Method for designing a multi-stage nested helmholtz type coil system

Abstract

The application discloses a design method of a multi-stage nested Helmholtz coil system and relates to the technical field of general instrument manufacturing. The application provides a mutual inverse analysis and design method of coil structure parameters and global sensitivity of magnetic field characteristics of a multi-stage nested Helmholtz coil system, based on which, the optimal design expression of each design parameter of the multi-stage nested Helmholtz coil system can be determined, the multi-parameter expression of the magnetic field characteristics can be obtained, the priority of the coil parameter design is determined, and the optimization design strategy aiming at the magnetic field design index is provided. When the macro design requirement of the target uniform magnetic field is provided, the optimal solution of each design parameter of the multi-stage nested Helmholtz coil system can be directly obtained. The application can efficiently and accurately improve the design of the Helmholtz coil according to the requirement.

Description

Technical Field

[0001] The present invention relates to the technical field of general instrument manufacturing, and in particular to a design method for a multi-stage nested Helmholtz coil system. Background Art

[0002] Generally speaking, the magnetic field, as a core physical quantity in the electromagnetic field, has its strength and uniformity as key indicators determining the performance of electromagnetic devices. In high-precision applications such as particle acceleration, material characterization, and biomedical imaging (such as magnetic resonance imaging (MRI)), magnetic field strength directly impacts key performance indicators such as particle manipulation efficiency and signal resolution, while magnetic field uniformity is essential for ensuring experimental reproducibility and device stability. For example, in quantum computing, insufficient magnetic field uniformity can cause rapid decay of quantum bit coherence, directly destabilizing the quantum state. In flow measurement, a stronger magnetic field enhances the apparent induced electromotive force signal caused by flow velocity, allowing for clearer capture and processing of fluid dynamics. A more uniform magnetic flux density distribution minimizes the deviation between the measured flow velocity and the true value, resulting in more accurate flow measurement per unit time. Therefore, achieving a synergistic improvement in both maximizing magnetic field strength and optimizing uniformity within a confined space has become a core technical challenge in current electromagnetic device design.

[0003] Currently, the devices used to generate uniform magnetic fields primarily include permanent magnet arrays, superconducting magnets, Bronck coils, Barker coils, Maxwell coils, and Helmholtz coils. Helmholtz coils, due to their simple structure, low cost, and highly adjustable magnetic field, are widely used in laboratory magnetic field calibration, magnetic compatibility testing, and other scenarios. As the most commonly used device for generating uniform magnetic fields, they are particularly irreplaceable in scenarios requiring a medium-intensity uniform magnetic field. The core principle is that two parallel coaxial coils are used. When the spacing between circular coils is equal to the coil radius and the spacing between square coils is 0.5445 times their length, a highly uniform magnetic field can be generated in the middle region.

[0004] A very high magnetic field uniformity can typically be achieved along the central axis of a Helmholtz coil, typically less than 0.1%. However, for larger areas, such as a circular region with a diameter equal to one-quarter the diameter of the circular coil, magnetic field uniformity of less than 1% is typically achievable. Furthermore, conventional Helmholtz coil designs lack clear design guidelines for microscopic parameters (parameters related to the coil windings), such as the number of winding layers, the number of turns per layer, and the winding gap. Because these coils are unable to generate a strong, uniform magnetic field over a large area, improvements are often required.

[0005] There are two existing methods for improving Helmholtz coils. The first method improves the uniformity and strength of the magnetic field generated by the coil by individually exploring and optimizing parameters such as the coil's shape, windings, or relative position. The second method uses global optimization algorithms based on the Biot-Savart law, such as differential evolution and particle swarm optimization. These algorithms iterate within constraints based on an objective function to calculate the optimal values ​​of the Helmholtz coil parameters for a desired fixed uniform magnetic field space.

[0006] However, the first method is highly dependent on the size and settings of the experimental equipment and has poor applicability. In the second method, the range of optimized variables of the Helmholtz coil is difficult to set, with high randomness and difficulty in convergence. Both methods make it difficult to efficiently and accurately improve the design of the Helmholtz coil as needed. Summary of the Invention

[0007] Based on this, it is necessary to provide a design method for a multi-level nested Helmholtz coil system to address the above technical issues.

[0008] The present invention adopts the following technical solutions:

[0009] The present invention provides a design method for a multi-stage nested Helmholtz coil system, wherein the Helmholtz coil includes two parallel coaxial nested coils, and the parallel coaxial nested coils include a plurality of coplanar and coaxial nested coils to form a plurality of nested Helmholtz coils;

[0010] The present invention first obtains a design indicator corresponding to a target uniform magnetic field; builds a simulation model of the Helmholtz coil based on preset parameters of the Helmholtz coil to determine the magnetic field distribution of the target area; then, by adjusting the winding current of a single Helmholtz coil, a first influence relationship between the winding current and the design indicator is determined based on changes in the magnetic field distribution of the target area; then, using the inner side dimensions of the single Helmholtz coil and the spacing between the coils on both sides as macro parameters, a second influence relationship between each macro parameter and the design indicator is determined; using the second influence relationship as a constraint and the coil winding setting as a micro parameter, a third influence relationship between each micro parameter and the design indicator is determined; thereby, based on the first influence relationship, the second influence relationship, and the third influence relationship, the optimal parameters of the macro and micro parameters of the single Helmholtz coil are determined;

[0011] Then, a reference coil is constructed according to the optimal macro parameters and the optimal micro parameters, and a Helmholtz coil with the same micro parameters is nested outside the reference coil. When the spacing between the coils on both sides is fixed, the fourth influence relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the design index is determined; the spacing between the coils on both sides is adjusted to determine the fifth influence relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the spacing between the coils on both sides when the design index is optimal; finally, based on the fourth and fifth influence relationships, the optimal nesting number is determined by adjusting the nesting number of coils on both sides according to the change of the magnetic field distribution in the target area; according to the optimal nesting number and the macro design requirements of the target uniform magnetic field, the optimal design parameters of the multi-level nested Helmholtz coil system are determined.

