PROCEEDINGS
of the Tomsk Order of the October Revolution and Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Vol. 229 1972

COMMUTATION STABILITY OF MACHINES WITH VALVE-MECHANICAL COMMUTATION

O. A. BRATKOVSKII, V. V. IVASHIN, I. A. MILORADOV, M. A. SUTORMIN

(Presented by the scientific seminar of the Department of Electrical Machines)

The Concept of Commutation Stability

At present, the operation of commutator electric machines with respect to commutation is evaluated mainly by the method of no-spark zones [1], which has found wide application for the experimental adjustment of interpoles. This method makes it possible to compare clearly the commutation state of machines of one and the same type. At the same time, it is not applicable, for example, to machines having unequal air gaps under the interpole [2]. Quantitatively, the width of the no-spark zone of these machines does not unambiguously determine the stability of their sparkless operation in various modes. Therefore, in the literature, along with the concept of the no-spark zone, such concepts as “commutation capability,” “commutation strength,” “commutation stability,” and others are often encountered, in most cases without a clear definition.

In the present article, the commutation stability (CS) of a commutator electric machine is understood as its resistance to the occurrence of brush sparking in various modes. As a rule, sparking of the trailing edge of the brushes is the most intense and dangerous. Therefore, the concept of CS is associated with sparkless operation specifically of the trailing edge.

In the general case, when the no-spark zone is asymmetric with respect to the abscissa axis, the CS of a machine in some mode is determined by the following coefficients:

\[ K_{1,2}=\frac{\Delta e_{1,2}}{e_0}, \tag{1} \]

where

\(e_0\) is the emf induced by the commutating current under the interpoles in the armature sections;

\(\Delta e_{1,2}\) are the absolute values of the maximum permissible increments of the emf \(e_0\) at which brush sparking still does not occur;

\(K_{1,2}\) are the coefficients of commutation stability.

In expression (1), subscript 1 refers to positive increments of the emf \(e_0\), and subscript 2 to negative ones.

The coefficients \(K_1\) and \(K_2\) are functions of the armature current, rotational speed, commutating properties of the brushes, type of armature winding, and other machine parameters. The criterion for stable sparkless operation is the inequality \(K_{1,2}>0\). The equality \(K_{1,2}=0\) means operation on the verge of sparking. In the general case, the coefficients \(K_1\) and \(K_2\) in some re-

may be unequal. Then the CS of the machine in this regime is determined by the smaller of them (operation of the machine not at the center of the sparkless zone). For operation at the center of the zone it is necessary to satisfy the condition \(K_1=K_2\).

The operating regimes of a machine are conventionally divided into two types: static and dynamic. Static regimes include operation of the machine with different, but time-constant, armature current and current in the excitation winding of the main poles. Dynamic regimes include operation of the machine with abrupt changes or pulsations of the armature currents and excitation-winding currents, which may lead to the appearance of short-time or periodic “unbalanced” EMFs in the commutated sections and to a change with time in the CS coefficients.

The introduction of \(\Delta e\) into the commutated sections of the machine in the experimental determination of CS is carried out by the method of boosting the winding of the auxiliary pole. The relation between the CS coefficients and the boosting currents is of interest.

For the case of boosting the entire winding of the auxiliary pole, with an unsaturated magnetic circuit, one may write

\[ \frac{i_{\mathrm{p}1,2}}{I_{\mathrm{a}}} = \frac{F_{\mathrm{k}0}}{F_{\mathrm{d}0}} \cdot \frac{e_{1,2}-e_0}{e_0} = \frac{W_{\mathrm{k}}}{W_{\mathrm{d}}} \cdot \frac{\Delta e_{1,2}}{e_0} = \frac{W_{\mathrm{k}}}{W_{\mathrm{d}}} \cdot K_{1,2}. \tag{2} \]

Here

\[ \begin{aligned} i_{\mathrm{p}}&\text{ is the absolute value of the boosting current of the auxiliary-pole winding;}\\ I_{\mathrm{a}}&\text{ is the armature current;}\\ F_{\mathrm{d}0}&\text{ is the MMF of the auxiliary-pole winding in the absence of boosting;}\\ F_{\mathrm{k}0}&\text{ is the part of the auxiliary-pole MMF that goes to creating the commutating flux;}\\ W_{\mathrm{d}}&\text{ is the number of turns of the auxiliary-pole winding;}\\ W_{\mathrm{k}}=W_{\mathrm{d}}-\frac{F_{\mathrm{r a}}}{I_{\mathrm{a}}} &\text{ is the part of the turns of the auxiliary-pole winding}\\ &\text{that creates the MMF }F_{\mathrm{k}0};\\ F_{\mathrm{r a}}&\text{ is the MMF of the transverse armature reaction;}\\ e_1;\ e_2&\text{ are the EMFs in the commutated sections at which}\\ &\text{the machine operates, respectively, at the upper and lower}\\ &\text{boundaries of the sparkless zone.} \end{aligned} \]

