CN116599261A - Permanent magnet hub motor with high torque performance and partition design method thereof - Google Patents
Permanent magnet hub motor with high torque performance and partition design method thereof Download PDFInfo
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- 230000010349 pulsation Effects 0.000 claims abstract description 29
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- 238000004804 winding Methods 0.000 claims abstract description 12
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- 229910000976 Electrical steel Inorganic materials 0.000 claims description 5
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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
- H02K1/2786—Outer rotors
- H02K1/2787—Outer rotors the magnetisation axis of the magnets being perpendicular to the rotor axis
- H02K1/2789—Outer rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets
- H02K1/279—Magnets embedded in the magnetic core
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60K—ARRANGEMENT OR MOUNTING OF PROPULSION UNITS OR OF TRANSMISSIONS IN VEHICLES; ARRANGEMENT OR MOUNTING OF PLURAL DIVERSE PRIME-MOVERS IN VEHICLES; AUXILIARY DRIVES FOR VEHICLES; INSTRUMENTATION OR DASHBOARDS FOR VEHICLES; ARRANGEMENTS IN CONNECTION WITH COOLING, AIR INTAKE, GAS EXHAUST OR FUEL SUPPLY OF PROPULSION UNITS IN VEHICLES
- B60K7/00—Disposition of motor in, or adjacent to, traction wheel
- B60K7/0007—Disposition of motor in, or adjacent to, traction wheel the motor being electric
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
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- H—ELECTRICITY
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- H02K7/00—Arrangements for handling mechanical energy structurally associated with dynamo-electric machines, e.g. structural association with mechanical driving motors or auxiliary dynamo-electric machines
- H02K7/006—Structural association of a motor or generator with the drive train of a motor vehicle
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- 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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Abstract
The invention discloses a high-torque performance permanent magnet hub motor and a partition design method thereof, and belongs to the field of hub motors for vehicles. The rotor of the motor comprises an iron core and a permanent magnet, wherein the permanent magnet is embedded on the rotor in a V-shaped structure so as to generate a permanent magnetic field with a magnetism gathering effect; the torque design domain on the rotor is divided into a torque lifting domain and a pulsation suppression domain, and the final output torque is improved by improving the output torque quantity generated by working harmonic waves; the resultant torque ripple is suppressed by suppressing the torque ripple amount generated by the non-operating harmonics. The stator comprises a stator core and an armature winding, the stator core consists of a stator yoke, armature teeth and modulation teeth, and the modulation effect of the motor is enhanced through the split slot type modulation teeth, so that the torque performance is improved; an armature winding is arranged in the stator slot and used for generating an armature magnetic field to couple with the permanent magnetic field to generate torque.
Description
Technical Field
The invention relates to the technology of hub motors for vehicles, in particular to a permanent magnet hub motor with high torque performance and a partition design method thereof.
Background
The magnetic field modulation permanent magnet motor works based on the magnetic gear principle, and is gradually applied to various fields of electric automobiles, aerospace, industrial and agricultural production and the like due to the remarkable advantages of diversified structures, high power density, high efficiency, low loss and the like. Meanwhile, the method is suitable for a direct-drive system, and the problems of vibration noise, mechanical loss and the like which are common in the traditional high-speed motor system adopting a reduction gear box are avoided.
The permanent magnet hub motor utilizes the modulation teeth to modulate the armature magnetic field and the permanent magnetic field in the air gap, modulates harmonic components with different rotational speed and pole pair numbers, and refers to the harmonic wave with the same pole pair number and rotational speed in the air gap density of the armature magnetic field and the air gap density of the permanent magnetic field as working harmonic wave, so that output torque can be generated, and the other harmonic waves are called non-working harmonic waves, which can have negative effects on the motor performance, such as loss and torque pulsation.
