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pGiNEERM^a
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CONNECTING
INDUCTION MOTORS

VlkQrobo-Mll Book QxJm

PUBIISHETIS OF, BOOKS FOR^

Electrical \\forld '^ Ei^ineerir^ News^Record
Power V Engineering and Mining Joumal-Ress
Chemical and Metallurgical Engineering
Electric Railway Journal v Coal Age
American Machinist ^ Ingenieria Intemadonal
Bectrical Merchandising ^ BusTiansportation
Journal of Electricity and Western Industry

Industrial Engineer,

iiii ii h i i iiin M ifi1iiiiif h !i!in ^ i m i fr i mr i1 i ii rn T i ii i ifftii iiii >i H

CONNECTING
INDUCTION MOTORS

The Practical Application of a Designing Engineer's
Experience to the Problems of Operating Engineers,
Armature Winders and Repair Men. Also the Presen-
tation to Students of Practical Questions Arising in
Winding and Connecting Alternating Current Motors.

A. M.'^pUDLEY, B.S. in E.E. (Michigan)

FBLZX>W AMBRICaW ZNBTITnTB KLBCTRICAIi BMaZNBBBS; MBMBBB SOCIBTT OF

AUTOMOTIYB BNOINBBB8: IIANAOBR AUTOMOTiyB BNOZNBBBINQ

DBPABTMBNT, WBSTINOHOnSB BLBCTBIC AND MAZOT-

FACTXTBINQ COMPAITr

FiBST Edition
Fourth Impbbssion

McGRAW-HILL BOOK COMPANY, Inc

NEW YORK: 370 SEVENTH AVENUE
LONDON: 6 A 8 BOUVERIE ST., E. C. 4

1921

• •• •

PRINTED IN THE UNITED STATES OF AMEBIC A

THE MAPLE PRESS • YORK PA

o
o

PREFACE

The material which later developed into this book appeared
first in the ''Electric Journal'' in February, 1916. It was pre-
pared as a general answer to questions which come to the Ques-
tion Box Editor, regarding Induction Motor Connections and
the possibility of making changes to meet varying conditions of
voltage, phase, etc. This article came to the attention of Mr.
F. A. Annett, Associate Editor of "Power," and at his request
was elaborated into a series of articles appearing at intervals from
January, 1917, for about 3 years. From the comments on these
articles, there appeared to be a justification for a permanent
form which is now presented in this book.

Owing to the fact that the articles appeared in this way and
-^ without definite plan at the start, the material lacks unity in

some details, and also bears evidence of being viewed from a
repair standpoint rather than as a book on winding. The
author still cherishes the hope that the future may bring time
and opportunity for a revision, which will permit a more orderly
r^ arrangement. In its present form it is offered for what it may

be worth to practical men engaged in operating and repair
work. It was these men who were always in mind and for whose
5^ use the material was intended.

^ The author takes this opportunity of expressing his grati-

tude to the Westinghouse Electric and Manufactiu'ing Company
for permission to present the material, and to the "Electric
Journal" and "Power" for the use of cuts and material appear-
ing in their columns. He wishes also to express a personal
appreciation of the assistance and inspiration afforded by Mr.
F. A. Annett, whose interest in the subject made this book
possible.

A. M. Dudley.

East Pittsbubgh, Pa.,
November, 1920.

CONTENTS

Pbeface

Paob
V

Introduction xi

CHAPTER I

What the Winding on an Induction Motor Accomplishes . . 1-4

Counter Electro-motive Force — Functions of the Windings
d.c. Motor — Synchronous Motor — Induction Motor.

CHAPTER II

The Rotating Magnetic Field 5-21

Why a Motor Drives its Load — How Torque is Produced —
Setting up a Rotating Magnetic Field by Alternating Cur-
rent — Direct Current Analogue — The Frequency of an Alter-
nating Current — ^The Counter Electro-motive Force — Method
of Building the Magnetic Field from Pictures — ^Setting up a
Magnetic Field with Three-phase Currents — Drawing a
Graphic Picture of the Magnetic Field — Interchanging Two
Leads Reverses Direction of Rotation.

CHAPTER III

Types of Windings 22-50

Effect of Form of Slot— Windings Used in Partly Closed Slots
— Windings Used in Open Slots — Master Diagrams for Polar
Grouped Windings — "Wave" or "Progressive" Diagrams —
Standard d.c. Form of Wave Winding Adapted to a.c. —
Voltage Relation of Individual Coils in this Winding — Con-
centric Coil Windings — Rearrangement of Concentric — Coil
Windings — Wave Windings — ^Passing to Open Slot Windings —
Standard "Lap" Winding — Phase Insulation — Schematic
Diagram — Check for Connecting Proper Ends of Phases to
Star Point — How to Draw a Diagram to Suit Any Case —
Three-phase Star Diagrams — Delta Diagrams.

CHAPTER IV

Chorded Windings or the Effect of Coil Throw on the

Magnetic Field 51-76

Advantages of Chording the Winding — Changing Poles with
Constant Throw — ^Explanation of Term "Chord Factor" —
Effect of Chording — Distribution Factor Less Important —
Phase Insulation Important — Plotting Pictures of the Mag-
netic Field — Effect of Chording Shown Graphically.

• •

Vll

VUl CONTENTS

CHAPTER V

Pagb

Effect of Voltage on Windings and PossiBiLiTr of Connect-
ing A Winding for Mobe than One Voltage 77-86

Checking Insulation for New Voltage — ^Insulation Tests —
Volts per Turn — General Tables Covering All Voltage Con-
nections.

CHAPTER VI

How THE Number of Phases Effect the Windings and the Re-
sult OF Changing Voltage and Phase at the Same Time . 87-104
Two-phase to Three-phase — Scott Connection or "Tee" —
Phase Changes and Voltage Changes Combined — ^Effect on
Voltage between Collector Rings and Control

CHAPTER VII

How THE Frequency Affects THE Windings 105-112

Checking the Speed when Operating at Higher Frequency —
Relation between Voltage and Frequency — Relation between
Torque, r.p.m. and Horsepower — Starting a Squirrel Cage
Motor by Bringing up the Generator from Rest.

CHAPTER VIII

The Number of Poles and the R.P.M. and the Possibility

OF Varying Them WITH THE Same Winding 113-122

Check Points in Changing Number of Poles — Slip — Chord
Factor — Counter e.m.f.

CHAPTER IX

Less Common Connections Used for Unsymmetrical Condi-
tions OR in an EBiERGENCY 123-133

Number of Slots not a Multiple of Phases Times Poles —
Consequent Pole Windings for Two Speeds — "SpUt Group"
Diagrams — "Tee" Connection.

CHAPTER X

Reconnecting an Old Winding for New Conditions 134-152

General Fundamental Considerations — Cross-section of Cop-
per and Iron — Generator Action of the Winding — Changing the
Throw — ^AU Changes Can be Handled as Voltage Changes —
1. Change in Voltage — 2. Change in Phase — 3. Change in
Frequency — 4. Change in Number of Poles or Speed — ^5.
Change in Horsepower — Example of Each.

CONTENTS ix

CHAPTER XI

Paqb

Locating Faults IN Induction Motor Windings 153-181

Noisd and Vibration — Separating Air Noise from Magnetic
Noise — Mechanical Vibration — Grounds — Short Circuits —
Reversed Coil — Reversed Group — ^Wrong Grouping — Re-
versed Phase — Connected for Wrong Voltage — ^Wrong Num-
ber of Poles — Open Circuits — First Fault — Second and Third
Faults— Fourth and Fifth Faults— Sixth Fault— Seventh
Fault— Eighth Fault— Ninth Fault— Tenth Fault— Compass
Test — Balance Test — Usual Order of Locating Defects.

CHAPTER XII

How TO Figure a New Winding for an Old Core 182-200

Effect of the Winding on the Performance — Nineteen Points
Considered in a Design — Output Coefficient and Table — ^Iron
below Slots — Flux per Pole — Conductors per Phase — FuU
Load Current per Lead — ^Insulation Space in Slot — Formula
for Figuring Volts between Collector Rings.

CHAPTER XIII

Standard Group Diagrams prom 2 to 14 Poles 201-219

How Standard Diagrams are Drawn — Changing from Star to
Delta.

CHAPTER XIV

Wave Diagrams 220-244

Why Rotor Winding is Always Three-phase — How Wave Dia-
gram is Drawn.

Index 246

INTRODUCTION

The best teirt books for students usually are written by those
most familiar with the art of teaching; so should the best techni-
cal books, for the active workers, be written by those who are in
the midst of such work. Otherwise the text is liable to lag be-
hind the actual practice. In the electrical art the growth has
been so rapid and the changes in practice so numerous, that
only those directly in touch with the many developments are
able to tell the up-to-date story. Unfortunately, it is only in
rare cases the doer is the teller, that is, too often he delegates the
telling of his work to others, while he continues to do. Lack of
practice in writing is often back of this. In Mr. Dudley's book
we have a very positive exception to the usual practice, for here
we have the case of a writer with fourteen years of active prac-
tical experience upon which to build his treatment of the sub-
ject. Consequently there is a sincerity in the facts presented
and a logic in their treatment which appeal strongly to the
practical man. The method given for checking phase rotation
on a three phase winding, is an example, as is also the table of
voltages showing how connections may be changed for any com-
bination of phases and voltages. Since the treatment does
represent good engineering practice, it also makes an appeal to
the student whose practical experience is still ahea^ of him.

like all highly technical subjects, the Induction Motor, in the
past, has been treated very completely from the theoretical stand-
point, while comparatively little has been published concerning
the really practical details, of which the windings are a prominent
part. This type of motor, while much later "in the running"
than its d.c. rival, has fairly pre-empted the field in general
power work. Therefore a practical treatise on the winding char-
acteristics of this apparatus, such as the author has presented,
is not only most timely, but is really a practical necessity.

It is with the greatest pleasure that I recommend this work
to those who are interested in both the theoretical and practical
side of the Induction Motor problem.

(Signed) B. G. Lamme.

CONNECTING
INDUCTION MOTORS

CHAPTER 1

WHAT THE WINDING ON AN INDUCTION MOTOR

ACCOMPLISHES

The simplest conception of any motor either direct or alter-
nating current is that it consists of a magnetic circuit inter-
linked with an electrical circuit in such a way as to produce a
mechanical turning force. A study of the reasons for this force
and its results leads naturally to the consideration of the magnetic
circuit and the way it is set up and of the electric circuit and the
interrelation of the two. It was recognized a long time ago that
a magnet could be produced by passing an electric current through
a coil wound around magnetic material and the fact was estab-
lished later that when a current is passed through a conductor
or a coil which is situated in a magnetic field there is set up a
force tending to produce motion of the coil relative to the field.
Since it is equally true that a magnet is most easily produced by
an electric current and that an electric current is most easily
produced by employing a magnet it is not material which of these
elements is considered the more fundamental and the better
starting point for study. One thing which becomes apparent
is that coils or turns of wire are essential both to the magnetic
and the electric circuit and it is the form and combination of these
coils in alternating-current motors which is 'the subject matter
of this book.

Functions of the Windings in a D. C. Motor.

In the familiar shunt-wound direct-current motor there are
two separate and distinct windings each serving a special pur-
pose. There are the shunt coils on the stator or field member
whose function it is to establish the magnetic circuit or ''field."
There are also the coils on the armature which constitute the
electric circuit or. the circuit carrying the working current.

2 CONNECTING INDUCTION MOTORS

In addition to carrying the working current the armature coils
are also acting as generator coils and generating a voltage which
prevents any more current flowing in the armature than is nec-
essary to produce exactly the required amount of torque. A Uttle
consideration shows that this must be the case. The full load
current in a 5-hp. 230-volt motor is in the neighborhood of 20
amperes and the resistance of the armature between brushes may
be 0.3 of an ohm. Since the armature brushes are put directly
across the 230-volt line, if there was no other condition existing
except Ohm's law, a current would flow in the armature having a
value of 230 -4- %o = 767 amperes. However, since the full-
load current of the motor is only 20 amperes it is evident that
only 6 volts are required to circulate this current in the armature
and the remaining 230 — 6 = 224 volts are absorbed or ac-
counted for in some other way. As a matter of fact these 224
volts are taken care of by the armature which actually generates
a voltage of 224 volts and opposes it to the line leaving only the dif-
ference between 230 and 224 or 6 volts available to force the needed
working current through the armature. The name of this voltage
generated in :the armature is the "back-electromotive force"
or "counter-electromotive force" and it is present in the case of all
motors of any type whether direct- or alternating-current.

, Direct Current Power Sapply [^Malns 1^

I Shunt Field Coll J n,,.ying ^ '^

llagnetlzlng
Carrent

Armature Colli /

Carrying Working Beilitance Bepresenting

Current Counter e.m.f.Qenerated by

the Armature Colli

Fig. 1. — Windings of a direct-current motor and their functions.

The foregoing is. mentioned to show that on a shunt- wound
direct-current motor the windings are exercising three distinct
functions, viz., first, the field coils are setting up the magnetic
field, second, the armature coils are carrying the working cur-
rent and, third, the armature coils are generating a voltage which
is opposed to the Une voltage and which determines how much
working current may flow in the armature and hence, directly,
how much torque will be produced.

This condition is shown diagranmiatically in Kg. 1 where the
shunt-field coil is shown setting up the magnetic field and the

WINDING ON AN INDUCTION MOTOR

'armature coils carrying the working current. The counter-elec-
tromotive force which is generated by the armature coils is rep-
resented as a resistance in series with the armature since its
action is to cut down the amount of current which would other-
wise flow in the armature.

S]mclironous Motor.

In an alternating-current motor of the synchronous type there
are also two windings exercising these same three functions, viz.,
first, the direct-current winding serving to set up the magnetic
field, second, the alternating-current winding carrying the work-

■AlteniBtlDg Current Fower jSupply Mains

Botor Colli
Carrying _

Direct Current

Magnetizing Current

Exciter Circuit or

Direct Circuit Supply Malm

Stator Colls
Carryiag Working
Current

Besiatance Bepre tenting
Ooonter e.m.f. Gfrerated
by Stator Colli

Fig. 2. — Windings of an alternating-current synchronous motor and their

functions.

ing current and, third, the alternating-current winding generating
the counter-electromotive force nearly equal to the appUed line
voltage.

The condition is represented by the diagram, Fig. 2, which
shows the magnetic-field circuit as separately excited from a
direct-current source of supply. The stator winding or alter-
nating-current winding is shown as carrying the working current
and in addition generating the counter-electromotive force which
is represented as a resistance in series with it.

Induction Motor.

In the case of the alternating-current induction motor there
are again two windings, one in the stator and one on the rotor
and these two windings are again exercising the same three
functions but with a slight difference which is well worth noting.
The rotor winding or secondary winding of a polyphase induc-
tion motor carries the working current. Since in this type of
motor there is no electrical connection between the stator and
rotor windings the only manner in which this current can be set
up in the rotor is by transforming it from stator to rotor using
the transformer action of the primary upon the secondary. This,
then, sets up in the primary or stator winding the very interesting

I
k

4 CONNECTING INDUCTION MOTORS N

condition that in one single winding or set of coils there exist
three separate actions. First, the magnetizing current is flowing ^
and setting up the magnetic field just as it does in theshunt direct-
current or synchronous alternating-current motor; second, the
working current is flowing and being transformed into the rotor
and, third, there is a generator action taking place in the coils
and generating a back or counter-electromotive force opposite
in direction and slightly less in amount than the appUed line
voltage.

This condition is shown graphically in the diagram of Fig. 3
where the three separate actions are indicated and shown to be
similar to the corresponding items in Fig. 1 and Fig. 2.

Alternating Carrent Power Supply Mains

Stator Colls Carrying Magnetizing Current
^^and the same Colli at
jfthe lame time also carrying
•^ "Working Current

RoMrCoQi

IDS WorkiBi
rmt laduotd-j

-jJi/WWWVWVV-

Staort Circuited, fiotor Circalt £eBi«tance Bepresenting
either Squrrel Cage Counter e.m.f. Generated

or Phase Wound by Stator Coila

FiQ. 3. — Windings of an alternating-current induction-motor and their functions.

Since these three conditions do exist in the single winding
it becomes evident that when changes in operating conditions
occur such as are covered by reconnecting a winding for different
phases and different speeds, etc., all three of these conditions
must be satisfied if the operation of the motor is to be normal.
That is to say, the cross section of the conductor in the windings
must be great enough to carry the combined magnetizing and
working current; the number of turns must be correct for setting
up the required magnetic field and the combination of magnetic
field and number of turns in the armature working together must
generate the required counter-electromotive force, which in all
cases is just sUghtly less than the appUed Une voltage. This
also shows the reason why one of the simplest methods of figur-
ing how many turns are required in the winding of a given
motor is to consider it as an alternating-current generator rather
than as a motor. This method is frequently referred to through-
out the text and an effort made to have it appear as a physical
picture of what is going on inside the motor rather than as
a set of mathematical formulae or an involved vector or circle
diagram.

CHAPTER II

THE ROTATING MAGNETIC FIELD

Why a Motor Drives its Load.

An induction motor rotates and drives its load because there
exists inside the motor a magnetic field which rotates and pulls
the iron of the rotor core and the rotor windings around with it.
This magnetic field has a number of north and south poles and in
its effect resembles several bar magnets riveted together in the
center and spaced radially Uke the spokes of a wheel. The dis-
covery that such a magnetic field could be estabUshed in an iron
core and made to rotate by exciting a winding with alternating
current is what made possible the development of the induction
motor. With the proper conception of how this field is set up
and caused to rotate and its effect upon the windings of the motor
as it rotates it is easier to understand the working of the motor
and also to form an opinion of the possibiUty of accommodating
the motor windings to changes in operating conditions. It is
the intent of this chapter to give a physical idea of the rotating
magnetic field followed by a graphical explanation of how it is
set up by alternating current.

How Torque is Produced.

It is now generally understood that an electric motor produces
torque or driving effort by utiHzing the effect of a magnetic field
upon a wire, or wires, which are carrying electric current. It is
also understood that a magnetic field may be produced in an
iron circuit by passing an electric current through a coil which
surrounds or is interUnked with that iron circuit. The action of
producing driving effort in a direct-current motor then becomes
very simple. First the magnetic field is set up by passing a
direct current through the field coils surrounding the poles. This
direct current is drawn from the same source of supply that is
to drive the motor. When the magnetic field is set up, another
direct current is drawn from the source of supply and caused to
flow through the armature coils which he in the magnetic field
just previously set up. The action of the magnetism of the field

6 CONNECTING INDUCTION MOTORS

on the current in the armature wires causes the rotor to develop
torque and start to turn.

The foregoing is elementary and exactly the thing that hap-
pens in the alternating-current motor, but in a Uttle different
way. In the direct-current motor just noted, two sets of coils
were used. The first set — the field coils — was used to excite the
magnetic field; the second set was the armature coils and was
used to carry the working current. In the induction motor
there is but one set of coils, which must at the same time exercise
the two functions of setting up the magnetic field and carrying
the working current. This fact is chiefly responsible for the
condition in the motor which is called power factor and which is
not present in the case of the direct-current motor.

It is worth while to consider as simply as possible the manner
in which the magnetic field is set up in the induction motor and
the reason it travels around the machine at a relatively high rate
of speed.

Long before the days of Tesla and Feraris, it was known that
if a magnet was passed over a sheet of copper close to its surface,
a force was produced which tended to cause the copper to move
in the same direction as the magnet. Although not then so
recognized, this was the fundamental principle on which all
modern dynamo-electric machines are based. The contribution
that Tesla and Feraris made was the discovery that such a
moving magnetic field could be set up by an alternating current
and need not rely on a permanent magnet or one excited by
direct current.

Setting up a Rotating Magnetic Field by Alternating Current.

The matter of setting up such a field by alternating current
and causing it to move can be shown by a few simple figures.
Figure 4 is a cross-section through a direct-current machine. It
shows an outside field yoke with inwardly projecting field poles
with a coil around each polepiece through which a direct current
is flowing. The usual convention is adopted to show the direc-
tion of the field current by marking the conductors with a dot
when the current is flowing toward the observer and with a cross
when it is flowing away. The armature is shown by the inside
circle carrying the conductors C on its periphery; in practice
these conductors would be connected to a commutator. The
magnetic field itself is represented by the dotted lines passing

THE ROTATING MAGNETIC FIELD 7

from one pole into the armature and out through adjacent poles,
as indicated by the arrows.

Direct-Current Analogue.

If now, contrary to the usual practice, the machine is suspended
by means of the shaft projecting on either side and the armature
held from turning by clamping the shaft, it would be possible
to take hold of the field frame and rotate it around the armature.
Mechanically such a rotation would not interfere with the usual
electrical functions of any of the parts of the machine since the
brushes would bear on the commutator as usual and move rela-
tively to the polepieces, the only difference being that now the
commutator is standing still and the brushes are moving.

Going a step farther, if the field was driven mechanically at
a fair rate of speed around the armature, this inverted direct-
current machine would give a very fair representation of what
is going on inside an induction motor. So far as the rotating
magnetism is concerned, it is just as surely present in the one
case as in the other and with just as plainly marked north and
south poles. The difference is that in the induction motor the
magnetic field alone rotates and the iron core with the windings
stands still, while in the case of the inverted direct-current
machine described, the iron core and the field coils are going
around with the magnetism.

The picture that the foregoing is intended to bring out is that
in any running induction motor a well-defined magnetic field is
actually rotating in the stator exactly the same as would be the
case if we excited a field of equal strength by direct current and
rotated it mechanically. The manner of setting up this field
by alternating current instead of direct current and making it
rotate electrically instead of driving it mechanically is explained
in Figs. 5 to 8.

Figure 5 shows the same machine as Fig. 4 except that it is
developed or rolled out flat the better to illustrate the point.
Suppose, for example, that it is desired to set up a magnetic
field as shown and cause it to travel from right to left in the
direction of the arrow. One method of doing this would be to
excite the pole marked No. ] , Fig. 5, with direct current to produce
a south pole as shown; a fraction of a second later No. 1 could be
cut off and No. 2 made a south pole; after the same interval of
time No. 2 could be cut off and No. 3 excited south ; followed, in

CONNECTING INDUCTION MOTORS

Fio. 4. — CroM tection of a d.c. machine showing th« ntagnetio field.

Fio, 5. — Development of Fiit. 4.

k—^

OOOOOOOOOOO'

o^oooooooooooo|
Fro. 6. — SimploBt form of four-pole einglo-phaae winding.

loooooooooo^oooooooooooa
FiQ. 7. — Two-phasa winding equivalent of Fig. 6.
C,C, B,B.*,A,C,C B,B, A,A,C,CB, t A, A,C,C, ^B, A.A,

FiQ. 8. — TliTBe-phasB w
How the magnetic field n

ading equivalent of Fig. 6
^atea in an induetion mote

THE ROTATING MAGNETIC FIELD 9

turn, after the same interval again, by cutting off No. 3 and ex-
citing No. 4. Thus a south pole would have traveled regularly
and steadily from right to left as desired. But this is using direct
current.

An analysis of what really happened shows that while No. 1
was excited as a south pole. No. 2 might just as well have been
excited as a north pole since the magnetism to flow into No. 1
and make it south must flow around and out of No. 2, as shown.
This is indicated by the dotted Unes, which represent the magnetic
field. At this instant, then, coil No. 1 would be excited minus
and plus and No. 2 excited plus and minus, as shown. However,
the next instant, when No. 2 is to be made a south pole, this
excitation would have to be reversed to minus and plus, and an
instant later, when No. 3 becomes a south, No. 2 can again be a
north and the excitation would again reverse to plus and minus.
Consideration of any particular coil in this way shows that
each time the field moves forward one pole, the excitation of all
the poles changes in direction and consequently each pole might
quite as well be excited by alternating current, which in efifect
is really rapidly reversing direct current.

The Frequency of an Alternating Current.

The rapidity of these reversals or the so-called frequency of
the alternating current would depend on how rapidly the field
was expected to advance a space represented by the distance
from center to center of adjacent poles. And this is exactly
what happens: If the motor has four poles the field will have to
advance four times to make one complete revolution around
the motor, and if it is desired that the field shall make 1,800
r.p.m., there will be required 4 X 1,800 = 7,200 reversals.
This is readily recognized as the sixty cycles of the commercial
alternating-current circuit. Conversely, since the r.p.m. of
the motor roter is nearly that of the magnetic field, if 60-cycle
current is available and power is wanted at 1,800 r.p.m. or
thereabouts, a four-pole motor is required.

From the foregoing it might appear that single-phase alternat-
ing cxurent for excitation is all that is needed, and for this reason
Figs. 6, 7 and 8 are shown. Since Fig. 5 is a direct-current struc-
ture, the field would progress by jumps and hitches from pole
to pole around the machine rather than steadily and evenly;
hence, in Fig. 6 the slot between poles is reduced to the size of

10 CONNECTING INDUCTION MOTORS

an armature slot, of which the necessary number are evenly
spaced around the machine. Also, for simplicity the field coils
are shown gathered into one coil per pole.

In Fig. 6 the step from pole to pole is still rather wide, so that
in Fig. 7 coils are introduced halfway in between and these are
excited by a second alternating current which is just as much
behind the first one in time as it takes the field to travel one-half
a pole, and such an arrangement of two alternating currents is
called two-phase. Similarly, if desired, three currents could be
used, as shown in Fig. 8, and this would represent the well known
three-phase arrangement.

From this explanation it must not be gathered that in the case
of the two-phase there are two rotating fields and three in the
case of three-phase. This would be true if the two currents or
three were acting entirely independently, but they are not — ^they
are all trying to excite the same iron circuit and the actual re-
sultant magnetism at any instant is due to the combination. In
other words, since one current is ahead or behind the others by a
fraction of a pole, the currents in the different phases have differ-
ent values at any given instant. In the case of three-phase one
may be zero, the second be increasing and be equal to one-half
its maximum value, and the third be decreasing and be actually
at one-half its maximum value. Since these three currents are
all acting on the same iron circuit, the magnetic field which
actually exists at that instant is due to the resultant of the three
currents. Thus the resulting field looks exactly Uke the field in
Fig. 4, which was set up by direct current, and it travels around
the stator iron just as did the field in the mechanically rotated
direct-current machine.

The Counter-Electromotive Force.

Having considered the manner of setting up the field and
causing its rotation, there is another action, easily understood,
which is perhaps as useful as any in giving a clear idea of how
many turns are required in a motor winding under different
conditions. This is what is called the generation of the counter-
electromotive force. Since the coils of the motor are standing
still and the magnetic field is rotating past them and threading
through them, there is of necessity a voltage generated in the
coils by the rotating field. This is the voltage which is referred
to as counter-electromotive force and is in all cases equal to the

THE ROTATING MAGNETIC FIELD 11

voltage of the supply line which is applied to the motor, except
for a small loss in the motor caused by producing the necessary
torque or driving force.

With this conception and the fundamental formula for the
generation of an electromotive force, it is a simple matter to
write expressions showing how the turns in a motor should vary
with different line voltages and for different speeds, etc. For
example, a motor to operate on 440 volts must have twice as
many turns in the coils as the same motor when operating on 220
volts, and a motor operating at 900 r.p.m. in general would
require twice as many turns as the same motor when operating
at 1,800 r.p.m. These are matters with which the designing en-
gineer is chiefly concerned, but they are sufficiently simple to be
borne in mind at all times, and in themselves offer the readiest
first-hand answer as to the probable result of operating a given
motor under changed conditions.

Having in mind this physical conception of the rotating mag-
netic field the next step is to be able to draw a picture of this field
as it would look if it might be arrested in space at any instant
and photographed. This can be most easily accomplished by the
simple graphical method explained below and sometimes called
"stair-step" pictures. By means of this method the rotating
magnetic field can be explained and studied and the readiest
possible answer given to such questions as, Why does reversing
two leads of a three-phase motor reverse its direction of rotation?
Why is a phase-wound rotor always three-phase^ whether the
stator is for two-phase or three-phasef Also such questions as
the effect of chording the coil and changing the number of poles
are readily analyzed.

The confidence that will be gained in the understanding of
induction-motor operation and troubles will well repay the
amount of study required to master it, and the amount of elec-
trical knowledge required is not so great as to discourage any-
one who has even a speaking acquaintance with alternating
current and its behavior. No claim is made that this is a new
method. This is how it applies, for example, to a three-phase
problem :

Method of Building the Magnetic Field from Pictures.

In each of the three wires of a three-phase circuit which is
carrying load is an alternating current which several times a

CONNECTING INDUCTION MOTORS

second increases from zero to a maximum value in one direction,
decreases to zero and increases in the opposite direction to a
maximum value and again decreases to zero, thus completing
one "round trip," which is called a "cycle." If a pencil could
be attached to this current and a piece of paper be drawn under
it as the current rose and fell, after the manner that indicator
cards are made on a steam engine, its "card," or curve, would
have the characteristic shape shown in Fig. 9. Here it will be
noticed that the time in fractions of seconds is along the hori-
zontal Une XX and the value of the current in amperes is along
the vertical line YY.

All three currents of a three-phase crcuit will trace a similar
card to that in Fig. 9, but they do not all reach a maximum at .

<Gr7e jiUfernaHon*
— iP/7e Cyc/e

Fio. 9. — The "indicator card" of a edngle-phase alternating current.

—>*

the same instant nor pass through zero at the same instant, but
are evenly spaced the same distance apart at all times so that if
the indicator be connected to all three Unes at once, the combined
card would be that shown in Fig. 10 where A is the card for phase
1, B for phase 2 and C for phase 3. The values above the XX
line are considered plus and the values below the Une negative.
It is the evenly spaced coils in the alternating-current generator
winding that keep the current in all three phases of equal value
and with a constant spacing with regard to each other.

Assume that each one of the three-phase Unes is wound an
equal number of times around the same iron bar, as in Fig. 12.
Whenever a coil is placed around iron and current flows in the coil,
it sets up magnetic Unes, or flux, and the iron becomes a magnet.
It is evident, then, from Fig. 12, that any one of the three coils
by itself would make a magnet of the iron bar which would have
its north pole at one end at one instant and a south pole at the
same end the next instant as the current changed its direction
according to the curve in Fig. 9.

THE ROTATING MAGNETIC FIELD 13

However, when all three coils work together on the bar (Fig.
12) there ia no magnetism set up, because at any instant the cur-
rent in one coil is equal in amount and opposite in direction to
the currents in the other two coils. This can be seen from Fig.
10. Take, for instance, the time marked by the vertical line
1. At this instant the A and C phases are measured above

Fio. 10. — Sine nave cepreseiitatioii of Uiree-phase alternating current.

the horizontal line XX and hence are positive or plus in value and
are each equal to +0.5, while the B phase is measured below the
X line and hence negative or minus value to —1. Therefore,
the sum of all three currents is zero because + (0.5 X 2) — 1 = 0.
At the instant 2, C = 0, A = +0.866 and 5 = -0.866
and the sum of the three currents is zero. At instant 3, A =
+ 1,B = -0.5, and C = -0.5, total = 0; at the instant 4,
A = +0.866, B = and C = -0.866, total = 0; and so on

Pio. II. — Hon the tlirae phases oombine to form one maenetizing current.

at all points the sum of the three currents is zero. Therefore
in Fig, 12 there will be no magnetism in the iron bar, since at all
times there is an equal number of ampere turns in the coils try-
ing to force the magnetism in each direction.

The next step is to reverse one coil, as shown at B in Fig. 13,
and the bar immediately becomes a strong magnet, reversing
its poles from instant to instant according to the change in direc-
tion of the curve D in Fig. 11. Reversing one coil in Fig. 13 is
the equivalent of reversing the current in one phase of the genesl-a-

CONNECTING INDUCTION MOTORS

tor. This is indicated in Fig. 1 1 , in which curve B is shown plotted
above the line where it is below the line in Fig. 10, and vice versa.
The sum of the three curves A, B and C, Fig. 11, gives a resultant
curve D, which represents the current that will be effective in
magnetizing the core. Fig. 13. It will be seen that the A and C
curves in Fig. 11 are the same as in Fig. 10, but the B curve is
turned over, or reversed, since the B coil is reversed in Fig. 13.
Curve D, Fig. 11, is obtained by adding the values of the three

Fig. 12. — Iron bar acted upon by three-phase currents as arranged in Fig. 10.

No resultant magnetism.

"?=v;?i;l*^*^vJi:i^f

M^:

iv.'.;":".-.-:;.*;;:;".:::?!!:
■■■.•-•-— ■.■••^'

----—■ •.—-•-

j..f •■'1

•5 * 3

Iron
Bar

Fig. 13. — Iron bar acted upon by three-phase currents as in Fig. 11. Strong

resultant magnetism alternately north and south.

currents at any point. For example, at the time marked by the
vertical line, 1, A = +0.5, C = +0.5 and B = +l,|[hence D
= +2. At the time marked by the vertical line 3, A = +1,
B = +0.5 and C = —0.5, hence* D = +1. Also at time 4, A
= + 0.866, B = and C = -0.866, hence D =0. In this
manner the curve. D is obtained, and it serves as an indicator
card of the magnetism in the iron bar in Fig. 13.

Setting up a Magnetic Field with Three-Phase Currents.

This conception of three-phase coils making a magnet whose
flux or field varies in value and direction*'according to the curve
D in Fig. 11 can be readily transferred to the stator of an induction
motor, as shown in Fig. 14. Here is shown part of a laminated

THE ROTATINO MAGNETIC FIELD 15

core slotted on the inner periphery, and in two of these slots are
shown three coils, A, B and C, to correspond to the coils in Fig.
13. Assume the three coils to be connected in star and to athree-
phaBe circuit. A magnetic field will then flow into the air gap
and back through the core, as shown by the curved dotted lines
and arrowheads. This magnetic field will flow in the direction
of the arrows for a fraction of a second, then fall to zero, and in-
crease to a maximum in the direction opposite to the arrowheads,
and 80 on. Id other words, the three coils working together
would make first a north pole and then a south pole on the inner
periphery, and repeat, and the amount and direction of the mag-

— Ccosa-aection of stator core with three coils similar to Fig. 13.

Fia. 15. — The three coils of Fig. 14 distributed as in normal induction motor.

netism in the iron between the two sides of the coil could be
measured by taking the distance from points on the curve D,
Fig. 11, from the horizontal reference line and calling all points
above that line north values and below the line south values.
For example, at the position marked 1 the magnetic value
would be a maximum north value, at 3 it would be 0.5 north, at
4 zero, at 5 it would be 0.5 south, and at 7 a maximum south value,
and so on. There would be no tendency, however, for this mag-
netic field to rotate or travel around the stator as it does in an
induction motor. It would simply stand still in space and alter-

16 CONNECTING INDUCTION MOTORS

nate backward and forward through the coil as described. In
order to get the rotating motion, it will be necessary to separate
the three coils and put each one in a separate slot, as shown in
Fig. 15, as they would be in any normal induction motor.

A section cut through the core and coils. Fig. 15, is shown in
Fig. 16 with one side of each coil in the bottom of slots 1, 2 and 3
and marked A, By G, respectively, and their other sides in the
top of slots 4, 5 and 6 and marked A', B\ C, respectively. By
means of Figs. 11 and 16 taken together, it is possible to build up
small pictures of the magnetic field from instant to instant and
show how it moves or rotates around in the stator core and air

Laminafecf-Iron Core

liUinAAAAAAMP

Fig. 16. — Cross-section of core and winding in Fig. 15.

gap. These small pictures, of which one series is shown in Fig.

17 and another in Fig. 18, can be very well compared to the in-
dividual small pictures on a moving-picture film as they appear
when the film is at rest, and the rotating magnetic field as it
really exists could be compared to the same film when in motion
and thrown on the screen. The method of making these small
pictures is very simple and is as follows:

Drawing a Graphical Picture of the Magnetic Field.

At the top of Fig. 17 is a section through the coils and core,
Fig. 16, the same as that given in Fig. 16. A current is assumed
to be flowing in each coil, and the value of that current is taken
from the curve marked with the same letter in Fig. 11. For
example, at the time represented by the vertical Une 1 in Fig. 11,
curve B is at its maximum value, which is called +1, because
it is above the horizontal reference line, and curves A and C
are each at a value of +0.5, since they are half their maximum
value and are also above the reference line XX, Similarly, at
the time represented by the vertical line 2, which is called posi-
tion 2, in Fig. 11, the value of the A and B curves is +0.866
and the C curve is zero. The value 0.866 is obtained because
these current curves are all what are known as sine curves and
the reference points or positions 1, 2, 3, etc., are taken 3^2 of ^
complete cycle apart.

