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Dec’. 1_0, 1946.
Filed May 25, 1945
2 Sheets-Sheet 1
Dvec. 1_0, 1_946.
Filed May 25, 1945
2 Sheets-Sheet 2
John E. Macih
v Í` «w
Parental Dee. 1o, 194s
John R. Macintyre, South Peabody,
signor to General
ration of New York
Application May 25,
Serial No. 595323
My invention relates to synchronous motors
netic core fl, andouter and inner stator magnetic
and is suitable for use in the construction of small
motors such as are used for
timing de
`pole piece sections
oi such a motorin which there is high utilization
of the material in the rotor and a high utilization
of the radial space'occupied by adjacent stator
and rotor parts for the production of torque. In
the usual motor the torque producing pole piece
parts of stator and rotor are located in concen
tric circles separated by an air gap, and the rotor
structure lying between its pole pieces and the
axis of rotation is used merely as supporting
structure. In accordance with my invention the '
and rotor are positioned in spaced parallel planes
perpendicular to the axis of rotation and utilize
and S, in the same radial i
The outer pole piece section ~5 _ may be
mechanically secured to the inner pole piece sec
tion 6, by means of the nonmasnetic ring 3l,
which is `welded to both pole piece sections. This
welded assembly may be magnetically secured to
andwithin cup l by a close iit at their contacting
surfaces,'the outer periphery of section 5 having
a bent-over rim section ‘lf to facilitate this. The
welded assembly of the inner stator pole piece
section 6 and outer pole piece section 5 is staked
to the inner end of core 4, and the opposite 'end
of the core is staked to the center of the end loi
_ vices. One object of the invention is the design
active torque producing ‘pole pieces of both'stator
@emp-any, a corpo
cup l. A coil 8 surrounds the core I and is housed
within the magnetic parts described as shown.
A dish-shaped spring washer 9 holds the coil
a very substantial portion of the entire radial
ñrmly in place so that it cannot rattle. Provi
space between the axis of rotation and the pe
sion is made for exciting coil 8 from an alternat
riphery of the rotor. By such an arrangement 20 ing current circuit Èby leads l0 brought out
the available torque producing surfaces of stator
through a bushing Il in the end wall of member
and rotor for a motor of given external dimen
i. The electrical resistance of the washer 9 and
sions may `be appreciably increased with a corres
the metal ring 3d are such as to limit the power
spending increase in the ratio of motor output
loss due to circulatingy currents to a minimum.
to motor size. Other advantageous features of 25 If necessary 'this can be accomplished by suitable
my invention will be mentioned as the description
slotting to increase the length and hence the re
sistance of the circulating current path.
The features of the invention` which are be->
The pole piece sections 5 and 6 have inter
lieved to be novel and patentable will be pointed
leaved ilngers or pole pieces l2 and i3, respec~
out in the claims appended hereto. For a better 30 tively. In the example shown there are eight
understanding of my invention, reference is made
pole pieces in each section, the pole pieces i 3 of
in the following description to the accompany
the inner section S extending radially outward
ing drawings in which Fig.,1 shows a- cross-sec
between inwardly extending radial pole pieces l2
tional view of my improved motor as constructed
in the outer section 5 in the same plane. The
with a suitable gear reduction and supporting 35 air gaps H between the pole pieces l2 and I3 are
casing. Fig. 2 represents an end view of such a
radially ‘symmetrical and are somewhat greater
motor with a one-way clutch included in the gear
near the periphery than* near the center. The
teeth or pole »pieces i3 are slightly wider at their
exploded perspective
in dotted view
lines.of the
than at their inner ends and the teeth
rotor and stator pole piece assemblies of the motor 40 l2 areends
approximately twice as wide at the outer
of Fig. 1, Fig. 4 is a perspective view of a shaded
ends as at their inner ends. The radial gap at
pole form of stator- pole piece assembly that may
the ends of the 'teeth are made at least as large
'be used and
5 is a schematic illustration of
as the greatest width or” the peripheral gap. The
gaps between the stator pole pieces are sufficient
rotor in a given torque position.
