Tangential magnetizing type 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 tangential magnetizing type 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, calculating an air-gap magnetic field generated by the rotor with the eccentric magnetic pole face by adopting Schw-Kg transformation; 3, calculating an armature reaction air-gap magnetic field in combination with a D-Q magnetic potential decomposition method and Schw-Kg transformation; 4, introducing complex relative permeability and conformal transformation to calculate a stator slotting effect in the air-gap magnetic field; and 5, calculating the saturation equivalent current of the iron core to consider the influence of the nonlinear stator iron core on the air-gap magnetic field. 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, in particular to a method for analytic calculation of the magnetic field of a tangential magnetizing eccentric permanent magnet motor. Background Art

[0002] Due to the development of rare earth materials, the inherent advantages of permanent magnet motors and the demand for applications, permanent magnet motors have been developed by leaps and bounds and are widely used in all walks of life. Compared with surface-mount and other embedded permanent magnet motor rotors, tangential magnetization permanent magnet motors have the advantages of strong rotor magnetic field concentration effect, different D-axis and Q-axis inductance, weak magnetic effect and good reluctance torque ratio, which are widely recognized by academia and application industries. The calculation of the electromagnetic field in the motor is the basis for the calculation of motor performance. With the development of computer computing performance and finite element technology, although numerical finite element methods are mostly used to calculate the magnetic field and performance of motors, 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 motor magnetic field analytical calculation method is combined with the finite element method. Generally, the analytical calculation method is used for preliminary design in the early stage, and the finite element method is finally used for precise optimization and verification.

[0003] The existing methods for calculating the magnetic field of permanent magnet motors mainly include the subdomain method (such as CN202311517735.7) and the magnetic circuit method (such as CN201810450264.5). The typical patent that considers eccentricity is CN110346719A. However, these methods have many assumptions and there are deviations in actual application. During the manufacturing and operation of the motor, a certain degree of eccentricity is inevitable; in order to reduce harmonics and improve performance, the shape of the magnetic poles will also be optimized; the nonlinearity of the stator core also exists inherently. In order to calculate the magnetic field of a tangentially magnetized permanent magnet motor and consider these factors, a method for calculating the magnetic field of a tangentially magnetized eccentric permanent magnet motor is needed that considers the nonlinear stator core and magnetic pole shape. Summary of the invention

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

[0005] According to the present invention, a method for calculating the magnetic field of a tangentially magnetized eccentric permanent magnet motor comprises the following steps:

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

[0007] Second, the air gap magnetic field generated by the rotor with eccentric magnetic pole faces is calculated using the Hsu-Ke transform;

[0008] 3. Calculate the armature reaction air gap magnetic field by combining DQ magnetic potential decomposition method and Xu-Ke transformation;

[0009] Fourth, complex relative permeability and conformal transformation are introduced to calculate the stator slotting effect in the air gap magnetic field;

[0010] 5. Calculate the core saturation equivalent current to consider the influence of the nonlinear stator core on the air gap magnetic field.

[0011] 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:

[0012]

[0013] 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;

[0014] So the air gap magnetic flux B in the polar coordinate system in the S plane S It is expressed as:

[0015] B S =B T [λ(e d ,β)] * (2)

[0016] 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:

[0017]

[0018] In the above formula,

[0019]

[0020] h(e d ) and k(e d ,β) is the intermediate parameter, j is the imaginary unit, R s and R rare the radii of the outer and inner circles respectively;

[0021] In the above formula,

[0022]

[0023] 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

[0024] 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).

[0025] Preferably, in step 2, after the conformal transformation, the electromagnetic field inside the motor of the non-eccentric rotor is combined with formula (2) to obtain the electromagnetic field inside the motor of the rotor eccentricity, and then the electromagnetic field inside the motor of the non-eccentric rotor is analytically calculated;

[0026] Air gap magnetic field B generated by the rotor permanent magnet m As shown below:

[0027]

[0028] In the above formula, F m is the magnetic potential on the rotor core surface, is the normalized magnetic flux density, the base value of magnetic flux density B max0 =μ 0 F m / δ min , δ min is the minimum air gap length, δ is the air gap length corresponding to any angle, and the radial component B mr is the radial magnetic flux density, the tangential component B mθ is the tangential magnetic flux density, μ 0 is the magnetic permeability of air; j is the imaginary unit;

[0029] According to the Xu-Ke transformation, the per-unit magnetic flux density Obtained by the following formula:

[0030]

[0031] In the above formula, α p is the polar arc coefficient, τ=R q π / P is the pole distance, θ m is the angle, δ(θm ) is the angle θ m The corresponding air gap length, P is the number of pole pairs, R q is the distance from the center of the circle to any point in the air gap.

