Electromagnetic torque hierarchical modeling method based on magnetic guide space attenuation characteristics

Abstract

The application discloses a kind of electromagnetic torque layered modeling method based on magnetic guide space attenuation characteristics, it is related to permanent magnet motor technical field, comprising: by motor parameter establishment electromagnetic parameter expression;By motor pole slot coordination and winding mode, determine armature and permanent magnet magnetic motive force parameter expression, and obtain magnetic motive force harmonic from it;According to the same condition of magnetic field pole pair number in electromagnetic parameter expression, limit the source of armature magnetic field that generates average torque, determine armature magnetic motive force source to modulate magnetic guide order;By conformal mapping, determine air gap space magnetic guide;For air gap space magnetic guide, carry out space layering and harmonic attenuation law analysis, by magnetic motive force harmonic and magnetic guide harmonic modulation coupling, calculate electromagnetic layered torque considering space attenuation characteristics, the total torque of motor is obtained by weighting electromagnetic layered torque.The application significantly improves the precision of permanent magnet vernier motor torque modeling.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet motor technology, and in particular to a method for hierarchical modeling of electromagnetic torque based on the spatial decay characteristics of magnetic permeability. Background Technology

[0002] In the research of permanent magnet vernier motors, torque modeling and analysis are among the key technologies. Traditional torque modeling methods for permanent magnet motors mainly focus on magnetic field analysis, magnetic flux distribution, and electromagnetic force calculation. However, for permanent magnet vernier motors, their unique magnetic permeability modulation mechanism makes torque generation more complex. Although existing technologies can provide basic torque expressions, they have not fully considered the influence of the spatial attenuation distribution of torque due to the weakening of air gap magnetic permeability with slotting effect.

[0003] When modeling the torque of multi-harmonic motors such as permanent magnet vernier motors, neglecting the slotting effect leads to spatial attenuation of magnetic permeability, resulting in layered torque attenuation and further reducing modeling accuracy. The spatial attenuation of magnetic permeability causes layering, which in turn affects the spatial attenuation of torque, impacting the accuracy of torque calculation. Because the spatial attenuation of magnetic permeability varies across different orders, the spatial attenuation patterns of torque modulated by each order of magnetic permeability are inconsistent, causing the total torque to deviate from a single magnetic permeability spatial attenuation pattern. For example, using the traditional equivalent magnetic circuit method only yields a set of overall curves characterizing the approximate air gap magnetic permeability. While this achieves motor torque modeling, it still suffers from insufficient modeling accuracy and fails to reflect the actual magnetic field modulation at various points 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 prior art and provide an electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability. The present invention is based on the modulation phenomenon in the motor and performs torque spatial hierarchical modeling for different modulated magnetic permeability, which improves the accuracy of motor torque modeling and makes the source of torque attenuation clearer.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A layered modeling method for electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability, proposed according to the present invention, includes:

[0007] Establish electromagnetic parameter expressions based on motor parameters;

[0008] By determining the motor pole slot matching and winding method, the magnetomotive force parameter expressions of the armature and permanent magnet are determined, and the magnetomotive force harmonics are obtained from this.

[0009] Based on the condition of the same number of magnetic field pole pairs in the electromagnetic parameter expression, the source of the armature magnetic field that generates the average torque is defined, and the source of the armature magnetomotive force is determined to modulate the magnetic permeability order.

[0010] The permeability of the air gap space was determined by conformal mapping.

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

[0012] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, the expressions for the magnetomotive force parameters of the armature and permanent magnet are determined by the motor pole-slot combination and winding method; specifically as follows:

[0013] Separate permanent magnet information, armature-side slot information, and pitch information to obtain the rotor permanent magnet magnetomotive force F. r (θ,t) and armature magnetomotive force F s The expression (x) is represented as:

[0014]

[0015] Among them, B r For remanence of permanent magnets, h m Where α is the thickness of the permanent magnet, α is the pole arc coefficient, v is the harmonic order, and p r ω is the number of pole pairs of the permanent magnet, t is time, i is the armature current, and N is the number of pole pairs of the permanent magnet. c k is the number of turns in the winding. sv k yv These represent the slot coefficient and pitch coefficient of the motor, respectively; x is the tangential position of the motor; μ0 is the spatial permeability; and μ r Where θ is the relative permeability and θ is the initial phase angle. The rotor mechanical angle; characterized in Fourier decomposition form:

[0016]

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

[0018] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, the equation for the source of armature magnetomotive force and the modulation order of magnetic permeability is determined as follows:

[0019] |k±j λ N s |=p r

[0020] Where, j λ N is the order of the magnetic permeability harmonic caused by a unit tooth cog. s This represents the number of stator slots.

