A method for field analytical analysis of an axial flux motor

Abstract

The present application relates to a kind of magnetic field analytical analysis method for axial flux motor, it is characterized in that, including the following steps: step 1: the analytical model of the axial flux ring electromagnetic mechanism of axial flux motor is established;Step 2: slot sub-domain model construction;Step 3: air gap sub-domain model construction;Step 4: rotor sub-domain model construction;Step 5: air gap magnetic density solution.The present application is applicable to any energizing mode, can reach the magnetic field analysis result consistent with finite element calculation under the premise of reducing the complexity of magnetic field analysis.

Description

Technical Field

[0001] This invention belongs to the field of air gap magnetic field of axial flux induction motors, and relates to the analysis of air gap magnetic field of axial flux induction motors considering the influence of eddy currents. Background Technology

[0002] With the new requirements for high-quality development and the widespread use of new energy sources, electric motors, as efficient devices for converting electrical energy into mechanical energy, have been widely applied. Furthermore, with the increasing specialization of industrial division of labor, the demand for high-tech products such as CNC machine tools, industrial robots, and electric vehicles is becoming more personalized and customized, leading to a growing emphasis on special motors suitable for specific applications.

[0003] Axial flux motors, as the earliest invented type of motor, are characterized by low rotational inertia, high power density, simple manufacturing process, high utilization rate of silicon steel sheets, and compact structure. Furthermore, their flat shape makes them particularly suitable for applications with strict space constraints. These characteristics allow axial flux motors to meet the demands for miniaturization, thinning, and low noise in motors, thus promoting the development and application of axial flux motors with different structures.

[0004] Solid rotor axial flux motors offer significant advantages over traditional asynchronous motors in specific applications. They feature excellent thermal stability, high mechanical reliability, strong heat dissipation, low vibration frequency, and low noise during operation. Therefore, even in harsh working environments, these motors can maintain high-speed, stable operation for extended periods, ensuring reliable performance. In terms of performance, solid rotor asynchronous motors exhibit high torque at startup, low current after startup, and smooth braking operation. They also maintain relative stability after frequent starts and reciprocating impacts, making them suitable for environments with frequent switching between power-on and power-off operation.

[0005] In the design of axial flux motors, magnetic flux density analysis is fundamental to motor performance research. However, the finite element method (FEM) is relatively slow in its calculations. Analytical methods, employing numerical calculations, offer a relatively coarse solution, but are faster and can be used in the initial design and optimization phases of the motor, thus improving design efficiency. Summary of the Invention

[0006] The purpose of this invention is to provide a method for analytical analysis of the magnetic field based on an axial flux induction motor. The technical solution adopted in this invention is as follows:

[0007] A method for analytical analysis of the magnetic field in an axial flux motor, characterized by comprising the following steps:

[0008] Step 1: Establish an analytical model of the axial flux loop electromagnetic mechanism of the axial flux motor.

[0009] A three-dimensional cylindrical coordinate system is constructed based on an axial flux motor, with the origin being the annular center point. The coordinates of the moving point in the coordinate system are (r, θ, z), where r is the radius of the plane circle from the moving point to the origin of the polar coordinates, θ is the angle from the polar axis to the line connecting the point and the pole, and z is the perpendicular distance from the moving point to the polar coordinate r-θ plane. Three layers of regions are established: the slot subdomain, the air gap subdomain, and the rotor subdomain.

[0010] Step 2: Slot Domain Model Construction

[0011] Let Q be the total number of slots in the stator of the axial flux motor. The pole axis at θ = 0 is positioned at the center of a certain slot and designated slot 1. The slots are then numbered counter-clockwise as slot 1, slot 2, ..., slot Q. The position corresponding to slot i is θ. i , and θ i =2π(i-1) / Q, and the corresponding armature current is sequentially applied to different slots according to the energizing method. This is the first layer of slot sub-domain region.

[0012] Based on the current excitation of the i-th stator slot, the slot subdomain vector magnetic potential A is introduced. I,i Write the Poisson equation for the i-th slot region of the stator:

[0013]

[0014]

[0015] In the formula, For the Laplace operator, A I,i (θ,z,t) represents the vector magnetic potential of the slot domain, μ0 is the free permeability, and J i (θ,z,t) represents the current density of the i-th slot;

[0016] Step 3: Air Gap Subdomain Model Construction

[0017] Considering that there is no current excitation in the air gap region, an air gap subdomain vector magnetic potential A is introduced. II Write the Laplace equation for the air gap region:

[0018]

[0019]

[0020] In the formula, A II (θ,z,t) represents the vector magnetic potential of the air gap subdomain;