[0032] As a preferred method, in step 3, according to the DQ magnetic potential decomposition method of the double reaction theory, the magnetic motive force F of the A phase winding A Divided into D-axis magnetic potential F Ad and Q-axis magnetic potential F Aq sum:

[0033] F A =F Ad +F Aq (10)

[0034] D-axis armature reaction magnetic field B Ad It is obtained by the following formula:

[0035]

[0036] Among them, h m is the thickness of the permanent magnet, n is the number of poles divided into discrete parts, σ ​​is the leakage coefficient, b m is the permanent magnet width;

[0037] In the above formula, It is obtained by Xu Ke transformation as follows:

[0038]

[0039] is the basic air gap magnetic field of the D-axis armature reaction when the air gap is uniform;

[0040] Q-axis armature reaction magnetic field B Aq It is obtained by the following formula:

[0041]

[0042] In the above formula, It is obtained by Xu Ke transformation as follows:

[0043]

[0044] In the above formula, u is the intermediate variable. From the first equation of the above formula, we can get the intermediate variable U = 2δ(θ m ) / b j , intermediate variable b j It represents half of the distance between poles at the pole shoe;

[0045] The armature reaction magnetic fields of phases B and C are obtained in a similar way;

[0046] The armature reaction magnetic field B generated by the three-phase winding w for:

[0047] B w =B Ad +B Aq +B Bd +B Bq +B Cd +B Cq (15)

[0048] B Bd , B Bq is the armature reaction magnetic field of the D and Q axes of the B phase, B Cd , B Cq is the armature reaction magnetic field of D and Q axes of phase C;

[0049] According to the principle of magnetic field superposition, the total air gap magnetic field B generated by the permanent magnet and armature reaction is expressed as:

[0050] B=B m +B w =B r +jB θ (16)

[0051] In the above formula, B r is the radial magnetic flux density, B θ is the tangential magnetic flux density.

[0052] Preferably, in step 4, the stator slotting effect is obtained by complex relative permeability and conformal transformation:

[0053]

[0054] In the above formula, B z Indicates the air gap flux density after slotting, B T =μ 0 F m / δ min represents the magnetic density base value, λ r and λ θ Respectively represent the real part and imaginary part of the complex relative permeability; λ is the complex relative permeability, w represents the coordinate in the W plane of the conformal change, and w is obtained by the following formula:

[0055]

[0056] In the above formula, the intermediate variable z = R q θ m +j(R s -R q ), b 0 is the slot width;

[0057] The radial air gap magnetic field B of the spoke permanent magnet motor with concentric rotor sr and the tangential air gap magnetic field B sθ They are

[0058]

[0059] As a preferred embodiment, in step 5, 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:

[0060] i si =V sj -V s(j-1) (20)

[0061] In the above formula, V sj and V s(j-1) Indicates the magnetic potential of the adjacent nodes;

[0062] 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 by magnetic density:

[0063]

[0064] In the above formula, l eff is the effective axial length of the motor, r x1 ,θ x1 and r x2 ,θ x2 To calculate two positions within the flux region entering the core;

[0065] According to the nonlinear magnetic network diagram, the node magnetic potential in the core is obtained by Kirchhoff's law:

[0066] f(V)=AAA T V-φ s =0 (22)

[0067] 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.

[0068] The present invention combines bilinear mapping conformal transformation, Hsu-Ker transformation, DQ magnetic potential decomposition method, magnetic field superposition principle, complex relative magnetic permeability and iron core saturation equivalent current method: firstly, bilinear mapping conformal transformation is adopted to calculate the rotor eccentricity effect, then Hsu-Ker transformation is adopted to calculate the air gap magnetic field generated by the rotor with eccentric magnetic poles, secondly, the DQ magnetic potential decomposition method and Hsu-Ker transformation are combined to calculate the armature reaction air gap magnetic field, then the complex relative magnetic permeability and conformal transformation are introduced to calculate the stator slotting effect in the air gap magnetic field, and finally the iron core saturation equivalent current is calculated to consider the influence of the nonlinear stator iron core on the air gap magnetic field. The present invention has the characteristics of strong practical application, high calculation accuracy and fast calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of a method for analytic calculation of magnetic field of a tangential magnetization type eccentric permanent magnet motor in an embodiment;

