A low-torque pulsating magnetic field modulation permanent magnet vernier motor and rotor "multi-harmonic injection" topology design method

Abstract

The present invention discloses a low-torque pulsating magnetic field modulated permanent magnet vernier motor and a rotor "multi-harmonic injection" topology design method. The motor rotor adopts a "V+-" type alternating pole permanent magnet topology structure, wherein the V-type permanent magnet has a magnetic concentration effect and can reduce internal leakage magnetic field. The I-shaped permanent magnet is attached to the surface close to the air gap side to guide the magnetic lines of force through the air gap, thereby increasing the air gap magnetic density amplitude to generate higher output torque and improving the permanent magnet utilization rate. In addition, the "V+-" type permanent magnet can withstand greater compressive stress and smaller tensile stress, thereby avoiding damage and falling off of the rotor permanent magnet, and making the motor have high mechanical strength. The design of the "multi-harmonic injection" rotor topology structure is proposed, and a non-uniform air gap length function model after multi-harmonic injection is derived. The function model of the permanent magnet magnetomotive force, the stator magnetic permeance and the "multi-harmonic injection" rotor magnetic permeance is established, thereby realizing the targeted design of the structure of the motor's "multi-harmonic injection" rotor magnetic permeance and the effective suppression of torque pulsation.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet motor design, specifically a design method based on a "multi-harmonic injection" rotor topology structure to improve air gap magnetic flux density, especially a design of a low-torque pulsating magnetic field modulation type permanent magnet motor. Background Art

[0002] In recent years, permanent magnet motors (PMMs) have been widely used and studied in the field of electric motors due to their advantages of high torque, high power density, and high efficiency. By introducing the design concept of "magnetic gears," PMMs have attracted widespread attention. Like magnetic gears, PMMs are based on the magnetic field modulation effect. In this type of motor, the stator teeth employ open slots and act as modulation poles. This results in a pole-pair number in the modulated armature winding that differs from that of the permanent magnets. The armature winding is designed for a high-speed magnetic field with a low pole-pair number, while the rotor permanent magnets can be designed with a high pole-pair number and maintain low-speed rotation, similar to a mechanical gear reducer. Furthermore, this unique stator-rotor structure influences the air gap flux waveform, resulting in a richer harmonic waveform that contributes to torque output. Overall, this type of motor offers high torque output at relatively low speeds, offering significant advantages and broad development prospects in the direct-drive hub field.

[0003] It's worth noting that the magnetic field modulation effect generated by the interaction between the open slots and salient pole teeth in a permanent magnet vernier motor enriches the air gap harmonics, giving this motor the advantage of high torque density. However, this also introduces numerous harmonics that generate torque ripple. Torque ripple significantly impacts motor stability and can also cause vibration and noise. In more severe cases, it can cause magnetic steel misalignment and damage the motor shaft. Existing methods for suppressing torque ripple are primarily based on motor control and motor design.

[0004] From the perspective of motor control, Chinese invention patent application No. 202310235244.7 proposes a method for suppressing torque ripple in a permanent magnet synchronous motor by controlling input current harmonics. This method injects a q-axis harmonic current into the input current of the permanent magnet motor, and suppresses the q-axis harmonic voltage caused by the introduction of the q-axis harmonic current by injecting a d-axis harmonic current into the current. This method not only suppresses the torque ripple of the permanent magnet synchronous motor, but also suppresses the fluctuation of the inverter output voltage vector amplitude, thereby improving voltage utilization compared to traditional strategies. However, the key to this invention is to determine an optimal injection current that includes appropriate harmonic components to reduce torque ripple. This requires accurate prediction of harmonic generation and injection location, requiring a more complex control system and more advanced algorithms, which increases the difficulty and cost of control.

[0005] From the perspective of motor design, Chinese invention patent application number 202211281246.1 proposes a modular permanent magnet motor. By dividing the stator into six modules, each with fault-tolerant teeth between them, interphase coupling can be effectively reduced. Changing the winding configuration increases the self-inductance amplitude, effectively suppressing short-circuit current. This structure not only effectively improves the fault tolerance of the permanent magnet motor, but also offsets the tooth boots, suppressing cogging torque and thus reducing torque ripple. Chinese invention patent application number 202311062096.X proposes a permanent magnet motor and a method for reducing torque ripple and electromagnetic vibration noise. By combining shallow and deep auxiliary slots on the rotor surface of the permanent magnet motor, the cogging torque and current harmonics can be simultaneously reduced, effectively suppressing the torque ripple and electromagnetic vibration noise of the permanent magnet motor.

