Halbach array axial flux motor and analytical method thereof

Abstract

The application discloses a Halbach array axial flux motor and an analytic method thereof. The motor is a double-stator single-rotor motor, and a magnetic pole array is arranged between each stator and the rotor, and the magnetic pole array comprises a plurality of magnetic poles. φ In the analytic method, a subdomain model method is used to divide subdomains, and a general expression of a scalar magnetic potential of three subdomains is calculated φ General expressions of a radius r , a circumferential angle θ and an axial height z , and general expressions of a magnetic field intensity H and a magnetic flux density B are solved; then, Carter coefficients are introduced to calculate an equivalent air gap g e as an actual effective air gap; finally, an expression of the magnetic flux density B is recalculated according to the actual effective air gap length, and counter electromotive forces and electromagnetic torques of each phase in the coil are calculated according to the electromagnetic induction law.

Description

Technical Field

[0001] This invention relates to the field of axial flux permanent magnet motors, specifically a Heilbeck array axial flux motor and its analytical method. Background Technology

[0002] The stator and rotor of an axial flux permanent magnet motor are arranged along the axial direction. Therefore, axial flux permanent magnet motors have a more compact axial structure, higher torque density, greater power density, and low loss and high efficiency. They are widely used in aerospace, defense, transportation, industrial and agricultural production and public life.

[0003] The axial flux permanent magnet motor employing a Halbach pole array is a type of axial flux permanent magnet motor. Compared to traditional surface-mounted pole arrays, motors using Halbach pole arrays offer significant advantages. The air gap magnetic field tends to have a sinusoidal distribution, reducing rotor magnetomotive force harmonic content and thus effectively reducing torque pulsation and cogging torque. The motor's air gap side exhibits unilateral magnetic focusing properties, increasing the motor's back EMF coefficient. The rotor side significantly reduces magnetic saturation, thus effectively reducing the motor's size and weight while increasing torque and power density.

[0004] Compared to two-dimensional analytical methods, three-dimensional analytical methods can more accurately simulate and analyze the electromagnetic field distribution and variations in axial flux motors. This includes modeling the electromagnetic interactions of the stator, stator windings, air gap, and permanent magnets in three-dimensional space. By establishing and analyzing using three-dimensional analytical methods, the electromagnetic performance of axial flux motors can be evaluated more accurately, and performance optimization and design improvements can be made.

[0005] Current research on dual-stator single-rotor axial flux motors is relatively limited, and their structures are quite simple. Although axial flux motors have been widely studied and used in some specific applications, research in the entire motor field is still in its early stages. Compared with traditional radial flux motors, axial flux motors produce higher average torque, but they also bring greater torque ripple, increasing noise and significantly impacting equipment use and the working environment. Therefore, there is still considerable room for improvement in motor topology. Analytical methods for axial flux motors are only applicable to slotless structures and cannot analytically model Halbach array structures with unequal thicknesses and different remanent magnetization materials. Furthermore, most methods simplify calculations by reducing the dimensionality of three-dimensional analysis, which is not suitable for all dual-stator single-rotor axial flux motors. Data processing is also complex, prone to significant errors, and the accuracy of calculation results is low. Summary of the Invention

[0006] This invention provides a Halbach array axial flux motor and its analytical method to solve the problems of insufficient torque density in existing axial flux motors, and the inapplicability of analytical methods to slotted structures and Halbach array structures with unequal thickness and different remanent magnetization materials.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A Helbeck array axial flux motor includes a dual-stator single-rotor motor. Both the stator and rotor are toroidal. The stator is used to wind coils. The two stators and the rotor are coaxially and linearly distributed, with the rotor located between the two stators. Each stator has multiple stator slots evenly distributed along the circumferential direction of the stator, and the slot openings all face the rotor. A Helbeck magnetic pole array is provided in the gap between each stator and the rotor. Each Helbeck magnetic pole array is composed of multiple circumferentially distributed magnetic poles. The multiple magnetic poles in each Helbeck magnetic pole array are evenly distributed, and the side of each magnetic pole facing the rotor is in close contact with the corresponding side of the rotor. An air gap is formed by the ring formed by the magnetic poles in each Helbeck magnetic pole array and the gap between the corresponding stator.

[0009] Each Helbeck pole array comprises three segments: a central permanent magnet, a clockwise permanent magnet adjacent to the clockwise side of the central permanent magnet, and a counterclockwise permanent magnet adjacent to the counterclockwise side of the central permanent magnet. The central, clockwise, and counterclockwise permanent magnets are all fan-shaped rings, and each pole's central, clockwise, and counterclockwise permanent magnets are coaxial with the rotor. The clockwise and counterclockwise permanent magnets of each pole span an angular phase. Similarly, the span angle of the intermediate permanent magnet is greater than that of the clockwise and counterclockwise permanent magnets, and the clockwise and counterclockwise permanent magnets are symmetrical about the central axis of the intermediate permanent magnet; the axial thickness of the clockwise and counterclockwise permanent magnets of each magnetic pole is half the axial thickness of the intermediate permanent magnet; the intermediate permanent magnet of each magnetic pole adopts a parallel magnetization method in the axial direction, and the magnetization angle of the clockwise and counterclockwise permanent magnets of each magnetic pole is the angle between the magnetization direction and the axial direction;

[0010] Each pair of adjacent magnetic poles in each circumferential direction is considered as a magnetic pole group. The magnetic flux path of each magnetic pole group starts from the first magnetic pole, passes through the air gap to the stator, then passes through the air gap from the stator to the second magnetic pole of the magnetic pole group, and then forms a closed loop with the first magnetic pole through the rotor core. The first magnetic pole in the magnetic flux path of each magnetic pole group is defined as the N pole and the second magnetic pole as the S pole, thus obtaining three segments of N pole and S pole.

