Surface-mounted eccentric permanent magnet motor magnetic field analytical calculation method

Abstract

The invention relates to the technical field of permanent magnet motor magnetic fields, in particular to a surface-mounted eccentric permanent magnet motor magnetic field analytical calculation method, which comprises the following steps of: 1, calculating a rotor eccentricity effect by adopting bilinear mapping conformal transformation; 2, solving a magnetic field generated by the permanent magnet and the winding by using a permanent magnet equivalent surface current method, a sub-domain method and a magnetic field superposition principle; and 3, solving the saturation equivalent current of the iron core according to the magnetic circuit Kirchhoff law. The method has the characteristics of strong practical application, high calculation precision and high calculation speed.

Description

Technical Field

[0001] The invention relates to the technical field of permanent magnet motor magnetic field, and in particular to a method for analyzing and calculating the magnetic field of a surface-mounted eccentric permanent magnet motor. Background Art

[0002] Rare earth permanent magnet motors have the following advantages: ① high efficiency; ② high power density and torque density; ③ high power factor; ④ small torque pulsation; ⑤ low vibration and noise; ⑥ small moment of inertia and fast response; ⑦ high speed and torque control accuracy; ⑧ flexible shape and structure design. Rare earth permanent magnet motors can achieve high performance that is difficult to achieve with ordinary electric excitation motors. With the development of rare earth permanent magnet materials and permanent magnet motor design technology, it has now become the mainstream trend of motor research and motor product development, and has been widely used in aviation, aerospace, national defense, equipment manufacturing, industry and agriculture, transportation and daily life. The surface-mounted permanent magnet motor is named because the permanent magnet is placed on the surface of the rotor core. Compared with the built-in permanent magnet motor, it has the advantages of simple structure, small magnetic circuit distortion, small inductance, and convenient control. It is one of the most commonly used rotor forms in permanent magnet motors. The calculation of the electromagnetic field in the motor is the basis for calculating the motor performance. With the development of computer computing performance and finite element technology, although numerical finite element method is now mostly used to calculate the motor magnetic field and performance, the finite element method not only has the problem of time-consuming modeling, pre-processing, solving and post-processing, but also is not conducive to beginners to better grasp the basic internal mechanism of motor design. The accurate analytical calculation method of the magnetic field of the surface-mounted permanent magnet motor is conducive to the rapid and accurate optimization design of the surface-mounted permanent magnet motor.

[0003] In the existing analytical calculation methods for surface-mounted permanent magnet motors, the subdomain method (such as CN201811453722.7), the magnetic circuit method (such as CN201911097266.1), the conformal transformation method (such as CN202110096521.1), etc. are often used separately, and certain assumptions are made in the analytical calculation process, such as infinite core magnetic permeability, the same thickness of permanent magnets, and no eccentricity of the rotor. However, the BH curve of the stator core of the actual surface-mounted permanent magnet motor is nonlinear, a special pole shape (permanent magnets of unequal thickness) is used to optimize the motor performance, and the motor rotor has a certain degree of eccentricity during actual production and operation. Summary of the invention

[0004] The present invention provides a method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor, which has the characteristics of strong practical application, high calculation accuracy and fast calculation speed.

[0005] A method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor according to the present invention comprises the following steps:

[0006] 1. Use bilinear mapping conformal transformation to calculate the rotor eccentricity effect;

[0007] 2. Use the permanent magnet equivalent surface current method, subdomain method and magnetic field superposition principle to solve the magnetic field generated by the permanent magnet and winding;

[0008] 3. Solve the core saturation equivalent current based on Kirchhoff's law of magnetic circuit.

[0009] As a preference, in step 1, the bilinear mapping transforms the S plane where the two eccentric circles are located into the T plane where the two concentric circles are located, and the air gap magnetic flux B of the polar coordinate system in the T plane is T It is expressed as:

[0010]

[0011] In the above formula, B Tr represents the radial air gap flux density in the T plane, B Tθ represents the tangential air gap flux density in the T plane, represents the radial unit direction vector, The unit direction vector representing the tangent direction;

[0012] So the air gap magnetic flux B in the polar coordinate system in the S plane S It is expressed as:

[0013] B S =B T [λ(e d ,β)] * (2)

[0014] In the above formula, e d is the center of the outer circle of the S plane O s and the inner circle center O r The distance between them, β is e d The angle between the X axis and d ,β)] * is the intermediate parameter λ(e d ,β),λ(e d ,β) is obtained through bilinear mapping:

[0015]

[0016] In the above formula,

[0017]

[0018] h(e d ) and k(e d ,β) is the intermediate parameter, j is the imaginary unit, R s and R r are the radii of the outer and inner circles respectively;

[0019] In the above formula,

[0020]

[0021] α is e s The angle between the X axis and the s O is the center of the outer circle s and the inner circle rotation center O b The distance between r The inner circle center O r and the inner circle rotation center O b The distance between

[0022] From equation (3), we can see that the effect of eccentricity on the magnetic field depends on the relative position between the center of the inner circle and the center of the outer circle (e d , β).

