Surface-mounted permanent magnet vernier motor modulation pole structure optimization method based on analytical model

Abstract

The invention discloses a surface-mounted permanent magnet vernier motor modulation pole structure optimization method based on an analytical model, and the method comprises the steps: constructing a magnetic conductivity function model containing modulation pole geometric parameters through employing a Fourier series method, and obtaining a space harmonic component in an air-gap magnetic field based on the magnetic conductivity function model; based on the space harmonic component in the air-gap magnetic field, the harmonic component of the magnetic conductivity function is finely regulated and controlled by using a genetic algorithm, the maximum working harmonic component is realized, and the optimal geometric dimension of the modulation pole is determined. According to the method, the design period is remarkably shortened, the output torque of the surface-mounted permanent magnet vernier motor is remarkably improved, the torque pulsation is greatly reduced, and the torque output capacity and the torque stability of the motor are effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of permanent magnet vernier motor optimization design, and in particular relates to a surface mounted permanent magnet vernier motor modulation pole structure optimization method based on an analytical model. Background Art

[0002] Permanent magnet vernier motor (PMVM) has attracted increasing attention in energy conversion systems such as wind power, electric propulsion, and robotic servo systems due to its high torque density and high efficiency. The number of stator winding pole pairs and rotor pole pairs of PMVM are not equal, but the magnetic field excited by the armature winding and the rotor permanent magnets has a magnetic transmission coupling effect. Compared with ordinary permanent magnet synchronous motors, this magnetic field coupling helps to achieve a larger torque density in PMVM. In order to effectively utilize the magnetic field modulation effect, PMVM requires modulation poles, which will cause the magnetic permeability in the air gap to change, thereby modulating the magnetic flux. In addition, the number of stator and rotor poles should be determined by considering the number of modulation poles. The stator structure of PMVM can be divided into two categories: (1) slotted stator with spur teeth and overlapping windings; (2) split teeth with non-overlapping windings. Spur teeth and split teeth play the role of magnetic field modulation poles. In recent years, PMVM with split tooth stator structure has attracted widespread attention due to its short end winding length and low copper loss.

[0003] The magnetomotive force of the armature winding of the surface-mounted permanent magnet vernier motor is modulated by the harmonics of the air gap permeability caused by the modulation poles, and the generated magnetic field is synchronized with the magnetic field generated by the rotor permanent magnet to generate output torque. The synchronous spatial harmonics of the air gap flux distribution generated by the armature winding are defined as working harmonics. In addition, the amplitude and output torque of the working harmonics depend on the structure of the modulation poles. Based on the magnetic transmission effect, the analytical equations in the existing literature explain the working principle of the surface-mounted permanent magnet vernier motor. In order to improve the output torque, researchers have proposed many new topological structures of permanent magnet vernier motors. However, previous studies have mainly focused on the flux modulation between the fundamental wave of the winding magnetomotive force distribution and the harmonics of the permeability corresponding to the number of modulation poles. Therefore, other harmonics of the winding magnetomotive force and permeability distribution are ignored in the analytical equations. In addition, the design of the modulation pole does not consider the harmonic components of the permeability. In the existing literature, the winding magnetomotive force harmonics in the surface-mounted permanent magnet vernier motor can generate output torque by interacting with specific harmonics of the permeability. In general, the design method of the modulation pole is to adjust its width and use the finite element method (FEM) to obtain the optimal width of the modulation pole to maximize the output torque. However, in this case, the winding magnetomotive force harmonics have no effect on the output torque because no matter how the modulation pole is designed, the permeability distribution only contains spatial harmonics that are multiples of the modulation pole width. To this end, a modulation pole shape with air gap permeability subharmonics is proposed to use the winding magnetomotive force harmonics to improve the output torque. The output torque of the surface-mounted permanent magnet vernier motor can be increased by 21.5% by simply changing the shape of the modulation pole. In addition, the existing literature also includes the effect of permeability subharmonics on back-EMF. The modulation pole with subharmonics can increase the output torque and back-EMF amplitude by 22%. The analytical results are verified by experiments. In order to improve the output torque, the shape and structural parameters of the modulation pole are proposed using analytical equations. However, the optimal combination of design variables is obtained by using a parametric study based on the finite element method. In order to adjust the subharmonics of the permeability, the number of geometric parameters for designing the modulation pole shape increases, so it takes a long time to complete the optimization design process.

[0004] The finite element method (FEM) is often used in traditional motor optimization design. This method has high accuracy and a wide range of applications, but it is computationally intensive and time-consuming. This challenge is particularly prominent when designing new special topology motors, such as vernier permanent magnet motors. In addition, although Fourier series analysis has been used in existing studies to obtain analytical expressions for winding magnetomotive force, air gap permeability, and magnetic flux density distribution, the amplitude of the permeance harmonics has not been taken as a function of the geometric variables of the modulation pole. Therefore, it is difficult to design the optimal modulation pole structure using analytical methods. Summary of the invention

[0005] In order to solve the problem of time-consuming and lengthy finite element analysis in the optimization design of permanent magnet vernier motors, the present invention provides a method for optimizing the modulated pole structure of a surface-mounted permanent magnet vernier motor based on an analytical model, comprising:

[0006] For the surface-mounted permanent magnet vernier motor, a magnetic permeability function model including the modulation pole geometry parameters is constructed by using the Fourier series method, and the spatial harmonic components in the air gap magnetic field are obtained based on the magnetic permeability function model;

[0007] Based on the spatial harmonic components in the air gap magnetic field, a genetic algorithm is used to finely control the harmonic components of the magnetic permeability function to maximize the working harmonic components and determine the optimal geometric size of the modulation pole.

