An asymmetric axial electromagnetic force wave calculation method for an axial magnetic field permanent magnet memory motor

Abstract

The application discloses an asymmetric axial electromagnetic force wave calculation method of an axial magnetic field permanent magnet memory motor, which mainly comprises the following steps: determining a solving coordinate system, respectively establishing Poisson equations and Laplace equations for the motor according to different solving regions of air gaps and Halbach array permanent magnets, solving static axial air gap magnetic flux density and circumferential air gap magnetic flux density according to boundary conditions that should be met by an open-circuit magnetic field analytical model on the basis of obtaining a Laplace general solution, calculating a Halbach array permanent magnet magnetic motive force during motor operation, respectively calculating a single-phase winding generated magnetic motive force and a three-phase winding generated magnetic motive force when the motor is supplied with three-phase symmetrical sinusoidal currents, and deducing and calculating a motor axial air gap magnetic field distribution formula in the case of considering air gap permeability. In the case of ignoring air gap saturation, axial electromagnetic force acting on a unit area of the axial magnetic field permanent magnet memory motor is calculated according to Maxwell tensor equations.

Description

Technical Field

[0001] This invention belongs to the field of drive motors, specifically relating to a method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor. Background Technology

[0002] Motor vibration and noise (NVH) is one of the performance indicators of a motor, especially in the design of electric vehicle drive motors, where the NVH performance of the motor and electric drive system has become a current focus. Motor noise mainly includes three categories: electromagnetic noise, mechanical noise, and aerodynamic noise. Electromagnetic noise refers to the noise radiated by the electromagnetic force acting on the air gap between the stator and rotor, generating rotational force waves or pulsating force waves that cause the stator to vibrate. Due to the pursuit of high power density, lightweight miniaturization, and wide speed range design, permanent magnet synchronous motors have complex rotor structures and low stiffness, making it more difficult to suppress electromagnetic vibration and noise.

[0003] There are many existing analytical methods for calculating electromagnetic force waves. Several scholars have proposed analytical calculation methods for electromagnetic force harmonics based on qualitative analysis methods. Many researchers have calculated and compared the effects of different motor structure shapes and pole-slot combinations on the electromagnetic force waves of motors. However, most of these methods are for calculating electromagnetic force waves of radial motors, and there are very few analytical calculation methods for electromagnetic force waves of axial motors. Summary of the Invention

[0004] To address the technical problems mentioned in the background section, this invention proposes a method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:

[0006] A method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor includes the following steps:

[0007] S1. Based on the actual motor model, determine the solution coordinate system, and establish Poisson's equation and Laplace's equation for the motor in different solution regions for the air gap and Halbach array permanent magnet respectively.

[0008] S2. Based on the general solution of the Laplace equation, the static axial air gap magnetic flux density and circumferential air gap magnetic flux density are solved according to the boundary conditions that the analytical model of the unloaded magnetic field should satisfy.

[0009] S3. During motor operation, calculate the magnetomotive force of the motor's Halbach array permanent magnets; when a three-phase symmetrical sinusoidal current is applied to the motor, calculate the magnetomotive force generated by the single-phase winding and the magnetomotive force generated by the three-phase winding respectively.

[0010] S4. Based on the air gap permeability, calculate the axial air gap magnetic field distribution of the motor to obtain the expression for the air gap magnetic field of the axial magnetic field permanent magnet memory motor.

[0011] S5. Based on Maxwell's tensor equations, calculate the axial electromagnetic force acting on a unit air gap area, and calculate the time and spatial harmonics for each electromagnetic force wave obtained from the calculation.

