A stress analysis method suitable for superconducting magnet winding of stellarator

Abstract

The application provides a stress analysis method suitable for a superconducting magnet winding of a stellarator, comprising: building a finite element model of the superconducting magnet of the stellarator; performing multi-physical field coupling on the finite element model, and performing cutting processing on the coupled finite element model to cut a local region from the finite element model as a cutting block; re-performing multi-physical field coupling on the cutting-processed finite element model to obtain a global model; performing detailed modeling on the winding and the filling layer corresponding to the cutting block to obtain a detailed model; mapping the deformation displacement of the cutting block corresponding to the global model to the detailed model; and solving the displacement-mapped detailed model to determine stress data corresponding to the cutting block. The application can quickly and accurately evaluate the stress of the winding by locally and in detail modeling the cutting block, combining the global model and the local model, and through the displacement mapping method.

Description

Technical Field

[0001] This invention relates to the field of stellarator-related technologies, and in particular to a method for stress analysis of superconducting magnet windings in stellarators. Background Technology

[0002] Stellarators are the mainstream magnetic confinement fusion devices, relying on superconducting magnets to generate magnetic fields and achieve stable plasma operation. The superconducting magnet windings are the core of the stellarator device, primarily used for load bearing and excitation. The internal stress distribution of the superconducting magnet windings directly determines whether the superconducting material can maintain a stable superconducting state. Excessive winding stress can easily lead to problems such as insulation layer cracking, armor plastic yielding, and damage to superconducting cable strands, ultimately causing magnet structure failure. Therefore, improving the accuracy of winding stress analysis is a core aspect of stellarator superconducting magnet structure design.

[0003] Currently, the generalized plane strain method is widely used for stress analysis of superconducting magnet windings in fusion reactors. This method is simple in principle and highly efficient, and has been widely applied in tokamak devices for winding stress analysis. However, the superconducting magnets in stellarators have a twisted, irregular, and irregular shape, which does not conform to the basic assumptions of the plane stress-strain method of the generalized plane strain method. If the generalized plane strain method is used, problems such as poor method adaptability and distortion of calculation results will occur.

[0004] To circumvent the limitations of traditional generalized plane strain methods, existing technologies attempt to employ a comprehensive, full-structure, fine-grained modeling approach for stress analysis, performing solid modeling and meshing of all microstructures within the magnet winding. However, the overall size of a stellarator superconducting magnet can reach tens of meters in diameter, while the thickness of the internal winding structure (such as the armor and insulation layer) is only on the order of millimeters. Detailed modeling of every part of the winding for stress analysis would result in an unacceptable computational burden and significantly increase the difficulty of convergence.

[0005] In summary, existing methods for stress analysis of superconducting magnet windings in stellarators cannot simultaneously meet the requirements of high analysis accuracy and low computational load. Summary of the Invention

[0006] The purpose of this invention is to address the problem that existing methods for stress analysis of superconducting magnet windings in stellarators cannot simultaneously meet the requirements of high analysis accuracy and low computational load.

[0007] To address the aforementioned problems, embodiments of the present invention disclose a method for stress analysis of stellarator superconducting magnet windings, comprising: constructing a finite element model of a stellarator superconducting magnet; wherein the stellarator superconducting magnet includes windings, a filler layer, and a coil box stacked sequentially from the inside out; performing multiphysics coupling on the finite element model, and cutting the coupled finite element model to extract local regions as cutting blocks; re-coupling the cut finite element model with multiphysics to obtain a global model; performing detailed modeling on the windings and filler layer corresponding to the cutting blocks to obtain a detailed model; mapping the deformation displacement of the cutting blocks corresponding to the global model to the detailed model; and solving the detailed model after displacement mapping to determine the stress data corresponding to the cutting blocks.

[0008] According to another specific embodiment of the present invention, the stress analysis method for stellarator superconducting magnet windings disclosed in this embodiment of the present invention constructs a finite element model of the stellarator superconducting magnet, including: treating the winding as a single uniform isotropic material and performing equivalent modeling of the winding; performing actual modeling of the filler layer and the coil box; setting the contact type between the winding and the filler layer as bonded contact; and setting the contact type between the filler layer and the coil box as frictional contact.

[0009] According to another specific embodiment of the present invention, the stress analysis method for superconducting magnet windings of stellarators disclosed in this embodiment of the present invention performs multi-physics coupling on a finite element model, including: performing multi-physics coupling of temperature field, electromagnetic field, and structural field on the finite element model. Furthermore, a local region is cut out from the finite element model as a cutting block, including: determining a critical region based on the multi-physics coupled finite element model, and determining the cutting block based on a pre-defined region of interest and the critical region; wherein, the critical region is the region with the highest calculated stress value; the region of interest is the region that needs to be verified; and the cutting block is a local region that simultaneously includes the critical region and the region of interest.

