A Hybrid Analytical Method for Solving the Air-gap Magnetic Field of a Permanent Magnet Motor with a Quasi-Regular Polygon Rotor Core

Abstract

The present invention belongs to the technical field of motors, and discloses a hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core, comprising the following steps: Step 1, using the equivalent surface current method to equivalent the permanent magnet into a current layer; Step 2, making the circumcircle of the quasi-regular polygon rotor core, converting the quasi-regular polygon rotor core of the permanent magnet motor into a regular circular rotor core, and obtaining the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots; Step 3, obtaining the complex air-gap specific permeance λ of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots; Step 4, using the complex air-gap specific permeance λ to correct the air-gap magnetic field of the permanent magnet motor with a circular rotor core and stator slots obtained by the subdomain method, so as to obtain the air-gap magnetic field of the actual permanent magnet motor. The method of the present invention can calculate the permanent magnet motor quickly and accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of motors, and particularly to a hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core, which can be applied to the analytical calculation of a surface-mounted permanent magnet motor with parallel magnetization and a quasi-regular polygon rotor core. Background Art

[0002] Permanent magnet motors have been widely used in various civilian and military fields such as high-speed railways, automobiles, aerospace, etc. due to their advantages of high efficiency, high power density, and high reliability. The surface-mounted permanent magnet motor with a quasi-regular polygon rotor core, also known as a bow-shaped surface-mounted permanent magnet motor, has a flat lower surface of the permanent magnet, which has the advantages of convenient processing and installation of the permanent magnet, and can reduce the generation of permanent magnet waste. It has been widely used in common propulsion systems at present, such as ship propulsion systems. At the beginning of the design of permanent magnet motors, the analytical method is often used to analyze and calculate permanent magnet motors and optimize their structures. This has the advantages of facilitating the adjustment of the motor structure, saving a large amount of calculation time and calculation resources compared with the finite element method for motor simulation calculation.

[0003] However, existing analytical methods, such as the magnetic network method, sub-domain method, and conformal transformation method, etc., are basically used to analytically calculate the performance such as the air-gap magnetic field of surface-mounted permanent magnet motors with regular circular rotor cores, and there is little analysis of permanent magnet motors with quasi-regular polygon rotor cores. Therefore, in order to facilitate the analytical optimization of surface-mounted permanent magnet motors with quasi-regular polygon rotor cores, that is, bow-shaped surface-mounted permanent magnet motors, at the beginning of the design, it is necessary to seek an analytical method applicable to such permanent magnet motors to improve the analytical calculation and optimization speed of bow-shaped surface-mounted permanent magnet motors, which is an urgent problem to be solved at present. Summary of the Invention

[0004] To solve the problem of difficult solution of the air-gap magnetic field of the above permanent magnet motor, and improve its analytical accuracy and speed up its analytical speed, the embodiment of the present invention proposes a hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core, which is applicable to the solution of the air-gap magnetic field of a surface-mounted parallel magnetization permanent magnet motor with a quasi-regular polygon rotor core. The hybrid analytical method combines the ideas of the sub-domain method and the conformal transformation method, and can calculate the above permanent magnet motor quickly and accurately. To provide a basic understanding of some aspects of the disclosed embodiments, a simple summary is given below. This summary part is not a general review, nor is it intended to identify key / important constituent elements or delineate the protection scope of these embodiments. Its sole purpose is to present some concepts in a simple form as a prelude to the detailed description below.

[0005] According to the first aspect of the embodiment of the present invention, a hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core is provided.

[0006] In one embodiment, a hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core includes:

[0007] Step 1: Using the equivalent surface current method, the permanent magnet is equivalent to a current layer.

[0008] Step 2: Make a circumcircle of the quasi-regular polygon rotor core, convert the quasi-regular polygon rotor core of the permanent magnet motor into a regular circular rotor core, and obtain the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots.

[0009] Step 3: Obtain the complex air-gap permeance λ1 of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots and the complex air-gap permeance λ0 of the permanent magnet motor with a circular rotor core and no stator slots. Then, the complex air-gap specific permeance λ of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots is the ratio of λ1 to λ0.

[0010] Step 4: Use the complex air-gap specific permeance λ to correct the air-gap magnetic field of the permanent magnet motor with a circular rotor core and stator slots obtained by the subdomain method, so as to obtain the air-gap magnetic field of the actual permanent magnet motor, where the complex air-gap specific permeance λ and the position of the air-gap magnetic density obtained by the subdomain method in the air gap are in one-to-one correspondence.