45 to prevent any appreciable leakage flux directly
I will refer ilrst to the form of motor repre
between these pole pieces in the operation ci the
sented -in Figs. l to 3 wherein like parts are in=
the overlapping tooth relationship of stator and
dicated by like reference characters. The casing
may comprise a magnetic cup part i with an end
motor, and the generally sector shaped pole pieces
and gaps are otherwise dimensloned with a view
of avoiding saturation at any point and of ob
closure 2, these parts being riveted together at 50 taininga
maximum useful tordus nur.
their rims by hollow rivets 3 which may then
serve as screw or bolt holes for securing the motor
assembly to' other apparatus. The motor stator
magnetic circuit includes the right portion of the
cup member l as shown in Fig. 1, a central mag
The rotor l5 shown at the left in Fig. 3 is es
sentially a disk withl eight radial slots I6 forming
eight radial pole piece sectors l?. A’l’he rotor is
rotatively mounted with a bushing i8 and a shaft
55 I9 on-the center axis of the casing and motor
i 2,412,461
stator land is positioned closely adjacent to the
Where a certain direction of rotation -is desired,
plane of thestator pole pieces with a suflîciently
small intervening axial air gap to cause the
greater part of the flux which passes between
sisting of a ratchet wheel 22 on one of theV driven
a one-way lock may be provided in the gear re--
duction unit as represented in Figs. 1 and 2, con
shafts and a ratchet pawl 23 cooperating there
y the stator pole pieces to do so through the rotor.
with to prevent rotation in the counterclockwise '
A thrust be'aring for the rotor shaft at the core
end comprises `a steel ball 20 ilxed in the center
of housing I8 against the end of shaft I9 and
bears against a suitable bearing surface 2| in
serted in the adjacent end of the core piece. This
bearing surface ZI may be a small piece of fab
direction as viewed in Fig. 2. The pawl is piv
oted at 24 and has a tail 25 which approaches
the ratchet Wheel 22 when the pawl 23 moves
away therefrom, and in case the pawl is not in
locking position when locking action is called for,
ricated plastic material such as is sold‘under
the trade-mark Textolite. The shaft I@ is other
wise supported for rotation in bearings in plates
the tail 25 will be, or will move the pawl to lock
ing position. This locking device perse is not
my invention, and any suitable one-way locking
2l’ which are riveted together in spaced relation
and support the gear reduction unit for the motor
securely in the left end of the housing as viewed
in Fig. 1. The rotor sectors i1 may be bent
-slightly as represented so as to bring their radial
mechanism may be used which will serve the pur
pose. Thus the motor is self-starting and runs
in a given direction at a 16-pole speed. Gener
ally, the gear reduction wili be such as to reduce
the speed to one rpm at the terminal or out
edges slightly closer to the stator pole pieces than 20 put shaft 25.
It will be apparent that due to endwise mag
the intermediate portions of the sectors. This
netic attraction between stator and rotor, there
assures a small motor air gap with sufficient
clearance at the axis to accommodate the thrust
bearing 2li and also makes the rotor more> diñi
cult> to demagnetize.
To facilitate the manufacture fof the rotor sec
tors I1 and their proper alignment with the stator
pole pieces, the inner ends of the slots I6 may
terminate in enlarged drill holes 36. In the formY
will be an end thrust on the ball bearing âêl-‘â l.
This bearing determines the air gap between sta
25 tor and rotor and will be designed for minimum
wear and long life. The bearing plates 2l', which
rotatively support the motor rotor shaft I9 and `
all of the shafts of the gear reduction unit, are
preferably made of an oil impregnated metal,
such as is sold under the trade name “oilite”
of synchronous motor represented in Figs. 1 to 3
The motor and gear reduction unit requires no
the rotor is preferably made of permanent mag
additional lubrication, and the motor unit is in
net material, such as the copper-nickel-cobalt
tended to run continuously for several years with
alloy described in United States Letters Patent
out attention. The motor has been found to be
No. 2,170,047 to Dannöhl et al., and is polarized
in a peripheral direction to have poles of opposite 35 exceptionally quiet in operation with relatively
polarity facing themselves across the radial slots
smooth torque pulsations. This is attributed to
the combination of low speed, high torque rotor
I6 at the edges of the sectors as indicated by the
inertia, and the range of overlapping ci the rotor
polarity marks on certain of the rotor .sectors in
and stator poles during synchronous torque pnl
Fig. l3. 'I'he radial length of the sectors I1 con
-forms to the radial length of active stator pole 40 sations. It will be observed that the useful torque
producing pole face length in the rotor is the
pieces, and the rotor is of the proper diameter
radial length of a rotor sector I1 measured from
so that when assembled the rotor sectors I1 can
the opening 36 to the periphery multiplied by
magnetically bridge across the gaps I4 of the
stator when in overlapping position.