[0010] According to another specific embodiment of the present invention, the stress analysis method for superconducting magnet windings of stellarators disclosed in this embodiment includes a cutting block comprising a side surface parallel to the winding centerline and two end faces perpendicular to the winding centerline; and mapping the deformation displacement of the cutting block corresponding to the global model to the detailed model includes: using a radial basis function interpolation algorithm to map the lateral displacement, longitudinal displacement, and vertical displacement of the side surface of the cutting block in the global model to the detailed model, and mapping the degrees of freedom of the cutting block in the normal direction of the end faces in the global model to the detailed model.

[0011] According to another specific embodiment of the present invention, the stress analysis method for superconducting magnet windings of stellarators disclosed in this embodiment uses a radial basis function interpolation algorithm to map the lateral, longitudinal, and vertical displacements of the side of the cut block in the global model to the detailed model in the spatial coordinate system. This includes: determining the reference node coordinates of all reference grid nodes corresponding to the filling layer within the cut block in the global model, and the lateral, longitudinal, and vertical displacements of the reference grid nodes in the spatial coordinate system; determining the coordinates of all undetermined grid nodes corresponding to the filling layer within the cut block in the detailed model; determining the radial basis function; determining the displacement interpolation formula based on the weight coefficient corresponding to each reference grid node; and calculating the lateral, longitudinal, and vertical displacements of each undetermined grid node in the spatial coordinate system based on the undetermined node coordinates and the interpolation formula.

[0012] According to another specific embodiment of the present invention, the radial basis function of the stress analysis method for superconducting magnet windings of stellarators disclosed in this embodiment is: ,in, Let the coordinates of the node to be determined be... ; The coordinates of the reference node are... ; Let be the linear Euclidean distance between the coordinates of the node to be determined and the coordinates of the reference node; ,in, These are Gaussian radial basis functions; The shape parameter is determined by calculating the spacing between any two reference mesh nodes in the global model according to the following formula.

[0013]

[0014] And order equal of the median.

[0015] The displacement interpolation formula is:

[0016]

[0017] Let be the displacement of the grid node to be determined in the spatial coordinate system; The weighting coefficients are determined as follows: The coordinates of each reference grid node, along with its lateral, longitudinal, and vertical displacements in the spatial coordinate system, are substituted into the displacement interpolation formula to obtain the values ​​related to the reference grid node. Solving multiple systems of equations simultaneously yields... .

[0018] According to another specific embodiment of the present invention, the stress analysis method for superconducting magnet windings of stellarators disclosed in this embodiment of the present invention provides stress data for the region of interest within the cut block; the winding includes cables, armor, turn insulation layers, and ground insulation layers stacked sequentially from the inside out; and the stress data includes at least one of the following: stress cloud diagrams of each layer structure of the winding inside the cut block, stress values, the location of the maximum stress, and stress distribution patterns.

[0019] According to another specific embodiment of the present invention, the stress analysis method for stellarator superconducting magnet windings disclosed in this embodiment of the present invention, after determining the stress data corresponding to the cutting block, further includes: establishing a global detailed model of the stellarator superconducting magnet; determining calibration stress parameters based on the global detailed model; comparing the stress data output by the detailed model corresponding to the cutting block with the calibration stress parameters, and verifying the output accuracy of the detailed model corresponding to the cutting block.

[0020] An embodiment of the present invention discloses an electronic device, including: a processor and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the stress analysis method for stellarator superconducting magnet windings as described in any of the above embodiments.

[0021] The present invention discloses a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the stress analysis method for stellarator superconducting magnet windings as described in any of the above embodiments.

[0022] The beneficial effects of this invention are:

[0023] The stress analysis method for stellarator superconducting magnet windings provided in this application is based on the modeling of stellarator superconducting magnets, which makes the stress analysis method adaptable to the space-torsional magnet structure of stellarators, avoiding the problem that the traditional generalized plane strain method is not applicable to tortuous magnet structures.

[0024] Furthermore, by combining global and detailed models, only local segments are modeled in detail, thus avoiding the problems of huge computational load and convergence difficulties caused by full-size detailed modeling.

[0025] Furthermore, by performing displacement mapping based on the global model of secondary multiphysics coupling after cutting, the precise nodal displacements at the side and end boundary of the cut block can be used as the data source for subsequent displacement mapping, thereby improving the accuracy of displacement mapping and thus improving the accuracy of subsequent stress analysis. Attached Figure Description

[0026] Figure 1This is a schematic flowchart of a method for stress analysis of superconducting magnet windings in stellarators provided in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram of a detailed local model in the stress analysis method for superconducting magnet windings of stellarators provided in this embodiment of the invention;

[0028] Figure 3 This is a schematic diagram of displacement mapping in the stress analysis method for superconducting magnet windings of stellarators provided in the embodiments of the present invention;

[0029] Figure 4 This is a schematic diagram showing the comparison between stress data and calibrated stress parameters in the stress analysis method for superconducting magnet windings of stellarators provided in this embodiment of the invention.

