CN116317430A - Halbach array magnetic flux reversing permanent magnet motor and design method thereof - Google Patents

Halbach array magnetic flux reversing permanent magnet motor and design method thereof Download PDF

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Publication number
CN116317430A
CN116317430A CN202310074721.6A CN202310074721A CN116317430A CN 116317430 A CN116317430 A CN 116317430A CN 202310074721 A CN202310074721 A CN 202310074721A CN 116317430 A CN116317430 A CN 116317430A
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permanent magnet
clockwise
stator
counter
angle
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倪有源
曹帮恒
黄亚
王佩
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Hefei University of Technology
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Hefei University of Technology
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    • 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
    • H02K21/38—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with rotating flux distributors, and armatures and magnets both stationary
    • H02K21/44—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with rotating flux distributors, and armatures and magnets both stationary with armature windings wound upon the magnets
    • 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
    • H02K1/12—Stationary parts of the magnetic circuit
    • H02K1/16—Stator cores with slots for windings
    • H02K1/165—Shape, form or location of the slots
    • 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
    • H02K1/12—Stationary parts of the magnetic circuit
    • H02K1/17—Stator cores with permanent magnets
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K15/00—Methods or apparatus specially adapted for manufacturing, assembling, maintaining or repairing of dynamo-electric machines
    • H02K15/0006—Disassembling, repairing or modifying dynamo-electric machines
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K29/00—Motors or generators having non-mechanical commutating devices, e.g. discharge tubes or semiconductor devices
    • H02K29/03—Motors or generators having non-mechanical commutating devices, e.g. discharge tubes or semiconductor devices with a magnetic circuit specially adapted for avoiding torque ripples or self-starting problems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/64—Electric machine technologies in electromobility

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  • Power Engineering (AREA)
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Abstract

The invention discloses a halbach array magnetic flux reversing permanent magnet motor and a design method thereof, wherein the motor comprises a rotor and a stator, the inner ring surface of the stator is provided with a plurality of stator grooves, the notch of each stator groove is respectively provided with a three-section halbach magnetic pole, each stator groove adopts a tooth point structural design, the span angles of a counter-clockwise permanent magnet and a clockwise permanent magnet in each three-section halbach magnetic pole are the same, the span angle of a middle permanent magnet is larger than that of the counter-clockwise permanent magnet, the middle permanent magnet is magnetized in parallel, and the magnetization angles of the counter-clockwise permanent magnet and the clockwise permanent magnet are included angles between the magnetization directions and circumferential tangential directions of corresponding directions. In the method, the halbach permanent magnet array is analyzed and optimized through modeling to obtain the design parameter of the maximum average electromagnetic torque. Compared with the traditional halbach array flux reversing permanent magnet motor, the invention has higher average electromagnetic torque.

Description

Halbach array magnetic flux reversing permanent magnet motor and design method thereof
Technical Field
The invention relates to the field of flux reversing permanent magnet motors, in particular to a halbach array flux reversing permanent magnet motor and a design method thereof.
Background
Because the permanent magnet and the winding of the magnetic flux reversing permanent magnet motor are both arranged on the stator, the winding of the magnetic flux reversing permanent magnet motor has high utilization rate, small inductance, good fault tolerance and high operation efficiency, is suitable for high-speed and low-speed rotation, and is widely applied to a plurality of fields of automobile manufacturing industry, aerospace and the like.
The Halbach array magnetic flux reverse permanent magnet motor is one of magnetic flux reverse permanent magnet motors, and because the Halbach permanent magnet array is adopted, larger air gap magnetic flux density fundamental wave amplitude and lower air gap magnetic flux density waveform distortion rate can be provided, torque pulsation can be reduced, and compared with the traditional radial and parallel magnetization, the Halbach array magnetic flux reverse permanent magnet motor is more suitable for occasions with higher accuracy control requirements. However, the existing Halbach array flux reversing permanent magnet motor has the problem of small average electromagnetic torque, so that in order to obtain larger electromagnetic torque under the condition of the same permanent magnet dosage, the existing Halbach array flux reversing permanent magnet motor needs to be improved.
Disclosure of Invention
The invention provides a halbach array magnetic flux reversal permanent magnet motor and a design method thereof, which are used for solving the problem that the halbach array magnetic flux reversal permanent magnet motor in the prior art has small average electromagnetic torque.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the halbach array magnetic flux reversing permanent magnet motor comprises a rotor and a stator coaxially sleeved outside the rotor, wherein a plurality of stator grooves are formed in the inner annular surface of the stator, the stator grooves are uniformly distributed at equal intervals in the stator ring, three-section halbach magnetic poles are respectively arranged at the notch of each stator groove, each three-section halbach magnetic pole comprises a middle permanent magnet, a counter-clockwise permanent magnet positioned at one counter-clockwise side of the middle permanent magnet and a clockwise permanent magnet positioned at one clockwise side of the middle permanent magnet, each stator groove respectively comprises a groove main body, a notch, a connecting groove main body and a middle section of the notch, and the groove width of the middle section is smaller than the groove width of the groove main body and the groove width of the notch;
in each three-section halbach pole, the crossing angles of the counter-clockwise permanent magnet and the clockwise permanent magnet are the same, the crossing angle of the middle permanent magnet is larger than the crossing angles of the counter-clockwise permanent magnet and the clockwise permanent magnet, the middle permanent magnet is magnetized in parallel, the magnetization angle of the counter-clockwise permanent magnet is an included angle between the magnetization direction of the counter-clockwise permanent magnet and the counter-clockwise circumferential tangential direction, the magnetization angle of the clockwise permanent magnet is an included angle between the magnetization direction of the clockwise permanent magnet and the clockwise circumferential tangential direction, and the counter-clockwise permanent magnet and the clockwise permanent magnet have symmetrical magnetization angles.