[0012] Preferably, step S1 specifically includes:

[0013] Based on the motor's appearance and size requirements, a two-dimensional rectangular coordinate system is established. According to this system, the axial magnetization function of the Halbach array permanent magnet is assumed to be an even function, and the axial magnetization function is assumed to be an odd function. The formula for the magnetization function of the Halbach array permanent magnet in the axial magnetic field permanent magnet memory motor is expressed as:

[0014]

[0015] In the formula, The coefficients of the Fourier series of the circumferential magnetization function are represented. The coefficients of the Fourier series of the axial magnetization function are represented; p is the number of pole pairs of the motor; r is the radius of the motor; n represents the odd magnetization function, and n = 1, 3, 5...;

[0016] The axial magnetization coefficient α of the Halbach array r The formula is expressed as follows:

[0017]

[0018] In the formula, τ y τ represents the width of the axially magnetized permanent magnet; p Indicates the pole pitch; p is the number of pole pairs of the motor; r is the radius of the motor;

[0019] The formulas for the magnetic flux density B1 inside the permanent magnet and the magnetic flux density B2 at the air gap are as follows:

[0020] B1 = B r =μH1=μ0M=μ0μ r H2

[0021] B2=μ0H2

[0022] In the formula, Br represents the remanence of the permanent magnet; μ r denoted as the relative permeability of the permanent magnet; μ0 is the permeability of free space; H1 and H2 are the magnetic field strengths of each region, respectively.

[0023] The Halbach array permanent magnet region, i.e., the Poisson equation formula, is expressed as follows:

[0024]

[0025] In the formula, For permanent magnet region magnetic flux; μ r denoted as , where is the relative permeability of the permanent magnet; x and y are the coordinates of the x-axis and y-axis, respectively; divM is the divergence of the magnetization function M.

[0026] The air gap region of the axial magnetic field memory motor, expressed by the Laplace equation, is as follows:

[0027]

[0028] In the formula, denoted as the air gap magnetic flux; x and y are the coordinates of the x-axis and y-axis, respectively.

[0029] Preferably, step S2 specifically includes:

[0030] S21. By combining the expression for magnetic field strength with the axial magnetization coefficient of the Halbach array, the magnetic flux density B1 inside the permanent magnet, and the magnetic flux density B2 at the air gap, the general solution formula for the Laplace equation is obtained as follows:

[0031]

[0032]

[0033]

[0034] In the formula, C1 is the first undetermined coefficient; C2 is the second undetermined coefficient; C3 is the third undetermined coefficient; and C4 is the fourth undetermined coefficient. These four coefficients depend on the boundary conditions of the equivalent model. The exponential function part of the general solution of the Laplace equation is represented; n represents the magnetization odd function; p represents the number of pole pairs of the motor; r represents the radius of the motor.

[0035] The expression for the magnetic field strength is:

[0036]

[0037]

[0038] In the formula, H x Let represent the magnetic field strength along the x-axis, and Hy represent the magnetic field strength along the y-axis.

[0039] S22. Calculate the Laplace general solution coefficients based on the boundary conditions of the analytical model of the unloaded magnetic field. The formula is expressed as follows:

[0040]

[0041]

[0042]

[0043] C4 = -C3

[0044] In the formula, M n h is the magnetization function for permanent magnets. m g is the height of the permanent magnet; g is the length of the air gap 1;

[0045] Δ=μ r cosh(u n h m sinh(u n g)+cosh(u n g)sinh(u n h m )

[0046] The boundary condition formulas for the analytical model of the unloaded magnetic field are expressed as follows:

[0047]

[0048] H x2 | y＝0 =0

[0049]

[0050]

[0051] In the formula, HX1 and HX2 are the magnetic field strengths of the x-axis; By1 is the magnetic flux density of the y-axis; and Hy2 is the magnetic field strength of the y-axis.

[0052] S23. Based on the Laplace coefficient solution obtained in S22, the formulas for calculating the axial and circumferential components of the air gap magnetic flux density of the axial magnetic field permanent magnet memory motor are expressed as follows:

[0053]

[0054]

[0055] In the formula, μ0 is the vacuum permeability; Hm is the magnetic field strength; M is the magnetization function; g is the length of the air gap 1; and hm is the height of the permanent magnet.