THE ROTATINO MAGNETIC FIELD

tetti

OnNo.3

A-

B-

C-

-05

U-

CONNECTING INDUCTION MOTORS

THE ROTATING MAGNETIC FIELD 19

A complete cycle is known as 360 electrical degrees similar
to the 360 mechanical degrees in a circle^ and hence the reference
positions 1, 2, 3, etc., are H2 of 360 deg. or 30 deg. apart. From
a table of natural sines such as is f oimd in any handbook, it will
be foimd that the sine of 30 deg. = 0.5, sine of 60 deg. = 0.866,
sine of 90 deg. = 1, sine of 120 deg. = 0.866, sine of 150 deg.
= 0.6 and sine of 180 deg. = 0. Continuing from 180 deg. to 360
deg., the same values recur with a minus sign since they are
measured below the horizontal reference Une. So that it is
these values which are used in plotting the pictures in Fig. 17,
and the values for different positions are given in the left-hand
colmnn in the figiu'e.

From Fig. 16 we have the position of the coils, and from Fig. 11
we have the value of the current in each coil as given in the
colmnn on the left of Fig. 17. Then if the values of these cur-
rents are plotted or drawn, the resulting curve is a measure of
the magnetic field, since such a field depends on the number of
tiu*ns of wire and the current flowing in the coil. It remains,
then, only to draw the small figures or curves in Fig. 17 in the
following manner:

Starting from any arbitrary point at as d. Fig. 17, the line
moves in direction and amount according to the value of the cur-
rent in slot 1. Slot 1 contains the A coil and the value of the
current is -[-0.5 as is shown on the left; since the direction of plus
is up, the Une is drawn upward from d to 6 and ef is drawn hori-
zontally, representing by its height above d the current in No. 1
slot and the magnetic field at that point. From / the line goes
up to fir, making fg twice as long as de because the B coil is in No.
2 slot and the value of the current in the B coil is -[-1, or twice
that in A, and the line gh is drawn horizontally, representing by
its height above d the current in slot 1 + slot 2 and therefore
the magnetic field at that point. From h the line goes up to i
because the C coil is in slot 3 and the current in the C coil as
shown at the left at that instant is +0.5. The Une ij is drawn
horizontally, representing by its height above d the combined
currents in slots 1 plus 2 plus 3 and therefore the magnetic field
at that point. From j the Une drops down to k because the A'
conductor is in slot 4 and the A' conductor is the other side of the
A coil and hence the current in it is in the opposite direction to
that in the A side. By referring to the column at the left of
the figure, if the current in the A side was considered H-0.6, the

20 CONNECTING INDUCTION MOTORS

current in the A' side must be —0.5 and hence the curve drops
down for a minus value from j to k. Similarly, it drops twice
as far from I to m, since B — +1 and therefore the other side of
the B coil or B' must = — 1. Following the ciu-ve in this manner
to n and o, it completes one cycle or one north and south pole.
The north pole is considered as that part above the horizontal
reference line and under the Une g, h, i, j, k, and I, which is shown
shaded, and the center of this north pole is indicated by the verti-
cal arrow.

In an actual machine the magnetic field would not have such
sharp corners, but would be smoothed out by the rotor winding
into a smooth curve practically a sine curve such as the current
ciu*ves in Fig. 11, but for purposes of illustration the "stair-step,"
or square-shouldered curves, may be considered as shown. In
a similar manner the Uttle stair-step picture may be drawn for
each position and the center of the north pole marked by an
arrow pointing up as shown. After drawing seven positions, the
very interesting fact may be noted that the center of the north
pole has traveled three slots to the left, which in this case means
180 electrical degrees, or a half revolution on a two-pole motor
or a quarter revolution on a four-pole machine.

Interchanging Two Leads Reverses Direction of Rotation.

Figure 18 is drawn to show the effect of interchanging the leads
to the coils A and C, or in other words, the line lead that was
connected to A is now connected tp C and vice versa. For this
reason in the little sketch at the top of Fig. 18, taken from Fig.
15, the C coil is now in slot 1 and the A coil is in slot 3, the B
coil remaining in slot 2 unchanged. The numerical values of
the currents are again taken from Fig. 11 just as it stands, because
it must be remembered that the curves in Fig. 11 represent cur-
rents in the line and that they depend on the generator and are
not changed by the change in the motor leads. These assump-
tions give the current values for the different positions, as shown
in the left-hand column in Fig. 18, and the small stair-step pic-
tures show the magnetic field in the same manner as in Fig. 17.
The interesting thing to note is that the center of the north pole
has now traveled from the center of slot 3 to the center of slot
6, or the magnetic field has now traveled three slots to the right,
which discloses the well-known fact that interchanging two leads
on a three-phase motor will reverse the mechanical direction of

THE ROTATING MAGNETIC FIELD 21

its rotation. As a problem the reader might attempt to produce
the same result for a two-phase motor and will find, as previously
pointed out, that this held plotting becomes a fascinating mentfil
diversion.

A comparison of Figs. 10 and 11 shows at once why the
middle leg of a three-phase winding is reversed in all the common
diagrams that will be shown in this book. Figs. 17 and 18
show how the magnetic field may be studied and how reversal
follows exchange of two leads.

Fio. le. — Open Fio. 20.— Partly closed Fio. 21.— Partly closed
slota. Blots — center openiaE- slots — side openinE.

Common forms of induction-motor stator and rotor slots.

After a designing engineer has determined how many turns
are required in the winding which he is calculating, the largest
single factor which decides the form or type of windings to be
used is the mechanical form of the slots; that is, whether they
are open. Fig. 19, or semiclosed, as in Figs. 20 and 21, and the
width of the opening if they are semiclosed. The factor of
next importance is whether the winding is on the rotor or on
the stator.

CHAPTER 111
TYPES OF WINDINGS

Effect of Form of Slot.

The question of open versus semiclosed slots has out-lasted
many controversies and is still open to argument. It is enough
to say that, other things being equal, the designing engineer
favors semiclosed slots. Slots of this type usually give the high-
est performance and the maximum efficiency in the use of ma-
terial. The repair man prefers open slots on accoimt of the
greater accessibiUty of the windings and the consequent ease of
repair. These factors will always remain somewhat divergent
and must be adjusted to suit the times and the local conditions.
The reason why a machine cannot be built with as good a per-
formance or as economically with open slots in both members is
that, broadly, its capacity and excellence may be measured by
the square inches of laminated-iron surface on the rotor periph-
ery or in the bore of the stator core. Since the slot openings
subtract directly from this useful surface, it is desirable to make
them as small as possible. If the slot is made wide open, it
subtracts the maximum amoimt from this useful working surface,
hence the core must be made longer axially or the rotor increased
in diameter to bring back the useful working surface to somewhere
near the value it would have if entirely inclosed or if semiclosed
slots were used. This problem is of more interest to the designer
than to the repair man, but is mentioned to explain the use of a
mechanical construction that is apparently undesirable from an
operating standpoint.

Windings Used in Partly Closed Slots.

The types of windings adapted to semiclosed slots and most
generally employed are :

1. Straight bars with involute end connectors.

2. Pushed-through coils. In this type the coils are formed in a
U-shape and pushed through two slots at once in a direction
parallel to the shaft. After the coil is in place, the separate
wires are bent around and connected together at the other side

of the core.

TYPES OF WINDINGS 23

3. Hand-wound or threaded coils. In this construction each
coil is formed in place in the machine itself, from a single piece of
wire, by the process of passing the wire through the length of one
slot, bending it around a wooden former to make a suitable end
and threading it back through another slot and repeating until
the coil is complete with the desired number of turns. When
completed, it resembles the pushed-through coil.

4, Fed-in, or dropped-in coils. In this type the coil ie formed
complete into a so-called diamond shape and then the turns are
fed one at a time through the opening at the top of the slot.

Fia. 22. — The bars and coanactors. Fio. 24. — Completai] winding.

Fia, 23. — Partially completed winding.

Bar and end-oonnactor winding.

The first of these types, bar and end connector, has been widely
used for both statora and rotors. The bars and connectors are
shown in Fig. 22, and a typical assembled winding in Figs. 23
and 24. This winding gave excellent satisfaction, the only real
criticism, from a mechanical standpoint, being that it was
difficult to brace the coil ends mechanically owing to their
form and relation to other parts. It has been ahnost aban-
doned on modem machines for the reason that it hmited the
winding to one conductor or two conductors per slot, and also
because modern practice has demonstrated that the use of

36 CONNECTING INDUCTION MOTORS

two coils per slot, which have a definite and final form before
being placed in the core and which resemble exactly, when com-
pleted, the well-known diamond-shaped coils wound into open
slots. The first of these forms is suited to small and the second

(B) (C)

Fia. 27. — (A) Hand-wound, threaded type of winding.

Fia. 28. — (B> "Fed^n" type — "muBh coil" or one coil par slot.

Fio. 20. — (C) "Fed-in" type — "diamond" or two coils per slot.

Stators with partly closed slots.

to larger machines. A modification of the second form makes
use of a slot shaped as in Fig. 21 and is shown in place in Fig. 33,
Each coil ia completely insulated from ground and inserted in the

TYPES OF WINDINGS

11 8.
'111

28 CONNECTING INDUCTION MOTORS

TYPES OF WINDINGS 29

slot as a unit, so that it might be considered as a combination
of the coils from two adjacent open slots brought together and
seeiu'ely held by the overhanging tooth tip, which leaves an open-
ing large enough for the passage of one complete coil while
winding. It is considered one of the most satisfactory forms for
use on the rotating part of machines up to the largest capacity.
A similar winding has been made by forming the coil of one or
two straps bent on one end only, as shown in Fig. 34, and insu-
lating it. The straight sides of this coil are then pushed through
two partly closed slots in an axial direction, and the two ends
are bent to the proper form to connect with other coils, as shown
in Fig. 35. This makes a good mechanical job, but is rather
difficult to repair owing to the fact that several straps must be
straightened out to get at the damaged coil.

Windings Used in Open Slots.

With open slots, as illustrated in Fig. 19, the most popular
and widely used form of winding is that shown in Figs. 36 and 38,
for which the coil is shown in Fig. 37. This is the well-known
diamond coil, so-called from its shape, and is entirely formed and
insulated before placing in the slots. It is also the simplest and
easiest coil to wind and is used by designers wherever the condi-
tions permit. The greater number of typical connection dia-
grams shown in this book have reference to windings of this
general type, since they lend themselves so readily to changes
of arrangement and various reconnections.

There have been many other modifications of coils or windings
employed with both open and closed slots in making special
machines or where unusual conditions justified their use, but the
forms described cover the great majority of machines found in
use today.

Master Diagrams for Polar Grouped Windings.

In discussing windings, frequent reference is made to the usual
forms of connection. For this reason much space in this and the
following chapters is devoted to illustrations of the typical forms
of diagrams that are employed by all manufacturers in connecting
induction motors. A passing consideration will indicate that
there would have to be an indefinitely large number of these
diagrams to cover all possible combinations. For example,
machines are usually connected either two-phase or three-phase.
The three-phase machines may be either Y (star) or A (delta),

CONNECTING INDUCTION MOTORS

-Typical "wave" disErtun for tHfee-phttae, rouT-pol«, aerieB-dalla o

no. 40.— Typical "wi

TYPES OF WINDINGS 33

the middle of eacli phase. When compared with the mass of
cross connections for the simples t form of pole-phase group winding,
the advantage is apparent. It will be noticed that the windings
shown in Figs. 39 and 40 are perfectly symmetrical and balanced
at all points, the number of slots being an exact multiple of the
number of phases times the number of poles; this is true in practi-
cally all cases for this type of winding.

Standard D. C. Form of Wave Winding Adapted to A. C.

An interesting variation from the foregoing type is illustrated
in Fig. 41 and is typical of a method of connection that has been

Fio. 41. — Special form of wave diaeram for threa-phase, aiz-pols, serieB-stBi'
connection.

widely employed, particularly on the rotors of motors of the
phase-wound type. Here it will be seen that the number of
slots, 62, is not an even multiple of 18 (3 X 6, phases times poles),
but follows the same law as a direct-current, series or wave,
armature winding; namely, the number of slots ± 1 divided by
the number of pairs of poles must equal an integer, and this

34 CONNECTING INDUCTION MOTORS

integer divided by 2 is equal to the proper pitch, or throw, of
the connector. In the case shown in Fig. 41,

Number of slots ± 1 _ 62 ± 1 _ ^^
Pairs of poles 3

The proper pitch of the coil is 21 -5-2 = 10.5 slots; that is, the
throw should be 10.5. Since this is not physically possible,
the throw is made 10 slots or 1 to 11 on one end, and 11 slots
or 1 to 12 on the other end, giving an average of 10.5.

Assume that a bar in the bottom of the slot 1 is connected
by the connector on the back of the core to the bar in the top
of slot 12, and that the front end of the bar in slot 12 is in turn
connected on the front end of the core to the bar in the bottom
of slot 22 and this again on the back end to the bar in the top of
slot 33. Tracing the winding through in this manner, after one
complete circuit has been made around the core it will be found
to connect to the bottom bar in slot 2 and for the second round to
the bottom bar in slot 3 and so on, imtil finally, when all the
slots are traced through both top and bottom, the last throw
will close the winding on itself by connecting to the front end of
the bottom bar of slot 1. This can be proved easily by setting
down a table of nimibers 1-12, 12-22, 22-33, 33-43, 43-54, 54-
2, 2-13, etc., representing the path of the winding around the
core as described until each number has appeared two times,
or until 2 X 62 = 124 bars have been passed through. This
would then give a completely closed winding, and if the middle
point of each end connector were attached to a bar on a suitable
commutator, it would represent exactly a direct-current series
armature winding.

To employ this winding on alternating current, the proper
phase leads must be brought out, and this can be accomplished
in several] ways. One method of doing this would be to leave the
winding closed and bring out three-phase taps 120 deg. apart,
as shown in Fig. 42, or four taps, as in Fig. 43. The first
would give three-phase and the second two-phase. A second
method is to open the winding at three proper places and use
these three pieces to form the usual star or delta connect
This is indicated in Fig. 44. It must not be assumed that the
winding is actually interrupted at the points -4, B and C since
each portion of the winding between these points actually runs
completely around the core several times. This can be readily

TYPES OF WINDINGS 36

grasped if the table as set down in the foregoing is separated into
three parts, each part having one-third of the total bars in it,

or — K — = 4:l^i; say 40 bars in one section and 42 bars in the

other two. The slight unbalancing so caused is, in this case, of
no consequence.

It is necessary to keep an even number of bars in each section
for the reason that the connections are all on one end of the core
and an odd number of bars in any section would mean ending
that section on the back end of the core. Or, in other words,
in tracing through the winding on the odd-numbered bars one is
always going from the front to the back and on the even-num-
bered bars always coming from the back to the front, hence to
end on the front an even number of bars must have been passed
through.

In the connection shown in Fig. 41 a still different method is
adopted by separating the winding into six sections, four of which
have 20 bars in them and two have 22 bars each. These six
sections are connected in pairs in series and the three pairs con-
nected in series star to form a three-phase winding. The reason
for this is a more eflScient use of the copper than either of the
two preceding methods. This follows from the fundamental
idea brought out in the first chapter that every induction motor
is at the same time an alternating-current generator, due to the
fact that the stationary windings are cut by the rotating field.
The output of an alternating-current generator is measured
by the product of the volts times the amperes. In Fig. 41 the
copper will carry a certain maximum current. It then follows
that to get the most out of it as an alternating-current generator,
the windings must be made to generate the maximum practicable
voltage, and this is the result accompUshed by the connection in
Fig. 41.

Voltage Relation of Individual Coils in This Winding.

In the complete closed winding, Fig. 41, each coil is generat-
ing a small voltage which is sUghtly out of phase with all its
neighbors. The situation can be described as a polygon having
62 equal sides, each side representing the voltage of a single coil.
Obviously, the maximum voltage would be obtained if we could
roll out this polygon into a straight line and use one-third of its
length for each of the three phases. This cannot be done in

CONNECTING INDUCTION MOTORS

practice; but it can be approached as shown in Fig. 46. Here
the circle represents the 62-sided polygon just mentioned. By
dividing the winding into six pieces, the efifective voltage of each
piece is reduced to the equivalent of one side of a hexagon. By
putting the opposite side of the hexagon in series and then the
three pairs in series star, the winding is made to develop almost
the maximum voltage. A slight gain could still be made in
the same way by dividing the winding in 12 pieces and using

Fro. 42.

Fig. 43.

Fig. 44.

^mt^

FiQ, 45.

T-19

B-l
"^ xT-39

T-iS'Top Bar SlofNalS
B-l-^BotfomBarSlffr/ih./

T-8V

B-18

LeadB

vB-25

LeadC T-2 S T '\S BH

^°^^ Point

\ ♦»>B-49

B-ll

Leadk

T-2S

Fig. 46.

Fig. 47.

Figs. 42, 43, 44, 45, 46 and 47. — Manner of connecting and bringing out leads

of the winding in Fig. 41.

these 6 pairs as a six-phase winding, but this is too complicated
for ordinary use.

The connection shown in Fig. 41 is obtained practically by
setting down a table, as previously stated, including all the bars
and then dividing it into 6 pieces as nearly equal as possible,
keeping an even number of bars in each. In this case sections
1, 2, 3 and 4 have 20 bars and 5 and 6, 22 bars each. Section
1 is then connected with 4 for phase -4, section 2 with 6 for phase
-B, and section 3 with 6 for phase C. The proper ends of these
connectors for star and the leads can be determined from Figs.

TYPES OF WINDINGS 37

46 and 47, the numbering on which corresponds to that on
Fig. 41. A little practice in this way will suggest how different
three-phase connections could be made for star or delta or series
or parallel to accommodate different voltages and how corre-
sponding two-phase or even six-phase connection, could be ob-
tained.

Concentric-Coil Windings.

In the pushed-through type of winding, previously described,
the coil is formed in the shape of a U and the two branches are
simultaneously pushed through the proper slots in the core, after
whicn the ends are bent toward each other and the individual
conductors connected in series. In the hand-wound type a single
long wire is threaded around and back through two slots until
the complete coil is formed. The completed coil is practically
identical in the two types, and the completed 'winding takes the
form shown in Figs. 48 to 53 inclusive. Figure 49 is typical
of a two-phase arrangement. The coils are concentric and there
are two shown per group, but in practice on induction motors
as high as five or even six have been used. The coils that are
inside on one end of the core are outside on the other end, thus
insuring symmetry and equal resistance in the two phases. Figure
48 shows a cross-section of the core and coils on the line XX and
indicates the relative position of the two banks of coil ends.

Figure 51 shows a three-phase winding similar to the two-phase
Fig. 49 except that only one coil per group is shown; however,
there might be four or more concentric coils per group, as in the
two-phase. It will be noticed at once from this figure and Fig.
50 that the winding is not so simple as the two-phase. Owing
to the passing of the coils at the ends of the core, three banks,
or tiers, are necessary instead of two, and the coil ends are cor-
respondingly longer. It will be noticed that the A phase oc-
cupies the middle tier all the way through and the B and C
phases are alternately in the inside and outside tiers. In this
manner the resistance is kept nearly equal in the three phases.

In order to be able to wind the three-phase with a two-bank
winding similar to the two-phase, the scheme shown in Fig. 53
is^employed. It can be seen that there are the same number of
slots as in Fig. 51 and that both are three-phase, four-pole,
series-star windings. However, Fig. 53 has only two tiers at
the ends and has two coils per group instead of one, but only two

CONNECTINO INDUCTION MOTORS

sit

3 lis

I III

llj

tit

TYPES OF WINDINGS 39

groups per phase instead of four. This is what is called a ''con-
sequent-pole winding/' because the current passes in the same
direction through all the coils forming, for example, two north
poles in each phase. Since there cannot be a north pole with-
out a corresponding south pole, the magnetism returns between
the groups in each phase, thus forming the two south poles, or
four in all. This winding is simpler to make than Fig. 61,
mechanically, but has some slight electrical disadvantages.
Figure 52 is a section through the core and winding on the line
ZZ and indicates the relative positions of the two banks of coils.

Rearrangement of Concentric-Coil Windings.

It wiU be seen that these concentric-coil windings do not lend
themselves readily to rearrangement or reconnection for different
poles or phases, and this is one reason why they have gradually
fallen into disuse. Two-phase windings such as Fig. 49 can
sometimes be connected in "T" and run on three-phase, and
mention of this will be made in a later chapter. Also, a compari-
son of Figs. 49 and 53 indicates that the winding in Fig. 49
might be connected for three-phase 8 poles by a consequent-pole
connection similar to Fig. 53, since the total number of groups,
being twelve, is half of 3 X 8, and this lines up with Fig. 53,
where the total number of groups is 6, or half of 3 X 4.

Where the coils are of the closed type similar to "diamond"
coils used in open slots, they may be grouped and connected
by the usual diagrams for that type, which will be discussed
under open-slot windings. There is, however, a large class
using one- or two-turn coils of the open end, or 'Vave," type
which form very interesting windings, two of which are shown in
Figs. 39 and 40. This type of winding is believed today to be the
form best adapted to the rotating member of phase-wound
motors up to the largest sizes. Since they are perfectly sym-
metrical, they can be equally well employed in the stator, where
the design permits a number of conductors not exceeding four per
slot. These diagrams are practically self-explanatory, but
their great utility and wide employment merits a brief comment.
They are typical three-phase diagrams connected both star and
delta. Three-phase is chosen as it is suitable for either stator
or rotor and is oftenest met with. Figure 39 shows a four-pole
series-delta winding, but it may be equally well connected paral-
lel-star. The winding. Fig. 39, has four conductors per slot.
In Fig. 40 is an eight-pole series-star connection where the two

40 CONNECTING INDUCTION MOTORS

wires in the top of the slot are connected in parallel, also the two
in the bottom of the slot, to form one conductor, or a total of
two conductors per slot.

Wave Windings.

In these windings it is of interest to note that the number of
cross-connections is a minimum, being reduced to the star or
delta connection, the leads and one short connection in the middle
of each phase. Such conditions are ideal for a rotor, and when
the coils are placed in a slot with the tip overhung from one side,
the winding forms one of the best mechanical jobs for a rotor that
is known at the present time.

Passing to Open-Slot Windings.

It is the object of the rest of this chapter to explain the
method of connecting up these windings with suflScient examples
to make it possible to lay out such a diagram when one is not
inmiediately available. It should be borne in mind that such dia-
grams can also be used with partly closed slot windings when they
are of the same form as "diamond coils." Such for example
are the so-called "fed-in" or "dropped-in" coils, which are really
"diamond" coils except that they are placed in partly closed
slots, one wire at a time, through the small opening at the top
of the slot. Such also are the strap coils referred to earlier, where
the slot is half open and the tooth tip overhangs from one side.
While there are four separate coils in such a slot, each coil is
insulated from ground and for purposes of connecting up may be
considered the equivalent of an open-slot winding laid in twice
the number of slots. Such a winding is shown in Figs. 21 and
33. Bar-and-end connector windings when of the "lap" and
not the "wave" type are also connected in the same manner.

Standard " Lap " Winding.

A completely developed picture of an open-slot winding is
stiown in Figs. 54 and 55. The straight radial lines are shown
in pairs. These radial lines represent the straight parts of the
"diamond" coils. The shorter line of each pair represents the
side of the coil lying in the bottom of the slot and the longer line
the side of the coil in the top of the slot. Taking Fig. 54, for
example, before any cross-connecting was done there were 24
separate coils with the beginning and ending of each coil project-
ing at the end of the winding as shown in Fig. 56, which is the
winding represented in Fig. 54 in place in the stator except laid

TYPES OF WINDINGS

n
I

'1
I

42 CONNECTING INDUCTION MOTORS

out flat. Since it is to be connected for three-phase four poles,
there is a total of 3 X 4 = 12 pole-phase groups required and
this results in 24 -^ 12 = 2 coils per group. The first step,
therefore, is to connect the coils in pairs, each pair forming a
pole-phase group, as in Fig. 57. These coU-to-coil connections,

Fia. 67. — Same coils "itubbed.up" or connected into pola-phase Etoups.

Fio. 58. — Completed winding same aa Pigs. 54 and 55.

or stubs, are shown at the group numbers. The resulting 12
pole-phase groups are then cross-connected to form the completed
winding as in Figs. 54 and 58.

A comparison of Fig. 54 with Fig. 55 shows that the cross-
connections or pole-phase-group connections are identical, the
only difference between the two being that Fig. 55 has 36 coils

TYPES OF WINDINGS 43

total instead of 24 and hence there are three coils in each pole-
phase group instead of two. The coils shown in heavy lines,
Fig. 55, represent the coils having heavier insulation, where the
phases change between adjacent coils and will be referred to in
a later chapter. A consideration of these figures leads at once to
two conclusions: First, that such a form of diagram as Figs. 64
and 65 is entirely too compUcated for use by the average winder
and a diagram like that in Fig. 58 requires too much time to
make and is therefore too expensive. Second, since the actual
cross-connections themselves are not affected by the number of
individual coils in the pole-phase group, the entire picture shown
in Figs; 54 to 68 may be replaced by the simple diagram shown
in Fig. 69. The spiral Unes representing the pole-phase groups,
which are numbered to correspond with Figs. 54, 67 and 68,
can be imagined as being the coils which form the pole-phase
groups. It is obvious that there might be any number of coils
connected in series to form the groups. If, for example, the
complete machine instead of having 24 or 36 slots had 48, 60, 72
or 96 slots, the cross-connections of the groups in any case would
be as shown in Fig. 69. A diagram of this type is therefore always
used for such windings, since it can be used for any three-phase
four-pole machine independently of the number of slots in a
particular machine.

Schematic Diagram.

Attention is called to the small "Y" diagram in the center of
Figs. 64 and 55 which is also reproduced in Fig. 69. It has
no electrical connection with, but is the "schematic equivalent''
of, the rest of the diagram. It is the designing engineer's
imaginary conception of the cross-connections reduced to their
simplest terms. By comparing the numbers of the groups on
this small diagram with the corresponding numbers on the larger
diagram, it will be seen that each pole-phase group is shown in
its proper phase and with the proper direction of its ends toward
the lead or toward the star connection. The arrows shown on
the larger diagram, Fig. 59, and also on the small schematic
equivalent represent a simple and positive check as to whether
the connections to the diflferent groups are correct.

Check for Connecting Proper Ends of Phases to Star Point.

There is a danger in a three-phase winding that the three
phases may be connected in a 60-deg. relation instead of a 120-

44 CONNECTING INDUCTION MOTORS

deg. relation, or as it might be expressed on the diagram, Fig. 59,
there is danger that the wrong end of the B phase, for example,
may be connected to the star point. As a check against this
each phase is traced through, starting from the lead or terminal
and proceeding to the common, or "star," point at the center
of the winding. As the successive groups are passed through,
an arrow is placed on each as shown, indicating in which direc-
tion that group was passed through. When all three phases
have been traced through and the arrows on the groups are in-
spected, the diagram is correct if the arrows on adjacent groups

Fig. 59. — Schematic, four-pole, series star diagram exact equivalent of pictured

winding in Figs. 54, 55 and 58.

reverse; that is, if they are alternately clockwise and coimter-
clockwise in passing aroimd the winding. This check should
be studied over and thoroughly mastered, as it is the one check
that the author has found in 15 years of practical experience
is always reUable and easily applied. The only exception to this
check is the case of consequent-pole machines, to be described
in another chapter, but these are so special and so infrequently
met with that they may be practically put out of the consider-
ation and the check be regarded as almost xmiversal.

It is the common practice of all manufacturers to send out
machines that can readily be connected for either one or two
voltages. This is accompUshed by a series or parallel arrange-
ment and can be understood by comparing Figs. 59 and 60.
By looking at the small "equivalent" diagram in the center, it

TYPES OF WINDINGS

will be seen that there are twice as many groups in series between
the terminal leads in Fig. 59 as there are in Fig. 60. This
means that if Fig. 59 is proper for 440 volts, Fig. 60 would be
right for 220 volts. The idea was given in an earlier chapter
that one function of the winding was to generate the counter-
electromotive force. It can be seen at once that if the coils
as connected in Fig. 59 are generating 440 volts, they will ob-
viously generate only half as many, or 220 volts, connected as
in Fig. 60. As another consideration, it is seen that if the
motor has the same horsepower at both voltages, it will have

AC B

Fia. 60. — Showing the diagram Fig. Fig. 61. — Showing the diagrams of

59 reconnected from series to parallel Figs. 59 and 60 reconnected to four
star. parallel star.

twice the number of full-load amperes at 220 as it has at 440
volts. This is properly taken care of, as will be seen from Fig.
60, since the winding being doubled has twice the copper cross-
section in Fig. 60 that it had in Fig. 59.

If the number of poles in the machine is divisible by 4 as,
for example, 4, 8, 12, 16, etc., the winding may be put in 4 paral-
lels as shown in Fig. 61 and by comparison with Figs. 59 and
60 would be good for 110 volts at the same horsepower. The
increased current at 110 volts is again taken care of by providing
4 times the copper section, as shown. This same principle can
be extended, and when the number of poles for which the machine
is woimd can be divided by 6, it is possible to have the winding
connected for 3 parallels or 6 parallels, as shown in Figs. 62

46 CONNECTINQ INDUCTION MOTORS

and 63, reapectively. If divisible by 8, there could be 2, 4
or 8 parallels, and if divisible by 10, there could be 2, 5, or
10 parallels. It will be explained in a later chapter on "Changes
in Voltage" that these possible changes when considered with
the possibility of "star" or "delta" allow in many cases the re-
connecting of motors for new conditions.

How to Draw a Diagram to Suit Any Case.

As regards the number of possible diagrams, these multiply very
fast. As an instance are shown the diagrams, Figs. 64, 65, 66, 67,

TYPES OF WINDINGS

68 and 69. Here the simplest case is studied — that of two poles —
and when two- and three-phase are considered, series and parallel,
and star and delta, there are six possible diagrams of connection,
as indicated. Considering for the moment a 12-pole winding,

CAB

BAG

Fig. 66. — Three-phase, two-pole wind-
ing connected series star.

CA B

Fig. 67. — Three-phase, two-pole wind
ing connected parallel delta.

Fig. 68. — Three-phase, two-pole wind- Fig. 69. — Three-phase, two-pole wind-
ing connected series delta. ing connected two parallel star.

there are possibilities for series, 2 parallel, 3 parallel, 4 parallel,
6 parallel and 12 parallel groups, which with two- and three-
phase and star and delta give 18 diagrams total, just for 12 poles.
It becomes plain that it is desirable to analyze these diagrams

CONNECTING INDUCTION MOTORS

and arrive at a simple scheme by which any one can be drawn
at need without the necessity of relying on a bulky collection of

^'^e../

Fia. 70. — Two-phase, four-pole series connection.

Fig. 71. — Same as 70 except **B" phase reversed.

V-

■t 'e' If 's' f,

-^—4

tH=t:

Fig. 72. — Three-phase, four-pole series star connection.

Fig. 73. — Same as Fig. 72 except leads brought out from different groups.
General scheme of laying out pole phase group diagrams.

diagrams which may not be available when needed. In Figs.
70, 71, 72 and 73 is shown the method of laying out diagrams

TYPES OF WINDINGS 49

of this general nature. The first operation in making the
connection is to connect the individual coils into pole-phase
groups. There are as many coils in series in each group as the
total number of coils in the winding divided by the number of
phases times the number of poles. In Figs. 70 and 71 this is
assumed to be 4 coils, and hence each pole-phase group is shown
as having 4 individual coils in series. The next step, as shown in
Figs. 70 and 71, for a two-phase machine is to letter the altern-
ate groups A, B, A, B, etc., to designate the groups in the A
phase from those in the B phase. The next step is to put on the
arrows, as shown, in groups of two pointing m the same direction
on two successive groups of coils. It does not matter what group
is used to start with. The only essential is that there shall be
first two arrows pointing clockwise and then two arrows pointing
coimterclockwise. The third step is to show the connections to
the different groups so that the current at any given instant will
pass through the groups in the same direction as the arrows. If
this method is followed in laying out the connections of two-phase
windings, the result will always be a diagram that shows the pole-
phase groups connected in their proper relation.

Figure 71 is produced to compare with Fig. 70 to verify the
statement already made that the arrows may be placed beginning
with any group. In Fig. 70, beginning at the right, there are
two arrows coimterclockwise on groups 1 and 2, whereas
in Fig. 71 the first two arrows counterclockwise are on groups
4 and 5. The only effect of this is to reverse the B phase,
or in other words, the motor in Fig. 71 would have the opposite
rotation of the motor in Fig. 70. Since this is at once corrected
by reversing the leads of one phase outside the motor, it wiU be
seen that if the internal connections are made according to Fig.
70 or 71, the motor will operate properly in all respects.

Three-Phase Star Diagrams.

The three-phase winding shown in Fig. 72 is even simpler.
Here there are 3 coils per pole-phase group, and as in the two-
phase winding the individual coils are first connected mto pole-
phase groups and the groups lettered consecutively A,B,C,A,B,
C, to separate the phases. Then the arrows are put on as shown,
first clockwise and then counterclockwise, alternately, beginning
with any convenient group, it matters not which. The lines are
then drawn in for the group connections as shown, following the

50 CONNECTING INDUCTION MOTORS

convention that the arrow enters the lead or terminal of each
phase and goes toward the star or common connection at the
center of the winding. If this rule is followed, the connection
will be correct and it is applicable to any combination of numbers
of slots and poles. By keeping in mind either Fig. 70 or Fig.
71 for two-phase and Fig. 72 for three-phase, all diagrams of
this type are mastered and can readily be reproduced at a
moment's notice.

Delta Diagrams.

In checking a delta diagram, check it first as if it were a star
diagram and then form the delta by connecting the star end of
the A phase to the B lead, the B star to the C lead and the C
star to the A lead. These three connections will be the delta
points from which the three external leads are brought out.
Another method of checking where it can be handled without
confusion is to imagine the current flowing aroimd inside the
closed delta. The arrows on adjacent pole-phase groups will
then alternate in direction as in the check on a star winding.
This latter check may be applied to Figs. 67 and 68 by starting
from terminal A, or any terminal for that matter, and following
around through all the pole-phase groups back to A. For ex-
ample, in Fig. 68, starting from A terminal, follow through
group 1, then through 4, 3, 6, 5 and 2 back to A ; thus a closed
circuit has been made through all the groups in the direction
of the arrows.

A further consideration of the arrows on the pole-phase groups
of Fig. 72 shows that there might be a number of different con-
nections, all correct, which check with these arrows and differ
only as to the particular group from which the lead or the star
connection are taken off. In fact, the lead or the star connec-
tion may be taken off from the proper end of any pole-phase
group in a given phase so long as the cross-connections, when
followed through, give the alternate arrows as shown. Fig.
73 is added to show one of these possible connections just as
correct as Fig. 72, but with the leads and stars taken off from
different pole-phase groups. Referring to the winding. Fig. 58,
and again applying this rule, it will be foimd to hold good as
indicated by the arrows. This demonstrates conclusively the
correctness of this method of checking three-phase diagrams
of this type.

CHAPTER IV

CHORDED WINDINGS OR THE EFFECT OF COIL THROW

ON THE MAGNETIC FIELD

The efifect of changes in frequency, phase, voltage or poles
upon the performance of an induction motor and the necessary
changes in the windings to preserve normal operation may be
considered from the viewpoint of a change in voltage only and
worked out by that method. By this is meant, for example, that
a three-phase motor may be considered as a two-phase machine
of a different voltage, in so far as the magnetic flux in the iron is
concerned, also the heating, efficiency, torques, power factor, etc.
Likewise a 25-cycle motor may be considered as a 60-cycle
machine at a different voltage and operated accordingly.

A change in the number of poles can be looked upon as chang-
ing the speed of rotation of the magnetic field. With a given
number of conductors this would at once affect the generated
voltage or counter-electromotive force. It was explained in the
second chapter that the coimter-e.m.f. was practically almost
equal to the appUed e.m.f., or Une voltage. Hence it may be
seen that even a change in the number of poles can be considered
as a voltage change and the number of wires in the coils corre-
spondingly changed so as to give the same performance imder
the new conditions.

Since all these changes can be considered as voltage changes
and will be so considered in the chapters to follow, it is necessary
to investigate closely all the considerations that directly affect
the voltage. The first one of these is the effect of winding the
coils less than full pitch, or "chording" the coils, as it is most
frequently called. The pitch, or span, is expressed in the number
of the slots included beween the two sides of the coil.

