The Repulsion Start Induction Motor

To be presented at the 314JΔ Meeting of the American Institute of Electrical Engineers, St. Louis, Mo., October 19, 1915.

THE REPULSION START INDUCTION MOTOR

BY JAMES L. HAMILTON

ABSTRACT OF PAPER The repulsion start induction motor for single-phase current has come into considerable prominence during the last 10 or 15 years as is fully attested by the large number of motors of this type now in operation, and by the increasing demand and pro duction. While there is considerable literature available on the subject of repulsion motors both compensated and non- compensated and on induction motors, there is comparatively little information available on the repulsion start induction motor which is really a combination of two distinct types of motors. The objects of this paper are: 1. To set forth the general characteristics of this type of motor and compare them with similar characteristics of direct- current motors and other alternating-current motors. 2. To outline a definite and commercially practicable method of studying the electrical design of existing motors and of pre determining the electrical design of new or proposed motors. 3. To discuss the mechanical design and construction.

1—GENERAL HE REPULSION start induction motor may be described T briefly as consisting of a field or stator of laminated toothed construction having a single winding, usually of the pyramidal type, wound thereon and connected to the supply circuit; a progressively wound armature or rotor with a com mutator and having brushes which bear on the commutator during the starting period, the brushes being removed from the commutator and the armature winding short circuited through the commutator after the armature has obtained sufficient speed. This type of motor therefore starts as a simple repulsion motor without compensating or auxiliary windings and operates as a simple repulsion motor until a predetermined speed has been attained at which time the armature winding is short circuited through the commutator and the brushes lifted. The motor then operates as a simple induction motor with an armature equivalent to the squirrel cage armature. Manuscript of this paper was received August 30, 1915. 2389 2390 HAMILTON: INDUCTION MOTOR [Oct. 19

The straight repulsion motor without compensation gives the most efficient starting torque possible and the single-phase induction motor with the squirrel cage armature or its equiv alent gives the simplest*and most efficient motor when running, hence the rapid development of this type of motor with its desirable characteristics throughout. The discovery that a single-phase motor with armature, commutator and brushes as described above would start and operate without any electrical connection to the armature was made by Elihu Thomson, and the experiments leading up to this discovery are described by him in the United States Patent No. 363,185 issued to him May 17, 1887 and later patents issued in that year and following years to Thomson and others.

FIG. 1 FIG. 2

These early patents describe a motor which started and oper ated on the repulsion principle by short circuiting a number of coils in favorable position with regard to the field magnetism by a comparatively wide brush as is shown in Fig. 1. This plan, as is well known, has the disadvantage of using a part of the armature coils only at any instant. It was soon discovered however, that the entire armature winding could be used to advantage by employing comparatively narrow brushes and by connecting these brushes together as shown in Fig. 2. It may be .observed by referring to Figs. 1 and 2, the direc tion of rotation will be different in the two types of motors and that the coils short circuited by the brushes as shown in Fig. 2, exert a torque opposite from the direction of the torque 1915] HAMILTON: INDUCTION MOTOR 2391 of the armature as a whole, and therefore the number of coils short circuited in practise are kept to a minimum by using a comparatively large number of commutator segments and narrow brushes. Objection has been raised to the term " repulsion " as apply ing to this type of motor. The word " repulsion " motor will be used here however as it is a well known term and engineers in general understand that the fundamental principles causing torque in this type of motor are the same as in all types of direct- current or alternating-current motors ; that is, that a current in a wire at right angles to and situated in a magnetic field tends to move out of that field, the direction of motion being well known when the direction of the magnetic field and the direc tion of the current in the wire are known. Little was done on the repulsion type of motor in a com mercial way for several years after these fundamental patents were granted, due to the limited demand for alternating-current power motors and due more particularly to the fact that about the date of these fundamental patents on repulsion motors, it was discovered and patents* were granted showing that a single-phase motor having a squirrel cage armature could be started by a double winding on the field which gave a form of rotating field. This type of motor is now the well known split- phase alternating-current motor. This latter type of motor without the auxiliary winding is the kind of induction motor which we have in the type of motor under discussion when it is up to speed. Most engineers in this country and abroad, as is shown by the electrical literature following the dates of these funda mental repulsion patents considered the split phase motor with its substantial armature better and more satisfactory as a basis for developing a single-phase power motor. During the period of 1894 to 1900 the demand for a prac ticable single-phase power motor having good starting torque and efficiency, and at the same time good running torque and efficiency, caused some of the engineers in this country to take up actively the question of developing a commercially satis factory single-phase motor. They realized that the repulsion motor had the starting characteristics so much desired and that the single phase induction motor with the squirrel cage armature or its equivalent possessed the desirable running characteristics, that is, a definite limiting or synchronous speed 2392 ' HAMILTON: INDUCTION MOTOR [Oct. 19 and comparatively small slip or dropping off of speed under load and the absence of brushes on the commutator when the mptor is up to speed. The repulsion start induction motor came into commercial prominence about the period of 1895 to 1900 first as a hand start or manually operated motor when starting and later in genious devices for automatically performing this function were' developed. During the period of 1900 to the present date no radical improvements have been made with reference to this type of motor. However, it has been consistently im proved in all of its electrical and mechanical details until at the present time it is doubtful if any other alternating-current or even any direct-current motor is more satisfactory alike to manufacturer, central station and user. Torque Efficiency at Start. As the starting efficiency of an alternating current power motor is one of the most interest ing points for discussion, the starting efficiency of this type of motor will be considered and comparisons made with direct current motors, polyphase motors and other types of single phase motors. Table I gives the starting torque in per cent of the full-load torque, starting current in per cent of full-load current, per cent of full-load torque at start for 100 per cent full-load cur rent and maximum pulling torque in per cent of full-load torque. As may be noted from these data, the direct-current shunt or compound motor, the two- and three-phase wound rotor in duction motor with resistance in rotor at starting, and the repulsion start induction motor have very much the same starting efficiency, and all other types of alternating-current motors are inferior particularly the two- and three-phase squirrel cage of the larger sizes and the single-phase motor of the split- phase type, so that the repulsion start induction motor com pares very favorably in regard to starting efficiency with the best type of direct-current or alternating-current motors avail able. The central stations are favorably inclined toward this type of7 single-phase motor as it causes a minimum line dis turbance, and it is quite usual nowadays for central stations to limit the starting current of single phase motors to 300 per cent of full-load current for motors up to and including 5 h.p. and to limit starting current to 150 to 175 per cent of full-load current for 1\ h.p. and larger. While starters are not required for any size of repulsion start induction motor up to 50 h.p., as they take not over 300 per cent full load current at starting, 1915] HAMILTON: INDUCTION MOTOR 2393 however, it is quite usual to use a resistance or compensator starter for sizes of 7? .h.p. and larger so as to cause a minimum of line disturbance. TABLE I

Starting tor Starting cur Per cent full Maximum Kind of motor. que in per rent in per load torque pulling cent of full cent of full- for full load torque in per load torque. load current current cent of full- load torque.

