A T-type Halbach plug-in axial flux motor and its analytical method

Abstract

The present invention discloses a T-type Halbach plug-in axial flux motor and an analytical method thereof. The motor structure is a double-stator single rotor, and a plug-in T-type Halbach magnetic pole array is provided between the rotor and each stator, and the magnetic pole array includes a plurality of magnetic poles. In the method, a subdomain model method is first used to divide the motor into three subdomains, and the magnetization intensity components of different subdomains are respectively given to establish a double Fourier decomposition expression of the total magnetization intensity. Secondly, according to the Poisson equation and the Laplace equation in a three-dimensional coordinate system, the separation of variables method is used to calculate the general solution expression of the scalar magnetic potential of each subdomain. Then, according to the interface connection condition of the Ampere circuit law and the flux continuity principle, the unknown coefficients in the scalar magnetic potential are solved, and based on the relationship between the magnetic field intensity and the magnetic flux density and the scalar magnetic potential, the general expressions of the magnetic field intensity and the magnetic flux density are calculated. Then, the Carter coefficient is introduced to correct the magnetic flux density to obtain the corrected magnetic flux density expression.

Description

Technical Field

[0001] The present invention relates to the field of axial flux permanent magnet motors, in particular to a T-type Halbach plug-in axial flux motor and an analysis method thereof. Background Art

[0002] Axial flux motors are highly efficient and reliable. Compared to traditional radial flux motors, axial flux motors utilize an axial flux design, which reduces magnetic resistance and energy loss. This results in higher efficiency, greater torque output within the same motor size, and a wider operating range, making them widely used in various fields, including industry, transportation, aerospace, and energy.

[0003] Although axial flux motors have been widely used in certain specific applications, research in the field of electric motors as a whole is still in its infancy. While axial flux motors produce higher average torque, they also produce greater torque ripple, which increases the noise of the motor equipment. Therefore, there is still significant room for improvement in motor topology, and it is necessary to improve existing axial flux motors. Currently, the main analytical methods for axial flux motors are dimensionality reduction and three-dimensional analytical methods. The dimensionality reduction method has the advantage of reducing the analytical calculation time of the model, but it also introduces relatively large calculation errors and has significant limitations. This method is not suitable for axial flux motors that require high computational accuracy. Although the three-dimensional analytical method has a more complex calculation model, it can effectively balance calculation time and accuracy, making it a more desirable analytical method. Currently, research on the three-dimensional analytical method is limited to analyzing surface-mount axial flux motor models and cannot analyze surface-mount three-dimensional axial flux motor models. The pole structure is relatively limited and is not suitable for slotted structures. Summary of the Invention

[0004] The present invention provides a T-type Halbach surface-mount axial flux motor and an analytical method thereof, so as to solve the problems of low magnetic flux density and large torque pulsation in the prior art axial flux permanent magnet motors; and the problem that the existing three-dimensional analytical method can only analyze the surface-mount motor model, is not suitable for the surface-mount structure, and can only calculate the fixed magnetic pole structure.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A T-type Halbach surface-inserted axial flux motor comprises a dual-stator single-rotor structure, wherein two stators and one rotor are coaxially distributed, the inner diameters and outer diameters of the rotor and the stator are correspondingly equal, and the rotor is located between the two stators, and each stator is provided with a plurality of stator slots on the axial end surface facing the rotor, and the plurality of stator slots of each stator are uniformly distributed at equal intervals along the circumferential direction on the corresponding axial end surface of the stator, and the rotor is provided with a plurality of T-type Halbach poles on the axial end surface facing each stator, each T-type Halbach pole is coaxial with the rotor, and the plurality of T-type Halbach poles on each axial end surface of the rotor are uniformly distributed at equal intervals along the circumferential direction, a Halbach pole array is formed by the plurality of T-type Halbach poles on each axial end surface of the rotor, and the axial end surface of each T-type Halbach pole facing the stator in the corresponding direction is flush with the corresponding axial end surface of the rotor, and an air gap is formed by the gap between each axial end surface of the rotor and the surface-inserted Halbach pole array and the stator in the corresponding direction;

[0007] Each T-shaped Halbach pole is composed of a middle permanent magnet, a counterclockwise permanent magnet located counterclockwise to the middle permanent magnet, and a clockwise permanent magnet located clockwise to the middle permanent magnet. The counterclockwise permanent magnet and the clockwise permanent magnet in each T-shaped Halbach pole have the same axial thickness, and the axial thickness of the middle permanent magnet is greater than the axial thickness of the counterclockwise permanent magnet and the clockwise permanent magnet, thereby forming a T-shaped Halbach pole in the axial direction.

[0008] In each T-type Halbach pole, the clockwise and counterclockwise permanent magnets have the same span angle, the clockwise and counterclockwise permanent magnets have the same magnetization angle, and both are angles between the magnetization direction and the axial direction. The magnetization angles of the clockwise and counterclockwise permanent magnets are symmetrical along the central axis of the middle permanent magnet. The span angle of the middle permanent magnet is smaller than the span angles of the clockwise and counterclockwise permanent magnets, and the middle permanent magnet is axially magnetized.

