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

Magnetic field calculation method for segmented oblique pole surface-mounted permanent magnet motor Download PDF

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CN112737173A
CN112737173A CN202011499888.XA CN202011499888A CN112737173A CN 112737173 A CN112737173 A CN 112737173A CN 202011499888 A CN202011499888 A CN 202011499888A CN 112737173 A CN112737173 A CN 112737173A
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permanent magnet
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magnetic field
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CN112737173B (en
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王慧敏
刘舒
郭丽艳
李新旻
张威
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Tianjin Polytechnic University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K1/00—Details of the magnetic circuit
    • H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
    • H02K1/22—Rotating parts of the magnetic circuit
    • H02K1/27—Rotor cores with permanent magnets
    • H02K1/2706—Inner rotors
    • H02K1/272—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis
    • H02K1/274—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets
    • H02K1/2753—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets the rotor consisting of magnets or groups of magnets arranged with alternating polarity
    • H02K1/278—Surface mounted magnets; Inset magnets
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
    • H02K21/12—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets
    • H02K21/14—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating within the armatures
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K3/00—Details of windings
    • H02K3/04—Windings characterised by the conductor shape, form or construction, e.g. with bar conductors
    • H02K3/28—Layout of windings or of connections between windings
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K2201/00—Specific aspects not provided for in the other groups of this subclass relating to the magnetic circuits
    • H02K2201/03—Machines characterised by aspects of the air-gap between rotor and stator
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K2213/00—Specific aspects, not otherwise provided for and not covered by codes H02K2201/00 - H02K2211/00
    • H02K2213/03—Machines characterised by numerical values, ranges, mathematical expressions or similar information
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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

Magnetic field calculation method for segmented oblique pole surface-mounted permanent magnet motor
Technical Field
The invention relates to a segmented oblique pole surface-mounted permanent magnet motor.
Background
From the perspective of the motor body, there are many methods for weakening 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 magnetic pole shape, adding an auxiliary slot or adopting a skewed slot, a skewed pole, and the like. Compared with other methods for reducing the cogging torque, the method has the advantages of simple manufacturing process of the rotor oblique pole, low cost and suitability for batch production and wide application due to the limitation of the processing of the permanent magnet and the manufacturing process of the motor. In the process of optimizing the motor by changing the structure of the motor, if an accurate analytical model is not calculated, a large number of finite element calculations are usually required to analyze the influence of the change of each structural parameter on the result. Compared with finite element calculation, the method has the advantages that an accurate analytic model is established for magnetic field analysis, calculation time can be shortened, analysis efficiency is improved, reference is provided for design and optimization of the segmented skewed pole motor, and important reference significance is provided for motor design and optimization and motor performance improvement.
Disclosure of Invention
The invention aims to provide a method capable of accurately calculating a magnetic field of a segmented skewed pole surface-mounted permanent magnet motor. The technical scheme of the invention is as follows:
1. a magnetic field calculation method for a segmented skewed pole surface-mounted permanent magnet motor comprises the following steps:
the first step is as follows: the modeling of the segmented skewed pole motor is that the magnetic field solving domain sections are axially divided in the whole magnetic field solving region in a three-dimensional space based on the segmented discrete idea, the motor structure of each discrete domain section is modeled, and each solving domain section belongs to a region.
The second step is that: aiming at different solution domain sections, respectively establishing a Laplace equation or a Poisson equation for each section of the motor;
the third step: calculating different circumferential segmentation modes of the segmented oblique-pole motor, and solving radial and tangential component amplitude values M under each harmonic of residual magnetization of the permanent magnetrkAnd MθkK is the harmonic number of the permanent magnet domain and the air gap domain;
the fourth step: calculating a winding arrangement mode, and performing Fourier decomposition on the current density of the stator to obtain the current density under each harmonic;
the fifth step: and (3) establishing a linear equation set in each axial solution domain section by combining boundary conditions among the regions, determining each coefficient to be determined, and further calculating the magnetic field of the segmented skewed pole motor: at the junction of the permanent magnet and the rotor core, the tangential component of the magnetic field intensity is; 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 notch and the stator slot body, the radial magnetic field is continuous, and the magnetic vectors are equal; at the junction of the stator notch and the air gap, the radial magnetic field is continuous, and the magnetic vectors are equal; combining M obtained in the third steprk、MθkSolving the Laplace equation and the Poisson equation established in the second step to obtain an expression of vector magnetic potential in the solved area, and further obtaining expressions of radial components and tangential components of magnetic densities of all areas;
and a sixth step: and calculating the torque and the back electromotive force of the motor by using a Maxwell stress equation and an electromagnetic induction law through the expression of the radial and tangential components of the air gap flux density obtained in the fifth step.
