Theory and Calculation of Electrical Apparatus (1917) — part 15 of 21

The compensating winding, or the “cross held,” thus fulfils the twofold purpose of reducing the armature self-inductance to that of the leakage flux, and of neutralizing the armature reac- tion and thereby permitting the use of very high armature am pore-turns.

The main purpose of the compensating winding thus is to de- crease the armature self-inductance; that is, increase the effect- ive armature reluctance and thereby its ratio to the field reluc-

Yl\

tame, b, and thus permit the use of a much higher ratio, q = ---,

before maximum power-factor is reached, and thereby a higher power-f actor.

Even with compensating winding, with increasing q, ultimately a point is reached where the armature self-inductance equals the field self-inductance, and beyond this the power-factor again decreases. It becomes possible, however, by the use of the com- pensating winding, to reach, with a mechanically good design, values of & as high as 16 to 20.

Assuming 6 = 16 gives, substituted in (11) and (12):

q = 4;

338

ELECTRICAL APPARATUS

that is, four times as many armature turns as field turns, = 4 n 0 and :

f

tan do =

AJ 0

hence, at synchronism:

/o = / : tan 0 O = 0.5, or 89 per cent, power-factor.

At double synchronism, which about represents maximum motor speed at 25 cycles :

fo = 2 / : tan 6o = 0.25, or 98 per cent, power-factor;

that is, very good power-factors can be reached in the single- phase commutator motor by the use of a compensating winding, far higher than are possible with the same air gap in polyphase induction motors.

III. Field Winding and Compensating Winding

192. The purpose of the field winding is to produce the maxi- mum magnetic flux, $, with the minimum number of turns, n Q . This requires as large a magnetic section, especially at the air gap, as possible. Hence, a massed field winding with definite polar projections of as great pole arc as feasible, as shown in Fig. 157, gives a better power-factor than a distributed field winding.

The compensating winding must be as closely adjacent to the armature winding as possible, so as to give minimum leakage flux between armature conductors and compensating conductors, and therefore is a distributed winding, located in the field pole faces, as shown in Fig. 157.

The armature winding is distributed over the whole circum- ference of the armature, but the compensating winding only in the field pole faces. With the same ampere-turns in armature and compensating winding, their resultant ampere-turns are equal and opposite, and therefore neutralize, but locally the two windings do not neutralize, due to the difference in the distribu- tion curves of their m.m.fs. The m.m.f. of the field winding is constant over the pole faces, and from one pole corner to the next pole corner reverses in direction, as shown diagrammatically by F in Fig. 158, which is the development of Fig. 157. The m.m.f. of the armature is a maximum at the brushes, midway between the field poles, as shown by A in Fig. 158, and from there decreases to zero in the center of the field pole. The m.m.f. of

SINGLE-PHASE COMMUTATOR MOTORS 339

the compensating winding, however, is constant in the space from pole corner to pole corner, as shown by C in Fig. 158, and since the total m.m.f. of the compensating winding equals that of the armature, the armature m.m.f. is higher at the brushes, the compensating m.m.f. higher in front of the field poles, as shown by curve R in Fig. 158, which is the difference between A and C; that is, with complete compensation of the resultant armature and compensating winding, locally undercompensation exists at the brushes, overcompensation in front of the field

Fig. 158. — Distribution of m.m.f. in compensated motor.

poles. The local undercompensated armature reaction at the brushes generates an e.m.f. in the coil short-circuited under the brush, and therewith a short-circuit current of commutation and sparking. In the conductively compensated motor, this can be avoided by overcompensation, that is, raising the flat top of the compensating m.m.f. to the maximum armature m.m.f., but this results in a lowering of the power-factor, due to the self- inductive flux of overcompensation, and therefore is undesirable.

