A three-dimensional square Helmholtz coil and its magnetic field compensation method

Abstract

This invention discloses a three-dimensional square Helmholtz coil and its magnetic field compensation method, comprising: a square Helmholtz coil, a platform and base disposed at the center of three sets of square Helmholtz coils, and a winding frame fixedly disposed on the base; the three sets of square Helmholtz coils are all disposed within the winding frame and are symmetrically distributed along the X-axis, Y-axis and Z-axis respectively to form a three-dimensional magnetic field, and the platform is detachably disposed at the center of the three-dimensional magnetic field. The symmetrical arrangement of the multi-layer square frame structure effectively improves its space utilization, reduces magnetic field coupling error and magnetic field distribution offset, and improves the magnetic field consistency and three-dimensional magnetic field control accuracy in the central region. Furthermore, based on theoretical magnetic field analysis and combined with environmental magnetic field error analysis, this invention proposes an active magnetic field compensation model, providing a theoretical basis for the structural design and parameter optimization of the three-dimensional magnetic field control system, further improving the magnetic field uniformity of the three-dimensional square Helmholtz coil.

Description

Technical Field

[0001] This invention relates to the field of Helmholtz coil technology, and specifically discloses a three-dimensional square Helmholtz coil and its magnetic field compensation method. Background Technology

[0002] A three-dimensional Helmholtz coil device is used to generate a uniform magnetic field. It typically consists of two coaxial, identical circular coils with currents flowing in the same direction and at the same magnitude, thus producing a relatively uniform magnetic field in the central region. Three-dimensional Helmholtz coil devices are widely used in laboratories, medicine, geological exploration, and other fields. However, existing three-dimensional Helmholtz coils are usually circular, and the highly uniform magnetic field region formed by a circular coil is typically approximately ellipsoidal. Because the range of the ellipsoidal uniform magnetic field is relatively small, and circular coils have limitations in terms of structural integration and space utilization, their use is somewhat inconvenient.

[0003] Although square Helmholtz coils are used in some fields of existing technology to simplify installation and increase the range of uniform magnetic fields, the size of the uniform magnetic field region generated by existing square Helmholtz coils is very limited, resulting in low space utilization (space utilization is defined as the volume of the uniform magnetic field region divided by the space occupied by the magnetic field generator). They can only be used in situations with ample space and cannot meet the requirements of situations where there are high requirements for the volume of the magnetic field generator, the uniform magnetic field region, and the uniformity of the magnetic field. Furthermore, existing square Helmholtz coils often fail to effectively form a uniform magnetic field when there is magnetic field interference in the environment. This makes it difficult for existing Helmholtz coils to ensure the uniformity of the magnetic field for experimental testing when there is environmental magnetic field interference.

[0004] Therefore, there is an urgent need to propose a three-dimensional square Helmholtz coil that can simplify installation and increase the range of uniform magnetic fields, while ensuring the uniformity of the magnetic field to improve the accuracy of experimental detection. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the aforementioned issues, this invention provides a three-dimensional square Helmholtz coil and its magnetic field compensation method. The three-dimensional square Helmholtz coil, through the arrangement of a multi-layer square frame structure, enables it to form a uniform magnetic field of sufficient range and intensity within a certain space. Furthermore, the establishment of the magnetic field compensation method can further reduce environmental interference with the experiment.

[0007] (II) Technical Solution

[0008] To solve the above-mentioned technical problems, the present invention proposes a three-dimensional square Helmholtz coil, which is used as a platform for multi-axis magnetic field control, magnetic drive experiments and related magnetic field research. The three-dimensional square Helmholtz coil includes: three sets of mutually independent and spatially orthogonal square Helmholtz coils, a platform set at the center of the three sets of square Helmholtz coils, a movable base, and a winding frame fixedly set on the base.

[0009] The three sets of square Helmholtz coils are all arranged in the winding frame and are symmetrically distributed along the X-axis, Y-axis and Z-axis to form a three-dimensional magnetic field. The platform is detachably arranged at the center of the three-dimensional magnetic field. An auxiliary space is preset below the platform to integrate a slide, power supply or heat dissipation mechanism.

