Dual rotor electric motor

The dual rotor electric motor integrates axial and radial flux paths with optimized magnetic saliencies and stator windings, addressing inefficiencies in existing designs by enhancing power density and heat management.

GB2643140APending Publication Date: 2026-02-11HART SIMON DAVID +1
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Patent Information

Application Number
GB2024011304
Authority / Receiving Office
GB · GB
Patent Type
Applications
Current Assignee / Owner
Filing Date
2024-07-31
Publication Date
2026-02-11

AI Technical Summary

Technical Problem

Existing electric motor designs face limitations in combining the benefits of axial and radial flux machines, such as efficiency, power density, and heat management, due to their distinct magnetic flux paths and structural differences.

Method used

A dual rotor electric motor design incorporating a single set of stator poles with varying magnetic saliencies and stator windings that integrate both axial and radial flux paths, utilizing grain-oriented steel and additive manufacturing for optimized magnetic flux distribution and cooling.

Benefits of technology

The design achieves enhanced power density, efficiency, and flexible installation while balancing heat management, leveraging the advantages of both axial and radial flux configurations.

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Abstract

An electric motor comprising a rotor 402 with a first and second group of magnetic saliencies, where the first group of magnetic saliencies is on a different plane to the second group of saliencies.
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Description

TECHNICAL FIELD The present invention relates to an electric motor design, in particular a method of using both a radial and an axial flux path. BACKGROUND Electric motor-based propulsion is becoming an attractive solution for road and air transport. Electric motors fall into two basic configurations depending on the primary flux direction. The key distinction lies in their flux direction: axial flux machines have a magnetic flux direction parallel to the machine's rotation axis, whereas radial flux machines have a radial magnetic flux direction. In radial machines, the flux path is considerably longer compared to axial machines. This elongated path spans from one rotor pole to the first stator tooth, then traverses through the stator back iron to the second tooth, ultimately returning to another rotor pole. Conversely, axial flux machines feature a shorter and more direct flux path, moving directly from one pole to another through the air gap. This shorter path helps maintain a strong magnetic field, contributing to increased efficiency and power density. In radial machines, the flux follows a 2-dimensional path, making the use of grain-oriented steel impractical. Conversely, in axial machines, the magnetic flux path is unidirectional, enabling the utilization of grain-oriented steel. This type of steel offers higher permeability, leading to reduced iron losses in axial flux machines and a potential efficiency increase of up to 2%. The axial flux machine holds a significant advantage over radial machines when it comes to winding configuration. With a higher active winding copper and reduced overhang, there is greater flexibility to increase the number of turns and minimize heat generated by end effects. Additionally, the winding can be in direct contact with aluminium, a superior heat conductor, facilitating a more efficient cooling system. In contrast, radial machines must dissipate heat through the stator core, typically composed of steel with lower thermal conductivity. Overall, the key benefits of axial flux motors include higher power density, enhanced efficiency, compact design, reduced weight, and installation flexibility, making them well-suited for a wide range of applications across different industries. Overall, radial flux motors offer simplicity in construction, efficient heat dissipation, durability, versatility, and cost-effectiveness, making them a preferred choice for many industrial and commercial applications. Regarding power (speed * torque) capability, the axial flux machine can produce more low speed torque due to the high-power density provided, and the radial flux machine can produce more speed as the rotor is of a smaller diameter, so the edge speed is less. Many uses of electric motors requires a mixture of the benefits offered by both the axial and radial flux machines and this invention looks to combine them. The combining of different flux path planes (for example axial or radial) within the same motor design has been considered before. US202201093561A1 teaches how two magnetic circuits, one radial and one axial, can be combined using two sets of stator poles, one set for the radial and one set for the axial magnetic circuits. The present invention has only one set of stator poles. The Radial-Axial flux (RADAX) hybrid motor configuration again has two magnetic circuits and choses which one to energise given the operating conditions. The present invention has only one set of stator poles. US1148289B2 teaches how two magnetic circuits with two separate stator yokes can be combined in the same motor. The present invention has only one set of stator poles and may have one yoke or alternately can be yokeless. US1148289B2 also teaches having two sets of stator windings. The present invention has only one set of stator windings. DEFINITIONS Concentrated windings type: A single coil is wound on each stator tooth. Distributed winding type. The coils are distributed around the stator. The advantage of a distributed winding is that the back-emf waveform is near to sinusoidal. Random coil winding: Where the wire is wound in no particular pattern, resulting in a coil with layers of wire stacked on top of each other Orthocyclic