Low-loss planar winding configurations for axial-flux machines.

Abstract

The planar stator includes conductive traces forming windings for the poles and at least first and second conductive vias extending between a first conductive layer and a second conductive layer, the first and second conductive vias being positioned to be radially located on a first side of an annular conductive region of an axial flux machine. The conductive traces include a first conductive trace in the first conductive layer and a second conductive trace in the second conductive layer. The first conductive trace includes a first end turn positioned to be radially located on the second side of the annular effective region, the second side facing the first side. The second conductive trace includes a second end turn positioned to be radially located on the first side of the annular effective region. All of the conductive vias interconnecting the first and second conductive traces are positioned to be radially located on the first side of the annular conductive region.

Description

[Background technology]

[0001] (background) Permanent magnet axial flux motors and generators are described in several patents, including U.S. Patent Nos. 7,109,625, 10,170,953, 9,859,763, 10,211,694, and 10,256,690. Summary of the Invention [Means for solving the problem]

[0002] (summary) This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. It is not intended to identify key or essential features, nor is it intended to limit the scope of the claims included herein.

[0003] In some of the disclosed embodiments, the stator includes one or more dielectric substrates adapted to be positioned within an annular effective area of ​​an axial-flux machine, including a rotor configured to rotate about an axis of rotation; conductive traces contained within at least first and second conductive layers defined by the one or more dielectric substrates, the conductive traces forming windings for the stator poles; and at least first and second conductive vias extending between the first and second conductive layers, the first and second conductive vias positioned radially on a first side of the annular effective area. The conductive traces include a first conductive trace within the first conductive layer and a second conductive trace within the second conductive layer. The first conductive trace includes a first end turn positioned radially on a second side of the annular effective area, the second side facing the first side. The first conductive trace extends along a first path starting from the first conductive via, passing through the first end turn, and terminating at the second conductive via. The second conductive trace includes a second end turn positioned so as to be located radially on the first side of the annular effective area. The second conductive trace extends along a second path starting from the second conductive via and passing through the second end turn. The second conductive trace is connected to the first conductive trace through the second conductive via such that the first and second paths are connected in series. All conductive vias interconnecting the first and second conductive traces are positioned so as to be located radially on the first side of the annular effective area.

[0004] In some embodiments, the stator includes one or more dielectric substrates adapted to be positioned within an annular effective area of ​​an axial-flux machine, the stator including a rotor configured to rotate about an axis of rotation; conductive traces contained within at least first and second conductive layers defined by the one or more dielectric substrates, the conductive traces forming windings for poles of the stator; and at least first and second conductive vias extending between the first and second conductive layers, the first and second conductive vias positioned radially on a first side of the annular effective area. The conductive traces include a first conductive trace within the first conductive layer and a second conductive trace within the second conductive layer. The first conductive trace includes a first end turn positioned radially on a second side of the annular effective area, the second side facing the first side. The first conductive trace follows a first path starting from the first conductive via, extending through the first end turn, and terminating at the second conductive via. The second conductive trace includes a second end turn positioned so as to be located radially on the second side of the annular effective area. The second conductive trace follows a second path starting from the first conductive via, extending through the second end turn, and terminating at the second conductive via. All conductive vias interconnecting the first and second conductive traces are positioned so as to be located radially on the first side of the annular effective area. The present invention provides, for example, the following. (Item 1) A planar stator, one or more dielectric substrates adapted to be positioned within an annular effective area of ​​an axial flux machine, the rotor being configured to rotate about an axis of rotation; conductive traces contained within at least first and second conductive layers defined by the one or more dielectric substrates, the conductive traces forming windings for poles of the stator; at least first and second conductive vias extending between and interconnecting portions of the conductive traces in the first and second conductive layers, the first and second conductive vias positioned so as to lie radially on a first side of the annular effective area; Equipped with the conductive traces include a first conductive trace in the first conductive layer; the first conductive trace includes a first end turn positioned to lie radially on a second side of the annular effective area, the second side facing the first side; the first conductive trace extends along a first path beginning at the first conductive via, passing through the first end turn, and terminating at the second conductive via; the conductive traces include a second conductive trace in the second conductive layer; the second conductive trace includes a second end turn positioned so as to be located radially on the first side of the annular effective area; the second conductive trace extends along a second path beginning at the second conductive via and passing through the second end turn; the second conductive trace is connected to the first conductive trace through the second conductive via such that the first and second paths are connected in series; a planar stator positioned such that all conductive vias interconnecting the first and second conductive traces are located radially on the first side of the annular effective area; (Item 2) Item 2. The planar stator of item 1, further comprising a third conductive via extending between the first conductive layer and the second conductive layer and positioned so as to be located radially on the first side of the annular effective area, along which the second conductive trace extends, the second path starting from the second conductive via, passing through the second end turn, and terminating at the third conductive via. (Item 3) Item 3. The planar stator of item 2, wherein the third conductive via is positioned such that the first conductive trace and the second conductive trace form part of a serpentine-shaped winding. (Item 4) Item 3. The planar stator of item 2, wherein the third conductive via is positioned such that the first conductive trace and the second conductive trace form part of a spiral-shaped winding. (Item 5) a fourth conductive via extending between the first conductive layer and the second conductive layer and positioned so as to be located radially on the first side of the annular effective area; a third conductive trace in the second conductive layer, the third conductive trace including a third end turn positioned so as to be located radially on the second side of the annular effective area, the third conductive trace extending along a third path starting at the third conductive via, passing through the third end turn, and terminating at the fourth conductive via; 5. The planar stator according to any one of items 2-4, further comprising: (Item 6) the one or more dielectric substrates further define a third conductive layer, the third conductive via extending through the third conductive layer; Item 6. The planar stator of item 5, wherein the stator further comprises a fourth conductive trace in the third conductive layer, the fourth conductive trace including a fourth end turn positioned so as to be located radially on the second side of the annular effective area, the fourth conductive trace extending along a fourth path starting from the third conductive via, passing through the fourth end turn, and terminating at the fourth conductive via. (Item 7) 7. The planar stator of claim 6, wherein all conductive vias interconnecting the third and fourth conductive traces are positioned so as to lie radially on the first side of the annular effective area. (Item 8) 8. The planar stator of any one of items 1-7, further comprising an additional via extending between the first conductive layer and the second conductive layer and positioned so as to be radially located on the first side of the annular effective area, wherein the second conductive trace is further connected to the first conductive trace through the additional conductive via. (Item 9) 9. The planar stator according to any one of items 1-8, wherein the first end turn is an inner end turn and the second end turn is an outer end turn. (Item 10) 9. The planar stator according to any one of items 1-8, wherein the first end turn is an outer end turn and the second end turn is an inner end turn. (Item 11) 11. An axial flux motor or generator comprising the planar stator according to any one of items 1-10. (Item 12) A planar stator, one or more dielectric substrates adapted to be positioned within an annular effective area of ​​an axial flux machine, the rotor being configured to rotate about an axis of rotation; conductive traces contained within at least first and second conductive layers defined by the one or more dielectric substrates, the conductive traces forming windings for poles of the stator; at least first and second conductive vias extending between the first conductive layer and the second conductive layer, the first and second conductive vias positioned so as to be located radially on the first side of the annular effective area; Equipped with the conductive traces include a first conductive trace in the first conductive layer; the first conductive trace includes a first end turn positioned to lie radially on the second side of the annular effective area, the second side facing the first side; the first conductive trace follows a first path beginning at the first conductive via, extending through the first end turn, and terminating at the second conductive via; the conductive traces include a second conductive trace in the second conductive layer; the second conductive trace includes a second end turn positioned so as to be located radially on the second side of the annular effective area; the second conductive trace follows a second path beginning at the first conductive via, extending through the second end turn, and terminating at the second conductive via; A planar stator, wherein all conductive vias interconnecting the first and second conductive traces are positioned to lie radially on the first side of the annular effective area. (Item 13) Item 13. The planar stator of item 12, wherein the first path has the same size and shape as the second path. (Item 14) 14. The planar stator according to item 12 or 13, wherein the first and second end turns are inner end turns. (Item 15) 14. The planar stator of claim 12 or 13, wherein the first and second end turns are outer end turns. (Item 16) a third conductive via extending between the first conductive layer and the second conductive layer, the third conductive via positioned so as to be located radially on the first side of the annular effective area; a third conductive trace in the second conductive layer, the third conductive trace including a third end turn positioned so as to be located radially on the first side of the annular effective area, the third conductive trace extending along a third path starting from the second conductive via, passing through the third end turn, and terminating at the third conductive via; 16. The planar stator according to any one of items 12-15, further comprising: (Item 17) the one or more dielectric substrates further define a third conductive layer, the third conductive via extending through the third conductive layer; The stator further comprises: a fourth conductive via extending through the first, second, and third conductive layers, the fourth conductive via positioned so as to be located radially on the first side of the annular effective area; a fourth conductive trace in the third conductive layer, the fourth conductive trace including a fourth end turn positioned so as to be located radially on the second side of the annular effective area, the fourth conductive trace extending along a fourth path starting from the third conductive via, passing through the fourth end turn, and terminating at the fourth conductive via; Item 17. A planar stator according to item 16, comprising: (Item 18) 18. An axial flux motor or generator comprising the planar stator according to any one of items 12-17. [Brief explanation of the drawings]

