Method and system for calculating magnetic field of partial elliptic cylinder magnet based on equivalent magnetic charge method

Abstract

The application discloses a local elliptic cylinder magnet magnetic field calculation method and system based on an equivalent magnetic charge method, establishes a local elliptic cylinder magnet magnetic field mathematical model, sets parameters of the local elliptic cylinder magnet, brings the parameters of the local elliptic cylinder magnet into the local elliptic cylinder magnet magnetic field mathematical model, solves the model, and obtains the magnetic field of the local elliptic cylinder magnet. The application can accurately and quickly calculate the space magnetic field of the local elliptic cylinder magnet magnetized in any direction in the xoy plane, is helpful for subsequent accurate solution of the magnetic field gradient, control of the space magnetic force, and analysis of the dynamic movement of the magnetic beads.

Description

Technical Field

[0001] This invention relates to the field of analytical calculation methods for the magnetic field of locally elliptical cylindrical magnets, and particularly to a method and system for calculating the magnetic field of locally elliptical cylindrical magnets with magnetization directions along arbitrary directions in the xoy plane based on the equivalent magnetic charge method. Background Technology

[0002] A magnetic field exerts a force on a magnet placed within it. This characteristic allows magnetic objects to interact without physical contact, and it has been applied in numerous fields, such as non-contact sensing and magnetic resonance imaging. High-precision analytical analysis of the magnetic field is essential for designing external magnetic field units in order to accurately control the movement of magnetic objects.

[0003] Compared to cylindrical micromagnets, elliptical cylindrical micromagnets have an aspect ratio of non-1. This increases the magnetic force along the major axis and decreases the magnetic force along the minor axis. Therefore, the spatial magnetic force can be precisely controlled by adjusting parameters such as the aspect ratio, magnetization direction, and shape of the elliptical cylindrical magnet, thereby indirectly controlling the direction of motion of the target particles.

[0004] Currently, the most common method for calculating the magnetic field distribution around such magnets is finite element analysis. This method mainly utilizes Maxwell's equations, and based on initial conditions and necessary boundary conditions, integrates the magnetic field as equivalent to magnetic charge elements or current elements to obtain a mathematical expression for the magnetic field distribution. Although this method has high practicality and effectiveness, its computational accuracy is greatly affected by the mesh size and the size of the computational domain. When the applied mesh is small, it becomes very time-consuming when solving high-precision problems; when the mesh is coarse, the solution will have a large error compared to the actual magnetic field value. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for calculating the magnetic field of a locally elliptical cylindrical magnet based on the equivalent magnetic charge method, in order to solve the problems existing in the prior art. This invention can accurately and quickly calculate the spatial magnetic field of a locally elliptical cylindrical magnet magnetized in any direction in the xoy plane, which helps to accurately solve the magnetic field gradient, control the spatial magnetic force, and analyze the dynamic motion of the magnetic bead.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The magnetic field calculation method for a locally elliptical cylindrical magnet based on the equivalent magnetic charge method includes the following steps:

[0008] Establish a mathematical model of the magnetic field of a local elliptic cylindrical magnet;

[0009] Set the parameters of the local elliptical cylindrical magnet;

[0010] By substituting the parameters of the local elliptical cylindrical magnet into the mathematical model of the local elliptical cylindrical magnet's magnetic field and solving for the magnetic field, the magnetic field of the local elliptical cylindrical magnet can be obtained.

[0011] Furthermore, the establishment of the mathematical model for the magnetic field of the local elliptical cylindrical magnet specifically involves:

[0012] Establish a magnetic field model for a uniformly magnetized magnet;

[0013] The surface of a local elliptical cylindrical magnet is divided into sections;

[0014] Based on the magnetic field model of a uniformly magnetized magnet, magnetic field models for each region of a locally elliptical cylindrical magnet are established.

