CN112737173A - Magnetic field calculation method for segmented oblique pole surface-mounted permanent magnet motor - Google Patents

Abstract

The invention relates to a magnetic field calculation method for a segmented skewed pole surface-mounted permanent magnet motor, which comprises the following steps: modeling the segmented oblique pole surface-mounted motor; aiming at different solution domain sections, respectively establishing a Laplace equation or a Poisson equation for each section of the motor; calculating different circumferential segmentation modes of the segmented oblique-pole motor, and solving radial and tangential component amplitudes of the permanent magnet under each subharmonic of residual magnetization intensity; calculating a winding arrangement mode, and performing Fourier decomposition on the current density of the stator to obtain the current density under each harmonic; calculating the magnetic field of the segmented skewed pole motor; and calculating the torque and the back electromotive force of the motor by using Maxwell stress equations and an electromagnetic induction law. The invention is suitable for the segmented skewed pole surface-mounted permanent magnet motors with different circumferential and axial segmentation modes, can reduce the calculation difficulty and shorten the calculation time by using the analytic model, and is convenient for analyzing the rule of the motor performance along with the magnetic pole segmentation and the skewed pole parameter change in the follow-up research work in an express and comprehensive manner.

Description

A method for calculating the magnetic field of a segmented sloping pole surface-mount permanent magnet motor

technical field

The invention relates to a segmented inclined pole surface-mounted permanent magnet motor.

Background technique

From the perspective of the motor itself, there are many ways to weaken the cogging torque by optimizing the structure and parameters of the motor, such as changing the pole-slot fit, optimizing the pole arc coefficient, the shape of the magnetic pole, adding auxiliary slots or using skewed slots, skewed poles, etc. method. Due to the limitation of permanent magnet processing and motor manufacturing process, compared with other methods for reducing cogging torque, the manufacturing process of the rotor sloping pole is simple, the cost is low, and it is more suitable for mass production and wide application. In the process of optimizing the motor by changing the motor structure, if there is no accurate analytical model for calculation, it is usually necessary to perform a large number of finite element calculations to analyze the influence of the structural parameter changes on the results. Compared with finite element calculation, establishing an accurate analytical model for magnetic field analysis can shorten the calculation time, improve the analysis efficiency, and provide a reference for the design and optimization of segmented sloping pole motors. D.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method capable of accurately calculating the magnetic field of a segmented inclined pole surface-mounted permanent magnet motor. The technical scheme of the present invention is as follows:

1. A method for calculating the magnetic field of a segmented inclined pole surface-mounted permanent magnet motor, comprising the following steps:

Step 1: Modeling a segmented slanted pole motor. Based on the idea of segmental discreteness, the entire magnetic field solution area is divided into the magnetic field solution segment along the axial direction in three-dimensional space, and the motor structure of each discrete segment is modeled. The region to which the segment belongs.

Step 2: For different solution domain segments, establish Laplace equation or Poisson equation for each motor segment;

The third step: taking into account the different circumferential segmentation modes of the segmented oblique pole motor, solve the radial and tangential component amplitudes M _rk and M _θk under each harmonic of the permanent magnet residual magnetization, where k is the permanent magnet domain and harmonic orders in the air-gap domain;

Step 4: Taking into account the winding arrangement, perform Fourier decomposition on the stator current density to obtain the current density at each harmonic;

Step 5: Combine the boundary conditions between the regions, establish a linear equation system in each axial solution domain segment, determine the undetermined coefficients, and then calculate the magnetic field of the segmented skew-pole motor: at the junction of the permanent magnet and the rotor core At the junction of the permanent magnet and the air gap, the radial magnetic field is continuous and the tangential magnetic field strength is equal; at the junction of the stator slot and the stator slot body, the radial magnetic field is continuous and the magnetic vector is equal; At the junction of the stator slot and the air gap, the radial magnetic field is continuous, and the magnetic vector is equal; combined with the M _rk and M _θk obtained in the third step and the current density obtained in the fourth step, the Laplace equation established in the second step is and Poisson equation to solve, get the expression of vector magnetic potential in the solution area, and then get the expression of radial component and tangential component of magnetic density in each area;

The sixth step: According to the radial and tangential component expressions of the air-gap flux density obtained in the fifth step, the torque and back EMF of the motor are calculated using Maxwell's stress equation and the law of electromagnetic induction.