Further, in the first step, the area to which each solution domain segment belongs is divided as follows: through the rotor outer diameter RrOuter diameter R of permanent magnetmAnd stator bore diameter RsThe motor is divided into 3 areas of a permanent magnet area, an air gap area and a stator part from inside to outside, and each area is described by using a radius coordinate r under a polar coordinate system, wherein when r is<RrWhen being a ferromagnetic material, when r>RrAnd r is<RmThen, it is a permanent magnet domain; when R ism<r<RsThen, is the air gap domain; when r is>RsAnd the stator part comprises a notch area and a groove body area.
The second step is specifically as follows: establishing Poisson's equation in the permanent magnet domain
Figure BDA0002843290790000021
Az1jFor the vector magnetic potential of the j-th motor-rotor region, Mθ、MrTangential and radial components, mu, of the remanent magnetization of the permanent magnet, respectively0For the vacuum magnetic conductivity, theta represents an angular coordinate under a polar coordinate system; establishing Laplace equation in air gap domain and notch domain
Figure BDA0002843290790000022
AzIs the vector magnetic potential of the region; establishing Poisson's equation in tank body area
Figure BDA0002843290790000023
Az3ijIs the vector magnetic potential of the ith slot body of the jth section of motor, JiThe current density of the ith slot body is regarded as 0 when the motor is in idle running.
When the magnetization mode of the permanent magnet is radial magnetization, the following solving method can be adopted in the third step:
(1) taking into account the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width, α, corresponding to the permanent magnet under each polepIs the polar arc coefficient, p is the polar logarithm, and the relationship is
Figure BDA0002843290790000024
αprIs the ratio of the actual width of the magnetic pole to the total pole arc width, αpr＝∑ls(n)/L,ls(n) is the width of the pole arc of each magnetic pole segment, n represents the nth segment magnetic pole, when alpha isprWhen 1, the number n of pole segments is indicatedsegIs 1, i.e. the pole is not segmented; d1Representing half of the gap under each two adjacent poles,
Figure BDA0002843290790000025
d2the gap between each segment of the pole under each pole is shown:
Figure BDA0002843290790000026
(2) determination of ls(n) and the angle theta corresponding to the midline of each segment of the magnetic poles(n): will be alphapm(n) is defined as the ratio of the nth segment magnetic pole to the total width of the magnetic polesA value of and satisfies Σ αpm(n)＝1，ls(n)＝Lαprαpm(n),θs(n)＝d1+(n-1)d2+∑ls(n)-ls(n)/2；
(3) The period of the radial component of the residual magnetization of the permanent magnet is 2 pi/p, and in one period, M isrAnd MθThe piecewise functions of (a) are:
Figure BDA0002843290790000031
Mθ＝0,-π/p≤θ≤π/p
where M is the magnitude of the remanent magnetization vector,
when the poles are segmented, at each pole, i.e. thetas(n)–ls(n)/2<θ<θs(n)+ls(n)/2, M is not zero.
When the magnetizing mode of the permanent magnet is parallel magnetizing, the following solving method can be adopted in the third step:
(1) taking into account the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width, α, corresponding to the permanent magnet under each polepIs the polar arc coefficient, p is the polar logarithm, and the relationship is
Figure BDA0002843290790000032
αprIs the ratio of the actual width of the magnetic pole to the total pole arc width, αpr＝∑ls(n)/L,ls(n) is the width of the pole arc of each magnetic pole segment, n represents the nth segment magnetic pole, when alpha isprWhen 1, the number n of pole segments is indicatedsegIs 1, i.e. the pole is not segmented; d1Representing half of the gap under each two adjacent poles,
Figure BDA0002843290790000033
d2the gap between each segment of the pole under each pole is shown:
Figure BDA0002843290790000034
(2) determination of ls(n) and the angle theta corresponding to the midline of each segment of the magnetic poles(n): will be alphapm(n) is defined as the ratio of the nth segment magnetic pole to the total width of the magnetic poles, and satisfies Σ αpm(n)＝1，ls(n)＝Lαprαpm(n),θs(n)＝d1+(n-1)d2+∑ls(n)-ls(n)/2；
(3) The period of the tangential component of the remanent magnetization of the permanent magnet is 2 pi/p, and in one period, M isrAnd MθThe piecewise functions of (a) are:
Figure BDA0002843290790000035
Figure BDA0002843290790000036
where M is the magnitude of the remanent magnetization vector,
when the poles are segmented, at each pole, i.e. thetas(n)–ls(n)/2<θ<θs(n)+ls(n)/2, M is not zero.
