CN113659899A - Low-torque ripple permanent magnet brushless motor design method based on harmonic injection - Google Patents

Low-torque ripple permanent magnet brushless motor design method based on harmonic injection Download PDF

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CN113659899A
CN113659899A CN202110824866.4A CN202110824866A CN113659899A CN 113659899 A CN113659899 A CN 113659899A CN 202110824866 A CN202110824866 A CN 202110824866A CN 113659899 A CN113659899 A CN 113659899A
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permanent magnet
harmonic
phase angle
torque
magnetomotive force
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CN113659899B (en
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全力
徐炀
朱孝勇
项子旋
樊德阳
浦尉玲
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Jiangsu University
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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
    • 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
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/20—Estimation of torque
    • 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
    • H02P21/26—Rotor flux based control
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • 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
    • 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
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation
    • 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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  • Permanent Field Magnets Of Synchronous Machinery (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a design method of a low-torque ripple permanent magnet brushless motor based on harmonic injection, (1) analyzing permanent magnet magnetomotive force composition of the permanent magnet brushless motor, verifying that an initial phase angle and torque performance of a permanent magnet magnetomotive force harmonic are related through a generation mechanism of output torque and torque ripple, (2) providing a permanent magnet magnetomotive force formula considering the harmonic injection phase angle according to the influence of the permanent magnet magnetomotive force phase angle on the torque performance, completing rotor modeling of the permanent magnet brushless motor after the harmonic injection according to the influence principle of different phase angles on the rotor shape, (3) analyzing the sensitivity of different subharmonics on the torque and the torque ripple, selecting injection harmonic times, (4) optimizing different subharmonic initial phase angles through parametric scanning, determining the optimal initial phase angle of each injection harmonic, and realizing the torque ripple optimization under the condition that the output torque is basically unchanged, and finishing the design of the low-torque ripple permanent magnet brushless motor.

Description

Low-torque ripple permanent magnet brushless motor design method based on harmonic injection
Technical Field
The invention relates to a low-torque ripple permanent magnet brushless motor design method based on harmonic injection, and belongs to the technical field of motors.
Background
Because of the advantages of high efficiency, high power density and the like, the permanent magnet brushless motor is widely applied and plays an important role in the fields of automobiles, aviation and the like. However, in high-performance occasions such as an electric automobile driving system and the like, higher requirements are put forward on torque ripple of the permanent magnet brushless motor. The torque pulsation is too high, so that large vibration and noise can be generated in the operation process, and the operation stability of the motor is influenced. Therefore, ensuring the output torque to be constant while reducing the torque ripple is a hot and challenging problem in the field of motor research.
Many current methods achieve low torque ripple by changing stator or rotor parameters, such as rotor offset, making auxiliary slots or teeth, changing permanent magnet shape and flux barriers, etc. The document "Material-Efficient Permanent Magnet for Torque Pulsation Minimization in SPM Motors for automatic Applications" (published in IEEE Transactions on Industrial Electronics 61 Vol. 10, page 5779-. However, this method is time-consuming because each segment of the permanent magnet is irregular, resulting in a time-consuming optimization and machining process. In the document "Torque Enhancement of Surface-driven Permanent Magnet Machine Using Third-Order Harmonic wave is injected into the Permanent Magnet to improve the Torque performance by analyzing the air gap magnetic density, wherein the output Torque is greatly improved under the condition that the Torque pulsation is basically unchanged. However, it is worth noting that the magnetomotive force is formed by adding different subharmonics, and the harmonics include three elements of amplitude, frequency and phase angle, and the current research mainly focuses on the amplitude and the frequency of the injected harmonics, and neglects the influence of the phase angle of the injected harmonics on the torque performance. The phase angle has great influence on the magnetomotive force, the difference of the phase angles can cause the deviation of corresponding injected harmonic wave forms, according to the principle that the shape of the rotor is changed by different initial phase angles during the injection of the harmonic waves, the shape change of the rotor along the air gap part can influence the magnetic density of the air gap, and therefore the effect of reducing the torque pulsation can be achieved through the phase angle optimization. Therefore, the invention provides a low-torque ripple permanent magnet brushless motor design method based on harmonic injection by comprehensively considering the amplitude and the initial phase angle of the injected harmonic.
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 based on harmonic injection, which can comprehensively consider the principle that harmonic amplitude and phase angle in harmonic injection influence the rotor shape under the condition of ensuring that the output torque is basically unchanged, and realize effective suppression of torque ripple.
