CONICAL MAGNETS AND ROTOR-STATOR STRUCTURES FOR ELECTRODYNAMIC MACHINES

BRIEF DESCRIPTION

[0001] Various embodiments of this invention relate generally to electrodynamic machines and the like, and more particularly, to conical magnets and rotor-stator structures for electrodynamic machines.

BACKGROUND

[0002] Both motors and generators have been known to use axial-based rotor and stator configurations, which can experience several phenomena during operation. For example, conventional axial motor and generator structures can experience detent, which is also known as "cogging torque" or "detent torque." Detent can be described as a periodic torque that can arise in motors and generators that co-axially integrate magnetically permeable elements, such as field poles, to form a stator structure, and use permanent magnets to form a rotor structure. When either the stator or rotor structure is rotated with respect to the other, a periodic varying torque can be created because the magnet structure typically prefers to align at a position that is centered with the magnetically permeable elements rather than at the intervening field pole gaps of air between the field pole elements.

[0003] FIG. IA illustrates a traditional electric motor exemplifying commonly-used stator and rotor structures. Electric motor 100 is a cylindrical motor composed of a stator structure 104, a magnetic hub 106 and a shaft 102. The rotor structure of motor 100 includes one or more permanent magnets 1 10, all of which are attached via magnetic hub 106 to shaft 102 for rotation within stator structure 104. Stator structure 104 typically includes field poles 1 IS, each having a coil winding 1 12 (only one is shown) that is wound about each field pole 1 18. Stator structure 104 includes slots 108 used in part to provide a wire passage for winding coil wire about stator field poles 1 18 during manufacturing. Slots 108 also provide magnetic separation between adjacent field poles 118. Stator structure 104 includes a peripheral flux- carrying segment 119 as part of magnetic return path 1 16. In many cases, stator structure 104 is composed of laminations 114, which typically are formed from isotropic (e.g., non-grain oriented), magnetically permeable material. Magnetic return path 116, which is one of a number of magnetic return paths in which permanent magnet-generated flux and AT-generated flux is present, is shown as being somewhat arcuate in nature at peripheral flux-carrying segment 119 but includes relatively sharp turns into the field pole regions 1 18.

[0004] Another drawback of conventional electric motors is that laminations 1 14 do not effectively use anisotropic materials to optimize the flux density and reduce hysteresis losses in flux-carrying poles, such as through field poles 1 18, and stator regions at peripheral flux- carrying segment 1 19. In particular, peripheral flux-carrying segment 1 19 includes a non- straight flux path, which limits the use of such anisotropic materials to reduce the hysteresis losses (or "iron losses"). Hysteresis is the tendency of a magnetic material to retain its magnetization. "Hysteresis loss" is the energy required to magnetize and demagnetize the magnetic material constituting the stator regions, wherein hysteresis losses increase as the amount of magnetic material increases. As magnetic return path 116 has one or more turns of ninety-degrees or greater, the use of anisotropic materials, such as grain-oriented materials, cannot effectively reduce hysteresis losses because the magnetic return path 1 16 in peripheral flux-carrying segment 119 would cut across the directional orientation of laminations 114, such as direction 120, which represents the orientation of grains for laminations 1 14.

[0005] While traditional motor and generator structures are functional, they have several drawbacks in their implementation. It would be desirable to provide improved techniques and structures that minimize one or more of the drawbacks associated with traditional motors and generators, including axial motors.

SUMMARY

[0006] Disclosed are conical magnets for rotors in electrodynamic machines, methods to design the same, and rotor-stator structures for electrodynamic machines, according to various embodiments. In various embodiments, a rotor-stator structure for electrodynamic machine can include field pole members and conical magnets. According to at least some embodiments, one or more of the conical magnets can include a magnetic region configured to confront one or more air gaps. The magnetic region can be substantially coextensive with one or more acute angles to the axis of rotation. The magnetic region can also include a surface (or a portion thereof) that is positioned at multiple radial distances from the axis of rotation (e.g., in a plane perpendicular to the axis of rotation).

BRIEF DESCRIPTION OF THE FIGURES

[0007] The various embodiments of the invention are more fully appreciated in connection with the following detailed description taken in conjunction with the accompanying drawings, in which:

[0008] FlG. 1 exemplifies commonly-used stator and rotor structures implemented in a traditional electric motor;

[0009] FIG. 2A depicts an example of a conical magnet including magnetic regions, according to at least one embodiment of the invention;

[0010] FIG. 2B depicts examples of sectional views for magnetic regions, according to various embodiments of the invention;

[0011] FIG. 2C depicts a cross-sectional view for an example of a magnetic region, according to at least one embodiment of the invention;

[0012] FIG. 2D depicts a cross-sectional view for an example of a specific magnetic region, according to at least one embodiment of the invention;

[0013] FIG. 2E depicts a cross-sectional view of an example of a specific implementation of a magnetic region, according to at least one embodiment of the invention;

[0014] FIG. 2F depicts a cross-sectional view of an example of a magnetic region, according to at least one embodiment of the invention;

[0015 j FIG. 2G depicts a cross-sectional view of another example of a magnetic region, according to at least one embodiment of the invention;

[0016] FIG. 3 is a diagram illustrating an example of a sinusoidal flux waveform generated by an arrangement of magnetic regions, according to at least one embodiment of the invention;

[0017] FIG. 4 depicts an example of spectrum diagram showing a Vbemf waveform, according to one embodiment of the invention;

[0018] FIG. 5A depicts a conical magnet structure in accordance with one embodiment of the invention;

[0019] FIG. 5B depicts a conical magnet structure in accordance with yet another embodiment of the invention;

[0020] FIGs. 6A to 6C depict another conical magnet structure in accordance with another embodiment of the invention;

[0021] FIG. 7 depicts yet another conical magnet structure in accordance with yet another embodiment of the invention;

[0022] FIG. 8 is a diagram illustrating a flux waveform generated by an arrangement of magnetic regions of FIG. 7, according to at least one embodiment of the invention;

[0023] FIG. 9 is an example of a spectrum diagram depicting an example of a Vbemf waveform, according to one embodiment of the invention;

[0024] FIGs. 1OA to IOC depict an example of an internal permanent magnet ("IPM")- based implementation of a conical magnet structure in accordance with at least one embodiment of the invention;

[0025] FIGs. HA to 11C depict another example of an internal permanent magnet ("IPM")-based implementation of a conical magnet structure in accordance with at least one embodiment of the invention;

[0026] FIGs. 12A to 12C depict yet another example of an internal permanent magnet ("IPM")-based implementation of a conical magnet structure in accordance with at least one embodiment of the invention;

[0027] FIG. 13 shows a rotor structure implementing an arrangement of offset conical magnets, according to one or more embodiments of the invention;

[0028] FIGs. 14A and 14B depict amplitudes of detent waveforms for rotor structures implementing arrangements of conical magnets with and without offsets, according to one or more embodiments of the invention;

[0029] FIGs. 15A and 15B depict amplitudes of composite detent waveforms for rotor struciures implementing arrangements of conical magnets with and without offsets, according to one or more embodiments of the invention;

[0030] FIG. 16 depicts a conical magnet structure having a magnetic region composed of multiple magnets, in accordance with at least one embodiment of the invention; and

[0031] FIG. 17 is an exploded view depicting an example of a rotor-stator structure, according to various embodiments of the invention.

[0032] Like reference numerals refer to corresponding parts throughout the several views of the drawings.

DETAILED DESCRIPTION Definitions

[0033] The following definitions apply to some of the elements described with respect to some embodiments of the invention. These definitions may likewise be expanded upon herein.

[0034] As used herein, the term "air gap" refers, in at least one embodiment, to a space, or a gap, between a magnet surface and a confronting pole face. Such a space can be physically described as a volume bounded at least by the areas of the magnet surface and the pole face. An air gap functions to enable relative motion between a rotor and a stator, and to define a flux interaction region. Although an air gap is typically filled with air, it need not be so limiting.

[0035] As used herein, the term "back-iron" commonly describes a physical structure (as well as the materials giving rise to that physical structure) that is often used to complete an otherwise open magnetic ciicuit. In particular, back-iron structures are generally used only to transfer magnetic flux from one magnetic circuit element to another, such as either from one magnetically permeable field pole member to another, or from a magnet pole of a first magnet to

a magnet pole of a second magnet, or both, without an intervening ampere-turn generating element, such as coil, between the field pole members or the magnet poles. Furthermore, back- iron structures are not generally formed to accept an associated ampere -turn generating element, such as one or more coils.

