Magnetic conductance space attenuation characteristic-based electromagnetic torque layered modeling method

Abstract

The invention discloses an electromagnetic torque layered modeling method based on magnetic conductance space attenuation characteristics, and relates to the technical field of permanent magnet motors, and the method comprises the steps: building an electromagnetic parameter expression through motor parameters; determining magnetomotive force parameter expressions of an armature and a permanent magnet through motor pole slot cooperation and a winding mode, and thus obtaining magnetomotive force harmonic waves; according to the condition that the number of magnetic field pole pairs in the electromagnetic parameter expression is the same, an armature magnetic field source generating average torque is limited, and an armature magnetomotive force source is determined to modulate the magnetic conductance order; determining air gap space magnetic conductance through conformal transformation; spatial layering and harmonic attenuation law analysis are carried out aiming at air gap space magnetic conductance, electromagnetic layering torque considering space attenuation characteristics is calculated through magnetomotive force harmonic and magnetic conductance harmonic modulation coupling, and weighting is carried out on the electromagnetic layering torque to obtain the total torque of the motor. According to the method, the torque modeling precision of the permanent magnet vernier motor is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet motors, and in particular to a layered modeling method of electromagnetic torque based on spatial attenuation characteristics of magnetic permeance. Background Art

[0002] Torque modeling and analysis are key technologies in the study of permanent magnet vernier motors. Traditional methods for torque modeling in permanent magnet motors focus on magnetic field analysis, flux distribution, and electromagnetic force calculation. However, the unique permeance modulation mechanism of permanent magnet vernier motors complicates torque generation. While existing technologies can provide basic torque expressions, they do not fully account for the impact of the air gap permeance on the spatial torque attenuation distribution that occurs as the slotting effect weakens.

[0003] When modeling motor torque for multi-harmonic motors such as permanent magnet vernier motors, the spatial attenuation of the slotting effect is not considered, resulting in spatial attenuation of the magnetic permeance, which leads to stratified torque attenuation and further reduces modeling accuracy. The spatial attenuation of magnetic permeance causes stratification, which further leads to spatial attenuation of torque, thus affecting the accuracy of torque calculation. Since the spatial attenuation of magnetic permeance is inconsistent for different orders of magnetic permeance, the spatial attenuation of torque modulated by each order of magnetic permeance is inconsistent, causing the total torque to not follow the spatial attenuation law of a single magnetic permeance. For example, the application of the traditional equivalent magnetic circuit method can only obtain a set of overall curves that represent the general situation of the air gap magnetic permeance. Although the modeling of the motor torque is achieved, there are still problems with insufficient modeling accuracy and the inability to reflect the actual magnetic field modulation conditions at various locations within the air gap. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide an electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance. The present invention subdivides the modulation phenomenon within the motor and performs torque spatial hierarchical modeling for different modulation magnetic permeances, thereby improving the accuracy of motor torque modeling and making the source of torque attenuation clearer.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] According to the present invention, a hierarchical modeling method of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeance is proposed, comprising:

[0007] Establish electromagnetic parameter expressions through motor parameters;

[0008] Through the motor pole slot matching and winding method, the armature and permanent magnet magnetomotive force parameter expressions are determined, and the magnetomotive force harmonics are obtained accordingly;

[0009] According to the same condition of magnetic field pole pairs in the electromagnetic parameter expression, the source of the armature magnetic field that generates the average torque is limited, and the source of the armature magnetomotive force is determined to modulate the permeance order;

[0010] Determine the air gap space magnetic permeability through conformal transformation;

[0011] The spatial stratification and harmonic attenuation law of the air gap magnetic permeability are analyzed. The electromagnetic stratification torque taking into account the spatial attenuation characteristics is calculated through the modulation coupling of the magnetomotive force harmonics and the magnetic permeability harmonics. The weighted electromagnetic stratification torque is the total torque of the motor.