193 . To get complete compensation even locally requires the compensating winding to give the same distribution curve as the armature winding, or inversely. The former is accomplished by distributing the compensating winding around the entire cir- cumference of the armature, as shown in Fig. 159. This, how- ever, results in bringing the field coils further away from the armature surface, and so increases the magnetic stray flux of the field winding, that is, the magnetic flux, which passes through the field coils, and there produces a reactive voltage of self-in-

j

340 ELECTRICAL APPARATUS

ductance, but does not pass through the armature conductors, and so does no work; that is, it lowers the power factor, just as over compensation would do. . The distribution curve of the

armature winding can, however, be made equal to that of the compen- sating winding, and therewith local complete compensation secured, by using a fractional pitch armature winding of a pitch equal to the pole arc. In this case, in the space be- tween the pole corners, the currents are in opposite direction in the upper and the lower layer of con- ductors in each armature slot, as shown in Fig. 160, and thus neutralize magnetically; that is, the armature reaction extends only over the space of the' armature circumference covered by the pole arc, where it is neutralized by the compensating winding in the pole face.

To produce complete compensation even locally, without im- pairing the power-factor, therefore, requires a fractional-pitch

Fig. 160. — Fractional pitch arma- Fig. 161. — Repulsion motor with ture winding. massed winding.

armature winding, of a pitch equal to the field pole arc, or some equivalent arrangement.

Historically, the first compensated single-phase commutator motors, built about 20 years ago, were Prof. Elihu Thomson's repulsion motors. In these the field winding and compensating

Fig. 159. — Completely distributed compensating winding. *

4

SINGLE-PHASE COMMUTATOR MOTORS

341

winding were massed together in a single coil, as shown diagram- matically in Fig. 161. Repulsion motors are still occasionally- built in which field and compensating coils are combined in a single distributed winding, as shown in Fig. 162. Soon after the first repulsion motor, conductively and inductively compensated series motors were built by Eickemeyer, with a massed field winding and a separate compensating winding, or cross eoi], either as single coil or turn or distributed in a number of coils or turns, as shown diagrammatically in Fig. 163, and by W. Stanley.

Fig. 162 . — Repulsion motor with distributed winding.

For reversible motors, separate field coils and compensating coils are always used, the former as massed, the latter as dis- tributed winding, since in reversing the direction of rotation either the field winding alone must be reversed or armature and compensating winding are reversed while the field winding re- mains unchanged.

IV. Types of Varying-speed Single-phase Commutator Motors

194 . The armature and compensating windings are in induc- tive relations to each other. In the single-phase commutator motor with series characteristic, armature and compensating windings therefore can be connected in series with each other, or the supply voltage impressed upon the one, the other closed upon itself as secondary circuit, or a part of the supply voltage im- pressed upon the one, and another part upon the other circuit, and in either of these cases the field winding may be connected in series either to the compensating winding or to the armature winding. This gives the motor types, denoting the armature by

SINGLE-PHASE COMMUTATOR MOTOI^S 343

A , the compensating winding by C, and the field winding by F, shown in Fig. 164.

Primary

Secondary

A + F

Series motor.

A +C + F

. . .

Conductively compensated

series motor. (1)

A+F

c

Inductively compensated

series motor. (2)

A

C + F

Inductively compensated

series motor with second- ary excitation, or inverted repulsion motor. (3)

C + F

A

Repulsion motor. (4)

C

A +F

Repulsion, motor with sec-

ondary excitation. (5)

A +F,C

• • • l

Series repulsion motors.

A,C +F

... J

(6) (7)

Since in all these motor types all three circuits are connected directly or inductively in series with each other, they all have . the . same general characteristics as the direct-current series motor; that is, a speed which increases with a decrease of load, and a torque per- ampere input which increases with increase of current, and therefore with decrease of speed, and the different motor types differ from each other only by their commutation as affected by the presence or absence of a . magnetic flux at the brushes, and indirectly thereby in their efficiency as affected by commutation losses.

In the conductively compensated series motor, by the choice of the ratio of armature and compensating turns, overcompensa- . tion, complete compensation, or undercompensation can be pro- duced. In all the other types, armature and compensating windings are in inductive relation, and the compensation there- fore approximately complete.