[0021] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, the air gap spatial magnetic permeability is determined through conformal transformation; specifically as follows:

[0022] First, the physical model boundary of the magnetic permeability is obtained by taking the unit slot topology of the circumferentially symmetrical motor and the corresponding rotor wall.

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

[0024] Then, based on the magnetic potential information, the air gap length h, and Maxwell's equations, the gradient of the air gap length direction is calculated for the magnetic potential to obtain the spatial permeability at each location in space, i.e., the spatial permeability of the air gap.

[0025] As a further optimization of the electromagnetic torque layering modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, spatial layering and harmonic attenuation law analysis are performed on the air gap spatial magnetic permeability. Through magnetomotive force harmonics and magnetic permeability harmonic modulation coupling, the electromagnetic layering torque considering spatial attenuation characteristics is calculated. The weighted sum of the electromagnetic layering torques yields the total motor torque; specifically as follows:

[0026] The magnetic permeability in the air gap space is divided into layers and Fourier decomposition is performed to analyze the distribution law of each order of magnetic permeability in the air gap space.

[0027] For different orders of magnetomotive force and different orders of magnetic permeability, the corresponding order of magnetomotive force and magnetic permeability are multiplied to obtain the modulated armature magnetic field and the modulated permanent magnet magnetic field, and the electromagnetic torque expression is derived. The air gap spatial magnetic permeability is traversed for all spatial positions and substituted into the electromagnetic torque expression to calculate the electromagnetic layered torque with spatial attenuation characteristics. The weighted sum of the layered torques is the total torque of the motor.

[0028] As a further optimization scheme of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, the distribution law of each order of magnetic permeability in the air gap space is as follows: the content of DC magnetic permeability in the space is stable, while the attenuation law of harmonic magnetic permeability is inconsistent.

[0029] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, conformal mapping is replaced by logarithmic mapping and Schwarz-Christopheel mapping.

[0030] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention, the method for obtaining the spatial permeability ratio at each spatial location is as follows:

[0031] The magnetic field strength H after slotting was obtained using Maxwell's equations. slot :

[0032]

[0033] in, For gradient operators, For air gap magnetic potential, This represents the magnetic potential information, where σ is the equivalent air gap length of the motor.

[0034] Magnetic field strength H without slotting noslot for

[0035]

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

[0037] H slot / H noslot The spatial permeability of each location after slotting is given, i.e., the spatial permeability of the air gap.

[0038] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial attenuation characteristics of magnetic permeability described in this invention,

[0039] According to the magnetic field modulation theory, substituting the condition that the order of the modulation permeability is no higher than 3, the magnetomotive force of the working armature 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 forces correspond to the 0th, 1st, 1st, 2nd, 2nd, 3rd, and 3rd magnetic permeability modulations in space, respectively.

[0040] As a further optimization of the electromagnetic torque hierarchical modeling method based on the spatial decay characteristics of magnetic permeability described in this invention, the electromagnetic hierarchical torque with spatial decay characteristics is calculated as follows:

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

[0042] 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 modulated magnetic permeability corresponds to the 0th, 1st, 1st, 2nd, 3rd, and 3rd order magnetic permeability, respectively; the specific magnetomotive force modulating the permanent magnet field is p. r The permanent magnet magnetomotive force has a specific modulated permeability of zero order permeability; where p r N is the number of pole pairs of the permanent magnet. s This refers to the number of stator slots;

[0043] With the same number of pole pairs, the formula for the electromagnetic torque T coupled between the armature magnetic field and the permanent magnet magnetic field in each group is:

