Calculation method for space magnetic field intensity generated by rectangular neodymium iron boron permanent magnet

Abstract

The invention discloses a calculation method for space magnetic field intensity generated by a rectangular neodymium iron boron permanent magnet, which comprises the following steps of: (1) enabling the permanent magnet to be equivalent to magnetic charges distributed according to a certain rule, and for the uniformly magnetized permanent magnet, only surface magnetic charges exist, and establishing a relationship between scalar magnetic potential and surface magnetic charge density; (2) calculating the distribution of a space magnetic field generated by the permanent magnet according to the distribution of the magnetic field in the space; and (3) establishing a space rectangular coordinate system for the rectangular neodymium-iron-boron permanent magnet, calculating the magnetic field intensity of a P (x, y, z) point on the rectangular neodymium-iron-boron permanent magnet, integrating three components of positive and negative magnetic charges of the permanent magnet, and calculating the total magnetic field intensity and the total magnetic induction intensity. According to the calculation method, high precision of space magnetic field distribution is ensured, and the requirement for fine adjustment of the magnetic field in different application scenes can be met.

Description

Technical Field

[0001] The invention relates to the technical field of magnets, and in particular to a method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet. Background Art

[0002] In scientific research and industrial applications, precise control and regulation of magnetic fields are key technologies, especially in the fields of material research, magnetic device design, and sensor manufacturing. Neodymium iron boron (NdFeB) permanent magnets are widely used in these fields due to their high magnetic energy product and stable magnetic properties, especially rectangular NdFeB permanent magnets, which are a common choice for magnetic field generation due to their simple structure and good magnetic field stability. However, how to accurately calculate the spatial magnetic field intensity generated by them is the core issue to ensure the effect of magnetic field application.

[0003] Traditional methods for calculating magnetic field strength are mostly based on empirical formulas or simplified mathematical models, but these methods often ignore the complex effects of the shape, size, and position distribution of permanent magnets on magnetic field strength, resulting in deviations between the calculation results and actual application scenarios. Especially in rectangular NdFeB permanent magnets, the distribution of the magnetic field is relatively uneven, and its strength changes significantly with changes in distance, position, and magnet size. Many existing calculation methods cannot accurately reflect the effects of these factors on magnetic field strength, and it is difficult to meet the needs of high-precision scenarios.

[0004] The calculation of the spatial magnetic field strength of rectangular NdFeB permanent magnets needs to consider multiple key factors, such as the geometric dimensions of the magnet, the magnetic properties of the material, the operating temperature, and the spatial distribution characteristics of the magnetic field. An accurate calculation method not only needs to be able to capture the changes in these parameters, but also has the ability to dynamically simulate and adjust the magnetic field strength to meet the application requirements under different experimental conditions. However, the calculation of the magnetic field strength of rectangular permanent magnets in the prior art is mostly based on idealized assumptions, which fails to fully consider the complexity and diversity of actual conditions.

[0005] Therefore, it is of great practical significance to develop a calculation method that can accurately calculate the spatial magnetic field intensity generated by rectangular NdFeB permanent magnets. Summary of the invention

[0006] The object of the present invention is to provide a method for calculating the spatial magnetic field strength generated by a rectangular NdFeB permanent magnet, which can more accurately calculate the spatial magnetic field strength generated by the rectangular NdFeB permanent magnet.

[0007] In one aspect of the present invention, the present invention proposes a method for calculating the spatial magnetic field strength generated by a rectangular NdFeB permanent magnet. According to an embodiment of the present invention, the method comprises the following steps:

[0008] (1) The permanent magnet is equivalent to the magnetic charge distributed according to a certain rule. For a uniformly magnetized permanent magnet, only the surface magnetic charge exists, and the relationship between the scalar magnetic potential and the surface magnetic charge density is established;

[0009] (2) Calculate the size of the spatial magnetic field generated by the permanent magnet based on the magnetic field distribution in space;

[0010] (3) Establish a spatial rectangular coordinate system for the rectangular NdFeB permanent magnet, calculate the magnetic field intensity at point P (x, y, z) on the rectangular NdFeB permanent magnet, and then integrate the three components of the positive and negative magnetic charges of the permanent magnet to calculate the total magnetic field intensity and total magnetic induction intensity.