Small d-c. comp. without] [starter. \ h.p. and smaller 350 450 78 Small d-c. shunt without starter. i h.p. and smaller 250 450 55 Large d-c. comp. with starter. θ h.p. and larger 200 170 118 Large d.c. shunt with starter. h h.p. and larger 180 170 106 Small two- and three-phase squirrel cage ind. motors with out starter. \ h.p. and smaller.. 215 475 45 Two- and three-phase squirrel | [cage ind. motors without starter. \ h.p. and larger, 225 550 41 Two- and three-phase .wound [rotor ind. motors with resistance! in rotor for starting. 5 h.p. and) up. 150 150 100 Single-phase ind. motor split phase start, up to \ h.p 220 500 44 Single-phase ind. motor with clutch and with hand or auto matic start, for cutting res. and reactance in and out of circuit, up to 15 h.p 140 250 56 Single-phase strongly compen sated repulsion motor up to 15 |h.p 225 500 50 Single-phase weakly compen sated repulsion motor up to 1 h.p] 360 270 133 Single-phase repulsion start ind. motors 1/10 to Jh.p. inc.. .. 450 260 175 Single-phase repulsion start ind. motors, \ h.p. and larger. 335 270 125 Single-phase repulsion start ind. motor, 7\ h.p. and larger with resistance starter 100 170 60 Single-phase repulsion start ind. motor 7i h.p. and larger, with compensator starter.... 100 100 100

With a resistance type of starter this motor causes a little greater line disturbance, and with a starting compensator causes substantially the same line disturbance, as does a direct-current 2394 HAMILTON: INDUCTION MOTOR [Oct. 19 motor with a starter. This type of motor like the direct-current motor in all sizes will bring up to speed promptly a load from 125 to 150 per cent of full-load torque. Weight, size and cost. The weight and size of the repulsion start induction motors are substantially the same as for direct- current and other types of alternating-current motors. There are considerable differences in the weights and sizes of any two lines of the same kind of motors due to different manu facturers emphasizing certain features of design, such as staunch ness in one case and lightness and compactness in another case. The cost of this motor is not materially different from the cost of a similar size and construction of direct-current motors or other types of alternating current motors. The installation cost of a multiphase motor of a given capacity is substantially greater than that of a repulsion start induction motor of the same size on account of the increased line construction, the multiphase motors requiring at least three wires and on account of increased transformer cost which will average about 30 per cent greater than the transformer cost for the single-phase repulsion start motor. The transformer losses will be about 25 per cent greater for the multiphase installation than for the repulsion start induction motor installation. Lse and field of application. This motor, possessing as it does high starting torque characteristics, is well adapted for operating such apparatus as requires large starting torque, that is, pumps starting under full head, air compressors start ing under a maximum pressure, rock crushers which are equipped with the necessary fly wheel, baker's machinery where the tub is full of dough ready for final mixing, meat choppers, coffee mills which have been stopped with the burrs full of coffee, etc. These motors because of their not requiring a starter are well suited for operating vacuum cleaners, pumps which are con trolled automatically, sewerage disposal pumps; and are in extensive use for the operation of organ blowers, and heating and ventilating apparatus because they can be started from a distance and because they start quickly, and the brushes being removed from the commutator after attaining speed makes it possible to produce exceedingly quiet and smooth operating motors of this type. The central stations are objecting more and more to the split- phase motors on their circuits on account of the large starting current, even in sizes of \ h.p. and smaller. 1915] HAMILTON: INDUCTION MOTOR 2395

As the result of the demand for small fractional horse power motors which may be operated on all lighting circuits with no inconvenience to the lighting service, repulsion start induction motors have recently been developed and are now on the market in all sizes down to 1/10 h.p. and are rapidly replacing the split-phase motor for operating small coffee mills, meat choppers, house pumpgj; etc. The field igr the application of this type of motor is therefore almost unliiSpted, and it is being used extensively not only in

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TORQU E JΔ^ o o o D :\ 1 e i \ HOFtSEP OWE R FIG. 3—PERFORMANCE CURVES—5 H.P.—208 VOLT—60 CYCLE MOTOR this country but in practically all foreign countries where alternating-current systems of distribution are used.

2—ELECTRICAL DESIGN Analysis of 5 h.p., 104/208 volt, four-pole, 1750 rev. per min., 60-cycle motor. In analyzing an existing motor it is well to make an accurate load test if practicable to check the calcula tions, taking sufficient readings to be sure of the performance. A running idle magnetization test should be made, beginning 2396 HAMILTON: INDUCTION MOTOR [Oct. 19 with a voltage'somewhat above normal and reducing the volt age, taking readings at suitable intervals until the voltage is reached where the current begins to increase. A further de crease in voltage causes the motor to stop. The blocked satura tion test is made by short circuiting the entire commutator by

120 160 200 VOLTS FIG. 4—RUNNING IDLE MAGNETIZATION CURVES SHOWING SEPARATION OF LOSSES—5 H.P.—208 VOLT—60 CYCLE MOTOR

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0 0 0 40 80 »0 u) 0 2CX ) 240 voLT S FIG. 5—BLOCKED SATURATION CURVES—5 H.P.—208· VOLT—60 CYCLE MOTOR some convenient method and beginning at a low voltage read watts, volts, and amperes to motor, taking readings up to full voltage of motor, or as near full voltage as is practicable. The results of load test, running idle magnetization test, and the blocked saturation test, are shown in Figs. 3, 4 and 5 re spectively, the observed points in each case being indicated. 1915] HAMILTON: INDUCTION MOTOR 2397

MOTOR DATA 48 field slots; 61 armature slots. Field winding 4£ coils per pole of 22 turns of No. 11 wire in each coil, connected in series parallel on 208 volts. Resistance of field on 208 volts = 0.287 ohms. Armature winding 122 coils of 3 turns of No. 12 wire in each coil. Diameter oFfield punching = 13 in. Bore of field punching = 8} in. Net amount of iron = 5 X 0.95 = 4.75 in. Single air gap = 0.035 in.

