Note: Descriptions are shown in the official language in which they were submitted.
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SHORT-FLUX PATH MOTORS / GENERATORS
RELATED APPLICATION
This application claims the benefit of U.S. Provisional Patent Application
Serial
No. 60/952,339 entitled "Method and System for Short-Flux Path
Motor/Generators"
filed July 7, 2007, the entire disclosure of which is hereby incorporated by
reference.
TECHNICAL FIELD OF THE INVENTION
This invention relates in general to electric machines and, more particularly,
to
short-flux path motors / generators.
BACKGROUND OF THE INVENTION
Electric machines using rotor/stator configurations (e.g., switched reluctance
motors (SRM) and permanent magnet motors (PMM)) generally include components
constructed from magnetic materials such as iron, nickel, or cobalt. In an
SRM, a pair of
opposing coils in the SRM may become electronically energized. The inner
magnetic
material is attracted to the energized coil causing an inner assembly to
rotate while
producing torque. Once alignment is achieved, the pair of opposing coils is de-
energized
and a next pair of opposing coils is energized. In a PMM, the inner assembly
may
include permanent magnets, which may provide both push and pull forces
relative to the
energized coils (as opposed to only pulling forces in an SRM).
SUMMARY OF THE INVENTION
According to certain embodiment of the present disclosure, an electric machine
includes a stator and a rotor. The stator includes a stator pole including a
first leg and a
second leg, and a gap defined between the first and second legs. The rotor
includes a
rotor pole. The rotor is configured to rotate relative to the stator such that
the rotor pole
rotates through the gap defined between the first and second legs of the
stator pole. The
stator pole includes a laminar stator pole structure including multiple
lamination layers.
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According to other embodiments of the present disclosure, an electric machine
includes a housing, a stator having a stator pole including a first leg and a
second leg,
and a rotor including a rotor pole. The rotor is configured to rotate relative
to the
stator. At least one of the stator and the rotor is adjustably coupled to the
housing to
allow a distance between the stator pole and the rotor pole to be adjusted.
According to other embodiments of the present disclosure, an electric machine
includes a first stator, a first rotor, a second stator, and a second rotor.
The first stator
has a first perimeter and a plurality of first stator poles arranged around
the first
perimeter, each first stator pole including a first leg and a second leg. The
first rotor
is configured to rotate relative to the first stator around a first axis. The
second stator
has a second perimeter and a plurality of second stator poles arranged around
the
second perimeter, each second stator pole including a first leg and a second
leg. The
second rotor is configured to rotate relative to the second stator around the
first axis.
The second stator is rotationally offset from the first stator about the first
axis such
that the second stator poles are offset from the first stator poles.
According to other embodiments of the present disclosure, an electric machine
includes a stator and a rotor. The stator has a plurality of stator pairs
arranged around
a stator perimeter, each stator pair including two legs. The rotor has a
plurality of
rotor blades arranged around a rotor perimeter, each rotor blade including two
legs.
The rotor rotates relative to the stator. At least three stator pairs are
energized
simultaneously to generate magnetic circuits with at least three corresponding
rotor
blades.
According to other embodiments of the present disclosure, an electric machine
includes a stator and a rotor. The stator has a plurality of stator pairs
arranged around
a stator perimeter, each stator pair including two legs. The rotor has a
plurality of
rotor blades arranged around a rotor perimeter, each rotor blade including two
legs.
All of the plurality of stator pairs are energized simultaneously and de-
energized
simultaneously, in an repeating manner, in order to cause the rotor to rotate
relative to
the stator.
According to other embodiments of the present disclosure, an electric machine
includes a stator and a rotor. The stator includes a plurality of stator
pairs, each stator
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pair including two legs defining a gap between the two legs. The rotor
includes a
plurality of rotor blades including a permanent magnet. The rotor is
configured to
rotate relative to the stator such that the rotor blade rotate through the
gaps between
the two legs of each stator pair.
According to other embodiments of the present disclosure, an electric machine
includes a stator including a stator pole, a rotor including a rotor pole and
configured
to rotate relative to the stator, and a housing configured to house a fluid
for cooling
the stator. A first portion of the stator pole projects through a wall in the
housing.
According to other embodiments of the present disclosure, an electric machine
includes a stator having a stator pole, a rotor including a rotor pole and
configured to
rotate relative to the stator, and a plurality of slots formed in the stator
or the rotor, the
plurality of slots configured to reduce eddy currents during operation of the
electric
machine.
Certain embodiments of the invention may provide numerous technical
advantages. For example, a technical advantage of some embodiments may include
the capability to produce very high torque and power densities in motors and
generators. Other technical advantages of other embodiments may include the
capability to balance forces in short-flux path motor / generators to reduce
cogging,
vibration, and/or noise. Other technical advantages of other embodiments may
include the capability to efficiently remove waste heat from electrical and
magnetic
circuits by evaporating or boiling a volatile fluid. Yet other technical
advantages of
other embodiments may include methods for laminating stators and rotors for
increased magnetic flux and reduced eddy currents. Yet other technical
advantages of
other embodiments may include methods for increasing the area of overlap
between a
stator core and a rotor blade, which may increase torque for a given
magnetomotive
force Ni. Yet other technical advantages of other embodiments may include
methods
for interrelating U-shaped stators and U-shaped rotors to increase torque. Yet
other
technical advantages of other embodiments may include methods for adjusting
the
stator poles and/or rotor poles in an axial direction in order to adjust the
area of
overlap between the stator poles and rotor poles, which may be used to control
the
torque output for a given magnetomotive force Ni. Yet other technical
advantages of
other embodiments may include methods for configuring and controlling a
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permanent-magnet flat-blade rotor/U-shaped stator design. Yet other technical
advantages of other embodiments may include methods for staggering stator sets
to
overcome noise, vibration, and/or "cogging" effects. Yet other technical
advantages
of other embodiments may include methods for cooling the electrical machine.
Yet
other technical advantages of other embodiments may include methods for
penetrating
a sealed housing wall with a magnetic circuit. Yet other technical advantages
of other
embodiments may include methods for reducing eddy currents in non-laminar
metal,
e.g., using slots. Yet other technical advantages of other embodiments may
include
methods for linking "magnetic legs" to reduce space, noise, vibration, and/or
cogging
effects.
Various embodiments according to the present disclosure may include none,
any one, or any combination of technical advantages discussed above, and/or
various
other technical advantages not discussed above.
BRIEF DESCRIPTION OF THE DRAWINGS
To provide a more complete understanding of the embodiments of the
invention and features and advantages thereof, reference is made to the
following
description, taken in conjunction with the accompanying FIGURES, wherein like
reference numerals represent like parts, in which:
FIGURE lA shows a schematic representation of an example conventional
switched reluctance motor (SRM);
FIGURE 1B is a dot representation of the example SRM of FIGURE 1A;
FIGURE 2 shows a schematic representation of a long flux path through the
conventional switched reluctance motor (SRM) of FIGURE lA;
FIGURE 3 shows in a chart the effect of MMF drop in the torque production
of an example one-phase, one horsepower machine;
FIGURE 4 shows a dot representation for an example switched reluctance
motor (SRM), according to an embodiment of the invention;
FIGURES 5A and 5B illustrate an example rotor/stator configuration,
according to an embodiment of the invention;
FIGURE 6 shows an outer rotor assembly of an example rotor/stator
configuration, according to an embodiment of the invention;
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FIGURE 7 shows an inner rotor assembly of an example rotor/stator
configuration, according to an embodiment of the invention;
FIGURE 8 shows an example stator/compressor case of an example
rotor/stator configuration, according to an embodiment of the invention;
5 FIGURE 9 shows a cutaway view of an example composite assembly of an
example rotor/stator configuration, according to an embodiment of the
invention; and
FIGURE 10 shows the composite assembly of FIGURE 9 without the
cutaway;
FIGURE 11 shows a side view of how a rotor can change shape when it
expands due to centrifugal and thermal effects;
FIGURE 12 shows an example rotor/stator configuration, according to another
embodiment of the invention;
FIGURE 13A and 13B show an example rotor/stator configuration, according
to another embodiment of the invention;
FIGURE 14 shows an example rotor/stator configuration, according to another
embodiment of the invention;
FIGURE 15 shows an unaligned position, a midway position, and an aligned
position;
FIGURE 16 shows an energy conversion loop;
FIGURE 17 shows an example rotor/stator configuration, according to another
embodiment of the invention;
FIGURE 18 shows an example rotor/stator configuration, according to another
embodiment of the invention;
FIGURE 19 shows an example rotor configuration, according to another
embodiment of the invention;
FIGURE 20 shows an example rotor/stator configuration, according to another
embodiment of the invention;
FIGURES 21A and 21B show an example rotor/stator configuration,
according to another embodiment of the invention;
FIGURE 22 illustrates the formation of flux lines in an example SRM drive;
FIGURES 23 and 24 shows the placement of easily saturated materials or flux
barriers under the surface of rotors;
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FIGURE 25 shows a chart of B-H curves for various alloys;
FIGURE 26A shows a representation of a magnetic circuit in an example flat
blade/U-shaped core rotor/stator configuration;
FIGURE 26B shows a cross-section taken along line 26B-26B in FIGURE
26A of a portion of a bundle of round wires in an example close-packed
configuration;
FIGURE 27 shows a relationship between magnetic field intensity and
magnetic flux density for a 0.012-inch-thick M-5 grain-oriented electrical
steel;
FIGURE 28 show the relationship between magnetic field density and
magnetic flux permeability for a 0.012-inch-thick M-5 grain-oriented
electrical steel;
FIGURE 29 shows that a force f is constant with respect to the fractional
closure (x/b) of a flat bade relative to a U-shaped core, except for high area
ratios
( Ag / Aj where the core starts to saturate;
FIGURE 30 shows that the magnetic flux ~ increases linearly with the
fractional closure (x/b) of a flat bade relative to a U-shaped core, except
for high area
ratios ( Ag / Aj when the core starts to saturate;
FIGURE 31 shows that the core magnetic flux density B, has a similar pattern
as the magnetic flux ~ relative to the fractional closure (x/b) of a flat bade
relative to a
U-shaped core;
FIGURE 32 shows that the gap magnetic flux density Bg (which is the same as
the blade magnetic flux density Bb) is nearly constant for each area ratio Ag
/ A, and
fractional closure (x/b) of a flat bade relative to a U-shaped core, except
when the core
starts to saturate at high area ratios;
FIGURE 33 shows a representation of an alternative geometry of a rotor/stator
configuration in which a U-shaped rotor blade slides past a U-shaped stator
core;
FIGURE 34 shows a representation of another alternative geometry of a
rotor/stator configuration, which is representative of a rotor moving relative
to a pair
of opposite stator poles in a conventional switched reluctance motor;
FIGURES 35A and 35B illustrate examples of how the linear motion shown in
FIGURES 26A and 33 can be converted to rotary motion;
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FIGURES 36A and 36B show that the U-shaped stators in the configurations
shown in FIGURES 26A and 33 may be similar, but rotated by 90 degrees relative
to
each other;
FIGURES 37A and 37B show an example orientation of lamination layers for
a U-shaped blade/U-shaped core configuration and a flat blade /U-shaped core
configuration, respectively, according to certain embodiments;
FIGURE 38 shows an example orientation of lamination layers for a stator
pair and a flat blade in a flat blade /U-shaped core rotor/stator
configuration,
according to certain embodiments;
FIGURE 39 shows an example method of making a laminar stator by
wrapping the laminations around a mandrel, according to certain embodiments;
FIGURE 40A shows an example technique for cutting a laminar structure at a
non-right angle to for a U-shaped stator having an area ratio Ag / A, > 1,
according to
certain embodiments;
FIGURE 40B and 40C show adjustment of a U-shaped stator in an axial
direction relative to a flat blade in order to adjust the gap area Ag between
the stator
legs and the flat blade, which adjusts the torque generated for a given Ni,
according to
certain embodiments;
FIGURES 41A and 41B show various housing aspect ratios L/r ranging from
1.0 to 4.0, which are used in the subsequent analysis of various rotor/stator
configurations;
FIGURE 42 shows a rotation of a 6/4 (6 stators, 4 rotors) conventional
switched reluctance motor;
FIGURE 43 shows an example stator firing sequence for the conventional 6/4
switched reluctance motor of FIGURE 42;
FIGURE 44 shows a rotation of a 12/10 (12 stators, 10 rotors) conventional
switched reluctance motor;
FIGURE 45 shows an example stator firing sequence for the conventional
12/10 switched reluctance motor of FIGURE 44;
FIGURE 46 shows the stator width for a 6/4 switched reluctance motor;
FIGURE 47 shows a "unit cell" for a stator pair of a conventional switched
reluctance motor;
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FIGURE 48 shows the rotation of an example U-shaped blade/U-shaped core
rotor/stator configuration with six stator pairs and four blades, according to
certain
embodiments;
FIGURE 49 shows an example stator firing sequence for the example U-
shaped blade/U-shaped core rotor/stator configuration of FIGURE 48, according
to
certain embodiments;
FIGURE 50 shows that the stator width c is c = 24 in the U-shaped blade/U-
24
core configuration of FIGURE 48;
FIGURE 51 shows a "unit cell" for a first U-shaped stator pair for use in a U-
shaped blade/U-shaped core rotor/stator configuration, and a second U-shaped
stator
pair offset from the first U-shaped stator pair, according to certain
embodiments;
FIGURE 52 shows the rotation of an example U-shaped blade/U-shaped core
rotor/stator configuration including double the number of rotor blades and
stator pairs
as FIGURE 48, according to certain embodiments;
FIGURE 53 shows an example stator firing sequence for the example U-
shaped blade/U-shaped core rotor/stator configuration of FIGURE 52, according
to
certain embodiments;
FIGURE 54 shows an example U-shaped blade/U-shaped core rotor/stator
configuration having an equal number of rotor blades and stator poles (12/12),
and
where all stator poles may be energized/de-energized simultaneously, according
to
certain embodiments;
FIGURE 55 shows an example stator firing sequence for the example U-
shaped blade/U-shaped core rotor/stator configuration of FIGURE 54, according
to
certain embodiments;
FIGURE 56 shows how the stator poles of a U-shaped blade/U-shaped core
rotor/stator configuration having an equal number of rotor blades and stator
poles
(16/16) can all be energized at the same time, according to certain
embodiments;
FIGURE 57 shows the rotation of an example flat blade/U-shaped core
rotor/stator configuration in a 6/4 configuration, according to certain
embodiments;
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FIGURE 58 shows an example stator firing sequence for the example 6/4 flat
blade/U-shaped core rotor/stator configuration of FIGURE 57, according to
certain
embodiments;
FIGURE 59 shows the rotation of an example flat blade/U-shaped core
rotor/stator configuration in a 12/8 configuration, according to certain
embodiments;
FIGURE 60 shows an example stator firing sequence for the example 12/8 flat
blade/U-shaped core rotor/stator configuration of FIGURE 58, according to
certain
embodiments;
FIGURES 61 A, 61 B, and 61 C show that for certain embodiments of a flat
blade/U-shaped core rotor/stator configuration, the stator width b is b = 2g
with a
denominator of 8 for the 6/4 configuration, 16 for a 12/8 configuration, and
32 for a
24/16 configuration;
FIGURE 62A shows a "unit cell" for a U-shaped stator pair for use in a flat
blade/U-shaped core rotor/stator configuration, along with a second U-shaped
stator
pair of an adjacent set of stators, showing how a wire bundle can be wrapped
around
the legs of adjacent stator pairs to form a "magnetic leg," according to
certain
embodiments;
FIGURE 62B shows mechanically coupling unit cells together to create a
series of "magnetic legs" that have a common core with the magnetic flux
flowing in
the same direction, according to certain embodiments;
FIGURE 63A shows a "unit cell" for a U-shaped stator pair for use in a flat
blade/U-shaped core rotor/stator configuration, which is similar to FIGURE
62A,
except the width of the core body is narrowed from b to b*, according to
certain
embodiments;
FIGURE 63B shows an unfolded view of the unit cell of FIGURE 63A,
according to certain embodiments;
FIGURE 64 shows the rotation of an example permanent-magnetic flat-blade
motor including permanent magnet flat blades on the rotor, according to
certain
embodiments;
FIGURE 65 shows an example stator energizing sequence for the flat-blade
permanent magnet motor of FIGURE 64, according to certain embodiments;
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FIGURE 66 shows an example system and method for cooling stators that
pierce a housing wall of a cooling system housing, according to certain
embodiments;
FIGURE 67 shows a configuration of a stator pole including a non-laminar
portion provided for piercing a housing wall of a cooling system, in order to
resist
5 leakage through the housing wall, according to certain embodiments;
FIGURE 68 shows details of a non-laminar portion of a stator pole (e.g., as
used in the configuration of FIGURE 67), including slots configured to align
with
lamination layers of a laminar portion of the stator pole, according to
certain
embodiments; and
10 FIGURE 69 shows details of a non-laminar leg portions of a U-shaped stator
pole (e.g., as used in the configuration of FIGURE 67), including slots
configured to
align with both (a) lamination layers of a laminar portion of the stator pole
and (b)
lamination layers or slots of a flat rotor blade configured to pass between
the U-
shaped stator leg portions; according to certain embodiments;
DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS
It should be understood at the outset that although example implementations
of embodiments of the invention are illustrated below, embodiments of the
present
invention may be implemented using any number of techniques, whether currently
known or in existence. The present invention should in no way be limited to
the
example implementations, drawings, and techniques illustrated below.