Further, in the first step, the area to which each solution domain segment belongs is divided as follows: the motor is divided from the inside _out into the permanent _{magnet domain} , the gas The three regions of the gap domain and the stator part are described by the radial coordinate r in the polar coordinate system: when r<R _r , it is a ferromagnetic material, and when r>R _r and r<R _m , it is a permanent magnet domain; when R _m <r<R _s , it is the air gap domain; when r>R _s , it is the stator part, including the slot domain and the slot body domain.

A_z1j为第j段电机转子域的矢量磁位，M_θ、M_r分别为永磁体剩余磁化强度的切向和径向分量，μ₀为真空磁导率，θ代表极坐标系下的角坐标；在气隙域和槽口域建立拉普拉斯方程

A_z为该区域的矢量磁位；在槽身域建立泊松方程

A_z3ij为第j段电机第i个槽身的矢量磁位，J_i为第i个槽身的电流密度，当电机空载运行时，视为0。The second step is specifically: establish Poisson equation in the permanent magnet domain

A _z1j is the vector magnetic potential of the j-th motor rotor domain, M _θ and M _r are the tangential and radial components of the residual magnetization of the permanent magnet, respectively, μ ₀ is the vacuum permeability, and θ represents the angle in the polar coordinate system Coordinates; Laplace equations are established in the air gap and notch domains

A _z is the vector magnetic potential in this region; establish Poisson equation in the slot body region

A _z3ij is the vector magnetic potential of the ith slot body of the j-th motor, and J _i is the current density of the ith slot body. When the motor runs without load, it is regarded as 0.

When the magnetization method of the permanent magnet is radial magnetization, the following solution method can be used in the third step:

α_pr为磁极实际宽度与总极弧宽度的比值，α_pr＝∑l_s(n)/L,l_s(n)为各段磁极的极弧宽度，n代表第n段分段磁极，当α_pr＝1时，表明磁极分段数n_seg为1，即磁极不分段；d₁表示每相邻两极下间隙的一半，

d₂表示每极下每段磁极间的间隙：(1) Considering the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width corresponding to the permanent magnet under each pole, α _p is the pole arc coefficient, p is the number of pole pairs, and their relationship is

α _pr is the ratio of the actual width of the magnetic pole to the total pole arc width, α _pr =∑l _s (n)/L, l _s (n) is the pole arc width of each segment, n represents the nth segment segmented magnetic pole, when When α _pr = 1, it indicates that the number of magnetic pole segments n _seg is 1, that is, the magnetic poles are not segmented; d ₁ represents half of the lower gap of each adjacent two poles,

d ₂ represents the gap between each pole under each pole:

(2) Determine l _s (n) and the angle θ _s (n) corresponding to the midline of each magnetic pole: define α _pm (n) as the ratio of the n-th magnetic pole to the total width of the magnetic pole, and satisfy ∑ α _pm (n )=1, l _s (n)=Lα _pr α _pm (n), θ _s (n)=d ₁ +(n-1)d ₂ +∑l _s (n)-l _s (n)/2;

(3) The period of the radial component of the residual magnetization of the permanent magnet is 2π/p. In one period, the piecewise functions of M _r and M _θ are:

M _θ =0,-π/p≤θ≤π/p

where M is the magnitude of the residual magnetization vector,

When the poles are segmented, M is not zero at each pole, ie θ _s (n) _–ls (n)/2<θ<θ _s (n)+ _ls (n)/2.

When the magnetization method of the permanent magnet is parallel magnetization, the following solution method can be used in the third step:

α_pr为磁极实际宽度与总极弧宽度的比值，α_pr＝∑l_s(n)/L,l_s(n)为各段磁极的极弧宽度，n代表第n段分段磁极，当α_pr＝1时，表明磁极分段数n_seg为1，即磁极不分段；d₁表示每相邻两极下间隙的一半，

d₂表示每极下每段磁极间的间隙：(1) Considering the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width corresponding to the permanent magnet under each pole, α _p is the pole arc coefficient, p is the number of pole pairs, and their relationship is

α _pr is the ratio of the actual width of the magnetic pole to the total pole arc width, α _pr =∑l _s (n)/L, l _s (n) is the pole arc width of each segment, n represents the nth segment segmented magnetic pole, when When α _pr = 1, it indicates that the number of magnetic pole segments n _seg is 1, that is, the magnetic poles are not segmented; d ₁ represents half of the lower gap of each adjacent two poles,

d ₂ represents the gap between each pole under each pole:

