CN114123912A - Low-torque ripple permanent magnet brushless motor design method considering harmonic injection phase angle - Google Patents
Low-torque ripple permanent magnet brushless motor design method considering harmonic injection phase angle Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
- H02P21/32—Determining the initial rotor position
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/22—Rotating parts of the magnetic circuit
- H02K1/27—Rotor cores with permanent magnets
- H02K1/2706—Inner rotors
- H02K1/272—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis
- H02K1/274—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets
- H02K1/2753—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets the rotor consisting of magnets or groups of magnets arranged with alternating polarity
- H02K1/276—Magnets embedded in the magnetic core, e.g. interior permanent magnets [IPM]
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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
- H02K21/12—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets
- H02K21/14—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating within the armatures
- H02K21/145—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating within the armatures having an annular armature coil
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple
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- 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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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Brushless Motors (AREA)
- Permanent Field Magnets Of Synchronous Machinery (AREA)
- Permanent Magnet Type Synchronous Machine (AREA)
Abstract
The invention discloses a design method of a low-torque ripple permanent magnet brushless motor considering a harmonic injection phase angle. (1) Analyzing the composition principle of the magnetomotive force of the permanent magnet field and the armature field of the permanent magnet brushless motor, and providing a low-torque ripple optimization method considering harmonic injection phase angles, wherein the method can be independently applied to a stator part or a rotor part, and can also be simultaneously applied to the stator part and the rotor part, (2) taking a surface-embedded permanent magnet brushless motor as an embodiment, the method is respectively applied to a rotor and a stator and a rotor at the same time, and modeling is carried out again, (3) analyzing the magnetomotive force of the permanent magnet field and the armature field of the surface-embedded permanent magnet brushless motor, selecting the times and the phase angles of main injection harmonic waves, and (4) optimizing different subharmonic phase angles of the permanent magnet field and the armature field through parametric scanning, determining the optimal phase angle of each injection harmonic, realizing optimal torque performance, and finishing the design of the low-torque ripple permanent magnet brushless motor.
Description
Technical Field
The invention relates to a design method of a low-torque ripple permanent magnet brushless motor considering a harmonic injection phase angle, and belongs to the technical field of motors.
Background
In recent years, with the rapid development of the engineering field, the permanent magnet brushless motor is widely applied and plays an important role in the fields of aviation, automobiles and the like. The brushless permanent magnet motor mainly benefits from the advantages of high power density, high efficiency and the like, but in high-performance occasions such as a servo system and the like, higher requirements are put forward on the performance of the brushless permanent magnet motor, and the brushless permanent magnet motor mainly reflects in two aspects of high required output torque and low torque ripple. The high torque ripple causes large vibration and noise during the operation of the motor, which affects the stability of the servo system operation, and the reduction of the torque ripple is usually accompanied with the weakening of the output torque. Reducing torque ripple without impairing output torque has therefore been a hot and challenging problem in the field of electric machine research.
The harmonic injection method changes the shape of the permanent magnet or the silicon steel sheet by introducing sine waves, reduces the content of invalid harmonic, makes the air gap flux density and back electromotive force waveform more sinusoidal, and achieves the purpose of reducing the integral torque pulsation. In the literature "Effects of magnetic Shape on Torque Capability of Surface-Mounted Permanent Magnet Machine for service Applications" (published in volume IEEE Transactions on Industrial Electronics67, No. 4, 2977 and page 2990 in 2020), by analyzing the air gap flux density, a plurality of sine harmonics with optimal amplitudes are injected into the Permanent Magnet to improve the Torque performance, so that the output Torque is greatly improved under the condition that the Torque ripple is basically unchanged. It is however noteworthy that: 1. the magnetomotive force comprises three elements of amplitude, frequency and phase angle, the current harmonic injection research mainly focuses on the number and amplitude of injected harmonics, and the influence of the phase angle of the injected harmonics on the torque performance is ignored; 2. the phase angle-dependent harmonic injection is applied mainly to the rotor alone, without taking into account the effect on the torque performance of the stator and rotor simultaneously.