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Winding Constant Calculations. Central or 1st coil 1 X18 = 18 2nd " 1 X25 = 25 3rd " 1 X30 = 30 4th " 1 X33 = 33 Outside i coil h X34 = 17

123 123 Winding constant = ^ = 0.805

The voltage on each pole, is 104. The number of turns on each pole is ,4£ X 22 = 99

Flux per pole = ^,χ^χ0,805 = **>,0001ines

41 Flux in central field tooth = rf X 490,000 = 65,000

The above winding constant calculation, it will be observed, is based on the theory that the magnetic flux in the various teeth is proportional to the ampere turns surrounding those teeth. If we assume a sinusoidal flux distribution and de termine the winding constant by integration we will get a wind ing constant of 0.786 in this case, and flux per pole and flux in central tooth of approximately the same values as were 2398 HAMILTON: INDUCTION MOTOR [Oct. 19 obtained above. The writer has found this method of getting the winding constant very simple and reliable.

MAGNETIC CIRCUIT CALCULATIONS

Amp. Width Length Area Length turns Amp. Section in in in sq. Flux Density -of per turns inches inches inches circuit inch

Field teeth 3/16-Min. 4.75 0.89 65000 73000 2-3/16 3-1/2 8 1/4 -Aver. 4.75 1.07 65000 60600 Field yoke 1-1/4 4.75 5.94 245000 41300 9.24 22 20 Arm. teeth 7/64-Min. 4.75 0.52 51200* 98500 1-3/4 19.5 34 9/64-Aver. 4.75 0.668 51200* 76700 1-5/16 4.75 6.24 245000 39300 4.25 2.0 8.5 Air gap per tooth.. . 15/32 5 2.34 65000 27800 0.070 609.Of

Total 679.5 field slots 48 *Flux per armature tooth = X flux per field tooth = — X 65,000 ~ 51,200 arm. slots 61 fAmpere turns absorbed in air gaps = 0.313 X 27,800 X 0.035 X 2 = 609

The magnetizing current required to produce this flux is

fi7Q ^ 707 2 43 2 x 98 X °· = · amperes.

Since there are two parallel circuits through the field we have 2 X 2.43 = 4.86 amperes magnetizing current for main field. In a single-phase induction motor the cross field magnetizing current (corresponding .to the magnetizing current in phase 2 of a two-phase motor) is also carried by the one winding and in a motor of this size the cross field can be assumed to be 95 per cent of the strength of the main field we have for total magnetiz ing current on 208 volts

4.86 X 1.95 = 9.48 amperes which checks substantially with the magnetizing current of Τ.25 amperes observed on this motor. The strength of the cross field of the single-phase induction motor may be determined by placing exploring coils in position corresponding to position of phase 2 of a two-phase motor and in this way it will be found that when the motor is running idle 1915] HAMILTON: INDUCTION MOTOR 2399 the cross flux will be about 90 per cent of the main flux for J-h.p. motor and about 95 per cent for 5-h.p. motor, and less than 90 per cent for motors smaller than \ h.p. and greater than 95 per cent for motors larger than 5 h.p. As the air gap reluctance is always a very large percentage of the total reluctance of the magnetic circuit it is well to exercise considerable care in determining the effective area of air gap per field tooth and also the length of the air gap or clearance. Experience shows that the effective width of the air gap per tooth is obtained very closely for partially closed slots in field and arma ture when 35 to 40 per cent of one field slot opening is added to the actual width of the field tooth at air gap. The dimension 15/32 in. of width of air gap per tooth given above was obtained by adding 37.5 per cent of one slot opening to width of iron of one tooth at air gap. The length of the air gap per tooth along the shaft should be the gross length of iron in motor exclusive of ventilating ducts. Circle diagram and calculation of performance. The data for getting the armature resistance and the running idle and blocked points for a circle diagram are taken from the idle magnetization curves Fig. 4 at 208 volts and the blocked magnetization curves Fig. 5 at 208 volts and is calculated as follows:

Res. of Power Watts Volts Amps. Cos

Idle 310 208 9.25 16.1 24.5 12.5 1.49 Blocked 7720 208 ' 94.5 39.2 2560 5160 0.577 37.

The circle diagram can now be constructed. The running idle point of the circle diagram is therefore on an arc of 9.25 amperes and at a height of 1.49 amperes. The blocked point is on an arc of 94.5 amperes and at a height of 37 amperes. The circle can now be drawn, the center being on a horizontal line passing through the running idle point and the circle pass ing thorough both the running idle point and the blocked point as shown in Fig. 6. The armature resistance now being known the various losses of the motor running idle can be separated and plotted as is shown in Fig. 4. The extension of the observed watt curve to 2400 HAMlLTON^lNbUCTlON MOTOR [Oct. 19

zero voltage gives the friction and windage losses. In calcula ting the armature or secondary copper loss one half of the primary current for that voltage is used, for, as we have previously stated, the current in the armature running idle is the cross inagnetiz- in,g current and is therefore approximately one-half of the total field or primary current. The loss remaining after the other losses are subtracted from the observed loss gives what we will call " added " iron loss. This subject of " added " iron loss is of sufficient importance to be given separate consideration which will be done later on in this paper. The free magnetization curves with the losses separated, Fig. 4, gives one at a glance the various losses in the motor running idle at different voltages on the motor, and therefore the action of the motor with different strength of windings. Lines showing

0 10 20 30 40 50 60. 70 80 90 100 FIG. 6—CIRCLE DIAGRAM—5, H.P., 208-VOLT, 60-CYCLE MOTOR the densities of different parts of the magnetic circuit may be drawn on this free magnetization curve if desired. We may now proceed to calculate the complete performance of this motor as follows : Columns 1, 2 and 3, as indicated, are taken from the current locus or circle diagram of the motor in the usual way, it being remembered that the secondary current is to be taken or measured from the point half way between the origin and the running idle point. The item 273 at head of column 7 is the sum of the iron losses (transformer and "added") 129 watts and the friction and wind age loss of 144 watts. Item 12.5 at the heading of column 12 is the copper loss in armature running idle. 1915] HAMILTON: INDUCTION MOTOR 2401

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The calculated performance curves can now be plotted on the curve sheet Fig. 3 with the points which were plotted from the observed load tesU. The observed and the calculated perform ance check sufficiently close for all practical purposes and any slight differences are due among other things to the difficulty of observing with precision the performance of a motor by loading, and due to it being almost impossible to eliminate changing temperature conditions which affect the performance to a con siderable extent. We now know the performance at various loads and the various losses in the motor at those loads with as great an ac curacy as is consistent with the nature of the problem.