[0030] Explanation of reference numerals in the attached figures:

[0031] 1. Cable; 2. Armor; 3. Turn insulation layer; 4. Ground insulation layer; 5. Filler layer; 6. Coil box. Detailed Implementation

[0032] As described in the background section, existing methods for stress analysis of stellarator superconducting magnet windings cannot simultaneously meet the requirements of high analysis accuracy and low computational complexity. To address these technical issues, this embodiment discloses a method for stress analysis of stellarator superconducting magnet windings, which achieves rapid assessment of stress in key areas of interest by combining a global model and a local detailed model.

[0033] To facilitate understanding, the relevant concepts will be explained.

[0034] Stellarator superconducting magnet: A twisted configuration superconducting magnet used in controlled nuclear fusion devices. It generates a magnetic field to confine plasma by energizing the superconducting windings, and the whole structure is a spatially irregular twisted structure.

[0035] Winding: A component formed after a superconducting conductor is wound along a specific path and then impregnated. Generally, a winding includes a superconducting conductor, turn insulation, and ground insulation. The superconducting conductor includes a superconducting cable and armor.

[0036] Ground insulation: Used for insulation between superconducting coils and external components.

[0037] Turn insulation: The insulation of a superconducting conductor itself, usually wrapped around the outside of an armor.

[0038] Armor: A stainless steel structure that wraps around the outside of the superconducting cable, usually round or square.

[0039] Superconducting cable: A type of cable structure made by twisting multiple superconducting strands.

[0040] Filler layer: A structure that fills the gap between the winding and the coil box.

[0041] Coil box: The outermost load-bearing protective shell that bears the overall weight, structural constraints, low-temperature sealing, and external support load.

[0042] Next, the stress analysis method applicable to the superconducting magnet windings of stellarators will be described in detail with reference to the accompanying drawings.

[0043] Example 1:

[0044] refer to Figure 1 The method for stress analysis of superconducting magnet windings in stellarators includes the following steps:

[0045] First, a finite element model of the stellarator superconducting magnet is constructed. The stellarator superconducting magnet consists of windings, filler layers, and coil boxes stacked sequentially from the inside out.

[0046] Second, multiphysics coupling is performed on the finite element model, and the coupled finite element model is then cut to extract local regions as cutting blocks.

[0047] Third, the finite element model after the cutting process is re-coupled into multiphysics to obtain a global model.

[0048] Fourth, detailed modeling is performed on the windings and filler layers corresponding to the cutting blocks to obtain a detailed model.

[0049] Fifth, map the deformation displacement of the cutting block corresponding to the global model to the detailed model.

[0050] Sixth, solve the detailed model after displacement mapping to determine the stress data corresponding to the cutting block.

[0051] Specifically, the finite element model is a numerical simulation model that discretizes the physical structure of the magnet into mesh nodes and elements. The stellarator magnet is a multi-layered nested assembly structure, and the force transmission path from the inside to the outside is: winding → filler layer → coil box. Therefore, in the first step, it is necessary to first establish a finite element model of the overall assembly of the stellarator superconducting magnet to balance the overall force transmission relationship and simulation efficiency. In implementation, it is necessary to construct a three-layer nested structure of coil box, filler layer, and winding according to the actual geometric dimensions of the magnet, and establish a finite element model for it. In the first step, only an initial global equivalent finite element model is built, and this model does not perform local detailed stress calculations.

[0052] In the second step, multiphysics coupling is used to calculate the actual operating conditions of the magnet under multiphysics conditions, thereby identifying high-risk areas; then, geometric cutting is used to delineate boundaries, defining the scope for subsequent local fine calculations. This step only involves the first multiphysics coupling, and the coupled model is only used for cutting and positioning.

[0053] In the third step, because the geometric cutting of the model creates new boundaries corresponding to the cut sides and end faces, the displacement and stress fields of the original model will be reconstructed. Therefore, multiphysics coupling needs to be performed again to obtain the displacements corresponding to the real nodes of the cut boundaries, serving as the reference data source for subsequent displacement mapping. In practice, based on the finite element model with completed geometric cutting, the loads, boundary conditions, material parameters, and coupling algorithms remain completely unchanged, and the temperature-electromagnetic-structural multiphysics coupling solution is performed again. After the solution is completed, a global model with secondary coupling after cutting is obtained, which can provide a reference data source for subsequent displacement mapping. By performing multiphysics coupling again on the global model after cutting, high-precision reference data can be provided for subsequent displacement mapping, avoiding boundary errors caused by using the original uncut model data, and ensuring the calculation accuracy of the local fine model from the source.

