A method for reducing torque ripple of a doubly salient permanent magnet motor with unequal air gaps and the motor

Abstract

A method for reducing torque ripple of a double-sided permanent magnet motor with unequal air gaps and the motor relate to the technical field of motors, and include the following steps: Step 101, the stator teeth of the motor are eccentrically designed, and the rotor teeth of the motor are eccentrically designed. The eccentricity is scanned through parameters to minimize the torque ripple; Step 102, the radial and tangential magnetic flux density amplitudes and phases of the air gap at multiple time points are obtained by using Maxwell finite element simulation; Step 103, the data obtained in Step 102 are substituted into the torque formula of the Maxwell stress tensor method to obtain the torque generated by each harmonic; Step 104, the torque data obtained in Step 103 are substituted into the torque ripple formula to calculate the torque ripple generated by each harmonic; Step 105, compare the changes in the amplitudes of the dominant harmonics of the torque ripple before and after the eccentricity of the stator teeth and rotor teeth to verify the results.

Description

Technical Field

[0001] The present invention relates to the technical field of motors, and particularly to a method and a motor for reducing torque ripple of an unequal air-gap bilateral permanent magnet motor. Background Art

[0002] Permanent magnet vernier motors (PMVMs) are widely studied because of their simple structure and high torque density, and are more suitable for direct drive applications with low speed and large torque, such as electric vehicles, ship propulsion, and wind power generation. Compared with unilateral permanent magnet vernier motors with permanent magnets only placed on the stator side or the rotor side, bilateral permanent magnet vernier motors (DPMVMs) have permanent magnets installed on both the stator and rotor sides, which can further improve the torque density. A DPMVM can be regarded as a combination of a stator vernier motor and a rotor vernier motor. However, due to the superposition of the stator-side torque and the rotor-side torque, and the influence of the phase relationship, this will inevitably bring larger torque ripple, especially having an adverse effect on actual application conditions such as low-speed direct drive.

[0003] Due to the bidirectional flux modulation effect in the structure of bilateral permanent magnet excitation of DPMVMs, the air-gap magnetic field contains richer harmonics. On the one hand, for permanent magnet vernier motors, the Maxwell stress tensor method can be used to establish the relationship between the output torque and the air-gap magnetic flux density, so that it can be obtained that the harmonics of the air-gap magnetic flux density are the key factors affecting the torque and torque ripple of permanent magnet vernier motors. On the other hand, the air-gap magnetic field distribution is mainly obtained by the magnetic conductance modulation of the armature magnetomotive force and the permanent magnet magnetomotive forces on the stator and rotor sides, which is the result of their interaction. Therefore, starting from the armature magnetomotive force, the permanent magnet magnetomotive forces on the stator and rotor sides, and the magnetic conductance on the stator and rotor sides, the air-gap magnetic field distribution can be improved to achieve the effect of improving torque ripple. Among them, improving the distribution of the permanent magnet magnetomotive force has a certain effect on reducing torque ripple, but the torque sacrifice is relatively large. And improving the distribution of the permanent magnet magnetomotive force by modifying the permanent magnets will increase the processing cost and material cost. Therefore, the present invention starts from the magnetic conductance on the stator and rotor sides to improve the torque characteristics. Summary of the Invention

[0004] Aiming at the deficiencies in the background art, the purpose of the present invention is to provide a method and a motor for reducing torque ripple of an unequal air-gap bilateral permanent magnet motor.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] A method for reducing torque ripple of an unequal air-gap bilateral permanent magnet motor, comprising the following steps:

[0007] Step 101: In the eccentric design of the motor stator teeth, there are point A, point O, and point O'. Point A is the top center point of the stator teeth, point O is the reference point of the stator teeth, and point O' is located on the extension line of the connection line between point A and the motor center and has an eccentricity from point O. An arc is formed with O' as the center and O'A as the radius to create the eccentric design of the stator teeth. In the eccentric design of the motor rotor teeth, there are point E, point O2, and point O2'. Point E is the top center point of the rotor teeth, point O2 is the motor center, and point O2' is located on the connection line between point E and the motor center and has an eccentricity from point O2. An arc is formed with O2' as the center and O'E as the radius to create the eccentric design of the rotor teeth. The torque ripple is minimized by parameter scanning of the eccentricity;

[0008] Step 102: Use Maxwell finite element simulation to obtain the radial and tangential air-gap magnetic flux density amplitudes and phases at multiple time points;

[0009] Step 103: Substitute the data obtained in Step 102 into the Maxwell stress tensor method torque formula to obtain the torque generated by each harmonic;

[0010] Step 104: Substitute the torque data obtained in Step 103 into the torque ripple formula to calculate the torque ripple generated by each harmonic;

[0011] Step 105: Compare the changes in the dominant harmonic amplitudes of the torque ripple before and after the eccentricity of the stator teeth and rotor teeth to verify the results.

[0012] Furthermore, in Step 101, the following quantitative relationships need to be satisfied among R, h, and OA: R = OA - h; where h is the eccentricity of the stator teeth and R is the distance between O' and point A; the following quantitative relationships need to be satisfied among R1, h1, and O2E: R1 = O2E - h1; where h1 is the eccentricity of the rotor teeth and R1 is the distance between O2' and point E.

[0013] Furthermore, in Step 103, the relationship between the output torque and the air-gap magnetic flux density is expressed as: where, T e (t) is the total output torque, r g is the air-gap radius, μ0 is the vacuum permeability, l a is the axial length of the motor, T q (t) is the output torque generated by the qth harmonic, B Rq 、B Tq are the qth radial and tangential air-gap magnetic flux density amplitudes respectively, θ Rq 、θ Tq are the qth radial and tangential air-gap magnetic flux density phases.

[0014] Further, the torque ripple is calculated based on the peak-to-peak values and average values of the harmonics obtained in the step 103, and the basic calculation formula of the torque ripple is as follows: where, T pk2pk (t) is the peak-to-peak value of the output torque, T max (t) is the maximum value of the output torque, T min (t) is the minimum value of the output torque, T avg (t) is the average value of the output torque.

[0015] Further, the torque ripple generated by the q-th harmonic is expressed as obtained from formula (1) and formula (2):

[0016] An unequal air-gap bilateral permanent magnet motor applicable to a method for reducing the torque ripple of an unequal air-gap bilateral permanent magnet motor, characterized in that it includes a stator and a rotor arranged in sequence from outside to inside, there is an air gap between the rotor and the stator, the stator includes a stator core, first stator slots and stator teeth are evenly spaced along the circumferential direction inside the stator core, stator armature windings are embedded in the stator slots, rotor slots and rotor teeth are evenly spaced along the circumferential direction on the outer side of the rotor core, and the tooth profiles of at least one of the stator teeth and rotor teeth are non-uniform geometric structures;

[0017] The non-uniform geometric structure of the stator teeth is that the end of the stator teeth extends towards the center of the motor to form a convex surface, a reference point is formed by connecting any fixed point on the extension line of the connection between the top center point of the convex surface of the stator teeth and the center of the motor, and the geometric center of the convex surface of each stator tooth has an eccentricity relative to the reference point, so that a non-uniform air gap is formed between the inner surface of the stator and the outer surface of the rotor, so as to reduce the content of specific sub-permeance harmonics and thus reduce the torque ripple.

[0018] Further, the non-uniform geometric structure of the rotor teeth is that the rotor teeth extend towards the outside of the motor with a convex surface with the center of the motor as the reference point, and the end of the rotor teeth forms a convex surface, and the geometric center of the convex surface of each rotor tooth has an eccentricity relative to the center of the motor.

