A method for contouring an airgap profile in an electromagnetic device comprising an airgap in a magnetic path and an electromagnetic device comprising a contoured airgap in a magnetic path

Abstract

The invention relates to a method for contouring an airgap (2) profile in an electromagnetic device comprising an airgap in a magnetic path to reduce airgap reluctance, and an electromagnetic device comprising a contoured airgap in a magnetic path. In the present invention, the airgap (2) is profiled such that the airgap profile corresponds to a contour of the guide profile line between the opposite faces forming the airgap between them at the midpoint of the airgap (2) thickness taken perpendicular to said guide profile line.

Description

[0001] A method for contouring an airgap profile in an electromagnetic device comprising an airgap in a magnetic path and an electromagnetic device comprising a contoured airgap in a magnetic path

[0002] TECHNICAL FIELD

[0003] Present invention relates to a method for contouring an airgap profile in an electromagnetic device comprising an airgap in a magnetic path to reduce airgap reluctance, and an electromagnetic device comprising such an airgap.

[0004] BACKGROUND ART

[0005] International patent application WO2021 / 083631A1 discloses solution relating to a varying the cross-sections of airgap-forming electromagnetic parts to mitigate rotor temperature imbalances and prevent local overheating. While it introduces modifications to the airgap geometry, it lacks specificity in the shape of these variations. Electromagnetic performance aspects are not addressed, and the stator outer diameter remains constant. This design choice can lead to significant localized magnetic saturation, increasing the overall reluctance and potentially decreasing the device's output performance.

[0006] United States patent application US2014 / 0021822A1 proposes a use of rectangular projections and recesses in the airgap-forming parts to increase the airgap surface area. While it acknowledges the effect of increased airgap surface area on electromagnetic performance, it limits the geometric variations to simple rectangular shapes. The solution emphasizes manufacturability through sectionalized sintered cores but does not provide a comprehensive strategy for optimizing electromagnetic performance across different size and types of devices.

[0007] United States patent US8653713B2 includes a solution, where one, two, and three-step protrusions are used to modify the airgap profile, maintaining the airgap constant only in the radial direction. However, it lacks a shaping strategy for triangular or V-shaped contours. The increased airgap length in directions other than the radial causes the magnetic flux to concentrate radially, which may reduce the utilization of the increased airgap surface area. Additionally, the patent suggests that step protrusions can solve saturation issues at high magnetomotive forces, aclaim not substantiated with comprehensive analysis applicable to various electromagnetic devices.

[0008] United States patents US6066908, US6034462 and US5777421 disclose serrated faces and sawtooth or conical shapes on the airgap-forming surfaces to reduce reluctance by increasing the airgap surface area. However, they do not define a precise contouring strategy or provide mathematical formulations for the shapes. The focus is on specific machine types and does not extend the applicability to devices like linear actuators or air-gapped transformers and inductors.

[0009] European patent applications EP2555389A1 and EP0944158A2 and French patent FR3109249B1 relate to concepts such as staggered (zigzag) airgap profiles, sinusoidal shapes, and increased rotor surface areas through varying crosssections. While they aim to reduce airgap reluctance and enhance electromagnetic performance, they often lack detailed contouring strategies and do not address the implications of core saturation, or the optimization of contour amplitude based on operating conditions applicable to a broad range of electromagnetic devices.

[0010] The design and optimization of airgap profiles in electrical machines have been the subject of numerous studies and patents, aiming to improve electromagnetic performance, thermal management, and mechanical integrity. Various approaches have been proposed to modify the airgap geometry, primarily focusing on radial flux machines with inner rotors. However, these prior art solutions exhibit limitations that the present invention addresses through a novel contoured airgap topology applied to axial flux machines.

[0011] The prior art in the field of airgap design has primarily focused on specific machine types or limited geometrical modifications, often without a comprehensive strategy applicable to a broad range of electromagnetic devices. The present invention advances the state of the art by providing a universally applicable contoured airgap topology supported by mathematical formulations and thorough electromagnetic evaluations.

[0012] SUMMARY OF INVENTION

[0013] Present invention provides a method for contouring an airgap profile in an electromagnetic device comprising an airgap in a magnetic path to reduce airgapreluctance, and an electromagnetic device comprising a contoured airgap in a magnetic path contoured according to said method.