[0011] Optionally, the step of obtaining the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots specifically includes:

[0012] Using the subdomain method, the converted permanent magnet motor model is divided into an air-gap subdomain and two slot subdomains. By writing the Laplace equation or Poisson equation in each subdomain to solve the vector magnetic potential of each subdomain, the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots is obtained.

[0013] Optionally, the magnetization method of the permanent magnet is parallel magnetization.

[0014] Optionally, the step of obtaining the complex air-gap permeance λ1 of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots is specifically:

[0015] Perform conformal transformation on the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots to obtain its complex air-gap permeance λ1.

[0016] Optionally, the step of obtaining the complex air-gap permeance λ0 of the permanent magnet motor with a circular rotor core and no stator slots is specifically:

[0017] Perform conformal transformation on the permanent magnet motor with a circular rotor core and no stator slots to obtain its complex air-gap permeance λ1.

[0018] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0019] This hybrid analysis method combines the subdomain method and the conformal transformation method, which can quickly and accurately calculate the above-mentioned permanent magnet motor and can be applied to the preliminary design optimization of such motors.

[0020] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present invention. Brief Description of the Drawings

[0021] The drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.

[0022] Figure 1 It is a schematic diagram of a quasi-regular dodecagon rotor core and arc-shaped permanent magnets shown according to an exemplary embodiment;

[0023] Figure 2 It is a schematic diagram of a subdomain method analysis model under one pole shown according to an exemplary embodiment;

[0024] Figure 3 It is a conformal transformation flow chart of a permanent magnet motor with a quasi-regular dodecagon rotor core shown according to an exemplary embodiment;

[0025] Figure 4 It is a schematic diagram of the air-gap polygon in the m-plane drawn by the Schuck toolbox shown according to an exemplary embodiment;

[0026] Figure 5 It is a conformal transformation flow chart of a permanent magnet motor with a circular rotor core shown according to an exemplary embodiment;

[0027] Figure 6a It is a waveform diagram of the radial component of the complex air-gap specific permeance at the air-gap center line of a permanent magnet motor with a quasi-regular dodecagon rotor core and no stator slots shown according to an exemplary embodiment;

[0028] Figure 6b It is a waveform diagram of the tangential component of the complex air-gap specific permeance at the air-gap center line of a permanent magnet motor with a quasi-regular dodecagon rotor core and no stator slots shown according to an exemplary embodiment. Detailed Description of the Invention

[0029] The following description and the accompanying drawings fully disclose specific embodiments herein, enabling those skilled in the art to practice them. Parts and features of some embodiments may be included in or replace parts and features of other embodiments. The scope of the embodiments herein includes the entire scope of the claims and all available equivalents of the claims. In this document, the terms "first", "second", etc. are only used to distinguish one element from another, without requiring or implying any actual relationship or order between these elements. In fact, the first element can also be called the second element, and vice versa. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, such that a structure, device or equipment comprising a series of elements not only includes those elements but also other elements not expressly listed, or elements inherent to such structure, device or equipment. Without further limitation, an element defined by the statement "comprising one..." does not exclude the presence of additional identical elements in the structure, device or equipment comprising the element. The embodiments herein are described in a progressive manner, with each embodiment highlighting the differences from other embodiments. For the same or similar parts among the embodiments, reference may be made to each other.

[0030] In this document, the orientation or positional relationships indicated by the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing this document 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, and thus should not be construed as a limitation of the present invention. In the description herein, unless otherwise specified and defined, the terms "mounted", "connected" and "coupled" shall be understood in a broad sense. For example, it may be a mechanical connection or an electrical connection, or may be the communication inside two elements. It may be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms may be understood according to specific circumstances.

[0031] In this document, unless otherwise stated, the term "plurality" means two or more.

[0032] In this document, the character " / " indicates that the objects before and after are in an "or" relationship. For example, A / B means: A or B.

[0033] In this document, the term "and / or" is an associative relationship describing an object, indicating that three relationships may exist. For example, A and / or B means: A or B, or, A and B.

[0034] Without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0035] The following further describes in detail the specific embodiments of the present invention with reference to the accompanying drawings.