Further, the crossing angle of the notch of the stator groove is 21 degrees, and the crossing angle of the middle section of the stator groove is 6 degrees.
Further, in the three-section halbach pole, the angle of the middle permanent magnet is 11.8 degrees, and the angles of the permanent magnet on the anticlockwise side and the permanent magnet on the clockwise side are 4.6 degrees.
Further, the magnetization angles of the counter-clockwise permanent magnet and the clockwise permanent magnet are 50 degrees.
The design method of the halbach array magnetic flux reversing permanent magnet motor comprises the following steps:
step 1, dividing a motor solving domain into a stator slot main body subdomain, a stator slot middle segment subdomain, a magnetic pole subdomain, an air gap subdomain and a rotor slot subdomain by adopting an accurate subdomain model method;
step 2, establishing a z component equation of the vector magnetic bit A of each subdomain in the step 1;
step 3, solving a z component equation of the vector magnetic potential A of each subdomain obtained in the step 2 to obtain the air gap flux density of the motor; based on the calculated air gap flux density, establishing an electromagnetic torque formula model corresponding to the air gap flux density;
and 4, optimizing the crossing angle of the middle permanent magnet of the three-section halbach pole and the magnetizing angles of the counter-clockwise permanent magnet and the clockwise permanent magnet based on the electromagnetic torque formula model obtained in the step 3 to obtain the optimal average electromagnetic torque, and taking the crossing angle of the middle permanent magnet, the magnetizing angle of the counter-clockwise permanent magnet and the magnetizing angle of the clockwise permanent magnet corresponding to the optimal average electromagnetic torque as the optimal design parameters of the middle permanent magnet, the counter-clockwise permanent magnet and the clockwise permanent magnet of the three-section halbach pole.
In step 2, a general solution expression of the vector magnetic potential A of each subdomain under the two-dimensional plane is deduced by ampere loop law and Gaussian law; and then establishing a matrix equation to solve each direct current component coefficient and harmonic component coefficient in each sub-field magnetic potential equation by using boundary conditions among each sub-field to obtain a z component equation of the vector magnetic potential A of each sub-field.
In step 4, the cross angle of the middle permanent magnet, the magnetization angle of the counterclockwise permanent magnet and the magnetization angle of the clockwise permanent magnet are optimized by adopting a parameter scanning method.
Compared with the prior art, the invention has the beneficial effects that:
compared with the traditional halbach array flux reversing permanent magnet motor, each stator slot comprises a slot main body, a slot opening, a connecting slot main body and a middle section of the slot opening, and the slot width of the middle section is smaller than that of the slot main body and that of the slot opening.
Drawings
Fig. 1 is a schematic view of a stator and a rotor according to a first embodiment of the present invention.
Fig. 2 is a schematic diagram of a stator and a rotor of a conventional permanent magnet motor according to a third embodiment of the present invention.
Fig. 3 is a radial air gap flux density analysis method and finite element comparison verification of a permanent magnet motor designed by the second method of the embodiment of the invention.
Fig. 4 is a schematic diagram of electromagnetic torque analysis and finite element comparison verification of a permanent magnet motor designed by the second method of the embodiment of the invention.
Fig. 5 is a comparison of electromagnetic torque of a permanent magnet motor according to an embodiment of the present invention and a conventional permanent magnet motor.
Detailed Description
In order to make the technical solution of the present invention better understood by those skilled in the art, the following detailed description will be given with reference to the accompanying drawings and examples, by which the technical means are applied to solve the technical problem, and the implementation process for achieving the corresponding technical effects can be fully understood and implemented. The embodiment of the invention and the characteristics in the embodiment can be mutually combined on the premise of no conflict, and the formed technical scheme is within the protection scope of the invention.
It will be apparent that the described embodiments are merely some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It is noted that the terms "comprises" and "comprising," and any variations thereof, in the description and claims of the present invention and in the foregoing figures, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or apparatus.
Example 1
As shown in fig. 1, this embodiment discloses a halbach array flux reversing permanent magnet motor, the axial length of the whole motor is 30mm, and the rated rotation speed is 600r/min. The embodiment comprises a rotor 1 and a stator 2 coaxially sleeved outside the rotor, wherein the rotor 1 is provided with a plurality of rotor grooves 3, the inner annular surface of the stator 2 is provided with a plurality of stator grooves 4, and 14 rotor grooves 3 and 12 stator grooves 4 are shared in the embodiment, so that a motor with a 14-pole 12-groove structure is formed.