[0014] According to present invention, the airgap is profiled such that the airgap profile corresponds to a contour of the guide profile line between the opposite faces forming the airgap between them at the midpoint of the airgap thickness taken perpendicular to said guide profile line, where said guide profile line lies in plane containing x- and y-axes, where said x-, y- and z-axes represent the first, second and third dimension, where x-axis is perpendicular to the general direction of flux flow in the magnetic path in the vicinity of said airgap, y-axis is in the general direction of the flux flow in said magnetic path and z-axis perpendicular both with x and y-axes.

[0015] This means that in a stationary electromagnetic device, x- and z-axes lie in the cross-section plane of the magnetic path core in the vicinity of the airgap and y-axis is perpendicular with said plane.

[0016] This means that in a rotating electromagnetic device in the case of an axial flux motor, the y-axis is parallel with the axis of rotation of motor, where the x-axis is perpendicular to said axis of rotation of motor. Said guide profile line and axis of rotation of motor both lie in the plane of longitudinal cut of said motor.

[0017] This means that in a rotating electromagnetic device in the case of a radial flux motor, the x-axis is parallel with the axis of rotation of motor, where the y-axis is perpendicular to said axis of rotation of motor. Said guide profile line and axis of rotation of motor both lie in the plane of longitudinal cut of said motor.

[0018] The airgap-facing surface profiles of the core components are offset by half the airgap thickness (g / 2) perpendicular to said guide profile line on both sides of said guide profile line to define the airgap-facing surfaces of the core components such that the normal distance between the airgap-facing components remains uniform and a distribution of flux lines throughout the airgap profile are both uniform, and a shape of said airgap guide profile line is triangular, sinusoidal or circular.

[0019] In an embodiment, where the shape of said airgap guide profile line is triangular, said triangular airgap contour corresponds to the following conditionsg ZAC(*i + x2)y = y»+2X1 <x< - 2 - g 2?icOi + x2) [y =y<) +-+2^ - (j— ^(x - xj - - - < x < x2

[0020]

[0021] where

[0022] xris the starting point of the core component, defining the starting point of airgap in first axis,

[0023] x2is the edge-point of the core component defining the end point of the airgap in the first axis,

[0024] y0is the midpoint of airgap thickness in the second axis,

[0025] ACis the amplitude of the central-guide contour profile.

[0026] In an embodiment, where the shape of said airgap guide profile line is sinusoidal, said sinusoidal airgap contour corresponds to the following conditions

[0027] f g n(x - xj y0y = y0+^+ Acsin--— 0.01 < AC<

[0028]

[0029] f 1^2X1J where

[0030] xxis the starting point of the core component, defining the starting point of airgap in first axis,

[0031] x2is the edge-point of the core component defining the end point of the airgap in the first axis,

[0032] y0is the midpoint of airgap thickness in the second axis,

[0033] ACis the amplitude of the central-guide contour profile.

[0034] In an embodiment, where the shape of said airgap guide profile line is circular, said circular airgap contour corresponds to the following conditions

[0035]

[0036] where

[0037] is the starting point of the core component, defining the starting point of airgap in first axis,x2is the edge-point of the core component defining the end point of the airgap in the first axis,

[0038] y0is the midpoint of airgap thickness in the second axis,

[0039] is the amplitude of the central-guide contour profile,

[0040] r is the radius of the circular contour profile.

[0041] Though the novel contoured airgap topology showcased here is unequivocally applicable to a wide range of electromagnetic devices involving airgap in their magnetic path. These include radial flux electrical machines (outer and inner rotor topologies), axial flux electrical machines (single stator-single rotor to multi stator-multi rotor configurations, air-gapped transformers / inductors, linear actuators and / or linear electrical machines).

[0042] The present invention introduces a novel method of reducing airgap reluctance and increasing power density without increasing the machine’s mass / volume. This is achieved by contouring the faces of the machine components adjacent to the airgap, effectively modifying the airgap profile to increase its surface area. By introducing contours to the airgap-facing surfaces, the electromagnetic performance is enhanced without the need for larger machine components. This design innovation leads to a reduction in airgap reluctance, thereby improving the magnetic flux production against a given MMF (MMF = magnetomotive force), enhancing energy conversion efficiency, and increasing the power density of the machine.