[0009] In the T-shaped Halbach magnetic pole array, two circumferentially adjacent T-shaped Halbach magnetic poles are used as a magnetic pole pair. The magnetic flux path of each magnetic pole pair is that the magnetic lines of force start from the first magnetic pole, pass through the air gap to the stator, then from the stator through the air gap to the second magnetic pole of the magnetic pole pair, and then return to the first magnetic pole through the rotor to form a closed loop. The first magnetic pole where the magnetic lines of force start in each magnetic pole pair is used as the north pole, and the second magnetic pole is used as the south pole.

[0010] Furthermore, each stator slot on the stator is a parallel slot structure.

[0011] Furthermore, in each T-shaped Halbach pole, the magnetization angles of the permanent magnet on the clockwise side and the permanent magnet on the counterclockwise side are both 42°.

[0012] Furthermore, in each T-shaped Halbach pole, the span angle of the middle permanent magnet is 3°, and the span angles of the clockwise permanent magnet and the counterclockwise permanent magnet are both 4.5°.

[0013] Furthermore, the outer diameter of each T-shaped Halbach pole is equal to the outer diameter of the rotor, and the inner diameter of each T-shaped Halbach pole is equal to the inner diameter of the rotor, so that the rotor and its surface-inserted T-shaped Halbach pole array form a complete ring.

[0014] An analytical method for the above-mentioned T-type Halbach plug-in axial flux motor includes the following steps:

[0015] Step 1: Using the precise subdomain model method, the area between the inner and outer radii of the rotor of the motor and between the upper and lower surfaces of the rotor axial direction and the interface between the air gap and the stator is divided into three annular cylindrical subdomains: the air domain, the upper magnetic pole domain, and the lower magnetic pole domain;

[0016] Step 2: Cut the N and S poles in each magnetic pole pair into odd numbers n according to the cylindrical surfaces of different radii. t The difference between the inner and outer radii of the fan-shaped magnetic poles is equal. t Calculate the fan-shaped magnetic poles separately;

[0017] Step 3: For the entire motor model, cut the rotor, stator, and T-type Halbach poles along the axial direction of the radius. After cutting, a rectangular linear motor model is obtained, in which the equivalent circumferential length is the circumference of the circle where the average radius is located, the equivalent width is the difference between the outer diameter and the inner diameter of the rotor, and the axial length remains unchanged. The circumferential direction is the x-axis direction, the width direction is the y-axis direction, and the axial direction is the z-axis direction.

[0018] Step 4: Perform odd, even and periodic extensions on different subdomains to establish the double Fourier decomposition expressions of the magnetization intensity of different subdomains and the general expressions of the scalar magnetic potential containing unknown coefficients;

[0019] Step 5: According to the interface connection conditions of Ampere's circuit law and the principle of magnetic flux continuity, solve the unknown coefficients in the expression of the scalar magnetic potential of each subdomain in step 4 to obtain the scalar magnetic potential of each subdomain. The general expressions for the x-axis, y-axis, and z-axis directions are based on the magnetic field intensity H, magnetic flux density B, and scalar magnetic potential. The relationship between the magnetic field intensity H and the magnetic flux density B is calculated to obtain the general expression;

[0020] Step 6: Based on the principle of minimum magnetic resistance, the Carter coefficient is introduced to correct the magnetic flux density B to obtain the corrected magnetic flux density expression.

[0021] Furthermore, in step 4, the determination of odd and even extensions needs to be determined based on the general expression of the magnetic flux density B under the three coordinate separation in step 5, which is specifically expressed as the x-axis direction component B x Do odd extension in the x-axis direction and periodic extension in the y-axis direction, and the z-axis component B z Perform even extension in the x-axis direction and periodic extension in the y-axis direction.

[0022] Furthermore, in step 5, the interface connection conditions derived from Ampere's circuit law and the principle of flux continuity are used to solve the unknown coefficients in the magnetic potential expression of each subdomain by establishing a matrix equation to obtain the scalar magnetic potential of each subdomain. The general expression of .

[0023] Furthermore, in step 2, the N and S poles of each magnetic pole pair are cut and in steps 3-6, the n t The scalar magnetic potential, magnetization intensity, magnetic flux density and magnetic field intensity are calculated for each group of T-type Halbach poles. The final magnetic flux density can be expressed as n t Linear superposition of the magnetic flux density generated by a set of T-type Halbach poles.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] Compared to traditional axial flux motors, the T-type Halbach surface-inserted axial flux motor in this invention utilizes a T-type Halbach pole array and a surface-inserted structure for its permanent magnets. While maintaining the same residual magnetization intensity per unit volume, the magnetization angle and span angle of the Halbach permanent magnet array are optimized. This results in a higher magnetic flux density and lower torque ripple than traditional axial flux motors, effectively utilizing the magnetic flux and improving the motor's torque performance. This also addresses the inability of existing three-dimensional analytical methods to analyze surface-inserted Halbach pole array structures. By introducing the Carter coefficient into the three-dimensional analytical calculations and adapting the analytical method to the three-dimensional surface-inserted structure, the results can be obtained for the case with slots. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a three-dimensional schematic diagram of the T-type surface-inserted axial flux motor structure in the first embodiment of the present invention.