sixteen, and is roughly double that which would
It will now be evident that when the stator coil 45 be practicable in a conventional motor of the
8 is energized with alternating current, the sta
same diameter where the useful ñux gap is across
tor pole pieces I2 and I3 will alternate in mag-A
a radial gap at the periphery of the rotor and
netic polarity, the poles I2 being south poles when
where the greater portion of the nonperipheral
poles I3 are north poles and vice versa, creating
portion of the rotor is used only as a spider sup
a magnetic ñeld which pulsates at a rate propor
porting structure.~ In the stator the useful pole
tional to the applied frequency. -Thus if the fre
face area is even greater in proportion since it is
quency be 60 cycles, the synchronous speed of the
v the total stator pole face area adjacent the rotor
16 pole rotor operating in cooperation _with the
section. Thus the sector-shaped pole pieces of
16 pole iield will be 450 rpm. The polarized rotor,
the stator have a radial length more thanvthree
although having eight sectors, is` in reality a 16 55 times their mean peripheral width with a cor
pole rotor, as the sectors have a pole at each of
responding'ly large useful pole face surface.
their two edges. At standstill with the ñeld de
The structure or material used in the gear case
energized, the rotor will, if sumciently free, seek
Y to the left of the rotordn Fig. 1 should be such
a position whereAits sectors I1 bridge gaps be
as not" to provide any appreciable magnetic leak
tween the stator pole pieces because the sectors 60 -age ñux path from the cup shell into the hub l
of the rotor being permanent magnets will move.
ysection of the rotor such as would rob the 'motor
to a position of least reluctance. When the field
is energized, it would appear that the rotor might
lock, as theoretically the opposing torques of re
pulsion and attraction can be equal in certain 65
rotor positions. However, such is not the case
because of the unbalanced magnetic and me
chanical conditions which will always exist. The .
rotor will vibrate momentarily moving` ?rst` in
one direction and then in the other because of 70
its low inertia and the high magnetic forces
active upon it. Therefore, it will jump into syn
chronous speed almost instantaneously, although
of useful ñux.
Where a shaded pole type of motor is desired,
the stator pole piece structure may be formed
as in Fig. 4. The stator pole pieces designated
I2a and I3a in Fig. 4 correspond to the pole pieces
I2 _and I3 of Fig. 3 but are provided with axially
, extending pole faces 21, 28, 29,7and 30 formed by
turning the edges sol as to extend toward the
rotor. A copper disk 3l having slots 33 extend
ing to the periphery to accommodate the pole
place _extensions 21 and 29, and openings 32 to
‘ accommodate pole face extensions 28' and 3D, is
-provided. The flux which threads the latter or
the direction of rotation is uncertain unless the
rotor is permitted to go in one direction only. 75 trailing pole face extensions is thus shaded or
, 2,412,461
retarded by the copper conductor surrounding
' all of the torques for this rotorposition and pro
such extensions. but that which threads the
leading pole face extensions 21 and 29 is not
duce» starting and synchronous operation in a
counterclockwise direction. There are of course
a great variety of rotor positions and stator pole
shaded. In order to equalize the flux in the un
shaded and shaded portions of the stator poles,
polarity conditions that could be similarly repre
the shaded »pole face extensions 23 and IU are
made slightly longer than the extensions 21 and
29 in an axial direction; hence, the air gap be
tween theshaded pole face extensions and rotor
sented but it is believed that the example given
will be suiiicient to an understanding of the op
eration of this form oi motor,
The operation of the shaded pole hysteresis
is made correspondingly less than for the un 10 form of motor of Fig. 4 is essentially the same as
shaded extensions. vThe shaded pole construction
in any shaded pole hysteresis motor except for
>may use a hysteresis> steel disk rotor without
, polar slotting as represented at 34a, Fig. 4. The
the greatly increased amount of active stator pole
piece and rotor area available for torque pro
shaded pole form of'motor will not require the
ducing action afforded by the novel construction.
one-'way locking device 22-23 of Fig. 2, since 15 In accordance with the provisions of the pat
it will rotate only in the direction-of the rotating
ent statutes I have described the principle of op
field produced by the shading poles.
eration of my invention, together with the ap
Fig. 5 is intended to show the manner in which
paratus which I now consider to represent the
the rotor and stator pole pieces overlap and to
best embodiment thereof, :but I desire to have it
illustrate theftorque action of the form of motor 20 understood that the apparatus shown is only il
of Fig. 3. `In Fig. 5 the stator pole pieces I2 and
lustrative and that the invention may be car
I3 are shown in full lines and the rotor sectors
I1 are represented in dot-dash lines for one par
ried out by other means.