Additionally,
the drawings are not necessarily drawn to scale.
Various electric machines such as motors and generators and type variations
associated with such motors and generators may benefit from one or more of the
embodiments described herein. Example type variations include, but are not
limited
to, switched reluctance motors (SRM), permanent magnet AC motors, brushless DC
(BLDC) motors, switched reluctance generators (SRG), permanent magnet AC
generators, and brushless dc generators (BLDCG). Although particular
embodiments
are described with reference to one or more type variations of motor and/or
generators, it should be expressly understood that such embodiments may be
utilized
with other type variations of motors or generators. Accordingly, the
description
provided with certain embodiments described herein are intended only as
illustrating
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examples type variations that may avail benefits of embodiments of the
invention.
For example, teachings of some embodiment of the invention increase the
torque,
power densities, and efficiency of electric motors, particularly switched
reluctance
motors (SRM) and permanent magnet AC motors (PMM). Such embodiments may
also be used with brushless DC (BLDC) motors, for example. Some of same
advantages described with reference to these embodiments may be realized by
switched reluctance generators (SRG), permanent magnet AC generators, and
brushless dc generators (BLDCG).
In conventional radial and axial SRMs, the magnetic flux flows through a long
path through the whole body of a stator and rotor. Due to the saturation of
iron,
conventional SRMs have a large drop in the magneto motive force (MMF) because
the flux path is so large. One way to reduce the loss of MMF is to design
thicker
stators and rotors, which reduces the flux density. However, this approach
increases
the weight, cost, and size of the machine. Accordingly, teachings of
embodiment of
the invention recognize that a more desirable approach to reduce these losses
is to
minimize the flux path, which is a function of geometry and type of machine.
Teachings of some embodiments additionally introduce a new family of
stator/pole interactions and configurations for SRMs and PMMs. In this family,
stator
poles have been changed from a conventional cylindrical shape to U-shaped pole
pairs. This configuration allows for a shorter magnetic flux path, which in
particular
embodiments may improve the efficiency, torque, and power density of the
machine.
To take full advantage of the isolated rotor/stator structures of this
invention,
sensorless SRM, PMM, and BLDC control methods may be utilized, according to
particular embodiments.
The switched reluctance motor (SRM) has salient poles on both the stator and
rotor. It has concentrated windings on the stator and no winding on the rotor.
This
structure is inexpensive and rugged, which helps SRMs to operate with high
efficiency over a wide speed range. Further, its converter is fault tolerant.
SRMs can
operate very well in harsh environments, so they can be integrated with
mechanical
machines (e.g., compressors, expanders, engines, and pumps). However, due to
the
switching nature of their operation, SRMs need power switches and controllers.
The
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recent availability of inexpensive power semiconductors and digital
controllers has
allowed SRMs to become a serious competitor to conventional electric drives.
There are several SRM configurations depending on the number and size of
the rotor and stator poles. Also, as with conventional electric machines, SRMs
can be
built as linear-, rotary-, and axial-flux machines. In these configurations,
the flux
flows 180 electrical degrees through the iron. Due to saturation of iron, this
long path
can produce a large drop in MMF, which decreases torque density, power, and
efficiency of the machines. Increasing the size of the stator and rotor back
iron can
avoid this MMF drop, but unfortunately, it increases the motor size, weight,
and cost.
Using bipolar excitation of phases can shorten the flux path, but they need a
complex
converter. Also, they are not applicable when there is no overlapping in
conduction
of phases.
In addition, many of the issues discussed above regarding switched reluctance
motor (SRM) apply also to permanent magnet motors (PMM).
FIGURE 1A shows a schematic representation of a conventional switched
reluctance motor (SRM) 100. The SRM 100 of FIGURE 1 A includes a stator 110
and
a rotor 140. The stator 110 includes eight stationary stator poles 120 (each
with its
own inductor coil 120) and the inner rotor 140 includes six rotating rotor
poles 150
(no coils). The components of the SRM 100 are typically constructed from
magnetic
materials such as iron, nickel, or cobalt. In particular configurations, the
materials of
the SRM 100 can be laminar to reduce the effect of eddy currents. At any one
time, a
pair of opposing coils 130 is energized electrically. The inner magnetic
material in
the rotor poles 150 of the rotor 140 are attracted to the energized coil 130
causing the
entire inner rotor 140 to rotate while producing torque. Once alignment is
achieved,
the pair of opposing coils 130 is de-energized and the next pair of opposing
coils 130
is energized. This sequential firing of coils 130 causes the rotor 140 to
rotate while
producing torque. An illustration is provided with reference to FIGURE 1 B.
FIGURE 1B is a dot representation of the SRM 100 of FIGURE 1A. The
white circles represent the stator poles 120 and the black circles represent
the rotor
poles 150. Stator poles 120A, 120B are currently aligned with rotor poles
150A,
150B. Accordingly, the coils associated with this alignment (coils associated
with
stator poles 120A, 120B) can be de-energized and another set of coils can be
fired.
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For example, if the coils associated with the stator poles 120C and 120D are
fired,
rotor poles 150C, 150D will be attracted, rotating the rotor 140 counter-
clockwise.
The SRM 100 of FIGURE 1 has inherent two-fold symmetry.
FIGURE 2 shows a schematic representation of a long flux path through the
conventional switched reluctance motor (SRM) 100 of FIGURE 1 A. In the SRM
100,
magnetic fluxes must traverse 180 degree through both the stator 110 and the
rotor
140 - for example, through stator pole 120G, rotor pole 150G, rotor pole 150H,
stator
pole 120H, and inner rotor 140, itself. Such long flux paths can lead to the
creation of
undesirably eddies, which dissipate energy as heat. Additionally, due to the
high flux
density, the magneto motive force (MMF) drop will be very high, particularly
if the
stator 110 and rotor 140 back iron are thin.
As an example of MMF drop, FIGURE 3 shows in a chart 105 the effect of
MMF drop in the torque production of a one-phase, one horsepower machine. In
FIGURE 3, output torque 170 is plotted against rotor angle 160. Line 180 show
torque without the effect of saturation in the rotor 140 and stator 110 back
iron and
line 190 shows torque with the effect of saturation in rotor 140 and stator
110 back
iron. As can be seen, the MMF drop in torque production can be more than 6%.
Accordingly, teachings of some embodiments reduce the length of the flux path.
Further details of such embodiments will be described in greater detail below.
FIGURE 4 shows a dot representation for a switched reluctance motor (SRM)
200, according to an embodiment of the invention. The SRM 200 of FIGURE 4 may
operate in a similar manner to the SRM described with reference to FIGURE 1 B.
However, whereas the SRM 100 of FIGURE 1 B fire two coils associated with two
stator pole 120 at a time, the SRM of FIGURE 4 fires four coils associated
with four
stator poles 220 at a time. The increased firing of such coils/stator poles
220
increases the torque.
The SRM 200 of FIGURE 4 has a rotor with eight rotor poles 250 and a stator
with twelve stator poles 220. The active magnetized sets of stator poles 220
are
denoted by arrowed lines 225 and the attractive forces through the flux
linkages (e.g.,
between a rotor pole 250 and stator pole 220) are shown by the shorter lines
235
through a counterclockwise progression of 40 of rotor rotation. At 45 , the
configuration would appear identical to the 0 configuration. As can be seen
with
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reference to these various rotor angles, as soon as a alignment between four
stator
poles 220 and four rotor poles 250 occur, four different stator poles 220 are
fired to
attract the rotor poles 250 to the four different stator poles 220.
The switched reluctance motor 200 in FIGURE 4 has four-fold symmetry.
That is, at any one time, four stator poles 220 (the sets denoted by arrowed
lines 225)
are energized, which as referenced above, is twice as many as a conventional
switched reluctance motor (e.g., SRM 100 of FIGURE 1). Because twice as many
stator poles 220 are energized, the torque is doubled.
In particular embodiments, adding more symmetry will further increase
torque. For example, six-fold symmetry would increase the torque by three
times
compared to a conventional switched reluctance motor. In particular
embodiments,
increased symmetry may be achieved by making the rotor as blade-like
projections
that rotate within a U-shaped stator, for example, as described below with
reference to
the embodiments of FIGURES 5A and 5B. In other embodiments, increased
symmetry may be achieved in other manners as described in more details below.
As used herein, the term "U-shaped" may refer to any shape defining a pair of
legs or elongated portions, or any curved or non-linear shape defining a pair
or ends
generally extending in the same direction, including, for example, generally U-
shaped, V-shaped, or C-shaped, or multi-pronged. "U-shaped" may also be
referred
to as "C-shaped" or "V-shaped."
FIGURES 5A and 5B illustrate a rotor/stator configuration 300, according to
an embodiment of the invention. For purposes of illustration, the embodiment
of the
rotor/stator configuration 300 of FIGURES 5A and 5B will be described as a
switched
reluctance motor (SRM). However, as briefly referenced above, in particular
embodiments, the rotor/state configuration 300 may be utilized as other types
of
motors. And, in other embodiments, the rotor/state configuration 300 may be
utilized
in other types of electric machines such as generators.
In the rotor/state configuration 300 of FIGURES 5A and 513, a blade-like rotor
pole or blade 350, affixed to a rotating body 340, is shown passing through a
U-
shaped electromagnet core or U-shaped stator pole 320. In this configuration,
the flux
path is relatively short, compared to conventional SRMs. For example, the
magnetic
flux produced by a coil 330 fired on the U-shaped pole 320 would pass through
one
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leg 322 of the U-shaped stator pole 320 through the blade 350 and to the other
leg 324
of the U-shaped stator pole 320 in a circular-like path. In particular
embodiments,
this short path - in addition to diminishing the long path deficiencies
described above
- enables increased symmetry because the path does not traverse the center of
the
5 rotating body 340 and has little effect, if any, on other flux paths.
Additionally, in
particular embodiments, the short path enables use of the center of the
rotating body
340 for other purposes. Further details of such embodiments will be described
below.
Furthermore, radial loads are applied to the rotor with this embodiment and
axial
loads on the rotor are balanced. Additionally, extra radius is afforded by the
blade
10 350, thus increasing generated torque.
In particular embodiments, a rotor/stator configuration (e.g., the
rotor/stator
configuration 300 of FIGURES 5A and 513) can be integrated with other features
such
as a gerotor compressor/expander and other embodiments described in the
following
United States Patents and Patent Application Publications: Publication No.
15 2003/0228237; Publication No. 2003/0215345; Publication No. 2003/0106301;
Patent No. 6,336,317; and Patent No. 6,530,211.
Desi= Case Implementation
FIGURES 6-10 illustrate a rotor/stator configuration 450, according to an
embodiment of the invention. The rotor/stator configuration 450 of FIGURES 6-
10 is
used with a compressor. However, as briefly referenced above, in particular
embodiments, the rotor/stator configuration 450 may be utilized as other types
of
motors and other types of electric machines such as generators. The
rotor/state
configuration 450 of FIGURES 6-10 includes three stacked arrays of twelve
stator
poles 444 and eight rotor blades 412. The rotor/stator configuration 450 for
the
compressor in FIGURES 6-10 may operate in a similar manner to the rotor/state
configuration 300 described above with reference to FIGURES 5A and 5B. FIGURE
6 shows an outer rotor assembly 400 of the rotor/stator configuration 450,
according
to an embodiment of the invention. The outer rotor assembly 400 in FIGURE 6
includes a bearing cap 402, a bearing sleeve 404, a port plate 406,
inlet/outlet ports
408, two rotor segments 410A/410B with rotor blades 412 mounted, a seal plate
414
to separate the dry compression region from the lubricated gear cavity, a
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16
representation of the outer gear 416 (internal gear), an end plate 418 with
blades 412
mounted, an outer rear bearing 420, and another bearing cap 422. In this
embodiment, the outer compressor rotor serves as the rotor for the SRM.
In this embodiment, there are eight outer rotor lobes 411 with eight blades
412
in each radial array 413 of rotor poles. In particular embodiments, such
symmetry
may be necessary to minimize centrifugal stress/deformation. In this
configuration,
ferromagnetic materials utilized for the operation of the rotor/stator
configuration 450
may only be placed in the blades 412 of the radial array 413.
FIGURE 7 shows an inner rotor assembly 430 of the rotor/stator configuration
450, according to an embodiment of the invention. The inner rotor assembly 430
of
FIGURE 7 includes an inner shaft 432, a stack of three (seven lobed) inner
rotors
434A/434B/434C, a spur gear 436, and an inner rear bearing 438.
Details of operation of the inner rotor assembly 430 with respect to the outer
rotor assembly 400, according to certain embodiments of the invention, as well
as
with other configuration variations are described in further detail in one ore
more of
the following United States Patents and/or Patent Application Publications:
Publication No. 2003/0228237; Publication No. 2003/0215345; Publication No.
2003/0106301; Patent No. 6,336,317; and Patent No. 6,530,211.
FIGURE 8 shows a stator/compressor case 440 of the rotor/stator
configuration 450, according to an embodiment of the invention. The
stator/compressor case 440 of FIGURE 8 in this embodiment includes three
stacks
442A, 442B, 442C of twelve stator poles 444, spaced at equal angles. Although
the
stator poles 444 could be mounted to the case 440 in many ways, an external
coil
embodiment is shown in FIGURE 8. There are two coils 446A, 446B per stator
pole
444, which are mounted in sets of three into a nonferromagnetic base plate
448,
forming a bolt-in pole cartridge 450. In particular embodiments, the coils
446A,
446B may be copper coils. In other embodiments, the coils 446A, 446B may be
made
of other materials. In particular embodiments, the number of coils 446 on a
given
stator pole 444 can be increased above two, thereby reducing the voltage that
must be
supplied to each coil. During operation of particular embodiments, all poles
in four
cartridges 450 (90 apart) may be magnetized simultaneously. The magnetization
occurs sequentially causing the outer rotor assembly 400 of FIGURE 6 to
rotate.
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17
FIGURE 9 shows a cutaway view of a composite assembly 460 of a
rotor/stator configuration 450, according to an embodiment of the invention.
The
composite assembly 460 shows an integration of the outer assembly 400, the
inner
assembly 430, and the stator/compressor case 440 of FIGURES 6 - 8 as well as
end
plates 462 providing bearing support and gas inlet/outlet porting through
openings
464. FIGURE 10 shows the composite assembly 460 without the cutaway.
In certain embodiments, during operation, the rotor may expand due to
centrifugal and thermal effects. To prevent contact between the rotor poles
and stator
poles, a large air gap is typically used. However, it is known that the torque
is
strongly affected by the air gap: a smaller gap results in more torque.
Accordingly,
there are advantages to reducing the gap as small as possible. Teachings of
some
embodiments recognize configurations for maintaining small gap during thermal
and
centrifugal expansion of a rotor.
FIGURE 11 shows a side view of how a rotor 540 changes shape when it
expands due to centrifugal and thermal effects. The rotor 540 has an axis of
rotation
503. The solid line 505 represents the rotor 540 prior to expansion and the
dotted line
507 represents the rotor 540 after expansion. Dots 510A, 512A, and 514A
represent
points on the rotor 540 at the cold/stopped position and dots 510C, 512C, and
514C
represent the same points on the rotor 540 at the hot/spinning position. The
left edge
or thermal datum 530 does not change because it is held in place whereas the
right
edge is free to expand. The trajectories 510B, 512B, and 514B of dots is
purely radial
at the thermal datum 530 and becomes more axial at distances farther from the
thermal datum 530.
