STUDY OF THE INFLUENCE OF THE MAIN FIELD ON THE COMMUTATION OF A MACHINE WITH AUXILIARY VALVES

V. V. Ivashin, I. A. Miloradov

(Presented by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering)

In [1] it is shown that the relative width of the sparkless-operation zone of a machine with valve-brush commutation, determined without taking into account the influence of the main field and the real properties of the brush contact, does not depend on the load; in the axes \(i_{\mathrm{п}} = f(I_{\mathrm{я}})\) the zone has the form of a trumpet: at a load current equal to zero, \(i_{\mathrm{п}}=0\); as the load increases, the upper and lower boundaries of the zone diverge uniformly \((1—1'\), Fig. 2).

In real machines, the field of the main poles is always present in the commutation zone. And if in machines without slot skew the effect of the main field may be neglected, then in machines with slot skew this is impermissible, since in this case the emf induced by the main field in the commutating section can cause a noticeable distortion of the sparkless zone. This applies above all to low-load conditions, when the commutating emf from the auxiliary poles is small and comparable with the emf from the main field.

Let us consider the influence of the main field on commutation, first making a number of assumptions:

1. The emf of the sections due to the auxiliary poles is constant throughout the entire commutation period.
2. The commutation conditions of all armature sections are identical.
3. The active resistance of the section is equal to zero.
4. There is no mutual inductive coupling of the sections.
5. The brushes do not possess commutating properties.
6. The excitation current and the rotational speed are constant.
7. The main field induces in the commutating section an emf independent of load, equal to the emf from the main field in the ideal no-load mode.

Under these assumptions it is possible to give only an approximate quantitative estimate of the influence of the main field on commutation, but it is nevertheless possible to draw some general conclusions regarding the qualitative change in the sparkless-operation zone under the action of the main field.

The emf of the section due to the field of the main poles as a function of time \(U_{\mathrm{г}}(t)\) is shown in Fig. 1 and in the general case has a nonlinear character. The action of the main field on commutation is determined by the integral

\[ \int_{0}^{T} U_{\mathrm{г}}(t)\,dt, \]

here \(T\) is the period of current commutation in the section. Obviously, the sign and magnitude of this integral depend on the position of the commutation period relative to the point at which the e.m.f. from the main field passes through zero. We shall agree to regard as positive that direction of the e.m.f. in the commutating section due to the commutating poles in the absence of auxiliary supply, i.e., if the e.m.f. is positive, it is always applied to the valve in the blocking direction [2]. The direction of the e.m.f. from the main field during commutation may vary and

Fig. 1. E.m.f. from the main field in the commutation zone.

depending on the sign of the integral \(\displaystyle \int_0^T U_\Gamma(t)\,dt\), the main field will either strengthen or weaken the commutating poles and distort the sparkless-operation zone. If, for example, at the upper boundary of the zone, where the commutation period is \(T_1\), the integral \(\displaystyle \int_0^{T_1} U_\Gamma(t)\,dt\) is positive, then the main field strengthens the field of the commutating poles and, consequently, the upper boundary of the zone is shifted somewhat into the region of negative excitations. At the lower boundary of the zone, where the period of current commutation in the section is \(T_2\), a positive sign of the integral \(\displaystyle \int_0^{T_2} U_\Gamma(t)\,dt\) likewise means a shift of the lower boundary of the zone into the region of negative currents of the auxiliary supply, while a negative sign, on the contrary, shifts it into the region of positive excitations, since in the first case the commutating poles are strengthened on average, and in the second they are weakened.

With the assumptions made above, for the current in the armature section one may write

\[ L\frac{di}{dt}=U=e+U_\Gamma(t). \tag{1} \]

Here \(i\) is the section current,
\(e\) is the e.m.f. in the section due to the commutating poles,
\(U\) is the total e.m.f. of the section

\[ i=\frac{e}{L}t+\frac{1}{L}\int_0^t U_\Gamma(t)\,dt-i_a. \tag{2} \]

The current in the trailing commutator segment is

\[ i_k=i_a-i=2i_a-\frac{e}{L}t-\frac{1}{L}\int_0^t U_\Gamma(t)\,dt. \tag{3} \]

From equation (3) it is clear that even in the absence of active resistance the current varies nonlinearly, which is associated with the character of the distribution of the e.m.f. from the main field in the commutation zone.

