A method for calculating the magnetic field of a high-speed permanent magnet motor

Abstract

This invention discloses a method for calculating the magnetic field of a high-speed permanent magnet motor. The method divides the solution domain of a hierarchical composite rotor high-speed permanent magnet motor into stator slots, stator slot openings, air gap, magnetic powder film layer, and carbon fiber layer. Based on the governing equations and boundary conditions of each subdomain, the general solution of the vector magnetic potential of each subdomain is solved. Considering the special characteristics of the rotor structure of the hierarchical composite rotor high-speed permanent magnet motor, the method can be extended to the analytical calculation of the magnetic field of quasi-hierarchical rotor permanent magnet motors. The hierarchical composite rotor high-speed permanent magnet motor allows for unified modeling, is applicable to various pole-slot combinations, avoids repeated motor model building, and saves modeling time.

Description

Technical Field

[0001] This invention relates to the field of high-speed permanent magnet motor technology, and in particular to a method for calculating the magnetic field of a high-speed permanent magnet motor. Background Technology

[0002] High-speed permanent magnet motors have a wide range of applications in aerospace, flywheel energy storage and other fields. However, the rotor temperature rise and stress concentration of high-speed permanent magnet synchronous motors limit their development towards high power and high speed.

[0003] To fully leverage the potential advantages of high-speed permanent magnet motors with composite rotors, particularly in parametric optimization, a fast and accurate analysis tool is needed. Basic analytical models for evaluating motors include finite element analysis (FEM) models, analytical models, and equivalent magnetic network models. All three can be applied to motor modeling and optimization. FEM models offer high accuracy and modeling flexibility, but their solution speed is relatively slow. Analytical models offer faster solution speeds, but are more challenging for complex topology modeling and have lower solution accuracy. Multilayer precise subdomain magnetic field analytical models achieve a balance between the solution speed of analytical models and the solution accuracy of finite element analysis models. Summary of the Invention

[0004] In view of this, the present invention provides a novel method for constructing an equivalent magnetic circuit model of a composite rotor high-speed permanent magnet motor, in order to solve the problem that the shape of the tooth tip affects the magnetic flux density of the air gap.

[0005] This invention provides a novel method for constructing an equivalent magnetic circuit model of a composite rotor high-speed permanent magnet motor, comprising the following steps:

[0006] A method for constructing a multi-layer accurate subdomain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor, characterized by the following steps:

[0007] S1: The solution domain for a high-speed permanent magnet motor with a hierarchical composite rotor structure can be divided as follows: composite magnetic material layer, which includes a magnetic powder film layer (R 1_mi i = 1, 2, ... N H ) and carbon fiber layer (R 1_ni i = 1, 2, ..., N H ); air gap (R2); groove (R) 3i i = 1, 2, ... N s ); Groove (R) 4i i = 1, 2…N s ), N H N represents the number of layers in the composite magnetic material. s This refers to the number of stator slots;

[0008] S2: Solve the governing equations and vector magnetic potential general solutions for each subdomain, including the composite magnetic material layer subdomain, air gap subdomain, stator slot subdomain, and stator slot opening subdomain. The composite magnetic material layer subdomain can be further divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain.

[0009] S3: Solve for the magnetic flux density expression of each subdomain, including the composite magnetic material layer subdomain, the air gap subdomain, the stator slot subdomain, and the stator slot opening subdomain. The composite magnetic material layer subdomain can be further divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain.

[0010] S4: Combining the boundary conditions of each subdomain, establish the governing equations for each subdomain and solve for the stiffness coefficient matrix. The simultaneous establishment of subdomain boundary conditions includes: boundary conditions between the magnetic powder film layer and the carbon fiber layer, boundary conditions between the composite magnetic material and the air gap, boundary conditions between the stator slot and the slot opening, and boundary conditions between the stator slot opening and the air gap.

[0011] S5: Substitute the solution of the coefficient matrix into the magnetic flux density formula of each subdomain to complete the solution of the motor magnetic field.