winding: Reduces resistance and improves the efficiency of the component by creating a more uniform magnetic field. Orthocyclic winding is commonly used in high-performance transformers and inductors where precision and consistency are essential. Helical winding: Involves winding the wire in a spiral pattern around a core, resulting in a coil with a cylindrical shape. Jumble winding: Randomly would on a bobbin. Multistrand wire: Is made of multiple conducting stands rather than one conductor. Litz wire: Designed to reduce skin effect and proximity effect losses in conductors. Additive manufacturing methods: Additive manufacturing (AM) is a process that creates objects by adding material in layers. Subtractive manufacturing methods: Removes material from a larger block to produce the part. Hybrid manufacturing methods: Combines additive and subtractive manufacturing methods. Magnetic saliency: Magnetic saliency describes the relationship between the rotor's main flux (d axis) inductance and the main torque-producing (q axis) inductance. 2 Magnetic reluctance and magnetic resistance: Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux and depends on the geometry and composition of an object. Flux path: A path which is followed by magnetic lines of force and in which the magnetic flux density is significant Stator yokeless: Where the stator poles do not require interconnection via magnetic material for example through a yoke. The requirements for a yoke include providing a magnetic flux path, providing mechanical stability and providing cooling of the stator poles. Flux for a sinusoidal machine rotor configuration: The flux defines a sinusoidal distribution around the stator. Flux for a switched reluctance machine rotor configuration: The flux is in a block distribution around the stator. Synchronous / asynchronous motors: In a synchronous motor the rotor turns synchronised with the stator field to produce maximum torque. In an asynchronous motor, the rotor turns at a different speed to that of the stator field to produce maximum torque. Magnetic saliency: Can be provided via permeant magnets, wound rotor poles, different magnetic reluctance paths, or asynchronous rotor features for example a closed cage (squirrel cage induction machine). Alternatively, can be provide by a combination, or all, of the above methods. SUMMARY A first aspect provides an electric motor comprising a rotor with a first and second group of magnetic saliencies; wherein the first group of magnetic saliencies is on a different plane to the second group of saliencies; wherein an element of the rotor is at a first angle to the electric machine axle and an element of the rotor is ata second angle to the electric machine axle; wherein the first group of magnetic saliencies are attached to the element of the rotor which is at a first angle to the electric machine axle; wherein the second group of magnetic saliencies are attached to the element of the rotor which is at a second angle to the electric machine axle. The electric motor further comprising a stator with a plurality of stator windings each around a stator pole; wherein each stator pole has two sides where the bulk of the magnetic flux leaves the stator material; wherein the two sides where the bulk of the magnetic flux leaves the stator material are at an angle greater than 0 degrees to each other; wherein the stator winding is between the two sides where the bulk of the magnetic flux leaves the stator material. The first and second group of magnetic saliencies on the rotor form magnetic circuits with the plurality of stator windings. A second aspect provides rotor magnetic saliency by permeant magnets. A third aspect provides rotor magnetic saliency by wound rotor poles. A fourth aspect provides rotor magnetic saliency by a series of different rotor magnetic reluctance paths. A fifth aspect provides rotor magnetic saliency by an asynchronous rotor topology. A sixth aspect provides rotor magnetic saliency by a combination of some or all of the methods of claims 2 to 5. A seventh aspect provides the motor magnetic saliency attached to the element of the rotor at a first angle to the electric machine axle can be provide by a different method to the motor magnetic saliency attached to the element of the rotor at a second angle to the electric machine axle. An eighth aspect provides the at a first angle is 0 degrees and the second angle is 90 degrees. A nineth aspect provides the stator pole is made of grain orientated material. A tenth aspect provides the stator pole is made of grain orientated material where the grain angle to each of the two sides is at half the angle between the two sides of the stator pole where the bulk of the magnetic flux leaves the stator material. An eleventh aspect provides the stator pole where the grain is at 45 degrees to each of the two sides of the stator pole where the bulk of the magnetic flux leaves the stator material. A twelfth aspect provides the stator windings are of the concentrated windings type. A thirteenth aspect provides the stator windings are of the distributed winding type. A fourteenth aspect provides the stator windings are of random coil winding and / or orthocyclic winding and / or helical winding and / or jumble winding, and / or multistrand wire, and / or Litz wire. A fifteenth aspect provides the stator windings are produced by hybrid manufacturing methods. A sixteenth aspect provides the stator windings are produced by additive manufacturing methods. A seventeenth aspect provides the stator windings are individually of different cross-sectional area. An eighteenth aspect provides the stator windings are of differing cross-sectional area that changes with position in the winding. A nineteenth aspect provides the stator poles provide flux for a sinusoidal (synchronous or asynchronous) motor rotor configuration. A