[0010] Preferably, the winding frame includes multiple sets of horizontal planar square frames and multiple sets of vertical planar square frames, wherein the multiple sets of horizontal planar square frames are connected to the multiple sets of vertical planar square frames and the multiple sets of horizontal planar square frames are perpendicular to each other.

[0011] Preferably, each of the multiple sets of horizontal planar square frames and vertical planar square frames includes a mounting beam and a rounded corner, adjacent mounting beams are connected by the rounded corner, and both the mounting beam and the rounded corner are made of polyoxymethylene material.

[0012] Preferably, the platform includes a connecting seat, a sample stage, and a lifting rod;

[0013] The connecting seat is fixedly mounted on the base and located at the center of the base. The fixed end of the lifting rod is located at the center of the connecting seat. The lifting end of the lifting rod is connected to the sample stage to drive the sample stage to move up and down.

[0014] Preferably, the sample stage has multiple M6 standard optical platform threaded holes to fix the sample to be tested.

[0015] Preferably, the three-dimensional square Helmholtz coil is used to form the three-dimensional magnetic field, and the magnetic field strength of the three-dimensional magnetic field is calculated as follows:

[0016] S1. Assume the side length of a single-turn square coil is 2. Furthermore, the square Helmholtz coil is located in the xy plane, and its center is located at the origin. Therefore, the expression for the magnetic field generated by a single turn of the square Helmholtz coil at its center is: When the number of coil turns is During the turn, the central magnetic field can be further expressed as: ;

[0017] S2. For a square Helmholtz structure consisting of two identical square Helmholtz coils, with the two coils placed symmetrically along the same axis and supplied with currents of the same direction and magnitude, the magnetic field at any position along the axis can be expressed as:

[0018] ;

[0019] in, The distance between the centers of the two coils is... These are the position coordinates along the axis. This is the magnetic field distribution function generated by a single coil along the axial direction;

[0020] S3. The three-dimensional square Helmholtz coil consists of three sets of mutually independent and spatially orthogonal square Helmholtz coils, respectively corresponding to... axis, axis, In the three directions of the axis, according to the principle of magnetic field vector superposition, the total magnetic field of the three-dimensional magnetic field can be expressed as:

[0021] ;

[0022] in, , , They are respectively , , Magnetic field components generated by a triaxial coil , , These are the unit vectors in the corresponding directions. The theoretical target magnetic field generated by a three-dimensional square Helmholtz coil.

[0023] Preferably, to further improve the stability and consistency of the magnetic field, the uniformity of the three-dimensional square Helmholtz coil is defined as:

[0024] ;

[0025] in, and These represent the maximum and minimum magnetic field values ​​within the target uniform region, respectively. The value of the magnetic field at the center point;

[0026] Furthermore, to improve the magnetic field uniformity in the central region of the three-dimensional magnetic field, the side length of the square coil and the spacing between the two coils are optimized to ensure that the axial magnetic field in the central region satisfies the following:

[0027] ;

[0028] Even if the second derivative of the axial magnetic field in the central region approaches zero, the uniform magnetic field region is expanded, thereby improving the stability and consistency of the magnetic field.

[0029] This invention also provides a magnetic field compensation method for a three-dimensional square Helmholtz coil, the magnetic field compensation method being implemented based on the aforementioned three-dimensional square Helmholtz coil, the magnetic field compensation method comprising:

[0030] S4. Magnetic field error is mainly caused by environmental interference magnetic fields. To quantify the systematic error, a magnetic field error index is introduced:

[0031] ;

[0032] in, This represents the percentage of magnetic field error. The allowable error threshold is set according to application requirements. :when < When the system is deemed to be working normally, ≥ When the system is found to be significantly affected by external magnetic field interference, compensation and correction are performed.