What I_ claim as new and desire to secure'by
Letters Patent of the United States, is:
ticular rotary position taken at random. It is
seen here that the peripheral width of a rotor 25
1. An _electric motor structure comprising co
sector I'I is roughly twice the width of the stator
operating stator and rotor members the stator
pole pieces and the same width as the spacing
member having a magnetic circuit provided with
_ between stator pole pieces of the same polarity
an air vgap formed between two equally numbered
at any given radius. Thus the distances DI 2, DI 3
sets of pole pieces, one set extending radially in
representing the spacing between stator poles I2 30 ward and the other set extending radially out
and between stator poles I3, respectively, are
ward in the same plane perpendicular to the axis
roughly equal to the width DI1 of the rotor sec- ' _ of rotation of the motor with the pole pieces
tors II‘I all measured at the same radius. Also
the spacing between rotor sectors I1 is roughly
the width of the stator pole pieces measured at
the same radius» `lïiachrotor sector Il is thus
within the influence of at least two stator poles
and possibly three stator poles rin all- rotor po
sitions and is always within the influence of stator
poles of opposite magnetic polarity, and each
rotor magnetic pole is always within the inñuence
of at least one stator magnetic pole. This lib
eral range of overlapping is advantageous in quick
and powerful .starting from any rotor position and
in smoothing out the torque pulsations at syn->
chronous speed, resulting in quiet operation.A
In Fig. 5 the outer group of stator poles _I2 is
represented as having an N polarity and the in
of one set interleaved between the pole pieces
oi' the other set, said pole pieces lbeing sector
shaped and of a radial length at least three times
their mean peripheral width, a single-phase al->
ternating-current coll for producing a flux in the
magnetic circuit such that when the pole pieces
of one set .are at one polarity the pole pieces of
40 the other set are of the opposite polarity, said
ner group of stator poles as having an S polarity
at the instant assumed. The permanent mag
netic polarity of Athe _rotor is represented by
small jn and s polarity designations along the
edges îfythesectors Il, From the knowledge that
like po es repel and unlike poles attract, the torque
relations between stator ,and rotor for this posi- '
tion of the rotor and stator pole polarity will be
evident. An outer circle of arrows pointing clock
wise represents attraction forces drawn between
pole pieces .being uniformly spaced and symmet
_ rically distributed about the axis of rotation, the
rotor including a magnetic member mounted
for rotation in a radial plane closely adjacent
to the radial plane occupied by said pole pieces,
the effective air gap between said rotor member
and said pole pieces being less than the eiIectiVe
air gap between the pole pieces whereby flux
passing between the adjacent stator pole pieces
of opposite magnetic polarity, does so primarily
through said rotor member,
_, 2. :An electric motor structure comprising co
operating stator'and rotor members said stator
member having two sets of magnetic pole pieces
equal in number, one set extending radially out
ward from the axis o! rotation of the motor and
the other set extending radially inward in the
same plane such that the pole pieces of one set
extend between the pole pieces of the other set
in stator and rotor. An inner circle of arrows ,60 with substantial air gap space between them in>
the edges oi the adjacent poles of unlike polarity
also pointing clockwise represents repulsion torque
forces at the points where they occur, 'I'he length
said plane, said pole pieces being equally 'spaced
and symmetrically distributed about the axis of
motor rotation, mans for producing an alternat
ing magnetomotive force between said two sets
of pole pieces,- said rotor member including a
radially slotted disk rotatively mounted closely
adjacent to and in axially spaced relation with
respect to the stator pole pieces, .the rotor slots
dividing the rotor into equal sectors equal in
of these arrows does not necessarily represent rel
ative values but rather the angular location of
the torque forces. Thus the arrow marked “At- ’
traction” represents the attraction of south stator
pole I3 for the northA pole- of adjacent rotor sec
tor I1 to the left thereof, and the arrow marked
“Repulsion” represents the repulsion force be
tween north stator pole I2` and the north pole 70 number to the stator pole pieces of one set and
oi.' sector I1 adjacent thereto. These forces exist
of approximately half the peripheral width of the
over the radial length of the pole pieces and will
stator pole pieces measured at the same radius,
obviously tend to produce clockwise rotation as
said rotor disk being made of permanent mag-z
. viewed in Fig. 5. If the rotor is blocked for clock
net material with its sectors similarly polarized
wise rotation, the next half-cycle will reverse 75 in a peripheral- direction such that permanent
tor-shaped stator pole pieces, both sets ex
magnet poles of opposite polarity are formed at
the two end edges of each sector, the eiîective
air gap between the stator and rotor pole pieces
tending in a radial direction relative to the
axis of rotation of the motor and in the '
same plane perpendicular to such axis of -
being less than the effective air gap between the
stator pole pieces of opposite polarity.
