An analytical method for the effective permeability of permanent magnets

Abstract

The application provides an analytical method for actual permeability of a permanent magnet, which comprises the following steps: in a two-dimensional axial section of a permanent magnet motor, an air gap and a permanent magnet region are equivalent to a rectangle according to an area equivalence principle; total magnetic resistance of the equivalent air gap and the equivalent permanent magnet is calculated by combining permeability of the air gap and the permanent magnet; the total magnetic resistance is magnetic resistance R ap ; the equivalent current method is adopted to equivalent the rectangular permanent magnet to a current layer, total magnetic resistance corresponding to the equivalent air gap and the equivalent permanent magnet in vacuum is calculated, and the total magnetic resistance is magnetic resistance R ta ; magnetic flux equations of the total magnetic resistance R ap and the total magnetic resistance R ta are listed according to a constant air gap flux principle, and the modified permanent magnet coercive force is obtained by solving, and then the actual permeability of the permanent magnet can be considered in the analytical calculation of the permanent magnet motor based on the equivalent current method. According to calculation, the air gap magnetic field calculation precision of the permanent magnet motor can be improved by nearly 7 times, the precision of the equivalent current method for calculating the air gap magnetic field is improved, and an accurate theoretical tool is provided for initial design and optimization of the permanent magnet motor.

Description

Technical Field

[0001] This invention belongs to the field of analytical calculation of permanent magnet motors, and relates to an analytical method for the actual magnetic permeability of permanent magnets. Background Technology

[0002] In recent years, permanent magnet motors have been widely used in many fields such as industrial and agricultural production, transportation, and aerospace due to their advantages such as high efficiency, high power density, high reliability, and low vibration and noise. The initial design and optimization stage of permanent magnet motors requires the calculation of numerous design schemes. Using the finite element method for simulation calculations would consume a significant amount of time and computational resources. Therefore, analytical methods, with their clear physical concepts, faster calculation speed, and acceptable computational accuracy, play a crucial role in the initial design and optimization stage of permanent magnet motors.

[0003] In analytical calculations of the magnetic field of permanent magnet motors, the permanent magnet needs to be treated equivalently. Two methods are commonly used for this: the magnetization vector method and the equivalent current method. The equivalent current method treats the surface of the permanent magnet as a current layer, while the actual permanent magnet region is considered a vacuum. This equivalence process assumes a relative permeability of 1, but the actual relative permeability should be slightly closer to 1. This assumption reduces the magnetomotive force generated by the permanent magnet, resulting in a calculated air gap magnetic flux density that is less than the actual air gap magnetic flux density. Consequently, the analytical model cannot accurately predict the electromagnetic performance of the permanent magnet motor.

[0004] Therefore, it is necessary to find a simple and quick analytical method that can take into account the actual permeability of permanent magnets in order to calculate the air gap magnetic field and electromagnetic performance of permanent magnet motors more accurately. This can also promote the widespread application of the equivalent current method in the analytical calculation of permanent magnet motors. Summary of the Invention

[0005] To overcome the limitation of the currently used equivalent current method in accounting for the actual permeability of permanent magnets, this invention proposes an analytical method for the actual permeability of permanent magnets, enabling more accurate prediction of the air gap magnetic field and electromagnetic performance of permanent magnet motors. Research indicates that this method has not been applied in the analytical calculations of permanent magnet motors.

[0006] To achieve the above-mentioned objectives, the technical solution of the present invention is as follows:

[0007] A method for analyzing the actual permeability of a permanent magnet includes the following steps:

[0008] In the two-dimensional axial section of a permanent magnet motor, based on the principle of area equivalence, the air gap and permanent magnet regions are equivalent to rectangles, and the total magnetic reluctance R of the equivalent air gap and permanent magnet is calculated. ap ;

[0009] The rectangular permanent magnet is represented by an equivalent current layer and a vacuum using the equivalent current method. The total magnetic reluctance R corresponding to the air gap and the permanent magnet being represented by a vacuum is then calculated. ta ;

[0010] Based on the principle of constant air gap magnetic flux, write the following regarding the total magnetic reluctance R. ap With total magnetic reluctance R ta The magnetic flux equation, where the magnetic reluctance R ap The corresponding magnetomotive force is the product of the coercivity of the permanent magnet (a known property parameter of the permanent magnet) and the projected length of the permanent magnet in the magnetization direction, while the magnetic reluctance R... ta The corresponding magnetomotive force is the product of the corrected coercivity of the permanent magnet and the projected length of the permanent magnet in the magnetization direction. The corrected coercivity of the permanent magnet is the quantity to be determined.

