CALCULATION OF THE MAIN POLE FIELD IN THE COMMUTATION ZONE TAKING INTO ACCOUNT SATURATION OF THE MAGNETIC CORE

E. G. Chebotkov, A. I. Skorospeshkin

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

The commutating stability of DC machines with deep speed regulation is significantly affected by the leakage field of the main poles, since such machines also operate in regimes of strong saturation. Saturation of the magnetic system increases the influence of the main-pole field on commutation, since the rotational speed then decreases somewhat more slowly than the growth of the m.m.f. of the main pole, which, accordingly, causes an increase in the rotational e.m.f. of the commutated sections from the field of the main poles.

Hence the need is evident to take the main-pole field into account in the calculation of commutation, especially when the magnetic system is saturated.

Existing methods for calculating leakage magnetic fields are applicable only for an unsaturated magnetic system.

In [1] a method was developed for calculating the field of the main poles in the commutation zone in the form of determining the parameters of flux tubes and their magnetic resistances as functions of the machine geometry. It is also noted there that reducing the potential of the pole-shoe tip relative to the pole potential to 50% leads to a change in the field pattern and in the parameters of the flux tubes by no more than 10%. Consequently, the method of [1] is applicable to a saturated magnetic system provided that the distribution of the potential along the pole shoe is known.

The distribution of the potential along the pole shoe can be calculated by applying Benedikt’s nomographic method [2].

The procedure for calculating the leakage field of the main pole in the neutral zone, taking into account saturation of the steel of the magnetic core, is adopted as follows:

I. Determination of the distribution of the magnetic potential along the pole shoe. It includes:

1. Construction of nomograms for the grades of steel used for the magnetic core of the given machine.

2. Neglecting the magnetic resistance of the pole shoe, for a specified value of the m.m.f. of the main pole, the fluxes through sections of the pole shoe I, II, III (Fig. 1) and the approximate values of the drops of magnetic potential in the indicated sections of the pole shoe are determined.

3. The approximate values of the magnetic-potential drop in the pole shoe are refined.

On the basis of the m.m.f. of the main pole and the calculated values of the magnetic-potential drops, the distribution of magnetic potential along the pole shoe is calculated.

Fig. 1

II. Calculation of the leakage field of the main pole in the neutral zone

The calculation includes:

1. According to expressions (5--8) [1], the parameters of the flux tubes are determined for the geometry of the given machine.

2. According to expressions (1--2) [1], taking into account the distribution of the magnetic potential over the pole shoe, the induction in the air gap of the neutral zone is determined.

Using the indicated method, a calculation was carried out for the field of the main poles in the neutral zone of a P51 machine with the following geometric parameters:

\[ \delta_{\mathrm{kr\ g.p.}} = 2.5\ \mathrm{mm} \]
-- air gap under the edge of the main pole,

\[ \delta_w = 2.5\ \mathrm{mm} \]
-- air gap under the center of the interpole,

\[ b_w = 22\ \mathrm{mm} \]
-- width of the interpole,

\[ D_a = 162.5\ \mathrm{mm} \]
-- armature diameter.

The calculation was performed for excitation currents \(0.8;\ 1;\ 1.2;\ 1.4\,a\), which, as is evident from the magnetization curve of the machine (Fig. 2), correspond to a saturated magnetic system.

The results of the calculation for determining the drop of magnetic potential in the pole shoe are summarized in Table 1, where

\[ i_v \]
-- excitation current,

\[ P_{os} \]
-- m.m.f. of the main pole,

\[ P_{\mathrm{nI}},\ P_{\mathrm{nII}},\ P_{\mathrm{nIII}} \]
-- drops of magnetic potential in sections I, II, III of the pole shoe,

\[ P_{\mathrm{oy1}} \]
-- drop of magnetic potential in the tooth--air-gap layer under section I of the pole shoe.

From the data presented in Table 1 it follows that the main portion of the m.m.f. of the main pole is spent on conducting the flux through the air-gap--tooth layer in the form of the magnetic potential drop \(P_{\mathrm{oy1}}\). For the given machine, at excitation currents \(1--1.4\,a\), 10 to 20 percent of the m.m.f. of the excitation winding is spent on conducting the flux through the main-pole shoe, which correspondingly reduces the magnetic potential of the pole shoe and the magnitude of the field in the neutral zone.

The principal drop of magnetic potential in the pole shoe occurs in sections III and II (Fig. 1). The drop of magnetic potential in section I of the pole shoe is insignificant, since in the given case it does not exceed 1% of the m.m.f. of the excitation winding. The latter

Fig. 2

is explained by the fact that through section III pass the fluxes \(\Phi_{III}\), \(\Phi_{\Gamma I}\), and \(\Phi_{\Gamma}\); through section II, the fluxes \(\Phi_{II}\) and \(\Phi_I\); and through section I, the flux \(\Phi_I\), respectively. Sections III and II are more saturated, and they account for a greater drop in magnetic potential than section I. This confirms the possibility of calculating the field of the main pole in the neutral zone, with saturation of the magnetic system, by the method set forth above, since the field tubes of the main-pole field in the neutral zone, resting on an insignificant part of the pole shoe, do not change their parameters, because the magnetic potential of section I of the pole shoe is practically constant along its length.

The results of calculating the field in the neutral zone for the P51 machine are presented in Fig. 3 in the form of curves 1, 2, 3, 4, corresponding to excitation currents of 0.8; 1; 1.2; 1.4 A.

To verify the reliability of this method for calculating the field with allowance for saturation, an experiment was carried out to determine the induction in the interpole gap of the P51 machine.

The distribution of induction was recorded using a Hall emf sensor fastened to an armature tooth. The experimental data are presented in Fig. 3 as points.

Analysis of the data presented in Fig. 3 shows that the discrepancy between experiment and calculation does not exceed 10%.

The results of this work confirm the possibility of calculating the field of the main poles in the commutation zone for a saturated magnetic system, using [1] and [2].

The calculations and experiments performed make it possible to conclude that it is necessary to take into account saturation of the pole shoe, since the drop of magnetic potential in them can reach 10–20% of the m.m.f. of the main pole.

The magnitude of the field of the main poles in the commutation zone may be considerable, since the width of the commutation zone is chosen to be somewhat greater than that of the interpole. Thus, for the excitation currents considered in these calculations, the field of the main poles at the beginning and end of the commutation zone reaches 500–600 G. This field magnitude corresponds to the beginning of the commutation zone—\(81^\circ\) of the P51 machine (Fig. 3), is comparable with the field of the interpole, and can exert a substantial influence on the nature of the commutation process.

Fig. 3

Table 1

References

1. A. I. Skorospelkin, E. G. Chebotkov. Calculation of the field of the main poles in the commutation zone of DC machines of series II. Proceedings of TPI, vol. 190, 1968.

2. O. V. Benedikt. Nomographic method for calculating complex highly saturated magnetic circuits of electrical machines. GEI, 1953.