(2) Determine l _s (n) and the angle θ _s (n) corresponding to the midline of each magnetic pole: define α _pm (n) as the ratio of the n-th magnetic pole to the total width of the magnetic pole, and satisfy ∑ α _pm (n )=1, l _s (n)=Lα _pr α _pm (n), θ _s (n)=d ₁ +(n-1)d ₂ +∑l _s (n)-l _s (n)/2;

(3) The period of the tangential component of the residual magnetization of the permanent magnet is 2π/p. In one period, the piecewise functions of M _r and M _θ are:

where M is the magnitude of the residual magnetization vector,

When the poles are segmented, M is not zero at each pole, ie θ _s (n) _–ls (n)/2<θ<θ _s (n)+ _ls (n)/2.

式中，F_m为槽身系数；J_i0为电流密度基波幅值；J_im为电流密度的各次谐波幅值；m为槽身域谐波次数；θ_i为第i个槽的位置；b_sa为槽身极弧宽度；F_m＝mπ/b_sa；J_i0＝(J_i1+J_i2)d/b_sa；J_im＝2[J_i1+J_i2cos(mπ)]sin(mπd/b_sa)/(mπ)；d为每层绕组在槽中占据面积的弧度；J_i1和J_i2分别为各层绕组的电流密度。Further, the following method can be adopted in the fourth step: for the concentrated winding with double-layer distribution, in the jth axial solution domain segment, J _i is decomposed into the Fourier series of the stator slot interval:

In the formula, F _m is the tank body coefficient; J _i0 is the fundamental wave amplitude of the current density; J _im is the harmonic amplitude of the current density; _m is the harmonic order of the tank body; position; b _sa is the pole arc width of the groove body; F _m =mπ/b _sa ; J _i0 =(J _i1 +J _i2 )d/b _sa ;J _im =2[J _i1 +J _i2 cos(mπ)]sin (mπd/b _sa )/(mπ); d is the radian of the area occupied by each layer of winding in the slot; J _i1 and J _i2 are the current density of each layer of winding, respectively.

The present invention has the following outstanding beneficial effects:

1. The present invention considers different magnetic pole positions in the axial direction and different segmentation methods in the circumferential direction when calculating the air-gap magnetic field, so that a more accurate air-gap magnetic field distribution can be obtained, and at the same time, the segmentation of different magnetization methods can be obtained. The magnetic field of the inclined pole surface mount permanent magnet motor is analyzed;

2. The calculation method of the present invention can be used to analyze the number of oblique pole segments, the oblique pole angle, the number of circumferential segments, the segment clearance, and the amplitude of the motor cogging torque in the circumferential segment mode and oblique pole mode, and the no-load reverse The variation law of the potential distortion rate has important reference significance for the initial design and optimal design of the segmented sloping pole surface-mounted permanent magnet motor.

Description of drawings

Figure 1 Schematic diagram of the motor structure

Figure 2 Subdomain model division diagram

Figure 3 Schematic diagram of the circumferential segment of the permanent magnet

Figure 4. Comparison of calculation results of segmented sloping pole surface-mounted permanent magnet motor calculated by analytical method and finite element method, (a) rotor structure diagram (b) comparison of opposite potential results of A (c) comparison of cogging torque results (d) Comparison of electromagnetic torque results

Detailed ways

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

The first step: determine the solution area;

As can be seen from Figure 1, based on the idea of piecewise discreteness, the entire magnetic field solution region is divided into N _z magnetic field solution regions along the axis in three-dimensional space. The slant angle of the jth magnetic pole is θ _j . The motor is modeled, and the solution area is divided into four, the area 1 _j is the permanent magnet domain, the area 2 _j is the air gap domain, the area 3 _ij is the slot body domain, and the area 4 _ij is the slot sub-domain.