IRON Loss CALCULATIONS The iron loss calculation is given below.

Field Teeth Field Yoke Total Per Total Loss Loss cale, cent observed Weight per lb. Loss Weight per lb. Loss loss added loss

18.7 1.75 32.7 65.6 0.68 45 77.7 66 129

The weight of the field teeth and the weight of the field yoke can be obtained with sufficient accuracy by calculating the volume of iron in teeth and yoke, and knowing the magnetic densities in these parts, and taking the loss per lb. from a loss curve of the iron used, we get the total calculated or transformer iron loss of 77.7. The total observed loss is taken from the idle magnetization curves. This loss was found to be 129 watts, which is 66 per cent more than the transformer loss for this motor and we have called it " added " iron loss. " Added " iron loss is a very profitable and interesting phenom enon for study but we can only touch on this subject here. The principal cause of the added iron loss seems to be the high fre quency ripples in the magnetic flux caused by armature teeth and gaps sweeping by the field teeth and gaps. The fundamental frequency of these ripples can be calculated as follows : For the motor under discussion when running at synchronous speed we have 1800 rev. per min. -s- by 60 the number of cycles = 30 rev. per sec. Since there is a complete change of conditions for each 1/61 of the armature rotation, the frequency of these 1915] HAMILTON: INDUCTION MOTOR 2403 changes = 61 X 30 = 1830 cycles per second or 30.5 times supplied frequency. This very high frequency ripple in the mag netism will cause considerable " added " iron loss even if the combination of field slots and armature slots and the shape of tooth tips, slot openings and surface of armature and field bore are correctly designed and made, but if some or all of these conditions are bad very high " added " iron loss will result. It has been the writers* experience that well proportioned 60- cycle induction motors, single-phase or multiphase, wound or squirrel cage armatures will have from 25 to 100 per cent " added " iron loss, and poorly designed motors may have up to 250 per cent and even higher " added " iron loss. Con siderable care should therefore be exercised to keep the chance for appreciable ripples in the magnetism to a minimum. When calculating the transformer iron loss of this motor, as may be observed from above data, no account has been taken of iron loss in the armature. There is a theory of single-phase motors which deals with the motor as though there were two revolving fields in the armature, which when the motor is run ning at synchronous speed, causes a double frequency in the armature. To determine in just what respect, if any, the iron losses of a single-phase motor differ from those of a two-phase motor, the following results were observed. A two-phase motor hav ing ball bearings to reduce the friction to a minimum and to maintain the friction loss constant was wound with a pyramidal winding for each phase, which gave the same magnetic flux distribution whether the motor was operating on one or both phases. This motor was tested and the performance and the losses completely analyzed. The total iron losses for the motor operating as a single phase motor was found to be substantially and for all practical purposes the same as when operating as a two phase motor, the total iron loss being from 1 to 2 per cent higher for all magnetic densities on two-phase than on single phase. We may therefore conclude that the iron losses in a multi phase and in a single-phase motor are the same for all practical purposes when the magnetic densities are the same, and that there are practically no transformer losses in the armature in either type of motor when running idle, as the rotating mag netism and the armature are almost in step. There is, however, an " added " iron loss in the armature as in the field and is due 2404 HAMILTON: INDUCTION MOTOR [Oct. 19 to the same causes. All of th„e " added " iron losses (field and armature) are therefore included in the term " added " iron loss. Circle coefficient calculations. The circle coefficient and maxi mum power factor of this motor may be calculated from the physical dimensions of the electrical design by Behn-Eschen- burgs empirical formula as follows:

3 . 10 A C , 5A X2 ' X Y T ' Li

ó = circle coefficient X = the mean number of slots per pole in field and armature Y = width of the slot openings in inches A = motors single air gap (clearance) in inches C = average tooth tip thickness of field and armature in inches T = pole pitch in inches Li = net iron length of the core in inches For this motor we have

= 3__ 10 X 0.035X0.031 5 X 0.035 σ 13.622 + 13.62X0.125X6.47 + 5 = 0.01610 + 0.00099 + 0.03500 = 0.0521 Since the maximum power factor for a single-phase induction motor = 1 1+4Χσ we have 1 83 per cent max. power factor calculated 1 + 4X0.0521 which is a fair agreement with the observed maximum power factor of 85 per cent for this motor, and the calculated maximum power factor of 85.5 per cent. Resistance of field and armature. The resistance of the field of 0.287 ohms used in these calculations was calculated from the weight of the field wire. The resistance of the field was also calculated from the length of wire by developing one quarter section of one field pole and laying out the various coils to scale, the resistance in this way was calculated to be 0.295 ohms which checks substantially with the figure by weight of 0.287 ohms. 1915] HAMILTON: INDUCTION MOTOR 2405

With a little time and care the resistance can be obtained quite accurately by the length method and assists greatly in pre determining the resistance of field of a proposed motor. The total cross section in circular mills of all the wires in all the slots of the field and of the armature is Field 2 X 18 X 22 X 8234 = 6,540,000 Armature 2 X 122 X 3 X 6530 = 4,800,000 The resistance of the armature is not

6,540,000 w Λ 00_ Λ ΟΛ1 , 4ΔΦΦ0 X °·287 = °·391 °hmS as might be expected, as the copper in the armature is not as effectively used as in the field which has a pyramidal winding. We therefore have for this motor

^SS'iiiiii X 0-287 X K = 0.577 = observed resistance of 4,800,000 ' armature from the blocked test or K = 1.47 This constant is usually of the proportion of 1.4 for four-pole motors 1.7 for six-pole motors. This we believe is the simplest and most practical method of dealing with the armature resist ance. We have now analyzed and calculated this motor completely for the running idle and various load conditions. We will now inquire into the various calculations and show how the performance of a proposed motor may be predetermined. Predetermining the performance of a proposed motor. Every designer has, more or less, his own method of starting a new electrical design and each method if correctly and consistently followed leads to substantially the same result in the end. The writer has found the following method quite satisfactory. Fig. 7 gives the total magnetic flux for four- and six-pole 60- cycle single-phase induction motors for various maximum horse powers up to 40 horse power. Data like these give a very conr venient and safe starting point for preliminary design for not only this type of motor but for any alternating-current induction motor, as the principal factors which may cau.se a variation in the total magnetic flux for a given maximum horse power or armature resistance and leakage both of which are fairly con stant for motors of same size and general construction. 2406 HAMILTON: INDUCTION MOTOR

