Magnetic field coupling analysis and modulation method of permanent magnet motor with magnetic field modulation based on harmonic group

Abstract

The present invention discloses a magnetic field coupling analysis and modulation method of a permanent magnet motor based on a harmonic group in the field of motor design. According to the permanent magnet excitation source being an outer surface mounted permanent magnet and an intermediate permanent magnet, and the armature magnetic source being an outer armature winding, a reference magnetic flux density component of the motor's outer air gap magnetic field is obtained. According to the permanent magnet excitation source being an inner surface mounted permanent magnet and an intermediate permanent magnet, and the armature magnetic source being an inner armature winding, a coupling magnetic flux density component of the outer air gap magnetic field is obtained. A coupling effect ratio, a harmonic characteristic factor, and a harmonic coupling efficiency are calculated in sequence from the air gap magnetic flux density. Positive and negative coupling harmonics are determined based on the harmonic coupling efficiency. Corresponding positive and negative coupling harmonic groups are established from the positive and negative coupling harmonics, and the positive and negative coupling efficiencies are calculated. Whether the motor magnetic field coupling meets the requirements is analyzed based on the positive and negative coupling efficiencies. The present invention effectively utilizes the positive effect of the coupling harmonics and improves the motor torque capacity by improving the air gap magnetic flux density harmonic coupling characteristics.

Description

Technical Field

[0001] The present invention belongs to the field of motor design, specifically to a method for analyzing the magnetic field coupling of a motor, specifically analyzing the mutual influence between the composite magnetic fields formed by a double-air-gap magnetic field modulation permanent magnet motor, analyzing the coupling effect of the composite magnetic field of the double-air-gap magnetic field modulation permanent magnet motor, and avoiding the negative impact caused by magnetic field coupling. Background Art

[0002] In recent years, field-modulated permanent magnet motors (FMMs), as an emerging type of permanent magnet motor, have attracted widespread attention. The modulation effect generates multiple magnetic field harmonics, giving these motors high torque density. To further enhance the torque density of FMMs, the concept of a dual-air-gap structure has been incorporated into their design, resulting in a FMM with high power density and torque density. For example, Chinese invention patent application No. 202010212515.3 discloses a dual-stator FMM motor with multiple operating modes. Its multiple operating harmonics improve output torque and magnetic modulation capability, and its dual-winding structure helps meet complex and diverse drive requirements. Chinese invention patent application No. 201610812433.6 proposes a brushless dual-mechanical-port permanent magnet motor based on the FMM principle. Its dual-air-gap structure enables a more compact motor structure and achieves higher torque density. Due to its high power density, outstanding torque capability, and flexible operating modes, FMMs are suitable for use in the power drive systems of electric vehicles, such as electric vehicles and electric tractors.

[0003] The dual-air-gap magnetic field modulated permanent magnet motor has a highly integrated design and assembly. Its two layers of air-gap magnetic fields constitute a composite magnetic field. There is a certain degree of mutual influence between the composite magnetic fields. This problem is usually called the magnetic field coupling effect. The coupling of the composite magnetic field will affect the coordinated control and mechanical reliability of the motor, and a reasonable motor topology can weaken the negative impact caused by the magnetic field coupling to a certain extent. For example, the dual-rotor magnetic field modulated motor disclosed in the document of Chinese invention patent application No. 202111284089.5 adopts a brushless structure, the permanent magnets are laterally segmented and staggered, and the rotors are independent of each other, avoiding the problem of synchronous control difficulties caused by motor coupling. The document of Chinese invention patent application No. 201810753354.1 discloses a bidirectional magnetic circuit coupled magnetic field modulated direct drive motor, whose magnetic isolation bridge structure reduces magnetic circuit coupling.

[0004] It can be seen from this that the mutual influence between the composite magnetic fields of a field-modulated permanent magnet motor (FMM) is the root cause of magnetic field coupling. For FMMs with abundant air-gap harmonics, while the composite magnetic field provides efficient energy conversion, it also introduces magnetic field coupling issues, which in turn impacts motor performance. It is well known that structural changes in the motor's magnetic source, modulator, and windings—the three main elements of a FMM—can lead to changes in the air-gap harmonics, further impacting motor performance. To overcome the issues of magnetic field coupling, existing dual-gap FMMs have all made improvements to their motor topology, without addressing the motor's magnetic source, modulator, and windings. Consequently, they fail to fully understand the coupling of the motor's composite magnetic fields. Air-gap flux density is a key entry point for addressing magnetic field coupling, and air-gap flux density harmonics are an important means of analyzing air-gap flux density. Therefore, analyzing the impact of magnetic field coupling on motor performance from the perspective of air-gap flux density harmonics can avoid coupling issues in FMMs and fully understand the coupling of the composite magnetic fields. Summary of the Invention

[0005] The purpose of the present invention is to address the coupling problem of the composite air gap magnetic field in the existing double-air-gap magnetic field modulation permanent magnet motor, propose a magnetic field coupling analysis method for the magnetic field modulation permanent magnet motor based on the harmonic group, comprehensively and accurately analyze the magnetic field coupling of the motor, and based on the analyzed magnetic field coupling results, propose a magnetic field modulation method for the magnetic field modulation permanent magnet motor to improve the torque performance of the motor.

[0006] The technical solution adopted by the harmonic group-based magnetic field modulation permanent magnet motor magnetic field coupling analysis of the present invention is:

[0007] According to the permanent magnet excitation source being the outer surface permanent magnet and the middle permanent magnet of the motor and the armature magnetic source being the outer armature winding of the motor, a reference magnetic flux density component of the outer air gap magnetic field of the motor is obtained;

[0008] According to the permanent magnet excitation source being the inner surface-mounted permanent magnet and the middle permanent magnet of the motor, and the armature magnetic source being the inner armature winding of the motor, the coupling magnetic flux density component of the outer air gap magnetic field of the motor is obtained by a method similar to that for obtaining the reference magnetic flux density component;

[0009] The air gap magnetic flux of the external air gap magnetic field is obtained by synthesizing the reference magnetic flux component and the coupling magnetic flux component;

[0010] The coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency are calculated in sequence from the air gap magnetic flux density;

[0011] Determining positive and negative coupling harmonics based on the harmonic coupling efficiency;

[0012] Establishing corresponding positive and negative coupling harmonic groups from the positive and negative coupling harmonics, respectively, and calculating the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups;

[0013] Whether the motor magnetic field coupling meets the requirements is analyzed based on the positive and negative coupling efficiencies.