It is conmion knowledge that this pitch, or throw, must be
somewhere near the quotient of the bore periphery of the core
divided by the number of poles. For example, if the stator of
a given motor had 72 slots and was woimd for four poles, an in-
dividual coil would be expected to lie in slots 1 and 19 or there-

CONNECTING INDUCTION MOTORS

CHORDED WINDINGS 53

abouts. The reason for this is that if there are four poles, the
span of each coil must be somewhere near one-quarter of the bore
periphery. In this case 72 -5- 4 = 18 slots, and 18 + 1 = 19,
hence the exact pitch for the coils of this winding would be 1 and
19. Similarly, a six-pole coil for the same core would Ue in some-
thing like slots 1 and 13 and an eight-pole coil in slots 1 and 10.
An examination of any induction motor woimd in the usual way
discloses the fact that the coils are seldom woimd full pitch, as in
Fig. 74, but always a few slots less, as in Fig. 75. It is the purpose
of this chapter to discuss the reasons for winding the coils less
than full pitch and the effect upon the voltage of the machine
caused by this practice, which gives a fractional-pitch winding. ^
One of the immediate results of spreading the coil less than
full pitch is to place in the same slot coils carrying currents of
different phases. This is illustrated in Figs. 74 and 75, which
show a two-phase four-pole winding placed in 32 slots. In Fig.
74 the throw of the coil is 1 and 9, or exact pitch, and it can
be seen, that all the slots contain coils entirely of the same phase;
that is, all slots contain either A or B coils. On the other hand,
in Fig. 75, the throw of the coil is one less than full pitch, or it
is chorded one slot and woimd in slots 1 and 8. As a result,
it is seen that in slots 1, 5, 9, 13, etc., the coil lying in the top of
the slot is of a different phase from the coil in the bottom of the
slot. At first thought this appears to be an interference, but
it is really not so, since the values of the currents in the two phases
at a given instant are different; and since one is increasing and
the other decreasing, the effect on the magnetic circuit is due not
only to the amount of current in the two coils, but also to their
phase relation. Hence the result of chording is not to make
the two phases interfere with each other in any way, but simply
to have a tendency to reduce the number of turns in the coils, as
wiU be described. That the resulting magnetic field which ro-
tates is due to the interaction of all the phases in this way was
mentioned in Chapter II.

Advantages of Chording the Winding.

There are three main reasons for winding the coils less than
full pitch: (1) The length of the mean turn is reduced; (2) it has

^ A longer theoretical discussion of fractional-pitch windings is found in the
"Transactions of the A. I. E. E.," Vol. XXVI, 1907, pp. 1485-1608, Messrs.
Adams, Cabot and Irving; and Vol. XXVII, 1908, pp. 1077-85, Jens Bache-
Wiig.

CONNECTING INDUCTION MOTORS

CHORDED WINDINGS

the efifect of changing the number of turns in the coil; (3) the
over-all length of the winding parallel to the shaft is reduced, thus
requiring less space in the end brackets which carry the bearings.

Discussing these effects in order, the reduction in the length of
the mean turn accompUshes two results: First, less wire is re-
quired to form the coils, which is a sUght economy; and second,
the total resistance of the winding is reduced. This reduction
in resistance, in turn, has two beneficial results — the one a reduc-
tion in copper loss with a corresponding gain in efficiency and
the other a reduction in heating, since the heating is measured
by the* total losses that must be dissi-
pated. The reduction in cost and the
improvement in performance are both of
a relatively small order, but they repre-
sent the minor details in which a nicely
balanced design has an advantage over
one more crude. The reason for the
shortening of the mean turn can be seen
from Fig. 76. The coil ABCDEF is
wound in slots 1 and 7 and the coil
AGHIJF is woimd in slots 1 and 6.
It will be noted that the gain in length
by the shorter coil is due not alone to

the fact that the chord AH is shorter than AC, but also
to the fact that the point G is considerably nearer the core
than the point B; or in other words, the angle AGH is greater
than ABC.^

The second effect of chording is that it acts in the same man-
ner as changing the number of turns in series in the coil. Sup-
pose, for example, that a designer of induction motors has made
a calculation and finds that if six turns of wire are put in a
coil there will be sUghtly too many turns for the best result,
and if five turns are used there will be sUghtly too few. If
there was not the recourse of chording the coil, it would be neces-
sary to decide which was the lesser of the two evils, or else to
change the number of slots. The latter might not be possible
as it is desirable to have the total number of slots a multiple of
the number of phases times the number of poles, and this could
not be shifted in fine adjustments. However, it is possible to

1 See article in "Electric Journal," Vol. VIII, 94, by Gray E. MiUer, on
"Determining the Fonn of a Diamond Coil."

Fia. 76.— "Chording"
shortens the length of wire
in the coil.

56 CONNECTING INDUCTION MOTORS

chord the coil and by the simple expedient of winding the coils
one or more slots less than fuU pitch, the effect can be produced
of putting 5J^ or 5% turns in a coil, or in fact a very fine ad-
justment to give exactly the best possible combination. There
would of course be six actual physical turns of wire in the coils,
but their magnetic eflfect would be reduced by the chording to
5J^ tiu-ns or whatever was desired.

The effect of the turns in the coil varies as the sine of half of
the angle in electrical degrees which the coil spans. To illus-
trate, if there are 72 slots in an eight-pole machine, the coils
would spread exactly full pitch if they lay in slots 1 and* 10; or
in other words, if there were eight slots between the two slots
in which the two sides of any coil were located. Such a coil
would span 180 electrical degrees. One-half of 180 deg. is 90
deg., and the sine of 90 deg. is 1; therefore the effect of the tiuns
in such a coil is 1, or maximum. Suppose, instead, the coil lies
in slots 1 and 8. It would then span 140 deg. electrically, since
72 -J- 8 = 9 slots represents 180 deg.; one slot therefore repre-
sents 20 deg. and seven slots 140 deg. The sine of half of 140 deg.,
or 70 deg., is 0.94. Hence it follows that the effect of the turns
in this coil is less than that of the full-pitch coil by the ratio of
0.94 to 1.

Changing Poles with Constant Throw.

The foregoing is of interest in the present problem, because it
is often possible in making alterations in the winding to change
at the same time the span of the coils by one slot, more or less,
by springing the coil mechanically, and so improve the per-
formance of the machine under the new conditions. The point
becomes of vital importance immediately when changing the
nimiber of poles without changing the throw of the coils.
Referring again to the 72-slot motor, assume that the coils are
wound in slots 1 and 8. For an eight-pole connection these coils
will have an effect of 0.94 as explained. If the connections are
changed for six poles, the effect is entirely different; 72 -^ 6 = 12
and 180 -^ 12 = 15, or each slot represents 15 electrical degrees.
A throw of 1 and 8 covers seven complete slots, or 7 X 15 = 105
deg.; the sine of half of 105, or 52.5 deg. = 0.79, which means
that when connected for six poles the coils have an effect of only
0.79, as against 0.94 when connected for eight poles.

It is possible to avoid using the sine of half the angle and se-

CHORDED WINDINGS 57

cure a factor that is sufficiently accurate for all practical pur-
poses by using the expression,

(Ntimber of slots per poley—2{N umber of slots dropped)^

{Number of slots per poleY

Using the same eight-pole example as above, the number of
slots per pole is 72 -7- 8 = 9, and the pole pitch is 1 and 10.
When the coil is woimd 1 and 8, it spans 7 slots and there are 9
— 7 = 2 slots dropped. The expression then becomes

(9)
and similarly for the six-pole.

V^^^- ^i - OM.

which agrees roughly with the other method.

Explanation of Term " Chord Factor."

A coil should in no case be chorded more than half of the pole
pitch, as secondary disturbances of the magnetic field are oc-
casioned by chording which become prohibitive at that point.
The expression, "sine of half the angle spanned by the coil," is
given the name "chord factor," and it should be considered in
the work of reconnecting. For example, if the poles are changed
from 8 to 6, as in the example given, and the chord factor changes
from 0.94 to 0.79, the new line voltage should be 0.79 -^ 0.94
times the old, neglecting the effect of other changes that are
being made. If nothing else was undergoing change and the

normal voltage was 440 in the first place, it should be 440 X

0.79

7^-^ = 370 after the change is made; or, expressing it another

way, if it was still operated at 440 volts after the change, the
motor should be thought of as operating at about 18 per cent,
over voltage.

Since the foregoing is one of the important points in induction-
motor winding, it is worth while to consider carefully how this
effect is produced. It could be stated briefly by saying that the
two sides of the coil, which of course are in series, are not strictly
in phase with each other. But this can be seen more clearly
from diagrams. Suppose, for example, that a two-pole motor is
considered and that a cross-section is taken through the core and

CONNECTING INDUCTION MOTORS

windings in a plane at right angles to the shaft, as shown in Fig.
77. The dotted parallel lines in the peculiar twin pattern
represent the lines of force, or magnetism of the rotating mag-
netic field, which is rotating in a clockwise direction, as shown by

the arrow outside. The small

^oiafiojl

ofAfo,

Stator^
(jarrwiations

Fig. 77. — Cross-section through a
two-pole stator showing magnetic
lines of force.

arrows on the lines of flux indi-
cate the magnetism coming from
the stator north pole at the top
into the rotor core and out again
into the stator at the bottom,
forming a south pole.

Of course this magnetic field
is being set up by polyphase
alternating currents, but it need
only be thought of as shown in
the figure and as if excited by
direct current. The six small
circles, in the stator and near
the bore, numbered 1 to 6, repre-
sent the conductors of the stator winding. Consider that these
six conductors constitute the complete winding. As the mag-
netic field swings around in a clockwise direction, it cuts these
six conductors because with6ut doing so it cannot get from the
stator into the rotor and back and at the same time rotate. As
the conductors cut this field, each one gen-
erates a voltage which in value and direc-
tion may be represented by the arrows or
vectors of Fig. 78.

The reason these voltages are shown in
a hexagon is because they are not all gen-
erated at the same time, but in a succession.
For example, the north pole sweeps by
conductor No. 1 and a fraction of a second
later past No. 2 and then past No. 3 and
so on around to No. 6, and this can be
represented by the sides of a hexagon
which finally closes on itself, as shown in Fig. 78. The reason
the arrows for conductors No. 1 and No. 4 are shown in the
same direction is because the north pole is sweeping past
No. 1 to the right at the same instant that the south pole is
sweeping past No. 4 to the left, so that the voltages in these two

Fig. 78. — Vector dia-
gram showing direction
at any instant of volt-
ages generated by con-
ductors in Fig. 77.

CHORDED WINDINGS 59

conductors are in the same direction at the same instant. Simi-
larly, Nos. 2 and 5, and Nos. 3 and 6 are aUke in pairs. Suppose
now that No. 1 and No. 4 had their ends connected together both
at the front and the back of the machine so that they formed a
short-circuited turn. The voltage then which would be effective
in forcing current around this short-circuit would be that generated
in No. 1 plus that in No. 4 and may be represented by line No. 1
plus No. 4, or KL, shown in Fig. 79. KL then would represent the
voltage of a coil wound exactly full pitch or from the center of
a north pole to the center of a south pole.

Suppose, instead of No. 1 and No. 4, that No. 1 and No. 6 had
their ends connected so as to form a short-circuited tiu-n. The
voltage which would be effective in forcing ciu-rent around

K U ^^L

Fia. 79. — Adding volt- Fia. 80. — Adding volt- Fio. 81. — Adding volt-
ages generated by con- ages of conductors 1 and ages of conductors 1 and
ductors 1 and 4, Fig. 77. 6, Fig. 77. 6, Fig. 77.

through this short-circuit would be MN, shown in Fig. 80,
which it will be seen is somewhat less than KL in Fig. 79. The
arrow MN is made by adding 1 and 5 which in themselves are
just as long as 1 and 4, but instead of lying in a straight line they
are at an angle to each other. This angle shows what is meant
by the two sides of the coil being out of phase with each other, or
still another way to say it would be that the magnetic field is not
working on No. 1 and No. 5 in exactly the same way at the same
instant as it was on No. 1 and No. 4. Therefore, when No. 1
and No. 5 are short-circuited giving the voltage MN, they repre-
sent a coil chorded to two-thirds of full pitch, or they have the
effect instead of being two conductors in series, of being only
2 X 0.866 conductors, or 1.73 conductors. This is because two-
thirds pitch would he % X 180 deg. = 120 deg. and the sine
(0.5 of 120 deg.) = sine 60 deg. = 0.866.

In the same way conductors No. 1 and No. 6 could be joined in
series to form a short-circuited turn, and the voltage of such a
turn would be represented by OP in Fig. 81 which is made up of
No. 1 and No. 6, which are at an angle of 60 deg. with each other.
In this case, instead of having the effect of two conductors in

60 CONNECTING INDUCTION MOTORS

series so far as voltage generation is concerned, the effect will
be that of only one, since 1 and 6 represent one-third pitch, and
yi of 180 deg. = 60 deg. and the sine (0.5 of 60 deg.) = sine
30 deg. =0.6. Therefore 2X0.5 = 1. Of course 6 slots per pole
is a small number and it can be seen that with 12 or 15 slots per
pole at his disposal the designer can chord to get almost any
value required.

Effect of Chording.

It will be noted that in this graphic explanation the conductors
were spoken of only as generating counter-e.m.f., as explained
in the first chapter and never as setting up the field. How-
ever, it should be understood that in the magnetizing function
of the winding, also, the chording produces the same effect as
explained here by means of the generator idea.

The third effect of chording has been mentioned as shortening
the coils axially. This is very useful, especially in the case of
two-pole and four-pole machines where the coils, if made full
pitch, would protrude so far at each end a£ to require special
end brackets. These long end brackets in turn would spread the
bearings farther apart and make necessary a larger shaft to keep
down the shaft deflection. Hence it is of prime importance to
shorten up on the coil ends in this manner. Also, the end wind-
ings are mechanically stiff er. There are other effects of chording
known to the designer, which are desirable. These are, for
example, a reduction in the leakage reactance, thereby giving
better torques and possibly better power factor and efficiency.
Also, it is very beneficial in reducing magnetic noise to employ
chording, depending on the combinations of slot numbers, so
that, taken all in all, chording is one of the prime features in
studying the effect of winding changes upon the performance of
a machine.

Distribution Factor Less Important.

Another winding factor that acts in a similar manner to the
chord factor just discussed is the one known as distribution factor.
This is not subject to control as is the chording and is relatively
much less important, but should be mentioned in passing, as its
neglect might occasion trouble if a combination was employed
which otherwise was on the ragged edge of failure. This distri-
bution factor has to do with the fact that the coils in one phase
of a two-phase motor are spread over half of the face of a pair of
poles and in a three-phase motor are spread over one-third of the

C HORDED WINDINGS 61

face of a pair of poles. This factor varies a trifle with the
number of slots per phase and pole, but a fair value for average
two-phase windings is 0.905, which is about the ratio of one side
of a square inscribed in a circle to one-fourth of the circumfer-
ence. For a three-phase machine a fair average value is 0.956,
which is practically the ratio of one side of a hexagon inscribed
in a circle to one-sixth the circumference, or 3 -^ 3.14.

Ordinarily this factor is not troublesome and if forgotten in
changing from two- to three-phase, or vice versa, would not cause
any great disturbance. However, in deaUng with special ma-
chines — as for example, motors woimd for two sets of poles —
the distribution factor may be more important than the other
factors. In such a case the two-phase distribution factor may
be as low as 0.707 and the three-phase as 0.866 because the coils
for a four-pole motor, for example, are spread over the pole
face of an eight-pole. Mention is made of this fact in connection
with Fig. 138, Chapter IX.

Phase Insulation Important.

Another general fa-ctor is that of "phase insulation." It is the
practice of many manuf actiu'ers to put heavier insulation on the
coils at the ends of the polar groups which are mechanically adja-
cent to one another and which are also subjected to the voltage
between phases, which may be the maximum voltage between sup-
ply lines. Such coils are drawn in heavy lines in Fig. 55. By rear-
ranging this diagram for two-phase it appears at once that both the
number and location of these so-called ''phase-coils" are changed,
and in changing the number of poles, the number and location of
the phase-coils must also be -changed. In fact, whatever recon-
nection is attempted, the phase coils should be checked and re-
arranged, since this is comparatively easy and adds considerably
to the protection of the machine from breakdowns of insulation.

To illustrate the manner in which the phase coils should be
rearranged when changing phases or poles. Figs. 82 to 85 are
shown. All four of these figiu-es show the same winding in 48
slots and with a coil throw of 1 and 9. In Fig. 82 the phase
coils are arranged for three-phase four-poles, in Fig. 83 for two-
phase four-poles, in Fig. 84 for two-phase eight-poles and in Fig.
85 for three-phase eight-poles. It will be noted that since the
throw of the coils remains unchanged, it represents a chord factor
corresponding to two-thirds pitch, or 120 deg. for the four-pole
winding (since 8 slots = % of 12) and a chord factorcorrespond-

CONNECTING INDUCTION MOTORS

CHORDED WINDINGS

■3

•s

64 CONNECTING INDUCTION MOTORS

ing to one and one-third or 240 deg. for the eight-pole winding
(since 8 slots = 1^^ of 6). Since the chord factor is equal to the
sine of }4 the spread angle and since the sine of 120 deg. = the
sine of 60 deg. = 0.866, the effect of the underchording on the
four-pole winding is exactly the same as the effect of the over-
chording on the eight-pole winding.

In all four diagrams the coils having heavier insulation than
the others are shown shaded, the different degrees of shading
representing the coil having additional insulation in the different
phases. In Fig. 82 there are 12 pole-phase groups of four coils
each. The two outside coils of each group have heavier insula-
tion, as indicated; this will give 24 phase coils, or one-half the
winding is phase coils. The winding Fig. 83 has eight pole-
phase groups, with 16 phase coils, or one-third of the total wind-
ing is phase coils. In Fig. 84 the winding has 16 pole-phase
groups, making it necessary that there be 32 phase coils. The
arrangement in Fig. 85 gives 24 pole-phase groups of only two
coils per group, hence all the coils must be phase coils with
increased insulation.

Plotting Pictures of the Magnetic Field.

In Chapter II there was shown a method of plotting a physical
representation of the rotating magnetic field as it varies from
point to point around the air gap of an actual machine. The
same method may be used to show what effect is produced on its
shape by changing the throw of the coil, or chording the winding
as it is called. The latter effect is thus investigated for a change
of one slot at a time from full pitch to less than half pitch. By
full pitch is meant that the span of the coil is exactly the same
distance as that from the center of a north pole to the center of
an adjoining south pole, and by half pitch that the coil spans or
throws only half that distance. Referring to Figs. 17 and 18 of
Chapter II the small "stair step'' figures represent cross-sections
of the magnetic field existing in the motor as the alternating
currents in the windings vary in value from instant to instant,
and a comparison of the small figiu-es shows that the magnetic
field actually travels around the stator bore or ''air gap*' at a
uniform rate. The number of revolutions that it makes in one
minute is equal to 120 times the number of cycles per second of
the supply circuit divided by the number of poles in the stator.

Expressed in symbols this would be S = 120 - ; where S is the

CHORDED WINDINGS

speed of rotation in r.p.m., / is the frequency in cycles per second,
and p is the number of poles.

In order to make clear the field photographs or diagrams of the
present chapter and to obviate the possibility of confusion regard-
ing them, attention is called to the fact that they represent the
conditions existing in the windings at an instant of time when the
current in one of them is at its maximum value. Since we are
dealing with three-phase motors, the currents in the windings
connected to the other two phases will at that instant both be
equal to one-half their maximum values. This may be ex-
plained by reference to Figs. 17 and 18 of Chapter II, which
represent the values of the currents in the three phases for

FiQ. 86. — Normal relation of the currents in a three-phase motor.

every 30 deg. of a complete cycle of 360 deg. Suppose these
three cm-rents are represented by the three branches. A, B
and C of the '' Y'' illustrated in Fig. 86, each of which is 120 deg.
from the other, and that a vertical reference line hh is drawn
through the center o. Now assume that the "Y" rotates in a
counterclockwise direction about this center while the line hh
remains stationary, and that the three branches assume the suc-
cessive positions represented in the second colunm of Fig. 87.
The values of the currents at any instant of time will be repre-
sented by the length of their horizontal projections upon the
line hh. If the maximum value of each current is assumed to be
one ampere, the instantaneous values of the three for each 30
deg. of a complete cycle would be those given in the last three

CONNECTING INDUCTION MOTORS

columns of Fig. 87. Projections that lie above the center o
are taken to be positive and those that lie below as being negative.
In Chapter II there was given a picture of the field corre-
sponding to each instantaneous value of the currents, but in the
present chapter the figures are given for only one of these values
and they have been chosen to be the ones existing when the con-

ANGLE,
DEG.

POSITION Of
BRANCHES
OF Y

CURRENT A
AMPERES

CURRENT B
AMPERES

CURRENT C
AMPERES

O-fB

-05

+ 1.0

-05

+ 0.60^

-OM<b

+ 0.5

+ 05

-1.0

B^f^^

+ 0.d(b(b

-0.6(b(b

120

B*^C

+ 1.0

-0.5

■

-03

150

Aw
I5<pl— C

+ 0.d(b(b

- O.Q(b(b

160

A<UC

+ 05

-1.0

+ 05

210

ZIO-^B

- O.Q(b(b

+ OA(b(b

240

-05

-0.5

+ 1.0

270

A ^'-''

'0.6(b(c

+ 0.6Q>(d

300

300°

-1.0

+ 05

+05

530

'^'

-0.600

+ 0.d<b(b

Z(bO

Same as
ODeg.

Fio. 87. — Instantaneous values of

out a

the currents in a three-phase motor through-
complete cycle.

dition is that shown for deg. in Fig. 87, that is, for the instant
when the current in the B phase is at its plus maximum value
and the currents in the A and C phases are at minus one-half
their maximum values. Of course, any other position could have
been chosen for conducting the investigation, but the values for
the deg. position are convenient ones to use when plotting the
results.

CHORDED WINDINGS 67

Meet of Chording Shown Graphically.

Since one of the efEecta of reconnecting for a diEEerent number
of poles is to affect the "chord" or throw of the coil, let us con-
sider first the effect of "chording." Pigs. 88 to 93 incluaive

Fio. SS. — Fioluca of mftKOBtio Gald set up by viadiog in Fig. 94.

Fio. 8S. — Magnelia field if winding in Fig. 94 is chorded to alota 1 and 9.

show the magnetic field constructed, as explained in Chapter II
for a 54-8lot three-phase 6-pole winding when the throw of the
coil is changed one slot at a time from slots 1 and 10, as in Fig.
94, which is full pitch or 180 deg., down to slots 1 and 5, as in
Fig. 95, which is less than half pitch; or to be precise, 80 deg.

68 CONNECTING INDUCTION MOTORS

The same magnetizing current is assmned to flow in the coils in
all six cases, although in an actual machine this would not be
the case; the magnetizing current would increase with decreased

(ca • ■ + 1-0 Ampera, Plwe B
(WO- -0,5 " "A

Fio. 90.— Macnellc field if wioding in Fi«. 94 is ohorded to alota 1 and 8.

FiQ. 01. — Similar to Fig. 90 except eborded to slots 1 and 7.

throw of coil due to the attempt of the motor to keep the field at
the constant v^ue necessary for the generation of the required
back or counter-electromotive force. To facilitate comparison,

■ CHORDED WINDINGS 69

however, this change in current has been disregarded in the
figures. The "stair steps" show the magnetic fields as they
would look if there were no winding on the rotor, and the smooth

Fia. 82.— Similar to Fin. 91 chorded to I and 6.

{d)©- + 1.0 Ampere, PhcjsoB
(e)©--0.5 - « A

(f)©--aB " " C

Fia. 03.— Similar to Fig. 92 chorded to 1 and 5 as in Fig. 95.

curves, having the sine shape, show the fields as they look after
being smoothed out by the currents in the rotor winding. It
will be noticed that the area of the field for one pole is given in
each case and that it varies from 32 for full pitch in Fig. SS,

CONNECTING INDUCTION MOTORS

down to 20 in Fig. 93. These areas correspond to what is
known as the "chord factor" of the winding. In the earlier
part of this chapter it was stated that the chord factor for a
chorded winding could be expressed in its effect on the magnetiz-
ing or no-load current and in its effect on the generated or counter-
electromotive force by the mathematical value of the sine of
one-half the electrical angle spanned by the coil. This relation
is shown in the following table:

Table I. — Chobd Factors fob Vabious Angles

Figure

Angle spanned by
coil — a deg.

Sine Ka, or chord
factor

Area of magnetic
pole figured from
chord factor

Area of ma^etie

pole granhically

from ngure

ISO

1.000

32.0

160

0.985

31.5

140

0.940

30.1

120

0.866

27.7

100

0.766

24.5

0.642

20.5

The sUght difference between the last two columns in the table
is due to the area imder the ''stair step'* curve not being quite
the same as the area imder the corresponding smooth sine curve.
The chord factor as shown in the third column at once indicates
two facts: First, that if the winding is chorded more current will
have to flow in the windings to produce the same magnetic field
strength; and second, that since the generated or counter-electro-
motive force in the windings set up by the rotating magnetic
field is reduced through chording by the amoimt indicated by
the chord factor, it is necessary to have a stronger magnetic
field in the motor if it is to operate at the same voltage when the
coil is chorded up. The way this shows up in reconnecting
for different numbers of poles, when the reconnection causes
chording of the coil, is that the same effect is produced as would
be if the motor were connected to a higher voltage. This will
be explained fully in a later chapter deaUng with the practical
appUcation of the principles presented in this chapter to the
actual work of reconnecting.

An examination of the shape of the magnetic field indicates
that the effect of chording is to flatten the top of the field and
make it lower for the same pole span. In Fig. 96 is shown the

CHORDED WINDINGS

CONNECTING INDUCTION MOTORS

CHORDED WINDINGS 73

effect of connecting the winding of Figs. 88 and 94 for four
poles instead of six. The mechanical throw of the coils is still
1 and 10, but the pole arc is longer for four poles, hence, the
coil is actually chorded to 120 electrical degrees for four poles,
although it was full pitch, or 180 deg., when connected for six
poles. It will be noted that with the 6-pole winding, Fig. 88
the entire area of the poles is 6 X 32 = 192, but that for the
4-pole winding. Fig. 96, the area is 4 X 61 = 244. In the 4-
pole winding, the speed of the rotating field is 1.5 times that of
the 6-pole one, and it would therefore seem reasonable that with
the same magnetic field density in the air gap and the same
currents in the windings, the horsepower when connected as a
4-pole machine should be 1.5 times that of the 6-pole rating.
However, since the coil throw on four poles is only 120 deg. the
chord factor is sine of 60 deg. = 0.866 and the rating will be
reduced by this fact so that only 1.5 X 0.866, or about 1.3 the
6-pole horsepower can be expected. The total areas of the two
fields as previously noted — namely, 244 and 192 — have the
relation ^^^92 = 1-27, which is very dose to 1.3, so it follows
that a close approximation of the output to be expected from
a reconnected motor can be obtained by this simple method of
plotting the magnetic fields and comparing the areas. The
difference in the saturation of the stator iron would affect this
result to some extent, but usually not enough to introduce a
serious error.

In Figs. 97, 98 and 99 is shown the effect upon the magnetic
field of reconnecting the winding shown in Figs. 88 and 94 for 8,
10 and 12 poles, respectively. The effect of chording becomes
more pronounced with each step, and the decreased area of the
magnetic field shows that with the decreasing speed the horse-
power decreases also until finally in Fig. 99 an impossible con-
dition is reached under which the motor could not run at all,
since the throw of the coil is exactly pitch for 6 poles and therefore
substantially becomes dead when connected for 12 poles; or
putting it another way, the throw of the coil is such that when
there are 12 poles both sides of any givea coil lie in exactly the
same polarity; one side is under a north pole and the other,
instead of being under a south pole, reaches clear across and hes
under the next north pole, so that the counter-electromotive
force, which is generated in one side of the coil, is exactly balanced
and neutralized by the voltage generated in the opposite side

CONNECTING INDUCTION MOTORS

^ '

5 =-

- -s

M^^lj-

- - s

#li

CHORDED WINDINGS 75

and there is no counter-electromotive force left to oppose the
applied electromotive force at the stator terminals, consequently,
the current in the stator winding is limited only by the ohmic
resistance of this winding, and would cause the circuit-breaker
to open, or, if the motor was not properly protected, cause the
windings to be destroyed in a very short period. Attention was

Fia. 100.

Fio. 101.

Fio, 100. — Stator o! Fig. 94 ooanected for two poles.

Fia. 101. — Stator of Fig. 94 rewound for two poles vrith coils of correct throw.

Note unprovement in Fig. 101 over Fig. 100.

called to this point in an earlier chapter when speaking of the pos-
sibility of connecting some windings as they stand for double or
half speed; that is, for half as many poles or twice as many poles.
The statement was then made that this should not be attempted
if the throw of the coils was exactly pitch on the original winding.

76 CONNECTING INDUCTION MOTORS

Fig. 99 explains why this is true and why such a reconnection is
not feasible.

In Figs. 100 and 101 is shown a very interesting comparison.
Fig. 100 shows the result of reconnecting the 6-pole winding of
Figs. 88 and 94 for two poles. Ordinarily, this would not be
possible because a 2-pole motor would require about three times
the radial depth of iron behind the slots as is required by a 6-pole
one; but assuming for illustration that such a reconnection had
been attempted, the field would have the appearance shown, and
it will be seen that the area of one magnetic pole would be 142.
Suppose, on the other hand, that instead of reconnecting, the
motor had been rewound with coils having a throw of 180 deg. for
two poles or full pitch, as shown in Fig. 101 ; then the area of the
field would be 284 for one pole or just twice the value for the
reconnected motor. Since, as has been shown, the comparative
areas of the two poles are some measure of the output to be
expected, it can be at once concluded from Figs. 100 and 101
that the use of a new set of coils would double the output of the
motor and that it would be poor economy in such a case to re-
connect instead of rewinding.

The comparisons made give a good idea of the effect upon any
motor of changing the throw of the coil. The main value of the
latter idea is that it is often possible when reconnecting a winding
to assist in getting normal conditions in the winding by changing
the throw of the coils by a slot or two in a certain direction.

CHAPTER V

EFFECT OF VOLTAGE ON WINDINGS AND POSSI-
BILITY OF CONNECTING A WINDING FOR
MORE THAN ONE VOLTAGE

Changing the winding connections of induction motors to
accommodate a changed voltage supply is more often considered
and accomplished than any other winding change. As was sug-
gested in an earUer chapter, this may arise from the purchase of
a used motor, a change in power supply from an isolated plant to
central-station power, the remodeUng of an old distributing sys-
tem or in other similar ways. It was stated in Chapter IV that
other changes, whether of phase or frequency or speed, could be
considered as voltage changes and so worked out. This chapter
outlines the considerations involved in the simplest form of
voltage changes, thus estabhshing a basis for the solution of
changes in the other characteristics.

In changes of voltage there are two main conditions that have
to be met if the operation of the motor is to be kept normal. The
first is to determine whether the insulation on the winding is
proper for the new voltage that is to be used, and the second is
how to adjust the niunber of turns in series in the winding, so that
there will be substantially the same voltage per turn or per coil
in the winding as existed under the original voltage. It is as-
sumed that there is to be no change in the frequency of the supply
circuit, the throw of the coils, the number of poles in the winding,
the horsepower output or the number of phases.

Checking Insulation for New Voltage.

In considering the insulation alone, if the new voltage is to
be lower than the old, no further attention need be given this
point other than to determine that the insulation is mechanically
in good condition and clean and dry. If the new voltage is
higher than the old, the amount of insulation must be considered,
and if there is any question as to this, it should be settled by the

78 CONNECTING INDUCTION MOTORS

insulation tests described in the foUowing, before proceeding with
the actual work of reconnection. This may sometimes save
work that would otherwise be lost by discovering too late that
the insulation is inadequate for the new conditions.

In many cases suitable facilities are not available for makmg
either of the insulation tests described, and it is well to have some
general information on the standard practice followed by good
manufacturers with regard to insulation. There is an old saying
among insulation engineers that "a winding that wiU stand any
insulation test at all will stand 1000 volts." Like most general
statements, this is not strictly true, perhaps, but it brings out
the fact that the insulation for all voltages up to 750 volts is
practically the same and is determined more by mechanical
strength than by strictly electrical considerations. This means
that usually a 110- or a 220-volt machine will be all right on
440 or 550 volts provided the number of turns in the winding is
suitable for the higher voltage.

Sometimes the insulation for 550 volts is increased over that
for 440, but most 440-volt insulation will stand 550 volts if in
good condition and the operating temperature of the machine is
reasonably cool. Voltages between 550 and 2200 are seldom
met with commercially, and the caution which needs to be ob-
served is that machines wound for 550 volts or below should not
be operated on 2200 volts even if the number of turns in the coils
could be properly arranged. However, there is no reason why
machines built for a higher voltage should not be operated on a
lower. The only handicap in such a case would be that the tem-
perature would be somewhat higher, owing to the insulation
being heavier than would be required for a machine normally
wound for the lower voltage. In order to indicate the limits on
different classes of insulation, the following shows broadly the
classification followed by many manufacturers: Class I, up to
and including 500 volts; Class II, from 500 to 1200 volts; Class
III, from 1200 to 3500 volts; Class IV, from 3500 to 6000 volts;
Class V, from 6600 to 8000 volts. Very few induction motors
are built at voltages higher than 6600.

The general statement may be made regarding these classes
that any machine of a higher-voltage class may be operated on a
lower voltage, but no machine in a lower class should be operated
on a higher voltage than its own clans.

EFFECT OF VOLTAGE ON WINDINGS

Insulation Tests.

Where a reference to classification will not settle this matter
or there are a number of units involved and the possibility of
reconnection is serious, tests should be made. The insulation of
electric machines may be tested in two ways — one measures its
ability actually to withstand the voltage strains that occur be-
tween the parts of the winding and the ground, and the second
determines the condition of the insulation as to dryness and clean-
liness. The first is called a test for dielectric strength and is
performed by appl3dng for one minute, between the winding and
the ground, an alternating voltage equal to twice the normal
voltage of the circuit to which the apparatus is to be connected,
plus 1000 volts. 1

To Source of D.C. Power

Windings of
Machine whose
lasnUtion Besistacce
is under Test

High-Besistance
Yoltmeter

Fig. 102. — Test for insulation resistance.

The second test is called a test for insulation resistance and is
usually made by applying a direct-current voltage of 600 volts
between the conductors in the winding and the ground, having a
direct-current voltmeter of high internal resistance in series with
the insulation. Since the insulation is in series with the circuit,
there will be practically no current flowing, but the direct-
current voltmeter will show a slight deflection and the insulation
resistance is measured thereby. The arrangement of this test
is shown in Fig. 102.

Then the insulation resistance R of the winding under test is
given by the following equation :

e
where

r = interna] resistance of the voltmeter, which must be known

and is usually given by the maker;
E = direct-current voltage which is used for the test;
e = reading of the voltmeter.

1 Standardization Rules of the Amer. Inst, of Elec. Engrs.

80 CONNECTINO INDUCTION MOTORS

For example, suppose the values for the test are, E = 646 volts,

. ,. J ..^r.^ ^ m,- T. (545-6)66,000
e = 6 volts and r = 66,000 ohms. Then R = ^^ ^ — - —

= 6,940,000 ohms, which would indicate that theinsulation was
in good condition.

This test is of secondary importance as compared with the
test for breakdown under high-voltage alternating current, since
the insulation resistance can be considerably increased by baking,
but this gives no real increase in the actual abiUty to withstand
voltage strains. Commenting on these two tests, the standard-
ization rules of the American Institute of Electrical Engineers
says: ''The insulation resistance of a machine at its operating
temperature shall be not less than that given by the following
formula:

Insulation resistance in megohms =
Normal terminal voltage

Raied capacity in kv.-a. + lOOO'

a megohm being 1,000,000 ohms and the sjrmbol kv.-a. or kilo-
volt-amperes being the voltage of the machine times the full-
load current, times 1.73 if three-phase, or times 2 if two-phase.
A general rule is that machines up to 1000 volts should show
somewhere near a megohm. The Institute rules say further:
"It should be noted that the insulation resistance of machinery
is of doubtful significance by comparison with the dielectric
strength. The insulation resistance is subject to wide variation
with temperature, humidity and cleanliness of the parts. When
the insulation resistance falls below that corresponding to the
foregoing rule, it can, in most cases of good design and where no
defect exists, be brought up to the required standard by cleaning
and drjring out the machine. The insulation resistance test may
therefore afford a useful indication as to whether the machine
is in suitable condition for the application of the dielectric test.''
These two tests indicate a method of settling any doubt as to
whether the insulation on a machine is suitable for a new voltage
higher than the old. The method of procedure would be to see
that the windings were clean and dry and free from grounds, the
latter point to be determined in the usual way with a 110-volt
lighting circuit or by ''ringing out'' with a magneto. If the
winding shows clear of grounds the insulation resistance should be
measured with any convenient source of direct-current supply,

EFFECT OF VOLTAGE ON WINDINGS

preferably 500 volts. If the insulation resistance is up to or
beyond the value specified by the A. I. E. E. formula, the winding
may be given the further dielectric or breakdown test for one
minute with high-voltage alternating current provided a suitable
small testing transformer is available. In making this test great
care should be used in handling the high voltage to guard against
personal injury and also a suitable circuit-breaker should be in
circuit which will open if the insulation breaks down.