[0019] Further, the rotor includes a rotor core, and rotor slots are circumferentially spaced on the outer surface of the rotor core; second stator slots are evenly spaced along the circumferential direction inside the stator core, and the second stator slots and the stator teeth are alternately distributed.

[0020] Further, stator permanent magnets and rotor permanent magnets are respectively embedded in the second stator slots and the rotor slots, so that both the stator and the rotor form an alternating pole structure, and the stator teeth and rotor teeth with non-uniform geometric structures are respectively adapted to the stator and rotor of the alternating pole structure.

[0021] Furthermore, the inner side of the stator core and the outer side of the rotor core are flux modulation poles with a double salient pole structure, forming a bidirectional flux modulation effect.

[0022] The beneficial effects of the present invention are as follows:

[0023] 1. A method for reducing torque ripple of a bilateral permanent magnet motor proposed by the present invention can significantly reduce torque ripple while sacrificing a small amount of output torque. It does not require complex structural deformation of the motor by changing the permeance period or other means, and only simple profile design of the stator or rotor modulation teeth is needed.

[0024] 2. A method for reducing torque ripple of a bilateral permanent magnet motor proposed by the present invention only performs eccentric profile design on silicon steel sheets, and the processing and material costs are lower than those of permanent magnet profile design. As the modulation harmonic is the dominant harmonic of torque ripple, the eccentricity of the stator and rotor modulation teeth can reduce the modulation harmonic amplitude by reducing the amplitude of specific sub-permeance harmonics. Compared with the case of reducing torque ripple by permanent magnet profile design, the torque sacrifice is relatively small. At the same time, the optimization results show that this method can significantly reduce the motor torque ripple and cogging torque, and also improve the electromagnetic performance including core loss, power factor, etc., which helps to improve the operating performance of the motor. Description of the Drawings

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0026] Figure 1 Schematic diagram of Embodiment 1 of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0027] Figure 2 is Figure 1 An enlarged view of part A;

[0028] Figure 3 Schematic diagram of Embodiment 2 of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0029] Figure 4 Schematic diagram of Embodiment 3 of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0030] Figure 5 Stator tooth eccentric design diagram of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0031] Figure 6Design diagram of rotor tooth eccentricity of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0032] Figure 7 Relationship diagram between harmonic orders and torque of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0033] Figure 8 Relationship diagram between harmonic orders and torque ripple of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0034] Figure 9 Comparison diagram of magnetic flux density amplitudes of harmonic orders between the initial structure and the modulated tooth eccentricity structure of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0035] Figure 10 Comparison diagram of torques at each electrical angle between the initial structure and the modulated tooth eccentricity structure of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0036] Figure 11 Comparison diagram of back electromotive forces at each electrical angle between the initial structure and the modulated tooth eccentricity structure of an unequal air-gap bilateral permanent magnet motor of the present invention;

[0037] Figure 12 Comparison diagram of cogging torques at each electrical angle between the initial structure and the modulated tooth eccentricity structure of an unequal air-gap bilateral permanent magnet motor of the present invention.

[0038] In the figure, 101, stator core; 102, stator permanent magnet; 103, stator armature winding; 104, stator tooth; 201, rotor core; 202, rotor permanent magnet; 203, rotor tooth. Detailed implementation manners

[0039] The following combines Figure 1 - 12 to describe the present invention in detail.

[0040] Example 1:

[0041] A method for reducing torque ripple of an unequal air-gap bilateral permanent magnet motor, comprising the following steps:

[0042] Step 101: The motor has points A, O, and O'. Point A is the top center point of the stator tooth, point O is the reference point, and point O' is located on the extension of the line connecting point A and the center of the motor and has an eccentricity from point O. An eccentric design of the bread-shaped stator tooth is formed by making an arc with O' as the center and O'A as the radius. The eccentric design of the motor rotor tooth has points E, O2, and O2'. Point E is the top center point of the rotor tooth, point O2 is the center of the motor, and point O2' is located on the line connecting point E and the center of the motor and has an eccentricity from point O2. An eccentric design of the bread-shaped rotor tooth is formed by making an arc with O2' as the center and O'E as the radius. The eccentricity is scanned by parameters to minimize the torque ripple;