twentieth aspect provides the stator poles provide flux for a switched reluctance machine rotor configuration A twenty-first aspect provides the stator poles are yokeless. OBJECTS OF THE INVENTION Accordingly, a primary object of the present invention is to provide the combination of an axial flux and a radial flux motor. Another object of the present invention is to provide stator windings that are individually of different cross-sectional area and that this differing cross-sectional area changes with position in the winding. Another object of the present invention is to provide the stator poles made of grain orientated material. Another object of the present invention is to provide rotor saliencies created through a range of techniques including, permeant magnets, wound rotor poles, a series of different rotor magnetic reluctance paths, or by an asynchronous rotor topology. Another object of the present invention is to provide concentrated windings type. Another object of the present invention is to provide a distributed winding type. Another object of the present invention is to provide a stator that is yokeless. Other further objects of the present invention will become apparent from a careful reading of the included drawing figures, the claims and detailed description of the invention. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 schematically depicts a comparison between radial and axial flux machines with particular attention paid to the magnetic flux path. Figure 2 schematically depicts a prior art axial flux machine. Figure 3 schematically depicts a prior art radial flux machine. Figure 4 schematically depicts and embodiment of the invention with an outer radial rotor. Figure 5 schematically depicts the embodiment of the invention with an inner radial rotor. Figure 6 schematically depicts the embodiment of the invention stator winding. Figure 7 schematically depicts a stator pole made of grain orientated material where the grain is at 45 degrees to each of the two sides of the stator pole where the bulk of the magnetic flux leaves the stator material. Figure 8 schematically depicts the motor magnetic field poles provided by rotor pole windings. Figure 9 schematically depicts the rotor magnetic saliency provided by varying the magnetic reluctance in the rotor. Figure 10 schematically depicts the embodiment of the invention with an inner radial rotor where the angles between the planes on which the rotor magnets are fixed and the axle is not either 0 or 90 degrees. DETAILED DESCRIPTION PRIOR ART Turning to figure 1 which schematically depicts a comparison between radial and axial flux machines with particular attention paid to the magnetic flux path (shown by the circular arrows). The flux path of a radial flux motor follows a plane that is perpendicular (90 degrees) to the axle. The flux path of an axial flux motor follows a plane that is parallel to the axle. These forms of electric motors operate through the interaction of the stator produced magnetic field and the rotors magnetic saliency (which may itself be created by a rotor field). The magnetic fields wish to move to a position where the magnetic flux path aligns to provide the path of least resistance between North and South poles. Alternately, some electric motors (for example reluctance motors) operate through the interaction of the stator produced magnetic field and the rotors saliency with regard to magnetic reluctance paths. In this case the rotor reluctance wishes to move to a position where the magnetic flux path has the least magnetic resistance. Turning to figure 2 which schematically depicts a prior art axial flux machine. Image 200 shows a side view of the motor. The axle (201) is connected to the rotor (202), which is the rotating element, on which are fixed the magnets (203). The example shown is a permeant magnet machine, however, the operation is applicable for other forms of rotor design, for example wound rotor poles. The stator (206) is the stationary element on which are mounted the stator poles (204) with their associated stator windings (205). The flux direction is shown by the thick arrow. The flux path of an axial flux motor follows a plane that is parallel to the axle. Image 210 shows a plan view of the stator (206) on which the stator poles (204) are mounted. The stator poles have associated stator windings (205). The example shown is of a concentrated winding type. Other winding types exist and are covered by the present invention. Those winding types include, but are not limited to, concentrated windings type, distributed winding type, random coil winding, orthocyclic winding, helical winding and the coils within can be, for example, jumble winding, multistrand wire, Litz wire etc. Image 220 is similar to image 210 with the superposition of the rotor magnets (203). This shows a typical magnetic polarity distribution (North and South poles) for a 2-pole pair motor. Note that in the diagram the stator stationary rotational angular reference (221) differs from the rotor magnetic rotational angular reference (222). Turning to figure 3 which schematically depicts a prior art radial flux machine. Image 300 shows a cut through view of the motor. The axle (301) is connected to the rotor (302), which is the rotating element, on which are fixed the magnets (303). The example shown is a permeant magnet machine, however, the operation is applicable for other forms of rotor design, for example wound rotor poles. The stator (306) is the stationary elementon which are mounted the stator poles (304) with their associated stator windings (305). The flux direction is shown by the thick arrow. The flux path of a radial flux motor follows a plane that is perpendicular (90 degrees) to the axle. Image 310 shows a plan view of the stator (306) on which the stator poles (304) are mounted. The stator poles have associated stator windings (305). The example shown is of a concentrated winding type. The rotor magnets (303) are attached to the rotor (302) which rotates with the axle (301). This shows a typical magnetic polarity distribution (North and South poles) for a 2-pole pair motor. 