The number of slots in the field and armature should now be decided upon. In general too few or too many slots in field or armature will be found disadvantageous. In general either a less number or greater number of armature slots than field slots may be used with substantially the same results providing the average number of slots per pole in field and armature is the same. The average number of slots per pole in field and arma ture varies from 5 to 15 in this kind of motor being near the smaller figure for small motors and nearer the larger for larger motors, say 5 h.p. and larger. One of the most important features of the design for smooth ness and quiet operation and as we have intimated while dis cussing " added " iron loss is the combination of field and arma-

0 4 8 12 16 20 24 28 32 .36 40 MAXIMUM HORSE-POWER OUTPUT-60 CYCLE MOTORS

FIG. 7—FLUX-HORSE POWER CURVES FOR 60 CYCLE, SINGLE-PHASE INDUCTION MOTORS ture slots. The principal features affected by this combination are noise, uniformity of starting torque, and " added " iron loss, but it should not be inferred that these features depend entirely on the combination of slots, as there are other things which may effect these features, such as, centering of field and armature» air gap, magnetic densities, shape and size of slots and tooth tips and the rigidity of general design, method of mounting field and armature iron and amount of twist in field or armature, all of which combine to form a problem far too complex to state definitely at the present time, but about which nevertheless considerable is known. In general then the combination of slots and general proportions should be restricted to those combinations which have been tried and not found wanting. 1915] HAMILTON: INDUCTION MOTOR 2407

Having decided on the number of slots in field and armature to be used, and knowing the number of poles and the voltage of the motor, the number of turns may be calculated from the formula used in analyzing the motor earlier in this paper. In calculating the winding constant and determining the number of slots to be left empty it can be borne in mind that there is no advantage in filling more than 75 per cent of the slots when there are eight or more slots per pole. Knowing the number of wires per slot, and by estimating the current taken by the motor at full load, the preliminary size of the field wire can be estimated allowing 500 to 800 circular mills per ampere. The smaller number of circular mills per ampere should be used only in motors that are well ventilated with definite air circulation, or in motors where it is known that the service will always be of such an intermittent character that the motor will never overheat. Knowing the field winding and therefore the resistance, the armature winding and resistance may be calculated as has been outlined. Having the magnetic flux per pole and having determined the number of coils per pole, the flux in the central field tooth can be determined as has previously been done. By fixing the magnetic densities in the different parts of the magnetic circuit the area of the different members can be calculated. The magnetic densities which may be used, of course, depend to a large extent upon the quality and kind of sheet steel used. How ever, practically all sheet steel used nowadays in alternating- current motors shows a permeability and watt loss substantially as good as is given in Fig. 8. With iron of this quality the

Lines per sq. in.

Field yoke can be worked at 60,000 to 80,000 Field teeth aver, section can be worked at 80,000 "110,000 " min. " " " " " 100,000 " 125,000 Armature teeth aver. " " " " " 90,000 "115,000 " min. " " " " " 100,000 " 130,000 " yoke " " " " " 75,000 " 90,000 for 60-cycle motors. The preliminary electrical design may now be drawn to scale, beginning either with an armature diameter or field iron diameter that is considered about correct or is desirable to be used. The preliminary design may be either too long along the shaft in which case a larger armature diameter is necessary or too short 2408 HAMILTON: INDUCTION MOTOR [Oct. 19

along the shaft in which case a smaller armature diameter should be used. The best general proportions as to the relation of polar pitch at the air gap and the length of iron along the shaft may be checked by the following observations on this type of motor. The length of iron along the shaft should be 50 per cent to 100 per cent of the polar pitch, 60 per cent to 70 per cent giving the best all around performance, but if the diameter of armature and field punchings are large a motor will be somewhat more expen sive in general to build. If, as is often the case with the larger motors, it is desirable to build four- six- and eight- pole motors

^1600 1400 22 14U 1200 — ^ϊόοό\ Λ 900 =^8 B "et —"m "- 7( 0 20 ε£ϊ 500 _ 120 r ^"δX) B ^» &* JΔSS?** lN^ - 18 ^ —*"""" ~ ^ίοο 7Λ .-*"!&"" 90 - 16 100 |—'40 —50 3 0 TJRNS PE UN( 3H^> - / —? 0 , i.MPER E T / Ë ) ^' -j 80 ,*' s' H y S - 60 M B=PERMEABIUTY CURVE > For No. 26 Elee. Steel = / / M=IRON LOSS CURVE ~~ 40 For No. 26 Elee. Steel 6 / 60 Cycles - 4

J 2 , - n 0 0 0. 50 1. 00 1. 50 2. 00 2. 50 3. 00 3. 50 4.() 0 4. 50 WAHS LOSS PER POUND FIG. 8 in the same frame, 50 per cent for four-pole motors may be used which will result in fair characteristics for each of the three motors. Having made the preliminary design and checked the general proportions if it is considered advisable in view of the facts con cerning these general proportions, new diameters and lengths may be determined for the electrical design. The second design will therefore usually be safe to proceed with. The magnetizing current, the field and armature copper loss and the iron lose may now be calculated as was done when ana lyzing the existing motor. The " added " iron loss and friction 1915] HAMILTON: INDUCTION MOTOR 2409 and windage loss may be estimated with fair degree of accuracy from data on existing motors. This gives the necessary data for plotting the running idle point of the circle diagram. The circle coefficient, the maximum power factor and hence the diameter of the circle may now be calculated from the physical dimensions of the electrical design as was done previously, the circle being drawn as before through the running free point and tangential to the maximum power factor line, the blocked point not as yet having been determined.. The complete performance may there fore now be calculated as was previously done. Having a complete lay out and calculated performance of the