[0015] Furthermore, the establishment of the magnetic field model for a uniformly magnetized magnet specifically involves:

[0016] For a uniformly magnetized magnet, the magnetic field strength it produces at any point in space satisfies:

[0017]

[0018] In the formula, μ0 is the free permeability, s refers to the surface of the local elliptical cylinder, v refers to the local elliptical cylinder, P is a point on the local elliptical cylinder, K is any point in space, and σ s Let σ be the surface charge density of the local elliptic cylindrical magnet. v The local elliptic cylindrical magnet's charge density;

[0019] Volume charge density formula:

[0020]

[0021] In the formula, For Hamiltonian operators, Let be the magnetization vector along any direction in the xoy plane. The magnitudes of the magnetization vectors at all points are equal, and their directions are parallel. Therefore... If the divergence is 0, then σ v =0;

[0022] Surface charge density formula:

[0023]

[0024] In the formula, It is a unit vector perpendicular to the surface of the local elliptical cylindrical magnet.

[0025] Furthermore, the process of dividing the surface of the local elliptical cylindrical magnet into sections specifically involves:

[0026] The surface of the local elliptical cylindrical magnet is divided into a first sector surface, a second sector surface, an arc-shaped side surface, a first rectangular surface, and a second rectangular surface. The first sector surface and the second sector surface are the upper and lower base surfaces of the local elliptical cylindrical magnet, respectively. The first rectangular surface is the side surface corresponding to the starting position of integration relative to the arc-shaped side surface, and the second rectangular surface is the side surface corresponding to the ending position of integration relative to the arc-shaped side surface.

[0027] Furthermore, the magnetic field model based on a uniformly magnetized magnet establishes magnetic field models for each region of a locally elliptical cylindrical magnet, specifically including:

[0028] Establish magnetic field models for the first and second sector surfaces;

[0029] Establish a magnetic field model for the curved side surface;

[0030] Establish magnetic field models for the first and second rectangular surfaces.

[0031] Furthermore, establishing the magnetic field model of the first and second sector surfaces specifically involves: the unit vectors of the first and second sector surfaces. with vector The angle between them is 90°, which does not affect the surrounding magnetic field.

[0032] Furthermore, the establishment of the magnetic field model for the arc-shaped side surface specifically involves:

[0033] Let the coordinates of point K be (x, y, z), which can be converted to cylindrical coordinates as (r, α, z). Point P1 is located on the curved side surface with coordinates (x0, y0, z0), which can be converted from rectangular coordinates to cylindrical coordinates as (r0, θ, z0).

[0034] The magnetization direction is decomposed into the x-axis and the y-axis. for The angle between the x-axis and the x-axis Decomposed into components along the x-axis J X and the component J along the y-axis Y :

[0035]

[0036]

[0037] The standard equation of an ellipse:

[0038]

[0039] Where a is the semi-major axis of the ellipse, and b is the semi-minor axis of the ellipse;

[0040] Plane P1'O”K is a plane with ordinate z and parallel to the xoy plane, where point O” is the intersection of plane P1'O”K and the y-axis, point P1' is the intersection of the perpendicular line drawn from point P1 to plane P1'O”K and the plane, and the distance from point P1' to the center point O” is:

[0041]

[0042] The unit normal vector of the ellipse at point P:

[0043]

[0044] By combining the expressions, we obtain the formula for the magnetic field strength at point K on the curved side:

[0045]

[0046] Where θ1 is the angle between the first rectangular plane and the xoz plane, θ2 is the angle between the second rectangular plane and the xoz plane, and h is the height of the elliptical cylinder;

[0047] Integrating this formula over the height yields the magnitude of the magnetic field in the z-direction:

[0048]

[0049] Magnitude of the magnetic field in the α direction:

[0050]

[0051] Magnitude of magnetic field in the r direction:

[0052]

[0053] In the formula:

[0054] η 2 =r 2 +r0 2 -2rr0cos(α-θ) (13).