[0033] S5. There is a corresponding relationship between the compensating magnetic field and the compensating current:

[0034] ;

[0035] ;

[0036] ;

[0037] in, These are the magnetic field transformation constants of the X, Y, and Z axis coils, used to characterize the magnetic field strength generated by a unit current;

[0038] S6. To reduce the impact of environmental interference, an active magnetic field compensation model is established: assuming that an environmental magnetic field is detected in the X direction. Then, the compensation current is adjusted by adjusting the X-axis coil. , so that:

[0039] ;

[0040] Similarly, the Y-axis and Z-axis coils achieve active compensation by adjusting the compensation current:

[0041] ;

[0042] ;

[0043] The triaxial compensated magnetic field vector is represented as: Therefore, the total magnetic field of the compensated three-dimensional magnetic field is: ,in, The environmental magnetic field vector can be represented as .

[0044] Preferably, when the compensation magnetic field satisfies: Then we get: That is, the total magnetic field of the output three-dimensional magnetic field is restored to the theoretical target magnetic field.

[0045] (III) Beneficial Effects

[0046] Compared with the prior art, the three-dimensional square Helmholtz coil of the present invention has the following advantages:

[0047] 1. The three-dimensional square Helmholtz coil, through the setting of a multi-layer square frame structure, can form a uniform magnetic field with sufficient range and intensity within a certain space, which effectively improves the space utilization of the three-dimensional square Helmholtz coil and enables it to effectively meet the requirements of the uniform magnetic field area scale of multi-axis magnetic field control, magnetic drive experiments and related magnetic field research platforms.

[0048] 2. The movable base in the three-dimensional square Helmholtz coil facilitates equipment movement and position adjustment, while taking into account the overall load-bearing capacity and structural stability, and reserving installation space for subsequent integration of accessories such as power supply, slide table and control module.

[0049] 3. The winding frame of the three-dimensional square Helmholtz coil adopts a multi-layer spatial symmetrical layout design. By optimizing the spatial positional relationship of the X, Y, and Z axis coils, the magnetic field coupling error and magnetic field distribution offset are reduced, and the magnetic field consistency and three-dimensional magnetic field control accuracy in the central area are improved.

[0050] 4. The magnetic field compensation method for the three-dimensional square Helmholtz coil starts from the theoretical magnetic field analysis of single-turn square coils, double-coil square Helmholtz structures and three-dimensional orthogonal square Helmholtz coil systems. Combined with the environmental magnetic field error analysis, a magnetic field compensation model is established to reduce the interference of the environmental magnetic field on the three-dimensional square Helmholtz coil and improve the uniformity of the three-dimensional magnetic field. Attached Figure Description

[0051] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a schematic diagram of the overall structure of the three-dimensional square Helmholtz coil of the present invention;

[0053] Figure 2 This is a front view schematic diagram of the overall structure of the three-dimensional square Helmholtz coil of the present invention;

[0054] Figure 3 This is a top view schematic diagram of the overall structure of the three-dimensional square Helmholtz coil of the present invention;

[0055] Figure 4 This is a schematic diagram of the splicing and installation structure of the three-dimensional square Helmholtz coil of the present invention.

[0056] Explanation of reference numerals in the attached figures:

[0057] 1. Winding frame; 2. Display platform; 21. Lifting rod; 22. Sample platform; 23. Connecting seat; 3. Base. Detailed Implementation

[0058] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0059] The following is in conjunction with the appendix Figure 1-4 The three-dimensional square Helmholtz coil of the present invention will be further described.

[0060] Please refer to this carefully. Figure 1-3 This invention discloses a three-dimensional square Helmholtz coil, which is used as a platform for multi-axis magnetic field control, magnetic drive experiments, and related magnetic field research. The three-dimensional square Helmholtz coil includes: three sets of independent and spatially orthogonal square Helmholtz coils, a platform 2 set in the common central area of ​​the three sets of square Helmholtz coils, a movable base 3, and a winding frame 1 fixedly set on the base 3. The three sets of square Helmholtz coils are all set in the winding frame 1 and are symmetrically distributed along the X-axis, Y-axis, and Z-axis to form a three-dimensional magnetic field. The platform 2 is detachably set in the center of the three-dimensional magnetic field. An auxiliary space is preset below the platform 2 to integrate a slide, power supply, or heat dissipation mechanism.