FIGURE 12 shows a rotor/stator configuration 600, according to an
embodiment of the invention. The rotor/stator configuration 600 includes a
rotor 640
that rotates about an axis 603. The rotor 640 includes rotor poles 650 that
interact
with stator poles 620, for example, upon firing of coils 630. The rotor/stator
configuration 600 of FIGURE 12 may operate in a similar manner to the
rotor/stator
configuration 300 of FIGURES 5A and 513, except for an interface 645 between
the
rotor pole 650 and the stator pole 620. In the rotor/stator configuration 600
of
FIGURE 12, an angle of interface 645 between the rotor pole 650 and stator
pole 620
is the same as the trajectory of a dot on the surface of the rotor 540 shown
in FIGURE
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18
11. By matching these angles, the surface of the rotor pole 650 and the
surface of the
stator pole 620 slide past each other without changing an air gap 647, even as
the
rotor 640 spins and heats up. This design allows for very small air gaps to be
maintained even at a wide variety of rotor temperatures. In particular
embodiments,
the housing that holds the stator pole 620 may be assumed to be maintained at
a
constant temperature. Various different angles of interface 645 may be
provided in a
single configuration for a rotor pole 650/stator pole 620 pair, dependent upon
the
trajectory of the dot on the surface of the rotor 640.
FIGURE 13A and 13B show a rotor/stator configuration 700A, 700B,
according to another embodiment of the invention. The rotor/stator
configurations
700A, 700B include rotors 740 that rotate about an axis 703. The rotor/stator
configurations 700A, 700B of FIGURES 13A and 13B may operate in a similar
manner to the rotor/stator configuration 300 of FIGURES 5A and 5B, including
rotor
poles 750, stator poles 720A, 720B, and coils 730A, 730B. The rotor/stator
configuration 700A of FIGURE 13A show three U-shaped stators 720A, operating
as
independent units. The rotor/stator configuration 700B of and FIGURE 13B shows
a
single E-shaped stators 710B operating like three integrated U-shaped stators
720A.
This E-shaped stator 720B allows for higher torque density. Although an E-
shaped
stator 720B is shown in FIGURE 13B, other shapes may be used in other
embodiments in integrating stator poles into a single unit.
FIGURE 14 shows a rotor/stator configuration 800, according to another
embodiment of the invention. In a similar manner to that described above with
other
embodiments, the rotor/stator configuration 800 of FIGURE 14 may be utilized
with
various types of electric machines, including motors and generators. The
rotor/stator
configuration 800 of FIGURE 14 may operate in a similar manner to the
rotor/stator
configuration 300 of FIGURES 5A and 5B, including rotor poles 850 and U-shaped
stator poles 820. However, the stator poles 820 have been axially rotated
ninety
degrees such that the rotor poles 850 do not transverse between a gap of the U-
shape
stator poles 820. Similar to FIGURES 5A and 5B, the flux path is relatively
short.
For example, the magnetic flux produced by a coil fired on the U-shaped pole
820
would pass through one leg 822 of the pole 820 through the rotor pole 850
through a
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19
periphery of the rotor through another rotor pole 850 and to the other leg 824
of the
pole 820 in a circular-like path.
The rotor/stator configuration 800 of FIGURE 14 is shown with three phases
A, B, and C and two pairs of stator poles 820 per each phase. In this
embodiment,
stator poles 820 are U- shaped iron cores with coils that are inserted into a
non-
ferromagnetic yoke 890. In other embodiments the stator poles 820 may be made
of
materials other than iron and may have other configurations. The stator poles
820 in
particular embodiments may be electrically and magnetically isolated from each
other. The rotor 840 in the embodiment of FIGURE 14 may operate like a rotor
of a
conventional SRM; however, unlike a conventional SRM, the pitches of the rotor
pole
850 and stator pole 820 are the same.
The magnetic reluctance of each phase changes with position of the rotor 840.
As shown in FIGURE 15, when a rotor pole 850 is not aligned with two stator
poles
820, the phase inductance is at a minimum and this position may be called an
unaligned position. When the rotor pole 850 is aligned with the stator pole
820, the
magnetic inductance is at a maximum and this position may be called an aligned
position. Intermediate between the aligned position and unaligned position is
an
intermediate position. SRM torque is developed by the tendency of the magnetic
circuit to find the minimum reluctance (maximum inductance) configuration.
The configuration of FIGURE 14 is such that whenever the rotor 840 is
aligned with one phase, the other two phases are half-way aligned, so the
rotor 840
can move in either direction depending which phase will be excited next.
For a phase coil with current i linking flux, the co-energy W' can be found
from the definite integral:
W' = JAdi (1)
0
The torque produced by one phase coil at any rotor position is given by:
T = rMl
I o (2)
I d
i=coi7stamt
The output torque of an SRM is the summation of torque of all phases:
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N
T,,, T(ij,B) (3)
l =1
If the saturation effect is neglected, the instantaneous torque can be given
as:
T - 2a2 dO (4)
5
From Equation 4, it can be seen that to produce positive torque (motoring
torque) in SRM, the phase has to be excited when the phase bulk inductance
increases, which is the time that the rotor moves towards the stator pole.
Then it
should be unexcited when it is in aligned position. This cycle can be shown as
a loop
10 in flux linkage (X) - phase current (iph) plane, which is called energy
conversion loop
as shown in FIGURE 16. The area inside the loop (S) is equal to the converted
energy
in one stroke. So the average power (PaVe) and the average torque of the
machine
(Ta,) can be calculated as follows:
15 P NpN,NSSw ave 4~ (5)
NpNrNp,,S
Tnve - 4~ (6)
where, Np, Nr, Nph, q are the number of stator pole pairs per phase, number of
rotor
poles, number of stator phases, and rotor speed, respectively.
By changing the number of phases, stator pole pitch, and stator phase-to-phase
20 distance angle, different types of short-flux-path SRMs can be designed.
FIGURE 17 shows a rotor/stator configuration 900, according to another
embodiment of the invention. The rotor/stator configuration 900 of FIGURE 17
is a
two-phase model, which operates in a similar manner to the model described
with
reference to FIGURE 14. The configuration 900 of FIGURE 17 includes rotor 940;
rotor poles 950; stator poles 920; legs 922, 924; and yoke 990.
FIGURE 18 shows a rotor/stator configuration 1000, according to another
embodiment of the invention. In a similar manner to that described above with
other
embodiments, the rotor/stator configuration 1000 of FIGURE 18 may be utilized
with
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21
various types of electric machines, including motors and generators. The
rotor/stator
configuration 1000 of FIGURE 18 may operate in a similar manner to
rotor/stator
configuration 1000 of FIGURE 14, including U-shaped stator poles 1020, rotor
poles
1050, a non-ferromagnetic yoke 1080, and phases A, B, and C. However, in the
rotor/stator configuration 1000 of FIGURE 18, the rotor poles 1050 are placed
radially outward from the stator poles 1020. Accordingly, the rotor 1040
rotates
about the stator poles 1020. Similar to FIGURE 14, the flux path is relatively
short.
For example, the magnetic flux produced by a coil fired on the U-shaped stator
pole
1020 would pass through one leg 1022 of the stator pole 1020 through the rotor
pole
1050 and to the other leg 1024 of the stator pole 820 in a circular-like path.
As one
example application of the rotor/stator configuration 1000 according to a
particular
embodiment, the rotor/stator configuration 1000 may be a motor in the hub of
hybrid
or electric (fuel cell) vehicles, and others. In this embodiment, the wheel is
the
associated with the rotor 1040, rotating about the stators 1020. This
rotor/stator
configuration 1000 may additionally be applied to permanent magnet motors, for
example, as shown in FIGURE 19.
FIGURE 19 shows a rotor configuration 1100, according to another
embodiment of the invention. The rotor/stator configuration 1100 of FIGURE 14
may operate in a similar manner to rotor/stator configuration 1100 of FIGURE
14,
including U-shaped stator poles 1120, a non-ferromagnetic yoke 1190, and
phases A,
B, and C, except that a rotor 1140 contains alternating permanent magnet poles
1152,
1154.
FIGURE 20 shows a rotor/stator configuration 1200, according to another
embodiment of the invention. In a similar manner to that described above with
other
embodiments, the rotor/stator configuration 1200 of FIGURE 20 may be utilized
with
various types of electric machines, including motors and generators. The
rotor/stator
configuration 1200 of FIGURE 20 integrates several concepts described with
reference to other embodiments, including blades 1250A, 1250B from FIGURES 5A
and 5B; E-shaped stator poles 1220A, 1220B from FIGURE 13B; stator poles 1220B
radially inward of rotor poles 1250B from FIGURES 6-10; and stator poles 1220A
radially outward of rotor poles 1250B from FIGURE 18. The stator poles 1220A
are
rigidly mounted both on the inside and outside of a drum 1285, which allows
torque
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22
to be applied from both the inside and outside thereby increasing the total
torque and
power density. In particular embodiments, the rotor poles 1250A, 1250B may be
made of a ferromagnetic material, such as iron, which is a component of a
switched
reluctance motor. In other embodiments, the rotor poles 1250A, 1250B could be
permanent magnets with the poles parallel to the axis of rotation, which would
be a
component of a permanent magnet motor.
FIGURES 21A and 21B show a rotor/stator configuration 1300, according to
another embodiment of the invention. In a similar manner to that described
above
with other embodiments, the rotor/stator configuration 1200 of FIGURES 21A and
21B may be utilized with various types of electric machines, including motors
and
generators. The rotor/stator configuration 1300 of FIGURES 21A and 21B may
operate in a similar manner to the rotor/stator configuration 1300 of FIGURES
5A
and 5B, including rotor poles 1350 and U-shaped stator poles 1320. However,
the
rotor poles 1350 and U-shaped stator poles 1320 have been rotated ninety
degrees
such that rotor poles 1350 rotate between a leg 1322 of the stator pole 1320
that is
radially inward of the rotor pole 1350 and a leg 1324 of the stator pole 1320
that is
radially outward of the rotor pole 1350. In the embodiment of the rotor/stator
configuration 1300 of FIGURES 21A and 21B, it can be seen that the axial and
radial
fluxes co-exist.
In this embodiment and other embodiments, there may be no need for a
magnetic back-iron in the stator. Further, in this embodiment and other
embodiments,
the rotor may not carry any magnetic source. Yet further, in particular
embodiments,
the back iron of the rotor may not need to be made of ferromagnetic material,
thereby
creating flexibility design of the interface to the mechanical load.
In this embodiment and other embodiments, configuration may offer higher
levels of power density, a better participation of stator and the rotor in
force
generation process and lower iron losses, thereby offering a good solution for
high
frequency applications. In various embodiments described herein, the number of
stator and rotor poles can be selected to tailor a desired torque versus speed
characteristics. In particular embodiments, cooling of the stator may be very
easy.
Further, the modular structure of certain embodiments may offer a survivable
performance in the event of failure in one or more phases.
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Optimization of the magnetic forces
FIGURES 22-25 illustrate an optimization of magnetic forces, according to
embodiments of the invention. The electromagnetic force on the surface of a
rotor
has two components, one that is perpendicular to the direction of motion and
one that
is tangent to the direction of motion. These components of the force may be
referred
to as normal and tangential components of the force and can be computed from
magnetic field quantities according to the following equations:
1 2 z
(Bn - Bt )
2,uo (7)
.f = 1 BnBt
Po
For an optimal operation, the tangential component of the force needs to be
optimized
while the normal component of the force has to be kept at a minimal level or
possibly
eliminated. This, however, is not the case in conventional electromechanical
converters. To the contrary, the normal force forms the dominant product of
the
electromechanical energy conversion process. The main reason for this can be
explained by the continuity theorem given below. As the flux lines enter from
air into
a ferromagnetic material with high relative permeability the tangential and
normal
components of the flux density will vary according to the following equations:
Bn,air Biron
1 (8)
Bt,air = Bt,iron
Pr,iron
The above equations suggest that the flux lines in the air gap will enter the
iron almost
perpendicularly and then immediately change direction once enter the iron.
This in
turn suggests that in a SRM and on the surface of the rotor we only have
radial forces.
FIGURE 22 illustrates the formation of flux lines in a SRM drive. The flux
density, B, is shown in Teslas (T). The radial forces acting on the right side
of the
rotor (also referred to as fringing flux - indicated by arrow 1400) create
radial forces
(relative to the rotor surface) that create positive propelling force for the
rotor. This is
the area that needs attention. The more fluxes are pushed to this corner, the
better
machine operates. This explains why SRM operates more efficient under
saturated
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24
condition. This is because due to saturation, the effective air gap of the
machine has
increased and more flux lines are choosing the fringing path.
To enhance the migration of flux lines towards the fringing area, one
embodiment of the invention uses a composite rotor surface. In the composite
rotor
surface, the top most part of the of the rotor is formed by a material that
goes to
saturation easier and at a lower flux density, thereby reinforcing the
fringing at an
earlier stage of the electromechanical energy conversion process. In
particular
embodiments, the shape of the flux barrier or the shape of the composite can
be
optimized to take full advantage of the magnetic configuration. In another
embodiment, flux barriers can be introduced in the rotor to discriminate
against radial
fluxes entering the rotor normally and push more flux lines towards the
fringing area.
FIGURES 23, 24 and 25 illustrate these embodiments.
FIGURES 23 and 24 show the placement of easily saturated materials or flux
barriers 1590A, 1590B, 1590C, and 1590D under the surface of rotors 1550A,
1550B,
and stators 1520A, 1520B. Example materials for easily saturated materials or
flux
barriers 1590 include, but are not limited to M-45. Example ferromagnetic
materials
for the rotors 1550 and stators 1520 include, but are not limited HyperCo-50.
The
shape, configuration, and placement of the easily saturated materials or flux
barriers
may change based on the particular configurations of the rotors and stators.
FIGURE 25 shows a chart 1600 of B-H curve for various alloys. The chart
1600 of FIGURE 25 charts magnetic flux density 1675, B, against magnetic field
1685, H, for alloys 1605, 1615, and 1625.
Theory for Analyzing Various Rotor/Stator Configurations
Various different rotor/stator configurations are disclosed herein. One type
of
rotor/stator configuration disclosed herein may be referred to at "U-shaped
core/flat
blade" rotor/stator configurations. Some examples of the U-shaped core/flat
blade
configuration are shown and discussed above with reference to FIGURES 5-13 and
20-21. In this configuration, the cores (or stator poles) are generally U-
shaped with a
pair of legs, and the blades (or rotor poles) pass through a gap defined
between the
legs of the U-shaped cores. Such blades may be referred to as "flat" blades.
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Another type of rotor/stator configuration disclosed herein may be referred to
as "U-shaped blade/U-shaped core" rotor/stator configurations. Some examples
of
the U-shaped blade/U-shaped core configuration are shown and discussed above
with
reference to FIGURES 14-18. In this configuration, both the cores (or stator
poles)
5 and the blades (or rotor poles) are generally U-shaped. The U-shaped cores
include a
pair of legs, and the U-shaped blades include a pair of legs. The U-shaped
cores in
this configuration are axially rotated 90 degrees as compared to the U-shaped
core/flat
blade configuration. Thus, unlike in the U-shaped core/flat blade
configuration, the
blades in the U-shaped blade/U-shaped core configuration do not pass through a
gap
10 between the legs of each U-shaped core. Instead, the ends of the two legs
of each U-
shaped blade slide just past the ends of the two legs of each U-shaped core,
e.g., as
shown in FIGURES 14, 15, 17, and 18.
Presented below are methods for calculating the theoretical torque and other
performance characteristics provided by various rotor/stator configurations.
In
15 particular,
FIGURES 26-32, along with the corresponding text and equations below, provide
theory and calculations for determining the torque and other performance
characteristics provided by various U-shaped core/flat blade rotor/stator
configurations. Similarly, FIGURES 33-41, along with the corresponding text
and
20 equations below, provide theory and calculations for determining the torque
and other
performance characteristics provided by various U-shaped core/flat blade
rotor/stator
configurations.
"Flat blade/U-shaped core" rotor/stator configurations
25 FIGURE 26A illustrates a magnetic circuit created in a Flat blade/U-shaped
core rotor/stator configuration when a flat blade 1700 enters a magnetized U-
shaped
core 1702 having an energized wire coil 1704. U-shaped core 1702 includes a
first
leg 1708 and a second leg 1710, and flat blade 1700 passes through the gap
defined
between legs 1708 and 1710. The magnetomotive force F of the magnetic circuit
is:
F= Ni = F, + Fg + Fb (9)
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where
F = magnetomotive force (A = turn)
F, = magnetomotive force dissipated in core 1702 (A = turn)
Fg = magnetomotive force dissipated in the air gaps between core 1702
and flat blade 1700 (A = turn)
Fb = magnetomotive force dissipated in flat blade 1700 (A = turn)
N = number of turns in coil 1704
i = current (A)
The dissipation of magnetomotive force in each section of the magnetic circuit
follows:
F= Ni = Hj, + Hg 2g + Hb w
(10)
where
H~ = magnetic field intensity in core 1702 (A = turn/m)
Hg = magnetic field intensity in the air gaps between core 1702 and flat
blade 1700 (A = turn/m)
Hb = magnetic field intensity in flat blade 1700 (A = turn/m)
lc = length of core 1702 re (m)
g =length of each of the two air gaps between core 1702 and flat blade
1700 (m)
w = width of flat blade 1700 (m)
The magnetic flux density is related to the magnetic field intensity as
follows:
B= H
(11)
where
B = magnetic flux density (Wb/m2 or tesla)
= magnetic permeability (Wb/(A = turn = m))
All or portions of blade 1700 and core 1702 may be formed from any suitable
materials. In certain applications, metals with high magnetic permeability may
be
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27
preferred. As an example only, blade 1700 and/or core 1702 may be formed from
0.012-inch-thick M-5 grain-oriented electrical steel.
