per ton in large furnaces under advantageous condi-tions and as high as 150 to 200 lb of carbon electrodes in small and poorly designed furnaces. The con-sumption of electrodes in the ferro-alloy industry varies widely depending, of course, upon the material produced; it may be as low as 25 lb of carbon elec-trodes per ton for 15 per cent ferrosilicon, 50 lb per ton for 50 per cent ferrosilicon, 65 lb for 80 per cent ferromanganese, and 150 to 300 lb per ton for silicon alloys containing the higher percentages of silicon when these materials are produced under good operating conditions, but 2 or 3 times these figures for the same alloys produced under less advantageous conditions.

In the nonferrous industry, figures as low as 2 y 2

to 3 lb of graphite electrodes per ton are reported, but the average is undoubtedly nearer double that quantity and figures much higher often are reported.

In making high-grade steel, alloy steel, tool steel, stainless steel, etc., electrode consumptions as low as 17 lb of carbon electrodes per ton have been reported, but figures in that neighborhood are rather unusual and the average is probably nearer 25 lb. The figures for graphite are not as low as the expected y 2 of the figures for carbon because of the long finishing time required for these metals. During that period the electrodes are consumed largely by oxidation ; and although this is less with the graphite electrode because of its smaller size, still the propor-tion is not maintained and graphite consumption of less than 12 lb per ton is unusual. In the steel cast-ing field, the consumption of graphite electrodes is very nearly half that of carbon ones, with graphite consumptions reported as low as 4 y 2 to 5 lb com-paring with carbon at 9 to 10 lb, and as high as 10 lb per ton, comparing with 20 lb for carbon. Such figures are influenced greatly by the rate of opera-tion, that is, the number of heats per day and the amount of power put into the furnace per hour; and if the oxidation loss is proportionately great, as in the production of high-grade steel, the figures for graphite do not appear to as good advantage as they do when the bulk of the electrode consumption is accounted for by the transmission of power to the charge. Electrode consumption for iron may be as low as 3 lb per ton of graphite electrodes for furnaces charged with hot iron from the cupola, or may run as high as that for steel castings. Relatively few carbon electrodes are used in the gray iron industry, either duplexing or straight.

CONCLUSION

The number of users of carbon and graphite elec-trodes is increasing year by year, and the field of application is constantly widening. The future growth of the industry depends largely upon the use of the right electrode in the right place to secure the desired result, whether that be a new product or an old product made in a new way at a lower cost.

Electrode manufacturers have made clear their desire to cooperate at all times with electrode users, and particularly in the later years operators have shown more inclination to benefit by the assistance the manufacturers were willing to give.

Induction Motors as Selsyn Drives The power Selsyn unit, an adaptation of the wound rotor induction motor, provides accurate remote control of angular motion, using only an electrical connection. The characteristics of these units are described briefly in this paper, and methods of calculating their performance are offered. Typical applications of Selsyn drives also are given.

By L. M. N O W A C K I General Elec C o . , A S S O C I A T E A . I . E . E . Schenectady, Ν . Y.

THE SELSYN device is used for repeating or reproducing by remote electrical control angular motion, both as to speed and total angle. The word ' 'Selsyn'' is an abbreviation of the expres-sion "self-synchronous" and indicates the normal use of the apparatus. The function of the Selsyn system is to transmit motion by electrical means between 2 points which cannot conveniently be interconnected mechanically.

The power Selsyn unit is an adaptation of the conventional wound rotor induction motor. The principle of operation is a familiar one. For sim-plicity, 2 identical 3-phase wound rotor induction motors will be considered. The stator windings are excited from a common power source, and the rotors electrically interconnected. One Selsyn unit is located at the point where the motion is generated and the other unit is located at the point where the motion is duplicated. Under these conditions, for each pair of poles, there is only one relative position of the rotors where the secondary voltages will be exactly opposed so that no current will circulate in the secondary windings. For other positions, a current will circulate in the rotor windings and torques will result tending to turn the rotors to that position where the voltages are again equal and opposite. If, therefore, one rotor is turned, the other rotor will tend to assume exactly the same position.