0 20 40 60 80 100 120 FAHRENHEIT DEGREES 22.2 33.3 44.4 55.5 CENTIGRADE DEGREES FIG. 9—CURVES SHOWING TEMPERATURE RISE design the different factors, such as, slip, power factor, efficiency, etc; may be considered in detail, and detail modifications made, and the effect on the other factors noted with comparative ease. For instance, the maximum efficiency can be made to occur at either less or greater than full load by arranging the iron losses and the copper losses accordingly. The point at which the maximum power factor occurs can to a certain extent be regu lated by modifications of the design. The temperature rise of the different parts of the motor de pends, of course, to a large extent on the mechanical design, construction and ventilation whether natural or by forced draft as with a definite fanning action. Fig. 9 will serve to indicate 2410 HAMILTON: INDUCTION MOTOR [Oct. 19 in general how much the temperature of the frame may be expected to rise above the surrounding air. Discussion of brush setting. The external characteristics of the repulsion motor being subjected to a wide variation due to the setting of the brushes in various positions with respect to the neutral axis or dead point, as it is more commonly known, it is of prime importance to determine the most advantageous position to set the brushes relative to the duty the motor is to perform. In general, the shifting of the brushes of a repulsion motor away from the dead point will increase its static torque up to a certain point, and thereafter the static torque will decrease with the further shifting of the brushes, while the

0 2 4 6 8 10 12 14 16 BRUSH SETTING ELEC. DEGREES FROM DEAD POINTS

FIG. 10—STARTING CHARACTERISTICS—5-H.P., 4-POLE, 60-CYCLE RE PULSION START INDUCTION MOTOR—FIELD RES. 0.287 OHMS. shifting of the brushes away from the dead point will decrease the strength of the repulsion motor for bringing the load up to speed. Test results on the 5-h.p. motor analyzed above are given here to bring out the pertinent points in the operation of a repulsion start motor. The resistance of the armature is approximately twice that of the field. The effect of the brush setting and starting characteristics are clearly shown in Fig. 10, where the blocked torque, amperes and power factor are plotted against the distance in electrical degrees that the brushes are set away from the dead point. It can be noted that the torque varies approximately as a sine curve reaching the maximum at 12 electrical degrees (four-pole motor) from dead point, while the torque decreases as the brushes are shifted further from the dead point. From a starting view point, the torque per ampere increases with the increase of the 1915] HAMILTON: INDUCTION MOTOR 2411

distance the brushes are set from the neutral axis, within the range that the motor can be operated. So from this viewpoint it is desirable to have th,e brushes set a considerable distance. from the dead point. Somewhat contrary results as to the proper brush setting are shown by the speed torque curves with the brushes in eight different positions, varying from 2 deg. to 16 deg. from the dead point. This shows that the motor as a repulsion motor, will develop the greatest torque at 1350 rev. per min. and at higher speeds when the brushes are set close to the dead point. It

S. 1 \ ιΝ4 Repulsion Motor S\J7 Curve No. 1 Brushes 2°(Elee.) from Neutral ] \ s " " 2 " 4° " ·' " _J " " 3 " 6° " " " Ί > " " 4 " 8° " " " 5 " 10° V\ " " 6 " 12° " " " 1 00 .. „ 7 „ 14o „ „ „ —i s "μ**" " " 8 " 16° " sz o^ 5^ * o 40 â ^Ν ^ fc^ -v 2 ""ί"" Js X ^> ^ = 30 S N": S^ ^ ^s ce 2^J x % S ^ Λ 6N". \ X ^ ^ ^ ^ \ \ [ S-Q \ Ë^ *Cl _-1 8* N ^v -"' r ^ ^ : \

o 0 2 )0 4(X ) 6(X ) 8(K ) 100 0 120 0 140 0 160 0 1800 SPEED-REV. PER MINUTE

FIG. 11—TORQUE-SPEED CURVES—5-H.P., 4-POLE—1750-REV. PER MIN. MOTOR can be noted by referring to Fig. 11 that after a speed of 1350 rev. per min. is reached the 2 deg. position has the greatest torque, with the running torque decreasing at that speed as the brushes are shifted away from the dead point. Fig. 12 shows the variation of horse power and torque and indi cates that the 4 deg. position develops the greatest horse power, showing that a shifting of the brushes in either direction from this point causes the motor as a repulsion motor to become weaker and the horse power it will pull up will be less. Thus we see that at the 12 deg. setting of the brushes the motor has the strongest starting torque and at the 4 deg. setting it de- 2412 HAMILTON: INDUCTION MOTOR [Oct. 19

velops the greatest horse power, so the final setting of the brushes is a balance between these two positions, depending upon the application of the motor. To consider the whole cycle of operation of the repulsion start induction motor as it comes up to speed as a repulsion motor, and is short circuited and converted into an induction motor; the curves of the repulsion motor for the 8 deg. setting are super imposed on the curves of the induction motor. Imposing the condition that the armature is short circuited at a predetermined speed the static torque and current, the maximum torque that

OL-SL· I I J I I I I ! I I 1 I 1 1 ! 1 0 1-2 3 4 5 6 7 8 HORSEPOWER OUTPUT FIG. 12—TORQUE-HORSE POWER CURVES— 5-H.P..4-POLE, 1750 REV. PER MIN. MOTOR

can be brought up to speed, the surge of current when the short circuiting occurs, and the maximum horsepower that can be brought up to speed can be analyzed in the following manner. Referring to Fig. 14, presupposing that the governor mechanism short circuits the armature at 1600 rev. per min. as indicated by position A on the repulsion motor speed curve, and follow ing the vertical line down to point B shows 16.5 lb-ft. torque was brought up to that speed;. Further, point C on the same vertical line shows the current then will be 28.0 amperes. A short circuiting of the armature then occurring at 1600 rev. per min. is at point D on the speed curve of the induction motor, 1915] HAMILTON: INDUCTION MOTOR 2413

and following the vertical line down from that point to point E on the torque curve of the induction motor it has 28 lb-ft. torque. Point F indicates that the current increases to 60 amperes. However, as just 16.5 lb-ft. torque was brought up ' to 1600 rev. per min. by the repulsion motor and the induction motor immediately after short circuiting occurs having 28 lb. ft. torque will rapidly carry the armature up to the speed where the induction motor will carry the torque that was brought up by the repulsion motor as shown by position G on the torque