[0043] Step 102: Use Maxwell finite element simulation to obtain the radial and tangential magnetic flux density amplitudes and phases at multiple time points in the air gap;

[0044] Step 103: Substitute the data obtained in Step 102 into the torque formula of the Maxwell stress tensor method to obtain the torque generated by each harmonic;

[0045] Step 104: Substitute the torque data obtained in Step 103 into the torque ripple formula to calculate the torque ripple generated by each harmonic;

[0046] Step 105: Compare the changes in the dominant harmonic amplitudes of the torque ripple before and after the eccentricity of the stator tooth 104 and the rotor tooth 203 to verify the results.

[0047] As Figure 5 - 6 shown, in Step 101, the motor also has point C. Point C is the intersection point of the line connecting point A and the center of the motor and the inner rotor. The distance AC, denoted as y, is the minimum air gap distance, which is 0.75 mm.

[0048] As Figure 5 shown, 1 is the outer contour line of the rotor, 2 is the inner contour line of the stator. Point B is the top center point of any stator tooth, point D is the intersection point of the line connecting point B and the center of the motor and the inner rotor. Points B and D are equivalent to points A and C; point O1 is the reference point, equivalent to point O; point O1' is located on the extension of the line connecting point B and the center of the motor and has an eccentricity from point O1.

[0049] Further, in Step 101, the following quantitative relationships need to be satisfied among R, h, and OA: R = OA - h; where h is the eccentricity and R is the distance between O' and point A. The following quantitative relationship needs to be satisfied among R1, h1, and O2E: R1 = O2E - h1; where h1 is the eccentricity of the rotor tooth and R1 is the distance between O2' and point E.

[0050] For the stator side, the larger the eccentricity, the smaller the R, and the greater the eccentricity of the stator teeth 104. The design process of the split stator teeth on the other side is the same. Since point O is on the opposite side of the motor center, even when the eccentricity is 0 mm, there is still a slight eccentricity effect. Therefore, when optimizing, a suitable point O needs to be selected and fixed as a fixed point, so that when the eccentricity is 0 mm, the eccentricity effect can be ignored, making the subsequent parameter scan for the eccentricity to select the optimal eccentricity more accurate and reasonable. In this example, point O is 180 mm away from the center of the circle.

[0051] Under the condition of ensuring that the shapes of the stator teeth 104 and the rotor teeth 203 do not deform, select a suitable range of eccentricities on the stator and rotor sides for scanning. Regarding the torque and torque ripple as the main objects and the core loss and eddy current loss as the secondary objects, view the optimization results. Taking the low torque ripple under the condition that the torque does not decrease too much as the selection criterion, select the optimal result.

[0052] Furthermore, to verify the accuracy of reducing torque ripple by the eccentric design of the stator and rotor modulation teeth, use the Maxwell stress tensor method to calculate the torque and torque ripple generated by each harmonic order, and obtain the harmonic orders that contribute more to the torque and torque ripple. At the same time, through simulation, analyze the amplitude changes of the main harmonic orders before and at the optimal eccentricity of the stator and rotor modulation teeth. Finally, compare and analyze the relationship between the amplitude changes of the main harmonic orders and the dominant harmonics of the torque and torque ripple to verify the effectiveness of the eccentric design of the stator and rotor modulation teeth.

[0053] In step 102, the radial air-gap magnetic density and tangential air-gap magnetic density of the motor can be expressed as: where B Rq and B Tq are the amplitudes of the q-th radial and tangential air-gap magnetic densities respectively, and θ Rq and θ Tq are the phases of the q-th radial and tangential air-gap magnetic densities.