Let us note that if boosting is applied not to all turns \(W_{\mathrm{d}}\) of the auxiliary-pole winding (“complete” boosting), but to a part \(W_{\mathrm{k}}\) of them (“partial boosting”), then, analogously to (2), one may obtain

\[ \frac{I_{\mathrm{p}1,2}}{I_{\mathrm{a}}} = \frac{e_{1,2}-e_0}{e_0} = \frac{\Delta e_{1,2}}{e_0} = K_{1,2}, \tag{3} \]

where \(I_{\mathrm{p}}\) is the absolute value of the “partial” boosting current. Thus, the CS coefficients are the ratio of the absolute values of the “partial” boosting currents to the armature current.

The relation of the CS coefficients to the width of the sparkless zone \(\vartheta\), plotted in the axes \(i_{\mathrm{p}1,2}, I_{\mathrm{a}}\), is expressed by the relation

\[ \vartheta=i_{\mathrm{p}1}+i_{\mathrm{p}2} = I_{\mathrm{a}}\frac{W_{\mathrm{k}}}{W_{\mathrm{d}}}(K_1+K_2). \tag{4} \]

From (4) the difference between the concepts of the width of the sparkless zone and commutation stability is evident.

If, on a graph above the abscissa axis, one plots the dependence of \(K_1\) on some parameter, and below the abscissa axis, \(K_2\), then the width of the region between the curves \(K_1\) and \(K_2\) will be proportional to the width of the sparkless zone in the axes \(i_{\mathrm{p}}/I_{\mathrm{a}}, I_{\mathrm{a}}\) (the proportionality coefficient is \(W_{\mathrm{k}}/W_{\mathrm{d}}\)).

In this case the magnitude of the CS coefficients is clearly related to the character of the sparkless zone. The indicated graphical method is used in the present article.

CS of a Machine with VMC and the Influence of Various Factors on It

Basic assumptions

1. Commutation stability is evaluated from the sparkless operation of only the trailing edge of the brushes.

2. The inductance, active resistance of the armature sections, and the commutating e.m.f. are constant quantities.

Fig. 1. Diagram of valve-mechanical commutation: 1—valves, 2—brushes, 3—commutator bars, 4—armature sections

1. Commutation of the current in the slot sections occurs simultaneously. This assumption presupposes a diametral winding pitch and a number of sections per slot equal to two, which, as a rule, is the case in machines with VMC.

2. Machines are considered with the VMC circuit of Fig. 1, with interpoles and independent excitation of the main poles.

Taking into account the adopted notation, the following expressions can be written for the CS coefficients of a machine with the VMC circuit:

\[ K_1=\frac{\Delta e_1}{e_0}=\frac{e_1-e_0}{e_0}=\frac{e_1}{e_0}-1, \tag{5} \]

\[ K_2=\frac{\Delta e_2}{e_0}=\frac{e_0-e_2}{e_0}=1-\frac{e_2}{e_0}. \tag{6} \]

From the operating principle of the VMC circuit of Fig. 1 it is known [3] that sparking of the trailing edge of the brushes is absent in it even for very large increments \(\Delta e_1\). That is, \(e_1 \gg e_0\), and \(K_1\) is theoretically equal to infinity. (In practice, the value of \(K_1\) is nevertheless limited, but not by sparking of the trailing edge, rather by the permissible value of the reverse voltage on the valve, and also by the increase in current density at the leading edge of the brushes.) Thus, the CS of a machine with VMC is determined by one coefficient, \(K_2\).