rotation with the pole pieces of one set spaced
-from and alternately interleaved with the pole
pieces of the other set over a radial distance ap
3. An alternating-current motor structure com
prising cooperating stator and rotor members,
said vstator member having a magnetic circuit
preciably greater than the maximum peripheral
pole-piece width, said pole pieces being equally
formed of a cup-shaped member with a central
core part therein on the axis of rotation of the 10 spaced and symmetrically disposed about the axis
motor and with a set oi sector-shaped pole pieces
of rotation of the motor, means for producing an
alternating ñux between the pole pieces of the '
extending radially inward from the rim of the
dirîerent sets, and a magnetic rotor ,mounted for
rotation in a plane parallel to and closely ad
cup toward the core and a set of an equal num-u
ber of sector-shaped pole pieces extendingradi
ally outward from the core toward the rim" ofthe 15 jacent the plane of- said pole pieces such' that it
magnetically overlaps stator pole pieces of both
cup at the outer end oi the core, said pole pieces
sets and comprises the principal path. for the
having a radial length more than twice their
alternating iiux between said sets of pole pieces
, mean peripheral width and being symmetrically
and whereby thearea oi' said stator pole pieces'
spaced and interleaved in the same radial plane
with sector-shaped gaps between their radial 20 facing and overlapped by said rotor is available
for producing torque ñuxes.
edges, an energizing coil within the cup and about
6. A shaded pole alterriating-current- motor
the core for producing a single-phase alternat
having cooperating stator and rotor members the
ing flux between said pole pieces, said rotor mem
stator having a magnetic circuit with two equal
Vber including a disk-shaped rotor of magnetic
material mounted for rotation on the axis of said 25 ly numbered sets of pole pieces in the same plane
perpendicular to' the axis of motor rotation the
core in a plane parallel to the plane of the stator
poles of one set extending lradially inward loe
pole pieces and closely adjacent to and opposite
said pole pieces such that the eiîective air gap be
tween the poles of the other set which extend ra
dially outward symmetrically with respect to such
tween stator pole pieces and rotor is less than
axis, means for producing' .la single-phase alter
' that between stator pole pieces of opposite mag
nating ñux >between the diñerent sets of pole l
netic polarity whereby the greater portion of the
pieces, a magneticrotor mounted for rotation' on
stator iiux passing between the pole pieces does
such axis and positioned in a plane parallel to
so 'through the rotor and a thrust bearing for
and closely adjacent the »plane of the stator pole
said rotor determining the axial air gap spacing
between stator and rotor.
35 pieces whereby the rotor overlaps and magneti
cally bridges the stator pole pieces, the pole pieces
d. A synchronous alternating-current motor
of said stator having their radial edges extended
comprising cooperating stator and rotor mem
toward the rotor, shading pole conductor means
bers, said stator member having a magnetic cir
surrounding said radial edges oi all of said pole
pieces only on the trailing sides oi said pole
cuitformed oi a cup-shaped member with a cen
tral core therein and with radially extending pole
,pieces between the core and the cup, there being
a set or” pole pieces magnetically connected to
the core extending toward the wall or" the cup,
said two groups of pole pieces being equally and
pieces, the eiîective air gap between stator pole
pieces and rotor being less than betweenv stator
pole pieces of the diñerent sets whereby ñux pms
ing between said sets of pole pieces does so
'through the rotor, and portions thereof from each
pole piece are lagged by said conductor means
symmetrically spaced about the axis of the core ,
causing a rotational shifting of such ilux and cor
the cup extending toward the core and an egual
number oi pole pieces magnetically connected to
responding rotation of the rotor.