[0036] As used herein, the term "coil" refers, in at least one embodiment, to an assemblage of successive convolutions of a conductor arranged to inductively couple to a magnetically permeable material to produce magnetic flux. In some embodiments, the term "coil" can be described as a "winding" or a "coil winding." The term "coil" also includes foil coils (i.e., planar-shaped conductors that are relatively flat).

[0037] As used herein, the term "coil region" refers generally, in at least one embodiment, to a portion of a field pole member around which a coil is wound.

[0038] As used herein, the term "core" refers to, in at least one embodiment, a portion of a field pole member where a coil is normally disposed between pole shoes and is generally composed of a magnetically permeable material for providing a part of a magnetic flux path. The term "core," in at least one embodiment, can refer, in the context of a conical magnet, to a structure configured to support magnetic regions. As such, the term core can be interchangeable with the term "hub" in the context of a rotor magnet, such as a conical magnet.

[0039] As used herein, the term "field pole member" refers generally, in at least one embodiment, to an element composed of a magnetically permeable material and being configured to provide a structure around which a coil can be wound (i.e., the element is configured to receive a coil for purposes of generating magnetic flux). In particular, a field pole member includes a core (i.e., core region) and at least one pole shoe, each of which is generally located near a respective end of the core. Without more, a field pole member is not configured to generate ampere -turn flux. In some embodiments, the term "field pole member" can be described generally as a "stator-core."

[0040] As used herein, the term "active field pole member" refers, in at least one embodiment, to an assemblage of a core, one or more coils, and at least two pole shoes. In particular, an active field pole member can be described as a field pole member assembled with one or more coils for selectably generating ampere-turn flux. In some embodiments, the term "active field pole member" can be described generally as a "stator-core member."

[0041] As used herein, the term "ferromagnetic material" refers, in at least one embodiment, to a material that generally exhibits hysteresis phenomena and whose permeability is dependent on the magnetizing force. Also, the term "ferromagnetic material" can also refer to

a magnetically permeable material whose relative permeability is greater than unity and depends upon the magnetizing force.

[0042] As used herein, the term "field interaction region" refers, in at least one embodiment, to a region where the magnetic flux developed from two or more sources interact vectorially in a manner that can produce mechanical force and/or torque relative to those sources. Generally, the term "flux interaction region" can be used interchangeably with the term "field interaction region." Examples of such sources include field pole members, active field pole members, and/or magnets, or portions thereof. Although a field interaction region is often referred to in rotating machinery parlance as an "air gap," a field interaction region is a broader term that describes a region in which magnetic flux from two or more sources interact vectorially to produce mechanical force and/or torque relative to those sources, and therefore is not limited to the definition of an air gap (i.e., not confined to a volume defined by the areas of the magnet surface and the pole face and planes extending from the peripheries between the two areas). For example, a field interaction region (or at least a portion thereof) can be located internal to a magnet.

[0043J As used herein, the term "generator" generally refers, in at least one embodiment, to an electrodynamic machine that is configured to convert mechanical energy into electrical energy regardless of, for example, its output voltage waveform. As an "alternator" can be defined similarly, the term generator includes alternators in its definition.

[0044] As used herein, the term "magnet" refers, in at least one embodiment, to a body that produces a magnetic field externally unto itself. As such, the term magnet includes permanent magnets, electromagnets, and the like. The term magnet can also refer to internal permanent magnets ("IPMs"), surface mounted permanent magnets ("SPMs"), and the like.

[0045] As used herein, the term "motor" generally refers, in at least one embodiment, to an electrodynamic machine that is configured to convert electrical energy into mechanical energy.

[0046] As used herein, the term "magnetically permeable" is a descriptive term that generally refers, in at least one embodiment, to those materials having a magnetically definable relationship between flux density ("B") and applied magnetic field ("H"). Further, the term "magnetically permeable" is intended to be a broad term that includes, without limitation, ferromagnetic materials such as common lamination steels, cold-rolled-grain-oriented (CRGO) steels, powder metals, soft magnetic composites ("SMCs"), and the like.

[0047] As used herein, the term "pole face" refers, in at least one embodiment, to a surface of a pole shoe that faces at least a portion of the flux interaction region (as well as the air

gap), thereby forming one boundary of the flux interaction region (as well as the air gap). In some embodiments, the term "pole face" can be described generally as including a "flux interaction surface." In one embodiment, the term "pole face" can refer to a "stator surface."

[0048] As used herein, the term "pole shoe" refers, in at least one embodiment, to that portion of a field pole member that facilitates positioning a pole face so that it confronts a rotor (or a portion thereof), thereby serving to shape the air gap and control its reluctance. The pole shoes of a field pole member are generally located near one or more ends of the core starting at or near a coil region and terminating at the pole face. In some embodiments, the term "pole shoe" can be described generally as a "stator region."

[0049] As used herein, the term "soft magnetic composites" ("SMCs") refers, in at least one embodiment, to those materials that are comprised, in part, of insulated magnetic particles, such as insulation-coated ferrous powder metal materials that can be molded to form an element of the stator structure of the invention.

Discussion

[0050] FIG. 2A depicts an example of a conical magnet including magnetic regions, according to at least one embodiment of the invention. As shown, conical magnet 2300 can include an arrangement of magnetic regions ("MR") 2302. In one or more embodiments, at least one magnetic region 2302 has a surface (or a portion thereof) that is coextensive (or is substantially coextensive) to one or more acute angles with respect to axis of rotation 2301. In the example shown, surface portion 2303a can be at acute angle 2306 to axis of rotation 2301, whereas surface portion 2303b can be at acute angle 2305. Further, the arrangement of magnetic regions 2302 can be mounted upon a hub 2304, such as a core (in the context of a rotor magnet, such as a conical magnet) or an equivalent structure. In at least one embodiment, magnetic regions 2302 can be configured to modify the thickness of at least a portion of an air gap (not shown) in, for example, a plane perpendicular to axis of rotation 2301, whereby the thickness of the air gap can vary during rotation relative to conical magnet 2300. The arrangement of magnetic regions 2302 can include one or more configurable structural attributes that modify magnetic regions 2302, which, in turn, can modify the generation of a sinusoidal flux waveform (or a substantially sinusoidal flux waveform), or an equivalent thereof. In a specific embodiment, the one or more magnetic region portions of magnetic regions 2302 can be configured to modify portions of the sinusoidal flux waveform. In at least one embodiment, magnetic regions 2302 can be configured to include one or more surfaces (or one or more portions thereof) that can provide for a substantially uniform thickness for at least a portion of an air gap (not shown) in a plane perpendicular to axis of rotation 2301. To illustrate, consider

that configuring magnetic region 2302 as an internal permanent magnet ("IPM") can provide for a uniform air gap thickness. In various embodiments, magnetic regions 2302 can include magnets or magnetically permeable material, or both, as well as other equivalent materials. As used herein, the term "conical magnet" can generally refer to, in at least one embodiment, a structure of a conical magnet that implements an assembly of magnet components including, but not limited to, magnetic regions and/or magnetic material and a hub structure. In at least some embodiments, the term "conical magnet" can be used interchangeably with the term "conical magnet structure." In at least one embodiment, the term "conical magnet" can refer to those magnets described in U.S. Pat. No. 7,061,152 and/or U.S. Pat. No. 7,294,948 B2.

[0051] In view of the foregoing, magnetic regions 2302 (and/or portions thereof) can provide for configuring, for example, the shape of a flux waveform, such as a magnetic flux waveform in field pole members (not shown) of an electrodynamic machine in which conical magnet 2300 is implemented. In at least some embodiments, the arrangement of magnetic regions 2302 can be configured to reduce higher-order harmonic frequencies in the flux waveform. This, in turn, can reduce the hysteresis and eddy current losses (both of which can be collectively referred to as "core losses") that otherwise might be generated by higher-order harmonic frequencies in, for example, magnetically permeable material (e.g., steel) of the field pole members. Therefore, the configuration of the magnetic regions 2302 (and portions thereof) can facilitate, among other things, a reduction in power losses due to the core losses, according to various embodiments. In at least some embodiments, the shape of a magnetic region can be determined in accordance with the multiple radial distances to provide flux, in a substantially sinusoidal manner, to one or more fixed point or area portions in space, such as a point or area associated with a pole face.