[0011] Based on the above flux equation, the corrected coercivity of the permanent magnet can be obtained, which is the coercivity considering the actual permeability of the permanent magnet in the equivalent current method.

[0012] Optionally, the permanent magnet motor is a surface-mounted permanent magnet motor.

[0013] Optionally, the permanent magnet is magnetized in a parallel manner.

[0014] Optionally, the permanent magnet is magnetized radially.

[0015] Optionally, the permanent magnet can have any shape.

[0016] This invention can easily and quickly calculate the actual permeability of permanent magnets using the equivalent current method, thereby improving the analytical model of permanent magnet motors and promoting the widespread application of the equivalent current method in the analytical calculation of permanent magnet motors. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the equivalent relationship between the air gap and the permanent magnet;

[0018] Figure 2 This is a comparison chart of air gap magnetic flux density with and without taking into account the actual permeability of the permanent magnet. Detailed Implementation

[0019] The specific embodiments of the present invention will be further described in detail with reference to the accompanying drawings.

[0020] Figure 1 A schematic diagram of the equivalent relationship between the air gap and the permanent magnet in a permanent magnet motor is given. The specific implementation process of considering the actual permeability of the permanent magnet in the equivalent current method is as follows:

[0021] (1) Figure 1The air gap in (a) is the air gap after considering the stator slotting effect using the Carter coefficient. To simplify the calculation, according to the principle of area equivalence, the air gap and the permanent magnet are respectively equivalent to two rectangles, such as... Figure 1 As shown in (b), the permeability of the air gap is μ0, which is the permeability of free space, and the length and width of the air gap rectangle are w and h, respectively. a The magnetic permeability of the permanent magnet is μ0μ r μ r Let be the relative permeability of the permanent magnet, and let w be the length and h be the width of the rectangle containing the permanent magnet. p The coercivity of the permanent magnet is H c At this point, the total magnetic reluctance model of the air gap and the permanent magnet is a cuboid, and the expression for the total magnetic reluctance is:

[0022]

[0023] Among them, L ef This is the effective axial length of the motor;

[0024] (2) Using the equivalent current method to Figure 1 The rectangular permanent magnet in (b) is equivalent to a current layer and a vacuum, such as Figure 1 As shown in (c), current layers exist on both sides of the rectangular permanent magnet. In this case, the permeability of the permanent magnet region is the vacuum permeability μ0. The expression for the total magnetic reluctance when the air gap and permanent magnet are equivalent to a vacuum is:

[0025]

[0026] To ensure that the magnetomotive force generated by the permanent magnet is consistent with that before it is equivalent to a current layer, the coercivity of the equivalent permanent magnet should be H. c_m The following will calculate H. c_m The expression;

[0027] (3) According to the principle of constant air gap magnetic flux, that is, to ensure the equivalent performance of the permanent magnet before and after ( Figure 1 (b) to Figure 1 (c) The magnetic flux in the equivalent air gap is equal, and the magnetic reluctance R is listed. ap With magnetic reluctance R ta The magnetic flux equation is as follows:

[0028]

[0029] Among them, H c h p For the magnetic reluctance R ap The corresponding magnetomotive force is the product of the coercivity of the permanent magnet and the projected length of the permanent magnet in the magnetization direction, H. c_m h p For the magnetic reluctance R taThe corresponding magnetic potential is the product of the corrected coercivity of the permanent magnet and the projected length of the permanent magnet in the magnetization direction.