[0056] The formula for the axial air gap magnetic flux density of an axial magnetic field permanent magnet memory motor is expressed as follows:

[0057]

[0058] Preferably, step S3 includes the following steps:

[0059] S31. Calculate the magnetomotive force generated by the permanent magnet. The formula is expressed as follows:

[0060]

[0061] In the formula, u is the harmonic order of the magnetomotive force of the permanent magnet, p is the number of poles of the permanent magnet, and θ is the rotation angle.

[0062] The formula for calculating the rotor magnetomotive force is expressed as follows:

[0063]

[0064] In the formula, μ0 is the air permeability; u is the harmonic order of the permanent magnet magnetomotive force. α is the amplitude of the magnetomotive force of the permanent magnet; p ω is the pole arc coefficient of the permanent magnet; w is the angular frequency of the motor rotation.

[0065] S32. Suppose that the axial magnetic field permanent magnet memory motor is composed of t unit motors, with Nc turns of fractional slot windings, ω angular frequency, and a total magnetomotive force iNc generated under the excitation of a sinusoidal current i with an effective value of Ic; the unit motor is a motor with Z0 slots and p0 pole pairs, Z0 / p0=Z / p; p is the number of permanent magnet rotor pole pairs, Z is the number of stator slots; Z0 is an integer multiple of m; m is the number of motor phases;

[0066] The formula for calculating the pulsating rectangular magnetomotive force generated by the armature winding magnetic field of an axial magnetic field permanent magnet memory motor, which is related to spatial θ and time t, is as follows:

[0067]

[0068] In the formula, w is the rotational angular velocity; θ is the rotation angle; v is the stator harmonic order; Fv is the amplitude of the v-th harmonic magnetomotive force of the stator winding; where,

[0069]

[0070] In the formula, k yv The short-pitch factor for the harmonic winding with a pole pair number of v;

[0071] S33. Calculate the axial magnetic field of a permanent magnet memory motor when three-phase current is applied to the armature winding. The formula is as follows:

[0072] F c (θ, t) = F cv cosvθsinωt+F cv cosv(θ-120°)sin(ωt-120°)+F cv cosv(θ+120°)sin(ωt+120°) When v=3k, F c (θ, t) = 0; when v = 6k + 1 When v = 6k-1

[0073] Preferably, step S4 includes the following steps:

[0074] S41. Calculate the air gap permeability of the axial magnetic field permanent magnet memory motor. The formula is as follows:

[0075] λ(θ, t) = λ00 + Σλk k cos(kZθ)

[0076] In the formula, λ0 is the air gap permeability constant, Z is the number of stator slots; k is the harmonic order of the stator teeth, and k is a natural number; Σλ k This represents the sum of the harmonic amplitudes of each order of the stator teeth;

[0077] S42. The axial air gap magnetic flux density is calculated based on the air gap permeability of the axial magnetic field permanent magnet memory motor. The formula is as follows:

[0078] B z (θ,t)=(f φ (θ,t)+F c (θ,t))·λ(θ,t)

[0079] Substituting the magnetomotive force of the permanent magnet, the magnetomotive force of the armature winding, and the air gap permeability into the equation, we obtain the following relationship:

[0080]

[0081] Preferably, step S5 includes the following steps:

[0082] The axial electromagnetic force acting on a unit air gap area is calculated using Maxwell's tensor method, ignoring the fourth term. The formula is as follows:

[0083]

[0084] 1) The square of ①

[0085] The time harmonics are μ1±μ2, and the spatial harmonics are ±μ1±μ2;

[0086] 2) The squared term of ②

[0087] The time harmonic is 2, and the spatial harmonic is (v1±v2)p;

[0088] 3) The square of ③

[0089] The time harmonics are μ1±μ2, and the spatial harmonics are (μ1±μ2)p±(k1±k2)Z;

[0090] 4) The square of ① × ②

[0091] The time harmonics are μ1±1, and the spatial harmonics are μp±v;

[0092] 5) The square of ① × ③

[0093] The time harmonics are μ1±μ2, and the spatial harmonics are (μ1±μ2)p±kZ;

[0094] 6) The square of ② × ③

[0095] The time harmonics are μ1±1, and the spatial harmonics are μp±v±kZ.

