CHAPTER XX. COMMUTATOR MOTORS. 213. Commutator motors — that is, motors in which the current enters or leaves the armature over brushes through a segmental commutator — have been built of various types, but have not found any extensive appli- cation, in consequence of the superiority of the induction and synchronous motors, due to the absence of commu- tators. The main subdivisions of commutator motcrs are the repulsion motor, the series motor, and the shunt motor. REPULSION MOTOR. 214. The repulsion motor -is an induction motor or transformer motor ; that is, a motor in which the main current enters the primary member or field only, while in the secondary member, or armature, a current is in- duced, arid thus the action is due to the repulsive thrust between induced current and inducing magnetism. As stated under the heading of induction motors, a multiple circuit armature is required for the purpose of having always secondary circuits in inductive relation to the primary circuit during the rotation. If with a single- coil field, these secondary circuits are constantly closed upon themselves as in the induction motor, the primary circuit will not exert a rotary effect upon the armature while at rest, since in half of the armature coils the cur- rent is induced so as to give a rotary effort in the one direction, and in the other half the current is induced to COMMUTATOR MOTORS. 355 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 157. In the induction motor a second magnetic field is used to act upon the currents induced by the first, or inducing magnetic field, and thereby cause a rotation. That means the motor consists of a primary electric circuit, inducing Fig. 157. in the armature the secondary currents, and a primary magnetizing circuit producing the magnetism to act upon the secondary currents. In the polyphase induction motor both functions of the primary circuit are usually combined in the same coils ; that is, each primary coil induces secondary currents, and pro- duces magnetic flux acting upon secondary currents induced by another primary coil. 356 AL TERNA TING-CURRENT PHENOMENA. 215. In the repulsion motor the difficulty due to the equal and opposite rotary efforts, caused by the induced armature currents when acted upon by the inducing mag- netic field, is overcome by having the armature coils closed upon themselves, either on short circuit or through resist- ance, only in that position where the induced currents give Fig. 158. a rotary effort in the desired direction, while the armature coils are open-circuited in the position where the rotary effort of the induced currents would be in opposition to the desired rotation. This requires means to open or close the circuit of the armature coils and thereby introduces the commutator. Thus the general construction of a repulsion motor is as shown in Figs. 158 and 159 diagrammatically as bipolar COMMUTATOR MOTORS. 357 motor. The field is a single-phase alternating field F, the armature shown diagrammatically as ring wound A consists of a number of coils connected to a segmental commutator C, in general in the same way as in continuous-current ma- chines. Brushes standing under an angle of about 45° with the direction of the magnetic field, short-circuit either a Fig. 159. part of the armature coils as shown in Fig. 158, or the whole armature by a connection from brush to brush as shown in Fig. 159. The former arrangement has the disadvantage of using a part of the armature coils only. The second arrangement has the disadvantage that, in the passage of the brush from segment to segment, individual armature coils are short- 358 AL TERNA TING-CURRENT PHENOMENA. circuited, and thereby give a torque in opposite direction to the torque developed by the main induced current flowing through the whole armature from brush to brush. 216. Thus the repulsion motor consists of a primary electric circuit, a magnetic circuit interlinked therewith, and a secondary circuit closed upon itself and displaced in Fig. 160. space by 45° — in a bipolar motor — from the direction of the magnetic flux, as shown diagrammatically in Fig. 160. * This secondary circuit, while set in motion, still remains in the same position of 45° displacement, with the magnetic flux, or rather, what is theoretically the same, when moving out of this position, is replaced by other secondary circuits entering this position of 45° displacement. For simplicity, in the following all the secondary quan- COMMUTATOR MOTORS. 359 titles, as E.M.F., current, resistance, reactance, etc., are assumed as reduced to the primary circuit by the ratio of turns, in the same way as done in the chapter on Induction Motors. 