Investigation of Sparkless Operation Zones of a DC Motor with Brush–Valve Commutation

V. V. Ivashin, I. A. Miloradov

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

The calculation of commutation in a direct-current machine with auxiliary valves, the operating principle of which is set forth in [1], consists in determining the brush dimensions and their relative arrangement that are optimal from the standpoint of commutation, and in determining the sparkless-operation zone characterizing the commutational reliability of the machine.

To determine the region of sparkless operation, it is necessary to find the limiting commutating e.m.f.’s at which a machine with the selected geometry of the commutator–brush assembly operates without sparking. In ordinary machines such a problem is extremely complicated because of the properties of the brush contact.

In a machine with auxiliary valves, the sparkless-operation zone is determined primarily by the position and width of the brushes. It is shown in [1] that, if the commutating properties of the brushes are neglected, then sparking at the upper boundary of the sparkless zone (under the main brush) will begin as soon as the period of commutation of the current in a section, determined by the magnitude of the commutating e.m.f., becomes less than the time during which the section is short-circuited by the main brush.

Sparking of the auxiliary brush determines the lower boundary of the zone and begins when the period of commutation of the current in the section becomes greater than the time during which it is short-circuited by the main and auxiliary brushes.

Thus, to calculate the sparkless zone it is necessary to find the commutating e.m.f.’s at which the section current, while varying, becomes equal to the current of the parallel branch precisely at the instant of disconnection of the main brush (the upper boundary of the zone) and of the auxiliary brush (the lower boundary of the zone). This problem can be solved relatively simply by methods for calculating linear electrical circuits.

Let us first adopt a number of assumptions:

a) The commutating e.m.f. is constant during the commutation period.
b) The magnetic system is unsaturated.
c) The resistance of the end connections is equal to zero.
d) The field of the main poles is absent in the commutation zone.
e) The brushes do not possess commutating properties.
f) The number of sections in a slot is equal to two: in the upper layer of the slot there is located the side of a section short-circuited by a brush of one polarity, and in the lower layer the side of a section short-circuited by a brush of the opposite polarity.

The last three assumptions are connected with the design and fundamental features of the machine with brush–valve commutati-

[1]. Since here we are interested primarily in the sparkless zone in operating conditions close to nominal, assumptions (d) and (e) are fully justified: in machines with auxiliary valves, under nominal conditions the commutating emf is of the order of 15–20 V, and secondary factors do not have a noticeable effect on the accuracy of the calculation.

It is not difficult to show that, in general form, the relative width of the sparkless zone can be written as follows:

\[ \Theta=\frac{F_0}{F_{\mathrm{do}}}\cdot \frac{e_1-e_2}{e_0}. \tag{1} \]

Here \(e_1\), \(e_2\), \(e_3\) are the commutating emf’s, respectively, at the upper and lower boundaries of the zone and in the absence of additional supply to the commutating poles;

\(F_0=ke_0\) is the air-gap ampere-turns under the commutating pole that go into producing the commutating emf \(e_0\), i.e., the calculated air-gap ampere-turns;

\(F_{\mathrm{do}}\) is the total ampere-turns of the commutating pole in the absence of additional supply.

If the zone is located symmetrically with respect to the armature-current axis, then

\[ \Theta^*=2\frac{F_0^*}{F_{\mathrm{do}}^*}\cdot \frac{e_1-e_2}{e_1+e_2}. \tag{2} \]

We shall begin determining the width of the sparkless zone with the simplest case, when only the leakage inductance of the armature sections is taken into account. This sequence makes it possible to establish, by a simple method, certain general regularities.

1. Sparkless zone in the absence of individual couplings and active resistances. For the commutating emf’s one may write:

\[ e_1=L\frac{2i_a}{T_1}; \qquad e_2=L\frac{2i_a}{T_2}; \qquad e_0=L\frac{2i_a}{T_0}. \tag{3} \]

Here

\(T_1\), \(T_2\), \(T_0\) are the periods of current commutation in a section, respectively, at the upper and lower boundaries of the zone and in the absence of additional supply;

\(i_a\) is the current of the parallel branch;

\(T_1\) and \(T_2\), in a machine with ideal geometry, are equal to the periods of short-circuiting of the section by the main brush \((T_1)\) and by the main and auxiliary brushes \((T_2)\).