[0055] Furthermore, when point P2 is located on the first rectangular surface formed by the semi-axis at the starting endpoint of the elliptic arc integral, the coordinates of point P2 are (x0, y0, z0), and the unit normal vector of the first rectangular surface is:

[0056]

[0057] Surface charge density:

[0058]

[0059] When θ≠±π / 2, by combining the expressions, we obtain the formula for the magnetic field strength of the first rectangular surface at point K:

[0060]

[0061] Integrating this formula over the height yields the magnitude of the magnetic field in the x-direction:

[0062]

[0063] Magnetic field strength in the y-direction:

[0064]

[0065] Magnitude of magnetic field in the z-direction:

[0066]

[0067] When θ = ±π / 2, by combining the expressions, we obtain the formula for the magnetic field strength of the first rectangular surface at point K:

[0068]

[0069] Magnetic field strength in the x-direction:

[0070]

[0071] Magnetic field strength in the y-direction:

[0072]

[0073] Magnitude of magnetic field in the z-direction:

[0074]

[0075] When point P2 lies on the second rectangular surface formed by the semi-axis at the endpoint of the elliptic arc integral, and the coordinates of point P2 are (x0, y0, z0), the unit normal vector of the second rectangular surface is:

[0076]

[0077] The remaining derivation steps are the same as those for the first rectangular surface.

[0078] Furthermore, the parameters of the local elliptical cylindrical magnet include: semi-major axis a, semi-minor axis b, height h, magnetization vector J, and magnetization direction. The angle θ1 between the first rectangular plane formed by the semi-axis at the starting endpoint of the elliptic arc surface integral and the xoz plane, and the angle θ2 between the second rectangular plane formed by the semi-axis at the ending endpoint of the elliptic integral and the xoz plane.

[0079] A magnetic field calculation system for locally elliptical cylindrical magnets based on the equivalent magnetic charge method includes:

[0080] Model building module: used to build a mathematical model of the magnetic field of a local elliptical cylindrical magnet;

[0081] Parameter setting module: Used to set the parameters of the local elliptical cylindrical magnet;

[0082] The solver module is used to input the parameters of a local elliptical cylindrical magnet into the mathematical model of the local elliptical cylindrical magnet's magnetic field, solve for the magnetic field of the local elliptical cylindrical magnet, and obtain the magnetic field of the local elliptical cylindrical magnet.

[0083] Compared with the prior art, the present invention has the following beneficial technical effects:

[0084] This invention establishes a mathematical model of the local elliptical cylindrical magnetic field and obtains an analytical solution for the spatial magnetic field through formulas, resulting in more accurate calculations. Secondly, it has advantages in the theoretical derivation of the magnetic field gradient, enabling precise calculation of the magnetic field gradient by differentiating the magnetic induction intensity. Furthermore, calculating the spatial magnetic field using analytical solutions eliminates the need for mesh generation, avoiding the limitations of the finite element method due to mesh size and computational domain size, thus improving calculation speed and solving the simulation time problem under fine mesh conditions. The calculation method using the magnetic field calculation expression is more accurate and faster, facilitating subsequent accurate solutions for the magnetic field gradient, control of spatial magnetic force, and analysis of the dynamic motion of magnetic beads. Attached Figure Description

[0085] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0086] Figure 1 This is a flowchart of the model analysis and calculation method in this invention;

[0087] Figure 2 The three-dimensional model established in this invention includes (a) a schematic diagram of the first sector surface, the arc-shaped side surface, and the second rectangular side surface of the partial elliptical cylinder, (b) a schematic diagram of the second sector surface and the first rectangular side surface of the partial elliptical cylinder, and (c) a top view of the partial elliptical cylinder.

[0088] Figure 3 This is a model diagram of the external magnetic field generated at any point on the arc-shaped side surface in this invention, where (a) is a schematic diagram of any point on the arc-shaped side surface of the local elliptical cylinder to any point in space, and (b) is a top view of the local elliptical cylinder.