[0027] Figure 2 It is a schematic diagram of a 1 / 4 expansion diagram of a cylinder with the outer diameter of the permanent magnet as the radius of the T-type surface-inserted axial flux motor in the first embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram of the geometric parameters of a pair of poles of a T-type surface-inserted axial flux motor in the first embodiment of the present invention.

[0029] Figure 4This is a comparative verification of the axial slotless air gap magnetic flux density of the T-type plug-in axial flux motor designed by the method of embodiment 2 of the present invention using the finite element method.

[0030] Figure 5 This is a comparative verification of the axial slotted air gap magnetic flux density of the T-type plug-in axial flux motor designed by the method of embodiment 2 of the present invention using the finite element method. DETAILED DESCRIPTION

[0031] The present invention will be further described below with reference to the accompanying drawings and examples.

[0032] Example 1

[0033] like Figure 1 As shown, this embodiment discloses a T-type Halbach plug-in axial flux motor, including a dual-stator single-rotor coaxial structure consisting of a rotor 1 and two stators 2. In the dual-stator single-rotor coaxial structure, the rotor 1 and the two stators 2 are coaxially distributed, and the rotor 1 is located between the two stators 2. The inner diameter and outer diameter of the rotor 1 are correspondingly equal to the inner diameter and outer diameter of the two stators 2.

[0034] Each stator 2 is provided with a plurality of stator slots 5 on the axial end surface facing the rotating shaft 1. The plurality of stator slots 5 are circumferentially and evenly spaced on the axial end surface of the stator 2. Each stator slot 5 includes a slot body, a stator slot opening 6, and a stator slot transition portion 7 connecting the slot body and the stator slot opening 6. The slot body, the stator slot opening 6, and the stator slot transition portion 7 of the stator slot 5 are all parallel slot structures, thereby forming a stator slot 5 with a parallel slot structure. The stator slot opening 6 of the stator slot 5 of each stator 2 faces the rotor 1.

[0035] In this embodiment, the rotor 1 and each stator 2 are made of 50WW470 silicon steel sheets. The inner and outer radii of the rotor 1 are 25mm and 35mm respectively, and the axial thickness is 7mm. The inner and outer radii of the stator 2 are 25mm and 35mm respectively, and the axial thickness is 10mm. The axial height of the stator slot 5 is 7mm, the circumferential width is 5mm, and the radial depth is 8mm. The axial height of the stator slot 6 is 0.5mm, the circumferential width is 2mm, the axial height of the stator slot transition part 7 is 0.5mm, the inclination angle is 18.43°, and the number of series turns of each phase winding is 64 turns. The axial length of the entire motor is 39mm, and the rated speed is 3000r / min.

[0036] A plurality of T-shaped Halbach poles 3 are installed on the axial end face of the rotor 1 facing each stator 2. Each T-shaped Halbach pole 3 is coaxial with the rotor. The plurality of T-shaped Halbach poles 3 on each axial end face of the rotor 1 are evenly distributed along the circumferential direction at equal intervals. A Halbach pole array is formed by the plurality of T-shaped Halbach poles 3 on each axial end face of the rotor 1.

[0037] The axial end face of each T-shaped Halbach pole 3 facing the corresponding stator direction is flush with the corresponding axial end face of the rotor 1. The outer diameter of each T-shaped Halbach pole 3 is equal to the outer diameter of the rotor 1, and the inner diameter of each T-shaped Halbach pole 3 is equal to the inner diameter of the rotor 1. As a result, the rotor and its surface-mounted T-shaped Halbach pole array form a complete ring. The gap between each axial end face of the rotor 1 and the surface-mounted Halbach pole array and the corresponding stator 2 forms an air gap 4.

[0038] Each T-shaped Halbach pole 3 consists of a center permanent magnet, a counterclockwise permanent magnet located counterclockwise of the center permanent magnet, and a clockwise permanent magnet located clockwise of the center permanent magnet. The counterclockwise and clockwise permanent magnets in each T-shaped Halbach pole 3 have the same axial thickness, while the center permanent magnet is thicker than the counterclockwise and clockwise permanent magnets, forming a T-shaped Halbach pole in the axial direction. The center permanent magnet and the counterclockwise and clockwise permanent magnets are all made of neodymium iron boron N30M, with a relative magnetic permeability of 1.05.