[0052] FIG. 2B depicts examples of sectional views for magnetic regions, according to various embodiments of the invention. For purposes of illustration, diagram 2310 depicts a cross section 231 1 of a conical magnet, the cross section 2311 showing a sectional view A-A of conical magnet 2300 of FIG. 2A with magnetic regions 2302 having different surfaces. As shown, magnetic regions 2302a, 2302b, and 2302c have surfaces 2307, 2308, and 2309, respectively. Surfaces 2307 and 2308 are shown as being positioned at multiple radial distances, "rd," from axis of rotation 2301 in a plane perpendicular to axis of rotation 2301. In particular, surface 2307 is positioned at multiple radial distances, which include radial distance ("rd(l)") 2317a and radial distance ("rd(2)") 2317b from axis of rotation 2301 , whereas surface 2308 is positioned at multiple radial distances that include radial distance ("rd(l)") 2318a and radial distance ("rd(2)") 2318b. In at least some embodiments, the multiple radial distances can

determine multiple angles with which a surface can be coextensive. The multiple angles can be determined with reference to axis of rotation 2301. For example, radial distance ("rd(l)") 2318a and radial distance ("rd(2)") 2318b can determine angles 2305 and 2306 of FlG. 2A, respectively, for surface portions 2303b and 2303a. The multiple radial distances can determine the variation of the thickness of an air gap as conical magnet 2300 rotates. Surface 2309 is positioned at a radial distance ("rd") 2319a from axis of rotation 2301, which can facilitate the establishment of an air gap having a uniform air gap thickness.

[0053] FIG. 2C depicts a cross-sectional view for an example of a magnetic region, according to at least one embodiment of the invention. Magnetic region 2320 can include any number of portions, at least a subset of which can be configured to define the rate at which flux is exchanged with a pole face (not shown). As such, portions of magnetic region 2320 can determine the portions of a flux waveform, such as a sinusoidal flux waveform. In this example, magnetic region 2320 includes a medial portion ("medial magnetic region portion") 2334 and lateral portions ("lateral magnetic region portions") 2332. Further, surface 2322 of magnetic region 2320, including the surface portions of medial portion 2334 and lateral portions 2332 can be configured to have a shape or shapes that facilitate the shaping of a flux waveform to establish a substantially sinusoidal flux waveform in, for instance, a field pole (not shown). Lines of flux can be established between magnetic region 2320 and a pole face, with the directions of flux oriented either toward magnetic region 2320 from a pole face or from magnetic region 2320 into the pole face. In at least one embodiment, surface 2322 associated with medial portion 2334 can be located at a thickness ("Thickness(Med)") 2324 that can be greater than the thicknesses ("Thickness(Lat)") 2326 at which lateral portions 2332 are located. In another embodiment surface 2322 associated with medial portion 2334 can be located at a thickness ("Thickness(Med)") 2324 that can be less than the thicknesses ("Thickness(Lat)") 2326 at which lateral portions 2332 are located.

[0054] In a specific embodiment, one or more shapes of surfaces associated with medial portion 2334 and lateral portions 2332 can be configured to modify a part of a sinusoidal flux waveform. In one embodiment, the part of the sinusoidal flux waveform can be in a range from approximately 20 degrees to approximately 80 degrees of a quadrant of a sinusoidal waveform (e.g., from an amplitude of zero to a positive peak amplitude). In other embodiments, the part can include fewer or more degrees, and can overlap other portions of the sinusoidal flux waveform. Note that the shape of surface 2322, including the shapes of medial portion 2334 and lateral portions 2332, can be configured to coincide (or substantially coincide) with a curved boundary, according to one embodiment. In at least some embodiments, the rate of change of

surface 2322 from one or more points on surface 2322 associated with medial portion 2334 to one or more points on surface 2322 associated with at least one of lateral portions 2332 can influence the shaping of the portion of a flux waveform, such as a sinusoidal flux waveform, from approximately 20 degrees to approximately 80 degrees, as an example. In at least some embodiments, the rate of change of surface 2322 can be represented by (and/or coextensive with) an angle of surface 2322, such as the angle ("A") 2325 of FIG. 2D. Referring back to FIG. 2C, magnetic region 2320 can be composed of one or more magnets having curved surfaces. In another embodiment, surface 2322 can be configured to coincide (or substantially coincide) with multiple straight boundaries (e.g., straight or flat boundary portions that reside in a plane tangent to a cone circumscribing a conical magnet). As such, magnetic region 2320 can be composed of one or more magnets having flat surfaces. Or, surface 2322 can include a combination of flat and curved surface portions.

[0055] In at least one embodiment, medial portion 2334 can be configured to modify another part of the sinusoidal flux waveform. In one embodiment, another pan of the sinusoidal flux waveform can be from approximately 70 degrees to approximately 90 degrees of the quadrant of a sinusoidal waveform. In other embodiments, this part can include fewer or more degrees, and can overlap other portions of the sinusoidal flux waveform. In one instance, medial portion 2334 can be configured to include an intra-magnetic region gap, the modification of which (e.g., in terms of size) can influence the shaping of a flux waveform to approximate, for example, a portion of sine wave from approximately 70 degrees to approximately 90 degrees. In a specific embodiment, different thicknesses(med) 2324 can be established over medial portion 2334 (or part of medial portion 2334) to produce the same effect as the intra-magnetic region gap at or near a surface portion (not shown) of surface 2322 that is configured to generate, for example, a relatively small air gap thickness (e.g., for at least a portion of surface 2322). In at least one embodiment, magnetic region 2320 can include multiple intra-magnetic region gaps of one or more shapes.

[0056] In at least one embodiment, any of lateral portions 2332 can be configured to modify yet another part of the sinusoidal flux waveform. In one embodiment, the part of the sinusoidal flux waveform can be from approximately 0 degrees to approximately 30 degrees of the quadrant of a sinusoidal waveform. In other embodiments, this part can include fewer or more degrees, and can overlap other portions of the sinusoidal flux waveform. As an example, consider that one or more of lateral portions 2332 can be configured to include an inter-magnetic region gap (or a portion thereof), the widening of which can influence the shaping of a flux waveform to approximate, for example, a portion of a sine wave from approximately 0 degrees

to approximately 30 degrees. In a specific embodiment, thicknesses(lat) 2326 can be negligible or non-existent (e.g., zero thickness) in association with lateral portions 2332 (or part of lateral portions 2332) to produce inter-magnetic region gaps with neighboring magnetic regions (not shown).

[0057] In various embodiments, magnetic region 2320 can include one or more permanent magnets formed to produce, for example, at least one magnet pole (e.g., a North pole or a South pole). In at least some embodiments, the polarity of a pole can be represented by a direction of polarization, which can be at any angle to, for example, at least a portion of a surface of magnetic region 2320 (or surface of a conical magnet). For example, a direction of polarization representing a north pole can be depicted as a ray extending at any angle with respect to surface of magnetic region 2320, the direction of the ray pointing away from the surface of magnetic region 2320. As another example, a direction of polarization can represent a south pole. Thus, the direction of polarization can be depicted as a ray intersecting a point on the surface of magnetic region 2320, the direction of the ray pointing into the surface of magnetic region 2320. Magnetic region 2320 can comprise magnet material, such as neodymium iron ("NdFe"), ceramic, Samarium Cobalt ("SmCo"), and/or any other magnet material. In some cases, a flux, such as the peak magnet flux, in a field pole member can also be a function of the angle of a surface of hub 2330 (e.g., with respect to the axis of rotation) at which magnetic region 2320 is mounted, the thickness of magnet material of magnetic region 2320, and/or the energy product of the magnet material to meet a target peak flux level, among other things. In at least one embodiment, magnetic region 2320 can be produced as an internal permanent magnet ("IPM"). As such, magnetic region 2320 can include magnetically permeable material disposed with or on magnets. As used herein, the term "medial" refers, in at least one embodiment, to being situated at or pertaining to the middle of a magnetic region (e.g., nearer the middle of the magnetic region). As used herein, the term "lateral" refers, in at least one embodiment, to being situated at or pertaining to the side of a magnetic region (e.g., at a portion that is farther from the middle of a magnetic region). Note that in various embodiments, one or more lateral portions and one or more medial portions can overlap each other or can be separate from each other. In at least some embodiments, magnetic region 2320 can include any number of lateral portions and/or any number of medial portions.