[0012] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeance described in the present invention, the armature and permanent magnet magnetomotive force parameter expressions are determined by the motor pole slot matching and winding method; the details are as follows:

[0013] Separate the permanent magnet information, armature side slot, and pitch information to obtain the rotor permanent magnet magnetomotive force F r (θ, t) and the armature magnetomotive force F s (x) expression, characterized by:

[0014]

[0015] Among them, B r is the remanence of the permanent magnet, h m is the thickness of the permanent magnet, α is the pole arc coefficient, v is the harmonic order, p r is the number of permanent magnet pole pairs, ω is the angular velocity of the permanent magnet, t is time, i is the armature current, N c is the number of winding turns, k sv 、k yv are the motor slot coefficient and pitch coefficient respectively, x is the motor tangential position, μ0 is the spatial magnetic permeability, μ r is the relative permeability, θ is the initial phase angle, is the rotor mechanical angle; it is represented by Fourier decomposition form:

[0016]

[0017] Where j is the harmonic order, A j is the j-order magnetomotive force amplitude, Ω r is the rotor mechanical speed, ω s is the electrical frequency, ω s =P r Ω r , k is the harmonic order, F k is the k-order magnetomotive force harmonic amplitude, is the magnetomotive force of the permanent magnet.

[0018] As a further optimization scheme of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of the magnetic permeance described in the present invention, the equation for determining the source of the armature magnetomotive force to modulate the magnetic permeance order is:

[0019] |k±j λ N s |=p r

[0020] Among them, j λ is the order of the permeance harmonics caused by the unit slot, N s is the number of stator slots.

[0021] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of the magnetic permeance described in the present invention, the air gap magnetic permeance is determined by conformal transformation; the details are as follows:

[0022] First, the unit slot topology of the circularly symmetric motor and the corresponding rotor wall composition are used to obtain the physical model boundary of the magnetic permeance;

[0023] Secondly, the magnetic potential information of each position of the concentric ring between the stator wall and the rotor wall is obtained through conformal mapping and physical model boundaries.

[0024] Then, based on the magnetic potential information, the air gap length h, and Maxwell's equations, the gradient of the magnetic potential in the direction of the air gap length is calculated to obtain the spatial relative magnetic permeance at each position in space, that is, the air gap spatial magnetic permeance.

[0025] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeance described in the present invention, the spatial stratification and harmonic attenuation law analysis of the air gap magnetic permeance is carried out. Through the modulation coupling of magnetomotive force harmonics and magnetic permeance harmonics, the electromagnetic layered torque taking into account the spatial attenuation characteristics is calculated. The total torque of the motor is obtained by weighting the electromagnetic layered torque; the details are as follows:

[0026] The air gap permeability is layered and Fourier decomposed to obtain the distribution law of each order permeability in the air gap space;

[0027] According to the coordination between different orders of magnetomotive force and different orders of magnetic permeance, the magnetomotive force of the corresponding order is multiplied by the magnetic permeance to obtain the modulated armature magnetic field and the modulated permanent magnet magnetic field, and the electromagnetic torque expression is derived; the air gap space magnetic permeance of all spatial positions is traversed and substituted into the electromagnetic torque expression to calculate the electromagnetic stratified torque with spatial attenuation characteristics, and the weighted stratified torque is the total torque of the motor.

[0028] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeance described in the present invention, the distribution law of each order of magnetic permeance in the air gap space is: the DC magnetic permeance has a stable content in the space, while the attenuation laws between the harmonic magnetic permeances are inconsistent.

[0029] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeability described in the present invention, the conformal mapping is a logarithmic mapping and a Schwarz-Christoffel mapping.