In the document with the Chinese patent application number of 202110633241.X, a layered multi-target optimization design method based on a hybrid permanent magnet synchronous motor is proposed, the optimization of a local topological structure is realized by analyzing the relation between the relative positions of two permanent magnet magnetic sources and a magnetic circuit, magnetic potential, magnetic conductance and magnetic linkage, a multi-target optimization model is established to obtain an optimal solution of design variables, and the torque density and anti-demagnetizing capability of the motor are improved. In the document of the Chinese patent application number 202110988212.5, a design method of a low-harmonic double-three-phase fractional slot permanent magnet synchronous motor is proposed, subharmonics are eliminated by adopting different winding coil turns, so that the eddy current loss, unbalanced magnetic tension and torque pulsation of a permanent magnet of the motor are effectively reduced, but the improvement on the torque output capability is not obvious enough. A winding dislocation method is proposed in the document of patent number CN108768016B to weaken even harmonic in counter potential and improve motor torque performance, however, the motor winding is complex in structure and difficult to process, and the large-scale application of the motor winding in the industrial field is limited.
Therefore, how to improve the output torque and reduce the torque ripple of the motor based on the magnetic field modulation principle is very necessary to achieve an overall improvement of the torque performance.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and realizes synchronous improvement of output torque and torque pulsation performance by providing a partition design method of a permanent magnet hub motor with high torque performance so as to ensure that a direct-drive system keeps running stably under low-speed and high torque. In the invention, the torque design domain on the rotor of the permanent magnet hub motor is divided into two parts, namely a torque lifting domain and a pulsation suppression domain, and torque pulsation can be further reduced on the basis of improving output torque by carrying out targeted design and optimization on the two regions.
The technical scheme adopted by the invention is as follows: a high-torque performance permanent magnet hub motor comprises an inner stator, an outer rotor and permanent magnets; an air gap is arranged between the inner stator and the outer rotor; the inner stator comprises a stator yoke iron core (1), armature teeth (2) and modulation teeth (3); armature windings (4) are wound on the armature teeth; the modulation teeth adopt a split tooth structure, and two small modulation teeth are arranged at the end part of each armature tooth. The outer rotor comprises a rotor core (5) and a permanent magnet (6), and the permanent magnet is embedded in the rotor by adopting a V-shaped structure; the distance from the center of a circle to the air gap side magnetic barrier (7) of the permanent magnet is R1, the distance from the center of a circle to the inner diameter of the outer rotor is R2, and a circular ring with the radius of (R1-R2) is formed and is called a torque design domain (8); the torque design domain includes a torque boost domain (9) and a ripple suppression domain (10).
Further, the permanent magnets (6) are magnetized in a V-shaped tangential mode, N-level and S-level are alternately arranged, and the magnetizing directions of the adjacent permanent magnets are opposite.
Further, the permanent magnet is made of neodymium iron boron materials.
Furthermore, the inner stator iron core and the outer rotor iron core are formed by laminating magnetic conductive materials such as silicon steel sheets.
Further, according to the number of modulated teeth N st And permanent magnet pole pair number P r Determining the pole pair number P of armature winding s Satisfy P s ＝∣N st -P r I= i 24-19 i=5, motor slot number z=n st 2=24/2=12. Further, the modulation tooth angle alpha and the crack angle alpha of the split modulation tooth (3) 0 Equal, satisfying the coefficient k=α/α 0 =1. In case of satisfying the magnetic field modulation principle, the slot pitch angle β=p of the motor s *360°/Z＝150°。
Further, structural design is carried out on a torque lifting domain part in the torque design domain;
further, structural design is performed on the pulsation suppression domain part in the torque design domain;
the partition design method of the permanent magnet hub motor with high torque performance comprises the following steps:
step 1, the initial motor M1 is first analyzed and processed. The stator teeth are slotted and split into two modulating teeth (3) which are kept at the same angle as the stator slots (alpha = alpha) 0 ) The torque design domain is all silicon steel sheet. The permanent magnet magnetomotive force F can be obtained by using discrete Fourier transform and considering the rotation of the rotor pm The expression along with the circumferential position θ is:
wherein P is r Is the pole pair number of the permanent magnet, omega r For the mechanical angular velocity of rotor rotation, i represents a positive odd number, θ is the rotor circumferential position, F i-M1 For the ith order harmonic amplitude generated in magnetomotive force by the initial motor permanent magnet, the expression is:
the air gap flux density of the permanent magnet (6) is calculated when acting independently, and the air gap flux density expression is as follows:
wherein F (θ, t) is a magneto-motive force of a permanent magnet, Λ s (θ) is air gap permeance, N s Is stator tooth number, j is zero or positive integer, P j Is the amplitude of the j-order harmonic. Determining the order and frequency of working harmonic waves by calculating an air gap flux density formula when the permanent magnet (6) is excited singly;
and 2, firstly, performing torque lifting design. The initial motor M1 is not subjected to partition design, namely the torque design domain is still a silicon steel sheet; combining with a permanent magnet hub motor partition design method, only designing a torque lifting domain in a torque design domain; calculating the optimal size of a torque lifting domain through a finite element algorithm, wherein the output torque of the motor reaches the maximum at the moment, and recording the maximum output torque as an M2 motor;
and step 3, performing pulsation suppression design. The optimal size of the pulsation suppression domain is calculated through a finite element algorithm on the basis of the M2 motor, and torque pulsation is reduced under the condition that the motor hardly influences output torque, so that high torque performance of the permanent magnet hub motor is achieved. The high-torque performance permanent magnet hub motor adopting the partition design method is recorded as an M3 motor.