The phase angle has great influence on the magnetomotive force, the injected harmonic wave forms can be deviated due to the difference of the phase angles, and the injected harmonic wave forms are simultaneously applied to the air gap part of the stator and the rotor according to the principle that the shape is changed by a harmonic injection method considering the phase angle, so that the shape of the air gap part of the stator and the rotor can be changed by optimizing the phase angle, and the effect of reducing the integral torque pulsation can be achieved by changing the coupling condition of the permanent magnetic field and the armature field. Therefore, the amplitude and the phase angle of injected harmonic waves are comprehensively considered, the method is applied to a stator part and is simultaneously applied to a stator part for comparison, and the design method of the low-torque-ripple permanent magnet brushless motor considering the harmonic wave injected phase angle is provided.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a design method of a low-torque ripple permanent magnet brushless motor considering a harmonic injection phase angle, which can comprehensively consider a harmonic amplitude and a phase angle in harmonic injection under the condition of ensuring that the output torque is basically unchanged, and realize effective suppression of torque ripple and improvement of output torque by utilizing the coupling of a permanent magnetic field and an armature field.
In order to achieve the purpose, the invention adopts the technical scheme that: a design method of a low-torque ripple permanent magnet brushless motor considering a harmonic injection phase angle comprises the following steps:
and 4, carrying out combined optimization on different main subharmonic phase angles in the permanent magnetic field and the armature field, and carrying out contrastive analysis on the optimal motor torque performance obtained by optimizing the initial harmonic phase angle after the independent application of the optimal motor torque performance to the rotor part and the fixed rotor part.
Further, in the step 1, a relation between an initial phase angle of a harmonic in the magnetomotive force of the permanent magnetic field and the armature field and the torque performance needs to be proved, which means that the initial phase angle of the harmonic injected in the magnetomotive force of the permanent magnetic field and the armature field is changed, and then the coupling condition is improved, so that the sine degree of the air gap flux density is higher, the specific subharmonic is adjusted to reduce the whole torque pulsation, and the torque performance of the permanent magnet brushless motor is improved.
Further, in step 2, the magnetomotive force harmonic injection formula considering the initial phase angle is as follows:
in the formula, Frp(θ, t) is the permanent magnet magnetomotive force, prIs the pole pair number of the permanent magnet, i is positive odd number, omegarAs mechanical angular velocity, AiIs the amplitude of the i-th harmonic in the magnetomotive force, theta is the air gap circumferential position angle, t is the time, thetaiIs the initial phase angle of the i-th harmonic in the magnetomotive force, AmAmplitude of the m-th injected harmonic, thetamIs the initial phase angle theta of the major subharmonic in the magnetomotive forcenTo inject the phase angle of the major subharmonic, NsNumber of stator slots, AmThe amplitude of the m-th order injection harmonic is (ip)r±jNs) Sub-harmonic, k1，k2，k3Is any of the m harmonics.
Further, in step 2, the method considers the harmonic injection on the permanent magnet, and is not only applied to the side of the rotor close to the air gap, but also applied to the side of the stator air gap.
Furthermore, in step 3, the contributions of different subharmonics to the torque and to the torque ripple are calculated by a stress-strain method, so as to determine the sensitivity of each harmonic to the torque performance, and a specific subharmonic is selected according to the sensitivity to perform phase angle optimization.
Further, in the step 4, different main sub-harmonic phase angles in the permanent magnetic field and the armature field are combined and optimized, the harmonic injection method of the phase angles is only applied to the rotor and is simultaneously applied to the stator and the rotor to influence the torque performance in a contrast analysis mode, the two optimal motors determined according to the method are subjected to the contrast analysis, the effectiveness of the method applied to the stator and the rotor to improve the torque performance is verified, the output torque is guaranteed to be unchanged, and meanwhile, the torque pulsation is reduced.
The invention has the beneficial effects that:
1. according to the design method of the low-torque ripple permanent magnet brushless motor considering the harmonic injection phase angle, the influence of the harmonic injection method considering the phase angle on the torque performance by only applying the harmonic injection method considering the phase angle to the rotor part and simultaneously applying the harmonic injection method to the stator part is contrastively analyzed, the defects that the conventional harmonic injection method does not consider the injection of the harmonic initial phase angle and only applies the harmonic initial phase angle to the rotor side are overcome, the permanent magnet field and the armature field are effectively coupled more efficiently through the optimization of the magnetomotive force harmonic initial phase angle on the stator side and the rotor side, the compensation effect of specific subharmonics on the torque performance is improved, and the effect of reducing the overall torque ripple is achieved.