[0008] Preferably, the surface-mounted permanent magnet vernier motor converts the outer rotor of the magnetic gear into the stator winding of the motor on the basis of the magnetic gear, and fixes the magnetic adjustment magnet block with the outer stator, and utilizes the magnetic field modulation effect of the magnetic gear to obtain a low-speed and high-torque motor on the inner rotor, thereby obtaining the surface-mounted permanent magnet vernier motor;

[0009] The stator of the surface-mounted permanent magnet vernier motor includes six slots and a three-phase winding to form a rotating magnetic field with two pole pairs; each stator tooth end is divided into four modulation poles, and the total number of modulation poles is 24;

[0010] The relationship between the stator and rotor pole pairs of the surface-mounted permanent magnet vernier motor is:

[0011] p r =|p FMP -p s |

[0012] In the formula, p s and p EMP are the stator winding pole pairs and modulation pole numbers respectively.

[0013] Preferably, the magnetic gear comprises a surface-mounted permanent magnet inner rotor and an outer rotor and a magnet adjustment block group, and the magnetic fields generated by the surface-mounted permanent magnet inner rotor and the outer rotor with different pole pairs are coupled through the magnet adjustment block, thereby realizing the transmission of speed and torque;

[0014] If only the magnetic field of the inner rotor permanent magnet is considered, the radial component of the magnetic flux density distribution in the outer air gap is expressed as:

[0015]

[0016] Where, the first term represents the radial flux density distribution without adjusting the magnet block, which is generated by the harmonic component of the magnetomotive force of the inner rotor permanent magnet; the second term represents the flux modulation function, which is actually the air gap permeability function considering the geometric shape of the adjusting magnet block, θ m is the rotational mechanical angle, ωir is the mechanical angular velocity of the inner rotor, p ir is the number of inner rotor pole pairs, p sp Adjust the number of magnets, B m is the radial magnetic flux density without adjusting the magnet block, P j is the flux modulation function;

[0017] The radial flux density distribution in the outer air gap is expressed as:

[0018]

[0019] Preferably, the magnetic field generated by the armature winding of the surface-mounted permanent magnet vernier motor is obtained by multiplying the winding magnetomotive force and the air gap permeance function;

[0020] The analytical equation of the output torque generated by the working harmonic is expressed as a function of the modulation pole design variables, and the magnetomotive force distribution of the three-phase winding is expressed as:

[0021]

[0022] In the formula, ω e is the electrical angular velocity, m is the harmonic order of the winding magnetomotive force distribution, mp s is the spatial harmonic order.

[0023] Preferably, the permeability function is determined by the geometry of the modulation poles, assuming that the modulation poles are equidistant and relative to θ m The reference axis is symmetrical, and the air gap permeability function is expressed as:

[0024]

[0025] In the formula, p FMPs is the number of modulation poles, j is an integer, jp FMPs is the harmonic order of the air gap permeance function. When the shape of the modulation pole is designed differently, the air gap permeance function contains p FMPs Multiple harmonics and other sub-space harmonics.

[0026] Preferably, the radial magnetic flux density distribution generated by the armature winding in the air gap is obtained based on the magnetomotive force distribution of the three-phase winding and the air gap permeability function, and the expression is:

[0027]

[0028] Preferably, the spatial harmonic component in the air gap magnetic field is obtained based on the magnetic permeability function model, the spatial harmonic component includes the winding magnetomotive force, the winding magnetomotive force is generated by the current flowing through the armature winding, and the magnetomotive force distribution in the air gap is obtained by the following assumptions:

[0029] The magnetic permeability of the stator and rotor cores is infinite;

[0030] The air gap flux density, winding magnetomotive force and magnetic permeability are consistent with the axial direction;

[0031] The value of the winding magnetomotive force varies linearly in the area before the slot opening;

[0032] The three-phase current is symmetrical and sinusoidal;

[0033]

[0034] Where ω is the electrical angular velocity, I rms is the effective value of the input current;

[0035] Using Fourier analysis method, the magnetomotive force distribution is expressed as:

[0036]

[0037] In the formula, θ m is the mechanical angle, θ so is the mechanical angle of the slot opening, N c is the number of turns for each coil;

[0038] The Fourier expression of the winding magnetomotive force distribution is:

[0039]

[0040] In the formula, F m It is the Fourier coefficient of the spatial harmonics of the total armature winding magnetomotive force distribution.

[0041] Preferably, the spatial harmonic components in the air gap magnetic field are obtained based on the permeability function model, and the spatial harmonic components include the air gap permeability function, and the air gap permeability function is obtained by the following assumptions:

[0042] The magnetic permeability of the stator and rotor cores is infinite;

[0043] The relative magnetic permeability of permanent magnets is consistent;

[0044] The modulation pole on each stator main tooth is symmetrical to the stator main tooth axis;

[0045] All teeth have the same structure;

[0046] The modulation pole height has no effect on the air gap permeability distribution;

[0047] The air gap permeability function is expressed as follows using Fourier analysis:

[0048]

[0049] In the formula, p FMPs is the modulation pole number, P0 is the DC bias value, Pj is the Fourier coefficient, corresponding to the air gap permeability function (j×N slot ) space harmonics; P0 and P j The design variables θ1, θ2, θ3, θ4 and θ so function.

[0050] Preferably, the spatial harmonic components in the air gap magnetic field are obtained based on the magnetic permeability function model, and the spatial harmonic components also include the air gap magnetic flux generated by the winding and the air gap magnetic flux generated by the modulation pole.

