An axial magnetic field double-rotor synchronous motor through-type stator tooth slot parameter design method

Abstract

The application discloses a kind of axial magnetic field double-rotor synchronous machine through stator tooth slot parameter design method, for main analysis rotor and open-slot stator, according to tooth slot torque pulsation amplitude design stator pitch, slot width and slot depth;Design method includes ignoring stator open circuit, ignoring the influence of stator and rotor slotting, according to the main analysis rotor excitation to obtain the spatial ideal rectangular superposition waveform of axial air-gap magnetic flux density;Then consider the influence of stator slotting, according to Carter coefficient, magnetic field modulation coefficient and its attenuation coefficient, the spatial distribution of double-air-gap axial magnetic flux density in the circumferential direction of the structure principle synchronous machine is realized analytically;According to the spatial distribution of axial air-gap magnetic flux density, the tooth slot torque of main analysis rotor is obtained by virtual position method;With motor installation process and material characteristics as constraint condition, select the parameter set element that makes the tooth slot torque pulsation amplitude of main analysis rotor minimum as design parameter.The application realizes tooth slot parameter rapid screening by analysis, without relying on a large number of simulation computing power, and improves design efficiency.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic field analysis and design technology for electric motors, specifically to a method for designing the through-type stator cog parameters of an axial magnetic field dual-rotor synchronous motor. Background Technology

[0002] Axial flux synchronous motors, due to their axial flux distribution, feature compact axial dimensions, high power density, and high torque density, and have received widespread attention in recent years for direct-drive power generation systems and low-speed, high-torque applications. Among them, AC drives of axial flux dual-rotor synchronous motors with fractional-slot concentrated windings not only easily achieve fewer slots and more pole pairs and low-speed, high torque, further improving the motor's electromagnetic performance under low-speed operating conditions, but also, with their open-slot stator cores, facilitate modular assembly of stator slotted units, automated winding, and efficient operation and maintenance, demonstrating promising engineering application prospects.

[0003] However, this type of motor still has the following technical shortcomings: (1) The stator adopts a fractional slot concentrated winding, and its spatial pole pair includes a pair of dominant components with large amplitude and several harmonic components with small amplitude. The two-choice scheme for the dominant components of the spatial pole pair will inevitably lead to a reduction in the winding utilization rate; (2) The counter-rotating dual rotor scheme is adopted, and the two DC excitation rotors are coupled with a pair of dominant components of the spatial pole pair of the stator respectively. There is no theoretical basis for the analysis of the cogging torque pulsation suppression for the dual air gap structure; (3) Due to the adoption of the dual air gap structure, the air gap length needs to be shortened to improve the power factor, but this will lead to an increase in the spatial harmonics of the axial air gap magnetic flux density distribution function in the circumferential direction, which in turn leads to an increase in the cogging torque; (4) This type of motor adopts a through stator slot structure, and the magnetomotive force of each stator tooth is not equal, which increases the difficulty of the analysis of the conventional one-dimensional equivalent magnetic circuit.

[0004] Some research attempts to theoretically derive cogging torque based on virtual displacement methods or magnetic circuit analysis. However, existing analytical methods are mostly focused on single-air-gap or radial flux structures. For dual-air-gap axial flux synchronous motors, there is still a lack of a systematic method that can effectively equivalently represent the dual-air-gap magnetic circuit and directly use the analytical calculation results for selecting cogging structure parameters. Especially in the engineering design process, how to quickly compare different combinations of cogging parameters based on the analytical expression of cogging torque, while meeting structural dimensional constraints, to determine reasonable cogging structure parameters, still requires further research.

[0005] Therefore, there is an urgent need for a parameter design method for the through-type stator cogging structure of this type of axial magnetic field dual-rotor synchronous motor. This method can achieve quantitative comparison of different cogging structure parameters through analytical calculation of cogging torque without relying on a large number of finite element simulations, and provide an effective technical means for motor cogging torque suppression and structural parameter design. Summary of the Invention

[0006] 1. The technical problem to be solved:

[0007] To address the aforementioned technical problems, this invention provides a method for designing the cogging parameters of a through-type stator of an axial magnetic field dual-rotor synchronous motor. This method, based on the characteristics of the dual-air-gap magnetic circuit, quantitatively characterizes the variation of cogging torque with cogging structural parameters through analytical calculations. Thus, under the premise of satisfying structural constraints, it provides a basis for the rational selection of cogging structural parameters of an axial flux dual-rotor synchronous motor.

[0008] 2. Technical Solution:

[0009] A method for designing the cogging parameters of a through-type stator of an axial magnetic field dual-rotor synchronous motor is characterized in that: the axial magnetic field dual-rotor synchronous motor includes discrete axial through-type yokeless stator cogging units and rotors on both sides of the stator axial direction; the rotors are DC excitation; the stator is composed of multiple independent and structurally identical cogging units, and the stator adopts open slots and fractional slot concentrated windings.

[0010] The stator tooth parameters include stator tooth pitch, stator slot width, and stator slot depth, and their design method includes the following steps;

[0011] Step 1: Calculate the least common multiple of the number of rotor poles and stator slots for both rotors. Select the rotor with the smallest least common multiple and define it as the main analysis rotor. Under the condition of stator open circuit and neglecting the influence of stator and rotor core slots, obtain the ideal axial air gap magnetic flux density distribution function in the rotor circumferential direction by superimposing ideal rectangular waves based on the winding distribution, number of winding turns, excitation current, and air gap length of the main analysis rotor. And perform a Fourier expansion on it;

[0012] Step Two: Calculate the multiple algebraic terms and coefficients of the per-unit distribution function of the magnetic permeability of the axial air gap magnetic circuit in the circumferential direction, considering the influence of stator core slotting. Specifically, this includes: ignoring the influence of rotor core slotting, considering the influence of stator core slotting, and calculating the average algebraic term of the per-unit distribution function of the magnetic permeability of the magnetic circuit based on the stator tooth width, stator slot width, and stator tooth pitch. The stator tooth pitch is the sum of the stator tooth width and the stator slot width. Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator tooth width, stator slot width, and stator tooth pitch. The stator tooth pitch is the sum of the stator tooth width and the stator slot width. Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator tooth width, stator slot width, and stator tooth pitch. attenuation coefficient The stator tooth pitch is the sum of the stator tooth width and the stator slot width; ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator slot depth. attenuation coefficient Where m is the spatial harmonic order of the per-unit distribution function of the magnetic permeability of the magnetic circuit;

[0013] Step 3: For a dual-air-gap dual-rotor synchronous motor with a through-type stator slot structure and axial magnetic field, using the magnetic permeability distribution function per unit cross-sectional area of ​​the axial air-gap magnetic circuit in the circumferential direction (ignoring the influence of stator and rotor core slotting) as the benchmark value, based on algebraic terms or coefficients... , , and The circumferential distribution function of this type of motor based on stator cogging effect compensation was obtained. Distribution function This represents the per-unit value of the magnetic permeability of the axial air gap magnetic circuit, where... The spatial position radian in the circumferential direction of the stator;

[0014] Step 4: Considering the cogging effect of the stator slots and ignoring the influence of the rotor core slots, the axial magnetic flux density circumferential distribution functions of the air gap between the stator and rotor 1, and between the stator and rotor 2 are approximately equal; the ideal air gap axial magnetic flux density distribution function obtained in Step 1 is then used as the basis for this step. The per-unit distribution function in the circumferential direction based on stator cogging effect compensation for this type of motor obtained in step three. Multiplying these together yields the axial air gap magnetic flux density distribution function in the circumferential direction of this type of motor, based on stator cogging effect compensation.

