CHAPTER XIX. COMMUTATOB MOTOBS. 192. 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 motors are the repulsion motor, the series motor, and the shunt motor. REPULSION MOTOR. 193. 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, and 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 292 ALTERNATING-CURRENT PHENOMENA, [§ 193 give a rotary effort in the opposite direction, as shown by the arrows in Fig. 141. 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. 14h 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 inchices secondary currents, and pro- duces magnetic flux acting upon secondary currents induced by another primary coil. §1941 COMMUTATOR MOTORS. 194. 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 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. 142 and 143 diagrammatically as bipolar 294 ALTERXATINC-CURRF.NT rJ/EA'aMEA'A. IS 104 motor. The field is a single-phase alternating field F, the armature shown diagram matically 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 part of the armature coils as shown in Fig. 142, or the whole armature by a connection from brush to brush as shown in Fig. 143. 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- § 196] COMMUTATOR MOTORS. 295 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. 195. 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 Bg. 144. space by 45° — in a bipolar motor — from the direction of the magnetic flux, as shown diagrammatically in Fig. 144. 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- 296 AL TERN A TJNG-CURRENT PHENOMENA. [ § 196 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. 196. Let ^ = maximum magnetic flux per field pdle ; e = effective E.M.F. induced thereby in the field turns; thus : ^^ n = number of turns, iV= frequency, thus : ^ , 10» V2irnN The instantaneous value of magnetism is sin )3 ; and the flux interlinked with the armature circuit <^i = 4> sin p, sin X ; when X is the angle between the plane of the armature coil and the direction of the magnetic flux. The E.M.F. induced in the armature circuit, of n turns, as reduced to primary circuit, is thus : ^ — _ «^^10-« = — « 4> — sin )3 sin X 10"* == — « 4> ) sin X cos p dp_ lit + s\npcos\—\ 10 ^ dt ) -8 If iV= frequency in cycles per second, N^ = speed in cycles per second (equal revolutions per second times num- ber of pairs of poles), it is : dt dt ' §197] COMMUTATOR MOTORS, 297 and since A = 45°, or sin X = cos X = 1 / V2, it is, sub- stituted : ^1= - V2fl-«*{iV^cos)3+^isin)3}10-» or, since * = ; ^1 = — ^ { cos )3 + ^ sin )3 } ; where * = A = ratio _^P??d_ . N frequency or the effective value of secondary induced E.M.F., 197. Introducing now complex quantities, and counting the time from the zero value of rising magnetism, the mag- netism is represented by the primary induced E.M.P\, E =^ — e\ the secondary induced E.M.F. : hence, if V2 Zi = /*! — j Xx = secondary impedance reduced to primary circuit, Z =^ r — j X = primary impedance, Y = g -\- jb = primary admittance, it is, secondary current, r _ E, _ e 1_±j±. -'i — — : — f primary exciting current, 298 AL TERN A TING-CURRENT PHENOMENA. [ § 198 hence, total primary current, Primary impressed E.M.F., or Neglecting in -C© ^^e last term, as of higher order, xSq — ^ ■^ -*- "1 _- : ( » or, eliminating imaginary quantities, ^ ^ ^ V(^ + nV^ + kxf + (x + x^V2 - krf ^ 198. The power consumed by the primary counter E.M.F., r, that is, transferred into the secondary circuit, is or, eliminating the imaginary quantities. 7^' = n + '^-''^i V2 n' + -^'i The power consumed by the secondary resistance is 2 n^ + ^/^ ' Hence, the difference, or the mechanical power at the motor shaft — §1981 COMMUTATOR MOTORS. 299 and, substituting for e, J, ..■(>-|(y5-1) + .i»,V3-yr,} (r + r, V2 + *»■)' + (■"■ + ■i = effective magnetic flux produced by armature current (cross magnetization), r = resistance of field (effective resistance, including hys- teresis), ri = resistance of armature (effective resistance, including hys- teresis), iV = frequency of alternations, JVi = 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). £ =4;/,i\^i*10-» E.M.F. of self-induction of field, J5" = 2fl-///i\'^*10-«, E.M.F. of self-induction of armature, E.M.P\ consumed by resistance, where / = current passing through motor, in amperes effective. Further, it is : Field magnetism : * « / 10« 9 = /" > 302 AL TEKA'A TING-CURRENT PHENOMENA, [§199 Armature magnetism : vi = -^ . Substituting these values, J' j^, ^ 2 irptl^NI , P ' E{ = * ; Thus the impressed E.M.F., ^^"i^L^ + . + ..y+4^A'«(/^+'^;j; or, smce ^ = 2 w N^-^ = reactance of field ; //,^ OTi = 2 fl- A'' — ^ = reactance of armature ; and ^» - v/(i^?2' a \Til P"' ,'1^^'' =v/(^^+'-+^'Y+(-^+-') a ^« =v/(r^ f ^+'- +'■■)"+ (^•+^-^- 1*200] COMMUTATOR MOTORS, 303 200. The power output at armature shaft is, P^ EI ( ( - ^ ^ •'^ + '- + '■lY + (•* + ^.)* The displacement of phase between current and E.M.F. tan 01 = F A- F — ^^— + '^ + n ? a ^. + .+ ... TT pn N Neglecting, as approximation, the resistances r + ri, it is, tan 01 = 2 nj Ni w pn N p = -ElSL K pn N 2 «, ^ 304 AL TERN A TING^CURRENT PHENOMENA, [§ 20 1 hence a maximum for, 2 pn ^1. N~ (- ?) n 2 «i 2% ' •K pn N 1+ ^» or, _ substituting this in tan w, it is : tan w = 1, or, ai = 45°. 201. Instance of such an alternating-curren*- motor, ^0=100 A^=60 / = 2. r = .03 rj = .12 jc: = .9 jTj = .5 « = 10 //i = 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 armat ure ampere-turns cy a field ampere-turns It is in this case, J ^ 100 V(.023 ^1 + .15)^ -f. 1.96 J, ^ 230 TV^i (.023 ^1 + .15y + 1.96 , . 1.4 . .023 A^, + .15 tan ID = , or, cos oi = *— ' .023 iV, + .15 ' ' V(".023 A\ + .15)"'"+TU0' Sa02] COMMUTATOR MOTORS. 305 In Fig. 147 are given, with the speed A^i as abscissae, the values of current /, power P, and power factor cos 2 of this motor. SER E3 MO OR IOf> '- r? ■^ -! H" ao p 2 0, w -- ■ ^ / 1= A/1 ,y, ID" / / p= Alfl nf Ml. / ( / C« M = -j-' — 1 Til' r™ i«i Am in* / « / is [^ * P3- Sti ■m „ 1 ■ ^ ■^ „ .^ / ~ ■— ~~& . / / /■ ^ '«h M • 10 W « » 202. 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 counter E.M.F. of the armature should be in phase with the impressed E.M.F., and thereby the armature current lag less, to represent power. Since how- ever, the field current, and thus the field magnetism, lag nearly 00°, the induced E.M.F, of the armature will lag nearly 90°, and thus not represent power. 806 AL TERN A TING-CURRENT PHENOMENA. [§ 202 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. 146, 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 armature. To overcome this difficulty various arrangements have been proposed, but have not found an application. §203] COMMUTATOR MOTORS. 307 203. 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. 147, 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 tr X 12 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. • 808 AL TERNA TING-CURRENT PHENOMENA. [§ 204