217. Let $ = maximum magnetic flux per field pole ; e = effective E.M.F. induced thereby in the field turns ; thus, where ;/ = number of turns, N= frequency. = — -- \&-anN The instantaneous value of magnetism is = <& sin (3 ; and the flux interlinked with the armature circuit <£x = sin /3 sin X ; when X is the angle between the plane of the armature coil and the direction of the magnetic flux. (Usually about 45°.) The E.M.F. induced in the armature circuit, of n turns, (as reduced to primary circuit), is thus, e = _ n ^1 10-8, = - n® 4- sin B sin X lO"8, at at = - n$> sin X cos (3 + sin (3 cos X 10~8. If N= frequency in cycles per second, N: = frequency of rotation or speed in cycles per second, and k = N^/ N speed we have frequency thus, gl = — 2-TrnJV® {sin X cos /? + k cos X sin B\ 10~8, or, since $ = — — — — , et = e V2 {sin X cos /3 + k cos X sin fi\. 360 ALTERNATING-CURRENT PHENOMENA. 218. Introducing now complex quantities, and counting the time from the zero value of rising magnetism, the mag- netism is represented by /4>, the primary induced E.M.F., E = — e, the secondary induced E.M.F., £1 = — e {sin X +j"k cos X|; hence, if Zl = r1—jx1= secondary impedance reduced to primary circuit, Z = r — jx = primary impedance, Y = g —jb = exciting admittance, we have, & sin X -f- jk cos A secondary current, 7X = — L = - e - _ - , primary exciting current, I0 = eY= e (g +jb}, hence, total primary current, Primary impressed E.M.F., E0= — E + IZ\ = e 1 + (sinX Neglecting in E0 the last term, as of higher order, £0 = e j 1 + sin X +jk cos X ^ ^4^ j ; or, eliminating imaginary quantities, e V(?i + r sin X -f- kx cos X)2 + (x^ + x sin X — kr cos X)2 The power consumed by the component of primary counter E.M.F., whose flux is interlinked with the secondary e sin X, is, f = [e sin X /]' = ^inXfosuiX-^cosX) , r\ + x\ the power consumed by the secondary resistance is, _ 2 _ **ri (sin2 x + ^ cos2 x) hence the difference, or the mechanical power developed by the motor armature, COMMUTATOR MOTORS. 361 and substituting for e, egk cos X (x^ sin X + r^k cos X) ~ fa + r sin X + kx cos X)2 + (xl + x sin \ — kr cos X)2 ' and the torque in synchronous watts, P sin X 7X cos A]' = [^/! cos X}> _ ^ cos X (xl sin X + r^k cos X) r2 + x2 The stationary torque is, k = 0, _ ifo2^ sin X cos X 0 = (rx + r sin X)2 + (^ + * sin X)2 ' and neglecting the primary impedance, r = 0 = x, _ e^x^ sin X cos X _ (fo2^ sin2 X which is a maximum at X = 45°. At speed k, neglecting r = 0 = x, , / no 1 / / R :PL LS ON M( 5TC 3R ;••') m 0 / V OC rt / / r= .! r, ' 05 joa > / X 2. x. 1. M / p- DO 1.17 0 1 j^ ^ <) g k 14 — i, -,] I 21 K I / UW K1 F^ £d_ / s 2. I) F/fir. 161. Repulsion Motor. As an instance is shown, in Fig. 161, the power output as ordinates, with the speed k = N^_ / N as abscissae, of a repulsion motor of the constants, X = 45° e0 = 100. r= .1 r1= .05 * = 2.0 *x = 1.0 giving the power, 10,000 f .02 + 1.41 k — .05 ffj ~~ .171 + 2 y&)2 + (3.14 - .1 Kf ' COMMUTATOR MOTORS. SERIES MOTOR. SHUNT MOTOR. 220. If, in a continuous-current motor, series motor as well as shunt motor, the current is reversed, the direction of rotation remains the same, since field magnetism and armature current have reversed their sign, and their prod- Fig. 162. Series Motor. net, the torque, thus maintained the same sign. There- fore such a motor, when supplied by an alternating current, will operate also, provided that the reversals in field and in armature take place simultaneously. In the series motor this is necessarily the case, the same current passing through field and through armature. With an alternating current in the field, obviously the 364 ALTERNATING-CURRENT PHENOMENA. magnetic circuit has to be laminated to exclude eddy cur- rents. Let, in a series 'motor, Fig. 146, = effective magnetism per pole, n = number of field turns per pole in series, «i = number of armature turns in series between brushes, / = number of poles, (R. = magnetic reluctance of field circuit,* (R! = magnetic reluctance of armature circuit,! 4>i = effective magnetic flux produced by armature current (cross magnetization) per pole, r = resistance of field (effective resistance, including hys- teresis), rj = resistance of armature (effective resistance, including hys- teresis), N = frequency of alternations, N± = speed in cycles per second. It is then, E.M.F. induced in armature conductors by their rotation through the magnetic field (counter E.M.F. of motor). E =4 E.M.F. of self-induction of field, E' = E.M.F. of self-induction of armature, ^/ = 27r«1^V110-8, E.M.F. consumed by resistance, Er = (r + *i) I, where / = current passing through motor, in amperes effective. Further, it is : Field magnetism : $ = n 7108 / (R * That is, the main magnetic circuit of the motor. t That is, the magnetic circuit of the cross magnetization, produced by the armature reaction. COMMUTATOR MOTORS. 365 Armature magnetism : Wj/108 1 = "V"; Substituting these values, (R ptfNI E' = (R E1 = ^^niNI . Er = (r + rj) / Thus the impressed E.M.F., or, since i,2 x = 2 TT N^- = reactance of field ; (R 2-n-jV— = reactance of armature fti and / « • «, 366 AL TERNA TING-CURRENT PHENOMENA. 221. The power output at armature shaft is, J>= El \ (R (R fi- *Ef 7T « 7V^ /2 n± N± x _j_ r _^_ The displacement of phase between current and E.M.F. tan CD = Neglecting, as approximation, the resistances r + rlf it 1 + |! lan W = ? «j ^ 7T /« 7V ^n2 1+^' ^ /« TV COMMUTATOR MOTORS. 