[0012] The present invention provides a multi-level nested Helmholtz coil system, wherein the multi-level nested Helmholtz coil system includes two parallel coaxial nested coils, wherein the parallel coaxial nested coils include a plurality of coplanar and coaxial nested coils, forming a plurality of nested Helmholtz coils;

[0013] The macroscopic parameters and microscopic parameters of the multi-level nested Helmholtz coil system are determined by any of the above-mentioned design methods for a multi-level nested Helmholtz coil system; the macroscopic parameters include the inner side dimensions of the nested reference coil and the spacing between the coils on both sides; the microscopic parameters are the corresponding parameters of the coil winding settings.

[0014] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects:

[0015] This invention provides a reciprocal analysis and design method for the global sensitivity of coil structural parameters and magnetic field characteristics in a multi-level nested Helmholtz coil system. This method can clarify the optimal design expressions for each design parameter of the multi-level nested Helmholtz coil system, derive a multi-parameter expression for the magnetic field characteristics, clarify coil parameter design priorities, and propose an optimization design strategy for magnetic field design indicators. When macroscopic design requirements for a target uniform magnetic field are provided, the optimal solution for each design parameter of the multi-level nested Helmholtz coil system can be directly obtained. This invention enables efficient and accurate design improvements of Helmholtz coils as needed. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0017] Figure 1 A schematic flow chart of a design method for a multi-stage nested Helmholtz coil system provided by the present invention;

[0018] Figure 2 A schematic diagram of a Helmholtz coil provided by the present invention;

[0019] Figure 3 A schematic diagram of a multi-stage nested Helmholtz coil system provided by the present invention;

[0020] Figure 4 A schematic diagram of magnetic field distribution provided by the present invention;

[0021] Figure 5 A schematic diagram of the design process of a multi-stage nested Helmholtz coil system provided by the present invention. DETAILED DESCRIPTION

[0022] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0023] Currently, there are two approaches to improving Helmholtz coils. The first involves individually exploring and optimizing parameters such as the coil's shape, windings, or relative position to improve the uniformity and strength of the magnetic field generated by the coil. However, this local sensitivity analysis approach, which refines coil parameters individually, is highly dependent on the size and setup of the experimental equipment, limiting its applicability.

[0024] The second approach involves global optimization algorithms based on the Biot-Savart law, such as differential evolution and particle swarm optimization. These algorithms iterate within constraints based on an objective function to calculate the optimal values ​​for the Helmholtz coil parameters for a fixed, uniform magnetic field. Changes in the desired uniform magnetic field domain require re-optimization of the parameters. To achieve optimal uniformity within the desired magnetic field space, these algorithms encounter challenges in defining the range of optimization variables (the boundary conditions of the search space), resulting in arbitrariness, uncertainty, randomness, and slow convergence.

[0025] In addition, these methods lack deterministic expressions for designing Helmholtz coil parameters, making it impossible to study the uncertainty propagation function of magnetic field characteristics such as magnetic flux density and uniformity indicators, and it is impossible to clearly optimize the design priority of Helmholtz coil parameters.

[0026] This invention proposes a novel multi-level nested Helmholtz coil system and a reciprocal analysis method for the global sensitivity of coil structural parameters to magnetic field characteristics. By analyzing the coupling effects between these parameters, the optimal design expressions for each parameter can be determined. The optimal structural design of the multi-level nested Helmholtz coil system can be achieved by providing the cross-sectional diameter of the required uniform magnetic field domain or the required coil spacing for the device. Furthermore, using the uncertainty propagation function of the magnetic field characteristics (intensity and uniformity), the contribution of various coil parameters to the magnetic field characteristics is studied, including coil shape, size, spacing, number of winding layers, number of turns per layer, axial and radial gaps between windings, nesting coefficient, and gaps between adjacent coils on the same side. This prioritizes the design of optimized Helmholtz coil parameters. This multi-level nested Helmholtz coil system not only improves the magnetic field intensity within the required magnetic field domain, but also maintains magnetic field uniformity within the central circular domain to within 0.2%.

[0027] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0028] Figure 1 The present invention provides a flow chart of a design method for a multi-stage nested Helmholtz coil system. The method is applied to the design of a multi-stage nested Helmholtz coil system. The Helmholtz coil includes two parallel coaxial nested coils. The parallel coaxial nested coils include a plurality of coplanar and coaxial nested coils, forming a plurality of nested Helmholtz coils. The method specifically includes the following steps:

[0029] S101: Obtain design indicators corresponding to the target uniform magnetic field.

[0030] S102: Determine a first influence relationship between the winding current and the design indicator by adjusting the winding current of a single Helmholtz coil according to a change in magnetic field distribution in a target area.

[0031] S103: Using the inner side size of a single Helmholtz coil and the spacing between the coils on both sides as macro parameters, determine the second influence relationship between each macro parameter and the design index; using the second influence relationship as a constraint and the coil winding setting as a micro parameter, determine the third influence relationship between each micro parameter and the design index.

[0032] S104: Determine optimal macroscopic parameters and optimal microscopic parameters of a single Helmholtz coil according to the first influence relationship, the second influence relationship, and the third influence relationship.

[0033] S105: Construct a reference coil according to the optimal macroscopic parameters and the optimal microscopic parameters, and nest a Helmholtz coil with the same microscopic parameters outside the reference coil, and determine the fourth influence relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the design index when the spacing between the coils on both sides is fixed; adjust the spacing between the coils on both sides to determine the fifth influence relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the spacing between the coils on both sides when the design index is optimal.

[0034] S106: Based on the fourth influence relationship and the fifth influence relationship, the optimal nesting number is determined by adjusting the nesting number of coils on both sides according to the change in the magnetic field distribution in the target area; based on the optimal nesting number and the macro design requirements of the target uniform magnetic field, the optimal design parameters of the multi-level nested Helmholtz coil system are determined.