[0014] Furthermore, the reference magnetic flux density component of the external air gap magnetic field is obtained by synthesizing the permanent magnet magnetic flux density and the armature magnetic flux density.

[0015] Furthermore, the air gap magnetic flux density is used to calculate the coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency in turn: first calculate the coupling effect ratio Then calculate the winding slot angle Harmonic slot angle of τ harmonic Determine when α w =α p When the harmonic characteristic factor k w =1, when α w ≠α p When the harmonic characteristic factor k w =-1; finally calculate the harmonic coupling efficiency η = k c ·k w ×100%,B cτ is the harmonic amplitude of the τ-th coupling magnetic flux density component, θ cτ (t) is the function of the phase of the harmonic of the coupling magnetic density component of τ times as a function of time, θ τ (t) is the function of the phase of the harmonic of the τ-order reference magnetic density component changing with time, B τ is the harmonic amplitude of the τth reference magnetic density component, P s is the number of pole pairs of the middle permanent magnet of the motor, N r Number of teeth on the outer rotor of the motor, N st is the number of stator teeth.

[0016] Furthermore, the positive and negative coupled harmonic groups are established respectively by the positive and negative coupled harmonics, and the positive coupled harmonic group pg={p1, p2, ..., p σ},σ∈N + , negative coupling harmonic group ng={n1,n2,...,n ε}, ε∈N + ,p1,p2…,p σ They are the 1st, 2nd,…,σth positive coupled harmonics, n1, n2…, n ε are the 1st, 2nd, …, εth negative coupling harmonics, N + represents a positive integer;

[0017] Calculate the positive coupling efficiency and negative coupling efficiency η p1 ,η p2 ,…,η pσ They represent the σ positive coupled harmonics p1, p2…, p in the positive coupled harmonic group pg. σ Harmonic coupling efficiency, η n1 ,η n2 ,…,η nε They represent the ε positive coupled harmonics n1, n2…, n in the negative coupled harmonic group ng. ε Harmonic coupling efficiency.

[0018] Furthermore, when the positive coupling efficiency η pg The value of is higher than 300%, and the negative coupling efficiency η ng When the value is lower than 150%, the coupling characteristics of the motor's harmonic groups meet the requirements; otherwise, they do not meet the requirements.

[0019] The technical solution adopted by the magnetic field coupling modulation method of a permanent magnet motor based on harmonic group magnetic field modulation described in the present invention is as follows: when the motor magnetic field coupling does not meet the requirements as analyzed by the positive and negative coupling efficiencies, the contour line of the outer surface of the surface-mounted permanent magnet of the motor stator on the radial cross section is designed to be a non-sinusoidal line, the radial thickness of the surface-mounted permanent magnet is changed, the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups are recalculated, and the motor magnetic field coupling is reanalyzed until the coupling characteristics of the harmonic group meet the requirements;

[0020] When the analysis of the positive and negative coupling efficiencies indicates that the motor magnetic field coupling does not meet the requirements, the contour line of the outer surface of the surface-mounted permanent magnet of the motor on the radial section is designed to be a sine line, the amplitude and phase of the sine contour line of the surface-mounted permanent magnet are adjusted, the amplitude of the permanent magnet magnetic potential harmonics before modulation is added to the amplitude change, and the initial phase of the magnetic potential harmonics before modulation is added to the phase change, to obtain the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups that meet the coupling characteristic requirements.

[0021] After adopting the above solution, the present invention has the following beneficial effects:

[0022] 1. Based on the differences in the magnetic source and modulator of the composite magnetic field of a magnetic field-modulated permanent magnet motor, the present invention establishes magnetomotive force and permeance models for the reference and coupled magnetic fields, respectively. Expressions for the reference and coupled magnetic density components are defined for the motor's composite magnetic field. The type of coupled magnetic density component harmonics is determined by the effect of the coupled magnetic density component harmonics on the air gap magnetic density harmonics and their harmonic characteristics. Unlike the traditional approach of weakening coupling, this analysis of the motor's composite magnetic field from the perspective of air gap magnetic density harmonics reveals the presence of positive coupling harmonics that have a positive effect on motor performance, allowing for accurate analysis of the coupling of the composite magnetic field of a magnetic field-modulated permanent magnet motor.

[0023] 2. This invention defines harmonic group coupling efficiency and establishes a basis for evaluating magnetic field coupling based on it. Positive and negative coupling harmonic groups are constructed based on this harmonic group coupling efficiency. The positive and negative coupling efficiencies of the harmonic group are calculated using the coupled harmonic group as a unit, and the coupling characteristics of the harmonic group are analyzed accordingly. The positive coupling efficiency of the harmonic group is positively correlated with the coupling characteristics, and a mapping relationship between the harmonic coupling characteristics and motor torque performance is established. Improving the coupling effect can improve motor performance.

[0024] 3. This invention proposes a method for improving the coupling characteristics of composite magnetic fields based on harmonic groups. By adjusting the amplitude and phase of the sinusoidal profile of the surface-mounted permanent magnet, harmonic modulation is achieved, increasing the positive coupling efficiency of the air gap flux density harmonic group and improving the coupling effect, thereby enhancing motor performance. The present invention's coupled harmonic group analysis method effectively utilizes the positive effect of coupled harmonics and improves the motor's torque capability by improving the air gap flux density harmonic coupling characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a topological structure diagram of a double-air-gap magnetic field modulation permanent magnet motor targeted by the method of the present invention;

[0026] Figure 2 for Figure 1 The expanded view of the local structure of the permanent magnet 2 attached to the middle and outer surfaces;

[0027] Figure 3 for Figure 1 The expanded view of the local structure of the inner surface permanent magnet 7;

[0028] Figure 4 for Figure 1 Schematic diagram of the permanent magnet potential of the middle permanent magnet 3;

[0029] Figure 5 for Figure 1 Schematic diagram of the permanent magnetic potential of the permanent magnet 2 attached to the middle and outer surfaces;