Step 2: For different solution regions, establish Laplace equation or Poisson equation respectively;

Establish Poisson's equation in the permanent magnet domain 1 _j

In the stator current-carrying region 3 _ij , the vector magnetic potential satisfies the equation

Laplace equations are established in passive regions 2 _j , 3 _ij , 4 _ij

The third step: taking into account the different circumferential segmentation modes of the segmented inclined pole motor, solve M _rk and M _θk ;

The schematic diagram of the circumferential segment is shown in Figure 2. The relationship between the pole arc coefficient and the pole arc width of each magnetic pole, the number of magnetic pole segments and the segment gap is shown in equations (4) to (7):

α _pr =∑l _s (n)/L (5)

After determining the ratio of the nth magnetic pole to the total width of the magnetic pole, the pole arc width of each magnetic pole and the angle corresponding to the center line of each magnetic pole can be calculated by equations (8) and (9):

l _s (n)=Lα _pr α _pm (n) (8)

θ _s (n)=d ₁ +(n-1)d ₂ +∑l _s (n)-l _s (n)/2 (9)

The period of the radial or tangential component of the residual magnetization of the permanent magnet is 2π/p. According to the magnetization method of the permanent magnet, it can be divided into two situations.

a. When the magnetization method of the permanent magnet _{is radial magnetization, in one cycle, the piecewise functions of Mr and M θ are} :

where M is the magnitude of the residual magnetization vector,

When the poles are segmented, at each pole, that is, θ _s (n)–l _s (n)/2<θ<θ _s (n)+l _s (n)/2, M only exists, when the permanent When the magnetization method of the magnet is radial magnetization, the Fourier decomposition of the piecewise functions of M _r and M _θ obtained in the above formula can be obtained as follows:

b. When the magnetization method of the permanent magnet _{is parallel magnetization, in one cycle, the piecewise functions of Mr and M θ are} :

where M is the magnitude of the residual magnetization vector,

When the poles are segmented, at each pole, that is, θ _s (n)–l _s (n)/2<θ<θ _s (n)+l _s (n)/2, M only exists, when the permanent When the magnetization method of the magnet _{is parallel magnetization, the Fourier decomposition of the piecewise functions of Mr and M θ obtained} in the above formula can be obtained as follows:

in,

Step 4: Perform Fourier decomposition on the stator current density to obtain the current density expression;

For the concentrated winding with double layer distribution, the current density can be decomposed into the Fourier series of the stator slot interval

in,

J _i0 =(J _i1 +J _i2 )d/b _sa

J _im =2[J _i1 +J _i2 cos(mπ)]sin(mπd/b _sa )/(mπ)

The fifth step: establish boundary conditions, solve the Laplace equation and Poisson equation established in the second step, obtain the expression of the vector magnetic potential in each region, and then obtain the radial component B of the air gap magnetic density _r2j and the tangential component B _θ2j of the air gap flux density;

Establishment of boundary conditions

At the junction of the permanent magnet and the rotor core, the magnetic field strength H has only the radial component and the tangential component is 0;

At the junction of the permanent magnet and the air gap, the radial components of the magnetic induction intensity B are equal;

At the junction of the stator slot and the stator slot body, the radial components of the magnetic induction intensity B are equal;

At the junction of the stator slot and the air gap, the radial components of the magnetic induction intensity B are equal.

The expressions of B _r2j and B _θ2j are

Among them, B _rsk2j is the sine component of B _r2j , B _rck2j is the cosine component of B _r2j , B _θsk2j is the sine component of B _θ2j , B _θck2j is the cosine component of B _θ2j , and its expression is shown in equation (17)

In the formula, A _2jk ~ D _2jk are undetermined coefficients, which can be solved by formulas (18) ~ (26) simultaneously

In the formula, A _1jk , B _1jk , C _3ijv , D _3ijv , D _4ijm are all undetermined coefficients, which are solved by equations (18) to (26) simultaneously; R _sb is the stator slot bottom radius; θ _t is the rotor rotation angle; μ _r is the relative permeability of the permanent magnet; v is the harmonic order of the notch domain; M _θck , M _θsk , Mr _rck , and _{Mr rsk} are the amplitudes of the cosine and sine components of the tangential and radial magnetization of the permanent magnet, respectively ; D _i is a special solution; G _1k , G _2k , G _3v , G _4m , E _v , η _i0 (k), η _i (m,k), σ _i0 (k), σ _i (m,k), τ _i (m,k), ξ _i0 (k), ξ _i (m,k), γ _i0 (v), γ _i (v,m) are the parameter coefficients of the motor, which are expressed by the following formulas;

M _θck =M _θk cos(kθ _t )

M _rsk =M _rk sin(kθ _t )

M _θsk =M _θk sin(kθ _t )