[0089] Figure 4 This is a model diagram of the external magnetic field generated at any point on the first rectangular side surface (the side surface corresponding to the starting position of the integral relative to the arc surface) in this invention, where (a) is a schematic diagram of any point on any rectangular side surface of the local elliptical cylinder to any point in space, and (b) is a top view of the local elliptical cylinder.

[0090] Figure 5The diagram shows the external magnetic field model generated on any point on the second rectangular side surface (the side surface corresponding to the integral endpoint of the arc surface) in this invention, where (a) is a schematic diagram of any point on the first rectangular side surface of the local elliptical cylinder to any point in space, and (b) is a top view of the local elliptical cylinder.

[0091] Figure 6 The figure shows a comparison of the calculation results of the analytical method and the finite element method in this invention. (a) shows the magnetic induction intensity in the x-axis direction of the two calculation methods, (b) shows the magnetic induction intensity in the y-axis direction of the two calculation methods, and (c) shows the magnetic induction intensity in the z-axis direction of the two calculation methods.

[0092] Wherein, 1 is the first sector surface, 2 is the second sector surface, 3 is the first rectangular surface, 4 is the arc-shaped side surface, and 5 is the second rectangular side surface. Detailed Implementation

[0093] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0094] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0095] Example 1

[0096] This invention proposes a method for deriving the analytical expression of the magnetic field distribution of a locally elliptical cylindrical magnet based on the equivalent magnetic charge method. It is important to note that the magnetization direction of the locally elliptical cylindrical magnet can be any direction within the xoy plane, and the locally elliptical cylinder is a complete elliptical cylindrical magnet cut arbitrarily along the radial direction. This method outperforms finite element analysis in terms of computation time and accuracy.

[0097] See Figure 1 Specifically, it includes the following steps:

[0098] Step 1: Establish a mathematical model of the magnetic field of a local elliptical cylindrical magnet;

[0099] Based on Maxwell's equations, it can be seen that, Figure 2 (c) For a uniformly magnetized magnet, the magnetic field strength generated at any point in space satisfies:

[0100]

[0101] In the formula, μ0 is the free permeability, s refers to the surface of the local elliptical cylinder, v refers to the local elliptical cylinder, P is a point on the local elliptical cylinder, K is any point in space, and σ s Let σ be the surface charge density of the local elliptic cylindrical magnet. v Let be the local elliptic cylinder charge density.

[0102] Volume charge density formula:

[0103]

[0104] In the formula, For Hamiltonian operators, Let be the magnetization vector along any direction in the xoy plane. The magnitudes of the magnetization vectors at all points are equal, and their directions are parallel. Therefore... If the divergence is 0, then σ v It is 0.

[0105] Surface charge density formula:

[0106]

[0107] in It is a unit vector perpendicular to the surface of the local elliptical cylindrical magnet.

[0108] like Figure 2 The unit vector of the two sector surfaces (first sector 1 and second sector 2) of the locally elliptical cylindrical magnet. with vector The included angle between them is 90°, and only the side of the cylinder affects the surrounding magnetic field. The side of the local elliptical cylinder is composed of an arc-shaped side 4 at an arbitrary angle, and a first rectangular surface 3 and a second rectangular surface 5 formed by two semi-axes passing through the two ends of this arc-shaped side.

[0109] Let the coordinates of point K be (x, y, z), which can be converted to cylindrical coordinates as (r, α, z), as follows: Figure 3 Point P1 is located on the curved side surface with coordinates (x0, y0, z0). The rectangular coordinate system is converted to a cylindrical coordinate system as (r0, θ, z0).