[0030] Figure 6 for Figure 1 Schematic diagram of permanent magnet potential of the air gap magnetic field 1 between the middle and outer parts;

[0031] Figure 7 for Figure 1 Schematic diagram of the magnetic permeance of the inner and outer rotors 4;

[0032] Figure 8 for Figure 1 Schematic diagram of the permanent magnet potential of the external air gap magnetic field 1 before and after medium modulation;

[0033] Figure 9 for Figure 1 The distribution diagram of the positive and negative coupling efficiency of the coupling harmonics of the external air gap magnetic field 1 before and after medium modulation;

[0034] Figure 10 for Figure 1 The distribution diagram of the positive and negative coupling efficiency of the coupled harmonics of the inner air gap magnetic field 10 before and after the medium modulation;

[0035] Figure 11 for Figure 1 The positive and negative coupling efficiency diagrams of the harmonic group of the external air gap magnetic field 1 before and after medium modulation;

[0036] Figure 12 for Figure 1 Graphs showing the fundamental amplitude of the back-EMF of the outer armature winding 5 and the average torque of the outer rotor 4 before and after medium modulation;

[0037] Figure 13 for Figure 1 The positive and negative coupling efficiency diagram of the 10 harmonic groups of the inner air gap magnetic field before and after medium modulation;

[0038] Figure 14 for Figure 1 Graphs showing the back EMF fundamental amplitude of the inner armature winding 6 and the average torque of the inner rotor 8 before and after medium modulation;

[0039] In the figure: 1. External air gap magnetic field, 2. External surface permanent magnet, 3. Middle permanent magnet, 4. External rotor, 5. External armature winding, 6. Inner armature winding, 7. Inner surface permanent magnet, 8. Inner rotor, 9. Stator, 10. Internal air gap magnetic field; 20. Sinusoidal contour line of external surface permanent magnet 2; 70. Sinusoidal contour line of internal surface permanent magnet 7: 21. Permanent magnet magnetomotive force curve of external air gap magnetic field 1 before modulation, 22. Permanent magnet magnetomotive force curve of external air gap magnetic field 1 after modulation. DETAILED DESCRIPTION

[0040] The following, combined with the accompanying drawings of the embodiments of the present invention, uses a dual-air-gap magnetic field modulation permanent magnet motor with a composite magnetic field as an example to clearly and completely describe the technical solutions of the present invention, including methods for analyzing composite magnetic field coupling using coupled harmonic groups and modulating the magnetic field. The embodiments described below with reference to the accompanying drawings are exemplary and intended only to explain the present invention, and are not to be construed as limiting the present invention.

[0041] like Figure 1As shown, the present invention is a dual-air-gap magnetic field modulation permanent magnet motor with a composite magnetic field. The motor comprises an outer rotor 4, a stator 9, and an inner rotor 8, arranged coaxially from outside to inside. The stator 9 includes 18 outer stator teeth and 18 inner stator teeth. The outer stator teeth are wound with outer armature windings 5, while the inner stator teeth are wound with inner armature windings 6. An outer air gap exists between the stator 9 and the outer rotor 4, generating an outer air gap magnetic field 1. An inner air gap exists between the stator 9 and the inner rotor 8, generating an inner air gap magnetic field 10. Eighteen outer permanent magnets 2 are attached to the side of the stator 9 near the outer air gap, and 18 outer and inner permanent magnets 7 are attached to the side of the stator 9 near the inner air gap. Eighteen intermediate permanent magnets 3 are evenly distributed between the inner and outer stator slots of the stator 9. These 18 intermediate permanent magnets 3 are magnetized alternately in the radial direction.

[0042] like Figure 2 The structure shown is a structure with a permanent magnet 2 attached to the surface, and the contour line of the outer side surface on the radial cross section is unfolded into a sinusoidal contour line 20.

[0043] like Figure 3 The structure shown is a structure with a permanent magnet 7 attached to the inner surface, and the contour line of the inner side surface on the radial cross section is unfolded into a sinusoidal contour line 70.

[0044] The present invention is based on the magnetic field coupling analysis method of the magnetic field modulation permanent magnet motor of the harmonic group. First, according to the permanent magnet excitation source is the external permanent magnet 2 and the middle permanent magnet 3, the armature magnetic source is the external armature winding 5, the reference magnetic density component B of the external air gap magnetic field 1 is obtained. n (θ, t); According to the permanent magnet excitation source is the inner surface permanent magnet 7 and the middle permanent magnet 3, the armature magnetic source is the inner armature winding 6 to obtain the coupling magnetic density component B of the external air gap magnetic field 1 c (θ, t). Then, according to the reference magnetic flux density component B of the external air gap magnetic field 1 n (θ,t) and the coupled magnetic flux density component B c (θ, t) synthesizes the air gap magnetic field 1 to obtain the air gap magnetic flux density B c_n (θ,t), is determined by the air gap magnetic flux density B c_n (θ, t) and the coupling effect ratio k c , harmonic characteristic factor k w And harmonic coupling efficiency η, then establish the positive and negative coupling harmonic groups pg, ng, and finally calculate the corresponding coupling efficiency η of the positive and negative coupling harmonic groups pg ,η ng , given by the coupling efficiency η pg ,η ng Analyze whether the coupling characteristics of the harmonic group meet the requirements. Analyze the positive effect of the composite magnetic field coupling of the magnetic field modulation motor on the motor performance from the perspective of the air gap harmonic group. This can quantitatively analyze the magnetic field coupling characteristics of the motor and improve the positive coupling characteristics through harmonic modulation. Figure 1 The magnetic field modulation permanent magnet motor in the embodiment has a composite magnetic field structure, with two air gap magnetic fields: an outer air gap magnetic field 1 and an inner air gap magnetic field 10. The outer air gap magnetic field 1 and the inner air gap magnetic field 10 are similar. The details are as follows:

[0045] Step 1: Based on the symmetry and periodicity of the magnetic circuit of the stator 9, establish an expression for the permanent magnetomotive force of the intermediate permanent magnet 3 on the stator 9.