[0054] The radial and tangential air-gap magnetic densities can be obtained through simulation at multiple time points, and the amplitude and phase FFT decompositions are respectively performed on the obtained radial and tangential air-gap magnetic densities, and finally the amplitudes and phases of the radial and tangential air-gap magnetic densities are obtained.

[0055] For the permanent magnet vernier motor, the Maxwell stress tensor method can be used to establish the relationship between the output torque and the air-gap magnetic density. In step 103, the relationship between the output torque and the air-gap magnetic density is expressed as: where T e (t) is the total output torque, r g is the air-gap radius, μ0 is the vacuum permeability, l a is the axial length of the motor, T q (t) is the output torque generated by the q-th harmonic, and BRq , B Tq are the amplitudes of the q-th radial and tangential air-gap magnetic fluxes respectively, and θ Rq , θ Tq are the phases of the q-th radial and tangential air-gap magnetic fluxes.

[0056] Through the above analysis, via the Maxwell stress tensor method, the relationship between the output torque and the air-gap magnetic flux can be established. Through simulation, the total average torque generated by each harmonic order at a single time point and the output torque of a certain harmonic order at multiple simulation time points can be obtained. Taking the number of multi-time points in the simulation as the superposition times and superimposing the total average torque generated by each harmonic order at a single time point, the average torque and torque waveform of the motor output can be obtained. Similarly, the average torque and torque waveform generated by a certain harmonic order can also be obtained.

[0057] After obtaining the output torque generated by each harmonic, calculate the torque ripple according to the peak-to-peak value and average value of each harmonic order obtained in step 103. The basic calculation formula of the torque ripple is as follows: where, T pk2pk (t) is the peak-to-peak value of the output torque, T max (t) is the maximum value of the output torque, T min (t) is the minimum value of the output torque, T avg (t) is the average value of the output torque.

[0058] Furthermore, according to formula (1) and formula (2), the torque ripple generated by the q-th harmonic is expressed as:

[0059] Through the above analysis, after ignoring the higher-order harmonics and the lower-amplitude harmonic orders, the contribution degrees of the main harmonic orders to the torque and torque ripple are obtained.

[0060] As Figure 7 shown, it can be seen that the 38th harmonic generates a torque of 83.86 Nm, accounting for 69% of the average torque, and the 48th harmonic generates a torque of 26.15 Nm, accounting for 21% of the average torque. The harmonics of these two orders contribute the vast majority of the torque. The remaining higher-order or lower-amplitude harmonics contribute a total of 10% of the torque component. From this, it can be concluded that the 38th and 48th harmonics are the torque-dominant harmonics. The dominant harmonic orders of the torque ripple can be obtained by dividing the peak-to-peak value of each harmonic order by the average torque of each harmonic order.

[0061] As Figure 8As shown, the harmonic orders that have a greater impact on torque ripple are 34, 72, 10, and 14, which are the dominant harmonics of torque ripple. The modulation harmonics are the dominant harmonics of torque ripple rather than the original magnetic field harmonics. Among them, the 10th harmonic involves rotor permeance modulation, the 72nd harmonic involves stator permeance modulation, and the 14th and 34th harmonics involve both stator and rotor permeance modulation. Without changing the original magnetic field harmonic components, changing the content of specific-order permeance harmonics is an effective method to optimize modulation harmonics and reduce torque ripple.

[0062] The optimal eccentricity has been determined by optimizing the eccentricity through the above steps. The amplitudes of the main harmonic orders of the motor with the initial structure and the amplitudes of the main harmonic orders of the motor under the optimal eccentricity are obtained through simulation respectively.

