CN112671135A - Method for optimizing four-section Halbach array surface-mounted permanent magnet motor - Google Patents
Method for optimizing four-section Halbach array surface-mounted permanent magnet motor Download PDFInfo
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Abstract
The invention discloses a method for optimizing a four-section Halbach array surface-mounted permanent magnet motor, wherein the magnetization angles of a first section and a second section of N-pole permanent magnet are included angles between the magnetization direction and the clockwise circumferential tangential direction; the magnetization angle of the third section and the fourth section of the N-pole permanent magnet is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the first section and the second section of the S pole permanent magnet is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the third section and the fourth section of the S pole is the included angle between the magnetization direction and the clockwise circumferential tangential direction; the pole-arc coefficient ratio of the second section of permanent magnet and the third section of permanent magnet of each pole is a certain value, and the rotor and the corresponding stator are matched to form the four-section Halbach permanent magnet motor. The invention can improve the radial air gap flux density fundamental wave amplitude of the motor and reduce the harmonic component of the air gap flux density, thereby improving the output torque and the torque density and the power density of the motor under the same volume and permanent magnet consumption, and having more excellent electromagnetic performance.
Description
Technical Field
The invention relates to the technical field of permanent magnet motors, in particular to an optimized four-section Halbach array surface-mounted permanent magnet motor.
Background
The permanent magnet motor has the advantages of high output efficiency, small volume, high power density and the like, and has very wide application in the fields of aerospace, national defense, transportation, new energy, public life and the like. The surface-mounted permanent magnet motor of the Halbach array can be divided into two sections, three sections, four sections and up to n sections according to the number of the sections of the permanent magnet under each pole. Theoretically, the larger the number of the sections of the Halbach array is, the closer the radial air gap flux density of the motor is to a sine wave, and the better the electromagnetic performance is. But as the number of stages increases, the complexity of the fabrication process increases. In view of production practice, permanent magnet machines with a few limited-section Halbach arrays are generally being investigated.
Disclosure of Invention
The invention aims to overcome the defects of low torque density, low power density and the like of a surface-mounted permanent magnet motor in the prior art, and provides a method for optimizing a four-section Halbach array surface-mounted permanent magnet motor.
The invention is realized by the following technical scheme:
the utility model provides an optimize four sections Halbach array table and paste formula permanent-magnet machine, including rotor and the stator that corresponds rather than the rotor, the rotor constitute by optimizing four sections Halbach arrays, four sections Halbach array every utmost point constitute by four sections adjacent and axisymmetric permanent magnetism, the symmetry axis is the geometric center of second section and third section permanent magnetism. The pole arc coefficient ratio of the permanent magnets of the second section and the third section is RmpThe magnetization angle of the first and fourth permanent magnets is delta theta1The magnetization angle of the second and third permanent magnets is delta theta2The N pole first section and the N pole second section of the permanent magnet are acute angles, and the magnetization angles of the N pole first section and the N pole second section of the permanent magnet are included angles between the magnetization direction and the clockwise circumferential tangential direction; the magnetization angle of the third section and the fourth section of the N-pole permanent magnet is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the first section and the second section of the S pole permanent magnet is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the third section of S pole permanent magnet and the fourth section of S pole permanent magnet is the included angle between the magnetization direction and the clockwise circumferential tangential direction, and the rotor and the corresponding stator are matched to form the four-section Halbach array surface-mounted permanent magnet motor.
The ratio of the magnetization angles and the permanent magnet pole arc coefficients of the four-section Halbach array is calculated by an analytical method to obtain: firstly, a function expression of the no-load radial air gap flux density of the slotless permanent magnet motor is obtained through an analytical method, and then the optimization parameter design is carried out on the no-load radial air gap flux density fundamental wave function of the slotless motor by utilizing a genetic algorithm, so that the magnetization angle and the permanent magnet pole arc coefficient ratio of the slotless motor when the no-load radial air gap flux density fundamental wave amplitude is maximum are obtained.