Further, the fourth step may employ the following method: for a double-layer distributed concentrated winding, in the jth axial solution domain section, JiDecomposition into fourier series of stator slot intervals:
Figure BDA0002843290790000037
in the formula, FmIs the tank body coefficient; j. the design is a squarei0Is the current density fundamental amplitude; j. the design is a squareimThe amplitude of each harmonic of the current density; m is the harmonic frequency of the tank body domain; thetaiIs the position of the ith slot; bsaThe width of the polar arc of the groove body; fm＝mπ/bsa；Ji0＝(Ji1+Ji2)d/bsa；Jim＝2[Ji1+Ji2cos(mπ)]sin(mπd/bsa) V (m π); d is the occupied surface of each layer of winding in the slotThe radian of the product; j. the design is a squarei1And Ji2The current densities of the windings of the respective layers.
The invention has the following outstanding advantages:
1. according to the invention, different magnetic pole positions in the axial direction and different segmentation modes in the circumferential direction are considered when the air gap magnetic field is calculated, more accurate air gap magnetic field distribution can be obtained, and the magnetic field of the segmented oblique pole surface-mounted permanent magnet motor with different magnetizing modes can be analyzed;
2. the calculation method can be used for analyzing the number of different oblique pole sections, the oblique pole angle, the circumferential number of sections, the sectional gap, the motor tooth socket torque amplitude in the circumferential sectional mode and the oblique pole mode, and the no-load back electromotive force distortion rate change rule, and has important reference significance for the initial design and the optimized design of the sectional oblique pole surface-mounted permanent magnet motor.
Drawings
FIG. 1 is a schematic view of the motor structure
FIG. 2 subdomain map
FIG. 3 permanent magnet circumferential segment schematic
FIG. 4 is a comparison graph of the calculation results of the segmented skewed pole surface-mounted permanent magnet motor calculated by the analytic method and the finite element method, (a) a rotor structure diagram, (b) an A counter potential result comparison, (c) a cogging torque result comparison, (d) an electromagnetic torque result comparison
Detailed Description
The invention is described below with reference to the figures and examples.
The first step is as follows: determining a solving area;
as can be seen from FIG. 1, the whole magnetic field solving area is axially divided into N in three-dimensional space based on the segmented discrete ideazSolving the domain section by each magnetic field, wherein the oblique polar angle of the jth magnetic pole is thetajModeling each discrete-segment motor, and dividing a solving area into four areas 1jBeing a field of permanent magnets, region 2jIs the air gap domain, region 3ijIs the channel region, region 4ijIs a notch subdomain.