[0096] The beneficial effects of adopting the above technical solution are as follows:

[0097] This invention provides a comprehensive and systematic analysis of the axial air gap magnetic flux density and electromagnetic force waves of an axial magnetic field permanent magnet memory motor, starting from both static and dynamic perspectives.

[0098] The electromagnetic force wave solution of the axial magnetic field permanent magnet memory motor of this invention can be applied not only to integer slot motors, but also to fractional slot motors.

[0099] The Halbach array selected in this invention is applied to an axial motor. By performing analytical calculations of electromagnetic force waves on the Halbach array permanent magnets and hybrid excitation windings, the selected calculation method is applicable not only to the calculation of Halbach array permanent magnets and hybrid excitation windings, but also to the calculation of electromagnetic force waves on ordinary permanent magnet arrays and ordinary armature windings. This lays the foundation for subsequent research on analytical calculations of electromagnetic force waves for other motor models. Attached Figure Description

[0100] Figure 1 This is a cross-sectional view of the motor's axial direction;

[0101] Figure 2 This is an exploded view of an axial magnetic field permanent magnet memory motor. Detailed Implementation

[0102] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0103] like Figure 1The figure shows an axial cross-sectional view of the permanent magnet, which includes permanent magnet 1 and permanent magnet 2 of the Halbach array, forming a Halbach array to enhance the air gap magnetic flux density. The intermediate rotor and the lower stator are made of ferromagnetic material, and the upper and lower stators and the intermediate rotor constitute a typical double-stator single-rotor structure. When solving for electromagnetic force waves, a solution coordinate system is first established. Based on the direct coordinate system established in Figure (1), the required equations are listed and then solved.

[0104] Step 1: Based on the actual motor model, determine the solution coordinate system, and establish Poisson and Laplace equations for different solution regions of the motor, specifically for the air gap and Halbach array permanent magnet region. Halbach array permanent magnet region (Poisson equation): Axial magnetic field permanent magnet memory motor air gap region (Laplace equation): In Cartesian coordinates, the axial magnetization function of a Halbach array permanent magnet is an even function, and the axial magnetization function is an odd function. Therefore, the magnetization function of the Halbach array permanent magnet in the axial magnetic field permanent magnet memory motor is: in, The axial magnetization coefficient α of the Halbach array r τ represents the width of the axially magnetized permanent magnet. y and polar distance τ p The ratio: The magnetic flux density B1 inside the permanent magnet and the magnetic flux density B2 at the air gap can be expressed as: B1 = B r +μH1=μ0M+μ0μ r H2; B2 = μ0H2.

[0105] Step 2: The magnetic field strength can be expressed as: By calculation and solving in conjunction with the first step, the general solution to the Laplace equation can be obtained as follows: in, Meanwhile, the analytical model of the unloaded magnetic field should satisfy the boundary conditions: H x2 | y＝0 =0, By simplifying the calculation, the general coefficients of the Laplace solution can be obtained, thus yielding the solution. C4 = -C3; where Δ = μ r cosh(u n h m sinh(u n g)+cosh(u n g)sinh(u n h mSubstituting the obtained coefficients into the Laplace general solution, we can obtain the Laplace coefficient solution. Then, substituting this into the first step, we can obtain the axial and circumferential components of the air gap magnetic flux density of the axial magnetic field permanent magnet memory motor:

[0106]

[0107]

[0108] The axial flux motor experiences forces primarily in the axial direction. The air gap magnetic field generates electromagnetic forces on the stator and rotor structures, causing vibrations and noise. Other noise sources include bearing noise and vibrations caused by rotor imbalance or eccentricity. The axial electromagnetic force is the primary source of vibration in the axial flux motor. Considering only the axial component of the air gap magnetic flux, the axial air gap magnetic flux of the axial magnetic field permanent magnet memory motor can be expressed as: B z =B y1 .