[0043] Electrical machines, including motors and generators of various types, fundamentally rely on magnetic circuits that incorporate an airgap to facilitate mechanical movement. The presence of this airgap is essential for the operational functionality of these devices. However, the airgap introduces a significant challenge, that is, due to its low magnetic permeability compared to ferromagnetic core materials, the airgap's magnetic reluctance dominates the overall reluctance of the magnetic circuit. This high reluctance impedes the production of magnetic flux against an applied magnetomotive force (MMF), consequently affecting the efficiency of energy conversion and the power density of the machine. Enhancing these parameters is a primary objective in the design and optimization of electrical machines, as they are highly desired characteristics that determine the effectiveness and competitiveness of the machines in various applications.In conventional designs, the reluctance of the magnetic circuit is lowered by enhancing the permeability of the core material on one side, and by reducing the airgap reluctance either through reduced airgap thickness or increased cross-sectional area of the airgap on the other side. While improving core material permeability is beneficial, it reaches a practical limit due to material properties and cost considerations. The thickness of the airgap is constrained by mechanical manufacturing tolerances and thermal expansion considerations during operation. As such, there is a lower limit to how much the airgap thickness can be reduced without compromising mechanical integrity and operational reliability. Therefore, the primary possibility for further reducing airgap reluctance lies in increasing the airgap's surface area.

[0044] Traditionally, the airgap surface area is uniform and straight, a design choice driven by conventional manufacturing technologies such as the use of laminated steel sheets. These manufacturing constraints limit the ability to modify the airgap surface without significantly altering the machine's overall dimensions. In conventional design topology, increased cross-sectional area of the airgap can be achieved by increasing the cross-sectional area of the airgap facing components of the electrical machine such as the rotor, and stator surface areas. This leads to an increase in the overall volume of the machine components. This trade-off improves energy conversion efficiency but adversely affects the power density, which is a critical parameter in many applications.

[0045] By addressing both the design and practical implementation aspects, the invention achieves significant enhancements in energy conversion efficiency and power density without increasing the device's external dimensions. This innovative approach not only overcomes the limitations of prior art but also offers a versatile solution that can be adapted to various electromagnetic devices, including rotating machines (both radial and axial flux), linear actuators, transformers, and inductors. The invention's universal applicability and optimization strategies provide a significant opportunity to develop more efficient and power-dense electromagnetic devices, meeting the ever-increasing demands for higher performance in diverse applications.

[0046] BRIEF DESCRIPTION OF DRAWINGSPresent invention is described below with reference to the accompanying schematic illustrations, in which:

[0047] Figure 1 a and 1 b depict respectively a magnetic circuit with airgap on Figure 1 a and its schematic representation on Figure 1b.

[0048] Figures 2a to 2d illustrate straight and contoured magnetic circuit profiles, where respectively:

[0049] Figure 2a depicts straight airgap profile,

[0050] Figure 2b depicts triangular airgap profile with triangular guide profile line, Figure 2c depicts sinusoidal airgap profile with sinusoidal guide profile line, Figure 2d depicts circular airgap profile with circular guide profile line.

[0051] Figure 3 illustrates a benchmark magnetic circuit with straight air gap topology.

[0052] Figures 4a to 4c depict coil flux linkage versus input coil current for core material with constant magnetic permeability in comparison respectively triangular, sinusoidal and circular airgap profile, where respectively:

[0053] Figure 4a depicts a comparison straight airgap profile versus triangular airgap profile,

[0054] Figure 4b depicts a comparison straight airgap profile versus sinusoidal airgap profile,

[0055] Figure 4c depicts a comparison straight airgap profile versus circular airgap profile.

[0056] Figure 5 illustrates a decreasing cross-sectional area of the core in the vicinity of the contoured air gap.

[0057] Figure 6 illustrates a central contour defining the airgap.

[0058] Figure 7 depicts an implemented contour profiles for various magnitudes of contour amplitudes according to the defined contouring strategy and the respective FEA (= Finite Element Analysis) plots for flux lines in the core material and the airgap.

[0059] Figures 8a to 8c depict coil flux linkage versus input coil current for M400-50A corematerial with non-linear magnetic permeability in comparison respectively triangular, sinusoidal and circular airgap profile, where respectively:

[0060] Figure 8a depicts a comparison straight airgap profile versus triangular airgap profile,

[0061] Figure 8b depicts a comparison straight airgap profile versus sinusoidal airgap profile,

[0062] Figure 8c depicts a comparison straight airgap profile versus circular airgap profile.