[0051] Preferably, based on the spatial harmonic components in the air gap magnetic field, the harmonic components of the permeability function are regulated by a genetic algorithm to maximize the working harmonic components and determine the optimal geometric dimensions of the modulation pole, which includes:

[0052] Construct the formula to maximize the working harmonics: Maximize|B 22 (x)|, where x is a set of design variables;

[0053] Considering the torque pulsation characteristics, three constraints of the harmonic components of the air gap permeability function are applied to the three optimal models respectively:

[0054]

[0055] Where p1(x) and p2(x) are the Fourier coefficients of the 6th and 12th spatial harmonics of the air gap permeability function, respectively. The torque ripple in the optimization process is reduced by adjusting the 6th and 12th harmonics of the air gap permeability function, while the output torque is improved.

[0056] Compared with the prior art, the present invention has the following advantages and technical effects:

[0057] The present invention innovatively proposes a method that integrates analytical equations and intelligent optimization algorithms to optimize the geometric structure of modulation poles. The core of this method is to deeply analyze the magnetic flux density distribution characteristics generated by the armature winding, and on this basis evaluate the influence of the modulation pole on the magnetic field modulation effect. In view of the fact that the torque generation mechanism of the permanent magnet vernier motor depends on the coupling effect between the winding magnetic field after modulation by the modulation pole and the magnetic field of the rotor permanent magnet, the present invention enhances the torque output capacity of the motor by optimizing the geometric structure of the modulation pole. Specifically, a Fourier series method is used to construct a magnetic permeability function model that includes changes in the geometric parameters of the modulation pole. The model can accurately capture the spatial harmonic components in the air gap magnetic field, especially those working harmonics that have a direct impact on the torque. Subsequently, the genetic algorithm, an efficient global optimization tool, is used to finely control the harmonic components of the magnetic permeability function, which can maximize the working harmonic components, thereby determining the optimal geometric size of the modulation pole. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0059] Figure 1 A typical magnetic gear topology diagram of an embodiment of the present invention;

[0060] Figure 2 The figure is a structural diagram of a surface mounted permanent magnet vernier motor according to an embodiment of the present invention.

[0061] Figure 3 A winding magnetic flux path diagram of the winding magnetomotive force generated by the A-phase winding according to an embodiment of the present invention;

[0062] Figure 4 An equivalent magnetic circuit diagram of the winding magnetomotive force generated by the A-phase winding in an embodiment of the present invention;

[0063] Figure 5 A winding magnetomotive force diagram of the winding magnetomotive force generated by the A-phase winding according to an embodiment of the present invention;

[0064] Figure 6 A single-phase winding diagram of the winding magnetomotive force distribution at time t=0 according to an embodiment of the present invention;

[0065] Figure 7 A three-phase winding diagram showing the magnetomotive force distribution of the winding at time t=0 according to an embodiment of the present invention;

[0066] Figure 8 A diagram showing the design variables of the modulation pole structure of the flux modulation pole and the air gap permeance distribution according to an embodiment of the present invention;

[0067] Fig. 9 An air gap permeance distribution diagram of a flux modulation pole and an air gap permeance distribution according to an embodiment of the present invention;

[0068] Fig.10 The magnetic flux density distribution diagram of the embodiment of the present invention when θ1=7.5°;

[0069] Fig.11 A radial air gap magnetic flux density diagram of an embodiment of the present invention;

[0070] Fig.12 Air gap magnetic permeance diagram of an embodiment of the present invention;

[0071] Fig.13 A graph showing the variation of air gap permeability with angle θ1 according to an embodiment of the present invention;

[0072] Fig.14 A diagram of the modulation pole pitch and the width of the auxiliary groove according to an embodiment of the present invention;

[0073] Fig.15A modulation optimization flow chart of an embodiment of the present invention;

[0074] Fig.16 Torque characteristic diagrams of the basic model and the optimal model of the embodiment of the present invention;

[0075] Fig.17 No-load back-electromotive force harmonic analysis diagram of the basic model and the optimized model of the embodiment of the present invention. DETAILED DESCRIPTION

[0076] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0077] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0078] like Figure 2 As shown, in this embodiment, a method for optimizing the modulation pole structure of a surface-mounted permanent magnet vernier motor based on an analytical model is provided, comprising:

[0079] For the surface-mounted permanent magnet vernier motor, a magnetic permeability function model including the modulation pole geometry parameters is constructed by using the Fourier series method, and the spatial harmonic components in the air gap magnetic field are obtained based on the magnetic permeability function model;

[0080] Based on the spatial harmonic components in the air gap magnetic field, a genetic algorithm is used to regulate the harmonic components of the magnetic permeability function to maximize the working harmonic components and determine the optimal geometric size of the modulation pole.

[0081] Furthermore, based on the magnetic gear, the surface-mounted permanent magnet vernier motor converts the magnetic gear outer rotor into the stator winding of the motor, and fixes the magnetic adjustment magnet block to the outer stator, thereby utilizing the magnetic field modulation effect of the magnetic gear to obtain a low-speed, high-torque motor on the inner rotor.