In order to achieve the purpose, the invention adopts the technical scheme that: a low-torque ripple permanent magnet brushless motor design method based on harmonic injection comprises the following steps:
step 1, analyzing the composition of permanent magnet magnetomotive force of a surface-embedded permanent magnet brushless motor in an embodiment, verifying that the phase angle is closely related to torque performance by analyzing the relationship between the phase angle of a harmonic wave of the permanent magnet magnetomotive force and output torque and torque ripple, and obtaining the amplitude and initial phase angle of main subharmonic wave of the magnetomotive force by Fourier decomposition.
And 2, according to the influence of the permanent magnet magnetomotive phase angle on the torque performance, providing a permanent magnet magnetomotive force formula considering the harmonic injection phase angle, and thus completing the rotor modeling of the surface-embedded permanent magnet brushless motor again. By combining the principle that the harmonic injection method changes the shape of the rotor, taking (ipr +/-jNs) subharmonic of the permanent magnet magnetomotive force as an example, the influence of the subharmonic initial phase angle change on the shape of the rotor is verified, and the rationality of the formula is further verified through magnetomotive force simulation and calculation.
And 3, according to the sensitivity analysis of different subharmonics to the torque ripple, selecting main subharmonics to combine, optimizing the initial phase angle of the subharmonics through parametric scanning, determining the optimal initial phase angle of the injected harmonic, minimizing the torque ripple under the condition that the output torque is basically unchanged, and finishing the optimization of the topological structure of the rotor of the surface-embedded permanent magnet brushless motor.
And 4, taking the output torque and the torque ripple of the designed surface-embedded permanent magnet brushless motor as optimization targets, selecting an optimal solution to compare and verify the initial phase angle of the injected harmonic as a design variable, and verifying the feasibility of the method in the aspects of electromagnetic properties such as air gap flux density, flux density cloud pictures, back electromotive force, output torque, torque ripple and the like.
Further, the step 1 proves the relationship between the initial phase angle of the harmonic in the permanent magnet magnetomotive force and the torque performance, and the air gap flux density is effectively adjusted by changing the initial phase angle of the harmonic in the permanent magnet magnetomotive force, so that the purpose of adjusting the initial phase angle of a specific subharmonic to reduce the torque ripple is achieved.
Further, in step 2, the magnetomotive force harmonic injection formula considering the initial phase angle is as follows:
Figure BDA0003173225240000021
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, NsFor the number of slots, the total length of the permanent magnets and the air gap is assumed to be constant, taking into account the change in the shape of the rotor, where the m harmonic is (ip)r±jNs) Dividing p in subharmonicrAnd pr±NsHarmonics, k, of relatively low sub-external amplitude1，k2，k3Is any of the m harmonics.
Figure BDA0003173225240000031
In the formula AmAmplitude of the m-th injected harmonic, AiAmplitude of i-th harmonic in magnetomotive force, AmaxMaximum amplitude of magnetomotive force,/pmIs the width of the permanent magnet, /)airThe width of the air gap.
Further, in the step 2, the trend of the magnetic circuit needs to be analyzed to determine the direction of harmonic injection; if the motor is a surface-embedded permanent magnet brushless motor, a rotor of the motor is divided into two parts, namely a permanent magnet and rotor teeth, the alternating pole magnetizing mode of the permanent magnet determines that the directions of magnetic circuits of the permanent magnet and the rotor teeth in a rotor structure are opposite, so that the directions of harmonic injection of the permanent magnet and the rotor teeth are opposite, and the principle that the shapes of the permanent magnet and the rotor teeth are changed when the initial phase angle is changed is described through initial phase angle injection with different (ipr +/-jNs) subharmonics.
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 step 4, according to the sensitivity analysis of the harmonic to the torque performance, the combination optimization is performed on different harmonic times and phase angles, and the influence of the multiple harmonic phase angles on the output torque and the effectiveness of reducing the torque ripple are explored and considered.
The invention has the beneficial effects that:
1. the design of the low-torque ripple permanent magnet brushless motor based on harmonic injection introduces optimization of phase angle in consideration of harmonic injection on the basis of the traditional harmonic injection, overcomes the defect that the initial phase angle of the injected harmonic is not considered in the traditional harmonic injection method, effectively improves the compensation of specific subharmonic on torque performance through the optimization of the initial phase angle, and achieves the effect of inhibiting torque ripple under the condition that the output torque performance is basically unchanged.
2. The invention can reasonably select the harmonic wave with larger influence on the torque performance by analyzing the sensitivity of different harmonic waves to the output torque and the torque ripple, so that the effect of reducing the torque ripple can be more easily achieved by aiming at the optimization of the phase angle of the corresponding subharmonic wave.