[0110] The magnetization direction is decomposed into the x-axis and the y-axis. for The angle between the x-axis and the x-axis Decomposed into components along the x-axis J X and the component J along the y-axis Y :

[0111]

[0112]

[0113] The standard equation of an ellipse:

[0114]

[0115] Where a is the semi-major axis of the ellipse, and b is the semi-minor axis of the ellipse;

[0116] like Figure 3 (b) Plane P1'O”K is a plane with ordinate z and parallel to the xoy plane, where point O” is the intersection of plane P1'O”K and the y-axis, point P1' is the intersection of the perpendicular line drawn from point P1 to plane P1'O”K and the plane, and the distance from point P1' to the center point O” is:

[0117]

[0118] The unit normal vector of the ellipse at point P:

[0119]

[0120] Combining the expressions, we obtain the formula for the magnetic field strength at point K on the curved side surface 4:

[0121]

[0122] Where θ1 is the angle between the first rectangular plane and the xoz plane, θ2 is the angle between the second rectangular plane and the xoz plane, and h is the height of the elliptical cylinder;

[0123] Integrating this formula over the height yields the magnitude of the magnetic field in the z-direction:

[0124]

[0125] Magnitude of the magnetic field in the α direction:

[0126]

[0127] Magnitude of magnetic field in the r direction:

[0128]

[0129] In the formula:

[0130] η 2=r 2 +r0 2 -2rr0cos(α-θ) (13)

[0131] like Figure 4 When point P2 is located on the first rectangular plane 3 formed by the semi-axis at the starting endpoint of the elliptic arc integral, the coordinates of point P2 are (x0, y0, z0). The unit normal vector of the first rectangular plane 3 is:

[0132]

[0133] Surface charge density:

[0134]

[0135] When θ≠±π / 2, by combining the expressions, we obtain the formula for the magnetic field strength of the first rectangular surface 3 at point K:

[0136]

[0137] Integrating this formula over the height yields the magnitude of the magnetic field in the x-direction:

[0138]

[0139] Magnetic field strength in the y-direction:

[0140]

[0141] Magnitude of magnetic field in the z-direction:

[0142]

[0143] When θ = ±π / 2, by combining the expressions, we obtain the formula for the magnetic field strength of the first rectangular surface at point K:

[0144]

[0145] Magnitude of magnetic field in the x direction:

[0146]

[0147] Magnetic field strength in the y-direction:

[0148]

[0149] Magnitude of magnetic field in the z-direction:

[0150]

[0151] like Figure 5When point P2 is located on the second rectangular surface 5 formed by the semi-axis at the endpoint of the elliptical arc integral, with coordinates (x0, y0, z0), the unit normal vector of the second rectangular surface 5 is:

[0152]

[0153] The remaining derivation steps are the same.

[0154] The calculation method proposed in this invention can calculate the spatial magnetic field strength of a locally elliptical cylindrical magnet with magnetization direction in any direction within the xoy plane and cut arbitrarily in the radial direction.

[0155] Step 2: Set the parameters of the local elliptical cylindrical magnet;

[0156] like Figure 2 As shown, the local elliptical cylinder data is as follows: semi-major axis a = 6 mm, semi-minor axis b = 3 mm, height h = 5 mm, magnetization vector J = 1 A / m, and magnetization direction is at a 30° angle to the x-axis. Figure 2 (c) The angle between the first rectangular plane formed by the semi-axis at the starting endpoint of the elliptic arc surface integral and the xoz plane is θ1, and the angle between the second rectangular plane formed by the semi-axis at the ending endpoint of the elliptic integral and the xoz plane is θ2, where θ1 = 0 and θ2 = 135°.

[0157] Step 3: Substitute the parameters of the local elliptical cylindrical magnet into the mathematical model of the local elliptical cylindrical magnet's magnetic field, solve for the magnetic field of the local elliptical cylindrical magnet.

[0158] The analytical calculation method for the magnetic field proposed in this invention is used to solve the following: Figure 3 The magnetic field of the local elliptical cylindrical magnet is shown, and the calculation results are compared with the finite element simulation results, such as... Figure 6 .

[0159] A line segment with a height of 7 mm and an angle of 60° to the x-axis (α = 60°) is selected, and the magnetic induction intensity on the line segment is calculated. The curves and points in the figure represent the results calculated by the analytical method and the finite element method, respectively. Although the calculation results show slight deviations, the waveform trends are consistent, and the error meets the requirements, which also proves that the analytical method used in this invention is correct and effective.