[0070] FIG2( a ) is a schematic diagram of the S plane in the bilinear mapping in the embodiment;

[0071] FIG2( b ) is a schematic diagram of the T plane in the bilinear mapping in the embodiment;

[0072] Figure 3 A two-dimensional structural diagram of a concentric tangential magnetization permanent magnet motor in an embodiment;

[0073] Figure 4 A schematic diagram of a nonlinear magnetic network showing the effect of stator core saturation on the magnetic field in an embodiment;

[0074] Figure 5 Schematic diagram of radial magnetic flux density of the air gap of the tangentially magnetized eccentric permanent magnet motor in the embodiment;

[0075] Figure 6 Schematic diagram of the radial magnetic flux density of the air gap of the tangentially magnetized eccentric permanent magnet motor in the embodiment. DETAILED DESCRIPTION

[0076] 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.

[0077] Example

[0078] like Figure 1 As shown, this embodiment provides a method for calculating the magnetic field of a tangentially magnetized eccentric permanent magnet motor (taking into account the nonlinear stator core and magnetic pole shape), which includes the following steps:

[0079] 1. Use bilinear mapping conformal transformation to calculate the rotor eccentricity effect.

[0080] 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 Relative magnetic permeability in the region μ=μ 0 , the X axis represents the 0° position. In the S plane of the figure, O 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 Tr are the radii of the outer and inner circles respectively.

[0081] 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 density B of the polar coordinate system in the T plane is T It is expressed as:

[0082]

[0083] 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;

[0084] So the air gap magnetic flux B in the polar coordinate system in the S plane S It is expressed as:

[0085] B S =BT [λ(e d ,β)] * (2)

[0086] 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:

[0087]

[0088] In the above formula,

[0089]

[0090] 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;

[0091] In the above formula,

[0092]

[0093] 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

[0094] 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).

[0095] Second, the Hsu-Ke transform is used to calculate the air gap magnetic field generated by the rotor with eccentric magnetic pole faces.

[0096] 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.

[0097] The two-dimensional structure of the concentric tangential magnetization permanent magnet motor is as follows Figure 3As shown in the figure, the magnetization direction of the permanent magnet is tangential to the circumference. The rotor magnetic pole arc surface (the center of the magnetic pole arc is O 1 ), the center of the entire tangential magnetization permanent magnet motor rotor is O, and the eccentric magnetic pole surface refers to O 1 It is not at the same point as O. r is the thickness of the pole edge, h m is the thickness of the permanent magnet, b m is the permanent magnet width, b j is half the distance between the poles, δ max is the maximum air gap, δ min is the minimum air gap, R s is the inner radius of the stator. m is the mechanical angle of any point Q in the air gap, δ(θ m ) is θ m The air gap length at R so is the stator outer radius.

[0098] Air gap magnetic field B generated by the rotor permanent magnet m As shown below:

[0099]

[0100] In the above formula, F m is the magnetic potential on the rotor core surface, is the normalized magnetic flux density, the base value of magnetic flux density B max0 =μ 0 F m / δ min , δ min is the minimum air gap length, δ is the air gap length corresponding to any angle, and the radial component B mr is the radial magnetic flux density, the tangential component B mθ is the tangential magnetic flux density, μ 0 is the magnetic permeability of air; j is the imaginary unit;

[0101] According to the Xu-Ke transformation, the per-unit magnetic flux density Obtained by the following formula:

[0102]

[0103] In the above formula, α p is the polar arc coefficient, τ=R q π / P is the pole distance, θ m is the angle, δ(θ m ) is the angle θ m The corresponding air gap length, P is the number of pole pairs, R q is the distance from the center of the circle to any point in the air gap.

[0104] 3. Combine the DQ magnetic potential decomposition method and Xu-Ke transformation to calculate the armature reaction air gap magnetic field.