[0109] Step 3: The axial magnetic field of the permanent magnet memory motor's stator flux linkage is mainly generated by the interaction of the stator magnetomotive force and the permanent magnet. The magnetomotive force excited by the permanent magnet is: If the rotor rotates synchronously in space, the rotor magnetomotive force can ultimately be expressed as: in, In the formula, F μ α is the amplitude of the magnetomotive force of the permanent magnet; p ω is the pole arc coefficient of the permanent magnet poles; w is the angular frequency of the motor rotation. Explanation of a unit motor: A motor with m phases, Z stator slots, and p permanent magnet rotor pole pairs. If Z and p have a greatest common divisor t, i.e., Z / p = Z0 / p0, where Z0 is an integer multiple of m, then a motor with Z0 slots and p0 pole pairs is called a unit motor. An axial magnetic field permanent magnet memory motor consists of t unit motors, with N turns in the fractional slot winding. c The angular frequency is ω, and the effective value is I. c Under the excitation of a sinusoidal current i, the total magnetomotive force generated is iN. c The pulsating rectangular magnetomotive force generated by the armature winding magnetic field of an axial magnetic field permanent magnet memory motor, which is related to spatial θ and time t, is: In the formula: v is the stator harmonic order; F v This represents the amplitude of the v-th harmonic magnetomotive force of the stator winding. Where F... v The calculation method for the derived formula is as follows: Among them, k yv The short-pitch factor for the harmonic winding with a pole pair number of v; A single coil generates harmonic magnetomotive force (MOMF) for all pole pairs except v = kZ0 (k = 1, 2, 3...). The amplitude of the harmonic MOMF is directly proportional to the effective value of the current and the harmonic short-pitch coefficient, and inversely proportional to the number of harmonic pole pairs. In an axial magnetic field permanent magnet memory motor, when three-phase current is applied to the armature winding:

[0110] F c (θ, t) = F cv cosvθsinωt+F cv cosv(θ-120°)sin(ωt-120°)+F cv cosv(θ+120°)sin(ωt+120°) When v=3k, F c (θ, t) = 0; when v = 6k + 1 When v = 6k-1

[0111] Step 4: The air gap permeability of the axial magnetic field permanent magnet memory motor is: λ(θ,t)=λ0+Σλ k cos(kZθ). Where: λ0 is the invariant part of the air gap permeability; Z is the number of stator slots; k is a natural number representing the harmonic order of the stator teeth; ∑λ k Let k be the sum of the harmonic amplitudes of the stator teeth, k = 0, 1, 2, ... . Ignoring magnetic field saturation, the expression for the axial air gap magnetic flux density is as follows:

[0112] B z (θ,t)=(f φ (θ,t)+F c (θ,t))·λ(θ,t)

[0113]

[0114] The calculated axial air gap magnetic flux density is:

[0115]

[0116] Step 5: The electromagnetic force of the axial magnetic field permanent magnet memory motor is mainly the axial electromagnetic force. According to Maxwell's tensor method, neglecting the saturation of the air gap magnetic field, the axial electromagnetic force acting on a unit air gap area can be expressed as (ignoring the fourth term of the axial electromagnetic force): The time harmonics are μ1±μ2, and the spatial harmonics are... The time harmonic is 2, and the space harmonic is... The time harmonics are μ1±μ2, and the spatial harmonics are... The time harmonics are μ1±1, and the spatial harmonics are... The time harmonics are μ1±μ2, and the spatial harmonics are...

[0117] The time harmonics are μ1±1, and the spatial harmonics are μp±v±kZ; where p z y is the axial electromagnetic force; μ0 is the free permeability; B z It is the axial air gap magnetic flux density.