[0006] In summary, motor control methods optimize stator current to compensate for periodic torque pulsation, as long as they produce a certain control effect. Motor design methods primarily optimize the shape and structure of the motor's stator and rotor to improve spatial harmonics and cogging torque in the magnetic flux density. It is worth noting that in permanent magnet vernier motors, the motor air gap magnetic flux density harmonics are rich, and the motor torque pulsation is often relatively high. However, the relationship between the air gap magnetic flux harmonics and motor performance is complex, making it difficult to achieve a comprehensive improvement in motor performance through traditional motor design and control methods. Therefore, how to achieve targeted suppression of torque pulsation in permanent magnet vernier motors based on the motor air gap magnetic flux harmonics has become a challenging topic in motor research. Summary of the Invention

[0007] The present invention addresses the difficulty of existing permanent magnet vernier motors in simultaneously achieving high torque density and low torque ripple. From a motor design perspective, this invention provides a permanent magnet vernier motor with a rotor "multi-harmonic injection" topology. This motor reduces torque ripple while maintaining high torque output. The present invention also provides a design method for this motor, including designing the shape and structure of the permanent magnets, selecting the harmonic injection amplitude on the rotor air gap side, and designing the stator slot structure.

[0008] In order to achieve the above-mentioned purpose, the technical solution adopted by the permanent magnet vernier motor with a rotor "multi-harmonic injection" topology structure provided by the present invention is: the rotor is placed on the outside of the stator, and the permanent magnets are arranged in a "V+1" structure around the rotor. The V-shaped permanent magnet is composed of two rectangular permanent magnets and is magnetized from the outside to the inside along the thickness. Triangular magnetic barriers are designed at both ends of the permanent magnet to avoid external magnetic leakage and reduce internal magnetic leakage; two virtual slots are arranged under each V-shaped permanent magnet, and the virtual slot corresponds to a mechanical angle of b. A straight-line permanent magnet is placed under the V-shaped permanent magnet on the side surface of the air gap to form a "V+1" type permanent magnet. The number of "V+1" type permanent magnets is P. rA magnetic core is left between each "V+-" type permanent magnet. The magnetic core is magnetized to different polarities accordingly, so that the permanent magnet poles and the iron core form a polarity alternating distribution structure as one pair of rotor poles. The pole pitch τ is the span of one pair of rotor poles, and the mechanical angle τ corresponding to the span is p =2*PI / P r The mechanical angle between each "V+-" type permanent magnet and the magnetic core is the same as τ θ =τ p / 2-b. Therefore, the inner circumference of the motor rotor will have P r The rotor core and P r There are a total of 1-shaped permanent magnets with an angle of τ θ . Each τ θ The corresponding rotor inner circumference introduces a multi-harmonic injection design, which is formed by superimposing the fundamental wave, third harmonic and fifth harmonic of the arc cosine function (1 / cos(x)), where the fundamental wave order is P r ; Therefore, the air gap between the rotor and stator teeth is non-uniform, and the air gap length is τ θ The internal harmonic injection function will change with the harmonic injection function. In order to prevent the maximum or minimum value of the harmonic injection function from conflicting with the stator model, the multi-harmonic injection function is multiplied by a coefficient k to ensure that the minimum air gap length remains constant at g (this value is the constant air gap length between the rotor teeth and stator teeth of a conventional permanent magnet vernier motor).

[0009] The stator teeth of the present invention adopt a mixed form of straight teeth and split teeth. The split tooth structure is formed by increasing the height of the stator tooth shoe and opening auxiliary slots on it. The straight teeth and split teeth are arranged alternately in a circle of the stator. The number of stator slots is Z; the number of split teeth is c, and the stator has a total of N. s =(c+1)*Z / 2 modulated teeth, the width of each modulated tooth is the same as the adjacent slot width, which is 360° / (2Z). The stator armature winding adopts a single-layer concentrated winding, and the number of armature winding pole pairs P a According to the parameters after modulation of the modulation teeth and permanent magnet pole pairs (N s -P r ) winding.

[0010] In view of the above-mentioned permanent magnet vernier motor, the present invention also proposes a "multi-harmonic injection" topology design method for the permanent magnet vernier motor rotor. A harmonic injection function design is introduced into the rotor. The air gap length g(θ) varies with the mechanical angle θ. The harmonic injection function uses the fundamental wave, third harmonic and fifth harmonic of the arc cosine function (1 / cos(x)) to superimpose each other. The expression of the air gap length g(θ) is:

[0011]

[0012] Among them, k is used to ensure that the minimum air gap length remains constant at g, which is the constant air gap length between the rotor tooth and the stator tooth without harmonic injection; s1 is the fundamental wave amplitude, s3 is the third harmonic amplitude, s5 is the fifth harmonic amplitude, τ p is the mechanical angle corresponding to the span;

[0013] The span mechanical angle required to correspond to half the pole pitch is 180° / P r Harmonic injection design is performed, so the fundamental angular velocity ω of the arc cosine function g Set to P r , P r is the number of permanent magnet pole pairs, and the period of the arc cosine function is T g =360° / ω g =360° / P r , where the function image of half a period is on the positive half axis, and the positive half axis function image is used in the harmonic injection design;

