Influence of the Winding Type on Some Performance Indicators of Motors with an Arc-Shaped Stator

N. M. Pirumyan, M. G. Rezin

(Presented by the scientific seminar of the departments of electrical machines and general electrical engineering)

G. I. Shturman [1] showed that the induction of the magnetic field in the air gap of an arc-shaped asynchronous machine, produced by a three-phase stator winding with an open magnetic circuit, varies along the gap according to the law

\[ B = B_{\mathrm{п}}\cdot \sin\left(\omega t-\frac{\pi}{\tau}x\right) -(-1)^p\cdot B_{\mathrm{mc}}\cdot \operatorname{ch}\beta x\cdot \sin\omega t -(-1)^p\cdot B_{\mathrm{ms}}\operatorname{ch}\beta x\cdot \cos\omega t. \tag{1} \]

The first term on the right-hand side of equation (1) represents the normal traveling field, while the second and third terms are the pulsating components of the field. Usually one may assume that \(\beta \approx 0\), and then instead of (1) we obtain

\[ B = B_{\mathrm{m}}\sin\left(\omega t-\frac{\pi}{\tau}x\right) -(-1)^p\cdot B_{\mathrm{mc}}\cdot \sin\omega t. \tag{2} \]

The available experimental data [2] also show that the field in the gap varies in accordance with equation (2), i.e., practically only one component of the pulsating field exists. The presence of pulsating fields in the air gap of a machine is extremely undesirable, since they increase the inductive reactances of the primary windings, distort the symmetry of the currents, cause additional losses in the secondary circuit, and reduce the efficiency. Therefore, a search has long been under way for effective means of reducing the pulsating component of the field. One promising direction is the proper choice of the stator winding.

In the present work, several types of two-layer windings are considered, with a linear current loading constant in amplitude in the wound zone of the stator: a partially corrected winding, the compensated winding of A. I. Voldek [4], and the proposed winding. The defining distinctive feature of the proposed winding is that, in the central phase, the coil group with a pitch equal to \(\tau\) is split into two coil groups having a smaller pole pitch and number of turns and placed at the edges of the magnetic circuit. Other methods of making windings and compensating pulsating fields are also known [2, 5]. The investigations were carried out on a two-pole stator, since it makes it possible to present in the clearest form certain characteristic features of the consequences of opening the magnetic circu-

drive. In practice, however, it is often necessary to use precisely two-pole motors.

The tests of all windings were carried out under identical conditions. The experimental investigation of the field in the air gap was performed by two methods: with direct current and with alternating current. The method for investigating magnetic fields with direct current consists in the fact that the instantaneous values of the alternating current are set by direct current for several instants of time of the alternating current. The induction is then determined by the ballistic method. As a result, a family of curves \(B=f(x)\) is obtained. Figure 1 shows the field-distribution pattern for the proposed winding. The method of measuring fields with direct current, on the basis of a family of curves, makes it possible to judge the distribution of the field along the length of the stator arc for each instant of time, and the speed of motion of the field in individual sections of the magnetic circuit. To measure the induction in the air gap, a measuring frame was used whose length was equal to the tooth pitch. With such a measurement, the induction is averaged and the higher harmonics, which here do not play a significant role, are excluded from consideration. Measurements were made with an M19-type webersmeter (fluxmeter).

Fig. 1

It is simpler to characterize the field not by a family of curves, but by the envelope of this family.

\[ B=\pm B_m\sqrt{1-(-1)^p\cdot 2k_c\cdot \cos ax+k_c^2}. \tag{3} \]

For this it is sufficient to measure the emf of a search coil in the gap when the winding is supplied with three-phase current. The emf was measured with a V3-3 tube voltmeter.

Comparing the magnetic-field measurement methods under consideration, it can be said that both methods differ substantially in labor input, the instruments used, and the results.