Selsyn units are synchronized at standstill by applying single-phase excitation. This introduces several problems which bear directly on the choice of control and winding connections. A study of

Full text of a paper recommended for publication by the A.I.E.E. committee on electrical machinery, and scheduled for discussion at the A.I.E.E. winter con-vention, Jan. 23-26, 1934. Manuscript submitted Oct. 17, 1933; released for publication Nov. 3, 1933. Not published in pamphlet form.

848 ELECTRICAL ENGINEERING

the several synchronizing characteristics is important to the thorough understanding of the Selsyn drive. Both operating and synchronizing torques are ex-pressed in terms of induction motor operating char-acteristics, thus enabling the direct translation of induction motor characteristics into synchronizing and operating data.

GENERAL

Selsyn devices were first built over 20 years ago. They were originally designed as instruments for transmitting and receiving an indication by an angu-lar movement. In these applications the Selsyn receiver carried on its shaft only a very light dial pointer or possibly a cam. The characteristics of the Selsyn device, however, soon made it desirable that the receiver be capable of exerting enough torque to perform such work as operating relay contacts or turning a valve. Simultaneously with this develop-ment came also requests for Selsyn control systems where the units were required to rotate continuously at high speeds in addition to carrying mechanical loads. In the last 5 years, considerable progress has been made in extending the Selsyn principle to indus-trial machine drives.

The study of Selsyn behavior has not been given much attention in technical literature. Several papers were published in trade journals bearing, in the main, on application problems. The increasing popularity of the Selsyn drive made urgent a thor-ough understanding not only of the underlying principle of the Selsyn system, but, also, of the operating and synchronizing characteristics. It is the purpose of this paper, therefore, to describe briefly the behavior of the Selsyn units, to offer a convenient method for determining their character-istics, and to suggest the possible arrangements of the Selsyn tie.

THREE-PHASE OPERATING CHARACTERISTICS

The 2 Selsyn units are connected as shown in Fig. 1. One unit, the transmitter, is driven. The second unit, the receiver, rotates in synchronism with the transmitter. The angle of deflection between the 2 rotors is given in electrical degrees and is designated by a. For any angle a and slip s, the transmitter and receiver torques, for rotation against the revolving field, are :

6.09 V(I - Im) sin 0 sin a + Γο sin2 -̂ lb-ft rpm 2

6.09 V{I — Im) . . _ . . a Tr = sin θ sin a — T0 sin2 -

rpm 2

where

lb-ft

(1)

(2)

V is the line voltage J is the induction motor current for slip 5 cos θ is the induction motor power factor for slip ^ Γο is the induction motor torque for slip s I M is the induction motor magnetizing current rpm is the induction motor synchronous speed

The above factors, as designated, are determined for an induction motor operating at the given slip. Thus the induction motor characteristics may be translated directly into Selsyn drive performance.

Similarly, the currents:

It = (lm cos | + jl sin | ^ Ζ - |

Ir = (j[m cos | - jl sin f ) z + f The line current:

J, = 2 ( / „ cos21+7 s i n 2 | )

The rotor current:

IR = jh sin |

(3)

(4)

(5)

(6)

Γ2 is All the currents are expressed vectorially. the rotor induction motor current for slip s.

Torque characteristics are shown in Figs. 2 and 3. The torque expressions of eq 1 and 2 consist of

2 components, the first a synchronizing component due to the rotor displacement, acting in the direction to decrease the angle, and a rotor loss torque, acting in the direction of the rotating field. On this ac-count, the receiver torque is higher for rotation with the field and the transmitter torque for rotation against the field. The synchronizing torque is highest and the induction motor torque is lowest for slips greater than unity. Therefore, to obtain the highest synchronizing torque efficiency, Selsyn units are recommended for operation against field rotation. Similarly, to obtain the highest motor torque effi-ciency, the units are recommended for operation in the direction of field rotation. Rotation in the direction of the revolving field is much limited by the loss of synchronizing torque in the neighborhood of synchronous speed. Here, if there should be a sudden change in speed, particularly if the inertia of the system is appreciable, the transmitter and