[0015] Step 5: Ignoring the core magnetic reluctance and assuming the rotor excitation current is constant, the axial air gap magnetic flux density distribution function of the stator in the circumferential direction based on the cogging effect compensation obtained in Step 4 is used to obtain the magnetic co-energy of the motor air gap magnetic field under different relative positions of the stator and the main analysis rotor; the virtual displacement derivative of this magnetic co-energy with respect to the change in the relative positions of the stator and the main analysis rotor is obtained to obtain the analytical expression of the cogging torque of the main analysis rotor under different relative positions of the stator and the main analysis rotor.

[0016] Step Six: Set the stator tooth width, stator slot width, and stator slot depth as candidate parameters, where the stator tooth width and stator slot width are arc lengths, and the slot depth is the length. Under the conditions of satisfying motor installation and electromagnetic constraints, pre-set the set of candidate elements for the stator tooth pitch, stator slot width, and stator slot depth. Substitute the elements in the set of candidate elements into the analytical expression of the rotor cogging torque in the main analysis, and select the stator tooth width, stator slot width, and stator slot depth that minimize the amplitude of the rotor cogging torque in the main analysis as the design result of the cogging geometry parameters.

[0017] Furthermore, step one specifically includes:

[0018] S11: Ignoring the influence of stator and rotor core slotting, assuming the stator winding is open-circuited, the rotor uses a single-layer distributed winding, and DC current excitation, calculate the ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction of this type of motor; specifically including:

[0019] Spatial position radian of stator circumference The spatial position radian of rotor No. 1 in the circumferential direction is represented by... The spatial position radian of rotor No. 2 in the circumferential direction is indicated by... The relative positional radian between the stator and the main analytical rotor is represented by θ; the position of the axis of any slot in the stator circumferential direction is predetermined as the reference zero position in the stator space. The position of the central axis of any N pole of rotor 1 on the teeth is preset as the reference zero position in rotor 1 space. Stator position and the position of rotor No. 1 The relative position radians between them are used This indicates that the position of the central axis of any N pole of rotor 2 on the teeth is preset as the reference zero position in rotor 2 space. Stator position Position of rotor No. 2 The relative position radians between them are used This indicates that if rotor 1 is defined as the main analysis rotor, then... If rotor number 2 is defined as the main analysis rotor, then At different radii of the axial magnetic field motor, the air gaps between the stator and rotor 1 and between the stator and rotor 2 in the circumferential direction have approximately equal axial magnetic flux density distributions, which can be approximately represented as a superposition of ideal rectangular waves. Furthermore, these superimposed rectangular waves exhibit abrupt changes within each pair of magnetic poles. Second-rate; ,in Main analysis of rotor slot number, The main analysis focuses on the number of rotor pole pairs; At that time, the ideal rectangular wave superposition expression of the axial air gap magnetic flux density distribution in the circumferential direction generated by the rotor excitation is analyzed. for:

[0020] (1);

[0021] In the formula, For each magnetic flux density jump, The periodicity of this expression on a circle is as follows: ; air permeability; The main analysis focuses on the number of turns in the rotor excitation winding. The main analysis focuses on the rotor excitation current; This is the air gap length; Indicates the first Whether the magnetic flux density jump is upward or downward is determined by the following formula:

[0022] (2);

[0023] S12: Performing a Fourier series expansion on the ideal rectangular wave superposition expression of the axial air gap magnetic flux density distribution in the circumferential direction, we obtain:

[0024] (3)

[0025] In the above formula, for The average value of this is 0, based on general knowledge theory; for of Second harmonic amplitude.

[0026] Furthermore, step two involves sequential calculations based on the following steps:

[0027] S21: Using the magnetic permeability distribution function per unit cross-sectional area of ​​the axial air gap magnetic circuit in the circumferential direction, ignoring the influence of stator and rotor core slotting, as the benchmark value, and ignoring the influence of rotor core slotting, a Carter coefficient is introduced to characterize the degree of reduction in the average magnetic permeability of the axial air gap caused by stator slotting. Based on the stator tooth width, stator slot width, and stator tooth pitch, calculate the algebraic term of the average value of the per-unit distribution function of the magnetic permeability of the axial air gap magnetic circuit in the circumferential direction. ;

[0028] S22: Order Let the spatial harmonic order of the per-unit distribution function of magnetic permeability of the axial air gap magnetic circuit in the circumferential direction be the reference value. Ignoring the influence of stator and rotor core slotting, the permeability distribution function of the axial air gap magnetic circuit in the circumferential direction is used as the benchmark value. Then, considering the influence of stator core slotting, the algebraic term of the harmonic components of the per-unit distribution function of magnetic permeability of the axial air gap magnetic circuit in the circumferential direction corresponding to the magnetic field modulation effect of stator core slotting is calculated based on the stator tooth width, stator slot width, and stator tooth pitch. ;

[0029] S23: Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the complex boundary region containing stator slots is mapped to a regularized domain using the Schwarz-Christophe transform; the regularized domain is either an upper half-plane regularized domain or a rectangular regularized domain; after solving, an inverse transform is performed to obtain the logarithmic terms generated by the stator tooth width, stator slot width, and stator tooth pitch. attenuation coefficient ;

[0030] S24: Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the complex boundary region containing stator slots is mapped to a regularized domain using the Schwarz-Christophe transform; after solving, an inverse transform is performed to obtain the logarithmic terms generated by the slot depth. attenuation coefficient .

[0031] Furthermore, the process of obtaining the distribution function of the per-unit value of magnetic permeability of the axial air gap magnetic circuit corresponding to the unit cross-sectional area in step three is as follows: For the through-type stator cogging effect of the dual-rotor synchronous motor with axial magnetic field, taking the distribution function of magnetic permeability of the axial air gap magnetic circuit per-unit cross-sectional area in the circumferential direction, ignoring the influence of stator and rotor core slotting, as the benchmark value, ignoring the influence of rotor core slotting, and considering the influence of stator core slotting, the distribution function of the per-unit value of magnetic permeability of the axial air gap magnetic circuit per-unit cross-sectional area is obtained as follows: :

[0032] (4);

[0033] In the formula, ; ; ; ; This refers to the number of stator slots; Carter's coefficient; For stator tooth width; This refers to the width of the stator slot; The length of the air gap; ; ; ; The stator slot depth is the stator slot opening; here, the stator tooth width is... and stator slot width All adopt the outer radius of the stator core of this axial magnetic field motor The arc length at the radius position.

[0034] Furthermore, step four obtains the axial air gap magnetic flux density distribution function in the circumferential direction of this type of motor based on stator cogging effect compensation, specifically as follows: the relative position arc between the main analysis rotor and stator obtained in step one. The time-major analysis of the ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction generated by the rotor excitation is a key feature. Based on this, ignoring the influence of stator and rotor core slotting, we consider the relative positions between the stator and the main analytical rotor. , to obtain ( - ( ) is an ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction of the independent variable. The following formula is multiplied by the function obtained in step three. The axial air gap magnetic flux density distribution function in the circumferential direction based on the stator slot cogging effect was obtained. :

[0035] (5).