M _rck =M _rk cos(kθ _t )

D _i =b _sa μ ₀ J _i0 (R _sb ² −R _t ² )/(2b _oa )

b_oa为槽口极弧宽度；

b _oa is the width of the notch pole arc;

η _i (m,k)= _{bo oa} σ _i (m,k)/(2π)

η _i0 (k)= _{bo oa} σ _i0 (k)/π

σ _i (m,k)=-2k[cos(mπ)sin(kθ _i +kb _oa /2)-sin(kθ _i -kb _oa /2)]/[b _oa (F _m ² -k ² )]

σ _i0 (k)=2sin(kb _oa /2)cos(kθ _i )/(kb _oa )

τ _i (m,k)=2k×[cos(mπ)cos(kθ _i +kb _oa /2)-cos(kθ _i -kb _oa /2)]/[b _oa (F _m ² -k ² )

ξ _i (m,k)=b _oa τ _i (m,k)/(2π)

ξ _i0 (k)= _{bo oa} τ _i0 (k)/π

γ _i (v,m)=b _oa ζ _i (v,m)/b _sa

γ _i0 (v)=2b _oa ζ _i0 (v)/b _sa

Step 6: Calculate the electromagnetic performance of the motor by using the radial component B _r2j of the air-gap flux density and the tangential component B _θ2j of the air-gap flux density obtained in the fourth step.

The cogging torque and electromagnetic torque of the motor can be calculated from the air-gap flux density at no-load and under load by formula (27), respectively.

In the formula, L _zj is the length of each section of the axially segmented motor

The flux linkage _ψx of each phase winding can be calculated by formula (28)

In the formula, x can be A, B, and C, respectively representing the A phase, B phase and C phase of the stator winding; N _c is the number of conductors per slot of the stator; a is the number of parallel branches of the stator winding

The back EMF of each phase winding E _x can be calculated by formula (29)

Taking a radially magnetized segmented sloping pole surface-mounted permanent magnet synchronous motor as an example to introduce the proposed magnetic field calculation method, the parameters of the motor are shown in Table 1.

Table 1 Inner rotor motor parameters

Determine the solution area

The motor is a segmented oblique pole structure, so it can be seen from Figure 1 that the motor is evenly segmented in the axial direction. Taking one of the segments as an example, its area division is shown in Figure 2.

For different solution regions, in the polar coordinate system, respectively establish Laplace equation or Poisson equation

Establish Poisson's equation in the permanent magnet domain 1 _j

In the stator current-carrying region 3 _ij , the vector magnetic potential satisfies the equation

Laplace equations are established in passive regions 2 _j , 3 _ij , 4 _ij

Calculation of the residual magnetization of permanent magnets

The magnetization method of the motor is radial magnetization

According to the ratio α _pm (n) of each magnetic pole to the total width of the magnetic pole, the pole arc width of each magnetic pole and the angle corresponding to the center line of each magnetic pole can be determined

l _m (n)=Lα _pr α _pm (n) (33)

θ _m (n)=d ₁ +(n-1)d ₂ +∑l _m (n)-l _m (n)/2 (34)

When the poles are segmented, M exists only at each pole, ie θ _m (n)-l _m (n)/2<θ<θ _m (n)+l _m (n)/2. According to different magnetization methods, the pole arc width of each segment of the magnetic pole and the angle relative to the initial position, the periodic function of the radial and tangential components of the residual magnetization is subjected to Fourier decomposition to obtain the expression. Radial and Tangential Component Expressions of Position Residual Magnetization

Establishment of boundary conditions

At the junction of the permanent magnet and the rotor core, the magnetic field strength H has only the radial component and the tangential component is 0;

At the junction of the permanent magnet and the air gap, the radial components of the magnetic induction intensity B are equal;

At the junction of the stator slot and the stator slot body, the radial components of the magnetic induction intensity B are equal;

At the junction of the stator slot and the air gap, the radial components of the magnetic induction intensity B are equal.