Various example dimensions are shown in FIGURE 26A. It should be
understood that these are example values only, and that the components shown
in
FIGURE 26A may be formed with any other suitable dimensions.
FIGURE 27 is a graph illustrating the relationship between B and H for an
example material: 0.012-inch-thick M-5 grain-oriented electrical steel. The
magnetic
permeability ( ) is the slope of the line 1720.
FIGURE 28 is a graph illustrating the magnetic permeability as a function of
B for 0.012-inch-thick M-5 grain-oriented electrical steel. Substituting
Equation 11
into Equation 10 gives:
F = Ni = B'l' + Bg2g + Baw
c o ~tb
(12)
where
c = magnetic permeability in core 1702 (Wb/(A = turn = m))
o = magnetic permeability in the air
= magnetic permeability of free space = 47c X 10-7 Wb/(A turn m)
b = magnetic permeability in flat blade 1700 (Wb/(A = turn = m))
The magnetic flux is the same everywhere in the circuit and follows:
0 = BcAc = BgAg = BbAb
(13)
where
= magnetic flux (Wb)
Ac = cross-sectional area of core 1702 (m2), as indicated at leg 1710 in
FIGURE 26A
Ag = area of the air gap (i.e., the area of overlap) between core 1702 and
flat blade 1700 at an instant of time (m2)
Ab = area of flat blade 1700 through which the magnetic flux passes at an
instant of time (m)
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If the flat blade width w is small, the magnetic field lines do not have
enough
space to spread out so the magnetic flux density of the air gap and flat blade
1700 are
about the same, thus allowing the following approximation to be made:
Ab = Ag
(14)
Using this relationship, the magnetic flux density can be calculated in each
portion of
the magnetic circuit.
B = ~
` A,
B = 0
g A
a
Bb 0
A
b
(15)
Substituting the relationships in Equations 15 into Equation 12 gives the
following:
F=Ni= 0" + 02g + Ow =0 l` + 2g + w
ltcAc N oAg bAb cAc oAg bAb
0 Ni
l, + 2g + w
eAc oAg bAb
(16)
The terms in the brackets are the reluctance R (A = turn/Wb) of each portion
of the
magnetic circuit.
F=Ni=O(Rc +Rg+Rb~
(17)
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where
R, = lc = reluctance of core 1702 (A = turn/Wb)
cAc
Rg = 2g = reluctance of the two air gaps between core 1702 and blade 1700 (A
turn/Wb)
oAg
Rb = W= reluctance of flat blade 1700 (A = turn/Wb)
!"~ b Ab
(18)
The work required to supply the energy to a magnetic field is:
Wfld 1 = 2 L(x)i 2
(19)
where
Wfld = work required to supply energy to the magnetic field (J)
L(x) = instantaneous inductance (Wb = turn /A), which is a function of the
position x of blade 1700 relative to core 1702 as blade 1700 moves
through the gap between legs 1708 and 1710 (i.e., the length of
overlap between blade 1700 and core 1702), indicated as distance
"x" in FIGURE 26A.
As the flat blade moves laterally through the air gap between legs 1708 and
1710 of
core 1702, the inductance of the circuit increases, thus allowing the magnetic
flux to
increase. The inductance is:
NZ
L(x) _
R, + Rg + Rb
(20)
Substituting the expressions in Equations 18 gives:
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NZ
L(x) = lc + 2g + w
~tcAc ltoAg bAb
(21)
5 The areas may be expressed relative to the core area Ac as follows:
N2 N2 Ac
L(x) = l, + 2gAc + wAc = lc + 2gA, +wA,
E'i' c Ac E-l o`4g Ac ~a b Ab Ac EA c EI' o Ag b Ab
(22)
10 Using the approximation shown in Equation 14, the following equation
results:
N2Ac NzA,
L(x) = lc + 2gAc + wAc = lc Ac (2g w
+ +
c oAg N0g c Ag o b
(23)
15 The instantaneous air gap Ag, which is the instantaneous area of overlap
between
blade 1700 and core 1702 as blade 1700 moves through the gap between legs 1708
and 1710, is:
Ag = b Ag
20 (24)
where
Ag = area of the closed air gap (i.e., at a position of maximum overlap
between blade 1700 and core 1702) (m2)
25 b = width of flat blade 1700 (m)
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31
x = position of flat blade 1700 relative to core 1702 as blade 1700 moves
through the gap between legs 1708 and 1710 (i.e., the length of
overlap between blade 1700 and core 1702), indicated as distance
"x" in FIGURE 26A (m).
Equation 24 may be substituted into Equation 23 to provide:
_ NZA~
L(x) l, A, b 2g w
+-- -+-
, Ag x o
(25)
Equation 25 may be substituted into Equation 19 to give the work required to
build
the magnetic field:
W_ 1 N2AC i2 = 1 (Ni~2A,
~ d 2 l , + Ac b 2g + w 2 lc Ac b 2g + w
- -- + -
c Ag x o e c Ag x Ito b
(26)
The following definitions
A= ~(Ni)ZA,
= Z
B ` = 0 (if the core is not saturated)
c
C A` b 2g + w = A` b 2g (if the blade is not saturated)
Ag No Nb Ao No
(27)
may be substituted into Equation 26 to provide:
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32
_ A
Wfld C
B+-
x
(28)
The force f acting on the flat blade as the magnetic flux increases follows:
fa~n``
(29)
Taking the derivative of Equation 28 gives
C
2
f=-A 2
CB+xJ
(30)
If the core and flat blade are not saturated (where saturated = maximum
magnetic flux
through the circuit) then Equation 30 simplifies to:
1(Ni)2A o
,
f=-C=-~ 2 =- 4 (Ni)z A, A A , b g g b ,
Ag
(31)
Equation 31 indicates that as long as core 1702 is not saturated, the force
acting on flat blade 1700 will be constant and independent of the position x
of flat
blade 1700. Further, for a given core area A, and magnetomotive force Ni, the
force
increases with a smaller gap g, increases with larger close air gap area Ag ,
and
decreases with greater flat blade width b.
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33
Using the following procedure, the equations above allow the calculation of
the force in a flat blade, allowing for saturation of the core:
1. Specify the following: A, Ag / A, b, l, w, g, Ni, x.
2. Guess ~.
3. Calculate B, Bg, and Bb (Equations 15).
4. Calculate , and b (e.g., see FIGURE 28).
For example, = 0.1422B5 - 0.6313B4 + 0.9695B3 - 0.6939B2 + 0.2954B +
0.0055
for 0.012 M-5 grain-oriented electrical steel, valid up to B= 1.9 Wb/m2
5. Calculate ~ (Equation 16).
6. Iterate Steps 2 to 5 until convergence.
7. Calculate A, B, and C (Equations 27).
8. Calculate f (Equation 30).
FIGURE 29 is a graph illustrating force f versus the fractional closure (xlb)
of
the flat blade, for three different area ratios Ag / A, in an example Flat
blade/U-
shaped core stator/rotor configuration. The parameters x, b, Ag , and A, are
defined
above with reference to FIGURE 26A. x/b is the fractional closure, or overlap,
of the
flat blade as the flat blade moves through the gap between the two legs of the
U-
shaped core. Ao / A, is the ratio of the surface area of the end of a stator
leg that
interfaces with the flat blade to the cross-section of that stator leg, as
shown in
FIGURE 26A.
As shown in FIGURE 29, the force f is constant with respect to the fractional
closure (x/b) of the flat blade, except for relatively high area ratios Ag /
A, (e.g., area
ratio = 3) when the core starts to saturate. A relatively high area ratio Ag /
A, may be
defined as an area ratio Ag l A, where saturation may have a significant
effect on the
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34
force as the fractional closure (x/b) increases, e.g., area ratio = 3, as
shown in
FIGURE 29.
FIGURE 30 is a graph illustrating magnetic flux ~ versus the fractional
closure (x/b) of the flat blade, for three different area ratios Ag / A. in an
example Flat
blade/U-shaped core stator/rotor configuration. The graph indicates that the
magnetic
flux ~ increases linearly with fractional closure, except for relatively high
area ratios
Ag / A, (e.g., area ratio = 3) when the core starts to saturate.
FIGURE 31 is a graph illustrating magnetic flux density B, versus the
fractional closure (x/b) of the flat blade, for three different area ratios Ag
/ A, in an
example Flat blade/U-shaped core stator/rotor configuration. The graph
indicates that
the core magnetic flux density B, has a similar pattern as ~, which is
expected because
the two quantities are related by the core area A, which is constant.
FIGURE 32 is a graph illustrating magnetic flux density in both the blade and
in the gap, Bg and Bb , versus the fractional closure (x/b) of the flat blade,
for three
different area ratios Ag / A. in an example Flat blade/U-shaped core
stator/rotor
configuration. The graph indicates that the gap and blade magnetic flux
density Bg
and Bb are nearly constant for each area ratio Ag / A, and fractional closure,
except for
relatively high area ratios Ag / A, (e.g., area ratio = 3) when the core
starts to saturate.
The graphs shown in FIGURES 29-32 were generated based on an example
Flat blade/U-shaped core stator/rotor configuration. The illustrated data
corresponding to the area ratios of 1, 2, and 3 corresponds to that example
configuration. Different configurations (e.g., different geometries,
dimensions,
materials, coil turns (N), current, etc.) will yield different results for
similar area
ratios. Thus, what is a "relatively high area ratio" (i.e., where saturation
has a
significant effect on the force and/or flux densities) depends on the
particular
configuration. For example, an area ratio of 3 may not be affected by
saturation --
and thus not a "relatively high area ratio" -- in other configurations.
In some embodiments, for a torque-dense electric motor, the core should
saturate (i.e., maximum B) just as the air gap is fully closed by the blade
(i.e., when
xlb = 1). This strategy may take maximum advantage of the flux carrying
capacity of
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the core. As shown in FIGURE 31, only an area ratio of 3 caused the core to
saturate
with the Ni used in that configuration (500 A= turns). With all other
parameters held
constant, the core of the smaller area ratios (1 and 2) can be saturated by
increasing
Ni; however, this comes at the expense of an increased wire bundle area. An
5 advantage of using an increased area ratio is that it can cause saturation
of the core
with a small Ni, and hence increase the force acting on the blade. This
increased force
with a small Ni must come from somewhere - it comes from an increase in
voltage
that delivers the current. Thus, when the area ratio increases, it allows for
a smaller
Ni, and a larger voltage.
10 To maximize the torque from an electric motor, the core should saturate
near
x/b =1 (full closure of the air gap between the blade and core). For the
condition of
saturation at closure (x/b = 1):
omax = Bc, max Ac
15 (32)
The maximum magnetic flux occurs with the maximum allowable magnetomotive
force From Equation 16 for a flat blade:
20 ~j = (Ni)inax
Ymax -
11 + 2g + w
A, Ag 6A~
(33)
where Ag = Ab = Ag @ xlb = 1. Substituting Equation 32 into Equation 33 gives:
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36
(Ni).. A,
11 2g w 1,2g A, w A,
+ o + o + o + o
,A, oAg bAg ~ R. Ag b Aa
(Ni )max ~Ni ~max
Bc, inax
2g + w A,
11 + 2g A, + w A. +
-- - - - -- -
, o Ag b Ag , R. b As
l~ 2g w A~
(NZ )~nax = B~, max + + Ao
, R. b g
(34)
The following example shows example parameter values, some of which are taken
from FIGURE 26A:
g = 0.0005 m
o =4z x10-' Wb/(A-turn=m)
,: = 0.0036 Wb/(A tum m)(@1.8 T)
b = 0.0072 Wb/(A turn m)(@0.6 T)
Ag l A, =3
w=0.2m
l, = 0.5 m
l, + (2g + w A, _ l, + 2g A, + w A,
- -- - -----
, o b Ag , o As b As
_ 0.5 m + 2(0.0005 m) 1+ 0.2 m 1
0.0036 Wb/(A = turn = m) 4z x 10-' Wb/(A = turn m) 3 0.0072 Wb/(A = turn = m)
3
=(139+265+9.3) A=turn m'
Wb
In this example, the reluctance of the blade is small, the reluctance of the
air gap is
large, and the reluctance of the core is significant. It should be understood
that these
values are examples only, and that any other suitable values may be used.
Equation 34 may be reformulated as:
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37
(Ni)max 1 2g
P o
(35)
where p for the example above is:
2g 265A=turn=m2
Wb = 0.641
P l, + (2g +w A, (139 + 265 + 9.3) A. turn m2
Wb
'Lc No Nb `48
(36)
Substituting Equation 35 into Equation 31 gives:
2 0 2 0
o 1 2g A~ Ag g B,,max Ac AS
.f =- 4g B~, max p Q b A, N o p b A,
(37)
The power density of a motor is determined by its average torque and speed.
The
analysis presented above describes the torque ability of a motor. The
volumetric
torque density can be calculated as follows:
Tave _ Yf / ave _ Yf n pairs eo,t f
V izyZL * 7rO2L *
(38)
where
rf = radius where force is applied (m)
npal,.s = number of stator pairs
Oon = fraction of the time that a stator pair is on
f = force on a stator pair (and rotor) (N)
ro = outer radius of motor (m)
L * = length of unit cell (m)
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38
where the "unit cell" is the repeated unit along the length of the motor.
(This concept
of the "unit cell" is explained below in greater detail.) Substituting
Equation 37
gives:
2 0
Tave = Yf nPairs eon g Bc, max A, Ag
V -xoL* o p b A,
(39)
FIGURE 26B is a cross-sectional view of round wires 1730 of coil 1704 in a
close-packed wire coil configuration, taken along line 26B-26B shown in FIGURE
26A. The packing factor P for individual wires 1730 of cross-sectional area Al
is
related to the cross-sectional area of the wire bundle forming the coil, A, as
follows:
1 2
~'w
P = A' = 2 = 7r = 0.907
Ax, /-3Yw 2r3-
(40)
The number of turns in a wire bundle is:
NPAW
A;
(41)
An individual wire of cross-sectional area A; has a maximum current capacity
im,,
which is determined by the electrical conductivity, the heat transfer
coefficient, and
the allowable temperature rise.
Zmax
A;
imax = aA;
(42)
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39
For 10-gauge copper wire (as an example only), standard tables recommend the
following:
i= 30A X 1000 mm 2= 5 7 x 106 A/m2 (10-gauge wire)
5.26 mm2 ( m )
Multiplying Equation 41 by Equation 42 gives:
(Ni)max = (iA; ~ A'" = iPAw
A;
(43)
Comparison of Equation 43 with Equation 35 shows that the wire bundle cross-
sectional areaAW is:
(Ni )max = i PAw = B,, max 1 2g
p [t
A = Bc, max 1 2g
ip p o
(44)
"U-shaped blade/U-shaped core" rotor/stator configurations
FIGURE 33 illustrates a U-shaped blade/U-shaped core rotor/stator
configuration 1790 in which a U-shaped blade 1800 slides past a magnetized U-
shaped core 1802 having an energized wire coil 1804, e.g., as shown in FIGURES
14,
15, 17, and 18.
Various example dimensions are shown in FIGURE 33. It should be
understood that these are example values only, and that the components shown
in
FIGURE 33 may be formed with any other suitable dimensions.
FIGURE 34 illustrates a rotor/stator configuration 1830 that is representative
of a conventional switched reluctance motor (e.g., as shown in FIGURES 1-2).
The
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configuration includes a U-shaped core (stator) 1832 including first and
second legs
1840 and 1842, and a blade (rotor) 1834. In this model, the U-shaped core 1832
represents one half of the stator assembly shown in FIGURES 1-2. Thus, core
legs
1840 and 1842 represent opposite stator poles that are simultaneously charged,
e.g.,
5 stator poles 120G and 120H shown in FIGURE 2. Blade 1834 represents rotor
140
shown in FIGURES 1-2, including rotor poles 150G and 150H. The rotation of
rotor
140 relative to stator poles 120G and 120H in FIGURES 1-2 may be modeled as
linear translation (as indicated by arrow "x" in FIGURE 34), as the movement
by
rotor poles 150G and 150H by stator poles 120G and 120H may be approximated as
10 linear translation.