[0058] Further to the example shown in FIG. 2C, magnetic portion 2320 can be mounted on hub 2330. Note that while FIG. 2C shows thickness 2324 and thickness 2326 of surface 2322 being referenced from hub 2330, these thicknesses can be referenced from the axis of rotation or any other point of reference. To illustrate, surface 2322 and portions thereof can be determined

with respected to a radial distance ("rd") 2340. As such, a rate of change of surface 2322 can be determined with respect to radial distance 2340, which in this example, is referenced from the centerline (not shown) of hub 2330. Hub 2330 can be of any shape, such as, but not limited to, conical shapes with curved and/or flat surfaces, as well as any other shapes suitable to support internal permanent magnets (such as in FIG. 12B). For instance, hub 2330 is shown to include a flat portion having width 2336. In various embodiments, hub 2330 can include "magnetically permeable" material such as, without limitation, ferromagnetic materials, soft magnetic composites ("SMCs"), steel, laminated metals (e.g., steel), pressed metal, and the like.

[0059] FIG. 2D depicts a cross-sectional view for an example of a specific magnetic region, according to at least one embodiment of the invention. In this example, magnetic region 2321 includes flat surfaces (or substantially flat surfaces) 2323a and 2323b for modifying portions of a sinusoidal flux waveform in field pole members (not shown). In this example, magnetic region 2321 includes a medial portion ("medial magnetic region portion") 2335 and lateral portions ("lateral magnetic region portions") 2333. In one embodiment, angie ("A") 2325 can be configured to modify the part of the sinusoidal flux waveform from approximately the range of 20 degrees to 80 degrees of the first quadrant of a sinusoidal waveform. Angle 2325 can describe the rate of change of a surface (e.g., surface 2323b) of either a magnet or magnetically permeable material, or both, approximately between at least one point in medial portion 2335 to at least one point in one of lateral portions 2333. Optionally, the surface portions of flat surfaces 2323a and 2323b for medial portion 2335 can be configured to modify another part of the sinusoidal flux waveform by, for example, implementing an intra-magnetic region gap 2327, which can be composed of flat, curved or any other type of surface portion and/or shape. In one embodiment, flat surfaces 2323a and 2323b can belong to two or more separate magnets. In a specific embodiment, the surface portions of flat surfaces 2323a and 2323b for lateral portions 2333 can be configured to modify yet another part of the sinusoidal flux waveform by, for example, implementing a reduced (e.g., a negligible) thickness or a zero thickness ("Thickness(lat)") at parts 2329 of lateral portions 2333, thereby providing for inter- magnetic region gaps. Portions 2399 of an inter-magnetic region gap at parts 2329 can facilitate formation of an inter-magnetic region gap with a neighboring magnetic region (not shown).

[0060] FIG. 2E depicts a cross-sectional view 2336 of an example of a specific implementation of a magnetic region, according to at least one embodiment of the invention. In this example, a magnetic region 2344 includes magnets 2348 having, for example, flat surfaces 2343a and 2343b, both of which can be configured to confront a pole face (not shown). An intra-magnetic region 2327a can be disposed between the two magnets 2348. Magnets 2348 can

be mounted on a hub region 2341 , which is a portion of hub 2342 that can extend into magnetic region 2344. In some embodiments, hub region 2341 can be composed of material or a structure other than that associated with hub 2342. In at least some embodiments, a magnetically permeable layer (not shown) can be disposed on or relating to surfaces 2343a and 2343b.

[0061] FIG. 2F depicts a cross-sectional view 2350 of an example of a magnetic region, according to at least one embodiment of the invention. In this example, a field pole member 2354 includes a field pole face 2356 having, for example, a curved cross-section configured to confront a conical magnet. Magnetic region 2362 can be mounted on hub 2364, and can include a surface 2359 for modifying portions of a sinusoidal flux waveform. As shown, the distances ("DIST(Lat)") 2358 from field pole face 2356 to surface 2359 can be greater than the distance ("DIST(Med)") 2357. As distances 2358 from field pole face 2356 to surface 2359 can be greater than the distance 2357, the thickness of air gap 2360 can generally be greater at the lateral portions of magnetic region 2362 than the medial portion. In at least some embodiments, magnetic region 2362 can include one or more magnets, whereby surface 2359 can include one or more surfaces of magnetic material associated with one or more magnets. In at least some embodiments, surface 2359 (or one or more portions thereof) of magnetic region 2362 (e.g., at a lateral portion thereof) can be located at a subset of one or more distances, including distance 2358, from a surface of field pole face 2356. Similarly, surface 2359 (or one or more portions thereof) of magnetic region 2362 (e.g., at a medial portion thereof) can be located at another subset of one or more distances, including distance 2357, from field pole face 2356. Note that distances 2357 and 2358 can each be coincident with a radial line (not shown) that extends from either a centerline of hub 2364 or an axis of rotation.

[0062] FIG. 2G depicts a cross-sectional view 2370 of another example of a magnetic region, according to at least one embodiment of the invention. In this example, elements having similar names and/or reference numbers can have (but need not have) similar structures and/or functions described in FIG. 2F. In this case, magnetic region 2374 can be mounted on hub 2364, and can include one or more magnets represented as magnet(s) 2377 on which a magnetically permeable layer ("MP layer") 2376 can be formed thereupon. In at least one embodiment, magnetically permeable layer 2376 can be disposed on one or more magnets ("magnet(s)") 2377 to form a substantially uniform air gap thickness for air gap 2372. As such, surface 2379 (or portions thereof) can be positioned at a substantially constant radial distance (not shown), which, in turn, can establish distances ("DϊST(Lat)") 2358a from field pole face 2356a to surface 2379 to be the same (or substantially the same) as distance ("DIST(Med)") 2357a. In at least some embodiments, magnetic region 2374 can include surface 2387 (or portions thereof) of magnetic

material that can be associated with one or more magnets ("magnet(s)") 2377. As such, magnet surface distance ("MSDIST(Lat)") 2388 can represent one or more distances from field pole face 2356a to surface 2387 of one or more magnets 2377 (e.g., at a lateral portion thereof), and magnet surface distance ("MSDIST(Med)") distance 2389 can represent one or more distances from field pole face 2356a to surface 2387 of one or more magnets 2377 (e.g., at a medial portion thereof). These examples of magnet surface distances demonstrate that one or more portions of surface 2387 can be irregular while being implemented in a magnetic region that provides uniform air gap 2372, according to at least some embodiments. As used herein, the term "irregular surface" can refer to a non-uniform magnet surface or surfaces of a magnetic region, such as surface 2387, the non-uniform magnet surface being determined by multiple distances between a magnet surface and an arc 2385 at a radial distance from hub centerline (not shown). Examples of hub centerlines are shown in FIGs. 5 A and 5B. In some embodiments, arc 2385 can be coextensive with one or more surface portions of a pole face, such as pole face 2356a of field pole member 2354a (e.g., active field pole member 2354a).

[0063] FIG. 3 is a diagram 2400 illustrating an example of a sinusoidal flux waveform generated by an arrangement of magnetic regions, according to at least one embodiment of the invention. Diagram 2400 depicts the voltage that results from the back electromagnetic force ("Vbemf" ), which can be induced, for example, in a coil about a field pole member (not shown) by a magnet flux waveform created by either a hub with magnet regions or field pole faces rotating relative to the other. For purposes of illustration, consider that Faraday's Law provides that the amplitude of the Vbemf is given by (or is related to) the following relationship: -d(Nφ)/dt, where "N" is the number of turns of a coil and "φ" is the magnetic flux. Integration of the Vbemf waveform can determine the shape of the flux waveform (e.g., the magnet flux waveform). In the example shown in FIG. 3, an arrangement of magnetic regions in a conical magnet structure can produce Vbemf ("trace 1") 2402 and magnet flux waveform ("trace 2") 2404, both of which are approximate sinusoids.

[0064] FIG. 4 depicts an example of spectrum diagram 2500 showing a Vbemf waveform, according to one embodiment of the invention. As shown in this example, an arrangement of magnetic regions can maintain the harmonics below, for example, -45dB. The fundamental frequency is shown in this example to be at or near spectral waveform portion 2502. Note that the proportions, amplitudes, frequencies and other depicted portions of the waveforms are provided for purposes of discussion and are not intended to be limiting.