[0030] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeance described in the present invention, the method of obtaining the spatial relative magnetic permeance at each position in space is:

[0031] The magnetic field intensity H after the slot is obtained by Maxwell's equations slot :

[0032]

[0033] in, is the gradient operator, is the air gap magnetic potential, is the magnetic position information, σ is the equivalent air gap length of the motor;

[0034] Magnetic field strength H when no slots are cut noslot for

[0035]

[0036] in, is the magnetic potential difference between the stator and rotor sides;

[0037] H slot / H noslot It is the spatial relative permeability of each position after slotting, that is, the air gap space permeability.

[0038] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeance described in the present invention,

[0039] According to the magnetic field modulation theory, the condition is that the modulation permeability order is not higher than 3, and the working armature magnetomotive force is determined as: p r 、p r +N s 、p r -N s 、p r +2N s 、p r -2N s 、p r +3N s 、p r -3N s The secondary armature magnetomotive force corresponds to the 0th, 1st, 1st, 2nd, 2nd, 3rd, and 3rd permeance modulation in space respectively.

[0040] As a further optimization scheme of the electromagnetic torque layered modeling method based on the spatial attenuation characteristics of magnetic permeance described in the present invention, the method for calculating the electromagnetic layered torque with spatial attenuation characteristics is as follows:

[0041] The modulated armature magnetic field and the modulated permanent magnetic field are obtained by multiplying the specific magnetomotive force obtained by Fourier decomposition with the specific modulation permeance, ensuring that the number of pole pairs of the modulation magnetic field is P. r antipodes;

[0042] Among them, the specific magnetomotive force that modulates the armature magnetic field is p r 、p r +N s 、p r -N s 、p r +2N s 、p r -2N s 、p r +3N s 、p r -3N s The specific modulation permeance corresponds to the 0th, 1st, 1st, 2nd, 3rd and 3rd order permeance respectively; the specific modulation permeance of the permanent magnetic field is p r Permanent magnetomotive force, specific modulation permeance is 0th order permeance; where p r is the number of permanent magnet pole pairs, N s is the number of stator slots;

[0043] The number of pole pairs is the same, and the formula for the electromagnetic torque T of each set of armature magnetic field coupled with the permanent magnet magnetic field is:

[0044] T=vπlrB am_v B pm_v sin(θ am_v -θ pm_v )

[0045] Among them, v is the harmonic order, which is fixed here as the number of permanent magnet pole pairs P r , l is the axial length of the motor, r is the air gap radius, B am_v is the vth harmonic of the armature modulation flux density, B pm_v is the vth harmonic of the permanent magnet modulated magnetic flux density, θ am_v is the phase angle of the harmonic of the vth armature modulation flux density, θ pm_v Modulate the magnetic density harmonic phase angle of the vth permanent magnet;

[0046] B pm_v The fundamental magnetomotive force of the permanent magnet is modulated by DC permeance, B am_v It is derived from the magnetic permeability of the corresponding layers at different air gap radii r, and the electromagnetic torque T represents the contribution of the corresponding armature magnetomotive force torque.

[0047] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0048] (1) The present invention breaks the conventional permanent magnet vernier motor torque modeling method and introduces conformal mapping for the first time to explain the attenuation and stratification distribution of torque in the air gap space, intuitively reflecting the influence of different permeability harmonics on the modulated torque.

[0049] (2) By analyzing the attenuation distribution law of magnetic permeance in space, the present invention makes the spatial attenuation of each torque formed by the modulation of each order of magnetic permeance more accurate, can accurately describe the relationship between each order of modulated magnetic permeance and the motor torque, and give the spatial distribution ratio of each type of electromagnetic torque. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The system structure of the method of the present invention.

[0051] Figure 2 The original topology of the motor being modeled and tested.

[0052] Figure 3 The spatial attenuation distribution of the air gap permeability harmonics of the motor is tested for this modeling.

[0053] Figure 4 Schematic diagram of the spatial attenuation distribution of the motor torque for this modeling test.

[0054] Figure 5 Schematic diagram of the attenuation law of the torque modulated by fundamental magnetic permeability in space and the magnetic permeability attenuation law.