[0023] Preferably, in step 2, after conformal transformation, the electromagnetic field inside the non-eccentric motor is combined with formula (2) to obtain the electromagnetic field inside the motor with rotor eccentricity; then, an analytical calculation of the electromagnetic field inside the non-eccentric motor is performed:

[0024] The magnetic flux density generated by the permanent magnet is equivalent to the current distributed on the surface of the permanent magnet; the permanent magnet surface current density J is obtained by the following formula:

[0025]

[0026] In the above formula, B r is the remanence of the permanent magnet, μ0 is the magnetic permeability of air, h is the angle between the magnetization direction and the tangent direction of the permanent magnet surface, m (θ) is the thickness of the permanent magnet at the position θ, R r is the outer radius of the rotor core, R s is the inner radius of the stator core;

[0027] The current i at each position c for:

[0028] i c =JΔl (9)

[0029] In the above formula, Δl is the microelement of the length of the permanent magnet surface;

[0030] When the core magnetic resistance is zero, the permanent magnet surface current equivalent method is used to establish a subdomain model with a pair of current coils in the air gap.

[0031] Since the permanent magnet and the air gap are simplified into a subdomain, namely region 1, the magnetic field generated by the permanent magnet surface current and the slot current is added together by the magnetic field superposition principle to obtain the synthetic air gap magnetic field, the vector magnetic potential A z1i The calculation formula is:

[0032]

[0033] In the above formula, θ represents the position angle;

[0034] The Laplace equation for the notch area 2j and the in-notch area 3j is:

[0035]

[0036] In the above formula, A z represents the vector magnetic potential, r represents the radius, J s represents the electric density, μ0 is the magnetic permeability of air;

[0037] The general solution A of the above partial differential equation in the 2j region z2j for:

[0038]

[0039] General solution A of vector magnetic potential in 3j region z3j for:

[0040]

[0041] In formulas (10), (12), and (13), A 1mi ,C 1mi ,A 2nj ,B 2nj and C 3kj is the unknown coefficient, and the center of the first slot is defined as the initial angle, θ i is the angle between the centerline of the ith pole and the centerline of the first slot, θ j is the angle between the center of the jth slot and the center of the first slot, b sa is the slot width angle, b oa is the slot width angle, m and n are the harmonic orders to be solved, R sb is the groove bottom radius, J i0 and J ik Represents the DC component and kth component of the Fourier decomposition of the current density in the slot, and the intermediate variable E n =nπ / b oa ; G 1m =(r / R r ) m +(R r / r) m ; E k =kπ / b sa ; k represents the kth harmonic, R p and ξ are the positions of the coil in the two-dimensional polar coordinate system;

[0042] A 1mi ,C 1mi ,A 2nj,B 2nj and C 3kj Through boundary conditions and interface solutions, the boundary conditions in each subdomain and the interface conditions between subdomains are constrained; the magnetic flux density and vector magnetic potential along the interface of the subdomains meet the conditions of equal tangential magnetic flux density and equal vector magnetic potential;

[0043] The constraints for the jth slot are:

[0044] When θ=θ j ±b oa / 2 and R s ≤r≤R t When B r2j =0 (14)

[0045] Among them, R t is the radius of the junction between the notch and the inside of the groove, B r2j is the radial magnetic flux density in the 2j region;

[0046] The constraints within the jth slot are:

[0047]

[0048] Among them, B θ3j and B r3j They are the tangential magnetic flux density and radial magnetic flux density in the 3j region respectively.