[0054] In the fourth step, only the small area corresponding to the cut block is not simplified, and its true structure is restored layer by layer. For other areas outside the cut block, equivalent simplification is still performed, thereby improving the accuracy of stress solution in key areas without increasing the overall computational load. In practice, the area covered by the cut block is modeled layer by layer with fine detail, establishing the true structure of the superconducting cable, armor, turn insulation, ground insulation, and filling layer from the inside out. Then, the local geometry is constructed and fine meshed according to the actual dimensions, material properties, and interlayer assembly relationships. The detailed model obtained through the above steps is a blank detailed model containing only mesh node coordinates and no simulation results. In subsequent displacement mapping, the displacement of the global model needs to be assigned to the blank detailed model.

[0055] In the fifth step, the actual deformation of the cutting boundary corresponding to the global model needs to be transferred to the local detailed model boundary, and displacement constraints that conform to the overall force are applied to the detailed model, thereby avoiding errors caused by artificial boundary assumptions.

[0056] Since the locally detailed model, after applying precise displacement boundaries, can accurately reproduce the interlayer stress, insulation, and armor stress states in key areas, the sixth step can use this detailed model to solve for and output stress results. Specifically, using the locally detailed model as the computational object, a structural mechanics finite element method is performed to obtain the global stress distribution of the entire cut block. Stress data for the region of interest, such as stress values ​​and the coordinates corresponding to the maximum stress, are then extracted from the stress distribution results. Finally, the stress data for the windings, armor, and each insulating layer are output for subsequent verification of the superconducting magnet structure strength or assessment of superconducting safety.

[0057] By employing these steps and modeling based on the stellarator's superconducting magnet, the stress analysis method becomes adaptable to the space-torsional magnet structure of the stellarator, avoiding the problem that traditional generalized plane strain methods are unsuitable for tortuous magnet structures. Furthermore, by combining global and detailed models, only local cut blocks are finely modeled, avoiding the enormous computational burden and convergence difficulties associated with full-size detailed modeling. Even further, displacement mapping is performed based on the global model with secondary multiphysics coupling after cutting. This allows precise nodal displacements at the sides and end faces of the cut blocks to serve as the data source for subsequent displacement mapping, improving the accuracy of displacement mapping and thus enhancing the accuracy of subsequent stress analysis.

[0058] Furthermore, in this method for stress analysis of stellarator superconducting magnet windings, a finite element model of the stellarator superconducting magnet is constructed, including the following steps:

[0059] First, the winding is equivalent to a single uniform isotropic material, and an equivalent model of the winding is performed.

[0060] Next, the filler layer and coil box are actually modeled.

[0061] Next, set the contact type between the winding and the filler layer to bonded contact, and set the contact type between the filler layer and the coil box to frictional contact.

[0062] Specifically, when establishing the finite element model, the winding is modeled using a homogeneous equivalent model, that is, only the overall mechanical stiffness and elastic parameters are retained, while the internal fine layered structure is ignored, and the winding is equivalent to a single homogeneous material, thereby reducing the overall model mesh size and computational load. For the filler layer and coil box structure, a refined solid model is created based on the actual geometry, wall thickness, and assembly relationships, without equivalent simplification. At the same time, it is necessary to define the contact relationships between components. The winding and filler layer are set as bonded contact to simulate the state without relative slippage after impregnation and curing; the filler layer and coil box are set as frictional contact to simulate the force characteristics of assembly gaps and small slippage. Since the filler layer and coil box are the main load-bearing, constraint, and force transmission components of the magnet, their geometry, wall thickness, and assembly position directly determine the overall stress and deformation. Actual modeling of the supporting structures such as the filler layer and coil box can ensure the realism and reliability of the global force boundary.

[0063] More specifically, the contact type determines the force transmission and relative motion relationship between components. Bonded contact refers to a complete fit between the winding and the filler layer, with no relative slippage, no separation, and consistent deformation. Setting the contact type between the winding and the filler layer as bonded contact better reflects the actual bonding state after impregnation and curing, thus improving the accuracy of subsequent analysis. Frictional contact refers to a situation where there are minute gaps and assembly stresses between the filler layer and the coil box assembly, which can produce slight relative slippage during operation. Setting frictional contact better reflects the actual assembly stress state in engineering, avoiding distortion of simulation results. Setting the contact type between the filler layer and the coil box as frictional contact better reflects the actual assembly stress state in engineering, avoiding distortion of simulation results.

[0064] Furthermore, in this method for stress analysis of superconducting magnet windings applicable to stellarators, multi-physics coupling is performed on the finite element model, including multi-physics coupling of temperature field, electromagnetic field, and structural field.