[0012] The method for constructing an analytical model of the magnetic field of a high-speed permanent magnet motor with a hierarchical composite rotor provided by this invention divides the solution domain of the high-speed permanent magnet motor into stator slots, stator slot openings, air gap, magnetic powder film layer, and carbon fiber layer. Based on the governing equations and boundary conditions of each subdomain, the general solution of the vector magnetic potential of each subdomain is solved. Considering the special characteristics of the rotor structure of the high-speed permanent magnet motor with a hierarchical composite rotor, it can be extended to the analytical calculation of the magnetic field of similar high-speed permanent magnet motors with hierarchical composite rotors. The high-speed permanent magnet motor with a hierarchical composite rotor can achieve unified modeling, is suitable for various pole-slot combinations, avoids repeated construction of motor models, and saves modeling time. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the analytical model of the magnetic field of the high-speed permanent magnet motor with a hierarchical structure composite rotor in Embodiment 1 of the present invention;

[0014] Figure 2 The figure shows a comparison between the air gap magnetic flux density obtained in Embodiment 1 of the present invention and the unloaded air gap magnetic flux density obtained by the existing finite element analysis model.

[0015] Figure 3 The figure shows a comparison between the air gap magnetic flux density obtained in Embodiment 1 of the present invention and the load air gap magnetic flux density obtained from the existing finite element analysis model. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely illustrative and are not intended to limit the present invention.

[0017] 1. A method for constructing a multi-layer accurate subdomain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor, characterized by comprising the following steps:

[0018] S1: The solution domain for a high-speed permanent magnet motor with a hierarchical composite rotor structure can be divided as follows: composite magnetic material layer, which includes a magnetic powder film layer (R 1_mi i = 1, 2, ... N H ) and carbon fiber layer (R 1_ni i = 1, 2, ..., N H ); air gap (R2); groove (R) 3i i = 1, 2, ... N s ); Groove (R) 4i i = 1, 2…N s ), N H N represents the number of layers in the composite magnetic material. s This refers to the number of stator slots;

[0019] S2: Solve the governing equations and vector magnetic potential general solutions for each subdomain, including the composite magnetic material layer subdomain, air gap subdomain, stator slot subdomain, and stator slot opening subdomain. The composite magnetic material layer subdomain can be further divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain.

[0020] S3: Solve for the magnetic flux density expression of each subdomain, including the composite magnetic material layer subdomain, the air gap subdomain, the stator slot subdomain, and the stator slot opening subdomain. The composite magnetic material layer subdomain can be further divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain.

[0021] S4: Combining the boundary conditions of each subdomain, establish the governing equations for each subdomain and solve for the stiffness coefficient matrix. The simultaneous establishment of subdomain boundary conditions includes: boundary conditions between the magnetic powder film layer and the carbon fiber layer, boundary conditions between the composite magnetic material and the air gap, boundary conditions between the stator slot and the slot opening, and boundary conditions between the stator slot opening and the air gap.

[0022] S5: Substitute the solution of the coefficient matrix into the magnetic flux density formula of each subdomain to complete the solution of the motor magnetic field.

[0023] 2. The method for constructing a multi-layer precise subdomain magnetic field analytical model for a high-speed permanent magnet motor with a hierarchical composite rotor as described in claim 1, characterized in that, in step S2, the governing equations of each subdomain and the general solution of the vector hedgehog are:

[0024] In a two-dimensional field, the vector magnetic potential A has only a z-axis component and is a function of polar coordinate variables r and θ. Its governing equations for each subdomain are expressed as follows:

[0025] 1) Layer subdomains of composite magnetic materials

[0026] Each layer of composite magnetic material needs to be divided into two layers: a magnetic powder film layer and a carbon fiber layer. The vector magnetic potential equation of the i-th layer of composite magnetic material is:

[0027]

[0028] The vector magnetic potential equation for the i-th carbon fiber layer is:

[0029]

[0030] In the formula, M r_m and M θ_m These represent the radial and tangential components of the magnetization intensity of the magnetic powder film, respectively.

[0031]

[0032] M rck_m =M rk_m cos(kω r t+kθ0) (5)

[0033] M rsk_m =M rk_m sin(kω r t+kθ0) (6)

[0034] M θck_m =-M θk_m sin(kω r t+kθ0) (7)

[0035] M θsk_m =M θk_m cos(kω r t+kθ0) (8)

[0036] For radial magnetization, its M rk_m With M θk_m They are represented as follows:

[0037]

[0038] M θk_m =0 k / p=1,3,5... (10)

[0039] In the formula, B rm The remanence of the magnetic powder film is given, θ0 is the initial position angle of the rotor, and ω is the remanence of the magnetic powder film. r ω is the angular velocity of the rotor.