[0061] In this embodiment, the three-dimensional square Helmholtz coil, through its multi-layered square frame structure, can generate a uniform magnetic field of sufficient range and intensity within a certain space, effectively improving the space utilization of the coil and meeting the requirements for the uniform magnetic field area scale of multi-axis magnetic field control, magnetic drive experiments, and related magnetic field research platforms. Furthermore, the movable base 3 within the coil facilitates equipment movement and position adjustment while maintaining overall load-bearing capacity and structural stability, and provides installation space for subsequent integration of power supplies, slides, control modules, and other accessories. The three-dimensional square Helmholtz coil features a high degree of modularity, clear spatial layout, ease of expansion, and applicability to AC or DC magnetic field systems, enabling its efficient application in multi-axis magnetic field control, magnetic drive experiments, and related magnetic field research platforms.

[0062] like Figure 4 As shown, the winding frame 1 includes multiple sets of horizontal planar square frames and multiple sets of vertical planar square frames. The horizontal planar square frames are all connected to the vertical planar square frames, and the horizontal and vertical planar square frames are perpendicular to each other. Both the horizontal and vertical planar square frames include mounting beams and rounded corners. Adjacent mounting beams are connected by rounded corners, and both the mounting beams and rounded corners are made of polyoxymethylene (POM) material.

[0063] In this embodiment, the winding frame 1 adopts a multi-layered square frame structure, forming a spatial three-dimensional skeleton through crossbeams and corner connections, which can be used to install square Helmholtz coils in the X, Y, and Z directions. The winding skeleton of the three-dimensional coil is made of POM (polyoxymethylene) material. POM has good mechanical strength, dimensional stability, and electrical insulation properties, which can effectively avoid the eddy current effect generated by the metal skeleton in an AC magnetic field environment, thereby reducing additional losses and local heating problems. The square skeleton adopts a multi-layered spatial symmetrical layout, which can meet the installation requirements of triaxial coils.

[0064] Furthermore, the winding frame 1 adopts a multi-layer spatial symmetrical layout design. By optimizing the spatial positional relationship of the X, Y, and Z axis coils, it reduces magnetic field coupling error and magnetic field distribution offset, thereby improving the magnetic field consistency in the central region and the three-dimensional magnetic field control accuracy.

[0065] In a preferred embodiment, the winding frame 1 has multiple sets of mounting holes and connection interfaces pre-drilled inside, allowing for position fixing according to the size and installation requirements of different axial coils. The winding frame 1 adopts a rounded corner transition design to accommodate the arc corners of the winding frame 1, reducing local stress concentration while ensuring mechanical strength, and facilitating winding, cable arrangement, and overall structural assembly.

[0066] like Figure 1As shown, the stage 2 includes a connecting seat 23, a sample stage 22, and a lifting rod 21. The connecting seat 23 is fixedly mounted on the base 3 and located at the center of the base 3. The fixed end of the lifting rod 21 is located at the center of the connecting seat 23, and the lifting end of the lifting rod 21 is connected to the sample stage 22 to drive the sample stage 22 to move up and down. The sample stage 22 has multiple M6 standard optical platform threaded holes to fix the sample to be tested.

[0067] In this embodiment, the sample stage 22 located in the middle is also made of POM material, mainly used for placing experimental samples, petri dishes, sensors, or testing devices. Meanwhile, POM material is lightweight and has high processing precision, facilitating platform opening, module installation, and position adjustment. The height-adjustable sample stage 22 in the middle can be used to place experimental objects, sensors, or culture devices, facilitating experimental operations and positioning in the central magnetic field area. A large space is reserved below the sample stage 22 for arranging a sliding stage, power connection, heat dissipation structure, and other auxiliary modules. The tabletop of the sample stage 22 has M6 standard optical platform threaded holes with a hole spacing of 25mm, facilitating sample positioning and fixation.

[0068] Furthermore, both the winding frame 1 and the sample stage 22 are made of POM material, which utilizes its good insulation properties and dimensional stability to reduce the disturbance of the magnetic field distribution by the metal structure and improve the system's operational stability and electromagnetic compatibility performance.