[0021] Step 4: Rotor Subdomain Model Construction

[0022] Considering that the rotor will generate eddy currents under changes in the external magnetic field, a rotor subdomain magnetic potential A is introduced. IIIWrite the Helmholtz equations for the solid rotor region:

[0023]

[0024]

[0025] In the formula, J Fe (θ,z,t) represents the induced current density of the rotor, j is the imaginary number, ω is the electric angular frequency, and μ r Let A be the relative permeability of the rotor, σ be the electrical conductivity of the rotor, and A be the relative permeability of the rotor. III (θ,z,t) represents the rotor subdomain vector magnetic potential;

[0026] Step 5: Solving the air gap magnetic flux density

[0027] By solving the partial differential equations listed in steps 2 through 4 simultaneously, the vector magnetic potential A of the air gap subdomain can be obtained. II The final expression for (θ,z,t) can then be obtained by solving for the axial component of the magnetic flux density in the air gap region based on the relationship between vector magnetic potential and magnetic flux density. and circumferential components

[0028]

[0029]

[0030] The magnetic field analysis described above is based on the following assumptions:

[0031] a) The axial flux motor is subdivided radially into several concentric circular ring units. It is assumed that only axial flux and circumferential flux exist in the magnetic circuit of each concentric circular ring unit, and radial flux is ignored.

[0032] b) The analysis region is the θ-z coordinate torus, and end effects are neglected;

[0033] c) The stator core has infinite permeability, and the effect of the core reluctance is negligible;

[0034] d) The stator slots are axially open slots, i.e., in the z-direction, and the current density is uniformly distributed within the slots;

[0035] e) The rotor is a solid rotor that is magnetically and electrically conductive, and its BH curve is considered to be linear;

[0036] f) Magnetic field lines will not cross the lower boundary of the rotor.

[0037] This invention takes a solid rotor axial flux induction motor as the research object and constructs an accurate analytical model that considers the effects of slotting and eddy current induced magnetic field. It is applicable to any power supply method and can achieve magnetic field analysis results that are consistent with finite element calculations while reducing the complexity of magnetic field analysis. Attached Figure Description

[0038] Figure 1 Figure (a) is a schematic diagram of the axial flux motor structure; Figure (b) is a schematic diagram of the analytical solution radius range of the axial flux motor.

[0039] Figure 2 Schematic diagram of the cross-sectional structure of an axial flux motor along the circumferential direction.

[0040] Figure 3 Axial flux motor cross-section unfolded schematic diagram

[0041] Figure 4 Schematic diagram of subdomain partitioning

[0042] Figure 5 Diagram of coordinate transformation for opening slot

[0043] Figure 6 : Slot current density mirror

[0044] Figure 7 Schematic diagram of winding current of a 12-slot 4-pole motor

[0045] Figure 8 Schematic diagram of winding current of a 12-slot 8-pole motor

[0046] Figure 9 Comparison diagram of axial magnetic flux density in the air gap of a 12-slot 4-pole motor

[0047] Figure 10 Comparison diagram of circumferential magnetic flux density in the air gap of a 12-slot 4-pole motor

[0048] Figure 11 Harmonic components of the air gap axial magnetic flux density of a 12-slot 4-pole motor

[0049] Figure 12 Harmonic components of the air gap circumferential magnetic flux density in a 12-slot, 4-pole motor

[0050] Figure 13 Comparison diagram of axial magnetic flux density in the air gap of a 12-slot 8-pole motor

[0051] Figure 14 Comparison diagram of circumferential magnetic flux density in the air gap of a 12-slot 8-pole motor

[0052] Figure 15 Harmonic components of the air gap axial magnetic flux density of a 12-slot 8-pole motor

[0053] Figure 16Harmonic components of the air gap circumferential magnetic flux density in a 12-slot 8-pole motor Detailed Implementation

[0054] This invention provides a method for solving axial flux induction motors. The invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0055] The specific steps of this invention are as follows:

[0056] 1. Subdomain Model Construction

[0057] Will as Figure 1 (a) shows an axial flux motor divided radially into equally spaced circular rings. A ring corresponding to a certain radius is taken as the basic unit for magnetic field analysis. The cross-section of the axial flux motor along the circumferential direction at this radius is as follows: Figure 2 As shown. Taking the center of the circle as the origin, in Figure 2 A cylindrical coordinate system is established on the cross-section, with the polar axis (θ = 0) located at the center of the open slot. For ease of description of the axial flux motor structure, as follows... Figure 3 As shown Figure 2 The cross-sectional diagram is expanded along θ = 0. Specific subdomain partitioning is as follows: Figure 4 As shown, the region corresponding to slot i is selected for principle explanation. Assuming the number of stator slots is Q, the position corresponding to slot i is:

[0058]

[0059] The opening groove adopts a parallel groove with a groove width of l. s The angle of the slot in cylindrical coordinates differs for different radii, such as... Figure 5 As shown, the width β corresponding to each opening slot can be expressed as:

[0060]

[0061] 2. Construction of the magnetic field in the slot domain

[0062] Based on the armature winding excitation method, the energizing conditions of different slots are calculated. Let the current density in slot i be J. i =Re{J i (θ)e jωt}e r Considering that the concentrated winding has a double-layer left and right winding structure in the slot, the same slot can be divided into two regions, left and right, with current densities of J in each region. i,l and J i,r .like Figure 6 As shown, the current density in the stator slot can be mirrored through the right boundary of the slot to form a periodic signal with a period of 2β. After Fourier decomposition, the current density in the slot can be obtained as follows:

[0063]

[0064] DC term:

[0065]

[0066] Harmonic terms:

[0067]

[0068] Introducing vector magnetic potential A in this region I,i =Re{A I,i (z,θ)e jωt}e r Without considering saturation and end effects, the vector magnetic potential equation for each slot can be written separately according to the excitation method. Since there is current excitation in the stator slots, the Poisson equation can be written within the stator slot region:

[0069]

[0070] Since the stator core is assumed to have infinite permeability, there is no circumferential component at the bottom of the slot (z = z3), and no circumferential component at the left and right boundaries of the slot. At a point where there is no axial magnetic flux density, the boundary condition can be expressed as:

[0071]

[0072] The general solution for the stator slot subdomains satisfying the boundary conditions can be obtained by the method of separation of variables:

[0073]

[0074] In the formula All of these are coefficients to be determined.

[0075] 3. Construction of the magnetic field in the air gap subdomain

[0076] Introducing vector magnetic potential A in this region II =Re{A II (θ,z)e jωt}e r Since there is no current excitation in the air gap, the Laplace equation can be written in the air gap region as follows:

[0077]

[0078] Therefore, the general solution of the magnetic vector potential of the air gap subdomain can be obtained as follows:

[0079]

[0080] In the formula All of these are coefficients to be determined.

[0081] 4. Construction of rotor subdomain magnetic field

[0082] Introducing vector magnetic potential A in this region III =Re{A III (θ,z)e jωt}e r Under the influence of an alternating magnetic field, a solid rotor will generate an induced electromotive force, which in turn will generate an induced current. The induced current density is denoted as J. Fe =Re{J Fe (θ,z)e jωt}e r Based on this, the Helmholtz equations can be written in the rotor region:

[0083]

[0084] Since it is assumed that the magnetic field lines will not cross the lower boundary of the rotor, that is, the magnetic flux density at the lower boundary of the rotor (z = z0) is 0, its vector magnetic potential is also zero, and its boundary condition can be expressed as:

[0085] A III (θ, z0) = 0

[0086] Therefore, the rotor subdomain vector magnetic potential flux solution can be obtained:

[0087]

[0088] In the formula The coefficients to be determined are denoted as .

[0089] 5. Simultaneous expression of subdomain magnetic field

[0090] Based on the requirement that the magnetic field continuity must be satisfied at the interface between different subdomains, i.e., the axial magnetic flux density is equal and the circumferential magnetic field strength is equal, the relevant harmonic coefficients to be determined can be obtained.

[0091] The equation can be written at z = z²:

[0092] A I,i (θ,z2)=A II (θ,z2)

[0093]

[0094] The equation can be written at z = z1:

[0095] A II (θ,z1)=A III (θ,z1)

[0096]

[0097] The system of equations obtained by combining the two equations can be written in matrix form:

[0098] [M] (Q+QM+6N)×(Q+QM+6N) ·[X] (Q+QM+6N)×1 =[C] (Q+QM+6N)×1

[0099] Where M is the coefficient matrix, X is the harmonic coefficient matrix to be determined, and C is the constant matrix. Specifically, it can be expanded as follows:

[0100]

[0101] 6. Solving for air gap magnetic flux density

[0102] Solving the above matrix yields the following results: By substituting the specific expression of the air gap subdomain vector magnetic potential equation into the equation, the final expression for the air gap magnetic flux density can be obtained:

[0103]

[0104]

[0105] 7. Simulation Experiment

[0106] Taking a 12-slot axial flux electromagnetic mechanism as an example, the winding energization methods are as follows: Figure 7 , 8 As shown, the air gap magnetic field is analyzed under two different methods, assuming the harmonic order of both the slot subdomain and the air gap subdomain is 50. The three-phase current is as follows:

[0107]

[0108] In the formula I m =200NA is the ampere-turns of the winding, and ω=100π is the angular frequency of the energized winding.

