor and with a defective rotor differ greatly from one another. The difference is most pronounced in the region of the dip caused by the third harmonic of the magnetic field. If, with a normal rotor, the dip in the mechanical characteristic extends into the region of negative torques, then with a defective rotor the dip is located

Fig. 3.

in the region caused by the third harmonic of the magnetic field. If, with a normal rotor, the dip in the mechanical characteristic extends into the region of negative torques, then with a defective rotor the dip is located

only in the motoring region and does not reach a zero value of the torque. It is precisely this circumstance that is used in the new inspection method: during startup of the installation, a normal rotor accelerates to a speed above the synchronous speed of the third harmonic of the magnetic field, whereas a rotor with a casting defect accelerates to a speed below the synchronous speed of the fundamental harmonic of the stator magnetic field.

Defective rotors can be identified by their rotational speed either visually or with the aid of a tachometer.

The duration of the inspection process is determined by the rotor acceleration time. With the aid of the installation, the following casting defects in the squirrel cage are detected:

1) one blowhole in one bar, reducing the cross section of the bar at that point by 30%;

2) complete breakage of a bar;

3) breakage of two or more bars.

It should be noted that this method is highly effective even with closed slots.

REFERENCES

1. Dan Teodorescu. A new method for determining casting defects in the bars of squirrel-cage rotors. VEP, No. 7, 1963.

2. Hiller, Ute-Maria. Eisfluß fehlender Läuferstäbe auf die elektrischen Eigenschaften von Kurzschlußläufer—Motoren. ETZ—A, No. 4, 1962.

3. A. I. Zaitsev, M. P. Tabinskii, L. A. Tsirina. Detection of damage to the rotor of a squirrel-cage induction motor. Abstracts of reports of the II Scientific and Technical Conference on Production Automation, Tomsk, 1964.

4. M. P. Kostenko, L. M. Piotrovskii. Electrical Machines. Part II, GEI, 1958.

5. V. P. Andreev, Yu. A. Sabinin. Fundamentals of Electric Drive. GEI, 1963.