If the e.m.f. from the commutating poles is represented in the form

\[ e=k_0\cdot 2i_a+k_1 i_n, \tag{4} \]

then, solving (3) and (4) jointly, one can find the supplementary-supply current for the upper boundary of the zone

\[ i_{n1}=2i_a\left(\frac{L}{k_1T_1}-\frac{K_0}{k_1}\right) -\frac{1}{k_1T_1}\int_0^{T_1} U_r(t)\,dt \tag{5} \]

and for the lower boundary of the zone

\[ i_{n2}=2i_a\left(\frac{L}{k_1T_2}-\frac{K_0}{k_1}\right) -\frac{1}{k_1T_2}\int_0^{T_2} U_r(t)\,dt. \tag{6} \]

The supplementary-supply currents are found from the condition that the current in the commutator bar is equal to zero at the instant when the main brush is switched off (upper boundary of the zone) and when the auxiliary brush is switched off (lower boundary of the zone) [2]. It follows from equations (5) and (6) that the supplementary-supply current consists of two components, the first of which determines the sparkless zone in the absence, in the commutation zone, of the main field

\[ (1—1' \text{ in Fig. 2}). \]

The second component

\[ \frac{1}{k_1T}\int_0^T U_r(t)\,dt \]

reflects the influence of the main field of the machine and shows the magnitude of the displacement of the boundaries of the sparkless-operation zone.

In the general case

\[ \frac{1}{k_1T_1}\int_0^{T_1} U_r(t)\,dt \ne \frac{1}{k_1T_2}\int_0^{T_2} U_r(t)\,dt, \]

therefore the upper and lower boundaries of the zone are displaced by different amounts and intersect at some load current.

The sparkless-operation zone, found from (5) and (6), for a particular distribution of the emf from the main field in the commutation zone is shown in Fig. 2 (ed—the upper boundary of the zone, mf—the lower boundary of the zone). The coordinates of the point of intersection of the zone boundaries (a, Fig. 2) are determined by the equality \(i_{n1}=i_{n2}\).

Equation (3) for the current in the commutator bar and the equations (5) and (6) derived from it for calculating the sparkless zone do not take into account the nonlinear properties of the commutating circuit that arise because of the presence of the auxiliary valve. Obviously, at the upper boundary of the zone there is no need to take the nonlinearity into account, since in this case the section is short-circuited by the main brush, bypassing the valve. Therefore the upper boundary of the zone is in any case determined by equation (5).

When the machine operates at the lower boundary of the zone, the valve is included in the section circuit in series, and the character of the change of current in the commutator bar has a substantial effect on the operation of the circuit.

Let us consider the time derivative of the current of the commutator bar at the instant when the auxiliary brush is switched off \((t_2)\):

\[ \left(\frac{di_k}{dt}\right)_{t=t_2} = -\frac{e_2}{L}-\frac{U_2}{L}. \tag{7} \]

Here \(U_2\) is the emf from the main field at the instant \(t_2\),

\(e_2\) is the emf from the interpoles at which the current in the commutator bar, determined by equation (3), becomes equal to zero precisely at the instant when the auxiliary brush is switched off. At large loads, when \(e_2\) is large, the derivative is always negative, since \(|U_2|<e_2\); the bar current decreases throughout the entire commutation period.

of section \(T_2\). At small loads, when \(e_2\) is comparable in magnitude with \(U_2\), the sign of the derivative
\[ \left(\frac{di_k}{dt}\right)_{t=t_2} \]
may change; the magnitude of the load at which this occurs depends on the magnitude and sign of the voltage \(U_2\).

Under the condition \(i_k=0\) at the instant \(t_2\), a change in the sign of the derivative means that the bar current, according to equation (3), passes through zero twice during the commutation period: at the instant \(t=t_2\) and somewhat earlier. A change in the sign of the current derivative at the instant \(t_2\) is accompanied by a change in the direction of the resultant e.m.f. in the section from positive to negative. Equation (3), as indicated above, was derived without taking into account the nonlinear properties of the commutating circuit. When the actual properties of the valve are taken into account, the current in the bar is determined by equation (3) throughout the commutation period only until its derivative changes sign. At small loads, at the instant when the bar current first passes through zero, the valve closes and remains in this state until the resultant e.m.f. of the section changes direction. It then is applied to the valve in the forward direction; the valve opens, and the switching-off of the auxiliary brush is accompanied by sparking, although according to equation (3) \(i_k=0\) precisely at the instant \(t_2\).

Thus, at small loads the condition \(i_k=0\) at the instant of switching off the auxiliary brush is insufficient for sparkless operation of the machine. It is necessary that the derivative of the bar current according to equation (7) be less than or equal to zero.

In this case the e.m.f. of the section does not change direction during the entire commutation period, and the valve remains closed.