311 shows the cut through line that was used for image 300. INVENTION Turning to figure 4 which schematically depicts and embodiment of the invention with an outer radial rotor. Image 400 shows a side view of the motor. The axle (401) is connected to the rotor (402), which is the rotating element, on which are fixed the magnets (403). The example shown is a permeant magnet machine, however, the operation is applicable for other forms of rotor design, for example wound rotor poles. The bearing is shown as 407. The stator (406) is the stationary elementon which are mounted the stator poles (404) with their associated stator windings (405). The flux direction is shown by the thick arrow. The flux path has sections in one plane (for example parallel to the axle) and other sections that are in another plane (for example perpendicular to the axle). Thus, the invention has combined both an axial flux and a radial flux motor and permits a design that combines and optimises the advantages of both configurations of motor. In this embodiment, the rotor elements parallel to the axle are on the outer diameter and the stator poles are nearer to the axle. Turning to figure 5 which schematically depicts the embodiment of the invention with an inner radial rotor. Image 500 shows a side view of the motor. The axle (501) is connected to the rotor (502), which is the rotating element, on which are fixed the magnets (503). The example shown is a permeant magnet machine, however, the operation is applicable for other forms of rotor design, for example wound rotor poles. The bearing is shown as 507. The stator (506) is the stationary elementon which are mounted the stator poles (504) with their associated stator windings (505). The flux direction is shown by the thick arrow. The flux path has sections in one plane (for example parallel to the axle) and other sections that are in another plane (for example perpendicular to the axle). Thus, the invention has combined both an axial flux and a radial flux motor and permits a design that combines and optimises the advantages of both configurations of motor. In this embodiment, the rotor elements parallel to the axle are on the inner diameter and the stator poles are further from the axle. Turning to figure 6 which schematically depicts the embodiment of the invention’s stator winding. Image 600 shows a cut through of a stator winding (605) around a stator pole (604) which is made up of multiple turns. Turn one (601) is separated from turn two (603) by insulation (602). This insulation could be a separate part or a coating on the turns. Note that in this embodiment, the turns are not of equal cross section and that an individual turns cross section changes through the length of the turn. The cross section between turns may be optimised based on the cooling availability and mutual heating experienced by that turn. The change of cross section by length within a turn is constrained by the stator windings’ mechanical package and is designed to provide the largest area near cooling surfaces. The diagram shows a concentrated winding type, but those skilled in the art will appreciate that the invention is applicable to a range of winding configurations. The winding design leads itself to being manufactured by additive methods (3D printing), although other methods may be used. Figure 7 schematically depicts a stator pole made of grain orientated material where the grain is at 45 degrees to each of the two sides of the stator pole where the bulk of the magnetic flux leaves the stator material. Image 700 shows a cut through view of a stator pole (704) with material grain orientated aligned with the black lines (702). The grain orientation may be provided through the grain structure of the pole material or through the lamination of several flat sheets of the stator material. 701 and 703 show examples of these sheets with a boundary between (702). The laminations guide the flux and also reduce the magnetic eddy losses. Those skilled in the art will realise that other paths are possible including those that provide the routes of least magnetic resistance when the sides of the stator, where the bulk of the magnetic flux leaves the stator material, are not at 90 degrees. Figure 8 schematically depicts the motor magnetic field poles provided by rotor pole windings. As described before, the rotor magnetic poles can be provided by permeant magnets or other means. Image 800 shows the motor of figure 5 with the substitution of the rotor magnets for rotor poles (801 and 803) and rotor pole windings, field windings, (802 and 804). As an alternative embodiment, image 810 shows that the rotor magnetic field parallel to the axle is provided by a permanent magnet (805) while the rotor magnetic field perpendicular to the axle is provided by a rotor pole and rotor winding. Figure 9 schematically depicts the rotor magnetic saliency provided by varying the magnetic reluctance in the rotor. Image 900 shows an alternative to rotor field poles (provided by either magnets or windings). The image shows the section of rotor that behaves like a radial flux motor. This form of motor is a reluctance motor and operates by providing sections of different magnetic reluctance with respect to angle aboutthe axle. 901 and 902 show paths of low reluctance. The flux travels predominantly through low magnetic resistance magnetic material. 