[0065] Specifically, the temperature field is used to simulate the thermal stress brought about by the ultra-low temperature refrigeration environment, the electromagnetic field is used to simulate the strong Lorentz electromagnetic force generated by energization, and the structural field is used to simulate mechanical deformation, compression, and tensile stress.

[0066] Furthermore, in this method for stress analysis of superconducting magnet windings in stellarators, a local region is cut out from the finite element model as a cutting block. This includes: determining the critical region based on the finite element model after multiphysics coupling, and determining the cutting block based on the pre-defined region of interest and the critical region. The critical region is the area with the highest calculated stress value; the region of interest is the area that needs to be checked; and the cutting block is a local region that includes both the critical region and the region of interest.

[0067] Specifically, when performing multiphysics coupling, it is necessary to apply low-temperature loads, electromagnetic excitation loads, and structural constraint loads to the initial global equivalent finite element model to conduct temperature-electromagnetic-structure multiphysics coupling calculations. After coupling, two regions need to be identified: the critical region and the region of interest. The critical region is the area with the highest stress value obtained from the simulation solution; the region of interest is a key engineering verification area manually set based on the weak points of the structure.

[0068] Specifically, the danger zone is automatically calculated based on the coupling of multiple physical fields, including temperature, electromagnetic, and structural fields. It identifies areas with the highest equivalent stress and principal stress values ​​across the entire field, and those most prone to insulation failure, armor yielding, superconductivity failure, and structural cracking. The region of interest, on the other hand, is pre-defined by designers based on structural layout, process characteristics, industry standards, and operational experience. It is typically defined as winding bends and twists, conductor joints, insulation overlaps, connections to coil boxes, and weak points in the manufacturing process. Spatially, the danger zone and the region of interest can overlap; that is, the location with the highest stress calculated in the simulation coincides with a critical structural component requiring special verification in engineering. The danger zone can be contained within the region of interest. For example, a large region of interest may be defined, and simulation may reveal that a point within this region has the highest stress across the entire field. The danger zone may also extend beyond the originally defined region of interest; that is, if the simulation shows abnormally high stress at a location not initially predicted, the danger point must be included in the region of interest, expanding the cut-off area.

[0069] When cutting the cutting block, two parallel cutting planes are used for cutting, with the cutting planes perpendicular to the winding centerline. This results in a more regular cutting section and a more regular boundary shape, which in turn makes the boundary conditions more regular during subsequent displacement mapping. This reduces the problems of errors or simulation non-convergence that are prone to occur during displacement mapping, and is more suitable for the structure of the astrolabe's twisted winding.

[0070] The cutting block needs to completely surround the region of interest, cover inherent structural weaknesses, and prevent the region of interest from falling on the cutting boundary, thereby eliminating boundary effect interference. At the same time, the cutting block should also completely include the danger zone, discovering high-stress failure points that could not be predicted in the early stages, and not omitting any risk points. In this way, it can avoid overlooking high-risk points in objective mechanics and also ensure that points that need to be checked in engineering design are not missed, achieving full coverage of critical areas and improving the accuracy of stress analysis.

[0071] The number of cutting blocks is determined based on the distribution of the regions of interest and the hazardous regions. When the regions of interest and the hazardous regions are concentrated in a contiguous area, only one cutting block is needed; when the regions of interest and the hazardous regions are scattered and isolated, multiple cutting blocks are required.

[0072] Furthermore, the winding comprises, from the inside out, stacked cables, armor, turn insulation layers, and a ground insulation layer. (Reference) Figure 2 The detailed model obtained after detailed modeling of the windings and filler layers corresponding to the cutting block shows, from the inside out, cable 1, armor 2, turn insulation layer 3, ground insulation layer 4, filler layer 5, and coil box 6. It can be seen that... Figure 2The geometric model corresponding to the layered structure of the winding within the cutting block range is shown. Through this detailed model, the stress state of each of the cable 1, armor 2, turn insulation layer 3, and ground insulation layer 4 can be analyzed separately, and it can be determined whether there are risks such as insulation layer damage, armor yielding, and superconductivity failure.

[0073] Further, refer to Figure 3 The cutting block includes a side surface parallel to the winding centerline and two end faces perpendicular to the winding centerline. Figure 3 The diagram shows the four sides and two end faces corresponding to the structural boundaries of the cutting block.

[0074] Specifically, the winding centerline is the centerline along the spatial twisting direction of the stellarator superconducting winding. The sides of the cutting block refer to the four vertical surfaces parallel to the winding centerline and surrounding the outer periphery of the filler layer, while the end faces of the cutting block refer to the two cross-sections formed by cutting with a parallel plane perpendicular to the winding centerline.