[0046] like Figure 4 , is the function distribution diagram of the permanent magnetomotive force of the middle permanent magnet 3, the horizontal axis θ represents the mechanical angle, the vertical axis is the permanent magnetomotive force of the middle permanent magnet 3, P s is the number of pole pairs of the middle permanent magnet 3, θ s is the stator tooth width, F M is the magnetic potential amplitude of the middle permanent magnet 3, Figure 4 The permanent magnetomotive force F of the middle permanent magnet 3 can be obtained by Fourier decomposition of the magnetic potential function in o The expression of (θ) is:

[0047]

[0048] Among them, θ o is the initial phase of the i-th harmonic of the magnetic potential of the middle permanent magnet 3, F oi is the amplitude of the i-th magnetic potential harmonic, the magnetic potential harmonic amplitude F oi It is obtained from the following formula:

[0049]

[0050] Step 2: At the same time as step 1, according to the structure of the surface-mounted permanent magnet 2, an expression for the permanent magnetomotive force of the surface-mounted permanent magnet 2 is established.

[0051] like Figure 5 The function distribution of the permanent magnetomotive force of the surface-mounted permanent magnet 2 is shown in FIG. The horizontal axis θ represents the mechanical angle, and the vertical axis represents the permanent magnetomotive force of the surface-mounted permanent magnet 2. When the outer surface of the surface-mounted permanent magnet 2 is unfolded into a non-sinusoidal contour line, that is, non Figure 2 When the sinusoidal contour line 20 is shown, the magnetic potential amplitude is F f When the outer surface of the permanent magnet 2 is expanded into the sinusoidal contour line 20 shown in Figure 2, the magnetic potential amplitude is F fs .right Figure 5 The permanent magnetomotive force F of the permanent magnet 2 can be obtained by Fourier decomposition of the magnetic potential function in surface The expression of (θ) is:

[0052]

[0053] Among them, θ fis the initial phase of the i-th harmonic of the magnetic potential of the permanent magnet attached to the surface, F surface_i is the harmonic amplitude of the magnetic potential of the i-th surface-mounted permanent magnet. For the surface-mounted permanent magnet 2, if the contour line is a non-sinusoidal contour line, then F fs = 0. Based on the magnetic potential amplitude F f and F fs , magnetic potential harmonic amplitude F surface_i Calculated by the following formula:

[0054]

[0055] Step 3: The permanent magnetomotive force F of the intermediate permanent magnet 3 obtained in step 1 o (θ) and the permanent magnetomotive force F of the external permanent magnet 2 surface (θ) synthesis, the permanent magnet potential F of the outer air gap magnetic field 1 superimposed by the middle permanent magnet 3 and the outer permanent magnet 2 is obtained. pm (θ), its expression is:

[0056]

[0057] Among them, θ pm is the initial phase of the i-th harmonic of the external air gap magnetic field 1, F i is the amplitude of the i-th harmonic of the permanent magnet potential.

[0058] Step 4: Simultaneously with steps 1-3, establish the permeance expression of the outer rotor 4 according to the structure of the outer rotor 4.

[0059] like Figure 7 The permeance function distribution diagram of the outer rotor 4 is shown in the figure. The horizontal axis θ represents the mechanical position and the vertical axis represents the permeance. The permeance function is Fourier decomposed to obtain the permeance Λ(θ,t) of the outer air gap magnetic field 1:

[0060]

[0061] Among them, Λ k is the kth permeability harmonic amplitude, N r is the number of teeth of the outer rotor, Ω r is the mechanical speed of the outer rotor 4, and t represents time.

[0062] Step 5: The permanent magnet potential F of the external air gap magnetic field 1 obtained in step 3 pm (θ) is multiplied by the permeability Λ(θ,t) obtained in step 4 to obtain the permanent magnet flux density B PM The expression for (θ, t);

[0063]

[0064] Step 6: At the same time as step 5, calculate the magnetomotive force F generated by the three-phase armature winding of the outer armature winding 5 ABC (θ,t) is:

[0065]

[0066] Where ω is the electrical angular velocity, θ represents the mechanical position, and F m and F n They represent the amplitudes of the mth and nth harmonic armature magnetomotive force harmonics respectively.

[0067] Step 7: The synthetic magnetomotive force F generated by the outer armature winding 5 in step 6 ABC Multiply (θ, t) by the permeability Λ(θ, t) of the external air gap magnetic field 1 in step 4 to obtain the armature flux density B AM The expression of (θ,t) is:

[0068]

[0069] Step 8: Place the permanent magnet B in step 5 PM (θ, t) and the armature flux density B in step 7 AM (θ, t) synthesis, the reference magnetic flux density component B of the external air gap magnetic field 1 is obtained n (θ,t) is:

[0070]

[0071] From the above formula, we can see that B τ is the harmonic amplitude of the τth sub-reference magnetic density component, θ τ (t) is the function of the phase of the harmonic of the τ-th reference magnetic density component changing with time.

[0072] It can be seen from this that the reference magnetic flux density component B of the external air gap magnetic field 1 is n The permanent magnet excitation sources of (θ, t) are the outer surface permanent magnet 2 and the middle permanent magnet 3, and the armature magnetic source is the outer armature winding 5.

[0073] Step 9: Based on steps 1-8, for the inner surface permanent magnet 7 and the inner armature winding 6, the permanent magnetic excitation source is the inner surface permanent magnet 7 and the middle permanent magnet 3, and the armature magnetic source is the inner armature winding 6. The method similar to steps 1-8 is used to obtain the coupling magnetic density component B of the external air gap magnetic field 1. c (θ,t).

[0074] In this process, the only difference is steps 2 and 6: In step 2, the outer surface permanent magnet 2 is replaced by the inner surface permanent magnet 7, and the permanent magnet magnetomotive force of the inner surface permanent magnet 7 is obtained in step 2. In step 6, the outer armature winding 5 is replaced by the inner armature winding 6, and the resultant magnetomotive force of the inner armature winding 6 is generated in step 6. Then, in step 8, the permanent magnet flux density in step 5 and the armature flux density in step 7 are combined to obtain the coupled flux density component B of the external air gap magnetic field 1. c (θ,t) is:

[0075]

[0076] From the above formula, we can see that B cτ is the harmonic amplitude of the τ-th coupling magnetic flux density component, θ cτ (t) is the function of the phase of the harmonic of the τ-order coupling magnetic density component changing with time.