2. The invention applies the method of considering the harmonic injection phase angle to the stator and the rotor, and can realize the improvement of the output torque while reducing the torque pulsation.
3. The invention can reasonably select the harmonic wave which has larger influence on the torque performance through the sensitivity analysis of different subharmonics on the output torque and the torque ripple, so that the effect of improving the torque performance of the motor can be more easily achieved by aiming at the optimization of a specific subharmonic phase angle.
4. The invention can be simultaneously applied to a plurality of harmonic phase angles of the stator and the rotor for optimization, and effectively balances the harmonic phase angles to obtain the comprehensive optimal solution of the torque performance. Meanwhile, the method takes a surface-embedded permanent magnet brushless motor as an embodiment, but has general applicability in the permanent magnet brushless motor.
Drawings
FIG. 1 is a flow chart of an optimal design method according to the present invention.
Fig. 2 shows a topology of an embedded permanent magnet brushless motor according to an embodiment of the present invention.
Wherein: 1 is a stator, 2 is a permanent magnet, 3 is an armature winding, 4 is a magnetic barrier, and 5 is a rotor.
Fig. 3 is a schematic diagram of the harmonic injection method considering phase angle according to the present invention applied to the stator and the rotor. (a) The change mechanism of the shape of the stator and rotor teeth when the initial phase angle of a certain injected harmonic in the initial stator and rotor teeth is changed from a degree to b degrees; (b) the shape of the rotor teeth is determined after the initial phase angle is changed.
Fig. 4 is a comparison graph of cogging torque of an initial motor and a phase angle-considered harmonic injection method applied only to a rotor portion and applied to a fixed rotor portion motor according to the present invention.
Fig. 5 is a comparison graph of back emf of the initial motor and the phase angle-considered harmonic injection method applied to the rotor portion only and to the stator portion motor of the present invention.
Fig. 6 is a diagram of back electromotive force harmonic analysis of the initial motor and the phase angle-considered harmonic injection method applied to the rotor portion only and the stator portion motor.
FIG. 7 is a graph comparing the output torque and torque ripple of the initial motor and the phase angle-considered harmonic injection method applied to the rotor portion only and to the stator and rotor portions.
Detailed Description
The invention is described in detail below with reference to specific embodiments and the attached drawings.
The invention provides a low-torque ripple permanent magnet brushless motor design method based on harmonic injection, and the specific optimization process of the method can be seen in figure 1, and the method mainly comprises the following steps:
and 4, after the topological optimization of the rotor of the surface-embedded permanent magnet brushless motor considering the harmonic injection phase angle is completed, comparing and analyzing the electromagnetic performance of the initial surface-embedded permanent magnet brushless motor and the harmonic injection method considering the angle when the method is applied to the rotor part and the stator part at the same time, and verifying the effectiveness of the method applied to the stator and the rotor for improving the torque performance.
Fig. 2 is a topological structure diagram of the motor according to the embodiment, in which 1 is a stator, 2 is a permanent magnet, 3 is an armature winding, 4 is a magnetic barrier, and 5 is a rotor. The embodiment of the invention relates to a 12-slot/8-pole surface-embedded permanent magnet brushless motor, wherein a permanent magnet adopts a surface-embedded structure and an alternating pole magnetizing mode. Magnetic barriers are adopted at two ends of the permanent magnet to reduce magnetic leakage at the end parts of two sides, and meanwhile, pole shoes are added on the stator part to reduce torque pulsation of the motor. The stator and the rotor are both made of silicon steel sheets M19-29G, and the permanent magnet is made of NdFeB 35.
According to the optimization flow chart of fig. 1, the embedded permanent magnet brushless motor in fig. 2 is used as an embodiment, and the specific implementation process is as follows:
in the formula, Frp(θ, t) is the permanent magnet magnetomotive force, prIs the pole pair number of the permanent magnet, i is positive odd number, omegarAs mechanical angular velocity, AiIs the amplitude of the i-th harmonic in the magnetomotive force, theta is the air gap circumferential position angle, t is the time, thetaiIs the initial phase angle of the i-th harmonic in the magnetomotive force, AmAmplitude of the m-th injected harmonic, thetamIs the initial phase angle theta of the major subharmonic in the magnetomotive forcenTo inject the phase angle of the major subharmonic, NsIs the number of grooves, AmThe amplitude of the m-th order injection harmonic is (ip)r±jNs) Sub-harmonic, k1，k2，k3Is any of the m harmonics.