The following is a specific calculation procedure.
The magnetization of a four-segment Halbach array in one electrical cycle can be written as a piecewise function as follows:
in the formula: delta1＝(1+Rmp)π/(4p)，δ2＝Rmpπ/(4p), p is the number of polar pairs, RmpThe ratio of permanent magnet pole arc coefficients of the second section and the third section, BrIs remanence of permanent magnet, Delta theta1Is the magnetization angle of the first and fourth permanent magnets, Delta theta2The magnetization angle of the second section of permanent magnet and the third section of permanent magnet, and theta is the position angle of the rotor.
To MrAnd MθRespectively carrying out Fourier decomposition to obtain
According to the Laplace equation, the quasi-Poisson equation and the boundary conditions of the magnetic field, the obtained no-load radial air gap flux density of the slotless permanent magnet motor is as follows:
Mn＝Mrn+npMθn
in the formula: r is the distance from a certain point in the air gap to the center of the circle, RsIs the stator inner radius, Rm1Is the outer radius of the permanent magnet, Rm2Is the inner radius of the permanent magnet, RrIs the outer radius of the rotor, and Rm2＝Rr，μ0Is magnetic permeability of vacuum, murIs the relative permeability of the permanent magnet.
In equation (10), let n be 1, and take the fundamental coefficient to obtain the fundamental amplitude of the radial air gap flux density of the slotless permanent magnet motor:
Br1＝f(Δθ1,Δθ2,Rmp) (11)
i.e. the fundamental amplitude B of the magnetic flux density of the slotless radial air gapr1Is an angle Δ θ with the magnetization1、Δθ2And the pole arc coefficient ratio RmpThe associated ternary function.
The ternary function is optimized and calculated by using a genetic algorithm, and an objective optimization function is as follows:
max{f(Δθ1,Δθ2,Rmp)} (12)
where Δ θ1Is the magnetization angle of the first and fourth permanent magnets, Delta theta2The magnetization angle R of the permanent magnet of the second section and the third sectionmpThe pole arc coefficient ratio of the permanent magnets of the second section and the third section is shown.
Wherein, inequality constraint conditions of each magnetization angle and permanent magnet pole arc coefficient ratio are as follows:
and when the optimization termination condition is met, selecting the optimal permanent magnet magnetization angle and the optimal pole arc coefficient ratio. The respective magnetization angles and pole-arc coefficient ratios in the objective function can then be obtained.
The invention has the advantages that: the invention applies the characteristic of the Halbach array to ensure that the flux density of the slotless air gap is close to sinusoidal distribution, so that the traditional four-section Halbach array is optimized and designed into the four-section Halbach array, the fundamental amplitude of the radial air gap flux density of the slotless motor can be improved, and the harmonic component of the air gap flux density is reduced. In a slotted motor, the optimized four-section Halbach array permanent magnet motor has larger amplitude of the fundamental wave of the air gap flux density and the air gap flux density is closer to a sine wave, so that the output torque can be improved under the same volume and the same permanent magnet consumption, the torque density and the power density of the motor can be improved, and the slot motor is also suitable for a rotor-free iron core motor and an outer rotor motor. For practical production, the four sections of magnetic poles are symmetrical pairwise, so that a large amount of extra work is not brought to practical production, and the complexity of processing and manufacturing is not increased remarkably.
Drawings
FIG. 1 is a schematic diagram of a four-stage Halbach array according to the present invention.
Fig. 2 is a schematic structural diagram of a four-segment Halbach permanent magnet motor of the present invention.