The second step is that: respectively establishing a Laplace equation or a Poisson equation aiming at different solving areas;
in the permanent magnet field 1jEstablishing Poisson's equation
Figure BDA0002843290790000041
In the stator current-carrying region 3ijThe vector magnetic potential satisfies the equation
Figure BDA0002843290790000042
In the inactive area 2j,3ij,4ijEstablishing the Laplace equation
Figure BDA0002843290790000051
The third step: calculating different circumferential segmentation modes of segmented oblique-pole motor and solving MrkAnd Mθk；
The schematic diagram of circumferential segment is shown in fig. 2, and the relationship between the pole arc coefficient, the pole arc width of each segment of magnetic pole, the number of segments of magnetic pole and the segment gap is shown in formulas (4) to (7):
Figure BDA0002843290790000052
αpr＝∑ls(n)/L (5)
Figure BDA0002843290790000053
Figure BDA0002843290790000054
after the ratio of the nth section of magnetic pole to the total width of the magnetic pole is determined, the pole arc width of each section of magnetic pole and the angle corresponding to the center line of each section of magnetic pole can be calculated through the formula (8) and the formula (9):
ls(n)＝Lαprαpm(n) (8)
θs(n)＝d1+(n-1)d2+∑ls(n)-ls(n)/2 (9)
the period of the radial or tangential component of the residual magnetization of the permanent magnet is 2 pi/p, and the permanent magnet is divided into two situations according to the magnetization mode of the permanent magnet,
a. when the permanent magnet is magnetized in a radial direction, M is in one periodrAnd MθThe piecewise functions of (a) are:
Figure BDA0002843290790000055
where M is the magnitude of the remanent magnetization vector,
when the poles are segmented, at each pole, i.e. thetas(n)–ls(n)/2<θ<θs(n)+ls(n)/2, M exists, when the magnetizing mode of the permanent magnet is radial magnetizing, the obtained relation M in the above formularAnd MθThe piecewise function of (a) is subjected to Fourier decomposition to obtain the following expression:
Figure BDA0002843290790000056
b. when the magnetizing mode of the permanent magnet is parallel magnetizing, M is in one periodrAnd MθThe piecewise functions of (a) are:
Figure BDA0002843290790000061
where M is the magnitude of the remanent magnetization vector,
when the poles are segmented, at each pole, i.e. thetas(n)–ls(n)/2<θ<θs(n)+ls(n)/2, M is present, whenWhen the magnetizing mode of the permanent magnet is parallel magnetizing, the magnetic flux is related to M obtained in the formularAnd MθThe piecewise function of (a) is subjected to Fourier decomposition to obtain the following expression:
Figure BDA0002843290790000062
wherein,
Figure BDA0002843290790000063
the fourth step: carrying out Fourier decomposition on the current density of the stator to obtain a current density expression;
for a double-layer distributed concentrated winding, the current density can be decomposed into Fourier series of stator slot intervals
Figure BDA0002843290790000064
Wherein,
Figure BDA0002843290790000065
Ji0＝(Ji1+Ji2)d/bsa
Jim＝2[Ji1+Ji2cos(mπ)]sin(mπd/bsa)/(mπ)
the fifth step: establishing boundary conditions, solving the Laplace equation and the Poisson equation established in the second step to obtain the expression of the vector magnetic potential in each area, and further obtaining the radial component B of the air gap flux densityr2jAnd the tangential component B of the air gap flux densityθ2j；
Establishment of boundary conditions
At the junction of the permanent magnet and the rotor core, the magnetic field intensity H only has a radial component and a tangential component is 0;
at the junction of the permanent magnet and the air gap, the radial components of the magnetic induction B are equal;
the radial components of the magnetic induction intensity B are equal at the junction of the stator notch and the stator slot body;
at the stator slot to air gap interface, the radial component of magnetic induction B is equal.
Br2jAnd Bθ2jIs expressed as
Figure BDA0002843290790000071
Wherein, Brsk2jIs Br2jOf the sinusoidal component, Brck2jIs Br2jCosine component of, Bθsk2jIs Bθ2jOf the sinusoidal component, Bθck2jIs Bθ2jIs expressed as formula (17)
Figure BDA0002843290790000072
In the formula A2jk～D2jkThe undetermined coefficient is obtained by simultaneous solution of equations (18) to (26)
Figure BDA0002843290790000073
Figure BDA0002843290790000074
Figure BDA0002843290790000075
Figure BDA0002843290790000076
Figure BDA0002843290790000077
Figure BDA0002843290790000078
Figure BDA0002843290790000079
Figure BDA00028432907900000710
Figure BDA00028432907900000711