[0040] Formula (4.1) can be rewritten in the following form:

[0041]

[0042] The vector magnetic potential flux solution of the i-th layer of composite magnetic material magnetic powder film can be expressed as:

[0043]

[0044] In the formula, R mi R is the outer diameter of the i-th layer of composite magnetic material magnetic powder film. ci-1 R is the outer diameter of the (i-1)th layer of composite magnetic material carbon fiber. When i = 1, R ci-1 =R r A 1_mi B 1_mi C 1_mi D 1_mi For the coefficients to be determined, its particular solution A p The expression is:

[0045]

[0046] The vector magnetic potential flux solution of the i-th layer of composite magnetic material carbon fiber can be expressed as:

[0047]

[0048] In the formula, R ci Let A be the outer diameter of the i-th layer of composite magnetic material carbon fiber. 1_ci B 1_ci C 1_ci D 1_ci These are coefficients to be determined.

[0049] 2) Air gap subdomain

[0050] The air gap vector magnetic potential equation is:

[0051]

[0052] The air gap vector magnetic flux solution can be expressed as:

[0053]

[0054] In the formula, R mN The outermost layer (i=N) H The outer diameter of the magnetic powder adhesive film layer, A2, B2, C2, and D2 are coefficients to be determined.

[0055] 3) Stator slot subdomain

[0056] The stator slot vector magnetic potential equation is:

[0057]

[0058] For double-layer lap windings, the vector magnetic flux solution at the bottom of the stator slot can be expressed as:

[0059]

[0060] The vector magnetic potential flux solution at the bottom of the stator slot can be expressed as:

[0061]

[0062] In the formula, J i1 and J i2 R is the current density of the upper and lower windings in the i-th slot. sm E n G3 and G3 are respectively represented as:

[0063]

[0064] E n =nπ / b sa (twenty one)

[0065]

[0066] 4) Stator slot sub-domain

[0067] The stator slot vector magnetic potential equation is:

[0068]

[0069] The vector magnetic flux solution of the stator slot can be expressed as:

[0070]

[0071] In the formula, F m Represented as:

[0072] F m =mπ / b oa (25)

[0073] 3. The method for constructing a multi-layer precise subdomain magnetic field analytical model for a high-speed permanent magnet motor with a hierarchical composite rotor as described in claim 1, characterized in that, in step S3, the magnetic flux density expression for each subdomain is:

[0074] The radial and tangential portions of the magnetic flux density can be obtained using vector magnetic potential, and their expressions are as follows:

[0075]

[0076] 1) Magnetic density of layer subdomains in composite magnetic materials

[0077] The boundary conditions between the first layer of magnetic powder adhesive film and the rotor yoke, i.e.

[0078]

[0079] The radial magnetic flux density of the first layer of magnetic powder film is:

[0080]

[0081] The tangential magnetic flux density of the first layer of magnetic powder film is:

[0082]

[0083] In the formula, C m1k C m2k C m3k C m4k C m5k C m6k They are represented as follows:

[0084]

[0085] In the formula, μ rm Let G1 be the relative permeability of the magnetic powder film, and G1 = (R r / R m1 ) k .

[0086] Radial magnetic flux density of the i-th layer (i≠1) magnetic powder film:

[0087]

[0088] Tangential magnetic flux density of the i-th layer (i≠1) magnetic powder film:

[0089]

[0090] Radial magnetic flux density of the i-th carbon fiber layer:

[0091]

[0092] Tangential magnetic flux density of the i-th carbon fiber layer:

[0093]

[0094] 2) Air gap subdomain magnetic flux density: The radial magnetic flux density of the air gap is:

[0095]

[0096] The air gap tangential magnetic flux density is:

[0097]

[0098] 3) Stator slot subdomain magnetic flux density: The stator slot radial magnetic flux density is:

[0099]

[0100] The tangential magnetic flux density at the bottom of the stator slot is:

[0101]

[0102] The tangential magnetic flux density at the top of the stator slot is:

[0103]

[0104] 4) Stator slot sub-domain magnetic flux density

[0105] The radial magnetic flux density of the stator slot is:

[0106]

[0107] The tangential magnetic flux density at the stator slot opening is:

[0108]

[0109] 4. The method for constructing a multi-layer precise subdomain magnetic field analytical model of a high-speed permanent magnet motor with a hierarchical composite rotor as described in claim 1, characterized in that, in step S4, the boundary conditions of each subdomain are:

[0110] 1) Boundary conditions between the magnetic powder film layer and the carbon fiber layer