[0077] Step 10: The reference magnetic flux density component B of the external air gap magnetic field 1 n (θ, t) and the coupling magnetic flux density component B c The projection of (θ, t) in the reference magnetic flux direction is synthesized to obtain the air gap magnetic flux B of the external air gap magnetic field 1. c_n (θ,t) is:

[0078]

[0079] From the above formula, we can know that the amplitude of the τth harmonic of the air gap magnetic flux density is {B τ +B cτ cos[θ cτ (t)-θ τ (t)]}, is the harmonic amplitude of the reference magnetic density component B τ and the coupling magnetic density component harmonic amplitude B cτ cos[θ cτ (t)-θ τ (t)] was synthesized.

[0080] Step 11: Since the τth harmonic amplitude of the air gap magnetic flux density {B cτ cos[θ cτ (t)-θ τ (t)]+B τ} is the harmonic amplitude of the reference magnetic density component B τ and the coupling magnetic density component harmonic amplitude B cτ cos[θ cτ (t)-θ τ (t)] is synthesized, so the harmonic amplitude of the reference magnetic density component B τ and the coupling magnetic density component harmonic amplitude B cτ cos[θ cτ (t)-θτ (t)] will affect the air gap magnetic density harmonic amplitude {B cτ cos[θ cτ (t)-θ τ (t)]+B τ}, and its influence is expressed by the coupling magnetic density component harmonic amplitude B cτ cos[θ cτ (t)-θ τ (t)] divided by the harmonic amplitude of the reference magnetic density component B τ The obtained coupling effect ratio k c express:

[0081]

[0082] According to the coupling effect ratio k c Evaluate the effect of coupling magnetic flux density harmonics on the air gap magnetic flux density harmonic amplitude {B cτ cos[θ cτ (t)-θ τ (t)]+B τ}. If k c >0, indicating that the component of the coupled magnetic flux harmonic in the direction of the reference magnetic flux harmonic is in the same direction as the reference magnetic flux harmonic, and the synthesized air gap magnetic flux harmonic amplitude {B cτ cos[θ cτ (t)-θ τ (t)]+B τ Higher than the reference magnetic density harmonic amplitude B τ , that is, the coupling magnetic flux density harmonic has an enhanced effect on the air gap magnetic flux harmonic. On the contrary, if k c <0, that is, the coupling magnetic density component harmonics weaken the air gap magnetic density harmonics. c = 0, the coupling magnetic flux density harmonics are orthogonal to the reference magnetic flux density harmonics and do not affect the amplitude of the air gap magnetic flux density harmonics {B cτ cos[θ cτ (t)-θ τ (t)]+B τ}.

[0083] Step 12: To determine the impact of the coupling flux density harmonics on the motor performance, we need to further determine whether the weakening or strengthening effect of the coupling flux density harmonics on the air gap flux harmonic amplitude occurs in the working magnetic field, thereby affecting the output torque. In other words, it is necessary to determine whether the air gap flux harmonics are working harmonics. Define the harmonic characteristic factor k w To determine whether the air gap harmonic is a working harmonic, first calculate the winding slot angle α w and harmonic slot angle α p , the specific expression is:

[0084]

[0085] Among them, N st is the number of stator teeth, α w is the winding slot angle, α p is the harmonic slot angle of the τth harmonic.

[0086] Define the harmonic characteristic factor k w To determine whether the τth air gap magnetic density harmonic is a working harmonic, if α w =α p , then the air gap magnetic density harmonic is the working harmonic, and the harmonic characteristic factor k w = 1. On the contrary, if α w ≠α p , then the air gap magnetic density harmonic is a non-working harmonic, and the harmonic characteristic factor is k w =-1, the specific expression is:

[0087]

[0088] Step 13: Based on the coupling effect ratio k obtained in step 11 c and the harmonic characteristic factor k obtained in step 12 w The harmonic coupling efficiency η of a single coupled harmonic is calculated as:

[0089] η=k c ·k w ×100%,

[0090] The harmonic coupling efficiency η can evaluate the harmonic coupling efficiency of the τ-th coupled harmonic of the coupled magnetic flux density component harmonic characteristics. The type of coupled magnetic flux density component harmonic can be determined based on the sign of the harmonic coupling efficiency η. If η>0, the τ-th coupled magnetic flux density component harmonic is a positive coupled harmonic; if η=0, the τ-th coupled magnetic flux density component harmonic is a neutral harmonic; if η<0, the τ-th coupled magnetic flux density component harmonic is a negative coupled harmonic. It can be specifically expressed by the following formula:

[0091]

[0092] Step 14: All positive coupled harmonics are established as a set, namely, the positive coupled harmonic group pg, and all negative coupled harmonics are established as a set of negative coupled harmonic group ng, which is expressed by the following formula:

[0093]

[0094] Among them, p1, p2…, p σ represents σ positive coupled harmonics, n1, n2…, n ε represents ε negative coupling harmonics, N + Represents a positive integer.

[0095] Harmonic coupling efficiency η=k based on a single coupled harmonic c ·k w × 100%, and the coupling efficiency η of the positive coupling harmonic group is obtained. pg and the coupling efficiency η of the negative coupling harmonic group ng :

[0096]

[0097] Among them, η p1 ,η p2 ,…,η pσ They represent the σ positive coupled harmonics p1, p2…, p in the positive coupled harmonic group pg. σ Harmonic coupling efficiency, η n1 ,η n2 ,…,η nε They represent the ε positive coupled harmonics n1, n2…, n in the negative coupled harmonic group ng. ε Harmonic coupling efficiency.

[0098] Coupling efficiency η of the positively coupled harmonic group pg and the coupling efficiency η of the negative coupling harmonic group ng The value is used to analyze the coupling characteristics of the harmonic group: when the coupling efficiency of the positive coupling harmonic group is η pg The value is higher than 300%, and the coupling efficiency η of the negative coupling harmonic group ng When the value is lower than 150%, the coupling characteristics of the motor's harmonic groups meet the requirements; otherwise, the coupling characteristics of the motor's harmonic groups do not meet the requirements.