[0065] FIG. 5A depicts a conical magnet structure in accordance with one embodiment of the invention. Conical magnet 2600 includes an arrangement of magnetic regions 2612

mounted on a hub 2610, at least one of magnetic regions 2612 including magnetic material 2604 for forming magnet poles. In at least on embodiment, hub 2610 can include a hub hole 261 1 through which a shaft (not shown) can pass to mount conical magnet 2600 thereupon. Hub hole 261 1 can be configured to align centerline 2605 of hub 2610 with an axis of rotation (not shown) when conical magnet 2600 is disposed upon the shaft. At least one of magnetic regions 2612, such as magnetic region 2612a, can be disposed on hub 2610 so that a centerline 2603 of magnetic region 2612a can be at an acute angle 2609 with centerline 2605 of hub 2610 (and/or hub hole 2611). In various embodiments, at least portions of curved surfaces 2606 can be coextensive with at least one acute angle with respect to centerline 2605 of hub 2610.

[0066] Further, at least one of magnetic regions 2612 can include a surface 2606 having a curvature (i.e., one or more curved surfaces) that has curved portions for producing sine wave- like flux waveforms. Curved surfaces 2606 facilitate a reduction in the number of magnet segments constituting a magnetic region (e.g., the use of a curved surface can reduce a quantity of multiple magnets to a single magnet, at least in some cases). One or more radii of curvature for one or more portions of surface 2606 can be selected to approximate a sinusoidal waveform shape to ensure a relatively small air gap (i.e., the closest distance of surface 2606 to a field pole face, which is not shown) is at or near the center of magnetic region 2612. In at least some embodiments, the radii of curvature can be described in a plane that is perpendicular to the axis of rotation. In at least one case, the one or more radii of curvature can be varied along the length of magnetic region 2612 (e.g., from the large diameter end of conical magnet 2600 to the small diameter end). In other cases, one or more radii of curvature can be constant along the length. In at least one embodiment, the radii of curvature can be referenced to or reside in one or more planes that are perpendicular (or substantially perpendicular) to a centerline of magnetic region, such as centerline 2603 of magnetic region 2612a (and/or magnetic material 2604). Production of sine wave-like flux waveforms can be affected by the implementation of an inter-magnetic region gap 2602, which can affect the sine flux waveform in approximately the 0 to 30 degree portion. For example, the thickness at a part 2614 of a magnetic region 2612 can be effectively zero to produce inter-magnetic region gap 2602. In a specific instance, hub 2610 can include a surface defined by an angle 2616. As shown, FIG. 5A depicts a cross-section 2613 of an example of magnetic material 2620 for a magnet region 2612 having a curved surface 2607. Also shown in relation to cross-section 2613 is a point that represents a centerline 2605, which can be similar to centerline 2603, of magnetic material 2620 (e.g., a magnet).

[0067] FIG. 5B depicts a conical magnet structure in accordance with yet another embodiment of the invention. Conical magnet 2650 includes an arrangement of magnetic

regions 2662 mounted on a hub 2660, at least one of magnetic regions 2662 including magnetic material, such as magnet(s) 2654, for forming magnet poles. In at least on embodiment, hub 2660 can include a hub hole 2661 through which a shaft (not shown) can pass to mount conical magnet 2650 thereupon. Hub hole 2661 can be configured to align a centerline 2690 of hub 2660 with an axis of rotation (not shown) when conical magnet 2650 is disposed upon the shaft. At least one of magnetic regions 2662 can be disposed on hub 2660 so that a centerline 2653 of magnetic region 2662a is at an acute angle 2692 with respect to centerline 2690 of hub 2660 (and/or hub hole 2661). In various embodiments, at least portions of surfaces 2655 can be coextensive with at least one acute angle with respect to centerline 2690 of hub 2660.

[0068] Further, at least one of magnetic regions 2662 can include a surface 2655 that has at least one beveled surface portion for producing sine wave-like flux waveforms. Beveled surfaces 2655 can be coextensive with, for example, an angle, such as angle 2656. As shown, FIG. 5B depicts a cross-section 2663 of an example of magnetic material 2670 for a magnet region 2662, the magnetic material 2670 having a beveled surface 2657. Inter-magnetic region gaps 2652 are also shown. According to various embodiments, magnetic regions 2662 can include one or more magnets. Also shown in relation to cross-section 2663 is a point that represents centerline 2690, which can be similar to centerline 2653, for magnetic material 2670 (e.g., a magnet).

[0069] FIGs. 6A to 6C depict another conical magnet structure in accordance with another embodiment of the invention. Conical magnet 2700 includes an arrangement of magnetic regions 2712 mounted on a hub 2710, at least one of magnetic regions 2712 including magnets 2703. As shown in this example, six magnetic regions 2712 can give rise to a six pole conical magnet structure 2700. Further to this example, there are two magnets 2703 within magnetic region 2712. Magnets 2703 include magnetic material for forming magnet poles. Further, magnetic regions 2712 can include surfaces 2706a and 2706b that can have relatively flat surface portions, and are configured to produce inter-magnetic region gaps 2702. In one embodiment, magnets 2703 can have flat-surfaced magnet having a trapezoid shape (e.g., a trapezoidal cross-section). In at least one case, flat magnets 2703 can consume fewer resources to be produced than, for example, magnets having curvature. In other embodiments, any number of magnets 2703 or other magnets can be used.

[0070] FIG. 6B depicts configurable structural attributes in accordance with at least one embodiment of the invention. A first configurable structural attribute is an angle 2722 in associations with at least two magnets 2723. In at least one case, angle 2722 can be selected to urge the surfaces of magnets 2723 and/or the medial portion 2727 of the magnet pole nearer to a

point or area that is physically closer to a field pole face (e.g., as the hub rotates). As such, angle 2722 can determine how closely a portion of the shape of the flux waveform approximates a sine wave (e.g., from 20 to 80 degree range). In some embodiments, the rate of change of a surface portion associated with a medial portion to a surface portion associated with at least one of lateral portions can determine a portion of a flux waveform, such from approximately 20 degrees to 80 degrees. As such, the rate of change between the surface portions can be considered a configurable structural attribute. A second configurable structural attribute can be an intra-magnetic region gap 2724 that optionally can be implemented, such as between at least two magnets 2723, to modify the shape of the flux waveform approximately from 70 to 90 degrees. Note that in the example shown, magnets 2723 are shown to abut each other, thereby excluding an intra-magnetic region gap 2724 in this instance. A third configurable structural attribute can be an inter-magnetic region gap 2726 that optionally can be implemented, for example, between at least two magnet groups 2721 of magnets 2723, at least one group 2721 of magnets 2723 providing for a magnet pole. Modification of the third configurable structural attribute can affect the shape of a flux waveform to approximate a sine wave approximately from 0 to 30 degrees. In one embodiment, the above-described configurable structural attributes can each be optimized to produce a conical magnet structure by implementing a computer-based simulation of, for example, the magnetic flux induced in a field pole member, which can be determined at several points of hub rotation using, for example, a 3D finite or boundary element magnet analysis software program. Also, a configurable structural attribute can be the angle of at least a portion of the surface of one of magnets 2723 to the axis of rotation (not shown) or to a centerline to the hub for conical magnet 2720, as well as the magnetic properties of magnets 2723. There are also several sequences that could be used to perform the design optimization, but one sequence can be as follows without limitation: (1) optimize the angle (e.g., an acute angle) between the centerline of a magnetic region and an axis of rotation to establish a desired level of peak flux (e.g., in a field pole member), (2) optimize a first configurable structural attribute (e.g., determine an angle 2722 of the surface (or a rate in change) for a magnetic region that includes magnets 2723 to produce a desired flux waveform shape (e.g., in the 20 to 80 degree region), (3) optimize the second configurable structural attribute (e.g., determine an intra- magnetic region gap 2724), and (4) optimize the third configurable structural attribute (e.g., determine an inter-magnetic region gap 2726).

[0071] FIG. 6C depicts a hub 2740 including support regions 2742 for supporting magnets 2723 (FIG. 6B) in accordance with at least one embodiment of the invention. Further, hub 2740 can optionally include raised sections 2744, or any other element providing for an

equivalent functionality and/or structure. Raised section 2744 can be implemented in the inter- magnetic region gaps to provide for physical alignment of magnetic regions and/or the magnetic material thereof. In some embodiments, the height of raised section 2744 relative to support regions 2742 can influence flux leakage between magnetic regions (not shown). As such, the size of an inter-magnetic region gap between the magnetic regions may be adjusted to compensate for the height of raised section 2744.