[0011] Furthermore, the stator slots of the stator adopt a parallel slot structure.

[0012] Furthermore, the remanence of the central permanent magnet of each magnetic pole is 1.3T, and the remanence of the clockwise and counterclockwise permanent magnets is 1.1T.

[0013] An analytical method for the above-mentioned Heilbeck array axial flux motor includes the following steps:

[0014] Step 1: Determine the magnetic field strength H and scalar magnetic potential in the above analytical method for the axial flux motor of the Heilbeck array. The relationship between them;

[0015] Step 2: Using the precise subdomain model method, the region between the inner and outer radii of the rotor and between the upper and lower surfaces of the rotor axis and the interface between the air gap and the stator is divided into three annular cylindrical regions: an inner subdomain, an intermediate subdomain, and an outer subdomain.

[0016] The internal subdomain is an annular cylindrical region with the inner diameter of the rotor core and the inner diameter of the permanent magnets in the N and S poles as its inner and outer diameters, and the sum of the axial thickness of the N and S pole permanent magnets and the axial height of the air gap as its height.

[0017] The intermediate subdomain is an annular cylindrical region with the inner and outer diameters of the permanent magnets in the N and S poles as the inner and outer diameters of the domain, and the sum of the axial thickness of the permanent magnets in the N and S poles and the axial height of the air gap as the height.

[0018] The outer subdomain is an annular cylindrical region with the outer diameter of the permanent magnets in the N and S poles and the outer diameter of the rotor core as its inner and outer diameters, and the sum of the axial thickness of the permanent magnets in the N and S poles and the axial height of the air gap as its height.

[0019] Then, Poisson's equation and Laplace's equation in three-dimensional coordinate system are established for the three subdomains respectively, and the scalar magnetic potential of each subdomain in cylindrical coordinate system is obtained by using the method of separation of variables. The general solution expression;

[0020] Step 3: Since the remanence of the intermediate permanent magnets of each N-pole and S-pole in the intermediate subdomain is different from that of the clockwise and counterclockwise permanent magnets, the intermediate subdomain is further divided into intermediate subdomain 1 and intermediate subdomain 2. In each magnetic pole group, the intermediate domain formed by the intermediate permanent magnets of each N-pole and S-pole is intermediate subdomain 1, and the intermediate domain formed by the clockwise and counterclockwise permanent magnets of each N-pole and S-pole is intermediate subdomain 2. The axial and circumferential magnetization expressions of intermediate subdomain 1 and intermediate subdomain 2 are given respectively, and odd extension and even extension are performed on them respectively to establish the axial and circumferential double Fourier decomposition expressions of magnetization.

[0021] Step 4: Based on the interface connection conditions of Ampere's circuital law and the principle of magnetic flux continuity, solve for the coefficients of the double Fourier series components in the magnetic potential expression of each subdomain in Step 2 to obtain the scalar magnetic potential of each subdomain. General expressions for radius r, circumferential angle θ, and axial height z, and derived from the magnetic field strength H and magnetic flux density B in step 1 and the scalar magnetic potential. The relationship between these factors is used to calculate the general expression for the magnetic field strength H and magnetic flux density B;

[0022] Step 5: Due to the presence of stator slots, the general expression for the magnetic flux density B obtained in Step 3 is not accurate. Based on the principle of minimum magnetic reluctance, the Carter coefficient is introduced to calculate the equivalent air gap g. e As the actual effective air gap;

[0023] Step 6: Recalculate the expression for the magnetic flux density B based on the actual effective air gap length obtained in Step 5, and calculate the back electromotive force and electromagnetic torque of each phase in the coil according to the law of electromagnetic induction.

[0024] Furthermore, in step 3, the determination of odd and even extensions needs to be based on the general expression of magnetic flux density B in the three coordinates of the cylindrical coordinate system, as described in step 4. Specifically, this is represented by the radial component B. r and circumferential component B θ For odd extension, axial component B z Perform even extension.

[0025] Furthermore, in step 3, the Poisson equation and Laplace equation for the three-dimensional scalar magnetic potential in cylindrical coordinates are solved using the method of separation of variables to obtain the scalar magnetic potential of each subdomain in cylindrical coordinates. The general solution expression is obtained, and the interface connection conditions are derived from Ampere's circuital law and the principle of magnetic flux continuity. The coefficients of each double Fourier series component in the magnetic potential expression of each subdomain are then solved to obtain the scalar magnetic potential of each subdomain. General expressions for radius r, circumferential angle θ, and axial height z.