Detailed Description
As shown in fig. 1 and 2, an optimized four-segment Halbach array surface-mounted permanent magnet motor comprises a rotor 2 and a stator 1 corresponding to the rotor 2, wherein the rotor 2 is formed by an optimized four-segment Halbach array, each pole of the four-segment Halbach array is formed by four adjacent permanent magnets which are symmetrical in pairs, a symmetry axis is a geometric center of the second segment permanent magnet and the third segment permanent magnet, all magnetization angles delta theta of the four segments of permanent magnets are acute angles, and the magnetization angles of a first segment permanent magnet 3 and a second segment permanent magnet 4 of an N pole are included angles between a magnetization direction and a clockwise circumferential tangential direction; the magnetization angle of the N-pole third-section permanent magnet 5 and the fourth-section permanent magnet 6 is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the S-pole first section permanent magnet 7 and the second section permanent magnet 8 is the included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the S pole third section permanent magnet 9 and the fourth section permanent magnet 10 is the included angle between the magnetization direction and the clockwise circumferential tangential direction; the ratio of the second-stage permanent magnet and the third-stage permanent magnet in each pole to the whole permanent magnet pole is Rmp(ii) a The rotor 2 and the corresponding stator 1 are matched to form a four-section Halbach array surface-mounted permanent magnet motor.
The magnetization angle and the permanent magnet pole-arc ratio of the optimized four-section Halbach array are calculated by an analytical method to obtain: firstly, a function expression of the no-load radial air gap flux density of the slotless permanent magnet motor is obtained through an analytical method, and then the fundamental wave function of the no-load radial air gap flux density is optimized and calculated through a genetic algorithm, so that the optimal magnetization angle and the pole arc coefficient ratio of each section of permanent magnet when the no-load radial air gap flux density fundamental wave amplitude is maximum are obtained.
The following is a specific calculation procedure.
The magnetization of a four-segment Halbach array in one electrical cycle can be written as a piecewise function as follows:
in the formula: delta1＝(1+Rmp)π/(4p)，δ2＝Rmpπ/(4p), p is the number of polar pairs, RmpThe ratio of permanent magnet pole arc coefficients of the second section and the third section, BrIs remanence of permanent magnet, Delta theta1Is the magnetization angle of the first and fourth permanent magnets, Delta theta2The magnetization angle of the second section of permanent magnet and the third section of permanent magnet, and theta is the position angle of the rotor.
To MrAnd MθRespectively carrying out Fourier decomposition to obtain
According to the Laplace equation, the quasi-Poisson equation and the boundary conditions of the magnetic field, the obtained no-load radial air gap flux density of the slotless permanent magnet motor is as follows:
Mn＝Mrn+npMθn
in the formula: r is the distance from a certain point in the air gap to the center of the circle, RsIs the stator inner radius, Rm1Is the outer radius of the permanent magnet, Rm2Is the inner radius of the permanent magnet, RrIs the outer radius of the rotor, and Rm2＝Rr，μ0Is magnetic permeability of vacuum, murIs the relative permeability of the permanent magnet.
In equation (10), let n be 1, and take the fundamental coefficient to obtain the fundamental amplitude of the radial air gap flux density of the slotless permanent magnet motor:
Br1＝f(Δθ1,Δθ2,Rmp) (11)
i.e. the fundamental amplitude B of the magnetic flux density of the slotless radial air gapr1Is an angle Δ θ with the magnetization1、Δθ2And the pole arc coefficient ratio RmpThe associated ternary function.
The ternary function is optimized and calculated by using a genetic algorithm, and an objective optimization function is as follows:
max{f(Δθ1,Δθ2,Rmp)} (12)
where Δ θ1Is the magnetization angle of the first and fourth permanent magnets, Delta theta2The magnetization angle of the second-stage permanent magnet and the third-stage permanent magnet is shown, and Rmp is the pole arc coefficient ratio of the second-stage permanent magnet and the third-stage permanent magnet.
Wherein, inequality constraint conditions of each magnetization angle and permanent magnet pole arc coefficient ratio are as follows:
and when the optimization termination condition is met, selecting the optimal permanent magnet magnetization angle and the optimal pole arc coefficient ratio. The respective magnetization angles and pole-arc coefficient ratios in the objective function can then be obtained.