Various example dimensions are shown in FIGURE 34. It should be
understood that these are example values only, and that the components shown
in
FIGURE 34 may be formed with any other suitable dimensions.
The analysis of the geometries shown in FIGURES 33 and 34 is very similar
15 to the analysis presented above for the Flat blade/U-shaped core
rotor/stator
configuration shown in FIGURE 26A, except that the flux path through the
blades in
the configurations of FIGURES 33 and 34 is much longer than in the flat blade
configuration of FIGURE 26A. In particular, in the U-shaped blade/U-shaped
core
configuration shown in FIGURE 33, the flux path must flow along the complete U-
20 shaped length of the blade. And in the conventional SRM configuration shown
in
FIGURE 34, the flux path must flow across the full length of the rotor (from
rotor
pole to opposite rotor pole) and around one half of the stator yoke, as shown
in
FIGURE 2.
As a consequence of this increased flux path distance in the configurations of
25 FIGURES 33 and 34, the field lines have the opportunity to spread out over
the entire
width of the blades, which affects its reluctance. Also, in such
configurations, the
cross-sectional area of the core, closed air gap, and blades are typically the
same, as
shown in FIGURES 33 and 34.
30 A, = Ag = Ab
(45)
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41
The inductance of the magnetic circuit in such configurations is as follows:
NZ
L(x) = lc + 2g + w
cAc oAg A
(46)
where
w = flux path the blade (m)
The instantaneous air gap between the core and blade is:
x o x
Ag=cAg=cAc
(47)
which may be substituted into Equation 46:
N 2 N2Ac
L(x) = lc 2g w= l, 2g w
+ + -+ +-
NcAc o xAc NbAc c o x b
c c
(48)
The work required to build the magnetic field follows:
W_ 1 N z Ac 1.2 = 1 (Na )Z A,
nd 2 lc 2g w 2 l` + c 2g w l ~to x b ~Lc x ~to ~t b
c
(49)
The following definitions:
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42
A ~(Ni)ZA,
B Z` + w= 0 (if the core and blade are not saturated)
~t, 6
C 2gc
o
(50)
may be substituted into Equation 49:
_ A
W fld C
B+-
x
(51)
The forcef acting on the blade as the magnetic flux increases follows:
fa~fld
(52)
Taking the derivative of Equation 51 gives:
C
2
f=-A x Z
CB+~J
(53)
If the core and blade are not saturated then Equation 53 simplifies to:
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43
1(Nl)2 A A
2 ~
f C c g 2 4g )(Ni)2 c
o
(54)
In certain embodiments, to maximize the torque from an electric motor, the
core
should saturate near x/c =1 (full closure of the air gap between the blade and
the core).
For the condition of saturation at closure (x/c = 1):
Omax = Bc, max A~
(55)
The maximum magnetic flux occurs with the maximum allowable magnetomotive
force (Ni),,aX.
(Nt )max
Y max ~ 2g w
+ +
,, oAc bAc
(56)
Assume b = ~ at xlc = 1 (i.e., the core and blade materials are the same).
Substituting Equation 55 into Equation 56 gives:
(Ni)~nax _ (Ni~max `4c
B~,max`4~ lc 2g + w lC + 2g w
eAc oAc bAc , o b
B lNz)max
~,max l 2g w
c + +
c o b
(57)
Equation 57 may be reformulated as
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44
(Nl)max 1 2g
p R.
(58)
wherep is:
2g
__ o
p lc
+ 2g + w
- - -
c o It6
(59)
Substituting Equation 58 into Equation 54 gives:
f B 1 2g 2 Ac g Bc,max Z Ac
4g c,max p o c o p c
(60)
The volumetric torque density can be calculated as follows:
2
Tave _r.1~ J{~ove _rf n pairs eon J_ rf n pairs eon g Bc, max Ac
V -x,,zL* 7rroL* 7rroL* a p c
(61)
FIGURES 35A and 35B illustrate two examples of how the linear motion
described in FIGURES 26A and 33 can be converted to rotary motion. FIGURES
35A illustrates a U-shaped blade/U-shaped core rotor/stator configuration 1850
including a U-shaped blade 1852 positioned on a rotor that rotates relative to
a U-
shaped stator 1854. The U-shaped blade 1852 includes a pair of legs 1855 and
1856,
and the U-shaped core 1854 includes a pair of legs 1857 and 1858. The core is
charged (indicated at "Start On") when the blade legs 1855 and 1856 approach
the
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core legs 1857 and 1858, and turned off (indicated at "End On") when the blade
legs
1855 and 1856 are aligned with the core legs 1857 and 1858.
FIGURES 35B illustrates a flat blade/U-shaped core rotor/stator configuration
1860 including a flat blade 1862 positioned on a rotor that rotates relative
to a U-
5 shaped core 1864. Flat blade 1862 passes between two legs of U-shaped core
1864,
e.g., as shown in FIGURES 5-13 and 26A. Core 1864 is charged (indicated at
"Start
On") when blade 1862 is at some predefined angular orientation relative to
core 1864,
and turned off (indicated at "End On") when blade 1862 is aligned with core
1864.
FIGURES 36A and 36B illustrate the orientation of the U-shaped cores, or
10 stators, in the configurations of FIGURES 33 and 26A, respectively. The
geometries
are generally similar, except rotated relative to each other by 90 degrees. In
particular, FIGURE 36A illustrates a U-shaped core 1880 of the U-shaped
blade/U-
shaped core configuration of FIGURE 33, wherein a U-shaped blade passes by the
two ends of U-shaped core 1880, but not between the two legs of U-shaped core
1880.
15 In contrast, FIGURE 36B illustrates a U-shaped core 1890 of the flat
blade/U-shaped
core configuration of FIGURE 26A, wherein a flat blade passes through legs
1892
and 1894 of U-shaped core 1890.
Laminations of stator and/or rotor components
20 In some embodiments, all or certain portions of the stator and/or rotor may
be
formed in a laminar manner, which may act to channel the magnetic flux in the
direction of the laminar layers, thus reducing undesirable eddy currents.
FIGURES 37A and 37B illustrate example orientations for laminating blade
and core components for various rotor/stator configurations disclosed herein,
25 according to certain embodiments. FIGURE 37A illustrates a U-shaped blade/U-
shaped core configuration including a U-shaped blade 1900 including first and
second
legs 1902 and 1904, and a U-shaped core 1910 including first and second legs
1912
and 1914. Each of blade legs 1902 and 1904 and core legs 1912 and 1914 may be
formed with laminations aligned in parallel planes. Although FIGURE 37A shows
30 two lamination layers A and B, it should be understood that any suitable
number of
layers may be used. FIGURE 37A also illustrates magnetic flux lines 1920
flowing
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46
between lamination layer A of stator leg 1912 and rotor leg 1902, and between
lamination layer A of stator leg 1914 and rotor leg 1904.
FIGURE 37B illustrates a flat blade/U-shaped core configuration including a
flat blade 1930 and a U-shaped core 1934 including first and second legs 1936
and
1938. As discussed above, in such configurations the flat blade 1930 passes in
the
direction of the arrow through the gap defined between first and second legs
1936 and
1938 of U-shaped core 1934. Blade 1930 and core legs 1936 and 1938 may be
formed with laminations aligned as shown in FIGURE 37B. Although FIGURE 37B
shows two lamination layers A and B, it should be understood that any suitable
number of layers may be used. FIGURE 37B also illustrates magnetic flux lines
1940
in lamination layer A flowing between stator legs 1936 and 1938 through blade
1930.
FIGURE 38 illustrates an example orientation for laminating blade and core
components for a flat blade/U-shaped core rotor/stator configuration,
according to
certain embodiments. FIGURE 38 is generally similar to FIGURE 37B, but shows
the full U-shaped core, the rotor to which the flat blade is connected, and
additional
lamination layers. As shown in FIGURE 38, a flat blade 1950 connected to a
rotor
1952, and a U-shaped core 1954 may include multiple lamination layers aligned
in a
similar manner as shown in FIGURE 37B.
In this example, flat blade 1950 has a laminar structure in which the layers
are
generally formed in planes perpendicular to a plane about which rotor 1952
rotates
(i.e., a plane defined by a pattern traced by a point on flat blade 1950 as
rotor 1952
rotates). Also, U-shaped core 1954 has a laminar structure that generally
bends
around the U-shaped length of the core. In this example, the laminar structure
turns
inward toward the end portion of each stator leg. Thus, with such
configuration, the
lamination layers of flat blade 1950 are aligned generally parallel with the
lamination
layers exposed at the ends of the two stator legs when flat blade 1950 passes
between
the stator legs. Thus, the magnetic flux may be channeled through flat blade
1950
from one stator leg to the other, and eddy currents may be reduced.
In this example, flat blade 1950 and U-shaped core 1954 each include five
lamination layers. Again, it should be understood that any suitable number of
layers
may be used.
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47
FIGURES 39 and 40A-40C illustrate an example technique for forming and
utilizing a laminar U-shaped stator 1960 having an area ratio Ag / A, > 1,
according to
certain embodiments. FIGURE 39 illustrates a laminar material 1970 being
wrapped
around a mandrel 1972. Mandrel 1972 may have one or more angled portions 1974,
which facilitate the formation of a U-shaped stator 1960 having an area ratio
Ag / A, > 1, as discussed below.
The laminar material 1970 may be wrapped around mandrel 1972 any desired
number of times to form any desired number of lamination layers. For example,
as
shown in FIGURE 40A, laminar material 1970 may be wrapped around mandrel 1972
to form three layers. The layered structure may then be cut to define the two
stator
legs 1980 and 1982 and the gap between the stator legs 1980 and 1982. For
example,
the layered structure may then be cut along lines 1984 and 1986, and the
remaining
portion 1988 may be removed. In some embodiments, e.g., as shown in FIGURE
40A, the layered structure may be cut at a non-right angle in order to create
an
exposed area Ag that is larger than the cross-sectional area A, of the stator
legs. In
this manner, U-shaped stator 1960 having an area ratio Ag / A, > 1 may be
formed.
FIGURES 40B and 40C illustrate the laminar U-shaped stator pair 1960 in use
in a flat blade/U-shaped core rotor/stator configuration including a laminar
flat blade
1990 configured to pass between legs 1980 and 1982 of U-shaped stator pair
1960,
and a pair of wire coils 1992 wrapped around stator pair 1960. U-shaped stator
pair
1960 may be axially adjusted toward or away from blade 1990 (e.g., toward or
away
from a center point about which the rotor rotates) in order to adjust a
distance between
a point on stator pair 1960 and a point on rotor blade 1990. By adjusting the
distance
between stator pair 1960 and rotor blade 1990, the maximum area of overlap
between
stator pair 1960 and blade 1990 (e.g., during full closure) may be controlled.
U-
shaped stator pair 1960 may be adjusted in any suitable manner, e.g., using a
screw
1994 connected to a stator yoke or support structure 1996, or any other
suitable
adjustment mechanism.
In alternative embodiments, the position of rotor blade 1990 may be axially
adjusted toward or away from stator pair 1960 (e.g., toward or away from a
center
point about which the rotor rotates) in order to adjust a distance between a
point on
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stator pair 1960 and a point on rotor blade 1990. In such embodiments, rotor
blade
1990 may be adjusted in any suitable manner, e.g., using a screw connected to
a rotor
yoke or support structure, or any other suitable adjustment mechanism.
In other embodiments, the positions of both stator pair 1960 and rotor blade
1990 may be independently adjusted.
FIGURE 40B shows U-shaped stator pair 1960 adjusted such that blade 1990
fully overlaps with the exposed area of stator legs 1980 and 1982, which
maximizes
Ag. This configuration may allow for the maximum flux density in core 1960,
which
maximizes the torque for a given Ni. FIGURE 40C shows U-shaped stator pair
1960
adjusted outward in the radial direction (e.g., using screw 1994), which
reduces Ag
and reduces the torque for a given Ni. In this manner, the position of each U-
shaped
stator pair 1960 in the motor may be mechanically adjusted to alter the torque
output
of the electric motor for a given Ni, as desired.
FIGURE 41 illustrates two different rotor/stator motor housings 2000 and
2002 having housing aspect ratios L/r of 1.0 and 4.0, respectively. Housing
aspect
ratios L/r ranging from 1.0 to 4.0 are used in the analysis presented below.
The
following example dimensions are used to illustrate these aspect ratios:
r = 0.50 m
ro = varies as required
L = 0.50 m
L = 2.0 m
Analysis of Various Rotor/Stator Configuration Options
Various rotor/stator configuration options are analyzed and compared below.
In particular, the torque density and power density generated by various
rotor/stator
configuration options are calculated and compared as described below.
Rotor/Stator Configuration Option A: Traditional Switched Reluctance Motor
(SRM)
FIGURE 42 illustrates a traditional 6/4 switched reluctance motor 2100
including a stator 2101 with six stator poles 2102 and a rotor 2110 with four
rotor
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poles 2112. Opposite stator pole pairs are energized sequentially (currently
energized
stator poles are indicated with dark shading) and the rotor 2110 completes the
magnetic circuit. As magnetic flux increases in the magnetic circuit, rotary
torque is
produced that drives rotor 2130. FIGURE 42 illustrates eight positions of
rotor 2110
at 15 degree increments to show the rotation of rotor 2110.
FIGURE 43 corresponds to FIGURE 42 and illustrates the sequence that each
of the three stator pairs 1-3 is fired throughout the 360 degree rotation of
rotor 2110.
Each stator pair is on for 2/6 of the time (Ooõ = 0.3333), and there are three
stator pairs
(npR1YS = 3). One drawback to the traditional SRM is that only one pair of
stators can
be energized at any given time.
FIGURE 44 illustrates a traditional 12/10 switched reluctance motor 2120
including a stator 2121 with 12 stator poles 2122 and a rotor 2130 with 10
rotor poles
2132. As with the 6/4 motor 2100, opposite stator pole pairs in the 12/10
motor are
energized sequentially (currently energized stator poles are indicated with
dark
shading) and rotor 2130 completes the magnetic circuit. As magnetic flux
increases
in the magnetic circuit, rotary torque is produced that drives rotor 2130.
FIGURE 44
illustrates eight positions of rotor 2130 at 15 degree increments to show the
rotation of
rotor 2130.
FIGURE 45 corresponds to FIGURE 44 and illustrates the sequence that each
of the six stator pairs 1-6 is fired throughout the 360 degree rotation of
rotor 2130.
Each stator pair is on for 1/6 of the time (0o, = 0.166667) and there are six
stator pairs
(npQl,-S = 6). Notice that in general, the product Oon npQl,-S = 1.
FIGURE 46 illustrates a geometry of a 6/4 switched reluctance motor. As
shown,
for a 6/4 switched reluctance motor, the rotor and stator width c may be
defined as:
27ar
c=
12
(62)
For 12/10 and 24/22 switched reluctance motors, the denominators are 24 and
48,
respectively (instead of 12).
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FIGURE 47 illustrates a "unit cell" for a stator pair of a standard switched
reluctance motor (e.g., as shown in FIGURES 1-2, 42, and 44). As used herein,
a
"unit cell" is the minimum geometry that includes the features of a stator
pair for
generating a magnetic circuit. For example, in a standard SRM configuration
(i.e., a
5 long-flux configuration), a "unit cell" includes a pair of stator poles on
opposite sides
of the rotor, as well as the wire bundles (coils) for energizing the pair of
stator poles.
In contrast, as discussed below, for short-flux configurations including U-
shaped
stator pairs, a "unit cell" includes a single U-shaped stator pair, along with
the wire
bundles (coils) for energizing the U-shaped stator pair. The "unit cell"
allows for a
10 fair comparison of different rotor/stator configuration options.
As shown in FIGURE 47, the "unit cell" for the standard SRM configuration
includes a pair of opposite stator poles 2150A and 2150B including the wire
bundles
(coils) 2152A and 2152B needed to provide the magnetomotive force. FIGURE 47
also indicates one-half of the circular stator yoke 2154 (in dashed lines) to
provide
15 context for the stator pair. The semi-circular half yoke is not part of the
unit cell.