[0105] In step 3, according to the DQ magnetic potential decomposition method of the double reaction theory, the magnetic motive force F of the A phase winding A Divided into D-axis magnetic potential F Ad and Q-axis magnetic potential F Aq sum:

[0106] F A =F Ad +F Aq (10)

[0107] D-axis armature reaction magnetic field B Ad It is obtained by the following formula:

[0108]

[0109] Among them, h m is the thickness of the permanent magnet, n is the number of poles divided into discrete parts, σ ​​is the leakage coefficient, b m is the permanent magnet width;

[0110] In the above formula, It is obtained by Xu Ke transformation as follows:

[0111]

[0112] is the basic air gap magnetic field of the D-axis armature reaction when the air gap is uniform;

[0113] Q-axis armature reaction magnetic field B Aq It is obtained by the following formula:

[0114]

[0115] In the above formula, It is obtained by Xu Ke transformation as follows:

[0116]

[0117] In the above formula, u is the intermediate variable. From the first equation of the above formula, we can get the intermediate variable U = 2δ(θ m ) / b j , intermediate variable b j It represents half of the distance between poles at the pole shoe;

[0118] The armature reaction magnetic fields of phases B and C are obtained in a similar way;

[0119] The armature reaction magnetic field B generated by the three-phase windingw for:

[0120] B w =B Ad +B Aq +B Bd +B Bq +B Cd +B Cq (15)

[0121] B Bd , B Bq is the armature reaction magnetic field of the D and Q axes of the B phase, B Cd , B Cq is the armature reaction magnetic field of D and Q axes of phase C;

[0122] According to the principle of magnetic field superposition, the total air gap magnetic field B generated by the permanent magnet and armature reaction is expressed as:

[0123] B=B m +B w =B r +jB θ (16)

[0124] In the above formula, B r is the radial magnetic flux density, B θ is the tangential magnetic flux density.

[0125] 4. Complex relative permeability and conformal transformation are introduced to calculate the stator slotting effect in the air gap magnetic field.

[0126] In step 4, the stator slotting effect is obtained by complex relative permeability and conformal transformation:

[0127]

[0128] In the above formula, B z Indicates the air gap flux density after slotting, B T =μ 0 F m / δ min represents the magnetic density base value, λ r and λ θ Respectively represent the real part and imaginary part of the complex relative permeability; θ is the complex relative permeability, w represents the coordinate in the W plane of the conformal change, and w is obtained by the following formula:

[0129]

[0130] In the above formula, the intermediate variable z = R q θ m +j(R s -R q ), b 0 is the slot width;

[0131] The radial air gap magnetic field B of the spoke permanent magnet motor with concentric rotor sr and the tangential air gap magnetic field B sθ They are

[0132]

[0133] 5. Calculate the core saturation equivalent current to consider the influence of the nonlinear stator core on the air gap magnetic field.

[0134] In step 5, in actual situations, the stator core is nonlinear and has magnetic voltage drop. According to the core BH curve, different magnetic flux density corresponds to different relative magnetic permeability and magnetic voltage drop. 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:

[0135] i si =V sj -V s(j-1) (20)

[0136] In the above formula, V sj and V s(j-1) Indicates the magnetic potential of the adjacent nodes;

[0137] A nonlinear magnetic network diagram of the effect of stator core saturation on the magnetic field is established, such as Figure 4 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 by magnetic density:

[0138]

[0139] In the above formula, l eff is the effective axial length of the motor, r x1 ,θ x1 and r x2 ,θ x2 To calculate two positions within the flux region entering the core;

[0140] According to the nonlinear magnetic network diagram, the node magnetic potential in the core is obtained by Kirchhoff's law:

[0141] f(V)=AAA T V-φ s =0 (22)

[0142] 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.

[0143] Figure 5 It is the radial magnetic flux density of the air gap of the 4-pole 24-slot tangential magnetization eccentric permanent magnet motor. Figure 6 This is the air gap tangential flux density of a 4-pole 24-slot tangentially magnetized eccentric permanent magnet motor. From the figure, we can see that the air gap flux density 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.

[0144] 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 tangentially magnetized eccentric permanent magnet motor, characterized in that: The following steps are involved:

1. Use bilinear mapping conformal transformation to calculate the rotor eccentricity effect; Second, the air gap magnetic field generated by the rotor with eccentric magnetic pole faces is calculated using the Hsu-Ke transform; 3. Calculate the armature reaction air gap magnetic field by combining DQ magnetic potential decomposition method and Xu-Ke transformation; Fourth, complex relative permeability and conformal transformation are introduced to calculate the stator slotting effect in the air gap magnetic field; 5. Calculate the core saturation equivalent current to consider the influence of the nonlinear stator core on the air gap magnetic field.

