Torque analysis modeling method for magnetic field modulation type speed regulator

Abstract

The invention relates to a torque analysis modeling method for a magnetic field modulation type speed regulator, belongs to the technical field of magnetic field modulation type speed regulators, and aims at solving the problem that an existing finite element method is too long in simulation time and improving design efficiency. According to the method, a magnetic field modulation type speed regulator is divided into a plurality of sub-domains such as a permanent magnet domain, a slot domain, a notch domain, a modulation domain, an inner air domain and an outer air domain, and the magnetic vector potential of each sub-domain is described in a polar coordinate form. By determining boundary conditions among the sub-domains, a magnetic vector potential control equation is established in the plurality of sub-domains by using a field method, and nonlinear magnetization characteristics of materials are considered. And solving the magnetic vector potential control equation by adopting a finite element method, and obtaining flux density distribution of the air gap layer by adopting an interpolation method. And finally, calculating the electromagnetic torque according to the flux density distribution by using a Maxwell stress tensor method. The calculation speed of the method is far higher than that of a finite element method, flux density distribution and torque can be rapidly obtained, design is aided, and the design process is accelerated.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic field modulation speed regulators, and relates to a torque analytical modeling method for magnetic field modulation speed regulators. Background Art

[0002] As a new type of non-contact transmission device, the magnetic field modulation speed regulator has the characteristics of complex structure and complex internal electromagnetic environment. It realizes precise control of speed and torque through magnetic field modulation technology and has broad application prospects in fields such as aerospace and electric vehicles.

[0003] At present, the electromagnetic torque calculation of magnetic field modulation speed regulators generally relies on the finite element method. The finite element method can accurately simulate the magnetic field distribution, but its calculation amount is huge, the simulation time is long, which seriously reduces the design efficiency. In addition, the finite element method requires a large amount of computing resources and high requirements for computer hardware, which limits its application in actual engineering. To overcome the deficiencies of the finite element method, some scholars have tried to use analytical methods for torque calculation of magnetic field modulation speed regulators. For example, methods based on the equivalent magnetic circuit method or the magnetic field superposition principle can simplify the calculation process and improve the calculation speed. However, these methods usually require simplifying the model or performing approximate calculations, resulting in reduced calculation accuracy.

[0004] Therefore, developing a torque analytical modeling method for magnetic field modulation speed regulators with fast calculation speed, high accuracy, and easy implementation is of great significance for improving design efficiency and reducing design costs. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a torque analytical modeling method for magnetic field modulation speed regulators.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] A torque analytical modeling method for magnetic field modulation speed regulators includes the following steps:

[0008] S1: Divide the magnetic field modulation speed regulator into multiple sub-domains, and the multiple sub-domains include a permanent magnet domain, a slot sub-domain, a slot opening domain, a modulation domain, an inner air domain, and an outer air domain;

[0009] S2: Describe the magnetic vector potential of each sub-domain in polar coordinate form;

[0010] S3: Determine the boundary conditions between each sub-domain;

[0011] S4: Use the field method to establish a magnetic vector potential control equation in multiple sub-domains;

[0012] S5: Solve the magnetic vector potential control equation to obtain the magnetic flux density distribution of the air gap layer;

[0013] S6: Calculate the electromagnetic torque according to the magnetic flux density distribution by using the Maxwell stress tensor method.

[0014] Furthermore, the magnetic vector potential control equations for the permanent magnet domain and the slot domain are Poisson equations, and the magnetic vector potential control equations for the slot opening domain, the modulation domain, the inner air domain, and the outer air domain are Laplace equations.

[0015] Furthermore, in S1, the permanent magnet domain includes a plurality of permanent magnets, the slot domain includes a plurality of slots, the slot opening domain includes a plurality of slot openings, the modulation domain includes a plurality of modulation teeth, and the inner air domain and the outer air domain are respectively the air gap regions between the permanent magnet domain and the slot domain.

[0016] Furthermore, in S2, the boundary condition is that the magnetic vector potential values at the junctions of the sub-domains are the same.

[0017] Furthermore, in S4, the solution method is the analytical method.

[0018] Furthermore, in S5, the Maxwell stress tensor is a second-order tensor.

[0019] Furthermore, the pole-pair ratio of the magnetic field modulation type speed regulator is 9:8:1.

[0020] A magnetic field modulation type speed regulator, which is used to execute the torque analytical modeling method described above.

[0021] The beneficial effects of the present invention are as follows:

[0022] (1) Compared with the traditional finite element method, the analytical modeling method provided by the present invention has a greatly improved calculation speed, can quickly obtain the magnetic flux density distribution and torque, effectively shortens the design cycle, and improves the design efficiency.

[0023] (2) The present invention takes into account the non-linear magnetization characteristics of the material and uses the interpolation method to obtain the magnetic flux density distribution of the air gap layer, improves the calculation accuracy, and ensures the reliability of the results.

[0024] (3) The present invention uses the field method to establish the magnetic vector potential control equation and solve it, which is easy to understand and implement, and is convenient for engineers to apply in actual engineering.