3-PHASE POWER SOURCE

ί ROTORS ί

η n u I 1 STATOR π

ί

Fig. 1 (left). Connection dia-gram of 2 Selsyn units

Fig. 2 (left below). Three-phase torque-angle character-istics at standstill, illustrated for 2 25-hp 8-pole 60-cycle 3-phase wound-rotor induc-

tion motors

Fig. 3 (below). Three-phase maximum torque character-istics, illustrated for same

motor as Fig. 2

§ 4 0 0

t 3 0 0

Λ 200

τ RANS MITT :R -4~L -REC EIVE

\ ÏECE VER

\ ISMO TER̂ \ \

I u 20 40 < 60 ' 80 I00 I20 MO I60 180

ELECTRICAL DEGREES DISPLACEMENT 2.0 1.8 1.6 1.4 1.2 1.0 OA 0.6 0.4 0 2

SLIP

receiver may momentarily interchange their func-tions and possibly fall out of step. Operating in each direction with respect to the revolving field has its definite applications, all factors considered.

DECEMBER 1933 849

S Y N C H R O N I Z I N G O F S E L S Y N U N I T S

Selsyn units are synchronized a t standstil l . Single-phase power is applied first, and, after a m o m e n t a r y t ime delay, 3-phase excitat ion is appl ied. A l though the units m a y be synchronized 3-phase, synchronizing single-phase is more pract ical and eliminates certain difficulties.

I f 3-phase power is applied to the 2 units and if the in i t ia l angle of displacement is large, then, if the 2 units are unrestrained, they m a y tend to come up in speed in the direction of the revolving field. One machine wi l l serve as a short circuit for the rotor of the other. T h e machines wi l l not assume any definite speed but wi l l f luctuate. I f one uni t is restrained, the other m a y come up to speed as an induct ion motor . W i t h single-phase excitat ion, this occurrence is avoided, for the only torque existing is the synchronizing torque and continuous t ract ion is not possible. Once the units are synchronized, 3-phase power is applied and the Selsyn t ie is operative.

Single-phase excitat ion m a y be applied in one of 3 ways as shown in Figs. 4, 5, and 6, respectively. I n a l l cases, the rotors are interconnected 3-phase. Each connection has its part icular torque-angle characteristic.

T h e connection of F ig . 6 is suitable for synchroniz-ing. T h e m a x i m u m torque is high and occurs in the neighborhood of 150 electrical degrees, the region where the synchronizing torque is least for the other connections. A possible objection to this connection, for some applications, is the rap id decrease in torque for angles less t h a n 90 deg. A convenient arrange-ment , f r o m an operat ing point of view, is the se-quence of connections of F ig . 6 and F ig . 4. T h e con-

motor action, but , on the same account, i t is best for single-phase Selsyn operat ion. C A S E I :

r 3.05 V(I - Im) sin θ . . Τ = sin a lb-ft (7)

rpm

Ii - ^ ( / » c o s « f + J s i n « f) (8)

C A S E I I :

_ 3.50 V(I - Im) sin θ . Τ = sin a lb-ft (9)

rpm

Ii = ^ ( / « cos* I + / sin' | ) (10)

T h e nomenclature is the same as for the 3-phase characteristics. T h e 3-phase induct ion motor values are determined for the slip of one and translated direct ly into single-phase synchronizing data .

T h e connection of F i g . 6 is a very special case and does not yie ld a simple solution. A n analysis of this

ELECTRICAL CABLES

CONTROL AND POWER CABLE

OPERATOR S CONTROL HOUSE

COUNTERWEIGHT

Fig. 7. Lift bridge operated by power Selsyn drive

CASE I

\ STATOR I /

f STATOR Π

^ 7

3 \ Λ

0 — L- -A

u / 1 Φ 0 ' 3 0 40 80 120 160

ELECTRICAL DEGREES DISPLACEMENT

H y

A / \ / \ / 1 \

\ \ I

0 40 80 120 160 ELECTRICAL DEGREES DISPLACEMENT

F19. 5. Case II.