For the simplest case, when in the commutated circuit only the self-induction e.m.f. and the commutating e.m.f. from the interpoles are taken into account, and with an unsaturated magnetic circuit, one may write

\[ e_2=(L_s+M)\frac{2i_a}{T_2} =\frac{(L_s+M)\pi D_k}{60ab_{\mathrm{sh}}} I_{\mathrm{ya}} n =m_1 I_{\mathrm{ya}} n, \tag{7} \]

\[ e_0=2B_k l_a v_a W_s =\frac{2W_s W_k \mu_0 l_a \pi D_a}{60\delta_d} I_{\mathrm{ya}} n =m_2 I_{\mathrm{ya}} n, \tag{8} \]

\[ K_2=1-\frac{e_2}{e_0} =1-\frac{(L_s+M)\delta_d D_k}{2W_s W_k ab_{\mathrm{sh}}\mu_0 l_a D_a} =1-\frac{m_1}{m_2}. \tag{9} \]

Here \(L_s, M\) are the inductance and mutual inductance of the slot sections;
\(i_a\) is the current of the parallel branch of the machine;
\(n\) is the angular speed of rotation of the armature;
\(a\) is the number of parallel branches of the armature winding;

$T_2$ — period during which the sections are short-circuited by the brushes;

$B_k$ — induction in the air gap under the auxiliary pole;

$\delta_d$ — air gap under the auxiliary pole;

$l_a, D_a, v_a$ — length, diameter, and peripheral speed of the armature;

$W_s$ — number of turns in an armature section;

$D_k$ — commutator diameter;

$b_{\text{sh}}$ — brush width;

$\mu_0$ — magnetic permeability of air;

$m_1, m_2$ — coefficients constant for the given machine.

Fig. 2. Dependence of the commutation-stability coefficient \(K\) on \(I_a\) and \(n\), taking into account various factors

It follows from (9) that, in the case under consideration, the commutation stability of a machine with VMC does not depend on the armature current and the rotational speed (Fig. 2, a). In machines with ordinary commutation, as is known, CS decreases sharply when they increase. By choosing the coefficients $m_1$ and $m_2$, for example by changing $\delta_d$ or $W_s$, in a machine with VMC it is always possible to obtain the required value $K_2 > 0$, i.e., to ensure sparkless operation of the trailing edge of the brushes. It is also seen from (9) that $K_2$ in this case is always less than unity, since the emf $e_2$ is always greater than zero, while the emf $e_0$ cannot be equal to infinity.

The principal factors affecting CS include:

a) the active resistance of the sections undergoing commutation;

b) the ability of the brushes to interrupt, without sparking, a certain residual current of the section (the commutating properties of the brushes);

c) the emf in the section from the main field penetrating into the commutation zone;

d) the degree of saturation of the magnetic circuit in the path of the flux of the auxiliary poles;

e) short-time or periodic emfs in the commutated sections, arising in dynamic regimes. They may be caused by the lag in time of the commutating flux relative to the armature current due to the action of eddy currents in the steel of the magnetic circuit, and also by the time variation of the flux of the main poles;

f) mechanical factors that determine the quality of contact between the brushes and the commutator.

It should be noted that in machines with VMC, in regimes close to nominal, the effect of the active resistance of the sections, of the main field in the commutation zone, and of the commutating properties of the brushes may be neglected. Therefore, in a first approximation (with an unsaturated magnetic circuit, in steady-state regimes and regimes close to nominal, and with good contact between the brushes and the commutator), the CS of machines with the VMC circuit (Fig. 1) may be determined from formula (9).

Let us briefly consider the influence of various factors on the CS of machines with VMC. The analysis was carried out for each factor separately.

All factors may be divided into those that reduce CS (active resistance of the sections, saturation of the magnetic circuit, mechanical factors, dynamic regimes), those that increase it (commutating properties of the brushes), and factors that may either reduce or increase it (the main field in the commutation zone).

The active resistance of the sections leads to a slight decrease in CS (Fig. 2, b) when \(I_a\) varies over a wide range and when \(n\) is close to nominal. At the same time, it has a strong effect at small \(n\), where a critical speed \(n_{\mathrm{cr}1}\) appears, below which \(K_2 < 0\) (without taking into account the commutating properties of the brushes). Analysis shows that the value of \(n_{\mathrm{cr}1}\) is usually no more than 17.5% of \(n_n\), i.e., the range \(0—n_{\mathrm{cr}1}\) is the starting range.

The influence of the commutating properties of the brushes is opposite to the influence of the active resistance (Fig. 2, c). As a result, it becomes possible to reduce substantially or completely eliminate the critical speed \(n_{\mathrm{cr}1}\).

The field of the main poles penetrating into the commutation zone may, on average, either strengthen or weaken the commutating field. In this case CS increases or decreases, as shown in Fig. 2, d. It is seen from Fig. 2, d that the main field may lead to the appearance of a critical current \(I_{a\mathrm{cr}1}\), usually much less than nominal. At a current less than \(I_{a\mathrm{cr}1}\), sparkless operation must be ensured by the commutating properties of the brushes.