[0025] (4) The analytical modeling method proposed by the present invention can be migrated to other similar equipment with magnetic field modulation structures or magnetic gear structures, and has wide applicability, such as permanent magnet motors, magnetic gear drive systems, etc.

[0026] (5) The parsing and modeling method provided by the present invention can assist engineers in the design of magnetic field modulation speed regulators, such as optimizing the size of permanent magnets, slot design, etc., to improve the design efficiency and product quality.

[0027] Other advantages, objectives, and features of the present invention will, to some extent, be described in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0028] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0029] Figure 1 is the schematic diagram of the present invention;

[0030] Figure 2 is the comparison between the present invention and the finite element method in terms of the calculation results of the radial magnetic density;

[0031] Figure 3 is the comparison between the present invention and the finite element method in terms of the calculation results of the tangential magnetic density Detailed Embodiments

[0032] The following uses specific specific examples to illustrate the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0033] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and should not be construed as limiting the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged, or reduced, and do not represent the dimensions of actual products; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0034] In the drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0035] The present invention will be described in detail below in conjunction with the drawings and specific examples.

[0036] 1. Magnetic field modulation type speed governor model

[0037] The present invention takes a magnetic field modulation type speed governor with a pole ratio of 9:8:1 as an example for illustration. The speed governor mainly consists of components such as a stator, a rotor, a permanent magnet PM, a modulation ring, and a coil. As Figure 1 shown, the magnetic vector potential of each region is described in polar coordinate form.

[0038] 2. Subdomain division

[0039] The magnetic field modulation type speed governor is divided into six subdomains, including a permanent magnet domain, a slot subdomain, a slot opening subdomain, a modulation domain, an inner air domain, and an outer air domain.

[0040] 3. Magnetic vector potential description

[0041] The magnetic vector potential of each subdomain is described in polar coordinate form.

[0042] 4. Boundary conditions

[0043] The boundary conditions between each subdomain are determined, including the continuity of the magnetic vector potential value and the equality of the normal magnetization intensity at the junction of each subdomain.

[0044] 5. Magnetic vector potential control equation

[0045] The magnetic vector potential control equation is established in multiple subdomains using the field method. The magnetic vector potential control equations for the permanent magnet domain and the slot subdomain are Poisson equations, and the magnetic vector potential control equations for the slot opening subdomain, the modulation domain, the inner air domain, and the outer air domain are Laplace equations, and the nonlinear magnetization characteristics of the material are considered.

[0046] 6. Finite element method solution

[0047] The magnetic vector potential control equation is solved using the finite element method, and the magnetic flux density distribution of the air gap layer is obtained through the interpolation method.

[0048] 7. Electromagnetic torque calculation

[0049] Calculate the electromagnetic torque according to the magnetic flux density distribution by using the Maxwell stress tensor method, where the Maxwell stress tensor is calculated by using the virtual displacement method.

[0050] 8. Result comparison

[0051] Compare the analytical modeling method proposed in the present invention with the finite element software method. The results show that the method proposed in the present invention has higher calculation accuracy for the radial magnetic flux density and the tangential magnetic flux density, and the calculation time is significantly shortened, effectively improving the design efficiency.

[0052] Perform analytical modeling on a magnetic field modulation type speed regulator with a pole ratio of 9:8:1 and compare it with the finite element method. Use the analytical method proposed in the present invention and the finite element software method respectively for magnetic flux density analysis and torque calculation. The comparison of the results is as Figure 2 and Figure 3 shown. It can be seen that the analytical method has higher calculation accuracy for the radial magnetic flux density and the tangential magnetic flux density. The calculation time of the finite element method is 50 seconds, while the time required for this analytical method is only 9.7 seconds, greatly improving the design efficiency. This shows the advantages of the method proposed in this patent.

[0053] The following are three embodiments including specific calculation parameters:

[0054] Embodiment 1 (standard parameter configuration)

[0055] Technical parameter configuration

[0056] Speed regulator structure: number of outer rotor pole pairs p 1 = 9, number of magnetic conduction blocks of modulation ring N m = 9, number of permanent magnet pole pairs of inner rotor p 2 = 8;

[0057] Permanent magnet parameters: remanence B r = 1.2 T, thickness h pm = 5 mm, Halbach magnetization method.

[0058] Air gap length: δ = 1.5 mm, axial length L z = 50 mm.

[0059] Calculation process

[0060] 1. Subdomain division and equation establishment

[0061] Slot subdomain (radius r 5 = 65 mm to r 6 = 70 mm): Poisson equation ▽ 2 A = -μ 0 J m where J m= 0 (No current);

[0062] Permanent magnet region (radius r 0 = 45 mm to r 1 = 50 mm): Poisson's equation ▽ 2 A = -μ 0 ▽×M, M = B r / μ 0 ;

[0063] Modulation region (radius r 2 = 60 mm to r 3 = 65 mm): Laplace's equation ▽ 2 A = 0.

[0064] 2. Simultaneous solution of boundary conditions

[0065] At the junction of the outer air region and the modulation region (r = 60 mm):

[0066] By solving using the method of separation of variables, the magnetic flux density at the air gap layer (r = 52.5 mm) is obtained: B r = 0.85 T, B θ = 0.12 T 3. Electromagnetic torque calculation

[0067] The Maxwell stress method is adopted:

[0068]

[0069] Verification result: The error compared with the finite element simulation is < 3%.