[0036] Furthermore, step five specifically includes:

[0037] S51: Approximating the core reluctance as 0, the magnetic co-energy equals the magnetic field energy. All magnetic field energy is stored in the air gap magnetic field, and the magnetic field energy in the slot region is ignored. The analytical expression for the magnetic co-energy of the magnetic fields in the two air gaps inside the motor is W. c (θ) is:

[0038] (6);

[0039] In the above formula: , and These are the inner and outer radii of the stator core of the axial magnetic field motor, respectively.

[0040] S52: The result obtained in step four Substituting the analytical expression for the magnetic co-energy of the magnetic field in the two air gaps inside the motor ;

[0041] S53: Will right Differentiating, we obtain the relative positions of the stator and the main rotor. The principal analysis expression for rotor cogging torque with independent variables. :

[0042] (7);

[0043] In the formula: and They are respectively function and The amplitude of the second harmonic component;

[0044] ;

[0045] ;

[0046] The Kronecker delta function is defined as follows: ;

[0047] Cut Amplitude calculations are performed on the finite-order harmonic components of the function; among them, for and The finite harmonic components are the first M harmonics that meet the preset calculation accuracy requirements, where M is a positive integer; Specifically, for... The finite harmonic components are the first N harmonics that meet the preset calculation accuracy requirements, where N is a positive integer.

[0048] Furthermore, step six specifically includes:

[0049] S61: Define the stator pitch using the selected stator tooth width, stator slot width, and stator slot depth as design parameters. The stator slot depth and stator slot depth respectively satisfy the following constraints:

[0050] Tooth width parameter set B t for ;

[0051] Slot width set B s for ;

[0052] groove depth set H s for ;

[0053] in and The element index of the corresponding parameter set; This represents the minimum value of the stator tooth width. This represents the maximum value of the stator tooth width; This is the minimum value of the stator slot width. This represents the maximum value of the stator slot width. This represents the minimum stator slot depth. W represents the maximum stator slot depth, and Y represents the maximum element index of the corresponding set.

[0054] S62: Select the stator tooth width according to the parameter value range of the constraint conditions in step S61. Stator slot width and stator slot depth Different combinations of these are used, and based on the fact that the stator pitch is the sum of the stator tooth width and the stator slot width, they are substituted into the circumferential distribution function of this type of motor based on stator cogging effect compensation in step three. And the main analysis of the rotor cogging torque expression in step five. The cogging torque ripple amplitude corresponding to each design parameter combination is obtained; the stator tooth width b is selected to minimize the cogging torque ripple amplitude of the main analysis rotor. t Stator slot width and stator slot depth These are the design parameters, representing the design results of the tooth groove structure parameters.

[0055] Furthermore, in step S61, the stator tooth width is included in the constraint conditions. Stator slot width and stator tooth pitch satisfy And stator tooth pitch It is determined by the size of the motor and the number of stator slots.

[0056] Further, in step S61, the width of the sub-tooth to be selected... The range of values, the width of the sub-slot to be selected The range of values, the depth of the sub-slot to be selected The range of values ​​is determined to ensure that the magnetic flux density of the motor core does not exceed the allowable magnetic flux density of the core material under rated operating conditions, and is based on the allowable magnetic flux density value with a safety margin for engineering purposes; minimum stator slot width. Minimum stator slot depth The dimensions of the stator winding conductors and the thickness of the insulation layer are determined to meet the requirements for winding installation space, taking into account the motor heat dissipation conditions and winding assembly process requirements in actual engineering projects; simultaneously, the stator slot width... Stator slot depth The value is determined to meet the requirements of the motor's magnetic circuit continuity, mechanical strength, or structural stability.

[0057] Furthermore, the tooth cogging parameter design method is applied to the preliminary design stage of this type of axial magnetic field dual-rotor synchronous motor based on a through-type stator tooth cogging structure, suppressing the tooth cogging torque pulsation amplitude of the main analysis rotor under the premise of satisfying the structural and electromagnetic constraint conditions of claim 9.

[0058] 3. Beneficial effects:

[0059] (1) The present invention provides a method for designing the cogging parameters of a through-type stator of a dual-rotor synchronous motor with an axial magnetic field. Based on the characteristics of the through-type stator cogging unit structure and the dual-air-gap magnetic circuit, the analytical calculation of the main rotor cogging torque can be performed under a unified magnetic circuit model through the dual-air-gap permeability function. This analytical method intuitively reflects the influence of stator slot width, tooth width, and slot depth parameters on the main rotor cogging torque, providing a clear physical basis for the selection of cogging structure parameters. This reduces the complexity of the dual-air-gap structure on the main rotor cogging torque analysis and facilitates its application in the motor design stage.

[0060] (2) The present invention provides a method for designing the cogging parameters of a through-type stator of a dual-rotor synchronous motor with axial magnetic field. The method selects the rotor with larger cogging torque for targeted optimization design, avoids the electromagnetic coupling effect between the two rotors, reduces the adverse effects of "approximation processing" and "nonlinear factors" in the comprehensive modeling process of the dual rotors, and the analysis results have higher accuracy. By combining and comparing the cogging structural parameters under the premise of meeting the stator pitch and structural constraints, the method described in the present invention is applicable to the preliminary stage of the design of this type of synchronous motor structure. The finite element fine analysis and prototype design provide a reasonable initial parameter selection range, which is conducive to shortening the motor structure design cycle.

[0061] (3) The present invention provides a design method for the cogging parameters of the through-type stator of a dual-rotor synchronous motor with axial magnetic field. It fully considers the average value of the space function of the air gap magnetic permeability of the dual air gap, the modulation coefficient and the two types of attenuation coefficients of the modulation coefficient. It also establishes the analytical expression of the cogging torque of the main analysis rotor by means of the virtual displacement method, and represents the variation law of the cogging torque of the main analysis rotor in an explicit analytical form. Thus, it is possible to adjust the parameters of this type of motor without relying on a large number of finite element simulations or experience.

[0062] (4) The method for designing the cogging parameters of the through-type stator of the dual rotor synchronous motor with axial magnetic field provided by the present invention has good versatility and can be extended to the process of cogging torque analysis and structural parameter design of axial flux and radial flux synchronous motors with double air gap structure. It provides an implementable technical means for the suppression of cogging torque and rapid selection of structural parameters of such motors in the engineering design stage. Attached Figure Description

[0063] Figure 1 This is an overall flowchart of the present invention;

[0064] Figure 2 This is an axial view of the stator core of the axial magnetic field dual rotor synchronous motor based on a through-type stator slot structure involved in this invention.

[0065] Figure 3 This is a radial view of the axial magnetic field dual rotor synchronous motor based on a through stator slot structure involved in this invention, unfolded in the circumferential direction.