Saturation of the magnetic circuit acts at large armature currents and leads to the appearance of a critical current \(I_{a\mathrm{cr}2}\) (Fig. 2, e), above which sparkless operation is impossible. Usually \(I_{a\mathrm{cr}2} \gg (3—5)I_{a n}\). Mechanical factors affect CS through a change in the period during which the sections are short-circuited by the brushes. Measures to combat mechanical factors in machines with VMC must be directed toward ensuring a guaranteed value of the period during which the sections are short-circuited by the brushes. Good results in this respect are given by split brushes and improvement of the commutator profile.

In dynamic regimes, CS is reduced by the action of “unbalanced” emfs in the commutated sections, due to eddy currents in the steel of the magnetic circuit and the time variation of the flux of the main poles. “Unbalanced” emfs may be reduced by lamination of the magnet—

wire and by measures that reduce pulsations and abrupt changes in the excitation current of the main poles.

Experimental Verification of CU

Experimental verification of CU was carried out on two identical direct-current machines with conventional commutation and with VMC. Figure 3 shows the dependences of the coefficients \(KУ\), \(K_1\), and \(K_2\) on the current \(I_{\mathrm{я}}\) and the speed \(n\) of a conventional machine having retarded commutation. The coefficients \(K_1\) and \(K_2\) were determined from formula (2) from the sparkless zones, obtained experimentally, in static modes.

Fig. 3. Dependence of \(K_1\) and \(K_2\) on \(I_{\mathrm{я}}\) and \(n\) of a machine with a conventional commutation system.

Figure 4 gives the dependences of \(K_2\) on \(I_{\mathrm{я}}\) and \(n\) for the same machine, but made with the VMC circuit. The method for determining \(K_2\) is the same as in the machine with conventional commutation. In this case, the sparkless zone in the machine with VMC was determined in two ways: by the appearance of sparking and by the disappearance of reverse-voltage pulses on the valves.

Fig. 4. Dependence of \(K_2\) on \(I_{\mathrm{я}}\) and \(n\) of a machine with VMC.

The latter method approximately shows the boundary of the zone without taking into account the commutating properties of the brushes. Accordingly, in Fig. 4, curves 1 show the dependence of \(K_2\) on \(I_{\mathrm{я}}\) and \(n\) without taking into account the commutating properties of the brushes, and curves 2 with them taken into account.

From Figs. 3 and 4 it is evident that the principal difference in the CU of machines with ordinary commutation and with VMC consists in the sharp decrease of CU with increasing armature current and rotational speed under ordinary commutation, and in its independence of them under VMC. On the whole, the results of the experimental determination of the CU of the machine with VMC agree well with the theoretical concepts of the operation of the VMC circuit in Fig. 1.

Conclusions

1. Determining commutation stability through the coefficients \(K_1\) and \(K_2\) as functions of the armature current and rotational speed makes it possible objectively to evaluate and compare the commutation stability of machines with an asymmetric sparkless zone in static and dynamic operating conditions.

2. The principal advantage of machines with VMC, in comparison with machines of conventional design, lies in the independence of commutation stability from the armature current and rotational speed when these vary over wide limits. The limitations are imposed mainly by saturation of the magnetic circuit (at very high armature currents) and by instability of contact between the brushes and the commutator (usually at speeds considerably above rated speed). The disadvantages of machines with VMC include a lower commutation stability at small armature currents and rotational speeds than in conventional machines.

3. The principal factors affecting commutation stability include: the active resistance of the armature sections, the commutating properties of the brushes, saturation, mechanical factors, dynamic operating conditions, and penetration of the main field into the commutation zone.

Among the factors that reduce commutation stability, there are none whose influence cannot in principle be reduced by known methods and that would call into question the serviceability of the VMC circuit.

References

1. V. T. Kas’yanov. Regulation of the additional poles of direct-current machines. Elektrichestvo, 1934, No. 20; 1935, No. 1.

2. V. V. Ivashin, I. A. Miloradov. Commutation stability of direct-current motors and its relation to the sparkless-operation zone. Izvestiya TPI, vol. 190, 1968.

3. O. A. Bratkovskii, V. V. Ivashin, I. A. Miloradov. Experimental verification of a direct-current machine with valve-mechanical commutation. Izvestiya TPI, vol. 212, 1969.