[0011] In addition, the method for calculating the spatial magnetic field strength generated by a rectangular NdFeB permanent magnet according to the above embodiment of the present invention may also have the following additional technical features:

[0012] In some embodiments of the present invention, in step (1), the relationship between the scalar magnetic potential and the surface magnetic charge density is as follows:

[0013]

[0014] In the formula, is the scalar magnetic potential, σ m is the surface magnetic charge density, r is the distance between the source point and the field point, S is the permanent magnet boundary surface, c is the integration constant, and μ0 is the vacuum permeability.

[0015] In some embodiments of the present invention, in step (2), the calculation formula for the magnitude of the spatial magnetic field generated by the permanent magnet is as follows:

[0016]

[0017] In the formula, H is the size of the spatial magnetic field generated by the permanent magnet, σ m is the surface magnetic charge density, S is the permanent magnet boundary surface, μ0 is the vacuum permeability, and r is the distance between the source point and the field point.

[0018] In some embodiments of the present invention, the surface magnetic charge density σ m The calculation formula is as follows:

[0019] σ m =n·M0=n·B r

[0020] Where n is the unit vector of the external normal of the permanent magnet boundary surface, M0 = B r is the residual magnetic induction intensity of the permanent magnet.

[0021] In some embodiments of the present invention, in step (3), the magnetic field strength at point P (x, y, z) is calculated as follows:

[0022]

[0023] In the formula, H + , H - are the magnetic fields generated by positive and negative magnetic charges, S + , S - are the source areas that generate positive and negative magnetic charges, r + 、r - are the distances from the source of positive and negative magnetic charges to the field point P respectively.

[0024] In some embodiments of the present invention, the first term in the magnetic field strength calculation formula at point P (x, y, z) is integrated as follows:

[0025]

[0026] Where (ξ,η,γ) represents the source coordinates, and i, j, and k represent the unit vectors along the x-axis, y-axis, and z-axis, respectively.

[0027] In some embodiments of the present invention, in step (3), the magnetic field components generated by the positive magnetic charge in the x, y, and z directions are represented by H x+ , H y+ , H z+ The calculation formula is as follows:

[0028]

[0029]

[0030] Where a and b represent the width and length of the rectangular magnet respectively.

[0031] In some embodiments of the present invention, in step (3), the magnetic field components generated by the negative magnetic charge in the x, y, and z directions are represented by H x- , H y- , H z- The calculation formula is as follows:

[0032]

[0033] Where a, b, and h represent the width, length, and height of the rectangular magnet, respectively.

[0034] In some embodiments of the present invention, in step (3), the total magnetic field strength and the total magnetic induction strength are calculated as follows:

[0035] The total magnetic field strength is:

[0036] The total magnetic field intensity is: B = μH

[0037] H x=H x+ -H x- , H y =H y+ -H y- , H z =H z+ -H z-

[0038] Where H is the total magnetic field intensity and B is the total magnetic induction intensity.

[0039] In some embodiments of the present invention, in step (3), a rectangular magnet with adjustable fixing and magnetic field strength control device is used to verify the calculation result, and the device includes two sets of fixing mechanisms, and the fixing mechanisms include two parallel flat bars with holes and a plurality of U-shaped aluminum grooves, and the two ends of the U-shaped aluminum grooves are respectively fixed on the two flat bars with holes, and the two sets of fixing mechanisms are symmetrically arranged up and down, so that the rectangular NdFeB permanent magnet is fixed between the U-shaped aluminum grooves of the two sets of fixing mechanisms.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. Accurate magnetic charge distribution model: This method equates permanent magnets to magnetic charges distributed in a certain pattern, and calculates the magnetic field strength based on the superposition principle of magnetic charges. This magnetic charge model is closer to the actual magnetic field distribution generated by permanent magnets in space, and is particularly suitable for complex geometric shapes, such as rectangular NdFeB permanent magnets. Compared with traditional empirical formulas, it can more accurately describe the distribution changes of magnetic fields in space.