A second series of motors of the same varying speed charac- teristics results by replacing the stationary field coils by arma- ture excitation, that is, introducing the current, either directly or by transformer, into the armature by means of a second set of brushes at right angles to the main brushes. Such motors are used to some extent abroad. They have the disadvantage of

344

ELECTRICAL APPARATUS

requiring two sets of brushes, but the advantage that their power-factor can be controlled and above synchronism even leading current produced. Fig. 165 shows diagrammatically such a motor, as designed by Winter-Eichberg-Latour, the so-called compensated repulsion motor. In this case, compensated means compensated for power-factor.

The voltage which can be used in the motor armature is limited by the commutator: the voltage per commutator segment is limited by the problem of sparkless commutation, the number

of commutator segments from brush to brush is limited by mechanical consideration of commutator speed and width of segments. In those motor types in which the supply cur- rent traverses the armature, the supply voltage is thus limited to values even lower than in the direct-current motor, while in the repulsion motor (4 and ,5), in which the armature is the secondary circuit, the armature voltage is independent of • the supply voltage, so can be chosen to suit the requirements of commutation, while the motor can be built for any supply voltage for which the stator can economically be insulated.

Alternating-current motors as well as direct-current series motors can be controlled by series parallel connection of two or more motors. Further control, as in starting, with direct-current motors is carried out by rheostat, while with alternating-current motors potential control, that is, a change of supply voltage by transformer or auto transformer, offers a more efficient method of control. By changing from one motor type to another motor type, potential control can be used in alternating-current motors without any change of supply voltage, by appropriately choosing the ratio of turns of primary and secondary circuit. For in- stance, with an armature wound for half the voltage and thus

twice the current as the compensating winding ^ratio of turns

~ = 2^ , a change of connection from type 3 to type 2, or from • type 5 to type 4, results in doubling the field current and there-

Pig. 165. — Type of alternating-cur- rent commutating motor.

SINGLE-PHASE COMMUTATOR MOTORS 345

with the field strength. A change of distribution of voltage be- tween the two circuits, in types 6 and 7, with A and C wound for different voltages, gives the same effect as a change of supply voltage, and therefore is used for motor control.

195 . In those motor types in which a transformation of power occurs between compensating winding, C, and armature winding,

A, a transformer flux exists in the direction of the brushes, that is, at right angles to the field flux. In general, therefore, the single-phase commutator motor contains two magnetic fluxes in quadrature position with each other, the main flux or field flux,

<E>, in the direction of the axis of the field coils, or at right angles to the armature brushes, and the quadrature flux, or transformer flux, or commutating flux, $ 1 , in line with the armature brushes, or in the direction of the axis of the compensating winding, that is, at right angles (electrical) with the field flux.

The field flux, $, depends upon and is in phase with the field current, except as far as it is modified by the magnetic action of the short-circuit current in the armature coil under the commu- tator brushes.

In the conductively compensated series motor, 1, the quad- rature flux is zero at complete compensation, and in the direc- tion of the armature reaction with undercompensation, in oppo- sition to the armature reaction at overcompensation, but in .either case in phase with the current and so approximately with the field.

In the other motor types, whatever quadrature flux exists is . not in phase with the main flux, but as transformer flux is due to the resultant m.m.f. of primary and secondary circuit.

In a transformer with non-inductive or nearly non-inductive secondary circuit, the magnetic flux is nearly 90° in time phase behind the primary current, a little over 90° ahead, of the sec- ondary current, as shown in transformer diagram, Fig. 166.

In a transformer with inductive secondary, the magnetic flux is less than 90° behind the primary current, more than 90° ahead of the secondary current, the more so the higher is the inductivity of the secondary circuit, as shown by the transformer diagram, Fig. 166.

Herefrom it follows that:

' In the inductively compensated series motor, 2, the quad- rature flux is very small and practically negligible, as very little voltage is consumed in the low impedance of the secondary cir- cuit, C; whatever flux there is, lags behind the main flux.