[0049] As a preferred embodiment, in step 3, according to the magnetic voltage drop equivalent principle, an iron core saturation equivalent current is introduced into the slot to replace the magnetic voltage drop in the iron core. The equivalent current i si The calculation formula is:

[0050] i si =V sj -V s(j-1) (39)

[0051] In the above formula, V sj and V s(j-1) Indicates the magnetic potential of the adjacent nodes;

[0052] A nonlinear magnetic network diagram of the effect of stator core saturation on the magnetic field is established. The nonlinear magnetic network diagram includes the node magnetic potential of the stator core, the core magnetic resistance, the magnetic flux entering the core, and the core saturation equivalent current in the slot; the magnetic flux entering the core φ sm Calculation via vector magnetic potential:

[0053] φ sm =[A z (r x1 ,θ x1 )-A z (r x2 ,θ x2 )] eff(40)

[0054] In the above formula, l eff A is the effective axial length of the motor, z (r x1 ,θ x1 ) and A z (r x2 ,θ x2 ) represents the two positions where the magnetic flux entering the core is calculated;

[0055] According to the nonlinear magnetic network diagram, the node magnetic potential in the core is obtained by Kirchhoff's law of magnetic circuit:

[0056] f(V)=AΛA T V-φ s =0 (41)

[0057] In the above formula, A is the correlation matrix, Λ is the magnetoresistance matrix, V is the magnetic potential matrix, φ s is the magnetic flux matrix entering the iron core; the above formula can be solved by the Newton-Raphson method.

[0058] The present invention combines conformal transformation, permanent magnet equivalent surface current method, subdomain method, magnetic field superposition principle and iron core saturation equivalent current method: firstly, bilinear mapping conformal transformation is used to calculate the rotor eccentricity effect, then the permanent magnet equivalent surface current method, subdomain method and magnetic field superposition principle are used to solve the magnetic field generated by the permanent magnet and the winding, and finally the iron core saturation equivalent current is solved according to Kirchhoff's law of magnetic circuit. The present invention has the characteristics of strong practical application, high calculation accuracy and fast calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of a method for analyzing and calculating the magnetic field of a surface-mounted eccentric permanent magnet motor in an embodiment;

[0060] FIG2( a ) is a schematic diagram of the S plane in the bilinear mapping in an embodiment;

[0061] FIG2( b ) is a schematic diagram of the T plane in the bilinear mapping in the embodiment;

[0062] Figure 3 Schematic diagram of a subdomain model of a surface-mounted permanent magnet motor taking into account the core magnetic resistance in an embodiment;

[0063] Figure 4 A schematic diagram of a subdomain model in which a pair of current coils are present in an air gap in an embodiment;

[0064] Figure 5 A schematic diagram of a nonlinear magnetic network showing the effect of stator core saturation on the magnetic field in an embodiment;

[0065] Figure 6Schematic diagram of radial magnetic flux density of the air gap of the surface-mounted eccentric permanent magnet motor in the embodiment;

[0066] Figure 7 Schematic diagram of the air gap tangential flux density of the surface mounted eccentric permanent magnet motor in the embodiment. DETAILED DESCRIPTION

[0067] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0068] Example

[0069] like Figure 1 As shown, this embodiment provides a method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor (taking into account the nonlinear stator core and magnetic pole shape), which includes the following steps:

[0070] 1. Use bilinear mapping conformal transformation to calculate the rotor eccentricity effect.

[0071] Bilinear mapping is a type of conformal transformation that can handle the eccentricity problem of magnetic field calculation within two circular boundaries. Bilinear mapping transforms the S plane where the two eccentric circles are located into the T plane where the two concentric circles are located, as shown in Figure 2(a) and Figure 2(b). In the S plane and T plane, the radius r <R r and r>R s Relative magnetic permeability μ=∞ in the region, radius r≤R r and r ≥ R s The relative magnetic permeability in the region is μ = μ0, and the X axis represents the 0° position. s and O r are the centers of the outer and inner circles, O b is the inner circle rotation center, e s O s and O b The distance between r O r and O b The distance between d O S and O r The distance between them, α, β, and γ are respectively s 、e d 、e r The angle between the X axis and the s and R r are the radii of the outer circle and the inner circle respectively. In the T plane of the figure, O s , O r and O b coincide with the same point, R Ts and R Trare the radii of the outer and inner circles respectively.