[0066] Figure 4 This is the equivalent magnetic circuit diagram of the axial magnetic field dual-rotor synchronous motor based on the through-type stator slot structure involved in this invention;

[0067] Figure 5 This is a comparison model of the Ansys Electronics finite element simulation results of the embodiments involved in this invention;

[0068] Figure 6-10 shows a comparison between the finite element simulation results of the embodiments involved in this invention and the calculation results of the design method proposed in the invention. Detailed Implementation

[0069] The present invention will now be described in detail with reference to the accompanying drawings.

[0070] As attached Figure 1 As shown, a method for designing the cogging parameters of a through-type stator of an axial magnetic field dual-rotor synchronous motor is characterized in that: the axial magnetic field dual-rotor synchronous motor includes discrete axial through-type yokeless stator cogging units and rotors on both sides of the stator axial direction; the rotors adopt DC excitation; the stator is composed of multiple independent and structurally identical cogging units, and the stator adopts open slots and fractional slot concentrated windings.

[0071] The stator tooth parameters include stator tooth pitch, stator slot width, and stator slot depth, and their design method includes the following steps;

[0072] Step 1: Calculate the least common multiple of the number of rotor poles and stator slots for both rotors. Select the rotor with the smallest least common multiple and define it as the main analysis rotor. Under the condition of stator open circuit and neglecting the influence of stator and rotor core slots, obtain the ideal axial air gap magnetic flux density distribution function in the rotor circumferential direction by superimposing ideal rectangular waves based on the winding distribution, number of winding turns, excitation current, and air gap length of the main analysis rotor. And perform a Fourier expansion on it;

[0073] Step Two: Calculate the multiple algebraic terms and coefficients of the per-unit distribution function of the magnetic permeability of the axial air gap magnetic circuit in the circumferential direction, considering the influence of stator core slotting. Specifically, this includes: ignoring the influence of rotor core slotting, considering the influence of stator core slotting, and calculating the average algebraic term of the per-unit distribution function of the magnetic permeability of the magnetic circuit based on the stator tooth width, stator slot width, and stator tooth pitch. The stator tooth pitch is the sum of the stator tooth width and the stator slot width. Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator tooth width, stator slot width, and stator tooth pitch. The stator tooth pitch is the sum of the stator tooth width and the stator slot width. Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator tooth width, stator slot width, and stator tooth pitch. attenuation coefficient The stator tooth pitch is the sum of the stator tooth width and the stator slot width; ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator slot depth. attenuation coefficient Where m is the spatial harmonic order of the per-unit distribution function of the magnetic permeability of the magnetic circuit;

[0074] Step 3: For a dual-air-gap dual-rotor synchronous motor with a through-type stator slot structure and axial magnetic field, using the magnetic permeability distribution function per unit cross-sectional area of ​​the axial air-gap magnetic circuit in the circumferential direction (ignoring the influence of stator and rotor core slotting) as the benchmark value, based on algebraic terms or coefficients... , , and The circumferential distribution function of this type of motor based on stator cogging effect compensation was obtained. Distribution function This represents the per-unit value of the magnetic permeability of the axial air gap magnetic circuit, where... The spatial position radian in the circumferential direction of the stator;

[0075] Step 4: Considering the cogging effect of the stator slots and ignoring the influence of the rotor core slots, the axial magnetic flux density circumferential distribution functions of the air gap between the stator and rotor 1, and between the stator and rotor 2 are approximately equal; the ideal air gap axial magnetic flux density distribution function obtained in Step 1 is then used as the basis for this step. The per-unit distribution function in the circumferential direction based on stator cogging effect compensation for this type of motor obtained in step three. Multiplying these together yields the axial air gap magnetic flux density distribution function in the circumferential direction of this type of motor, based on stator cogging effect compensation.

[0076] Step 5: Ignoring the core magnetic reluctance and assuming the rotor excitation current is constant, the axial air gap magnetic flux density distribution function of the stator in the circumferential direction based on the cogging effect compensation obtained in Step 4 is used to obtain the magnetic co-energy of the motor air gap magnetic field under different relative positions of the stator and the main analysis rotor; the virtual displacement derivative of this magnetic co-energy with respect to the change in the relative positions of the stator and the main analysis rotor is obtained to obtain the analytical expression of the cogging torque of the main analysis rotor under different relative positions of the stator and the main analysis rotor.

[0077] Step Six: Set the stator tooth width, stator slot width, and stator slot depth as candidate parameters, where the stator tooth width and stator slot width are arc lengths, and the slot depth is the length. Under the conditions of satisfying motor installation and electromagnetic constraints, pre-set the set of candidate elements for the stator tooth pitch, stator slot width, and stator slot depth. Substitute the elements in the set of candidate elements into the analytical expression of the rotor cogging torque in the main analysis, and select the stator tooth width, stator slot width, and stator slot depth that minimize the amplitude of the rotor cogging torque in the main analysis as the design result of the cogging geometry parameters.

[0078] Furthermore, step one specifically includes:

[0079] S11: Ignoring the influence of stator and rotor core slotting, assuming the stator winding is open-circuited, the rotor uses a single-layer distributed winding, and DC current excitation, calculate the ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction of this type of motor; specifically including:

[0080] Spatial position radian of stator circumference The spatial position radian of rotor No. 1 in the circumferential direction is represented by... The spatial position radian of rotor No. 2 in the circumferential direction is indicated by... The relative positional radian between the stator and the main analytical rotor is represented by θ; the position of the axis of any slot in the stator circumferential direction is predetermined as the reference zero position in the stator space. The position of the central axis of any N pole of rotor 1 on the teeth is preset as the reference zero position in rotor 1 space. Stator position and the position of rotor No. 1 The relative position radians between them are used This indicates that the position of the central axis of any N pole of rotor 2 on the teeth is preset as the reference zero position in rotor 2 space. Stator position Position of rotor No. 2 The relative position radians between them are used This indicates that if rotor 1 is defined as the main analysis rotor, then... If rotor number 2 is defined as the main analysis rotor, then At different radii of the axial magnetic field motor, the air gaps between the stator and rotor 1 and between the stator and rotor 2 in the circumferential direction have approximately equal axial magnetic flux density distributions, which can be approximately represented as a superposition of ideal rectangular waves. Furthermore, these superimposed rectangular waves exhibit abrupt changes within each pair of magnetic poles. Second-rate; ,in Main analysis of rotor slot number, The main analysis focuses on the number of rotor pole pairs; At that time, the ideal rectangular wave superposition expression of the axial air gap magnetic flux density distribution in the circumferential direction generated by the rotor excitation is analyzed. for:

[0081] (1);

[0082] In the formula, For each magnetic flux density jump, The periodicity of this expression on a circle is as follows: ; air permeability; The main analysis focuses on the number of turns in the rotor excitation winding. The main analysis focuses on the rotor excitation current; This is the air gap length; Indicates the first Whether the magnetic flux density jump is upward or downward is determined by the following formula:

[0083] (2);

[0084] S12: Performing a Fourier series expansion on the ideal rectangular wave superposition expression of the axial air gap magnetic flux density distribution in the circumferential direction, we obtain:

[0085] (3)

[0086] In the above formula, for The average value of this is 0, based on general knowledge theory; for of Second harmonic amplitude.