And 4, calculating sensitivity analysis of different subharmonics to torque and torque pulsation by a stress-tensor method, selecting main subharmonics to perform optimization analysis, and obtaining a torque performance optimal model of different harmonic and phase angle combinations under the condition that the method is only applied to a rotor part and is simultaneously applied to a fixed rotor part. The optimal motor which only applies the harmonic injection method considering the phase angle to the rotor part is named as an optimized motor I, and the optimal motor which simultaneously applies the harmonic injection method considering the phase angle to the stator part is named as an optimized motor II.
And 5, after the optimization is completed, verifying the effectiveness of the optimization method. In the embodiment of the invention, after the initial phase angle of the injected harmonic wave of the rotor part only and the initial phase angle of the injected harmonic wave of the rotor part at the same time reach the optimal value through optimization, the electromagnetic performance before and after the optimization of the motor is analyzed and compared, and the results are shown in fig. 4, fig. 5, fig. 6 and fig. 7. It can be seen from fig. 4 that the cogging torque on the stator and rotor is reduced by a small amount compared to before using the harmonic injection taking into account the phase angle, and the peak-to-peak value is reduced from 1.79Nm to 1.54 Nm. Fig. 5 and fig. 6 are analyzed from the back electromotive force angle, and it can be seen from the figure that the back electromotive force amplitudes of the three and the ratio of each harmonic to the fundamental wave are basically unchanged. Reflecting the torque performance comparison of the initial motor and the optimized motor in fig. 7, it can be seen that the torque ripple is greatly reduced when the harmonic injection method considering the phase angle is only applied to the rotor, and is reduced from 38.1% to 13.9%, and the output torque is kept unchanged. When the method is further applied to the stator and the rotor simultaneously, the torque pulsation is further reduced to 10.9%, and the output torque is slightly improved. The effectiveness of the design method is verified through the electromagnetic performance comparison analysis.
The present invention has been described above with reference to the surface-mount permanent magnet brushless motor of fig. 2 as an example, but the present invention is not limited to the motor of fig. 2, and is also applicable to permanent magnet brushless motors of other configurations.
The invention analyzes the composition of the permanent magnetic field and the armature field magnetomotive force of the surface-embedded permanent magnet brushless motor in the embodiment, proves that the phase angle is closely related to the torque performance by analyzing the relationship between the phase angle of the magnetomotive force harmonic and the output torque and the torque ripple, and provides a magnetomotive force formula considering the phase angle of the injected harmonic. And obtaining the amplitude and the initial phase angle of the main subharmonic of the magnetomotive force of the initial permanent magnet brushless motor through Fourier decomposition. And respectively completing the modeling of the surface-embedded permanent magnet brushless motor of which the method is only applied to the rotor part and is simultaneously applied to the stator part by utilizing the magnetomotive force formula considering the injected harmonic phase angle. According to the contribution of different subharmonics to the torque, main subharmonics are selected to be combined with the aim of optimal torque performance, the harmonic phase angle is optimized through parametric scanning, the optimal phase angle of the injection harmonic of the magnetomotive force of the permanent magnetic field and the armature field is obtained, and therefore the motor structure with the optimal torque performance, in which the harmonic injection method considering the phase angle is only applied to the rotor part and the fixed rotor part at the same time, is determined. And comparing the electromagnetic performance of the initial surface-embedded permanent magnet brushless motor with the electromagnetic performance of two optimized motor structures applied to different parts, and verifying the effectiveness of the method applied to the stator and rotor parts for improving the torque performance.