[0072] Air gap magnetic flux density B of polar coordinate system in T plane T It is expressed as:

[0073]

[0074] In the above formula, B Tr represents the radial air gap flux density in the T plane, B Tθ represents the tangential air gap flux density in the T plane, represents the radial unit direction vector, The unit direction vector representing the tangent direction;

[0075] So the air gap magnetic flux B in the polar coordinate system in the S plane S It is expressed as:

[0076] B S =B T [λ(e d ,β)] * (2)

[0077] In the above formula, e d is the center of the outer circle of the S plane O s and the inner circle center O r The distance between them, β is e d The angle between the X axis and d ,β)] * is the intermediate parameter λ(e d ,β),λ(e d ,β) is obtained through bilinear mapping:

[0078]

[0079] In the above formula,

[0080]

[0081] h(e d ) and k(e d ,β) is the intermediate parameter, j is the imaginary unit, R s and R r are the radii of the outer and inner circles respectively;

[0082] In the above formula,

[0083]

[0084] α is e s The angle between the X axis and the s O is the center of the outer circle s and the inner circle rotation center Ob The distance between r The inner circle center O r and the inner circle rotation center O b The distance between

[0085] From equation (3), we can see that the effect of eccentricity on the magnetic field depends on the relative position between the center of the inner circle and the center of the outer circle (e d , β).

[0086] 2. Use the permanent magnet equivalent surface current method, subdomain method and magnetic field superposition principle to solve the magnetic field generated by the permanent magnet and winding.

[0087] After the conformal transformation, the electromagnetic field inside the non-eccentric motor is combined with equation (2) to obtain the electromagnetic field inside the motor with rotor eccentricity. Next, the analytical calculation of the electromagnetic field inside the non-eccentric motor will be performed.

[0088] like Figure 3 As shown in FIG. 1 , this is a subdomain model of a surface-mounted permanent magnet motor taking into account the core magnetic resistance. The permanent magnet and the air gap are subdomain 1 (Region 1), the winding slot is subdomain 2j (j=1, 2, …), and the slot is subdomain 3j (j=1, 2, …).

[0089] The magnetic flux density generated by the permanent magnet is equivalent to the current distributed on the surface of the permanent magnet; the permanent magnet surface current density J is obtained by the following formula:

[0090]

[0091] In the above formula, B r is the remanence of the permanent magnet, μ0 is the magnetic permeability of air, h is the angle between the magnetization direction and the tangent direction of the permanent magnet surface, m (θ) is the thickness of the permanent magnet at the position θ, R r is the outer radius of the rotor core, R s is the inner radius of the stator core;

[0092] The current i at each position c for:

[0093] i c =JΔl (9)

[0094] In the above formula, Δl is the microelement of the length of the permanent magnet surface;

[0095] When the core magnetic resistance is zero, the permanent magnet surface current equivalent method is used to establish a subdomain model with a pair of current coils in the air gap, such as Figure 4 As shown;

[0096] Since the permanent magnet and the air gap are simplified into a subdomain, namely region 1, the magnetic field generated by the permanent magnet surface current and the slot current is added together by the magnetic field superposition principle to obtain the synthetic air gap magnetic field, the vector magnetic potential A z1i The calculation formula is:

[0097]

[0098] In the above formula, θ represents the position angle;

[0099] The Laplace equation for the notch area 2j and the in-notch area 3j is:

[0100]

[0101] In the above formula, A z represents the vector magnetic potential, r represents the radius, J s represents the electric density, μ0 is the magnetic permeability of air;

[0102] The general solution A of the above partial differential equation in the 2j region z2j for:

[0103]

[0104] General solution A of vector magnetic potential in 3j region z3j for:

[0105]

[0106] In formulas (10), (12), and (13), A 1mi ,C 1mi ,A 2nj ,B 2nj and C 3kj is the unknown coefficient, and the center of the first slot is defined as the initial angle, θ i is the angle between the centerline of the ith pole and the centerline of the first slot, θ j is the angle between the center of the jth slot and the center of the first slot, b sa is the slot width angle, b oa is the slot width angle, m and n are the harmonic orders to be solved, R sb is the groove bottom radius, J i0 and J ik Represents the DC component and kth component of the Fourier decomposition of the current density in the slot, and the intermediate variable E n =nπ / b oa ; G 1m =(r / R r ) m +(R r / r) m ; E k =kπ / bsa ; k represents the kth harmonic, R p and ξ are the positions of the coil in the two-dimensional polar coordinate system;

[0107] A 1mi ,C 1mi ,A 2nj ,B 2nj and C 3kj Through boundary conditions and interface solutions, the boundary conditions in each subdomain and the interface conditions between subdomains are constrained; the magnetic flux density and vector magnetic potential along the interface of the subdomains meet the conditions of equal tangential magnetic flux density and equal vector magnetic potential;

[0108] The constraints for the jth slot are:

[0109] When θ=θ j ±b oa / 2 and R s ≤r≤R t When B r2j =0 (14)

[0110] Among them, R t is the radius of the junction between the notch and the inside of the groove, B r2j is the radial magnetic flux density in the 2j region;

[0111] The constraints within the jth slot are:

[0112]

[0113] Among them, B θ3j and B r3j They are the tangential magnetic flux density and radial magnetic flux density in the 3j region respectively.