[0005] [Figure 1] FIG. 1 shows a partial cutaway interior perspective view of a stator constructed in accordance with the teachings of the prior art patent.

[0006] [Figure 2] FIG. 2 shows a top view of the stator shown in FIG.

[0007] [Figure 3] FIG. 3 shows the flux-in-gap solution for an axial flux machine with alternating pole geometry.

[0008] [Figure 4A] FIG. 4A shows certain components of the stator, including the inner vias, as they are oriented within the stator.

[0009] [Figure 4B]FIG. 4B shows the structure shown in FIG. 4A as it would appear unwrapped and drawn flat, illustrating the eddy current paths within the structure due to the θ-directional magnetic flux.

[0010] [Figure 5A] FIG. 5A illustrates certain components of a stator when oriented within the stator such that inner vias are omitted in accordance with certain aspects of the present disclosure.

[0011] [Figure 5B] FIG. 5B shows the structure shown in FIG. 5A as it would appear unwrapped and drawn flat, illustrating the eddy current paths within the structure due to the θ-directional magnetic flux.

[0012] [Figure 6] FIG. 6 illustrates a first layer of a stator constructed in accordance with certain teachings of the present disclosure.

[0013] [Figure 7] FIG. 7 shows a second layer of a stator constructed in accordance with certain teachings of the present disclosure that is complementary to the first layer shown in FIG.

[0014] [Figure 8] FIG. 8 shows an overlay of the layers of FIGS. 6 and 7, showing that radial traces can be uniformly incorporated into a stator with this construction using two layers (or multiples of two layers).

[0015] [Figure 9] FIG. 9 illustrates how the structure of FIGS. 6 and 7 can be extended to a practical 18-layer stator.

[0016] [Figure 10] FIG. 10 shows a complete single-phase connection for a 16-pole, 3-turn winding, omitting the inner end turn and all other features associated with other phases, which may be established by superimposing three layers such as those shown in FIGS. 6 and 7.

[0017] [Figure 11] FIG. 11 illustrates the three layers of FIG. 10 in a perspective view.

[0018] [Figure 12] FIG. 12 shows a first exemplary structure embodied in the stator shown in FIGS.

[0019] [Figure 13] FIG. 13 shows a second exemplary structure embodied in the stator shown in FIGS. DETAILED DESCRIPTION OF THE INVENTION

[0020] (Detailed explanation) Permanent magnet axial flux motors and generators, described by several patents, including U.S. Patent Nos. 7,109,625, 10,170,953, 9,859,763, 10,211,694, and 10,256,690, the entire contents of which are incorporated herein by reference, feature a planar stator assembly, typically a printed circuit board between the rotor and supporting permanent magnets. Current in the windings in the stator interacts with the magnetic flux density in the gap established by the magnets, producing torque in motor operation. Similarly, when the machine is mechanically driven, it can function as a generator.

[0021] In either mode of operation, the machine's stator experiences a time-varying magnetic flux. This time-varying flux interacts with the copper in the stator, inducing currents that circulate in loops and within the copper-filled areas. These effects cause a loss of efficiency in operation. While much of the flux driving these losses is axially, or z-oriented, there are also auxiliary components that are θ- and radially oriented. The magnitude of these components varies as a function of the displacement z within the air gap.

[0022] The stator construction disclosed herein incorporates novel features that can be applied to planar compound stators to mitigate losses associated with θ, i.e., directional flux leakage in planar stators, and may provide additional benefits.

[0023] Electric machines of the type described in the above-mentioned patents generally comprise a planar stator ("stator") disposed within the gap of a magnetic structure ("rotor"), exhibiting a pattern of alternating magnetic poles and corresponding magnetic flux densities within the gap. When the stator is energized by an external drive circuit, the interaction of the current in the stator and the magnetic flux within the gap generates a force density within an effective area that can result in motion of the rotor. Similarly, when the rotor is set into motion by an external mechanical source, the resulting time-varying magnetic flux captured by the windings results in a voltage across the windings in the stator.