[0087] Furthermore, step two involves sequential calculations based on the following steps:

[0088] S21: Using the magnetic permeability distribution function per unit cross-sectional area of ​​the axial air gap magnetic circuit in the circumferential direction, ignoring the influence of stator and rotor core slotting, as the benchmark value, and ignoring the influence of rotor core slotting, a Carter coefficient is introduced to characterize the degree of reduction in the average magnetic permeability of the axial air gap caused by stator slotting. Based on the stator tooth width, stator slot width, and stator tooth pitch, calculate the algebraic term of the average value of the per-unit distribution function of the magnetic permeability of the axial air gap magnetic circuit in the circumferential direction. ;

[0089] S22: Order Let the spatial harmonic order of the per-unit distribution function of magnetic permeability of the axial air gap magnetic circuit in the circumferential direction be the reference value. Ignoring the influence of stator and rotor core slotting, the permeability distribution function of the axial air gap magnetic circuit in the circumferential direction is used as the benchmark value. Then, considering the influence of stator core slotting, the algebraic term of the harmonic components of the per-unit distribution function of magnetic permeability of the axial air gap magnetic circuit in the circumferential direction corresponding to the magnetic field modulation effect of stator core slotting is calculated based on the stator tooth width, stator slot width, and stator tooth pitch. ;

[0090] S23: Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the complex boundary region containing stator slots is mapped to a regularized domain using the Schwarz-Christophe transform; the regularized domain is either an upper half-plane regularized domain or a rectangular regularized domain; after solving, an inverse transform is performed to obtain the logarithmic terms generated by the stator tooth width, stator slot width, and stator tooth pitch. attenuation coefficient ;

[0091] S24: Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the complex boundary region containing stator slots is mapped to a regularized domain using the Schwarz-Christophe transform; after solving, an inverse transform is performed to obtain the logarithmic terms generated by the slot depth. attenuation coefficient .

[0092] Furthermore, the process of obtaining the distribution function of the per-unit value of magnetic permeability of the axial air gap magnetic circuit corresponding to the unit cross-sectional area in step three is as follows: For the through-type stator cogging effect of the dual-rotor synchronous motor with axial magnetic field, taking the distribution function of magnetic permeability of the axial air gap magnetic circuit per-unit cross-sectional area in the circumferential direction, ignoring the influence of stator and rotor core slotting, as the benchmark value, ignoring the influence of rotor core slotting, and considering the influence of stator core slotting, the distribution function of the per-unit value of magnetic permeability of the axial air gap magnetic circuit per-unit cross-sectional area is obtained as follows: :

[0093] (4);

[0094] In the formula, ; ; ; ; This refers to the number of stator slots; Carter's coefficient; For stator tooth width; This refers to the width of the stator slot; The length of the air gap; ; ; ; The stator slot depth is the stator slot opening; here, the stator tooth width is... and stator slot width All adopt the outer radius of the stator core of this axial magnetic field motor Arc length at the radius. Here, tooth pitch. and slot width All adopted Figure 2 As shown The arc length at the radius position.

[0095] Furthermore, step four obtains the axial air gap magnetic flux density distribution function in the circumferential direction of this type of motor based on stator cogging effect compensation, specifically as follows: the relative position arc between the main analysis rotor and stator obtained in step one. The time-major analysis of the ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction generated by the rotor excitation is a key feature. Based on this, ignoring the influence of stator and rotor core slotting, we consider the relative positions between the stator and the main analytical rotor. , to obtain ( - ( ) is an ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction of the independent variable. The following formula is multiplied by the function obtained in step three. The axial air gap magnetic flux density distribution function in the circumferential direction based on the stator slot cogging effect was obtained. :

[0096] (5).

[0097] Furthermore, step five specifically includes:

[0098] S51: Approximating the core reluctance as 0, the magnetic co-energy equals the magnetic field energy. All magnetic field energy is stored in the air gap magnetic field, and the magnetic field energy in the slot region is ignored. The analytical expression for the magnetic co-energy of the magnetic fields in the two air gaps inside the motor is W. c (θ) is:

[0099] (6);

[0100] In the above formula: , and These are the inner and outer radii of the stator core of the axial magnetic field motor, respectively.

[0101] In this step, the result obtained in step four is first processed. Performing the squaring operation on the following formula, we get:

[0102]

[0103] Then, the obtained Substituting the result into the analytical expression for the magnetic co-energy of the magnetic field in the two air gaps inside the motor... .

[0104] S52: The result obtained in step four Substituting the analytical expression for the magnetic co-energy of the magnetic field in the two air gaps inside the motor ;

[0105] S53: Will right Differentiating, we obtain the relative positions of the stator and the main rotor. The principal analysis expression for rotor cogging torque with independent variables. :

[0106] (7);

[0107] In the formula: and They are respectively function and The amplitude of the second harmonic component;

[0108] ;

[0109] ;

[0110] The Kronecker delta function is defined as follows: ;

[0111] Cut Amplitude calculations are performed on the finite-order harmonic components of the function; among them, for and The finite harmonic components are the first M harmonics that meet the preset calculation accuracy requirements, where M is a positive integer; Specifically, for... The finite harmonic components are the first N harmonics that meet the preset calculation accuracy requirements, where N is a positive integer.

[0112] Furthermore, step six specifically includes:

[0113] S61: Stator tooth width to be selected Stator slot width and stator slot depth Define the stator tooth pitch as a design parameter. Stator slot depth and stator slot depth The following constraints must be satisfied respectively:

[0114] Tooth width parameter set B t for ;

[0115] Slot width set B s for ;

[0116] groove depth set H s for ;

[0117] in and The element index of the corresponding parameter set; This represents the minimum value of the stator tooth width. This represents the maximum value of the stator tooth width; This is the minimum value of the stator slot width. This represents the maximum value of the stator slot width. This represents the minimum stator slot depth. W represents the maximum stator slot depth, and Y represents the maximum element index of the corresponding set.

[0118] S62: Select the stator tooth width according to the parameter value range of the constraint conditions in step S61. Stator slot width and stator slot depth Different combinations of these are used, and based on the fact that the stator pitch is the sum of the stator tooth width and the stator slot width, they are substituted into the circumferential distribution function of this type of motor based on stator cogging effect compensation in step three. And the main analysis of the rotor cogging torque expression in step five. The cogging torque pulsation amplitude corresponding to each combination of design parameters is obtained; the stator tooth width that minimizes the cogging torque pulsation amplitude of the main analysis rotor is selected. Stator slot width and stator slot depth These are the design parameters, representing the design results of the tooth groove structure parameters.

[0119] Furthermore, in step S61, the stator tooth width is included in the constraint conditions. Stator slot width and stator tooth pitch satisfy And stator tooth pitch It is determined by the size of the motor and the number of stator slots.

[0120] Further, in step S61, the width of the sub-tooth to be selected... The range of values, the width of the sub-slot to be selected The range of values, the depth of the sub-slot to be selected The range of values ​​is determined to ensure that the magnetic flux density of the motor core does not exceed the allowable magnetic flux density of the core material under rated operating conditions, and is based on the allowable magnetic flux density value with a safety margin for engineering purposes; minimum stator slot width. Minimum stator slot depth The dimensions of the stator winding conductors and the thickness of the insulation layer are determined to meet the requirements for winding installation space, taking into account the motor heat dissipation conditions and winding assembly process requirements in actual engineering projects; simultaneously, the stator slot width... Stator slot depth The value is determined to meet the requirements of the motor's magnetic circuit continuity, mechanical strength, or structural stability.