[0082] like Figure 1 The figure shows a typical magnetic gear topology, which consists of a surface-mounted permanent magnet inner rotor and outer rotor, and a magnetic block. Figure 1 It can be seen that the magnetic fields generated by the permanent magnets with different pole pairs in the inner and outer rotors are coupled through the magnetic adjustment blocks, thereby realizing the transmission of speed and torque. If only the magnetic field of the inner rotor permanent magnet is considered, the radial component of the magnetic flux density distribution in the outer air gap can be written as follows:

[0083]

[0084] In formula (1), the first term represents the radial flux density distribution without the tuning magnet block, which is generated by the harmonic components of the magnetomotive force of the inner rotor permanent magnet. The second term represents the flux modulation function, which is actually the air gap permeability function and takes into account the geometric shape of the tuning magnet block. It should be noted that the flux modulation function is defined based on the assumption that the tuning magnet blocks have the same shape. If the shape and distribution design of the tuning magnet block are different, the flux modulation shape is defined under the assumption that the flux modulation shape is the same. If the shape and distribution design of the tuning magnet block are different, the flux modulation function will be different except for p sp In addition to multiples of , it can also include harmonics of other spatial orders. In this case, j, P in the equation j ,jp sp You can use v, P respectively v and vp sp Instead, where v is an integer describing the spatial harmonic order of the flux modulation function. m is the rotational mechanical angle, ω ir is the mechanical angular velocity of the inner rotor, p ir is the number of inner rotor pole pairs, p sp Adjust the number of magnets, B m is the radial magnetic flux density without adjusting the magnet block, P j is the flux modulation function.

[0085] According to formula (1), the radial flux density distribution in the outer air gap can be expressed as:

[0086]

[0087] Considering the influence of the magnetic modulation block, the harmonic distribution of radial magnetic flux density is divided into two components. The first component is generated only by the magnetomotive force harmonics of the inner rotor permanent magnet, that is, the first term of equation (2). The second component is generated by the magnetic modulation between the magnetomotive force harmonics of the inner rotor permanent magnet and the harmonics of the flux modulation function. The magnetic gear uses the modulated component of the magnetic field to work normally. Among the modulated harmonics of the radial magnetic flux density distribution in the outer air gap caused by the inner rotor permanent magnet, the harmonic with the highest amplitude is selected as the working harmonic. In the outer air gap of the magnetic gear, the working harmonic refers to the spatial harmonic of the magnetic flux distribution in the outer air gap generated by the inner rotor permanent magnet and affecting the output torque of the outer rotor. Therefore, the working harmonic generates an output torque on the outer rotor by interacting with the magnetic field of the outer rotor permanent magnet. When m=1 and j=1, the working harmonic is generated by the third term of equation (2). In order to generate useful torque on the outer rotor, the number of pole pairs of the outer rotor should be equal to the working harmonic order, and can be expressed as:

[0088] p or =|p ir -p sp | (3)

[0089] Mechanical angular velocity of the outer rotor:

[0090]

[0091] It can be seen from equation (4) that the inner rotor and outer rotor of the magnetic gear rotate at different speeds, and the torque is transmitted between the rotors at the ratio of the rotor speeds.

[0092] The output torque characteristics of the outer rotor of the magnetic gear depend on the amplitude of the working harmonics in the outer air gap. In addition, the working harmonics of the inner rotor permanent magnet in the outer air gap are generated only by the interaction between the fundamental wave of the inner rotor permanent magnet magnetomotive force distribution and the spatial harmonics of the flux modulation function, and the spatial harmonics of the flux modulation function correspond to the number of magnetic modulation magnets. As shown in the first term of formula (1), all harmonics of the inner rotor permanent magnet magnetomotive force distribution rotate at the same speed as the mechanical angular velocity of the inner rotor. Therefore, according to formula (2), it is difficult to transform the harmonics of the inner rotor permanent magnet magnetomotive force distribution into the same harmonic components of the radial flux density distribution of the outer air gap. That is, the harmonics of the inner rotor permanent magnet magnetomotive force distribution cannot be modulated into working harmonics with the same spatial order and angular velocity.

[0093] like Figure 1 As shown, when the number of pole pairs of the inner rotor permanent magnet is 4 and the number of the tuning magnet blocks is 26, according to formula (3), the number of pole pairs of the outer rotor permanent magnet is 22. The spatial harmonic order of the outer air gap is 22, and the working harmonic angular velocity is -4 / 22×ω ir . Table 1 shows the combination of harmonic components modulated into the 22nd spatial harmonic of the radial flux density distribution in the outer air gap. For example, according to the second term of formula (2), the 12th spatial harmonic of the inner rotor permanent magnet magnetomotive force distribution can generate the 22nd spatial harmonic of the radial flux density distribution in the outer air gap by interacting with the 10th spatial harmonic of the flux modulation function. However, the modulated harmonics rotate at different angular speeds. Studies have shown that the working harmonics generated by the fundamental wave of the inner rotor permanent magnet magnetomotive force distribution produce output torque on the outer rotor, while other harmonics cause torque pulsations through their different angular speeds.

[0094] Table 1

[0095]

[0096] Figure 2 The structure of the concentrated winding surface-mounted permanent magnet vernier motor is shown. The stator has six slots and three-phase windings to form a rotating magnetic field with two pole pairs. Each stator tooth end is divided into 4 modulation poles, so the total number of modulation poles is 24. According to the relationship between the stator and rotor pole pairs of the surface-mounted permanent magnet vernier motor, the rotor pole pair number p r is 22. That is:

[0097] p r =|pFMP -p s | (5)

[0098] In the formula, p s and p EMP are the stator winding pole pairs and the modulation pole number, respectively. For the surface-mounted permanent magnet vernier motor, the magnetic field generated by the armature winding is obtained by multiplying the winding magnetomotive force and the air gap permeance function. The analytical equation for the output torque generated by the working harmonics is derived as a function of the modulation pole design variables. The magnetomotive force distribution of the three-phase winding can be expressed as:

[0099]

[0100] In the formula, ω e is the electrical angular velocity, m is the harmonic order of the winding magnetomotive force distribution, mp s is the spatial harmonic order.