Each stator slot 4 is uniformly distributed at equal intervals in the circumferential direction of the stator, each stator slot 4 comprises a fan-shaped slot main body 4.1, a slot opening, a connecting slot main body 4.1 and a middle section 4.2 of the slot opening, the slot opening is positioned at the innermost side of the stator 2 and faces the center of the stator 2, and the slot width of the middle section 4.2 is smaller than that of the slot main body 4.1, and the slot width of the slot opening, so that the stator slot 4 with the tooth tip structure is formed.
In this embodiment, the stator 2 and the rotor 1 each use 50WW470 silicon steel sheets. The outer radius of the rotor groove 3 from the rotor center is 33.5mm, the inner radius of the rotor groove 3 from the rotor center is 25.5mm, and the span angle of the rotor groove 3 is 17.1 degrees.
The outer radius of the stator 2 from the center of the rotor is 55mm, the outer radius of the stator groove 4 from the center of the rotor is 50mm, the inner radius of the stator groove 4 from the center of the rotor is 34mm, and the crossing angle of the stator groove 4 is 21 degrees. The outer radius of the middle section 4.2 from the center of the rotor is 40mm, the inner radius of the middle section 4.2 from the center of the rotor is 37mm, and the groove span angle of the middle section 4.2 is 6 degrees. The permanent magnet is placed at the position of the slot opening of the stator, the outer radius of the slot opening of the stator is 37mm from the center of the rotor, the inner radius of the slot opening of the stator is 34mm from the center of the rotor, the angle of the slot opening of the stator 4 is 21 degrees, and the angle of the slot of the middle section of the stator is 6 degrees.
In this embodiment, the notch of each stator slot 4 is respectively provided with a three-section halbach pole, and each three-section halbach pole includes a middle permanent magnet 5.1, a counter-clockwise permanent magnet 5.2 located at one counter-clockwise side of the middle permanent magnet 5.1, and a clockwise permanent magnet 5.3 located at one clockwise side of the middle permanent magnet 5.1. Wherein:
the angles of the counter-clockwise permanent magnet 5.2 and the clockwise permanent magnet 5.3 are the same, and in the embodiment, the angles of the counter-clockwise permanent magnet 5.2 and the clockwise permanent magnet 5.3 are all 4.6 degrees.
The span angle of the middle permanent magnet 5.1 is larger than that of the anticlockwise permanent magnet 5.2 and the clockwise permanent magnet 5.3, the span angle of the middle permanent magnet 5.1 is 11.8 degrees in the embodiment, and the middle permanent magnet 5.1 is magnetized in parallel.
The magnetization angle of the counter-clockwise permanent magnet 5.2 is an included angle between the magnetization direction of the counter-clockwise permanent magnet 5.2 and the counter-clockwise circumferential tangential direction, the magnetization angle of the clockwise permanent magnet 5.3 is an included angle between the magnetization direction of the clockwise permanent magnet 5.3 and the clockwise circumferential tangential direction, and the counter-clockwise permanent magnet 5.2 and the clockwise permanent magnet 5.3 have symmetrical magnetization angles. In this embodiment, the magnetization angles of the counter-clockwise permanent magnet and the clockwise permanent magnet are both 50 °.
In the embodiment, the three permanent magnets 5.1, 5.2 and 5.3 in the three-section halbach pole are neodymium iron boron N35UH, the relative magnetic permeability of the three permanent magnets 5.1, 5.2 and 5.3 is 1.05, the remanence of the three permanent magnets 5.1, 5.2 and 5.3 is 1.2T, the outer radius of the three permanent magnets 5.1, 5.2 and 5.3 is 37mm, the inner radius of the three permanent magnets 5.1, 5.2 and 5.3 is 34mm, and the number of turns of each phase winding in series connection is 88.
Example two
The embodiment discloses a design method of a permanent magnet motor, which comprises the following steps:
and 1, dividing a motor solving domain into a stator slot main body subdomain, a stator slot middle segment subdomain, a magnetic pole subdomain, an air gap subdomain and a rotor slot subdomain by adopting an accurate subdomain model method. The specific process is as follows:
defining the initial position as the position of the first stator slot, alpha 0 Is the position angle of the first rotor slot relative to this position. The stator slot numbers are sequentially arranged in the 2 nd stator slot in the positive direction counterclockwise 1 A stator slot; the rotor groove numbers are sequentially arranged in the 2 nd rotor groove.
Figure BDA0004065754660000051
Is the kth 1 An included angle between the center line of the stator slot and the center line of the 1 st stator slot; θ k Is the angle between the kth rotor slot centerline and the 1 st rotor slot centerline. Obviously, for a rotor having K rotor slots and K 1 Motor with stator slot, theta k And->
Figure BDA0004065754660000052
The expressions of (2) are respectively:
Figure BDA0004065754660000053
the general solution expression of the vector magnetic potential A of each subdomain under the two-dimensional plane is deduced by ampere loop law and Gaussian law, a partial differential equation is established for the z-direction component of the vector magnetic potential A under each subdomain, and the radial component B of the magnetic field density in the two-dimensional polar coordinate system r And tangential component B θ The relationship with magnetic bit a can be expressed as:
Figure BDA0004065754660000054
wherein: r is the distance between the position of the magnetic field density and the center of the rotor, and θ is the included angle between the position of the magnetic field density and the initial position.