[0026] Compared with the prior art, the advantages of the present invention are:

[0027] In this invention, the Halbach array axial flux motor with unequal thickness and different remanence has the advantage of being a Halbach pole array with unequal axial thickness and different remanence compared to the traditional axial flux motor. The Halbach permanent magnet array is optimized, resulting in a higher torque density than the traditional axial flux motor. It also reduces torque ripple to a certain extent, thus solving the problem in the prior art of being unable to perform three-dimensional analysis of axial flux motors with Halbach arrays of unequal thickness and different remanence.

[0028] The analytical method of this invention takes into account the influence of the presence of stator slots on the back electromotive force and torque of the axial flux permanent magnet motor, and analyzes the electromagnetic characteristics of the motor more accurately. It is a general three-dimensional analytical method for dual-stator single-rotor axial flux permanent magnet motors. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the axial flux permanent magnet motor in Embodiment 1 of the present invention.

[0030] Figure 2 This is a 1 / 4 unfolded view of the axial flux permanent magnet motor in Embodiment 1 of the present invention, with the outer diameter of the permanent magnet body as the radius.

[0031] Figure 3 This is a structural diagram of the axial flux permanent magnet motor 1 with N and S poles in Embodiment 1 of the present invention.

[0032] Figure 4 This is the magnetic flux path diagram for calculating the effective air gap of the slot in Embodiment 2 of the present invention.

[0033] Figure 5 This is a comparative verification of the axial air gap magnetic flux density analysis method and finite element method for the axial flux permanent magnet motor designed by the method in Embodiment 2 of the present invention.

[0034] Figure 6 This is a comparative verification of the electromagnetic torque analysis method and finite element method for the axial flux permanent magnet motor designed by the method in Embodiment 2 of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] Example 1

[0037] like Figure 1 , Figure 2 As shown, this embodiment discloses a Heilbeck array axial flux motor, which is a dual-stator single-rotor motor, including a rotor 1, a stator 2, and a stator 3. Coils are wound on stators 2 and 3, and stators 2, 3, and rotor 1 are all toroidal. The two stators 2 and 3 and rotor 1 are coaxially and linearly distributed, with rotor 1 located between the two stators 2 and 3. The entire motor has an axial length of 38 mm and a rated speed of 3000 r / min.

[0038] Halbach pole arrays 4 are present between stator 2 and rotor 1, and between stator 3 and rotor 1. Stator 2 and stator 3 each have multiple stator slots 5 near the rotor surface. Each stator slot 5 is evenly spaced along the circumferential direction of the stator and includes an inner slot portion, a slot opening 6, and a slot transition portion 7. The slot openings 6 face the rotor 1. Air gaps 8 are formed between the Halbach pole arrays 4 and stators 2 and 3, respectively, with an axial height of 0.5 mm.

[0039] Each Halbach pole array 4 includes a central permanent magnet, a clockwise permanent magnet attached to the clockwise side of the central permanent magnet, and a counterclockwise permanent magnet attached to the counterclockwise side of the central permanent magnet. The central, clockwise, and counterclockwise permanent magnets are all fan-shaped rings, and all three are coaxial with the rotor 1. The clockwise and counterclockwise permanent magnets of each pole have the same span angle. The span angle of the intermediate permanent magnet is greater than that of the clockwise and counterclockwise permanent magnets, and the clockwise and counterclockwise permanent magnets are symmetrical about the central axis of the intermediate permanent magnet; the axial thickness of the clockwise and counterclockwise permanent magnets of each magnetic pole is half the axial thickness of the intermediate permanent magnet; the intermediate permanent magnet of each magnetic pole adopts a parallel magnetization method in the axial direction, and the magnetization angle of the clockwise and counterclockwise permanent magnets of each magnetic pole is the angle between the magnetization direction and the axial direction.

[0040] In this embodiment, the Halbach magnetic pole array 4 has a total of 20 magnetic poles. Each pair of adjacent magnetic poles in each circumferential direction is considered as a magnetic pole group. The magnetic flux path of each magnetic pole group starts from the first magnetic pole, passes through the air gap to the stator, and then passes through the air gap from the stator to the second magnetic pole of the magnetic pole group. Then, it forms a closed loop with the first magnetic pole through the rotor core. The first magnetic pole in the magnetic flux path of each magnetic pole group is defined as the N pole and the second magnetic pole as the S pole. This results in N poles and S poles composed of three permanent magnets of different thicknesses and different remanences, with a total of 10 pairs of N poles and S poles.

[0041] Since each of the 10 pairs of N-pole and S-pole pairs is repetitive, they will all be used in subsequent analysis. Figure 3 Taking a pair of N and S poles as an example for analysis. In this embodiment, each stator has 24 stator slots 5, thus forming a motor with a 20-pole, 24-slot structure.

[0042] In this embodiment, rotor 1, stator 2, and stator 3 are all made of 50WW470 silicon steel sheets. The inner and outer radii of rotor 1 are 25mm and 35mm respectively, and its axial thickness is 7mm.

