High-speed permanent magnet motor magnetic field calculation method

Abstract

The invention discloses a method for calculating a magnetic field of a high-speed permanent magnet motor, and the method comprises the steps: carrying out the solution domain division of the high-speed permanent magnet motor with a hierarchical composite rotor, namely a stator groove, a stator notch, an air gap, a magnetic powder adhesive film layer and a carbon fiber layer. And solving a vector magnetic potential general solution of each sub-domain based on the control equation and the boundary condition of each sub-domain. The particularity of the rotor structure of the hierarchical composite rotor high-speed permanent magnet motor is considered, and the method can be expanded to magnetic field analytic calculation of a rotor permanent magnet motor with a class hierarchical structure. The hierarchical structure composite rotor high-speed permanent magnet motor can realize unified modeling, is suitable for cooperation of various pole slots, can avoid repeated construction of a motor model, and saves modeling time.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed permanent magnet motors, and in particular to a method for calculating the magnetic field of a high-speed permanent magnet motor. Background Art

[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] In order to give full play to the potential advantages of composite rotor high-speed permanent magnet motors, especially in the direction of parametric optimization, a fast and accurate analysis tool is needed. The basic analysis models used to evaluate motors include finite element analysis models, analytical models, and equivalent magnetic network models. All three models can be applied to motor modeling and optimization. The finite element analysis model has the characteristics of high accuracy and flexible modeling, but the solution speed is slow; the analytical model has a fast solution speed, but it is difficult to model complex topologies and has low solution accuracy; the multi-layer accurate subdomain magnetic field analytical model achieves a balance between the solution speed of the analytical model and the solution accuracy of the finite element analysis model. 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, so as to solve the problem that the tooth top shape affects the air gap magnetic flux density.

[0005] The present 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 sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor, characterized by comprising the following steps:

[0007] S1: The solution area of ​​the hierarchical composite rotor high-speed permanent magnet motor can be divided into the following: composite magnetic material layer, which includes the 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); slot (R 3i ,i=1,2,…N s ); notch (R 4i , i=1,2…N s ), N H is the number of composite magnetic material layers, N s is the number of stator slots;

[0008] S2: Solve the control equations of each subdomain and the general solution of the vector magnetic potential, which includes the composite magnetic material layer subdomain, the air gap subdomain, the stator slot subdomain, and the stator slot subdomain. The composite magnetic material layer subdomain can also be divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain;

[0009] S3: Solve 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 subdomain. The composite magnetic material layer subdomain can also be divided into a magnetic powder film layer subdomain and a carbon fiber layer subdomain.

[0010] S4: Combine the boundary conditions of each subdomain, and solve the stiffness coefficient matrix by combining the control equations of each subdomain. The boundary conditions of the subdomains include: 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, and boundary conditions between the stator slot and the air gap;

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

[0012] The method for constructing the analytical model of the magnetic field of the hierarchical composite rotor high-speed permanent magnet motor provided by the present invention divides the solution domain of the hierarchical composite rotor high-speed permanent magnet motor into stator slots, stator slots, air gaps, magnetic powder film layers, and carbon fiber layers. Based on the control equations and boundary conditions of each subdomain, the general solution of the vector magnetic potential of each subdomain is solved. Considering the particularity of the rotor structure of the hierarchical composite rotor high-speed permanent magnet motor, it can be expanded to the analytical calculation of the magnetic field of the hierarchical structure rotor permanent magnet motor. The hierarchical composite rotor high-speed permanent magnet motor can realize unified modeling, which is suitable for a variety of pole slot combinations, can avoid repeated construction of motor models, and save modeling time. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0014] Figure 2 This is a comparison diagram of the air gap magnetic flux obtained by Example 1 of the present invention and the no-load air gap magnetic flux obtained by the existing finite element analysis model.

[0015] Figure 3 This is a comparison diagram of the air gap magnetic flux obtained in Example 1 of the present invention and the load air gap magnetic flux obtained by the existing finite element analysis model. DETAILED DESCRIPTION

[0016] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only for illustration and are not intended to limit the present invention.