[0069] In one specific embodiment, the base 3 is preferably an aluminum profile base 3, with universal casters installed at the bottom for easy movement and position adjustment of the equipment, while ensuring overall load-bearing capacity and structural stability, and reserving installation space for subsequent integration of accessories such as power supplies, slides, and control modules. The base 3 adopts an aluminum profile composite structure, using modular connections to improve assembly strength and expandability, while reducing the impact of overall structural deformation on the spatial positioning accuracy of the coil. Furthermore, its three-dimensional square Helmholtz coil adopts an open frame structure design, which is beneficial for air circulation, cable routing, and observation in the experimental area, while also facilitating the subsequent addition of air cooling, water cooling, or other auxiliary heat dissipation structures, improving the system's long-term operating capability.

[0070] In one embodiment, to further improve the installation accuracy, structural stability, and magnetic field control accuracy of the three-dimensional square Helmholtz coil, the square frames in each direction are designed and manufactured using a unified installation benchmark, and a positioning structure is set up to achieve rapid assembly and fixation. This ensures that the X-axis, Y-axis, and Z-axis coils maintain a stable spatial orthogonal relationship, guaranteeing that the geometric centers of the coils in each direction coincide as much as possible in the same spatial position. By improving the center coincidence, parallelism, and orthogonality of the three-axis coils, the magnetic field distortion caused by assembly errors can be reduced, making the actual assembly state closer to the theoretical design model, thereby improving the magnetic field uniformity, magnetic field direction consistency, and system operational stability in the central region.

[0071] Based on the Biot-Savart law, the magnetic field element generated by a current-carrying conductor at any point in space is:

[0072] ;

[0073] in, Permeability of free space; The coil current; It is the length vector of the current element on the current-carrying conductor, and its direction is the same as the current direction; The position vector of the current element pointing towards the target field point; Position vector The modulus length, i.e. .

[0074] The aforementioned three-dimensional square Helmholtz coils form a three-dimensional magnetic field. The calculation process for the magnetic field strength of this three-dimensional magnetic field is as follows:

[0075] S1. Assume the side length of the square Helmholtz coil is 2. Furthermore, the square Helmholtz coil is located in the xy plane, and its center is located at the origin. Therefore, the expression for the magnetic field generated by a single-turn square Helmholtz coil at its center is: When the number of coil turns is During the turn, the central magnetic field can be further expressed as: ;

[0076] S2. For a square Helmholtz structure consisting of two identical square Helmholtz coils, symmetrically placed along the same axis and supplied with currents of the same direction and magnitude, the magnetic field at any position along the axis can be expressed as:

[0077] ;

[0078] in, The distance between the centers of the two coils is... These are the position coordinates along the axis. This is the magnetic field distribution function generated by a single coil along the axial direction;

[0079] S3, the three-dimensional square Helmholtz coil consists of three sets of independent and spatially orthogonal square Helmholtz coils, respectively corresponding to... axis, axis, In the three directions of the axis, according to the principle of magnetic field vector superposition, the total magnetic field of the three-dimensional magnetic field can be expressed as:

[0080] ;

[0081] in, , , They are respectively , , Magnetic field components generated by a triaxial coil , , These are the unit vectors in the corresponding directions.

[0082] The magnetic field characteristics generated by the coil are related to the form of the excitation current. When a constant DC current is input, the coil generates a stable static magnetic field; when an alternating AC current is input, the coil generates a dynamic AC magnetic field that varies with time. Therefore, to further improve the stability and consistency of the magnetic field, the uniformity of a three-dimensional square Helmholtz coil is defined as:

[0083] ;

[0084] in, and These represent the maximum and minimum magnetic field values ​​within the target uniform region, respectively. The value of the magnetic field at the center point;

[0085] To improve the magnetic field uniformity in the central region of the three-dimensional magnetic field, the side length of the square coil and the spacing between the two coils are optimized to ensure that the axial magnetic field in the central region satisfies the following:

[0086] ;

[0087] Even if the second derivative of the axial magnetic field in the central region approaches zero, the uniform magnetic field region is expanded, thereby improving the stability and consistency of the magnetic field.