[0039] In each T-type Halbach pole 3, the span angle of the clockwise permanent magnet and the counterclockwise permanent magnet is the same, the magnetization angle of the clockwise permanent magnet and the counterclockwise permanent magnet is the same and both are the angles between the magnetization direction and the axial direction, and the magnetization angles of the clockwise permanent magnet and the counterclockwise permanent magnet are symmetrical along the central axis of the middle permanent magnet; the span angle of the middle permanent magnet is smaller than the span angle of the clockwise permanent magnet and the counterclockwise permanent magnet, and the middle permanent magnet is axially magnetized.

[0040] In a T-type Halbach magnetic pole array, two circumferentially adjacent T-type Halbach magnetic poles are regarded as a magnetic pole pair. The magnetic flux path of each magnetic pole pair is that the magnetic lines of force start from the first magnetic pole, pass through the air gap to the stator, then from the stator through the air gap to the second magnetic pole of the magnetic pole pair, and then return to the first magnetic pole through the rotor to form a closed loop. The first magnetic pole where the magnetic lines of force start in each magnetic pole pair is regarded as the north pole, and the second magnetic pole is regarded as the south pole.

[0041] like Figure 2As shown, in this embodiment, a certain magnetic pole pair is used as an example. The north pole of the magnetic pole pair includes a middle permanent magnet 3.2, a counterclockwise permanent magnet 3.1 located counterclockwise to the middle permanent magnet 3.2, and a clockwise permanent magnet 3.3 located clockwise to the middle permanent magnet 3.2. The south pole of the magnetic pole pair includes a middle permanent magnet 3.5, a counterclockwise permanent magnet 3.4 located counterclockwise to the middle permanent magnet 3.5, and a clockwise permanent magnet 3.6 located clockwise to the middle permanent magnet 3.5. In this embodiment, the axial thickness of the permanent magnets 3.1, 3.3, 3.4, and 3.6 on both sides is 3.9 mm, the residual magnetization is 1.1 T, the span angle is 4.5°, and the magnetization angle is 42°. The middle permanent magnets 3.2 and 3.5 have an axial thickness of 5 mm, a residual magnetization of 1.1 T, and a span angle of 3°.

[0042] In this embodiment, there are 10 sets of magnetic pole pairs, namely 10 sets of N poles and S poles. Since each set of magnetic pole pairs in the 10 pairs of N poles and S poles is repetitive, Figure 3 The analytical process for each set of magnetic pole pairs shown is the same. In this embodiment, each stator has a total of 24 stator slots 5, thereby forming an axial flux motor with a 20-pole 24-slot structure.

[0043] Example 2

[0044] This embodiment discloses a three-dimensional magnetic field analytical model of the T-type Halbach plug-in axial flux motor described in the first embodiment, including the following steps:

[0045] Step 1: Using the precise subdomain model method, the area between the inner and outer radii of the motor rotor and between the upper and lower axial surfaces of the rotor and the interface between the air gap and the stator is divided into three annular cylindrical subdomains: the air domain, the upper magnetic pole domain, and the lower magnetic pole domain; the details are as follows:

[0046] Air domain:

[0047]

[0048] Upper magnetic pole domain:

[0049]

[0050] Lower magnetic pole domain:

[0051]

[0052] Where: R1 and R2 are the inner and outer radii of the rotor respectively; h1 is the axial thickness of the middle permanent magnet; h2 is the difference in axial thickness between the middle permanent magnet and the permanent magnets on both sides; τ p is the span angle of the N pole or S pole; g is the axial height of the air gap; r is the radial direction coordinate variable; z is the axial direction coordinate variable; τ is the circumferential direction coordinate variable.

[0053] Step 2: Figure 3 As shown, the different sub-domains of the N and S poles of each magnetic pole pair are cut into odd numbers n according to the cylindrical surfaces of different radii. t The difference between the inner and outer radii of the T-type Halbach pole is equal. t Calculate the T-type Halbach poles separately. The details are as follows:

[0054] Based on the inner diameter of the rotor, the T-type Halbach poles cut along the radial direction to the outer diameter of the rotor are defined as the first group, the jth group to the nth group. t A set of sector-shaped magnetic poles, as follows:

[0055] (2.1) Upper magnetic pole domain

[0056] The first set of T-type Halbach magnetic pole range:

[0057]

[0058] The range of the jth group of T-type Halbach magnetic poles:

[0059]

[0060] nth t Halbach T-type magnetic pole range:

[0061]

[0062] (2.2) Lower magnetic pole domain

[0063] The first set of T-type Halbach magnetic pole range:

[0064]

[0065] The range of the jth group of T-type Halbach magnetic poles:

[0066]

[0067] …………

[0068] nth t Halbach T-type magnetic pole range:

[0069]

[0070] Among them, 1≤j≤n t .