[0024] These primary modes of operation for electric machines abstractly depend solely on the axial magnetic flux established by the magnetic circuit. Thus, machines of the type presented in the above-mentioned patents are referred to as "axial flux" machines, and the magnetic circuit in such machines is designed to support magnetic flux primarily in the z-direction, i.e., perpendicular to the plane of the stator.

[0025] 1 and 2 show partial cutaway interior perspective and top views, respectively, of one embodiment of a stator constructed in accordance with the above-mentioned patent. As shown, the winding structure within the stator of such an axial-flux machine is organized to present radial current densities (carried by radial traces 106) for interaction with axial magnetic flux. The portion of the stator with such radial features, i.e., the annular region extending between radial distance r1 (measured from a center point 116 of the stator, which coincides with the axis of rotation of the machine's rotor) and radial distance r2 (also measured from the center point 116), is located within the machine's "active" region, primarily in the sense of torque production within the machine. The inner and outer diameters of magnets attached to the machine's rotor are typically located at or near radial distance r1 (measured from the axis of rotation of the stator) and radial distance r2 (also measured from the axis of rotation of the stator), respectively, and therefore generate axially directed magnetic flux within the annular active region. The remaining features, e.g., "end turns" 102, 104 radially adjacent to the annular active area of ​​the stator, exist solely to connect the radial portions in series and parallel combinations and transmit the associated currents and voltages to the terminals 112 of the machine.

[0026] Although machine operation relies on axial flux in the gap, there are regions throughout the gap where the flux can have significant radial and angular components. In particular, theta-directional leakage resulting from transitions between poles on the rotor can be very significant and can interact with adjacent radial traces 106. Theta components depend on magnet spacing and increase in magnitude toward the positive and negative z-extents of the gap. At the center of the gap (radially and axially) and at the pole centers, the flux solution is primarily axial. Figure 3, described in more detail below, shows the in-gap flux solution where theta-directional leakage flux component 302 in the gap 304 between opposing magnets 306 is readily apparent.

[0027] The effect of these non-axial components on motor or generator performance arises from their interaction with stator structures, which form conductive loops or surfaces. To approach this mathematically, it is helpful to visualize the "soap film surface" of a loop or conductive structure—i.e., the surface across which the magnetic flux density can be integrated to find the magnetic flux coupled by the conductive structure. When the magnetic flux penetrating the surface is time-varying, a potential is induced within the loop. When the loop is closed, a current will flow with a magnitude related to the resistance of the loop. The direction of the current can be intuitively understood as the current that would be required to oppose changes in the coupled magnetic flux, according to Lenz's law. Specifically, loops within a stator exposed to a time-varying magnetic flux density establish a current that attempts to "cancel" the imposed field. The resulting currents can reduce the currents in the motor structure that are producing torque, they can interact with any orthogonal components of the magnetic flux depending on the path of the loop, and can create drag, and finally, these currents can combine with the currents associated with the windings to result in unexpectedly high current densities and localized heating within the specific stator structure. In short, the effects of these trapped leakage flux components are to reduce the efficiency of the machine, increase losses, reduce thermal performance, etc. The magnitude of these effects increases proportionally with the speed of operation of the machine.

[0028] A fundamental part of the teachings of U.S. Pat. No. 7,109,625 ("the '625 patent") is that radial sections of a stator at a prescribed angle can be connected in parallel at the inner and outer diameters by conductive paths or vias. The vias form conductive paths perpendicular to the plane of the stator. As shown in FIGS. 1 and 2, for example, sets of radial traces 106 at different angles may be interconnected using inner vias 108 and outer vias 110. The use of such vias 108, 110 provides design flexibility for establishing connections around the stator. For example, using vias 108, 110, the inner end turn 102 for a particular set of radial traces 106 can be on a different layer than the corresponding outer end turn 104. The vias 108, 110 provide connection points to all radial traces 106 at the inner and outer radii, allowing for the construction and distribution of features to layers that would not otherwise be feasible. In effect, the vias 108, 110 allow the distribution of conductive structures needed to form the windings onto different layers so that they do not interfere.

[0029] In U.S. Patent No. 10,170,953 ("the '953 patent"), a corresponding observation is that functionality on different layers at the outer radius can include thermal paths to the outer edge of the stator. Furthermore, these thermal paths can include cross-layer thermal interactions as well as radial thermal paths. Radial thermal paths 114 are evident in FIGS. 1 and 2 at the outer edge of the winding structure, and they can be effectively coupled to the case or other heat sink.

[0030] U.S. Pat. No. 10,256,690 ("the '690 patent") discloses a structure that allows for accumulation of turns in a planar stator in both the axial and θ directions. A key aspect of this is the construction in which vias are conductive across a subset of adjacent layers. The '690 patent observes, as important to the embodiments disclosed therein, that a higher density of inner end turns can be achieved by packing the end turns as tightly as possible on each layer. This is distinct from previous designs in which the inner and outer end turns associated with a given phase were distributed to a particular layer to the exclusion of the inner and outer end turns for other phases. When the inner end turns are distributed to maximum density, two unique patterns exist for a three-phase machine. Together, these two patterns can result in complete connection of the inner end turns in only two layers. The winding scheme in the '625 patent first supports repeating the winding over the turns of adjacent poles, then linking the pole pairs, i.e., first the turns, then the poles. Figure 6 shows an example of a high-density inner end turn 602, which can be contrasted with the low-density end turns described in the '625 patent and shown in Figures 1 and 2.

[0031] Returning to the construction of the '625 patent, and with reference to FIGS. 1 and 2, consider a path that begins with a single radial trace 106 on the outer radius, continues radially to the inner radius, follows the path of the inner end turn 102, and returns to the outer radius. In plan view, this path is "U" shaped. Several such paths are evident in the structure 400a illustrated in FIG. 4A. The illustrated path includes a first set of radial traces 106a extending between the first outer via 110a and the first inner via 108a, a set of inner end turns 102 extending between the first inner via 108a and the second inner via 108b, and a second set of radial traces 106b extending between the second inner via 108b and the second outer via 110b. If the parallel, axially displaced layers corresponding to this path are considered, which Figure 1 may help to visualize, the result is a "ribbon" of traces punctured with vias 108, 110. This is illustrated in Figure 4B, where the U-shaped structure 400a of Figure 4A has been unwrapped and depicted flattened as a corresponding planar structure 400b.