[0075] More specifically, the stellarator winding is generally a three-dimensional twisted strip structure, and the cut-out block is a hexahedral structure including four side faces and two end faces. For the side faces of the cut-out block, due to the multi-directional deformation in three-dimensional space, the X, Y, and Z displacements need to be fully mapped. For the end faces of the cut-out block, since they only deform along the normal direction and have no obvious relative slip in the tangential direction, only their normal degrees of freedom need to be constrained, which can avoid problems such as over-constraint, non-convergence, and stress distortion in the simulation.

[0076] Furthermore, in this method for stress analysis of superconducting magnet windings in stellarators, the deformation displacement of the cutting block corresponding to the global model is mapped to the detailed model. This includes: using a radial basis function interpolation algorithm to map the lateral, longitudinal, and vertical displacements of the side of the cutting block in the spatial coordinate system in the global model to the detailed model, and mapping the degrees of freedom of the cutting block in the normal direction at the end face in the global model to the detailed model.

[0077] Specifically, in a spatial coordinate system, lateral displacement, longitudinal displacement, and vertical displacement refer to deformation displacements in three orthogonal directions under the X, Y, and Z rectangular coordinates.

[0078] The degree of freedom of the cutting block in the normal direction of the end face refers to the displacement constraint component perpendicular to the direction of the end face tangent.

[0079] More specifically, the sides of the cutting block are used as the main boundaries for displacement mapping, and a radial basis function interpolation algorithm is employed to fully map the lateral, longitudinal, and vertical displacements of the cutting block's sides. For the two end faces of the cutting block, only the displacement degrees of freedom in the normal direction of the end faces are mapped, without constraining the tangential sliding degrees of freedom. Through these steps, the displacements of the global model cutting block boundary are assigned to the local detailed model boundary.

[0080] Furthermore, in this method for stress analysis of superconducting magnet windings applicable to stellarators, the radial basis function interpolation algorithm is used to map the lateral, longitudinal, and vertical displacements of the side surfaces of the cut blocks in the spatial coordinate system from the global model to the detailed model, including the following steps:

[0081] First, determine the reference node coordinates of all reference mesh nodes corresponding to the filling layer within the cut block in the global model, as well as the lateral, longitudinal, and vertical displacements of the reference mesh nodes in the spatial coordinate system.

[0082] Secondly, determine the coordinates of all undetermined mesh nodes corresponding to the infill layer within the cut block in the detailed model. The reference mesh nodes are known nodes on the global model after the cut and secondary multiphysics coupling, whose coordinates and displacements have been calculated on the side of the infill layer. Undetermined mesh nodes are mesh nodes on the side of the infill layer of the local detailed model that only have coordinates and no displacement assignments yet.

[0083] Next, the radial basis functions are determined. Specifically, the radial basis functions are:

[0084]

[0085]

[0086] in, Let the coordinates of the node to be determined be... ; The coordinates of the reference node are... . Let be the linear Euclidean distance between the coordinates of the node to be determined and the coordinates of the reference node.

[0087] ,in, These are Gaussian radial basis functions; The shape parameter is a key parameter controlling the influence range and decay rate of the radial basis function fitting. The spacing between any two reference mesh nodes in the global model is determined using the following method: Calculate the spacing between any two reference mesh nodes in the global model according to the following formula; and let... equal of the median.

[0088]

[0089] Next, the displacement interpolation formula is determined based on the weight coefficient corresponding to each reference grid node. Specifically, the displacement interpolation formula is:

[0090]

[0091] Let be the displacement of the grid node to be determined in the spatial coordinate system; The weighting coefficients are weighting factors that represent the contribution of each reference node to the displacement of any point to be determined in the radial basis interpolation. The weighting coefficients are determined by substituting the reference node coordinates of each reference grid node, as well as the lateral, longitudinal, and vertical displacements of the reference grid nodes in the spatial coordinate system, into the displacement interpolation formula, and obtaining the values ​​related to... Solving multiple systems of equations simultaneously yields... .

[0092] Finally, based on the coordinates of each node to be determined, the horizontal, vertical, and longitudinal displacements of each node in the spatial coordinate system are calculated using interpolation formulas.