[0072] FIG. 7 depicts yet another conical magnet structure in accordance with yet another embodiment of the invention. Conical magnet 2800 includes an arrangement of magnetic regions 2812 mounted on a hub 2810, at least one of magnetic regions 2812 including magnetic material in magnets 2802 for forming magnet poles. Magnets 2802 can be described as trapezoid magnets 2802 having a trapezoidal shape that confronts an air gap (not shown). Further, at least one of magnets 2802 includes a surface 2806 that has flat portions. While this arrangement of magnetic regions 2812 excludes both inter-magnetic region gaps and intra- magnetic region gaps, either of which, or both, can be implemented in some embodiments.

[0073] FIG. 8 is a diagram 2900 illustrating a flux waveform generated by an arrangement of magnetic regions 2812 of FIG. 7, according to at least one embodiment of the invention. In the example shown in FIG. 8, an arrangement of magnetic regions in a conical magnet structure 2800 of FIG. 7 can yield Vbemf ("trace 1") 2902 and magnet flux waveform ("trace 2") 2904, both of which are nonlinear. In particular, Vbemf 2902 is shown as a flat- topped or clipped waveform, and flux waveform 2904 is shown be somewhat triangular. This means that both waveforms in this example are composed of a fundamental frequency and several higher order harmonics. Note that if it is desired to modify flux waveform 2904 toward a sinusoidal shape, then any combination of the waveform shaping techniques described herein can be used.

[0074] FIG. 9 is spectrum diagram 3000 depicting an example of a Vbemf waveform, according to one embodiment of the invention. As shown, conical magnet structure 2800 of FIG. 7 can produce harmonics 3004 and a fundamental frequency at or near waveform portion 3002. Fourier transform theory generally provides that the integral of Vbemf, which can represent the magnet flux waveform, will have the higher order harmonics, but with amplitudes scaled (e.g., divided) by the order of the harmonic. For the example shown in FIG. 9, the 3rd, 5th, 7th, 9th, and 1 1th harmonics are shown to be -13dB, -32dB, -38dB, -4OdB, and -47dB below the fundamental frequency, respectively. When adjusted to reflect the harmonic levels in the integrated waveform that corresponds to the magnetic flux, the respective values for the 3rd, 5th, 7th, 9th and 1 1th harmonics are -23dB, -46dB, -56dB, -59dB, -68dB. These amplitude

levels may be irrelevant in applications where power loss is not critical. But note that core losses in field pole members can increase with frequency by, for example, an amount equivalent to the frequency (as the base of an exponential expression) raised to a power of approximately 1.5 (as the exponent). So when the core losses are summed together over the adjusted harmonics in the magnetic flux, the sum of the core losses can be, for example, 1.66 times the core losses that might be associated with a pure sine wave at the fundamental frequency. Thus, configurable structural attributes can be used and/or modified to produce an approximate sinusoidal flux waveform that can reduce or exclude higher-order harmonics 3004, thereby reducing the core losses in the field pole members by, for example, about 40% compared to the case shown in this example.

[0075] FIGs. 1 OA to 1 OC depict an example of an internal permanent magnet ("IPM")- based implementation of a conical magnet structure in accordance with at least one embodiment of the invention. FIG. 1OA shows a conical magnet structure 3100 that includes magnetic regions 3101. In this example, at least one of magnetic regions 3101 can include magnetically permeable material 3103, such as steel (e.g., powdered metal) or soft composite material ("SMC"), layered upon one or more magnets or magnet segments, as shown in FIG. 1OB. Conical magnet structure 3100a can produce a sinusoidal flux waveform using at least some of the above-described techniques.

[0076] FIG. 1OB depicts one or more magnets embedded (entirely or partially) and/or mounted in magnetically permeable material. For example, magnetic region 3105 includes magnets 3102 that are embedded in magnetically permeable material, such as magnetically permeable material 3107, which is depicted as being transparent for purposes of illustration. Magnets 3102, which are shown to form a South pole, can be mounted on a hub 3104. Magnets 3102 can be oriented on hub 3104 with respect to an angle 31 10 (angle "C"), which can set the general shape for a portion of a flux waveform. One or more inter-magnetic region gaps 3130 and one or more intra-magnetic region gaps 3120 can be implemented to modify the 0 to 30 degree and 70 to 90 degree portions, respectively, of a flux waveform. In at least some embodiments, angle 3110 (i.e., the rate of change in the surface curvature between medial and lateral portions) can control the degree of shaping of a flux waveform (e.g., in the 20 to 80 degree portion of a sine wave.

[0077] FIG. 1 OC depicts one or more magnets embedded in magnetically permeable material. As shown in cross-sectional diagram 3150, magnets 3180 are shown embedded in magnetically permeable material 3152 to form, for example, magnetic regions 3151 , which can implement an inter-magnetic region gap 3170 and intra-magnetic region gap 3172. Magnets

3180 are mounted on hub 3 ] 54. As shown, magnetically permeable material 3152 is disposed on magnets 3180 to form substantially uniform air gaps 3160 between magnetic regions 3151 and field poles 3153 (e.g., pole faces), with surface 3198 of the magnetic material (e.g., surfaces of magnets 3180) being an irregular surface, according to at least some embodiments. In at least one embodiment, substantially uniform air gaps 3160 can produce relatively higher output torque than might otherwise be the case. Note that inter-magnetic region gap 3170 can facilitate a reduction of leakage between magnetic regions 3151, as well as provide a structure configurable to shape a flux waveform.

[0078J FIGs. HA to HC depict another example of an internal permanent magnet ("IPM")-based implementation of a conical magnet structure in accordance with at least one embodiment of the invention. FIG. HA shows a conical magnet structure 3200 that includes magnetic regions 3201. In this example, at least one of magnetic regions 3201 can include magnetically permeable material 3203 layered upon one or more magnets or magnet segments, as shown in FIG. HB. Conical magnet structure 3200 can produce a flux waveform using at least some of the above-described techniques to approximate a sine wave.

[0079] FIG. 1 IB depicts conical magnet structure 3200a including one or more magnets, such as magnets 3202, that are embedded in magnetically permeable material, such as magnetically permeable material 3207, which is depicted as being transparent for purposes of illustration. Magnets 3202, which are shown to form a North pole, can be mounted on a hub 3204. Magnets 3202 can be oriented on hub 3204 with respect to an angle ("D") 3210, which can set the shape for a portion of a flux waveform. In some embodiments, one or more inter- magnetic region gaps 3230 and one or more intra-magnetic region gaps 3220 can modify the 0 to 30 degree and 70 to 90 degree portions, respectively, of a flux waveform. In at least some embodiments, angle 3210 (angle "D") is an angle that configures the lateral portions to be at a greater radial distance from an axis of rotation (not shown) than the radial distance for a medial portion. In some instances, angle 3210 can be an obtuse angle.

[0080] FIG. I IC depicts one or more magnets that are embedded in magnetically permeable material. As shown in cross-sectional diagram 3250, magnets 3280 are shown to be embedded in magnetically permeable material to form, for example, magnetic regions 3251, which can implement a relatively larger quantity of magnetically permeable material 3252 than in the configuration shown in FIG. 1OC (e.g., more magnetically permeable material 3252 can be disposed between magnets 3280 and field poles 3253 than magnetically permeable material between magnets 3180 and field poles 3153 of FIGs. 10C). Referring back to FIG. 1 1 C, magnets 3280 are shown to be mounted on hub 3254. As shown, magnetically permeable

material 3252 is disposed on magnets 3280 to form substantially uniform air gaps 3260 between magnetic regions 3251 and field poles 3253 (e.g., pole faces). In at least some embodiments, angle ("E") 3290 can be an obtuse angle that is substantially coextensive with surfaces of magnets 3280, which, in turn, facilitates the use of a relatively larger quantity of magnetically permeable material 3252. This enables relatively more flux to pass through the surface 3263 (e.g., the surface area) of magnetic region 3251 . In particular embodiments, an inter-magnetic region gap 3270 and an intra-magnetic region gap (not shown) can modify the 70 to 90 degree and 0 to 30 degree portions, respectively, of a flux waveform, as described above.