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

[0045] Where v is the harmonic order, and here it is fixed as the number of permanent magnet pole pairs P. r l is the axial length of the motor, r is the air gap radius, and B am_v For the v-th armature modulated magnetic flux density harmonic, B pm_v For the modulation of magnetic flux density harmonics by the v-th permanent magnet, θ am_v The phase angle of the armature modulation magnetic flux density harmonic of the v-th order is θ. pm_v Modulate the phase angle of the magnetic flux density harmonics for the v-order permanent magnet;

[0046] B pm_v The fundamental magnetomotive force of the only permanent magnet is obtained through DC permeability modulation, B am_v It is derived from the layered magnetic permeability 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, employing the above technical solution, has the following technical effects:

[0048] (1) This invention breaks with the conventional torque modeling method of permanent magnet vernier motor and introduces conformal mapping for the first time to explain the attenuation layer distribution of torque in the air gap space, which intuitively reflects the influence of different magnetic permeability harmonics on the torque formed by modulation.

[0049] (2) By analyzing the attenuation distribution law of magnetic permeability in space, this invention makes the spatial attenuation of each torque formed by the modulation of each order of magnetic permeability more accurate, can accurately describe the relationship between each order of modulated magnetic permeability and motor torque, and give the spatial distribution ratio of various electromagnetic torques. Attached Figure Description

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

[0051] Figure 2 The original topology of the motor for modeling and testing.

[0052] Figure 3 The spatial attenuation distribution of harmonics in the air gap of the test motor was modeled.

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

[0054] Figure 5 This is a schematic diagram showing the attenuation law of the torque modulated by the fundamental magnetic permeability in space and the attenuation law of the magnetic permeability.

[0055] Figure 6 This is a schematic diagram showing the attenuation law of the torque in space and the attenuation law of the magnetic permeability in second harmonic magnetic permeability modulation. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] This invention provides a method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability. Its innovation lies in obtaining the spatial attenuation characteristics of air gap magnetic permeability through conformal mapping, then deriving the modulation of armature magnetomotive force and spatial magnetic permeability harmonics based on pole-slot coordination, and finally analyzing the spatial attenuation characteristics of each order of magnetic permeability in combination with the modulated armature magnetomotive force to obtain the spatial hierarchical attenuation distribution of electromagnetic torque contributed by each order of magnetic permeability 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 magnetic permeability modeling can be performed in any order.

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

[0060] by Figure 2 Taking a motor characterized by a motor topology as an example, the implementation method of this patent will be explained.

[0061] Establish electromagnetic parameter expressions based on motor structural parameters:

[0062] Separate permanent magnet information, armature-side slot information, 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 condition that the number of magnetic field pole pairs is the same, the source of the armature magnetic field that produces the average torque is defined.

[0064] Based on the magnetic field modulation theory, the magnetomotive force of the working armature and the corresponding modulation permeability order are determined.

[0065] The value of the air gap permeability is determined by conformal mapping:

[0066] The physical boundary of the magnetic permeability model is determined by taking the unit slot topology of the circumferentially symmetrical motor and the corresponding rotor wall.

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

[0068] By using conformal mapping and the aforementioned boundary information, the magnetic potential information at each position of the concentric ring between the stator wall and the rotor wall is obtained;

[0069] Based on magnetic potential information, air gap length h, and Maxwell's equations, the gradient along the air gap length is calculated to obtain the spatial permeability at various locations. The air gap is divided into 5 layers, and Fourier decomposition is performed on the spatial permeability of each layer to obtain the spatial distribution of the 0th to 3rd harmonics. Figure 3 As shown.

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

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

[0072] Solving for magnetic potential information at any point in the analytic domain Then, through the Maxwell equations:

[0073]

[0074] The magnetic field strength H after slotting can be obtained, and the magnetic field strength 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] Its expression for modeling electromagnetic parameters using structural parameters is as follows:

[0078]

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

[0080] Characterized in Fourier decomposition form:

[0081]

[0082] Where i is the harmonic order, A i Let Ω be the amplitude of the i-th order magnetomotive force. r θ represents the rotor's mechanical speed, and θ represents the circumferential position. s For 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, we usually have w. s =P r Ω r k is the harmonic order, F k It represents the amplitude of the k-th order magnetomotive force harmonic.