The vector magnetic potential A is obtained through analyzing the magnetic field of each subdomain, and the coefficient is scaled to obtain the final form, which is specifically as follows:
(1.1) sub-field magnetic field analysis of the stator slot Main body
Under the two-dimensional polar coordinates
Figure BDA0004065754660000061
Is the kth 1 The z-component equation of the vector magnetic position A in the sub-domain of the slot body in the stator slot, where k 1 ＝1，2，3，...，K 1 . Then, when the excitation current in the coil is zero, the kth is considered 1 The main body of each groove is +.>
Figure BDA0004065754660000062
The range of partial differential equations and domains of (c) can be expressed as:
Figure BDA0004065754660000063
wherein: r is R so Is the outer diameter of the middle section of the stator slot, R sl Is the outer diameter of the stator groove, h 3 The arc of the corresponding central angle of the fan-shaped stator groove.
The differential equation can be solved using a separate variable method, and the original form of the solution of the differential equation can be finally obtained as follows:
Figure BDA0004065754660000064
to facilitate subsequent calculation, coefficients are calculated
Figure BDA0004065754660000065
And->
Figure BDA0004065754660000066
And (3) carrying out coefficient scaling, wherein scaling of the coefficients does not affect a final result according to the property of the differential equation solution. The solution of the coefficient scaled differential equation is:
Figure BDA0004065754660000067
wherein:
Figure BDA0004065754660000068
and->
Figure BDA0004065754660000069
Direct current component coefficient and harmonic component coefficient of stator slot main body subdomain magnetic potential equation respectively, u 3 The harmonic order of the magnetic potential equation is a subdomain of the stator slot body.
(1.2) stator slot mid-section subzone magnetic field analysis
Under the two-dimensional polar coordinates
Figure BDA00040657546600000610
Is the kth 1 The z-component equation of the vector magnetic potential A of the mid-segment subdomain in the stator slot, where k 1 ＝1，2，3，...，K 1 Regarding the kth 1 Middle segment subdomain of the stator slot +.>
Figure BDA00040657546600000611
The partial differential equation and domain range of (2) can be expressed as:
Figure BDA00040657546600000612
wherein: r is R m Is the outer diameter of the magnetic pole, R so Is the outer diameter of the middle section of the stator slot, h 2 The slot which is the middle section of the fan-shaped stator slot corresponds to the radian of the central angle. The form and domain of the differential equation are similar to those of the main body subdomain of the slot without exciting current, and can be solved by using a separation variable method, and meanwhile, each coefficient is scaled, and the solution of the differential equation after processing is as follows:
Figure BDA0004065754660000071
wherein:
Figure BDA0004065754660000072
and->
Figure BDA0004065754660000073
Direct current component coefficient and harmonic component coefficient of stator slot middle segment subdomain magnetic potential equation respectively, u 2 The harmonic order of the magnetic potential equation of the sub-field in the middle section of the stator slot.
(1.3) magnetic pole sub-field analysis
The solving domain is located at the outer diameter R of the magnetic pole m With an air gap outer diameter R s Annular pole areas therebetween. Under the two-dimensional polar coordinates
Figure BDA0004065754660000074
The z-component equation for the vector magnetic potential A of the magnetic pole sub-field, for +.>
Figure BDA0004065754660000075
The range of partial differential equations and domains of (c) can be expressed as:
Figure BDA0004065754660000076
wherein: mu (mu) 0 Is the magnetic permeability of the vacuum and,
Figure BDA0004065754660000077
and->
Figure BDA0004065754660000078
Respectively the radial and tangential components of the magnetization of the permanent magnet, h 1 For the radian of the corresponding central angle of the slot opening of the stator, for the annular permanent magnet with the polar arc coefficient of 1 of Halbach magnetization, the radial and tangential component expressions of the magnetization intensity are as follows:
Figure BDA0004065754660000079
calculated by mirror image method, where
Figure BDA00040657546600000710
And->
Figure BDA00040657546600000711
The method comprises the following steps of:
Figure BDA00040657546600000712
when the permanent magnet Halbach is magnetized, in one mirror period
Figure BDA00040657546600000713
And->
Figure BDA00040657546600000714
Can be expressed as:
Figure BDA0004065754660000081
Figure BDA0004065754660000082
Figure BDA0004065754660000083
where θ is the radian of the corresponding central angle between the permanent magnet and the initial position, θ 1 For angle of magnetization, sigma 1 Is the radian and sigma of the central angle corresponding to the permanent magnets at the two sides 2 The radian of the central angle corresponding to the middle permanent magnet is B rr Is residual magnetism.