[0093] Specifically, during displacement mapping, the surface of the cutting block needs to be divided into two parts for differentiated mapping. For the side surfaces of the cutting block corresponding to the filling layer, the displacement degrees of freedom in the X, Y, and Z directions need to be mapped. For the two end faces of the cutting block, only the displacement degrees of freedom in the normal direction of the end faces are mapped, without considering the tangential displacement, thus preventing slow convergence caused by over-constraint. Next, the X, Y, and Z coordinates corresponding to the side nodes of the cutting block, as well as the corresponding three-dimensional displacements, are derived from the quadratically coupled global model. Then, the X, Y, and Z coordinates corresponding to the side nodes of the cutting block are derived from the local detailed model. Next, a Gaussian radial basis function is constructed, and the shape parameters are adaptively determined by the median of the global node spacing. Finally, the coordinates of all reference nodes and the three-dimensional displacements in the X, Y, and Z directions are substituted into the formulas sequentially to form an N-variable, Nth-order linear equation system. The simultaneous equations are solved directly to obtain all weighted coefficients, and independent interpolation is performed in the X, Y, and Z directions respectively. Finally, the global model displacement field is interpolated and fitted to all boundary nodes of the detailed model to complete the displacement mapping assignment.

[0094] In this way, displacement mapping is performed using a radial basis function interpolation algorithm. Because the Gaussian function has good smoothness, it is suitable for the displacement field of the distorted and irregular curved surface of the stellarator.

[0095] Furthermore, in this method for stress analysis of superconducting magnet windings applicable to stellarators, the stress data are the stress data of the region of interest within the cut block.

[0096] Specifically, during subsequent engineering verification, only the areas of interest inside the cut blocks are focused on, and only the core critical areas are assessed for strength, reducing redundant data analysis.

[0097] Furthermore, in this stress analysis method applicable to the superconducting magnet windings of stellarators, the stress data includes at least one of the following: stress cloud diagrams of each layer of the winding structure inside the cutting block, stress values, the location of the maximum stress, and the stress distribution pattern.

[0098] Furthermore, in this method for stress analysis of superconducting magnet windings applicable to stellarators, after determining the stress data corresponding to the cutting block, the following steps are also included:

[0099] First, a global detailed model of the stellarator's superconducting magnet is established.

[0100] Then, the calibration stress parameters are determined based on the global detailed model.

[0101] Next, refer to Figure 4 The stress data output by the detailed model corresponding to the cutting block will be compared with the calibrated stress parameters to verify the output accuracy of the detailed model corresponding to the cutting block.

[0102] Specifically, a global detailed model refers to a full-size reference model in which the stellarator magnet is not simplified in any way, and the windings, insulation, armor, filler layer, and coil box are all modeled in detail.

[0103] The calibrated stress parameters refer to the stress values ​​and distribution patterns based on the simulation results of the global detailed model.

[0104] Comparing the stress data with the calibrated stress parameters is a comparison of the results obtained using the stress analysis method provided in this embodiment. Figure 4 (shown on the right) and global precision model benchmark results ( Figure 4 (As shown on the left), thus quantifying the error to verify the reliability of the method. Specifically, the peak stress errors of the two methods can be compared. If the error is less than 5%, it indicates that the accuracy of the stress analysis method for stellarator superconducting magnet windings provided in this embodiment meets the requirements. Alternatively, the similarity of the stress distribution patterns of the two methods can be compared. If the similarity reaches 95% or more, it indicates that the accuracy of the stress analysis method for stellarator superconducting magnet windings provided in this embodiment meets the requirements.

[0105] Figure 4 The figure shows the stress data obtained after establishing two models using a four-turn conductor as the verification object. Figure 4 The stress cloud map of the global detailed model shown on the left and the stress cloud map obtained using the analysis method of this embodiment shown on the right have the same stress concentration location and distribution height. The calculated maximum stress values ​​of the two differ by only 2%. It can be seen that the stress analysis method for stellarator superconducting magnet windings in this embodiment combines global equivalence, local fine modeling, and displacement mapping, achieving accuracy close to that of fully fine modeling while significantly reducing the amount of computation.

[0106] Example 2:

[0107] Based on the stress analysis method for stellarator superconducting magnet windings described in Embodiment 1, this embodiment provides an electronic device, including: a processor and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the stress analysis method for stellarator superconducting magnet windings as described in Embodiment 1.

[0108] Example 3:

[0109] Based on the stress analysis method for stellarator superconducting magnet windings described in Embodiment 1, this embodiment provides a computer-readable storage medium storing computer-executable instructions. When executed by a processor, the computer-executable instructions are used to implement the stress analysis method for stellarator superconducting magnet windings as described in Embodiment 1.

[0110] While the present invention has been illustrated and described with reference to certain preferred embodiments, those skilled in the art should understand that the above description is a further detailed explanation of the invention in conjunction with specific embodiments, and should not be construed as limiting the specific implementation of the invention to these descriptions. Various changes in form and detail can be made by those skilled in the art, including several simple deductions or substitutions, without departing from the spirit and scope of the invention.