[0063] Figures 9a to 9d depict a structure for an axial flux motor with straight / conventional airgap profile, where respectively:

[0064] Figure 9a is an exploded view of components assembly with one coil-side cutaway to expose the stator tooth-side (forming the airgap),

[0065] Figure 9b a cross-sectional view on the motor components assembly at the line B-B, Figure 9c a bottom view of the rotor at the line C-C shown in figure 9b and Figure 9d a top view of stator assembly at the line D-D shown in figure 9b.

[0066] Figures 10a and 10b depict respectively a structure for an axial flux motor with contoured airgap profile, where Figure 10a contains an exploded view of components assembly and figure 10b a cross-sectional view on the motor components assembly at the line E-E shown in figure 10a.

[0067] Figure 11a depicts a cross-section of the radial flux motor.

[0068] Figures 11b and 11c depict respectively a radial flux motor with straight and contoured airgap profile in a cross-sectional view at the line F-F shown on Figure 11a.

[0069] DESCRIPTION OF EMBODIMENTS

[0070] ANALYTICAL AND SIMULATION EVIDENCE

[0071] To substantiate the effectiveness of the contoured airgap design, analytical calculations and finite element analysis (FEA) simulations can be employed using abasic gapped core magnetic circuit with a coil of N turns. In this setup, the magnetic circuit's performance is evaluated based on the flux linkage of the coil under a fixed applied MMF, represented by a current i flowing through the coil.

[0072] Reluctance (ft) of a magnetic circuit component is given by the analytical approximation formula:

[0073] I

[0074] R = —

[0075]

[0076] |ii4

[0077] where I is the length of the magnetic path, p. is the magnetic permeability of the material, and A is the cross-sectional area of the magnetic flux path. A basic magnetic circuit illustrating these terms is presented in Figure 1.

[0078] The magnetomotive force (MMF) is given by

[0079] MMF = Ni

[0080] and the flux in the magnetic circuit is then given by:

[0081] MMF

[0082] 0 = T? - •'''total

[0083] Rfotal =

[0084] lc

[0085] Rc=

[0086] Il

[0087]

[0088] where lcis the length of the magnetic path in core, p. is the magnetic permeability of the material, and Acoreis the cross-sectional area of the magnetic path in the core. g is the airgap length and Agis the cross-sectional area of the air gap.

[0089] Flux Linkage: A Key Performance Indicator of Magnetic Circuits

[0090] To measure and evaluate the performance of electromagnetic systems, flux linkage is often used as a key indicator. Flux linkage ( ) combines the magnetic flux ( ) with the number of turns (N) in a coil.

[0091] = N(p

[0092] Substituting for the term of flux ( ) in above equation gives:N XMMF

[0093] (A)

[0094]

[0095] •^total

[0096] This shows that for a given number of turns in a coil and the applied MMF, the flux linkage depends on the reluctance of the magnetic path. Another representation of flux linkage is deduced by expanding the term MMF in previous equation

[0097] N x N x i

[0098] A = — - ' 'total

[0099] Whereas

[0100] N2

[0101] L

[0102]

[0103] =V •''' -total

[0104] So, the alternate formulation for flux linkage becomes

[0105] = Li (B)

[0106] where L is the inductance of the coil.

[0107] In circuits with airgaps, since the airgap reluctance dominates, the flux linkage is mainly influenced by the airgap reluctance. A lower airgap reluctance leads to a higher flux production and consequently higher flux linkage. Both representations of flux linkage give the same results and the choice among them depends on how you are measuring it. For simulations using numerical methods, equation (A) is utilized and for practical measurements, equation (B) is utilized.

[0108] Focusing on the airgap section of the core 1 , the basic concept of contouring the airgap 2 is illustrated in Figure 2. Figure 2 shows the front view of the area of interest (marked with dotted line in Figure 3), that is, the airgap 2 portion and is uniform in the third dimension. For reference purposes, the airgap 2 length g is given a value of 0.5mm here and is kept same for all the contour illustrations of triangular, sinusoidal and circular airgap profile.