The area of the core A, relative to the surface area of the rotor Ar at radius
r
follows:
A, ce _ ce
Ar 2(c+2(0.5c))(e+2(0.5c)) 2(2c)(e+c)
20 1
e
e c elc
4(e+c) 4(e+c) 1 4(e/c+1)
c
(63)
The core area Ac can be calculated as:
A
25 q= ~Ac-
e/ c 27crL ` A, ' 4(e1c+1)
(64)
where
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r = radius of rotor (m)
L* = length of unit cell (m)
Substituting Equation 64 into Equation 61 provides:
elc 2TrrL*
T~Ve rf n pa;rs ean g Z Bc, max 4(e / c+ l)
V irrZL * o p c
(65)
For this geometry, r = rf
2 2
TaYe r g Bc, max 1 e/ c
V - npa;rseo,t ro o p c 2(elc+1)
(66)
wherep is:
2g 2g
p o _ o
lc + 2g + w Tro + 2d + 2g + 2r
----
c o b c R. b
(66a)
FIGURE 47 shows that the outer radius ro is related to the height of the wire
bundle d
as follows:
ro =r+d+0.5c
(67)
From Equation 44, an expression for d follows:
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d= A" = 1 B,,maX 1 2g
0.5c 0.5c iP p o
(68)
The length of a unit cell is the same as the overall length of the motor:
L* = L
(69)
FIGURE 47 shows that length e:
e = L * -2(0.5c)
(70)
Rotor/Stator Configuration Option B1: U-Shaped Blade/U-Shaped Core
FIGURE 48 illustrates rotor/stator configuration Option B 1, which is a U-
shaped blade/U-shaped core configuration, according to certain embodiments.
The
illustrated example is a 12/8 configuration, analogous to a standard 6/4
switched
reluctance motor. The rotor/stator configuration 2200 includes a stator 2202
with six
U-shaped stator pairs 1-6 and a rotor 2206 with four U-shaped blades 2208.
Opposite
stator pairs 1-6 are energized sequentially (currently energized stators are
indicated
with dark shading) and the relevant U-shaped blades 2208 complete the magnetic
circuits. FIGURE 48 illustrates eight positions of rotor 2206 at 15 degree
increments
to show the rotation of rotor 2206. In some embodiments, each U-shaped stator
pair
1-6 is turned on (i.e., energized) when there is a slight overlap between (a)
the leading
corners of the two legs of the U-shaped rotor blade 2208 coming into alignment
with
that particular stator and (b) the two legs of the particular stator. These
areas of
overlap between stator pair 1 and the approaching U-shaped rotor blade 2208
are
indicated in FIGURE 48 at 2210.
FIGURE 49 corresponds to FIGURE 48 and illustrates the sequence that each
of the six U-shaped stator pairs 1-6 is fired throughout the 360 degree
rotation of rotor
2206. Each stator pair is on for 1/6 of the time (00õ = 0.16666), and there
are six stator
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pairs (nPQI,.s = 6). As shown in FIGURE 49, during every other interval, none
of the
stator pairs are firing.
FIGURE 50 illustrates a geometry of a 12/8 U-shaped blade/U-shaped core
configuration, e.g., as shown in FIGURE 48. In such configuration, the rotor
and
stator width c may be defined as:
2)ar
c=-
24
(71)
FIGURE 51 illustrates a "unit cell" for a U-shaped stator pair 2300 for use in
a
U-shaped blade/U-shaped core rotor/stator configuration, e.g., as shown in
FIGURE
48. The unit cell includes the wire bundle (coil) needed to provide the
magnetomotive force. The area of the core A, relative to the surface area of
the rotor
A,- at radius r follows:
A, ce _ e _ e c _(e l c)
A, 4c(e+c) 4(e+c) 4(e+c) 1 4(e/c+1)
(72)
The core area A, can be calculated as:
A= A ' IA= (e / c) 2~rL *
` A,. r 4(e/c+1)
(73)
where
r = radius of rotor (m)
L* =length of unit cell (m)
Substituting Equation 73 into Equation 61 gives the torque density:
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(e/c) *
2 2;TrL
Tave rf npairs eon g Bc, max 4(e l c+ 1)
V 7zro L* o p c
(74)
For this geometry, r rf (where rf is the effective radius at which the torque
is
applied)
z
Tave = n B Y Z g Bc, max I (e l C)
v pairs on ro o p c 2(e l c+ 1)
(75)
wherep is:
2g 2g
p = R. o
lc + 2g + w 2;7r + 2d 2;zr
c o b nstators + 2g + nstators
c o b
(75a)
As shown in the unit cell (FIGURE 51):
ro =r+d+c
(76)
From Equation 44, an expression for d follows:
d A'" = 1 B~,max 1 2g
0.5c 0.5c aP p o
(77)
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The parameter e depends upon the length and the number of stator sets provided
along
the axis indicated by arrow A.
As discussed above, FIGURE 49 indicates that half the time, no torque is
applied to the rotor, which in some embodiments or applications may cause the
rotor
5 to "cog." Thus, multiple staggered stator sets may be provided to eliminate
the
periods of no-torque. For example, as shown in FIGURE 51, a first set of U-
shaped
stators (extending around a perimeter of the motor) including U-shaped stator
2300
may be complemented by a second set of U-shaped stators including U-shaped
stator
2310 offset rotationally offset from the first set of U-shaped stators about
the first axis
10 of rotation of the rotor. The second stator set may be rotationally offset
from the first
stator set by any suitable degree. For example, where the first stators are
arranged
around a perimeter at intervals of x degrees, the second stator set may be
rotationally
offset from the first stator set about the axis of rotation by x/2 degrees.
Similarly,
where three stator sets are used, each second stator set may be rotationally
offset from
15 each other by x/3 degrees. And so on. It should be understood that these
are only
example configurations, and any suitable number of stator sets and degree
offset of
each stator set may be used according to the application and desired
performance.
In the example configuration shown in FIGURE 51 including two staggered
stator sets, the motor length must be divided into two parts; i.e.
L*=%2L
(78)
As shown in the unit cell (FIGURE 51):
e = L * -2(0.5c)
(79)
Rotor/Stator Configuration Option B2: U-Shaped Blade/U-Shaped Core with Double
Number of Rotors and Stators
FIGURE 52 illustrates rotor/stator configuration Option B2, which is a U-
shaped blade/U-shaped core configuration, according to certain embodiments.
Option
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B2 is similar to the 12/8 configuration of Option B1, but with double the
number of
rotor blades and stator pairs as Option B 1. The rotor/stator configuration
2400 of
FIGURE 52 includes a stator 2402 with 12 U-shaped stator pairs 1-12 and a
rotor
2406 with eight U-shaped blades 2408.
In the example embodiment shown in FIGURE 52, each U-shaped stator pair
shares one of its stator legs with the adjacent U-shaped stator pair to the
right, and
shares its other stator leg with the adjacent U-shaped stator pair to the
left. Thus, each
of the 12 stator legs of stator 2402 is shared by two U-shaped stator pairs. A
wire coil
may be formed around each of the 12 stator legs. The wire coil around each leg
may
be used for energizing each of the two U-shaped stator pairs that shares that
leg. For
example, the around the leg shared by U-shaped stator pairs 2 and 3 shown in
FIGURE 52 includes a wire coil that may be energized (a) along with the coil
on
adjacent stator leg to the left in order to energize U-shaped stator pair 2
(as shown in
the snapshot at 345 degrees rotation), and (a) along with the coil on the
adjacent stator
leg to the right in order to energize U-shaped stator pair 3 (as shown in the
snapshot at
15 degrees rotation).
Opposite stator pairs 1-12 are energized sequentially (currently energized
stators are indicated with dark shading) and the relevant U-shaped blades 2408
complete the magnetic circuits. The configuration of FIGURE 52 generally
allows
more stator pairs to be energized at a given time, as compared with certain
other
configurations. For example, while some other configurations are limited to
two
stator pairs being energized at a time, the configuration of FIGURE 52 allows
more
than two stator pairs to be energized at a time. In an example operation of
the
configuration of FIGURE 52, two groups or opposite stator pairs (i.e., a total
of four
U-shaped stators) may be energized at a time, as opposed to one pair of
opposite
stator pairs (i.e., a total of two U-shaped stators) energized at a time in
Option B1.
FIGURE 52 illustrates eight positions of rotor 2406 at 15 degree increments to
show
the rotation of rotor 2406.
FIGURE 53 corresponds to FIGURE 52 and illustrates the sequence that each
of the 12 U-shaped stator pairs 1-12 is fired throughout the 360 degree
rotation of
rotor 2406. Each stator pair is on for 1/3 of the time (00õ = 0.33333) and
that there are
12 stator pairs (npQlrs = 12). As shown in FIGURE 53, four of the stator pairs
are
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firing at any given time; there are no time periods during which none of the
stator
pairs are firing (as compared to Option B 1).
Because the geometry of Option B2 is similar to that of Option B1 (but with
double the number of rotors and stators), the rotor and stator width c for
Option B2
may be defined with reference to FIGURE 50 as:
27zr
c=-
24
(80)
If the number of stator pairs is halved to six, then the denominator is 12. If
number of
stator pairs is doubled to 24, then the denominator is 48.
As shown in FIGURE 53, there are no gaps in torque, so there is no need to
double the number of stators along the length; therefore,
L*=L
(81)
The other formulas are identical to Option B1.
Rotor/Stator Configuration Option B3: U-Shaped Blade/U-Shaped Core with All
Stators Energized/De-energized SimultaneouslX
FIGURE 54 illustrates rotor/stator configuration Option B3, according to
certain embodiments. Option B3 is similar to Option B2, except the number of
rotor
blades and stator poles is identical (e.g., 12/12 in the example illustrated
embodiment). The rotor/stator configuration 2500 of FIGURE 54 includes a
stator
2502 with 12 U-shaped stator pairs 1-12 and a rotor 2506 with 12 U-shaped
blades
2508. All stator pairs 1-12 are energized and de-energized simultaneously (the
energized state is indicated with dark shading) to complete 12 magnetic
circuits with
the 12 U-shaped blades 2508 (each circuit includes one U-shaped stator and one
U-
shaped blade). FIGURE 54 illustrates four positions of rotor 2506 at 15 degree
increments to show the rotation of rotor 2506.
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FIGURE 55 corresponds to FIGURE 54 and illustrates the sequence that each
of the 12 U-shaped stator pairs 1-12 is fired throughout the 360 degree
rotation of
rotor 2506. Each stator pair 1-12 is on for 1/2 of the time (00õ= 0.5) and
that there are
12 stator pairs (npQi,.s = 12).
FIGURE 56 illustrates another example rotor/stator configuration 2526 of
Option B3, according to certain embodiments. Configuration 2526 is similar to
configuration 2520 shown in FIGURE 54, except configuration 2526 is a 16/16
configuration (rather than a 12/12 configuration). FIGURE 56 illustrates the
arrangement of the 16 U-shaped stator pairs such that the all 16 stator pairs
can be
energized at the same time. Each U-shaped stator pair forms a magnetic circuit
with a
corresponding U-shaped blade 2528. The flux paths for each of the 16 magnetic
circuits are indicated at 2530.
Referring back to the 12/12 configuration shown in FIGURE 54, the rotor and
stator width c for Option B2 may be defined with reference to FIGURE 50 as:
27rr
c=-
24
(82)
If the nuinber of stator pairs is halved to six, then the denominator is 12.
If number of
stator pairs is doubled to 24, then the denominator is 48. If number of stator
pairs is
16 (e.g., the configuration shown in FIGURE 56), then the denominator is 32.
As shown in FIGURE 55, there are gaps in torque in the Option B3
configurations, and thus for modeling the system, two stators are present
along the
length L, as compared to one in Option B1; therefore,
L*='/2L
(83)
The other formulas are identical to Option B 1.
Rotor/Stator Configuration Option C1: Flat Blade/U-Shaped Core
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FIGURE 57 illustrates rotor/stator configuration Option Cl, which is a flat
blade/U-shaped core configuration, according to certain embodiments. The
illustrated
example is a 6/4 configuration. The rotor/stator configuration 2600 includes
six U-
shaped stator pairs 1-6 and a rotor 2606 with four flat blades 2608. Each U-
shaped
stator pair includes two legs, and the flat rotor blades 2608 pass through the
gap
formed between the stator legs, e.g., as shown and discussed above regarding
FIGURES 5-13 and 26A. Opposite stator pairs 1-6 are energized sequentially
(currently energized stators are indicated with dark shading) and the relevant
flat
blades 2608 complete the magnetic circuits.
FIGURE 57 illustrates eight positions of rotor 2606 at 11.25 degree
increments to show the rotation of rotor 2606. In some embodiments, each U-
shaped
stator pair 1-6 is turned on (i.e., energized) when there is a slight overlap
between (a)
the leading edge of a flat rotor blade 2608 coming into alignment with that
particular
stator and (b) the two legs of the particular stator. In some embodiments,
each U-
shaped stator pair 1-6 is turned off (i.e., de-energized) when the flat blade
2608 is
fully aligned between the two legs of the stator (i.e., full closure). As
shown, one or
two sets of stator pairs 1-6 (i.e., a total of two or four U-shaped stators)
are energized
at any given time.
FIGURE 58 corresponds to FIGURE 57 and illustrates the sequence that each
of stator pairs 1-6 is energized throughout the 360 degree rotation of rotor
2606. As
shown, one or two sets of stator pairs 1-6 (i.e., a total of 2 or 4 U-shaped
stators) are
energized at any given time. Each stator pair is on for 4/9 of the time (00, =
0.444)
and that there are six stator pairs (nPalrs = 6). Notice that there is overlap
as the pairs
are fired, which will lead to smooth rotation.
FIGURE 59 illustrates another example rotor/stator configuration of Option
Cl, according to certain embodiments. This example includes a 12/8
configuration
2620 including 12 U-shaped stator pairs 1-12 and a rotor 2626 with eight flat
blades
2628. Each U-shaped stator pair includes two legs, and the flat rotor blades
2628 pass
through the gap formed between the stator legs, e.g., as shown and discussed
above
regarding FIGURES 5-13 and 26A. Opposite stator pairs 1-12 are energized
sequentially (currently energized stators are indicated with dark shading) and
the
relevant flat blades 2628 complete the magnetic circuits.
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FIGURE 59 illustrates eight positions of rotor 2626 at 5.625 degree
increments to show the rotation of rotor 2626. In some embodiments, each U-
shaped
stator pair 1-12 is turned on (i.e., energized) when there is a slight overlap
between (a)
the leading edge of a flat rotor blade 2628 coming into alignment with that
particular
5 stator and (b) the two legs of the particular stator. In some embodiments,
each U-
shaped stator pair 1-12 is turned off (i.e., de-energized) when the flat blade
2628 is
fully aligned between the two legs of the stator (i.e., full closure). As
shown, two or
four sets of stator pairs 1-12 (i.e., a total of four or eight U-shaped
stators) are
energized at any given time.
10 FIGURE 60 corresponds to FIGURE 58 and illustrates the sequence that each
of stator pairs 1-12 is energized throughout the 360 degree rotation of rotor
2626. As
shown, two or four sets of stator pairs 1-12 (i.e., a total of 4 or 8 U-shaped
stators) are
energized at any given time. Each stator pair is on for 4/9 of the time (0on =
0.444)
and that there are 12 stator pairs (npa,,.s = 12). Thus, it can be seen that
the fraction of
15 time on (00õ = 0.444) for a rotor/stator configuration of Option Cl is the
same
regardless of the number of stator pairs. This is in sharp contrast to the
traditional
switched reluctance motor in which the fraction of time on decreases as the
number of
stator pairs increases.
FIGURES 61 A-61 C illustrate the stator width b for various configurations of
20 the flat blade/U-shaped core of Option Cl. As shown in FIGURE 61A, for the
6/4
configuration, b is:
27rr
8
(84)
with a denominator of 8. The denominator for b is 16 for a 12/8 configuration
(see
FIGURE 6113), and 32 for a 24/16 configuration (see FIGURE 61 C).
FIGURE 62A illustrates a "unit cell" for a U-shaped stator 2700 for use in a
flat blade/U-shaped core rotor/stator configuration of Option Cl. The unit
cell
includes the wire bundle (coil) needed to provide the magnetomotive force.
Notice
that a single unit cell including a pair of stator legs 2702 and 2704 services
a single
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flat blade. As the flat blade passes between the magnetic legs 2702 and 2704,
there is
an attractive force that acts to pull the magnetic legs 2702 and 2704 inward
towards
the blade. Thus, by mechanically coupling sets of stator pairs together as
shown in
FIGURE 62A, a series of "magnetic legs" 2710 formed from two abutting stator
legs
(e.g., legs 2704 and 2706) may be created, with the magnetic flux flowing in
the same
direction through such abutting stator leg pairs, as shown in FIGURE 62B. To
form a
"magnetic leg" 2710, two stator legs (e.g., legs 2704 and 2706) may be abutted
and
then the coils may be wrapped around the pair of legs. The forces acting on a
common magnetic leg 2710 to pull the leg 2710 toward the flat blades on either
side
of the leg 2710 will act in opposite directions so the net force acting on the
magnetic
leg 2710 is zero or substantially zero. A net force of zero eliminates
movement of the
magnetic leg 2710 and thus may eliminate or reduce a source of vibration and
noise.