[0035] This invention uses the improvement of magnetic field characteristics on a circular pipe cross section as an example. Specifically, using the magnetic field characteristics on a circular pipe cross section as the target parameter, a design method for a multi-stage nested Helmholtz coil system is proposed. The resulting multi-stage nested Helmholtz coil system can be directly used in flow measurement applications, such as electromagnetic flowmeters and electromagnetic flow tomography. However, the resulting sphere, formed by rotating the circular cross section about its central axis, can serve as the circumscribed sphere for any desired uniform magnetic field geometric domain, thus also finding applications in materials, electronics, biology, and other fields.

[0036] It should be noted that in the parameter design of the multi-level nested Helmholtz coil system, it is necessary to ensure that the number of winding layers and the number of turns per layer are both integers of at least 1. In addition, according to the required uniform magnetic field cross-sectional diameter or the coil spacing required by the equipment, when designing the coil using the optimal expressions of the various parameters obtained by the present invention, there are certain constraints (coil radial length n×d Need to be smaller than the spacing between the coils on both sides h ,in, n is the number of turns per layer of coil winding, d is the diameter of the coil winding wire), that is, to avoid the designed multi-level nested Helmholtz coil system being embedded in the required uniform magnetic field domain.

[0037] In one or more embodiments of the present invention, when designing a multi-stage nested Helmholtz coil system, it is first necessary to clarify the design indicators, that is, to clarify the target parameters for the optimization design of the multi-stage nested Helmholtz coil system. Specifically, in one or more embodiments of the present invention, the design indicators include the magnetic flux density index and uniformity index of the target uniform magnetic field in the target area. To this end, an index parameter for judging the uniformity of the magnetic field is proposed. , represents the overall normalized standard deviation (coefficient of variation) of the magnetic field, and is a dimensionless parameter. Its value is the ratio of the standard deviation of the magnetic flux density in the measured area to the average value: .

[0038] in, Indicates the standard deviation of the magnetic flux density within the entire target area, Indicates the average value of the magnetic flux density in the target area.

[0039] It is defined as follows: .

[0040] Where, n represents the number of cells in the target area, It is the average value of the magnetic flux density in each small area.

[0041] It is defined as follows: .

[0042] Where, is the area of ​​each unit.

[0043] After that, the multi-level nested Helmholtz coil system can be designed based on the design indicators. Here, the composition structure of the multi-level nested Helmholtz coil system can be analyzed to clarify the parameters that need to be studied in the design optimization process.

[0044] Figure 2 A schematic diagram of a Helmholtz coil in the present invention is shown in FIG. Figure 2 It can be seen that the shapes of Helmholtz coils include traditional circular and rectangular Helmholtz coils. For rectangular coils, the inner dimensions of the coil can be expressed as length L and width W For a circular coil, the inner side of the coil can be expressed by the radius R The distance between the coils on both sides of the Helmholtz coil is expressed as h The diameter of the coil winding wire is expressed in d It limits the current i The size of the coil winding is k Indicates the number of coil winding layers, n Indicates the number of turns per layer of the coil winding. The gap between windings includes the gap between winding layers (inter-layer gap of coil winding) and the gap between two adjacent turns in each layer of winding (inter-turn gap of coil winding). Assuming that they are uniform, that is, the gap between two adjacent layers is equal, and the gap between two adjacent turns in each layer is also equal, they are defined as axial gap, d z , radial clearance d r .

[0045] For the multi-level nested Helmholtz coil system proposed in this invention, the innermost coil among the nested coils on the same side is used as the reference coil. That is, the number of coils is increased outside the reference coil. Except for the inner dimensions, the parameters of the increased coils are identical to those of the reference Helmholtz coil. In this case, in addition to all the design parameters of a single Helmholtz coil, the designable parameters of the multi-level nested Helmholtz coil system will also introduce three new parameter variables, namely, the number of coils nested on both sides, N 、Inner side dimensions of the standard Helmholtz coil ( R 1. L 1. W 1) and the gap between two adjacent coils on the same side d L ,like Figure 3 As shown, Figure 3 This is a schematic diagram of a multi-stage nested Helmholtz coil system in the present invention. It should be noted that the gap here d L It can only be greater than zero (corresponding to external nesting). For a group of coils with a fixed nesting coefficient, the optimal values ​​of the parameters of the Helmholtz coil under the optimal magnetic field are unique.

[0046] After the design parameters of the multi-stage nested Helmholtz coil system are determined, a three-dimensional model may be established to facilitate the design process through simulation. In one or more embodiments of the present invention, establishing the three-dimensional model includes:

[0047] 1) Build a geometric model with known parameters, including the Helmholtz coil, fluid pipe, and air domain.

[0048] 2) Setting the material properties of each part of the geometric model.

[0049] 3) Add the Magnetic Field physics interface, select the Coil domain, and define the wire model, coil type, excitation, number of turns, wire cross-sectional area, and current direction.

[0050] 4) Grid division.

[0051] 5) Add a steady-state study for the Magnetic Field physics interface. For numerical coils, a coil geometry analysis study must be added before adding a steady-state study.

[0052] 6) Calculate the magnetic field distribution in the entire space domain and pipeline, such as Figure 4 As shown, Figure 4 This is a schematic diagram of a magnetic field distribution in the present invention.

[0053] 7) Define global variables for calculating the average magnetic flux density and uniformity index at the pipeline cross section.

[0054] Next, the present invention designs a multi-level nested Helmholtz coil system using a global sensitivity reciprocal analysis method. Unlike the local sensitivity analysis method that improves magnetic field uniformity by changing one parameter at a time, this method analyzes the impact of each parameter and their interactions on the magnetic field characteristics. In one or more embodiments of the present invention, the spacing between the coils on both sides is h and inner dimensions R 、 L 、 W are considered as macroscopic parameters, whereas the parameters related to the winding are considered as microscopic parameters.

[0055] The present invention proposes a more accurate method for determining the macroscopic parameter design equations of a multi-level nested Helmholtz coil system as the main constraint equation for initialization and subsequent iterative processes. As the microscopic parameters related to the windings change, the macroscopic parameters and other microscopic parameters will also be adjusted accordingly, so that their global impact on the magnetic field characteristics can be studied, such as Figure 5 As shown, Figure 5 The figure is a schematic diagram of the design process of a multi-stage nested Helmholtz coil system in the present invention.