[0111] In the solution domain of the composite magnetic material, the radial magnetic induction and tangential magnetic field intensities of the i-th magnetic powder film layer and the carbon fiber layer are continuous, and their boundary conditions are expressed as follows:

[0112]

[0113] In the formula,

[0114]

[0115] When it is in the first layer of the magnetic powder adhesive film, its boundary conditions can be described as follows:

[0116]

[0117] Since the outermost layer of the composite magnetic material is a carbon fiber layer, the outermost carbon fiber layer, along with the sheath and air gap, will be divided into a single computational domain. The number of outermost layers in the solution domain for the carbon fiber layer is N. H -1. When the magnetic powder adhesive film is in its i-th layer, its boundary conditions can be written as follows:

[0118]

[0119] In the formula,

[0120]

[0121] The radial magnetic induction intensity and tangential magnetic field intensity are continuous between the i-th carbon fiber layer and the (i+1)-th magnetic powder film layer, and their boundary conditions are expressed as follows:

[0122]

[0123] When the carbon fiber layer is in the i-th layer, its boundary conditions can be written as follows:

[0124]

[0125] In the formula,

[0126] G cm =(R ci / R mi+1 ) k (65)

[0127] 2) Composite magnetic materials and air gap boundary conditions

[0128] Nth H The radial magnetic induction intensity and tangential magnetic field intensity are continuous between the layer of magnetic powder adhesive film and the air gap. The boundary conditions are described as follows:

[0129]

[0130] The outermost layer of the magnetic powder film (i=N) H The computational domain and air gap boundary conditions of the ) layer are consistent with the structural forms of formulas (4.55) to (4.58), the difference being G ci The formula definition of G ci It needs to be replaced with G N Its expression is:

[0131]

[0132] 3) Stator slot and slot opening boundary conditions

[0133] At the interface between the stator slot and the slot opening, the tangential component of the magnetic induction intensity and the vector magnetic potential are continuous, and the boundary conditions are as follows:

[0134]

[0135] 4) Stator slot and air gap boundary conditions

[0136] At the interface between the stator slot and the air gap, the tangential component of the magnetic induction intensity and the vector magnetic potential are continuous, and the boundary conditions are written as follows:

[0137]

[0138] The boundary conditions between stator slots and between stator slots and the air gap are consistent with those of the precise subdomain model of a traditional surface-mounted motor, and will not be elaborated further in this paper. Solving the coefficient matrix by simultaneously applying the above boundary conditions yields the following matrix equation:

[0139] A c Xc =Y c (70)

[0140] In the formula, A c Y is the overall stiffness matrix. c Let X be a vector of constant terms. c Let X be the coefficient vector to be determined, where X is the coefficient vector to be determined. c Represented as X c =[A 1_m1 C 1_m1 A 1_c1 B 1_c1 C 1_c1 D 1_c1 A 1_m2 B 1_m2 C 1_m2 D 1_m2 …A 1_mN B 1_mN C 1_mN D 1_mN A2 B2 C2 D2C 4t D 4t D 3t ] T .

[0141] The method for constructing an analytical model of the magnetic field of a high-speed permanent magnet motor with a hierarchical composite rotor provided by this invention divides the solution domain of the high-speed permanent magnet motor into stator slots, stator slot openings, air gap, magnetic powder film layer, and carbon fiber layer. Based on the governing equations and boundary conditions of each subdomain, the general solution of the vector magnetic potential of each subdomain is solved. Considering the special characteristics of the rotor structure of the high-speed permanent magnet motor with a hierarchical composite rotor, it can be extended to the analytical calculation of the magnetic field of similar high-speed permanent magnet motors with hierarchical composite rotors. The high-speed permanent magnet motor with a hierarchical composite rotor can achieve unified modeling, is suitable for various pole-slot combinations, avoids repeated construction of motor models, and saves modeling time.