[0043] Stator 2 and stator 3 have inner and outer radii of 26mm and 34mm respectively, and an axial thickness of 10mm. Stator slot 5 has an axial height of 7mm, a circumferential width of 5mm, and a radial depth of 8mm. Stator slot opening 6 has an axial height of 0.5mm and a circumferential width of 2mm. The stator slot transition portion 7 has an axial height of 0.5mm and an inclination angle of 18.43°. Each phase winding has 64 turns in series.

[0044] In this embodiment, 10 pairs of N poles and S poles are placed on the upper and lower surfaces of the rotor along the axial direction, respectively. Each pair of N poles and S poles consists of three permanent magnets of unequal thickness and different remanence. The N pole includes a clockwise permanent magnet 4.1, a middle permanent magnet 4.2, and a counterclockwise permanent magnet 4.3; the S pole includes a clockwise permanent magnet 4.4, a middle permanent magnet 4.5, and a counterclockwise permanent magnet 4.6. Since each pair of poles is repetitive, subsequent analytical processes will use... Figure 3 Let's take a pair of N and S poles as an example to illustrate.

[0045] In this embodiment, the permanent magnets under the N and S poles, the clockwise permanent magnets 4.1 and 4.4 and the counterclockwise permanent magnets 4.3 and 4.6 all have an axial thickness of 2.5 mm, a remanent magnetization of 1.1 T, and a span angle of 2.4°; the intermediate permanent magnets 4.2 and 4.5 have an axial thickness of 5 mm, a remanent magnetization of 1.3 T, and a span angle of 7.8°.

[0046] In this example, the magnetization angle of the clockwise permanent magnet 4.1 is the angle between the magnetization direction and the clockwise circumferential tangential direction, and the magnetization angle of the counterclockwise permanent magnet 4.3 is the angle between the magnetization direction and the counterclockwise circumferential tangential direction. The clockwise and counterclockwise permanent magnets 4.1 and 4.3 have symmetrical magnetization angles. In this embodiment, the magnetization angles of both the clockwise and counterclockwise permanent magnets are 27°.

[0047] In this embodiment, the middle permanent magnet is made of neodymium iron boron (N42M), and the two side permanent magnets are made of neodymium iron boron (N30M), with a relative permeability of 1.05.

[0048] Example 2

[0049] This embodiment discloses the analytical method for the Heilbeck array axial flux motor described in Embodiment 1, including the following steps:

[0050] Step 1: Establish the magnetic field strength H and scalar magnetic potential in the analytical model of the motor magnetic field. The relationship between them can be represented as:

[0051]

[0052] Expanded to:

[0053]

[0054] The relationship between magnetic flux density B, magnetic field strength H, and magnetization M in the analytical model of the electric motor's magnetic field can be expressed as:

[0055] B=μ0μ r H+μ0M (3)

[0056] Expanded to:

[0057]

[0058] In the formula: μ0 is the free permeability, μ r is the relative permeability.

[0059] Step 2: Using the precise subdomain model method, the region between the inner and outer radii of the motor rotor, and between the upper and lower surfaces of the rotor axis and the interface between the air gap and the stator, is divided into three annular cylindrical regions: an inner subdomain, a middle subdomain, and an outer subdomain. Wherein:

[0060] The internal subdomain is an annular cylindrical region with the inner diameter of the rotor core and the inner diameter of the permanent magnets in the N and S poles as its inner and outer diameters, and the sum of the axial thickness of the N and S pole permanent magnets and the axial height of the air gap as its height.

[0061] The intermediate subdomain is an annular cylindrical region with the inner and outer diameters of the permanent magnets in the N and S poles as the inner and outer diameters of the domain, and the sum of the axial thickness of the permanent magnets in the N and S poles and the axial height of the air gap as the height.

[0062] The outer subdomain is an annular cylindrical region with the outer diameter of the permanent magnets in the N and S poles and the outer diameter of the rotor core as its inner and outer diameters, and the sum of the axial thickness of the permanent magnets in the N and S poles and the axial height of the air gap as its height.

[0063] Then, Poisson's equation and Laplace's equation in a three-dimensional coordinate system are established for the three subdomains, and the scalar magnetic potential of each subdomain in a cylindrical coordinate system is obtained by using the method of separation of variables. The general solution expression is as follows:

[0064] (2.1) Establishment of the subdomain model

[0065] 1) The internal subdomain is an annular cylindrical domain with the rotor inner diameter R1 and the inner diameter r1 of the N and S pole permanent magnets as its inner and outer diameters, and the sum of the axial thickness h1 of the N and S pole permanent magnets and the axial height g of the air gap (both axial thickness and axial height are measurements in the axial direction of the motor, and since the N and S pole permanent magnets are adjacent to the air gap, h1+g is the distance from the stator to the rotor in the axial direction of the motor).