[0032] In the following, first consider the effect of inter-pole leakage flux 302, as shown in FIG. 3, in conjunction with the “unwrapped ribbon” structure 400b illustrated in FIG. 4B. As shown in FIG. 4B, this leakage flux 302a-d is perpendicular to the “segments” bounded by vias 108, 110. In FIG. 4B, the size of the circles representing leakage flux 302 indicates the relative magnitude of the depicted flux vectors, and the symbols inside the circles represent the relative directions of the flux vectors, with “X” symbols indicating flux vectors pointing into the page and dot symbols indicating flux vectors pointing out of the page. The vias 108, 110 and radial traces 106 within these segments form a mesh within which eddy currents will circulate in response to the time-varying θ-directional flux that integrates across the individual segments “(r,z surfaces)” as the rotor turns.

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[0033] The above equation is for this effect, where any armature reaction that may occur is ignored. The important consideration is the θ rate of change of the flux linkage across the loop, i.e.,

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[0034] As will be described, current circulating within the structure 400 with the inner vias 108 is indicated in FIG. 4B by arrows 404. Note how the inner vias 108a-b divide the structure 400 into three regions. Due to the presence of the inner vias 108a-b, the three regions are divided into local

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[0035] 5A-B show a structure 500 similar to FIG. 4B, but omitting the inner vias 108a-b. In this case, the current (indicated by arrow 504) is determined by the change in the net magnetic flux coupled thereto.

[0036] To conveniently describe the drag forces associated with the distribution of current within the stator structure, a dot product is introduced, as follows:

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[0037] The interpretation here is that α (vector) is the B ⊥The goal is to generate a vector with (z) components (capturing the z variations of the magnetic flux density in the stator), where γ generates currents in the individual traces in the mesh at the corresponding z values. The relative components in each trace are therefore the scalar B for a particular θ and positive z range of the stator. ⊥ and linearly dependent on the induced current. Finally, there is a geometric factor k0 to contribute to the torque, which takes into account the radius at which the individual force densities appear. Radial directional flux leakage and armature reaction resulting from currents are ignored. In this framework, the focus is on comparing the torque contribution as a function of theta-directional flux linkage and quadrature flux density.

[0038] With respect to structure 400 in FIGS. 4A-B, and using the notation definitions above, the torque is the combined effect of the mesh at the first angle (subscript 1) and the mesh at the second angle (subscript 2), i.e.,

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[0039] Alternatively, rewriting the θ-dependent flux terms coupled to a first loop λ1 at a first angle and a second loop λ2 at a second angle gives:

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[0040] Considering Figure 3 for z>0, τ α There are four cases to consider at either "end" of structure 400. These cases move across the rotor pole transition and are as follows:

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[0041] where B ⊥ The >>0 notation indicates that the location under consideration has a strong axial component, i.e., is in the center of the poles. A weaker inequality indicates that the transition between poles is on either side of the center point. For all possible combinations, τ α The component added to the torque is negative, i.e., drag. For the two center cases, i.e., for angles close to the transition between poles, the drag varies as structure 400 passes through the transition, and the majority of the drag associated with θ-directional leakage arises from these interactions. The terms driving the effects in structure 400 of FIGS. 4A-B can be compared to those significant in structure 500 of FIGS. 5A-B.

[0042] These conditions can occur at both ends of the structure 400 and in combinations depending on the "end" spacing and rotor position as follows: [Table 1]

[0043] In the table above, the notation τ α < 0, τ α indicates that one of the terms in contributes substantially, and t α <<0 indicates that two such drag terms contribute.

[0044] If the inner vias 108a-b are omitted as in Figures 5A-B, the structure 500 behaves very differently. The induced voltage depends on the magnetic flux coupled by all "faces" of the structure 500, i.e.,

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[0045] In the following, the λ3 magnetic flux from the radial direction will be neglected as being small for geometric reasons (displaced inner end turn at r). Under this assumption, the drag term for structure 500 of FIGS. 5A-B, comparable to the first equation for structure 400 of FIGS. 4A-B, can be written as follows:

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[0046] B ⊥1 and B ⊥2 The way in which the axial components (at the first and second locations) are incorporated can be understood by considering the case where they are equal. The end turn causes any current induced in the loop to flow in opposite directions at the individual locations, resulting in torque cancellation. In addition, the end turn causes any current induced in the loop to flow in opposite directions at the individual locations, resulting in torque cancellation.

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[0047] As was done previously, in this case, the interactions can be enumerated considering both ends of the structure 500, since the magnetic flux coupled at one end can now change the drag at the other end. Note that not all of the situations below are possible within one structure 500 with a given angular separation between radial sections, but they represent all possible combinations. As the rotor turns, a given structure 500 fixed within the stator will have varying angles relative to the magnetic structure and will transition between the cases listed below. Figure 3 can be helpful in considering these combinations. [Table 2]

[0048] In the table above, the middle four entries show cancellation behavior. These entries correspond to situations where both sides of the structure 500 are in the transition region between pole and coupled θ-directional flux. Where λ1, λ2 are shown, there is the possibility of partial cancellation of the rate of change of λ as the rotor moves relative to the structure 500. This will occur due to the spacing of the traces as a function of θ, such that leakage increases on one side while decreasing on the other. In the complementary case, B ⊥ If is shown in the table, B ⊥ There is complete or partial cancellation of torque due to the induced current. In these cases, the torque due to the induced current may be low, but relatively high currents flow. In the four corners of the table, the θ-directional loss term is small because there is minimal θ-directional flux from both sides.

[0049] The remaining eight cases are significant at one end of the structure 500.

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[0050] In summary, the inner via configuration of a typical stator following the teachings of the '625 patent confines eddy currents induced by inter-pole leakage on the rotor. These eddy currents interact with the axial flux component to produce drag and may also produce armature reactions not considered here. If the inner vias were eliminated, these currents would be distributed between the radial windings associated with the two poles. This would also increase the perceived resistance and the area across which the leakage flux integrates and forms EMF loops in an otherwise equivalent design. However, the integration of magnetic flux over the expanded loops formed by a stator without inner vias offers the potential for elimination of coupled flux, lower eddy currents between poles, and a lower rate of change of net drag.

[0051] Finally, it should be noted that the description provided here is for an "internal runner" type machine, in which the shaft is built into the stator. If the machine is of "external runner" construction, i.e., the stator is supported at the inner radius, and phase connections, thermal connections, and the like are located at the inner radius, the description provided here can similarly be reversed. Specifically, the outer end turns in a machine of external runner construction would be similar to the inner end turns described here, and vias would similarly be located at the inner radius and omitted at the outer radius.