[0121] Furthermore, the tooth cogging parameter design method is applied to the preliminary design stage of this type of axial magnetic field dual-rotor synchronous motor based on a through-type stator tooth cogging structure, suppressing the tooth cogging torque pulsation amplitude of the main analysis rotor under the premise of satisfying the structural and electromagnetic constraint conditions of claim 9.

[0122] Example:

[0123] This embodiment uses the design of through-type stator cogging parameters of an axial magnetic field dual-rotor synchronous motor as an example to illustrate and verify the method. This embodiment is based on the design parameters of a laboratory prototype for verification, and its structure is as follows: Figure 2 , Figure 3 As shown. Figure 2 This is an axial view of the stator core of an axial magnetic field dual-rotor synchronous motor based on a through-type stator slot structure, as described in this invention. R1 and R2 are the inner and outer radii of the stator core, respectively. Figure 3 This is a radially unfolded view of the axial magnetic field dual-rotor synchronous motor based on a through-type stator slot structure involved in this invention. The two reference zero positions of the rotor and stator space are marked in the figure. Reference location Reference location and Reference location.

[0124] Besides the tooth pitch, slot width, and slot depth parameters to be designed in this invention, the main parameters are as follows: Table 1:

[0125] Table 1. Main parameters of the axial magnetic field dual-rotor synchronous motor based on the through-type stator slot structure.

[0126]

[0127] The prototype stator employs a three-phase symmetrical six-slot double-layer fractional-slot concentrated winding; both rotors use the same 24-slot iron core with single-layer integer-slot windings. The stator has 2 and 4 dominant pole pairs respectively. Both rotor windings use DC excitation, with rotor number one having 2 dominant pole pairs and rotor number two having 4 dominant pole pairs. This structure allows the stator to couple with the dominant poles of the two rotors for energy exchange, and the magnetic field coupling is as follows: Figure 4 As shown.

[0128] Since the number of dominant pole pairs on rotor 1 of this prototype is 2, and the number of dominant pole pairs on rotor 2 is 4, the least common multiple of the number of dominant pole pairs and the number of stator slots on the two rotors is 12 and 24, respectively. Therefore, rotor 1 is the main analysis rotor when designing the cogging parameters of this prototype.

[0129] Based on this parameter design method and the design accuracy requirements, a set of stator tooth width parameters is set. Slot width set and the set of groove depths H s The number of elements W in the tooth width and slot width sets is 5, and the number of elements Y in the slot depth set is 5. Table 2 shows the main analytical rotor cogging torque obtained from the theoretical calculation of the axial magnetic field motor based on the parameters in Table 1. In this process, the slot depth set element 1: slot depth 26.4mm; slot depth set element 2: slot depth 31.4mm; slot depth set element 3: slot depth 36.4mm; slot depth set element 4: slot depth 41.4mm; slot depth set element 5: slot depth 46.4mm are used. Based on the above elements, the slot width and tooth width are further adjusted to obtain the optimal analytical solution.

[0130] Table 2. Main analysis rotor cogging torque calculated based on the parameters in Table 1 of the axial magnetic field motor.

[0131]

[0132] Table 3 shows the rotor cogging torque obtained from the two-dimensional finite element simulation. Figure 5 This is a comparison model of the finite element simulation results in Ansys Electronics; combined with Table 3 and... Figure 5 The amplitude of rotor cogging torque pulsation was compared with that in Table 2 for main analysis.

[0133] Table 3. Main analysis rotor cogging torque obtained from two-dimensional finite element simulation.

[0134]

[0135] like Figures 6-10 As shown, the analytical waveform and finite element analysis waveform of the cogging torque of the main rotor during one mechanical cycle of the main rotor rotation are compared: Figure 6 (a)-(e) correspond to groove depth set element 1: groove depth 26.4mm, 5 waveforms correspond to different tooth widths and groove widths. Figure 6 of (f), Figure 7 (g)-(j) corresponds to groove depth set element 2: groove depth 31.4mm, 5 waveforms correspond to different tooth widths and groove widths. Figure 7 (k), (l), Figure 8 The (m)-(o) corresponds to the groove depth set element 3: groove depth 36.4mm, and the 5 waveforms correspond to different tooth widths and groove widths. Figure 8 (p)-(r), Figure 9 (s) and (t) correspond to groove depth set element 4: groove depth 41.4mm, and the 5 waveforms correspond to different tooth widths and groove widths. Figure 9 (u)-(x), Figure 10 (y) Corresponding to groove depth set element 5: groove depth 46.4mm, 5 waveforms correspond to different tooth widths and groove widths.

[0136] According to Table 2, Table 3, Figure 6 The results show that the optimal solution for the tooth groove parameters obtained by theoretical calculation is basically consistent with the finite element simulation results from Ansys Electronics. Figure 6 The horizontal axis represents the rotor rotation angle, which is the relative position of the stator and rotor. Based on the optimal solution, after adjusting the cogging parameters, the theoretically calculated cogging torque results are basically consistent with the Ansys Electronics finite element simulation results.

[0137] Through Table 2, Table 3, Figure 6It can also be seen that there is still a certain proportion of difference between theoretical calculations and simulation results. The main reasons include, but are not limited to, the following: (1) Carter coefficient The calculation uses the slot width and tooth width positions located in Figure 2 In (1) The position was not analyzed point by point using the radius position, which led to errors; (2) The one-dimensional equivalent magnetic circuit was still used, which led to errors; (3) Since the finite element simulation model required by the present invention has many parameter types and the three-dimensional simulation has a huge amount of computation, two-dimensional modeling is adopted. However, in order to ensure that the tooth width and slot width of the two-dimensional model are as consistent as possible in the radial magnetic circuit direction, the model radius was "artificially enlarged". However, this measure will increase the "nonlinearity" of the conversion relationship between "analytical calculation based on axial magnetic field motor model" and "numerical calculation based on two-dimensional finite element model". Therefore, the average tooth width, average slot width, magnetic circuit cross-sectional area, slot depth and air gap length introduced in the above conversion process will inevitably introduce nonlinear errors, which is also an inherent technical problem in this field; (4) The error introduced by ignoring the influence of rotor slot is ignored.

[0138] Although the present invention has been disclosed above with reference to preferred embodiments, these are not intended to limit the invention. Any person skilled in the art can make various changes or modifications without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention should be defined by the scope of the claims of this application.