Volts per Turn.

Assuming that the question of the adequacy of the insulation
is settled, the second main consideration in all voltage changes
may be taken up. This is the question of rearranging the coils or
coil groups in the windings so that the voltage on each coil under

|< no Volts •--■^ ---no Vo/fs--->^--.-//0 Volfs-->r^--—JIO \/(7//5-->j

m5^

440 Volts— -H

Fig. 103. — Four 110 volt coils connected in series across 440 volts.

< llOVolis ->i< --no Volts --■■>\

U - 220 Volts

Fig. 104. — Same coils connected
two in series in two parallels across
220 volts.

<---IIO Volts— >

Fig. 105. — Same coils con-
nected four in parallel across
110 volts.

the i^ew conditions may be substantially the same as under the
original. In this regard an induction motor is similar to a trans-
former. It is designed originally for a certain voltage across
each coil or group of coils. These coils or groups may be ar-
ranged in series or in various parallels to accommodate different
line voltages, and so long as the voltage across each coil remains
at the figure originally calculated, the operation of the motor will
be normal in all respects. This can be shown graphically as in
Figs. 103 to 105. In these figures A-B represents one phase of a
two-phase, 4-pole winding. It will be seen that the voltage
across one pole-phase group, or X-Y, is 110 volts at all times.
When the motor is connected for 440 volts. Fig. 103, all four
pole-phase groups are in series. When the line is 220 volts,
there are two parallels with two pole-phase groups in series in

82 CONNECTING INDUCTION MOTORS

each parallel, Fig. 104. When the line voltage is 110 volta, all
four pole-phase groups are in parallel and each group is across
the line, Fig. 105, since each group has within itself the proper

Fio. 106, — Four-pola, w

lo. 107, — Foui^pole, t

Fio. 108. — Four-pole, four parallela,
— Different sroupinsB of a two-phue, fouc-pole winding.

number of turns for 110 volts. Figs. 106, 107 and 108 show a
24-coil four-pole two-phase winding connected in series, 2 par-
allels and 4 parallels respectively, as shown schematically in Figs,

EFFECT OF VOLTAGE ON WINDINGS

CONNECTING INDUCTION MOTORS

103, 104 and 106 respectively. If the connection, Fig. 106, is to
operate on 440 volts, for 220 volts the winding will be connected
as in Fig. 107 and for 110 volts as in Fig. 108.

The foregoing is very simple and is all that need be borne in
mind for changes of this nature. One caution needs to be ob-
served, and that is to handle the pole-phase groups as units and
not attempt to split them in the middle again — to make 8 par-
allels, for example, for a 55-volt connection. Such attempts re-
sult in improper connections as will be pointed out in Chapter
IX Fig. 140. If the number of poles is divisible by 3 or 6 or
7 corresponding numbers of parallels may be made, which is often
convenient.

For example, .if a three-phase six-pole 2200-volt motor is to.
be reconnected for 440 volts, it may be connected 3 parallel delta.

Fig. 111. Fig. 112.

FiGB. Ill and 112. — Equivalent voltage for star and delta connection.

Fig. 110, and would give 423 volts, if it had been connected series

2200
star, as in Fig. 109, on 2200 volts. The quotient of q^~i 70 =

423; the 3 comes from the 3 parallels and the 1.73 is due to chang-
ing from star to delta. The latter change is one of the advantages
or points of greater flexibility of three-phase over two-phase.
This is illustrated in Figs. Ill and 112. The ''star" diagram
shows the winding connected for a line voltage of 440. The
voltage which then exists between any lead and the star point is
254 volts, as shown on the B phase. Since this is true, the wind-
ing can be connected in delta as shown in Fig. 112, and operated
on a line voltage of 254. This change is sometimes made to
operate a 440-volt motor on 220 volts, but since 254 volts is

EFFECT OF VOLTAGE ON WINDINGS

normal, the delta-connected winding will compare with the star

220
winding as though operated on ^cT of normal voltage, or 87 per

cent. Many motors have sufficient margin to stand this reduc-
tion, but the copper heating will be ^i as great and the starting
and maximum torques only ^ as great as on the winding con-
nected in star and run on 440 volts.

Changes of this nature can be summed up in convenient form
as in Tables II and III for three-phase and two-phase motors
respectively. // a motor connected originally as shown in any
horizontal column has a voUage of 100, its voltage when recon-
nected, as indicated in any vertical column is shown at the inter-
section of the two columns.

Table II. — ^Comparison of Motor Voltages

PHASE Connections

WITH Various

Three-

aa
1

0,
n

100

125

150

130

173

216

260

•d
%

Ok
eo

1
1

Series star

100
200
300
400
500
600
173
346
619
692
865
1038

50
100
150
200
250
300

86
173
259
346
433
619

33
67
100
133
167
200
58
115
173
231
288
346

100

120

104

138

173

208

100

115

144

173

58
116
173
232
289
346
100
200
300
400
500
600

116

144

173

100

150

200

250

300

115

100

133

167

200

100

126

150

12
23
35
46
58
69
20
40
60
80
100
120

2 parallel star

3 parallel star

4 parallel star

5 parallel star

6 parallel star

Series delta

2 parallel delta

3 parallel delta

4 parallel delta

6 parallel delta

100

Table III. — Comparison op Motor Voltages with Various Two-
phase Connections

•c

•a

•S
A

Series —

2 parallel

3 parallel

4 parallel

5 parallel

6 parallel

100
200
300
400
500
600

50
100
150
200
250
300

33
67
100
133
167
200

.75

100

125

150

20
40
60
80
100
120

17
33
50
67
83
100

86 CONNECTING INDUCTION MOTORS

General Tables Covering All Voltage Connections.

The figures in the tables should be considered as percentages or
comparative values rather than actual voltages. For example,
in the case just cited, of the 2200-volt motor to be reconnected for
440 volts, assume that an inspection of the existing winding con-
nection shows it to be series star. Since 440 is 20 per cent, of 2200,
the problem resolves itself into how a series-star connection may be
changed so that the resulting voltage will be 20 per cent, of its value.
Looking at Tablell, locate the horizontal line reading ''series star,''
or the existing connection. Since 20 per cent, is required, read
along the same horizontal line till the figure 20 is reached. This
is found under the vertical heading "5 parallel star." In other
words, if the number of poles is divisible by 6, the winding can be
put in 5 parallels and operated on 440 volts, since 2200 -^ 6 =
440. Since six poles were assumed, the number of poles is not di-
visible by 6 and a 6-parallel connection is not possible. A further
search across the table shows the figure 19 under the vertical
heading "3 parallel delta"; 19 per cent, of 2200 is 418, which is
95 per cent, of 440. This varies from the figure 423 previously
mentioned, for the reason that the table is made to the nearest

whole number and ^ ^ i 70 = 19-2 per cent. It will be near

enough right to reconnect in 3 parallel delta and operate on 440
volts. Similar problems can thus be solved by inspection, mak-
ing such a table a very convenient reference. In Chapter VI
this table will be elaborated and combined with changes in phase
also, thus covering a large percentage of the possible changes
in windings at a glance.

CHAPTER VI

HOW THE NUMBER OF PHASES AFFECTS THE WIND-
INGS AND THE RESULT OF CHANGING VOLTAGE AND

PHASE AT THE SAME TIME

It was shown in Chapter V that changes in voltage of the
supply circuit can be taken care of with comparative ease and
simplicity by the proper changes in connection of the motor wind-
ings, provided that the maximum number of turns which can be
placed in series in the coils is equal to or greater than the number
required under the new conditions. For example, a 220-volt
motor may be reconnected for 440 volts, provided the windings
can be so arranged that there will be twice as many turns in
series between the terminals of each phase as there were with the
original connection. These changes, when possible, offer no
particular difficulty.

On the other hand, changes in the number of phases of the
supply circuit are usually difficult to accommodate by changes in
the motor connections and many times when they can be ac-
complished are attended with a loss in capacity of the motor or a
serious reduction in the excellence of the motor's performance as
regards torque, heating, power factor and efficiency.

Changes in Phase.

By far the commonest change of this nature is changing from
two-phase to three-phase and vice versa. Of the two changes, that
from two-phase to three-phase can more often be taken care of
for the reason that a normal two-ph^-se motor has approximately
25 per cent, more turns in series in its windings than a three-
phase motor of the same characteristics. Thus it is usually
possible to cut out 20 per cent, of the turns in a two-phase wind-
ing, leaving them dead, and have left the proper number of turns
for the corresponding three-phase winding. However, in going
from three-phase to two-phase a corresponding increase of 25
per cent, of the total number of turns in series is required; and
if the three-phase winding as it stood had all the turns in series,

CONNECTING INDUCTION MOTORS

any further increase is not possible and a set of new two-phase
coils will be required.

There are three methods of reconnecting from two-phase to
three-phase, which are here given in the order of their desirability:
(1) Twenty per cent, of the coils are cut out and left dead and the
motor operated on 80 per cent, of the two-phase turns; (2) the
number of coils is not changed, and the coils are reconnected
according to the proper diagram; (3) a "T" or Scott two-phase
to three-phase connection is used.

Ai Az

Fig. 113. — Normal two-phase, six-pole series connection, nine coils per group.

None of these is ideal, and in general it is a good investment to
rewind the motor with proper three-phase coils. In the first

method it must be borne in mind that the full-load current of a

2
three-phase motor is ^-y^ or about 115 per cent, of the current

in a two-phase motor. This means that for the same heating the
horsepower output when reconnected for three-phase can only
be in the neighborhood of 87 per cent, of what it was on two-
phase. This loss of 13 per cent, of the horsepower when capital-
ized in the proper manner will be found to pay a high rate of

HOW NUMBER OF PHASES AFFECTS WINDINGS

interest on the money that would be invested in a new set of
coils for normal three-phase operation which would give the
same horsepower output a^ the original two-phase windmg.

Another way of arriving at the foregoing conclusion is as fol-
lows: If one-sixth of the two-phase coils are to be cut out of cir-
cuit and left dead, as shown in Fig. 114, the amount of active
copper is reduced by the same percentage; and it might be ex-
pected that the horsepower output would be similarly reduced,
which is the case. This method of reconnecting from two-phase

.C A

Fio. 114. — Winding of Fig. 113 reconneoted for three-phase by leaving "dead

coils.

to three-phase is shown in Figs. 113 and 114. Fig. 113 shows a

winding with 108 coils connected in series for two-phase and six

108
poles. There are 2 X 6 = 12 pole-phase groups and -j^ = 9

coils in each group. As already stated, if this winding is to be
reconnected for three-phase, six poles, there should be only 80 per
cent, as many coils in series in the winding, or 0.80 X 108 = 86.4
coils.
Since there are to be 3 X 6 = 18 pole-phase groups in the new

90 CONNECTING INDUCTION MOTORS

connection, there should be the same number of coils in each
group; the nearest integer is 6, and 6 X 18 = 90 coils, which will
be used instead of 86.4, which is theoretically correct. This

leaves 108 — 90 = 18 coils dead, or 1 dead coil in each group, as

90
shown in Fig. 114. Since yqo = 0.833, then 83.3 per cent, of

the coils are active instead of 80 per cent., and this will have the

eflfectof operating a three-phase motor on ^;5^«> or 96 per cent.

of normal voltage, as compared with the two-phase motor. The
starting and maximum torques of the three-phase motor will be

/8oy^

\83.3/

about ( oQ o ) ~ ^2 P®^ ^®^*- ^^ *^®^ value on a two-phase

connection; but this is sufficiently close for all practical purposes,
especially as the horsepower rating will have to be reduced 13
per cent., as stated above, if the original maximum heating in the
stator coils is not to be exceeded. A comparison of Figs. 113
and 114 indicates that the position of the coils, which are specially
insulated to stand the voltage between phases, will have to be
changed. This was mentioned in the Chapter IV under "phase
insulation."

A consideration of the fact that there are 18 dead coils in the
three-phase windmg which are active on the two-phase con-
nection suggests at once that 'if the reconnection was attempted
from three-phase to two-phase there might in many cases be in-
sufficient coils to put in series for the two-phase connection. If
the coils are regrouped for two-phase and run on the same volt-
age, the motor shows all the signs of a machine operating on
25 per cent, overvoltage and may even overheat when running
light and not connected to any load whatever. On the other
hand, if a two-phase winding is regrouped and operated three-
phase on the same voltage without cutting out any coils, as ex-
plained in connection with Fig. 114, the three-phase motor shows
all the effects of a motor operating on 80 per cent, of normal
voltage; that is, the starting and maximum torques will be con-
siderably reduced and the heating increased. These two latter
conditions are covered by the second method of reconnecting
Usted in the foregoing— namely, changing the grouping and con-
nections properly, but neglecting the change in the total number
of coils in series.

The third method occasionally employed is that of making a

HOW NUMBER OF PHASES AFFECTS WINDINGS 91

"T" connection of the two-phase windings or a Scott connection
inside the motor and operating the resulting winding on a three-
phase circuit. This should not be confused with the use of Scott
connected transformers for changing from two-phase to three-
phase or vice versa. The latter may be an excellent solution in
many cases where there are several motors affected by the change
in phase. Let us assimae, for example, that a user of motors has
15 machines of various sizes from 1 to 60 hp., which have been
operating from his own steam-driven plant at two-phase, 220
volts. He decides to purchase power from a neighboring dis-
tribution system at three-phase, 220 volts. It is a matter of
considerable expense to rewind all the motors for three-phase,
and if simply reconnected the losses on the rated capacity are as
previously suggested. In addition, it is desired to hold the old
generating plant as a stand-by, in case of interruption to the
purchased service. All these results can be secured by putting
in transformers equivalent to 50 or 60 per cent, of the capacity
of motors installed and by means of a Scott connection on the
transformers operate the two-phase motors from the three-phase
supply in a perfectly normal manner. This is one very neat
solution for a problem in reconnecting induction motors which
does not involve any reconnection whatever.

On the other hand, assume that in the same plant the generat-
ing system has broken down and, in the emergency, power can
be purchased from the same neighboring power line at three-
phase. There is no time to secure transformers, and there is no
time to secure three-phase coils for the motors — ^it then becomes
essential to make some kind of reconnection so that the two-phase
motors will operate on three-phases. One of the possibilities in
such a case is a Scott connection inside the motor winding itself.
This is shown in Chapter IX and Fig. 115.

Table IV shows comparative performances of a two-phase
motor reconnected for operation on three-phase by a "T" con-
nection and the performance of the same motor when supplied
with new three-phase coils and connected in a normal three-
phase manner.

In order to make this connection clear. Fig. 116 shows the
windings on the motor connected for two-phase, and Fig. 117
the motor as reconnected with a "T" connection, corresponding
to the schematic diagram. Fig. 115.

CONNECTING INDUCTION MOTORS

Table IV. — Compabison op a Two-phasb Motob Connbctbo "T" to
Opebatb on Three-phasb with Normal Thbee-phabe Winding

Normal

two-phase

winoing

Thiee^phaie
oonneetion

Normal

three-phase

winoing

Full-load efficiency

Pull-load power factor

Starting torque

88.0
89.0
1.75
3.3

22.5
20.0
22.0

86.9
84.8
1.20
3.17

32.0
32.5
30.0

88.5
90.0
1.94

Mft^iTn^jin to''n!ie

3.3

Deg. C. Rise at Full Load :
Stator copper

21.0

Stator iron

19.0

Rotor copper

22.0

8 Coils

TCoils

►T Coi'/s removetf from Circu/f
U. KX)

Jt^ jr

\ie £ )-dy

60" /

W
I

/
/
/

'B2

Fia. 115. — Sohematio diagram of "Tee" connection.

The principle of the Scott connection is well understood and
explains the reason for omitting the coils in one leg, as indicated.
It may be of interest, however, to consider what would happen
if these coils were not omitted. This is indicated in the voltage
diagram. Fig. 118; BD represents the voltage generated in the
phase B\B\ of Fig. 115, by the rotation of the magnetic field
and AC the voltage generated in the phase A\A^, The result is

HOW NUMBER OF PHASES AFFECTS WINDINGS

three perfectly balanced voltages, AB, BC and CA, which cor-
respond to the voltage of the line in the three phases and allow
normal operation. If the coils had not been cut out of the B
phase, as shown in Fig. 116, the voltage generated in that phase
by the rotating magnetic field would have been the same in
value as that in the A phase and would be represented by DE in
Fig. 118. The voltages AE and EC would then be represented by

Fig. 116. — Normal two-phase, six-pole, series connection, eight coils per group.

Ill, while CA would be 100. This would be equivalent to having
one alternating-current generator representing the lines with
balanced voltages of 100 each, or AB, BC and CA connected in
parallel with another, alternating-current generator representing
the motor windings and having unbalanced voltages, AE, EC
and CA of 111, 111 and 100 respectively. The result of this
would be a component BE equal to 14, which would spend itself
driving useless wattless currents through the motor windings
in an effort to balance properly the voltages and make them equal
to AB, BC and CA, The immediate result of this useless cur-

94 CONNECTING INDUCTION MOTORS

rent would be to increase the heating of the machine and de-
crease its torque and efficiency and power factor.

It is characteristic of an induction motor that it always makes
this attempt to balance by circulation of wattless current any
eccentricities either existing in its own windings or in the circuit
to which it is connected. At times when such eccentricities exist
in the stator winding, there will be wattless currents Sowing in
the rotor winding trying to correct them through the medium,

always, of the rotating magnetic field. At other times when a
power circuit of relatively large power is somewhat unbalanced
and is connected to an induction motor, the motor will take upon
itself the burden of correcting the dissymmetry of the entire line
with disastrous results to the motor from overheat due to exces-
sive corrective currents, although the motor may have been
running idle at the- time and developing no actual power.
This explains why the coils are cut out of one phase, as shown
in Fig. 115.

HOW NUMBER OF PHASES AFFECTS WINDINGS

Poor Results of the "T" Connection.

The reason for the comparatively poor results on the "T''
connection, as shown in Table IV is that the motor was con-
nected as shown in Fig. 117. The result of this connection,
if the air gap was not absolutely the same all around the rotor,
would be to make AD and DC in Fig. 118 unequal; and a voltage
diagram, as shown in Fig. 119, might result. When the voltage
triangle A'B'C of Fig. 119 is connected in parallel with the
symmetrical line triangle represented by ABC in Fig. 118, the
result is that corrective current will flow and these corrective cur-
rents pull down the performance, as shown in the table. A much
better connection is the one shown in Fig. 120, since this will have
a tendency to keep the point D in Fig. 118 in the middle of the
side AC and not let it be moved to one side, as in Fig. 119.

A comparison of Figs. 117 and 120 shows that in Fig. 117 the
half legs AiBi and B1A2 of the A-phase, represented by AD and

FiO. 118. — Voltage diagram
for Fig. 117.

Fio. 119. — Effect on voltages
of uneven air gap.

DC, Fig. 118, each contain both north and south polar groups,
while in Fig. 120 the half leg AiB^ represented by AD, Fig. 118,
contains only north poles and B1A2 only south poles. The result
of this is that if the rotor is displaced slightly in the stator bore
from any cause, when the motor is connected as in Fig. 117, it
may narrow the air gap opposite to B1A2 and widen it opposite to
AiBij which means the field will be stronger opposite -81^4.2.
Consequently, the voltage generated in this section will be greater,
as represented by D'C in Fig. 119. However, when connected
as in Fig. 120, no matter if the rotor is near the stator at some
point, it cannot affect any north pole without affecting the
corresponding south pole, since all the lines of force that start
out from a north pole must return through a south pole. Since

CONNECTING INDUCTION MOTORS

the legaAiBi and BiAt are so arranged that one has all the north
poles and the other all the south poles, this means that they will
be affected exactly alike by any displacement of the rotor, and
the voltage in the two sections will be maintained equal as
represented by the lines AD and DC in Fig. 118. Therefore,
in connecting a two-phase motor in ''T" for operation on three-
phase a diagram similar to Fig. 120 should be used, in which case
the three-phase results will be much more favorable than shown
in the table.

The statement has been made above that the winding of a
normal two-phase motor has approximately 25 per cent, more

AgA,

Fig. 120. — Preferable connection to Fig. 117 so-called "top to top" connection.

turns in series than the corresponding three-phase motor. This
is, of course, true only if the turns are all in series in either case
and the three-phase motor is arranged for connection in series
star. If the three-phase motor under consideration is connected
delta instead of star, it should be thought of as a star-connected
motor at a corresponding voltage before reducing it to terms of a
two-phase winding. For example, if a motor is connected series
delta for operation on 220 volts, it could be reconnected series
star and operated on 1.73 X 220 = 381 volts; or connected for

HOW NUMBER OF PHASES AFFECTS WINDINGS 97

two-phase, it would be suitable for approximately 80 per cent,
of 381 volts, or 305 volts. It will thus be seen that a delta-con-
nected three-phase motor when reconnected for two-phase has
about 38 per cent, more turns in series than are actually required,
and this condition will have to be balanced up by some one of
the various schemes suggested.

In general, manufacturers prefer a star to a delta connection,
for the reason that the delta connection requires 1.73 times as
many turns for the same operating voltage and these turns are
of a correspondingly smaller-sized wire. The greater number of
turns of smaller wire is an objectionable condition for several
reasons, among which may be mentioned that more space is oc-
cupied in the slots by insulation, leaving less for copper; the coils
mechanically are less rigid and self-supporting; the smaller-sized
wire costs more per pound and the same number of pounds are
required; and it is more expensive to wind a coil with a greater
number of turns. For these reasons, if there is no other good rea-
son to the contrary, a three-phase wmding is apt to be arranged
for star connection.

It often happens that in changing the winding of a motor to
accommodate a change in the number of phases, it is necessary
to arrange for a change in the operating voltage at the same time;
as for example, changing a three-phase 440-volt winding to
operate on two-phase 220 volts. Reference was made above to
the fact that on a given winding the normal three-phase voltage
would be 125 per cent, of the normal two-phase voltage. Ex-
pressing the same condition in another way, if two motors that
are otherwise identical are made to operate on the same voltage
except that one is two-phase and the other is three-phase, the
three-phase winding will have only about 80 per cent, of the
number of turns in series that are necessary in the two-phase
winding. The foregoing is on the assmnption that the three-
phase winding is star-connected, which is usually the case. This
fact permits one very convenient reconnection of this nature;
namely, the one where a two-phase 440-volt winding is to be
reconnected for three-phase 650 volts or vice versa.

Since 440 is 80 per cent, of 550, the niunber of turns in series is
exactly right for either the two-phase or the three-phase com-
bination, and the only thing that has to be done is to regroup the
coils for the proper number of pole-phase groups, which in a
three-phase motor is 50 per cent, greater than in a two-phase,

98 CONNECTING INDUCTION MOTORS

and to shift the so-called "phase coils" or coils with heavier in-
sulation to their proper positions at the beginning and end of
each pole-phase group. Other combinations of change of phase
and voltage are met with, and it is useful to make up a table such
as Table V, which indicates at a glance the possible changes
between two- and three-phase, star and delta, series, 2, 3, 4, 6
and 6 parallels.

Phase Changes and Voltage Changes Combined.

This table is a combination of the two given in Chapter V under
voltage changes and shows the combination of phases as well.
The manner of using this table has been explained under voltage
changes, but further examples will be given here showing the way
to apply it, since it gives a ready answer to practically any ques-
tions that may be asked regarding the possibiUty of changing
windings when a change of voltage or phase or a combination of
the two is involved. It will be noticed that the table as ar-
ranged is really given in percentages. That is to say, the original
connection on the motor is called 100 or assumed to be good for a
normal voltage of 100, and then if the winding is assumed as
reconnected in some other way, the normal voltage on which the
reconnected motor should be operated is shown at the intersection
of the horizontal and vertical columns.

Take, for example, a motor which was originally connected
three-phase 2 parallel delta. Following across this horizontal
Une, the number 100 is found under the vertical heading that
also reads "three-phase 2 parallel delta," or, in other words,
when a motor is normally connected for three-phase 2 parallel
delta and is operated as three-phase 2 parallel delta, it is being
operated at 100 per cent., or exactly as the designer intended it
should be operated. Suppose, however, that the winding is
reconnected two-phase series, the question at once arises upon
what voltage the motor should be operated to give normal opera-
tion. Following the same horizontal column, "three-phase 2
parallel delta" (since that is the original connection) across until
it intersects the vertical column marked "two-phase series,"
the number 280 appears at the intersection of the two columns.
In other words, if the three-phase 2 parallel delta-connected wind-
ing is regrouped and reconnected two-phase series it must be
operated on a voltage 280 per cent, of the original voltage for
which it was designed.

HOW NUMBER OF PHASES AFFECTS WINDINGS 99

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100 CONNECTING INDUCTION MOTORS

The reason these values are given in percentages instead of
actual voltages is to make the table more flexible and of wider
application. The percentages, however, can be very simply
changed to voltages by using them as a multipUer. Applying
this to the case just used as an example, assume that the voltage
on which the original motor operated was 220. This then repre-
sents the 100 per cent, which was called "three-phase 2 parallel
delta." When changed to two-phase series, it has been shown
that a voltage of 280 per cent, would be required. From this it
follows at once that the new operating voltage for the motor when
reconnected two-phase series must be 280 per cent, of 220 volts,
or 2.8 X 220 = 616 volts.

As another example of appl3ning the table take a case where a
four-pole motor connected two-phase 2 parallels, as in Fig. 121, and
operated on 220 volts is to be changed, if possible, for operation
on a three-phase 550-volt circuit and it is desired to know what
particular kind of a three-phase connection on the winding will
give normal operation when the motor is run on 550 volts. In
this case the horizontal line two-phase 2 parallels represents 100
per cent. If the original voltage was 220 and that was 100 per
cent., the new voltage 550 must be 250 per cent., since it is 2.5
times 220. To find the proper form of three-phase connection,
follow the horizontal column "two-phase 2 parallels" (since
that was the original connection) across until it shows the value
250 under some vertical column which is headed "three-phase."
This is seen to be the first vertical column, marked "three-phase
series star." From this the conclusion is at once correctly drawn
that if a motor is connected two-phase 2 parallels and run on 220
volts and it is reconnected to three-phase series star, it will be
suitable for operating normally on a three-phase 550-volt circuit.
It is assumed, of course, in this problem that the number of poles
and the frequency and horsepower remain the same on the new
circuit as on the old, the only difference being that the old circuit
was two-phase 220 volts and the new circuit three-phase 550
volts. The changed connection is shown in Fig. 122.

To illustrate further the use of the table, assume that an eight-
pole motor is connected series star, as in Fig. 123, and operated
on a three-phase 2200-volt circuit, what form of reconnection
would make it suitable for operation on a two-phase 440-volt
circuit? In this case "series star" is 100 per cent, in the hori-
zontal column and 100 per cent, equals 2200 volts. The desired

HOW NUMUEn OF PHASES AFFECTS WINDINGS 101

102 CONNECTING INDUCTION MOTORS

voltage is 440, which equals }^i or 20 per cent, of 2200. Follow-
ing the ''three-phase series star" horizontal column across to the
value 20, it is found first under "three-phase 6 parallels," but
this is discarded since a two-phase connection is wanted; further-
more, an eight-pole winding cannot be connected in 5 parallels.
The value 20 is seen the second time under the vertical column
marked "two phase, 4 parallels." If the number of poles is
divisible by 4, as in this case, the winding can be put in 4 paral-
lels, therefore the conclusion is reached that this is the desired
connection, or in other words, if a three-phase motor is connected
series-star and operated on 2200 volts and is reconnected to
two-phase 4 parallels, it will be suitable for operation on 440
volts. This connection is shown in Fig. 124. Again, assume
that the motor has only six poles, as in Fig. 109, and it is to be
changed from three-phase 2200 volts to three-phase 440 volts.
In this case 2200 volts is again 100 per cent, and 440 volts is 20
per cent. Following the horizontal column marked "three-
phase series star" the value 20 is found under ''three-
phase 5 parallel star," meaning that if the winding could be put

2200
in 5 parallels it would be good for 440 volts, since — r— = 440.

However, a six-pole winding cannot be connected in 5 parallels
and the horizontal column is followed farther. There is not
another 20 under the three-phase vertical columns, but there is a
19, which is nearly right, under "three-phase 3 parallel delta."
Since a six-pole winding can be arranged in 3 parallel delta, as
in Fig. 1 10, this is the connection desired, and the normal operating
voltage will be 19 per cent, of 2200 = 418, which is near enough
to operate satisfactorily on a 440-volt circuit.

From these scattered examples it can be seen that the table is
of wide application and answers two types of questions. The
first of these is what will be the new operating normal voltage if
a winding is reconnected in a certain way, and the second is,
what will be the form of the connection to get a new operating
voltage which is desired. Indirectly, the table answers the ques-
tion of whether it is at all possible to get the desired combination
of changes without new coils, and if not exactly possible, what
degree of approximation may be obtained by means of the work-
ing combination utilized.

In the case of woimd-rotor machines it may be noted that
changing either the phase or voltage of the stator has no effect

HOW NUMBER OF PHASES AFFECTS WINDINQS 103

i I

104 CONNECTING INDUCTION MOTORS

on the rotor winding as long as the table shows that the recon-
nection gives exactly the right conditions. The reason for this
is that the real magnetic rotating field is neither two-phase nor
three-phase, but is just the same as if set up by direct current.
This was described in Chapter II. Since this rotating field re-
mains at the same value before and after the reconnection, it will
clearly have the same effect on the rotor winding in generating
counter-electromotive force. Hence there will be the same voltage
between collector rings as existed with the original connection,
and there need be no change in the controller or the external re-
sistance used in starting and running the motor.

« •

• • •
i •• • •

« c • «

CHAPTER VII
HOW THE FREQUENCY AFFECTS THE WINDINGS

The necessity for operating motors on a frequency differing
from that for which they were originally designed may be the
result of actually changing the frequency of the power supply
and thereby affecting a number of motors in one installation, or
it may result from applying used or repurchased motors on new
circuits. At times such as those at the outbreak of the European
War, when numbers of concerns were undertaking the manu-
facture of explosives and all sorts of munitions, the sudden
demand for motors for the operation of machine tools and other
purposes greatly overtaxed the available stocks and created a
brisk demand for second-hand motors wherever they could be
found. The installation of these machines on new circuits neces-
sitated a change in frequency in many cases as well as changes in
phase and voltage. Another instance of a wholesale change of
frequency is the retiring of an existing isolated plant for the pur-
chase of central-station power which may differ in frequency.
This may result sometimes in changing the motors in a single
plant, or it may involve a plant serving a town, in which case
the motors in the entire district served must be arranged for
the new frequency.

The commonest changes of this kind are from 26 cycles to
60 cycles and vice versa. There is also some changing from 60
cycles to 60 and infrequently 40-cycle motors are changed to
60 or the reverse.

Checking the Speed when Operating at Higher Frequency.

The most important and immediately noticeable change in the
motor when the frequency is changed, is that the motor operates
at a different speed. This change in speed is directly propor-
tional to the change in frequency. It was explained in Chapter
II that the so-called synchronous speed, or the number of revo-
lutions per minute made by the magnetic field of the stator is
equal to the alternations per minute of the supply circuit di-

105

e •
e e «

* r t «

e e e *

106 CONNECTING INDUCTION MOTORS

vided by the number of poles, or it is equal to the expression

— T- — -? — ~| - From this it follows at once that if the cycles

are changed and the poles remain the same, the revolutions per
minute will change exactly as the frequency.
As an example, a 4-pole motor operated on 26 cycles will have

a synchronous speed (practically the no-load speed) equal to

25 X 120

- - X ~ 760 revolutions per minute. The full-load speed

is usually about 3 per cent, to 6 per cent, less than the synchron-
ous speed. If now this same motor is operated on 60 cycles,

the speed will be - -^ = 1800 revolutions per minute.

This immediately brings up two serious mechanical questions:
First is the mechanical design of the rotor such that it will stand
this increase in speed, 240 per cent, of the original value?
The peripheral speed of the rotor (that is, diameter in feet X 3.14
X revolutions per minute) should not be permitted to go beyond
7600 ft. per minute without consulting the manufacturer of the
machine. Second, can the belting or gearing be suitably adjusted
so that the speed of the driven machine or apparatus will remain
practically unchanged? If these two questions cannot be satis-
factorily taken care of, it will be necessary to change the number
of poles in the motor winding also, so that the speed on the new
frequency and with the new number of poles will be nearly the
same as the speed on the old frequency and with the original
number of poles.

For example, in the case just cited, a 4-pole motor operated
on a 25-cycle circuit runs at about 760 revolutions per minute.
The nearest combination to give this speed on 60 cycles would be
to wind the motor for ten poles, and the resulting revolutions

per minute would be .?: = 720. There are, therefore,

two conditions in case of a change in frequency — the first, when
the number of poles remains the same and the speed changes
with the cycles, and the second, when the number of poles is
changed so as to keep the original speed or as nearly so as possible.
Consider first the case where the frequency is changed and the
number of poles remains the same. The resulting change in
the speed in this case is assumed to be proper for the motor in
question, and the gears or pulleys are changed so that the driven
load will operate at the same speed.

HOW THE FREQUENCY AFFECTS THE WINDINGS 107

Relation between Voltage and Frequency.

The next thing that is affected by the change in frequency is
the operating voltage. That is to say, if the frequency is raised,
the voltage should be raised also and vice versa, if the conditions
in the magnetic and electric circuits are to be kept normal
Assuming that the rotating magnetic field is to be kept at the
same value and the frequency raised, this field will rotate at a
faster rate and cut more conductors in a given time, which will
immediately result in the generation of more voltage, or counter-
electromotive force as it is called in a motor. It will be remem-
bered that in the first chapter attention was called to the fact
that one of the easiest ways of thinking of an induction motor
is as an alternating-current generator generating a counter-
electromotive force almost exactly equal to the line voltage on
which it is operated. In the present instance, then, if raising the
frequency causes the motor to generate more of this back vol-
tage, it will be necessary to oppose it by a higher applied voltage;
or, 3peaking simply, if the frequency is to be raised the line vol-
tage should be raised by the same amount to keep the same
magnetic conditions as existed in the original motor.

Relation between Torque, R.P.M., and Horsepower.

Suppose that the frequency is raised and the voltage is not
raised. If the same magnetic field existed and rotated faster,
it has been shown that an increased back voltage would be gen-
erated. However, if the line voltage is not raised, the motor does
not require any increased back voltage and hence it does the
only other thing it can to keep the generated voltage equal to
the line voltage, and that is automatically to decrease its own
magnetic field to such a point that the new field rotating at the
new speed will generate the same back voltage as the old field
rotating at the old speed, and this electromotive force will be
nearly the same as the applied line voltage, which has been as-
sumed to be the same on both frequencies. The result of a
decrease in the magnetic field would be a decrease in torque or
turning effort, and this might result in a reduced horsepower
output were it not for the fact that the speed increases and tries
to make up for the decrease in torque

Torque at one foot radius X r,p.m.
Horsepower = ^^ko

From this it follows that if the frequency was raised and the vol-

108 CONNECTING INDUCTION MOTORS

tage left the same, the magne tic field migh t decrease and the torque
decrease without lowering the horsepower by the same aniount,
since the speed increases and partly makes up for it. On most
of the loads that are driven by motors, the driving effort, or pull,
or torque is practically the same at all speeds. This is not true
of centrifugal pumps or fans or similar apparatus, but is generally
true of- a great deal of industrial machinery. Since this is the
case, it may be seen from the horsepower formula just given that
if the torque is constant the horsepower will vary directly as
the speed; that is, a higher speed will call for more horsepower
and a lower speed for less horsepower. Going back to the fre-
quency, a higher frequency means a higher speed and hence,
directly, a higher horsepower, and a lower frequency means a
lower speed and a lower horsepower. All these things work
out automatically if the voltage and frequency are varied on
the motor at the same time and by the same amount. This is
for the reason that torque is the product of the magnetic field
acting on the currents in the windings. To keep the heating
reasonably the same, the magnetic field and the currents in the
coils should be kept as nearly the same as possible.

It was shown in the foregoing that if the field is kept constant
and the speed increased, the generated voltage would increase,
and hence the applied voltage should be increased also. This
brings about a rule which may be most easily remembered in
this form: If the frequency on a motor is changed, the voltage should
be changed in the .same direction and by the same amount. If this
is done and the torque against which the motor is working is
constant, the magnetic field in the iron will remain constant, the
currents in the windings will remain constant, the speed and the
horsepower will vary directly with the change in voltage and
frequency, and the heating will vary somewhat due to the vari-
ation of the iron loss with the frequency and the variation of
the ventilating effect with the speed.

A concrete instance of the foregoing would be to take a ^hp.