[0056] The reciprocal analysis method under global sensitivity helps to explore the optimal solution for the interaction between multiple parameters of the Helmholtz coil. In one or more embodiments of the present invention, the iterative steps of the reciprocal analysis method under global sensitivity are as follows:

[0057] 1) By changing the winding current of a single Helmholtz coil, the first influence relationship between the current and the design indicators (average magnetic flux density and uniformity) is determined according to the change of the magnetic field distribution in the target area (circular cross-section of the pipeline).

[0058] 2) The inner side size of a single Helmholtz coil and the spacing between the two coils are used as macro parameters, and the diameter of the target uniform magnetic field is used as the size normalization factor of the macro parameters to normalize the macro parameters. By adjusting the inner side size ratio of a single Helmholtz coil, the ratio of the inner side size to the diameter after size normalization, and the ratio of the spacing between the two coils to the diameter, according to the changes in the magnetic field distribution in the target area, the second influence relationship between each macro parameter and the design index is determined, and a more accurate macro design constraint equation for the Helmholtz coil is obtained.

[0059] 3) On the basis of satisfying the macro design constraint equation, the micro parameters related to the coil winding are changed. At this time, the macro parameters will change with the change of the micro parameters, so as to study the influence of the micro parameters on the magnetic field characteristics in the global analysis.

[0060] 4) By studying the influence relationship between each microscopic parameter and the average magnetic flux density and uniformity index, a new parameter constraint equation can be obtained to determine the third influence relationship between each microscopic parameter and the design index.

[0061] 5) As the number of parameter constraint equations increases, when the design parameters are equal to the number of constraint equations, if the cross-sectional diameter of the required uniform magnetic field domain or the coil spacing required for the device is known, the optimal macroscopic parameters and optimal microscopic parameters of a single Helmholtz coil can be determined based on the first influence relationship, the second influence relationship, and the third influence relationship according to the cross-sectional requirements of the target uniform magnetic field or the spacing requirements between the coils on both sides.

[0062] 6) A reference coil is constructed based on the optimal macroscopic and microscopic parameters. Based on the optimal parameters of the reference coil, a Helmholtz coil with the same winding-related microscopic parameters except for different inner edge dimensions is nested outside the reference coil.

[0063] 7) When the spacing between the coils on both sides is fixed, by adjusting the gap between adjacent coils on the same side and the inner size of the reference coil, the fourth influencing relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the average magnetic flux density index and uniformity index is determined according to the change in the magnetic field distribution in the target area.

[0064] 8) Adjust the spacing between the coils on both sides. For each spacing traversed, determine the optimal microscopic parameters of the nested Helmholtz coils at that spacing, the optimal gap between adjacent coils on the same side, and the optimal inner edge size of the reference coil. This is to determine the fifth influencing relationship between the gap between adjacent coils on the same side, the inner edge size of the reference coil, and the spacing between the coils on both sides when the design index is optimized.

[0065] 9) Based on the fourth and fifth influence relationships, the number of nested coils on both sides is adjusted according to the change in the magnetic field distribution in the target area. The relationship between the gap between adjacent coils on the same side and the relationship between the inner edge size of the reference coil and the spacing between the coils on both sides when the design index is optimal for each number of nested coils on both sides is determined.

[0066] 10) Determine the optimal number of nested coils based on the optimal design index values ​​for each adjusted nesting coefficient. That is, determine the optimal number of nested coils for each Helmholtz coil based on the magnetic field characteristics within the desired magnetic field domain for each nesting coefficient.

[0067] 11) The optimal number of nestings is determined. When the cross-sectional diameter of the required uniform magnetic field or the coil spacing required by the device is known, the optimal solution for each parameter of the Helmholtz coil can be obtained.

[0068] In one or more embodiments of the present invention, the optimal spacing between coils on either side can be determined based on the optimal nesting number and the cross-sectional requirements of the target uniform magnetic field, thereby determining the optimal microscopic parameters corresponding to each nested Helmholtz coil. Furthermore, based on the relationship between the gap between adjacent coils on the same side and the inner dimension of the reference coil when the design index is optimized under the optimal nesting number, the optimal gap between adjacent coils on the same side and the optimal inner dimension of the reference coil are determined, thereby determining the optimal macroscopic parameters of each nested Helmholtz coil.

[0069] Alternatively, the optimal microscopic parameters for each nested Helmholtz coil can be determined based on the required spacing between coils on either side of the target uniform magnetic field. Based on the relationship between the gap between adjacent coils on the same side and the inner dimensions of the reference coil when the design index is optimized under the optimal nesting number, the optimal gap between adjacent coils on the same side and the optimal inner dimensions of the reference coil can be determined to determine the optimal macroscopic parameters for each nested Helmholtz coil.

[0070] Under different uniform magnetic field cross-sectional diameters or device coil spacings, the optimal solutions for the parameters of the multi-level nested Helmholtz coil system are different. The magnetic field characteristics of the coils under different conditions can be obtained, and multi-parameter expressions for the average magnetic flux density and uniformity index of the magnetic field can be established: P ( h 、 R 、 L 、 W 、 d 、 k 、 n 、 i 、 d r 、 d z 、 d L ) = f ( , ).

[0071] Based on this, the present invention can establish the uncertainty propagation function of the target parameter (uniform field index):

[0072] ,or .

[0073] The partial derivatives in the uncertainty propagation function reflect the degree of influence of each parameter on the uniformity index. Since a smaller uniformity index is preferred, the larger the absolute value of the partial derivative, the greater the potential contribution of that parameter to reducing the uniformity index and improving magnetic field uniformity. (A negative partial derivative means that increasing the parameter can reduce the uniformity index; a positive partial derivative means that decreasing the parameter can also reduce the uniformity index.) The contribution of each parameter to the uniformity index is evaluated and the coil design parameters are ranked. Parameters with higher contributions are designated as higher design priority and are prioritized for optimization and adjustment during coil design.