[0081] FIGs. 12A to 12C depict yet another example of an internal permanent magnet ("IPM")-based implementation of a conical magnet structure in accordance with at least one embodiment of the invention. FIG. 12A shows a conical magnet structure 3300 that includes magnetic regions 3301. In this example, at least one of magnetic regions 3301 can include magnetically permeable material 3303 disposed between magnets or magnet segments 3380, as shown in FIG. I2C. In some embodiments, conical magnet structure 3300 can produce a flux waveform using at least some of the above-described techniques to approximate a sine wave.

[0082] FIG. 12B depicts a conical magnet 330Oa including magnets, such as magnets 3302, that can be arranged to receive or be located adjacent magnetically permeable material at regions 3394. Magnets 3302 can be mounted on a hub 3304. Magnets 3302 can be arranged on hub 3304 with polarities being oriented, for example, normal to surface areas 3392. As such, the directions of polarization can be perpendicular (or substantially perpendicular), or at acute angles, to surface areas 3392. In some instances, the number of magnet poles associated with hub 3304 and widths 3308 of magnets 3302 can determine region angle 3306. Width 3308 of the magnet segment 3302 can be adjusted (including optional beveling of the edges) to reduce, for example, the relatively high amplitudes of a flux waveform. In some instances, region 3394 can be described as an intra-magnetic gap iocated between two surfaces (e.g., surfaces 3392) of magnets 3302 that, in the case of a North pole, provide flux to magnetically permeable material in region 3394, thereby establishing a magnetic region, such as magnetic region 3301.

[0083] FIG. 12C depicts one or more magnets that are arranged adjacent to magnetically permeable material, according to one embodiment. As shown in cross-sectional diagram 3350, magnets 3380 are shown to be arranged adjacent to magnetically permeable material 3399 to form, for example, magnetic regions 3351, which can implement a relatively larger amount of magnetically permeable material 3399 than in the configuration shown in FIG. 1OC. Referring back to FIG. 12C, magnets 3380 are mounted on a hub. Magnetically permeable material 3399 can be disposed adjacent to magnets 3380 to form air gaps 3360 that can be optionally uniform

(or substantially uniform) thicknesses between magnetic regions 3351 and field poles 3353 (e.g., pole faces). In at least some embodiments, surface areas 3392a provide for relatively higher flux for magnetic region 3351 via magnetically permeable material 3399 than otherwise might be the case. This enables a relatively higher flux amount to pass through the surface 3389 (e.g., the surface area) of magnetic region 3351. In at least one embodiment, magnetic regions 3351 can have a curved surface, such as curved surface 3395, or any other type of surface shape.

[0084] FIG. 13 shows a rotor structure implementing an arrangement of offset conical magnets, according to one or more embodiments of the invention. Rotor structure 3400 is shown to include conical magnets 3420a and 3420b disposed on a shaft 340 ] , which can define an axis of rotation 3402. Conical magnets 3420a and 3420b are shown to include magnet regions 3482, which, in turn, can include magnets 3480. Conical magnets 3420a and 3420b can include intra-magnetic region gaps 3428 and inter-magnetic region gaps 3430. As conical magnets 3420a and 3420b each can contribute to a detent waveform when positioned to interact with field poles (not shown) in the stator. Flux from either conical magnets 3420a and 3420b can contribute to detent waveforms. The detent waveforms produced in association with conical magnets 3420a and 3420b can be substantially similar in shape and amplitude, and, as such, the amplitudes of the detent waveforms for conical magnets 3420a and 3420b can be added together (e.g., through the principles of superposition). The detent waveforms can add together to form a composite detent waveform.

[0085] According to at least some embodiments, offsetting conical magnets 3420a and 3420b by an angle (e.g., alpha 3410) can provide for a composite detent waveform that has an amplitude less than if there was no offset. In some examples, alpha 3410 can be determined to offset the detent waveforms to be out of phase (or substantially out of phase), where alpha 3410 can be any number of degrees. In at least some examples, alpha 3410 can be any angle between 0 to 30 degrees (i.e., in the range of -330 to +30 degrees). A composite detent waveform can have a reduced amplitude, with the offset conical magnets 3420a and 3420b causing the detent waveforms to be offset relative to each other. In some cases, offset detent waveforms can cancel (or substantially cancel) each other. By canceling additive effects of the individual detent waveforms, a rotor-stator structure implementing rotor structure 3400 in a motor, for example, can provide for a magnetic circuit (or at least a portion thereof) having waveforms with relatively low detent content. In some cases, lower detent content can provide for enhanced position control of a motor and relatively smoother operation, according to various embodiments.

[0086] Angle alpha 3410 can be referenced in relation to conical magnets and/or between any points of reference associated with the conical magnets, and can be expressed in terms of mechanical degrees about shaft 3401. In at least some embodiments, alpha 3410 is an angle between poles between conical magnets 3420a and 3420b, such as an angle between one pole associated with conical magnet 3420a and another pole associated with conical magnet 3420b. For example, a north pole associated with conical magnet 3420a can be positioned on shaft 3401 at an angle 3410 relative to a south pole associated with conical magnet 3420b. In at least some embodiments, alpha 3410 can be referenced relative to a first reference point associated with conical magnet 3420a and a second reference point associated with conical magnet 3420b. As shown in this example, reference points, such as center points 3499a and 3499b of corresponding magnetic regions 3482, can be used to determine an offset from each other by angle alpha 3410. A center, such as either center points 3499a or 3499b, can be an intersection between a centerline (not shown) passing longitudinally through one of magnetic regions 3482 and a radial line (not shown) from shaft 3401 in a plane perpendicular to shaft 3401. A centerline can be located in intra-magnetic region gaps, such as intra-magnetic region gap 3428, according to some embodiments. Or, the centers of opposing conical magnets 3420a and 3420b can be offset from each other by an angle, such as alpha 3410, as measured in mechanical degrees between two planes (not shown), a first plane passing through shaft 3401 and bisecting conical magnet 3420a and a second plane passing through shaft 3401 and bisecting conical magnet 3420b.

[0087] Alpha 3410 can be determined as function of the number of detent cycles per revolution of shaft 3401, according to at least some embodiments. For example, alpha 3410 can be determined by dividing 180 by the number of detent cycles ("Ndc") in one mechanical revolution of rotor 3400. A number of detent cycles, Ndc, can be established by determining the least common multiple ("LCM") of the number of field poles (not shown) and the number of magnet poles for each of conical magnets 3420a and 3420b. To illustrate, consider that an electrodynamic machine has six field poles (i.e., field pole members) and two magnet poles. Such an electrodynamic machine can be referred to as a "6/2" electrodynamic machine. In this case, the electrodynamic machine has a least common multiple of 6, thereby establishing 6 detent cycles for a mechanical revolution of 360 degrees (i.e., Ndc=LCM(6,2)=6). Thus, alpha can be 30 degrees (i.e., 180/6), as an angle about shaft 3401 between, for example, a magnetic region 3482 representing a north pole on one magnet and another magnetic region 3482 representing a south pole on another magnet. Similarly, consider an example of an electrodynamic machine having nine field poles and six magnet poles (i.e., a "9/6"

electrodynamic machine). In this case, the electrodynamic machine has a least common multiple of 18, thereby establishing 18 detent cycles. Thus, alpha in this case can be 10 degrees (i.e., 180/18). An electrodynamic machine having twelve field poles and 10 magnet poles (i.e., a " 12/10" electrodynamic machine) has a least common multiple of 60, thereby establishing an alpha of 3 degrees (i.e., 180/60). Note that in some embodiments, rotor structure 3400 can include more or fewer conical magnets 3420a and 3420b, and conical magnets 3420a and 3420b can be any shaped magnet, such as cylindrical magnets. Rotor structure 3400 need not have an offset (i.e., alpha can be zero), according to some embodiments. According to other embodiments, rotor structure 3400 using an arrangement of offset magnets (conical or otherwise) can also be used in combination with other techniques, some of which are discussed herein, to reduce detent and its effects, among other things. Note that in some cases, offsetting conical magnets 3420a and 3420b can reduce the torque production of a motor in which rotor structure 3400 is implemented. So while a specific value for an offset angle, such as alpha 3410, can minimize detent, that specific value for the offset may cause an unacceptable reduction in torque production for the motor. Thus, a designer can back off and reduce the specific value of the offset angle to achieve an optimal detent reduction that keeps the reduction in the torque production of the motor above an acceptable threshold.