25 X 440
440- volt 60- cycle motor and operate it on 25 cycles and w^ —

25 X 50
= 183 volts, in which case it would develop — ^ — = 20.8 hp.

If 183 volts was not available, a connection of the windings should
be selected which would have been equivalent to 880 volts on

HOW THE FREQUENCY AFFECTS THE WINDINGS 109

26 X 880
60 cycles and this would be suitable for >,^> — = 366.6 volts

on 25 cycles, which in many cases would operate satisfactorily
on a commercial 440-yolt circuit. In the case which is most
commonly met with, which is changing from 26 to 60 cycles, this
condition can often be taken care of by impressing twice the
voltage on the motor on 60 cycles that was used on 26 cycles,
such as operating a 220-volt 26-cycle motor on a 440-volt 60-
oycle circuit, at about double the horsepower.

Theoretically, to follow the rule already given, the voltage
on 60 cycles should be 2.4 times the value on 26 cycles, since ^%&
= 2.4. Thii^ would result in 2.4 times the speed and 2.4 times the
horsepower. Practically, it is easier to get twice the voltage than
2.4, so the voltage is doubled and the horsepower considered
as double also. In case it is not possible to get double the vol-
tage on 60 cycles, the same result can be secured in another
way. Suppose the original motor is operating on a 220-volt
26-cycle circuit and is connected series star as in Fig. 109. Sup-
pose, also, that the available 60-cycle voltage upon which it is
to run is 220. To get the effect of doubling the voltage, the motor
can have its pole-phase groups connected in two parallel star.
Fig. 126, for 60 cycles and it will then be affected in the same way
as it would if the windings had not been reconnected but had
been operated on 440 volts 60 cycles. On 60 cycles the motor
would then run 2.4 times as fast and develop about twice the
horsepower.^

In some cases it would happen that the same horsepower was
required on the new frequency and at the increased speed as on
the original frequency. Hence, it would be imdesirable to recon-
nect the motor so as to raise the voltage with the frequency, since
this would result in twice the required horsepower and would
mean operating the motor at all times at half-load and conse-
quently somewhat lower efficiency and power factor than if it
were fully loaded.

Considering again the horsepower formula, it can be noted that
if the horsepower is to remain constant, the torque must decrease
as the speed increases and vice versa. Since the torque varies
as the square of the applied voltage, it is evident that approxi-
mately the same horsepower can be kept with a changing fre-

1 See articles in the "Electric Journal," Vol. Ill, p. 400, by G.[ B. Werner,
and Vol. VII, p. 680, by R. E: Hellmund.

CONNECTING INDUCTION MOTORS

HOW THE FREQUENCY AFFECTS THE WINDINGS 111

quency by varying the voltage applied to the motor as the square
root of the change in frequency instead of directly as the first
power. An example of this would be operating a 440-volt
25-cycle motor on a 560-volt 40-cycle circuit. The square root
of ^%5 = 1.26. Then if 1.26 X 440 = 564 volts be used on 40

cycles, the magnetic density in the iron will be about 80 per cent.

80^
of its 26-cycle value and the torque will be jtta = 64 per cent

of the 25-cycle value. Since the speed will be ^%5 of that on 25
cycles, the resulting horsepower will be ^%5 X ^Koo = 1.02
times its 25-cycle value or practically the same.

A similar instance would be operating a 50-cycle motor on
60 cycles and at 110 per cent, voltage to keep the same horse-
power. Suppose in the latter instance it was not possible to
juggle the generator or the transformers so as to get a 10 per
cent, increase in voltage. It would then be necessary to re-
connect the motor so that there would be ^®%io = 91 per cent,
as many turns in series. One way of accomplishing this if the
50-cycle motor was originally connected series delta, as in Fig.
126, would be to reconnect it two parallel star (Fig. 125) for

60 cycles and the same horsepower. This would have the effect

(200 \
y>fo) — 100 = 15 per cent.

However, since the frequency has increased 20 per cent. (50
to 60 cycles) and the speed also has increased the same amount,
if the voltage is increased only 15 per cent, the magnetic density
in the iron will be only ^ ^^20 of its 50-cycle value and the torque
will be only (^^^20)* X 100 = 92 per cent, of its 50-cycle value.
The resulting 60-cycle horsepower rating as compared with the
50-cycle will be ^Koo X -^^^oo = HO per cent, (since the
torque is 0.92 and the speed 1.2 of its 60-cycle value). Instances
could be multipUed of this, and some further examples will be
given in a later chapter giving practical applications of the princi-
ples laid down here.

The fact that raising the frequency, and hence the speed also
sometimes results in a horsepower rating greater than that actu-
ally required, leads at once to a word of caution regarding the
converse proposition; namely, that in reducing the frequency on a
motor and keeping the same number of poles, it should be figured
that the horsepower will decrease exactly in proportion to the
decrease in frequency and the consequent decrease in speed. The

112 CONNECTING INDUCTION MOTORS

physical conception of this is that if the frequency and voltage
are varied together and the motor is working against the same
torque, the magnetic density in the iron will remain the same and
the current in the copper of the stator and rotor will remain sub-
stantially the same, but the horsepower will rise and fall with the
voltage and frequency, since it is the product of the torque and
the speed divided by a constant. If it be imagined that the
voltage and the frequency be carried down to zero and the motor
just came to a standstill, it could be seen that the motor was de-
veloping full-load torque at standstill with no more than full-
load current flowing in its windings.

The foregoing at once suggests a method that is sometimes used
for starting a large squirrel-cage motor or a group of small motors
where such motors constitute practically the only load on the
generating unit from which they are operated. While the motors
and the generator are at standstill, the motors are connected
electrically to the generator by closing all line switches. The
generator field is next excited to its normal value. The steam
engine or the waterwheel is then started slowly from rest, and as
the generator builds up in speed the motors come right up along
with it and no more current is required in the motor windmgs
than is represented by the torque against which they are starting.
This gives the best physical picture of the voltage and frequency
building up together from zero to normal value and yet themotoris
exerting a constant torque from standstill to normal full-load
speed under these varying conditions.

The example just cited brings out the fact, also, which will
be mentioned in Chapter X, that practically all changes in
operating conditions can be considered equivalent to changes
in voltage and so calculated and used. So it is with the change
in frequency — ^if the torque is to be kept constant with the
same number of poles and the horsepower is to vary with the
speed, the voltage should be varied with the frequency or the
winding connections changed to produce the equivalent. How-
ever, if the horsepower is to be kept constant at any and all
speeds with the varying frequency, then the voltage should be
varied as the square root of the change in cycles.

CHAPTER VIII

THE NUMBER OF POLES AND THE R.P.M. AND THE
POSSIBILITY OF VARYING THEM WITH THE

SAME WINDING

The speed of an induction motor expressed in revolutions per
minute = (cycles X 120) -r- number of poles. The speed so
determined is called synchronous speed and is very nearly the
same as the no-load speed. When operating under full load the
speed will be a few revolutions lessthanthis— for ordinary motors,
on an average of about 96 to 97 per cent, of the synchronous
speed. The synchronous speed is the speed at which the rotating
magnetic field is traveling around in the stator, and the difference
between this and the full-load speed of the rotor (3 to 6 per cent.)
is called the "slip" of the motor.

From the equation for revolutions per minute it can be seen
at once that if the speed of the motor is to be changed, it is neces-
sary to change either the cycles or the number of poles. Or,
assuming that the cycles have been changed and that it is neces-
sary to keep the same speed as before, it will be necessary to
change the number of poles. So far as the cross-connections
themselves are concerned, and admitting windings where all the
pole-phase groups do not have the same number of coils, as dis-
cussed in Chapter IX, it is evident that any winding might be
connected for several different numbers of poles and for either
two-phase or three-phase, by the simple expedient of changing
the number of coils in each pole-phase group.

For example, a winding having 54 slots and 54 coils if arranged
for three-phase 6 poles would have 3 coils per group and 18
pole-phase groups. If the same winding is rearranged for three-
phase 4 poles there will be 12 pole-phase groups having alternately
4 and 6 coils per group. Or, if the same winding is arranged for
two-phase 4 poles there will be 8 pole-phase groups, 6 of which
would have 7 coils and 2 of which would have 6 coils, or 54 total.
There are practical limits beyond which this form of reconnection
cannot properly be carried and which are discussed farther on
8 113

CONNECTING INDUCTION MOTORS

THE NUMBER OF POLES AND THE R.P.M.

CONNECTING INDUCTION MOTORS

THE NUMBER OF POLES AND THE R.P.M.

117

in this chapter, but before proceeding to a discussion of them
attention is called to some typical cases of reconnection of this
nature.

Fig. 127 shows a 54-slot winding having a coil pitch of 1 and 7
as arranged for 6 poles and connected series star. There are 3
coils in every group. Fig. 128 shows the same winding as Fig.
127 except grouped and connected for 4 poles. It will be noted
that there are now 3 X 4 = 12 pole-phase groups containing
alternately 4 and 6 coils per group. Fig. 129 shows the same wind-
ing as in Fig. 127 arranged and connected for 8 poles; there are
18 pole-phase groups with 2 coils and 6 with 3, making total of
24 groups and 54 coils. Fig. 130 is the same winding as Fig. 127
connected for 10 poles. There are 24 groups having 2 coils each
and 6 groups with 1 coil, making a total of 30 pole-phase groups
and 64 coils. Fig. 131 shows the winding, Fig. 127, connected for
12 poles. There are 18 groups of 2 coils each and 18 groups of 1
coil each, making a total of 36 groups and 54 coils.

Of course all these connections would not normally operate
at the same voltage, nor would the horsepower developed be the
same, and the speed would vary inversely as the number of poles.
Assuming, for example, that the motor was 100-hp. 60-cycle
three-phase 440- volts and run at 1160 r.p.m. on the 6-pole con-
nection, the characteristics for the other connections are shown
in Table VI. Three-phase is assumed throughout.

Table VI. — Characteristics op a Three-phase Motor Connected

AS IN Figs. 127 to 131

Poles

Hp.

Voltage

R.P.M.

Connection

100

440

1,160

Fig. 127

110

484

1,750

Fig. 128

375

860

Fig. 129

300

690

Fig. 130

220

580

Fig. 131

The only commercial voltages in Table VI are the first and last,
440 and 220. To operate the motor on the other connections
would require special taps from the transformer, unless some
other change could be made in the motor's winding at the same
time that the number of poles was changed. For example, the
8-pole connection requires 375 volts. If it so happened that the

118 CONNECTING INDUCTION MOTORS

6-poIe motor was connected in parallel star, then the 8-pole
motor could be connected series delta, which would be the same
thing as operating the motor on a voltage in the ratio of 1.73 to 2

or^y-^ = 434, which is approximately the voltage required.

Table VI of horsepowers and normal voltages is figured by
taking account of the speed and of the chord factor in the follow-
ing way :

One of the functions of the winding is to be acted upon by the
rotating magnetic field and to actually generate a counter-electro-
motive force which is opposed to and almost equal to the applied
line voltage. If, then, in reconnecting for a different number of
poles, the assumption is made that the magnetic field in the teeth
and air gap remains at a constant value irrespective of the con-
nections, it is at once evident that the generated electromotive
force, and consequently the applied line voltage, should vary
directly as the speed of the rotating magnetic field, which is
practically the same as the revolutions per minute of the motor at
no load. For example, in the case cited in the foregoing, if the
normal voltage on the 6-pole connection is 440, everything else
being equal, the normal voltage on the 12-pole connection should
be 220, since the revolutions per minute of a 12-pole motor are
just one-half those of a 6-pole machine.

Practically, the only condition which enters to change the
voltage from varying directly as the speed is the "chord factor,"
which is due to the throw or pitch of the coil. This is de-
scribed under "Fractional Pitch Windings" in Chapter IV. It
will be recalled that tlup is a factor which reduces the voltage
generated in a coil because one side of a coil is not exactly
under the center of a north pole when the other side is exactly
under the center of a south pole. The numerical value of this
factor is expressed as the sine of one-half the electrical angle
which is spanned by the coil. It may appear in the example
given in Figs. 127 to 131 that the chord factor should remain con-
stant since the physical throw of the coils is unchanged. It should
be carried in mind, however, that while the coil spread remains
unchanged, the number of poles is changed, consequently the pole
arc is changed; hence, the relation of tho throw of the coil to the
pole arc is different in each case. The foregoing can be best
shown by Table VII, remembering that the throw of the coils is
slots 1 and 7 in all cases.

THE NUMBER OF POLES AND THE R.P.M.

119

Table VII. — ^Effdcts of Changinq thb Numbbb of Poles in an Indug-

TioN-MOTOB Winding

Number of poles

Throwof coil

Slots spanned by coil

Number of slots equivalent to 180

electrical degrees =» :ir= -, — =—

No. of poles

Electrical degrees represented by
six slots

Sine of half the electrical angle
covered by the coil throw or
pitch = chord factor

1-7

13.5

6.75

5.4

120

160

200

0.64

0.866

0.99

1-7

4.5

240

0.866

Table VII indicates that the normal 6-pole voltage of 440 must
be modified by two factors to find its value for other speeds.
These factors and their results are combined in Table VIII.

On first comparison of Tables VII and VIII it seems peculiar that
the 4-pole connection having the lowest chord factor, which is
0.64 operates, at 484 volts, which is the highest voltage, while the

Table VIII. — ^Factobs, Dub to Change in Numbeb op Poles, Modiftino

iNDUCnON-MOTOB VOLTAGE

Number of poles

Factor for changing voltage on
account of changing speed

Factor for changing voltage on
account of change in chord fac-
tor for new No. of poles -5- 6-
pole chord factor

Product of both factors

Resulting voltage = (440 X No. 4) .

1.5

0.75

0.60

0.74

1.14

1.11

0.855

0.685

484

440

375

330

0.50

220

8- and 10-pole connections, having a high chord factor of 0.99,
operate at 376 and 300 volts respectively. It must be re-
membered that the speed at which the magnetic field is rotating
comes into effect and changes the result of the chord factor.
Throughout this book we have considered the induction motor as
being an alternating-current generator, generating the counter-
electromotive force, or back voltage. Hence, in this case, the
assumption has been made that the magnetic field in the air
gap remains the same in density for all these connections, and

120 CONNECTING INDUCTION MOTORS

when connected for 4-pole this iSeld will rotate twice as fast
as when connected for 8-pole, and thus generate twice as much
voltage. This is the reason that the two factors, one due to
changing the speed of the field and the other due to changing the
throw of the coil, are introduced, as shown in Table VIII. The
product of these two factors governs the voltage which must be
appUed to the windmgs to give normal operation.

Table VIII determines the value of the proper voltage for the
new connections as given in Table VI. The horsepower is de-
termined just as if it were an alternating-current generator by
taking the product of the volts X amperes X 1.73 X power
factor and dividing by 746. The cross-section of the copper has
not been changed, hence the amperes remain constant. The
power factor is assumed the same, although it will be somewhat
higher on high speeds and lower on low speeds. Therefore, the
output in horsepower will vary as the voltage, assuming 100 hp.
at 440 volts. The horsepower for the new connections is figured
in this manner, as given in Table VI. Some general observations
might be made about the examples chosen in this chapter: First,
the question of starting torque or maximum torque required, or
the saturation of the core when connecting for higher speeds
might require a voltage somewhat higher or lower than Table VI;
second, as pointed out in Chapter IV, on fractional-pitch windings
it is not wise, in general, to chord up a coil so far that the chord
factor is less than 0.707, which means that the coils span only
halfway from the center of a north to the center of a south pole.
The reason for this was shown in Chapter IV by plotting the
shape of the magnetic field set up by windings having different
coil pitches. For this reason the 4-pole connection, as shown
and discussed in this chapter, should be avoided in practice, but
the 6-, 8-, 10- and 12-pole connections would be satisfactory if the
proper operating voltage could be secured.

Check Points in Changing Number of Poles.

From the foregoing it may be seen that there are three factors
to be taken care of in changing the number of poles. These are :

First, if the new speed is to be higher than the original speed,
the peripheral speed should not be allowed to exceed 7500
to 8000 ft. This figure is the diameter of the rotor in feet X
3.14 X revolutions per minute.

Second, the chord factor of the winding.

THE NUMBER OF POLES AND THE R.P.M. 121

£1
I-

122 CONNECTING INDUCTION MOTORS

Third, the phase-insulation coils should be shifted so as to
come at the beginning and ending of the new pole phase groups,
as discussed in Chapter IV.

Sometimes, when a winding is connected in parallel star it is
possible to reconnect it in series star with consequent poles, as
explained in Chapter IX, and have the motor operate at one-half
its original speed. This reconnection is shown in Figs. 132 and
133. Conversely, if the motor was originally connected for
series star, it might be reconnected for parallel star and operate
at double speed if the motor would stand up mechanically. The
counter-electromotive force generated by the consequent-pole
connection is only 86.6 per cent, as much as with the salient-pole
connection, which means that if the motor was ru^ on normal

rated voltage on the consequent-pole connection it would operate

100
as if it had an overvoltage of ^o^a — 100 = 16 per cent. Such a

reconnection should not be attempted if the throw of the coils is
exactly or nearly full pitch for the high speed. The reason for this
was explained in Chapter IV.

The effect of chording the coils or making the throw less than
full-pole pitch, as in Figs. 132 and 133, brings out the point that
it is often possible in reconnecting a winding to raise the side of
all the coils lying in the top of the slots, and to spring the coils
one or two slots longer or shorter and thus help out materially
on the operating conditions after the change is made. For
example, in Fig. 133, if the coils are raised and wound in slots 1
and 6 instead of 1 and 7, the new chord factor would be sine one-

half of ^g X 180 deg. = 200 deg., or 0.98 instead of 0.866. The

winding connected, as shown in Fig. 133, would then operate as if
on 102 per cent, of normal voltage instead of 115 per cent., which
would have cut down the iron losses and improved the power
factor.

In Chapter IV a graphical explanation was given of the effect
of chord factor and reconnecting for a different number of poles.
This was shown by plotting the shape of the magnetic field set
up by a three-phase winding connected for different numbers of
poles and whose coils had different pitches. It showed the mag-
netic conditions inside the motor which give rise to the practical
results discussed in this chapter.

CHAPTER IX

LESS COMMON CONNECTIONS USED FOR UNSYM-
METRICAL CONDITIONS OR IN AN EMERGENCY

Chapter III discussed the usual forms of connection for wind-
ings using "diamond" coils in open slots. It is the purpose of
this chapter to present some of the less usual forms. These are
often of more importance in reconnecting old machines than are
the standard forms, because it is by their help and "judicious"
use that a job is pulled through in a hurry or a temporary work-
able connection made that will carry on an essential part of a
larger work until such a respite can be obtained as will allow a
more permanent connection. .

The word "judicious" is used for the reason that short-cut
methods of this type are sometimes used where there is no need
for them and where their use is a positive detriment, since the
extra operating expense caused by them soon offsets any im-
mediate apparent gain. Such a case, for example, would be
represented by reconnecting a three-phase 440-volt series-star
winding for two phase 440 volts with the same coils, making no
other change. The machine would probably operate in many
cases, but the increased power bill would pay the interest on a
considerably larger sum than would be represented by the cost
of a proper set of two-phase coils. If this point is understood
and given proper consideration, it is desirable to know some of
these semistandard or possible schemes, as they may be of service
in an emergency.

Number of Slots Not a Multiple of Phases Times Poles.

Among these schemes one which is not usually found in text-
books, but which is perfectly legitimate and largely employed
by all manufacturers, is the use of a core having a number of
slots that is not an exact multiple of the number of phases times
the number of poles — ^for example, a 90-slot core wound for
three-phase, eight poles. This connection is represented by Fig.
134. The Roman numerals on each pole-phase group represent
the number of coils in that group, and it will be seen that each

123

124 CONNECTING INDUCTION MOTORS

phase consists of 6 groups of 4 coils each and 2 groups of 3 coils
each, or a total of 30 coils, and 90 coils in the complete winding.
This irregularity introduces a slight displacement of the phase
angle at certain places, but these places are so chosen around the
machine that the net result is a perfectly balanced three-phase
voltage at the terminals of the machine. E. M. Tingley origi-
nated an ingenious and simple method for arranging such
windings with mathematical accuracy to give perfectly balanced
voltage.*

It does not follow, however, that only the slot numbers rec-
ommended by Mr. Tingley can be made to give operating results.
Other combinations are practically workable along the same gen-
eral lines and can be laid out by inspection with reasonable regard
to the best sjmametry. But it is true that only the combinations
pointed out by him can be made to give a theoretically perfect
voltage balance at the motor terminals on all phases. This ex-
planation is made in reply to the question frequently asked as to
whether it is essential that the number of primary slots shall be a
multiple of the niunber of phases times the number of poles. It
does not necessarily have to be such a multiple, and connections
of the type shown in Fig. 134 give practically as good operating
results as any other.

The manufacturers make use of this type of connection in
order to use the same core for as many combinations of phase,
voltage, poles, cycles and horsepower as possible, thereby greatly
reducing the stock of punchings or stampings that must be carried
and also the expense necessary for dies to produce these punchings.

Particular reference is made to such diagrams in this chapter
to insure that no one who is contemplating a reconnection need
be discouraged or , give up the attempt if it is discovered that
the number of pole-phase groups does not divide exactly into
the number of slots. In general, if the total number of coils in
the winding is right for the voltage to be used, it will be satis-
factory to put as many coils in each group as can be obtained
by the even division of pole-phase groups into total number of
slots and then to distribute the odd coils equally among the
phases and insert them mechanically in various groups to give
the greatest symmetry. Of course, if there are two or more
parallels in each phase, there must be the same number of coils
in each parallel. For example, in the case of Fig. 134 there are

Un the "Electical Review" for Jan. 23, 1915, Vol. LXVI, pp. 116-8.

LESS COMMON CONNECTIONS

125

three phases and eight poles; 3 X 8 = 24 and 90 -5- 24 = 3^;
therefore there will be four coils in each group excepting in the
case of six groups which will have three coils. .Two of these six
groups are in each of the three phases, and one of these groups
is in each of the two parallel legs of each phase. E this be
followed, it may not give the perfectly balanced condition of Fig.
134, but when done by a careful man, it will usually give a safe
operating condition.

Fig. 134. — Three-phase, eight-pole, parallel star diagram with uneven grouping

for a ninety-slot stator.

Consequent-Pole Windings for Two Speeds.

A second expedient which may be employed to connect a
given winding for twice the original number of poles is the use
of what is known as a ''consequent-pole*' connection. This
is illustrated by Figs. 135 and 136, which show the usual con-
nections for the three-phase motor wound to give two sets of
poles or two speeds in the ratio of two to one. This change is
accompUshed by a single winding. In Fig. 135 the high-speed
is parallel-star and the low-speed series-star. In Fig. 136 the
high-speed is parallel-star and the low-speed series-delta. Either

126

CONNECTING INDUCTION MOTORS

may be used at the discretion of the designer. Fig. 135 usually
gives better results where a constant torque is desired and gives
twice the horsepower on the high-speed that it develops on the
lowHspeed. Fig. 136 gives somewhat better results where a con-
stant horsepower is desired at both speeds, as is the case with
most machine-tool applications.

Fig. 137 is an explanatory diagram showing schematically how
the two sets of poles are produced by such windings. Considered

no 2

C, B,A,

C B A

Fio. 135.— Two-speed, three-phase, four- and eight-pole parallel and series star

diagram.

with Fig. 135, the inside set of arrows shows the parallel-star con-
nection where four salient poles are produced directly by the
winding, two north and two south. The set of arrows outside
the winding circle shows the winding connected in series- tar
and the current direction such as to produce four north poles
by the winding. Since it is not possible to have north poles
alone, there immediately result four consequent south poles,
indicated by the dotted arrows, where the magnetic flux returns
to the primary. This results in eight poles and half-speed. For
the sake of simplicity the arrows shown are for one phase only.

LESS COMMON CONNECTIONS

127

The three phases interact to produce the combined magnetic
pole as in any normal three-phase winding. These diagrams
are shown to indicate that it may be possible in some cases to
reconnect motors for half-speed by making use of a diagram of
this nature. Such a connection, for example, makes it possible
at times to reconnect a 25-cycle motor for 60 cycles and twice
the number of poles, and so keep the r.p.m. of the motor nearly
the same.

C E FAB

Fig. 136. — Two-speed, three-phase, four- and eight-pole parallel star and series

delta diagram.

It will be noticed that the outside arrows on the pole-phase
groups for checking the slow-speed, or eight-pole, connection
in Figs. 135 and 136 all point in the same direction instead of
alternately in opposite directions as the inside arrows do. This
is because the eight-pole connection is "consequent-pole," or
so connected that the current produced the same polarity in all
the pole-phase groups, instead of alternate north and south as is
usually the case. It will be recalled that in Chapter III men-
tion was made of the fact that in such a case the check
with the alternate arrows did not hold. It will be seen

128

CONNECTING INDUCTION MOTORS

from Figs. 135 and 136 that in checking windings of this type,
or consequent-pole, by placing arrows on the pole-phase groups
in the direction from the lead toward the star in all three phases,
the arrows will all point in the same direction. This can be ex-
plained in another way by saying that in a winding of this type
there are only half as many pole-phase groups for the same total
number of poles as there are in the usual form of winding. This
is equivalent to saying that alternate pole-phase groups are

S A

Fig. 137.— 1

Schematic magnetic diagram explaining the eight-pole connection

of Figs. 135 and 136.

omitted. Since in the check of the usual winding the arrows
are alternately opposed, if alternate arrows are omitted the re-
mainder will all be in the same direction, as is indicated in the
check of the eight-pole connection of Figs. 135 and 136.

A diagram for a two-phase two-speed connection where the
winding is in parallel on the high-speed and in series on the low-
speed is shown in Fig. 138. This winding is of particular and
especial interest in that it overcomes one of the disadvantages
of the corresponding three-phese connections shown in Figs.
135 and 136 by putting half of the winding in one phase for the

LESS COMMON CONNECTIONS

129

lowHspeed connection and in the other phase for the high-speed
connection. This is an advantage, because the so-called " winding
factor," or "distribution factor,'' remains the same on both
speeds as in a normal two-phase machine, while in the three-
phase connections shown in Figs. 135 and 136 the winding factor
is only 86.6 per cent, as good on the low-speed connection as on
the high. This is because there are only four winding groups

•^^lyy^vs^biBi

Fig. 138. — Twonspeed, two-phase, four- and eight-pole, parallel and series dia-
gram for same distribution factor on both connections.

per phase spread over the entire periphery, and yet eight poles
are being produced.

Expressed in another way, the coils for one of the eight poles
are spread over the usual span for a four-pole machine. Since
the distribution factor is a measure of the induced voltage or
counter-electromotive force generated, and since the capacity of
the motor may be measured by its current-carrying capacity
multipUed by the induced voltage, it can be concluded at once
that the loss of 14.3 per cent, in the three-phase connection on

130

CONNECTING INDUCTION MOTORS

the slow speed is avoided in the two-phase diagram, Fig. 138.
In reality the gain is greater than this, for the reason that the
two-phase distribution factor caused by consequent poles is
only 70.7 per cent., as against 86.6 per cent, in the three-phase.
Speaking simply, if a series-parallel two-phase connection
were used, similar to the three-phase. Fig. 135, and without
changing the coils from one phase to the other as does Fig.

ABC

Fig. 139. — Three-phase, six-pole, series star diagram in four parallels,
called "split group" diagram. Emergency make shift.

So-

138, the loss in horsepower on the slow speed would be approxi-
mately 30 per cent., which is certainly a matter of prime im-
portance. It is mechanically possible to make such an arrange-
ment on a two-phase winding, but there seems to be no practical
way of accomplishing the same result on a three-phase winding.
As in the case of the three-phase two-speed diagrams, this con-
nection shows the possibility of changing a standard motor to
half-speed by the mediimi of such a connection.
When operating from a three-wire two-phase system or any

LESS COMMON CONNECTIONS 131

system having the two phases interconnected in any way, all
four of the leads that connect to y and y', Fig. 138, should be
brought out instead of tying them together in pairs and bringing
out y and y' as shown. This is in order that the phase windings
may be kept clean of each other on both speed connections.

Splitting Groups.

Fig. 139 illustrates a connection that is sometimes attempted,
but usually with disastrous results. In all the foregoing dia-
grams the phase-pole group has been treated as a unit. That is
to say, if there were four coils per pole per phase, these four were
connected in series into a group and handled as a unit. Fig.
139, on the other hand, breaks up some of the groups into halves.
Suppose, for example, that a three-phase six-pole motor has 72
coils total and is connected in series for 440 volts and it is de-
sired to reconnect it for 110 volts. It can be parallel for 220
volts, and there will be three pole-phase groups in each of the two
parallel legs of the winding. It cannot be paralleled four times,
since 6 is not divisible exactly by 4. Since there are 6 poles and
3 phases, there are 18 pole-phase groups and 72 4- 18 = 4 coils
per group. It is therefore possible to spUt 6 of the 18 groups into
halves of two coils each, and by putting a half-group in series
with a whole group to get 4 parallels per phase having 1.5 pole-
phase groups in each of the 4 parallel circuits. Such a connec-
tion is shown in Fig. 139. This is rather difficult to do properly
tmless there is an expert winder available, and it leaves the motor
in an unsatisfactory operating condition when it has been done.
This is explained by the vector diagrams in Figs. 140 to 144.

Let ag represent the voltage vector of one magnetic pole made
by combining the three pole-phase vectors ae, ef and fg, Fig. 140.
For clearness, one pole-phase vector ae is shown in Fig. 141 drawn
to a larger scale and made up of the vectors of the four separate
coils ab, bCy cd and de. The length of the Une a&, for example,
represents the voltage generated by the rotating field in a single
coil of the winding, and four of them are considered together
because there are foiu* coils in series in any complete pole-phase
group; as for example, group 16 in Fig. 139. If two or more
circuits, each made up of one whole pole plus one half-pole,
are to be connected in parallel, the two resulting vectors should
be the same length and have the same direction or phase. Such
a condition is shown in Fig. 142. This is a true parallel, and there

132

CONNECTING INDUCTION MOTORS

will be no circulating current around the closed loop formed by
the two parallels in the winding, since two equal voltages in phase
with each other are opposed.

An inspection of the four vectors of which ae is composed will
show that it cannot readily be divided into two parts and paral-
leled without there being circulating current. Suppose, first,
that the winding group is split in the middle at c, leaving ab + be
for one half and cd + de for the other. The two resulting vec-
tors are ac and ce. When each of these vectors is added to

^^,- —

— ->.

^^^

/ /

\ \

/ /

\ \

/ /
//

" Fig, UO ^

Whole Pole

X y z

Fig. m

Half Pole

Whole Pole Half Pole

Fig. U2
c

[

z e \

^ a ss fy

Fig. US ^ Fig. lU

Figs. 140-141-142-143-144. — Vector diagrams of group voltages in Fig. 139.

another complete pole and the two connected in parallel, the
result is indicated in Fig. 143, where ra + ac is paralleled with
sc + ce. Since ac and ce are not in phase, there is left a voltage
equivalent to em + nc, which will set up current around the closed
loop and produce increased heating. In order to avoid this to a cer-
tain extent, the two outside coils of the group, ab and de, are some-
times paralleled against the two inside coils, be and cd. The
two resulting vectors ax + ze and bd are in parallel, but they are
of different lengths. The results are shown in Fig. 144, where
a whole pole ib plus the half -pole bd is in parallel with ra -{- ax-^-
ze. While these vectors are in phase, the difference in their
numerical value leaves a component efc, which is unbalanced and
which is free to cause circulating current in the closed loop of
the parallel circuit.

LESS COMMON CONNECTIONS

133

Table IX. — Comparison op a Two-phasb Motor Connected **T" to
Operate on Three-phase with Normal Winding

Normal .
two-phase
windins

Three-phase
connection

Normal

three-phase

windins

Pull-load efficiency

Full-load power factor

Startinir toraue

88.0
89.0
1.75
3.3

22.5
20.0
22.0

86.9
84.8
1.20
3.17

32.0
32.5
30.0

88.5
90.0
1.94

Maximum torou^

3.3

Deg. C. Rise at Full Load :
Stator copper

21.0

Stator iron

19.0

Rotor copper

22.0

In addition to the difficulty of making this connection properly
and the fact that there is at all times some circulating current,
there is also likely to be trouble in keeping the phases insulated
from each other. All things considered, this is an expedient
which had better be left untried except in cases of emergency.
For all ordinary operating conditions much better results will
be secured by replacing the old coils in the machine by new coils
wound for the proper voltage.

Table IX shows comparative performances of a two-phase
motor reconnected for operation on three-phase by a "T'' con-
nection and the performance of the same motor when supplied
with new three-phase coils and connected in a normal three-phase
manner.

Fig. 115 shows a possible three-phase "T'' connection which
may be made from a two-phase winding by a method similar
to the Scott transformer connection. The efifect of this connec-
tion upon the performance is shown in the table and was dis-
cussed in Chapter VI under "Changes in Phases." It is a
connection that should be used only as a temporary expedient
until better arrangements can be made. It is possible to devise
other makeshifts, but they are usually attended with so great
a sacrifice in the heating and efficiency of the motor, that it
is safer to leave them untried. It happens that a connection
that looks feasible from the standpoint only of the number of
coils in series, falls down on trial because these coils are not strictly
in phase. Experiments of this nature are better left to the
electrical manufacturing establishments.

CHAPTER X

RECONNECTING AN OLD WINDING FOR NEW

CONDITIONS

General Ftmdamental Considerations.

An electric motor is a device for transforming energy in the
form of an electric current into mechanical energy in the form of
turning effort, or rotating force. This turning effort, or driving
force, is called torque and is measured in the pounds pull that a
motor would develop at the rim of a pulley one foot radius. This
torque is produced by the force exerted by a current flowing
through a conductor located in a magnetic field. From this it is
evident that the capacity of a motor to produce torque is limited
both by the capacity of the copper circuit to carry current and
the iron circuit to carry magnetic lines of force.

The amount of current, or flux, that is being carried by a given
crossHsectionof copper or iron determines the heating of the motor.
It may be assumed that in a normal motor operating under the
conditions for which it was designed, there is a reasonable current
flowing in the copper and a reasonable flux in the iron, which the
designer believes will give the most satisfactory operating results.
Therefore, if changes are to be made in the speed, phase, fre-
quency and voltage at which the machine is to operate, the wind-
ing must be reconnected so as to have approximately the same
number of magnetic Unes per unit cross-section of iron and the
same current density in the copper that existed before the change
was made in the motor. This statement is true over a wide range
of conditions, and would be true universally if it were not for the
fact that the high-speed machine will generally run cooler than
the same machine operated at low speed with the same current
density in the copper and number of magnetic lines per unit cross-
section of iron, because of the larger amount of air that the high-
speed machine will force through its parts. For this reason it is
generally true that the capacity of a motor may increase in the
same proportion as the speed when the speed is being increased,
but may decrease somewhat faster than the speed is being re-

134

RECONNECTING AN OLD WINDING 135

duced. As a concrete example of this, it may be stated that a 75-
hp. motor operating at 450 r.p.m. may be made to develop 150
hp. at 900 r.p.m., assuming that the mechanical design will
stand the stresses due to the increased speed; but conversely, a
motor originally designed for 150 hp., at 900 r.p.m., when cut
down to 450 r.p.m. might not be able to develop more than 65 hp.,
on account of reduced ventilation.

There are certain fundamental mechanical relations that gov-
ern all motors whether alternating or direct current. The idea
given in the foregoing of the reaction of the electric current upon
a magnetic field concerns the production of a mechanical pull
tending to rotate the movable member of the motor. This pull
is usually expressed in pounds at one foot radius. This in turn
is expressed in horsepower when multiplied by r.p.m. and by
2 w and divided by 33,000, and may be expressed by the equation :

rj __ Torque X r.p.m. X 27r _ Torque X r.p.m.
^' " SpOO 5;252

from which

„ hp. X 5,252

Torque = -^

* r.p.m.

Since the current in the copper and the flux in the iron are to
be held approximately constant whatever change may be made
in the motor winding, it' follows that the torque will be kept
constant and the horsepower will vary with the speed. In
other words, if the copper and iron are carrying the same current
and flux at all times, twice the horsepower will be developed at
twice the speed or approximately one-half the horsepower at
one-half the speed.

It is essential, in getting a clear conception of the motor, either
for purposes of making changes or for other reasons, that a plain
distinction be made between torque and horsepower. It is the
function of a motor to produce torque, or turning effort. It is
incidental that when the same force is allowed to rotate at one
speed or another, a different horsepower is produced. For this
reason it is incorrect to speak of a motor and say "It required 20
hp. to start the load,'' because, when starting, the motor was
generally at a standstill; therefore there was no rotation and
hence no horsepower. The motor, however, was taking current
and developing torque, and the correct expression would be the

136 CONNECTING INDUCTION MOTORS

current taken at start was equivalent to the current taken by
the motor when developing 20 hp. at full speed.