[0074] Implementation process of adaptive uniform intensity control of multi-stage nested Helmholtz coil system:

[0075] 1) Based on the current magnetic field parameters obtained by the magnetic field state monitoring system, a magnetic field characteristic prediction model is established to predict the changing trend of the uniformity index in the future.

[0076] 2) Set the target magnetic field parameters, that is, the uniformity index and magnetic flux density that are expected to be achieved, and calculate the deviation between the current required magnetic field parameters and the target magnetic field parameters.

[0077] 3) Design an adaptive control algorithm based on the model predictive control (MPC) principle, set the parameter adjustment priority and step size according to the contribution, and use the uncertainty propagation function to predict the uniformity index or average magnetic flux density after adjustment. The parameter adjustment scheme calculated by the adaptive control algorithm is transmitted to the actuator, such as the current controller and the number of turns adjustment device, to achieve coordinated adjustment of the coil design parameters.

[0078] 4) During the adjustment process, the changes in the magnetic field state are monitored in real time, and the new uniformity index and magnetic field data such as flux density are fed back to the adaptive control algorithm to form a closed-loop control.

[0079] By evaluating the contribution of each parameter to the magnetic field characteristics and clarifying the priority of coil design, a uniform magnetic field collaborative adaptive strategy was constructed, and the adaptive uniform intensity characteristic control of the Helmholtz field was realized.

[0080] based on Figure 1The present invention provides a design method for a multi-level nested Helmholtz coil system, which uses a reciprocal analysis of coil structural parameters and magnetic field characteristics under global sensitivity. This method can identify optimal design expressions for each design parameter of the multi-level nested Helmholtz coil system, derive a multi-parameter expression for the magnetic field characteristics, clarify coil parameter design priorities, and propose an optimization strategy for magnetic field design indicators. When macroscopic design requirements for a target uniform magnetic field are provided, the optimal solution for each design parameter of the multi-level nested Helmholtz coil system can be directly obtained. This method enables efficient and accurate design improvements of Helmholtz coils as needed.

[0081] The present invention can obtain multi-parameter expressions and uncertainty propagation relationships of magnetic field characteristics, identify key weight parameters that have the greatest impact on magnetic field uniformity, clarify coil parameter design priorities, and propose optimization strategies for magnetic field design indicators.

[0082] The above is a design method for a multi-level nested Helmholtz coil system provided in one or more embodiments of the present invention. Based on the same concept, the present invention also provides a corresponding multi-level nested Helmholtz coil system. The multi-level nested Helmholtz coil system includes two parallel coaxial nested coils. The parallel coaxial nested coils include a plurality of coplanar and coaxial nested coils, forming a plurality of nested Helmholtz coils.

[0083] The macroscopic parameters and microscopic parameters of the multi-level nested Helmholtz coil system are determined by any of the above-mentioned design methods for a multi-level nested Helmholtz coil system; wherein the macroscopic parameters include the inner side dimensions of the nested reference coil and the spacing between the coils on both sides; and the microscopic parameters are the corresponding parameters of the coil winding settings.

[0084] This new multi-stage nested Helmholtz coil system has high precision, high stability and broad application prospects, and can significantly improve the performance of electromagnetic measurement and sensing technology. It has the following technical advantages:

[0085] 1. High magnetic field uniformity: Through nested structure and multi-parameter optimization, the uniformity of the magnetic field is significantly improved to meet the needs of high-precision measurement.

[0086] 2. High magnetic field strength: The nested introduction of inner and outer Helmholtz coils enhances the magnetic field strength, making it suitable for applications requiring high magnetic field strength.

[0087] 3. Multi-parameter collaborative optimization: Multi-parameter collaborative optimization is achieved through a three-dimensional multi-physics field coupling simulation platform and a reciprocal analysis method under global sensitivity.

[0088] 4. Adaptive Adjustment: Provides optimal parameter design formulas, making coil design more flexible. Constructs an uncertainty propagation model between target magnetic field characteristics and structural parameters to identify the key weighted parameters that have the greatest impact on magnetic field uniformity. Through uncertainty analysis, coil parameter design priorities are clarified, and optimization strategies for magnetic field uniformity and field strength are proposed.

[0089] 5. Applicability of three-dimensional design: Although the present invention only lists the optimal design of Helmholtz coils that generate a strong uniform magnetic field in a single direction, it can be extended to three-dimensional space. By using three sets of Helmholtz coils in different orientations, a specific uniform magnetic field of any direction and intensity can be generated in space.

[0090] 6. Wide application: It can be used in flow meter, electromagnetic measurement, magnetic field design, regulation, calibration and other fields to improve measurement accuracy.

[0091] In addition, the present invention also provides an embodiment of the design method of the present invention:

[0092] 1. Calculation of optimal parameters for a multi-level nested Helmholtz coil system:

[0093] (1) When the nesting coefficient of the multi-level nested Helmholtz coil system of the present invention is N =1, only the third-level influence relationship is involved, and its implementation example is as follows:

[0094] The first influencing relationship: the diameter of the coil d =0.8mm enameled copper wire. The current carrying capacity of general copper wire is 5-8A / mm 2 , so the coil winding is fed with current i It should not be too large and should be within the range of 2.5-4A. When studying the first influence relationship, select the winding current. i The average magnetic flux density can be adjusted by varying the injection current of the coil windings, ranging from 1 to 3 A. It was found that increasing the injection current of circular or rectangular coil windings can exponentially increase the magnetic flux density without affecting the uniformity index. Therefore, the average magnetic flux density index can be adjusted by varying the injection current of the coil windings. The uniformity index will be a key consideration in subsequent studies of Helmholtz coil parameters.

[0095] Second influence relationship: required uniform magnetic field domain diameter D =100mm. Based on the principle that the magnetic flux density in the use space should not be too small, the number of winding layers can be selected k =11, turns per layer n = 14. Taking the target uniform magnetic field cross section as the size normalization factor, the geometric center size of the coil (2 R + kd ) / D 、( L + kd ) / D , L / W , and the coil spacing h / D The second influence relationship between the average magnetic flux density index and the uniformity index in the required uniform magnetic field domain is used to obtain the precise macro-design constraint equation of the Helmholtz coil, such as (2 R + kd ) / h =1.97,( L + kd ) / h =1.82, L / W = 1. With the coil spacing h As the space increases, the average magnetic flux density index and uniformity index in the use space continue to decrease, and both show a trend of slowing down the attenuation speed and finally becoming flat. Therefore, if space allows, h The value of can be appropriately larger to obtain a smaller uniformity index.