Using the separation variant method, taking into account the nature of the non-homogeneous partial differential equation solution and ampere's loop law, it can be calculated as:
Figure BDA0004065754660000084
wherein:
Figure BDA0004065754660000085
and->
Figure BDA0004065754660000086
Direct current component coefficient and harmonic component coefficient of magnetic potential equation of magnetic pole subdomain respectively, u 1 Is the harmonic order of the magnetic pole subdomain magnetic bit equation. Function->
Figure BDA0004065754660000087
The expression of (2) is:
Figure BDA0004065754660000091
(1.4) air gap sub-field magnetic field analysis
The solution domain is located at the air gap outer diameter R s With rotor outer diameter R p An annular region therebetween. Let A be under two-dimensional polar coordinates za (r, θ) is the vector of the air gap sub-fieldThe z-component equation for magnetic bit A, for A in the air gap subzone za The range of partial differential equations and fields of (r, θ) can be expressed as:
Figure BDA0004065754660000092
the differential equation is also solved using the separation variant method, the solution of which is in its original form:
Figure BDA0004065754660000093
unlike the main body sub-region and the intermediate sub-region of the slot, the air gap sub-region is a continuous annular region, so that the integral of the magnetic field strength at the circumference of any radius r in the air gap region is equal to the total current through the circumference range according to ampere's loop law, and the current through this region is always zero, so that the solution of the differential equation should not contain a direct current component. Simplifying and coefficient scaling the solution of the differential equation, wherein the final form of the solution is as follows:
Figure BDA0004065754660000094
wherein: a is that a ，B a For the DC component coefficients of the air gap sub-field magnetic potential equation, n a a ， n b a ， n c a and n d a and n is the harmonic component coefficient of the air gap sub-field magnetic potential equation.
(1.5) rotor groove sub-field magnetic field analysis
The solution domain is located at the outer diameter R of the rotor p With the inner diameter R of the rotor r An annular region therebetween. Under the two-dimensional polar coordinates k A zp (r, θ) is the z-component equation for the vector magnetic flux level a in the slot subzone in the kth slot, where k=1, 2, 3. Regarding the groove sub-field k A zp (r, θ) biasThe differential equation and domain range can be expressed as:
Figure BDA0004065754660000101
solving by using a separation variable method, simultaneously scaling each coefficient, and solving the differential equation after processing into:
Figure BDA0004065754660000102
wherein:
Figure BDA0004065754660000103
and->
Figure BDA0004065754660000104
The direct current component coefficient and the harmonic component coefficient of the rotor groove subdomain magnetic level equation are respectively, and u is the harmonic order number of the rotor groove subdomain magnetic level equation.
In summary, magnetic potential equations of five regions containing coefficients to be solved are established. Wherein the method comprises the steps of
Figure BDA0004065754660000105
Figure BDA0004065754660000106
n a a ， n b a ， n c a ， n d a ，/>
Figure BDA0004065754660000107
And
Figure BDA0004065754660000108
the total of 20 sets of coefficients (including the direct current component coefficient and the harmonic component coefficient) will be determined by the boundary conditions between the regions.
And step 2, a general solution expression of the vector magnetic bit A of each subdomain under the two-dimensional plane is deduced by ampere loop law and Gaussian law. And then is used inr＝R sl ，R so ，R m ，R s ，R p ，R r And establishing a matrix equation to solve each harmonic component coefficient in each sub-field magnetic potential equation according to boundary conditions at six positions to obtain a z component equation of the vector magnetic potential A of each corresponding sub-field. Consider that at r=r sl And r=r r The partial subdomain magnetic potential equation can be partially simplified at the positions, so that the two positions are analyzed first, and then the other positions are analyzed sequentially. The process is as follows:
(2.1) at r=r r Boundary condition analysis at
At r=r r The junction is the junction of the rotor groove subdomain and the rotor iron of the inner diameter of the rotor groove. The surface of the rotor iron is provided with:
Figure BDA0004065754660000109
by substituting the formula (19) into the formula (20), it can be obtained:
Figure BDA00040657546600001010
Figure BDA00040657546600001011
equation (23) is solved as a subsequent equation, equation (21) and equation (22) are substituted into equation (19), and the rotor slot subfield magnetic potential equation is simplified into:
Figure BDA0004065754660000111
in the following, the expression for the rotor groove sub-region is calculated using the expression (23).
(2.2) at r=r sl Boundary condition analysis at
At r=r sl The junction between the stator slot main body subdomain and the stator iron of the stator slot outer diameter. The surface of the stator iron is provided with:
Figure BDA0004065754660000112
substituting equation (24) into equation (5) can be solved:
Figure BDA0004065754660000113
Figure BDA0004065754660000114
substituting equation (25) and equation (26) into equation (5) yields a simplified magnetic potential equation for the sub-domain of the slot body as:
Figure BDA0004065754660000115
in the following, expressions for the stator slot main body subdomains are all operated using the formula (27).