It is often possible to reconnect a motor and adapt it to new
conditions leaving it entirely normal, and the performance in all
essential respects remains the same as before reconnection. Such
changes, for example, are represented by connecting the polar
groups of a winding in series for 440 volts and in parallel for 220
volts. These are classified as strictly legitimate changes.

A second class of changes leaves the performance in some
respects unchanged and alters it in others. These may be repre-
sented by operating a motor in star on 440 volts, and in delta on
220 volts. In this change there is little change in efficiency or
power factor; the starting and maximum torques on 220 volts,
however, are only 75 per cent, of their value on 440 volts. In
such a case the advisabiUty of the change depends entirely on
the work that the motor is doing. If the torques at their altered
values are sufficient to start and carry the driven load easily,
there is no objection to operating the motor indefinitely as so
reconnected, since the motor will not run any warmer than before
and its efficiency and power factor may be better. Such changes
may be classified as possible changes.

A third class of changes leaves a motor operative in the sense
of producing torque enough to do the work required, but so
alters its performance as to heating, or efficiency, or power factor,
or insulation, that it is undesirable to leave the motor operating
indefinitely in such a condition. Such changes might be ex-
empUfied by taking a three-phase motor and reconnecting the
coils as they stand for two-phase. This is equivalent to operating
the three-phase motor at 125 per cent, of normal voltage, and
in addition, the coils which should have extra insulation where
the phases change, have only group insulation. The iron loss and
heating may be increased to a dangerous degree and the power
factor greatly decreased. Such changes should be used only in
an emergency and the proper permanent changes made at as
early a date as possible. These changes should be classified
as make shift or undesirable changes.

The main principles which operate to fix the limits of the dif-
ferent combinations, such as series, parallel, series star, parallel
star, series delta, parallel delta, etc., possible with a single wind-
ing, may be enumerated somewhat in the following manner:

1. The mechanical output of a motor is limited by the cross-

RECONNECTING AN OLD WINDING 137

section of copper available to carry current and by the cross-
section of iron available to carry magnetic flux.

2. An induction motor is also at all times an alternating-cur-
rent generator as well, and the voltage generated by its own rotat-
ing field cutting the conductors of its own stator coils must at
all times very closely approximate the appUed line voltage.

3. It is necessary that the pitch or throw of the coils bear
some reasonable physical relation to the number of poles that the
machine has. For example, in a 4-pole motor the coils should
throw somewhere near J^ of the circiunference of the stator bore,
in a 6-pole motor somewhere near 3^^ the circumference, and so
on. The practical limits to the throw are from 3^^ to l}4 times

this full-pitch value. That is to say, in a 72-slot 6-pole motor

72
the full or exact pitch for the coil throw would be ^ = 12 slots,

or the coil wo uld be in slots 1 and 13. Using the limits 3^ to Ij^
as given, the throw of the coil should be not less than 6 slots
nor more than 18 slots for possible operation; that is, the coils
should not spread less than slots 1 and 7 nor more than slots 1
and 19.

4. All changes in operating conditions whether of horsepower,
voltage, phases, frequency or poles, may be reduced to terms
of change in voltage and so considered.

5. An induction motor is similar to a transformer in that the
niunber of turns in series in the winding must be varied in the
same direction and by the same percentage as any change in the
voltage appUed. In addition to these principles the following
practical considerations must be remembered:

(a) The new voltage which is appUed to a reconnected motor
must not exceed the Umiting value of the insulation which is
on the coils. For example, 2200 volts should not be applied to
a 550-volt winding even though it has been reconnected with
four times as many turns in series.

(b) In reconnecting for higher speeds the peripheral speed of
the rotor must be kept down to a safe value so that the cen-
trifugal force does not damage the rotor core or winding
mechanically.

(d) In a squirrel-cage motor if radical changes are made in the
number of poles, a change may also be required in the short-

138 CONNECTING INDUCTION MOTORS

circuiting rings of the equirrel-cage rotor windii^ in order to
keep the proper staxtiug torque.

(e) In a polar-group winding the individual coils at the begin-
ning and end of the phase groups have usually heavier InBulation
than the inside coils of the groups. Where this is the case,
when reconnecting for change in phase or poles the coils with the
heavier insulation should be shifted to their proper new places
in the winding.

These principles have been thoroughly covered in preceding
chapters, but in recapitulation some additional comments may be
made bearing on the practical appUcation.

1. Cross-Section of Copper and Iron.

From the existing connection of the winding in the machine
which is to be reconnected, it is a simple matter to check the

Fio. 145.
Flos. 146 and 146.— Chackinji c

current flowing in the turns of the coils which are in series.
This is done by checking the connection of the winding; that is,
whether it is series or parallel, star or delta, etc. From this
fact and the rated current of the machine can be derived directly
the current in the coils themselves. For example, a three-phase
machine has a normal rating of 50 Mnperes per terminal and is
connected 2-parallel delta. Fig. 145. The current in the indi-
vidual coils themselves is - . -„ = 14.5 amperes, as shown.
Then the load which is put on the motor after reconnection

RECONNECTING AN OLD WINDING

139

should not be greater than that which would cause 14.5 amperes
to flow in the coils themselves. Under the new connection the
polar groups might be 5-parallel star, as in Fig. 146, in which
case the new current per lead would be 6 X 14.6 amperes =
72.5 amperes, but the current in the individual coils would still
be 14.5 amperes as indicated.

If the new connection is for a greater number of poles and hence
a slower speed, it would be well not to put quite so much current

MAGNETIC
FIELD UN ES
ORFWX

^TAWJf
PUNCNIN60R
LAMINATION

Fio. 147. — Cross-section of stators wound for four, six, eight, ten and twelve
poles showing radial depth of iron behind slots required for the magnetic field.

through as originally on account of the reduction in ventilation.
Regarding the cross-section of iron, this remains constant so far
as the teeth are concerned, but in the core back of the slots this
changes with the number of poles. This is illustrated by Fig.
147, which shows a cross-section of a motor indicating the mag-
netic conditions in the iron when the motor is connected for 4, 6,
8, 10 or 12 poles.

Considering the 4-pole sector, the coils in the stator slots B set
up a magnetic field represented by the 15 concentric circles
causing a north pole where they leave the stator and a south pole

140 CONNECTING INDUCTION MOTORS

where they reenter the stator, as indicated by the arrowheads.
The proximity of these 15 circles at the air gap indicates the
density of the magnetic field at this location. It will be noted
that all 15 of these circles must pass through the core back of the
slots or through a cross-section represented by the dimension W.

If, now, consideration is given to the sector marked 6-pole, it
will be noticed that the magnetic density in the air gap as indi-
cated by the proximity of the concentric circles is the same as in
the case, of 4 poles, but the iron back of the slots now has to carry
only 10 circles and hence has only "^^^ the magnetic density as in
the case of 4 poles. There is still the same total flux in the
machine, since 4 X 15 = 60 = 6 X 10, and this explains why
the air-gap density stays the same, but this total flux is now
separated into six magnetic circuits instead of four and hence the
iron in the core back of the slots is not worked nearly so hard.

Similarly, in the case of 8 poles there are only 73^ circles, since
8 X 7J^ = 60, and in the case of 10 poles 6 circles and 12 poles 5
circles, since 10 X 6 = 60 and 12 X 5 = 60. In other words,
there is the same total flux in the machine for all these connec-
tions and the same magnetic density in the air gap, but the core
iron back of the slots works at a higher density the smaller the
number of poles and at a lower density the larger the nimiber of
poles for which the winding is connected. The obvious precau-
tion to be drawn from this consideration is that when reconnect-
ing a winding for a smaller number of poles some check should be
made to insure that the magnetic density in the core does no t exceed
a safe value. Reference will be made to this in Chapter XII
on estimating a new winding for an old core.

2. Generator Action of the Winding.

This has been referred to several times and will not be elabo-
rated here beyond calUng attention to the fact that the rotating
magnetic field will always assume such a value that as it cuts the
stator coils it will generate in them a voltage practically equiva-
lent to the applied Une voltage. Since both the number of
turns in series in the coils and the magnetic density in the iron
may be varied, there are evidently several combinations that
would generate the Une voltage, some having more turns and less
field and some having less turns and more field. The practical
difference between these combinations would be that the fewer
the turns and the stronger the field the greater would be the
maximum torque, this being limited by the saturation of the

RECONNECTING AN OLD WINDING

141

iron in the core. A little thought brings out the fact that this is
equivalent to raising and lowering the voltage on a fixed winding.
The higher the voltage the greater will be the magnetic field and
the greater the torque. This consideration of the generated
voltage or counter-electromotive force or back electromotive
force is one of the simplest checks on the number of turns
required in a winding.

o
U

o
O

•o

u
V

ca
>

c
0«

100
90

•

^ --)

.--L-

80
£70

/ L = Limit of Practical
^V/otkins Range, Coil should

not be chorded below one
Half Pitch

260

1^50

Per Cent Eleotr'l Chord
Pitch Degrees Factor

i ICO ISO LOGO
; 90 162 0.987
1 80 144 0.951
1 70 126 0.891
■ 60 106 0.8U9
1 50 90 0.707
1 40 72 0.588
1 30 54 0.454

*-'40

1 20
1 10

36
18

0.3C9
0.150

20 30 40 50 60 70

Per Cent, of Full Pitch

80 90

100

Fia. 148. — Curve showing the variation of the "chord factor" with the throw

of the coil.

3. Changing the Throw.

The effect of changing the throw has been thoroughly covered,
and only the effect on the appHed voltage will be shown here as
a curve, Fig. 148. In this figure full pitch is called 100 per cent.
For example, in a 72-slot 6-pole motor the winding would be 100
per cent, pitch if the coils lay in slots 1 and 13, it would be
66.66 per cent, pitch if the coils lay in slots 1 and 9 or 50 per
cent, if they lay in slots 1 and 7. The curve indicates how the
voltage applied to a coil or a winding should be reduced as the
coil is chorded up if the same magnetic conditions are to be kept,
or the reciprocal of the curve values indicates how the density
of the magnetic field will increase if the voltage is held constant
while the throw of the coils is decreased. .

142 CONNECTING INDUCTION MOTORS

4. All Changes can be Handled as Voltage Changes.

The statement is here made that any change in the operat-
ing characteristics of a motor may be reduced to terms of a vol-
tage change and that if the corresponding voltage be appUed the
operation imder the new conditions will approximate the normal
operating conditions under the original conditions. Since there
are five main operating characteristics — namely, volts, phase,
poles, cycles and horsepower — a brief r6sum6 is in order stating
how each one of these may be considered as a voltage change.
In other words if, for example, the horsepower or phase of a
motor is to be arbitrarily changed, what will be the new operating
voltage to seciu*e this result? Taking these characteristics in
order, a voltage change is self-evident since everything is to be
reduced to voltage. In the case of a phase change, two to three
or vice versa, the voltage on a three-phase connection should be
^ of that on the corresponding two-phase connection. For
example, if a two-phase motor is connected for three-phase and
everything else left the same, the three-phase connection should be
operated at ^ the rated voltage of the two-phase, or a two-phase
440-volt motor when reconnected for three-phase becomes a
550-volt motor, etc. In Fig. 149 is shown a 48-coil winding
grouped for two-parallels two-phase 4-poles, if this winding
will operate on 220 volts two-phase it will also operate on 660
volts three-phase when grouped 4-pole series star, as in Fig. 160.

In the case of a change in the number of poles, if the voltage
be changed in the same direction and by the same amount as
the change in speed, the torque will remain essentially constant
and the horsepower will vary with the speed, being greater at
higher speed and less at lower speed in exact proportion. How-
ever, if for reasons explained in connection with Fig. 147, there
is not enough iron back of the slots to permit of keeping the
same total flux and dividing it into fewer circuits with greater
flux per circuit, the voltage may be kept constant and the horse-
power will remain practically constant. The latter condition
would mean that there is less total magnetic flux and less torque
at higher speeds and greater total flux and greater torque at lower
speeds, as must necessarily be expected since the horsepower is
constant and horsepower = torque X r.p.m. -r- 5252.

A varying frequency can be readily reduced to a corresponding
voltage change by remembering that a change in frequency with-
out any other change would result in a change in speed and since

RECONNECTING AN OLD WINDING

144 CONNECTING INDUCTION MOTORS

the basic idea of this method is that the motor is also an alter-
nating-cmrent generator, generating the applied voltage, it is
evident that with an increased speed the generated voltage
will be increased and with decreased speed the generated voltage
will be decreased. Hence, it follows directly that when the fre-
quency or cycles of the supply circuit are changed the voltage
should be changed by the same amount and in the same direc-
tion. For example, if a 60-cycle motor is run on 50 cycles it
should have appUed only % the voltage if the same magnetic
condition is to be kept, and consequently the horsepower will
be only % of the 60-cycle value. Viewed mechanically, the
torque remains the same on 50 cycles, but the speed is only 5^
as great, hence there is only % the horsepower which checks the
electrical result.

There remains only a change in horsepower to be converted
into a voltage change, and this is apparent from the fact that
in any motor the horsepower is proportional to the product of
the voltage and amperes. Since the cross-section of the copper
conductor remains the same and hence the amperes remain the
same, the only thing that can vary is the voltage, and it follows
directly that to get more horsepower out of a motor requires the
application of a higher voltage and less horsepower will permit
the use of a lower voltage.

From these considerations it appears that the effect of a change
in any of the characteristics of the motor can be balanced by the
proper change in the voltage. This statement at once arouses
the comment that while it might be found that 273 volts or 346
volts or something of the kind was proper to give normal opera-
tion on a motor under changed conditions of phase or poles or
what not, still such information would be of Uttle use since there
are no commercial circuits having such voltage values. The
answer to this is that the number of turns in the winding or the
connection of the groups may be changed so as to increase the
total number of turns in series by the amount that the voltage
should be decreased; and vice versa j it may be possible to de-
crease the total number of turns per phase in series by the
amount that the voltage should be increased.

Consideration of a simple case under each of the five char-
acteristics of horsepower, poles, cycles, phase and voltage will
bring out the manner of applying the "voltage method" to any
and all changes in the motor-operating conditions.

RECONNECTING AN OLD WINDING

145

•s

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146 CONNECTING INDUCTION MOTORS

1. Change in Voltage.

A motor is connected series-star for three-phase 440 volts, as
in Fig. 151. How should it be connected for 220 volts? [For
convenience Table V is here reproduced.] Looking at the table
and following the horizontal line "Three-phase Series Star," there
appears under vertical heading "Three-phase Series Star," also,
the figures " 100." That is to say, the motor as it stands on 440
volts is considered 100 per cent. The new voltage is to be 220,
which is 50 per cent, of 440. Hence, the same horizontal line in
the table, namely, "Three-phase Series Star," is followed along
until the desired figure of 50 is found, which is imder the ver-
tical heading "Three-phase 2-Parallel Star." This is the cor-
rect answer: that is, if a motor is connected three-phase series-star
for operation on 440 volts, it must be connected three-phase
2-parallel star, as in Fig. 152, to operate correctly on 220 volts.

2. Change in Phase.

Refer again to the table and assume that a three-phase
440-volt motor is to be reconnected for two-phase 440 volts.
Inspection shows that the winding as it stands on 440 volts
is four-pole three-phase series-delta, as in Fig. 153. Select
the horizontal column in the table marked "Three-phase
Series Delta" and follow it across, looking for a vertical column
showing the value "100," since the desired two-phase voltage
is the same as the present three-phase voltage, or 100 per cent.
Inspection shows that there is no "100" under any two-phase
connection. This indicates at once that a three-phase series-
delta connected motor which is normally operated on 440 volts
cannot be changed and operated on two-phase 440 volts, with-
out rewinding. The nearest value to "100" imder a two-phase
colunm is "70," shown under "Two-phase 2-Parallels." This
means that if a three-phase 440-volt motor which is connected
series delta, be reconnected for 2-parallel two-phase, as in Fig.
154, it should be operated on 70 per cent, of 440, or 308 volts.

3. Change in Frequency.

It is desired to operate a three-phase 440-volt 60-cycle motor
on 50 cycles at the same voltage. What change should be made
in the connections? Inspection indicates that as the motor
stands it is connected for three-phase 5-parallel star on 60 cycles.
A change in frequency should be offset by a change in voltage
in the same direction and by the same amoimt; hence, if a motor
is operated on 100 per cent, voltage on 60 cycles, it should be

RECONNECTING AN OLD WINDING

CONNECTING INDUCTION MOTORS

RECONNECTING AN OLD WINDING 149

connected for % of 100, or 83J^ per cent., voltage on 60 cycles.
However, the voltage is to remain the same on 50 cycles as on
60 cycles, so this result must be obtained in another way. If
the voltage cannot be decreased the number of turns in series
can be increased. Another way of saying this is that we can
reconnect the winding so that ordinarily it would be good for a
higher voltage and then if it is operated on the same voltage the
efifect will be the same as if a lower voltage had been applied to
the original connection. In the case in hand the motor should,
when connected on 50 cycles, be operated on 83J^^ per cent, of
the 60-cycle voltage. Only 100 per cent, is available, so the

winding will have to be reconnected with w^i/ = 120 per cent.

of the original number of turns in series. This would ordi-
narily mean the winding was good for 120 per cent, of the
original voltage. Hence, in looking up the change in the con-
nection table the figure "120" is located instead of SS^i.

Referring to the table and following the horizontal Une " Three-
phase 6-Parallel Star" across, search is made for the figure " 120, "
the nearest thing to it is '' 125, " foimd under the vertical heading
"4-Parallel Star." The number of poles in the motor would have
to be divisible by both 4 and 5, in order to make this change
possible; or, in other words, it would have had to be either 20
poles or 40 poles. As it may have been 10 poles, for example,
the nearest connection that could be made would be for 144

under "Three-phase 2-Parallel Delta." This would mean the

144 X 440
correct operating voltage on 50 cycles would be - .^Ty — ~ ^28

volts; or, if operated on 440 volts, it would be working under

440

Vrto = 83J^^ per cent, normal voltage, which would usually not

be permissible on account of lowered torque and increased heating.

4. Change in Number of Poles or Speed.

A 60-cycle three-phase motor is operating on 550 volts at 850
r.p.m.; it is desired to operate at 690 r.p.m. on the same voltage.
What change in connections should be made, if any, in addition
to changing the number of poles? Inspection shows the motor
is connected 4-parallel star for 8 poles, as in Fig. 155. To get 690
r.p.m. would require to connect for 10 poles, since this would give
a no-load speed of about 720 r.p.m. and a full-load speed of about
690 r.p.m. Since the motor is a generator also, it will generate

150 CONNECTING INDUCTION MOTORS

only okn — = *46 volts when connected for 10 poles and a

slower speed. However, it is desired to continue at 550 volts, so
that the connections will have to be changed to get the effect of

j£Vfl = 123 per cent, of the old voltage. In the table opposite
the horizontal line "Three-phase 4-ParaUel Star," the nearest
figure to "123" is "116," which is found in the vertical column
headed " Three-phase, 2-ParaUel Delta. " Hence, the conclusion
is drawn that if an 8-poIe motor. Fig 155 is connected three-

Fio. 16S. — Normal three-phase, eight-pole, four parallel Btar
phase 4-parallel star and operated on 550 volts and it is recon-
nected for lO-poles 2-parallel delta, Fig. 156, it may be still
operated on 550 volts, although, strictly speaking, its normal

voltage would be ^h-i — =520 volts. In this example

no consideration was given to the fact that the throw of the coil
in electrical degrees was changed in changing from S poles to 10
poles. This can be taken account of in the following way:

Suppose the motor as it stood had 120 stator slots and the
coils lay in slots 1 and 13. Full pitch would be 1 and 16, since
120
-s- - 15. Since the coils throw 12 slots and full pitch is 15

RECONNECTING AN OLD WINDING

151

slots, the per cent, pitch = ^r = 80 per cent., and from Kg. 148

the chord factor for 80 per cent, pitch = 0.96. When recon-
nected for 10 poles, the throw of the coils is still 1 and 13, but this

120
is now 100 per cent, pitch sincey^j- = 12 and 1 and 13 does span

12 slots. Therefore, when connected for 10 poles the coils are

more effective in the ratio of ^^ri^ since the chord factor for 100

0.95

Fio. 156. — Same winding as Fig. 155 reconnected for three-phase, ten-pole

parallel delta.

per cent, pitch = 1.00 from Fig. 148. Therefore, when the
change in chord factor is also taken accoimt of, the new normal

operating voltage is 520, as obtained in the foregoing, multi-

1 00
plied by tt^^ = 548 volts, or almost exactly right for operation

on 550 volts.

5. Change in Horsepower.

A 10-hp. 220-volt motor is operating above the allowable safe
temperature, on its normal voltage, and it is found by experiment
that when the voltage is raised to 250 its temperature is reduced

152 CONNECTING INDUCTION MOTORS

to within safe limits. Can any change be made in the connec-
tions which will allow the motor to be operated still on 220 volts
and duplicate the conditions when operating on 250 volts? An
inspection of the winding shows the motor to be connected three-
phase series delta, as in Fig. 153. The experiment which was

250
made showed that the voltag6 should be increased to ^on =114

per cent, of its original value. It has been pointed out that re-
ducing the niunber of turns in series in a winding has the same
effect as increasing the voltage on the same number of turns.
In this case if the voltage was raised to 114 per cent, the same

effect could be obtained by reducing the turns to iprr = 87.5

per cent. Consequently, in referring to the voltage change
table, in this case, search is made for "87.5" and not "114."

Selecting, therefore, the horizontal line '*Three-phase Series
Delta" in the table and looking across the nearest figure to "87.5
is "86," which occurs under the vertical heading "Three-phase
Parallel Star." Consequently, the conclusion is at once drawn
that if a 220-volt motor has its connections changed from series-
delta. Fig. 153, to parallel-star, Fig. 152, it will act in every way

220
as though Q-^ = 256 volts had been applied to the series-delta

connection. This is equivalent to increasing the horsepower of
the motor, since on the original connection the motor was over-
loaded when carrying its rated load, but when the connections of
the winding were changed the machine could drive its rated full
load without distress. The reason for this is that, although the
density of the magnetic flux was increased the cross-section of
the copper in the winding was increased, consequently the copper
losses were reduced. The latter being considerably greater than

the former resulted in a reduced temperature. The capacity in

256
horsepower has actually been increased to ^on = 116 per cent.

of its original value.

From these five examples, which could be multiplied many
times and from all sorts of combinations that could be made by
changing the characteristics in pairs, it can be readily seen that
any contemplated change can be reduced to an equivalent change
in the applied voltage and the proper connection, if it is a feasible
and rational change, selected from the table of phase and voltage
given herewith.

CHAPTER XI

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS

NOISE AND VIBRATION

After the coils have been placed in a motor and the cross-
connections completed according to the desired diagram, a check
is necessary to insure that the connections are properly made
before load is put on. The simplest way of making this check
is to start up the motor and run it Ught on a circuit of the proper
phase, frequency and voltage. Observation of the behavior of
the motor under these conditions indicates to the trained ob-
server whether there are any serious discrepancies in the winding
or connections. This observation should cover five points;
namely, speed, noise, mechanical vibration, general heating of
the whole winding and local heating of one or more separate
coils.

The speed, if correct, should be of nearly synchronous value
when the motor is running without load; that is, equal to cycles
times 120 divided by the number of poles.

The motor should give a low himiming noise similar to that
made by transformers, but there should be no irregular or " growl-
ing" noise. There may also be a considerable volimie of air noise
or whistle caused by the ventilating air passing through the air
ducts in the rotor and stator. The magnetic noise may be
distinguished from the air noise by the expedient of opening the
switch for a second or two while the motor is running full speed
without load. Opening the switch breaks the current and re-
moves the magnetic field, and consequently the magnetic noise
ceases, but leaves the rotor running at practically the same speed
owing to its inertia or stored energy, and hence the windage, or
air noise, is practically unaffected. In this way, by opening and
closing the switch two or three times, it becomes readily apparent
what part of the total sound made by the motor is magnetic
and what part is windage. It also indicates whether either or
both of these sounds are abnormal. If the speed is correct and
the motor makes no more than a reasonable singing or humming

153

154 CONNECTING INDUCTION MOTORS

noise, the hand should be placed on the frame to note the me-
chanical vibration.

If there is noticeable mechanical vibration, it may be due to
purely mechanical causes or to magnetic causes or possibly to
both. By opening and closing the switch, as described in the
foregoing, the mechanical vibration due to the magnetic field
can be easily separated from that due to strictly mechanical
causes, because when the switch is open there is no magnetic
field present. Suppose, for example, that when the motor is
running at full speed there is a marked vibration or trembling that
can be felt when the hand is laid on the frame of the motor
Suppose, then, that when the switch is opened for a second or two
the vibration disappears and the motor rotates smoothly at
nearly the same rate of speed. This, then, is evidence that the
vibration was caused by the action of the magnetic field on the
stator and rotor. However, if the motor vibrates whether the
switch is open or closed, it is evidence that the action is purely
mechanical and is affected little or not at all by the presence of
the magnetic field.

When the trouble is traceable to the magnetic field, it may indi-
cate improper connection of the winding or it may indicate that
the mechanical clearance between stator and rotor is not sjnn-
metrical or that there is some similar combination of mechanical
and magnetic features that is responsible for the vibration notice-
able. The commonest mechanical causes for vibration are rotor
out of balance, either standing or running; bent shaft; too great
clearance between shaft and bearings; unbalanced or eccentric
coupling or pulley or a combination of two or more of these
faults. These mechanical conditions are easily determined and
can be corrected. The commonest causes of mechanical vibra-
tion due to a combination of mechanical and magnetic conditions
are rotor out of roimd, stator out of round, too great clearance
in the bearings, or rarely, xmeven or eccentric air gap or clearance
between stator and rotor. The latter point seldom gives trouble
and a pol3rphase motor will practically always run without giving
any trouble xmtil the bearing wear allows the rotor to strike on
the stator. Single-phase motors are more sensitive to eccentrici-
ties in the air gap or clearance between stator and rotor and
sometimes show a considerable variation in torque in motors
otherwise dupUcate due to such irregularities.

There are a number of elements that may cause the rotor or

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 155

stator to be out of round. In the first place there is a slight
variation due to the punch-and-die work, which may amount to
0.005 in. between individual pimchings. In the second place
some allowance around the outside of the punching must be made
in the fixture or frame in which they are built up so that they will
assemble readily, and this allows the punchings to stagger more
or less. In the third place when the punchings are actually
assembled in the frame, the frame may spring out of shape slightly
after machining, owing to the release of casting strains when re-
moving the material in the cut. Of course none of these varia-
tions is in itself large, but when they all accumulate in the same
direction, perceptible eccentricity may result amounting to a
good many thousandths of an inch. This is not serious, since it
is present to some extent in all motors, but under extreme or
extraordinary conditions it may cause mechanical vibration.

Mechanical vibration caused by the windings may be due to
either the rotor or the stator. For example, in a squirrel-cage
rotor there may be bad contacts between certain bars and the
short-circuiting rings, resulting in more resistance in some parts
of the winding than in others. This in turn affects the distri-
bution of current in the different bars and hence affects the mag-
netic field and varies the mechanical pull from point to point.
Or if the winding on the rotor of a wound-rotor type motor is
ground in a number of places, it will also cause unequal distri-
bution of the current in the windings, which in turn causes severe
vibration during the starting period. However, this generally
disappears to a large extent after the motor comes up to full
speed. From this it may be seen that where mechanical vibra-
tion is absent the conclusion may be drawn that the windings
are sjnnmetrical and are functioning properly, but where vibra-
tion is present it may be caused by a niunber of things, some of
them obscure, and must not immediately be attributed to im-
proper winding connections until a further examination is made.

The next point to be observed is the general temperature of
the entire winding as determined by passing the hand around the
ends of the windings. It is best practice in making this examina-
tion to shut down the motor after it has run three to five minutes.
If the examination is made while the motor is running, care should
be taken to avoid injury by coming in contact with moving parts
and also to avoid injury from electric shock, if the circuit is 550
volts or over. If the winding as a whole is cool, inspection should

156 CONNECTING INDUCTION MOTORS

be made for individual coils that are much hotter than the rest
of the winding, as these may indicate short-circuits or improper
connections in that particular coil.

If a motor is operating freely and easily at the proper speed
without undue noise or mechanical vibration and if there is no
general or local heating of the winding, the next step is to meas-
ure the current in each phase. This may be done a sindicated in
Figs. 157, 158 and 159. If possible an ammeter should be con-
nected in each phase so that the readings of all phases may be
taken simultaneously. For a two-phase motor two ammeters are
required, as in Figs. 157 and 158, and for a three-phase motor

Pio. 157.— Two-phaaa, Fio. 158.— Two-phaso,

Fio. 169.— Three-

four wire circuit. three wire oirouit.

phase circuit.

Meaauring the current in each p

haae.

three ammeters are required, as in Fig. 159. The no-load, or
magnetizing current as it is called, will usually be somewhere
between 15 and 35 per cent, of the full-load current with an aver-
age value of perhaps 25 per cent. If the no-load current in all
phases is equal and approxunately 25 per cent, of the full load,
it is safe to assume that the winding connections are properly
made. If a wattmeter is available, a further check might bemade
on the total watts taken by the motor nmning light, but that
does not add greatly to the ammeter check. The connections
for connecting two wattmeters in a two-phase four-wire circuit
are given in Fig. 160 and for a three-phase circuit in F^. 161.
The connections for a three-wire two-phase would also be the
same as those in Fig. 161; where only one wattmeter is available,
it may be connected into a three-phase circuit with a single-pole

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 157

switch, as in Fig. 162, so that the two readings may be taken by
simply throwing the switch. In a two-phase circuit the total
watts will always be the sum of the two readings, hut in a three-
phase circuit this is true only when the power factor is greater
than 0.50. Where two wattmeters are used to measure the no-
load watts of a three-phase motor, the difference of the two read-
ings gives the correct value of the watts, since the power factor
of an induction motor at no load is always less than 0.50. The
watts taken at no load and full speed and voltage cover the iron
loss, bearing friction, windage and a small amount of copper loss.
The total no-load watts wiU in general be in the order of 5 per

Fio. 160.— Two-
phaae, four-wire oirouit
with two wattmeters.

Measuring the total watts.

cent, to 8 per cent, of the rating of the motor in watts varying with
the capacity and speed of the motor. The motor rating in watts
would be the horsepower from the nameplate multipled by 746.

If the foregoing checks indicate that the motor is not acting
normally, they should also give some evidence that there is a
fault in the coils of the winding or in the manner in which these
coils are connected, and further search is made to analyze the
nature of this fault so that it may be located and corrected

The winding of an induction motor is made up of a number
of similar coils connected into groups. These groups in turn are
connected in such a manner that when an alternating current
of the proper characteristics flows through them, a magnetic
field having alternate north and south poles is set up and caused
to rotate in the motor. The coil itself is usually made up of

158 CONNECTING INDUCTION MOTORS

two or more turns of wire or strap so that there are at least ten
chances for defects in the winding after the coils are all in place
and connected. Some of these faults are simple and readily
rectified, while others are more obscure and difficult to handle.

The Ten Most Common Defects.

These ten most common defects in the order of their likelihood
are:

1. The winding grounded on the core.

2. One or more turns in one or more coils short-circuited.

a the CI

3. One or more complete coils short-circuited at the coil ends
or at the "stubs."

4. A complete coil reversed or connected so that the current
flows through it in the wrong direction.

5. A complete group of coils or pole-phase group is reversed;
that is, connected so that the current flows through the group
in the wrong direction, making a north pole where a south should
be or vice versa.

LOCATlNa FAULTS IN INDUCTION MOTOR WINDINGS 159

6. Owing to lack of care in couoting, two or more pole-phase
groups may include the wrong number of coils.

7. A complete phase in a three-phase star or delta winding is
reversed.

FiQ. 165. — Coils in placB imoonnected.

Fio. 166. — Coila coQDeotod into Fia. 167. — The flompleted oonneotioa

pole phase groups. of windins.

The three Btsgea o! ooODeoting a windins-

8. The winding connections may be properly made in them-
selves, but not right for the volt^e upon which the motor is
to be operated. That is, the motor may be connected properly
for HO or 440 volts, but the motor is to operate on 220 volts.

9. The winding connections are properly made, but they are

160

CONNECTING INDUCTION MOTORS

for the wrong number of poles, and hence the motor runs at a
different speed from that which was intended.

10. An open circuit somewhere in the winding, or one or more
coils are omitted and left out of the winding, known as "dead"
coils.

The manner in which these various faults occur can be best
understood by referring to what takes place, first, in winding
and insulating the coils, and, second, in placing them in the core
and connecting them.

Fig. 164 shows a coil of the usual form wound up from several
turns of wire and insulated ready to be used in the slot; Fig. 163,

Fig. 168.-

-Individual coil with insulation removed to show "shorts" and

"grounds." •

the operation of winding these coils in place in the core; and Fig.
165, the coils all in place ready for connecting. The coils con-
nected into pole-phase groups, with the coil ends at the begin-
ning of each group bent into the bore and the coil ends at the end
of each group bent out toward the frame are shown in Fig. 166.
The cross-connections are made in Fig. 167, thus completing
the winding connections. Fig. 168 shows the coil in Fig. 164
as it would appear if the insulation were stripped off and in-
dividual turns of wire separated.

Grounds.

The first fault listed — ^grounding of the winding on the core —
occurs when in some manner the insulation becomes stripped
from the coil and also the cotton covering from the wire so that
at some point, as at A, Fig. 169, the bare-copper conductor
touches the laminated-iron core and by so doing "grounds"
the winding. This means that a Uve current-carrying part is
touching the metal structure of the motor, and when this con-

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 161

dition exists anyone who touches the frame of the motor actually
touches a live conductor. This may not be detected if the entire
winding and the supply circuit otherwise is free from grounds,
but it often happens that other grounds are present somewhere
in the system so that in standing on the ground and touching
the frame of the machine the chances are very good of getting a
shock at a voltage that may equal that of the supply circuit.

Fia. 109. — Coil grounded on core.

Referring to Figs. 168 and 169, should two grounds occur
simultaneously, as for example, at A and B, a short-circuit would
be formed in the'loop, Fig. 168, from B through 11, 12 ajid 13 to
A ; and if the normal voltage remained on the motor, this short-
circuited turn would immediately become hot enough to destroy
the insulation on the complete coil. This is the second fault
listed and may occur without grounding by the touching of the
bare conductor of adjacent turns as at C, where the complete
short-circuit follows the path of C 2, 3, 4, 5, 6, 7 and C.

Short-Circuits.

The third fault — short-circuiting a complete coil — can also be
seen from Fig. 168 and exists when the insulation of the ends of the
coil 1 and 14 become damaged and allow these two wires to
touch, as at D. A current then flows in the entire coil, in addi-
tion to and aside from the line current, equal to the voltage of the
coil divided by its impedance. In other words, what happens is

162 CONNECTING INDUCTION MOTORS

equivalent to removing that particular coil from the main winding
where it is generating its share of the useful counter-electro-
motive force and using up this same generated or induced counter-
voltage, simply, to force current through the coil itself. This
coil would heat up practically as fast as would any induction
motor winding if the rotor was held from rotating and full-Une
voltage applied to the stator winding.

Reversed Coil.

The foiu*th fault occurs when the two leads of a coil are inter-
changed, as at X, Fig. 170. This has the effect of causing the
one coil, or in this case coil Y, to ''buck" all the other coils in
the same pole-phase group. Expressing this in another way,
the cross-connected coil is trying to produce a magnetic north
pole when all the other coils in its group are producing a south
pole. The effect of this is magnetic dissynametry and manifests
itself, as do most irregularities in winding, in noise and heating.

Reversed Group.

The fifth fault, and one that can occur readily in connecting,
is when an entire pole-phase group is reversed, as at Z, Fig. 170.
This can be understood from Fig. 166. The beginnings of all
pole-phase groups are bent in toward the center of the bore, and
the endings are all bent out. Should one of the ends bent out be
used as a beginning and the other end as an ending, the entire
group would be reversed with consequent magnetic distortion
and trouble due to noise and heating.

Wrong Grouping.

The sixth fault is one due wholly to wrong counting in grouping
the coils. In a three-phase four-pole motor with 48 coils there
should be in each group 48 -^ (3 X 4) = 4 coils, and the presence
of 3 coils or 5 coils in any group constitutes the sixth fault as
they are here listed. This is also shown in Fig. 170, where all
the groups have 4 coils except A^ and jBS which have 5 and 3
coils respectively.

Reversed Phase.