[0014] In addition, the cosine function of the expression for the air gap length g(θ) is in the denominator. This expression has a domain restriction, and within half a period θ=±T g / 4=±90° / P r = ±τ p The point of / 4 cannot be obtained, and the harmonic injection function is designed as τ θ The value should satisfy τ θ =λ*τ p / 2, where λ∈(0,1), τ θ It represents the mechanical angle between each pair of V+ type permanent magnets and the magnetic core. The remaining angle is used to set the virtual slot, that is, angle b = τ p / 2-τ θ Therefore, by determining the value of λ, the design angle τ of the harmonic injection function can be determined. θ , and then substitute the air gap length g(θ) into the expression to get the vertical coordinate of the end point of the harmonic injection function y=g(τ θ / 2),

[0015] The arc radius R above the I-shaped permanent magnet 2-2 pm1 The values ​​are:

[0016]

[0017] The radius of the second triangular magnetic barrier 2-4 can be determined as: R pm2 =R pm1 +0.8mm, and then determine the spatial position of the V-shaped permanent magnet according to the angle α between the first magnetic bridge width and the V-shaped permanent magnet.

[0018] Furthermore, it also includes: if the change of the length of the air gap (6) with time t is not considered, the expression of the air gap length g(θ) can be improved to the relative permeance form expression:

[0019]

[0020] Among them, Λ r (θ) is the rotor specific permeability without considering time;

[0021] If the Fourier expression of the rotor after rotating with time t is considered, it is:

[0022]

[0023] Among them, Λ r (θ, t) is the rotor specific permeability considering time, k' is the reciprocal of k; Λ r-min is the minimum value of relative permeability, which is related to the virtual slot depth; s i is the i-th harmonic injection amplitude; m is a positive integer.

[0024] Furthermore, it also includes:

[0025] Design of stator permeance. The stator permeance has no time component and its Fourier expression is:

[0026]

[0027] In order to facilitate calculation, the tooth width w of the straight tooth (3-1) is t1 The width w of the split tooth (3-2) t2 Set to the same tooth width w t ; Straight tooth (3-1) tooth width w s1 The width of the split tooth (3-2) w s2 Set to the same slot width w s ; N s is the number of teeth; st is the stator tooth permeability; ss is the magnetic permeability of the stator slot;

[0028] The design of no-load air gap flux density is to inject harmonics into the rotor to reduce the permanent magnet magnetomotive force F pm (θ,t) and rotor specific permeability Λ r (θ,t), stator magnetic permeability Λ s (θ) is multiplied to obtain the no-load air gap magnetic flux B pm The expression of (θ,t) is:

[0029] B pm (θ,t)=F pm (θ,t)*Λ r (θ,t)*Λ s (θ)

[0030] The design of the average air gap length, the average air gap length l at half the pole pitch avg The expression is:

[0031]

[0032] Beneficial effects of the present invention:

[0033] 1. The motor rotor of the present invention utilizes a "V+-" alternating-pole permanent magnet topology. The V-shaped permanent magnets have a magnetic field-concentrating effect and can reduce internal magnetic flux leakage. The I-shaped permanent magnets are attached to the side close to the air gap to guide magnetic lines of force through the air gap, increasing the air gap flux density amplitude and thus generating higher output torque, effectively improving the utilization rate of the permanent magnets. Furthermore, the "V+-" permanent magnets can withstand greater compressive stress and less tensile stress, preventing damage and loss of the rotor permanent magnets, and endowing the motor with relatively high mechanical strength.

[0034] 2. The stator teeth of the motor of this invention utilize a hybrid structure of split and spur teeth. The split teeth provide a larger slot area, improving heat dissipation in the armature winding. They also increase the number of fundamental cycles of the cogging torque, thereby reducing the cogging torque amplitude. The combination of split and spur teeth increases the permeance harmonics, which helps increase the amplitude of the magnetic flux density harmonics and thus improve the torque density of the motor.

[0035] 3. Based on the pole-slot combination and magnetic field modulation principles of a permanent magnet vernier motor, and analyzing the impact of a non-uniform air gap on the permanent magnet magnetic field and its magnetic flux harmonics, this paper proposes a design method for a "multi-harmonic injection" rotor topology and derives a functional model for the non-uniform air gap length after multi-harmonic injection. Based on this, functional models for the permanent magnet magnetomotive force, stator permeance, and "multi-harmonic injection" rotor permeance are established, and corresponding expressions are derived. Finally, the desired permanent magnet air gap magnetic flux waveform is obtained, enabling the targeted design of the motor's "multi-harmonic injection" rotor permeance structure and effective suppression of torque ripple.