[0160] This invention establishes an analytical formula for the magnetic field of a locally elliptical cylindrical magnet and calculates the magnetic induction intensity of a straight line in space along different directions using an example model. Comparison with finite element method (FEM) results demonstrates the correctness and effectiveness of this method. This method can calculate locally elliptical cylindrical magnets with arbitrary magnetization directions in the xoy plane and arbitrary radial cuts. It boasts high calculation accuracy and speed, is independent of spatial mesh generation, and facilitates accurate solution of the magnetic field gradient. It ensures the accuracy of the calculation results while reducing computation time and improving efficiency. This provides convenience for further research on the design of locally elliptical cylindrical magnetic fields, aiding in the accurate solution of magnetic field gradients and control of spatial magnetic forces. Based on locally elliptical cylinders, it designs spliced ​​magnetic fields, controls the trajectory of magnetic beads through changes in magnetic field and magnetic force, and analyzes the dynamic motion of the beads. This provides convenience for subsequent directional control of particle motion and separation of particles with different properties by adjusting parameters and the properties of the magnetic system.

[0161] Example 2

[0162] This invention also provides a magnetic field calculation system for a locally elliptical cylindrical magnet based on the equivalent magnetic charge method, comprising:

[0163] Model building module: used to build a mathematical model of the magnetic field of a local elliptical cylindrical magnet;

[0164] Parameter setting module: Used to set the parameters of the local elliptical cylindrical magnet;

[0165] The solver module is used to input the parameters of a local elliptical cylindrical magnet into the mathematical model of the local elliptical cylindrical magnet's magnetic field, solve for the magnetic field of the local elliptical cylindrical magnet, and obtain the magnetic field of the local elliptical cylindrical magnet.

[0166] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied 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.

[0167] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. 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 illustrations and / or block diagrams. Figure 1One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0168] 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.

[0169] 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.