[0052] Development of a stator that eliminates the inner vias 108, as in the structure 500 of FIGS. 5A-B, but preserves the distribution of end turns and thermal functions across layers at the outer radius, proceeds with consideration of the role of the inner vias 108 in a stator of the type described in the '625 patent. Essentially, the inner via construction serves two functions. First, the radial traces 106 are explicitly connected in parallel, and second, the inner end turns 102 can be arranged in a wide variety of ways on any layer. The '625 patent discloses a specific distribution of the inner end turns 102, i.e., a construction in which the inner end turns 102 are located on layers associated with a single phase. The requirement is simply to create a fully connected winding without competing paths that would result in a "short circuit." If the inner vias 108 are omitted, it is still possible to create a winding using only the radial traces 106 that correspond to the inner end turns 102 present on a given layer. Radial traces 106 present on two or more layers with the same set of inner end turns 102 are still connected in parallel, but the parallel connection extends from an outer via 110 at a first angle to an outer via 110 at a second angle. Radial traces 106 on a given layer without a corresponding inner end turn 102 serve no purpose, so they may be eliminated to reduce eddy current losses due to axial field components.

[0053] FIG. 6 shows an example of a single layer 600 of a stator with a construction that omits inner vias 108, as described above. As shown, layer 600 may include radial traces 606, inner end turns 602, outer end turns 604, and thermal features 608. In layer 600, each radial trace 606 may be connected to a corresponding inner end turn 602, and radial traces 606 without an inner end turn 602 may be omitted. The inner end turns 602 may be packed as tightly as possible. To ensure that the radial traces 606 omitted in layer 600 of FIG. 6 appear on a different layer, the new layer may rotate or shift its inner end turns 602 so that they are complementary to those shown in FIG. 6. An example of such a complementary layer (including radial traces 706, inner end turns 702, outer end turns 704, and thermal features 708) is shown in FIG. 7. Figure 7 also depicts the angle α corresponding to the poles on the stator. From here, the stator poles may span one or two groups of windings on the stator layer shown, depending on the rotor angle. At any angle, the rotor may interact uniformly with the stator as a whole, since traces at all angles may reside on other layers.

[0054] An overlay of the layers of Figures 6 and 7 is provided in Figure 8, showing that radial traces 606, 706 can be uniformly incorporated into a stator with this construction using two layers (or multiples of two layers). The annular region of the illustrated stator, extending between a first radial distance r1 (measured from a center point 802 of the stator, which coincides with the axis of rotation of the machine's rotor) and a second radial distance r2 (also measured from the center point 802), may be located within the annular effective area of ​​the machine. The inner and outer diameters of magnets attached to the machine's rotor (not shown) may be located at or near radial distance r1 (measured from the rotor's axis of rotation) and radial distance r2 (also measured from the rotor's axis of rotation), respectively, and thus generate axially directed magnetic flux within the annular effective area. Flux density measurements demonstrate that the flux density within this region is typically greater than about 40 percent of the peak axial flux density within the gap of the machine, while the flux density outside of this region is typically less than 40 percent of the peak flux density within the gap.

[0055] In Figures 6 and 7, the outer end turns 604, 704 are associated with the first phase (Figure 6) and the second phase (Figure 7), requiring three layers to achieve a complete set of outer end turns. A complete set of inner end turns 602, 702 can be achieved within two layers. While the outer end turns 604, 705 can be distributed more densely, distributing these connections across at least three layers allows room for thermal features 608, 708, phase connections, and neutral connections. The outer vias 110 allow the thermal, end turns, neutral, and connection structures to be distributed across multiple layers. The outer vias 110 also allow similar layers to be connected in parallel. Figure 9 shows this extended to a practical 18-layer stator 900. Working inward from the outer vias, all layers in this structure correspond to either Figure 6 or Figure 7 in alternating order.

[0056] The trajectory of a single phase through the winding scheme described here is somewhat more complex than the phases in the planar stator corresponding to the '625 patent. Using the same stator as shown in Figures 6-9, Figures 10 and 11 show a complete single-phase connection 1000, omitting the inner end turns 602, 702 and all other features associated with other phases. Figure 11 shows that this winding can be distributed across three layers due to the selection of the distribution of the outer end turns 604. Inside the radius of the vias 110, there are only two unique arrangements of radial traces 606, 706 and inner end turns 602, 702, one of which occurs in the illustrated structure with multiples of two (i.e., on the top and middle layers shown in Figure 11). Of the two identical inner sections depicted in Figure 11, the outer functionality is split between the outer end turns 604 and the thermal features 608, 708. If the thermal features 608, 708 are omitted, the complete stator can be made in only two layers (e.g., the top and bottom layers shown in FIG. 11), for example, by reconfiguring the outer end turns 604, 704.

[0057] The winding arrangement described herein has several advantages over the end windings described above. First, under high-speed operation, eddy current losses within the stator are reduced compared to stators of conventional design. This facilitates loss-related tradeoffs to achieve higher efficiency, higher speed operation at a given efficiency level and the like. Second, losses sustained within the designs described herein are moved from the inner radius to the outer radius of the machine compared to stators of conventional construction. For example, there are no circulating current losses in the inner radius vias 108. Third, with respect to stator fabrication, the inner vias 108 are often "drilled" in a separate operation from trace fabrication. This requires that planar stator layers be aligned and precisely positioned for drilling. In practice, this means that copper clearance is required around the inner vias. This limits the minimum spacing between features at the inner radius, which controls the number and combination of radial features that can be accommodated within a given overall size. In other words, higher trace density is often possible on a stator without inner vias 108 compared to stators of conventional design.

[0058] The design described herein allows for the construction of machines that operate efficiently at speeds in excess of 20,000 rpm, which in turn allows for the construction of machines that are less than two centimeters in diameter.

[0059] 1 shows a partial cutaway interior perspective view of the layers of a stator 100 designed in accordance with the '625 patent, in which the functions of the inner end turn 102 and outer end turn 104 are distributed across multiple layers. Radial traces 106 are connected in parallel by both inner vias 108 and outer vias 110 across all layers.

[0060] Figure 2 shows a single layer of the stator of Figure 1. Vias (shown in Figure 1) allow radial traces 106 that are not connected by the inner end turn 102 or outer end turn 104 on a particular layer to contribute to the reduced resistance of the radial traces 106 through parallel connections.

[0061] Figure 3 shows a numerical solution of the air-gap flux density for a particular geometry. In particular, Figure 3 represents the sections in the z and θ directions at constant r. The major components include magnets 306, back iron 308, and a primarily axial solution in the gap 304 between magnets 306 of opposite polarity. Flux leakage between the poles exhibits a θ-directional component 302 that can interact with stator features and cause losses.