[0036] 4. By injecting harmonics into the rotor, this invention effectively improves the air gap flux density waveform and harmonics. Compared to permanent magnet vernier motors of the same size and type without harmonic injection, this significantly reduces cogging torque and torque ripple, while slightly reducing output torque. This improves the quality of the motor's output torque and its operational stability. It also weakens higher-order air gap flux density harmonics, reducing the additional losses caused by these harmonics and effectively reducing core losses. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a radial topological structure diagram of a multi-harmonic injection permanent magnet vernier motor of the present invention;

[0038] Figure 2for Figure 1 An enlarged view of the partial structure of the middle rotor and a marked diagram of the permanent magnet magnetization method;

[0039] Figure 3 for Figure 1 A magnified structural diagram of the permanent magnet area and a diagram with geometric dimensions;

[0040] Figure 4 for Figure 1 An enlarged structural diagram of the middle stator teeth and a diagram with geometric dimensions;

[0041] Figure 5 for Figure 1 Schematic diagram of the magnetomotive force of the permanent magnet;

[0042] Figure 6 for Figure 3 Enlarged view of the middle air gap structure;

[0043] Figure 7 for Figure 1 Schematic diagram of the magnetic permeance of the middle rotor;

[0044] Figure 8 for Figure 1 Schematic diagram of the magnetic permeability of the stator;

[0045] Figure 9 The figure is a waveform curve diagram of the calculated and simulated no-load air gap flux density of the motor of the present invention;

[0046] Figure 10 The waveform curve of the no-load air gap magnetic flux before and after harmonic injection;

[0047] Figure 11 The harmonic distribution diagram of the no-load air gap magnetic flux before and after harmonic injection;

[0048] Figure 12 It is the no-load flux waveform curve before and after harmonic injection;

[0049] Figure 13 The waveform graph of the no-load back EMF before and after harmonic injection;

[0050] Figure 14 The no-load back EMF harmonic distribution diagram before and after harmonic injection;

[0051] Figure 15 The comparison diagram of cogging torque before and after harmonic injection;

[0052] Figure 16 The comparison diagram of output torque and pulsation before and after harmonic injection;

[0053] Figure 17 Comparison of torque contribution of each air gap magnetic density harmonic before and after harmonic injection.

[0054] In the figure: 1. Rotor; 2. Permanent magnet; 3. Stator; 4. Stator slot; 5. Armature winding; 6. Air gap; 7. Multi-harmonic injection design; 2-1. V-shaped permanent magnet; 2-2. I-shaped permanent magnet; 2-3. First triangular magnetic barrier; 2-4. Second triangular magnetic barrier; 2-5. Virtual slot; 2-6. First magnetic bridge; 2-7. Second magnetic bridge; 3-1. Stator straight teeth; 3-2. Stator split teeth; 3-3. Stator yoke. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings.

[0056] See also Figure 1 The present invention discloses a multi-harmonic injection magnetic field modulation permanent magnet vernier motor. The motor comprises, from the outside to the inside, a rotor 1, a permanent magnet 2, an air gap 6, and a stator 3. The rotor 1 is coaxially sleeved on the outside of the stator 3, and the rotor near the air gap adopts a multi-harmonic injection design 7.

[0057] See also Figure 2 and Figure 3 , the rotor 1 is uniformly embedded with several V-shaped permanent magnets 2-1 along the circumferential direction, and the number of V-shaped permanent magnets 2-1 is P r In the embodiment of the present invention, P r =19, the V-shaped permanent magnet 2-1 consists of two rectangular permanent magnets placed along the y-axis at an angle of α. The magnetization direction of the permanent magnets is from the outside to the inside along the thickness. The length of the two permanent magnets is l pm , thickness is w pm , a straight permanent magnet 2-2 is placed below each V-shaped permanent magnet 2-1 on the side surface of the air gap to form a V+ straight permanent magnet. The arc radius above the straight permanent magnet 2-2 is R pm1 There are triangular magnetic barriers 2-3 and 2-4 at both ends of the V-shaped permanent magnet. The arc radius below the second triangular magnetic barrier 2-4 is R pm2 . Two virtual slots 2-5 are set under each V-shaped permanent magnet 2-1. The mechanical angle corresponding to the virtual slot is b. In the embodiment of the present invention, b=1.894°. The first magnetic bridge 2-6 is formed between the first triangular magnetic barriers at the upper end of the V-shaped permanent magnet, and the second magnetic bridge 2-7 is formed between the second triangular magnetic barriers at the lower end and the inner edge of the rotor. The widths of the first magnetic bridge 2-6 and the second magnetic bridge 2-7 are both 0.8mm. A magnetic core is left between each V+ type permanent magnet, and the magnetic core is magnetized to different polarities accordingly, so that the permanent magnet poles and the iron core form a polarity alternating distribution structure. This structure is combined into one pair of poles of the rotor, so P r is the number of permanent magnet pole pairs. The pole pitch τ is the span of one pair of rotor poles, and the mechanical angle τ corresponding to the span is p =360° / P r The mechanical angle between each pair of V+ type permanent magnets and the magnetic core is the same as τ θ =τp / 2-b. Each τ θ A multi-harmonic injection design is introduced into the rotor surface near the air gap corresponding to the angle 7.