[0109] Analytically, it is evident that while the reluctance of the core remains largely unchanged, the introduction of a contoured airgap results in a decreased airgap reluctance due to the increased surface area. This reduction in reluctance leads to a higher flux linkage in the coil for the same applied MMF, indicating an improvement in the magnetic circuit's performance.

[0110] FEA simulations can be utilized to further validate this effect by comparing the fluxlinkage in circuits with straight and contoured airgap profiles for various values of contour amplitude and the coil current.

[0111] The magnetic circuit utilized for the current FEA analysis is shown in Figure 3. The shape and dimensioning of the magnetic circuit is done to uniformly distribute the flux in the airgap 2 and the magnetic core 1 components adjacent to the airgap 2. Figure 4 presents the coil flux linkage versus input coil current for core material with constant magnetic permeability, for straight airgap profile in comparison with the varying amplitudes of triangular, sinusoidal and circular airgap profiles. The simulations demonstrate that the contoured design enhances the magnetic flux path’s permeability, leading to improved performance indicator, that is, flux linkage without necessitating an increase in the magnetic circuit’s overall size.

[0112] DETAILED ANALYSIS OF THE CONTOURED AIRGAP TOPOLOGY

[0113] Limitations of Contour Amplitude in Circular Profiles

[0114] The effectiveness of contoured airgap profiles in reducing magnetic reluctance and enhancing the performance of electrical machines depends on several interrelated factors. Concerning the shape of the contour profile, one significant observation is the limitation on the amplitude of the contour, particularly in circular profiles. In these profiles, the amplitude, defined by the radius of the circular shape, cannot be increased beyond half the width of the core limb.

[0115] On Figure 3 the width of the core limb in the reference region of interest is 5mm leading to the constraint that the amplitude of the circular profile cannot be increased beyond half the length of this, that is in this reference example, 2.5mm.

[0116] This geometric constraint inherently limits the potential increase in airgap surface area achievable through contouring. Designers must consider this limitation when selecting the contour amplitude to optimize performance.

[0117] Non-proportional Relationship Between Airgap Surface Area and Flux Linkage

[0118] Furthermore, when examining the results closely, even with core materials exhibiting very high and constant magnetic permeability against the applied magnetomotive force (MMF), the gains in flux linkage are not directly proportional tothe increase in airgap surface area. For instance, an increase of 20% in airgap surface area does not necessarily translate to a 20% increase in flux linkage; the actual gain is somewhat lower.

[0119] This discrepancy arises because, although the overall reluctance of the core remains largely unchanged, the cross-sectional area of the core decreases in the immediate vicinity of the contour due to the shaping of the core faces. This fact is illustrated in Figure 5.

[0120] This reduction increases the local core reluctance, partially offsetting the potential gains from the increased airgap surface area. The impact of this effect is a function of the contour amplitude. The amplitude of the contour significantly affects the core's reluctance. As the contour amplitude increases, the reduction in the core's cross-sectional area near the airgap becomes more pronounced. This reduction leads to an increase in local core reluctance, especially in the immediate vicinity of the contoured airgap.

[0121] Thus, while a higher contour amplitude can decrease airgap reluctance by increasing surface area, it can simultaneously increase core reluctance due to the decreased cross-sectional area of the magnetic path inside the core components. This trade-off must be carefully balanced to optimize the overall performance of the magnetic circuit, which has been ignored in a prior art.

[0122] Impact of Contouring Strategy on Airgap Thickness

[0123] The geometrical shape of the core faces adjacent to the airgap is crucial in determining the performance gains from contoured airgap profiles. It is essential to maintain a consistent airgap thickness in the direction of the magnetic flux flow, to achieve the best and most uniform airgap reluctance distribution. This uniformity ensures that the magnetic field is evenly distributed across the airgap, minimizing localized flux density peaks that could lead to saturation or increased losses.

[0124] Achieving a uniform airgap thickness necessitates a specific contouring strategy. Starting from a straight airgap profile, a guide profile line is established at the midpoint of the airgap thickness. This line is then offset by half the airgap thickness (g / 2) on both sides to define the airgap-facing surfaces of the core components. This method ensures that the direct, or normal distance between the airgap-facingcomponents remains uniform in the direction of the magnetic flux flow in the airgap.

[0125] Contouring Strategy

[0126] Defining the contour mathematically is essential for precise implementation. Mathematical eguations representing the contour shapes, such as triangular, sinusoidal and circular profiles are given below along with the implementation strategy.