[0030] (4) Based on the magnetic flux equation in (3), the corrected coercivity H of the permanent magnet can be obtained. c_m This refers to the coercivity considering the actual permeability of the permanent magnet in the equivalent current method, as shown below.

[0031]

[0032] Among them, S a With S p They are respectively Figure 1 (a) The area of ​​the air gap and the permanent magnet.

[0033] (5) Furthermore, the equivalent current value i, considering the actual permeability of the permanent magnet, can be calculated using the equivalent current method. c As shown below

[0034] i c =H c_m l

[0035] Where l is the length of the equivalent current projected onto the magnetization direction of the permanent magnet.

[0036] In summary, this completes the process of considering the actual permeability of permanent magnets in the equivalent current method. The no-load air gap magnetic field of a permanent magnet motor is calculated using the subdomain method (a commonly used analytical method for calculating the magnetic field of permanent magnet motors), and the results considering and not considering the actual permeability of the permanent magnets are compared with the finite element simulation results. Figure 2 As shown. From Figure 2 (a) It can be seen that the air gap radial magnetic flux density considering the actual permeability of the permanent magnet is in good agreement with the finite element results, while the air gap magnetic flux density without considering the actual permeability of the permanent magnet has a large error with the finite element results. Figure 2 (b) shows the results of Fourier decomposition of the radial magnetic flux density in the air gap. Calculations show that the error between the fundamental amplitude of the magnetic flux density considering the actual permeability of the permanent magnet and the finite element result is only 0.44%, while the error is 3.02% for the result without considering the actual permeability of the permanent magnet. This verifies that considering the actual permeability of the permanent magnet in the equivalent current method allows for more accurate calculation of the air gap magnetic field of the permanent magnet motor, providing a more precise theoretical tool for the initial design optimization of the permanent magnet motor.

[0037] The above description is merely a preferred embodiment of the present invention, and while the description is quite specific and detailed, it should not be construed as limiting the scope of the present invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for analyzing the actual permeability of a permanent magnet, characterized in that, Includes the following steps: Based on the principle of area equivalence, the air gap and permanent magnet regions are equivalent to rectangles, denoted as the air gap rectangle and the permanent magnet rectangle, respectively. The length and width of the air gap rectangle are w and h, respectively. a The length and width of the permanent magnet rectangle are w and h, respectively. p The effective axial length of the motor is L ef The permeability of the air gap is μ0, which is the permeability of free space, and the relative permeability of the permanent magnet is μ0. r Calculate the equivalent air gap of the permanent magnet motor and the total magnetic reluctance R of the permanent magnet. ap Its calculation expression is: The equivalent current method for permanent magnets is used to treat a rectangular permanent magnet as an equivalent current layer and a vacuum. The total magnetic reluctance R corresponding to the air gap of the permanent magnet motor and the permanent magnet being equivalent to a vacuum is calculated. ta Its calculation expression is: Write the total magnetic reluctance R based on the principle of constant air gap magnetic flux of the motor. ap Total magnetic reluctance R ta Coercivity H of the original permanent magnet c From the flux equation, the corrected coercivity H of the permanent magnet can be obtained. c_m This refers to the coercivity corresponding to the actual permeability of the permanent magnet in the equivalent current method for permanent magnets. The above magnetic flux equation is: Total magnetic reluctance R ap The corresponding magnetic potential H c h p The total magnetic reluctance R is the product of the coercivity of the permanent magnet and the projected length of the permanent magnet in the magnetization direction. ta The corresponding magnetic potential H c_m h p The corrected coercivity of the permanent magnet is the product of the projected length of the permanent magnet in the magnetization direction. c_m That is, the quantity to be determined, its expression is: Where S a With S p These represent the air gap and the area of ​​the permanent magnet motor, respectively.

2. The method for analyzing the actual permeability of a permanent magnet according to claim 1, characterized in that, The permanent magnet motor is a surface-mounted permanent magnet motor.

3. The method for analyzing the actual permeability of a permanent magnet according to claim 1, characterized in that, The permanent magnet is magnetized either in parallel or radially.

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