[0170] 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 its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A method for calculating the magnetic field of a locally elliptical cylindrical magnet based on the equivalent magnetic charge method, characterized in that, Includes the following steps: Establish a mathematical model of the magnetic field of a local elliptic cylindrical magnet; Set the parameters of the local elliptical cylindrical magnet; By substituting the parameters of the local elliptic cylindrical magnet into the mathematical model of the local elliptic cylindrical magnet's magnetic field and solving it, the magnetic field of the local elliptic cylindrical magnet can be obtained. The establishment of the mathematical model for the magnetic field of a local elliptical cylindrical magnet is specifically as follows: Establish a magnetic field model for a uniformly magnetized magnet; The surface of a local elliptical cylindrical magnet is divided into sections; Based on the magnetic field model of a uniformly magnetized magnet, a magnetic field model for each region of a locally elliptical cylindrical magnet is established. The process of dividing the surface of the local elliptical cylindrical magnet into sections specifically involves: The surface of the local elliptical cylindrical magnet is divided into a first sector, a second sector, an arc-shaped side, a first rectangular surface, and a second rectangular surface. The first sector and the second sector are the upper and lower base surfaces of the local elliptical cylindrical magnet, respectively. The first rectangular surface is the side surface corresponding to the starting position of integration relative to the arc-shaped side, and the second rectangular surface is the side surface corresponding to the ending position of integration relative to the arc-shaped side. The magnetic field model based on a uniformly magnetized magnet establishes magnetic field models for each region of a locally elliptical cylindrical magnet, specifically including: Establish magnetic field models for the first and second sector surfaces; Establish a magnetic field model for the curved side surface; Establish magnetic field models for the first and second rectangular surfaces; The establishment of the magnetic field model for the first and second sector surfaces specifically involves: the unit vectors of the first and second sector surfaces. with vector The angle between them is 90°, which has no effect on the surrounding magnetic field; The establishment of the magnetic field model for the arc-shaped side surface is specifically as follows: Let the coordinates of point K be... Converted to cylindrical coordinates , The point is located on the curved side, with coordinates of The transformation from Cartesian coordinate system to cylindrical coordinate system is ; The magnetization direction is decomposed into the x-axis and the y-axis. for The angle between the x-axis and the x-axis Decomposed into components along the x-axis and the component along the y-axis : (4) (5) The standard equation of an ellipse: (6) Where a is the semi-major axis of the ellipse, and b is the semi-minor axis of the ellipse; flat Let be a plane with ordinate z, parallel to the xoy plane, where Point is a plane Intersection with the y-axis Point for Point to plane The perpendicular line to the plane, the point of intersection. Point to center point Distance: (7) The unit normal vector of the ellipse at point P: (8) By combining the expressions, we obtain the formula for the magnetic field strength at point K on the curved side: (9) in, The angle between the first rectangular face and the xoz plane. Let h be the angle between the second rectangular face and the xoz plane, and h be the height of the elliptical cylinder. Integrating this formula over the height yields the magnitude of the magnetic field in the z-direction: (10) Magnitude of directional magnetic field: (11) Magnitude of magnetic field in the r direction: (12) In the formula: (13) when The point lies on the first rectangular surface formed by the semi-axes at the starting endpoints of the elliptic arc integral. The coordinates of the point are The unit normal vector of the first rectangular face: (14) Surface charge density: (15) when When the equations are combined, the formula for the magnetic field strength of the first rectangular surface at point K is obtained: (16) Integrating this formula over the height yields the magnitude of the magnetic field in the x-direction: (17) Magnetic field strength in the y-direction: (18) Magnitude of magnetic field in the z-direction: (19) when When the equations are combined, the formula for the magnetic field strength of the first rectangular surface at point K is obtained: (20) Magnitude of magnetic field in the x direction: (21) Magnetic field strength in the y-direction: (22) Magnitude of magnetic field in the z-direction: (23) when The point lies on the second rectangular surface formed by the semi-axis at the endpoint of the elliptic arc integral. The coordinates of the point are The unit normal vector of the second rectangular face: (24) The remaining derivation steps are the same as those for the first rectangular surface.

2. The method for calculating the magnetic field of a locally elliptical cylindrical magnet based on the equivalent magnetic charge method according to claim 1, characterized in that, The establishment of the magnetic field model for a uniformly magnetized magnet is specifically as follows: For a uniformly magnetized magnet, the magnetic field strength it produces at any point in space satisfies: (1) In the formula, The permeability of free space, s The surface of a local elliptical cylinder. v Let P be a point on the local elliptic cylinder, and K be any point in space. The surface charge density of a local elliptic cylindrical magnet. The local elliptic cylindrical magnet's charge density; Volume charge density formula: (2) In the formula, For Hamiltonian operators, Let be the magnetization vector along any direction in the xoy plane. The magnitudes of the magnetization vectors at all points are equal, and their directions are parallel. Therefore... If the divergence is 0, then =0; Surface charge density formula: (3) In the formula, It is a unit vector perpendicular to the surface of the local elliptical cylindrical magnet.

3. The method for calculating the magnetic field of a locally elliptical cylindrical magnet based on the equivalent magnetic charge method according to claim 1, characterized in that, The parameters of the local elliptic cylindrical magnet include: semi-major axis a, semi-minor axis b, height h, magnetization vector J, and magnetization direction. The angle between the first rectangular surface formed by the semi-axis at the starting endpoint of the elliptical arc surface integral and the xoz plane. The angle between the second rectangular plane formed by the semi-axis at the endpoint of the elliptic integral and the xoz plane. .