[0071] Step 3: For the entire motor model, cut the rotor, stator, and T-type Halbach poles along the axial direction of the radius. After cutting, the resulting linear motor model has a rectangular parallelepiped structure with an equivalent circumferential length equal to the circumference of the circle containing the average radius, an equivalent width equal to the difference between the rotor's outer and inner diameters, and an unchanged axial length. The circumferential direction is the x-axis, the width is the y-axis, and the axial direction is the z-axis; the details are as follows:

[0072] In the original cylindrical coordinate system, assuming that the center axis of an N-pole is located at θ = 0, the motor model is split along the θ = 0 plane and unfolded along the circumferential direction. t The circumference of the circle formed by the average radius of the j-th magnetic pole group calculated in the group of T-type Halbach poles is used as the length of the unfolded cuboid, and the difference between the outer diameter and the inner diameter of the rotor is taken as the width of the unfolded cuboid. The axial length remains unchanged.

[0073] A spatial rectangular coordinate system is established with the positive circumferential direction of the original cylindrical coordinate system as the positive direction of the x-axis, the negative direction along the original radial direction as the positive direction of the y-axis, and the positive direction along the axial direction as the positive direction of the z-axis. The original θ=0 is defined as the zero point of the x-axis, the original rotor average radius is defined as the zero point of the y-axis, and the junction of the original magnetic pole and the rotor is defined as the zero point of the z-axis.

[0074] The average radius of the jth group of T-type Halbach poles can be written as:

[0075]

[0076] Step 4: Perform odd, even, and periodic extensions on different subdomains to establish the double Fourier decomposition expressions of the magnetization intensity of different subdomains and the general expressions of the scalar magnetic potential containing unknown coefficients. The process is as follows:

[0077] (4.1) Expression of magnetization intensity components in different subdomains

[0078] The axial centerline of the N-pole middle permanent magnet 3.2 is defined as the circumferential initial position θ=0, and the counterclockwise direction is the positive direction; α1 is the pole arc ratio of the upper magnetic pole domain permanent magnet; α2 is the pole arc ratio of the lower magnetic pole domain permanent magnet.

[0079]

[0080] Where: τ1 is the span angle of the middle permanent magnet; τ2 is the span angle of the T-type permanent magnet; 2τ p is the angle between a pair of poles of a permanent magnet.

[0081] Air domain:

[0082] Since there is no permanent magnet in the air domain, its magnetization intensity components are all 0.

[0083]

[0084] Where: and are the x-, y-, and z-axis components of the magnetization in the air domain, respectively.

[0085] Upper magnetic pole domain:

[0086] The upper magnetic pole region consists of three equal-thickness Halbach permanent magnet regions, whose magnetization intensity components and their odd and even extensions can be expressed as:

[0087]

[0088]

[0089]

[0090] Where: p is the number of motor pole pairs; and are the x-, y- and z-axis components of the magnetization intensity of the j-th group of magnetic poles in the upper magnetic pole domain; B r is the residual magnetization intensity; μ0 is the vacuum permeability; θ is the Halbach pole magnetization angle.

[0091] Lower magnetic pole domain:

[0092] The lower magnetic pole region is a permanent magnet region with conventional magnetization. Its magnetization intensity components and their odd and even extensions can be expressed as:

[0093]

[0094] Where: and are the x-, y-, and z-axis components of the magnetization intensity of the j-th group of magnetic poles in the lower magnetic pole domain, respectively.

[0095] (4.2) Solution of magnetization intensity in different subdomains

[0096] Upper magnetic pole domain:

[0097] In the rectangular domain S1(- 1 T x / 2≤x≤3 1 T x / 2,- 1 T y ≤y≤ 1 T y ) is subjected to double Fourier decomposition, and the magnetization intensity of the x-axis component and the y-axis component is in the form of:

[0098]

[0099] in:

[0100]

[0101] Where: 1 T x =α1πR j / p is the half period of the jth group of magnetic poles in the upper magnetic pole domain in the x-axis direction; 1 T y =R2-R1 is the half period of the magnetic pole in the y-axis direction; 1 M xmi j and 1 M zmi j are the coefficients of the double Fourier series of the x-axis component and the z-axis component of the magnetization intensity of the j-th group of magnetic poles in the upper magnetic pole layer in the x-axis direction and the y-axis direction respectively; ω m j is the periodic frequency of the magnetic pole in the y-axis direction; ω i j is the periodic frequency of the upper magnetic pole domain in the x-axis direction; m is a non-negative integer; i = 1, 3, 5, 7…

[0102] Lower magnetic pole domain:

[0103] In the rectangular domain S2(- 2 T y / 2≤x≤3 2 T y / 2,- 2 T y ≤y≤ 2 T y ) is subjected to double Fourier decomposition, and the magnetization intensity of the x-axis component and the y-axis component is in the form of:

[0104]

[0105] in:

[0106]