In the formula A1jk、B1jk、C3ijv、D3ijv、D4ijmAll the undetermined coefficients are simultaneously solved by the formulas (18) to (26); rsbThe radius of the bottom of the stator slot is; thetatIs the rotor rotation angle; mu.srIs the relative magnetic conductance of the permanent magnet; v is the notch domain harmonic number; mθck、Mθsk、Mrck、MrskCosine and sine component amplitudes of the tangential magnetization and radial magnetization of the permanent magnet respectively; diIs a special solution; g1k、G2k、G3v、G4m、Ev、ηi0(k)、ηi(m,k)、σi0(k)、σi(m,k)、τi(m,k)、ξi0(k)、ξi(m,k)、γi0(v)、γi(v, m) are parameter coefficients of the motor and are expressed by the following formula;
Mθck＝Mθkcos(kθt)
Mrsk＝Mrksin(kθt)
Mθsk＝Mθksin(kθt)
Mrck＝Mrkcos(kθt)
Di＝bsaμ0Ji0(Rsb 2-Rt 2)/(2boa)
Figure BDA0002843290790000081
Figure BDA0002843290790000082
Figure BDA0002843290790000083
Figure BDA0002843290790000084
Figure BDA0002843290790000085
boathe width of the notch polar arc;
ηi(m,k)＝boaσi(m,k)/(2π)
ηi0(k)＝boaσi0(k)/π
σi(m,k)＝-2k[cos(mπ)sin(kθi+kboa/2)-sin(kθi-kboa/2)]/[boa(Fm 2-k2)]
σi0(k)＝2sin(kboa/2)cos(kθi)/(kboa)
τi(m,k)＝2k×[cos(mπ)cos(kθi+kboa/2)-cos(kθi-kboa/2)]/[boa(Fm 2-k2)
ξi(m,k)＝boaτi(m,k)/(2π)
ξi0(k)＝boaτi0(k)/π
γi(v,m)＝boaζi(v,m)/bsa
γi0(v)＝2boaζi0(v)/bsa
and a sixth step: the radial component B of the air gap flux density obtained by the fourth stepr2jAnd the tangential component B of the air gap flux densityθ2jAnd calculating the electromagnetic performance of the motor.
The cogging torque and the electromagnetic torque of the motor can be respectively calculated by the air gap flux density in no-load and load through the formula (27)
Figure BDA0002843290790000091
In the formula LzjLength of motor segments for axial segmentation
Flux linkage psi of each phase windingxCan be calculated by the formula (28)
Figure BDA0002843290790000092
In the formula, x can be A, B, C and respectively represents a stator winding A phase, a stator winding B phase and a stator winding C phase; n is a radical ofcThe number of conductors in each slot of the stator is; a is the number of parallel branches of the stator winding
Counter-potential E of each phase windingxCan be calculated by the formula (29)
Figure BDA0002843290790000093
The proposed magnetic field calculation method is described by taking a radially magnetized segmented skewed pole surface-mounted permanent magnet synchronous motor as an example, and the parameters of the motor are shown in table 1.
TABLE 1 inner rotor Motor parameters
Figure BDA0002843290790000094
Figure BDA0002843290790000101
Determining a solution region
The motor is of a segmented oblique pole structure, so that as can be seen from fig. 1, the motor is axially uniformly segmented, and the area division is shown in fig. 2 by taking one segment as an example.
Respectively establishing Laplace equation or Poisson equation under a polar coordinate system according to different solving areas
In the permanent magnet field 1jEstablishing Poisson's equation
Figure BDA0002843290790000102
In the stator current-carrying region 3ijThe vector magnetic potential satisfies the equation
Figure BDA0002843290790000103
In the inactive area 2j,3ij,4ijEstablishing the Laplace equation
Figure BDA0002843290790000104
Calculation of residual magnetization of permanent magnets
The magnetizing mode of the motor is radial magnetizing
According to the ratio alpha of each magnetic pole to the total width of the magnetic polepm(n) determining the width of the pole arc of each segment of magnetic pole and the angle corresponding to the centerline of each segment of magnetic pole
lm(n)＝Lαprαpm(n) (33)
θm(n)＝d1+(n-1)d2+∑lm(n)-lm(n)/2 (34)
When the poles are segmented, at each pole, i.e. thetam(n)-lm(n)/2<θ<θm(n)+lm(n)/2, M is present. According to different magnetizing modes, the width of the pole arc of each section of magnetic pole and an included angle relative to the initial position, Fourier decomposition is carried out on the periodic function of the residual magnetization radial and tangential components to obtain an expression, and the radial and tangential component expressions of the residual magnetization at each position in a period are obtained
Figure BDA0002843290790000105
Establishment of boundary conditions
At the junction of the permanent magnet and the rotor core, the magnetic field intensity H only has a radial component and a tangential component is 0;
at the junction of the permanent magnet and the air gap, the radial components of the magnetic induction B are equal;
the radial components of the magnetic induction intensity B are equal at the junction of the stator notch and the stator slot body;
at the stator slot to air gap interface, the radial component of magnetic induction B is equal.