[0063] As Figure 9 shown, no new harmonic orders are generated before and after the eccentricity of the stator and rotor modulation teeth, only the harmonic amplitudes change. This is because the eccentric design of the stator and rotor modulation teeth does not change the period of the permeance, but only changes the waveform of the permeance. According to the magnetic field modulation theory, both the permanent magnet magnetomotive force and the armature magnetomotive force will be modulated by the stator and rotor permeances to generate new harmonic orders. Therefore, the change in the amplitudes of the permeances of each order of the stator and rotor will directly affect the amplitudes of the harmonics generated by modulation. Among them, the amplitude of the 38th harmonic decreases by the largest proportion of 7.7%, and at the same time, the torque proportion of the 38th harmonic reaches 69%. Although the amplitudes of the 24th and 48th harmonics increase by 3.9% and 3.2% respectively, the total torque proportion of the two is only 28.5%, which is not enough to offset the impact of the decrease in the amplitude of the 38th harmonic on the torque. On the other hand, the amplitudes of the 34th, 72nd, 10th, and 14th harmonics all decrease, and the decrease proportions are 15%, 20%, 2.8%, and 6.5% respectively, and these order harmonics are the dominant harmonics of torque ripple. In summary, the eccentric design of the stator and rotor modulation teeth causes changes in the air-gap magnetic flux density amplitude, and the changes in torque and torque ripple are consistent with the theoretical analysis, verifying its effectiveness.

[0064] Taking the 24-slot 38-pole double-sided permanent magnet motor of this embodiment as an example, after the eccentric design of the stator and rotor modulation teeth, the optimal eccentricity is selected for simulation, and the torque, back electromotive force, and cogging torque before and after simulation are obtained, as Figure 10 - 12 shown:

[0065] The comparison of the main performances of the motor before and after the eccentricity of the stator and rotor modulation teeth is shown in the following table:

[0066] Content Un-eccentric After 55mm Eccentricity Remarks Effective Value of Back EMF of Load Line (V) 212.9 197.1 THD of Back EMF of Load Line 1.2％ 0.84％ Rated Torque (N·m) 118.8 113.3 Decrease by 4.6% Rated Torque Fluctuation Rate 4.79％ 1.12％ Decrease by 76.6% Core Loss (W) 18.15 13.04 Decrease Power Factor 0.607 0.621 Increase Peak-to-Peak Value of Cogging Torque (N·m) 3.62 0.46 Decrease by 87.3%

[0067] From the optimization results, when the output torque drops by 4.6%, the torque ripple drops by 76.6%, showing a significant effect. The peak-to-peak cogging torque drops by 87.3%. The core loss is reduced to a certain extent. The eccentric design of the stator and rotor modulation teeth saves the amount of silicon steel sheet and reduces the manufacturing cost of the motor.

[0068] For this example, the eccentric design of the stator and rotor teeth can significantly reduce the torque ripple without sacrificing much output torque, while reducing the loss and achieving good results.

[0069] An unequal air-gap bilateral permanent magnet motor is applicable to a method for reducing the torque ripple of an unequal air-gap bilateral permanent magnet motor, as Figure 1 - 2 shown, including a stator and a rotor arranged in sequence from outside to inside. There is an air gap between the rotor and the stator. The stator includes a stator core 101. First stator slots and stator teeth 104 are evenly spaced along the circumferential direction inside the stator core 101. Stator armature windings 103 are embedded in the stator slots. Rotor slots and rotor teeth 203 are evenly spaced along the circumferential direction on the outer side of the rotor core. The tooth profiles of the stator teeth 104 and the rotor teeth 203 are non-uniform geometric structures. A non-uniform air gap is formed between the inner surface of the stator and the outer surface of the rotor, aiming to reduce the content of specific sub-permeance harmonics and thus reduce the torque ripple.

[0070] In this embodiment, the non-uniform geometric structure on the stator side is that the end of the stator tooth 104 extends towards the center of the motor to form a convex surface. The top center point of the convex surface of the stator tooth 104 forms a reference point with any fixed point on the extension line of the connection line between the center of the motor and the center of the convex surface. The geometric center of the convex surface of each stator tooth 104 has an eccentricity relative to the reference point. The non-uniform geometric structure on the rotor side is that the rotor tooth 203 has a convex surface. The geometric center of the convex surface of each rotor tooth 203 has an eccentricity relative to the center of the motor.