[0118] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0119] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0120] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0121] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0122] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0123] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor, characterized in that, Includes the following steps: S1. Based on the actual motor model, determine the solution coordinate system, and establish Poisson's equation and Laplace's equation for the motor in different solution regions for the air gap and Halbach array permanent magnet respectively. S2. Based on the general solution of the Laplace equation, the static axial air gap magnetic flux density and circumferential air gap magnetic flux density are solved according to the boundary conditions that the analytical model of the unloaded magnetic field should satisfy. S3. During motor operation, calculate the magnetomotive force of the motor's Halbach array permanent magnets; when a three-phase symmetrical sinusoidal current is applied to the motor, calculate the magnetomotive force generated by the single-phase winding and the magnetomotive force generated by the three-phase winding respectively. S4. Based on the air gap permeability, calculate the axial air gap magnetic field distribution of the motor to obtain the expression for the air gap magnetic field of the axial magnetic field permanent magnet memory motor. S5. Calculate the axial electromagnetic force acting on a unit air gap area according to Maxwell's tensor equation, and calculate the time and spatial harmonics for each electromagnetic force wave obtained by calculation. Step S1 specifically includes: Based on the motor's appearance and size requirements, a two-dimensional rectangular coordinate system is established. According to this system, the axial magnetization function of the Halbach array permanent magnet is assumed to be an even function, and the axial magnetization function is assumed to be an odd function. The formula for the magnetization function of the Halbach array permanent magnet in the axial magnetic field permanent magnet memory motor is expressed as: ； In the formula, , representing the coefficients of the Fourier series of the circumferential magnetization function; , represents the coefficient of the Fourier series of the axial magnetization function; p is the number of pole pairs of the motor; r is the radius of the motor; Let n represent a magnetization odd function, and n = 1, 3, 5…; Axial magnetization coefficient of Halbach array The formula is expressed as follows: ； In the formula, Indicates the width of the axially magnetized permanent magnet; Indicates the pole pitch; p is the number of pole pairs of the motor; r is the radius of the motor; magnetic flux density inside the permanent magnet and magnetic flux density at the air gap The formula is expressed as: ； ； In the formula, Br represents the remanence of the permanent magnet; The relative permeability of the permanent magnet; H is the vacuum permeability; H1 and H2 are the magnetic field strengths of each region, respectively. The Halbach array permanent magnet region, i.e., the Poisson equation formula, is expressed as follows: ； In the formula, For the magnetic flux of the permanent magnet region; ρ represents the relative permeability of the permanent magnet; x and y are the coordinates of the x-axis and y-axis, respectively. Let M be the divergence of the magnetization function M; The air gap region of the axial magnetic field memory motor, expressed by the Laplace equation, is as follows: ； In the formula, denoted as the air gap magnetic flux; x and y are the coordinates of the x-axis and y-axis, respectively.