[0096] The third influence relationship: h =170mm, L = W , coil spacing h and coil inner dimensions R 、 L The coil macro design constraint expression must be satisfied between them, namely (2 R + kd ) / h =1.97,( L + kd ) / h =1.82 is always true. Constantly change the number of coil winding layers k and the number of turns per layer n , when the uniformity index in the use space is the smallest, for the circular coil, k and n Roughly satisfied k =1.3 n -14.21, and when k =38, n =40 to obtain the optimal value; for rectangular coils, k and n Roughly satisfied k =0.95 n +6.37, and when k =25, n =20 to obtain the optimal value. Constantly change the coil spacing h , the number of winding layers can be obtained k and the number of turns per layer nThe third influence relationship with the uniformity index is to obtain their relationship with the coil spacing h The newly added microscopic parameter design constraint equation. When considering the winding gap, the coil geometric center size still satisfies [2 R + kd +( k -1) d z ] / h =1.97, [ L + kd +( k -1) d z ] / h =1.82, L / W =1. Change the winding axial gap respectively d z and winding radial clearance d r , when the coil spacing h =190mm, winding diameter d =0.8mm, number of turns per layer n =1, number of winding layers k =11, in order to ensure the minimum uniformity index in the use space, the circular coil must meet d z =0mm, d r =0.7mm; rectangular coils must meet d z =0mm, d r =0.9mm. Change the coil spacing h and winding diameter d , the winding axial clearance can be obtained d z and winding radial clearance d r The third influence relationship with the uniformity index is to obtain their h New micro-parameter design constraint equations.

[0097] According to the above embodiment, the optimal parameters of the circular and rectangular coils are as follows:

[0098] 1) Circular coil: Coil spacing between Helmholtz coils h =200mm, number of layers of coil winding k =33, the number of turns of each layer of winding n =49, diameter of enameled copper wire d =0.8 mm, the magnitude of the current flowing through the coil winding i=1A, the inner radius of the coil is R=183.8mm. The average magnetic flux density in the circular cross section of the pipe is obtained at this time. B avg =72.315G, uniformity index B hom =8.2957×10 -4 .

[0099] 2) Rectangular coil: Coil spacing between Helmholtz coils h =200mm, number of layers of coil winding k =18, the number of turns per winding layer n =24, diameter of enameled copper wire d =0.8mm, the magnitude of the current flowing through the coil winding i =1A, inner dimension of coil L =W=349.6mm. The average magnetic flux density in the circular cross section of the pipe is obtained at this time. B avg =18.996G, uniformity index B hom =8.4998×10 -4 .

[0100] (2) When the nesting coefficient N of the circular multi-stage nested Helmholtz coil system of the present invention is 2, the embodiment thereof is as follows:

[0101] The coil spacing between single circular Helmholtz coils can be obtained by the first influence relationship, the second influence relationship and the third influence relationship. h =200mm, the inner radius of the coil is R=183.8mm; the optimal microscopic parameters of each nested Helmholtz coil: the number of layers of coil winding k =33, the number of turns of each layer of winding n =49, diameter of enameled copper wire d =0.8mm.

[0102] Fourth influence relationship: When the inner dimension of the reference coil 2R1 = 300mm, the gap between adjacent coils on the same side d L =73mm, the magnetic field uniformity index in the circular cross section of the pipe achieves the optimal value B hom =3.123×10 -3 When the inner dimension of the reference coil is 2R1=280mm, the gap between adjacent coils on the same side is d L =79mm, the magnetic field uniformity index in the circular cross section of the pipe achieves the optimal value B hom =5.967×10-3 When the inner dimension of the reference coil is 2R1=260mm, the gap between adjacent coils on the same side is d L =84mm, the magnetic field uniformity index in the circular cross section of the pipe achieves the optimal value B hom =9.647×10 -4 . Continue to change the gap between adjacent coils on the same side under different reference coil inner edge dimensions, and explore the relationship between the gap between adjacent coils on the same side and the reference coil inner edge dimensions and the average magnetic flux density index and uniformity index. When the reference coil inner edge dimensions and the gap between adjacent coils on the same side meet 2R1=-0.275 d L +155.667, the uniformity of the magnetic field in the circular cross section of the pipe is optimal. According to this formula, by continuously changing the inner edge size of the reference coil and the gap between adjacent coils on the same side, the optimal uniformity of the magnetic field in the circular cross section of the pipe can be obtained, that is, B hom =8.0626×10 -4 、 B avg =137.82G, the corresponding inner edge size of the reference coil and the gap between adjacent coils on the same side is 2R1=328mm, d L =65.5mm.

[0103] The fifth influencing relationship: changing the coil spacing between circular Helmholtz coils will change the optimal microscopic parameters of each nested coil. For example, when the coil spacing between Helmholtz coils is h=240mm, the optimal microscopic parameters of each nested Helmholtz coil are: the number of coil winding layers k =31, the number of turns of each layer of winding n =58, diameter of enameled copper wire d =0.8mm. Using the fourth influence relationship, we can find the optimal design expression for the inner size of the reference coil and the gap between the adjacent coils on the same side, as well as the optimal value for the inner size of the reference coil and the gap between the adjacent coils on the same side. When the coil spacing between the Helmholtz coils is h=240mm, the optimal design relationship expression for the inner size of the reference coil and the gap between the adjacent coils on the same side is 2R1=0.025 d L +92; When the magnetic field uniformity in the circular cross section of the pipe is optimal, that is, B hom =3.7889×10 -4 , the corresponding inner edge size of the reference coil and the gap between adjacent coils on the same side is 2R1=402mm, d L= 102.05mm. By continuously changing the coil spacing between the circular Helmholtz coils and using the fourth influence relationship, we can explore the optimal values ​​for the inner edge size of the reference coil and the gap between adjacent coils on the same side under different coil spacings. The relationship between the inner edge size of the reference coil, the gap between adjacent coils on the same side, and the coil spacing is expressed as 2R1=1.8179 when the nesting coefficient N=2. h -34.3571, d L =0.7374 h -76.6904. At this point, based on the coil spacing between the circular Helmholtz coils, the optimal reference coil inner edge size R1 and the optimal gap between adjacent coils on the same side can be calculated. d L Then, the optimal macroscopic parameters of each nested Helmholtz coil are obtained when the nesting coefficient N=2.