3. The invention can simultaneously optimize a plurality of harmonic phase angles, and effectively balance the plurality of optimized harmonic phase angles to obtain the comprehensive optimal solution of the torque performance according to the principle analysis of different injected harmonic initial phase angles on the shape of the rotor. 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 is a schematic diagram of an initial surface-mount 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 illustrates the principle of rotor shape change when the initial phase angle changes, using a 16 th harmonic as an example; (a) a mechanism of change in rotor tooth shape when the initial phase angle of the 16 th injected harmonic in the initial rotor tooth changes from-8 degrees to 55 degrees; (b) the shape of the rotor teeth after 16 initial phase angle changes; (c) the change mechanism of the permanent magnet shape when the initial phase angle of 16 times of injected harmonics in the initial permanent magnet is changed from-8 degrees to 55 degrees; (d) the shape of the permanent magnet after 16 initial phase angle changes.
FIG. 4 is a diagram illustrating the correctness of a harmonic injection formula verified by a permanent magnet magnetomotive force formation mechanism; (a) an initial permanent magnet magnetomotive force formation mechanism; (b) comparing the initial permanent magnet magnetomotive force simulation value with a calculated value of a phase angle magnetomotive force formula; (c) a permanent magnet magnetomotive force formation mechanism after 16 times of injection of harmonic initial phase angle changes; (d) and comparing the simulated value of the permanent magnet magnetomotive force after the initial phase angle change of the harmonic wave is injected for 16 times with a calculated value of a phase angle magnetomotive force formula.
FIG. 5 is an analysis of output torque and torque ripple sensitivity of a surface-embedded permanent magnet brushless motor for different major sub-harmonics; (a) analyzing the sensitivity of different subharmonics to output torque; (b) and analyzing the sensitivity of different subharmonics to torque ripple.
FIG. 6 is a waveform diagram of air gap flux densities before and after optimization of an initial phase angle of a surface-embedded permanent magnet brushless motor; (a) comparing the air gap flux densities of the initial motor and the optimized motor I; (b) comparing the amplitude and phase angle of the primary subharmonic of the initial motor and the optimized motor I; (c) comparing the air gap flux densities of the initial motor and the optimized motor II; (d) the primary subharmonic amplitudes and phase angles for the initial motor and the optimized motor II are compared.
FIG. 7 is a diagram of counter potential waveforms before and after optimization of the initial phase angle of the surface-embedded permanent magnet brushless motor; (a) comparing counter electromotive forces of the initial motor, the optimized motor I and the optimized motor II; (b) comparing the main harmonic wave of the back electromotive force of the initial motor, the optimized motor I and the optimized motor II.
FIG. 8 is a torque waveform diagram before and after optimization of an initial phase angle of a surface-embedded permanent magnet brushless motor; (a) comparing the cogging torque and the peak value of the initial motor, the optimized motor I and the optimized motor II; (b) the output torque and torque ripple of the initial motor, the optimized motor I and the optimized motor II are compared.
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:
step 1, analyzing the magnetomotive force of an initial motor permanent magnet, and obtaining the amplitude and the initial phase angle of the main subharmonic of the magnetomotive force through Fourier decomposition;
step 2, selecting main permanent magnet magnetomotive force harmonic waves and initial phase angles, and re-modeling the initial surface-embedded permanent magnet brushless motor rotor according to a proposed formula considering the harmonic injection phase angles;
step 3, establishing a mechanism of different harmonic injection angles and rotor shape change by using the proposed harmonic injection formula, analyzing and comparing the influence of different subharmonic combinations and different phase angles on the performance of the motor by combining a parameterized scanning method, comprehensively considering the output torque and the torque ripple of the motor, and selecting the optimal injection times of the harmonic injection and the corresponding initial phase angle to realize the torque ripple minimization under the condition that the output torque is basically unchanged;
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 the performance of the initial surface-embedded permanent magnet brushless motor with the performance of the motor considering the harmonic injection angle, detecting whether the torque performance is optimal or not, otherwise, considering more initial phase angles for injecting the harmonic waves for optimization, and finally verifying the effectiveness of the electromagnetic performance testing method before and after the optimization through comparison.
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:
step 1, taking a surface-embedded permanent magnet brushless motor as an example, deducing a formation equation of the magnetomotive force of a permanent magnet, and obtaining the amplitude and the initial phase angle of the primary sub-magnetomotive force harmonic wave through Fourier decomposition. The amplitude, frequency and initial phase angle are the three elements that make up the magnetomotive force. When the initial phase angle is changed, the magnetomotive force is correspondingly changed. The air gap flux density is obtained by multiplying magnetomotive force and magnetic conductance, and the flux density change is closely related to the torque performance.