[0071] In this embodiment, the non-uniform geometric structure of the rotor tooth 203 is that the rotor tooth 203 extends towards the outside of the motor with a convex surface based on the center of the motor as the reference point. The end of the rotor tooth 203 forms a convex surface. The geometric center of the convex surface of each rotor tooth 203 has an eccentricity relative to the center of the motor.

[0072] In this embodiment, the rotor includes a rotor core 201, and rotor slots are circumferentially and spacedly distributed on the outer surface of the rotor core 201; second stator slots are evenly and spacedly distributed along the circumferential direction on the inner side of the stator core 101, and the second stator slots and the stator teeth 104 are alternately distributed. Further, a stator permanent magnet 102 and a rotor permanent magnet 202 are respectively embedded in the second stator slot and the rotor slot, and the rotor permanent magnet 202 and the rotor teeth 203 form an array of alternating pole structures, and the stator permanent magnet 102 and the stator teeth 104 form an array of alternating pole structures. Further, flux modulation poles are provided on the inner side of the stator core 101 and the outer side of the rotor core 201, and a non-magnetic air gap is provided between the two flux modulation poles.

[0073] In this embodiment, the structures of the motor stator permanent magnet 102 and the rotor permanent magnet 202 remain unchanged, and the contour configurations of the eccentric stator teeth 104 and the rotor teeth 203 change the content of specific harmonics of the magnetic conductance function of the flux modulation poles, thereby reducing the modulation harmonic amplitude of the dominant torque ripple.

[0074] Embodiment 2:

[0075] As Figure 3 shown, the number of split teeth of the bilateral permanent magnet excited vernier motor can be arbitrarily selected under the condition of satisfying the slot-pole number relationship. Therefore, eccentric design can be carried out for multiple stator split teeth, Figure 3 which is a bilateral permanent magnet vernier motor with 12 slots and 3 stator split teeth.

[0076] Embodiment 3:

[0077] As Figure 4 shown, the shape of the stator teeth 104 of the bilateral permanent magnet excited vernier motor can be approximately equivalent to a stepped shape, and its essence is to make the magnetic conductance waveform on the stator side have a higher sinusoidality.

[0078] The above embodiments are only used to illustrate the technical concept and characteristics of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement it, and cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the spirit and essence of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for reducing torque ripple of a permanent magnet motor with unequal air gaps on both sides, characterized in that It includes the following steps: Step 101: In the eccentric design of the stator teeth of the motor, points A, O, and O' are provided. Point A is the top center point of the stator teeth, point O is the reference point of the stator teeth, and point O' is located on the extension line of the connection line between point A and the center of the motor and has an eccentricity from point O. An arc is formed with O' as the center and O'A as the radius to form the eccentric design of the stator teeth. In the eccentric design of the rotor teeth of the motor, points E, O2, and O2' are provided. Point E is the top center point of the rotor teeth, point O2 is the center of the motor, and point O2' is located on the connection line between point E and the center of the motor and has an eccentricity from point O2. An arc is formed with O2' as the center and O'E as the radius to form the eccentric design of the rotor teeth. The torque ripple is minimized by scanning the eccentricity parameter. Step 102: Use Maxwell finite element simulation to obtain the radial and tangential magnetic flux density amplitudes and phases at multiple time points in the air gap. Step 103: Substitute the data obtained in Step 102 into the torque formula of the Maxwell stress tensor method to obtain the torque generated by each harmonic. The relationship between the output torque and the air-gap magnetic flux density is expressed as: where, T e (t) is the total output torque, r g is the air-gap radius, μ0 is the vacuum permeability, l a is the axial length of the motor, T q (t) is the output torque generated by the q-th harmonic, B Rq , B Tq are the amplitudes of the q-th radial and tangential air-gap magnetic flux densities respectively, θ Rq , θ Tq are the phases of the q-th radial and tangential air-gap magnetic flux densities; Calculate the torque ripple according to the peak and average values of each harmonic obtained. The basic calculation formula for torque ripple is as follows: Among them, T pk2pk (t) is the peak-to-peak value of the output torque, T max (t) is the maximum value of the output torque, T min (t) is the minimum value of the output torque, T avg (t) is the average value of the output torque; Step 104: Substitute the torque data obtained in Step 103 into the torque ripple formula to calculate the torque ripple generated by each harmonic. According to Equation (1) and Equation (2), the torque ripple generated by the q-th harmonic is expressed as: Step 105: Compare the changes in the amplitudes of the dominant harmonics of the torque ripple before and after the eccentricity of the stator teeth and rotor teeth to verify the results.