[0127] The contour in the airgap profile will be introduced in the general direction of flow of flux in the adjacent core components. As part of the air gap contouring strategy, a central contour guideline is established at the mid-height of the air gap based on specified geometrical eguations that follow. To maintain uniformity, the contour is offset by g / 2 on either side, ensuring a consistent direct / normal distance between the offset lines. These offset lines subseguently define the surfaces of the core components adjacent to the air gap.

[0128] The conditional geometric eguations defining the central airgap contour are as follows and are illustrated in Figure 6. The illustration of Figure 6 is relative and shows the cross-sectional view of the airgap forming component in a magnetic circuit, where x, y and z axes represent the first, second and third dimension and can be modified / interchanged according to the specific design plane.

[0129] In the eguations below,

[0130] x±is the starting point of the core component, defining the starting point of airgap in first axis,

[0131] x2is the edge-point of the core component defining the end point of the airgap in the first axis,

[0132] y0is the midpoint of airgap thickness in the second axis,

[0133] is the amplitude of the central-guide contour profile,

[0134] r is the radius of the circular contour profile.

[0135] The eguations are presented in x and y axis parameters where the contour is introduced in the direction of flow of flux i.e. perpendicular / normal to the direction of flow of flux.

[0136] Whereas, the third dimension, i.e. z-axis can be uniformly straight or curved,according to the electromagnetic device’s specific topology.

[0137] Triangular airgap contour

[0138] , 9 > Oi + x2)

[0139] X1 < X < - - - y = y°+2 + 5—

[0140] 9 ?Ac fri + x2) - 7. - < X < x2

[0141]

[0142] Sinusoidal airgap contour

[0143] f a n(x - xt) y0K

[0144]

[0145] 7o +2+^Sm— M1 < AC< ~ Circular airgap contour

[0146]

[0147] Figure 7 presents the implemented contour profiles for various magnitudes of contour amplitudes according to the previously defined contouring strategy, the respective FEA simulation results for the flux flow in the core material and the airgap. The flux lines shown in individual FEA plots demonstrate the efficacy of the current contouring strategy in ensuring the uniform airgap thickness, through the uniform distribution of flux lines throughout the airgap profile.

[0148] Influence of Magnetic Material Properties

[0149] Up to this point, the analysis has considered core materials with constant magnetic permeability. However, practical magnetic core materials exhibit non-linear magnetic permeability that varies with the applied MMF. At higher MMFs, the magnetic core material begins to saturate, leading to an increase in core reluctance. This effect is particularly pronounced in regions near the contoured airgap, where the core cross-sectional area is reduced due to the contouring. The localized saturation in these areas increases the core reluctance, which can significantly limit the gains from the decreased airgap reluctance, especially at higher contouramplitudes.

[0150] Finite element analysis (FEA) simulations can be utilized to demonstrate this effect by comparing the flux linkage in circuits with straight and contoured airgap profiles for different values of coil current using practical core materials, such as M400-50A. The coil flux linkage versus input coil current for M400-50A core material with nonlinear magnetic permeability, for straight airgap profile in comparison with the varying amplitudes of triangular, sinusoidal and circular airgap profiles is presented in Figure 8.

[0151] The simulations show that at higher levels of applied MMF, the core saturation in the immediate vicinity of the contoured airgap becomes more significant. This increased core reluctance in these regions partially offsets the benefits gained from the increased airgap surface area, reducing the overall performance gains from contouring.

[0152] This observation underscores that the gains from any contour shape and its respective amplitude are a function of the magnetic circuit's operating point. At lower values of applied MMF, the gains are more substantial, while at higher MMFs, the benefits diminish.

[0153] This dependency on the operating point implies that the contour shape and amplitude need to be optimized according to the specific operating conditions of the magnetic circuit or electrical machine. The proposed design strategy involves iteratively increasing the contour amplitude from a minimal value to an optimal one, assessing the performance gains at each increment. This iterative process continues until the maximum gains in flux linkage are achieved at the selected operating point without causing excessive core saturation.

[0154] In conclusion, the implementation of contoured airgap profiles requires a comprehensive strategy that includes defining the contour mathematically, ensuring a uniform airgap thickness through precise offsetting, and optimizing the contour amplitude based on the magnetic circuit's operating point. Only by balancing these factors, it is possible to enhance the energy conversion efficiency and increasing power density without increasing the electrical machine’s mass / volume.