[0107] Where: 2 T x =α2πR j / p is the half period of the jth group of magnetic poles in the lower magnetic pole domain in the x-axis direction; 2 T y =R2-R1 is the half period of the magnetic pole in the y-axis direction; 2 M xmi j and 2 M zmi j are the coefficients of the double Fourier series of the x-axis component and the z-axis component of the magnetization intensity of the j-th group of magnetic poles in the lower magnetic pole domain in the x-axis direction and the y-axis direction respectively; ω n jis the periodic frequency in the x-axis direction of the air domain; ω q j is the periodic frequency of the lower magnetic pole domain in the x-axis direction; n = 1, 3, 5, 7…; q = 1, 3, 5, 7…

[0108] (4.3) Scalar magnetic potential Establishment and solution of Poisson and Laplace equations

[0109] The relative magnetic permeability of the permanent magnet is approximately 1. Based on the three regions in step 1, the Poisson equation and Laplace equation in its three-dimensional coordinate system can be expressed as:

[0110]

[0111] Where: Represents the scalar magnetic potential; μ r Represents relative magnetic permeability; M j A vector representing the magnetization.

[0112] According to the periodic symmetry, the above formula is simplified:

[0113]

[0114] Where: and They represent the scalar magnetic potential of the jth group of T-type Halbach poles in the air domain, the upper magnetic pole domain, and the lower magnetic pole domain, respectively.

[0115] The total scalar magnetic potential of different subdomains is obtained, and the expression is:

[0116]

[0117] in are variables, and have:

[0118]

[0119] Where: are the scalar magnetic potentials of the jth group of magnetic poles in the air domain, the upper magnetic pole domain, and the lower magnetic pole domain, respectively; A 1mn j 、A 2mi j and B 2mi j 、A 3mq j are the unknown coefficients of the scalar magnetic potential of the jth group of magnetic poles in the air domain, the upper magnetic pole domain, and the lower magnetic pole domain, respectively, which are defined by the subsequent boundary conditions.

[0120] Step 5: According to the interface connection conditions of Ampere's circuit law and the principle of magnetic flux continuity, solve the unknown coefficients in the expression of the scalar magnetic potential of each subdomain in step 4 to obtain the scalar magnetic potential of each subdomain. The general expressions for the x-axis, y-axis, and z-axis directions are based on the magnetic field intensity H, magnetic flux density B, and scalar magnetic potential. The relationship between the magnetic field intensity H and the magnetic flux density B is calculated to obtain the general expression;

[0121] Magnetic field intensity H, scalar magnetic potential in magnetic field The relationship between the magnetization density M and the magnetic flux density B can be expressed as:

[0122]

[0123] Where: H x 、H y and H z Represent the x-, y-, and z-axis components of the magnetic field intensity; B x 、B y and B z Represent the x-, y-, and z-axis components of the magnetic flux density; M x 、M y and M z represent the x-, y-, and z-axis components of the magnetization density, respectively.

[0124] (5.1) Boundary condition analysis

[0125] The boundary z=h1 is the interface between the air domain and the upper magnetic pole domain, and it is necessary to ensure that the z-axis component B of the magnetic flux density z and the x-axis and y-axis components of the magnetic field strength H x,y equal:

[0126]

[0127] Where: 1 B z j and 2 B z j are the z-axis components of the magnetic flux density in the air domain and the upper magnetic pole domain respectively; 1 H x,y j and 2 H x,y j are the x-axis and y-axis components of the magnetic field strength in the air domain and the upper magnetic pole domain, respectively.

[0128] Boundary z = h2 is the interface between the upper and lower magnetic pole domains, and it is necessary to ensure that the z-axis component B of the magnetic flux density z and the x-axis and y-axis components of the magnetic field strength Hx,y equal:

[0129]

[0130] Where: 3 B z j is the z-axis component of the magnetic flux density of the lower magnetic pole domain; 3 H x,y j are the x-axis and y-axis components of the magnetic field strength of the lower magnetic pole domain.

[0131] Combining equations (29), (31) and (32), and simplifying equations (33) and (34), we can obtain:

[0132]

[0133] (5.2) Solving the unknown coefficients of scalar magnetic potential and magnetic flux density

[0134] According to the orthogonality of trigonometric functions, equation (35) is simplified to the following matrix form:

[0135]

[0136] Where: C 1m j is an n×n matrix with respect to variables m and n; C 2m j and C 3m j is an n×i matrix with respect to variables m, n, and i; C 4m j is an n×q matrix with respect to variables m, n, and q; D 1m j and E 1m j is an i×n matrix with respect to variables m, n, and i; D 2m j 、D 3m j 、E 2m j and E 3m j is an i×i matrix of variables m and i; D 4m j and E 4m j is an i×j matrix of variables m, i, and q; F 1m j is a j×n matrix with respect to variables m, n, and q; F 2m j and F 3m jis a q×i matrix of variables m, i, and q; F 4m j is a q×q matrix with respect to variables m and q; G 1m j , G 2m j , G 3m j and G 4m j are i×1 matrices respectively; A 1m j 、A 2m j 、B 2m j and A 2m j are respectively i×1 order unknown coefficient matrices.