346

ELECTRICAL APPARATUS

In the inductively compensated series motor with secondary excitation, or inverted repulsion motor, 3, the quadrature flux, 4>i, is quite large, as a considerable voltage is required for the field excitation, especially at moderate speeds and therefore high currents, and this flux, $i, lags behind the field flux, $, but this lag is very much less than 90°, since the secondary circuit is

Fig. 106. — Transformer diagram, inductive and non-inductive load.

highly inductive; the motor field thus corresponding to the con- ditions of the transformer diagram, Fig. 166. As result hereof, the commutation of this type of motor is very good, flux, $ 1 , having the proper phase and intensity required for a commu- tating flux, as will be seen later, but the power-factor is poor.

In the repulsion motor, 4, the quadrature flux is very consid- erable, since all the voltage consumed by the rotation of the armature is induced in it by transformation from the compen-

SINGLE-PHASE COMMUTATOR MOTORS 347

sating winding, and this quadrature flux, $ 1 , lags nearly 90° be- hind the main flux, <£, since the secondary circuit is nearly non- inductive, especially at speed.

In the repulsiqn motor with secondary excitation, 5, the quad- rature flux, 4>i, is also very large, and practically constant, corre- sponding to the impressed e.m.f., but lags considerably less than 90° behind the main flux, 4>, the secondary circuit being induct- ive, since it contains the field coil, F. The lag of the flux, 4>i, increases with increasing speed, since with increasing speed the e.m.f. of rotation of the armature increases, the e.m.f. of self- inductance of the field decreases, due to the decrease of current, and the circuit thus becomes less inductive.

The series repulsion motors 6 and 7, give the same phase rela- tion of the quadrature flux, #i, as the repulsion motors, 5 and 6, but the intensity of the quadrature flux, <3?i, is the less the smaller the part of the supply voltage which is impressed upon the com- pensating winding.

V. Commutation

196. In the commutator motor, the current in each armature coil or turn reverses during its passage under the brush. In the armature coil, while short-circuited by the commutator brush, the current must die out to zero and then increase again to its original value in opposite direction. The resistance of the arma- ture coil and brush contact accelerates, the self-inductance re- tards the dying out of the current, and the former thus assists, the latter impairs commutation. If an e.m.f. is generated in the armature coil by its rotation while short-circuited by the commutator brush, this e.m.f. opposes commutation, that is, retards the dying out of the current, if due to the magnetic flux of armature reaction, and assists commutation by reversing the armature current, if due to the magnetic flux of overcompensa- tion, that is, a magnetic flux in opposition to the armature reaction.

Therefore, in the direct-current commutator motor with high field strength and low armature reaction, that is, of negligible magnetic flux of armature reaction, fair commutation is produced with the brushes set midway between the field poles — that is, in the position where the armature coil which is being commu- tated encloses the full field flux and therefore cuts no flux and has no generated e.m.f. — by using high-resistance carbon brushes,

348

ELECTRICAL APPARATUS

as the resistance of the brush contact, increasing when the arma- ture coil begins to leave the brush, tends to reverse the current. Such “resistance commutation” obviously can not be perfect; perfect commutation, however, is produced by impressing upon the motor armature at right angles to the main field, that is, in the position of the commutator brushes, a magnetic field oppo- site to that of the armature reaction and proportional to the armature current. Such a field is produced by overcompensa- tion or by the use of a commutating pole or interpole.