[0058] See also Figure 4 The stator 3 includes a stator yoke 3-3 and straight teeth 3-1 and split teeth 3-2 alternately used in the circumferential direction. The number of stator slots 4 is Z, and Z=3j, j is a positive even number; the outer radius of the stator teeth is R st The number of straight teeth 3-1 and split teeth 3-2 is Z / 2, the number of split teeth 3-2 is c, and the stator 3 has a total of N modulated teeth. s =(c+1)*Z / 2. Straight tooth 3-1 tooth width w t1 、Groove width w s1 、Split tooth 3-2 split tooth width w t2 、Groove width w s2 The angles are set to be the same. Considering the situation that the split tooth 3-2 has a large magnetic flux density and is saturated, the split tooth width w st2 The angle setting is wider than the straight teeth w st1 In the embodiment of the present invention, the straight tooth 3-1 tooth width w t1 The angle relative to the center of the circle is 7.5° and the tooth width is w s1 The angle relative to the center of the circle is 7.5°, and the width of the split tooth (3-2) is w t2 The angle relative to the center of the circle is 7.5°, and the width of the tooth groove is w s2 The angle relative to the center of the circle is 7.5°, and the width of the split teeth is w st2 The angle relative to the center of the circle is 18°, and the straight tooth width is w st1 The angle relative to the center of the circle is 11.22°.

[0059] When harmonic injection is not considered, the surface of the rotor 1 near the air gap is a smooth arc, and the thickness of the air gap 6 along the circumferential direction is uniform. According to the arrangement of the permanent magnets, the following is obtained: Figure 5 The permanent magnet magnetomotive force distribution diagram shown in the figure has the mechanical angle θ as the horizontal axis and the magnetomotive force amplitude F as the vertical axis. pm (θ,t), the Fourier expression is:

[0060]

[0061] Among them, ω r is the mechanical rotation speed of the rotor; P r is the number of permanent magnet pole pairs; F m is the amplitude of the magnetomotive force of the air gap per pole; n is a positive odd number.

[0062] like Figure 6As shown in Figure 1, the air gap length g(θ) changes with the mechanical angle θ after the harmonic injection function is introduced into the rotor. The harmonic injection function uses the inverse cosine function (1 / cos(x)) to superimpose odd harmonics such as the fundamental wave, third harmonic, and fifth harmonic. The expression for the air gap length g(θ) is:

[0063]

[0064] Where g is the constant air gap length between the rotor teeth and stator teeth without harmonic injection; k is a variable whose value is the maximum value of the denominator in the expression. When calculating the minimum value of the air gap length g(θ), the expression only has the constant value g, thereby ensuring that the minimum value of the air gap length g(θ) is constant; s1 is the fundamental amplitude; s3 is the third harmonic amplitude; and s5 is the fifth harmonic amplitude.

[0065] Since the span mechanical angle corresponding to half the pole pitch is 180° / P r Harmonic injection design is performed, so the fundamental angular velocity ω of the arc cosine function g Set to P r , so the period of the inverse cosine function is T g =360° / ω g =360° / P r , where the function image of half a period is on the positive half axis. The positive half axis function image is used in the harmonic injection design. In addition, since the cosine function of the expression of the air gap length g(θ) is on the denominator, the expression has a domain restriction. Within half a period, θ=±T g / 4=±90° / P r = ±τ p The point of / 4 cannot be obtained, and the harmonic injection function design angle τ θ The value should satisfy τ θ =λ*τ p / 2, where λ∈(0,1). The remaining angle is used to set the virtual slot, which is angle b=τ p / 2-τ θ Therefore, determining the value of λ can determine the design angle τ of the harmonic injection function. θ , and then substitute the air gap length g(θ) into the expression to get the vertical coordinate of the end point of the harmonic injection function y=g(τ θ / 2). The arc radius R above the I-shaped permanent magnet 2-2 pm1 The values ​​are:

[0066]

[0067] Therefore, the radius of the second triangle magnetic barrier 2-4 position can be determined: R pm2 =R pm1 +0.8mm, in the embodiment of the present invention, R pm1 =126.7mm, Rpm2 =127.5mm; and then the spatial position of the V-shaped permanent magnet is determined according to the first magnetic bridge width and the angle α between the V-shaped permanent magnet.

[0068] Considering that the surface of the rotor 1 near the air gap is an uneven curve when harmonic injection is applied, the length of the air gap 6 along the circumferential direction varies with the arc cosine function. When the change with time t is not considered, the expression of the air gap length g(θ) is improved to the relative permeance form for the convenience of calculation:

[0069]

[0070] According to this expression, we can get Figure 7 The rotor magnetic permeance distribution diagram at t = 0 is shown in the figure. The horizontal axis is the mechanical angle θ and the vertical axis is the rotor magnetic permeance amplitude Λ r (θ), whose range is (0,1].

[0071] Considering the rotor rotating with time t, the Fourier expression is:

[0072]

[0073] Among them, Λ r (θ, t) is the rotor specific permeability considering time, k' is the reciprocal of k; Λ r-min is the minimum value of relative permeability, which is related to the virtual slot depth; s i is the i-th harmonic injection amplitude; m is a positive integer.