[0104] Through comparative studies, it was found that when the coil spacing between the circular Helmholtz coils h =200mm. When the magnetic field index is optimized, the average magnetic flux density on the circular cross-section of a circular Helmholtz coil with a nesting coefficient of N = 2 is 1.91 times that of a circular Helmholtz coil with a nesting coefficient of N = 1, improving the magnetic field uniformity by 5.2%. By adjusting the number of coil nests on both sides and exploring five new influencing relationships, the optimal solution for each Helmholtz coil parameter for a given coil spacing and optimal magnetic field index is obtained. Furthermore, the optimization of magnetic field index under different coil nesting numbers is explored to determine the optimal nesting number.

[0105] 2. Physical construction:

[0106] 1) Material selection and coil production

[0107] Coil material: Choose high conductivity copper wire, diameter 0.8mm.

[0108] Skeleton material: Choose non-magnetic material with high magnetic permeability, such as glass fiber.

[0109] Fabricate the inner coil: Use a precision winding machine to fabricate the inner coil according to the parameters optimized by simulation, ensuring the coil's geometric dimensions and winding accuracy.

[0110] Fabricate the outer coil: Fabricate the outer coil according to the parameters optimized by simulation. Ensure the coaxial arrangement and spacing accuracy of multiple parallel coils.

[0111] 2) Coil testing and connection:

[0112] Electrical performance test: Use an LCR meter to test the resistance and inductance of the coil to ensure that it meets the design requirements. At the same time, test the current carrying capacity of the coil to ensure that it can work stably.

[0113] Connect the current source: Connect the inner and outer coils to the adjustable current source, ensuring they are secure and provide good contact. Test the output stability of the current source to ensure it can provide an adjustable current of 0-5A.

[0114] 3) Assemble the sensor

[0115] Fix the coils: Fix the inner and outer Helmholtz coils in the sensor housing, ensuring that the coils are coaxial and in the same plane. Use insulating material to fix the coils and ensure that the spacing between the coils meets the design requirements.

[0116] Install a magnetic field detection device: Install a high-precision magnetometer and a mesh plane divider in the central area of ​​the sensor to ensure that the magnetic field detection device can monitor the magnetic field characteristics on the plane in real time.

[0117] 4) Testing and Optimization

[0118] Magnetic field distribution test: Use a magnetic field detection device to measure the magnetic field distribution on the center plane of the sensor. Obtain the average magnetic flux density and uniformity index.

[0119] Data comparison and analysis: Compare measured data with simulation results to evaluate model accuracy. Analyze the differences between measured data and simulation results to determine optimization directions.

[0120] Parameter adjustment: Based on the comparison results, adjust the coil design parameters (such as size, spacing, number of turns, etc.). Repeat the test and adjustment process until the magnetic field characteristics reach the optimized target.

[0121] By designing a multi-stage nested Helmholtz coil system, when currents in the same direction are passed through the coils on both sides, the magnetic field in the required uniform magnetic field domain can be made highly uniform, that is, the first-order derivative ∂ B y / ∂ y ≈0 (guaranteed by the geometric symmetry of the Helmholtz coil), the second-order derivative ∂ 2 B y / ∂ y 2 ≈0, and by reducing the high-order derivatives to expand the uniform magnetic field area. When the opposite currents are passed through the coils on both sides, the same Helmholtz coil generates a gradient field G=∂ B y / ∂ y , the symmetry of uniform magnetic field optimization reduces the high-order derivatives (such as ∂ 3 B y / ∂ y 3 ), the linearity of the gradient field (i.e. ∂ 2B y / ∂ y 2 The optimized magnetic field of the Helmholtz coil provides a high-intensity and well-linear foundation for the gradient field, enabling more consistent spatial encoding in applications such as magnetic resonance imaging (MRI) to distinguish and localize signals at different locations in space. Therefore, the design of a multi-stage nested Helmholtz coil system can also significantly improve the gradient field characteristics when currents in opposite directions flow through the coils on both sides.

[0122] That is, the above description of the present invention is based on the design of a multi-stage nested Helmholtz coil system using a uniform magnetic field as the target magnetic field. However, the present invention can also be applied to the design of a multi-stage nested Helmholtz coil system using a gradient magnetic field as the target magnetic field. The only difference lies in the change of design parameters, which will not be further described in the present invention.

[0123] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware using a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes in the above-described method embodiments. Any reference to memory, storage, database, or other media used in the various embodiments provided herein may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0124] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A design method for a multi-stage nested Helmholtz coil system, characterized in that: The multi-stage nested Helmholtz coil system includes two parallel coaxial nested coils, wherein the parallel coaxial nested coils include a plurality of coplanar and coaxial nested coils, forming a plurality of nested Helmholtz coils; the method includes: Obtaining design indicators corresponding to the target uniform magnetic field; By adjusting the winding current of a single Helmholtz coil and according to the change of the magnetic field distribution in the target area, the first influence relationship between the winding current and the design index is determined; Taking the inner side dimensions of a single Helmholtz coil and the spacing between the coils on both sides as macroscopic parameters, the second influence relationship between each macroscopic parameter and the design index is determined. Taking the second influence relationship as a constraint and the coil winding setting as a microscopic parameter, the third influence relationship between each microscopic parameter and the design index is determined. determining optimal macroscopic parameters and optimal microscopic parameters of a single Helmholtz coil according to the first influence relationship, the second influence relationship, and the third influence relationship; A reference coil is constructed based on the optimal macroscopic parameters and the optimal microscopic parameters, and a Helmholtz coil with the same microscopic parameters is nested outside the reference coil. A fourth influencing relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the design index is determined when the spacing between the coils on both sides is fixed. The spacing between the coils on both sides is adjusted to determine a fifth influencing relationship between the gap between adjacent coils on the same side and the inner size of the reference coil and the spacing between the coils on both sides when the design index is optimal. Based on the fourth and fifth influence relationships, the optimal nesting number is determined by adjusting the nesting number of coils on both sides according to the change of the magnetic field distribution in the target area; according to the optimal nesting number and the macro design requirements of the target uniform magnetic field, the optimal design parameters of the multi-level nested Helmholtz coil system are determined.