FIG. 1 is a schematic diagram of an optimized four-segment Halbach array permanent magnet structure. Each pole is composed of four sections of adjacent permanent magnets which are symmetrical in pairsThe axis is the geometric center of the middle second section of permanent magnet 4 and the third section of permanent magnet 5. All angles of magnetization Δ θ1、Δθ2Are all acute angles and are defined as: the magnetization angle of the first section of N-pole permanent magnet 3 and the second section of N-pole permanent magnet 4 is an included angle between the magnetization direction and the clockwise circumferential tangential direction; the magnetization angle of the N-pole third-section permanent magnet 5 and the fourth-section permanent magnet 6 is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the S-pole first section permanent magnet 7 and the second section permanent magnet 8 is the included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the S pole third section permanent magnet 9 and the fourth section permanent magnet 10 is the included angle between the magnetization direction and the clockwise circumferential tangential direction; the permanent magnet arc ratio of the second section and the third section of each pole is a certain value Rmp. Thus forming N, S poles alternating with each other.
Fig. 2 is a schematic structural diagram of an optimized four-segment Halbach array surface-mounted permanent magnet motor according to the invention. For comparison, an example motor is given. The example motor is a 4-pole slotless motor. The stator core and the rotor core are both made of 50W470 silicon steel sheets, and the permanent magnet is made of NdFeB N35H. The main structural parameters of the motor in the embodiment are as follows: the outer diameter of the stator is 100mm, the inner diameter of the stator is 80mm, the outer diameter of the rotor is 64mm, the shaft length of the rotor is 30mm, the height of a rotor yoke is 12mm, and the height of the permanent magnet is 6.4 mm. And obtaining the optimal magnetization angle and the optimal permanent magnet pole arc coefficient ratio by an analytical method.
In the optimized four-section Halbach structure, the magnetization angle delta theta of the permanent magnet at the first section and the fourth section1Is 23.6 degrees, and the magnetization angle delta theta of the permanent magnets of the second section and the third section277.2 degrees, and the pole arc coefficient ratio R of the permanent magnets of the second section and the third sectionmpIs 0.896; in the traditional four-section Halbach structure, the magnetization angle delta theta of the four-section permanent magnet1、Δθ2Are respectively 30 degrees, 45 degrees and 60 degrees, and the pole arc coefficient ratio R of the permanent magnets of the second section and the third section ismpIs 0.5, and the polar arc coefficients of each segment are equal. As can be seen from the data in the table, after the magnetization angle and the pole arc coefficient ratio are optimized, the air gap flux density amplitude of the motor is changedThe harmonic distortion ratio is reduced, and the electromagnetic performance of the motor is improved.
The optimized four-section Halbach array surface-mounted permanent magnet motor fully utilizes the characteristics of the Halbach array, can increase the fundamental wave amplitude of the radial air gap flux density of a slotless motor, and simultaneously reduces the harmonic distortion ratio of the radial air gap flux density. In the slotted motor, the optimized four-section Halbach array permanent magnet motor has larger amplitude of the fundamental wave of the air gap flux density and the air gap flux density is closer to a sine wave, so that the output torque can be improved under the condition of the same volume and the same permanent magnet consumption, and the torque density and the power density of the motor can be improved. Therefore, the invention has better electromagnetic performance on the premise of not changing the volume of the motor and the consumption of the permanent magnet.
Claims (4)
1. The utility model provides a four sections Halbach array table pastes formula permanent-magnet machine, including the rotor and with the stator that the rotor corresponds, its characterized in that: the rotor is composed of four sections of Halbach arrays, each pole of the four sections of Halbach arrays is composed of four sections of adjacent permanent magnets which are axisymmetric, and a symmetry axis is the geometric center of the second section of permanent magnet and the third section of permanent magnet; the pole arc coefficient ratio of the permanent magnets of the second section and the third section is RmpThe magnetization angle of the first and fourth permanent magnets is delta theta1The magnetization angle of the second and third permanent magnets is delta theta2The N pole first section and the N pole second section of the permanent magnet are acute angles, and the magnetization angles of the N pole first section and the N pole second section of the permanent magnet are included angles between the magnetization direction and the clockwise circumferential tangential direction; the magnetization angle of the third section and the fourth section of the N-pole permanent magnet is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the first section and the second section of the S pole permanent magnet is an included angle between the magnetization direction and the counterclockwise circumferential tangential direction; the magnetization angle of the third section of S pole permanent magnet and the fourth section of S pole permanent magnet is the included angle between the magnetization direction and the clockwise circumferential tangential direction, and the rotor and the corresponding stator are matched to form the four-section Halbach array surface-mounted permanent magnet motor.