[0088] In real-world applications, there is often interference from ambient magnetic fields. The actual magnetic field is:

[0089] ;

[0090] in, The environmental interference magnetic field can be further represented as:

[0091] ;

[0092] in, These represent the components of the ambient magnetic field along the X, Y, and Z axes, respectively.

[0093] Therefore, the error between the actual magnetic field and the theoretical magnetic field can be defined as:

[0094] ;

[0095] From the above formula, we can obtain: That is, the magnetic field error is mainly caused by environmental interference magnetic fields.

[0096] Therefore, the present invention also provides a magnetic field compensation method for a three-dimensional square Helmholtz coil, wherein the magnetic field compensation method is implemented based on the above-mentioned three-dimensional square Helmholtz coil, and the magnetic field compensation method includes:

[0097] S4. Magnetic field error is mainly caused by environmental interference magnetic fields. To quantify the systematic error, a magnetic field error index is introduced:

[0098] ;

[0099] in, This represents the percentage of magnetic field error. The allowable error threshold is set according to application requirements. :when < When the system is deemed to be working normally, ≥ When the system is found to be significantly affected by external magnetic field interference, compensation and correction are performed.

[0100] S5. There is a corresponding relationship between the compensating magnetic field and the compensating current:

[0101] ;

[0102] ;

[0103] ;

[0104] in, These are the magnetic field transformation constants of the X, Y, and Z axis coils, used to characterize the magnetic field strength generated by a unit current;

[0105] S6. To reduce the impact of environmental interference, an active magnetic field compensation model is established: assuming that an environmental magnetic field is detected in the X direction. Then, the compensation current is adjusted by adjusting the X-axis coil. , so that:

[0106] ;

[0107] Similarly, the Y-axis and Z-axis coils achieve active compensation by adjusting the compensation current:

[0108] ;

[0109] ;

[0110] The triaxial compensated magnetic field vector is represented as: Therefore, the total magnetic field after compensation in the three-dimensional magnetic field is: .

[0111] When the compensation magnetic field satisfies: Then we get: That is, the total magnetic field of the output three-dimensional magnetic field is restored to the theoretical target magnetic field.

[0112] This invention analyzes the theoretical magnetic field from single-turn square coils and double-coil square Helmholtz structures to three-dimensional orthogonal square Helmholtz coil systems. Combined with environmental magnetic field error analysis and active compensation models, it realizes integrated modeling of magnetic field generation, magnetic field evaluation and magnetic field compensation, providing a theoretical basis for the structural design and parameter optimization of three-dimensional magnetic field control systems.

[0113] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components; and they can also refer to a "transmission connection," that is, a power connection through various suitable methods such as belt drive, gear drive, or sprocket drive. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

Claims

1. A three-dimensional square Helmholtz coil, wherein the three-dimensional square Helmholtz coil is used for multi-axis magnetic field control, magnetic drive experiments, and related magnetic field research platforms, characterized in that, The three-dimensional square Helmholtz coil includes: three sets of mutually independent and spatially orthogonal square Helmholtz coils, a platform set at the center of the three sets of square Helmholtz coils, a movable base, and a winding frame fixedly set on the base. The three sets of square Helmholtz coils are all arranged in the winding frame and are symmetrically distributed along the X-axis, Y-axis and Z-axis to form a three-dimensional magnetic field. The platform is detachably arranged at the center of the three-dimensional magnetic field. An auxiliary space is preset below the platform to integrate a slide, power supply or heat dissipation mechanism.

2. The three-dimensional square Helmholtz coil according to claim 1, characterized in that, The winding frame includes multiple sets of horizontal planar square frames and multiple sets of vertical planar square frames. The multiple sets of horizontal planar square frames are all connected to the multiple sets of vertical planar square frames, and the multiple sets of horizontal planar square frames and the multiple sets of vertical planar square frames are perpendicular to each other.

3. The three-dimensional square Helmholtz coil according to claim 2, characterized in that, The multiple sets of horizontal and vertical square frames each include mounting beams and rounded corners. Adjacent mounting beams are connected by the rounded corners, and both the mounting beams and the rounded corners are made of polyoxymethylene material.