[0066]

[0067] 2) Since the intermediate subdomain contains Halbach pole arrays of different thicknesses and unequal remanence, the intermediate subdomain is further subdivided into intermediate subdomain 1 and intermediate subdomain 2, wherein:

[0068] Intermediate subdomain 1 is a ring-shaped cylindrical domain with inner diameter r1 and outer diameter r2 of the intermediate permanent magnet (4.2 and 4.5 mm) of the N-pole and S-pole as its inner and outer diameters, and the sum of the axial thickness h1 of the intermediate permanent magnet and the axial height g of the air gap as its height.

[0069]

[0070] Intermediate subdomain 2 is defined by the inner and outer diameters r1 and r2 of the clockwise and counterclockwise permanent magnets 4.1, 4.3, 4.4, and 4.6 of the N and S poles, respectively. The axial thicknesses of the permanent magnets 4.1, 4.3, 4.4, and 4.6 on the clockwise and counterclockwise sides of the N and S poles are also defined. The annular cylindrical region whose height is the sum of the axial height of the air gap and g:

[0071]

[0072] The axial height of the air gap refers to its length along the axial direction of the motor. Both axial thickness and axial height are measurements along the axial direction of the motor. Since the N-pole and S-pole permanent magnets are adjacent to the air gap, h1+g is the distance from the stator to the rotor along the axial direction of the motor. The superposition here is because the relative permeability of the permanent magnets and the air gap air are approximately equal. Therefore, the N-pole and S-pole permanent magnets and the corresponding air gap air above them are divided into a single region to facilitate the subsequent analysis of boundary conditions.

[0073] 3) The outer subdomain is an annular cylindrical domain with the outer diameters r2 of the N-pole and S-pole permanent magnets and the outer diameter R2 of the rotor as its inner and outer diameters, and the sum of the axial thickness h1 of the N-pole and S-pole permanent magnets and the axial height g of the air gap as its height:

[0074]

[0075] (2.2) Establishment and solution of Poisson equation and Laplace equation in three-dimensional coordinate system

[0076]

[0077] In the formula: M is the magnetization intensity. It is a scalar magnetic potential.

[0078] Using the separation of variables method for the Poisson equation, let Simplifying, we get:

[0079]

[0080] In the formula: f(r), g(θ), and h(z) are assumed to be equations containing only r, θ, and z as independent variables.

[0081] Solving the partial differential equation (10) yields:

[0082]

[0083]

[0084] In the formula: C, D, E, F, G, J, u, and v are all unknown coefficients.

[0085] Due to scalar magnetic potential It has periodicity and symmetry, and can be simplified by equation (13):

[0086]

[0087] In the formula: p is the number of magnetic pole pairs, z g =h1+g.

[0088] The general solutions of the Poisson equation and the Laplace equation for the inner subdomain, intermediate subdomain, and outer subdomain are obtained respectively:

[0089]

[0090] In the formula: C mn D mn E mn F mn G mn J mn The unknown coefficients of the scalar magnetic potential can be obtained by solving the matrix equations when applying the analytical boundary conditions. mn K mn This is a Bessel function.

[0091]

[0092] Where: m = 1, 2, 3…, n = 1, 2, 3…, M rmn M θmn M zmn Let M be the component of the magnetization intensity.

[0093] Step 3: Because the remanence of the intermediate permanent magnets of each N-pole and S-pole in the intermediate subdomain differs from that of the clockwise and counterclockwise permanent magnets, the intermediate subdomain is further divided into intermediate subdomain 1 and intermediate subdomain 2. Here, we take one pair of N-pole and S-pole as an example... Figure 3 As shown, intermediate subdomain 1 includes an intermediate permanent magnet 4.2 for the N pole and an intermediate permanent magnet 4.5 for the S pole. Intermediate subdomain 2 includes clockwise permanent magnets 4.1 and 4.4 for the N pole and counterclockwise permanent magnets 4.3 and 4.6 for the S pole. The structures of the remaining pole pairs are the same as these pole pairs. The axial and circumferential magnetization expressions for intermediate subdomain 1 and intermediate subdomain 2 are given respectively, and odd and even extensions are performed to establish the axial and circumferential double Fourier decomposition expressions for the magnetization, as follows:

[0094] Define the initial circumferential position θ = 0 as the axial centerline of the N-pole intermediate permanent magnet 4.2, with the counterclockwise direction as the positive direction; α is the ratio of the polar arcs of the N-pole and S-pole permanent magnets; β is the ratio of the intermediate permanent magnet 4.2 or 4.5 of the N-pole or S-pole permanent magnet to the three Halbach permanent magnet segments.

[0095] (3.1) Expressions for the axial and circumferential magnetization of the intermediate permanent magnets 4.2 and 4.5 in intermediate subdomain 1:

[0096]

[0097] Extending it with respect to the odd and even sides of the z=0 plane, the expression is:

[0098]

[0099] Where: M r11 M θ11 M z11 M represents the magnetization components of the intermediate permanent magnets 4.2 and 4.5 in intermediate subdomain 1; r12 M θ12 M z12 For M r11 M θ11 M z11 B represents the magnetization components after odd and even extensions. r2 The remanent magnetization of permanent magnets 4.2 and 4.5.