(2.3) at r=r so Boundary condition analysis at
At r=r so The junction of the stator slot main body subdomain and the stator slot middle section subdomain. The radial air gap flux density is continuous according to the boundary condition, and can be expressed as:
Figure BDA0004065754660000116
obviously, the stator slot main body and the stator slot middle section are in one-to-one correspondence, and according to the property of the Fourier series and the formula (28) considering the boundary condition, the correlation equations (29) and (30) of the DC component coefficient and the harmonic component coefficient can be obtained:
Figure BDA0004065754660000117
Figure BDA0004065754660000121
at r=r so Another boundary condition at which the tangential magnetic field strength is continuous can be expressed as:
Figure BDA0004065754660000122
likewise, r=r so Substituting equations (7) and (27), taking into consideration boundary condition equation (31), and based on the nature of the fourier series, correlation equations (32), (33) of the dc component coefficient and the harmonic component coefficient can be obtained:
Figure BDA0004065754660000123
Figure BDA0004065754660000124
at r=r so The substitution process of the boundary conditions is finished, and the formula (29) and the formula (32) are direct current component coefficient equations; equation (30) and equation (33) are equations for harmonic component coefficients. The substitution process of each subsequent boundary condition is similar, and in order to avoid repetition, only the boundary condition and the corresponding direct current component coefficient equation and harmonic component coefficient equation are given in the subsequent boundary condition analysis process.
(2.4) at r=r m Boundary condition analysis at
r＝R m Is the interface between the stator slot middle segment subdomain and the magnetic pole subdomain. The two boundary conditions are:
Figure BDA0004065754660000125
and carrying out Fourier decomposition on the magnetic potential function to obtain the correlation equation of the direct current component coefficient and the harmonic component coefficient of the magnetic potential function, wherein the correlation equation is as follows:
Figure BDA0004065754660000131
Figure BDA0004065754660000132
Figure BDA0004065754660000133
Figure BDA0004065754660000134
(2.5) at r=r s Boundary condition analysis at
r＝R s Is the interface of the air gap sub-field and the magnetic pole sub-field. The boundary conditions here are:
Figure BDA0004065754660000135
substituting the magnetic potential function into the equation to obtain the correlation equation of the direct current component coefficient and the harmonic component coefficient:
Figure BDA0004065754660000136
/>
Figure BDA0004065754660000141
Figure BDA0004065754660000142
Figure BDA0004065754660000143
(2.6) at r=R p Boundary condition analysis at
r＝R p The interface between the air gap subdomain and the rotor groove subdomain. The position of the rotor is time-dependent, so that a time variable a is added, where a=a 0 +ωt, where a 0 The initial position angle of the rotor is ω, the rotational angular velocity of the motor, and t is the rotor rotation time. Its boundary condition and substitution process and r=r s Similar to the above. The boundary conditions are as follows:
Figure BDA0004065754660000144
and carrying out Fourier decomposition on the magnetic potential function to obtain the equation of the direct current component coefficient and the harmonic component coefficient of the magnetic potential function, wherein the equation is as follows:
Figure BDA0004065754660000145
Figure BDA0004065754660000151
/>
Figure BDA0004065754660000152
Figure BDA0004065754660000153
finally, the direct current component coefficient and harmonic component coefficient of each sub-field magnetic potential equation can be solved by the combined equation of 20 sets of equations, namely, equation (21), equation (22), equation (25), equation (26), equation (29), equation (30), equation (32), equation (33), equation (35), equation (36), equation (37), equation (38), equation (40), equation (41), equation (42), equation (43), equation (45), equation (46), equation (47) and equation (48).
Step 3, corresponding air gap subdomain magnetic potential equation A za (r, θ) is substituted into formula (2),solving to obtain the air gap flux density of the motor. And establishing an electromagnetic torque formula model corresponding to the air gap flux density based on the air gap flux density. The process is as follows:
for any rotor position, the flux linkage ψ of one coil is interlinked x Can be defined by the upper layer edge psi x+ And the lower layer edge psi x- The difference between the average vector magnetic potential of (c) and the no-load induced electromotive force can be obtained by differential solution of the coil flux linkage. Its flux linkage can be expressed as:
ψ x ＝ψ x+ -ψ x- (49)
Figure BDA0004065754660000154
wherein: l is the axial length of the motor, N c For the number of turns, k 1 And k is equal to 2 The stator slots corresponding to the upper and lower layer edges of the coil are respectively provided, S is the transverse section area of the upper layer edge or the lower layer edge of the coil, and the expression is as follows:
Figure BDA0004065754660000161
for any phase winding, there are N coils connected in series, and then the total flux linkage of the phase is:
Figure BDA0004065754660000162
the no-load induced electromotive force of this phase is:
Figure BDA0004065754660000163
the electromagnetic torque expression of the permanent magnet motor in the first embodiment is:
Figure BDA0004065754660000164
wherein: e (E) A ，E B ，E C Is the induced electromotive force of each phase; i.e A ，i B And i C Is a three-phase symmetric armature current.