[0155] The practical realization of these contoured airgap profiles is facilitated by advanced manufacturing technologies, such as additive manufacturing (3D printing). Thistechnology allows for the precise fabrication of complex geometries required for the contoured profiles, overcoming the limitations imposed by conventional manufacturing methods, which might involve increased complexity and cost when producing such shapes. While it is possible to achieve these profiles with traditional manufacturing techniques, additive manufacturing offers greater flexibility and precision, making it a more efficient and practical solution.

[0156] By adopting this innovative approach, electrical machine designers can effectively reduce airgap reluctance, improve magnetic flux production against a given MMF, and enhance the overall performance of the machine. This advancement provides a significant opportunity to develop more efficient and power dense electrical machines, meeting the ever-increasing demands for higher performance in various applications.

[0157] APPLICATION OF CONTOURED AIRGAP TOPOLOGY TO AXIAL FLUX ELECTRICAL MACHINES

[0158] The magnetic circuit structure developed based on the analytical and simulation results described earlier is applied to a dual-rotor axial flux electrical machine, as detailed below.

[0159] An example of the present invention is an axial flux motor, though the contoured airgap topology is equally applicable to the generators and other electromagnetic devices requiring an airgap, be it an axial flux or a radial flux electrical machine, including, among other things, a single stator-single rotor, a multi stator-multi rotor and an outer rotor or an inner rotor configuration.

[0160] The axial flux motor comprises a rotor and a stator arranged along a common rotational axis. The rotor is configured to rotate about the axis, while the stator remains stationary.

[0161] Next references are made to Figures 9a, 9b and 9c illustrating the structure of a conventionally designed dual rotor, single stator axial flux motor. The rotor consists of a series of rotor-side magnetic poles (these magnetic poles could be made from permanent magnets (PM) for PM machines and from magnetic core material, for reluctance machines or wound rotor machines) distributed circumferentially around the axis. Similarly, the stator features stator-side magnetic poles aligned with therotor poles across the airgap.

[0162] The rotor and stator are constructed from soft magnetic composite materials or laminated steel to minimize eddy current losses, depending on manufacturing preferences. The magnetic poles could be made from permanent magnets (PM) for PM machines and from magnetic core material, for reluctance machines or wound rotor machines.

[0163] Implementation of the Contoured Airgap

[0164] As illustrated in Figures 10a and 10b, the facing surfaces of the rotor-side magnetic poles 4 and stator-side magnetic poles 5 are contoured according to the strategies outlined previously. The contours are introduced axially, increasing the effective airgap surface area and increasing power density without increasing the electrical machine’s mass / volume.

[0165] Figure 10b provides a cross-sectional view along line B-B' in Figure 10a, showing the alignment of the rotor and stator poles with the contoured airgap between them. The airgap thickness g remains constant across the contour due to the precise offsetting method described earlier, ensuring uniform magnetic flux distribution. Figure 11a depicts a cross-section of the radial flux motor, where on Figures 11b and 11c are depicted respectively a radial flux motor with straight airgap 2 and contoured airgap 2 profile in a cross-sectional view at the line F-F shown on Figure 11a. In figure 11 c, the airgap 2 thickness g remains constant across the contour due to the precise offsetting method described earlier, ensuring uniform magnetic flux distribution.

[0166] Design Considerations and Variations

[0167] The contours applied to the airgap-facing surfaces can adopt various mathematical profiles, such as sinusoidal, triangular, or circular shapes, as defined in the earlier mathematical expressions. The selection of the contour shape and amplitude depends on the desired performance characteristics and operating conditions.

[0168] In the embodiment shown, a sinusoidal contour is utilized with an amplitude optimized based on the motor's operating point. The optimization process involvesiteratively adjusting the contour amplitude and assessing the performance gains through simulation and experimental validation.

[0169] Manufacturing and Material Considerations

[0170] The rotor and stator can be fabricated using additive manufacturing techniques, such as 3D printing, to accurately produce complex contoured geometries. Alternatively, conventional manufacturing methods can be adapted, though they may involve increased complexity.