[0100] (3.2) Expressions for the axial and circumferential magnetization of the clockwise and counterclockwise permanent magnets 4.1, 4.3, 4.4, and 4.6 in intermediate subdomain 2:

[0101]

[0102] Extending it with respect to the odd and even sides of the z=0 plane, the expression is:

[0103]

[0104] Where: M r21 M θ21 M z21 M represents the magnetization components of the clockwise and counterclockwise permanent magnets 4.1, 4.3, 4.4, and 4.6 in the intermediate subdomain 2; r22 M θ22 M z22 For M r21 M θ21 M z21 B represents the magnetization components after odd and even extensions. r1 The remanent magnetization of the clockwise and counterclockwise permanent magnets are 4.1, 4.3, 4.4, and 4.6.

[0105] In the formula: B r1 and B r2 These are the remanent magnetizations of the two permanent magnets on the sides and the middle permanent magnet, respectively, and μ0 is the vacuum permeability.

[0106] (3.3) Solving for the circumferential and axial components of magnetization

[0107] Perform double Fourier decomposition on intermediate subdomain 1 and intermediate subdomain 2 respectively, and then superimpose the obtained magnetization expressions to obtain the total magnetization expression for the intermediate subdomain:

[0108] Intermediate subdomain 1:

[0109]

[0110] Intermediate subdomain 2:

[0111]

[0112] Double Fourier decomposition:

[0113]

[0114] Where: period When i=1, 2; n=0, When n≠0, λ mn =1. M θ1mn M z1mn These represent the total magnetization components in the θ and z directions of the intermediate subdomain 1, respectively; M θ2mn M z2mn These are the total magnetization components in the θ and z directions of the intermediate subdomain 2, respectively; M θ M z These are the total magnetization components in the θ and z directions of the intermediate subdomain, respectively;

[0115] Step 4: Based on the interface connection conditions of Ampere's circuital law and the principle of magnetic flux continuity, solve for the coefficients of the double Fourier series components in the magnetic potential expression of each subdomain in Step 2 to obtain the scalar magnetic potential of each subdomain. General expressions for radius r, circumferential angle θ, and axial height z, and derived from the magnetic field strength H and magnetic flux density B in step 1 and the scalar magnetic potential. Based on the relationship between them, the general expression for the magnetic field strength H and magnetic flux density B is calculated as follows:

[0116] (4.1) Boundary condition analysis at r = r1

[0117] r = r1, as the interface between the inner and intermediate subdomains, needs to simultaneously guarantee the radial component B of the magnetic flux density. r Equal circumferential and axial components H of magnetic field strength θ,z equal:

[0118]

[0119] Substituting equation (14) into equations (1) to (4) and simplifying, we get:

[0120]

[0121] (4.2) Boundary condition analysis at r = r2

[0122] r = r2, serving as the interface between the intermediate and outer subdomains, needs to simultaneously guarantee the radial component B of the magnetic flux density. r Equal circumferential and axial components H of magnetic field strength θ,z equal:

[0123]

[0124] Substituting equation (14) into equations (1) to (4) and simplifying, we get:

[0125]

[0126] (4.3) Boundary condition analysis at r = R1 and r = R2

[0127] r = R1 and r = R2 are the interfaces between the inner and outer subdomains and the air, respectively. It is necessary to simultaneously ensure the radial component B of the magnetic flux density. r All are 0:

[0128]

[0129] Substituting equation (14) into equation (4) and simplifying, we get:

[0130]

[0131] In the formula: 1,2,3 B r (r,θ,z) and 1,2,3 H θ,z (r, θ, z) represent the magnetic flux density and magnetic field strength components at the interface between the inner subdomain, the middle subdomain, and the outer subdomain, respectively; C mn D mn E mn F mn G mn J mn The unknown coefficients in the boundary conditions can be solved using equation (30).

[0132] (4.4) Scalar magnetic potential Analysis and solution of unknown coefficients

[0133] Combining equations (24), (26), and (28), we can obtain the result with unknown coefficient C. mn D mn E mn Fmn G mn J mn Let the system of six linear equations with variable A be the independent variable:

[0134]

[0135]

[0136] X = [C mn D mn E mn F mn G mn J mn ] T

[0137] The system of equations is in matrix form:

[0138] QX=Y (29)

[0139] Solving this problem yields the expressions for each coefficient:

[0140] X = Q -1 Y (30)

[0141] Substituting the coefficients into equations (14) and (1) to (4), the magnetic field strength H and magnetic flux density B are obtained, and the waveforms are as follows. Figure 5 As shown.

[0142] Step 5: Due to the presence of stator slots, the general expression for the magnetic flux density B obtained in Step 3 is not accurate. Here, based on the principle of minimum magnetic reluctance, the Carter coefficient is introduced to calculate the equivalent air gap g. e The actual effective air gap is as follows:

[0143] like Figure 4 As shown, based on the designed stator slot structure, there are five main magnetic circuit paths:

[0144] 1) Path a enters the stator teeth vertically through the air gap, and the path length is:

[0145] l1=g (31)

[0146] 2) Path b enters the stator slot sidewall from the slot opening via the air gap in an arc, with a path length of:

[0147]

[0148] 3) Path c passes perpendicularly through the air gap and the slot opening, and enters the inner wall of the transition section in an arc shape in the middle section connecting the main body of the slot and the slot opening. The path length is:

[0149]

[0150] 4) According to the principle of minimum magnetic reluctance, when the magnetic flux path is path d and path e, the circumferential width of the stator slot and stator slot opening will exceed the structure designed in this paper, so it will not be considered.