[0099] When the coupling characteristics of the motor's harmonic group do not meet the requirements, modulation is required. Then, the magnetic field coupling modulation method of the permanent magnet motor based on the magnetic field modulation of the harmonic group of the present invention is adopted. The specific modulation method is as shown in steps 15-16:

[0100] Step 15: When the coupling characteristics of the motor's harmonic group do not meet the requirements, the contour line of the outer surface of the motor's surface-mounted permanent magnet on the radial section is designed to be a sine line. When the contour line of the motor's surface-mounted permanent magnet 2 is a non-sinusoidal line, the radial thickness of the surface-mounted permanent magnet 2 can be changed first, and then steps 1 to 14 can be repeated until the coupling characteristics of the harmonic group meet the requirements.

[0101] When the coupling characteristics of the motor's harmonic group do not meet the requirements, and the contour line of the motor's outer surface adjacent to the permanent magnet 2 is a sine line, that is, Figure 2 The sinusoidal contour line 20 shown in FIG. 2 needs to adjust the amplitude and phase of the sinusoidal contour line of the external permanent magnet 2 to achieve amplitude modulation and phase modulation of the harmonics. The specific method includes the following:

[0102] Step A: If Figure 8 , is the permanent magnetomotive force distribution of the external air gap magnetic field 1 before and after modulation, the horizontal axis θ represents the mechanical position, and the vertical axis is the permanent magnetomotive force of the external air gap magnetic field 1 before and after modulation. Figure 8 The permanent magnetomotive force curve 21 of the outer air gap magnetic field 1 before modulation and the permanent magnetomotive force curve 22 of the air gap magnetic field I after modulation are compared with the permanent magnetomotive force curve 21 of the outer air gap magnetic field 1 before modulation. Figure 6 The permanent magnet magnetomotive force curve 21 shown, Figure 8 The modulated permanent magnet magnetomotive force curve 22 shows that the structure of the surface-attached permanent magnet 2 has changed. Figure 8 The amplitude change of the sinusoidal contour line of the permanent magnet 2 is ΔF i , the phase change is Δθ pm .

[0103] Before modulation, the permanent magnet potential F in step 3 pm (θ) is:

[0104]

[0105] After modulation, the permanent magnet potential expression in step 3 becomes F' pm (θ):

[0106]

[0107] In the expression of permanent magnet potential after modulation, the amplitude of the i-th harmonic of permanent magnet potential before modulation and the amplitude change are Δ F i Add together the initial phase of the i-th magnetic potential harmonic before modulation and the phase change is Δθ pm When the contour line of the external permanent magnet is non-sinusoidal, since only the radial thickness of the external permanent magnet 2 is changed, the permanent magnet potential F' pm (θ) only contains the amplitude change of the permanent magnet potential harmonic ΔF i , phase change Δθ pm =0.

[0108] It can be seen from this that the change in the amplitude and phase of the sinusoidal contour line of the external permanent magnet 2 brings about the change in the harmonics of the permanent magnet magnetic potential, thereby achieving a modulation effect on the harmonics.

[0109] Step B: Repeat the above steps 4 to 14. The difference is that due to the change of the sinusoidal contour line 20 of the external permanent magnet 2, the amplitude and phase of the air gap harmonics are affected. After modulation, the positive and negative coupling efficiency of the harmonic group in step 14 becomes η' pg and η' ng , the positive coupling efficiency of the modulated harmonic group η' pg The value is higher than 300%, and the negative coupling efficiency η' of the harmonic groupng If the value is lower than 150%, the harmonic coupling characteristics of the motor meet the requirements.

[0110] Step 16: Similar to the outer air gap magnetic field 1, repeat steps 1-15 to obtain the coupling efficiency of the positive and negative coupled harmonic groups of the inner air gap magnetic field 10. The analysis method for the harmonic coupling characteristics of the inner air gap magnetic field 10 is similar to that of the outer air gap magnetic field 1, except that step 2 is replaced by the permanent magnetomotive force of the inner surface-mounted permanent magnet 7, step 3 is replaced by the permanent magnetomotive force of the inner air gap magnetic field 10, step 4 is replaced by the magnetic permeance of the inner rotor 8, the three-phase armature winding composite magnetomotive force in step 6 is generated by the inner armature winding 6, and step 8 is replaced by the reference flux density component of the inner air gap magnetic field 10. Step 9 is the coupled flux density component of the inner air gap magnetic field 10, which is the synthesis of the permanent magnet flux density generated by the middle permanent magnet 3 and the outer surface-mounted permanent magnet 2 and the armature flux density formed by the outer armature winding 5.

[0111] Figure 9 and Figure 10 These are the harmonic coupling efficiency distributions of the positive and negative coupling harmonics of the outer air gap magnetic field 1 and the inner air gap magnetic field 10 , respectively, corresponding to the calculation result of the harmonic coupling efficiency η in step 13 .

[0112] Figure 9 is a coupling efficiency distribution diagram of the coupled harmonics of the external air gap magnetic field 1 before and after modulation. Among them, the coupling efficiencies of the 5th, 13th, and 31st harmonics of the external air gap magnetic field 1 are positive. According to the definition of positive and negative coupled harmonic groups in step 14, the 5th, 13th, and 31st harmonics of the external air gap magnetic field 1 constitute a positive coupled harmonic group; the coupling efficiencies of the 19th and 33rd harmonics are negative, constituting a negative coupled harmonic group.

[0113] Figure 10 is the coupling efficiency distribution of the coupled harmonics of the inner air gap magnetic field 10 before and after modulation. Similar to the external air gap magnetic field 1, the 5th, 13th, and 41st harmonics of the inner air gap magnetic field 10 constitute a positive coupled harmonic group, and the 37th harmonic is a negative coupled harmonic.

[0114] Depend on Figure 9 and Figure 10 It can be seen that the harmonic coupling efficiency has changed after modulation, and the positive harmonic coupling efficiency has increased after modulation, which to a certain extent confirms the effectiveness of using harmonic modulation to improve the harmonic coupling characteristics.