Step 4, utilizing discrete Fourier transformation and considering the rotation of a rotor, the ith harmonic amplitude generated in magnetomotive force by the permanent magnet of the M3 motor can be obtained:
therefore, the air gap flux density expression of the M3 motor is:
wherein, when i is 1 and j is 0, the magnetic flux density is the fundamental wave; the balance is harmonic component.
Step 5): comparing the contributions of the harmonics of the M1, M2 and M3 motors to the output torque and the torque ripple;
step 6): finally, the torque performance of the three motors is compared, and the feasibility and effectiveness of the partition design method of the permanent magnet hub motor are verified.
After the design scheme is adopted, the invention has the following beneficial effects:
1. the invention is based on the magnetic field modulation principle, by carrying out two-layer design on the torque design domain, the first layer firstly designs the torque lifting domain, and the fundamental wave amplitude is improved, thereby improving the output torque;
2. the second layer is designed for the pulsation suppression domain, so that torque pulsation generated by non-working harmonic waves is reduced, and the torque pulsation of final output torque is reduced, and the method is a high-torque performance design method of the permanent magnet hub motor;
3. compared with the initial motor, the partition design method of the permanent magnet hub motor has the advantages of being simple in structure, light in weight, obviously improved in torque performance and the like.
Description of the drawings:
in order that the invention may be more readily understood, the invention is further described below in connection with the following detailed description of the invention when taken in conjunction with the accompanying drawings:
FIG. 1 is an initial permanent magnet in-wheel motor
FIG. 2 is a schematic diagram of an initial motor without zoning
FIG. 3 shows a high torque permanent magnet in-wheel motor after zoning design
FIG. 4 is a torque design domain partitioning diagram
FIG. 5 is a graph of equivalent air gap magnetomotive force contrast for M1, M3 motors
FIG. 6 is a flow chart of a partition design
FIG. 7 is a graph comparing the air gap harmonics versus torque contributions of M1, M3 motors
FIG. 8 is a graph comparing the contributions of the air gap harmonics of M1, M3 motors to torque ripple
FIG. 9 is a graph showing torque performance comparisons of M1, and M3 motors
Reference numerals in the drawings denote: 1-a stator yoke core; 2-armature teeth; 3-modulating teeth; 4-armature winding; 5-a rotor core; 6-permanent magnets; 7-permanent magnet magnetic barriers; 8-turnA moment design field; 9-torque boost domain; 10-pulsation suppression domain; r1 is the distance from the center of a circle to the magnetic barrier at the air gap side of the permanent magnet; r2 is the distance from the center of the circle to the inner diameter of the outer rotor; alpha t -torque boost domain span; h is a t -torque boost domain height; alpha r -a ripple rejection domain span; h is a r Pulsation suppression domain height.
The specific embodiment is as follows:
in order that the present disclosure may be readily understood, a further description is provided below in connection with specific embodiments of the invention and the accompanying drawings.