367 hence a maximum for, 3r 7T substituting this in tan w, it is : tan o> = 1, or, w = 45°. 222. Instance of such an alternating-current motor, ^ = 100 AT=60 p = 2. r = .03 ri = .12 x = .9 *! = .5 n = 10 »j = 48 Special provisions were made to keep the armature re- actance a minimum, and overcome the distortion of the field by the armature M.M.F., by means of a coil closely surrounding the armature and excited by a current of equal phase but opposite direction with the armature current (Eickemeyer). Thereby it was possible to operate a two- circuit, 96-turn armature in a bipolar field of 20 turns, at a ratio of armature ampere-turns r> A field ampere-turns It is in this case, 100 V(.023 vVi + ,15)2 + 1.96 230 ./v; (.023 A! + .15)2 + 1.96 368 AL TERNA TING-CURRENT PHENOMENA. In Fig. 163 are given, with the speed Nv as abscissae, the values of current /, power P, and power factor cos o> of this motor. SER ES MO FOP Er 00 ^ Vaf- 3 r = n= 03 .12 =(, x _.y = .5 >->w N = 60 P= 2 0,, hi TUMI _x ^ ^~~~ ^« < ^ 2Stt> s V( J23 ]( ~ QjF 1.9 gem / / 1Z'_. NI •-il(N) / \'(. [23 ^, - -•)- ' 9 •>->00 / * / | •JIHIII / V( ).n ^ ^ 'SI-' 1.9 M Am P- 1S'K> / u SO icon / cos £>___ -sr _70 ij •\ po* ev ^ 70 H £ ' — — ______ ^J •< GO 50 1000 ^ ><~~ •*-. ^_/ M g % 01 111 HI 'oN no 20 30 40 50 00 Q B 0 Fig. 163. Series Motor. 223. The shunt motor with laminated field will not operate satisfactorily in an alternating-current circuit. It will start with good torque, since in starting the current in armature, as well as in field, are greatly lagging, and thus approximately in phase with each other. With increasing speed, however, the armature current should come more into phase with the impressed E.M.F., to represent power. Since, however, the field current, and thus the field mag netism, lag nearly 90°, the induced E.M.F. of the armature rotation will lag nearly 90°, and thus not represent power. COMMUTATOR MOTORS. 369 Hence, to make a shunt motor work on alternating-cur- rent circuits, the magnetism of the field should be approxi- mately in phase with the impressed E.M.F., that is, the field reactance negligible. Since the self-induction of the field is far in excess to its resistance, this requires the insertion of negative reactance, or capacity, in the field. If the self-induction of the field circuit is balanced by capacity, the motor will operate, provided that the armature reactance is low, and that in starting sufficient resistance is inserted in the armature circuit to keep the armature current approximately in phase with the E.M.F. Under these conditions the equations of the motor will be similar to those of the series motor. However, such motors have not been introduced, due to the difficulty of maintaining the balance between capacity and self-induction in the field circuit, which depends upon the square of the frequency, and thus is disturbed by the least change of frequency. The main objection to both series and shunt motors is the destructive sparking at the commutator due to the in- duction of secondary currents in those armature coils which pass under the brushes. As seen in Fig. 162, with the normal position of brushes midway between the field poles, the armature coil which passes under the brush incloses the total magnetic flux. Thus, in this moment no E.M.F. is induced in the armature coil due to its rotation, but the E.M.F. induced by the alternation of the magnetic flux has a maximum at this moment, and the coil, when short- circuited by the brush, acts as a short-circuited secondary to the field coils as primary ; that is, an excessive current flows through this armature coil, which either destroys it, or at least causes vicious sparking when interrupted by the motion of the arm'ature. To overcome this difficulty various arrangements have been proposed, but have not found an application. 370 ALTERNATING-CURRENT PHENOMENA. 224. Compared with the synchronous motor which has practically no lagging currents, and the induction motor which reaches very high power factors, the power factor of the series motor is low, as seen from Fig. 163, which repre- sents about the best possible design of such motors. In the alternating-series motor, as well as in the shunt motor, no position of an armature coil exists wherein the coil is dead; but in every position E.M.F. is induced in the armature coil : in the position parallel with the field flux an E.M.F. in phase with the current, in the position at right angles with the field flux an E.M.F. in quadrature with the current, intermediate E.M.Fs. in intermediate positions. At the speed irJV/2 the two induced E.M.Fs. in phase and in quadrature with the current are equal, and the armature coils are the seat of a complete system of symmetrical and balanced polyphase E.M.Fs. Thus, by means of stationary brushes, from such a commutator polyphase currents could be derived. REACTION MACHINES. 371