2. The method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor according to claim 1, characterized in that, Step S2 specifically includes: S21. Based on the expression for magnetic field strength and the axial magnetization coefficient of the Halbach array, the magnetic flux density inside the permanent magnet... and magnetic flux density at the air gap Solving the equation jointly, we obtain the general solution formula for the Laplace equation as follows: ； ； ； In the formula, C1 is the first undetermined coefficient; C2 is the second undetermined coefficient; C3 is the third undetermined coefficient; and C4 is the fourth undetermined coefficient. These four coefficients depend on the boundary conditions of the equivalent model. Represent the exponential function part of the general solution of the Laplace equation; The magnetization function is represented by p; the number of pole pairs of the motor is represented by r; The expression for the magnetic field strength is: ； ； In the formula, H represents the magnetic field strength along the x-axis. y The magnetic field strength is in the y-axis direction; S22. Calculate the Laplace general solution coefficients based on the boundary conditions of the analytical model of the unloaded magnetic field. The formula is expressed as follows: ； ； ； ； In the formula, The magnetization function for permanent magnets; g is the height of the permanent magnet; g is the length of the air gap 1; ； The boundary condition formulas for the analytical model of the unloaded magnetic field are expressed as follows: ； ； ； ； In the formula, H X1 H X2 B represents the magnetic field strength along the x-axis. y1 H is the magnetic flux density along the y-axis; y2 The magnetic field strength is along the y-axis. S23. Based on the Laplace coefficient solution obtained in S22, the formulas for calculating the axial and circumferential components of the air gap magnetic flux density of the axial magnetic field permanent magnet memory motor are expressed as follows: ； ； In the formula, H is the permeability of free space; m ρ is the magnetic field strength; M is the magnetization function; g is the length of the air gap 1; h is the magnetic field strength. m The height of the permanent magnet; The formula for the axial air gap magnetic flux density of an axial magnetic field permanent magnet memory motor is expressed as follows: 。 3. The method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor according to claim 2, characterized in that, Step S3 includes the following steps: S31. Calculate the magnetomotive force generated by the permanent magnet. The formula is expressed as follows: ； In the formula, u is the harmonic order of the magnetomotive force of the permanent magnet, p is the number of poles of the permanent magnet, and θ is the rotation angle; The formula for calculating the rotor magnetomotive force is expressed as follows: ； In the formula ρ is the permeability of air; u is the harmonic order of the magnetomotive force of the permanent magnet. The amplitude of the magnetomotive force of the permanent magnet; The polar arc coefficient of the permanent magnet pole; The angular frequency of the motor; S32. Assume that the axial magnetic field permanent magnet memory motor consists of t unit motors, and the number of turns of the fractional slot winding is N. c The angular frequency is ω, and the effective value is I. c Under the excitation of a sinusoidal current i, the total magnetomotive force generated is iN. c ; The unit motor is a motor with Z0 slots and p0 pole pairs. p represents the number of permanent magnet rotor pole pairs, Z represents the number of stator slots; Z0 is an integer multiple of m; m represents the number of motor phases. The formula for calculating the pulsating rectangular magnetomotive force generated by the armature winding magnetic field of an axial magnetic field permanent magnet memory motor, which is related to spatial θ and time t, is as follows: ； In the formula, w is the rotational angular velocity; θ is the rotation angle; v is the stator harmonic order; F v is the amplitude of the v-th harmonic magnetomotive force of the stator winding; where, In the formula, The short-pitch factor for the harmonic winding with a pole pair number of v; ; S33. Calculate the axial magnetic field of a permanent magnet memory motor when three-phase current is applied to the armature winding. The formula is as follows: when hour, ;when hour, ;when hour, .

4. The method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor according to claim 3, characterized in that, Step S4 includes the following steps: S41. Calculate the air gap permeability of the axial magnetic field permanent magnet memory motor. The formula is as follows: ； In the formula, Z is the air gap permeability constant, Z is the number of stator slots; k is the harmonic order of the stator teeth, and k is a natural number. This represents the sum of the harmonic amplitudes of each order of the stator teeth; S42. The axial air gap magnetic flux density is calculated based on the air gap permeability of the axial magnetic field permanent magnet memory motor. The formula is as follows: ； Substituting the magnetomotive force of the permanent magnet, the magnetomotive force of the armature winding, and the air gap permeability into the equation, we obtain the following relationship: 。 5. The method for calculating asymmetric axial electromagnetic force waves in an axial magnetic field permanent magnet memory motor according to claim 4, characterized in that, Step S5 includes the following steps: The axial electromagnetic force acting on a unit air gap area is calculated using Maxwell's tensor method, ignoring the fourth term. The formula is as follows: ； 1) The square of ① Time harmonics are Spatial harmonics are ; 2) The squared term of ② The time harmonic is 2, and the space harmonic is... ; 3) The square of ③ Time harmonics are Spatial harmonics are ; 4) The square of ① × ② Time harmonics are Spatial harmonics are ; 5) The square of ① × ③ Time harmonics are Spatial harmonics are ; 6) The square of ② × ③ Time harmonics are Spatial harmonics are .

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