[0101] When the magnetomotive force harmonics generated by each phase winding are added, the third harmonic of the winding magnetomotive force distribution is cancelled. In addition, the m=3i+1 harmonic rotates in the same direction as the fundamental wave of the winding magnetomotive force distribution, while the m=3i-1 harmonic rotates in the opposite direction, where i is an integer. The mechanical angular velocity of the mth harmonic can be expressed as:

[0102]

[0103] Where, when m = 3i + 1, sgn = +1, and when m = 3i - 1, sgn = -1. This is a significant feature of the permanent magnet vernier motor compared to magnetic gears where all rotor permanent magnet magnetomotive force harmonics rotate at the same speed and direction.

[0104] The air gap permeability function is determined by the geometry of the modulation poles. Figure 2 As shown, it is assumed that the modulation poles are equidistant and relative to θ m The reference axis is symmetrical, and the air gap permeability function can be expressed as:

[0105]

[0106] In the formula, p FMPs is the number of modulation poles, j is an integer, jp FMPs is the harmonic order of the air gap permeance function. When the shape of the modulation pole is designed differently, the air gap permeance function includes p FMPs In addition to the multiple harmonics, it also contains other sub-space harmonics.

[0107] By multiplying equations (6) and (8), the radial magnetic flux density distribution generated by the armature winding in the air gap is obtained as:

[0108]

[0109] When m = 1 and j = 1

[15] , the operating harmonics of the radial flux density distribution are mainly generated in the fifth term of equation (9).

[0110] The mechanical angular velocity of the rotor is:

[0111]

[0112] The magnetic field modulation phenomenon in a permanent magnet vernier motor is the same as the modulation of a magnetic gear. However, the angular velocity characteristics of the winding MMF harmonics in a permanent magnet vernier motor are different from the rotor permanent magnet MMF harmonics in a magnetic gear. The winding MMF harmonics contribute to the operating harmonics by interacting with certain harmonics of the air gap permeability function.

[0113] When the number of winding pole pairs is 2 and the number of modulation poles is 24, according to formula (5), the number of rotor permanent magnet pole pairs is 22. The order of the working harmonic is 22, and the angular velocity is Table 3 shows the combination of harmonic components modulated into working harmonics. As can be seen from Table 2, unlike traditional permanent magnet motors and magnetic gear motors, all winding magnetomotive force harmonics in permanent magnet vernier motors can be modulated into working harmonics. For example, based on the fourth term of formula (9), the fourth spatial harmonic (mp s =4) interacts with the 18th spatial harmonic (k=18) of the air gap permeability function and becomes the 22nd operating harmonic. However, in general, the modulation poles are equidistant, so the air gap permeability function only contains multiple harmonics of 24 corresponding to the number of modulation poles. This shows that, except for the 2nd and 22nd spatial harmonics of the winding magnetomotive force distribution, other harmonics usually have no effect on the operating harmonics. Therefore, in order to improve the operating harmonics and output torque, the shape of the modulation pole should be designed considering the harmonic components of the air gap permeability function.

[0114] Table 2

[0115]

[0116] Furthermore, the winding magnetomotive force is generated by the current flowing through the armature winding, and the magnetomotive force distribution in the air gap can be obtained by the following assumptions:

[0117] The magnetic permeability of the stator and rotor cores is infinite.

[0118] The air gap flux density, winding magnetomotive force and magnetic permeability are consistent with the axial direction.

[0119] The value of the winding magnetomotive force changes linearly in the area before the slot opening.

[0120] The three-phase current is symmetrical and sinusoidal.

[0121]

[0122] Where ω is the electrical angular velocity, I rms is the effective value of the input current.

[0123] for Figure 2 In the 6-slot permanent magnet vernier motor shown, the winding of phase A includes two coils, and the magnetic flux path generated by each coil of the phase A winding is independent, such as Figure 3 The reluctance in the flux path shown is caused by the area of ​​the air gap and the permanent magnet. In addition, by assuming that all teeth are constructed identically, the reluctance R per slot pitch is m equal.

[0124] According to Ampere's law and Gauss's law, the equivalent magnetic circuit is as follows: Figure 4 The magnetomotive force generated by the A-phase winding along the air gap circumference is a function of the current flowing into the winding and is affected by the number of winding turns. Therefore, the amplitude of the winding magnetomotive force can be regarded as the number of winding turns N. c and the instantaneous value of current i a If the number of turns and current value are given, the magnetomotive force amplitude at a certain moment can be calculated. According to the assumption (3), the magnetomotive force distribution of phase A winding is obtained as follows: Figure 5 shown.

[0125] A rectangular coordinate system is established on the inner surface of the stator, with the origin at the axis of the A-phase winding. The horizontal coordinate is the central angle of the air gap at different positions on the circumference from the origin, measured in spatial electrical angles, with the counterclockwise direction as the positive direction of the spatial electrical angle, and the vertical coordinate is the magnitude of the magnetomotive force. Using the Fourier analysis method, the magnetomotive force distribution can be expressed as:

[0126]

[0127] In the formula, θ m is the mechanical angle, θ so is the mechanical angle of the slot opening, N c is the number of turns for each coil.

[0128] The magnetomotive force distribution generated by phase B and phase C can also be obtained in the same way. The total winding magnetomotive force distribution is calculated by the sum of the magnetomotive force of each phase. Figure 6 The magnetomotive force distribution of the single-phase winding and the three-phase winding at time t = 0. The Fourier expression of the magnetomotive force distribution of the winding is as follows:

[0129]

[0130] In the formula, F m It is the Fourier coefficient of the spatial harmonics of the total armature winding magnetomotive force distribution.

[0131] Furthermore, the air gap permeance function makes the following assumptions in order to predict the air gap permeance distribution:

[0132] (1) The magnetic permeability of the stator and rotor cores is infinite.