2. A method for reducing torque ripple of a double-sided permanent magnet motor with unequal air gaps as claimed in claim 1, wherein In step 101, the following quantitative relationship needs to be satisfied among R, h, and OA: R = OA - h; where h is the eccentricity of the stator teeth and R is the distance between O' and point A; the following quantitative relationship needs to be satisfied among R1, h1, and O2E: R1 = O2E - h1; where h1 is the eccentricity of the rotor teeth and R1 is the distance between O2' and point E.

3. A non-uniform air-gap bilateral permanent magnet motor, applicable to a method for reducing torque ripple of a non-uniform air-gap bilateral permanent magnet motor as described in any one of claims 1-2, characterized in that, It includes a stator and a rotor arranged from outside to inside in sequence. There is an air gap between the rotor and the stator. The stator includes a stator iron core. First stator slots and stator teeth are evenly spaced along the circumferential direction inside the stator iron core. A stator armature winding is embedded in the stator slots. The rotor includes a rotor iron core. Rotor slots and rotor teeth are evenly spaced along the circumferential direction on the outer side of the rotor iron core. The tooth profile of at least one of the stator teeth and rotor teeth is a non-uniform geometric structure. The non-uniform geometric structure of the stator teeth is that the end of the stator teeth extends towards the center of the motor with a convex surface. The connection line between the top center point of the convex surface of the stator teeth and any fixed point on the extension line of the center of the motor forms a reference point. The geometric center of the convex surface of each stator tooth has an eccentricity relative to the reference point, so that a non-uniform air gap is formed between the inner surface of the stator and the outer surface of the rotor, thereby reducing the content of specific magnetic conductance harmonics and further reducing the torque ripple.

4. The unequal air-gap bilateral permanent magnet motor according to claim 3, wherein, The non-uniform geometric structure of the rotor teeth is that the rotor teeth extend towards the outside of the motor with a convex surface with the center of the motor as the reference point. The end of the rotor teeth forms a convex surface. The geometric center of the convex surface of each rotor tooth has an eccentricity relative to the center of the motor.

5. The unequal air-gap bilateral permanent magnet motor according to claim 4, wherein The outer side surface of the rotor iron core is circumferentially spaced with rotor slots; second stator slots are evenly spaced along the circumferential direction on the inner side of the stator iron core, and the second stator slots and the stator teeth are alternately distributed.

6. The unequal air-gap bilateral permanent magnet motor according to claim 5, characterized in that, Stator permanent magnets and rotor permanent magnets are respectively embedded in the second stator slots and the rotor slots, so that both the stator and the rotor form an alternating pole structure. The stator teeth and rotor teeth with non-uniform geometric structures are respectively adapted to the stator and rotor of the alternating pole structure.

7. A dual-sided permanent magnet motor with unequal air gaps as described in claim 5, characterized in that The inner side of the stator core and the outer side of the rotor core are flux modulation poles with a double salient pole structure, forming a bidirectional flux modulation effect.

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