[0042] 2. Consider the residual magnetism effect: This calculation method fully considers the residual magnetism effect of NdFeB permanent magnets. By introducing the residual magnetism intensity into the formula, it can more accurately reflect the magnetization characteristics of permanent magnets in practice, especially the high residual magnetism characteristics of rare earth permanent magnets. This improvement makes the calculation results more in line with the actual situation, while traditional methods often ignore or simplify this effect.

[0043] 3. Flexibility of analytical and numerical solutions: This method provides a choice of analytical or numerical solutions in magnetic field calculations. For some magnets with regular geometric shapes (such as rectangular permanent magnets), the magnetic field intensity distribution can be directly calculated through analytical solutions, which makes the calculation process more efficient. At the same time, for complex geometries or special boundary conditions, numerical solutions can provide effective supplements, enhancing the applicability and flexibility of this method. Traditional methods usually rely on a single numerical calculation or limited analytical solutions, and have a narrow scope of application.

[0044] 4. Multi-factor consideration: This calculation method not only considers factors such as the geometric size, magnetization direction and boundary conditions of the permanent magnet, but also comprehensively analyzes the area of ​​the positive and negative magnetic charge source and the distance from the source point to the field point through the integral formula expanded by formulas (3) and (4). This multi-factor calculation method ensures the high accuracy of the spatial magnetic field distribution and can meet the needs of fine adjustment of the magnetic field in different application scenarios. In contrast, the traditional method considers these factors roughly, resulting in insufficient accuracy of the calculation results.

[0045] 5. Optimization application of analytical formula: Through integral calculation, the magnetic field distribution of a field point located at a specific position in space (such as a point on the Z axis) can be accurately described. This field strength calculation for a specific position provides great convenience for engineering practice, especially in experimental devices or industrial applications, analytical results can be directly applied to guide design and debugging. Traditional methods are usually unable to effectively handle specific point field strength calculations in complex scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a rectangular coordinate system of a rectangular permanent magnet established in an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of the structure of a U-shaped aluminum trough in an embodiment of the present invention;

[0048] Figure 3 It is a schematic diagram of the structure of the U-shaped aluminum channel and the flat bar with holes in the embodiment of the present invention;

[0049] Figure 4 It is a structural schematic diagram of a rectangular magnet adjustable fixing and magnetic field strength control device in an embodiment of the present invention;

[0050] Figure 5 1 is a diagram of an apparatus for conducting an experiment using an adjustable rectangular magnet fixing and magnetic field strength control device in an embodiment of the present invention, wherein a, c, and e are installation schematic diagrams of magnet spacings of 69 mm, 94 mm, and 118 mm, respectively, and b, d, and f are actual measurement diagrams of magnetic field strengths of magnet spacings of 69 mm, 94 mm, and 118 mm, respectively;

[0051] In the picture, 1. U-shaped aluminum groove, 2. Flat bar with holes, 3. Screws, 4. Rectangular magnet. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] A method for calculating the spatial magnetic field strength generated by a rectangular NdFeB permanent magnet comprises the following steps:

[0054] (1) The magnetic field generated by a permanent magnet of finite size in space can be regarded as the superposition of magnetic fields generated by magnetic charges distributed in a certain pattern in space. Therefore, the permanent magnet can be equivalent to magnetic charges distributed in a certain pattern, and the following rules apply (about the calculation model of permanent magnets):

[0055]

[0056] In the formula, ρ m is the magnetic charge density, μ0 is the vacuum magnetic permeability, and M0 is the remanent magnetization intensity.