[0115] Figure 11 is the harmonic group coupling efficiency before and after modulation of the external air gap magnetic field 1, corresponding to η in step 14 pg is the harmonic group coupling efficiency of the positive coupling harmonic group pg, and the harmonic group coupling efficiency η of the negative coupling harmonic group ng ng .Depend on Figure 11 It can be seen that the positive coupling efficiency η of the harmonic group before modulation pgIt is 253.1%, which is lower than 300% and does not meet the requirements. Corresponding to step 15, if the coupling characteristics do not meet the requirements, the harmonics are amplitude and phase modulated, and the positive coupling efficiency of the modulated harmonic group is η' pg Reaching 321.9%, higher than 300%, and the harmonic group negative coupling efficiency η' ng It is 133.0%, lower than 150%, which meets the requirements.

[0116] Figure 12 The back-EMF fundamental amplitude of the outer armature winding 5 and the average torque output by the outer rotor 4 before and after modulation are compared. As can be seen from the figure, the back-EMF fundamental amplitude and the average torque are improved after modulation.

[0117] Similar to the external air gap magnetic field 1, Figure 13 is the harmonic group coupling efficiency before and after modulation of the inner air gap magnetic field 10, given by Figure 13 It can be seen that the positive coupling efficiency η of the harmonic group before modulation pg It is 285.7%, which is lower than 300% and does not meet the requirements. After harmonic modulation, the positive coupling efficiency of the harmonic group η' pg Reaching 345.3%, higher than 300%, and the harmonic group negative coupling efficiency η' ng It is 135.3%, which is lower than 150% and meets the requirements.

[0118] Figure 14 Comparing the back-EMF fundamental amplitude of inner armature winding 6 and the average torque output by inner rotor 8 before and after modulation, both the back-EMF fundamental amplitude and average torque increase after harmonic modulation. This indicates that harmonic modulation improves the positive coupling efficiency of the harmonic group, ensuring it meets harmonic characteristic requirements, and improves the coupling characteristics of the air gap magnetic field harmonics, thereby enhancing motor performance.

[0119] In summary, the present invention discloses a magnetic field coupling analysis and modulation method of a magnetic field modulated permanent magnet motor based on a harmonic group. According to the magnetic source and modulator structure of the composite magnetic field, the benchmark and coupling magnetic density models are established respectively, and the coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency are defined. The coupling harmonic type is judged by the harmonic coupling efficiency, and the positive and negative coupling harmonic groups of the motor are determined. The harmonic coupling characteristics are evaluated according to the positive and negative coupling efficiencies of the harmonic group. Harmonic modulation is achieved by adjusting the amplitude and phase of the sinusoidal contour line of the surface-mounted permanent magnet, and the harmonic coupling characteristics after modulation are improved, thereby improving the average torque of the motor. The present invention proposes a method for constructing a composite magnetic field coupled harmonic group of a magnetic field modulated motor, and realizes a quantitative evaluation of the harmonic coupling characteristics by defining the harmonic group coupling efficiency, and improves the coupling characteristics by improving the positive coupling efficiency of the harmonic group, thereby improving the torque performance of the motor.

[0120] 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 method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups, characterized by: According to the permanent magnet excitation source being the outer surface permanent magnet and the middle permanent magnet of the motor and the armature magnetic source being the outer armature winding of the motor, a reference magnetic flux density component of the outer air gap magnetic field of the motor is obtained; According to the permanent magnet excitation source being the inner surface mounted permanent magnet and the middle permanent magnet of the motor, and the armature magnetic source being the inner armature winding of the motor, the coupling magnetic flux density component of the outer air gap magnetic field of the motor is obtained by a method similar to that for obtaining the reference magnetic flux density component; The air gap magnetic flux of the external air gap magnetic field is obtained by synthesizing the reference magnetic flux component and the coupling magnetic flux component; The coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency are calculated in sequence from the air gap magnetic flux density; Determining positive and negative coupling harmonics based on the harmonic coupling efficiency; Establishing corresponding positive and negative coupling harmonic groups from the positive and negative coupling harmonics, respectively, and calculating the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups; Analyze whether the motor magnetic field coupling meets the requirements based on the positive and negative coupling efficiencies; The reference magnetic flux density component of the external air gap magnetic field is B n (θ, t), is determined by the permanent magnet flux density B PM (θ, t) and armature flux density B AM (θ, t) is synthesized to obtain: B n (θ,t)=B PM (θ,t)+B AM (θ,t)=∑B τ ∠[τθ-θ τ (t)],τ=|iP s +kN r |, The coupling magnetic flux density component of the external air gap magnetic field θ is the mechanical angle of the motor, t is the time, B τ is the harmonic amplitude of the τth sub-reference magnetic density component, θ τ (t) is the function of the phase of the harmonic of the τth reference magnetic density component changing with time, i is the order of the magnetic potential harmonic, which is an odd number 1, 3, 5, ..., k is the order of the magnetic permeability harmonic, which is 0, ±1, ±2, ..., P s is the number of pole pairs of the middle permanent magnet of the motor, N r Number of teeth on the outer rotor of the motor, B cτ is the harmonic amplitude of the τ-th coupling magnetic flux density component, θ cτ (t) is the function of the harmonic phase of the τ-order coupling magnetic flux density component changing with time.

2. The magnetic field coupling analysis method of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 1 is characterized by: The permanent magnet magnetic density B PM (θ,t) is determined by the permanent magnet potential F of the external air gap magnetic field pm Multiplying (θ) and permeance Λ(θ,t) yields: F i is the amplitude of the i-th harmonic of permanent magnet potential, Λ k is the kth permeability harmonic amplitude, Ω r is the mechanical speed of the motor's outer rotor, θ pm is the initial phase of the i-th magnetic potential harmonic of the external air gap magnetic field.

3. The magnetic field coupling analysis method of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 2 is characterized by: The permanent magnet potential F of the external air gap magnetic field pm (θ) is determined by the permanent magnetomotive force F of the middle permanent magnet of the motor. o (θ) and the permanent magnetomotive force F of the permanent magnet attached to the surface surface (θ) is synthesized to obtain: The magnetic permeability 4. The method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 3 is characterized by: The permanent magnetomotive force of the intermediate permanent magnet The amplitude of the i-th magnetic potential harmonic θ o is the initial phase of the i-th harmonic magnetic potential of the middle permanent magnet, F M is the magnetic potential amplitude of the middle permanent magnet; The permanent magnetomotive force of the surface-mounted permanent magnet θ f is the initial phase of the i-th harmonic of the magnetic potential of the surface-mounted permanent magnet, and the i-th harmonic amplitude of the magnetic potential of the surface-mounted permanent magnet F f is the magnetic potential amplitude when the outer side of the permanent magnet is unfolded into a non-sinusoidal contour line on the radial section. On the contrary, when it is a sinusoidal contour line, the magnetic potential amplitude is F fs ,θ s is the stator tooth width.