[0137] By solving the above matrix, the unknown coefficients of the scalar magnetic potential in each subdomain can be obtained.

[0138] The unknown coefficients obtained by solving equations (29), (31), (32) and (36) can be used to obtain the magnetic field intensity H of the j-th group of magnetic poles. j and magnetic flux density B j , n t The magnetic flux density B generated by the magnetic pole group j The magnetic flux density B generated by the T-type Halbach pole is obtained by superposition:

[0139]

[0140] Step 6: Considering the influence of stator slots on motor performance, the general expression of magnetic flux density B obtained in step 5 is not accurate. Therefore, based on the principle of minimum magnetic resistance, the Carter coefficient is introduced to correct the magnetic flux density B to obtain a corrected magnetic flux density expression;

[0141] According to the stator slot structure of the motor in this paper, the Carter coefficient C s It can be expressed as:

[0142]

[0143] Where: S a The area occupied by the path in three dimensions is 23.4144 mm 2 ; g is the axial height of the air gap; x α 、x β are the maximum radius of the arc in different paths of the stator slot; l is the radial depth of the stator slot; S e =π(R2 2 -R1 2 ) / 48.

[0144] The magnetic flux density under the slotted air gap can be expressed as

[0145]

[0146] The waveforms of the slotless and slotted magnetic flux density of the T-type Halbach axial flux motor designed by the present invention are compared with the finite element method. Figure 4 and Figure 5 .pass Figure 4 and Figure 5 It can be seen that the analytical method and the finite element waveform are consistent, which verifies the effectiveness of the analytical method in the present invention. The analytical method can be used to perform analytical optimization design on the motor structure.

[0147] The preferred embodiments of the present invention are described in detail above with reference to the accompanying drawings. The embodiments described in the present invention are merely descriptions of the preferred embodiments of the present invention and do not limit the concept and scope of the present invention. The various specific technical features described in the above specific embodiments can be combined in any suitable manner unless there is any contradiction. Such combinations should also be regarded as the contents disclosed in this disclosure as long as they do not violate the concept of the present invention. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

[0148] The present invention is not limited to the specific details of the above-mentioned embodiments. Within the scope of the technical concept of the present invention and without departing from the design concept of the present invention, various modifications and improvements made to the technical solution of the present invention by those skilled in the art should fall within the scope of protection of the present invention. The technical contents for which protection is sought in the present invention have been fully recorded in the claims.

Claims

1. A T-type Halbach plug-in axial flux motor, comprising a dual-stator single-rotor structure, wherein two stators and one rotor are coaxially arranged, the inner and outer diameters of the rotor and stator are correspondingly equal, and the rotor is located between the two stators. Each stator has a plurality of stator slots on its axial end surface facing the rotor, and the plurality of stator slots of each stator are uniformly distributed along the circumferential direction at equal intervals on the corresponding stator axial end surface. The invention is characterized in that: The rotor has a plurality of T-shaped Halbach magnetic poles installed on its axial end surface facing each stator. Each T-shaped Halbach magnetic pole is coaxial with the rotor. The plurality of T-shaped Halbach magnetic poles on each axial end surface of the rotor are evenly distributed along the circumferential direction at equal intervals. A Halbach magnetic pole array is formed by the plurality of T-shaped Halbach magnetic poles on each axial end surface of the rotor. The axial end surface of each T-shaped Halbach magnetic pole facing the stator in the corresponding direction is flush with the corresponding axial end surface of the rotor. An air gap is formed by the gap between each axial end surface of the rotor, the inserted Halbach magnetic pole array, and the stator in the corresponding direction. Each T-shaped Halbach pole is composed of a middle permanent magnet, a counterclockwise permanent magnet located counterclockwise to the middle permanent magnet, and a clockwise permanent magnet located clockwise to the middle permanent magnet. The counterclockwise permanent magnet and the clockwise permanent magnet in each T-shaped Halbach pole have the same axial thickness, and the axial thickness of the middle permanent magnet is greater than the axial thickness of the counterclockwise permanent magnet and the clockwise permanent magnet, thereby forming a T-shaped Halbach pole in the axial direction. In each T-type Halbach pole, the clockwise and counterclockwise permanent magnets have the same span angle, the clockwise and counterclockwise permanent magnets have the same magnetization angle, and both are angles between the magnetization direction and the axial direction. The magnetization angles of the clockwise and counterclockwise permanent magnets are symmetrical along the central axis of the middle permanent magnet. The span angle of the middle permanent magnet is smaller than the span angles of the clockwise and counterclockwise permanent magnets, and the middle permanent magnet is axially magnetized. In the T-shaped Halbach magnetic pole array, two circumferentially adjacent T-shaped Halbach magnetic poles are used as a magnetic pole pair. The magnetic flux path of each magnetic pole pair is such that the magnetic flux lines start from the first magnetic pole, pass through the air gap to the stator, then from the stator through the air gap to the second magnetic pole of the magnetic pole pair, and then return to the first magnetic pole through the rotor to form a closed loop. The first magnetic pole from which the magnetic flux lines start in each magnetic pole pair is used as the north pole, and the second magnetic pole is used as the south pole. The analytical method of T-type Halbach plug-in axial flux motor includes: based on the principle of minimum magnetic resistance, introducing the Carter coefficient to the magnetic flux density B After correction, the corrected magnetic flux density expression is obtained: According to the stator slot structure of the motor, the Carter coefficient C s It can be expressed as: (38) Where: S a The area occupied by the path in three dimensions is 23.4144 mm 2 ; g is the axial height of the air gap; x α 、 x β are the maximum radius of the arc in different paths of the stator slot; l is the radial depth of the stator slot; ,in R 1 and R 2 are the inner and outer radii of the rotor respectively.