[0057] In general, the permanent magnet is uniformly magnetized along the magnetization direction, M0 is a constant vector, ρ m Therefore, for a uniformly magnetized permanent magnet, only the surface magnetic charge exists, and the scalar magnetic potential and surface magnetic charge density σ m There is the following relationship (numerical analysis of engineering electromagnetic fields):

[0058]

[0059] Where r is the distance between the source point and the field point, S is the permanent magnet boundary surface, and c is the integration constant, which depends on the choice of the magnetic potential reference point.

[0060] (2) In the actual calculation of magnetic field, the focus is on the distribution of magnetic field in space, rather than the distribution of magnetic potential, so from the above formula we can get:

[0061]

[0062] In the formula, H represents the size of the spatial magnetic field generated by the permanent magnet;

[0063] Considering the residual magnetism of the permanent magnet, we have

[0064] B=(1+χ)μ0H+μ0M0

[0065] In the formula, M0 = B r is the residual magnetic induction of the permanent magnet, χ represents the magnetic susceptibility, μ0 is the vacuum magnetic permeability, and H is the size of the spatial magnetic field generated by the permanent magnet. When there is no other medium in the space under consideration, the above formula becomes:

[0066] B=μ0H+μ0M0

[0067] From the boundary conditions between the magnet surface and the air, we can get:

[0068] σ m =n·M0=n·B r

[0069] Where n is the unit vector of the external normal of the permanent magnet boundary surface.

[0070] For rare earth permanent magnets, HB is basically a straight line, so ε0 can be considered a constant, and equation (2) can be expressed as:

[0071]

[0072] The spatial magnetic field distribution generated by the permanent magnet can be calculated from equation (3).

[0073] (3) In practical applications, equation (3) can be solved analytically or numerically according to the actual situation. The solution conditions of the analytical solution usually depend on the geometric shape of the surface source S. The solution conditions include: symmetry, the location of the field point is on the symmetry axis or at a specific geometric position, and σ m is a constant or has a simple function form. If one of the above conditions is met, the solution can be obtained according to the actual situation. The solution steps are mainly divided into three steps: first, define the integral variable and the geometric relationship, then use symmetry to simplify the integral, and finally substitute the integral expression into the formula, expand the integral and calculate the result to obtain the numerical solution. Figure 1 For the rectangular permanent magnet shown, an analytical solution can be obtained.

[0074] according to Figure 1 A rectangular coordinate system is established as shown, and the magnetic field intensity at point P (x, y, z) is obtained by equation (3):

[0075]

[0076] In the formula, H + , H - , respectively, the magnetic fields generated by positive and negative magnetic charges, S + , S - is the source area of ​​positive and negative magnetic charges, r + , r - is the distance from the source of positive and negative magnetic charge to the field point P, and the first term in (4) is expanded:

[0077]

[0078] Since the integral is performed on the source, to avoid confusion, the source coordinates are represented by (ξ,η,γ). During the integration process, these coordinates are integral variables, representing every point in the source distribution area. + Integrate and convert the magnetic field components H generated by the positive magnetic charge in the x, y, and z directions x+ , H y+ , H z+ If it is expressed as:

[0079]

[0080]

[0081] In the formula, a and b represent the width and length of the rectangular magnet respectively. Similarly, the integral result of the second term of formula (4) is:

[0082]

[0083]

[0084] Where a, b, and h represent the width, length, and height of the rectangular magnet, respectively.

[0085] The components of the total magnetic field are then:

[0086] H x =H x+ -H x- , H y =H y+ -H y- , H z =H z+ -H z-

[0087] The total magnetic field strength is:

[0088] The total magnetic field intensity is: B = μH

[0089] In the formula, μ represents magnetic permeability, H x , H y , H z They respectively represent the components of the total magnetic field intensity in the x, y, and z directions.