In summary, the invention provides a design method of a low-torque ripple permanent magnet brushless motor based on harmonic injection for the first time, the design method is simultaneously applied to the sides of a stator and a rotor along an air gap, the structure of the motor is changed by adjusting the injection harmonic frequency and a phase angle, and the torque performance of the motor is further improved by changing the air gap flux density. The method can change the phase angle of specific subharmonic to effectively compensate the output torque on the premise of ensuring that the torque performance is basically unchanged, thereby achieving the purpose of reducing the torque pulsation while the output torque is unchanged. The method is simple and effective, is suitable for most permanent magnet brushless motors, is easy to implement, has strong universality, and can provide reference for later-stage design optimization of the motor.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (6)
1. A design method of a low-torque ripple permanent magnet brushless motor considering a harmonic injection phase angle is characterized by comprising the following steps:
step 1, analyzing the principle of the magnetomotive force composition of a permanent magnet field and an armature field of a permanent magnet brushless motor, and providing a low-torque ripple optimization method considering a harmonic injection phase angle, wherein the harmonic phase angle in the magnetomotive force composition is changed to change the injection angles of different harmonics, so that the coupling between the harmonics is improved, and the purpose of reducing torque ripple is achieved;
step 2, if the motor is a surface-embedded permanent magnet brushless motor, a magnetomotive force harmonic injection formula considering a phase angle is provided, and a low-torque ripple optimization method considering the harmonic injection phase angle is respectively applied to a rotor part and a fixed rotor part of the surface-embedded permanent magnet brushless motor;
step 3, determining the harmonic frequency of the optimized phase angle according to the sensitivity analysis of the main subharmonic in the magnetomotive force of the permanent magnetic field and the armature field to the output torque and the torque ripple;
and 4, carrying out combined optimization on different main subharmonic phase angles in the permanent magnetic field and the armature field, and carrying out contrastive analysis on the optimal motor torque performance obtained by optimizing the initial harmonic phase angle after the independent application of the optimal motor torque performance to the rotor part and the fixed rotor part.
2. The method for designing a low-torque-ripple permanent magnet brushless motor considering a harmonic injection phase angle according to claim 1, wherein in the step 1, a relationship between a harmonic initial phase angle and a torque performance in a permanent magnet field magnetomotive force and an armature field magnetomotive force needs to be proved, and the initial phase angle of the injected harmonic in the permanent magnet field magnetomotive force and the armature field magnetomotive force is changed, so that the coupling condition is improved, the sine degree of air gap flux density is higher, specific subharmonics are adjusted to reduce overall torque ripple, and the torque performance of the permanent magnet brushless motor is improved.
3. The design method of the low-torque ripple permanent magnet brushless motor considering the harmonic injection phase angle according to the claim 1, wherein in the step 2, the magnetomotive force harmonic injection formula considering the initial phase angle is as follows:
in the formula, Frp(θ, t) is the permanent magnet magnetomotive force, prIs the pole pair number of the permanent magnet, i is positive odd number, omegarAs mechanical angular velocity, AiIs the amplitude of the i-th harmonic in the magnetomotive force, theta is the air gap circumferential position angle, t is the time, thetaiIs the initial phase angle of the i-th harmonic in the magnetomotive force, AmAmplitude of the m-th injected harmonic, thetamIs the initial phase angle theta of the major subharmonic in the magnetomotive forcenTo inject the phase angle of the major subharmonic, NsNumber of stator slots, AmThe amplitude of the m-th order injection harmonic is (ip)r±jNs) Sub-harmonic, k1，k2，k3Is any of the m harmonics.
4. The design method of the low-torque-ripple permanent magnet brushless motor considering the phase angle of the harmonic injection is characterized in that in the step 2, the method considers the harmonic injection on the permanent magnet and is applied to the air gap side of the stator and the air gap side of the rotor.
5. The method as claimed in claim 1, wherein in step 3, the contributions of different subharmonics to the torque and to the torque ripple are calculated by a stress-strain method, so as to determine the sensitivity of each harmonic to the torque performance, and a specific subharmonic is selected according to the sensitivity for phase angle optimization.
6. The method according to claim 1, wherein in step 4, different major sub-harmonic phase angles in the permanent magnetic field and the armature field are combined and optimized, the harmonic injection method considering the phase angles is only applied to the rotor and is simultaneously applied to the stator and the rotor to influence the torque performance, and the two optimal motors determined according to the method are subjected to comparative analysis to verify the effectiveness of the method applied to the stator and the rotor to improve the torque performance and reduce the torque ripple while ensuring that the output torque is unchanged.
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