\STATQRI /

f STAT6RI\

1

/ \ f /

/

0 40 80 120 160 ELECTRICAL DEGREES DISPLACEMENT

Fi3. 6 . Case II Fig. 4. Case I.

Figs. 4, 5, and 6. Single-phase torque-angle characteristics at standstill for 3 different connections

of same motors as illustrated in Fig. 2

case is given in detai l in Appendix I I . For one th ing, the magnetic flux varies w i t h the displacement

•-angle, increasing in the rat io of V2 for 90 deg dis-placement. T h e increased flux results i n saturat ion and in an appreciable change in the several circuit constants. For this reason, the problem becomes involved and a rigorous solution difficult. I t is to be noted t h a t a definite second harmonic is present in the torque characteristic, which, i n par t , accounts for the decreased torque for the low values of dis-placement angle, and for the increased torque for the high values of displacement angle.

A P P L I C A T I O N O F S E L S Y N D R I V E S

nection of F i g . 4 prepares for the next step, the simultaneous application of the 3-phase excitat ion to all units.

T h e connection of F ig . 5 has the advantage t h a t the magnetic flux is increased in the rat io of 2 / V 3 . T h e torque, l ike tha t of the connection shown in Fig . 4, varies as the sine of the displacement angle. For a given flux, the 2 connections have identical torque-angle characteristics a t standsti l l . T h e con-nection of F ig . 5 has part icular value when single-phase excitat ion is employed under running condi-t ion. Th is arrangement is poorest for induct ion

A common and a simple applicat ion of Selsyn units is the t ie of 2 paral lel drives. A n interesting ar-rangement is the synchronized dr ive for the long l i f t bridge, as shown in F i g . 7. T h e 2 ends of the bridge are l i f ted b y separate motors. A power Selsyn un i t is direct connected to each m a i n motor and the 2 Selsyn rotors are electrically intercon-nected. T h e m a i n motors, as wel l as the 2 Selsyn units, are energized f r o m the same power source. T h e Selsyn units are first synchronized, and, after a short t ime delay, 3-phase power is applied to the 4 machines. B y this t ie, the 2 m a i n motors are held

E L E C T R I C A L E N G I N E E R I N G

in step during acceleration and running, and the 2 ends of the bridge are lifted and lowered in syn-chronism. In addition to this feature, the syn-chronized drive embodies several other points of interest. By using 4 duplicate units, 2 for the main drives and 2 for the synchronous tie, the entire

of interconnecting drive shafts, gears, and bearings commonly associated with the usual form of press drives, with possible savings in cost of labor and maintenance.

Selsyn units are used to synchronize auxiliaries with the main drive in many industrial equipments. A Selsyn generator is direct connected to the main motor and the several auxiliary units are driven by separate Selsyn motors. This form of a Selsyn tie is shown in Fig. 11, for the poidometer drive. In mill operations, it is often necessary to vary the kiln speed, and it is desirable to vary the feed in like manner. The tube mills, for instance, are fed with 2 materials and it is necessary to have close regula-tion of the proportions of the materials in order to insure uniformity of product. Also, to obtain a maximum satisfactory output of the mill, it is important to have control of the quantity of material carried on the conveyors. By adapting the Selsyn tie to the poidometer drive, the kiln may be operated at any desired rate with a corresponding change in

Fig. 8. Lifting motor and Selsyn unit on top of tower of bridge span

bridge may be lifted by one driving motor in case the other fails. Although this will impose a double load on the acting motor, nevertheless, in an emer-gency, this factor may prevent delay to railway traffic and navigation. Furthermore, the operating machinery is removed to the towers, the long-haulage cables and sheaves are eliminated, and thereby the weight of the total span is substantially reduced. A lifting motor and Selsyn unit of this type are shown in Fig. 8.