As seen in the foregoing, in the direct-current motor the counter e.m.f. of self-inductance of commutation opposes the reversal of current in the armature coil under the commutator brush, and this can be mitigated in its effect by the use of high-resistance brushes, and overcome by the commutating field of overcompen- sation. In addition hereto, however, in the alternating-current commutator motor an e.m.f. is generated in the coil short-cir- cuited under the brush, by the alternation of the magnetic flux, and this e.m.f., which does not exist in the direct-current motor, makes the problem of commutation of the alternating-current motor far more difficult. In the position of commutation no e.m.f. is generated in the armature coil by its rotation through the magnetic field, as in this position the coil encloses the maxi- mum field flux; but as this magnetic flux is alternating, in this position the e.m.f. generated by the alternation of the flux en- closed by the coil is a maximum. This “e.m.f. of alternation” lags in time 90° behind the magnetic flux which generates it, is proportional to the magnetic flux and to the frequency, but is independent of the speed, hence exists also at standstill, while the “e.m.f. of rotation” — which is a maximum. in the position of the armature coil midway between the brushes, or parallel to the field flux — is in phase with the field flux and proportional thereto and to the speed, but independent of the frequency. In the alternating-current commutator motor, no position therefore exists in which the armature coil is free from a generated e.m.f., but in the position parallel to the field, or midway between the brushes, the e.m.f. of rotation, in phase with the field flux, is a maximum, while the e.m.f. of alternation is zero, and in the posi- tion under the commutator brush, or enclosing the total field flux, the e.m.f. of alternation, in electrical space quadrature with the field flux, is a maximum, the e.m.f. of rotation absent, while in any other position of the armature coil its generated e.m.f. has

SINGLE-PHASE COMMUTATOR MOTORS

349

a component due to the rotation — a power e.m.f. — and a com- ponent due to the alternation — a reactive e.m.f. The armature coils of an alternating-current commutator motor, therefore, are the seat of a system of polyphase e.m.fs., and at synchronism the polyphase e.m.fs. generated in all armature coils are equal, above synchronism the e.m.f. of rotation is greater, while below synchronism the e.m.f. of alternation is greater, and in the latter case the brushes thus stand at that point of the com- mutator where the voltage between commutator segments is a maximum. This e.m.f. of alternation, short-circuited by the armature coil in the position of commutation, if not controlled, causes a short-circuit current of .excessive value, and therewith destructive sparking; hence, in the alternating-current commuta- tor motor it is necessary to provide means to control the short- circuit current under the commutator brushes, which results from the alternating character of the magnetic flux, and which does not exist in the direct-current motor; that is, in the alternating- current motor the armature coil under the brush is in the posi- tion of a short-circuited secondary, with the field coil as primary of 'a transformer; and as in a transformer primary and secondary ampere-turns are approximately equal, if n 0 — number of field turns per pole and i = field current, the current in a single arma- ture turn, when short-circuited by the commutator brush, tends to become io = n 0 i, that is, many times full-load current; and as this current is in opposition, approximately, to the field cur- rent, it would demagnetize the field; that is, the motor field vanishes, or drops far down, and the motor thus loses its torque. Especially is this the case at the moment of starting; at speed, the short-circuit current is somewhat reduced by the self-induc- tance of the armature turn. That is, during the short time during which the armature turn or coil is short-circuited by the brush the short-circuit current can not rise to its full value, if the speed is considerable, but it is still sufficient to cause destruc- tive sparking.

197. The character of the commutation of the motor, and therefore its operativeness, thus essentially depends upon the value and the phase of the short-circuit currents under the com- mutator brushes. An excessive short-circuit current gives de- structive sparking by high-current density under the brushes and arcing at the edge of the brushes due to the great and sud- den change of -current in the armature coil when leaving the

350

ELECTRICAL APPARATUS

brush. But even with a moderate short-circuit current, the sparking at the commutator may be destructive and the motor therefore inoperative, if the phase of the short-circuit current greatly differs from that of the current in the armature coil after it leaves the brush, and so a considerable and sudden change of

Fig. 167. — E.m.f. consumed at contact of copper brush.

current must take place at the moment when the armature coil leaves the brush. That is, perfect commutation occurs, if the short-circuit current in the armature coil under the commutator brush at the moment when the coil leaves the brush has the same value and the same phase as the main-armature current in

Fig. 168. — E.m.f. consumed at contact of high-resistance carbon brush.

the coil after leaving the brush. The commutation of such a motor therefore is essentially characterized by the difference between the main-armature current after, and the short-circuit current before leaving the brush. The investigation of the short- circuit current under the commutator brushes therefore is of

SINGLE-PHASE COMMUTATOR MOTORS 351

fundamental importance in the study of the alternating-current commutator motor, and the control of this short-circuit current the main problem of alternating-current commutator motor design.