Substituting (3) into (1), we obtain

\[ \Theta=\frac{F_0}{F_{\mathrm{do}}}\cdot T_0\cdot \frac{T_2-T_1}{T_1\cdot T_2}. \tag{4} \]

Thus, all other conditions being equal, the width of the sparkless zone is determined by the width and position of the brushes and does not depend on the load, since the ratio

\[ \frac{F_0\cdot T_0}{F_{\mathrm{do}}} \]

does not change with a change in load. But the width and position of the zone relative to the armature-current axis depend on the choice of the calculated air-gap ampere-turns. If, at an unchanged armature current, the ampere-turns of the commutating pole are changed, then the product \(F_0T_0=e_0T_0\) does not change; therefore, as the ampere-turns of the commutating pole decrease, the width of the sparkless zone increases, and vice versa. The position of the zone relative to the armature-current axis also changes in this case.

2. Sparkless zone taking mutual inductance into account, but without taking active resistances into account.

The equations of electrical equilibrium for inductively coupled short-circuited circuits have the form:

\[ L\frac{di_1}{dt}+M\frac{di_2}{dt}=e, \tag{5} \]

\[ L\frac{di_2}{dt}+M\frac{di_1}{dt}=e. \tag{6} \]

It follows from the equations that, during the period in which inductive coupling exists, the rates of change of the currents in the inductively coupled sections are identical; and since, in those time intervals when mutual induction is absent, the rate of change of current in both sections increases by the same amount, the periods of current commutation in both sections are identical, although the times at which the sections are short-circuited by the brushes may be different.

Fig. 1.

If the period of commutation of the current \(i_1\) in the section short-circuited by the brushes earlier is equal to \(T\), and the time interval from the beginning of commutation of this section to the beginning of commutation of the section inductively coupled with it is equal to \(T_M\) (Fig. 1), then in the interval during which inductive coupling exists the current of the section varies according to the law

\[ i_1=\frac{e}{L+M}\,t+I_1(\Theta). \tag{7} \]

\(I_1(\Theta)\) is the value of the current at the moment when the action of inductive coupling begins \((t_M)\):

\[ I_1(0)=\frac{e}{L}T_M-i_a. \tag{8} \]

Solving equations (7) and (8) simultaneously and taking into account that for \(t=t_1\), \(i_1=i_a\), we obtain

\[ e=\frac{L(L+M)\cdot 2i_a}{LT+MT_M}. \tag{9} \]

At the upper boundary of the zone \(T=T_1\), and at the lower boundary \(T=T_2\); therefore, for a symmetrical zone we obtain:

\[ \Theta^*=2\frac{F^*_o}{F^*_{\mathrm{do}}}\cdot \frac{L(T_2-T_1)}{L(T_2+T_1)+2MT_M}. \tag{10} \]

The relative width of the zone still does not depend on the load, but now depends not only on the time during which the sections are short-circuited by the brushes, but also

from the interval \(T_m\). Analysis shows that, other conditions being equal, the dependence \(\Theta=f(T_m)\) has the form shown in Fig. 2.

In actual machines, because of unavoidable technological deviations in the manufacture of the commutator, the periods during which different sections are short-circuited by the brushes at the upper and lower boundaries of the zone \((T_1; T_2)\) are not the same. In addition, different pairs of inductively coupled sections have different time intervals between the starts of commutation.

Fig. 2.

In this case, each pair of sections will have its own values of the commutating emf’s at which sparkless switching-off of only these sections is ensured. And for each pair of inductively coupled sections there will be its own value

\[ \frac{F_0}{F_{\text{do}}}, \]

at which the region of sparkless operation of these sections is located symmetrically.