The seventh fault is present only in the case of three-phase
motors and consists in reversing the ends of one-third of the
winding so that one leg of the star or one side of the delta is con-
nected in such a way that the voltages generated in the three
phases are only 60 electrical degrees apart, whereas the currents

WCATim FAULTS IN INDUCTION MOTOR WINDINGS 163

164 CONNECTING INDUCTION MOTORS

supplied from any normal three-phase generator are 120 electrical
degrees apart, and hence these three voltages and currents cannot
combine to produce power as they properly should. This can
be understood by referring to Figs. 172 and 173. Fig. 172 shows
th6 three voltages generated in a three-phase winding as repre-
sented by three arrows or vectors arranged 120 deg. apart. If,
however, one phase of the winding was reversed and the lead con-
nected to the star point and vice versa, the back, or counter-
electromotive, force generated in that winding would be reversed
and would no longer be 120 deg. from the voltages in the other
two phases, but would be 60 deg. from them, as in Fig. 173. This

Fig. 172. — Normal winding Fio. 173. — Wrong connection in

relation. one phase as in Fig. 171.

Effect of reversing a phase.

would mean that the magnetic field in the stator, instead of
being a balanced succession of north and south poles rotating
and pulling the rotor around, would become unbalanced and
would no longer rotate properly. According to another method
of looking at the matter, there would be one field rotating clock-
wise and another different kind of a field rotating counterclock-
wise, and the natural result would be that these two fields would
interfere, and instead of rotating, the motor would remain at a
standstill, emitting an unusual amount of noise and reaching a
dangerous temperature in a very short time.

A four-pole three-phase winding with the B phase reversed is
shown in Fig. 171. It will be observed that instead of the arrows
on the pole-phase groups pointing in alternate opposite directions,
as they should for a correct connection, they point in opposite
directions in groups of three. Further consideration will be
given this feature later in this chapter.

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 165

Connected for Wrong Voltage.

In the eighth fault the winding connections are all made prop-
erly to form the magnetic poles in their proper sequence, but
there are only half as many turns in series or perhaps twice as
many as there should be. When this is discovered, the winding
may be such as to permit connecting in series instead of parallel
or vice versa, but under the worst conditions it may be necessary
to remove the entire set of coils and replace with a new set having
the proper number of turns for the required voltage.

Wrong Number of Poles.

The ninth fault is sometimes overlooked imless the speed is
taken with a tachometer or speed counter, in which case it is
readily detected. Its correction is not always either evident or
simple, but can often be accomplished without change in coils
by following some one of the various methods described in
Chapters IV and VIII.

Open-Circuits.

The tenth fault, ''open-circuits," may be due to failure to
solder a joint properly or to a joint being broken mechanically
after having been once made. "Dead'' coils are usually purely
inadvertent and are sometimes present without being discovered
at all. Such an occurrence could hardly happen \mless there
were a large nimiber of small coils crowded together.

After the enumeration of the commonest errors made by the
winder, as outlined above, the next step is to consider them in
turn with particular reference to how each may be detected and
corrected.

First Fault : Grounds. If the ground is fairly low resistance —
that is, the bare copper of the winding touches the core — the
defect may be detected by using an incandescent lamp arranged
as shown in Fig. 174. One of the lamp leads is touched to a bare
spot on the winding — for example, a terminal connector or a
"stub" where two adjacent coils are connected — and the other
is touched to the bare metal of the motor frame at some point not
protected by paint. If there is a ground present, the lamp lights
up. Another common method is by "ringing out" with a mag-
neto similar to that used in telephone work. In this method the
terminals of the magneto are appUed, one to the winding and the
other to the frame similar to the procedure in Fig. 174, and the
handle is turned. If the bell rings, there is probably a ground

166 CONNECTING INDUCTION MOTORS

in the winding. A third method employs a "testing box,"
which is really a transformer for obtaining voltage much higher
than the normal voltage of the motor under test. These boxes
give 2,000 or 3,000 or more volts and readily detect grounds on
windings of 550 volts and below. The test box is so arrsjiged
that when the terminals are appUed as in Fig. 174, the presence
of a ground instantly opens a circuit-breaker on the side of the
box.

Having established the fact that the winding is grounded by
some one of the foregoing methods, the next problem is to locate
in which coil or what part of the winding it has occurred. This

Fia. 174. — Lamp teat for grounds.

can sometimes be done by inspection, but sometimes requires
other means. The most usual of these is to put enough voltage
on the ground with the lamp device of Fig, 174, or the test box,
so that the resulting current heats up the contact that is causing
the ground and it becomes evident through smoke or shght arcing.
This will generally require two or more lamps connected in par-
allel. When the ground is definitely located, it is corrected by
repairing the insulation at this point by retaping the coil, or
replacing the defective slot cell or whatever may be causing the
trouble. Sometimes the ground cannot be "smoked out" in
this manner, and it then becomes necessary to open up the wind-
ing at two or three places and test out the different pieces to find
in which one the groimd is present. If it is still not evident, the

LOCATINO FAULTS IN INDUCTION MOTOR WINDINGS 167

defective section of the winding is further broken into smaller
pieces and the search pursued until the trouble is finally run down
to the individual coil which is defective. It is seldom necessary
to go so far, as the ground furnishes evidence of its location as
soon as the voltage is put across it.

Second and Third Faults: Short-circuit of a few turns in a
coil, or a single coil completely short-circuited, becomes hot in a
short time if the motor is run light on normal voltage. Their
presence can be detected by feeling around the wioding with the

hand immediately after starting the machine and noting if some
individual coils are much warmer than others. A device for
detecting such short-circuits before the rotor is put in the stator
and without applying any voltage to the winding itself is shown
in Fig. 175. This device is somewhat similar to a large horseshoe
magnet excepting that the iron part is built up of laminations,
or it may be considered as a core-type transformer having a
primary coil only with one side of the iron core missing. The
coil is excited with alternating current of suitable voltage, and
then the complete device is passed slowly around the bore of the
machine being tested as shown in Fig. 176. In passing around, if
the testing device passes over any short-cu-cuited turn or coil,

168 CONNECTim INDUCTION MOTORS

such ehort-circuit immediately acts as a short-circuited secondary
coil on a transformer of which the exciting coil on the testing
device is the primary and whose magnetic circuit is made partly
by the testing device and partly by the core of the machine under
test. As in any shortr-circuited transformer, an increased cur-
rent flows both in the primary and secondary coil and can be
detected by an ammeter in series with the device or by the heating

Fio. 176. — Method of using the device shown in Fii- 175.

that immediately takes place in the defective coil, or by the
attraction that the short-circuited coil has for a strip of sheet
iron. By passing the device slowly around the core and observ-
ing its behavior from point to point, short-circuits can readily be
detected. This refers particularly to short-circuits in individual
turns or in one complete coil. A short-circuit of a complete
pole-phase group is more readily located by a compass test, and a

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 169

short-circuit of an entire phase can be located by a ''balance
test."

The ''compass test" referred to in the preceding paragraph
consists in passing a compass slowly around the bore of the stator
from which the rotor has been removed and which has the wind-
ing excited by direct current of the value of about one-third the
full-load alternating current. The effect of this direct current is
to set up north and south poles alternately in the phase which is
excited; and as the compass is passed slowly around the bore its
needle reverses with the polarity, and by marking the polarity
plus and minus with chalk marks in the bore, the chalk marks
immediately indicate the correctness or faults in the winding.
If it is a two-phase machine, the direct current is put on each
phase separately and the check is made. For a three-phase star
winding cause the direct current to flow from each lead to the
star by making three observations, and mark the polarity only on
the groups from the lead to the star in each phase separately.
This can be readily understood by referring to Fig. 177 and 177a.
For the first observation put the direct-current plus lead on A and
the minus on the star connection, then pass the compass around the
bore and mark the polarity of the groups from A to the star
point with an arrow, the arrow pointing in the same direction as
the compass needle. For the second observation put the direct-
current plus lead on B and the minus lead on the star connection
and passing the compass around marking the polarity of the
groups from B to the star point. For the third observation put
the direct-current plus lead on C and the minus on the star, and
by means of the compass determine and mark the polarity of the
groups from C to the star point. If the three observations have
been made correctly, there will be a chalk arrow on each pole-
phase group of the winding, and if the winding is correctly con-
nected, these chalk arrows will alternate north and south, as
shown in the Fig. 177. In case of a short-circuit of a complete
pole-phase group the compass needle will not be deflected. If a
three-phase delta winding is being checked, open the delta con-
nection at one lead, as in Fig. 178, and 178a connect the direct-
current source in so that the current flows through the three
phases in series, and if the pole-phase groups be checked for
polarity, the arrows will reverse as just described for the star
winding.

The "balance test" referred to consists in checking each phase

CONNECTING INDUCTION MOTORS

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 171

CONNECTING INDUCTION MOTORS

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 173

of the winding separately with low-voltage alternating current,
say 20 per cent, of normal full voltage, and measuring the am-
peres to check the impedance roughly and see if it is the same in
all phases. The connections for a star-connected winding are
made, as in Fig. 179, so that the current can be measured in each
phase, with an ammeter. The low-voltage alternating-current
source is, in all cases, connected across one terminal. A, B, or C,
and the star as in the figure. The ammeter should read the
same in all three leads. For a delta-connected winding it is
necessary to open the delta connections at some point, as at A,
then test across each phase separately. This test is made on the
stator only and with the rotor removed.

Fourth and Fifth Faults: Reversal of one or more coils in a
group or group of coils. It happens that individual coils or
sometimes entire groups are connected in backward. If the
error is confined to one coil it does not usually show up on a
''balance test" and would not be found on a resistance test,
since the resistance would be the same no matter which way the
coil was connected. Such reversed coils or groups can be located
by means of the compass test described under "Short-Circuits."
If an individual coil is reversed, it will show a tendency to reverse
the compass needle when the needle is directly over that coil.
If an entire pole-phase group is reversed, the compass needle
will indicate the same direction of field on three successive groups,
as at Z, Fig. 180. Also if a coil is left out of circuit, or "dead,"
as listed under the tenth fault, the compass needle will indicate
an irregularity at the instant of passing over that particular coil.
By checking the three phases of a three-phase winding separately,
with a compass, as described under the second and third faults,
it is possible to check for the reversal of an entire phase.

Sixth Fault : This is the case where one coil too many or too
few is connected in a pole-phase group, as at A' and B', Fig. 180.
The best check on this is a visual inspection and count of the
"stubs" at the end of each group, and when the trouble is located
it is corrected by disconnecting, regrouping and reconnecting.

Seventh Fault: The reversal of an entire phase in a three-
phase winding usually manifests itself in a very pronounced man-
ner when the motor is run light. If the rotor turns over at all
it is probably at a speed very much less than normal and emits a
loud, growling noise and immediately becomes hot. This fault
may also be detected by the compass test, as described under

CONNECTING INDUCTION MOTORS

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 175

faults two and three. The arrows on the windings will point in
groups of three in opposite directions, as in Fig. 181. The remedy
when the defect is found is to open the star point and use the star
point on the defective phase, which is the B phase in Fig. 181, for
a lead and bringing the end that was a lead to the star, thus giv-
ing the connection. Fig. 177. In a two-phase winding there is no
trouble with reversed phase for the reason that if the direction
of rotation of the motor is wrong, the leads may be easily
reversed outside of the motor and the correct rotation secured.

Eighth Fault : Connection for wrong voltage. If a motor is
connected for a lower voltage than the circuit upon which it is
operating, the no-load current becomes excessive and may even
approach full-load value. There is a pronounced magnetic hum
and a vibration indicating that the field is very strong, which is
the case. On the other hand, if the motor is connected for a
higher voltage than that upon which it is being tried, the no-load
current is very small and the motor apparently ''pulls out" on
much less than its rated full load. If these faults are a matter of
half-voltage or double voltage, for example, they can usually be
detected without much trouble; but if the variation is less, this
becomes a more difficult matter and in the absence of any other
official data it sometimes becomes necessary to take a brake test
to determine what the trouble is. After the difficulty and its
extent have been determined, a reconnection of the groups can
usually be made which will give the proper operating conditions.
For example, if it is found that the winding is connected series-
star as in Fig. 177, and the motor is connected for 440 volts,
when it is to be operated on a 220-volt circuit the winding should
be changed to parallel star, as in Fig. 182, and the operation will
be normal.

Ninth Fault : The easiest way to detect a connection for the
wrong number of poles is to run the motor light and take the
speed with a tachometer or speed counter. When it is found that
the winding is connected for the wrong number of poles, the pos-
sibiUty of reconnecting can be determined by methods suggested
in Chap. X.

Tenth Fault: Open-circuits are manifest from the fact that
the motor will not start, but acts as if it were operating single-
phase. It is easy to determine, in a star-connected winding, in
which phase the open-circuit exists by connecting all phase leads
to the starting transformer and opening them one at a time to

CONNECTING INDUCTION MOTORS

LOCATINQ FAULTS IN INDUCTION MOTOR WINDINGS 177

178 CONNECTING INDUCTION MOTORS

see in which lead no current is flowing. In Fig. 183 assume that
the open is in phase C at X. Then if lead A is open, no current
will flow through the motor, since the path is from B to C and
is open at X. If the B lead is disconnected with A, and C con-
nected, no cxirrent can flow, since the C phase is still in circuit. If
C is disconnected with A and B lead connected in circuit, then
C, the defective phase, will be cut out of circuit and current will
flow in the A and B windings of the motor and it will act as if
operating single-phase, which will be indicated by the motor
emitting a humming sound. When the defective phase is located,
it is not always apparent just where the break is. A visual in-
spection may fail to show the break on account of tape over the
defect or for some other reason. If this point cannot be located
by inspection, a simple method of finding it electrically is indi-
cated by referring to Fig. 183. A test voltage somewhat lower
than normal or whatever is convenient is then applied to B and C,
and a suitable voltmeter is used to measure the voltage between
B and various points along the C phase, as, for example, 1, 2, and
3, which are chosen at random along the "studs," or coil-to-coil
connections, or on the group cross-connections, as in the figure.
With the condition as shown in Fig. 183, assume that 110 volts
has been applied to the B and C terminals of the winding, as
shown. If one lead from the voltmeter be attached to B and the
other lead touched successively to C and 1, 2 and 3, the voltmeter
will read 110 volts between B and C, B and 1, B and 2, and zero
volts between B and 3, since the C phase is open at X. The con-
clusion is immediately and properly reached that the break is
between 2 and 3 and with the inspection narrowed down to this
small section of the winding the break is usually apparent. How-
ever, should the break not be discovered by inspection, points can
be selected with finer steps between 2 and 3 and voltage readings
taken until the defect is narrowed to the exact coil or piece of
cross-connection where it exists.

In the case of a delta connection one of the simplest ways to
detect an open-circuit would be to open the connection at one
terminal of the delta, such as A in Fig. 178, and connect a test
circuit across the open. If the winding is open no current will
flow. The phase with the open in may be located by testing
across each phase separately. If a lamp is used to make the test,
the defective phase will be indicated by failure of the lamp to
light. After the faulty phase has been located, the location of

LOCATINO FAULTS IN INDUCTION MOTOR WINDINGS 179

180 CONNECTING INDUCTION MOTORS

the defect can be detennined as for the star connection, Fig. 183.
There are all manaere of parallel-star and other groupings in
which it is difficult to locate an open-circuit, since an open in one
parallel group does not open the circuit through the phase, but
in only one of the parallel groups. For example, in Fig. 184 an
open in phase C at X will not open the phase between terminals
B and C, but only through C". Therefore, to detect the open
group it will be necessary to break the winding up into its parallel
groups and test each group separately. The defective phase
could be detected by the balance test as previously described.

Fio. 184. Fia. 185.

Fta. 184 and 185. — IiocBtiuE open circuits in parallel delta coanection.

Firet, open the delta connection, for example, at A, Fig. 185,
then apply the low-voltage alternating current between points
A and B and measure the current with an ammeter, test between
A and B, B and C and between C and At- The phase with the
open circuit, which in this case is C, will show a lower reading
than the other two phases, after which all that is necessary is
to break the phase up into its parallel groups and test the defect-
ive group for opens, as explained in Fig, 183.

Usual Order of Locating Defects.

These are the defects that commonly occur and the usual
method of locating ttem. In checking for these defects the order
usually observed is as follows : After the winder has completed
the connection of the entire winding, his work is checked, pref-
erably by a second winder, against the winding diagram speci-
fied for that particular job. The coils per group are counted and
a visual inspection made for short-circuits, open circuits and

LOCATING FAULTS IN INDUCTION MOTOR WINDINGS 181

reversed coils, groups or phases. A balance test is made on the
stator alone with low voltage to see if, roughly, the same current
flows in the various phases. A high-voltage test is then made on
the insulation to insure that the coils are not grounded on the
iron core, or that there is no short-circuit between the conductors
of the different phases. If everything is satisfactory up to this
point, the rotor is then assembled in the stator and the machine
prepared for a running test. The resistance of the winding is
measured on all phases, and if alike, the machine is passed for
running test without load. Sufficient voltage is applied to start
the rotor, and if it comes up to speed quickly without apparent
distress or irregularity of any kind, the speed is checked, to verify
whether the winding has the proper number of poles. The tem-
perature of the winding is then tested with the hand, passing com-
pletely around the machine and using care that the rotating
member and its parts do not strike the observer. If neither
general heating nor hot spots are observed, the voltage is raised
to normal and the no-load current in all phases and the total
watts are read. If these values check with the previous tests on
similar machines or with calculations, the windings are considered
to be correctly connected. If the motor does not readily come
up to speed or the phases do not balance or there are signs of
unequal heating in the winding or other distress, the rotor is
removed and the connections again checked. If the error is
still not apparent and a source of direct current is available, the
compass test may be applied. Having exhausted this resource
without avail, the problem is one that can be solved only by
some expedient at the command of an experienced designing
engineer, but such appeals are very seldom required, as the
trouble usually appears from the simple tests described.

CHAPTER XII

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE

It is felt by the author that this book is not quite complete
without giving some idea of how a winding may be figured for
a given core without reference to any winding that might pre-
viously have been on the core, but simply with a view to getting
a given horsepower out of it at a given voltage, speed, phase and
frequency. Obviously in a chapter with the limited space as-
signed to this one, there cannot be attempted a complete treatise
on the design of induction motors with detailed methods of cal-
culation which will make him who reads a finished designer.
There are many excellent books on this subject and a few which
are so written as to be useful to the practical man in his work,
If the foregoing chapters have aroused suflScient interest in the
general matter of design, some of these longer works can be
consulted for an exhaustive treatment of the entire subject.
The author feels, however, after personal knowledge of many
cases of windings roughly estimated by practical winders which
performed satisfactorily, that an approximate idea of what is
required in a winding to do a certain job can be had without
involving so great a mass of calculation that errors creep in
through the volume of fig\u*es alone, or without an advanced
theoretical training in all the phenomena of alternating cur-
rents which are involved in the operation of induction motors.
It should be understood that with the short cut methods and
the abbreviated consideration herewith presented, it is not in-
tended or expected that anyone will produce finished and ele-
gant designs; but it is believed that in an emergency, when time
is of the essence of the consideration and some chances can cheer-
fully be taken, the niethod presented will give an approximation
to the correct winding which will be satisfactorily operative in
a high percentage of cases. If the writer is checked by his
peers, the designing engineers, he should Uke to have it under-
stood thal^ he is not attempting to tell all the experience he has
accumulated nor to elaborate a new system of design calculation,

182

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 183

but he is attempting to tell our friends^ whose concern it is to
make motors run and keep them running, what they may do to
help themselves when all these designing engineers are a thousand
miles away and the job has to be running next week. Therefore
in this discussion while reference is made to all the points consid-
ered by the designing engineer only those points are covered in
detail which it is felt are the most vital and these are handled in
as elementary a manner as possible.

Effect of the Winding on the Performance.

The performance of an induction motor is made up of a number
of different things. It must be able to start its load without
drawing from the supply circuit an abnormal amount of current.
It must be able to carry its load, as long as it runs, with a reason-
able temperature rise and at a reasonable power factor.

It must have a good efficiency, that is to say it must not draw
from the supply circuit an amount of energy greatly in excess of
that represented by the work being done. It must have as much
mechanical clearance as possible between the stationary and
rotating members so as to increase the life of the bearings. It
must have a momentary overload capacity of from one and one
half to two times normal full load torque without "pulling out"
or stalling. And it must have all these things without an appreci-
able amount of noise due to magnetism or windage. Some of
these characteristics may be favored at the expense of others as,
for example, it is possible to get a high power factor at the
expense of having a very small clearance between stator and
rotor, or it is possible to have a high efficiency at a cost of low
starting torque and high starting current. For this reason in
selling motors the selling talk is often confined to those points
which are high in that particular design and the corresponding
points of disadvantage are dwelt upon lightly; but to get a true
comparison of the relative merits of two competitive ratings or
designs all these points must be considered and given their due
weight in view of the service in which it is intended to use the
motor.

It is understood that all these characteristics are affected in
various ways by the different features of the design, that is to
say by the axial length of the iron core as compared to the rotor
diameter, or by the number of slots, or the kind and thickness of
the laminated steel used and matters of this kind; but the thing

184 CONNECTING INDUCTION MOTORS

which has the greatest effect and which can most easily be modi-
fied is the number of turns in the stator or primary winding. In
figuring this detail, which is of prime importance, it is therefore
wise to have at all times a mental picture of what happens to
each characteristic when the cross-section of the conductors or
the number of turns in the primary winding is changed. In
order to summarize this quickly the various characteristics are
listed in order and considered separately. The main consid-
erations in the operation of any induction motor are — starting
torque, starting current, air gap or clearance, power factor, effici-
ency, heating, maximum torque, or pull out, noise, and mechani-
cal vibration.

If there were two motors which were exact duplicates in ma-
terials and all mechanical dimensions, except that one motor had
more turns in the winding than the other, when comparing the
characteristics just named, the motor having the most turns
would have a lower starting torque and a lower starting current.
It would probably have a higher power factor. It might have a
higher or a lower efficiency for the reason that the copper loss
would be higher and the iron loss lower and whichever one pre-
ponderated would determine whether the efficiency was higher
or lower, in other words, whether the copper loss increased faster
than the iron loss decreased and vice versa. Similarly the heat-
ing would be more or less, depending on the sum of the losses. In
general this motor would be a little more quiet and have less
tendency toward mechanical vibration.

On the other hand, considering the motor with the fewer num-
ber of turns, it will have relatively, a higher starting torque and a
higher starting current. It will probably have a lower power
factor. It will have a higher or lower efficiency depending on the
proportion of iron to copper loss, as explained in the preceding
paragraph; similarly, the heating will vary with the amoimt of
total losses. This motor would have a tendency to be noisier and
have more mechanical vibration.

It will be noted that these changes are the same as would occur
if the voltage were raised or lowered on any motor. Increasing
the number of turns in a winding has the same effect as lowering
the voltage and decreasing the number of turns has the same
effect as raising the voltage on the winding. This can be seen
from Pig. 186 where three windings are shown across 100 volts in
parallel. Winding number 1 has eight turns in series and there

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 185

are 12-J^ volts effective on each turn. Winding No, 2 has ten turns
and there are 10 volts effective on each turn; similarly winding
No. 3 has 12 turns and the effective voltage on each turn is 8 J-^
volts. Since the performance of the motor as regards torque
and other characteristics is proportional to the voltage per turn
in the winding, the No. 1 or 8 turn winding will operate as if on
over-voltage and the No. 3 or 12 turn winding will operate as if on
undervoltage. Expressing this another way, if we consider the
No . 2 winding as the normal winding for 100 volts the No. 1 winding
on 100 volts would operate and give the same result as the No. 2
winding if there were 125 volts applied to the No. 2 winding and
similarly the No. 3 winding on 100 volts would operate and give
the same result as would the No. 2 winding if the No. 2 winding had

Fig. 186. — The voltage per turn or "transformer volts" on a winding.

83}'i volts applied to it. From this it may be seen that perhaps
the most essential thing to determine in figuring a winding is the
proper number of turns in series in the stator winding which will
be put across the line voltage. Another vital consideration is the
cross section of the copper wire or conductor used in the winding,
necessary to carry the amperes required to develop the desired
horsepower. In order to get an idea of all the points which have
to be considered in making the complete design of an induction
motor a brief enumeration is here given of the different items
considered by the designing engineer with a brief statement of
how and why each is taken in to account.

1. Diameter and length of laminated iron core necessary to get
the horsepower desired at the given speed and voltage.

2. Magnetic flux or field required to generate the line voltage.

3. Number of turns of wire in series in the stator winding
which, when cut by the rotating field, will generate the line volt-
age.

4. Cross-section of stator conductor to carry the current re-
quired to develop desired horsepower at the power factor and
efficiency that the design will probably give.

186 CONNECTING INDUCTION MOTORS

5. Number and size of stator slots, width and depth, to ac-
commodate winding (3) and (4) when insulated for the required
voltage.

6. Magnetic densities in the stator teeth, core, rotor teeth, core
and air gap due to magnetic field (2).

7. Magnetizing or no load current required to set up the field
mentioned in (2) with the number of turns in (3) with lengths
of path required by (1) and (5).

8. Iron loss due to densities (6J.

9. Iron loss due to primary slot openings.

10. Number and size of slots in rotor.

11. Is rotor winding squirrel cage or phase wound.

12. Figure rotor volts and amps, if phase wound.

13. Figure "SUp" or rotor copper loss.

14. Figure stator copper loss.

15. Estimate bearing friction and windage.

16. Figure leakage reactance for stator and rotor slots and coil
ends, also zigzag, and belt, or differential leakage.

17. From (7) and (16) figure power factor.

18. From (13) and (16) figure starting and maximum torque.

19. From output and (8), (9), (13), (14) and (15) figure
efficiency.

Since the consideration for the moment assumes an old core
which already exists, many of these things are already deter-
mined and some can be assumed. The facts that require check-
ing in determining a new winding for new conditions of speed or
horsepower or voltage or phase or frequency, and which may be
considered as fundamental are:

1. Is the core large enough to wind for the horsepower and
speed that is desired?

2. Is there cross-section of iron enough below the slots to carry
the magnetic field that is needed in the air gap to do the work
desired?

3. How many turns are required in the stator winding?

4. What should be the cross-section or size of the wire or con-
ductor used in the stator winding?

5. What should be the cross-section of the bars in the rotor and
what should be the cross-section of the resistance rings at the
ends of the rotor bars, assuming a squirrel-Cage rotor winding?

6. Will the rotor diameter permit operating at the proposed
r.p.m.?

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 187

These are comparatively few questions that can be readily
answered and broad general limits laid down against which the
individual case can be checked. This will assume some points
but in general if the winding falls within these Umits the motor
will be sufficiently operative to fill the immediate requirement.

Proceeding at once to the determination of these quantities
(1) is answered by checking the so-called "output coefficient,"
that is to say, the horsepower of which a given core is capable at
a given r.p.m. This may be expressed by the formula:

Hp. = KXD^XLX r.p.m.

Where K is the so called "output coefficient" which varies
somewhat with the size and speed of the motor and the operating
voltage, D = diameter of the stator bore in inches, L = axial
length of the laminated iron core in inches measured parallel
to the shaft and r.p.m. = revolutions per minute. Suitable values
for this output coefficient may be found in several textbooks but
perhaps the most convenient reference is to the Standard Hand-
book published by McGraw-Hill Book Co., Inc. The table given
in Section 7 paragraph 246 of the fourth edition is reproduced
herewith.

Table X. — Output Coefficient Values

Pole pitch
in in<uies

Values of output coefficient, K, when output is expressed in horsepower,
linear dimensions in inches, and speed in rev. per min.

4 pole

8 pole

12 pole

16 pole

20 pole

24 pole

0.000025

0.0000320

0.000039

0.0000436

0.0000482

0.0000505

0.0000205
0.0000331
0.0000394
0.0000438
0.0000484

0.0000263
0.0000331
0.0000394
0.0000440
0.0000486

0.0000254
0.0000331
0.0000394
0.0000443

0.0000246

7
10
12
16
20

0.0000222
0.0000330
0.0000392
0.0000434
0.0000454

0.0000331
0.0000394
0.0000443

The following example is given to illustrate the use of this

table. A stator core having a bore of 17 inches and an axial

length of 6 inches was brought into a repair shop and a request

made to put in a winding for 50 hp. at about 730 r.p.m. on 25

cycles. To determine whether it was phjrsically possible

the following calculation was made. Pole pitch in inches =

Diameter XS.U 17X3.14 -^ ^ rnu ^n ^ ^u- •

jTf — I ^ — r~ = A = 13.4. The nearest figure to this in

Number of poles 4 ^

188 CONNECTING INDUCTION MOTORS

the table above is 12 inches and opposite 12 inches under 4 poles
is the figure .0000392. Then the horsepower that this core will
develop at 730 r.p.m. is given by the equation:

h.p. = .0000392 X 17« X 6 X 730 = 49.6

Hence the conclusion is reached that this core would wind
satisfactorily for 50 hp. at 730 r.p.m. since the output coefficient
for 13.4 inches would be a Uttle greater than for 12 inches in
the table which was used in the trial calculation.

The second question as to whether there is sufficient cross
section of iron in the core between the bottom of the slots and the

NORTH

Sfcitor
laminaHons

Fig. 187. — Cross-section of two-pole motor showing distribution of magnetic field.

outside periphery can be determined by figuring the actual
amount of magnetic flux per pole that must be set up to do the
required work. This can be readily understood by a reference
to Figs. 187 and 188, which illustrate the manner in which the
magnetic flux is divided into as many groups or circuits as
the motor has poles. In passing from the stator to the rotor
through the teeth, then behind the rotor slots and back to the
stator and again behind the stator slots to the starting point, it
will be noted that there must be enough iron behind the slots to
to carry the flux or the motor will overheat. Referring again to
Fig. 188 it is evident that the more poles the motor has, the less
iron is required in the core behind the slots of both stator and

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 189

rotor. Therefore, the correct way to determine this point is to
figure the amount of magnetic flux per pole and figure the cross
section of the core behind the slots and see that there are not
more than 80,000 to 100,000 magnetic lines per square inch and
if so, and other conditions are proper, the core should be satis-
factory for the assumed conditions of the winding. Here we are
confronted with a peculiar problem which often faces the de-
signer, which is, that he must know part of his answer before he

MAQNETIC
FIELD UHES
OR FLUX

STATOR
PUNCHING OR
LAMINATION

FiQ. 188. — Core section, showing effect on magnetic field by changing number

of poles.

can solve the problem and find the rest of it. In other words
the amount of magnetic flux in the core will depend on the num-
ber of turns of wire in the coils and the problem which he is
trying to solve is how many turns should be put in the coils.
So it is apparent that he must either guess the number of turns
required and find out if the amount of magnetic flux is reasonable
or else he must figure how much flux can be carried in the core he
is using and from that figure check back and see how many turns
are required in the winding to give this magnetic result. When
the number of turns is settled and the cross-section of the copper

190 CONNECTING INDUCTION MOTORS

is figured for the desired horse power and voltage, there is at
once a question whether the slots will accommodate that many
conductors of that cross-section after taking room enough to
allow for the insulation required on the coil at that particular
voltage. If the result is unfavorable and the copper so figured
will not go in the slot at all, it means that the motor is not good
for that much horsepower and the desired rating will have to be
reduced. The number of turns cannot readily be reduced as
that would mean more magnetic flux and the core back of the
slots is already figured for 80,000 to 100,000 lines per square inch
which is all it will stand. The reason why the number of con-
ductors and the magnetic flux are tied in together in this way is
because the conductors which are in series, when cut by the
rotating magnetic field must generate or produce practically line
voltage. This fact has been referred to many times in previous
chapters.

The formula for the field flux per pole or per magnetic circuit is
45 000,000 X Volts per phase

ux p p — Qy^^^y^ Conductors per phase X KiX K%

where

Volts per phase = line volts in the case of a two-phase winding

or a delta-connected three-phase winding

and = — :r-j^ — in the case of a star-connected

three-phase winding.
Cydes = the frequency of the supply circuit as

expressed in cycles, that is, 60 or 25 or
whatever the circuit may be.

Conductors per phase = number of wires per slot which are
in series X number of slots -^ number of phases. ^

Ki is a so-called "distribution factor" and is .905 for two-phase
and .955 for three-phase.

Kt is the so-called "chord factor'' and depends on the pitch or
throw of the coil. Its technical value is the sine of one-half
of the electrical angle spanned by the coil.

A practical method of getting this factor which is close enough
for general purposes is to use the expression

Chord factor = Ki =

Number of slots per poley'-2{N umber of slots dropped)

(Number of slots per poUy

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 191

or taking a concrete example: suppose there is a 72 slot motor
wound for six poles and having a coil throw of 1 and 8, what is
the chord factor or K±, which is under discussion? Since there
are 72 slots and six poles there are 12 slots per pole and full pitch
would be slots 1 and 13. Winding 1 and S drops 5 slots and
thus our formula above becomes the square root of twelve squared
minus two times five squared divided by twelve squared, or
mathematically

1 12* - 2(5)' _ j lM'- 50 _ / 94
\ 12* V 144 ^144 '

.80

To illustrate how this flux formula is applied, assume a core
having dimensions as shown in Fig. ISd which it is desired to

Fio. 189,— Stator oore in frame.

wind for 50 h.p., 25 cycles, 3 phase, 4 poles, 440 volts and 730
r.p.m. full load speed. The outside diameter of the stator
laminations = 25^ in., the inside bore D of the stator laminations
= 17 in. The axial length of the core L = 6^ in. but it con-
tains two ventilating ducts each ^ in. wide so that the net iron
core length = 6 in. The primary slots are 1.7 in. deep, so that
the dimension C or the radial depth of the latninations below the
slots = (25H - 17) -^ 2 - 1.7 = 2.55 in. and the actual cross-
section of the core below slots through which all of the flux per
Note. — Do not figure the new winding from the core density alone, but
check the density in the teeth also, as cautioned on page 194, since the
density in the teeth is frequently the limiting factor.

192 CONNECTING INDUCTION MOTORS

pole must pass is equal to C X L or id this case 2.55 X 6 =
15.3 square inches. A reference to Fig. 188 indicate that
when the Sux per pole passes from the rotor into the stator, it
divides and half goes one way and half the other way. Hence
in the present case the total available cross section of u-on to
cany the flux per pole is not 15.3 square inch^, but twice that
or 30.6 square inches. As stated above 80,000 Unas per square
inch is a permissible density, so that a total flux per pole of 30.6
X 80,000 can be used or 2,448,000 lines. The only other factor
missing from the flux per pole formula which is necessary to give

Fio. 189a.— Section of sUtor core,

at once the total number of conductors per phase is the chord
factor. This depends upon the slots in which the two sides of
any coil are placed. In the core which is under consideration
there are 48 slots and since a 4-pole winding is under calculation,
the full pitch for the winding would be slots 1 and 13. Full
pitch is too long mechanically and some space endwise can be
saved and some copper as well by chording it a few slots, so for
illustration it is assumed that the coils lie in slots 1 and 10.
Using the approximate formula given for chord factor above,
this factor becomes

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 193

Expressing the flux per pole formula in terms of conductors
per phase, this expression follows:

Conductors per phase =

45,000,000 X volts per phase

cycles X flux per pole X chord factor X dist. fact.

Remembering that the distribution factor for 3 phase equals
.955 and substituting the values calculated above, and assuming
a delta connected winding,

Conductors per pha^e =

45,000 000 X 440 ^

25 X 2,448,000 X .93 X .955

Since there are 3 phases, there will be required a total number of
conductors 3 X 362 = 1086 and since there are 48 slots there
will be 1086 -r- 48 = 22.6 conductors per slot. What a designer
would do in this case would be to either wind 22 conductors per
slot and throw the coil 1 and 11 instead of 1 and 10 or else wind
it 24 per slot and throw the coil 1 and 9, either of which would
be a good winding without much difference between the two.

The reason for this is that there are 2 coils per slot and hence
with 22 wires per slot there would be 11 wires in each coil. As
the wires are arranged in 2 or 3 layers, 11 would not be exactly-
divisible by either 2 or 3, hence, in the case of a two layer coil
there would be one layer of 5 wires and one layer of 6 wires side
by side, or in the case of a 3 layer coil there would be 2 layers of
4 wires each and one layer of 3 wires. Either of these arrange-
ments would be wasteful of space and hence it would be prefer-
able to have 12 wires per coil which is evenly divisible by either
2 or 3. If the coil is wound in slots 1 and 11 the chord factor is
.97 and if it is wound in 1 and 9 the chord factor is .866. Hence,
the real, effective number of wires in one case is 22 X .97 =
21.3 and in the other case is 24 X .866 = 20.78 which would
give very close to the same result so far as torques are concerned.

In this calculation it was noted that the figure 440 was used
for the voltage. This assumed a series delta connection. If,
for example it had been desired to connect the winding in two
parallel delta for the same voltage, there would have been re-
qurired twice as many conductors per phase and each conductor
would have had one half the cross section, since there would be
two paths in parallel for the current instead of one in series.

194 CONNECTING INDUCTION MOTORS

Similarly, if the winding was to have been connected in series

star instead of series delta the voltage used in the equation would.