Various means have been proposed and tried to mitigate or eliminate the harmful effect of this short-circuit current, as high resistance or high reactance introduced into the armature coil during commutation, or an opposing e.m.f. either from the out- side, or by a commutating field.

High-resistance brush contact, produced by the use of very narrow carbon brushes of high resistivity, while greatly improv- ing the commutation and limiting the short-circuit current so that it does not seriously demagnetize the field and thus cause the motor to lose its torque, is not sufficient, for the reason that the resistance of the brush contact is not high enough and also is not constant. The brush contact resistance is not of the nature of an ohmic resistance, but more of the nature of a counter e.m.f. ; that is, for large currents the potential drop at the brushes becomes approximately constant, as seen from the volt-ampere characteristics of different brushes given in Figs. 167 and 168. Fig. 167 gives the voltage consumed by the brush contact of a copper brush, with the current density as abscissae, while Fig. 168 gives the voltage consumed by a high-resistance carbon brush, with the current density in the brush as abscissae. It is seen that such a resistance, which decreases approximately in- versely proportional to the increase of current, fails in limiting the current just at the moment where it is most required, that s, at high currents.

Commutator Leads

198 . Good results have been reached by the use of metallic resistances in the leads between the armature and the commuta- tor. As shown diagrammatically in Fig. 169, each commutator segment connects to the armature, A , by a high non-inductive resistance, CB , and thus two such resistances are always in the circuit of the armature coil short-circuited under the brush, but also one or two in series with the armature main circuit, from brush to brush. While considerable power may therefore be consumed in these high-resistance leads, nevertheless the effi- ciency of the motor is greatly increased by their use; that is, the reduction in the loss of power at the commutator by the reduction

352

ELECTRICAL APPARATUS

of the short-circuit current usually is far greater than the waste of power in the resistance leads. To have any appreciable effect, the resistance of the commutator lead must be far higher than that of the armature coil .to which it connects. Of the e.m.f. of rotation, that is, the useful generated e.m.f., the armature re- sistance consumes only a very small part, a few per cent. only. The e.m.f. of alternation is of the same magnitude as the e.m.f. of rotation — higher below, lower above synchronism. With a short-circuit current equal to full-load current, the resistance of

A

j: j}p

miMiOTiirJiir

riiiiiij

TP

Ll

i i f n m i

1 1 °

. * _ i

Fig. 169. — Commutation with resistance leads.

the short-circuit coil would consume only a small part of the e.m.f. of alternation, and to consume the total e.m.f. the short- • circuit current therefore would have to be about as many times larger than the normal armature current as the useful generated e.m.f. of the motor is larger than the resistance drop in the arma- ture. Long before this value of short-circuit current is reached the magnetic field would have disappeared by the demagnetizing force of the short-circuit current, that is, the motor would have lost its torque.

To limit the short-circuit current under the brush to a value not very greatly exceeding full-load current, thus requires a re- sistance of the lead, many times greater than that of the armature coil. The i 2 r in the lead, and thus the heat produced in it, then, is many times greater than that in the armature coil. The space available for the resistance lead is, however, less than that avail- able for the armature coil.

It is obvious herefrom that it is not feasible to build these resistance leads so that each lead can dissipate continuously, or even for any appreciable time, without rapid self-destruction, the heat produced in it while in circuit.

When the motor is revolving, even very slowly, this is not nec- essary, since each resistance lead is only a very short time in

SINGLE-PHASE COMMUTATOR MOTORS

353

circuit, during the moment when the armature coils connecting to it are short-circuited by the brushes; that is, if n\ — number of

2

armature turns from brush to brush, the lead is only — - of the

'Wi

time in circuit, and though excessive current densities in mate- rials of high resistivity are used, the heating is moderate. In starting the motor, however, if it does not start instantly, the current continues to flow through the same resistance leads, and thus they are overheated and destroyed if the motor does not start promptly. Hence care has to be taken not to have such motors stalled for any appreciable time with voltage on.