903 shows a path that moves through less low magnetic resistance magnetic material due to pockets of a different material (or in some cases air). Note that the rise of additive manufacturing (3D printing) has led to optimised designs of reluctance paths on rotors. Those skilled in the art will appreciate that although the preceding description has focused on synchronous motors, the invention is also applicable to asynchronous motors. Figure 10 schematically depicts the embodiment of the invention with an inner radial rotor where the angles between the planes on which the rotor magnets are fixed and the axle are neither 0 nor 90 degrees. Image 1000 shows a side view of the motor. The axle (1001) is connected to the rotor (1002), which is the rotating element, on which are fixed the magnets (1003). The example shown is a permeant magnet machine, however, the operation is applicable for other forms of rotor design, for example wound rotor poles. The bearing is shown as 1007. The stator (1006) is the stationary element on which are mounted the stator poles (1004) with their associated stator windings (1005). The flux direction is shown by the thick arrow. In this embodiment, when compared to figure 5, the vertical elements are no longer perpendicular to the axle and the horizontal elements are no longer parallel to the axle. Note that those skilled in the art will appreciate how figure 4 may also be converted to have vertical elements that are no longer perpendicular to the axle and horizontal elements that are no longer parallel to the axle. This disclosure is provided to reveal a preferred embodiment of the invention and a best mode for practicing the invention. Having thus described the invention in this way, it should be apparent that various different modifications can be made to the preferred embodiment without departing from the scope and spirit of this invention disclosure. When structures are identified as a means to perform a function, the identification is intended to include all structures which can perform the function specified. When structures of this invention are identified as being coupled together, such language should be interpreted broadly to include the structures being coupled directly together or coupled together through intervening structures. Such coupling could be permanent or temporary and either in a rigid fashion or in a fashion which allows pivoting, sliding or other relative motion while still providing some form of attachment, unless specifically restricted. 1 CLAIMS The invention claimed is: 1. An electric motor comprising: a rotor with a first and second group of magnetic saliencies; wherein the first group of magnetic saliencies is on a different plane to the second group of saliencies; wherein an element of the rotor is at a first angle to the electric machine axle and an element of the rotor is at a second angle to the electric machine axle; wherein the first group of magnetic saliencies are attached to the element of the rotor which is at a first angle to the electric machine axle; wherein the second group of magnetic saliencies are attached to the element of the rotor which is at a second angle to the electric machine axle; a stator with a plurality of stator windings each around a stator pole; wherein each stator pole has two sides where the bulk of the magnetic flux leaves the stator material; wherein the two sides where the bulk of the magnetic flux leaves the stator material are at an angle greater than 0 degrees to each other; wherein the stator winding is between the two sides where the bulk of the magnetic flux leaves the stator material. the first and second group of magnetic saliencies on the rotor form magnetic circuits with the plurality of stator windings. 2. The rotor magnetic saliency is provided by permeant magnets. 3. The rotor magnetic saliency is provided by wound rotor poles. 4. The rotor magnetic saliency is provided by a series of different rotor magnetic reluctance paths. 5. The rotor magnetic saliency is provided by an asynchronous rotor topology. 6. The rotor magnetic saliency is provided by a combination of some or all of the methods of claims 2 to 5. 7. The motor magnetic saliency of claim 1 attached to the element of the rotor at a first angle to the electric machine axle of claim 1 can be provide by a different method to the motor magnetic saliency of claim 1 attached to the element of the rotor at a second angle to the electric machine axle of claim 1. 8. The at a first angle of claim 1 is 0 degrees and the second angle is 90 degrees. 9. The stator pole of claim 1 is made of grain orientated material. 10. The stator pole of claim 1 is made of grain orientated material where the grain angle to each of the two sides is at half the angle between the two sides of the stator pole where the bulk of the magnetic flux leaves the stator material. 11. The stator pole of claim 10 where the grain is at 45 degrees to each of the two sides of the stator pole where the bulk of the magnetic flux leaves the stator material. 12. The stator windings of claim 1 are of the concentrated windings type. 13. The stator windings of claim 1 are of the distributed winding type. 14. The stator windings of claim 13 are of random coil winding and / or orthocyclic winding and / or helical winding and / or jumble winding, and / or multistrand wire, and / or Litz wire. 15. The stator windings of claim 1 are produced by hybrid manufacturing methods. 16. The stator windings of claim 1 are produced by additive manufacturing methods. 17. The stator windings of claim 1 are individually of different cross-sectional area. 18. The stator windings of claim 1 are of differing cross-sectional area that changes with position in the winding. 19. The stator poles of claim 1 provide flux for a sinusoidal (synchronous or asynchronous) motor rotor configuration. 20. The stator poles of claim 1 provide flux for a switched reluctance machine rotor configuration 21. The stator poles of claim 1 are yokeless. Amendments to the Claims have been filed as follows: 25 06 25