[0114] 3. Solve the core saturation equivalent current based on Kirchhoff's law of magnetic circuit.

[0115] In actual situations, the stator core is nonlinear and has a magnetic voltage drop, and the core magnetic resistance is not zero. According to the core BH curve, different magnetic densities correspond to different relative magnetic permeabilities and magnetic voltage drops.

[0116] According to the magnetic voltage drop equivalent principle, the core saturation equivalent current is introduced into the slot to replace the magnetic voltage drop in the core. The equivalent current i si The calculation formula is:

[0117] i si =V sj -V s(j-1) (39)

[0118] In the above formula, V sj and V s(j-1) Indicates the magnetic potential of the adjacent nodes;

[0119] A nonlinear magnetic network diagram of the effect of stator core saturation on the magnetic field is established, such as Figure 5 As shown in the figure, the nonlinear magnetic network diagram includes the node magnetic potential of the stator core, the core magnetic resistance, the magnetic flux entering the core and the core saturation equivalent current in the slot; the magnetic flux entering the core φ sm Calculation via vector magnetic potential:

[0120] φ sm =[A z (r x1 ,θ x1 )-A z (r x2 ,θ x2 )]l eff (40)

[0121] In the above formula, l eff A is the effective axial length of the motor, z (r x1 ,θ x1 ) and A z (r x2 ,θ x2 ) represents the two positions where the magnetic flux entering the core is calculated;

[0122] According to the nonlinear magnetic network diagram, the node magnetic potential in the core is obtained by Kirchhoff's law of magnetic circuit:

[0123] f(V)=AΛA T V-φ s =0 (41)

[0124] In the above formula, A is the correlation matrix, Λ is the magnetoresistance matrix, V is the magnetic potential matrix, φ s is the magnetic flux matrix entering the iron core; the above formula can be solved by the Newton-Raphson method.

[0125] Figure 6 It is the air gap radial flux density of the 2-pole 12-slot surface-mounted eccentric permanent magnet motor. Figure 7 This is the air gap tangential flux density of a 2-pole 12-slot surface-mounted eccentric permanent magnet motor. From the figure, we can see that the air gap flux density of the surface-mounted eccentric permanent magnet motor calculated by this method is very consistent with the calculation result of the finite element method, and the calculation time of this method is shorter than that of the finite element method.

[0126] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.

Claims

1. A method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor, characterized in that: The following steps are involved:

1. Use bilinear mapping conformal transformation to calculate the rotor eccentricity effect; 2. Use the permanent magnet equivalent surface current method, subdomain method and magnetic field superposition principle to solve the magnetic field generated by the permanent magnet and winding; 3. Solve the core saturation equivalent current based on Kirchhoff's law of magnetic circuit.

2. The method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor according to claim 1, characterized in that: In step 1, the bilinear mapping transforms the S plane where the two eccentric circles are located into the T plane where the two concentric circles are located. The air gap magnetic flux B of the polar coordinate system in the T plane is T It is expressed as: In the above formula, B Tr represents the radial air gap flux density in the T plane, B Tθ represents the tangential air gap flux density in the T plane, represents the radial unit direction vector, The unit direction vector representing the tangent direction; So the air gap magnetic flux B in the polar coordinate system in the S plane S It is expressed as: B S =B T [λ(e d ,b)] * (2) In the above formula, e d is the center of the outer circle of the S plane O s and the inner circle center O r The distance between them, β is e d The angle between the X axis and d ,β)] * is the intermediate parameter λ(e d ,β),λ(e d ,β) is obtained through bilinear mapping: In the above formula, h(e d ) and k(e d ,β) is the intermediate parameter, j is the imaginary unit, R s and R r are the radii of the outer and inner circles respectively; In the above formula, α is e s The angle between the X axis and the s O is the center of the outer circle s and the inner circle rotation center O b The distance between r The inner circle center O r and the inner circle rotation center O b The distance between From equation (3), we can see that the effect of eccentricity on the magnetic field depends on the relative position between the center of the inner circle and the center of the outer circle (e d , β).