The most serious objection to the use of high-resistance leads, therefore, is their liability to self-destruction by heating if the motor fails to start immediately, as for instance in a railway motor when putting the voltage on the motor before the brakes are released, as is done when starting on a steep up-grade to keep the train from starting to run back.

Thus the advantages of resistance commutator leads are the improvement in commutation resulting from the reduced short- circuit current, and the absence of a serious demagnetizing effect on the field at the moment of starting, which would result from an excessive short-circuit current under the brush, and such leads are therefore extensively used ; their disadvantage, however, is that when they are used the motor must be sure to start im- mediately by the application of voltage, otherwise they are liable to be destroyed.

It is obvious that even with high-resistance commutator leads the commutation of the motor can not be as good as that of the motor on direct-current supply; that is, such an alternating- current motor inherently is more or less inferior in commutation to the direct-current motor, and to compensate for this effect far more favorable constants must be chosen in the motor design than permissible with a direct-current motor, that is, a lower voltage per commutator segment and lower magnetic flux per pole, hence a lower supply voltage on the armature, and thus a « larger armature current and therewith a larger commutator, etc.

The insertion of reactance instead of resistance in the leads connecting the commutator segments with the armature coils of the single-phase motor also has been proposed and used for limiting the short-circuit current under the commutator brush.

Reactance has the advantage over resistance, that the voltage

23

354

ELECTRICAL APPARATUS

consumed by it is wattless and therefore produces no serious heating and reactive leads of low resistance thus are not liable to self-destruction by heating if the motor fails to start im- mediately.

On account of the limited space available in the railway motor considerable difficulty, however, is found in designing sufficiently high reactances which do not saturate and thus decrease at larger currents.

At speed, reactance in the armature coils is very objectionable in retarding the reversal of current, and indeed one of the most important problems in the design of commutating machines is to give the armature coils the lowest possible reactance. There- fore, the insertion of reactance in the motor leads interferes seriously with the commutation of the motor at speed, and thus requires the use of a suitable commutating or reversing flux, that is, a magnetic field at the commutator brushes of sufficient strength to reverse the current, against the self-inductance of the armature coil, by means of an e.m.f. generated in the armature coil by its rotation. This commutating flux thus must be in phase with the main current, that is, a flux of overcompensation. Reactive leads require the use of a commutating flux of over- compensation to give fair commutation at speed.

Counter E.m.fs. in Commutated Coil

199 . Theoretically, the correct way of eliminating the de- structive effect of the short-circuit current under the commu- tator brush resulting from the e.m.f. of alternation of the main flux would be to neutralize the e.m.f. of alternation by an equal but opposite e.m.f. inserted into the armature coil or generated therein. Practically, however, at least with most motor types, considerable difficulty is met in producing such a neutralizing e.m.f. of the proper intensity as well as phase. Since the alter- nating current has not only an intensity but also a phase displace- ment, with an alternating-current motor the production of com- mutating flux or commutating voltage is more difficult than with direct-current motors in which the intensity is the only variable.

By introducing an external e.m.f. into the short-circuited coil under the brush it is not possible entirely to neutralize its e.m.f. of alternation, but simply to reduce it to one-half. Several such arrangements were developed in the early days by Eickemeyer,

SINGLE-PHASE COMMUTATOR MOTORS 355

for instance the arrangement shown in Fig. 170, which represents the development of a commutator. The commutator consists of alternate live segments, S, and dead segments, S', that is, seg- ments not connected to armature coils, and shown shaded in Fig. 170. Two sets of brushes on the commutator, the one, B i,

Fig. 170. — Commutation with external e.m.f.

ahead in position from the other, B%, by one commutator seg- ment, and connected to the first by a coil, N , containing an e.m.f. equal in phase, but half in intensity, and opposite, to the e.m.f. of alternation of the armature coil; that is, if the armature coil contains a single turn, coil N is a half turn located in the main

Fig. 171. — Commutation by external e.m.f.

77 %

field space; if the armature coil, A, contains m turns, turns in

the main field space are used in coil, N. The dead segments, S', are cut between the brushes, Bi and B%, so as not to short-circuit between the brushes.