Claims

1. A method for stress analysis of superconducting magnet windings in stellarators, characterized in that, include: A finite element model of a stellarator superconducting magnet is constructed; wherein, the stellarator superconducting magnet includes windings, a filler layer and a coil box stacked sequentially from the inside out; Multiphysics coupling is performed on the finite element model, and the coupled finite element model is cut to extract local regions as cutting blocks. The finite element model after the cutting process is re-coupled into multiphysics to obtain a global model; Detailed modeling is performed on the winding and the filler layer corresponding to the cutting block to obtain a detailed model; Map the deformation displacement of the cutting block corresponding to the global model to the detailed model; The detailed model after displacement mapping is solved to determine the stress data corresponding to the cutting block.

2. The method for stress analysis of superconducting magnet windings in stellarators as described in claim 1, characterized in that, The finite element model for constructing the stellarator superconducting magnet includes: The winding is equivalent to a single uniform isotropic material, and the winding is modeled equivalently. The filling layer and the coil box are actually modeled; Set the contact type between the winding and the filler layer to bonded contact; The contact type between the filling layer and the coil box is set to frictional contact.

3. The method for stress analysis of superconducting magnet windings in stellarators as described in claim 1, characterized in that, The multiphysics coupling of the finite element model includes: Multiphysics coupling of temperature field, electromagnetic field, and structural field is performed on the finite element model; and The step of cutting a local region from the finite element model as a cutting block includes: The danger zone is determined based on the finite element model after multiphysics coupling, and the cutting block is determined based on the pre-defined region of interest and the danger zone; wherein The danger zone is the area with the highest calculated stress value; The area of ​​concern is the area that needs to be verified. The cutting block is a local area that simultaneously includes the danger zone and the area of ​​interest.

4. The method for stress analysis of superconducting magnet windings in stellarators as described in claim 1, characterized in that, The cutting block includes a side surface parallel to the winding centerline and two end faces perpendicular to the winding centerline; and Mapping the deformation displacement of the cut block corresponding to the global model to the detailed model includes: The radial basis function interpolation algorithm is used to map the lateral, longitudinal, and vertical displacements of the side of the cutting block in the spatial coordinate system in the global model to the detailed model, and the degrees of freedom of the cutting block in the normal direction of the end face in the global model are mapped to the detailed model.

5. The method for stress analysis of superconducting magnet windings in stellarators as described in claim 4, characterized in that, The step of mapping the lateral, longitudinal, and vertical displacements of the side surfaces of the cutting block in the global model to the detailed model using a radial basis function interpolation algorithm includes: Determine the reference node coordinates of all reference mesh nodes corresponding to the filling layer within the cut block in the global model, as well as the lateral, longitudinal, and vertical displacements of the reference mesh nodes in the spatial coordinate system; Determine the coordinates of all the mesh nodes to be determined in the detailed model and the filling layer corresponding to the cut block; Determine the radial basis functions; The displacement interpolation formula is determined based on the weight coefficient corresponding to each of the reference grid nodes; Based on the coordinates of each node to be determined, the interpolation formula is used to calculate the lateral, longitudinal, and vertical displacements of each node in the spatial coordinate system.

6. The method for stress analysis of superconducting magnet windings in stellarators as described in claim 5, characterized in that, The radial basis function is: in, Let be the coordinates of the node to be determined. ; The coordinates of the reference node are... ; The linear Euclidean distance between the coordinates of the node to be determined and the coordinates of the reference node; ,in, These are Gaussian radial basis functions; The shape parameter is determined by calculating the spacing between any two reference mesh nodes in the global model according to the following formula; And order equal the median; The displacement interpolation formula is as follows: Let be the displacement of the grid node to be determined in the spatial coordinate system; The weighting coefficients are determined according to the following method: Substituting the coordinates of each reference grid node, along with its lateral, longitudinal, and vertical displacements in the spatial coordinate system, into the displacement interpolation formula, we obtain the following information: Solving a system of multiple equations simultaneously yields... .

7. The method for stress analysis of superconducting magnet windings in stellarators as described in claim 3, characterized in that, The stress data is the stress data of the region of interest within the cutting block; The winding includes, from the inside out, a cable, an armor, a turn insulation layer, and a ground insulation layer stacked sequentially. and The stress data includes at least one of the following: stress cloud diagram, stress value, location of maximum stress, and stress distribution pattern of each layer of the winding structure inside the cutting block.

8. The method for stress analysis of superconducting magnet windings in stellarators as described in any one of claims 1-7, characterized in that, After determining the stress data corresponding to the cutting block, the process also includes: Establish a global detailed model of the superconducting magnet of the stellarator; The calibration stress parameters are determined based on the global detailed model. The stress data output by the detailed model corresponding to the cutting block is compared with the calibrated stress parameters to verify the output accuracy of the detailed model corresponding to the cutting block.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes the computer execution instructions stored in the memory to implement the stress analysis method for stellarator superconducting magnet windings as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the stress analysis method for stellarator superconducting magnet windings as described in any one of claims 1-8.

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