Claims

The invention claimed is:

1. An electric motor comprising:a stator with a plurality of stator poles around each is a single stator winding: wherein the winding has at least one turn;wherein each stator pole has at least one winding surface onto which its stator winding is wound;wherein each stator pole has a first and a second stator flux surface which are additional to the winding surface;wherein the firstand second stator flux surfaces are not parallel with respect to each other;a rotor with a first and second group of magnetic saliencies:wherein the first group of magnetic saliencies are on a plane parallel to the first stator flux surface;wherein the second group of magnetic saliencies are on a plane parallel to the second stator flux surface;the groups of magnetic saliencies on the rotor form magnetic circuits with the plurality of stator poles.

2. The electric motor of claim 1 wherein the rotor magnetic saliency is provided by permanent magnets.

3. The electric motor of claim 1 wherein the rotor magnetic saliency is provided by wound rotor poles.

4. The electric motor of claim 1 wherein the rotor magnetic saliency is provided by a series of different rotor magnetic reluctance paths.

5. The electric motor of claim 1 wherein the rotor rotates asynchronously with respect to the stator field.

6. The rotor magnetic saliency is provided by a combination of some or all of the apparatus of claims 2 to 5.

7. The rotor of claim 1 wherein the angle between the first stator flux surface and the rotor axis of rotation is 0 degrees, which is the radial plane.

8. The rotor of claim 1 wherein the angle between the second stator flux surface and the rotor axis of rotation is 90 degrees, which is the axial plane.

9. The stator pole of claim 1 is made of grain orientated material.10.11.

12. The stator windings of claim 1 are of the concentrated windings type.25 06 2513. The stator windings of claim 1 are of the distributed winding type.

14. The stator windings of claim 13 are of random coil winding and / or orthocyclic winding and / or helical winding and / or jumble winding, and / or multistrand wire, and / or Litz wire.

15. The stator windings of claim 1 are produced by hybrid manufacturing methods that combine additive and subtractive processes.

16. The stator windings of claim 1 are produced by additive manufacturing methods.

17. The stator windings of claim 1 are individually of different cross-sectional area.

18. The stator windings of claim 1 are of differing cross-sectional area that changes with position in the winding.

19. The stator poles of claim 1 provide flux for a sinusoidal (synchronous or asynchronous) motor rotor configuration.

20. The stator poles of claim 1 provide flux for a switched reluctance machine rotor configuration.

21. The stator poles of claim 1 are yokeless.

Citation Information

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