4. The three-dimensional square Helmholtz coil according to claim 3, characterized in that, The placement platform includes a connecting base, a sample stage, and a lifting rod; The connecting seat is fixedly mounted on the base and located at the center of the base. The fixed end of the lifting rod is located at the center of the connecting seat. The lifting end of the lifting rod is connected to the sample stage to drive the sample stage to move up and down.

5. The three-dimensional square Helmholtz coil according to claim 4, characterized in that, The sample stage has multiple M6 standard optical platform threaded holes to fix the sample to be tested.

6. The three-dimensional square Helmholtz coil according to claim 5, characterized in that, The three-dimensional square Helmholtz coil surrounds and forms the three-dimensional magnetic field. The calculation process of the magnetic field strength of the three-dimensional magnetic field includes: S1. Assume the side length of a single-turn square coil is 2. Furthermore, the square Helmholtz coil is located in the xy plane, and its center is located at the origin. Therefore, the expression for the magnetic field generated by a single turn of the square Helmholtz coil at its center is: When the number of coil turns is During the turn, the central magnetic field can be further expressed as: ; S2. For a square Helmholtz structure consisting of two identical square Helmholtz coils, with the two coils placed symmetrically along the same axis and supplied with currents of the same direction and magnitude, the magnetic field at any position along the axis can be expressed as: ； in, The distance between the centers of the two coils is... These are the position coordinates along the axis. This is the magnetic field distribution function generated by a single coil along the axial direction; S3. The three-dimensional square Helmholtz coil consists of three sets of mutually independent and spatially orthogonal square Helmholtz coils, respectively corresponding to... axis, axis, In the three directions of the axis, according to the principle of magnetic field vector superposition, the total magnetic field of the three-dimensional magnetic field can be expressed as: ； in, , , They are respectively , , Magnetic field components generated by a triaxial coil , , These are the unit vectors in the corresponding directions. The theoretical target magnetic field generated by a three-dimensional square Helmholtz coil.

7. The three-dimensional square Helmholtz coil according to claim 6, characterized in that, To further improve the stability and uniformity of the magnetic field, the uniformity of a three-dimensional square Helmholtz coil is defined as: ； in, and These represent the maximum and minimum magnetic field values ​​within the target uniform region, respectively. The magnetic field value at the center point; Furthermore, to improve the magnetic field uniformity in the central region of the three-dimensional magnetic field, the side length of the square coil and the spacing between the two coils are optimized to ensure that the axial magnetic field in the central region satisfies the following: ； Even if the second derivative of the axial magnetic field in the central region approaches zero, the uniform magnetic field region is expanded, thereby improving the stability and consistency of the magnetic field.

8. A method for magnetic field compensation of a three-dimensional square Helmholtz coil, characterized in that, The magnetic field compensation method is implemented based on the three-dimensional square Helmholtz coil according to any one of claims 1-7, and the magnetic field compensation method includes: S4. Magnetic field error is mainly caused by environmental interference magnetic fields. To quantify the systematic error, a magnetic field error index is introduced: ； in, This represents the percentage of magnetic field error. A permissible error threshold is set based on application requirements. :when < When the system is deemed to be working normally, ≥ When the system is found to be significantly affected by external magnetic field interference, compensation and correction are performed. S5. There is a corresponding relationship between the compensating magnetic field and the compensating current: ； ； ； in, These are the magnetic field transformation constants of the X, Y, and Z axis coils, used to characterize the magnetic field strength generated by a unit current; S6. To reduce the impact of environmental interference, an active magnetic field compensation model is established: assuming that an environmental magnetic field is detected in the X direction. Then, the compensation current is adjusted by adjusting the X-axis coil. , so that: ； Similarly, the Y-axis and Z-axis coils achieve active compensation by adjusting the compensation current: ； ； The triaxial compensated magnetic field vector is represented as: Therefore, the total magnetic field of the compensated three-dimensional magnetic field is: ,in, The ambient magnetic field vector can be represented as .

9. The magnetic field compensation method for a three-dimensional square Helmholtz coil according to claim 8, characterized in that, When the compensation magnetic field satisfies: Then we get: That is, the total magnetic field of the output three-dimensional magnetic field is restored to the theoretical target magnetic field.

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