Step 2, combining a harmonic injection method according to the principle of forming the magnetomotive force of the permanent magnet, providing a harmonic injection formula considering different harmonic injection initial angles, and selecting 16 (-p)r+2Ns) The accuracy of the proposed formula is verified by the rotor shape change when the subharmonic initial phase angle changes. The formula is as follows:
Figure BDA0003173225240000061
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 slots. Considering the change in rotor shape, the total length of the permanent magnets and the air gap is assumed to be constant, where the m-th harmonic is (ip)r±jNs) Dividing p in subharmonicrAnd pr. + -. NsHarmonics, k, of relatively low sub-external amplitude1，k2，k3Is any of the m harmonics.
Figure BDA0003173225240000062
In the formula AmAmplitude of the m-th injected harmonic, AiAmplitude of i-th harmonic in magnetomotive force, AmaxMaximum amplitude of magnetomotive force,/pmIs the width of the permanent magnet, /)airThe width of the air gap.
And step 3, providing the correctness of a formula for verification, taking the initial phase angle of 16(-pr +2Ns) times of injected harmonics as an example for verification, and describing the principle of changing the shape of the rotor by different initial phase angles as shown in FIG. 3. When the initial angle of 16 th harmonic injection is changed, because the permanent magnets adopt alternating poles for magnetization, the magnetic circuit directions of adjacent permanent magnets and rotor teeth are opposite, the injection directions are opposite when the harmonic injection formula is applied to the permanent magnets and the rotor teeth. As can be seen from the shape change of the rotor teeth, the initial phase angle of the 16 th harmonic is-8 deg, when the initial phase angle of the injected 16 th harmonic is 55deg, the harmonic of the two harmonics has a shift of-63 deg, and the change causes the shape change of the rotor teeth due to the phase angle shift, and similarly, the shape change of the rotor teeth is opposite due to the opposite injection directions of the permanent magnets and the rotor teeth.
After describing the mechanism of phase angle change to rotor shape, fig. 4 shows the change of magnetomotive force after the rotor shape is changed under different phase angles, and the verification is carried out by comparing finite element analysis with theoretical calculation. When the initial phase angle of the 16 th harmonic is not changed, the shape of the rotor is consistent along the circumferential direction of the air gap, so that the corresponding magnetomotive force schematic diagram is unchanged on the permanent magnet and the rotor tooth, and meanwhile, the magnetomotive force calculated by finite element analysis and theory is basically consistent. When the phase angle changes, due to the change of the permanent magnet and the rotor teeth, the rotor shape is inconsistent along the air gap circumference, the corresponding magnetomotive force schematic diagram is correspondingly changed, the trend of the magnetomotive force schematic diagram calculated by finite element analysis and theory is basically consistent, and the analysis verifies the correctness of the initial phase angle formula considering the injected harmonic.
Step 4 and fig. 5 show the sensitivity analysis of torque and torque ripple by calculating different subharmonics by a stress-strain method, and it can be seen that the output torque is mainly generated by 8 subharmonics, and 4, 8, 16, 24, 32, 40 and 48 subharmonics have larger contribution to the torque ripple. According to the selection principle of injecting m-th harmonic in step 2, under the condition that the total length of the permanent magnet and the air gap is not changed, because the amplitudes of 4 th harmonic and 8 th harmonic are larger, the influence on the rotor shape is larger, and therefore 16 th harmonic, 24 th harmonic, 32 th harmonic and 48 th harmonic are selected for optimization.
Figure BDA0003173225240000071
Figure BDA0003173225240000072
In the formula, Tk(t) is torque generated by the k-th harmonic，lefIs the axial length of the motor, mu0For vacuum permeability, r is the air gap radius, BrkAnd BtkIs the k-th harmonic radial and tangential air gap flux density, θrkAnd thetatkInitial phase, F, of the k-th harmonic in radial and tangential directions, respectivelyrk(theta, t) is k-th harmonic permanent magnet magnetomotive force, and Λk(theta, t) is k-th harmonic permanent magnetic conductance, k, j is positive integer, ΛjAmplitude of permeance of j-th harmonic, NsIs the number of grooves, PrFor the permanent magnet pole pair number, theta is the air gap circumferential position angle, T is the time, TkripIs the torque ripple, T, produced by the k harmonickmaxIs the maximum output torque produced by the k harmonic, TkminIs the minimum output torque, T, produced by the k harmonickavgIs the average output torque produced by the k harmonic.