[0090] As a special case, consider the case where the field point is located at point d on the Z axis, that is, point P(0, 0, d). At this time:

[0091]

[0092] B x =B y =0

[0093] In the formula, B x , B y , B z They represent the components of magnetic field intensity in the x, y, and z directions respectively.

[0094] (4) A rectangular magnet with adjustable fixation and magnetic field strength control device is used to verify the correctness of the calculation results.

[0095] The device comprises two parallel flat bars with holes 2 and a plurality of U-shaped aluminum grooves 1. Through holes are set at both ends of the U-shaped aluminum grooves 1. The plurality of U-shaped aluminum grooves 1 are installed in parallel between the two flat bars with holes 2, so that the two ends of the U-shaped aluminum grooves 1 are respectively fixed to the two flat bars with holes 2, and the fixing is fixed by screws 3 and nuts.

[0096] The device installation method is as follows:

[0097] a. According to the required magnetic field strength and coverage, roughly determine the size of the rectangular magnet 4.

[0098] b. Determine the U-shaped aluminum groove 1 with a matching inner width according to the size of the rectangular magnet 4, and determine the length of the U-shaped aluminum groove 1 at the same time.

[0099] c. Drill holes at both ends of the U-shaped aluminum channel 1 and assemble it with the perforated flat bar 2 using screws 3, nuts and gaskets.

[0100] d. Place a rectangular magnet 4 in the U-shaped aluminum groove 1, and place the upper and lower ends of the rectangular magnet 4 in the U-shaped aluminum groove 1 respectively, that is, two sets of perforated flat bars 2 fixed with the U-shaped aluminum groove 1 are required to complete the assembly of the entire device.

[0101] e. Insert the standard test piece that needs to be placed in the magnetic field from the side of the U-shaped aluminum groove 1 between the two magnets so that the test section is completely within the magnetic field.

[0102] The rectangular magnet 4 is placed in the U-shaped aluminum groove 1 and fixed to the perforated flat bar 2 by screws 3, washers and nuts to form a stable structure. This design ensures that the magnet is not easy to move during use, thereby improving the reliability of the equipment. And by replacing the U-shaped aluminum groove 1 with different inner widths, it can adapt to rectangular magnets 4 of different thicknesses. In this way, not only can the coverage area and uniformity of the magnetic field be changed, but it can also be flexibly adjusted to adapt to magnets of various specifications, making the control of the magnetic field more diversified. Using the adjustable U-shaped aluminum groove 1, the relative position between the magnets can be easily adjusted without complicated adjustment procedures, which greatly simplifies the use process of the equipment and improves the convenience of operation. The magnetic field strength and distribution can be controlled by adjusting the distance between the magnets and changing the thickness and specifications of the magnets.

[0103] like Figure 5As shown, the NdFeB permanent magnet is installed by using the above-mentioned rectangular magnet adjustable fixing and magnetic field strength control device, and two NdFeB permanent magnets of grade N52 with the same size of 60mmⅹ40mmⅹ10mm are respectively installed in the U-shaped aluminum groove, so that the distance between the two magnets is 118mm, 94mm, and 69mm, and then the magnetic field generated at the midpoint on the central axis between the two magnets is calculated by the method described in the embodiment, and the magnetic field strength generated at this point is measured by using the Japanese Sanliang TS500 handheld digital Tesla meter. The calculation results and the measured results are shown in the following table:

[0104] Table 1 Calculation and measurement results of magnetic field strength at the midpoint of the central axis of two NdFeB permanent magnets

[0105]

[0106] The above contents are merely examples and explanations of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they shall all fall within the protection scope of the present invention.