[0142] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for constructing a multi-layer precise subdomain magnetic field analytical model for a hierarchical composite rotor high-speed permanent magnet motor, characterized in that, Includes the following steps: S1: The solution domain for a high-speed permanent magnet motor with a multi-layered composite rotor can be divided as follows: composite magnetic material layer, air gap. R 2. Tank R 3j ,notch R 4j The composite magnetic material layer includes a magnetic powder film layer. R mi With carbon fiber layer R ci , i =1,2,… N H , j =1,2… N s , N H The number of layers in a composite magnetic material. N s This refers to the number of stator slots; S2: Solve the governing equations and vector magnetic potential general solutions for each subdomain, including the composite magnetic material layer subdomain, air gap subdomain, stator slot subdomain, and stator slot opening subdomain. The composite magnetic material layer subdomain can be further divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain. S3: Solve for the magnetic flux density expression of each subdomain, which includes the composite magnetic material layer subdomain, air gap subdomain, stator slot subdomain, and stator slot opening subdomain. The composite magnetic material layer subdomain can be further divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain. S4: Combine the boundary conditions of each subdomain, solve the governing equations of each subdomain, and solve the stiffness coefficient matrix. The boundary conditions of each subdomain include: boundary conditions between magnetic powder film layer and carbon fiber layer, boundary conditions between composite magnetic material and air gap, boundary conditions between stator slot and slot opening, and boundary conditions between stator slot opening and air gap. S5: Substitute the results of the stiffness coefficient matrix into the magnetic flux density expression of each subdomain to complete the solution of the motor magnetic field; In step S2, the governing equations and general solutions for each subdomain and the vector magnetic potential are: In a two-dimensional field, the vector magnetic potential... A Only exist z Axis components, and are polar coordinate variables. r and θ The function, whose governing equations for each subdomain are expressed as follows: 1) Layer subdomains of composite magnetic materials Each layer of composite magnetic material needs to be divided into two layers: a magnetic powder film layer and a carbon fiber layer. i The vector magnetic potential equation for the layered composite magnetic material layer magnetic powder film is: （1） ； No. i The vector magnetic potential equation for the carbon fiber layer is: (2) ； In the formula, M r_m and M θ_m These represent the radial and tangential components of the magnetization intensity of the magnetic powder film, respectively. (3) ； (4) ； (5)； (6) ； (7) ； (8) ； For radial magnetization, M rk_m and M θk_m They are represented as follows: (9) ； (10) ； In the formula, B rm Residual magnetism in the magnetic powder film, θ 0 is the initial position angle of the rotor. ω r The rotor's angular velocity. Formula (1) can be rewritten in the following form: (11) ； No. i The vector magnetic potential flux solution of the magnetic powder film layer of the composite magnetic material can be expressed as: (12)； In the formula, R mi For the first i The outer diameter of the composite magnetic material magnetic powder film layer, R ci-1 For the first i -1 layer of composite magnetic material carbon fiber layer outer diameter, when i When =1, R ci-1 = R r ; A 1_mi , B 1_mi , C 1_mi , D 1_mi For the coefficients to be determined, its particular solution A p The expression is: (13) ； No. i The vector magnetic potential flux solution of the carbon fiber layer composite magnetic material can be expressed as: (14) ； In the formula, R ci For the first i The outer diameter of the carbon fiber layer in the composite magnetic material A 1_ci , B 1_ci , C 1_ci , D 1_ci These are coefficients to be determined; 2) Air gap subdomain The air gap vector magnetic potential equation is: (15) ； The air gap vector magnetic flux solution can be expressed as: (16) ； In the formula, R mN The outermost magnetic powder film layer is the outer diameter. A 2. B 2. C 2. D 2 is an undetermined coefficient; 3) Stator slot subdomain The stator slot vector magnetic potential equation is: (17) ； For double-layer lap windings, the vector magnetic flux solution at the bottom of the stator slot can be expressed as: (18) ； The vector magnetic potential flux solution at the top of the stator slot can be expressed as: (19) ； In the formula, J j1 and J j2 For the first j Current density of upper and lower windings in each slot R sm , E n and G 3 is represented as: (20) ； (21) ； (22) ； 4) Stator slot sub-domain The stator slot vector magnetic potential equation is: (23) ； The vector magnetic flux solution of the stator slot can be expressed as: (24) ； In the formula, F m Represented as: (25) 。 