The radial and tangential expressions of the magnetic density of the air gap domain are
Figure BDA0002843290790000111
Wherein,
Figure BDA0002843290790000112
in the formula A2jk～D2jkThe undetermined coefficient is obtained by simultaneous solution of equations (38) to (46)
Figure BDA0002843290790000113
Figure BDA0002843290790000114
Figure BDA0002843290790000115
Figure BDA0002843290790000116
Figure BDA0002843290790000117
Figure BDA0002843290790000118
Figure BDA0002843290790000119
Figure BDA00028432907900001110
Figure BDA0002843290790000121
Calculation of electromagnetic properties of an electric machine
Calculation of cogging torque at no-load and electromagnetic torque at load
Figure BDA0002843290790000122
Flux linkage psi of each phase windingxIs calculated by
Figure BDA0002843290790000123
Counter-potential E of each phase windingxIs calculated by
Figure BDA0002843290790000124
Verification of correctness of magnetic field calculation method provided by the invention
Setting the axial number of segments of the motor to be 5, the oblique pole angle to be 20 degrees, the circumferential number of segments to be 5, and the ratio alpha of each magnetic pole to the total width of the magnetic polespm(n) are respectively 0.1, 0.2, 0.3, 0.2 and 0.1, establishing a finite element model of the segmented skewed pole surface-mounted permanent magnet synchronous motor, and comparing the result obtained by the calculation method of the invention with the result obtained by the calculation of the finite element model. The rotor structure and resulting ratio is shown in fig. 4. As can be seen from the figure, the calculation result is basically consistent with the calculation result of the finite element model, and the correctness of the calculation method of the invention is verified.

Claims (8)

1. A magnetic field calculation method for a segmented skewed pole surface-mounted permanent magnet motor comprises the following steps:
the first step is as follows: the modeling of the segmented skewed pole motor is that the magnetic field solving domain sections are axially divided in the whole magnetic field solving region in a three-dimensional space based on the segmented discrete idea, the motor structure of each discrete domain section is modeled, and each solving domain section belongs to a region.
The second step is that: aiming at different solution domain sections, respectively establishing a Laplace equation or a Poisson equation for each section of the motor;
the third step: calculating different circumferential segmentation modes of the segmented oblique-pole motor, and solving radial and tangential component amplitude values M under each harmonic of residual magnetization of the permanent magnetrkAnd MθkK is the harmonic number of the permanent magnet domain and the air gap domain;
the fourth step: calculating a winding arrangement mode, and performing Fourier decomposition on the current density of the stator to obtain the current density under each harmonic;
the fifth step: and (3) establishing a linear equation set in each axial solution domain section by combining boundary conditions among the regions, determining each coefficient to be determined, and further calculating the magnetic field of the segmented skewed pole motor: in thatThe tangential component of the magnetic field intensity at the junction of the permanent magnet and the rotor core is; 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 notch and the stator slot body, the radial magnetic field is continuous, and the magnetic vectors are equal; at the junction of the stator notch and the air gap, the radial magnetic field is continuous, and the magnetic vectors are equal; combining M obtained in the third steprk、MθkSolving the Laplace equation and the Poisson equation established in the second step to obtain an expression of vector magnetic potential in the solved area, and further obtaining expressions of radial components and tangential components of magnetic densities of all areas;
and a sixth step: and calculating the torque and the back electromotive force of the motor by using a Maxwell stress equation and an electromagnetic induction law through the expression of the radial and tangential components of the air gap flux density obtained in the fifth step.
2. The method for calculating the magnetic field of the segmented skewed pole surface-mounted permanent magnet motor according to claim 1, wherein in the first step, the regions to which each solution domain segment belongs are divided as follows: through the rotor outer diameter RrOuter diameter R of permanent magnetmAnd stator bore diameter RsThe motor is divided into 3 areas of a permanent magnet area, an air gap area and a stator part from inside to outside, and each area is described by using a radius coordinate r under a polar coordinate system, wherein when r is<RrWhen being a ferromagnetic material, when r>RrAnd r is<RmThen, it is a permanent magnet domain; when R ism<r<RsThen, is the air gap domain; when r is>RsAnd the stator part comprises a notch area and a groove body area.