2. The T-type Halbach plug-in axial flux motor according to claim 1, characterized in that: Each stator slot on the stator is a parallel slot structure.

3. The T-type Halbach plug-in axial flux motor according to claim 1, characterized in that: In each T-type Halbach pole, the magnetization angles of the clockwise permanent magnet and the counterclockwise permanent magnet are both 42°.

4. The T-type Halbach plug-in axial flux motor according to claim 1, characterized in that: In each T-type Halbach pole, the span angle of the middle permanent magnet is 3°, and the span angles of the clockwise and counterclockwise permanent magnets are both 4.5°.

5. The T-type Halbach plug-in axial flux motor according to claim 1, characterized in that: The outer diameter of each T-type Halbach pole is equal to the outer diameter of the rotor, and the inner diameter of each T-type Halbach pole is equal to the inner diameter of the rotor, so that the rotor and its surface-inserted T-type Halbach pole array form a complete ring.

6. A method for analyzing a T-type Halbach plug-in axial flux motor according to any one of claims 1 to 5, characterized in that: The following steps are involved: Step 1: Using the precise subdomain model method, the area between the inner and outer radii of the rotor of the motor and between the upper and lower surfaces of the rotor axial direction and the interface between the air gap and the stator is divided into three annular cylindrical subdomains: the air domain, the upper magnetic pole domain, and the lower magnetic pole domain; Step 2: Cut the N and S poles of each magnetic pole pair into odd numbers according to the cylindrical surfaces of different radii. n t The difference between the inner and outer radii of a T-type Halbach pole is equal. n t The calculations for each group of T-type Halbach poles are performed separately; Step 3: For the entire motor model, cut the rotor, stator, and T-type Halbach poles along the axial direction of the radius. After cutting, a rectangular linear motor model is obtained, in which the equivalent circumferential length is the circumference of the circle where the average radius is located, the equivalent width is the difference between the outer diameter and the inner diameter of the rotor, and the axial length remains unchanged. The circumferential direction is the x-axis direction, the width direction is the y-axis direction, and the axial direction is the z-axis direction. Step 4: Perform odd, even and periodic extensions on different subdomains to establish the double Fourier decomposition expressions of the magnetization intensity of different subdomains and the general expressions of the scalar magnetic potential containing unknown coefficients; Step 5: According to the interface connection conditions of Ampere's circuit law and the principle of magnetic flux continuity, solve the unknown coefficients in the expression of the scalar magnetic potential of each subdomain in step 4 to obtain the scalar magnetic potential of each subdomain. φ The general expressions for the x-axis, y-axis, and z-axis directions are based on the magnetic field strength H and magnetic flux density B scalar magnetic potential φ The relationship between the two is used to calculate the magnetic field strength. H and magnetic flux density B The general expression of ; Step 6: Based on the principle of minimum magnetic resistance, introduce the Carter coefficient to the magnetic flux density B Make corrections to obtain the corrected magnetic flux density expression.

7. The analytical method for a T-type Halbach plug-in axial flux motor according to claim 6, characterized in that: In step 4, the determination of odd and even extensions needs to be based on the magnetic flux density in step 5 B The general expression of the three coordinate separation is determined as follows: x Axial component B x Do x Axial odd extension and y Axial periodic extension, z Axial component B z Do x Axial direction extension and y Axial periodic extension.

8. The analytical method for a T-type Halbach plug-in axial flux motor according to claim 6, characterized in that: In step 5, the interface connection conditions derived from Ampere's circuit law and the principle of flux continuity are used to solve the unknown coefficients in the magnetic potential expression of each subdomain by establishing a matrix equation to obtain the scalar magnetic potential of each subdomain. φ The general expression of .

9. The analytical method for a T-type Halbach plug-in axial flux motor according to claim 6, characterized in that: In step 2, cut the N and S poles of each magnetic pole pair and in steps 3-6 n t The scalar magnetic potential, magnetization intensity, magnetic flux density and magnetic field intensity are calculated for each group of T-type Halbach poles. The final magnetic flux density can be expressed as n t Linear superposition of the magnetic flux density generated by a set of T-type Halbach poles.

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