[0171] Materials with suitable magnetic properties, such as soft magnetic composites or high-permeability steel laminations, are selected to complement the contoured design. These materials help mitigate core saturation effects, particularly in regions where the cross-sectional area is reduced due to contouring.

[0172] Applicability to Other Devices

[0173] While the example provided focuses on an axial flux motor, the contoured airgap topology is equally applicable to other electromagnetic devices, including axial flux generators and transformers. The principles of increasing the airgap surface area to reduce reluctance and enhance performance remain consistent across radial flux topology in electrical machines too.

[0174] REFERENCE SIGNS LIST

[0175] 1 core

[0176] 2 airgap

[0177] 3 coil

[0178] 4 rotor-side magnetic pole

[0179] 5 stator-side magnetic pole

[0180] 6 stator winding

[0181] 7 shaft

[0182] 8 rotor back iron

[0183] 9 rotor

[0184] 10 stator

Claims

AMENDED CLAIMSreceived by the International Bureau on 15 April 2026 (15.04.26)AMENDED CLAIMS (PCT art 19)1. A method for contouring an airgap profile in an electromagnetic device comprising an airgap in a magnetic path to reduce airgap reluctance,characterized byprofiling the airgap such that the airgap profile corresponds to a contour of the guide profile line between the opposite faces forming the airgap between them at the midpoint of the airgap thickness taken perpendicular to said guide profile line, where said guide profile line lies in plane containing x and y axes,where x, y and z axes represent the first, second and third dimension, where x-axis is perpendicular to the general direction of flux flow in the magnetic path in the vicinity of said airgap, y-axis is in the general direction of the flux flow in said magnetic path and z-axis perpendicular both with x and y-axes,where the airgap-facing surface profiles of the core components are offset by half the airgap thickness (g / 2) perpendicular to said guide profile line on both sides of said guide profile line to define the airgap-facing surfaces of the core components such that the normal distance between the airgap-facing components remains uniform and a distribution of flux lines throughout the airgap profile are both uniform, and a shape of said airgap guide profile line is sinusoidal and corresponds to the following conditionsg - xx) y0y= y0+^-+ Acsin-r- - 0.01 < Ac<<IMG file=null he=null id=imgf000023_0001 img-content=null img-format=null inline=null orientation=null wi=null>y y° 2c(x2-X1)c2 whereX1is the starting point of the core component, defining the starting point of airgap in first axis,x2is the edge-point of the core component defining the end point of the airgap in the first axis,y0is the midpoint of airgap thickness in the second axis,ACis the amplitude of the central-guide contour profile.

2. The method according to claim 1, characterized in that, said electromagnetic device is an axial flux electrical machine, a radial flux electrical machine, a linear electrical machine, or an air-gapped transformer or inductor.

3. An electromagnetic device comprising a contoured airgap in a magnetic path to reduce airgap reluctance,characterized in thatthe airgap is profiled such that the airgap profile corresponds to a contour of the guide profile line between the opposite faces forming the airgap between them at the midpoint of the airgap thickness taken perpendicular to said guide profile line, where said guide profile line lies in plane containing x and y axes,where x, y and z axes represent the first, second and third dimension, where x-axis is perpendicular to the general direction of flux flow in the magnetic path in the vicinity of said airgap, y-axis is in the general direction of the flux flow in said magnetic path and z-axis perpendicular both with x and y-axes,where the airgap-facing surface profiles of the core components are offset by half the airgap thickness (g / 2) perpendicular to said guide profile line on both sides of said guide profile line to define the airgap-facing surfaces of the core components such that the normal distance between the airgap-facing components remains uniform and a distribution of flux lines throughout the airgap profile are both uniform, and a shape of said airgap guide profile line is sinusoidal and corresponds to the following conditionsg - xx) y0y= y0+^-+ Acsin-r- - 0.01 < Ac<<IMG file=null he=null id=imgf000024_0001 img-content=null img-format=null inline=null orientation=null wi=null>y y° 2c(x2-X1)c2 whereX1is the starting point of the core component, defining the starting point of airgap in first axis,x2is the edge-point of the core component defining the end point of the airgap in the first axis,y0is the midpoint of airgap thickness in the second axis,ACis the amplitude of the central-guide contour profile.

4. The device according to claim 3, characterized in that, said electromagnetic device is an axial flux electrical machine, a radial flux electrical machine, a linear electrical machine, or an air-gapped transformer or inductor.

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