[0036] Taking a surface-mounted permanent magnet motor with a quasi-regular dodecagon rotor core and parallel magnetization as an example, the hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core specifically includes the following steps:

[0037] Step 1: Equivalent the bow-shaped permanent magnet in Figure 1 to a current layer as shown in Figure 2 by using the equivalent surface current method. Since the permanent magnet adopts the parallel magnetization method, according to the principle of the equivalent surface current method, there is no current layer on the lower edge of the permanent magnet, and this equivalent process has no influence on the total magnetic potential generated by the permanent magnet.

[0038] Step 2: Draw the circumcircle of the quasi-regular dodecagon in Figure 1 , and convert the quasi-regular dodecagon rotor core of the permanent magnet motor into a circular rotor core as shown in Figure 2 .

[0039] In Figure 2 , the permanent magnet model under one pole is divided into three sub-domains, namely the air-gap sub-domain (sub-domain I) and two slot sub-domains (sub-domain II (i) , sub-domain III (i) ). Write the Laplace equation or Poisson equation in each sub-domain and solve it by using the method of separation of variables. Each time, only calculate the air-gap magnetic field generated by two symmetric surface currents on both sides of the coordinate axis. Finally, obtain the total air-gap magnetic field generated by all surface currents through the superposition theorem of the magnetic field. Taking the magnetic field distribution at the air-gap center line as an example, use B sr and B sθ to represent the radial component and tangential component of the magnetic flux density at the air-gap center line obtained by using the sub-domain method respectively.

[0040] Step 3: Perform three-step conformal transformation on the permanent magnet motor with a quasi-regular dodecagon rotor core and no stator slots, as shown in Figure 3 . Step 1: Convert the s-plane of the actual motor to the straight-line m-plane through the logarithmic equation, and the transformation formula is as follows

[0041] m = ln(s)

[0042] where s and m represent the coordinates on the air-gap center line of the s-plane and m-plane respectively.

[0043] Step 2: Divide the lower edge of the air-gap into several small segments in the m-plane to construct an air-gap polygon as shown in Figure 4 , Figure 4Among them, 1, 2, 3, and 4 are the vertices of the air-gap polygon. With the help of the Schuck toolbox, the m-plane is transformed into the air-gap rectangle of the z-plane, and the transformation formula is as follows:

[0044] z = f SC Toolbox (m)

[0045] where z represents the coordinate on the air-gap center line of the z-plane, and f SC Toolbox is the transformation function that transforms the m-plane into the z-plane in the Schuck toolbox.

[0046] Step 3, the transformation from the z-plane to the k-plane adopts the following formula:

[0047]

[0048] where k represents the coordinate on the air-gap center line of the k-plane, j is the imaginary unit, and z1, z2, z3 are as Figure 3 shown. The transformation formulas between the above planes are all reversible. Then, the complex air-gap permeance λ1 at the air-gap center line of the permanent magnet motor with a quasi-regular dodecagon rotor core and a stator without slots is:

[0049]

[0050] Repeating the above three-step transformation (Step 1 to Step 3) can obtain the complex air-gap permeance λ0 at the air-gap center line of the permanent magnet motor with a circular rotor core and a stator without slots. As Figure 5 shown, in Step 1, the permanent magnet motor with a circular rotor core and a stator without slots is transformed into the straight-line m-plane, and the transformation formula is as follows

[0051] m′ = ln(s′)

[0052] where s' and m' respectively represent the coordinates on the air-gap center line of the s-plane and the m-plane of the permanent magnet motor with a circular rotor core and a stator without slots.

[0053] Step 2, with the help of the Schuck transformation toolbox, the m-plane of the permanent magnet motor with a circular rotor core and a stator without slots is transformed into the air-gap rectangle of the z-plane, and the transformation formula is as follows:

[0054] z′ = f SC Toolbox (m′)

[0055] where z' represents the coordinate on the air-gap center line of the z-plane of the permanent magnet motor with a circular rotor core and a stator without slots.

[0056] Step 3, the transformation from the z-plane to the k-plane of the permanent magnet motor with a circular rotor core and a stator without slots adopts the following formula:

[0057]

[0058] where k' represents the coordinate on the k - plane air - gap center line of a permanent - magnet motor with a circular rotor core and a stator without slots, z'1, z'2, z'3 are as Figure 5 shown. Since the transformation formulas between the above - mentioned planes are all reversible, the complex air - gap permeance λ0 at the air - gap center line of a permanent - magnet motor with a circular rotor core and a stator without slots is:

[0059]

[0060] Therefore, the expression of the complex air - gap specific permeance λ at the air - gap center line of a permanent - magnet motor with a quasi - regular dodecagon rotor core and a stator without slots is:

[0061]

[0062] where λ r and λθ are the radial and tangential components of λ respectively, and their waveforms are as Figure 6a and Figure 6b shown.