[0017] 1. A method for constructing a multi-layer accurate sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor, characterized in that it comprises the following steps:

[0018] S1: The solution area of ​​the hierarchical composite rotor high-speed permanent magnet motor can be divided into the following: composite magnetic material layer, which includes the 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); slot (R 3i ,i=1,2,…N s ); notch (R 4i , i=1,2…N s ), N H is the number of composite magnetic material layers, N s is the number of stator slots;

[0019] S2: Solve the control equations of each subdomain and the general solution of the vector magnetic potential, which includes the composite magnetic material layer subdomain, the air gap subdomain, the stator slot subdomain, and the stator slot subdomain. The composite magnetic material layer subdomain can also be divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain;

[0020] S3: Solve 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 subdomain. The composite magnetic material layer subdomain can also be divided into a magnetic powder film layer subdomain and a carbon fiber layer subdomain.

[0021] S4: Combine the boundary conditions of each subdomain, and solve the stiffness coefficient matrix by combining the control equations of each subdomain. The boundary conditions of the subdomains include: 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, and boundary conditions between the stator slot and the air gap;

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

[0023] 2. The method for constructing a multi-layer precise sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor according to claim 1, characterized in that in step S2, the control equations of each sub-domain are solved by the vector hedgehog:

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

[0025] 1) Composite magnetic material layer subdomain

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

[0027]

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

[0029]

[0030] Where M r_m and M θ_m They 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, M rk_m With M θk_m Respectively expressed as:

[0037]

[0038] M θk_m =0 k / p=1,3,5... (10)

[0039] In the formula, B rm is the residual magnetism of magnetic powder film, θ0 is the initial position angle of the rotor, ω r is the rotor rotation angular velocity.

[0040] Formula (4.1) can be rewritten as follows:

[0041]

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

[0043]

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

[0045]

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

[0047]

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

[0049] 2) Air Gap Subdomain

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

[0051]

[0052] The general solution of the air gap vector magnetic potential can be expressed as:

[0053]

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

[0055] 3) Stator slot sub-domain

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

[0057]

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

[0059]

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

[0061]

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

[0063]

[0064] E n =nπ / b sa (twenty one)

[0065]

[0066] 4) Stator slot sub-area

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

[0068]

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

[0070]

[0071] In the formula, F m It is expressed as:

[0072] F m =mπ / b oa (25)

[0073] 3. The method for constructing a multi-layer accurate sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor according to claim 1, characterized in that in step S3, the magnetic flux density expression of each sub-domain is:

[0074] The radial and tangential parts of the magnetic flux density can be obtained by the vector magnetic potential, and its expression is:

[0075]

[0076] 1) Magnetic density of sub-domain of composite magnetic material layer

[0077] The boundary condition between the first magnetic powder film layer and the rotor yoke is:

[0078]

[0079] The radial magnetic 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 Respectively expressed as:

[0084]

[0085] In the formula, μ rm is the relative magnetic 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) of magnetic powder film:

[0087]

[0088] Tangential magnetic flux density of the i-th layer (i≠1) of 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 sub-domain magnetic density The radial magnetic density of the air gap is:

[0095]

[0096] The air gap tangential flux density is:

[0097]

[0098] 3) Stator slot sub-domain magnetic flux density The radial magnetic flux density of the stator slot is:

[0099]

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

[0101]

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

[0103]

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

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

[0106]

[0107] The stator slot tangential flux density is:

[0108]

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

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

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

[0112]

[0113] In the formula,

[0114]

[0115] When in the first layer of magnetic powder film, the boundary condition can be expressed as:

[0116]

[0117] Since the last outer layer of the composite magnetic material is a carbon fiber layer, the outermost carbon fiber layer will be divided into a calculation domain with the sheath and the air gap. The outermost layer number of the carbon fiber layer solution domain is N H -1. When the magnetic powder film is the i-th layer, its boundary condition can be written as:

[0118]

[0119] In the formula,

[0120]

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

[0122]

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

[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 of the magnetic powder film layer and the air gap are continuous, and the boundary condition is expressed as:

[0129]

[0130] The outermost layer of magnetic powder film (i=N H ) layer calculation domain and air gap boundary conditions are consistent with the structure of formula (4.55) to formula (4.58), the difference is that G ci The formula definition of G ci Need to be replaced by G N , whose expression is:

[0131]

[0132] 3) Boundary conditions between stator slots and slot openings

[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:

[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:

[0137]

[0138] The boundary conditions between stator slots and slots, and between stator slots and air gaps are consistent with the boundary conditions of the traditional surface-mounted motor precise subdomain model, and will not be repeated in this article. The above boundary conditions are combined to solve the coefficient matrix, and the matrix equation is:

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

[0140] In the formula, A c is the total stiffness matrix, Y c is a constant term vector, X c is the coefficient vector to be determined, where X 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 the analytical model of the magnetic field of the hierarchical composite rotor high-speed permanent magnet motor provided by the present invention divides the solution domain of the hierarchical composite rotor high-speed permanent magnet motor into stator slots, stator slots, air gaps, magnetic powder film layers, and carbon fiber layers. Based on the control equations and boundary conditions of each subdomain, the general solution of the vector magnetic potential of each subdomain is solved. Considering the particularity of the rotor structure of the hierarchical composite rotor high-speed permanent magnet motor, it can be expanded to the analytical calculation of the magnetic field of the hierarchical structure rotor permanent magnet motor. The hierarchical composite rotor high-speed permanent magnet motor can realize unified modeling, which is suitable for a variety of pole slot combinations, can avoid repeated construction of motor models, and save modeling time.

[0142] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for constructing a multi-layer accurate sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor, characterized in that: The steps include: S1: The solution area of ​​the hierarchical composite rotor high-speed permanent magnet motor can be divided into the following: composite magnetic material layer, which includes the 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); slot (R 3i ,i=1,2,…N s ); notch (R 4i , i=1,2…N s ), N H is the number of composite magnetic material layers, N s is the number of stator slots; S2: Solve the control equations of each subdomain and the general solution of the vector magnetic potential, which includes the composite magnetic material layer subdomain, the air gap subdomain, the stator slot subdomain, and the stator slot subdomain. The composite magnetic material layer subdomain can also be divided into the magnetic powder film layer subdomain and the carbon fiber layer subdomain; S3: Solve 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 subdomain. The composite magnetic material layer subdomain can also be divided into a magnetic powder film layer subdomain and a carbon fiber layer subdomain. S4: Combine the boundary conditions of each subdomain, solve the control equations of each subdomain, and solve the stiffness coefficient matrix. The sub-domain boundary conditions 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 coefficient matrix solution into the magnetic flux density formula of each subdomain to complete the motor magnetic field solution.

2. The method for constructing a multi-layer accurate sub-domain magnetic field analytical model of a hierarchical structure composite rotor high-speed permanent magnet motor according to claim 1, characterized in that: In step S2, the control equations of each subdomain are solved with the vector hedgehog general solution: In a two-dimensional field, the vector magnetic potential A has only a z-axis component and is a function of the polar coordinate variables r and θ. The control equations of each subdomain are expressed as follows: 1) Composite magnetic material layer subdomain Each layer of composite magnetic material needs to be divided into two layers, namely the magnetic powder film layer and the carbon fiber layer. The vector magnetic potential equation of the magnetic powder film of the i-th composite magnetic material layer is: The vector magnetic potential equation of the i-th carbon fiber layer is: Where M r_m and M θ_m They represent the radial and tangential components of the magnetization intensity of the magnetic powder film respectively. M rck_m =M rk_m cos(kω r t+kθ0) (5) M rsk_m =M rk_m sin(kω r t+kθ0) (6) M θck_m =-M θk_m sin(kω r t+kθ0) (7) M θsk_m =M θk_m cos(kω r t+kθ0) (8) For radial magnetization, M rk_m With M θk_m Respectively expressed as: M θk_m =0 k / p=1,3,5... (10) In the formula, B rm is the residual magnetism of magnetic powder film, θ0 is the initial position angle of the rotor, ω r is the rotor rotation angular velocity. Formula (4.1) can be rewritten as follows: The general solution of the vector magnetic potential of the i-th composite magnetic material magnetic powder film layer can be expressed as: In the formula, R mi is the outer diameter of the magnetic powder film layer of the i-th composite magnetic material, R ci-1 is the outer diameter of the i-1th composite magnetic material carbon fiber layer. When i=1, R ci-1 =R r . A 1_mi , B 1_mi , C 1_mi , D 1_mi is the unknown coefficient, and its particular solution A p The expression is: The general solution of the vector magnetic potential of the i-th composite magnetic material carbon fiber layer can be expressed as: In the formula, R ci is the outer diameter of the i-th composite magnetic material carbon fiber layer, A 1_ci , B 1_ci , C 1_ci , D 1_ci is the coefficient to be determined. 2) Air Gap Subdomain The air gap vector magnetic potential equation is: The general solution of the air gap vector magnetic potential can be expressed as: In the formula, R mN The outermost layer (i = N H ) The outer diameter of the magnetic powder film layer, A2, B2, C2, D2 are unknown coefficients. 3) Stator slot sub-domain The stator slot vector magnetic potential equation is: For double-layer windings, the general solution of the vector magnetic potential at the bottom of the stator slot can be expressed as: The general solution of the vector magnetic potential at the bottom of the stator slot can be expressed as: In the formula, J i1 and J i2 is the current density of the upper and lower windings in the i-th slot, R sm 、E n and G3 are respectively expressed as: E n =nπ / b sa (21) 4) Stator slot sub-area The stator slot vector magnetic potential equation is: The general solution of the stator slot vector magnetic potential can be expressed as: In the formula, F m It is expressed as: F m =mπ / b oa (25) 3. The method for constructing a multi-layer accurate sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor according to claim 1, characterized in that: In step S3, the magnetic density expression of each sub-domain is: The radial and tangential parts of the magnetic flux density can be obtained by the vector magnetic potential, and its expression is: 1) Magnetic density of composite magnetic material layer subdomain The boundary condition between the first magnetic powder film layer and the rotor yoke is: The radial magnetic flux density of the first layer of magnetic powder film is: The tangential magnetic flux density of the first layer of magnetic powder film is: In the formula, C m1k , C m2k , C m3k , C m4k , C m5k , C m6k Respectively expressed as: In the formula, μ rm is the relative magnetic permeability of the magnetic powder film, and G1=(R r / R m1 ) k . Radial magnetic flux density of the i-th layer (i≠1) of magnetic powder film: Tangential magnetic flux density of the i-th layer (i≠1) of magnetic powder film: Radial magnetic flux density of the i-th carbon fiber layer: Tangential magnetic flux density of the i-th carbon fiber layer: 2) Air gap sub-domain magnetic density The radial magnetic density of the air gap is: The air gap tangential flux density is: 3) Stator slot sub-domain magnetic flux density The radial magnetic flux density of the stator slot is: The tangential flux density at the bottom of the stator slot is: The tangential flux density at the top of the stator slot is: 4) Stator slot sub-field magnetic flux density The radial magnetic flux density of the stator slot is: The stator slot tangential flux density is:

4. The method for constructing a multi-layer accurate sub-domain magnetic field analytical model of a hierarchical composite rotor high-speed permanent magnet motor according to claim 1, characterized in that: In step S4, the boundary conditions of each subdomain are: 1) Boundary conditions between magnetic powder film layer and carbon fiber layer In the composite magnetic material solution area, the radial magnetic induction intensity and tangential magnetic field intensity of the i-th magnetic powder film layer and the carbon fiber layer are continuous, and the boundary conditions are expressed as: In the formula, When in the first layer of magnetic powder film, the boundary condition can be expressed as: Since the last outer layer of the composite magnetic material is a carbon fiber layer, the outermost carbon fiber layer will be divided into a calculation domain with the sheath and the air gap. The outermost layer number of the carbon fiber layer solution domain is N H -1. When the magnetic powder film is the i-th layer, its boundary conditions can be written as: In the formula, The radial magnetic induction intensity and tangential magnetic field intensity of the i-th carbon fiber layer and the i+1-th magnetic powder film layer are continuous, and the boundary conditions are expressed as: When the carbon fiber layer is in the i-th layer, its boundary condition can be written as: In the formula, G cm =(R ci / R mi+1 ) k (65) 2) Composite magnetic materials and air gap boundary conditions Nth H The radial magnetic induction intensity and tangential magnetic field intensity of the magnetic powder film layer and the air gap are continuous, and the boundary condition is expressed as: The outermost layer of magnetic powder film (i=N H ) layer calculation domain and air gap boundary conditions are consistent with the structure of formula (4.55) to formula (4.58), the difference is that G ci The formula definition of G ci Need to be replaced by G N , whose expression is: 3) Boundary conditions between stator slots and slot openings 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: 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: The boundary conditions between stator slots and slots, and between stator slots and air gaps are consistent with the boundary conditions of the traditional surface-mounted motor precise subdomain model, and will not be repeated in this article. The above boundary conditions are combined to solve the coefficient matrix, and the matrix equation is: TO c X c =And c (70) In the formula, A c is the total stiffness matrix, Y c is a constant term vector, X c is the coefficient vector to be determined, where X 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 D2 C 4t D 4t D 3t ] T .

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