[0055] Figure 6 Schematic diagram of the attenuation law of the torque modulated by second harmonic permeability in space and the attenuation law of permeability. DETAILED DESCRIPTION

[0056] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] The present invention provides a hierarchical modeling method for electromagnetic torque based on the spatial attenuation characteristics of magnetic permeance. Its innovation lies in: obtaining the spatial attenuation characteristics of air gap magnetic permeance through angle-conformal mapping, then deducing the modulation of armature magnetomotive force and spatial magnetic permeance harmonics based on pole-slot coordination, and finally analyzing the spatial attenuation characteristics of each order of magnetic permeance and combining them with the modulated armature magnetomotive force to obtain the spatial hierarchical attenuation distribution of electromagnetic torque contributed by each order of magnetic permeance and magnetomotive force.

[0058] The system structure of the method of the present invention is as follows Figure 1 As shown, the magnetomotive force modeling and the magnetic permeance modeling can be performed in no particular order.

[0059] The present invention is specifically implemented in the following steps:

[0060] by Figure 2 The implementation method of this patent is explained by taking the motor represented by the motor topology as an example.

[0061] Establish electromagnetic parameter expressions through motor structural parameters:

[0062] Separate the permanent magnet information, armature side slot, and pitch information to obtain the rotor permanent magnet magnetomotive force and the armature magnetomotive force expression F r and F s ;

[0063] Based on the same number of magnetic field pole pairs, the source of the armature magnetic field that produces the average torque is limited;

[0064] According to the magnetic field modulation theory, the working armature magnetomotive force and the corresponding modulation permeance order are determined.

[0065] By conformal transformation, the value of the air gap permeability is determined:

[0066] The physical boundary of the magnetic permeance model is obtained by taking the unit slot topology of the circularly symmetric motor and the corresponding rotor wall composition;

[0067] The magnetic potential difference between the stator and rotor walls is selected as φ0, the air gap length between the stator and rotor is h, and the stator slot topology is assumed to be closed to the rotor wall at infinity, and the infinity on both ends is set to +∞ and -∞.

[0068] By using conformal mapping and the above-mentioned set boundary information, the magnetic position information of each position of the concentric ring between the stator wall and the rotor wall is obtained;

[0069] Based on the magnetic potential information, the air gap length h, and the Maxwell equations, the gradient of the air gap length direction is calculated for the magnetic potential, and the spatial magnetic permeance at each position in the space is obtained. The air gap is divided into 5 layers, and the spatial magnetic permeance of each layer is Fourier decomposed to obtain the spatial distribution of harmonics from 0 to 3 as shown in the figure. Figure 3 shown.

[0070] The mapping relationship among the armature magnetomotive force, permeance and electromagnetic torque is determined by the modulation correspondence, and the spatial distribution of the electromagnetic torque contributed by the armature magnetomotive force from different sources is calculated by the spatial permeance distribution.

[0071] When performing conformal mapping on the stator and rotor topology, logarithmic mapping and SC mapping are mainly used, and the final parameter to be solved is the magnetic potential information of any point in the solution domain.

[0072] Calculate the magnetic potential information of any point in the analytical domain Then, through the Maxwell equations:

[0073]

[0074] The magnetic field intensity H after slotting can be obtained, and the magnetic field intensity without slotting is

[0075]

[0076] The ratio of the two is the relative air gap permeability function after slotting. Since the magnetic potential information covers the entire air gap domain, the permeability information also covers the entire air gap domain.

[0077] The expression for modeling electromagnetic parameters using structural parameters is:

[0078]

[0079] B r is the remanence of the permanent magnet, h m is the thickness of the permanent magnet, α is the pole arc coefficient, v is the harmonic order, P is the number of permanent magnet pole pairs, ω is the angular velocity of the permanent magnet, t is time, i is the armature current, N c is the number of winding turns, k sv 、k yv are the motor slot coefficient and pitch coefficient, and x is the motor tangential position.