3. The method for calculating the magnetic field of the segmented skewed pole surface-mounted permanent magnet motor according to claim 2, wherein the second step is specifically as follows: establishing Poisson's equation in the permanent magnet domain
Figure FDA0002843290780000011
Az1jFor the vector magnetic potential of the j-th motor-rotor region, Mθ、MrRespectively the remanent magnetization of the permanent magnetThe radial and radial components, μ0For the vacuum magnetic conductivity, theta represents an angular coordinate under a polar coordinate system; establishing Laplace equation in air gap domain and notch domain
Figure FDA0002843290780000012
AzIs the vector magnetic potential of the region; establishing Poisson's equation in tank body area
Figure FDA0002843290780000013
Az3ijIs the vector magnetic potential of the ith slot body of the jth section of motor, JiThe current density of the ith slot body is regarded as 0 when the motor is in idle running.
4. The method for calculating the magnetic field of the segmented skewed pole surface-mounted permanent magnet motor according to claim 2, wherein when the permanent magnet is magnetized in a radial direction, the third step adopts the following solving method:
(1) taking into account the gap between the circumferential segments of the magnetic poles, L is defined as the total pole arc width, α, corresponding to the permanent magnet under each polepIs the polar arc coefficient, p is the polar logarithm, and the relationship is
Figure FDA0002843290780000021
αprIs the ratio of the actual width of the magnetic pole to the total pole arc width, αpr＝∑ls(n)/L,ls(n) is the width of the pole arc of each magnetic pole segment, n represents the nth segment magnetic pole, when alpha isprWhen 1, the number n of pole segments is indicatedsegIs 1, i.e. the pole is not segmented; d1Representing half of the gap under each two adjacent poles,
Figure FDA0002843290780000022
d2the gap between each segment of the pole under each pole is shown:
Figure FDA0002843290780000023
(2) determination of ls(n) and the angle theta corresponding to the midline of each segment of the magnetic poles(n): will be alphapm(n) is defined as the ratio of the nth segment magnetic pole to the total width of the magnetic poles, and satisfies Σ αpm(n)＝1，ls(n)＝Lαprαpm(n),θs(n)＝d1+(n-1)d2+∑ls(n)-ls(n)/2；
(3) The period of the radial component of the residual magnetization of the permanent magnet is 2 pi/p, and in one period, M isrAnd MθThe piecewise functions of (a) are:
Figure FDA0002843290780000024
Mθ＝0,-π/p≤θ≤π/p
where M is the magnitude of the remanent magnetization vector,
when the poles are segmented, at each pole, i.e. thetas(n)–ls(n)/2<θ<θs(n)+ls(n)/2, M is not zero.
5. The method for calculating the magnetic field of a segmented skewed pole surface-mounted permanent magnet motor according to claim 4, wherein the M is obtained in step (3)rAnd MθThe piecewise function of (a) is subjected to Fourier decomposition to obtain the following expression:
Figure FDA0002843290780000025
Mθk＝0。
6. the method for calculating the magnetic field of the segmented skewed pole surface-mounted permanent magnet motor according to claim 2, wherein when the magnetizing mode of the permanent magnet is parallel magnetizing, the third step adopts the following solving method:
(1) taking into account the gaps between the circumferential segments of the magnetic poles, L is defined as the total pole arc corresponding to the permanent magnet under each poleWidth, αpIs the polar arc coefficient, p is the polar logarithm, and the relationship is
Figure FDA0002843290780000026
αprIs the ratio of the actual width of the magnetic pole to the total pole arc width, αpr＝∑ls(n)/L,ls(n) is the width of the pole arc of each magnetic pole segment, n represents the nth segment magnetic pole, when alpha isprWhen 1, the number n of pole segments is indicatedsegIs 1, i.e. the pole is not segmented; d1Representing half of the gap under each two adjacent poles,
Figure FDA0002843290780000027
d2the gap between each segment of the pole under each pole is shown:
Figure FDA0002843290780000028
(2) determination of ls(n) and the angle theta corresponding to the midline of each segment of the magnetic poles(n): will be alphapm(n) is defined as the ratio of the nth segment magnetic pole to the total width of the magnetic poles, and satisfies Σ αpm(n)＝1，ls(n)＝Lαprαpm(n),θs(n)＝d1+(n-1)d2+∑ls(n)-ls(n)/2；
(3) The period of the tangential component of the remanent magnetization of the permanent magnet is 2 pi/p, and in one period, M isrAnd MθThe piecewise functions of (a) are:
Figure FDA0002843290780000031
Figure FDA0002843290780000032
where M is the magnitude of the remanent magnetization vector,
when the magnetic poleAt each pole, i.e. theta, during segmentations(n)–ls(n)/2<θ<θs(n)+ls(n)/2, M is not zero.