2. The method for calculating the magnetic field of a tangentially magnetized 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 tangentially magnetized eccentric permanent magnet motor according to claim 2, characterized in that: In step 2, after conformal transformation, the electromagnetic field inside the motor with a non-eccentric rotor is combined with equation (2) to obtain the electromagnetic field inside the motor with an eccentric rotor. Next, the electromagnetic field inside the motor with a non-eccentric rotor is analytically calculated. Air gap magnetic field B generated by the rotor permanent magnet m As shown below: In the above formula, F m is the magnetic potential on the rotor core surface, is the normalized magnetic flux density, the base value of magnetic flux density B max0 =μ0F m / δ min , δ min is the minimum air gap length, δ is the air gap length corresponding to any angle, and the radial component B mr is the radial magnetic flux density, the tangential component B mθ is the tangential magnetic flux density, μ0 is the magnetic permeability of air; j is the imaginary unit; According to the Xu-Ke transformation, the per-unit magnetic flux density It is obtained by the following formula: In the above formula, α p is the polar arc coefficient, τ=R q π / P is the pole distance, θ m is the angle, δ(θ m ) is the angle θ m The corresponding air gap length, P is the number of pole pairs, R q is the distance from the center of the circle to any point in the air gap.

4. The method for calculating the magnetic field of a tangentially magnetized eccentric permanent magnet motor according to claim 3 is characterized in that: In step 3, according to the DQ magnetic potential decomposition method of the double reaction theory, the magnetic motive force F of the A phase winding A Divided into D-axis magnetic potential F Ad and Q-axis magnetic potential F Aq sum: F A =F Ad +F Aq (10) D-axis armature reaction magnetic field B Ad It is obtained by the following formula: Among them, h m is the thickness of the permanent magnet, n is the number of poles divided into discrete parts, σ ​​is the leakage coefficient, b m is the permanent magnet width; In the above formula, It is obtained by Xu Ke transformation as follows: is the basic air gap magnetic field of the D-axis armature reaction when the air gap is uniform; Q-axis armature reaction magnetic field B Aq It is obtained by the following formula: In the above formula, It is obtained by Xu Ke transformation as follows: In the above formula, u is the intermediate variable. From the first equation of the above formula, we can get the intermediate variable U = 2δ(θ m ) / b j , intermediate variable b j It represents half of the distance between poles at the pole shoe; The armature reaction magnetic fields of phases B and C are obtained in a similar way; The armature reaction magnetic field B generated by the three-phase winding w for: B w =B Ad +B Aq +B Bd +B Bq +B Cd +B Cq (15) B Bd , B Bq is the armature reaction magnetic field of the D and Q axes of the B phase, B Cd , B Cq is the armature reaction magnetic field of D and Q axes of phase C; According to the principle of magnetic field superposition, the total air gap magnetic field B generated by the permanent magnet and armature reaction is expressed as: B=B m +B w =B r +jB θ (16) In the above formula, B r is the radial magnetic flux density, B θ is the tangential magnetic flux density.

5. The method for calculating the magnetic field of a tangentially magnetized eccentric permanent magnet motor according to claim 4, characterized in that: In step 4, the stator slotting effect is obtained by complex relative permeability and conformal transformation: In the above formula, B z Indicates the air gap flux density after slotting, B T =μ0F m / δ min represents the magnetic density base value, λ r and λ θ Respectively represent the real part and imaginary part of the complex relative permeability; λ is the complex relative permeability, w represents the coordinate in the W plane of the conformal change, and w is obtained by the following formula: In the above formula, the intermediate variable z = R q θ m +j(R s -R q ), b0 is the slot width; The radial air gap magnetic field B of the spoke permanent magnet motor with concentric rotor sr and the tangential air gap magnetic field B sθ They are 6. The method for calculating the magnetic field of a tangentially magnetized eccentric permanent magnet motor according to claim 5, characterized in that: In step 5, 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) (20) 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 by magnetic density: In the above formula, l eff is the effective axial length of the motor, r x1 ,θ x1 and r x2 ,θ x2 To calculate two positions within the flux region entering the core; According to the nonlinear magnetic network diagram, the node magnetic potential in the core is obtained by Kirchhoff's law: f(V)=AAA T V-φ s =0 (22) 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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