Fig. 1 is an initial vernier motor, denoted M1 motor. The M1 motor comprises an inner stator, an outer rotor and a permanent magnet; an air gap is arranged between the inner stator and the outer rotor; the inner stator comprises a stator yoke iron core (1), armature teeth (2) and modulation teeth (3); armature windings (4) are wound on the armature teeth; the modulation teeth adopt a split tooth structure, and two small modulation teeth are arranged at the end part of each armature tooth. The outer rotor comprises a rotor core (5) and permanent magnets (6), wherein the permanent magnets are magnetized in a V-shaped tangential direction, N-level and S-level are alternately arranged, and the magnetizing directions of adjacent permanent magnets are opposite; the distance from the center of the circle to the air gap side magnetic barrier (7) of the permanent magnet is R1, the distance from the center of the circle to the inner diameter of the outer rotor is R2, and a circular ring with the radius of (R1-R2) is formed and is called a torque design domain (8), as shown in fig. 2.
Carrying out partition design on a torque design domain (8) of an M1 motor, wherein a torque lifting domain is separated, and the motor subjected to the torque lifting design is recorded as an M2 motor; and then the pulse suppression domain is partitioned on the basis of the M2 motor, so that the permanent magnet hub motor with high torque performance, which is designed by the partition, is obtained and is recorded as the M3 motor, as shown in fig. 3. The partition design is shown in FIG. 4, where α t To lift the domain span for torque, h t For torque boost domain length, α r To pulse inhibit domain span, h r Is the pulse suppression domain length.
The expression of the permanent magnet magnetomotive force F (theta, t) of the permanent magnet hub motor along with the circumferential position theta is as follows:
wherein P is r Is the pole pair number of the permanent magnet, omega r For the mechanical angular velocity of rotor rotation, i represents a positive odd number, θ is the rotor circumferential position, F i The motor permanent magnet generates the ith harmonic amplitude in magnetomotive force.
Combining the permanent magnet magnetomotive force distribution of M1, M2 and M3 shown in fig. 5, the ith harmonic amplitude generated in magnetomotive force by the permanent magnets of the three motors can be obtained by using discrete fourier transform and considering the rotation of the rotor:
wherein F is 0 ，F 1 ，F 2 ，F 3 Respectively magnetomotive force step amplitude, beta rt1 For rotor tooth span, beta rs1 For rotor slot span, beta rs2 For the pulsation suppression domain span, the magnetomotive force harmonic amplitude can be obviously improved through the permanent magnet hub motor partition design method. On the basis, the air gap flux density expression of the M3 motor is as follows:
wherein F (θ, t) is a magneto-motive force of a permanent magnet, Λ s (θ) is air gap permeance, N s Is stator tooth number, j is zero or positive integer, P j Is the amplitude of the j-order harmonic. Wherein, when i is 1 and j is 0, the magnetic flux density is the fundamental wave; the balance is harmonic component.
Based on Fourier series, radial component B of air gap flux density can be obtained r And tangential component B t Expressed as:
wherein B is rq And B tq As radial component B r And tangential component B t The q-th Fourier coefficient after Fourier series expansion, theta rq And theta tq Is the q-th air gap harmonic phase. Torque T generated by the q-th harmonic outq The method comprises the following steps:
wherein R is the air gap radius, l ef Is the axial length of the motor, mu 0 Is the magnetic permeability of the vacuum and is equal to the magnetic permeability of the vacuum,
torque ripple T generated by the q-th harmonic rq The method comprises the following steps:
based on classical electromechanics theory, the expression of output torque is:
the torque ripple is expressed as:
it can be seen that the air gap harmonics play an important role in the generation of output torque and torque ripple, as derived from the above equation, and therefore the contribution of the air gap harmonics to the torque performance will be varied by the zonal design to increase the output torque and reduce the torque ripple.