[0109] Figures 9-16 The figure compares the calculated air gap magnetic flux density and corresponding harmonic analysis results obtained using the present invention at an air gap inner radius of 35 mm with the results obtained using the finite element method at a time interval of 5 ms. As can be seen from the figure, the results of the present invention and the finite element method calculations agree very well.

Claims

1. A method for analytical analysis of the magnetic field in an axial flux motor, characterized in that, Includes the following steps: Step 1: Establish an analytical model of the axial flux loop electromagnetic mechanism of the axial flux motor. A three-dimensional cylindrical coordinate system is constructed based on an axial flux motor, with the origin at the center point of the ring. The coordinates of the moving point in the coordinate system are: ,in Let be the radius of the plane circle from the moving point to the origin of the polar coordinates. The angle is the distance from the polar axis to the line connecting that point and the pole. From the moving point to the polar coordinates Vertical distance in the plane; establish three layers of regions: slot subdomain, air gap subdomain, and rotor subdomain; Step 2: Slot Domain Model Construction Let the total number of stator slots of the axial flux motor be... , polar axis The location is set at the center of a slot and designated slot 1. The slots are then numbered sequentially counter-clockwise as slot 1, slot 2, ... Slot number 1, numbered as i The position corresponding to the slot is ,and According to the energizing method, the corresponding armature current is sequentially applied to different slots, which is the first layer of slot sub-domains. According to the stator i The current excitation of slot number 1 introduces the vector magnetic potential of the slot subdomain. Write about the stator in parallel. i Poisson's equation for region #1: In the formula, For the Laplace operator, For the slot subdomain vector magnetic potential, The permeability of free space, For the first i Slot current density; Step 3: Air Gap Subdomain Model Construction Considering that there is no current excitation in the air gap region, a vector magnetic potential of the air gap subdomain is introduced. Write the Laplace equation for the air gap region: In the formula, The vector magnetic potential of the air gap subdomain; Step 4: Rotor Subdomain Model Construction Considering that the rotor will generate eddy currents under changes in the external magnetic field, a rotor subdomain magnetic potential is introduced. Write the Helmholtz equations for the solid rotor region: In the formula, The induced current density of the rotor, j It is the symbol for imaginary numbers. It is the electric angular frequency. is the relative permeability of the rotor. The conductivity of the rotor, The rotor subdomain vector magnetic potential; Step 5: Solving the air gap magnetic flux density By solving the partial differential equations listed in steps 2 through 4 simultaneously, the vector potential magnetic potential of the air gap subdomain is obtained. The final expression; based on the relationship between vector magnetic potential and magnetic flux density, the axial component of the magnetic flux density in the air gap region is then solved. and circumferential components The specific method is as follows: (1) Simultaneous expression of subdomain magnetic field Based on the requirement that the magnetic field continuity must be satisfied at the interface between different subdomains, i.e., the axial magnetic flux density is equal and the circumferential magnetic field strength is equal, the relevant harmonic coefficients to be determined can be obtained. Let Z2 be the boundary between the air gap subdomain and the slot subdomain. Write the equation at the point: ， In the formula, The width corresponding to each opening slot, Let Z1 be the boundary between the air gap subdomain and the rotor subdomain. Write the equation at the point: Based on the system of equations obtained by combining the two equations, we can write it in matrix form: in M The coefficient matrix, X The harmonic coefficient matrix to be determined is... C For a constant matrix, its specific expansion can be written as: (2) Solution of air gap magnetic flux density Solving the above matrix yields , , , , , , , By substituting the specific expression of the air gap subdomain vector magnetic potential equation into the equation, the final expression for the air gap magnetic flux density can be obtained: 。 2. The magnetic field analytical method according to claim 1, characterized in that, The magnetic field analysis described above is based on the following assumptions: a) The axial flux motor is subdivided radially into several concentric circular ring units. It is assumed that only axial flux and circumferential flux exist in the magnetic circuit of each concentric circular ring unit, and radial flux is ignored. b) The analysis region is Coordinate torus, neglecting end effects; c) The stator core has infinite permeability, and the effect of the core reluctance is negligible; d) The stator slots are axially open slots, i.e., in the z-direction, and the current density is uniformly distributed within the slots; e) The rotor is a solid rotor that is magnetically and electrically conductive, and its BH curve is considered to be linear; f) Magnetic field lines will not cross the lower boundary of the rotor.

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