[0062] Figure 4A shows a generally U-shaped structure 400a in a conventional stator, such as that shown in Figure 1. The vertical axis is exaggerated for clarity.

[0063] FIG. 4B shows a planar structure 400b representing how the U-shaped structure 400a of FIG. 4A would appear if it were unwound and drawn flat. As with FIG. 4A, the vertical axis is exaggerated for clarity. FIG. 4B illustrates the distribution of current driven within a pair of radial traces 106a, 106b connected by an inner end turn 102. As shown, the overall structure begins at an outer via 110a, travels along a first set of radial traces 106a, encounters a first inner via 108a, traverses the set of inner end turns 102, encounters a second inner via 108b, travels along a second set of radial traces 106b, and terminates on a second outer via 110b. The structure includes multiple layers as shown in FIG. 3 and is nominally centered within the gap 304 shown. When the structure encounters leakage flux 302 (shown in FIGS. 3 and 4), it responds with a current indicated by arrows 404 in FIG. 4B. FIG. 4B shows diagrammatically how the leakage flux 302a-d coupled by the structure's windows decreases as the offset from the gap centerline decreases. For clarity, the response current indicated by arrows 404 is shown only on the right side of FIG. 4B for flux coupled within that portion of structure 400. Any response in the remainder of structure 400 will be to flux coupled at those locations and will be unrelated to response current 404 due to vias 108a, 108b.

[0064] 5A shows a generally U-shaped structure 500a similar to the generally U-shaped structure 500a, but in which the inner vias 108a, 108b are omitted, the vertical axis being exaggerated for clarity.

[0065] Figure 5B shows a planar structure 500b that represents how the U-shaped structure 500a of Figure 5A would appear if it were unwrapped and drawn flat. As with Figure 5A, the vertical axis is exaggerated for clarity. Figure 5B illustrates the current response of this structure (indicated by arrows 504) to an imposed time rate of change of leakage flux 302. As shown, the response current flows on both sides of the structure 500.

[0066] 6 shows a first layer 600 of a stator in which inner end turns 602 are present with the highest possible density, and only radial traces 606 corresponding to the inner end turns 602 are present on the layer. Because there are no radial traces 606 on this layer that need to be connected by inner end turns on another layer, there is no need for inner vias 108. Outer end turns 604 on layer 600 terminate on outer vias 110, regardless of whether corresponding radial traces 606 are present on that layer.

[0067] Figure 7 shows a second layer 700 of the stator depicted in Figure 6. As shown, the inner end turn 702 and associated radial traces 706 are complementary to the inner end turn 602 and radial traces 606 shown in Figure 6.

[0068] Figure 8 shows a combination 800 of layer 600 shown in Figure 6 and layer 700 shown in Figure 7, with layer 600 highlighted and layer 700 shaded. Figure 8 shows that the inner end turns 602, 702 and radial traces 606, 706 from the individual layers collectively provide a full complement of radial traces and inner end turns across the two layers.

[0069] FIG. 9 shows the assembly and combination of several layers where the inner end turns 602, 702 and radial traces 606, 706 follow the pattern established in FIG. 8, and outer vias 110 are used to distribute end turns, heat, and connection features across multiple layers.

[0070] FIG. 10 shows a complete single-phase connection 1000 for a 16-pole, three-turn winding, omitting the inner end turns 602, 702 and all other features associated with other phases, which may be established by overlapping three layers, such as layers 600 and 700 shown in FIGS. 6 and 7. The illustrated path starts at the phase connection 1002 and includes the radial traces 606a, 606b, 706a, 706b, the inner end turns 602, 702, the outer end turns 604a, 604b, and the outer via 110. As shown, a portion of the neutral connection 1004 may connect the illustrated phase to another and form the neutral. Not all features in FIG. 10 can be located on a single layer, particularly when similar features for other phasings are considered.

[0071] FIG. 11 illustrates the three layers of FIG. 10 in a perspective view. The single phase of FIG. 10 is supported by both types of layers 600 and 700 shown in FIGS. 6 and 7. In the illustrated embodiment, one of those types of layers is employed in both the top and middle layers of the stack, and the other type of layer is employed in the bottom layer. The outer end turns 604 for that phase appear on the top layer. The thermal features for that phase appear on the bottom layer where they do not interfere with the end turns of another phase. Also on the bottom layer is a power connector 1002. The middle layer includes a neutral connection 1004.

[0072] 12 and 13 illustrate a first example structure 1200 and a second example structure 1300, respectively, that may be embodied in stator 1000 shown in FIGS. 10 and 11 and provide various performance benefits for axial-flux machines as outlined herein. In this regard, it should be understood that structures 1200, 1300 have applicability to structures other than stator 1000 and may provide similar benefits. Thus, additional features and / or nuances of the specific configurations shown in FIGS. 10 and 11 should not be considered limiting.

[0073] Referring initially to FIG. 12 , the radial traces 706 a, 706 b and the inner end turn 702 a may be included in a first conductive layer, and the outer end turn 604 a may be included in a second conductive layer. While not specifically shown, it should be understood that the structure 1200 may additionally include one or more dielectric substrates supporting such conductive layers. Such dielectric substrates may be adapted to be positioned within an annular active region of an axial-flux machine, including a rotor configured to rotate about an axis of rotation. As described above, the annular portion of the stator in which the radial traces 706 a, 706 b are located may be positioned within the “active” region of the machine because it is the region primarily responsible for producing torque within the machine.

[0074] 12, the structure 1200 may also include at least a first conductive via 110a and a second conductive via 110c extending between the first and second conductive layers. The first conductive via 110a and the second conductive via 110d may be positioned radially on a first side of the annular effective area. In some implementations, additional conductive vias 110b and 110d may similarly extend between the first and second conductive layers (e.g., in parallel with the first and second conductive vias 110a and 110c, respectively) and may also be positioned radially on the first side of the annular effective area. The radial traces 706a and 706b and the inner end turn 702a may together form a first conductive trace within the first conductive layer. The inner end turn 702a may be positioned to lie radially on a second side of the annular effective area, the second side facing the first side. As shown, the first conductive trace may extend along a first path starting from the first conductive via 110a, passing through the inner end turn 702a, and terminating at the second conductive via 110c.