7. The method for calculating the magnetic field of a segmented skewed pole surface-mounted permanent magnet motor according to claim 6, wherein the M is obtained in step (3)rAnd MθThe piecewise function of (a) is subjected to Fourier decomposition to obtain the following expression:
Figure FDA0002843290780000033
Figure FDA0002843290780000034
wherein A is1k，A2kAre respectively represented by the following formula:
Figure FDA0002843290780000035
Figure FDA0002843290780000036
8. the method for calculating the magnetic field of the segmented skewed pole surface-mounted permanent magnet motor according to claim 1, wherein the fourth step adopts the following method: for a double-layer distributed concentrated winding, in the jth axial solution domain section, JiDecomposition into fourier series of stator slot intervals:
Figure FDA0002843290780000037
in the formula, FmIs the tank body coefficient; j. the design is a squarei0Is the current density fundamental amplitude; j. the design is a squareimThe amplitude of each harmonic of the current density; m is the harmonic frequency of the tank body domain; thetaiIs the position of the ith slot; bsaThe width of the polar arc of the groove body; fm＝mπ/bsa；Ji0＝(Ji1+Ji2)d/bsa；Jim＝2[Ji1+Ji2cos(mπ)]sin(mπd/bsa) V (m π); d is the radian of the occupied area of each layer of winding in the slot; j. the design is a squarei1And Ji2The current densities of the windings of the respective layers.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113944713A (en) * 2021-09-18 2022-01-18 浙江工业大学 Method for increasing magnetic force of permanent magnet spring
CN113992092A (en) * 2021-11-02 2022-01-28 浙江大学先进电气装备创新中心 Analytical method-based field-path coupling analysis method for surface-mounted permanent magnet motor driving system
CN114142640A (en) * 2021-10-27 2022-03-04 天津工业大学 Surface-mounted modulation magnetic pole structure design method based on specific harmonic elimination method

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103984864A (en) * 2014-05-16 2014-08-13 天津大学 Different-thickness-magnetic-pole-containing surface-pasting type permanent magnet motor magnetic field computing method
CN105005692A (en) * 2015-07-08 2015-10-28 三峡大学 Analytical method based permanent magnet motor field analysis and torque calculation method
CN109600006A (en) * 2018-11-30 2019-04-09 浙江大学 A kind of method for solving for surface-mounted permanent magnet machine electromagnetic design
CN109948298A (en) * 2019-04-10 2019-06-28 天津工业大学 Using the Magnetic Field for Permanent Magnet Electrical Machines calculation method of uneven segmentation Halbach array

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103984864A (en) * 2014-05-16 2014-08-13 天津大学 Different-thickness-magnetic-pole-containing surface-pasting type permanent magnet motor magnetic field computing method
CN105005692A (en) * 2015-07-08 2015-10-28 三峡大学 Analytical method based permanent magnet motor field analysis and torque calculation method
CN109600006A (en) * 2018-11-30 2019-04-09 浙江大学 A kind of method for solving for surface-mounted permanent magnet machine electromagnetic design
CN109948298A (en) * 2019-04-10 2019-06-28 天津工业大学 Using the Magnetic Field for Permanent Magnet Electrical Machines calculation method of uneven segmentation Halbach array

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113944713A (en) * 2021-09-18 2022-01-18 浙江工业大学 Method for increasing magnetic force of permanent magnet spring
CN114142640A (en) * 2021-10-27 2022-03-04 天津工业大学 Surface-mounted modulation magnetic pole structure design method based on specific harmonic elimination method
CN114142640B (en) * 2021-10-27 2024-01-12 天津工业大学 Surface-mounted modulation magnetic pole structure design method based on specific resonance elimination method
CN113992092A (en) * 2021-11-02 2022-01-28 浙江大学先进电气装备创新中心 Analytical method-based field-path coupling analysis method for surface-mounted permanent magnet motor driving system
CN113992092B (en) * 2021-11-02 2023-06-02 浙江大学先进电气装备创新中心 Surface-mounted permanent magnet motor driving system field path coupling analysis method based on analysis method

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