If the load at which
\[ \left(\frac{di_k}{dt}\right)_{t=t_2}=0 \]
already at the supplementary-supply current found from equation (6) is regarded as critical, then at smaller loads the lower boundary of the zone is determined by the equality:
\[ \left(\frac{di_k}{dt}\right)_{t=t_2} = -\frac{e_2}{L}-\frac{U_2}{L}=0. \tag{8} \]

Hence
\[ i'_{n2}=-2i_a\frac{k_0}{k_1}-\frac{U_2}{k_1}. \tag{9} \]

Here \(i'_{n2}\) is the supplementary-supply current at the lower boundary of the sparkless zone for loads smaller than the critical one. For any distribution of the e.m.f. from the main field in the commutation zone, sparkless switching-off of the auxiliary brush at small loads requires a certain strengthening of the interpoles as compared with the data obtained from equation (6), i.e. \(i'_{n2}>i_{n2}\).

The zone of sparkless operation, constructed with allowance for the actual properties of the valve, is shown in Fig. 2. In this figure \(I_k\) is the critical load, and \(I_v\) is the load current at which the upper and lower boundaries of the zone intersect. The critical load is determined by the simultaneous solution of equations (6) and (8), since at point \(k\), \(i_{n2}=i'_{n2}\).

In Fig. 2 the lines \(de\) and \(ckf\) correspond to the limiting supplementary-supply currents at which, respectively, the main and auxiliary brushes operate without sparking. The region bounded by the broken line \(eb, kf\) is the sparkless zone of the machine. In the region \(cbd\) both brushes operate with sparking. The point of intersection of the zone boundaries is characterized by the fact that, at the current \(I_v\), the bar current passes through zero at the instant the main brush is switched off and, at the same time, condition (8) is satisfied. At currents less than \(I_v\), it is impossible to achieve sparkless operation of the machine by changing the supplementary-supply current.

Fig. 2. Theoretical sparkless-operation zone.

It is not difficult to show that the point of intersection of the zone boundaries is always located to the right of the axis of the auxiliary-supply current, i.e., \(I_{\mathrm{B}}>0\). This means that, in the presence of the main field in the commutation zone, sparkless operation of the machine is impossible over the entire load range from \(2i_a=0\) and above.

It was indicated above that, when the main field is taken into account, the auxiliary-supply currents consist of two components: the auxiliary-supply current in the absence of the main field and the auxiliary-supply current “compensating” the main field. Obviously, the same will also hold in the case when the active resistance of the section is not zero and there is mutual inductive coupling of the commutating sections. But here the auxiliary-supply currents in the absence of the main field must be determined by the general method for calculating the sparkless zone of a machine with auxiliary valves [1]. The auxiliary-supply current “compensating” the main field can, in the first approximation, be determined by the formula derived for the case of zero active resistance:

\[ \frac{1}{k_1 T}\int_{0}^{T} U_{\mathrm{r}}(t)\,dt . \tag{10} \]

At a load below the critical value and with a nonzero active resistance of the section, the auxiliary-supply current must also be such that the total e.m.f. of the section does not change direction at the moment when the auxiliary brush is switched off; this, as was shown above, is achieved when equality (8) is fulfilled.

Taking these considerations into account, the sparkless-operation zone was calculated for an experimental machine, the main data of which are given in [2].

In doing so, the actual distribution of the e.m.f. from the main field in the commutation zone was approximated by a straight line. The results of the calculation are shown in Fig. 3, where \(1—1'\) is the sparkless-operation zone, po-

Fig. 3.

1—1′ — the sparkless-operation zone obtained experimentally; 2—2′ — the calculated sparkless-operation zone.

As can be seen from this figure, the agreement between the calculated and experimental zones is quite good.

Conclusions

1. The presence of the main field in the commutation zone generally leads to a displacement of the sparkless-operation zone upward or downward from the armature-current axis.

2. The e.m.f. due to the main field makes sparkless operation of the machine impossible over the entire load range: at small loads the zone is absent.

3. The design, manufacture, and adjustment of machines must be carried out so that the armature current at the point of intersection of the boundaries of the sparkless-operation zone is less than the actual no-load current.

4. The proposed method for taking account of the main field quite fully reflects the processes occurring in the machine. The calculation results agree well with experimental data.

Literature

1. V. V. Ivashin, I. A. Miloradov. Study of the sparkless-operation zones of a direct-current motor with brush-valve commutation, Izvestiya TPI, vol. 172, 1967.

2. V. V. Ivashin, I. A. Miloradov. On valve-mechanical commutation of direct-current machines, Izvestiya TPI, vol. 160, 1966.