[0070] Example 2 (Optimization of the number of magnetic conduction blocks)

[0071] Technical parameter change

[0072] The number of magnetic conduction blocks in the modulation ring is adjusted to N m = 12

[0073] The other parameters are the same as those in Example 1

[0074] Calculation of difference points

[0075] 1. The magnetic field modulation effect in the modulation region is enhanced, and the harmonic components of the air gap magnetic flux density are reduced

[0076] 2. It is calculated that B r = 0.88 T, B θ = 0.09 T, torque T = 38.6 Nm;

[0077] Technical effect: The torque ripple is reduced by 15%, verifying the regulation effect of the magnetic conduction block distribution on the magnetic field modulation. Example 3 (Optimization of Halbach magnetization)

[0078] Technical parameter change

[0079] The magnetization method of the permanent magnet is changed to radial magnetization (original Halbach array).

[0080] The thickness of the permanent magnet is increased to h pm = 6 mm to maintain the same magnetic flux

[0081] Calculate the difference points

[0082] 1. Equivalent magnetization current density J in the permanent magnet domain m Recalculate:

[0083] 2. Change in the air-gap magnetic flux density distribution: B r = 0.78 T, B θ = 0.18 T;

[0084] 3. The calculated torque result T = 35.1 Nm, a 17% decrease compared to the Halbach scheme;

[0085] Technical effect: Verify the improvement effect of the Halbach array on torque density.

[0086] Example 4 (Verification of pole-pair ratio)

[0087] Parameter configuration

[0088] Adopt p 1 :p m :p 2 = 9:8:1

[0089] Outer rotor speed ω 1 = 1500 rpm, inner rotor load speed ω 2 = 1681.25 rpm, electrical frequency is 50 Hz; Dynamic process calculation

[0090] 1. According to the magnetic field modulation theory, the speed relationship should satisfy:

[0091] Example 5 (Transient response analysis)

[0092] Calculation conditions

[0093] The outer rotor step speed rises from 0 to 1500 rpm, time t = 0.2 s;

[0094] Load inertia J = 0.5 kg·pm 2 ;

[0095] Dynamic torque calculation

[0096] 1. Simultaneously establish the motion equations

[0097] 2. The acceleration time t = 0.18 s calculated by the analytical model has an error of <5% compared with the experimental measurement.

[0098] The torque analytical modeling method of the magnetic field modulation type speed governor provided by the present invention has the advantages of fast calculation speed, high accuracy, easy implementation, wide application range, etc., and can be widely applied to the design and optimization of the magnetic field modulation type speed governor, and has important engineering application value.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A torque analytical modeling method for a magnetic field modulation speed regulator, characterized in that: The following steps are involved: S1: Divide the magnetic field modulation speed regulator into a plurality of subdomains, wherein the plurality of subdomains include a permanent magnet domain, a slot subdomain, a slot domain, a modulation domain, an inner air domain, and an outer air domain; S2: Use polar coordinates to describe the magnetic vector potential of each subdomain; S3: Determine the boundary conditions between each subdomain; S4: Establish the governing equations of the magnetic vector potential in multiple subdomains using the field method; S5: Solve the magnetic vector potential governing equation to obtain the magnetic flux density distribution in the air gap layer; S6: Calculate the electromagnetic torque according to the magnetic flux density distribution using the Maxwell stress tensor method.

2. The torque analytical modeling method for a magnetic field modulation speed regulator according to claim 1, characterized in that: The magnetic vector potential control equations of the permanent magnet domain and the slot subdomain are Poisson's equations, and the magnetic vector potential control equations of the slot domain, the modulation domain, the inner air domain and the outer air domain are Laplace equations.

3. The torque analytical modeling method for a magnetic field modulation speed regulator according to claim 1, characterized in that: In S1, the permanent magnet domain includes multiple permanent magnets, the slot subdomain includes multiple slots, the slot opening domain includes multiple slots, the modulation domain includes multiple modulation teeth, and the inner air domain and the outer air domain are respectively the air gap regions between the permanent magnet domain and the slot subdomain.

4. The torque analytical modeling method for a magnetic field modulation speed regulator according to claim 1, characterized in that: In S2, the boundary condition is that the magnetic vector potential values ​​at the boundaries of each subdomain are the same.

5. The torque analytical modeling method for a magnetic field modulation speed regulator according to claim 1, characterized in that: In S4, the solution method is an analytical method.

6. The torque analytical modeling method for a magnetic field modulation speed regulator according to claim 1, characterized in that: In S5, the Maxwell stress tensor is a second-order tensor.

7. The torque analytical modeling method for a magnetic field modulation speed regulator according to claim 1, characterized in that: The pole pair ratio of the magnetic field modulation speed regulator is 9:8:

1.

8. A magnetic field modulation speed regulator, characterized in that: The magnetic field modulation speed regulator is used to execute the torque analysis modeling method according to any one of claims 1 to 7.

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