The Selsyn tie is applied to synchronize a group of unit motor drives, as shown in Fig. 9, for the straight-line high-speed newspaper press. The Selsyn unit is built integral with each driving motor, as shown in Fig. 10. The entire group of Selsyn elements is energized from a common power source and all the rotor windings are electrically interconnected. The Selsyn units are first locked in step and when driven by their respective motors, start simultaneously and rotate in synchronism. Any unbalance in power between the several driving motors is equalized through the Selsyn units. The movement of any individual rotor in this combination is accompanied by a simultaneous and equivalent movement of each of the other rotors. The inherent function, there-fore, of such a group of Selsyn units is to hold in step and resist any external force to pull them apart. In the event of failure of any driving motor, con-tinuity of operation is assured. The Selsyn unit, deriving its energy from the other Selsyn units, will carry the total load of the individual drive. Such loading of the Selsyn unit is not generally recom-mended for long periods, but in an emergency, this feature is desirable. The application of the Selsyn tie to the segregated drive for newspaper presses made for greater flexibility and convenience. It made possible the complete elimination of all forms

Fig. 9. Arrangement of motor drive with Selsyn tie-in, for straight line high-speed newspaper press

the conveyor speeds. In this manner, the propor-tions of the raw materials are fixed irrespective of the kiln speed.

The examples given are but a few of the possible applications of the Selsyn tie. A detailed and a specific description of the several drives is beyond the scope of the paper. The field of application is broad, ranging from fractional horsepower ratings for small auxiliary drives to main drives of 75 and

Fig. 10. Selsyn unit printing press drive

Fig. 11. Arrangement of Selsyn tie for poidometer

drive

100 hp. The practicability of the Selsyn tie is fully recognized and its usefulness is more and more realized by the industrial engineer. The flexibility of the drive, the simplicity of operation, and the resulting economy will, no doubt, lead to the further adoption of the Selsyn principle to the synchronized motor drive.

DECEMBER 1933 851

Appendix I—Calculation οί 3-Phase Characteristics

The equivalent circuit of 2 identical Selsyn units is the combined induction motor circuit for the 2 rotors in series. The electrical angle of displacement between the 2 rotors is equivalent to the same displacement between the Selsyn terminal voltages. The circuit constants are per phase star and are referred to the stator.

The equivalent circuit of Fig. 12 is resolved into the 2 component circuits of Fig. 13 and Fig. 14, respectively. The currents and voltages are determined for each component circuit, and, by super-position, are combined to give the currents and voltages of the original circuit.

The power transferred across the air gap is EgI2 cos 0 2, where Eg

is the air gap voltage, I2 is the rotor current, and θ2 is the angle between them. In terms of the 2 component circuits, the power transferred is

Fig. 12. The equivalent circuit of 2 identical Selsyn

units

Fig. 1 3. The first component circuit

Ρ = p> + p " (Π)

This is permissible, for the secondary current is common to the air gap voltages of the 2 component circuits.

Ρ = Eg'I2" cos φ' + Ε/Ι/' cos φ"

where :

Eg' is air gap voltage of 1st component circuit Eg'

f is air gap voltage of 2nd component circuit I2" is secondary current of 2 n d component circuit φ' is angle between Eg' and I2" φ" is angle between Eg" and I2"

E0' = jxmE

ri + j(xi + xm) 2

*m Ε α 7Γ

= -γτ cos - Ζ - 0i + -

72" = h sin - Ζ -

where :

Z' Ζ 0 i ' is the impedance of 1st component circuit I2 Ζ — 0 2 " is the induction motor rotor current for slip s xm is the induction motor magnetizing reactance

p> = Eh sin - cos - cos ( 0 / - θ2")

(12)

P" = 7 2

2 r2 . a

I2 r2 / a = (1 - ab) sin2 -

J 2

Fig. 14. The second compo-nent circuit

(15)

Combining eq 14 and 15, the Selsyn transmitter torque, for rotation opposite to the magnetic field, is:

T t - r^m 1 ( 1 - a b ) L W * ~2~) S m a + 7 S i n 2

2J l b " f t ( 1 6 )

Similarly, the receiver torque :

Γ ' - w 7 ( 1 - û è ) I À 2 - - R )

s i n α - 7 s i n 2 J l b " f t ( 1 7 >

where :

rpm is the induction motor synchronous speed r2 is the induction motor secondary resistance s is the induction motor slip

a is the displacement angle between rotors in electrical degrees

^ 7 EI2 sin a [sin 0 / sin 0 2 " + cos 0 / cos 0 2"]