The radial and tangential expressions of the magnetic density in the air-gap domain are as follows:

in,

In the formula, A _2jk ~ D _2jk are the undetermined coefficients, which can be solved by formulas (38) ~ (46) simultaneously

Calculation of Electromagnetic Performance of Motors

Calculation of cogging torque under no-load and electromagnetic torque under load

Calculation of each phase winding flux linkage ψ _x

Calculation of the back EMF of each phase winding E _x

Verification of the correctness of the magnetic field calculation method proposed by the present invention

Set the number of axial segments of the motor to 5, the inclined pole angle to 20°, and the number of circumferential segments to 5. The ratio of each magnetic pole to the total width of the magnetic pole α _pm (n) is 0.1, 0.2, 0.3, 0.2, respectively. 0.1, establish a finite element model of a segmented sloping pole surface-mounted permanent magnet synchronous motor, and compare the results obtained by the calculation method of the present invention with the results obtained by the finite element model. The rotor structure and result comparison are shown in Figure 4. It can be seen from the figure that the calculation results are basically consistent with the calculation results of the finite element model, which verifies the correctness of the calculation method of the present invention.

Claims (8)

1. A method for calculating the magnetic field of a segmented inclined pole surface-mounted permanent magnet motor, comprising the following steps: Step 1: Modeling a segmented slanted pole motor. Based on the idea of segmental discreteness, the entire magnetic field solution area is divided into the magnetic field solution segment along the axial direction in three-dimensional space, and the motor structure of each discrete segment is modeled. The region to which the segment belongs. Step 2: For different solution domain segments, establish Laplace equation or Poisson equation for each motor segment; The third step: taking into account the different circumferential segmentation modes of the segmented oblique pole motor, solve the radial and tangential component amplitudes M _rk and M _θk under each harmonic of the permanent magnet residual magnetization, where k is the permanent magnet domain and harmonic orders in the air-gap domain; Step 4: Taking into account the winding arrangement, perform Fourier decomposition on the stator current density to obtain the current density at each harmonic; Step 5: Combine the boundary conditions between the regions, establish a linear equation system in each axial solution domain segment, determine the undetermined coefficients, and then calculate the magnetic field of the segmented skew-pole motor: at the junction of the permanent magnet and the rotor core At the junction of the permanent magnet and the air gap, the radial magnetic field is continuous and the tangential magnetic field strength is equal; at the junction of the stator slot and the stator slot body, the radial magnetic field is continuous and the magnetic vector is equal; At the junction of the stator slot and the air gap, the radial magnetic field is continuous, and the magnetic vector is equal; combined with the M _rk and M _θk obtained in the third step and the current density obtained in the fourth step, the Laplace equation established in the second step is and Poisson equation to solve, get the expression of vector magnetic potential in the solution area, and then get the expression of radial component and tangential component of magnetic density in each area; The sixth step: According to the radial and tangential component expressions of the air-gap flux density obtained in the fifth step, the torque and back EMF of the motor are calculated using Maxwell's stress equation and the law of electromagnetic induction. 2. The method for calculating the magnetic field of a segmented inclined-pole surface-mounted permanent magnet motor according to claim 1, wherein in the first step, the regions to which each solution domain segment belongs is divided as follows: by the rotor outer diameter R _r , The outer diameter of the permanent magnet R _m and the inner diameter of the stator R _s divide the motor from the inside out into three areas: the permanent magnet domain, the air gap domain, and the stator part, and the radius coordinate r in the polar coordinate system is used to describe each area: when r < When R _r , it is a ferromagnetic material, when r>R _r and r<R _m , it is a permanent magnet domain; when R _m <r<R _s , it is an air gap domain; when r>R _s , it is a stator section, including the slot field and the slot body field. 3. The method for calculating the magnetic field of a segmented inclined-pole surface-mounted permanent magnet motor according to claim 2, wherein the second step is specifically: establishing a Poisson equation in the permanent magnet domain

A _z1j is the vector magnetic potential of the j-th motor rotor domain, M _θ and M _r are the tangential and radial components of the residual magnetization of the permanent magnet, respectively, μ ₀ is the vacuum permeability, and θ represents the angle in the polar coordinate system Coordinates; Laplace equations are established in the air gap and notch domains

A _z is the vector magnetic potential in this region; establish Poisson equation in the slot body region

A _z3ij is the vector magnetic potential of the ith slot of the j-th motor, and J _i is the current density of the ith slot, which is regarded as 0 when the motor runs without load. 4. segmented oblique pole surface-mounted permanent magnet motor magnetic field calculation method according to claim 2, is characterized in that, when the magnetization mode of permanent magnet is radial magnetization, the 3rd step adopts following solution method: (1) Considering the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width corresponding to the permanent magnet under each pole, α _p is the pole arc coefficient, p is the number of pole pairs, and their relationship is