Claims

1. A method for designing slot parameters of a through-type stator of an axial field doubly-fed synchronous machine, characterized in that: The axial magnetic field dual-rotor synchronous motor includes discrete axial through-type yokeless stator slotted units and rotors on both sides of the stator axially; the rotors are DC excitation; the stator is composed of multiple independent and structurally identical slotted units, and the stator adopts open slots and fractional slot concentrated windings; Stator tooth parameters include stator tooth pitch, stator slot width, and stator slot depth, and their design methods. Includes the following steps; Step 1: Calculate the least common multiple of the number of rotor poles and stator slots for both rotors. Select the rotor with the smallest least common multiple and define it as the main analysis rotor. Under the condition of stator open circuit and neglecting the influence of stator and rotor core slots, obtain the ideal axial air gap magnetic flux density distribution function in the rotor circumferential direction by superimposing ideal rectangular waves based on the winding distribution, number of winding turns, excitation current, and air gap length of the main analysis rotor. And perform a Fourier expansion on it; Step Two: Calculate the multiple algebraic terms and coefficients of the per-unit distribution function of the magnetic permeability of the axial air gap magnetic circuit in the circumferential direction, considering the influence of stator core slotting. Specifically, this includes: ignoring the influence of rotor core slotting, considering the influence of stator core slotting, and calculating the average algebraic term of the per-unit distribution function of the magnetic permeability of the magnetic circuit based on the stator tooth width, stator slot width, and stator tooth pitch. The stator tooth pitch is the sum of the stator tooth width and the stator slot width. Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator tooth width, stator slot width, and stator tooth pitch. The stator tooth pitch is the sum of the stator tooth width and the stator slot width. Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator tooth width, stator slot width, and stator tooth pitch. attenuation coefficient The stator tooth pitch is the sum of the stator tooth width and the stator slot width; ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the algebraic terms of the harmonic components of the per-unit distribution function of the magnetic circuit are calculated based on the stator slot depth. attenuation coefficient Where m is the spatial harmonic order of the per-unit distribution function of the magnetic permeability of the magnetic circuit; Step 3: For a dual-air-gap dual-rotor synchronous motor with a through-type stator slot structure and axial magnetic field, using the magnetic permeability distribution function per unit cross-sectional area of ​​the axial air-gap magnetic circuit in the circumferential direction (ignoring the influence of stator and rotor core slotting) as the benchmark value, based on algebraic terms or coefficients... , , and The circumferential distribution function of this type of motor based on stator cogging effect compensation was obtained. Distribution function This represents the per-unit value of the magnetic permeability of the axial air gap magnetic circuit, where... The spatial position radian in the circumferential direction of the stator; Step 4: Considering the cogging effect of the stator slots and ignoring the influence of the rotor core slots, the axial magnetic flux density circumferential distribution functions of the air gap between the stator and rotor 1, and between the stator and rotor 2 are approximately equal; the ideal air gap axial magnetic flux density distribution function obtained in Step 1 is then used as the basis for this step. The per-unit distribution function in the circumferential direction based on stator cogging effect compensation for this type of motor obtained in step three. Multiplying these together yields the axial air gap magnetic flux density distribution function in the circumferential direction of this type of motor, based on stator cogging effect compensation. Step 5: Ignoring the core magnetic reluctance and assuming the rotor excitation current is constant, the axial air gap magnetic flux density distribution function of the stator in the circumferential direction based on the cogging effect compensation obtained in Step 4 is used to obtain the magnetic co-energy of the motor air gap magnetic field under different relative positions of the stator and the main analysis rotor. The virtual displacement derivative of the magnetic co-energy with respect to the change in the relative position of the stator and the main analytical rotor is obtained, and the analytical expression of the cogging torque of the main analytical rotor under different relative position conditions of the stator and the main analytical rotor is obtained. Step Six: Set the stator tooth width, stator slot width, and stator slot depth as candidate parameters, where the stator tooth width and stator slot width are arc lengths, and the slot depth is the length. Under the conditions of satisfying motor installation and electromagnetic constraints, pre-set the set of candidate elements for the stator tooth pitch, stator slot width, and stator slot depth. Substitute the elements in the set of candidate elements into the analytical expression of the rotor cogging torque in the main analysis, and select the stator tooth width, stator slot width, and stator slot depth that minimize the amplitude of the rotor cogging torque in the main analysis as the design result of the cogging geometry parameters.

2. The method for designing the through-type stator cogging parameters of an axial magnetic field dual-rotor synchronous motor according to claim 1, characterized in that: Step one specifically includes: S11: Ignoring the influence of stator and rotor core slotting, assuming the stator winding is open-circuited, the rotor uses a single-layer distributed winding, and DC current excitation, calculate the ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction of this type of motor; specifically including: Spatial position radian of stator circumference The spatial position radian of rotor No. 1 in the circumferential direction is represented by... The spatial position radian of rotor No. 2 in the circumferential direction is indicated by... The relative positional radian between the stator and the main analytical rotor is represented by θ; the position of the axis of any slot in the stator circumferential direction is predetermined as the reference zero position in the stator space. The position of the central axis of any N pole of rotor 1 on the teeth is preset as the reference zero position in rotor 1 space. Stator position and the position of rotor No. 1 The relative position radians between them are used This indicates that the position of the central axis of any N pole of rotor 2 on the teeth is preset as the reference zero position in rotor 2 space. Stator position Position of rotor No. 2 The relative position radians between them are used This indicates that if rotor 1 is defined as the main analysis rotor, then... If rotor number 2 is defined as the main analysis rotor, then At different radii of the axial magnetic field motor, the air gaps between the stator and rotor 1 and between the stator and rotor 2 in the circumferential direction have approximately equal axial magnetic flux density distributions, which can be approximately represented as a superposition of ideal rectangular waves. Furthermore, these superimposed rectangular waves exhibit abrupt changes within each pair of magnetic poles. Second-rate; ,in Main analysis of rotor slot number, The main analysis focuses on the number of rotor pole pairs; At that time, the ideal rectangular wave superposition expression of the axial air gap magnetic flux density distribution in the circumferential direction generated by the rotor excitation is analyzed. for: （1） ； In the formula, For each magnetic flux density jump, The periodicity of this expression on a circle is as follows: ; air permeability; The main analysis focuses on the number of turns in the rotor excitation winding. The main analysis focuses on the rotor excitation current; This is the air gap length; Indicates the first Whether the magnetic flux density jump is upward or downward is determined by the following formula: （2）； S12: Performing a Fourier series expansion on the ideal rectangular wave superposition expression of the axial air gap magnetic flux density distribution in the circumferential direction, we obtain: （3） In the above formula, is the average value, which is 0 based on the general theory; is the average value, which is 0 based on the general theory; is the second harmonic amplitude.​​ 3. The method for designing the through-type stator cogging parameters of an axial magnetic field dual-rotor synchronous motor according to claim 1, characterized in that: Step two involves performing calculations sequentially based on the following steps: S21: Using the magnetic permeability distribution function per unit cross-sectional area of ​​the axial air gap magnetic circuit in the circumferential direction, ignoring the influence of stator and rotor core slotting, as the benchmark value, and ignoring the influence of rotor core slotting, a Carter coefficient is introduced to characterize the degree of reduction in the average magnetic permeability of the axial air gap caused by stator slotting. Based on the stator tooth width, stator slot width, and stator tooth pitch, calculate the algebraic term of the average value of the per-unit distribution function of the magnetic permeability of the axial air gap magnetic circuit in the circumferential direction. ; S22: Order Let the spatial harmonic order of the per-unit distribution function of magnetic permeability of the axial air gap magnetic circuit in the circumferential direction be the reference value. Ignoring the influence of stator and rotor core slotting, the permeability distribution function of the axial air gap magnetic circuit in the circumferential direction is used as the benchmark value. Then, considering the influence of stator core slotting, the algebraic term of the harmonic components of the per-unit distribution function of magnetic permeability of the axial air gap magnetic circuit in the circumferential direction corresponding to the magnetic field modulation effect of stator core slotting is calculated based on the stator tooth width, stator slot width, and stator tooth pitch. ; S23: Ignoring the influence of rotor core slotting, but considering the influence of stator core slotting, the complex boundary region containing stator slots is mapped to a regularized domain using the Schwarz-Christophe transform; the regularized domain is either an upper half-plane regularized domain or a rectangular regularized domain; after solving, an inverse transform is performed to obtain the logarithmic terms generated by the stator tooth width, stator slot width, and stator tooth pitch. attenuation coefficient ; S24: ignoring the rotor core slotting effect, considering the stator core slotting effect, mapping the complex boundary region containing the stator opening slot to the regular domain through Schwarz-Christoffel transformation, and then inverse transforming to obtain the attenuation coefficient of the algebraic term generated by the slot depth . .