[0151] The permeability of each path is:

[0152]

[0153] The equivalent total permeability is equal to the sum of the permeabilities of each path:

[0154]

[0155] In the formula: P1, P2, and P3 are the permeabilities of paths a, b, and c; P e x is the equivalent permeability of the total path; α x β , respectively, represent the maximum radii of the arcs in paths b and c; l is the radial depth of the stator slot, and S1 is the surface area of ​​the stator teeth in path a.

[0156] So Figure 4 The Carter coefficient C of the stator slot structure shown s for:

[0157]

[0158] The axial air gap length of the unequal thickness magnetic poles is:

[0159]

[0160] In the formula: g1 is the air gap height from 4.2 and 4.5 in the intermediate permanent magnet of N pole and S pole to the surface of the stator slot, and g2 is the air gap height from 4.1, 4.3, 4.4 and 4.6 in the clockwise and counterclockwise permanent magnets of N pole and S pole to the surface of the stator slot.

[0161] The total effective air gap length is:

[0162]

[0163] Where: g e This represents the effective air gap when there is a slot.

[0164] Step 6: Recalculate the expression for the magnetic flux density B based on the effective air gap length obtained in Step 5, and calculate the back electromotive force and electromagnetic torque of each phase in the coil according to the law of electromagnetic induction, as follows:

[0165] The magnetic flux density B in the air gap is obtained from equation (4). z for:

[0166]

[0167] The magnetic flux linkage Ψ is:

[0168]

[0169] In the formula: N is the number of turns of the coil, α cp It is the span angle of the coil, and j is the j-th slot rotated counterclockwise from 0°.

[0170] The back electromotive force E is:

[0171]

[0172] The back electromotive force of the three phases is:

[0173]

[0174] Electromagnetic torque T e for:

[0175]

[0176] In the formula: E i These correspond to the back electromotive force of the i-th stator winding of the motor; E A,B,C and I A,B,C These represent the back electromotive forces and currents of A, B, and C, respectively; ω r It is the angular velocity of the rotor.

[0177] The waveforms of the analytical method and the finite element method for electromagnetic torque are compared as follows: Figure 6 As shown. (Through) Figure 6 It can be seen that the analytical method and the finite element waveform are consistent, which verifies the effectiveness of the analytical method in this invention. The analytical method can be used to perform analytical optimization design of the motor structure.

[0178] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. These embodiments are merely descriptions of preferred embodiments and are not intended to limit the scope or concept of the invention. The specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. Such combinations, as long as they do not violate the spirit of the present invention, should also be considered as part of this disclosure. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

[0179] This invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this invention and without departing from the design idea of ​​this invention, all modifications and improvements made by those skilled in the art to the technical solutions of this invention should fall within the protection scope of this invention. The technical content for which protection is sought in this invention has been fully described in the claims.