1800

1600

1400

1200

* 1000 50 100 Q. z ξ 800, 40 80

600 2 30 ,„ 60 ! 1 400 £ 20 "* 40

200 10 20

0 0 0 0 2 4 6 8

HORSEPOWER FIG. 13—EXTERNAL CHARACTERISTICS 5-H.P., 208-VOLT, 60-CYCLE MOTOR—BRUSH SETTING 6 DEG. (ELEC) FROM DEAD-POINT—STANDARD ARMATURE—RESISTANCE ARM. =0.577—FIELD 0.287 OHMS curve of the induction motor, which is the same torque as that of position B of the repulsion motor. Position G shows that at 16.5 lb-ft. torque the load on the machine will be 5.4 horse power. At that horse power the speed is 1735 rev. per min. and the current is 27.5 amperes, so this case shows a condition where the repulsion motor brought up to speed 5.4 horse power ' with an increase of current from 28.0 to 60 amperes which is 240 per cent of full-load current when the governor short cir cuits the armature. The torque of the motor after short cif- 2414 HAMILTON: INDUCTION MOTOR [Oct. 19

cuiting being considerably greater than before short circuiting, the load is brought up to speed so quickly that an ordinary damped ammeter will show only 5 to 10 amperes increase of current at the time of short circuiting. The lower the speed at which the short circuiting occurs, the greater the torque that can be brought to speed and the greater the current at short circuiting until the speed is reached where the induction motor has its maximum torque, at lower speeds the amount of torque that can be brought to speed decreases

FIG. 14—EXTERNAL CHARACTERISTICS 5-H.P., 208-VOLT, 60-CYCLE MOTOR—BRUSH SETTING 8 DEG. (ELEC.) FROM DEAD-POINT—STANDARD ARMATURE—RESISTANCE ARM. = 0.577—FIELD 0.287 OHMS rapidly. So here again the determining factor is a balance between the horse power that is desired to be brought up to speed and the increase of current that occurs when the arma ture is short circuited. Table III shows» a complete analysis with the brushes set 8 deg. from the dead point, and the short circuiting occurring at various speeds. The curves Figs. 13, 14, and 15 and tables II, III and IV, for the 6 deg., 8 deg., and 10 deg. brush settings show that considerable flexibility can be obtained. Their an- 1915] HAMILTON: INDUCTION MOTOR 2415

alysis brings out these facts when the governor operates at 1600 rev. per min. With the brushes in the 6 deg. position the starting torque will be 34 lb-ft. or 225 per cent full-load torque, and the current at start, 325 per cent of full-load cur rent and the load 5.6 h.p. At the 8 deg. position the starting torque will be 50 lb-ft. or 335 per cent of full-load torque, start ing amperes will be 295 per cent of full-load amperes and will bring to speed 5.4 h.p. The 10 deg. setting shows

FIG. 15—EXTERNAL CHARACTERISTICS—5-H.P., 208-VOLT, 60-CYCLE MOTOR—BRUSH SETTING 10 DEG. (ELEC) FROM DEAD POINT—STANDARD ARMATURE—RESISTANCE ARM = 0.577—FIELD 0.287 OHMS. a starting torque of 64 lb-ft. or 425 per cent of full-load torque, starting current 280 per cent of full-load current and will bring up to speed 4.65 h.p. As the governor op erates at the same speed of 1600 rev. per min. the increase of current at short circuiting will be the same in each case. So where a large load is to be brought up to speed and a heavy starting torque is not necessary the 6 deg. position is the best; where a great starting torque is necessary, such as on a pump installation, etc., the 10 deg. position shows the 2416 HAMILTON: INDUCTION MOTOR [Oct. 19 best, but for best average results the 8 deg. position is the most desirable.

TABLE IL—5 H.P., 104-208 VOLT, 60 CYCLE, 4 POLE, 1750 R.P.M. REPULSION START INDUCTION MOTOR STANDARD ARMATURE BRUSHES SET 6 Elee. Degrees FROM DEAD POINT

Repulsion motor. Induction motor.

Starting Short cir. spd. Short cir. spd Running Short cir. Speed speed Torque Amp. Torque Amp. Torque Amp. Torque H.P. Amp. rev. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. per min.

1300 34 81 25.25 40.5 21.25 84 25.25 1350 34 81 23.5 38.5 23 81.5 23.5 1400 34 81 22.25 37 24.5 78 22.25 7.2 40 1680 1450 34 81 21 35.5 26 75 21 6.85 37 1695 1500 34 81 19 33 27 71 19 6.25 32.5 1710 1550 34 8 18.5 32 28 65.5 18.5 6.1 31.5 1712 1600 34 81 17 30 28 60 17 5.6 28.5 1722 1650 34 81 16 28.5 26 50 16 5.3 27 1730 1700 34 81 14.5 27 20.5 36 14.5 4.85 24.5 1738

TABLE III.—5 H.P., 104-208 VOLT, 60 CYCLE, 4 POLE, 1750 R.P.M. REPULSION START INDUCTION MOTOR STANDARD ARMATURE BRUSHES SET 8 Elee. Degrees FROM DEAD POINT

Repulsion motor. Induction motor.

Starting Short cir. spd. Short cir. spd Running Short cir. Speed speed Torque Amp. Torque Amp. Torque Amp. Torque H.P. Amp. rev. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. per min.

1300 50 74 24.5 37 21.25 84 1350 50 74 23 36 23 81.5 23 7.4 42 1680 1400 50 74 21.5 33 24.5 78 21·. 5 6.95 38 1695 1450 50 74 20.4 32.1 26 75 20 Θ.5 34.5 1705 1500 50 74 19 30.5 27 71 19 6.2 32.5 1715 1550 50 74 18 29 28 66.5 18 5.9 30.5 1720 1600 50 74 16.5 28 28 60 16.5 5.4 27.5 1730 1650 50 74 15.5 26.25 26 50 15.5 5.1 26 1735 1700 50 74 14.0 25 20.5 36 14 4.65 23.5 1742

The effect of increasing armature resistance. An armature with approximately two times the resistance of that of the stand ard motor, making resistance of this armature four times that 1915] HAMILTON: INDUCTION MOTOR 2417 of a field or stator, brings out the following facts. The starting condition relative to the brush setting is shown on Fig. 10. Up to the 8 deg. position the starting torque was practically equal to that of the standard motor, but it only developed 56 lb-ft. torque at its maximum position (12 deg. from the dead point) against 74 lb-ft. with the standard armature at its maxi mum position. The current was about 10 per cent lower in all positions. It was perceptibly weaker as a repulsion motor than when the standard armature was used, compare Fig. 16 and Table V with Fig. 14 and Table III, it bringing up to speed but 5.4 h.p. with the governor operating at 1500 rev. per

TABLE IV.—5 H.P., 104-208 VOLT, 60 CYCLE, 4 POLE, 1750 R.P.M. REPULSION START INDUCTION MOTOR STANDARD ARMATURE BRUSHES SET 10 Elee. Degrees FROM DEAD POINT

Repulsion motor. Induction motor.