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 each injected harmonic reaches the optimal value through optimization, the electromagnetic performance before and after optimization of the motor is analyzed and compared, and the results are shown in fig. 6, 7 and 8. The optimal initial phase angle considering the 16 th and 24 th injection harmonics is named as an optimized motor I, and the optimal initial phase angle considering the 16 th, 24 th, 32 th and 48 th injection harmonics is named as an optimized motor II. As can be seen from FIG. 6, although the phase angle of each major subharmonic of the optimized air gap flux density changes, the amplitude of each major subharmonic remains substantially unchanged, which is consistent with the theoretical analysis in step 3. As can be seen from fig. 7, the back emf amplitude and the harmonic distortion rate after optimization are substantially unchanged. As can be seen from FIG. 8, after optimization, the torque ripple of the motor is obviously reduced and the output torque is kept basically unchanged, and the effectiveness of the design method is verified by comparison results before and after optimization.
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.
In conclusion, the invention firstly provides a design method of a low-torque ripple permanent magnet brushless motor based on harmonic injection, the structure of a rotor is changed by injecting the combination of the harmonic times and the phase angle, and the torque performance of the motor is further influenced by 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.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (6)

1. A low-torque ripple permanent magnet brushless motor design method based on harmonic injection is characterized by comprising the following steps:
step 1, determining the relation between an initial phase angle of harmonic in a permanent magnet magnetomotive force and output torque and torque ripple according to the permanent magnet magnetomotive force composition of a permanent magnet brushless motor, and extracting the amplitude and the initial phase angle of main subharmonic in the magnetomotive force through Fourier decomposition;
step 2, according to a permanent magnet magnetomotive force formula, a multi-harmonic injection formula considering an initial phase angle is provided, modeling considering the multi-harmonic injection phase angle by taking a surface-embedded permanent magnet brushless motor as an embodiment is completed according to the formula, and the correctness of the multi-harmonic injection angle formula is considered by combining simulation and analysis verification through the principle of the change of the m-th harmonic injection to the shape of a rotor;
step 3, determining the harmonic frequency of the optimized initial phase angle according to the sensitivity analysis of the main subharmonic to the output torque and the torque ripple;
and 4, carrying out combined optimization on different primary subharmonic initial phase angles, and verifying the effectiveness of the method on torque ripple reduction.
2. The design method of the low-torque ripple permanent magnet brushless motor based on the harmonic injection according to claim 1, wherein the relationship between the initial phase angle of the harmonic in the permanent magnet magnetomotive force and the torque performance is proved in step 1, and the air gap flux density is effectively adjusted by changing the initial phase angle of the harmonic in the permanent magnet magnetomotive force, so that the purpose of adjusting the initial phase angle of a specific subharmonic to reduce the torque ripple is achieved.
3. The design method of the harmonic injection-based low-torque ripple permanent magnet brushless motor according to claim 1, wherein in the step 2, the magnetomotive force harmonic injection formula considering the initial phase angle is as follows:
Figure FDA0003173225230000011
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, NsFor the number of slots, the total length of the permanent magnets and the air gap is assumed to be constant, taking into account the change in the shape of the rotor, where the m harmonic is (ip)r±jNs) Dividing p in subharmonicrAnd pr±NsHarmonics, k, of relatively low sub-external amplitude1，k2，k3Is any of the m harmonics.
Figure FDA0003173225230000021
In the formula AmAmplitude of the m-th injected harmonic, AiAmplitude of i-th harmonic in magnetomotive force, AmaxMaximum amplitude of magnetomotive force,/pmIs the width of the permanent magnet, /)airThe width of the air gap.
4. The design method of the harmonic injection-based low-torque ripple permanent magnet brushless motor according to claim 1, wherein in the step 2, the trend of the magnetic circuit needs to be analyzed to determine the direction of the harmonic injection; if the motor is a surface-embedded permanent magnet brushless motor, a rotor of the motor is divided into two parts, namely a permanent magnet and rotor teeth, the alternating pole magnetizing mode of the permanent magnet determines that the directions of magnetic circuits of the permanent magnet and the rotor teeth in a rotor structure are opposite, so that the directions of harmonic injection of the permanent magnet and the rotor teeth are opposite, and the principle that the shapes of the permanent magnet and the rotor teeth are changed when the initial phase angle is changed is described through initial phase angle injection with different (ipr +/-jNs) subharmonics.
5. The design method of the harmonic injection-based low-torque-ripple permanent magnet brushless motor according to claim 1, wherein in the step 3, the contributions of different subharmonics to the torque and 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.
6. The design method of the harmonic injection-based low-torque ripple permanent magnet brushless motor according to claim 1, wherein in the step 4, different harmonic times and phase angles are optimized in a combined manner according to the sensitivity analysis of harmonics to torque performance, and the effects of multiple harmonic phase angles on the output torque and the effectiveness of reducing the torque ripple are explored and considered.
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