[0133] (2) The relative magnetic permeability of permanent magnets is consistent.

[0134] (3) The modulation pole on each stator main tooth is symmetrical to the stator main tooth axis.

[0135] (4) All teeth have the same structure.

[0136] (5) The modulation pole height has no effect on the air gap permeability distribution.

[0137] In order to study the harmonic characteristics of the air gap permeability function, the finite element method was used to calculate the magnetic field distribution of PMVM. Figure 8 is the structure of the modulation pole and the distribution of magnetic permeance formed in the air gap. The air gap magnetic permeability per unit area is determined by the length of the magnetic flux path l, and the calculation formula is as follows

[0138]

[0139] Where μ0 is the magnetic permeability of air.

[0140] In the air gap region directly in front of the modulation pole, the length of the flux path remains constant and the permeance reaches the maximum value Pmax, such as Figure 8 As shown. On the contrary, the air gap flux path connecting the auxiliary slot and the stator slot changes along the circumferential direction, which is due to the existence of the edge flux. The edge flux reduces the permeance due to the increase in the length of the flux path. In addition, the permeance distribution caused by the edge flux is symmetrical in the area between any two modulation poles. Therefore, the air gap permeance distribution in the auxiliary slot and stator slot area can be approximated by a quadratic polynomial function, as shown in Fig. 9 As shown. In contrast, the flux path in front of the auxiliary slot and the stator slot opening changes along the circumferential direction, which is due to the edge flux. As the flux path length increases, the permeance of the edge flux decreases. In addition, the permeance distribution caused by the edge flux is symmetrical in the area between any two modulation poles. Therefore, the air gap permeability distribution of the auxiliary slot and slot opening area can be approximated by using a second-order polynomial function, such as Fig. 9 From 0 to The analytical expression of the air gap permeance distribution within the arc range is as follows:

[0141]

[0142] Where P θ1 and P θ3 is the minimum value of the permeance in the auxiliary slot, P so is the minimum value of the stator slot permeance. Using Fourier analysis and equation (17), the air gap permeance function can be expressed as follows:

[0143]

[0144] In the formula, p FMPs is the modulation pole number, P0 DC bias value, P j Fourier coefficients, corresponding to the air gap permeability function (j×N slot ) space harmonics. In addition, P0 and P j The design variables θ1, θ2, θ3, θ4 and θ so function.

[0145] The harmonic characteristics of the air gap permeance function depend on the size of the design variables and the length of the permanent magnet and the air gap. Based on equation (16) Among them l m and g are the lengths of the permanent magnet and the air gap, respectively. In addition, P max Does not depend on design variables, such as Figure 8 Shown P θ1 , P θ3 and P so Depends on θ1, θ3 and θ respectively so If the path of the edge flux is assumed to be a circular trajectory, the permeance can be predicted to be minimum in the region where the edge flux exists. However, this method has errors in the harmonic amplitudes of the air gap permeance function. In particular, the error value varies with θ1, θ3 and θ so Therefore, in order to improve the accuracy of the air gap permeability function, the finite element method (FEM) is used to analyze θ1, θ3 and θ so The change of P is then θ1 , P θ3 and P so Expressed as design variables θ1, θ3 and θ so The function is then substituted into (17) and (18).

[0146] Under the condition that the effective value of the phase current is 5.6A at time t=0, the radial magnetic flux density distribution caused by the armature winding in the air gap can be obtained by using the commercial software Maxwell. In addition, the winding magnetomotive force distribution is calculated by equations (14) and (15) under the same conditions as FEM. After obtaining the radial magnetic flux density of the armature winding in the air gap by using finite element analysis, the air gap permeability function can be calculated by the following formula:

[0147]

[0148] Figure 10-13 The radial magnetic flux density distribution in the air gap caused by the armature winding and the corresponding magnetic permeance distribution are obtained according to θ1. Fig.10As shown in the figure, the maximum values ​​of the magnetic flux density at the stator and rotor yokes are 0.96T and 0.75T, respectively, which indicates that the stator and rotor cores are not saturated by the winding magnetomotive force. Therefore, P is calculated by the analytical equation assuming infinite magnetic permeability. max Similar to the values ​​obtained by FEM, the latter takes into account the nonlinear properties of the core material, such as Fig.12 As shown in Figure 2. Since the magnetomotive force distribution of the windings is the same, it can be found that the change in the radial magnetic flux density distribution is caused by the change in the air gap permeance distribution. Fig.12 and Fig.13 As shown, the increase of θ1 leads to P θ1 The value of P max , P θ3 and P so The value of has no direct impact. θ1 It can be expressed as a function of θ1 using the least squares method. Similarly, P θ3 and P so According to θ3 and θ so The changes can be Figure 7 According to the analysis results, P θ1 , P θ3 and P so As shown below:

[0149]

[0150] Where θ1, θ3 and θ so The value is in radians.

[0151] Substituting equations (21) and (22) into equations (8) and (9), we can accurately predict the harmonic characteristics of the air gap permeance function as the modulation pole shape changes.

[0152] Furthermore, the air gap flux density generated by the winding is multiplied by (5) and (10), and the radial flux density distribution in the air gap generated by the armature winding can be expressed as:

[0153]

[0154]

[0155] In permanent magnet vernier motors, such as Figure 1 As shown, the operating harmonic of the air gap flux density distribution generated by the armature winding is the 22nd space harmonic, which corresponds to the number of rotor pole pairs and is arranged as follows.