Neglecting edge effects, the area of the core A, relative to the surface area
of
the rotor A,- at radius r follows:
A, ab _ ab _ a
A, (2a+0.333b)(b+2(0.16667b)) 1.33333b(2a + 0.3333b) 1.33333(2a + 0.3333b)
1
_ ab _ a/b
1.3333(2a + 0.3333b) 1 1.3333(2a / b + 0.3333)
b
(85)
The core area A, can be calculated as:
_ (A' )A,. _ alb *
A` A,. 1.3333(2a1b+0.3333) 2nrL
(86)
where
r = radius of rotor (m)
L* = length of unit cell (m)
= 2a +0.3333 b
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Equation 86 may be substituted into Equation 38:
a/b
Tave rfnpa;rse ,= g B ,max 2 1.3333(2a/b+0.3333) 2~L Ag
V 7rro2L * o p b A
r r f g Bc, 21 1.5a/b Ag
_ max
np"irse " r02 p b(2a/b+0.3333) A,
(87)
This equation allows the independent specification of Ag / A, and a/b, where p
is
2g 2g
p _ o
2g lv 2(r-rf)+2d+L+2g+0.33333b
Itc o '"tb N'b
(87a)
The value for a is
a = (a l b)b
(88)
From the unit cell (FIGURE 62):
L* = 2a + 0.3333b
(89)
The radius where the force is applied, rf, is:
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Ag 1
rf=r- a
A, 2
(90)
and ro is:
ro =r+d+a
(91)
From Equation 44, an expression for d follows:
d = `4w = 1 Bc,max 1 2g
0.166667b 0.166667b aP p o
(92)
Rotor/Stator Configuration Option C2: Flat Blade/U-Shaped Core with Reduced
Core
Width
FIGURES 63A and 63B illustrate a configuration Option C2, which is similar
to configuration Option Cl, except the width of the core is narrowed to b*,
according
to certain embodiments. FIGURE 63A illustrates a "unit cell" for a U-shaped
stator
pair 2720 of configuration Option C2, and FIGURE 63B illustrates a cross-
section of
the U-shaped stator pair 2720 if the U-shaped stator pair 2720 were laid-out
flat.
The ratioj shown in FIGURE 63B is defined as follows:
b*
b
(93)
FIGURES 61 A-61 C shows that the stator width b for configuration Option C2
is:
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2RY
b=-
8
(94)
with a denominator of 8 for the 6/4 configuration, 16 for a 12/8
configuration, and 32
for a 24/16 configuration. (Note: this is the same as Option Cl.)
The width of the wire bundle (coil) is m:
m=6b+~(b-b*)=6b+~(b- jb)=6b+~b(1- j)=L6+~(1- j)Jb
(95)
Neglecting edge effects, the area of the core A, relative to the surface area
of the rotor
AY at radius r follows:
A, ab* _ ajb _ ajb
A, [b*+2m][2a+2m] b-b+2mI2a+2m] (6 [Jb+2+!(1_f)Jb][2a+2[+i(1_I)Jb]
ajb ajj+2(6 +~(1-j)J b 2a+2(6 +2(1-j) lb1 1.3333[2a+(1.3333-j)bj
C _ ai
b _ jalb
1.3333[2a + (1.3333 - j)b] ~ 1.3333[2a/b+1.3333- j]
(96)
The core area A, can be calculated as:
_ (A, A_ jalb )2,TrL
A` A,. r 1.3333(2a/b+1.3333- j)
(97)
where
r = radius of rotor (m)
L* = length of unit cell (m)
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= 2a + 2m
Equation 97 may be substituted into Equation 38:
jalb
Tave rfnpairseon g B,ax z 1.3333(2a/b+1.3333- j) 27rrL Ag
5 V Rr o L* o p b A,
r r f g B 21 1.5jalb Ag
c, max
- npairseo r02 o p b 2a/b+1.3333- j A,
(98)
This equation allows the independent specification of j, Ag / A, and a/b where
p is:
2g 2g
p = o a
l~ 2g yv 2(r-rf)+2d+L*+2g+2m
-+-+ - - --
, o b o b
(98a)
The value for a is:
a=(alb)b
(99)
From the unit cell (FIGURE 63):
L* = 2a + 2m
(100)
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The radius where the force is applied is:
A I
rf=r- g-aj
A, 2
(101)
The relationship for ro is:
ro = r+d +a
(102)
From Equation 44, an expression for d follows:
d= Aw = 1 B,, max 1 2g
m m iP p o
(103)
Rotor/Stator Configuration Option D: Flat Blade/U-Shaped Core with Permanent
Magnet Blades
FIGURE 64 illustrates rotor/stator configuration Option D, which is a flat
blade/U-shaped core configuration 2800 including permanent magnet blades,
according to certain embodiments. Option D is generally similar to Option C2,
except
that permanent magnet flat blades are placed on the rotor in Option D. Thus, a
motor
formed in accordance with Option D may be referred to as a permanent magnet
motor
(PMM).
In the example embodiment shown in FIGURE 64, the rotor/stator
configuration 2800 includes a stator 2802 with eight U-shaped stator pairs 1-8
and a
rotor 2806 with six flat permanent magnet blades 2808. Each U-shaped stator
pair
includes two legs, and the flat permanent magnet blades 2808 pass through the
gap
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formed between the stator legs, e.g., as shown and discussed above regarding
FIGURES 5-13 and 26A.
As shown in FIGURE 64, the permanent magnet blades 2808 may be
positioned around the perimeter of rotor 2806 in alternating arrangement of
north (N)
and south (S) magnets. At any given time, half of the stator pairs (every
other stator
pair along the perimeter of stator 2802) are energized with a north (N)
polarity, and
the other half of the stator pairs are energized with a south (S) polarity. In
this
manner, the permanent magnet blades 2808 are both pushed and pulled into
alignment
with the nearest stator pair having the opposite charge, thus causing rotor
2806 to
rotate. As rotor 2806 continues to rotate, the polarity of all eight stator
pairs is
switched simultaneously, back and forth between north (N) and south (S)
polarity.
FIGURE 64 illustrates eight positions of rotor 2806 at 22.5 degree increments
to show
the rotation of rotor 2806.
FIGURE 65 corresponds to FIGURE 57 and the sequence that each of stator
pairs 1-8 is energized throughout the 360 degree rotation of rotor 2806. Each
stator
pair is energized all the time (Oo,T = 1.0), but the magnetic field switches
directions.
In some embodiments, the blade magnets need not be particularly strong
because an area ratio Ag l A, greater than 1 may be used, which concentrates
the flux
density in the core. For example, as shown in FIGURES 31 and 32, at an area
ratio of
3, the flux density in the blade is about 1/3 that of the flux density in the
core. Thus,
due to the area ratio advantage, high torque may be generated using relatively
low
strength magnets for blades 2808.. Thus, relatively low strength (and thus
relatively
inexpensive) magnets (e.g., Alnico magnets) may be used to generate high
torque.
This class of magnets has the added advantage of very high thermal stability.
With configuration Option D, an equal number of stators and blades can be
employed. For example, FIGURE 64 shows an 8/8 configuration with nPQirs = 8.
FIGURE 61 shows that the stator width b is:
b 2nr
8
(104)
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with a denominator of 8 for the 6/6 configuration, 16 for a 16/16
configuration, and
32 for a 32/32 configuration.
Because the stators are adjacent to each other, if multiple stator sets are
used
in a particular machine, they may be configured as shown in FIGURE 63. In
particular, the stator legs from one stator set may be abutted directly
against the stator
legs from an adjacent stator set, and wire coils may be wrapped around the
abutted leg
pairs. The ratio j is defined as before:
_b*
J b
(105)
The width of the wire bundle is m:
m=~(b-b*)=~(b- jb)=2(1-j)b
(106)
Neglecting edge effects, the area of the core A, relative to the surface area
of the rotor
A,- at radius r follows:
A, ab* _ ajb _ ajb
A, [b*+2ml2a+2m] b-b+2m][2a+2m] 1 1 1r 1
(1- j)Jb
Cjb+2 (1- j))bJl 2a+2 ~2
(2 L
ajb aj ai b ja / b
-`j+1- j]b[2a+(1- j)b] - 2a+(1- j)b -[2a+(1- j)b]~ 2a/b+l- j
(107)
The core area A, can be calculated as:
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A- A A (_jaIb 2nrL
` Ar ' 2alb+1- j
(108)
where
r = radius of rotor (m)
L* = length of unit cell (m)
= 2a + 2m
Equation 108 may be substituted into Equation 38:
ja l b 2)rrL
Tave Yf nPairs 0 g B , max 2 2a l b+ 1- j Ag
V Tr,,ZL* a p b A
YY1 - g Bc,max 2 1 2 ja l b Ag
np "se õ Yo o p b 2a/b+l-j A
(109)
This equation allows the independent specification of j, Ag / A, and alb. The
relationship forp is identical to Option C2. The value for a is
a = (alb)b
(110)
From the unit cell (FIGURE 63):
L* = 2a + 2m
(111)
The radius where the force is applied is:
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A 1
rf =r- g 2aj
A, (112)
and ro is:
5
ro =r+d+a
(113)
From Equation 44, an expression for d follows:
d= Aw = 1 Bc, max 1 2g
m m iP p o
(114)
Sample Calculations
Provided below are sample calculations for determining the torque density and
power density generated by various configuration options discussed above,
including
configuration Options A, B1, B2, B3, Cl, C2, and D. The calculations are based
on
the "unit cell" methodology explained above such that the different
configurations can
be fairly compared to each other, generally on a torque-per-physical-volume
basis or a
power-per-physical-volume basis. In addition, the calculations are based on
example
dimensions and other physical parameter values. It should be understood that
these
dimensions and other values are examples only and in no way limit the scope of
any
embodiments to such dimensions or values.
Option A: Traditional SRM Rotor/Stator Confi r_u~ ation
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Number stators = 6
npar,-s =3
0, = 0.3333
L/r = 1.0
2nr 2;T(0.5 m)
c = - _
= -0.262m
12 12
L*=L=0.5m
e = L * -2(0.5c) = 0.5 m - 2(0.5)(0.262 m) = 0.238 m
e/c = 0.238 m/0.262 m = 0.908
rf =r=0.5m
p = 0.487 (guess)
d 1 Bc,max 1 2g
0.5c iP p o
- 1 1.8 Wb/m2 ( 1 1 2(0.0005 m)
0.5(0.262 m) (5.7 x 106 A/mZ )(0.907) 0.487 J 4/T x 10-' Wb/A = turn m
= 0.00434 m
ro =r+d+0.5c=0.5m+0.00434m+0.5(0.262m)=0.635m
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2g 2g
p = o o
l, + 2g + w T7r + 2d + 2g + 2,
- - -
'"tc ~to ~a' b It c Ito ~tb
2(0.0005 m)
47z x 10-' (Wb/A = turn = m)
)r(0.635 m) + 2(0.00434 m) + 2(0.0005 m) + 2(0.5 m)
( 0.0036 Wb/A = turn = m 4TC x 10-' Wb/A = turn = m 0.0036 Wb/A = turn m
J
= 0.488
2 2
Tave = n 6 r g Bc, max 1 e/ c
v pairs lt o ~to p c 2(e l c+ 1)
= 3(0.33333) (0.5 m)2 (0.0005 m) 11.8 Wb/m2 2 1 0.908
(0.635m)2 4)r x10-' (Wb/A=turn=m) 0.488 0.262m 2(0.908+1)
=3048N=m/m3
Option B 1: U-Shaped Blade/U-Shaped Core Rotor/Stator Confi rug ation
Number stators = 12
npQ1rs =6
8on = 0.16666
Llr = 1.0
c-2nr-27z(0.5m)=0.131m
24 24
L = (L / r)r = (1. 0) 0. 5 m = 0. 5 m
L*=%2L='h(0.5m)=0.25m
e=L*-2(0.5c)=0.25m-2(0.5)(0.131m)=0.119m
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e/c=0.119m/0.131m=0.908
rf =r=0.5m
p = 0.823 (guess)
d 1 Bc,max 1 2g
0.5c iP p o
_ 1 1.8 Wb/m2 ~ 1 2(0.0005 m)
0.5(0.131 m) (5.7 x 106 A/mz )(0.907) 0.823 J 47t x 10-' Wb/A = turn m
= 0.00514 m
ro =r+d+c=0.5m+0.00514m+0.131m=0.636m
2g 2g
p = o o
+ 2g + w 2m + 2d 2,7r
''tc ILo Itb nstators + 2g + nstators
~to Ilb
2(0.0005 m)
4)r x 10-' (Wb/A = turn = m)
2;z(0.636 m) + 2(0.00513 m) 2g(0.5 m)
12 2(0.0005 m) + 12
0.0036Wb/A=turn=m 4TCx10-' (Wb/A=turn=m) 0.0036Wb/A=turn=m
= 0.826
2 z
Tave = n B r g Bc, max 1 (e l c)
V pairs o,' Yo o p c 2(e / c+ 1)
= 6(0.16666) (0.5 m)2 (0.0005 m) 11.8\Tm2Y 1 0.908
(0.636 m)2 4)c x 10-' (Wb/A = turn = m) 0.826 0.131 m 2(0.908 + 1)
=2126N=m/m3
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Option B2: U-Shaped Blade/U-Shaped Core Rotor/Stator Configuration with Double
Number of Rotors and Stators
Number stators = 12
nPQl,.s =12
0071= 0.3333
L/r = 1.0
27rr 2)c(0.5 m)
c=-= 0.131m
24 24
L=(L/r)r=(1.0)0.5m=0.5m
L*=L=0.5m
e=L*-2(0.5c) =0.5m-2(0.5)(0.131m)=0.369m
e / c = 0.369 m/0. 131 m = 2.817
rf. = r = 0.5 m
p = 0.823 (guess)
d 1 Bc,maX 1 2g
0.5c aP p o
- 1 1.8 Wb/m2 r 1 1 2(0.0005 m)
0.5(0.131 m) (5.7 x 106 A/mz )(0.907) 0.823 J 47r x 10-' Wb/A = turn m
= 0.00514 m
ro =r+d+c=0.5m+0.00514m+0.131m=0.636m
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2g 2g
o o
= =
p
Z + 2g + W 2~ +2d 2)7r
, o b nstators + 2g + nstators
~ o b
2(0.0005 m)
47c x 10-' (Wb/A = turn = m)
2)r(0.636 m) 2~(0.5 m)
12 + 2(0.00513 m) + 2(0.0005m) + 12
0.003 6 Wb/A = turn = m 47z x 10-' (Wb/A = turn = m) 0.003 6 Wb/A = turn = m
= 0.826
2
7ave = n 8r Z g B,, maX 1 (e / c)
V pairs a,t Yo o p c 2(e/c+l)
=12(0.3333) (0.5 m)2 (0.0005 m) 11.8w1m2Y 1 2.817
(0.636m)2 47cx10-' (Wb/A=turn=m) 0.826 0.131m 2(2.817+1)
=13,182 N = m/m3
5 Option B3: U-Shaped Blade/U-Shaped Core Rotor/Stator Configuration with All
Stators Energized/De-energized SimultaneouslX
Number stators = 12
npairs =12
10 epn=0.5
L/r = 1.0
c_ 2~r _ 27c(0.5 m) = 0.131 m
24 24
15 L = (L / r)r = (1.0) 0. 5 m = 0.5 m
L*=%2L=%2(0.5m)=0.25m
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e = L * -2(0.5c) = 0.25 m - 2(0.5)(0.131 m) = 0.119 m
e/c=0.119m/0.131m=0.908
rf =r=0.5m
p = 0.823 (guess)
d 1 Bc,maX 1 2g
0.5c aP p o
_ 1 1.8 Wb/m2 r 1 1 2(0.0005 m)
0.5(0.131 m) (5.7 x 106 A/mz )(0.907) 0.823 J 4;T x 10-' Wb/A = turn = m
= 0.00514 m
ro =r+d+c=0.5m+0.00514m+0.131m=0.636m
2g 2g
- l
P- N. ~t
l` + 2g + w 2;v +2d 2;Tr
'"Lc 'to Itb nstators + 2g + nstators
' c ~to ~tb
2(0.0005 m)
47c x 10-' (Wb/A = turn = m)
2z(0.636 m) + 2(0.00513 m) 2)r(0.5 m)
12 + 2(0.0005m) + 12
0.0036 Wb/A = turn = m 4)z x 10-' (Wb/A = turn = m) 0.0036 Wb/A = turn = m
= 0.826
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2
Tave = n 8 r Z g Bc, max 1 (e / c)
V pairs n r2 [t. p c 2(e/c+l)
=12(0.5) (0.5 m)2 (0.0005 m) 111 0.908
(0.636 m)z 47r x 10' (Wb/A = turn = m) 0.826 0.131 m 2(0.908 + 1)
=12,761N=m/m3
Option Cl: Flat Blade/U-Shaped Core Rotor/Stator Configuration
Number stators = 24
npairs = 24
0on = 0.4444
L/r > 4.0
alb = 0.5
Ag l A, = 3
2~r 2~(0.5 m) _
b=-= -0.0982m
32 32
a=(a / b)b = 0.5(0.0982 m) = 0.0491 m
L* = 2a + 0.333b = 2(0.0491 m) + 0.3333(0.0982 m)= 0.131 m
A 1 1
rf =r - Ag 2a=0.5m-32(0.0491m)=0.426m
, 20 p = 0.895 (guess)
d= 1 Bc, max 1 2g
0.166667b aP p o
- 1 1.8 Wb/m2 ~ 1 2(0.0005 m)
0.166667(0.0982 m) (5.7 x 106 A/m2 )(0.907) 0.895 J 41r x 10-' Wb/A = turn = m
= 0.0189 m
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ro =r+d+a=0.5m+0.0189m+0.0491m=0.568m
2g 2g
p _ f'='0 ~0
(,+2g+w)-(2,r-rf)+2d+L*+2g + 0.3333'di
~ o b , o b
2(0.0005m)
47r x 10-' (Wb/A turn= m)
2(0.5-0.426)m+2(0.0206m)+0.131m+ 2(0.0005m) + 0.333310.0982m)