α _pr is the ratio of the actual width of the magnetic pole to the total pole arc width, α _pr =∑l _s (n)/L, l _s (n) is the pole arc width of each segment, n represents the nth segment segmented magnetic pole, when When α _pr = 1, it indicates that the number of magnetic pole segments n _seg is 1, that is, the magnetic poles are not segmented; d ₁ represents half of the lower gap of each adjacent two poles,

d ₂ represents the gap between each pole under each pole:

(2) Determine l _s (n) and the angle θ _s (n) corresponding to the midline of each magnetic pole: define α _pm (n) as the ratio of the n-th magnetic pole to the total width of the magnetic pole, and satisfy ∑ α _pm (n )=1, l _s (n)=Lα _pr α _pm (n), θ _s (n)=d ₁ +(n-1)d ₂ +∑l _s (n)-l _s (n)/2; (3) The period of the radial component of the residual magnetization of the permanent magnet is 2π/p. In one period, the piecewise functions of M _r and M _θ are:

M _θ =0,-π/p≤θ≤π/p where M is the magnitude of the residual magnetization vector, When the poles are segmented, M is not zero at each pole, ie θ _s (n) _–ls (n)/2<θ<θ _s (n)+ _ls (n)/2. 5. The method for calculating the magnetic field of a segmented inclined-pole surface-mounted permanent magnet motor according to claim 4, wherein the Fourier decomposition is carried out to the segmental function obtained in step (3) about M _r and M _θ Get the following expression:

M _θk =0. 6. segmented oblique pole surface-mounted permanent magnet motor magnetic field calculation method according to claim 2, is characterized in that, when the magnetization mode of permanent magnet is parallel magnetization, the 3rd step adopts following solution method: (1) Considering the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width corresponding to the permanent magnet under each pole, α _p is the pole arc coefficient, p is the number of pole pairs, and their relationship is

α _pr is the ratio of the actual width of the magnetic pole to the total pole arc width, α _pr =∑l _s (n)/L, l _s (n) is the pole arc width of each segment of the magnetic pole, n represents the nth segment segmented magnetic pole, when When α _pr = 1, it indicates that the number of magnetic pole segments n _seg is 1, that is, the magnetic poles are not segmented; d ₁ represents half of the lower gap of each adjacent two poles,

d ₂ represents the gap between each pole under each pole:

(2) Determine l _s (n) and the angle θ _s (n) corresponding to the midline of each magnetic pole: define α _pm (n) as the ratio of the n-th magnetic pole to the total width of the magnetic pole, and satisfy ∑ α _pm (n )=1, l _s (n)=Lα _pr α _pm (n), θ _s (n)=d ₁ +(n-1)d ₂ +∑l _s (n)-l _s (n)/2; (3) The period of the tangential component of the residual magnetization of the permanent magnet is 2π/p. In one period, the piecewise functions of M _r and M _θ are:

where M is the magnitude of the residual magnetization vector, When the poles are segmented, M is not zero at each pole, ie θ _s (n) _–ls (n)/2<θ<θ _s (n)+ _ls (n)/2. 7. The method for calculating the magnetic field of a segmented inclined-pole surface-mounted permanent magnet motor according to claim 6, wherein the Fourier decomposition _is carried out to the segmental function obtained in step (3) about Mr and M _θ Get the following expression:

Among them, A _1k and A _2k are respectively represented by the following formulas:

8. segmented oblique pole surface-mounted permanent magnet motor magnetic field calculation method according to claim 1, is characterized in that, the 4th step adopts following method: for the concentrated winding of double-layer distribution, solve in the jth axial direction In the domain segment, J _i is decomposed into the Fourier series of the stator slot interval:

In the formula, F _m is the tank body coefficient; J _i0 is the fundamental wave amplitude of the current density; J _im is the harmonic amplitude of the current density; _m is the harmonic order of the tank body; position; b _sa is the pole arc width of the groove body; F _m =mπ/b _sa ; J _i0 =(J _i1 +J _i2 )d/b _sa ;J _im =2[J _i1 +J _i2 cos(mπ)]sin (mπd/b _sa )/(mπ); d is the radian of the area occupied by each layer of winding in the slot; J _i1 and J _i2 are the current density of each layer of winding, respectively.

Images