In this manner, during the motion of the brush over the com-

356

ELECTRICAL APPARATUS

mutator, as shown by Fig. 171 in its successive steps, in position:

1. There is current through brush, B,

2. There is current through both brushes, Bi and B 2 , and the

armature coil, A, is closed by the counter e.m.f. of coil,

N, that is, the difference, A — N, is short-circuited;

3. There is current through brush B 2 ]

4. There is current through both brushes, Bi and B 2) and the

coil, N, is short-circuited;

5. The current enters again by brush S x ;

thus alternately the coil, N, of half the voltage of the armature coil, A, or the difference between A and N is short-circuited, that is, the short-circuit current reduced to one-half.

Complete elimination of the short-circuit current can be pro- duced by generating in the armature coil an opposing e.m.f. This e.m.f. of neutralization, however, can not be generated by the alternation of the magnetic flux through the coil, as this would require a flux equal but opposite to the full field flux travers- ing the coil, and thus destroy the main field of the motor. The neutralizing e.m.f., therefore, must be generated by the rotation of the armature through the commutating field, and thus can occur only at speed; that is, neutralization of the short-circuit current is possible only when the motor is revolving, but not while at rest.

200 . The e.m.f. of alternation in the armature coil short-cir- cuited under the commutator brush is proportional to the main field, <£, to the frequency, /, and is in quadrature with the main field, being generated by its rate of change; hence, it can be rep- resented by

e 0 = 2 t/<£10 _8 j. (17)

The e.m.f., e h generated by the rotation of the armature coil through a commutating field, <F, is, however, in phase with the field which produces it; and since e\ must be equal and in phase with Co to neutralize it, the commutating field, <F, therefore, must be in phase with c 0 , hence in quadrature with <£; that is, the com- mutating field, of the motor must be in quadrature with the main field, 4>, to generate a neutralizing voltage, ei, of the proper phase to oppose the e.m.f. of alternation in the short-circuited coil. This e.m.f., e h is proportional to its generating field, <$>', and to the speed, or frequency of rotation, /o, hence is:

e x = 2 tt/oF' 10~ 8 ,

( 18 )

SINGLE-PHASE COMMUTATOR MOTORS

357

and from ei = e 0 it then follows that:

<*>' = jA 1 ; (. 10 )

Jo

that is, the commutating field of the single-phase motor must be in quadrature behind and proportional to the main field, pro- portional to the frequency and inversely proportional to the speed; hence, at synchronism, f 0 = /, the commutation field equals the main field in intensity, and, being displaced therefrom in quadrature both in time and in space, the motor thus must have a uniform rotating field, just as the induction motor.

Above synchronism, /o > /, the commutating field, is less than the main field; below synchronism, however, / 0 < /, the commutating field must be greater than the main field to give complete compensation. It obviously is not feasible to increase the commutating field much beyond the main field, as this would require an increase of the iron section of the motor beyond that required to do the work, that is, to carry the main field flux. At standstill <£' should be infinitely large, that is, compensation is not possible.

Hence, by the use of a commutating field in time and space quadrature, in the single-phase motor the short-circuit current under the commutator brushes resulting from the e.m.f. of alter- nation can be entirely eliminated at and above synchronism, and more or less reduced below synchronism, the more the nearer the speed is to synchronism, but no effect can be produced at standstill. In such a motor either some further method, as re- sistance leads, must be used to take care of the short-circuit cur- rent at standstill, or the motor designed so that its commutator can carry the short-circuit current for the small fraction of time when the motor is at standstill or running at very low speed.

The main field, <£, of the series motor is approximately inversely proportional to the speed, fo, since the product of speed and field strength, / 0 < I>, is proportional to the e.m.f. of rotation, or useful e.m.f. of the motor, hence, neglecting losses and phase displace- ments, to the impressed e.m.f., that is, constant. Substituting

f

therefore $ = y cj> 0; where <£ 0 == main field at synchronism, into Jo

equation (19):

( 20 )

358

ELECTRICAL APPARATUS