Fig. 6 shows a design flow of the permanent magnet hub motor partition design method proposed herein. The initial motor M1 is first determined and its air gap harmonics are analyzed by finite element calculations to obtain 5, 7, 17, 19, 29, 43, 57 harmonics as the main harmonics of the M1 motor, and the 19 th harmonics are calculated using equation (5)The contribution to the output torque is greatest. By adjusting the structural parameters of the torque boost domain (9), the structural parameters when the output torque reaches the maximum value are determined by finite element simulation. The main structural parameters of the torque boost domain are: torque boost domain span alpha t Torque boost domain length h t 。
When the output torque reaches the maximum value, the contribution of 29 th harmonic to the torque ripple is calculated by using the formula (6). By adjusting the structural parameters of the ripple suppression domain (10), the structural parameters at which torque ripple is lowest are determined using finite element simulation. The main structural parameters of the ripple suppression domain are: pulse suppression domain span alpha r Pulse suppression domain length h r 。
As can be seen by comparing the torque performance of the three motors in fig. 7 and 8, the output torque generated by the 19 th fundamental wave and the 43 rd harmonic wave of the motor after the design of the torque boost domain is obviously increased, but the torque pulsation generated by the 29 th harmonic wave is greatly increased; and then, through the design of a pulsation suppression domain, the torque pulsation generated by 29 th harmonic waves is reduced under the condition of not influencing the output torque, the partition design of the permanent magnet hub motor is realized, and the aim of high torque performance is fulfilled.
By adopting the design scheme, the output torque of the motor can be obviously improved, and the torque pulsation which is improved along with the improvement of the output torque can be further reduced.
In summary, the invention discloses a permanent magnet hub motor with high torque performance and a partition design method thereof. The method comprises the steps of carrying out partition design on a torque design domain on a motor rotor silicon steel sheet by utilizing a magnetic field modulation principle, dividing the torque design domain into a torque lifting domain and a pulsation suppression domain, and improving the contribution of working harmonic waves to output torque and reducing the contribution of non-working harmonic waves to torque pulsation, so that the output torque of the motor is improved and the torque pulsation is reduced; the permanent magnet is magnetized in a V-shaped tangential manner, so that a magnetism gathering effect can be generated, magnetic leakage is less, and the installation and the manufacture are convenient; the structural parameters of the motor are reasonably optimized, the magnetic field utilization rate is improved, and the motor performance is fully exerted; the stator teeth adopt a split groove structure, so that the modulation effect is enhanced, and the output torque is improved.
The foregoing description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. The high-torque performance permanent magnet hub motor is characterized by comprising an inner stator, an outer rotor and permanent magnets; an air gap is arranged between the inner stator and the outer rotor; the inner stator comprises a stator yoke iron core (1), armature teeth (2) and modulation teeth (3); armature windings (4) are wound on the armature teeth; the modulation teeth adopt a split tooth structure, and two small modulation teeth are arranged at the end part of each armature tooth; the outer rotor comprises a rotor core (5), permanent magnets (6) and a magnetic barrier (7), and the permanent magnets are embedded in the rotor in a V-shaped structure; the distance from the center of a circle to the air gap side magnetic barrier (7) of the permanent magnet is R1, the distance from the center of a circle to the inner diameter of the outer rotor is R2, and a circular ring with the radius of (R1-R2) is formed and is called a torque design domain (8); the torque design domain comprises a torque lifting domain (9) and a pulsation suppression domain (10); wherein the stator core and the rotor core are made of silicon steel sheet magnetic conductive materials, and the permanent magnet (6) is made of neodymium iron boron materials.
2. The high torque performance permanent magnet in-wheel motor of claim 1 wherein, according to the modulated number of teeth N st And permanent magnet pole pair number P r Determining the pole pair number P of armature winding s Satisfy P s ＝∣N st -P r ∣＝∣24-19∣＝5。
3. A high torque performance permanent magnet hub motor according to claim 1, characterized in that the permanent magnets (6) are of V-type structure and adjacent permanent magnets are magnetized in opposite directions.
4. The high-torque performance permanent magnet hub motor according to claim 1, wherein the included angle theta of the V-shaped structure formed by the permanent magnets (6) meets the condition that theta is more than or equal to 50 degrees and less than or equal to 100 degrees.
5. A high torque performance permanent magnet hub motor according to claim 1, characterized in that triangular magnetic barriers (7) are arranged at both ends of each permanent magnet (6).