[0156] B 22nd (θ m ,ω e t)=B 22 cos(22·θ m +ωe t) (24)

[0157] B 22 =[F 11 P0+0.5×(F1P4+F2P3+F4P5+F5P2+F7P6+F8P1+F 10 P7+…)] (25)

[0159] In the formula, F m is the magnetomotive force distribution of the winding (m×p s ) Fourier coefficients of subspatial harmonics, P j is the air gap permeability function (j×N slot ) Fourier coefficients of sub-spatial harmonics. s and N slot 2 and 6 respectively. It can be seen that all winding magnetomotive force harmonics can affect the amplitude of the operating harmonics according to the harmonic characteristics of the air gap permeance function. m and P j The function can be expressed by the design variables of the modulation pole shape, so the size of the design variables can be obtained from equation (25) to maximize the operating harmonics.

[0160] Furthermore, the air gap flux density generated by the modulation pole is generally constant, the pitch τ of the modulation pole is constant, and the width θ of the auxiliary slot is constant. as , including the width of the slot, such as Fig.14 In addition, the slot width ratio k, i.e. the ratio of the auxiliary slot width to the modulation pole pitch, is selected as a design parameter.

[0161]

[0162]

[0163] Furthermore, the output torque of the PMSM in the optimization of the modulation pole is proportional to the operating harmonics. Therefore, the optimal combination of design variables can be obtained by using formula (25) to maximize the output torque and operating harmonics. To perform the optimization, the genetic algorithm toolbox in MATLAB was applied. The design optimization problem can be constructed as maximizing the operating harmonics in formula (26):

[0164] Maximize|B 22 (x)| (28)

[0165] Where x is a set of design variables, such as Figure 3 In order to consider the torque pulsation characteristics, three constraints on the harmonic components of the air gap permeability function are applied to the three optimal models respectively:

[0166]

[0167] Where p1(x) and p2(x) are the Fourier coefficients of the 6th and 12th spatial harmonics of the air gap permeance function, respectively. The torque ripple of the permanent magnet vernier motor is significantly affected by the cogging torque, which varies according to the shape of the modulation pole. When the modulation pole is designed by adjusting the slot width ratio, the air gap permeance function is changed by N EMP In this case, the torque ripple and cogging torque are small, and its characteristics are similar to the model with a slot width ratio of 1. However, the Fourier expression (9) of the air gap permeance function of this embodiment includes a number less than N EMP of spatial harmonics, which increase the cogging torque, such as the 6th, 12th, and 18th spatial harmonics. In Equation (25), the 18th spatial harmonic of the air gap permeance can significantly generate working harmonics and output torque by interacting with the 4th spatial harmonic of the winding magnetomotive force (with the second highest amplitude). In contrast, the 6th and 12th spatial harmonics have less effect on the working harmonics. Therefore, the torque ripple in the optimization process can be reduced by adjusting the 6th and 12th harmonics of the permeance, while improving the output torque. The constraints in Equation (18) are to reduce the cogging torque and torque ripple by eliminating the effects of p1(x) and p2(x) in OM2 and OM3, respectively.

[0168] Table 3 lists the optimization results. Fig.15 The modulation pole geometry of the base model and the optimized model are shown. Compared with the base model, the operating harmonics of OM1, OM2 and OM3 increase by 32%, 27% and 24% respectively. Fig.16 The torque characteristics are shown. As shown in Table 3, compared with the basic model, the average torque of the optimized model increases with the increase of the operating harmonics at a similar proportion. In addition, it can be seen that the torque pulsation has a similar trend to the cogging torque. In OM1, the operating harmonics and average torque are the largest, but the torque pulsation increases by 10%. Compared with OM1, the cogging torque and torque pulsation in OM2 and OM3 are reduced by eliminating the 6th and 12th spatial harmonics of the permeance function, respectively. In particular, as Fig.16 As shown in Figure 2, after eliminating the 12th spatial harmonic of the permeance function in OM3, the value of the cogging torque is similar to that of the basic model. The results show that the minimum value of the torque ripple is 1.83% in OM3. Fig.17 The back electromotive force (EMF) characteristics of the basic model and the optimized model at a rotor speed of 500 rpm are shown. The total harmonic distortion values ​​of the back EMF for all models are less than 2%. In addition, the fundamental principle of the back EMF waveform of the optimized model is improved in a similar proportion as the output torque increases compared to the basic model.

[0169] Compared with the traditional optimization method relying on finite element simulation, this embodiment not only significantly shortens the design cycle, but also achieves a significant increase in the output torque of the surface-mounted permanent magnet vernier motor (up to 19%). At the same time, by finely controlling the harmonic distribution of the magnetic permeability, the torque pulsation phenomenon is effectively suppressed, and a significant improvement in torque smoothness is achieved (torque pulsation is reduced by 69%). This achievement not only demonstrates the great potential of deeply integrating analytical theory with advanced optimization algorithms in the field of motor design, but also provides new ideas for the efficient development of high-performance permanent magnet motors.

[0170] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for optimizing the modulated pole structure of a surface-mounted permanent magnet vernier motor based on an analytical model, characterized in that: include: For the surface-mounted permanent magnet vernier motor, a magnetic permeability function model including the modulation pole geometry parameters is constructed by using the Fourier series method, and the spatial harmonic components in the air gap magnetic field are obtained based on the magnetic permeability function model; Based on the spatial harmonic components in the air gap magnetic field, a genetic algorithm is used to finely control the harmonic components of the magnetic permeability function to maximize the working harmonic components and determine the optimal geometric size of the modulation pole.