7 i / 2 sin α rxm(xi + xm) . n „ • rxxm Ί _ 2 ~ L (ZT sm 0 2 " + ( — 2 c o s 0 2 j (13)

Equation 13 is rigorous, but, for convenience, it may be simplified by making the following assumptions:

Xm (Xl + Xm) 1 - ab

r^7j2 is negligible

I2 sin 0 2 " = 7 sin 0 / — 7 m

P ~ l ~ 2 2~J ( 1 - a h ) s i n α

where :

7 is the induction motor current for slip 5 7 m is the induction motor magnetizing current Xo is total induction motor leakage reactance xm is induction motor magnetizing reactance

ab IM Χα

Ε

(14)

The transmitter current :

( a oc\ a

Imcos-+jl sm-) Δ - -

The receiver current :

( a a\

7 m c o s ~ -jls'm-J Ζ 2

ri = 2 ( / m c o s 2 s i n 2 1 )

The line current :

II

The rotor current :

(X

IR = j7 2 sin -

(18)

(19)

(20)

(21)

But for a small error, eq 16 and 17 may be written in the following form, as presented in the text:

=

6 0 9 V (/ _ IM) sin 0 sin a + T0 sin2 - lb-ft rpm 2 (22)

6.09 V a r = rpm ^ ~~ ' S i n θ S i n α "" Γ ° s i n 2 2 l b " f t ^

852 ELECTRICAL ENGINEERING

T H E S I N G L E - P H A S E S Y N C H R O N I Z I N G T O R Q U E S

The method employed for the 3-phase calculations may be ex-tended for the first 2 cases of the single-phase excited units. The direct-phase and reverse-phase-sequence voltages are determined and the corresponding currents and torques calculated. For case I, the component voltages at standstill are:

(24)

Where D denotes direct-phase sequence and R reverse-phase se-quence.

- J O

4 L r

' 6 . 0 9 7 , χ . . ^ . {I — Im) sin θ sin a — T0 sin

rpm Δ

09 F

rpm (J — Im) sin θ sin a + To sin

il ib-ft

in2 |J lb-ft

Τ = TD + TR = (I - Im) sin θ sin a lb-ft rpm

Similarly for case II :

Ε ED = ER =

And 3.50 V(I - Im) .

Τ = TD + TR = — sin 0 sin a lb-ft rpm

(25)

(26)

(27)

(28)

(29)

The nomenclature is the same as for the 3-phase case. All the factors are determined for locked-rotor 3-phase induction motor.

Appendix II—Single-Phase Characteristics of Case III

The stators and rotors are connected as shown in Fig. 6. De-flecting one rotor from the other is equivalent to displacing the 2 stator fields by the same angle. If the angle of deflection between

Fig. 15. Schematic diagram of the 2 single-phase fields

a r, Jx» b ψ j*i γ M r, J*i

Fig. 16. Three-phase imped-ance offered to the in-phase voltage component

Fig. 17. Three-phase im-pedance offered to the quad-rature voltage component

the 2 rotors is a, the stators may be represented diagrammatically as shown in Fig. 15.

Let voltage Ε Ζ - a/2 = 0. Refer Ε Ζ a/2 to the direct axis of stator II, namely (EZa/2) (cos a — j sin a). £ cos α Ζ a/2 induces no voltage in phase Ο'α'. For this component, the short

circuit may be considered 3 phase. The impedance offered to Ε cos α Ζ a/2 is a balanced 3-phase secondary impedance as repre-sented by the circuit of Fig. 16.

— jE sin α Ζ a/2 induces no voltage in phases Q'b' and 0'c''. For this component, the 2 phases may be considered open circuited. The impedance offered to — jE sin α Ζ a/2 is a balanced 3-phase secondary impedance represented by the circuit of Fig. 17.

Similarly let Ε Ζ α/2 = 0. Refer voltage Ε Ζ - a/2 to the direct axis of stator / , namely (Ε Ζ — a/2) (cos a + j sin a). The impedance of Fig. 16 and Fig. 17 is now offered to Ε cos a Ζ — a/2 SLnajE sin a Ζ — a/2, respectively.