[0080] It can be represented as Fourier decomposition:

[0081]

[0082] Where i is the harmonic order, A i is the i-th order magnetomotive force amplitude, Ω r is the rotor mechanical speed, and θ is the circumferential position. s is the electrical frequency. In order to ensure that the rotational speed of the magnetic flux density on the armature side and the rotor side is the same, there is usually w s =P r Ω r , k is the harmonic order, F k is the k-th order magnetomotive force harmonic amplitude.

[0083] The equations for determining the armature magnetomotive force and different order permeance modulation modes are:

[0084] |F k ±jN s |=P r

[0085] Among them F k is the harmonic order of the armature magnetomotive force, j is the order of the permeance harmonic caused by the unit tooth slot, N s is the number of armature tooth slots.

[0086] According to the magnetic field modulation theory, the working armature magnetomotive force is determined, usually P r 、P r +N s 、P r-N s 、P r +2N s 、P r -2N s 、P r +3N s 、P r -3N s The secondary armature magnetomotive force corresponds to 0, 1, 1, 2, 2, 3, and 3 magnetic permeability modulations in space, and in fact, two or several of them should occupy the absolute majority.

[0087] The way to calculate the armature and permanent magnet magnetic fields is to multiply the specific magnetomotive force obtained by Fourier decomposition with the specific modulation permeance, ensuring that the number of pole pairs of the modulation magnetic field is P r The corresponding electromagnetic torque formula is:

[0088] T=vπlrB am_v B pm_v sin(θ am_v -θ pm_v )

[0089] Where v is the number of rotor permanent magnet pole pairs P r , l is the axial length of the motor, r is the air gap radius, B am_v is the vth harmonic of the armature modulation flux density, B pm_v is the vth harmonic of the permanent magnet modulated magnetic flux density, θ am_v is the phase angle of the harmonic of the vth armature modulation flux density, θ pm_v Modulate the magnetic density harmonic phase angle of the vth permanent magnet.

[0090] Among them B pm_v The fundamental magnetomotive force of the permanent magnet is modulated by DC magnetomotive force, B am_v The torque can be obtained by modulating the corresponding magnetic flux density with different magnetic flux density. The torque result represents the output result of the magnetic flux density. Since the magnetic flux density has a spatial distribution characteristic, the torque also has a spatial distribution characteristic. The overall torque spatial distribution of the motor modeled in this patent application is as follows: Figure 4 As shown, the spatial distribution of the torque obtained by modulating the fundamental wave and the secondary magnetomotive force of the 5th and 7th armature magnetomotive force are respectively as follows: Figure 5 、 6 shown.

[0091] This study proposes a spatial permeance analysis-based modeling method for the air-gap torque distribution of a permanent magnet vernier motor. Its technical features are reflected in the following innovative research paths: First, by establishing a parametric topological model of the tooth structure and assigning boundary conditions, the complex air gap domain is analytically solved using multiple conformal transformations to obtain an expression for the permeance function with spatial attenuation distribution characteristics. Then, the permeance function is spatially analyzed using the Fourier harmonic decomposition method. Combined with magnetic field modulation theory, a harmonic coupling model of the armature magnetomotive force and the permanent magnet magnetomotive force is established. Harmonic pairs of effective torque generation are selected based on the principle of equal pole pairs. Finally, a spatial attenuation model of torque contributed by each order of permeance and magnetomotive force is constructed based on the spatial distribution characteristics of permeance attenuation. This modeling system breaks through the theoretical limitations of the traditional equivalent magnetic circuit method, which assumes uniform air gap parameters. By establishing a mapping relationship between torque and spatial permeance harmonics, the constructed model analytically obtains the spatial attenuation of torque contributed by different magnetomotive forces and permeances, providing a new theoretical analysis framework for optimizing magnetic field modulation effects and high-precision torque modeling and analysis.