0.003 6 Wb/A= turn= m 4gx 1OF' (Wb/A= turn= m) 0.0072 Wb/A= turn= m
= 0.895
7 rrf B~ max 2 1 1.5a l b Ag
ave = yl Pairs Bon 2 g
v ro o p b(2a1b+0.3333) A,
= 24(0.44444) (0.5 m)(0.426 m) 0.0005 m 11.8 Wb/m2 2 1 1.5(0.5)
(0.568 m)z 4,Tx 10-' (Wb/A = turn = m) 0.895 0.0982 m(2(0.5) + 0.333
=194,571N=m/m3
Option C2: Flat Blade/U-Shaped Core Rotor/Stator Configuration with Reduced
Core
Width
Number stators = 24
npairs = 24
Ooõ = 0.4444
Llr > 4.0
alb = 0.5
j = 0.9
AglA, =3
27zr 2/z(0.5 m)
b== 0.0982m
32 32
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a = (a/ b)b = 0.5(0.0982 m) = 0.0491 m
m=(0.16667 + 0.5(1- j))b = (0.16667 + 0.5(1- 0.9))0.0982 m= 0.0213 m
L* = 2a + 2m = 2(0.0491 m) + 2(0.0213 m) = 0. 141 m
A
rf =r - Ag ~aj =0.5m-3~(0.0491m)0.9=0.434m
c
p = 0.90 (guess)
d= 1 Bc, max 1 2g
m iP p o
= 1 1.8 Wb/m2 ~ 1 2(0.0005 m)
0.0213 m(5.7 x 106 A/mZ )(0.907) 0.90 J 41r x 10-' Wb/A = turn m
= 0.0145 m
ro = r + d +a =(0.5m)+(0.0145m)+(0.0491m)=0.564m
2g
o
p 2(r-rf)+2d+L* + 2g + 2m
c o b
2(0.0005m)
4/7x 10-' (Wb/A turn= m)
2(0.5-0.434)m+2(0.015hn)+0.141m+ 2(0.0005m) + 2(0.0213m)_
0.003 6 Wb/A turn= m 47t x 10-' (Wb/A turn= m) 0.0072 Wb/A turn= m
= 0.898
7QVe - n 9 rY! g Bc max 2 1 1.5 ja l b Ag
v pairs on o2 ~o ( p) b(2a/b+1.3333- j Ac
~
= 24(0.44444) (0.5 m)(0.434 m) 0.0005 m 1.8 Wb/m2 1 1.5(0.9)(0.5)
(0.564 m)Z 4;T x 10' (Wb/A = turn = m) 0.898 0.0982 m(2(0.5) + 1.3333 - 0.5
=167,359N=m/m3
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Option D: Flat Blade/U-Shaped Core Rotor/Stator Configuration with Permanent
Magnet Blades
Number stators = 32
5 nPQ=,.,s = 32
Ooõ= 1.0
L/ro > 4.0
a/b = 0.5
j = 0.9
10 AgIA, =3
2nr 27r(0.5 m) _
b=-= -0.0982m
32 32
a=(a/b)b=0.5(0.0982m)=0.0491m
m 0.5(1- j)b = 0.5(1- 0.9)0.0982 m = 0.00491 m
L* = 2a + 2m = 2(0.0491 m) + 2(0.00491 m) = 0.108 m
rf =r- AA ~aj =0.5m-3~(0.0491m)0.9=0.434m
, p = 0.90 (guess)
d 1 Bc,max 1 2g
m iP p o
- 1 1.8 Wb/m2 r 1 2(0.0005 m)
0.00491 m(5.7 x 106 A/m2 )(0.907) 0.90 J 47r x 10-' Wb/A = turn = m
= 0.0627 m
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ro =r+d+a = (0.5 m) + (0.0627 m) + (0.0491 m) = 0.612 m
2g
o
p 2(r-rf)+2d+L* 2g 2m
+ +
o b
2(0.0005m)
4;7 x 10-' (Wb/A turn= m)
2(0.5-0.434)m+2(0.0627m)+0.108m+ 2(0.0005m) + 2(0.00491m)
0.0036Wb/A turn= m 47rx 10-' (Wb/A turn= m) 0.0072 Wb/A= turn= m
=0.886
TQVe = n 6 YrJ g(BM"Z 1 1.5 ja l b Aa
V pairs on z ~Op) b2a1b+1.3333-j)
o A,
= 32(1.0) (0.5 m)(0.434 m) 0.0005 m 1.8 Wb/m' 2 1 1.5(0.9)(0.5) 3
~ (Wb/A=turn=m)( 0.886 ) 0.0982m((2(0.5)+1.3333-0.9))( >
0.612m)2 4~x10'
= 437,839 N = m/m3
Tables 1 and 2 summarize the torque density and power density, respectively,
resulting from the parametric evaluation of the seven different configurations
options.
By examining Tables 1 and 2, the following conclusions may be made:
= As the aspect ratio Llr increases, the torque and power density increases.
This
occurs because the unproductive wire wrap at the ends becomes a smaller
percentage of the entire device.
= As the number of stators increases, the torque and power density increases.
This results because the maximum flux density of the core is limited to
saturation. Arriving at the maximum flux density over a shorter angular
displacement causes the torque to rise.
= Option B3 > Option B2 > Option B1 in terms of power density and torque
density. The differences are primarily due to the difference in 0on between
these options.
= Option A has the advantage of a much larger core area A. than Options B 1-
B3.
This advantage is helpful with a smaller number of stators where Option A is
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always better than Options B in terms of power density and torque density.
With a large number of stators, Options B2 and B3 can overcome Option A.
= Compared to Option B3, Options Cl and C2 are more torque and power dense
because their area ratio Ag / A, is greater than 1.
= In Option A, the product of nPa1rs 0O7z = 1 regardless of the number of
stators;
therefore, as the number of stators increases, 00, must decrease. In contrast,
with Options C and D, 00õ is constant regardless of the number of stators.
This
advantage dominates at large numbers of stators.
= There is an optimal a/b for Options C 1 and C2.
= There is an optimal j(-0.90) for Option D. For Option C2, the optimalj is 1.
= The permanent magnet (Option D) has the highest torque density because 0,
=1 and there are more stator pairs.
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Table 1. Parametric evaluation of torque density for various motor options.
Torque Density (N=m/m )
Opt A / Ac L/r a/b j 6 Stators 12 Stators 24 Stators
8
A 1 1 3,050 10,900 27,300
4 5,560 13,800 30,400
B1 1 impossible 2,130 13,400
4 833 3,880 17,000
B2 1 2,150 13,200 63,200
4 3,920 16,700 70,400
B3 1 impossible 12,800 80,600
4 5,000 23,300 102,000
C1 3 >4 0.2 1 8,800 38,700 158,000
0.5 6,160 41,400 195,000
1.0 impossible 26,500 180,000
C2 0.5 0.98 6,130 40,400 189,000
0.95 6,060 38,800 181,000
0.90 5,920 36,300 167,000
D 8 Stators 16 Stators 32 Stators
0.95 15,500 97,700 417,000
0.90 15,700 97,500 438,000
0.85 15,400 92,900 422,000
r = 0.5 m
i =5.7x106A/m2
0.0036 Wb/(A turn = m) @ 1.8 Wb/m2
0.0072 Wb/(A turn m) @ 0.6 Wb/m2
g = 0.0005 m
P = 0.907
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Table 2. Parametric evaluation of power density for various motor options.
Power Density (MW/m ) @ 60 Hz
Opt A / Ac L/r alb j 6 Stators 12 Stators 24 Stators
8
A 1 1 1.14 4.11 10.3
4 2.10 5.20 11.5
B1 1 impossible 0.803 5.05
4 0.314 1.46 6.41
B2 1 0.811 4.98 23.8
4 1.48 6.30 26.5
B3 1 impossible 4.83 30.4
4 1.88 8.78 38.5
C1 3 >4 0.2 1 3.32 14.6 59.6
0.5 2.32 15.6 73.5
1.0 impossible 9.99 67.9
C2 0.5 0.98 2.31 15.2 71.3
0.95 2.28 14.6 68.2
0.90 2.23 13.7 63.0
D 8 Stators 16 Stators 32 Stators
0.95 5.84 36.8 157
0.90 5.92 36.8 165
0.85 5.81 35.0 159
r = 0.5 m
i =5.7x106 A/mZ
0.0036 Wb/(A turn m) @ 1.8 Wb/m2
0.0072 Wb/(A = turn m) @ 0.6 Wb/m2
g = 0.0005 m
P = 0.907
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The above description has focused on applying this technology to an electric
motor in which electrical energy is converted to rotating shaft power. The
concepts
may be equally well applied to generators in which rotating shaft power is
converted
to electrical energy.
5 FIGURE 66 illustrates an example system for cooling a rotor/stator
configuration 3000 (e.g., a switched reluctance motor or a permanent magnet
motor),
according to certain embodiments. Rotor/stator configuration 3000 may have any
configuration disclosed herein (e.g., any of Options A-D) or any other known
rotor/stator configuration. Rotor/stator configuration 3000 may include a
stator 3002
10 including a number of stator poles 3004, and a rotor 3006 including a
number of rotor
poles 3008.
A housing 3010 may be provided for housing a cooling fluid. An end portion
of each stator pole leg (or stator pole for conventional SRM configurations)
3004 may
extend or pierce through a housing wall 3014 of housing 3010. The interface
between
15 each stator pole 3004 and housing wall 3014 may be sealed in any suitable
manner to
prevent cooling fluid 3012 from escaping housing 3010.
Housing wall 3014 may serve to isolate gases, indicated at 3020, that may
have a composition and/or pressure different than the surrounding atmosphere.
For
example, housing wall 3014 may be used to contain gases that are being
compressed
20 or expanded using a gerotor compressor/expander, e.g., as described in any
of the
following United States Patents and Patent Application Publications:
Publication No.
2003/0228237; Publication No. 2003/0215345; Publication No. 2003/0106301;
Patent No. 6,336,317; and Patent No. 6,530,211.
Because thermal energy is typically generated from electrical resistance in
the
25 wire bundles, and hysteresis losses in the core, stator 3002 may become
overheated.
To prevent this possibility, stator poles 3004 may be immersed in a cooling
fluid 3012
(e.g., gas and/or liquid), as shown in FIGURE 66. Cooling fluid 3012 may
comprises
an gas and/or liquid suitable for providing heat transfer. In some
embodiments, the
cooling fluid 3012 may be a heat transfer fluid that is (a) non-electrical-
conducting,
30 (b) volatile, and/or (c) compatible with the coatings on the coil wires
(i.e., non-
dissolving).. In some embodiments, cooling fluid 3012 may comprise a known
refrigerant.
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The thermal energy produced by operation of the device may cause the
volatile fluid 3012 to change phase from a liquid to a vapor, which phase
change
removes thermal energy in the form of latent heat. Because the liquid is
boiling, the
heat transfer coefficients may be very high, and may thus prevent overheating
of
stator 3002. In some embodiments, the vapors can be condensed in a heat
exchanger
3026, which converts the vapors back into a liquid. In essence, the system is
a heat
pipe, which is one of the most efficient means for removing heat from systems.
FIGURE 67 is a cut away view of a portion of the system of FIGURE 66,
illustrating a portion of stator 3002 having a stator pole 3004 extending
through
housing wall 3014, according to certain embodiments. Stator 3002 may have a
laminar construction including a number of laminar metal plates 3030. The
laminations allow for the efficient conduction of magnetic flux, while
limiting
electrical eddy currents that lower the efficiency of the system. If the
laminar metal
of stator 3002 were allowed to pierce through housing wall 3014, the laminate
coatings may provide a path through which the gases and/or liquids contained
by
housing wall 3014 may leak. Thus, as shown in FIGURE 67, the portion of the
stator
pole 3004 that pierces through housing wall 3014 may be constructed on non-
laminar
material. This non-laminar component of stator pole 3004 is indicated at 3034.
In
addition, the joint between the non-laminar portion 3034 of stator pole 3004
and
housing wall 3014 may be sealed in any suitable manner. For example, the non-
laminar portion of stator pole 3004 may be welded to housing wall 3014, which
may
be formed from a non-magnetic material, e.g., stainless steel.
In addition, the laminar and non-laminar portions of stator pole 3004 may be
intimately joined together in any suitable manner to eliminate air gaps that
would
resist the magnetic flux between the two stator pole components. For example,
the
two stator pole components may be mechanically joined, e.g., using a dovetail
joint
3040 shown in FIGURE 67, welded, brazed, or otherwise joined.
In addition, in some embodiments, as shown in FIGURE 68, thin slots 3050
may be formed in the non-laminar component 3034. The slotted portion of
component 3034 is indicated in the Front View by the dashed lines. The slots
3050 in
non-laminar component 3034 may be aligned in the same direction as the
laminations
in the laminar portion of stator pole 3004, and may serve the same purpose as
the
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laminations (e.g., to reduce eddy currents). The slot orientation shown in
FIGURE 68
may be used in various rotor/stator configurations, including, for example,
conventional SRM configurations (e.g., configuration Option A) and U-shaped
blade/U-shaped core configurations (e.g., configuration Options B1-B3).
FIGURE 69 illustrates an example configuration of a U-shaped stator pair
3060 having two partially-laminar legs 3062 and 3064 extending through housing
wall 3014, according to certain embodiments. U-shaped stator pair 3060 is
generally
laminar, except each leg 3062 and 3064 may include a non-laminar portion 3034
extending through housing wall 3014, e.g., to reduce the possibility of leaks
across
housing wall 3014, as discussed above regarding FIGURE 67. Non-laminar
portions
3034 may be connected to laminar portions of stator pair 3060, and to housing
wall
3014 in any suitable manner, e.g., as discussed above regarding FIGURE 67.
In this configuration, a flat blade 3070 passes between stator legs 3062 and
3064, as discussed above regarding FIGURES 5-13 and 26A. Flat blade 3070 may
be
laminar in the orientation shown in FIGURE 69. Thus, in order to provide a
continuous magnetic flux path, non-laminar portions 3034 stator legs 3062 and
3064
may include slots 3050 oriented as shown in FIGURE 69. For example, slots 3050
may turn or curve in order to align with both (a) the laminar portions of
stator legs
3062 and 3064 and (b) the laminations of flat blade 3070. This slot
orientation may
be used in various rotor/stator configurations, including, for example,
various flat
blade/U-shaped core configurations (e.g., configuration Options Cl, C2, and
D).
The short-flux-path configurations described with reference to the various
embodiments herein may be implemented for various SRM motors and/or generators
applications by changing the number of stator and rotor poles, sizes, and
geometries.
Similar configuration may also be utilized for axial-field and linear motors.
Several
embodiments described herein (e.g., configuration Option D discussed above)
may
additionally be used for permanent magnet AC machines where the rotor contains
alternating permanent magnet poles. Additionally, the embodiments described
above
may be turned inside out and used as an interior stator SRM or BLDC machines,
with
the rotor on the outside. These in turn can be used as motor, generators, or
both.
Numerous other changes, substitutions, variations, alterations, and
modifications may be ascertained to one skilled in the art and it is intended
that the
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present invention encompass all such changes, substitutions, variations,
alterations,
and modifications as falling within the scope of the appended claims.