[0088] According to at least some embodiments, offsetting conical magnets 3420a and 3420b can be referenced relative to directions of polarization. As shown, a direction of polarization depicted as a ray extending out from conical magnet 3420a can be offset from a direction of polarization depicted as a ray for conical magnet 3420b. In particular, a plane including the ray into conical magnet 3420a, such as ray 3489a, can be offset by an angle (e.g., alpha 3410) from another plane that includes the ray for conical magnet 3420b, such as ray 3489b. While planes including rays 3489a and 3489b can pass though axis of rotation 3402, the planes need not be so limited. In the example shown, ray 3489a represents a north pole for a magnet region on conical magnet 3420a, and ray 3489b represents a south pole for a magnet region on conical magnet 3420b. In various embodiments, the directions of polarization (e.g., as illustrated by rays 3489a and 3489b) can be in substantially opposite directions. For example, alpha 3410 between the directions of polarization can be, for example, 0 to 30 degrees. In at least some embodiments, the directions of polarization can be in substantially opposite directions as viewed, for example, in an end view of rotor structure 3400. For example, rays 3489a and 3489b are shown to be in substantially opposite directions as viewed, for example, from the end of shaft 3401. Note that while FIG. 13 depicts rays 3489a and 3489b being perpendicular to axis of rotation 3402, they need not be. For example, rays 3489a and 3489b

can be normal (not shown) to portions of magnetic regions for respective conical magnets 3420a and 3420b. In at least some embodiments, directions of polarization (e.g., rays 3489a and 3489b) can be at any angle (with respect to at least portions of magnetic regions 3480), and can be referenced from any point or area on either a portion of a conical magnet or on a magnetic region. Also, the directions of polarization can represent either a north pole or a south pole. According to at least some embodiments, conical magnets 3420a and 3420b can be offset from each other about axis of rotation 3402 by offsetting a magnetic region associated with conical magnet 3420a relative to a magnetic region associated with conical magnet 3420b, where both magnetic regions can be arranged about axis of rotation 3402 to form a portion of a closed flux path between the magnetic regions (e.g., via a field pole member, which is not shown). Thus, the magnetic regions need not be symmetric, and can be offset relative to each other so that their respective detent waveforms can be out of phase (or are substantially out of phase).

[0089] FIGs. 14 and 15 depict amplitudes of detent waveforms for rotor structures implementing arrangements of conical magnets with and without offsets, according to one or more embodiments of the invention. FIG. 14A is a diagram 3500 showing simulated detent waveforms for a rotor structure in which the directions of polarization of conical magnets are aligned, according to an embodiment of the invention. As such, the detent waveforms can add together in phase to create a composite waveform with an equivalent shape and approximately twice the amplitude of an individual detent waveform. In the example shown, a first conical magnet ("CM #1") can be modeled to produce a detent waveform 3506 and a second conical magnet ("CM #2") can be modeled to produce a detent waveform 3508. Here, the first and second conical magnets are aligned (i.e., alpha angle is about 0 degrees), and, thus, their detent waveforms are in phase. Composite detent waveform 3510 results from adding amplitudes of simulated detent waveforms 3506 and 3508. For purposes of illustration, consider that the first conicai magnet is configured to produce detent waveform 3506 with an amplitude of 1.5 units (with a second harmonic of amplitude 0.4 units), whereas second conical magnet is configured to produce detent waveform 3508 with an amplitude of 1.7 units (with a second harmonic of amplitude 0.4 units). Given these amplitudes, composite detent waveform 3510 has an amplitude of approximately 3.2 units. Further to the example, detent waveforms 3506 and 3508 are shown to have a saw tooth-like shape, with the slope of the falling edge being much steeper than the leading edge. Note further that there are six detent cycles 3504 shown for 360 electrical degrees. For a 6/2 electrodynamic machine, the 360 electrical degrees represent 1 revolution of a shaft (i.e., 360 mechanical degrees), whereas for a 9/6 electrodynamic machine, the 360 electrical degrees represent one-third revolution of the shaft (e.g., 120 mechanical degrees).

[0090] FIG. 14B is a diagram 3520 showing detent waveforms for a rotor structure in which the directions of polarization of conical magnets are offset by one-half a detent cycle, according to an embodiment of the invention. In the example shown, the first conical magnet ("CM #1") of FIG. 14A can be modeled to produce a simulated detent waveform 3526 and the second conical magnet ("CM #2") of FIG. 14A can be modeled to produce a simulated detent waveform 3528, which is shifted by one-half of detent cycle 3524. In FIG. 14B, while detent waveforms 3526 and 3528 have the same amplitudes and harmonics as in FIG. 14A, composite waveform 3530 has a lower amplitude than either of detent waveforms 3526 and 3528. Note that the apparent frequency of composite waveform 3530 can effectively double, depending on, for example, the shape of detent waveforms 3526 and 3528.

[0091] FIG. 15A is a diagram 3600 illustrating composite detent waveform 3530 of FIG. 14B having a lower amplitude than composite detent waveform 3510 of FIG. 14A. Note that further to the example shown, simulated composite detent waveforms 3510 and 3530 can be respectively derived by modeling detent waveforms 3506 and 3508 of FIG. 14A and detent waveforms 3526 and 3528 of FIG. 14B.

[0092] FIG. 15B shows a comparison between other composite waveforms, according to an example of an embodiment. In particular, FIG. 15B provides a diagram 3650 illustrating an example of measured composite detent waveforms 3660 and 3670 that, in this instance, are based on conical magnets that produce detent waveforms that deviate from those shown in FIGs. 14A and 14B due to, for example, differences in manufacturing tolerances. In this example, detent waveform 3660 relates to an arrangement of aligned conical magnets (i.e., alpha ~ 0 degrees), whereas detent waveform 3670 relates to an arrangement of conical magnets that are offset by, for example, 10 mechanical degrees with respect to each other (not shown) in, for example, a 9(6 electrodynamic machine (e.g., a 9/6 motor).

[0093] FIG. 16 depicts a conical magnet structure having a magnetic region composed of multiple magnets, in accordance with at least one embodiment of the invention. In this example, conical magnet 3700 includes two magnetic regions, with one magnetic region being a north pole and another magnetic region being a south pole. As such, conical magnet 3700 is a two pole conical magnet structure. As shown, magnetic region 3710 can include multiple magnets, such as magnet 3720, magnet 3722, and magnet 3724. Magnetic region 3710 can include one or more intra-magnetic region gaps 3702 and/or one or more inter-magnetic region gaps 3740 (or one or more portions thereof). In the example shown, surfaces 3730 of magnets 3720 and 3724 are flat (or substantially flat), whereas surface 3732 of magnet 3722 includes curvature. In

various embodiments, other numbers of magnets and/or magnetic regions can be implemented, as well as other surface shapes.

[0094] FIG. 17 is an exploded view depicting an example of a rotor-stator structure, according to various embodiments of the invention. Rotor-stator structure 3800 includes a number of field pole members, one field pole member of which is depicted as field pole member 3802. Rotor structure 3810 includes any conical magnet, such as conical magnets 3812a and 3812b, that can be arranged — with or without an offset — on a shaft 3814. To illustrate, consider that conical magnets 3812a and 3812b each had 10 magnetic regions (e.g., 10 poles), and 12 active field pole members that can include field pole member 3802 as well as eleven other field pole members that are not shown. As such, an electrodynamic machine using rotor-structure 3800 can be referred to as a 12/10 electrodynamic machine. In accordance with the various embodiments of the invention, conical magnets 3812a and 3812b conical magnet structures can be composed of any kind of magnet, including the various magnets discussed herein. According to various embodiments, field pole member 3802 and other field pole members (not shown) can be active field pole members.

[0095] The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the various embodiments of the invention. However, it will be apparent to one skilled in the art that specific details are not required in order to practice the various embodiments of the invention. In fact, this description should not be read to limit any feature or aspect of the various embodiments of the invention to any embodiment; rather features and aspects of one embodiment may readily be interchanged with other embodiments. For example, although the above description of the embodiments relate to a motor, the discussion is applicable to all electrodynamic machines, such as to a generator.

[0096] Thus, the foregoing descriptions of specific embodiments of the invention are presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed; obviously, many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles the various embodiments of the invention and its practical applications; they thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. Notably, not every benefit described herein need be realized by each embodiment of the invention; rather any specific embodiment can provide one or more of the advantages discussed above. It is intended that the following claims and their equivalents define the scope of embodiments of the invention.