4. A magnetic field calculation system for locally elliptical cylindrical magnets based on the equivalent magnetic charge method, characterized in that, include: Model building module: used to build a mathematical model of the magnetic field of a local elliptical cylindrical magnet; Parameter setting module: Used to set the parameters of the local elliptical cylindrical magnet; The solver module is used to input the parameters of a local elliptical cylindrical magnet into the mathematical model of the local elliptical cylindrical magnet's magnetic field, solve for the magnetic field of the local elliptical cylindrical magnet, and obtain the magnetic field of the local elliptical cylindrical magnet. The establishment of the mathematical model for the magnetic field of a local elliptical cylindrical magnet is specifically as follows: Establish a magnetic field model for a uniformly magnetized magnet; The surface of a local elliptical cylindrical magnet is divided into sections; Based on the magnetic field model of a uniformly magnetized magnet, a magnetic field model for each region of a locally elliptical cylindrical magnet is established. The process of dividing the surface of the local elliptical cylindrical magnet into sections specifically involves: The surface of the local elliptical cylindrical magnet is divided into a first sector, a second sector, an arc-shaped side, a first rectangular surface, and a second rectangular surface. The first sector and the second sector are the upper and lower base surfaces of the local elliptical cylindrical magnet, respectively. The first rectangular surface is the side surface corresponding to the starting position of integration relative to the arc-shaped side, and the second rectangular surface is the side surface corresponding to the ending position of integration relative to the arc-shaped side. The magnetic field model based on a uniformly magnetized magnet establishes magnetic field models for each region of a locally elliptical cylindrical magnet, specifically including: Establish magnetic field models for the first and second sector surfaces; Establish a magnetic field model for the curved side surface; Establish magnetic field models for the first and second rectangular surfaces; The establishment of the magnetic field model for the first and second sector surfaces specifically involves: the unit vectors of the first and second sector surfaces. with vector The angle between them is 90°, which has no effect on the surrounding magnetic field; The establishment of the magnetic field model for the arc-shaped side surface is specifically as follows: Let the coordinates of point K be... Converted to cylindrical coordinates , The point is located on the curved side, with coordinates of The transformation from Cartesian coordinate system to cylindrical coordinate system is ; The magnetization direction is decomposed into the x-axis and the y-axis. for The angle between the x-axis and the x-axis Decomposed into components along the x-axis and the component along the y-axis : (4) (5) The standard equation of an ellipse: (6) Where a is the semi-major axis of the ellipse, and b is the semi-minor axis of the ellipse; flat Let be a plane with ordinate z, parallel to the xoy plane, where Point is a plane Intersection with the y-axis Point for Point to plane The perpendicular line to the plane, the point of intersection. Point to center point Distance: (7) The unit normal vector of the ellipse at point P: (8) By combining the expressions, we obtain the formula for the magnetic field strength at point K on the curved side: (9) in, The angle between the first rectangular face and the xoz plane. Let h be the angle between the second rectangular face and the xoz plane, and h be the height of the elliptical cylinder. Integrating this formula over the height yields the magnitude of the magnetic field in the z-direction: (10) Magnitude of directional magnetic field: (11) Magnitude of magnetic field in the r direction: (12) In the formula: (13) when The point lies on the first rectangular surface formed by the semi-axes at the starting endpoints of the elliptic arc integral. The coordinates of the point are The unit normal vector of the first rectangular face: (14) Surface charge density: (15) when When the equations are combined, the formula for the magnetic field strength of the first rectangular surface at point K is obtained: (16) Integrating this formula over the height yields the magnitude of the magnetic field in the x-direction: (17) Magnetic field strength in the y-direction: (18) Magnitude of magnetic field in the z-direction: (19) when When the equations are combined, the formula for the magnetic field strength of the first rectangular surface at point K is obtained: (20) Magnitude of magnetic field in the x direction: (21) Magnetic field strength in the y-direction: (22) Magnitude of magnetic field in the z-direction: (23) when The point lies on the second rectangular surface formed by the semi-axis at the endpoint of the elliptic arc integral. The coordinates of the point are The unit normal vector of the second rectangular face: (24) The remaining derivation steps are the same as those for the first rectangular surface.

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