2. The method according to claim 1, characterized in that The surface-mounted permanent magnet vernier motor is based on the magnetic gear, and the outer rotor of the magnetic gear is converted into the stator winding of the motor, and the magnetic adjustment magnet block is fixed together with the outer stator, and the magnetic field modulation effect of the magnetic gear is used to obtain a low-speed and high-torque motor on the inner rotor, thereby obtaining the surface-mounted permanent magnet vernier motor; The stator of the surface-mounted permanent magnet vernier motor includes six slots and a three-phase winding to form a rotating magnetic field with two pole pairs; each stator tooth end is divided into four modulation poles, and the total number of modulation poles is 24; The relationship between the stator and rotor pole pairs of the surface-mounted permanent magnet vernier motor is: p r =|p FMP -p s | In the formula, p s and p EMP are the stator winding pole pairs and modulation pole numbers respectively.

3. The method according to claim 2, characterized in that The magnetic gear comprises a surface-mounted permanent magnet inner rotor and outer rotor and a magnet adjustment block group. The magnetic fields generated by permanent magnets with different pole pairs in the surface-mounted permanent magnet inner rotor and outer rotor are coupled through the magnet adjustment block, thereby realizing the transmission of rotation speed and torque. If only the magnetic field of the inner rotor permanent magnet is considered, the radial component of the magnetic flux density distribution in the outer air gap is expressed as: Where, the first term represents the radial flux density distribution without adjusting the magnet block, which is generated by the harmonic component of the magnetomotive force of the inner rotor permanent magnet; the second term represents the flux modulation function, which is actually the air gap permeability function considering the geometric shape of the adjusting magnet block, θ m is the rotational mechanical angle, ω ir is the mechanical angular velocity of the inner rotor, p ir is the number of inner rotor pole pairs, p sp Adjust the number of magnets, B m is the radial magnetic flux density without adjusting the magnet block, P j is the flux modulation function; The radial flux density distribution in the outer air gap is expressed as:

4. The method according to claim 1, characterized in that: The magnetic field generated by the armature winding of the surface-mounted permanent magnet vernier motor is obtained by multiplying the winding magnetomotive force and the air gap permeance function; The analytical equation of the output torque generated by the working harmonic is expressed as a function of the modulation pole design variables, and the magnetomotive force distribution of the three-phase winding is expressed as: In the formula, ω e is the electrical angular velocity, m is the harmonic order of the winding magnetomotive force distribution, mp s is the spatial harmonic order.

5. The method according to claim 1, characterized in that The permeability function is determined by the geometry of the modulation poles, assuming that the modulation poles are equidistant and relative to θ m The reference axis is symmetrical, and the air gap permeability function is expressed as: In the formula, p FMPs is the number of modulation poles, j is an integer, jp FMPs is the harmonic order of the air gap permeance function. When the shape of the modulation pole is designed differently, the air gap permeance function contains p EMPs Multiple harmonics and other sub-space harmonics.

6. The method according to claim 5, characterized in that Based on the magnetomotive force distribution of the three-phase winding and the air gap permeability function, the radial magnetic flux density distribution generated by the armature winding in the air gap is obtained, and the expression is:

7. The method according to claim 1, characterized in that The spatial harmonic components in the air gap magnetic field are obtained based on the magnetic permeability function model. The spatial harmonic components include the winding magnetomotive force, which is generated by the current flowing through the armature winding. The magnetomotive force distribution in the air gap is obtained by the following assumptions: The magnetic permeability of the stator and rotor cores is infinite; The air gap flux density, winding magnetomotive force and magnetic permeability are consistent with the axial direction; The value of the winding magnetomotive force varies linearly in the area before the slot opening; The three-phase current is symmetrical and sinusoidal; Where ω is the electrical angular velocity, I rms is the effective value of the input current; Using Fourier analysis method, the magnetomotive force distribution is expressed as: In the formula, θ m is the mechanical angle, θ so is the mechanical angle of the slot opening, N c is the number of turns for each coil; The Fourier expression of the winding magnetomotive force distribution is: In the formula, F m It is the Fourier coefficient of the spatial harmonics of the total armature winding magnetomotive force distribution.

8. The method according to claim 1, characterized in that The spatial harmonic components in the air gap magnetic field are obtained based on the permeability function model, wherein the spatial harmonic components include the air gap permeability function, and the air gap permeability function is obtained by the following assumptions: The magnetic permeability of the stator and rotor cores is infinite; The relative magnetic permeability of permanent magnets is consistent; The modulation pole on each stator main tooth is symmetrical to the stator main tooth axis; All teeth have the same structure; The modulation pole height has no effect on the air gap permeability distribution; The air gap permeability function is expressed as follows using Fourier analysis: In the formula, p FMPs is the modulation pole number, P0 is the DC bias value, P j is the Fourier coefficient, corresponding to the air gap permeability function (j×N slot ) space harmonics; P0 and P j The design variables θ1, θ2, θ3, θ4 and θ so function.

9. The method according to claim 1, characterized in that: The spatial harmonic components in the air gap magnetic field are obtained based on the magnetic permeability function model, and the spatial harmonic components also include the air gap magnetic flux generated by the winding and the air gap magnetic flux generated by the modulation pole.

10. The method according to claim 1, characterized in that Based on the spatial harmonic components in the air gap magnetic field, the process of using a genetic algorithm to regulate the harmonic components of the magnetic permeability function to maximize the working harmonic components and determine the optimal geometric size of the modulation pole includes: Construct the formula to maximize the working harmonics: Maximize|B 22 (z)|, where x is a set of design variables; Considering the torque pulsation characteristics, three constraints of the harmonic components of the air gap permeability function are applied to the three optimal models respectively: Where p1(x) and p2(x) are the Fourier coefficients of the 6th and 12th spatial harmonics of the air gap permeability function, respectively. The torque ripple in the optimization process is reduced by adjusting the 6th and 12th harmonics of the air gap permeability function, while the output torque is improved.

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