[0075] The outer end turn 604a may form a second conductive trace within the second conductive layer. The outer end turn 604a may be positioned radially on a first side of the annular effective area. As shown, the second conductive trace may extend along a second path that begins at the second conductive via 110c and passes through the outer end turn 604a. The second conductive trace (e.g., including the outer end turn 604a) may be connected to the first conductive trace (e.g., including the radial traces 706a, 706b and the inner end turn 702) through the second conductive via 110c such that the first and second paths are connected in series. In some implementations, the second conductive trace (e.g., including the outer end turn 604a) may terminate on an additional conductive via (not shown in FIG. 12) that may be positioned to extend between the first and second conductive layers and be located radially on a first side of the annular effective area, thus allowing connection from the additional conductive via to another radial trace (also not shown in FIG. 12). The location of such additional conductive via may depend on whether the stator windings are arranged in a serpentine pattern or a coil pattern.

[0076] 12, in structure 1200, all conductive vias interconnecting first conductive traces (e.g., including radial traces 706a, 706b and inner end turn 702) and second conductive traces (e.g., including outer end turn 604a) are positioned so as to be radially located on a first side of the annular effective area. The omission of conductive vias on the second side of the annular effective area, as well as elsewhere, may provide numerous benefits, such as reducing losses due to eddy currents caused by the θ-directional magnetic flux, as outlined above.

[0077] 13 , radial traces 606c, 606d and inner end turn 602a may be included in a first conductive layer, and radial traces 606e, 606f and inner end turn 602b may be included in a second conductive layer. While not specifically shown, it should be understood that structure 1300 may additionally include one or more dielectric substrates supporting such conductive layers. Such dielectric substrates may be adapted to be positioned within an annular active region of an axial-flux machine, including a rotor configured to rotate about an axis of rotation. As described above, the annular portion of the stator in which radial traces 606c, 606d, 606e, 606f are located may be positioned within the “active” region of the machine because it is the region primarily responsible for producing torque within the machine.

[0078] 13, structure 1300 may also include at least a first conductive via 110e and a second conductive via 110g extending between the first and second conductive layers. First conductive via 110e and second conductive via 110g may be positioned radially on a first side of the annular effective area. In some implementations, additional conductive vias 110f and 110h may similarly extend between the first and second conductive layers (e.g., in parallel with first and second conductive vias 110e and 110g, respectively) and may also be positioned radially on the first side of the annular effective area.

[0079] The radial traces 606c, 606d and the inner end turn 602a may together form a first conductive trace in the first conductive layer. The inner end turn 602a may be positioned to lie radially on a second side of the annular effective area, the second side facing the first side. As shown, the first conductive trace may extend along a first path starting from the first conductive via 110e, passing through the inner end turn 602a, and terminating at the second conductive via 110g. Similarly, the radial traces 606e, 606f and the inner end turn 602b may together form a second conductive trace in the second conductive layer. The inner end turn 602b may be positioned to lie radially on the second side of the annular effective area. As shown, the second conductive trace may extend along a second path that starts at the first conductive via 110e, passes through the inner end turn 602b, and terminates at the second conductive via 110g.

[0080] 13, in structure 1300, all conductive vias interconnecting first conductive traces (e.g., including radial traces 606c, 606d and inner end turn 602a) and second conductive traces (e.g., including radial traces 606e, 606f and inner end turn 602b) are positioned so as to be radially located on a first side of the annular effective area. The omission of conductive vias on the second side of the annular effective area, as well as elsewhere, may provide numerous benefits, such as reducing losses due to eddy currents caused by theta-directional magnetic flux, as outlined above.

[0081] While several aspects of at least one embodiment have been described above, it should be understood that various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of this disclosure. Accordingly, the foregoing description and drawings are by way of example only.

[0082] Various aspects of the present disclosure may be used alone, in combination, or in various arrangements not specifically discussed in the above-described embodiments, and therefore this application is not limited to the details and arrangements of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments.

[0083] Also, the disclosed aspects may be embodied as methods, examples of which are provided. The acts performed as part of a method may be ordered in any suitable manner. Thus, although illustrated embodiments show acts as sequential, embodiments may be constructed in which acts are performed in an order different from that shown, which may include performing some acts simultaneously.

[0084] The use of ordinal terms such as "first," "second," "third," etc. in the claims to modify claim elements does not, of itself, imply any priority, precedence, or sequence of one claim element over another, or the chronological order in which acts of a method are performed, but merely distinguishes one claimed element having a certain name from another element having the same name (but for the use of the ordinal term) and is used as a marker to distinguish between claim elements.

[0085] Also, the phraseology and terminology used herein is for purposes of description and should not be regarded as limiting. The use of "including," "comprising," "having," "containing," "involving," and variations thereof, as used herein, is meant to encompass the items listed thereafter, and equivalents thereof, as well as additional items.

[0086] The claims are as follows:

Claims

1. A planar stator, the planar stator comprising: one or more dielectric substrates adapted to be positioned within an annular effective area of ​​an axial flux machine, the one or more dielectric substrates including a rotor configured to rotate about an axis of rotation, the rotor configured to present a pattern of alternating magnetic poles that generate axial magnetic flux within gaps between axially displaced components of the rotor; a plurality of conductive traces contained within at least first and second conductive layers defined by the one or more dielectric substrates, the plurality of conductive traces forming windings for a plurality of poles of the planar stator; and at least first and second conductive vias extending between and interconnecting portions of the plurality of conductive traces in the first and second conductive layers, the first and second conductive vias being positioned so as to be radially disposed on a first side of the annular effective area; Equipped with the plurality of conductive traces includes a first conductive trace in the first conductive layer; the first conductive trace includes a first end turn positioned so as to be radially disposed on a second side of the annular effective area, the second side facing the first side; the first conductive trace extends along a first path, the first path starting at the first conductive via, passing through the first end turn, and terminating at the second conductive via; the plurality of conductive traces includes a second conductive trace in the second conductive layer; the second conductive trace includes a second end turn positioned so as to be radially disposed on the first side of the annular effective area; the second conductive trace extends along a second path, the second path starting at the second conductive via and passing through the second end turn; the second conductive trace is connected to the first conductive trace through the second conductive via such that the first path and the second path are connected in series; all conductive vias interconnecting the first conductive traces and the second conductive traces are positioned so as to be radially disposed on the first side of the annular effective area; the first conductive layer includes a first set of the plurality of conductive traces, the first set of the plurality of conductive traces being supported by the one or more dielectric substrates and disposed in a first plane; the second conductive layer includes a second set of the plurality of conductive traces, the second set of the plurality of conductive traces supported by the one or more dielectric substrates and disposed in a second plane, the second plane being parallel to the first plane and axially offset from the first plane; the annular effective area is a region of the planar stator in which the axial magnetic flux density is greater than 40% of the peak value of the axial magnetic flux density in the gap; A planar stator, wherein either (i) the first side is inside the annular effective area and the second side is outside the annular effective area, or (ii) the first side is outside the annular effective area and the second side is inside the annular effective area.