[0092] The present invention proposes a model that analyzes the spatial attenuation distribution of air gap magnetic permeability and maps this property to torque calculation. It not only improves the modeling accuracy of permanent magnet vernier motors by considering the spatial attenuation of torque, but also accurately analyzes the influence of magnetic permeabilities of various orders with different attenuation laws on the spatial attenuation distribution of torque, providing a more accurate reference for optimizing the torque ratio.

[0093] This method can accurately describe the relationship between the attenuation-modulated magnetic permeance of each order and the motor torque, and gives the spatial attenuation distribution of the electromagnetic torque contributed by the modulation of magnetic permeance with different spatial attenuation characteristics. It significantly improves the accuracy of the electromagnetic torque calculation of the vernier motor and has strong theoretical value.

[0094] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A hierarchical modeling method for electromagnetic torque based on the spatial attenuation characteristics of magnetic permeance, characterized in that: include: Establish electromagnetic parameter expressions through motor parameters; Through the motor pole slot matching and winding method, the armature and permanent magnet magnetomotive force parameter expressions are determined, and the magnetomotive force harmonics are obtained accordingly; According to the same condition of magnetic field pole pairs in the electromagnetic parameter expression, the source of the armature magnetic field that produces the average torque is limited, and the source of the armature magnetomotive force is determined to modulate the permeance order; Determine the air gap space magnetic permeability through conformal transformation; The spatial stratification and harmonic attenuation law of the air gap magnetic permeability are analyzed. The electromagnetic stratification torque taking into account the spatial attenuation characteristics is calculated through the modulation coupling of the magnetomotive force harmonics and the magnetic permeability harmonics. The weighted electromagnetic stratification torque is the total torque of the motor.

2. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 1 is characterized in that: The armature and permanent magnet magnetomotive force parameter expressions are determined by the motor pole slot matching and winding method; the details are as follows: Separate the permanent magnet information, armature side slot, and pitch information to obtain the rotor permanent magnet magnetomotive force F r (θ, t) and the armature magnetomotive force F s (x) expression, characterized by: Among them, B r is the remanence of the permanent magnet, h m is the thickness of the permanent magnet, α is the pole arc coefficient, v is the harmonic order, p r is the number of permanent magnet pole pairs, ω is the angular velocity of the permanent magnet, t is time, i is the armature current, N c is the number of winding turns, k sv 、k yv are the motor slot coefficient and pitch coefficient respectively, x is the motor tangential position, μ0 is the spatial magnetic permeability, μ r is the relative permeability, θ is the initial phase angle, is the rotor mechanical angle; it is represented by Fourier decomposition form: Where j is the harmonic order, A j is the j-order magnetomotive force amplitude, Ω r is the rotor mechanical speed, ω s is the electrical frequency, ω s =P r Ω r , k is the harmonic order, F k is the k-order magnetomotive force harmonic amplitude, is the magnetomotive force of the permanent magnet.

3. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 2 is characterized in that: The equation for determining the source of the armature magnetomotive force to modulate the permeance order is: |k±j λ N s |=p r Among them, j λ is the order of the permeance harmonics caused by the unit slot, N s is the number of stator slots.

4. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 1 is characterized in that: The air gap permeability is determined through conformal transformation; the details are as follows: First, the unit slot topology of the circularly symmetrical motor and the corresponding rotor wall composition are used to obtain the physical model boundary of the magnetic permeance; Secondly, the magnetic potential information of each position of the concentric ring between the stator wall and the rotor wall is obtained through conformal mapping and physical model boundaries. Then, based on the magnetic potential information, the air gap length h, and Maxwell's equations, the gradient of the magnetic potential in the direction of the air gap length is calculated to obtain the spatial relative magnetic permeance at each position in space, that is, the air gap spatial magnetic permeance.

5. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 1 is characterized in that: The spatial stratification and harmonic attenuation law of the air gap magnetic permeance are analyzed. Through the modulation coupling of magnetomotive force harmonics and magnetic permeance harmonics, the electromagnetic stratification torque taking into account the spatial attenuation characteristics is calculated. The total torque of the motor is obtained by weighting the electromagnetic stratification torque. The details are as follows: The air gap permeability is layered and Fourier decomposed to obtain the distribution law of each order permeability in the air gap space; According to the coordination between different orders of magnetomotive force and different orders of magnetic permeance, the magnetomotive force of the corresponding order is multiplied by the magnetic permeance to obtain the modulated armature magnetic field and the modulated permanent magnet magnetic field, and the electromagnetic torque expression is derived; the air gap space magnetic permeance of all spatial positions is traversed and substituted into the electromagnetic torque expression to calculate the electromagnetic stratified torque with spatial attenuation characteristics, and the weighted stratified torque is the total torque of the motor.

6. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 5 is characterized in that: The distribution law of each order of magnetic permeance in the air gap space is as follows: the DC magnetic permeance is stable in the space, while the attenuation laws of the harmonic magnetic permeances are inconsistent.

7. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 4 is characterized in that: Conformal mappings are the logarithmic map and the Schwarz–Christoffel map.

8. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 4 is characterized in that: The method to obtain the spatial magnetic permeance at each position in space is: The magnetic field intensity H after the slot is obtained by Maxwell's equations slot : in, is the gradient operator, is the air gap magnetic potential, is the magnetic position information, σ is the equivalent air gap length of the motor; Magnetic field strength H when no slots are cut noslot for in, is the magnetic potential difference between the stator and rotor sides; H slot / H noslot It is the spatial relative permeability of each position after slotting, that is, the air gap space permeability.

9. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 3 is characterized in that: According to the magnetic field modulation theory, the condition is that the modulation permeability order is not higher than 3, and the working armature magnetomotive force is determined as: p r 、p r +N s 、p r -N s 、p r +2N s 、p r -2N s 、p r +3N s 、p r -3N s The secondary armature magnetomotive force corresponds to the 0th, 1st, 1st, 2nd, 2nd, 3rd, and 3rd permeance modulation in space respectively.

10. The electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeance according to claim 5, characterized in that: The electromagnetic stratified torque with spatial attenuation characteristics is calculated as follows: The modulated armature magnetic field and the modulated permanent magnetic field are obtained by multiplying the specific magnetomotive force obtained by Fourier decomposition with the specific modulation permeance, ensuring that the number of pole pairs of the modulation magnetic field is P. r antipodes; Among them, the specific magnetomotive force that modulates the armature magnetic field is p r 、p r +N s 、p r -N s 、p r +2N s 、p r -2N s 、p r +3N s 、p r -3N s The specific modulation permeance corresponds to the 0th, 1st, 1st, 2nd, 3rd and 3rd order permeance respectively; the specific modulation permeance of the permanent magnetic field is p r Permanent magnetomotive force, specific modulation permeance is 0th order permeance; where p r is the number of permanent magnet pole pairs, N s is the number of stator slots; The number of pole pairs is the same, and the formula for the electromagnetic torque T of each set of armature magnetic field coupled with the permanent magnet magnetic field is: T=vπlrB am_v B pm_v sin(θ am_v -θ pm_v ) Among them, v is the harmonic order, which is fixed here as the number of permanent magnet pole pairs P r , l is the axial length of the motor, r is the air gap radius, B am_v is the vth harmonic of the armature modulation flux density, B pm_v is the vth harmonic of the permanent magnet modulated magnetic flux density, θ am_v is the phase angle of the harmonic of the vth armature modulation flux density, θ pm_v Modulate the magnetic density harmonic phase angle of the vth permanent magnet; B pm_v The fundamental magnetomotive force of the permanent magnet is modulated by DC permeance, B am_v It is derived from the magnetic permeability of the corresponding layers at different air gap radii r, and the electromagnetic torque T represents the contribution of the corresponding armature magnetomotive force torque.

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