2. A four-segment Halbach array surface-mounted permanent magnet machine according to claim 1, characterised in that: the ratio of two magnetization angles and the pole arc coefficient of the optimized four-section Halbach array is calculated by an analytic method to obtain: firstly, a function expression of the no-load radial air gap flux density of the slotless permanent magnet motor is obtained through an analytical method, and then the fundamental wave function, the permanent magnet magnetization angle and the pole-arc coefficient ratio of the radial air gap flux density are optimized through a genetic algorithm, so that the optimal magnetization angle and the pole-arc coefficient ratio of the slotless permanent magnet motor when the fundamental wave amplitude of the radial air gap flux density is maximum are obtained.
3. A four-segment Halbach array surface-mounted permanent magnet machine according to claim 2, characterized in that: the analysis method comprises the following specific steps:
the magnetization intensity of the permanent magnet motor with four Halbach arrays in one electric cycle is written as a piecewise function as follows:
in the formula: delta1＝(1+Rmp)π/(4p)，δ2＝Rmpπ/(4p), p is the number of polar pairs, RmpThe ratio of the pole arc coefficients of the permanent magnets of the second section and the third section, BrIs remanence of permanent magnet, Delta theta1Is the magnetization angle of the first and fourth permanent magnets, Delta theta2Is the magnetization angle of the second and third permanent magnets, theta is the position angle of the rotor, mu0Magnetic permeability in vacuum;
to MrAnd MθRespectively carrying out Fourier decomposition to obtain
According to the Laplace equation, the quasi-Poisson equation and the boundary conditions of the magnetic field, the obtained no-load radial air gap magnetic density of the slotless motor is as follows:
Mn＝Mrn+npMθn
in the formula: r is the distance from a certain point of the air gap to the center of the circle, RsIs the stator inner radius, Rm1Is the outer radius of the permanent magnet, Rm2Is the inner radius of the permanent magnet, RrIs the outer radius of the rotor, and Rm2＝Rr，μ0Is magnetic permeability of vacuum, murIs the relative permeability of the permanent magnet;
in equation (10), let n be 1, and take the fundamental coefficient to obtain the fundamental amplitude of the radial air gap flux density of the slotless permanent magnet motor:
Br1＝f(Δθ1,Δθ2,Rmp) (11)
i.e. the fundamental amplitude B of the magnetic flux density of the slotless radial air gapr1Is related to the magnetization angle Delta theta1、Δθ2And the pole arc coefficient ratio RmpThe associated ternary function.
4. The optimized four-segment Halbach array surface-mounted permanent magnet motor according to claim 3, wherein: after the permanent magnet consumption is determined, the Halbach permanent magnet array is optimized in a magnetizing mode and a pole-arc coefficient ratio, the fundamental wave of the radial air gap flux density of the slotless motor is optimized by using a genetic algorithm, and the objective optimization function is as follows:
max{f(Δθ1,Δθ2,Rmp)} (12)
where Δ θ1Is the magnetization angle of the first and fourth permanent magnets, Delta theta2The magnetization angle R of the permanent magnet of the second section and the third sectionmpThe pole arc coefficient ratio of the second-stage permanent magnet and the third-stage permanent magnet is obtained; determiningThe boundary of each magnetization angle and pole arc coefficient ratio and linear inequality constraint conditions; and when the optimization termination condition is met, selecting the magnetization angle and the pole arc coefficient ratio of each section of permanent magnet under the optimization condition.
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