3. The method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor according to claim 2, characterized in that: In step 2, after conformal transformation, the electromagnetic field inside the non-eccentric motor is combined with equation (2) to obtain the electromagnetic field inside the motor with rotor eccentricity; next, the electromagnetic field inside the non-eccentric motor is analytically calculated: The magnetic flux density generated by the permanent magnet is equivalent to the current distributed on the surface of the permanent magnet; the permanent magnet surface current density J is obtained by the following formula: In the above formula, B r is the remanence of the permanent magnet, μ0 is the magnetic permeability of air, h is the angle between the magnetization direction and the tangent direction of the permanent magnet surface, m (θ) is the thickness of the permanent magnet at the position θ, R r is the outer radius of the rotor core, R s is the inner radius of the stator core; The current i at each position c for: i c =JΔl (9) In the above formula, Δl is the microelement of the length of the permanent magnet surface; When the core magnetic resistance is zero, the permanent magnet surface current equivalent method is used to establish a subdomain model with a pair of current coils in the air gap. Since the permanent magnet and the air gap are simplified into a subdomain, namely region 1, the magnetic field generated by the permanent magnet surface current and the slot current is added together by the magnetic field superposition principle to obtain the synthetic air gap magnetic field, the vector magnetic potential A z1i The calculation formula is: In the above formula, θ represents the position angle; The Laplace equation for the notch area 2j and the in-notch area 3j is: In the above formula, A z represents the vector magnetic potential, r represents the radius, J s represents the electric density, μ0 is the magnetic permeability of air; The general solution A of the above partial differential equation in the 2j region z2j for: General solution A of vector magnetic potential in 3j region z3j for: In formulas (10), (12), and (13), A 1mi ,C 1mi ,A 2nj ,B 2nj and C 3kj is the unknown coefficient, and the center of the first slot is defined as the initial angle, θ i is the angle between the centerline of the ith pole and the centerline of the first slot, θ j is the angle between the center of the jth slot and the center of the first slot, b sa is the slot width angle, b oa is the slot width angle, m and n are the harmonic orders to be solved, R sb is the groove bottom radius, J i0 and J ik Represents the DC component and kth component of the Fourier decomposition of the current density in the slot, and the intermediate variable E n =nπ / b oa ; G 1m =(r / R r ) m +(R r / r) m ; E k =kπ / b sa ; k represents the kth harmonic, R p and ξ are the positions of the coil in the two-dimensional polar coordinate system; A 1mi ,C 1mi ,A 2nj ,B 2nj and C 3kj Through boundary conditions and interface solutions, the boundary conditions in each subdomain and the interface conditions between subdomains are constrained; the magnetic flux density and vector magnetic potential along the interface of the subdomains meet the conditions of equal tangential magnetic flux density and equal vector magnetic potential; The constraints for the jth slot are: When θ=θ j ±b oa / 2 and R s ≤r≤R t When B r2j =0 (14) Among them, R t is the radius of the junction between the notch and the inside of the groove, B r2j is the radial magnetic flux density in the 2j region; The constraints within the jth slot are: Among them, B θ3j and B r3j They are the tangential magnetic flux density and radial magnetic flux density in the 3j region respectively.

4. The method for calculating the magnetic field of a surface-mounted eccentric permanent magnet motor according to claim 3 is characterized in that: In step 3, according to the magnetic voltage drop equivalent principle, the core saturation equivalent current is introduced into the slot to replace the magnetic voltage drop in the core. The equivalent current i si The calculation formula is: i si =V sj -V s(j-1) (39) In the above formula, V sj and V s(j-1) Indicates the magnetic potential of the adjacent nodes; A nonlinear magnetic network diagram of the effect of stator core saturation on the magnetic field is established. The nonlinear magnetic network diagram includes the node magnetic potential of the stator core, the core magnetic resistance, the magnetic flux entering the core, and the core saturation equivalent current in the slot; the magnetic flux entering the core φ sm Calculation via vector magnetic potential: f sm =[A z (r x1 ,i x1 )-A z (r x2 ,i x2 )]l eff (40) In the above formula, l eff A is the effective axial length of the motor, z (r x1 ,θ x1 ) and A z (r x2 ,θ x2 ) represents the two positions where the magnetic flux entering the core is calculated; According to the nonlinear magnetic network diagram, the node magnetic potential in the core is obtained by Kirchhoff's law of magnetic circuit: f(V)AΛA T V-φ s H0 (41) In the above formula, A is the correlation matrix, Λ is the magnetoresistance matrix, V is the magnetic potential matrix, φ s is the magnetic flux matrix entering the iron core; the above formula can be solved by the Newton-Raphson method.

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