2. The planar stator of claim 1, further comprising an additional third conductive via extending between the first conductive layer and the second conductive layer and positioned so as to be radially disposed on the first side of the annular effective area, the second path along which the second conductive trace extends starting from the second conductive via, passing through the second seat winding, and terminating at the third conductive via.

3. The planar stator of claim 2 , wherein the third conductive via is positioned such that the first conductive trace and the second conductive trace form part of a serpentine-shaped winding.

4. The planar stator of claim 2 , wherein the third conductive via is positioned such that the first conductive trace and the second conductive trace form part of a spiral-shaped winding.

5. The planar stator further comprises an additional fourth conductive via and a third conductive trace in the second conductive layer; the additional fourth conductive via extends between the first conductive layer and the second conductive layer and is positioned so as to be radially disposed on the first side of the annular effective area; 5. The planar stator of claim 2, wherein the third conductive trace includes a third end turn positioned so as to be radially disposed on the second side of the annular effective area, the third conductive trace extending along a third path, the third path starting from the third conductive via, passing through the third end turn, and terminating at the fourth conductive via.

6. the one or more dielectric substrates further define a third conductive layer, the third conductive layer including a third set of the plurality of conductive traces, the third set of the plurality of conductive traces supported by the one or more dielectric substrates and disposed in a third plane, the third plane being parallel to the first plane and the second plane, and the third conductive via extending through the third conductive layer; 6. The planar stator of claim 5, further comprising a fourth conductive trace in the third conductive layer, the fourth conductive trace including a fourth end turn positioned so as to be radially disposed on the second side of the annular effective area, the fourth conductive trace extending along a fourth path, the fourth path starting from the third conductive via, passing through the fourth end turn, and terminating at the fourth conductive via.

7. 7. The planar stator of claim 6, wherein all conductive vias interconnecting the third conductive trace and the fourth conductive trace are positioned so as to be radially disposed on the first side of the annular effective area.

8. A planar stator as described in any of claims 1 to 7, further comprising an additional conductive via extending between the first conductive layer and the second conductive layer and positioned so as to be radially disposed on the first side of the annular effective area, and the second conductive trace further connected to the first conductive trace through the additional conductive via.

9. 9. A planar stator according to claim 1, wherein the first end turn is an inner end turn and the second end turn is an outer end turn.

10. 9. A planar stator according to claim 1, wherein the first end turn is an outer end turn and the second end turn is an inner end turn.

11. An axial flux motor or generator, the axial flux motor or generator having a planar stator as described in any one of claims 1 to 10.

12. A planar stator as described in any one of claims 1 to 10, wherein the first conductive trace is approximately U-shaped.

13. A planar stator as described in any one of claims 1 to 10 and 12, wherein the first path forms less than a complete turn for a pole of the planar stator.

14. A planar stator, the planar stator comprising: one or more dielectric substrates adapted to be positioned within an annular effective area of ​​an axial flux machine, the one or more dielectric substrates including a rotor configured to rotate about an axis of rotation, the rotor configured to present a pattern of alternating magnetic poles that generate axial magnetic flux within gaps between axially displaced components of the rotor; a plurality of conductive traces contained within at least first and second conductive layers defined by the one or more dielectric substrates, the plurality of conductive traces forming windings for a plurality of poles of the planar stator; and at least a first conductive via and a second conductive via extending between the first conductive layer and the second conductive layer, the first conductive via and the second conductive via positioned so as to be radially disposed on a first side of the annular effective area; Equipped with the plurality of conductive traces includes a first conductive trace in the first conductive layer; the first conductive trace includes a first end turn positioned so as to be radially disposed on a second side of the annular effective area, the second side facing the first side; the first conductive trace follows a first path, the first path starting at the first conductive via, extending through the first end turn, and terminating at the second conductive via; the plurality of conductive traces includes a second conductive trace in the second conductive layer; the second conductive trace includes a second end turn positioned so as to be radially disposed on the second side of the annular effective area; the second conductive trace follows a second path, the second path starting at the first conductive via, extending through the second end turn, and terminating at the second conductive via; all conductive vias interconnecting the first conductive traces and the second conductive traces are positioned so as to be radially disposed on the first side of the annular effective area; the first conductive layer includes a first set of the plurality of conductive traces, the first set of the plurality of conductive traces being supported by the one or more dielectric substrates and disposed in a first plane; the second conductive layer includes a second set of the plurality of conductive traces, the second set of the plurality of conductive traces supported by the one or more dielectric substrates and disposed in a second plane, the second plane being parallel to the first plane and axially offset from the first plane; the annular effective area is a region of the planar stator in which the axial magnetic flux density is greater than 40% of the peak value of the axial magnetic flux density in the gap; A planar stator, wherein either (i) the first side is inside the annular effective area and the second side is outside the annular effective area, or (ii) the first side is outside the annular effective area and the second side is inside the annular effective area.

15. The planar stator of claim 14 , wherein the first path has the same size and shape as the second path.

16. 16. A planar stator according to claim 14 or claim 15, wherein the first end turn and the second end turn are inner end turns.

17. 16. A planar stator according to claim 14 or claim 15, wherein the first end turn and the second end turn are outer end turns.

18. The planar stator further comprising an additional third conductive via and a third conductive trace in the second conductive layer; the additional third conductive via extends between the first conductive layer and the second conductive layer and is positioned so as to be radially disposed on the first side of the annular effective area; 18. The planar stator of claim 14, wherein the third conductive trace includes a third end turn positioned so as to be radially disposed on the first side of the annular effective area, the third conductive trace extending along a third path, the third path starting from the second conductive via, passing through the third end turn, and terminating at the third conductive via.

19. the one or more dielectric substrates further define a third conductive layer, the third conductive layer including a third set of the plurality of conductive traces, the third set of the plurality of conductive traces supported by the one or more dielectric substrates and disposed in a third plane, the third plane being parallel to the first plane and the second plane, and the third conductive via extending through the third conductive layer; the planar stator further comprises an additional fourth conductive via and a fourth conductive trace in the third conductive layer; the additional fourth conductive via extends through the first conductive layer, the second conductive layer, and the third conductive layer and is positioned so as to be radially disposed on the first side of the annular effective area; 19. The planar stator of claim 18, wherein the fourth conductive trace includes a fourth end turn positioned so as to be radially disposed on the second side of the annular effective area, the fourth conductive trace extending along a fourth path, the fourth path starting from the third conductive via, passing through the fourth end turn, and terminating at the fourth conductive via.

20. An axial flux motor or generator, wherein the axial flux motor or generator is provided with a planar stator as described in any one of claims 14 to 19.

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