"\ have been 440 -^ 1.73 = 254 instead of 440. Hence, in the re-

suit, the conductors required per phase would have beeuys^

= 209 instead of 362. It is well to remember this fact: that
with a star connection only about one half as many turns are
required in series as with a delta connection. It sometimes
makes an easier coil to wind and a coil which is mechanically
stiffer and stronger, if less turns of a larger size wire can be used.
This is one of the principal reasons why a star connection is
used much more frequently than a delta connection.

Having found the number of conductors per slot from the above
equation there would seem to be nothing more to do but figure
the required cross section of the conductor to carry the full load
current, and the space required for insulation and see if the coil
so figured and insulated would go into the slot. There is a check
calculation that should be made first to see how hard the iron
is working in the stator teeth. The calculation that was made
concerned itself only with the density of the magnetic flux in
the stator core behind the slots and was checked first to make
sure the required field had room to get through the core. -How-
ever, before accepting this figure the teeth should be checked also
to see how hard they are working. This is a simple check from
the figures already employed. The diameter of the stator bore
of the core under calculation is 17 in- The depth of the slots is
1.7 in., therefore the diameter to the middle of the slot = 18.7 in.

and the slot pitch at this point or the dimension P from Fig. 189a,

iQ 7 V ^ 14
C = ^ — = 1.22 in. The slot width W = .65 in. Hence

the tooth width P—TT = 1.22 — .65 = .57 in. and since the net
core length L = 6 in., the cross section of one tooth at its mid-
section = 6 X .57 = 3.42 square inches. There are 48 teeth
total and 4 poles, hence there are 12 teeth per pole through
which the magnetic flux of one pole may pass. Therefore, the
total iron cross section of 12 teeth = 12 X 3.42= 41.04 square
inches. It was calculated above that there were 2,448,000
magnetic lines per pole and it would seem that all that was ne-
cessary to check the tooth density would be to divide this figure
by 41.04. This is not the case as in the core for the reason that
all the teeth do not carry the flux equally but those in the center

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 195

of a pole at a given section carry a maximum and those half way
between poles carry nothing so that in order to take care of the

maximum^ the result above is divided by .636. Hence in the prob-

2 448 000
lem in hand the maximum density in the teeth is 41 04. y ttoa =

94,000 lines per square inch. As a matter of fact it is actually
about 96,000 lines since the 2,448,000 was figured with 362 con-
ductors per phase and a throw of one and ten, whereas there are
now 24 X 48 -7- 3 = 384 conductors per phase, but the throw is
only one and nine and substituting back in the original flux
equation,

Flux per pole =

45,000,000 X 440 o.onnnnr

25 X 384 X .955 X .866 = 2,480,000 hnes.

This value namely, 96,000 for density in the teeth is perfectly
permissible. It should not be allowed to exceed, say, 130,000 for
25 cycle machines, nor about 110,000 for 60 cycle machines.

Figuring the cross section of the stator conductor. — Having
determined the number of conductors required in the slot, that
is 24, the next step is to figure the. necessary size of the con-
ductor or cross section and see if the coils will go in the slot after
being properly insulated. In order to figure this it is necessary
to know what the full load current of the motor will be. The
formula for finding the full load current of a two phase motor is.

Full load current per lead =

. Horsepowe r X 746
2 X volts per phase X efficiency X power factor
Where the efiiciency and the power factor are the full load
values and are expressed in hundredths, that is with a decimal
point in front of each. For example 90 per cent, is written .90
and 85 per cent, power factor is written. 85, etc. For a three
phase motor the formula changes to.

Full load current per lead =

Horsepower X 746
1.73 X volts per phase X effi^ency X power factor

which it will be noted is similar to the two phase formula except
1.73 is used in the denominator instead of 2. One thing must
be specially noted about the three phase and that is that the full
load current so found is the current in the outside motor lead or

196 CONNECTING INDUCTION MOTORS

the current drawn from the line. If the motor is star connected
inside this same current flows in the motor winding itself and hence
in the conductors in the slots, unless the winding is in 2 or more
parallels in which case of course, the lead or line current splits
up into as many parts as there are parallel paths. On the other
hand if the windings inside th^ motor are delta connected as they
are in the case we are considering, the current in the windings
will be less than the current coming in the lead as figured above
and it is necessary to divide by 1.73 a second time to find out
what the current is, which must actually be provided for in the
coils themselves.

Preparing to apply the above formula, at once the problem
arises, What is the full load efficiency and the full load power
factor of the motor for which this winding is being figured?
Of course there is a wide variation in these figures between small
and large motors, and between high and low speeds, and between
25 and 60 cycles and these variations are shown as well as may
be in the Standard Hand Book referred to in the foregoing and
other text books. For the purpose here, which as has been stated,
is somewhat rough and ready, an approximation must be assumed.
The handiest approximation the author has ever used and one
that has given good results is to assume that a three phase, 550
volt motor, draws from the line in each lead just about one am-
pere per horsepower. This is very closely true in most lines of
commercial motors over a wide range of sizes and speeds. Then
if the motor in question is not 3 phase or if it is not 550 volts
the current can readily be changed to other voltages. For ex-
ample assume a 40 hp. motor. Then at 550 volts 3 phase it
follows that its full load current per lead is 40 amperes, at 440

550
volts its full load current Would be Tjn X 40 = 50 amperes and

550
at 220 volts it would be ^on X 40 = 100 amperes and at 110 volts

550
it would be \rr^ X 40 = 200 amperes and so on. Similarly to

1 73
convert to two phase multipy these values by ^t^q = '86 because

the current of any two phase motor is always that much less than
the corresponding three phase.

Referring again to the formula above for the full load current
of a 3 phase motor, to give one ampere per horsepower at 550
volts would mean that the product of the efficiency and power

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 197

factor would be .785. This might be assumed to be 89 per cent,
efficiency and 88 per cent, power factor or any other combination
whose product gave .785. At all events this is an average value
and sufficiently near correct for the present purpose.

Since the present calculation assumes a 50 hp. 3 phase
440 volt rating it may be assumed that the full load current per

lead is ~~aa7) — ~ 62.5 amperes. Since the winding is to be

delta connected the current in the coils themselves will be

62.5

YYo = 36.1 amperes. There is no fixed rule that can be followed

for the cross section of copper required in the coil per ampere.
It may be as low as 400 circular mils in some cases and may have
to be as high as 1,000 circular mils in others. Slow speed motors
and higher voltages (where there is more insulation to pass the
heat through) require larger copper than do higher speeds and
lower voltages. In the present case and in most average cases
a figure of 750 circular mils can be used. For the present case
then the circular mils required would be 36.1 X 750 = 27,075
circular mils. Looking in a Brown and Sharpe wire table the
nearest size to this is No. 6 round wire which shows 26,250 circular
mils. This is near enough and it is selected. The problem now
is, will 24 No. 6 wires go in a slot .65 in. wide by 1.70 in. deep
and allow for the retaining wedge at the top and the proper insu-
lation for 440 volts? To answer this it is necessary to know some-
thing about insulation requirements. As there are commonly
only two voltage classes met with, it can be stated that voltages
up to and including 550 volts wiU require a space in the width of
the slot of about .1 of an inch and in the depth of the slot of about
.15 inches and voltages above 550 up to and including 2,200 will
require about .16 inches in width and .26 inches in depth. These
figures in depth do not include any retaining wedges or so called
" top sticks, " but must be allowed in addition to the wires between
the bottom of the wedge, and the bottom of the slot. In the
case just being figured the wires will evidently go in better 3X8
than any other way. The diameter of No. 6 round wire over double
cotton covering is .178 inches. Three wires in width would be
3 X .178 = .534 in. adding .1 in. for insulation gives .534 -f- .1 =
.634 which goes very well in the width of the slot which is .65 in.
In depth 8 wires would require 8 X .178 inches = 1.424. The
allowance for insulation is .150 in. and the usual coil retaining

198 CONNECTING INDUCTION MOTORS

wedge requires .125 in. so that the total required depth will be
1.424 + .150 + .125 = 1.699 in. which just exactly fills the avail-
able depth. It should be under stood that the 24 wires are not
3 X 8 in one coil but 3 X 4 in each coil and two coils in the slot
according to the usual practice. If the wires had not fitted in
the slot as shown it would have been necessary to choose a wire
small enough to go in the space and then by trial after the winding
was complete find out how many horsepower the winding would
carry without over heating. If it were not possible to get 50
horsepower it would probably develop 45 hp. without trouble
if the output coefficient checked to 50 as shown in the beginning
of this chapter.

With regard to the rotor winding if it is of the wound rotor
type the number of wires per slot can. be made any number
that is convenient, provided the total weight of copper in the rotor
winding is made approximately 80 per cent, to 85 per cent, of
that in the complete stator winding.

Voltage Between Collector Rings. — In the case of a wound
rotor motor it is often useful to know the voltage at stand still
between the rotor collector rings in order to determine how much
resistance should be used in the starting or speed regulating
controller. This may be determined very closely from the
formula:

Volts between collector rings = j^ .. Trr v^ tz

Ax X It 1 X A3

Where Ei = line voltage applied to the stator

Wi = number of conductors in series per phase in the

stator
W2 = number of conductors in series per phase in the

rotor
Ki = Hi stator winding is two phase or three phase delta
Ki = 1.73 if stator winding is three phase star
jfiTa = 1 if rotor is connected delta
K2 = 1.73 if rotor is connected star
Ki = chord factor of the stator coils as explained in

Chapter IV

The number of conductors in series per phase in either stator
or rotor is equal to the total number of slots multipUed by the
number of wires in each slot, divided by the number of phases
and divided by the number of parallels in which the winding
diagram shows the winding to be connected.

HOW TO FIGURE A NEW WINDING FOR AN OLD CORE 199

For example, what is the voltage between collector rings on
a wound rotor motor with the following data? The line voltage
is 220. There are 72 slots in the stator and 10 wires per slot.
The stator winding is three phase, two parallel star, 6 pole and
the coil throw is slots 1 and 9. There are 54 slots in the rotor,
two conductors per slot and the rotor winding is connected
series star.

Setting down the data for use in the formula given above

El = 220, Wi = ^3^^" = 120, TF2 = ^^^ = 36, Ki =

1.73, K2 = 1.73, Kz = primary chord factor = sine of 60 deg. =
.866, because '^^ = 12 slots = 180 deg. and one slot = 15 deg.
Hence, a throw of 1 and 9 spans 8 slots or 8 X 15 = 120 deg.
and the chord factor = the sine of one-half the angle spanned
by the coil = J^ X 120 deg. = 60 deg. = .866. Therefore, voUs
between collector rings =

E1XW2X K2 _ 220 X 36 X 1.73
KiXWiXKz~ 1.73 X 120 X .866 " ^^ *'^^^^-

If phase wound the coils must, of course, be connected for the
same number of poles as the stator. If there should be an old
winding on the rotor for a different number of poles it may be
possible to reconnect it for the number desired, but as rotor wind-
ings are nearly always of the "wave" type or something of the
same order it is usually impossible to reconnect for any other
number of poles.

If the rotor winding is squirrel cage the number of bars and
their cross section is probably fixed. The cross section of the
end rings if of rolled or drawn copper should be so chosen that
the weight of bars plus rings is about. 75 per cent, to 80 per cent,
of the total weight of the stator coils. If the rings are cast copper
or cast brass it should be remembered that a larger cross section
will be required since the conductivity of the best cast copper
is only 80 per cent, to 85 per cent, of the conductivity of rolled
copper and cast brass is as low as 18 per cent, to 25 per cent, of
the conductivity of drawn or rolled copper. This would mean
that a ring of cast brass would have to be 4 to 5 times the cross
section of the corresponding rolled copper ring to carry the same
current. It should also be remembered that a two pole motor
would have proportionately the heaviest ring on the squirrel
cage, a four pole next, then a six and so on, and that when 10 poles

200 CONNECTING INDUCTION MOTORS

or 12 poles are reached the ring would probably be no larger in
cross section than would be required for mechanical strength and
construction.

Such in its briefest form is the simplest calculation that can be
made which it is safe to make in the hope of getting the desired
result. It will be noted that no attention has been paid to cal-
culating the leakage reactance, nor the no load current, nor the
starting and maximum torques, nor the circle diagram nor any
of the refinements which the designing engineer commonly
employs; and yet if care is used in employing the checks that are
made the experimenter should be rewarded with reasonable
results.

To sum up, the available core is first checked by the output
coefiicient to see if it will develop the horsepower at the desired
speed. Next a check is made to see how much magnetic field
can be handled in the core and teeth. Then the proper number
of conductors is chosen to generate the line voltage when acted
upon by the permissible magnetic field. These conductors are
then made of the proper size to carry the working current and
insulated for the working voltage and fitted in the slots. This is
all that is attempted and it is assumed that if these conditions
are met, all the other conditions of operation will fall reasonably
in line or can be adjusted after trial without too much change to
meet the desired requirements.

Naturally, such broad assumptions may not result in a design
of finished nicety, but they may sometimes give quick results
where results must be had quickly or not at all.

CHAPTER XIII
STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES

The form of diagram which is most often used in connecting
induction motor windings is the so-called " group *' diagram so
often illustrated in the foregoing chapters where the coils are
''stubbed" or grouped into pole-phase groups and then cross
connected to form magnetic poles. This form of diagram is
practically universally used for stators with open slots and be-
cause it is so often employed, it is considered desirable to give
in this chapter a series of diagrams covering all possible combina-
tions both two and three phase, star and delta, from two to
fourteen poles.

To attempt to show "developed" windings, that is a picture
of the actual coils rolled out flat for all possible numbers of poles,
phases, slots, coils per slot, etc. would require several hundred
diagrams even for full pitch windings and with the slots always
an integral multiple of the phases times the poles, and if to this is
added the possibilities of chording and using a total number of
slots not an even multiple of the phases time the poles, the num-
ber of pictures required to show all the connections would run
into thousands. However, by the relatively simple scheme of
considering the group of coils which forms one pole-phase group
as a unit, the possible number of combinations becomes greatly
limited, and as shown by the following diagrams all the combina-
tions from two to fourteen poles can be shown by means of
diagrams shown in Figs. 190 to 270 inclusive.

From the nature of the diagrams here given it will be seen that
they are not dependent on the total number of slots in the ma-
chine, nor upon the number of coils per group, nor upon the throw
or pitch of the coils, but are general for all machines of the same
number of phases and poles. Each one of the small arcs in the
circle represents the ends of the coils in a single pole-phase group
in the winding. In order to illustrate this, photographs have

201

202

CONNECTING INDUCTION MOTORS

♦ Ji^

Fig. 190. — Two pole, two phase, series. Fio. 193. — Two pole, three phase, parallel

star.

C Ji 6

Fio. 191. — Two pole, two phase, parallel.

Fig. 194. — Two pole, three phase, series

delta.

B A c

Fig. 192. — Two pole, three phase, series Fig. 195. — Two pole, three parallel, phase

star. delta.

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 203

Fio. 196. — Four pole, two phase, series.

Fig. 197. — Four pole, two phase, two parallel.

I t

8g B, A, Az

Fio. 198. — Four pole, two phase, four parallel.

CONNECTING INDUCTION MOTORS

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES, 205

CONNECTING INDUCTION MOTORS

ABC

I, three Fio. 214. — Sii pole, three phaa

parallel delta.

ABC
Fio. 213. — Six pole, three phase, a
deltK.

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 207

Fia. 221. — Eight pole, throe phase,

CONNECTIffa INDUCTION MOTORS

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 209

Pio. 229. — Ten pole, two phase.

Fid. 233.— Ten polo, threB phaao,

CONNECTING INDUCTION MOTORS

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 213

CONNECTING INDUCTION MOTORS

A, A^ 8, Bz
Fio. 259. — Fourteen pole, two phase

Fig. 261— Fourteen pole, two phase, Fio. 264. — Fourteen pole, three
■even puiUleL phase, two parAllel star.

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 215

216 CONNECTING INDUCTION MOTORS

been taken of & machine in three stages. In Fig. 271 a machine
is shown in which the coils have simply been placed in the slots
by the winder and no connections have been made. The wires
which are the beginnings and endings of the coils are sticking

Fta. 271. — Coila wound but unconaected.

Via. 273.— The completed

out at random. In Fig. 272 the coils have been connected into
several distinct groups, and the remaining wireSjWhich protrude
radially toward and away from the center of the machine, form
the beginning and the end of each pole-phase group. The opera-
tion which has been performed between Fig. 271 and Fig. 272
can be described in this way: — Suppose, for example, that there
are 96 total coils in the winding and that it is to be connected

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 217

for three phases and four poles. There will then be 3 X 4 =* 12
pole phase groups, and 96 -r- 12 = 8 coils in each group. Start-
ing at any arbitrary point, the winder connects the first eight
coils in series by connecting the end of coil 1 to the beginning of
coil 2, and the end of coil 2 to the beginning of coil 3, etc., until
eight coils are in series. The beginning of coil 1 is then bent
outward and left long and the end of coil 8 is bent inward and
left long. Between these two are seven short "stubs" or coil-
to-coil connections, which are shown taped up in Fig. 272. The
winder then proceeds to connect coils 9 to 16 in series in the
same manner to form pole-phase group No. 2, and so on around
the machine until he has completed 12 pole phase groups and
used all the coils, and the winding looks as shown in Fig. 272.

In case the winding has certain coils provided with heavier
insulation on the end turns to take the strain of the full voltage
of the machine where different phases are adjacent, the operation
is slightly different. Then, the number of coils per pole phase
group must be checked before the windings are inserted in the
slots, and specially insulated phase coils placed on both ends of
each group. In this case the location of the pole phase groups
is definitely determined by the winder before he starts connect-
ing the coils together.

The next step is to mark the pole phase groups A-B-C-A-B-C ,
etc., around the machine and then to connect all the groups to-
gether in the proper manner to form a three-phase winding by
means of a diagram of the same form as those shown in this
chapter. The completed winding will then appear as shown
in Fig. 273.

While it is intended to reproduce here only the standard dia-
grams over a wide range of speeds, it is useful to review
the general theory of their construction and the simple methods
by which any winding may be checked for phase polarity.
This is shown in Figs. 274 to 277, inclusive. In Fig. 274 a wind-
ing chosen at random is shown ''stubbed'' into pole-phase groups
for a two-phase connection, and in Fig. 276 stubbed for a three-
phase connection. To determinfe the proper connections for the
pole-phase groups in a two-phase winding, the rule is to mark on
the groups arrows alternating in direction in pairs, i.e., on two
successive groups the arrows are clockwise and on the two im-
mediately adjacent the arrows are counter-clockwise. Such
arrows, for example, are shown in Fig. 274 just above the wind-

218

CONNECTING INDUCTION MOTORS

ings. If now one end of any group in a phase is chosen as a lead
and all the groups are followed through and connected as indi-
cated by the arrows, the connection will be correct. Such a

fi^n^.

Fia. 274. — Checking a two-phase connection.

• • • • 1

r • 1 i

'^«o<yj

Fio. 275. — Similar to Fig. 274, but **B" phase reversed.

\i \.,

Fxo. 276. — Checking a three-phase connection.

*" -^ JL A

! '' f-'^'I!JTr!hM

Fio. 277. — Similar to Fig. 276, but leads taken off different groups.

connection is shown in Fig. 274. However, suppose the arrows
had alternated in pairs, but started with a different group, as
shown just above the windings in Fig. 275. The result is shown

STANDARD GROUP DIAGRAMS FROM 2 TO 14 POLES 219

in Fig. 276, which is just as correct as Fig. 274, except that the
motor would run with the opposite direction of rotation. Since
the rotation can be changed by reversing the two leads of either
phase outside of the motor, it is evident that the rule using the
arrows alternating in pairs is correct in all cases. It should also
be noted that it makes no diflference from what group the lead
is taken, provided all the groups are followed through with the
arrows.

In the three-phase machine it is even simpler. The rule in
that case is to put arrows on the groups alternating in direction
from group to group, as shown in Fig. 276. Any group may then
be chosen as a "lead'' group or a "star" group so long as the
arrows are followed in passing
from the lead to the star in each
phase. Figure 276 shows one ar-
rangement and Fig. 277 another
equally correct, and there might
be an indefinite number more,
simply by choosing the lead from
another group and following the
arrows through to the star in each
phase. Although shown for a de-
veloped four-pole winding only,
these diagrams may be considered
as strictly general, as additional groups may be added to make
six, eight, or any other number of poles, and the current
passed through them in any order, so long as the phases are kept
in the correct rotation, and the current in the right direction, as
indicated by the arrows.

In case a delta connection is wanted instead of a star, check
the connections through as for a star and then connect the A star
to the B lead, the B star to the C lead, and the C star to the A
lead, as shown in Fig. 278; or connect the A lead to the B neutral,
the B lead to the C neutral, and the C lead to the A neutral. The
three new leads will be taken from the corners of the delta so
formed.

Fig. 278. — Changing from star to
delta.

CHAPTER XIV
WAVE DIAGRAMS

With the exception of one or two diagrams briefly mentioned in
Chapter III practically all the diagrams discussed in the book
and those shown in Chapter XIII are of the type usually employed
for the stator winding. These could be used for the rotor also
so far as any electrical considerations are concerned. • It will be
noticed, however, when the cross connections are considered
that they are not arranged with mechanical symmetry
around the machine and, hence, if a diagram of this type were
used on the rotor there would be a tendency toward mechanical
unbalance which would set up mechanical vibration when the
rotor was running at full speed. In addition to this objection,
cross connections of this type are difficult to arrange and secure
in place on the rotor on account of their irregular shape and the
considerable space which they occupy. For this reason, so-
called "wave" diagrams, as shown in Figs. 279 to 289 in-
clusive, are ordinarily employed. on the rotor. They are of the
old, well known D. C. armature type sometimes called "pro-
gressive" or "retrogressive" windings. On examination they
will be found to be very regular mechanically and distributed with
practically perfect symmetry around the machine. They have
also the advantage of requiring a minimum of cross connections —
these being reduced to the three leads to the collector rings, one
jumper joining the two halves of each phase winding and in case
of a star connection the additional "star ring" with 3 taps, one
to each phase.

The rotor winding is practically always three phase and may be
connected either star or delta depending on the voltage which is
desired between the collector rings. A star connection would
give 1.73 times the voltage between rings that would exist with a
delta connection. This would mean a smaller current with
consequently smaller rings and brushes but would, in turn,
require insulation for the higher voltage throughout the wind-
ing and between collector rings.

220

WAVE DIAGRAMS 221

A two phase winding is practicafly never used on the rotor
as it would require four collector rings and an added set of brushes.
When the rotating magnetic field is set up by the primary winding
it is practically the same whether created by two phase or three
phase current and is the same as if it were set up by D. C. as
described in Chapter II. Hence, when the field is set up it can
act on a three phase rotor as well as a two phase and advantage
is taken of this fact to reduce the required number of collector
rings and brush holders to a minimum.

In checking over these wave diagrams it will be noticed that
the number of slots is always a multiple of the number of phases
times the number of poles and hence an even figure whereas a
true ''progressive" or ''retrogressive" winding as ordinarily
used on direct current for a two coil per slot winding must satisfy
the expression

Number of slots ±1 • . i i_

— ^7^ — ^ — = = an mtegral nimiber

Pairs of poles

in order that the conductor after passing around the machine
may fall into the slot adjacent to the one in which it started. In
the diagrams, Figs. 279 to 289, this is avoided mechanically
in the following way: Since the total number of slots is a multi-
ple of the number of poles and since the throw of the coil on a
rotor is exactly pitch the natural result would be that after once
passing around the rotor the conductor would fall again into
slot No. 1 in which it started. For example assume a 72 slot rotor
wound for 8 poles. Starting in the bottom of slot No. 1 the conduc-
tor passes successively through the top of slot 10, bottom of 19,
top of 28, bottom of 37, top of 46, bottom of 64, top of 63 and
would again fall into the bottom of slot No. 1. However, the
winder at this point bends the coil to one slot shorter throw and
arbitrarily places it in the bottom of slot 72 and again around the
rotor when he throws it in slot 71 and winds a third time around
the rotor and stops when he comes out of the top of slot No. 61.
He then leaves the two ends of this section of winding, viz.,
bottom of slot No. 1 and top of slot No. 61. This completes one
sixth of the winding and he proceeds to complete the other five
sixths in the same manner. At the finish there are left six com-
plete sections and twelve loose ends or leads. The winder then
takes the lead from the top of slot No. 61 described above and
looks for the section of the winding which lies in the tops of slots

CONNECTING INDUCTION MOTORS

WAVE DIAGRAMS

223

CONNSCTINO INDUCTION MOTORS

WAVE DIAOBAMS

CONNECTlUa INDUCTION MOTORS

WAVE DIAGRAMS

228 CONNECTING INDUCTION MOTORS

WAVE DIAOBAUS

CONNECTING INDUCTION MOTORS

WAVE DIAGRAMS

CONNECTINQ INDUCTION MOTORS

WA VE DIAGRAMS

CONNECTING INDUCTION MOTORS

WAVE DIAGRAMS

CONNECTING INDUCTION MOTORS

WAVE DIAGRAMS

238

CONNECTING INDUCTION MOTORS

WAVE DIAGRAMS

CONNECTING INDUCTION MOTORS

WAVE DIAQRAMS

CONNECTING INDUCTION MOTORS

WAVE DIAGRAMS

i
I
I
I

li
P

244 CONNECTING INDUCTION MOTORS

1-72-71, etc. Having located this section which may be called
section No. 4, the end of section No. 1 is connected to the end of
No. 4 so that the completed phase will have passed three times
around the armature clockwise and three times counter-clock-
wise. This is very similar to the case explained by Figs. 45,
46, and 47 in Chapter III. A little study of the diagrams, Fig-
ures 279 and 289, will show how this is done. After the three
separate phases are complete they are connected in star or delta
and the leads brought out as shown in the diagrams.

GENERAL INDEX

Air-gap, effect on performance, 183, 184

Balance test, 169, 172

Bar and end connector windings, 22

Changing volts, phase, poles, cycles, r.p.m., h.p., 134

examples of, 146, 149, 151
Chord factor, 56, 57, 118, 119
Chording a winding, advantage of, 53

effect of, 55, 60, 141
Coil throw, 141, see also ^ ^Chording."
Coils reversed, 173
Compass test, 169, 171
Concentric coil windings, 37
Conductor, cross section required, 138, 195
Conductors per phase, formula for, 193
Consequent pole windings, 39, 44, 125
Core iron, cross section required, 138^ 188, 189, 191, 192
Count, wrong number of coils in group, 173, 174
Counter electro-motive force, 2, 10, 51, 107, 118, 140
Current per lead, formula for, 195, 196

quick approximation, 196

Defects, ten most common in windings, 158

order of locating, 180, 181
Delta connections, 11, 50, 219
Design, points considered in making, 185, 186
Diagrams, see special index for, 249

delta, 50, 219

how to draw for any winding, 46, 217, 218

schematic equivalent, 43

standard ''group," Chapter XIII

typical "wave," Chapter XIV

wave, how drawn, 221
Diamond coil windings, 29

245

246 GENERAL INDEX

E
Efficiency, 183, 184

Faults, locating, 153, 180, 181

ten most common, 158, 159, 160

Ferraris, 6

Figuring a new winding, 182

Flux per pole, 190

Frequency, of an alternating current, 9
how it affects the winding, 105
how it affects r.p.m., 105

Functions of windings, d.c. motor, 1
a.c. induction motor, 4
a.c. synchronous motor, 3

Grounded windings, 160

locating grounds, 165, 166
Group reversed, 173, 174

Hand wound coils, 25

Horse power, relation to torque and r.p.m., 107, 135

Insulation, phase, 61, 97, 122

A. I. E. E. formula for resistance, 80
checking for voltage, 77
space required in slot, 197
tests, 79

Lap windings, 40
Locating faults, 153

Magnetic field, affected by chording, 64

Magnetic field, or flux per pole, 190

Magnetic noise, how separated from windage noise, 153

Maximum torque, 183, 184

Mechanical troubles, caused by windings, 153, 154, 155

Open circuits, 165, 178, 179
Output coefficient, 187

GENERAL INDEX 247

Performance, how affected by winding, 183, 184
Peripheral speed, of rotor, 120

safe value for, 106
Phase and voltage table, 99, 145
Phase insulation, 61, 97, 122, 217
Phase reversed, 173, 176
Phases, how the number affects the windings, 87

changing phase and voltage, 87
Poles and r.p.m., 113
Poles, changing number of, 113

changing affects chord factor, 56
Poles, how number affects cross section of iron core, 139

connection for wrong number of, 165, 175
Power factor, 183, 184
"Pull out," see "Maximum torque."
"Pushed through" windings, 22

Reconnecting old windings, 134, 136, 137

examples of, 146, 149, 151
Reversal of part of winding, 162, 173, 174
Reversing rotation, by reversing leads, 11, 20
Rotating magnetic field, 5

d.c. analogue, 7

graphical representation, 16

set up by a.c, 6, 14

sine wave shape, 13

"stair step" pictures of, 11
Rotor winding, why three phase, 11, 220
R.P.M., relation to horse power and torque, 107, 135

and poles, 9, 106, 113

connected for wrong, 165

Schematic equivalent diagram, 43

Scott connection or "Tee," 91

Secondary voltage, 102

Secondary voltage, how, to figure, 198, 199

Shorted windings, 161, .167, 168

"SUp," definition of, 113

Slots, number of, 123

"Split group," connection, 130, 132

Star connected winding, changing to delta, 219

Starting current and starting torque, 183, 184

Starting squirrel cage motor, 112

"Stubbing" and connecting, 216

248 GENERAL INDEX

"Tee" connection, 91, 133

Tesla, 6

Testing, volts and watts, 156, 157

balance test, 169, 172

compass test, 169, 171
Torque, how produced, 5

relation to h.p. and r.p.m., 107, 135
Two speed windings, 125

Uns3rmmetrical connections, 123

Vibration, mechanical, 154

Voltage, per turn in a winding, 81

all kinds of changes reduced to voltage changes, 142

and phase, table for different connections, 99, 145

between collector rings, how to figure, 198, 199

table of, 86

two- and three-phase compared, 85

wrong connection, 175

Windage noise, 153
Windings, types of, 22

bar and end coimector, 22

"diamond'' coils, 29

fed in coils, 25

for open slots, 29

hand wound, 25

partly closed slots, 22
Windings, wave, 31, 40

chorded, 51

concentric coil, 37

consequent pole, 39, 44, 125

effect of voltage on, 77

figuring a new winding, 182

generator action of, 140, see also Counter e.m.f.

grounded, 160

lap, 40

points considered in figuring, 185, 186

possibility of reconnecting, 77

reconnecting for new conditions, 134

reversal of part, 162, 173

shorted, 161

INDEX OF DIAGRAMS

Standard Gboup Diagrams

Two-pole, two-phase, series, Figure 190, page 202.
Two-pole, two-phase, parallel. Figure 191, page 202.
Two-pole, three-phase, series star. Figure 192, page 202.
Two-pole, three-phase, parallel star, Figure 193, page 202.
Two-pole, three-phase, series delta. Figure 194, page 202.
Two-pole, three-phase, parallel delta. Figure 195, page 202.
Four-pole, two-phase, series. Figure 196, page 203.
Four-pole, two-phase, two parallel, Figure 197, page 203.
Four-pole, two-phase, four parallel. Figure 198, page 203.
Four-pole, three-phase, series star. Figure 199, page 204.
Four-pole, three-phase, two parallel star. Figure 200, page 204.
Four-pole, three-phase, four parallel star. Figure 201, page 204.
Four-pole, three-phase, series delta. Figure 202, page 204.
Four-pole, three-phase, two parallel delta. Figure 203, page 204.
Four-pole, three-phase, four parallel delta. Figure 204, page 204.
Six-pole, two-phase, series, Figure 205, page 205.
Six-pole, two-phase, two parallel. Figure 206, page 205.
Six-pole, two-phase, three parallel. Figure 207, page 205.
Six-pole, two-phase, six parallel. Figure 208, page 205.
Six-pole, three-phase, series star, Figure 209, page 205.
Six-pole, three-phase, two parallel star. Figure 210, page 205.
Six-pole, three-phase, three parallel star. Figure 211, page 206.
Six-pole, three-phase, six parallel star, Figure 212, page 206.
Six-pole, three-phase, series delta, Figure 213, page 206.
Six-pole, three-phase, two parallel delta. Figure 214, page 206.
Six-pole, three-phase, three parallel delta, Figure 215, page 206.
Six-pole, three-phase, six parallel delta. Figure 216, page 206.
Eight-pole, two-phase, series. Figure 217, page 207.
Eight-pole, two-phase, two parallel. Figure 218, page 207.
Eight-pole, two-phase, four parallel. Figure 219, page 207.
Eight-pole, two-phase, eight parallel. Figure 220, page 207.
Eight-pole, three-phase, series star. Figure 221, page 207.
Eight-pole, three-phase, two parallel star, Figure 222, page 207.
Eight-pole, three-phase, four parallel star. Figure 223, page 208.
Eight-pole, three-phase, eight parallel star. Figure 224, page 208.
Eight-pole, three-phase, series delta, Figure 225, page 208.
Eight-pole, three-phase, two parallel delta, Figure 226, page 208.
Eight-pole, three-phase, four-parallel delta. Figure 227, page 208.
Eight-pole, three-phase, eight parallel delta. Figure 228, page 208.
Ten-pole, two-phase, series. Figure 229, page 209.
Ten-pole, two-phase, two parallel. Figure 230, page 209.

249

260 INDEX OF DIAGRAMS

Ten-pole, two-phase, five parallel, Figure 231, page 209.
Ten-pole, two-phase, ten parallel, Figure 232, page 209.
Ten-pole, three-phase, series star. Figure 233, page 209.
Ten-pole, three-phase, two parallel star, Figure 234, page 209.
Ten-pole, three-phase, five parallel star, Figure 235, page 210.
Ten-pole, three-phase, ten parallel star. Figure 236, page 210.
Ten-pole, three-phase, series delta. Figure 237, page 210.
Ten-pole, three-phase, two parallel delta, Figure 238, page 210.
Ten-pole, three-phase, five parallel delta, Figure 239, page 210.
Ten-pole, three-phase, ten parallel delta. Figure 240, page 210.
Twelve-pole, two-phase, series. Figure 241, page 211.
Twelve-pole, two-phase, two parallel, Figure 242, page 211. '
Twelve-pole, two-phase, three parallel. Figure 243, page 211.
Twelve-pole, two-phase, four parallel, Figure 244, page 211.
Twelve-pole, two-phase, six parallel. Figure 245, page 211.
Twelve-pole, two-phase, twelve parallel. Figure 246, page 211.
Twelve-pole, three-phase, series star, Figure 247, page 212.
Twelve-pole, three-phase, two parallel star. Figure 248, page 212.
Twelve-pole, three-phase, three parallel star. Figure 249. page 212.
Twelve-pole, three-phase, four parallel star. Figure 250, page 212.
Twelve-pole, three-phase, six parallel star. Figure 251, page 212.
Twelve-pole, three-phase, twelve parallel star, Figure 252, page 212.
Twelve-pole, three-phase, series delta. Figure 253, page 213.
Twelve-pole, three-phase, two parallel delta. Figure 254, page 213.
Twelve-pole, three-phase, three parallel delta, Figure 255, page 213.
Twelve-pole, three-phase, four parallel delta. Figure 256, page 213.
Twelve-pole, three-phase, six parallel delta. Figure 257, page 213.
Twelve-pole, three-phase, twelve parallel delta. Figure 258, page 213.
Fourteen-pole, two-phase, series. Figure 259, page 214.
Fourteen-pole, two-phase, two parallel. Figure 260, page 214.
Fourteen-pole, two-phase, seven parallel, Figure 261, page 214.
Fourteen-pole, two-phase, fourteen parallel, Figure 262, page 214.
Fourteen-pole, three-phase, series star, Fi^re 263, page 214.
Fourteen-pole, three-phase, two parallel star. Figure 264, page 214.
Fourteen-pole, three-phase, seven parallel star, Figure 265, page 215.
Fourteen-pole, three-phase, fourteen parallel star. Figure 266, page 215.
Fourteen-pole, three-phase, series delta, Figure 267, page 215.
Fourteen-pole, three-phase, two parallel delta, Figure 268, page 215.
Fourteen-pole, three-phase, seven parallel delta. Figure 269, page 215.
Fourteen-pole, three-phase, fourteen parallel delta, Figure 270, page 215.

Typical Wave Diaqbams

Four-pole, three-phase, series delta^ 84 slots, Figure 279, pages 222 and 223.
Six-pole, three-phase, series delta, 108 slots, Figure 280, pages 224 and 225.
Eight-pole, three-phase, series delta, 144 slots. Figure 281, pages 226 and

227.
Ten-pole, three-phase, series star, 180 slots. Figure 282, pages 228 and 229.
Twelve-pole, three-phase, series star, 144 slots. Figure 283, pages 230 and

321.

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