[0074] Since the stator teeth 3-1 and 3-2 of the stator 3 and the slot width angle are set to be consistent, the thickness of the air gap 6 along the circumferential direction changes regularly, and the following is obtained: Figure 8 The stator magnetic permeance distribution diagram shown in the figure has the mechanical angle θ as the horizontal axis and the magnetic permeance amplitude Λ as the vertical axis. s (θ), since the stator 3 is fixed, the stator permeance has no time component, and its Fourier expression is:

[0075]

[0076] In order to facilitate calculation, the tooth width w of the straight tooth (3-1) is t1 The width w of the split tooth (3-2) t2 Set to the same tooth width w t ; Straight tooth (3-1) tooth width w s1 The width of the split tooth (3-2) w s2 Set to the same slot width w s ; N s is the number of teeth; st is the stator tooth permeability; ss is the magnetic permeability of the stator slot.

[0077] After the rotor is injected with harmonics, the permanent magnet magnetomotive force F pm (θ,t) and rotor specific permeability Λ r (θ,t), stator magnetic permeability Λ s (θ) is multiplied to obtain the no-load air gap magnetic flux B pm The expression of (θ,t) is:

[0078] B pm (θ,t)=F pm (θ,t)*Λ r (θ,t)*Λ s (θ)

[0079] Based on this expression, the no-load air gap flux density waveform is plotted and compared with the waveform given by finite element simulation, see Figure 9 Comparison of no-load air gap magnetic flux density. The comparison results are calculated using the root mean square error (RMSE) and goodness of fit R 2 The values ​​represent the deviation between the calculated value and the simulated value of the no-load air gap magnetic flux density and the degree of fit. The closer the RMSE value is to 0, the better the degree of fit. 2 The value range is between 0 and 1. The closer to 1, the better the fit. Root mean square error (RMSE) and goodness of fit R 2 The expressions are:

[0080]

[0081] Where n is the number of waveform comparison points; i is a positive integer; is the corresponding value of the finite element simulation waveform points; y i is the corresponding value of the calculated waveform points; is the average value of the finite element simulation waveform and the calculated waveform at point i. The final RMSE is 0.330, R 2 It is 0.733, indicating a good degree of fit. However, the deviation is large near the peak value and 0, which may be related to the calculation of the slot magnetic permeance. The calculation method of the magnetic permeance needs to be further improved.

[0082] according to Figure 6 , the average air gap length l at half the pole pitch avg The expression is:

[0083]

[0084] Since the no-load air gap flux density is multiplied by the rotor harmonic permeance compared to the case without harmonic injection, Figure 10The no-load air gap flux waveform before and after harmonic injection will change at the peak of the air gap flux; in addition, the rotor harmonic permeability also causes the average air gap length to change. The average air gap length of the permanent magnet vernier motor without harmonic injection is a constant g. Generally speaking, the average air gap length after harmonic injection is l avg Will be slightly larger than g, l avg It is approximately equal to (1-2)*g. The average air gap length will affect the amplitude of the air gap magnetic flux density. Figure 11 This is a comparison chart of the harmonic amplitudes of the no-load air gap magnetic flux greater than 0.1T before and after harmonic injection. It can be seen that the harmonic amplitude of the no-load air gap magnetic flux is reduced after harmonic injection.

[0085] Torque ripple is caused by the distortion of the cogging torque and the no-load back EMF. Therefore, the no-load back EMF needs to be analyzed step by step, starting from the no-load flux density to the no-load flux linkage, and then calculating the no-load back EMF.

[0086] Figure 12 The figure below shows the comparison of no-load flux before and after harmonic injection. The no-load flux is the product of the number of flux turns and the single-turn flux. The single-turn flux is equal to the magnetic flux within the circle, and its expression is:

[0087]

[0088] in, is the no-load flux linkage, N is the number of turns; Ф is the magnetic flux; L stk is the axis length; R g is the air gap radius.

[0089] Figure 13 The figure below shows the comparison of no-load back EMF before and after harmonic injection. The no-load back EMF is equal to the rate of change of no-load flux. The flux needs to be differentiated with respect to time t, and the expression is:

[0090]

[0091] Figure 14 The figure below is a comparison of the no-load back EMF harmonic distribution before and after harmonic injection. It can be seen that after harmonic injection, the no-load back EMF has a slightly lower fundamental amplitude due to the reduction in the average air gap length, but the odd harmonics are significantly suppressed. This increases the sinusoidality of the back EMF waveform after harmonic injection, which is consistent with the sinusoidality of the input current and reduces the generation of torque ripple.

[0092] The cogging torque of a motor is the torque generated by the interaction between the permanent magnet and the iron core when the motor is unloaded. It is caused by the change in air gap magnetic resistance due to the alternation of teeth and slots in the motor. The cogging torque is also a factor that causes motor torque pulsation. Figure 15 The cogging torque comparison chart shows that the cogging torque is significantly reduced after harmonic injection, with the peak value reduced by about 75%, effectively reducing torque pulsation.