2. The design method of a multi-stage nested Helmholtz coil system according to claim 1, characterized in that: The inner side size of a single Helmholtz coil and the spacing between the coils on both sides are used as macro parameters to determine the second influencing relationship between each macro parameter and the design index, specifically including: The macro parameters are normalized using the inner side size of a single Helmholtz coil and the spacing between the two coils as macro parameters, and the diameter of the target uniform magnetic field as the size normalization factor of the macro parameters. By adjusting the inner side size ratio of a single Helmholtz coil, the ratio of the inner side size to the diameter after size normalization, and the ratio of the spacing between the two coils to the diameter, the second influencing relationship between each macro parameter and the design index is determined according to the change in the magnetic field distribution in the target area. Determining the optimal macroscopic parameters and the optimal microscopic parameters of a single Helmholtz coil according to the first influence relationship, the second influence relationship, and the third influence relationship specifically includes: According to the cross-sectional requirements of the target uniform magnetic field or the spacing requirements between the coils on both sides, the optimal macroscopic parameters and optimal microscopic parameters of a single Helmholtz coil are determined based on the first influence relationship, the second influence relationship and the third influence relationship.

3. The design method of a multi-stage nested Helmholtz coil system according to claim 1, characterized in that: The fourth influencing relationship between the gap between adjacent coils on the same side and the inner side dimension of the reference coil and the design index is determined when the spacing between the coils on both sides is fixed; and the fifth influencing relationship between the gap between adjacent coils on the same side and the inner side dimension of the reference coil and the spacing between the coils on both sides is determined when the design index is optimized, specifically including: Under the condition that the spacing between the coils on both sides is fixed, by adjusting the gap between adjacent coils on the same side and the inner side size of the reference coil, according to the change of the magnetic field distribution in the target area, the fourth influencing relationship between the gap between adjacent coils on the same side and the inner side size of the reference coil and the design index is determined; Adjust the spacing between the coils on both sides, and for each spacing traversed, determine the optimal microscopic parameters of each nested Helmholtz coil at that spacing, so as to determine the fifth influencing relationship between the gap between adjacent coils on the same side and the inner edge size of the reference coil and the spacing between the coils on both sides when the design index is optimal.

4. The design method of a multi-stage nested Helmholtz coil system according to claim 1, wherein: The method of determining the optimal nesting number by adjusting the nesting number of coils on both sides based on the fourth influence relationship and the fifth influence relationship according to the change in magnetic field distribution in the target area specifically includes: Based on the fourth and fifth influence relationships, the number of coil nestings on both sides is adjusted according to the magnetic field distribution in the target area. The relationship between the gap between adjacent coils on the same side and the relationship between the inner edge size of the reference coil and the spacing between the coils on both sides when the design index is optimal under each number of coil nestings traversed is determined. The optimal number of nestings is determined based on the optimal value of the design indicator under each adjusted nesting coefficient traversed.

5. The design method of a multi-stage nested Helmholtz coil system according to claim 4, characterized in that: The optimal design parameters of the Helmholtz coil are determined based on the optimal nesting number and the macroscopic design requirements of the target uniform magnetic field, specifically including: According to the cross-sectional requirements of the target uniform magnetic field, the optimal spacing between the coils on both sides is determined to determine the optimal microscopic parameters corresponding to each nested Helmholtz coil; According to the relationship between the gap between adjacent coils on the same side and the inner edge size of the reference coil when the design index is optimal under the optimal nesting number, and the spacing between the coils on both sides, the optimal gap between adjacent coils on the same side and the optimal inner edge size of the reference coil are determined to determine the optimal macro parameters of each nested Helmholtz coil.

6. The design method of a multi-stage nested Helmholtz coil system according to claim 4, characterized in that: The optimal design parameters of the Helmholtz coil are determined based on the optimal nesting number and the macroscopic design requirements of the target uniform magnetic field, specifically including: Determine the optimal microscopic parameters of each nested Helmholtz coil based on the required spacing between the coils on both sides of the target uniform magnetic field; According to the relationship between the gap between adjacent coils on the same side and the inner edge size of the reference coil when the design index is optimal under the optimal nesting number, and the spacing between the coils on both sides, the optimal gap between adjacent coils on the same side and the optimal inner edge size of the reference coil are determined to determine the optimal macro parameters of each nested Helmholtz coil.

7. The design method of a multi-stage nested Helmholtz coil system according to claim 1, wherein: The design indicators include: a magnetic flux density indicator and a uniformity indicator of the target uniform magnetic field in the target area.

8. The design method of a multi-stage nested Helmholtz coil system according to claim 1, wherein: The coil winding is set as a microscopic parameter, specifically including: The microscopic parameters include the diameter of the coil winding wire, the number of coil winding layers, the number of turns in each coil winding layer, the gap between coil winding layers, and the gap between turns in each coil winding layer.

9. A multi-stage nested Helmholtz coil system, characterized in that: The multi-stage nested Helmholtz coil system includes two parallel coaxial nested coils, wherein the parallel coaxial nested coils include a plurality of coplanar and coaxial nested coils, forming a plurality of nested Helmholtz coils; The macroscopic parameters and microscopic parameters of the multi-level nested Helmholtz coil system are determined by any one of the methods in claims 1 to 8 above; the macroscopic parameters include the inner side dimensions of the nested reference coil and the spacing between the coils on both sides; the microscopic parameters are the corresponding parameters of the coil winding settings.

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