[0063] Step 4: Using the complex air - gap specific permeance λ obtained above to correct the magnetic flux density at the air - gap center line obtained by the sub - domain method, the actual air - gap magnetic flux density at the air - gap center line of a permanent - magnet motor with a quasi - regular dodecagon rotor core can be obtained. The correction formula is shown as follows:

[0064] B r +jB θ =(λ r +jλ θ )·(B sr +jB sθ )

[0065] where the specific expressions of the radial and tangential components of the required actual air - gap magnetic flux density are shown as follows:

[0066] B r =λ r B sr -λ θ B sθ

[0067] B θ =λ θ B sr +λ r B sθ

[0068] where B r is the radial component of the actual air - gap magnetic flux density, B θ is the tangential component of the actual air - gap magnetic flux density, B sr is the radial component of the magnetic flux density at the air - gap center line obtained by the sub - domain method, and B sθ is the tangential component of the magnetic flux density at the air - gap center line obtained by the sub - domain method.

[0069] In summary, the hybrid analytical calculation of the air-gap magnetic field of the surface-mounted permanent magnet motor with a quasi-regular dodecagon rotor core and parallel magnetization is completed.

[0070] This implementation process is carried out taking the quasi-regular dodecagon rotor core as an example. For permanent magnet motors with other quasi-regular polygon rotor cores, the same solution process can also be used to analytically calculate their air-gap magnetic fields. Therefore, this hybrid analytical method has strong applicability.

[0071] The above description is only a preferred embodiment of the present invention, and its description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention are all included in the protection scope of the present invention.

[0072] The present invention is not limited to the structure already described and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. A hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core, characterized in that, It includes the following steps: Step 1: Use the equivalent surface current method to equivalent the permanent magnet to a current layer; Step 2: Make the circumcircle of the quasi-regular polygon rotor core, convert the quasi-regular polygon rotor core of the permanent magnet motor into a regular circular rotor core, and use the subdomain method to obtain the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots; Step 3: Adopt the conformal transformation method to obtain the complex air-gap permeance λ1 of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots and the complex air-gap permeance λ0 of the permanent magnet motor with a circular rotor core and no stator slots. Then, the complex air-gap specific permeance λ of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots is the ratio of λ1 to λ0; Step 4: Use the complex air-gap specific permeance λ to correct the air-gap magnetic density of the permanent magnet motor with a circular rotor core and stator slots obtained by the subdomain method, so as to obtain the air-gap magnetic density of the actual permanent magnet motor, where the position of the complex air-gap specific permeance λ and the air-gap magnetic density obtained by the subdomain method in the air gap corresponds one by one.

2. The hybrid analytical method for solving the air-gap magnetic field of a quasi-regular polygon rotor core permanent magnet motor according to claim 1, characterized in that, The step of obtaining the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots specifically includes: Use the subdomain method to divide the converted permanent magnet motor model into an air-gap subdomain and two slot subdomains, and solve the vector magnetic potential of each subdomain by writing the Laplace equation or Poisson equation in each subdomain to obtain the air-gap magnetic density distribution of the permanent magnet motor with a circular rotor core and stator slots.

3. A hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core as described in claim 1, characterized in that The magnetization mode of the permanent magnet is parallel magnetization.

4. A hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core as described in claim 1, characterized in that The step of obtaining the complex air-gap permeance λ1 of the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots is specifically: Perform conformal transformation on the permanent magnet motor with a quasi-regular polygon rotor core and no stator slots to obtain its complex air-gap permeance λ1.

5. A hybrid analytical method for solving the air-gap magnetic field of a permanent magnet motor with a quasi-regular polygon rotor core as described in claim 1, characterized in that The step of obtaining the complex air-gap permeance λ0 of the permanent magnet motor with a circular rotor core and no stator slots is specifically: Perform conformal transformation on the permanent magnet motor with a circular rotor core and no stator slots to obtain its complex air-gap permeance λ0.

Images