The several voltages are further resolved into the in-phase and quadrature components :

Voltages at « Voltages at d

Ε cos α cos a /2 Ε cos α cos a /2 jE cos a sin a /2 — jE cos a sin a /2

—jE sin a cos a /2 jE sin a cos a /2 Ε sin a sin a /2 Ε sin a sin a /2

jKE sin a cos a /2 —jKE sin a cos a /2 KE sin a sin a /2 KE sin a sin a /2

Inspecting the 6 sets of component voltages, it may be noted that 3 pairs are in phase addition and 3 in phase opposition. One set of 3 operates on the open-circuit impedance of Fig. 13 and the other on the short-circuit impedance of Fig. 14. The 2 voltages are designated by E' and E".

E' = £(cos a cos a/2 + (1 + K) sin a sin a/2)

E" = jE(cos a sin a/2 — (1 — K) sin a cos a/2)

(30)

(31)

E' and E" are single-phase voltages producing pulsating fields. The 2 pulsating fields are each resolved into the 2 rotating fields of direct and reverse-phase sequence which, at standstill, are E'/2 and £ 7 2 .

As for case I and case II :

21.1 Τ = TD + TR = r — Eg'h" cos φ' lb-ft 2 rpm

(32)

where :

Eg' is the air gap voltage of the open circuit J2 " is the secondary current of the short circuit φ' is the angle between Eg' and I2" rpm is the synchronous speed

The factor Κ is an impedance ratio. It is determined from the circuit of Fig. 17.

Κ = (33)

where Ea and Ed are the voltages at a and d, respectively.

Ref erences 1. S Y N C H R O N I Z E D D R I V E S W I T H O U T M E C H A N I C A L C O N N E C T I O N S , H. W.

Reding. Elec. Jl., v. 30, 1933, p. 277-80. 2. T H E A P P L I C A T I O N O F T H E S Y N C H R O N O U S T I E T O M O D E R N C O N T R O L

P R O B L E M S , R. H. Wright. Iron and Steel Engr., v. 10, 1933, p. 123-30. 3. S Y N C H R O N I Z E D M E C H A N I C A L M O T I O N W I T H O U T M E C H A N I C A L C O N N E C -

T I O N , C W. Drake. Maintenance Engg., v. 90, 1932, p. 441-3. 4. S E L S Y N C O N T R O L F O R P A P E R M A C H I N E S , F. M . Roberts. Paper Trade

Jl., v. 95, 1932, p. 18-20. 5. S A F E G U A R D I N G A N D C O N T R O L L I N G S E Q U E N C E O P E R A T I O N S , R. H. Rogers.

Elec. World, v. 99, 1932, p. 372-5. 6. S Y N C H R O N I Z I N G C O N V E Y O R S B Y P H O T O C E L L S A N D S E L S Y N S , W. B. Snyder.

Elec. World, v. 99, 1932, p. 327. 7. S E L S Y N D E V I C E S A N D T H E I R A P P L I C A T I O N S , L. W. Bailey. Combustion,

v. 3, 1931, p. 21-5, 39, 46. 8. V E R S A T I L I T Y O F A P P L I C A T I O N O F S E L S Y N E Q U I P M E N T , R. A . Corley.

Gen. Elec. Rev., v. 33, 1930, p. 706-11. 9. A P P L I C A T I O N O F S E L S Y N R E M O T E C O N T R O L I N T H E O I L R E F I N I N G I N D U S T R Y ,

L. De Florez. Gen. Elec. Rev., v. 33, 1930, pp. 378-83. 10. P R I N C I P L E S O F S E L S Y N E Q U I P M E N T S A N D T H E I R O P E R A T I O N , L. F. Holder.

Gen. Elec. Rev., v. 33, 1930, p. 500-4. 11. M E T E R R E A D I N G S A N D S I G N A L S T R A N S M I T T E D B Y S E L S Y N M O T O R S , A . E .

Bailey. Power, v. 68, 1928, p. 434-5.

DECEMBER 1933 853