And 5, optimizing the span angle of the middle permanent magnet of the three-section halbach pole and the magnetization angles of the counter-clockwise permanent magnet and the clockwise permanent magnet by adopting a parameter scanning method based on the electromagnetic torque formula model obtained in the step 4 so as to obtain the optimal average electromagnetic torque, and taking the span angle of the corresponding middle permanent magnet, the magnetization angle of the counter-clockwise permanent magnet and the magnetization angle of the clockwise permanent magnet as the optimal design parameters of the middle permanent magnet, the counter-clockwise permanent magnet and the clockwise permanent magnet of the three-section halbach pole when the optimal average electromagnetic torque is obtained. The magnetization angle theta of the permanent magnets at the two sides of the embodiment 1 And an intermediate permanent magnet span angle theta 2 The average electromagnetic torque under determination is set forth in table 1.
Table 1 shows the magnetization angle θ of the permanent magnets on both sides 1 And an intermediate permanent magnet span angle theta 2 Average electromagnetic torque meter under determination
Figure BDA0004065754660000165
Through the design of the method of the embodiment, the span angle of the middle permanent magnet 5.1 of the permanent magnet motor in the first embodiment of the invention is 11.8 degrees. The magnetization angles of the permanent magnets on the counterclockwise side and the permanent magnets on the clockwise side are 50 degrees, and the average electromagnetic torque is the largest.
FIG. 3 is a comparison of the analysis result of the radial air gap flux density of the permanent magnet motor at the air gap middle position and the finite element result according to the embodiment designed by the method of the present embodiment. The result calculated by the accurate subdomain model method is basically consistent with the finite element result within the error allowable range, and the correctness of the method of the embodiment is verified.
Fig. 4 is a comparison between the analysis result of the electromagnetic torque of the permanent magnet motor and the finite element result, which are designed by the method of the embodiment, and the error between the analysis result and the finite element result is smaller, so that the correctness of the method of the embodiment is verified.
Example III
In the embodiment, the existing traditional halbach array flux reversing permanent magnet motor is taken as a comparison example, and the advantage of the motor in the embodiment of the invention is illustrated by comparison.
As shown in FIG. 2, the axial length of the conventional halbach array flux reversing permanent magnet motor in the comparative example is 30mm, the rated rotation speed is 600r/min, the motor comprises a rotor 1 and a stator 2 coaxially sleeved outside the rotor, the rotor 1 is provided with a plurality of rotor grooves 3, the inner annular surface of the stator 2 is provided with a plurality of stator grooves 4, and 14 rotor grooves 3 and 12 stator grooves 4 are all arranged, so that the motor with a 14-pole 12-groove structure is the same as the motor in the first embodiment.
In the comparative example, the stator slots 4 are uniformly distributed at equal intervals in the circumferential direction of the stator, and the notch of each stator slot 4 is respectively provided with three-section halbach poles, each three-section halbach pole comprises a middle permanent magnet 5.1, a counter-clockwise permanent magnet 5.2 positioned at one counter-clockwise side of the middle permanent magnet 5.1 and a clockwise permanent magnet 5.3 positioned at one clockwise side of the middle permanent magnet 5.1.
In the comparative example, 50WW470 silicon steel sheets were used for both the stator 2 and the rotor 1. The outer radius of the rotor groove 3 from the rotor center is 33.5mm, the inner radius of the rotor groove 3 from the rotor center is 25.5mm, and the span angle of the rotor groove 3 is 17.1 degrees.
In the comparative example, the outer radius of the stator 2 from the center of the rotor is 55mm, the outer radius of the stator slot 4 from the center of the rotor is 50mm, the inner radius of the stator slot 4 from the center of the rotor is 34mm, the span angle of the stator slot 4 is 21 degrees, and the permanent magnet is placed at the position of the stator slot.
In the comparative example, the notch of each stator slot 4 is respectively provided with a three-section halbach pole, and each three-section halbach pole comprises a middle permanent magnet 5.1, a counter-clockwise side permanent magnet 5.2 positioned at one counter-clockwise side of the middle permanent magnet 5.1 and a clockwise side permanent magnet 5.3 positioned at one clockwise side of the middle permanent magnet 5.1. The span angles of the middle permanent magnet 5.1, the anticlockwise permanent magnet 5.2 and the clockwise permanent magnet 5.3 are the same and are all 7 degrees.
In the comparative example, the intermediate permanent magnet 5.1 was magnetized in parallel, and the magnetization angles of the counter-clockwise side permanent magnet 5.2 and the clockwise side permanent magnet 5.3 were each 0 °.
In the comparative example, neodymium iron boron N35UH is adopted for the three-section permanent magnets 5.1, 5.2 and 5.3, the relative magnetic permeability of the three-section permanent magnets 5.1, 5.2 and 5.3 is 1.05, the remanence of the three-section permanent magnets 5.1, 5.2 and 5.3 is 1.2T, the outer radius of the three-section permanent magnets 5.1, 5.2 and 5.3 is 37mm, the inner radius of the three-section permanent magnets 5.1, 5.2 and 5.3 is 34mm, and the serial turns of each phase winding is 88.