Claims

1. A method for analyzing a Hellbeck array axial flux motor, the Hellbeck array axial flux motor comprising a dual-stator single-rotor, wherein both the stator and rotor are toroidal, the stator is used for winding coils, the two stators and the rotor are coaxially and linearly distributed, and the rotor is located between the two stators, each stator is provided with multiple stator slots evenly distributed along the circumferential direction of the stator, and the slot openings of the stator slots all face the rotor, a Hellbeck magnetic pole array is provided in the gap between each stator and the rotor, each Hellbeck magnetic pole array is composed of multiple circumferentially distributed magnetic poles, the multiple magnetic poles in each Hellbeck magnetic pole array are evenly distributed, and the side of each magnetic pole facing the rotor is in close contact with the corresponding side of the rotor, and an air gap is formed by the ring formed by the magnetic poles in each Hellbeck magnetic pole array and the gap between the corresponding stator; Each Helbeck pole array comprises three segments: a central permanent magnet, a clockwise permanent magnet adjacent to the clockwise side of the central permanent magnet, and a counterclockwise permanent magnet adjacent to the counterclockwise side of the central permanent magnet. The central, clockwise, and counterclockwise permanent magnets are all fan-shaped rings, and each pole's central, clockwise, and counterclockwise permanent magnets are coaxial with the rotor. The clockwise and counterclockwise permanent magnets of each pole span an angular phase. Similarly, the span angle of the intermediate permanent magnet is greater than that of the clockwise and counterclockwise permanent magnets, and the clockwise and counterclockwise permanent magnets are symmetrical about the central axis of the intermediate permanent magnet; the axial thickness of the clockwise and counterclockwise permanent magnets of each magnetic pole is half the axial thickness of the intermediate permanent magnet; the intermediate permanent magnet of each magnetic pole adopts a parallel magnetization method in the axial direction, and the magnetization angle of the clockwise and counterclockwise permanent magnets of each magnetic pole is the angle between the magnetization direction and the axial direction; Each pair of adjacent magnetic poles in a circumferential direction forms a magnetic pole group. The magnetic flux path of each magnetic pole group starts from the first magnetic pole, passes through the air gap to the stator, then from the stator through the air gap to the second magnetic pole of the same magnetic pole group, and then forms a closed loop with the first magnetic pole through the rotor core. The first magnetic pole in the magnetic flux path of each magnetic pole group is defined as the N pole and the second magnetic pole as the S pole, thus resulting in three segments for each N and S pole. Its characteristic is: The analytical method for the Heilbeck array axial flux motor includes the following steps: Step 1: Determine the relationship between magnetic field strength H and scalar magnetic potential φ; Step 2: Using the precise subdomain model method, the region between the inner and outer radii of the rotor and between the upper and lower surfaces of the rotor axis and the interface between the air gap and the stator is divided into three annular cylindrical regions: an inner subdomain, an intermediate subdomain, and an outer subdomain. The internal subdomain is an annular cylindrical region with the inner diameter of the rotor core and the inner diameter of the permanent magnets in the N and S poles as its inner and outer diameters, and the sum of the axial thickness of the N and S pole permanent magnets and the axial height of the air gap as its height. The intermediate subdomain is an annular cylindrical region with the inner and outer diameters of the permanent magnets in the N and S poles as the inner and outer diameters of the domain, and the sum of the axial thickness of the permanent magnets in the N and S poles and the axial height of the air gap as the height. The outer subdomain is an annular cylindrical region with the outer diameter of the permanent magnets in the N and S poles and the outer diameter of the rotor core as its inner and outer diameters, and the sum of the axial thickness of the permanent magnets in the N and S poles and the axial height of the air gap as its height. Then, Poisson's equation and Laplace's equation in three-dimensional coordinate system are established for the three subdomains respectively, and the general solution expression of the scalar magnetic potential φ of each subdomain in cylindrical coordinate system is obtained by using the method of separation of variables. Step 3: Since the remanence of the intermediate permanent magnets of each N-pole and S-pole in the intermediate subdomain is different from that of the clockwise and counterclockwise permanent magnets, the intermediate subdomain is further divided into intermediate subdomain 1 and intermediate subdomain 2. In each magnetic pole group, the intermediate domain formed by the intermediate permanent magnets of each N-pole and S-pole is intermediate subdomain 1, and the intermediate domain formed by the clockwise and counterclockwise permanent magnets of each N-pole and S-pole is intermediate subdomain 2. The axial and circumferential magnetization expressions of intermediate subdomain 1 and intermediate subdomain 2 are given respectively, and odd extension and even extension are performed on them respectively to establish the axial and circumferential double Fourier decomposition expressions of magnetization. Step 4: Based on the interface connection conditions of Ampere's circuital law and the principle of magnetic flux continuity, solve the double Fourier series component coefficients in the magnetic potential expression of each subdomain in Step 2 to obtain the general expression of the scalar magnetic potential φ of each subdomain with respect to radius r, circumferential angle θ and axial height z. And through the relationship between magnetic field strength H and magnetic flux density B and scalar magnetic potential φ in Step 1, calculate the general expression of magnetic field strength H and magnetic flux density B. Step 5: Due to the presence of stator slots, the general expression for the magnetic flux density B obtained in Step 3 is not accurate. Based on the principle of minimum magnetic reluctance, the Carter coefficient is introduced to calculate the equivalent air gap g. e As the actual effective air gap; Step 6: Recalculate the expression for the magnetic flux density B based on the actual effective air gap length obtained in Step 5, and calculate the back electromotive force and electromagnetic torque of each phase in the coil according to the law of electromagnetic induction.

2. The analytical method for a Heilbeck array axial flux motor according to claim 1, characterized in that, The stator slots of the stator adopt a parallel slot structure.

3. The analytical method for a Heilbeck array axial flux motor according to claim 1, characterized in that, The residual magnetization of the central permanent magnet of each magnetic pole is 1.3T, and the residual magnetization of the clockwise and counterclockwise permanent magnets is 1.1T.

4. The analytical method for a Heilbeck array axial flux motor according to claim 1, characterized in that, In step 3, the determination of odd and even extensions needs to be based on the general expression of magnetic flux density B in the three coordinates of the cylindrical coordinate system, as described in step 4. Specifically, this is represented by the radial component B. r and circumferential component B θ For odd extension, axial component B z Perform even extension.

5. The analytical method for a Heilbeck array axial flux motor according to claim 1, characterized in that, In step 3, the Poisson equation and Laplace equation for the three-dimensional scalar magnetic potential in cylindrical coordinates are solved using the method of separation of variables. This yields the general expression for the scalar magnetic potential φ of each subdomain in cylindrical coordinates. Then, the interface connection conditions derived from Ampere's circuital law and the principle of magnetic flux continuity are used to solve for the coefficients of each double Fourier series component in the magnetic potential expression of each subdomain. This yields the general expression for the scalar magnetic potential φ of each subdomain with respect to radius r, circumferential angle θ, and axial height z.

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