5. The method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 1 is characterized by: The armature magnetic flux B AM (θ, t) is the resultant magnetomotive force F generated by the outer armature winding of the motor ABC (θ, t) is multiplied by the magnetic permeability Λ(θ, t) of the external air gap magnetic field, and the synthetic magnetomotive force is obtained. The magnetic permeability ω is the electrical angular velocity, F m and F n are the amplitudes of the mth and nth harmonic armature magnetic potential harmonics, Λ k is the kth permeability harmonic amplitude, N r is the number of teeth of the outer rotor of the motor, Ω r is the mechanical speed of the motor's outer rotor, and t is time.

6. The method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 1 is characterized by: The air gap magnetic field of the external air gap magnetic field 7. The method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 6 is characterized by: The coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency are calculated in sequence from the air gap magnetic density: first calculate the coupling effect ratio Then calculate the winding slot angle Harmonic slot angle of τ subharmonic Determine when α w =α p When the harmonic characteristic factor k w =1, when α w ≠α p When the harmonic characteristic factor k w =-1; finally calculate the harmonic coupling efficiency η = k c ·k w ×100%,N st is the number of stator teeth.

8. The method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 7 is characterized by: The positive and negative coupling harmonics are used to establish corresponding positive and negative coupling harmonic groups, respectively. The positive coupling harmonic group pg = {p1, p2, ..., p σ },σ∈N + , negative coupling harmonic group ng={n1,n2,…,n ε }, ε∈N + ,p1,p2…,p σ They are the 1st, 2nd,…,σth positive coupled harmonics, n1, n2…, n ε are the 1st, 2nd, …, εth negative coupling harmonics, N + represents a positive integer; Calculate the positive coupling efficiency and negative coupling efficiency η p1 ,η p2 ,…,η pσ They represent the σ positive coupled harmonics p1, p2…, p in the positive coupled harmonic group pg. σ Harmonic coupling efficiency, η n1 ,η n2 ,…,η nε They represent the ε negative coupled harmonics n1, n2…, n in the negative coupled harmonic group ng. ε Harmonic coupling efficiency.

9. The method for analyzing magnetic field coupling of a permanent magnet motor with magnetic field modulation based on harmonic groups according to claim 8 is characterized by: When the positive coupling efficiency η pg The value of is higher than 300%, and the negative coupling efficiency η ng When the value is lower than 150%, the coupling characteristics of the motor's harmonic groups meet the requirements; otherwise, they do not meet the requirements.

10. A magnetic field coupling modulation method for a permanent magnet motor based on magnetic field modulation of a harmonic group, characterized by: According to the permanent magnet excitation source being the outer surface permanent magnet and the middle permanent magnet of the motor and the armature magnetic source being the outer armature winding of the motor, a reference magnetic flux density component of the outer air gap magnetic field of the motor is obtained; According to the permanent magnet excitation source being the inner surface mounted permanent magnet and the middle permanent magnet of the motor, and the armature magnetic source being the inner armature winding of the motor, the coupling magnetic flux density component of the outer air gap magnetic field of the motor is obtained by a method similar to that for obtaining the reference magnetic flux density component; The air gap magnetic flux of the external air gap magnetic field is obtained by synthesizing the reference magnetic flux component and the coupling magnetic flux component; The coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency are calculated in sequence from the air gap magnetic flux density; Determining positive and negative coupling harmonics based on the harmonic coupling efficiency; Establishing corresponding positive and negative coupling harmonic groups from the positive and negative coupling harmonics, respectively, and calculating the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups; Analyze whether the motor magnetic field coupling meets the requirements based on the positive and negative coupling efficiencies; When the analysis of the positive and negative coupling efficiencies shows that the motor magnetic field coupling does not meet the requirements, the contour line of the outer surface of the motor's stator surface-mounted permanent magnet on the radial section is designed to be a non-sinusoidal line, the radial thickness of the surface-mounted permanent magnet is changed, the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups are recalculated, and the motor magnetic field coupling is reanalyzed until the coupling characteristics of the harmonic group meet the requirements.

11. A magnetic field coupling modulation method for a permanent magnet motor based on magnetic field modulation of a harmonic group, characterized by: According to the permanent magnet excitation source being the outer surface permanent magnet and the middle permanent magnet of the motor and the armature magnetic source being the outer armature winding of the motor, a reference magnetic flux density component of the outer air gap magnetic field of the motor is obtained; According to the permanent magnet excitation source being the inner surface mounted permanent magnet and the middle permanent magnet of the motor, and the armature magnetic source being the inner armature winding of the motor, the coupling magnetic flux density component of the outer air gap magnetic field of the motor is obtained by a method similar to that for obtaining the reference magnetic flux density component; The air gap magnetic flux of the external air gap magnetic field is obtained by synthesizing the reference magnetic flux component and the coupling magnetic flux component; The coupling effect ratio, harmonic characteristic factor and harmonic coupling efficiency are calculated in sequence from the air gap magnetic flux density; Determining positive and negative coupling harmonics based on the harmonic coupling efficiency; Establishing corresponding positive and negative coupling harmonic groups from the positive and negative coupling harmonics, respectively, and calculating the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups; Analyze whether the motor magnetic field coupling meets the requirements based on the positive and negative coupling efficiencies; When the analysis of the positive and negative coupling efficiencies shows that the motor magnetic field coupling does not meet the requirements, the contour line of the outer surface of the surface-mounted permanent magnet of the motor on the radial section is designed to be a sine line, the amplitude and phase of the sine contour line of the surface-mounted permanent magnet are adjusted, the amplitude of the permanent magnet magnetic potential harmonic before modulation is added to the amplitude change, and the initial phase of the magnetic potential harmonic before modulation is added to the phase change, so as to obtain the corresponding positive and negative coupling efficiencies of the positive and negative coupling harmonic groups that meet the coupling characteristic requirements.

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