Fig. 5 is a schematic illustration showing a comparison of electromagnetic torque between a permanent magnet motor and a conventional halbach array flux reversal permanent magnet motor according to an embodiment of the present invention, and when the permanent magnet usage amounts are the same, the torque ripple of the permanent magnet motor according to the embodiment of the present invention is reduced, and the average electromagnetic torque is improved significantly compared with the conventional halbach array flux reversal permanent magnet motor.
The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, and the examples described herein are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the spirit and scope of the present invention. The individual technical features described in the above-described embodiments may be combined in any suitable manner without contradiction, and such combination should also be regarded as the disclosure of the present disclosure as long as it does not deviate from the idea of the present invention. The various possible combinations of the invention are not described in detail in order to avoid unnecessary repetition.
The present invention is not limited to the specific details of the above embodiments, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the protection scope of the present invention without departing from the scope of the technical concept of the present invention, and the technical content of the present invention is fully described in the claims.

Claims (7)

1. The utility model provides a halbach array magnetic flux reverse permanent magnet motor, including rotor and coaxial ring cover outside the rotor's stator, the interior ring face of stator is equipped with a plurality of stator grooves, each stator groove is equidistant evenly distributed in stator ring, the notch in every stator groove is equipped with syllogic halbach magnetic pole respectively, every syllogic halbach magnetic pole includes middle permanent magnet, the anticlockwise side permanent magnet that is located middle permanent magnet anticlockwise one side, the clockwise side permanent magnet that is located middle permanent magnet one side clockwise, characterized in that, every stator groove includes the groove main part respectively, notch and the junction groove main part, the intermediate section of notch, the slot width of intermediate section is less than the slot width of groove main part, the slot width of notch;
in each three-section halbach pole, the crossing angles of the counter-clockwise permanent magnet and the clockwise permanent magnet are the same, the crossing angle of the middle permanent magnet is larger than the crossing angles of the counter-clockwise permanent magnet and the clockwise permanent magnet, the middle permanent magnet is magnetized in parallel, the magnetization angle of the counter-clockwise permanent magnet is an included angle between the magnetization direction of the counter-clockwise permanent magnet and the counter-clockwise circumferential tangential direction, the magnetization angle of the clockwise permanent magnet is an included angle between the magnetization direction of the clockwise permanent magnet and the clockwise circumferential tangential direction, and the counter-clockwise permanent magnet and the clockwise permanent magnet have symmetrical magnetization angles.
2. A halbach array flux reversing permanent magnet machine according to claim 1, wherein the angle of the notch of the stator slot is 21 ° and the angle of the middle section of the stator slot is 6 °.
3. The halbach array flux reversing permanent magnet machine of claim 1, wherein in the three-section halbach pole, the angle of the middle permanent magnet is 11.8 ° and the angles of the counter-clockwise permanent magnet and the clockwise permanent magnet are 4.6 °.
4. A halbach array flux reversing permanent magnet machine according to claim 3, wherein the angles of magnetization of the counter-clockwise side permanent magnet and the clockwise side permanent magnet are each 50 °.
5. A method of designing a halbach array flux reversing permanent magnet motor as claimed in any one of claims 1 to 4, comprising the steps of:
step 1, dividing a motor solving domain into a stator slot main body subdomain, a stator slot middle segment subdomain, a magnetic pole subdomain, an air gap subdomain and a rotor slot subdomain by adopting an accurate subdomain model method;
step 2, establishing vector magnetic bits of each subdomain in step 1AA kind of electronic devicezA component equation;
step 3, vector magnetic potential of each subdomain obtained in step 2AA kind of electronic devicezSolving a component equation to obtain the air gap flux density of the motor; based on the calculated air gap flux density, establishing an electromagnetic torque formula model corresponding to the air gap flux density;
and 4, optimizing the crossing angle of the middle permanent magnet of the three-section halbach pole and the magnetizing angles of the counter-clockwise permanent magnet and the clockwise permanent magnet based on the electromagnetic torque formula model obtained in the step 3 to obtain the optimal average electromagnetic torque, and taking the crossing angle of the middle permanent magnet, the magnetizing angle of the counter-clockwise permanent magnet and the magnetizing angle of the clockwise permanent magnet corresponding to the optimal average electromagnetic torque as the optimal design parameters of the middle permanent magnet, the counter-clockwise permanent magnet and the clockwise permanent magnet of the three-section halbach pole.
6. The halbach array flux reversal permanent magnet motor design method according to claim 5, wherein in step 2, vector magnetic potential of each sub-field in the two-dimensional plane is deduced from ampere loop law and gaussian lawAA general solution expression of (2); then using boundary conditions among all subfields to establish a matrix equation to solve all direct current component coefficients and harmonic component coefficients in all subfield magnetic potential equations to obtain vector magnetic potential of each subfieldAIs described.
7. The halbach array flux reversing permanent magnet motor design method of claim 5, wherein in step 4, a parameter scanning method is adopted to optimize a crossing angle of the intermediate permanent magnet, a magnetization angle of the counter-clockwise permanent magnet and a magnetization angle of the clockwise permanent magnet.
CN202310074721.6A 2023-01-16 2023-01-16 Halbach array magnetic flux reversing permanent magnet motor and design method thereof Pending CN116317430A (en)

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