[0083] The equations for determining the armature magnetomotive force and different orders of magnetic permeability modulation are as follows:

[0084] |F k ±jN s |=P r

[0085] Where F k N is the order of the armature magnetomotive force harmonics, j is the order of the permeability harmonics caused by a unit tooth slot, and N is the order of the armature magnetomotive force harmonics. s This represents the number of armature slots.

[0086] According to the theory of magnetic field modulation, the magnetomotive force of the working armature is determined, which is 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 the magnetic permeability modulation of 0, 1, 1, 2, 2, 3, 3 in space, and in reality, two or more of them should occupy the absolute majority.

[0087] The armature and permanent magnet magnetic fields are calculated by multiplying a specific magnetomotive force obtained through Fourier decomposition with a specific modulation permeability, ensuring that the number of pole pairs of the modulation magnetic field is P. r For each pole, 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 pole pairs of the rotor permanent magnet P r l is the axial length of the motor, r is the air gap radius, and B am_v For the v-th armature modulated magnetic flux density harmonic, B pm_v For the modulation of magnetic flux density harmonics by the v-th permanent magnet, θ am_v The phase angle of the armature modulation magnetic flux density harmonic of the v-th order is θ. pm_v The phase angle of the magnetic flux density harmonics is modulated for the v-order permanent magnet.

[0090] Among them B pm_v B is the only permanent magnet fundamental magnetomotive force obtained through DC magneto-modulation. am_v The torque result represents the output of the magnetomotive force (MOMF) corresponding to different magnetic permeabilities. Since magnetic permeability has spatial distribution characteristics, torque also has spatial distribution characteristics. The overall torque spatial distribution of the motor modeled in this patent application is as follows: Figure 4 As shown, the spatial distributions of the fundamental waves modulated by the 5th and 7th armature magnetomotive forces and the torques obtained from the second magnetomotive force are respectively as follows: Figure 5 , 6 As shown.

[0091] This study proposes a modeling method for air gap torque distribution of permanent magnet vernier motors based on spatial magnetic permeability analysis. Its technical features are reflected in the following innovative research path: First, a parameterized topological model of the toothed structure is established and boundary conditions are assigned. Multiple conformal transformations are used to analytically solve the complex air gap domain, obtaining an expression for the magnetic permeability function with spatial attenuation distribution characteristics. Then, Fourier harmonic decomposition is used to perform spatial spectrum analysis of the magnetic permeability function. Combined with magnetic field modulation theory, a harmonic coupling model of the armature magnetomotive force and the permanent magnet magnetomotive force is established. The effective torque generation harmonic pairs are selected based on the principle of equal pole pair numbers. Finally, a spatial attenuation model is constructed based on the spatial distribution characteristics of magnetic permeability attenuation, building a model for the torque spatial attenuation contributed by each order of magnetic permeability and magnetomotive force. This modeling system overcomes the theoretical limitations of the homogenization assumption of air gap parameters in the traditional equivalent magnetic circuit method. The established model, by establishing a mapping relationship between torque and spatial magnetic permeability harmonics, analytically obtains the attenuation of torque contributed by different magnetomotive forces and magnetic permeabilities in space, providing a new theoretical framework for optimizing magnetic field modulation effects and high-precision torque modeling and analysis.

[0092] This invention proposes a model that analyzes the spatial attenuation distribution of air gap magnetic permeability and maps this property to torque calculation. This model 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 different orders of magnetic permeability with different attenuation laws on the spatial attenuation distribution of torque, providing a more accurate reference for optimizing torque ratio.

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

[0094] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within 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 permeability, characterized in that, include: Establish electromagnetic parameter expressions based on motor parameters; By determining the motor pole slot matching and winding method, the magnetomotive force parameter expressions of the armature and permanent magnet are determined, and the magnetomotive force harmonics are obtained from this. Based on the condition of the same number of magnetic field pole pairs in the electromagnetic parameter expression, the source of the armature magnetic field that generates the average torque is defined, and the source of the armature magnetomotive force is determined to modulate the magnetic permeability order. The permeability of the air gap space was determined by conformal mapping. The spatial stratification and harmonic attenuation law of the air gap magnetic permeability are analyzed. By modulating and coupling the magnetomotive force harmonics and magnetic permeability harmonics, the electromagnetic stratification torque taking into account the spatial attenuation characteristics is calculated. The weighted sum of the electromagnetic stratification torque is the total torque of the motor.