4. The axial field doubly-fed synchronous machine through-axial stator tooth slot parameter design method of claim 3, wherein: Step 3, specifically the process of obtaining the distribution function of the per-unit value of magnetic permeability of the axial air gap magnetic circuit per unit cross-sectional area, is as follows: For the through-type stator cogging effect of the dual-rotor synchronous motor with axial magnetic field, the distribution function of magnetic permeability of the axial air gap magnetic circuit per unit cross-sectional area in the circumferential direction, ignoring the influence of stator and rotor core slotting, is used as the reference value. Ignoring the influence of rotor core slotting and considering the influence of stator core slotting, the distribution function of the per-unit value of magnetic permeability of the axial air gap magnetic circuit per unit cross-sectional area is obtained as follows: : （4）； In the formula, ; ; ; ; This refers to the number of stator slots; Carter's coefficient; For stator tooth width; This refers to the width of the stator slot; The length of the air gap; ; ; ; The stator slot depth is the stator slot opening; here, the stator tooth width is... and stator slot width All adopt the outer radius of the stator core of this axial magnetic field motor The arc length at the radius position.

5. The axial field doubly-fed synchronous machine through-axial stator tooth parameter design method of claim 4, wherein: Step four obtains the axial air gap magnetic flux density distribution function in the circumferential direction of this type of motor based on stator cogging effect compensation, specifically as follows: the relative position arc between the main analysis rotor and stator obtained in step one. The time-major analysis of the ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction generated by the rotor excitation. Based on this, ignoring the influence of stator and rotor core slotting, we consider the relative positions between the stator and the main analytical rotor. , to obtain ( - ( ) is an ideal rectangular wave superposition function of the axial air gap magnetic flux density distribution in the circumferential direction of the independent variable. The following formula is multiplied by the function obtained in step three. The axial air gap magnetic flux density distribution function in the circumferential direction based on the stator slot cogging effect was obtained. : （5）。 6. The axial field doubly-fed synchronous machine through- shaft stator tooth slot parameter design method of claim 1, wherein: Step five specifically includes: S51: Approximating the core reluctance as 0, the magnetic co-energy equals the magnetic field energy. All magnetic field energy is stored in the air gap magnetic field, and the magnetic field energy in the slot region is ignored. The analytical expression for the magnetic co-energy of the magnetic fields in the two air gaps inside the motor is W. c (θ) is: （6）； In the above formulae: , and are the inner radius and the outer radius of the axial magnetic field motor stator core, respectively. S52: obtaining the magnetic field of the motor from the magnetic field of the motor obtained in step S51 Substitute the analytical expression of the magnetic field in the two air gaps of the motor ; S53: Will right Differentiating, we obtain the relative positions of the stator and the main rotor. The principal analysis expression for rotor cogging torque with independent variables. : （7）； wherein: and are respectively function and the amplitude of the second harmonic component; ； ； is the Kronecker delta function, which is defined as: ; Cut Amplitude calculations are performed on the finite-order harmonic components of the function; among them, for and The finite harmonic components are the first M harmonics that meet the preset calculation accuracy requirements, where M is a positive integer; Specifically, for... The finite harmonic components are the first N harmonics that meet the preset calculation accuracy requirements, where N is a positive integer.

7. The method for designing the through-type stator cogging parameters of an axial magnetic field dual-rotor synchronous motor according to claim 1, characterized in that: Step six specifically includes: S61: Stator tooth width to be selected Stator slot width and stator slot depth Define the stator tooth pitch as a design parameter. Stator slot depth and stator slot depth The following constraints must be satisfied respectively: set of tooth width parameters B t to ; Slot width set B s To ; Set of groove depths H s To ; in and The element index of the corresponding parameter set; This represents the minimum value of the stator tooth width. This represents the maximum value of the stator tooth width; This is the minimum value of the stator slot width. This represents the maximum value of the stator slot width. This represents the minimum stator slot depth. W represents the maximum stator slot depth, and Y represents the maximum element index of the corresponding set. S62: Select the stator tooth width according to the parameter value range of the constraint conditions in step S61. Stator slot width and stator slot depth Different combinations of these are used, and based on the fact that the stator pitch is the sum of the stator tooth width and the stator slot width, they are substituted into the circumferential distribution function of this type of motor based on stator cogging effect compensation in step three. And the main analysis of the rotor cogging torque expression in step five. The cogging torque pulsation amplitude corresponding to each combination of design parameters is obtained; the stator tooth width that minimizes the cogging torque pulsation amplitude of the main analysis rotor is selected. Stator slot width and stator slot depth These are the design parameters, representing the design results of the tooth groove structure parameters.

8. The axial field doubly-fed synchronous machine through- shaft stator tooth slot parameter design method of claim 7, wherein: In step S61, the stator tooth width is a constraint condition. Stator slot width and stator tooth pitch satisfy And stator tooth pitch It is determined by the size of the motor and the number of stator slots.

9. The axial field doubly-fed synchronous machine through- shaft stator tooth slot parameter design method of claim 8, wherein: In step S61, the width of the sub-tooth to be selected The range of values, the width of the sub-slot to be selected The range of values, the depth of the sub-slot to be selected The range of values ​​is determined to ensure that the magnetic flux density of the motor core does not exceed the allowable magnetic flux density of the core material under rated operating conditions, and is based on the allowable magnetic flux density value with a safety margin for engineering purposes; minimum stator slot width. Minimum stator slot depth The dimensions of the stator winding conductors and the thickness of the insulation layer are determined to meet the requirements for winding installation space, taking into account the motor heat dissipation conditions and winding assembly process requirements in actual engineering projects; simultaneously, the stator slot width... Stator slot depth The value is determined to meet the requirements of the motor's magnetic circuit continuity, mechanical strength, or structural stability.

10. The axial field doubly-fed synchronous machine through- shaft stator tooth slot parameter design method of claim 9, wherein: The tooth cogging parameter design method is applied to the preliminary design stage of this type of axial magnetic field dual-rotor synchronous motor based on a through-type stator tooth cogging structure. Under the premise of satisfying the structural and electromagnetic constraint conditions of claim 9, the tooth cogging torque pulsation amplitude of the main analysis rotor is suppressed.

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