2. The method for constructing a multi-layer precise sub-domain magnetic field analytical model for a hierarchical composite rotor high-speed permanent magnet motor as described in claim 1, characterized in that, In step S3, the magnetic flux density expression for each subdomain is as follows: The radial and tangential portions of the magnetic flux density can be obtained using vector magnetic potential, and their expressions are as follows: (26)； 1) Magnetic density of layer subdomains in composite magnetic materials The boundary conditions between the first layer of magnetic powder adhesive film and the rotor yoke, i.e. (27) ； The radial magnetic flux density of the first layer of magnetic powder film is: (28) ； The tangential magnetic flux density of the first layer of magnetic powder film is: (29) ； In the formula, C m1k , C m2k , C m3k , C m4k , C m5k , C m6k They are represented as follows: (30) ； (31)； (32) ； (33) ； (34) ； (35) ； In the formula, µ rm The relative permeability of the magnetic powder film is given, and G 1=( R r / R m1 ) k ; No. i The radial magnetic flux density of the layered magnetic powder film, wherein i 1: (36) ； (37) ； No. i Tangential magnetic flux density of the layered magnetic powder film, wherein i 1: (38)； (39)； No. i Radial magnetic flux density of carbon fiber layers: (40) ； No. i Tangential magnetic flux density of carbon fiber layers: (41) ； 2) Magnetic flux density of the air gap subdomain The radial magnetic flux density of the air gap is: (42) ； The air gap tangential magnetic flux density is: (43) ； 3) Stator slot subdomain magnetic flux density The radial magnetic flux density of the stator slot is: (44) ； The tangential magnetic flux density at the bottom of the stator slot is: (45) ； The tangential magnetic flux density at the top of the stator slot is: (46) ； 4) Stator slot sub-domain magnetic flux density The radial magnetic flux density of the stator slot is: (47) ； The tangential magnetic flux density at the stator slot opening is: (48) 。 3. The method for constructing a multi-layer precise subdomain magnetic field analytical model for a hierarchical composite rotor high-speed permanent magnet motor as described in claim 2, characterized in that, In step S4, the boundary conditions for each subdomain are as follows: 1) Boundary conditions between the magnetic powder film layer and the carbon fiber layer In the solution region of composite magnetic materials, the first i The radial magnetic induction intensity and tangential magnetic field intensity are continuous between the magnetic powder film layer and the carbon fiber layer, and their boundary conditions are described as follows: (49) ； In the formula, (50) ； When it is in the first layer of the magnetic powder adhesive film, its boundary conditions can be described as follows: (51) ； (52) ； (53) ； (54) ； Since the outermost layer of the composite magnetic material is a carbon fiber layer, the outermost carbon fiber layer, along with the sheath and air gap, will be divided into a single computational domain. The number of outermost layers in the solution domain for the carbon fiber layer is... N H -1; when in the magnetic powder film... i When the layer is defined, its boundary conditions can be written as follows: (55) ； (56) ； (57) ； (58) ； In the formula, (59) ； No. i The first layer of carbon fiber and the second layer i The radial magnetic induction intensity and tangential magnetic field intensity of the +1 layer magnetic powder adhesive film are continuous, and its boundary conditions are expressed as follows: (60) ； When the carbon fiber layer is in the first i When the layer is defined, its boundary conditions can be written as follows: (61) ； (62) ； (63) ； (64) ； In the formula, (65) ； 2) Composite magnetic materials and air gap boundary conditions No. N H The radial magnetic induction intensity and tangential magnetic field intensity are continuous between the layer of magnetic powder adhesive film and the air gap. The boundary conditions are described as follows: (66) ； The outermost computational domain and air gap boundary conditions of the magnetic powder film are consistent with the structural forms of formulas (55) to (58), the difference being that G ci The formula definition, G ci It needs to be replaced with G N Its expression is: (67) ； 3) Stator slot and slot opening boundary conditions At the interface between the stator slot and the slot opening, the tangential component of the magnetic induction intensity and the vector magnetic potential are continuous, and the boundary conditions are as follows: (68) ； 4) Stator slot and air gap boundary conditions At the interface between the stator slot and the air gap, the tangential component of the magnetic induction intensity and the vector magnetic potential are continuous, and the boundary conditions are written as follows: (69) ； The boundary conditions between stator slots and between stator slots and the air gap are consistent with the boundary conditions of the precise subdomain model of a traditional surface-mounted motor. Solving the coefficient matrix by simultaneously applying the above boundary conditions yields the following matrix equation: (70) ； In the formula, A c Y is the overall stiffness matrix. c Let X be a vector of constant terms. c Let X be the coefficient vector to be determined, where X is the coefficient vector to be determined. c Represented as X c =[ A 1_m1 C 1_ m1 A 1_c1 B 1_c1 C 1_c1 D 1_c1 A 1_m2 B 1_m2 C 1_m2 D 1_m2 … A 1_mN B 1_mN C 1_mN D 1_mN A 2 B 2 C 2 D 2 C 4t D 4t D 3t ] T .

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