Claims

1. A method for calculating the spatial magnetic field strength generated by a rectangular NdFeB permanent magnet, characterized in that: The following steps are involved: (1) The permanent magnet is equivalent to the magnetic charge distributed according to a certain rule. For a uniformly magnetized permanent magnet, only the surface magnetic charge exists, and the relationship between the scalar magnetic potential and the surface magnetic charge density is established; (2) Calculate the size of the spatial magnetic field generated by the permanent magnet based on the magnetic field distribution in space; (3) Establish a spatial rectangular coordinate system for the rectangular NdFeB permanent magnet, calculate the magnetic field intensity at point P (x, y, z) on the rectangular NdFeB permanent magnet, and then integrate the three components of the positive and negative magnetic charges of the permanent magnet to calculate the total magnetic field intensity and total magnetic induction intensity.

2. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 1, characterized in that: In step (1), the relationship between the scalar magnetic potential and the surface magnetic charge density is as follows: In the formula, is the scalar magnetic potential, σ m is the surface magnetic charge density, r is the distance between the source point and the field point, S is the permanent magnet boundary surface, c is the integration constant, and μ0 is the vacuum permeability.

3. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 1, characterized in that: In step (2), the calculation formula for the spatial magnetic field generated by the permanent magnet is as follows: In the formula, H is the size of the spatial magnetic field generated by the permanent magnet, σ m is the surface magnetic charge density, S is the permanent magnet boundary surface, μ0 is the vacuum permeability, and r is the distance between the source point and the field point.

4. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 3, characterized in that: Surface magnetic charge density σ m The calculation formula is as follows: σ m =n·M0=n·B r Where n is the unit vector of the external normal of the permanent magnet boundary surface, M0 = B r is the residual magnetic induction intensity of the permanent magnet.

5. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 4, characterized in that: In step (3), the formula for calculating the magnetic field strength at point P (x, y, z) is as follows: In the formula, H + , H - are the magnetic fields generated by positive and negative magnetic charges, S + , S - are the source areas that generate positive and negative magnetic charges, r + 、r - are the distances from the source of positive and negative magnetic charges to the field point P respectively.

6. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 5, characterized in that: The first term in the calculation formula for the magnetic field strength at point P (x, y, z) is integrated as follows: Where (ξ,η,γ) represents the source coordinates, and i, j, and k represent the unit vectors along the x-axis, y-axis, and z-axis, respectively.

7. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 6, characterized in that: In step (3), the magnetic field components generated by the positive magnetic charge in the x, y, and z directions are represented by H x+ , H y+ , H z+ The calculation formula is as follows: Where a and b represent the width and length of the rectangular magnet respectively.

8. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 7, characterized in that: In step (3), the magnetic field components generated by the negative magnetic charge in the x, y, and z directions are represented by H x- , H y- , H s- represents, respectively represent negative magnetic charge, and the calculation formula is as follows: Where a, b, and h represent the width, length, and height of the rectangular magnet, respectively.

9. The method for calculating the spatial magnetic field strength generated by a rectangular NdFeB permanent magnet according to claim 6, characterized in that: In step (3), the total magnetic field strength and total magnetic induction strength are calculated as follows: The total magnetic field strength is: The total magnetic field intensity is: B = μH H x =H x+ -H x- ,H y =H y+ -H y- ,H z =H z+ -H z- Where H is the total magnetic field intensity and B is the total magnetic induction intensity.

10. The method for calculating the spatial magnetic field intensity generated by a rectangular NdFeB permanent magnet according to claim 1, characterized in that: In step (3), the calculation results are verified using a rectangular magnet adjustable fixing and magnetic field strength control device, the device comprising two sets of fixing mechanisms, the fixing mechanisms comprising two parallel flat bars with holes and a plurality of U-shaped aluminum grooves, the two ends of the U-shaped aluminum grooves being respectively fixed on the two flat bars with holes, the two sets of fixing mechanisms being symmetrically arranged up and down, so that the rectangular NdFeB permanent magnet is fixed between the U-shaped aluminum grooves of the two sets of fixing mechanisms.

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