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

3. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 2, characterized in that, The equation for determining the source of the armature magnetomotive force and modulating the order of magnetic permeability is as follows: |k±j λ N s |=p r where j λ is the order of the tooth slot induced magnetic flux harmonic, N s is the number of stator slots.

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

5. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 1, characterized in that, Spatial stratification and harmonic attenuation law of air gap magnetic permeability are analyzed. Electromagnetic stratification torque, considering spatial attenuation characteristics, is calculated by modulation coupling of magnetomotive force harmonics and magnetic permeability harmonics. The weighted sum of these electromagnetic stratification torques yields the total motor torque. Details are as follows: The magnetic permeability in the air gap space is divided into layers and Fourier decomposition is performed to analyze the distribution law of each order of magnetic permeability in the air gap space. For different orders of magnetomotive force and different orders of magnetic permeability, the corresponding order of magnetomotive force and magnetic permeability are multiplied to obtain the modulated armature magnetic field and the modulated permanent magnet magnetic field, and the electromagnetic torque expression is derived. The air gap spatial magnetic permeability is traversed for all spatial positions and substituted into the electromagnetic torque expression to calculate the electromagnetic layered torque with spatial attenuation characteristics. The weighted sum of the layered torques is the total torque of the motor.

6. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 5, characterized in that, The distribution patterns of different orders of magnetic permeability in the air gap space are as follows: the content of DC magnetic permeability is stable in the space, while the attenuation patterns of harmonic magnetic permeability are inconsistent.

7. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 4, characterized in that, Conformal mappings include logarithmic mappings and Schwarz-Christopheir mappings.

8. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 4, characterized in that, The method for obtaining the spatial permeability ratio at various locations in space is: The magnetic field intensity H after slotting is obtained by Maxwell's equations slot : in, For gradient operators, For air gap magnetic potential, This represents the magnetic potential information, where σ is the equivalent air gap length of the motor. Magnetic field strength H without slot noslot For in, The magnetic potential difference between the stator and rotor sides; H slot / H noslot The space ratio of each position after slotting is the permeance, i.e. the air gap space permeance.

9. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 3, characterized in that, According to the magnetic field modulation theory, substituting the condition that the order of the modulation permeability is no higher than 3, the magnetomotive force of the working armature 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 forces correspond to the 0th, 1st, 1st, 2nd, 2nd, 3rd, and 3rd magnetic permeability modulations in space, respectively.

10. The method for hierarchical modeling of electromagnetic torque based on the spatial attenuation characteristics of magnetic permeability according to claim 5, characterized in that, The electromagnetic stratification torque with spatial attenuation characteristics is calculated as follows: The modulated armature magnetic field and the modulated permanent magnet magnetic field are obtained by multiplying the specific magnetomotive force obtained by Fourier decomposition with the specific modulated magnetic permeability, ensuring that the number of pole pairs of the modulated magnetic field is P. r opposite pole; 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 modulated magnetic permeability corresponds to the 0th, 1st, 1st, 2nd, 3rd, and 3rd order magnetic permeability, respectively; the specific magnetomotive force modulating the permanent magnet field is p. r The permanent magnet magnetomotive force has a specific modulated permeability of zero order permeability; where p r N is the number of pole pairs of the permanent magnet. s This refers to the number of stator slots; With the same number of pole pairs, the formula for the electromagnetic torque T coupled between the armature magnetic field and the permanent magnet magnetic field in each group is: T=vπlrB am_v B pm_v sin(θ am_v -θ pm_v ) Where v is the harmonic order, and here it is fixed as the number of permanent magnet pole pairs P. r l is the axial length of the motor, r is the air gap radius, and B am_v For the v-th armature modulated magnetic flux density harmonic, B pm_v For the modulation of magnetic flux density harmonics by the v-th permanent magnet, θ am_v The phase angle of the armature modulation magnetic flux density harmonic of the v-th order is θ. pm_v Modulate the phase angle of the magnetic flux density harmonics for the v-order permanent magnet; B pm_v The fundamental magnetomotive force of the only permanent magnet is obtained through DC permeability modulation, B am_v It is derived from the layered magnetic permeability 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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