Starting Short cir. spd. Short cir. spd Running Short cir. Speed speed Torque Amp. Torque Amp. Torque Amp. Torque H.P. Amp. rev. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. per min.

1300 64 70 21.25 32 21.25 84 21.25 6.9 38 1695 1350 64 70 20 30.5 23 81.5 20 6.5 34.5 1705 1400 64 70 19 29 24.5 78 19 6.2 32.5 1712 1450 64 70 17.75 28.5 26 75 17.75 5.8 30 1720 1500 64 70 16.5 26.5 27 71 16.5 5.4 28 1730 1550 64 70 15.25 25 28 66.5 15.25 5.05 26 1735

1600 64 70 23.5 60 14 4.65 1740 14 28 i 24 1650 64 70 13 22 26 50 13 4.35 22.5 1745 1700 64 70 12.5 21.5 20.5 36 12.5 4.2 21 1750 min.; at this speed the increase of current at short circuiting is the same as at 1600 rev. per min. with the standard armature. This shows, however, the possibility of increasing the arma ture resistance so that the short circuiting can occur at a lower speed and thus the load broug.it up\ to speed with a given amount of static torque can be increased. But with an armature resistance, as in this case, of four times that of the field there is no advantage to be gained in either the starting or bringing the load to speed, and there is a defi nite disad vanta gθ when the motor is running as an induction motor. In general, the best average results will be secured 2418 HAMILTON: INDUCTION MOTOR [Oct. 19 by using an armature resistance of from two to three times that of the field.

3—MECHANICAL DESIGN The distinguishing feature of the mechanical design of the repulsion start induction motor is the commutator short cir cuiting device. The success of this type of motor has been due to a very large extent to the fact that this device has been developed so that it is entire ly dependable, even under adverse conditions. All of these devices work on the centrifugal principle and the better designs are arranged so that the short circuiting takes place instant- g ly when the proper speed has i been reached even though £ the motor is accelerating very | slowly. This quick action at g the make and the break in- * sures smooth and efficient action of the short circuiting members for an indefinite period. This type of motor is usually made with a radial commutator for convenience of arranging the short circuit HORSEPOWER ing device and so that the FIG. 16—EXTERNAL CHARACTERIS brushes may be lifted from the TICS 5-H.P., 208 VOLT, 60-CYCLE MOTOR commutator after the short Brush setting 8 deg. (Elee.) from dead circuiting. Lifting the brushes point— high resistance · armature—res. arm. after motor has started elim 99 ohms.—field 287 ohms. inates all friction wear and noise and has therefore assisted to a considerable extent in making this motor a success. The mechanical design in general of this type of motor is not different from other types of motors. Designers are now well agreed for the most part that a certain rigidity of frame, shaft and other parts is as essential to produce quiet, smooth run ning and efficient motors as is a good electrical design and that an otherwise good electrical design can be spoiled by a poor mechanical construction. Modern shop practise has made it 1915] HAMILTON: INDUCTION MOTOR 2419 possible to employ satisfactorily as small an air gap or clear ance as is desired in most cases. Pressed steel is being used to a considerable extent in this type of motor to lighten, strength en and at the same time lower the cost. The use of forced ventilation is helping materially to improve this type as well as other types of motors. One of the most commendable features of modern motor designing as in other apparatus is to appeal to the esthetic, to improve the looks, to harmonize the design with the apparatus it is to operate as far as it is practicable. Fig. 17 shows the cross sectional view of the repulsion start induction motor. This view shows the arrangement and con-

TABLE V.—5 H.P., 104-208 VOLT, 60 CYCLE, 4 POLE, 1750 R.P.M. REPULSION START INDUCTION MOTOR High Resistance Armature* BRUSHES SET 8 Elee. Degrees FROM DEAD POINT

Repulsion motor. Induction motor.

Starting Short cir. spd. Short cir. spd Running Short cir. Speed speed Torque Amp. Torque Amp. Torque Amp. Torque H.P. Amp. rev. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. lb-ft. 208 V. per min.

1300 48 67 . 22.3 33.5 24.7 68.5 22.3 6.75 40.7 1590 1350 48 67 21 32.2 25.2 65 21 6.42 38 1615 1400 48 67 19.5 30.7 25.5 61.5 19.5 6.1 35 1635 1450 48 67 18.2 29.5 25.5 > 57 18.2 5.7 32 1650 1500 48 67 17 28 25.0 52 17 5.4 30 1665 1550 48 67 15.8 26.7 24.3 47 15.8 5.03 28 1680 1600 48 67 14.5 25 21.7 40 14.5 4.65 25.8 1695 1700 48 67 12.5 23 13.5 24 12.5 4.0 22.3 1710 struction of a type of automatic commutator short circuiting device and brush lifting device which has proved entirely satisfactory. SUMMARY The starting efficiency of the repulsion start induction motor is substantially the same as for the shunt and compound-wound direct-current and the multiphase-wound with rotor with resist ance in rotor for starting, which has the highest starting efficiency of the various multiphase motors. This type of motor in all sizes may be started by closing the switch without the use of a starter of any kind as they take less than 300 per cent of full- 2420 HAMILTON: INDUCTION MOTOR [Oct. 19 load current at start and have over 300 per cent full-load start, and are therefore simpler to install and operate than the direct- current or the multiphase motors, as these require some form of starter to limit the starting current. We may, therefore, conclude that this type of motor compares favorably in all respects to the best direct-current and multiphase motors and is now the standard type of single-phase motor and has largely replaced less satisfactory types of single-phase motors. We have observed that a motor of this type can be easily

FIG. 17 analyzed and the different losses determined accurately and that such an analysis gives a definite and scientifically accurate basis for improving or modifying existing designs or for pre determining the performance of new designs. A definite and simple method has been set forth for calculating a new design of motor. The excellent performance and the comparative freedom from trouble and annoyance of the automatic short circuiting devices have helped materially to establish this type of motor.