[0093] Figure 16 The output torque comparison diagram shows that the output torque is reduced by 5.64% compared with before harmonic injection, but the torque ripple is reduced by 73.70% at the same time. Figure 17 The comparison diagram of the load air gap magnetic flux harmonic torque contribution before and after harmonic injection is shown in the figure. The torque generated by the load air gap magnetic flux harmonic of each order is calculated using the Maxwell tensor method. The zth load air gap harmonic torque T z The contribution expression is:

[0094]

[0095] Among them, μ0 is the relative magnetic permeability of air, and its value is 4π*10 -7 ; B rz B is the z-th radial load air gap flux density; tz is the z-th tangential load air gap flux density; θ rz is the z-th radial load air gap flux density angle; θ tz is the zth tangential load air gap magnetic flux angle. According to the magnetic field modulation principle, the harmonic order of the air gap magnetic flux can be expressed by the formula: m*N s ±n*P r (m=1,2,3…;n=1,3,5…), the harmonics greater than 0.1T in the obtained load air gap magnetic density are analyzed, and it is calculated through the formula that the 5th, 19th, and 43rd harmonics of the air gap magnetic density participate in the synthesis of stable output torque, while the DC component of the torque generated by the 29th, 33rd, 53rd, and 57th harmonics is very low and fluctuates, thereby affecting the torque pulsation. It can be seen that the torque pulsation generated by the 29th, 33rd, 53rd, and 57th harmonics is reduced after the harmonic injection.

[0096] The series of detailed descriptions listed above are only specific descriptions of feasible implementation methods of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent methods or changes that do not deviate from the technology of the present invention should be included in the scope of protection of the present invention.

Claims

1. A low-torque pulsating magnetic field modulation permanent magnet vernier motor, comprising a rotor (1) and a stator (3), wherein the rotor (1) is coaxially sleeved on the outside of the stator (3), and is characterized in that: The rotor is embedded with a plurality of permanent magnets (2) along the circumferential direction, wherein each permanent magnet (2) comprises a V-shaped permanent magnet (2-1) and a straight-shaped permanent magnet (2-2), and the number of the V-shaped permanent magnets (2-1) is P. r The V-shaped permanent magnet (2-1) consists of two rectangular permanent magnets placed along the y-axis at an angle of α. The magnetization direction of the permanent magnets is from the outside to the inside along the thickness. The length of the two permanent magnets is l pm , thickness is w pm Two virtual slots (2-5) are provided below each V-shaped permanent magnet (2-1), and the virtual slots correspond to a mechanical angle b. A straight-line permanent magnet (2-2) is provided below each V-shaped permanent magnet (2-1) on the side surface of the air gap, thereby forming a V+I type permanent magnet; There is a magnetic core between each V+ type permanent magnet, and the magnetic core is magnetized into different polarities accordingly, so that the permanent magnet poles and the iron core form a polarity alternating distribution structure, which is combined into one pair of poles of the rotor, so P r is the number of permanent magnet pole pairs, the pole pitch τ is the span of one pair of rotor poles, and the mechanical angle τ corresponding to the span p =360° / P r The mechanical angle between each pair of V+ type permanent magnets and the magnetic core is the same as τ θ =τ p / 2-b, each τ θ The rotor surface near the air gap corresponding to the angle adopts a multi-harmonic injection function topology design, and the air gap between the rotor and stator teeth is non-uniform. The air gap length is τ θ The internal changes with the harmonic injection function; The stator (3) is alternately provided with straight teeth (3-1) and split teeth (3-2) along the circumferential direction, the number of stator slots (4) is Z, the number of straight teeth (3-2) and split teeth (3-1) is Z / 2, the number of splits of the split teeth (3-2) is c, and the stator (3) has a total number of modulated teeth N. s =(c+1)*Z / 2, the width of each modulated tooth is the same as the adjacent slot width, both 360° / (2Z); the width of the straight tooth (3-1) is w t1 , tooth width is w s1 , the crack width of the split tooth (3-2) is w t2 , the width of the tooth groove is w s2 , split tooth width w st2 The angle setting is wider than the straight teeth w st1 big.

2. The low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: The arc radius above the I-shaped permanent magnet (2-2) is R pm1 =126.7mm; There are two triangular magnetic barriers at both ends of the V-shaped permanent magnet, namely the first triangular magnetic barrier (2-3) and the second triangular magnetic barrier (2-4). The arc radius below the second triangular magnetic barrier (2-4) is R pm2 =127.5mm.

3. The low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: Straight tooth (3-1) tooth width w t1 The angle relative to the center of the circle is 7.5° and the tooth width is w s1 The angle relative to the center of the circle is 7.5°, and the width of the split tooth (3-2) is w t2 The angle relative to the center of the circle is 7.5°, and the width of the tooth groove is w s2 The angle relative to the center of the circle is 7.5°, and the width of the split teeth is w st2 The angle relative to the center of the circle is 18°, and the straight tooth width is w st1 The angle relative to the center of the circle is 11.22°.