In reality, the ratio

\[ \frac{F_0}{F_{\text{do}}} \]

is the same for all sections of the machine, whereas it is necessary to know the region of sparkless operation of the machine as a whole. In this case, in formula (1) for calculating the zone it is necessary to substitute the minimum commutating emf at the upper boundary of the zone \((e_{1\min})\) for the given machine, obtained with allowance for the actual tolerances in commutator manufacture, and the maximum emf at the lower boundary of the zone \((e_{2\max})\). The emf in the absence of additional supply is determined from the calculated ampere-turns of the air gap. The sparkless zone of the machine obtained in this way will represent a region common to the regions of sparkless switching-off of the individual sections of the machine.

Obviously, the minimum emf at the upper boundary of the zone occurs for the section for which, for example, \(T_1=T_{1\max}\) and simultaneously \(T_m=T_{m\max}\). The maximum emf at the lower boundary is obtained for the section for which \(T_2=T_{2\min}\) and \(T_m=T_{m\min}\).

For different versions of the structural design of the valve-commutation circuit [1], technological tolerances affect the sparkless-operation zone in different ways. In the single-commutator version, the periods during which the sections are short-circuited by the brushes \((T_1; T_2)\) are the same for all sections, and the variability of the commutation conditions of different pairs of inductively coupled sections is explained only by the fact that \(T_m=\mathrm{var}\).

For the two-commutator version, it may also be assumed that the periods during which different sections are short-circuited by the main brushes are identical. But, in addition to the variability of the time interval between the starts of commutation of inductively coupled sections, here it is necessary to take into account the possible unfavorable superposition of tolerances on the main and auxiliary commutators, which may cause inequality of the periods during which the sections are short-circuited by the main and auxiliary brushes \((T_2)\). From this point of view, the single-commutator design is preferable.

In any calculation of the sparkless zone of a machine being newly designed, it is advisable to carry it out in two stages: a) determine the maximum possible sparkless zone for the given machine, which is obtained if the commutator is manufactured with zero tolerances; b) determine the minimum possible zone under the most unfavorable distribution of tolerances.

In the manufactured machine the width of the sparkless zone will assume some intermediate value.

3. Sparkless zone with allowance for active resistances. The expressions for the commutating emf’s at the upper and lower boundaries of the zone are complicated functions of the form

\[ e=i_a \cdot r \cdot f(r,L,M,T_1,T_2,T_M) \tag{11} \]

and are not given here.

Let us note that when \(r \ne 0\), the periods of current commutation in inductively coupled sections, if the sections begin to commutate at different times, are not identical: the period of current commutation in the section that begins commutation later is shorter. This is connected with the effect on commutation of the voltage drop across the active resistance [2].

Therefore the limiting commutating emf at the upper boundary of the sparkless zone must be determined from the sparkless switching-off of the section that is short-circuited by the brushes later than the section inductively coupled with it. Conversely, at the lower boundary of the zone the commutating emf is determined by the section that begins commutation earlier.

As calculations have shown, the influence of active resistance on the zone of sparkless operation at rated rotational speed is insignificant; therefore, in most cases it may be neglected, and the calculation is then considerably simplified.

Using the proposed method, the relative width of the sparkless zone was calculated for the experimental machine. In the rated mode the calculation gave a value of 18%, whereas the actual width of the zone was 20%. In this case the brush dimensions and winding data were somewhat different from those in the first experiments [1].

Conclusions

1. Under the assumptions made, the relative width of the zone of sparkless operation does not depend on load.

2. The width and position of the sparkless zone depend on the choice of the calculated ampere-turns of the air gap.

3. The calculation of the sparkless zone must be carried out with allowance for the technological tolerances in manufacturing the commutator.

4. The zone of sparkless operation of a motor with auxiliary valves in regimes close to the rated one can be calculated with sufficient accuracy by the proposed method.

References

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

2. O. G. Wegner. Theory and Practice of Commutation of Direct-Current Machines, Gosenergoizdat, 1961.