with outwardly extending pole pieces between the
7. A shaded, pole alternating-current motor'
inwardly extending pole pieces in the saine radial
piane, said pole pieces being sector-shaped and 50 having cooperating stator and rotor members, the
oi such dimensions as to provide~ a high reluc
tance air gap between the two sets, an energiz
ing coil within the cup and about the core for
producing an alternating iiux potential between
the sets oi pole pieces, a rotor in the I’onn of a
disk having radial slots dividing the dislzinto
sectors equal in number to one set of
stator pole pieces, said rotor being mounted for
stator' having a magnetic circuit formed with a
cup-shaped outer part, a core part extending con
centrically within the cup from the base there
of and a pole piece assembly between the outer
end of the core and inner walloi the cup, a coil
within the cup and about the core ior producing
an alternating linx through the magnetic circuit
and pole piece assembly, said pole piece assembly
allel to that of the statorpole 'pieces and closely
including a plurality of evenly spaced magnetic
pole pieces extending inwardly from the cup to
adjacent thereto so that its sectors simultane
. ward the core and an equal number of evenly
-rotation on the axis of the core in a plane par
ously overlap stator pole pieces in the two sets,
spaced magnetic Ipole pieces extending outward
said rotor being made of permanent magnet ma
terial with its sectors similarly polarized in a
ly from the core symmetrically between the in
wardly extending core pieces and in the same
plane, a vrotor containing magnetic material ro
tatively mounted on the axis of the cup in a plane
peripheral direction to form poles of opposite
. magnetic polarity atopposite ends of each sector,
said sectors having their end edges symmetrically
‘bent toward the stator pole pieces, and a thrust
bearing for said rotor spacing the rotor from the
stator pole pieces by an eiïective'air gap less than
the'air sap between stator pole pieces of the _
'_ diii’erent sets whereby the ñux path between dif
ferent sets of stator pole pieces is through the
_ 5.'.iin electric motor having two sets of
parallel and closely adjacent to the plane oi said
pole pieces, the leading and trailing edges of said
pole pieces having projections facing the rotor
with the projections on the trailing edges being
longer and extending nearer the rotor than the
A others, and shading coil means on the longer pro
` jections, the air gap relations between stator pole
pieces and between stator pole piece projections
75 and rotor being such that the greater portion oi
Athe flux between thetpoie pieces passes through
on the opposite side oi' the ilux air gap from the
the rotor and is approximately evenly divided
`.between the longer and shorter pole piece ex
8. A single-phase alternating-current motor
structure comprising cooperating stator and ro
tor members separated by a iiux air gap lying in
a plane perpendicular to the axis ot motor rota
Astator pole pieces having magnetic material ad
»jacent and magnetically bridging the stator pole
pieces of opposite magnetic' polarity causing the
tion, said stator meínber having a group of even
' net Mmaterial and slotted radially so as to divide
flux between said two groups of pole pieces to
cross said air gap and pass through the rotor.
9. A circular motor rotor member for a syn
chronous motor composed of permanent mag
ly spaced pole pieces of one magnetic polarity 10 -the peripheral portion thereof into a plurality
of equal sectors, said rotor being permanently
facing the air gap in circular formation about the
axis of rotation, and a second group, equal in
magnetized in a peripheral direction so as to pro
numberto the ñrst group, of evenly spaced pole
pieces of the opposite magnetic polarity facing
duce a permanent magnet pole of one polarity at
the leading edge of each sector and a. permanent
the’aix gap in circular formation about the axisl 15 magnetic .pole of the opposite polarity at the trail
of rotation and lying between and in the same
ing edge of each of said sectors whereby the rotor
radial plane with the ñrst group of pole pieces,
has twice as many magnetic poles as there are
said pole pieces being sector-shaped and being
sectors, which poles alternate in polarity about
interleaved a radial distance greater than twice
the rotor.
' the mean peripheral pole piece width, a rotor
mounted for rotation about the axis of rotation
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