6. A high torque performance permanent magnet in-wheel motor according to claim 1, characterized in that the number of torque lifting domains (9) corresponds to the number of permanent magnets (6); the number of the permanent magnets (6) is twice as large as that of the pulsation suppression domains (10).
7. A high torque performance permanent magnet in-wheel motor according to claim 1, characterized in that there is a pulsation suppression domain (10) of equal area on both sides of each torque boost domain (9).
8. The partition design method of the permanent magnet hub motor with high torque performance is characterized by comprising the following steps of:
step 1: the initial motor M1 is firstly analyzed, and the permanent magnet magnetomotive force F can be obtained by using discrete Fourier transform and considering the rotation of the rotor pm The expression along with the circumferential position θ is:
wherein P is r Is the pole pair number of the permanent magnet, omega r For the mechanical angular velocity of rotor rotation, i represents a positive odd number, θ is the rotor circumferential position, F i-M1 For the ith order harmonic amplitude generated in magnetomotive force by the initial motor permanent magnet, the expression is:
wherein F is 0 The magnetic potential amplitude determined for the rotor structure, i representing the positive odd number, beta rs0 For initial motor M1 rotor slot span, P r Is the pole pair number of the permanent magnet,
the air gap flux density of the permanent magnet (6) is calculated when acting independently, and the air gap flux density expression is as follows:
wherein F (θ, t) is a magneto-motive force of a permanent magnet, Λ s (θ) is air gap permeance, N s Is stator tooth number, j is zero or positive integer, P j For the amplitude of the j-order harmonic wave, determining the order and frequency of the working harmonic wave by calculating an air gap flux density formula when the permanent magnet (6) is excited singly;
step 2: then analyzing the permanent magnet hub motor after the partition design, and obtaining the ith harmonic amplitude generated in magnetomotive force by the permanent magnets of the three motors, namely the initial motor M1, the motor M2 only designed in the torque lifting domain and the high-torque performance permanent magnet hub motor M3 with the partition design, according to the magnetomotive force distribution:
wherein F is 0 ，F 1 ，F 2 ，F 3 Respectively magnetomotive force step amplitude, i represents positive odd number, P r The pole pair number of the permanent magnets is; beta rs0 For initial motor M1 rotor slot span, beta rs1 For the rotor slot spans of M2 and M3 motors, beta rs2 The permanent magnet hub motor partition design method provided by the invention can obviously improve the magnetomotive force harmonic wave amplitude for the pulsation suppression domain span, and an air gap flux density expression of the M3 motor is obtained on the basis;
step 3: analyzing air gap flux density harmonic waves, selecting harmonic components with the largest contribution to output torque in an initial motor M1, then adjusting structural parameters of a torque lifting domain (9), and determining the structural parameters when the output torque is largest by utilizing finite element simulation;
step 4: the motor designed by the torque lifting domain is recorded as M2, the air gap harmonic wave of the M2 motor is analyzed, the harmonic component with the largest contribution to the torque pulsation in the M2 is selected, the structural parameter of the pulsation suppression domain (10) is adjusted, and the structural parameter when the torque pulsation reaches the minimum value is determined by utilizing finite element software simulation;
step 5): comparing the contributions of the harmonics of the M1, M2 and M3 motors to the output torque and the torque ripple;
step 6): finally, the torque performance of the three motors is compared, and the feasibility and effectiveness of the partition design method of the permanent magnet hub motor are verified.
9. The method for zoning design of a high torque performance permanent magnet hub motor of claim 8, wherein the air gap flux density of the M3 motor is expressed as:
wherein F (θ, t) is a magneto-motive force of a permanent magnet, Λ s (θ) is air gap permeance, N s Is stator tooth number, j is zero or positive integer, P j The amplitude of the j-order harmonic wave is the fundamental wave magnetic density when i is 1 and j is 0; the balance is harmonic component.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117550050A (en) * | 2023-11-15 | 2024-02-13 | 德州市等磁科技有限公司 | Intelligent regulation type marine propulsion device |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117550050A (en) * | 2023-11-15 | 2024-02-13 | 德州市等磁科技有限公司 | Intelligent regulation type marine propulsion device |
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