The distribution of the envelopes of the magnetic induction at no load along the stator arc is shown in Fig. 2. If the longitudinal end effect were absent, the amplitude of the magnetic-field induction would be constant along the stator arc in the wound part and would be equal to zero outside this region. But, as can be seen from Fig. 2, the induction amplitude is not constant along the wound part and is not equal to zero outside it. Moreover, this depends on the type of winding. In some cases an increase is observed

field at that edge of the stator from which the field runs off. Such phenomena indicate the presence of considerable pulsating fluxes. It should be noted that, when the secondary system is taken into account, the structure of the field in the gap becomes considerably more complicated [6].

Fig. 2. 1 — corrected, 2 — compensated winding of A. I. Voldek

A comparison was made of the distribution of magnetic induction when each phase was supplied separately, with no supply to the other two phases. Studying the fluxes produced by the individual phases of the winding makes it possible to find more quickly ways of forming the resultant flux.

Experiments showed that the distribution of active powers among the phases was determined by the direction of motion of the traveling magnetic field. Along the length of the stator the phase coils were arranged in the order A, C, B. The distribution of active powers had the form: \(P_A > P_C > P_B\) when the field moved from A to B, and \(P_A < P_C < P_B\) in the opposite direction. The total powers of the phases in this case remained approximately the same. The reason for the nonuniform distribution of active power among the phases is the longitudinal end effect, as a result of which there is nonuniform mutual inductance and inductance of the winding phases. For any shape and any arrangement of the magnetically coupled coils, the mutual inductance “\(M\)” between them can be determined experimentally from the current in one phase and the induced voltages in the other phases. Below are the results of the experimental determination of the mutual inductances.

1. Partially corrected winding

\[ M_{AB}=0.0015\ \text{H}, \qquad M_{AC}=0.0040\ \text{H}, \qquad M_{BC}=0.0040\ \text{H}. \]

1. Corrected winding

\[ M_{AB}=0.0021\ \mathrm{H}, \qquad M_{AC}=0.0040\ \mathrm{H}, \qquad M_{BC}=0.0040\ \mathrm{H}. \]

1. Compensated winding of A. I. Voldek

\[ M_{AB}=0.0046\ \mathrm{H}, \qquad M_{AC}=0.0028\ \mathrm{H}, \qquad M_{BC}=0.0028\ \mathrm{H}. \]

1. Proposed winding

\[ M_{AB}=0.0043\ \mathrm{H}, \qquad M_{AC}=0.0033\ \mathrm{H}, \qquad M_{BC}=0.0033\ \mathrm{H}. \]

At no load of the motor, the dependence \(I_{\phi}=f(H_{\mathrm{p}})\) was recorded. From a comparison of these characteristics it is possible to determine the degree of asymmetry of the phase currents for each winding. The greatest difference between the phase currents is for the partially corrected winding, 35%; the smallest is for the proposed winding, 4%; for A. I. Voldek’s winding it is 7%. A consequence of the asymmetry is the appearance of negative-sequence currents and a nonuniform distribution of magnetic energy among the windings.

The mechanical forces developed by the stator were determined with the rotor braked \((s=1)\). The tests were carried out at different supply voltages. Figure 3 presents the dependences \(F=f(I^2)\) for each winding.

Fig. 3

Thus, according to all the compared criteria, preference should be given to the proposed winding.

REFERENCES

1. G. I. Shturman. Elektrichestvo, 1946, 10, 43.
2. G. A. Voldek. NDVSh, Electromechanics and Automation, 1959, 2, 130.
3. Ya. Ya. Lielpeter and others. Proceedings of the Academy of Sciences of the Latvian SSR, Series of Physical and Technical Sciences, 2, 53, 1964.
4. A. I. Voldek. Elektrichestvo, 1965, 4, 50.
5. M. G. Rezin. Proceedings of UPI. Electrical Engineering, 1959, 90, 30.
6. M. G. Rezin. Elektrichestvo, 1950, 2, 20.