4. The low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: The virtual slot (2-5) corresponds to a mechanical angle of b=1.894°.

5. The low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: A first magnetic bridge (2-6) is formed between the first triangular magnetic barriers at the upper end of the V-shaped permanent magnet, and a second magnetic bridge (2-7) is formed between the second triangular magnetic barriers at the lower end and the inner edge of the rotor. The widths of the first magnetic bridge (2-6) and the second magnetic bridge (2-7) are both 0.8 mm.

6. The low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: The number Z of the stator slots (4) satisfies Z=3j, where j is a positive even number.

7. The low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: The stator armature winding (5) adopts a single-layer concentrated winding, and the armature winding (5) has a pole pair number P a According to the parameters after modulation of the modulation teeth and permanent magnet pole pairs (N s -P r ) winding.

8. A method for designing a rotor of a permanent magnet vernier motor with a multi-harmonic injection topology of a low-torque pulsating magnetic field modulation permanent magnet vernier motor according to claim 1, characterized in that: After the harmonic injection function design is introduced into the rotor, the air gap length g(θ) changes with the mechanical angle θ. The harmonic injection function uses the fundamental wave, third harmonic, and fifth harmonic of the arc cosine function (1 / cos(x)) to superimpose each other. The expression of the air gap length g(θ) is: Among them, k is used to ensure that the minimum air gap length remains constant at g, which is the constant air gap length between the rotor tooth and the stator tooth without harmonic injection; s1 is the fundamental wave amplitude, s3 is the third harmonic amplitude, s5 is the fifth harmonic amplitude, τ p is the mechanical angle corresponding to the span; The span mechanical angle required to correspond to half the pole pitch is 180° / P r Harmonic injection design is performed, so the fundamental angular velocity ω of the arc cosine function g Set to P r , P r is the number of permanent magnet pole pairs, and the period of the arc cosine function is T g =360° / ω g =360° / P r , where the function image of half a period is on the positive half axis, and the positive half axis function image is used in the harmonic injection design; In addition, the cosine function of the expression for the air gap length g(θ) is in the denominator. This expression has a domain restriction, and within half a period θ=±T g / 4=±90° / P r = ±τ p The point of / 4 cannot be obtained, and the harmonic injection function is designed as τ θ The value should satisfy τ θ =λ*τ p / 2, where λ∈(0,1), τ θ It represents the mechanical angle between each pair of V+ type permanent magnets and the magnetic core. The remaining angle is used to set the virtual slot, that is, angle b = τ p / 2-τ θ Therefore, by determining the value of λ, the design angle τ of the harmonic injection function can be determined. θ , and then substitute the air gap length g(θ) into the expression to get the vertical coordinate of the end point of the harmonic injection function y=g(τ θ / 2), The radius R of the arc above the I-shaped permanent magnet (2-2) pm1 The values ​​are: The radius of the second triangular magnetic barrier 2-4 can be determined as: R pm2 =R pm1 +0.8mm, and then determine the spatial position of the V-shaped permanent magnet according to the angle α between the first magnetic bridge width and the V-shaped permanent magnet.

9. The "multi-harmonic injection" topology design method for a permanent magnet vernier motor rotor according to claim 8 is characterized in that: Also includes: If the length of the air gap (6) does not change with time t, the expression of the air gap length g(θ) can be improved to the relative permeance form: Among them, Λ r (θ) is the rotor permeability amplitude; If the Fourier expression of the rotor after rotating with time t is considered, it is: Among them, Λ r (θ, t) is the rotor specific permeability considering time, k' is the reciprocal of k; Λ r-min is the minimum value of relative permeability, which is related to the virtual slot depth; s i is the i-th harmonic injection amplitude; m is a positive integer.

10. The "multi-harmonic injection" topology design method for a permanent magnet vernier motor rotor according to claim 8, characterized in that: Also includes: Design of stator permeance. The stator permeance has no time component and its Fourier expression is: In order to facilitate calculation, the tooth width w of the straight tooth (3-1) is t1 The width w of the split tooth (3-2) t2 Set to the same tooth width w t ; Straight tooth (3-1) tooth width w s1 The width of the split tooth (3-2) w s2 Set to the same slot width w s ; N s is the number of teeth; st is the stator tooth permeability; ss is the magnetic permeability of the stator slot; The design of no-load air gap flux density is to inject harmonics into the rotor to reduce the permanent magnet magnetomotive force F pm (θ,t) and rotor specific permeability Λ r (θ,t), stator magnetic permeability Λ s (θ) is multiplied to obtain the no-load air gap magnetic flux B pm The expression of (θ,t) is: B pm (θ,t)=F pm (θ,t)*Λ r (θ,t)*Λ s (i) The design of the average air gap length, the average air gap length l at half the pole pitch avg The expression is:

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