A method for mechanical modeling and analysis of superconducting magnets

Abstract

The application belongs to the field of superconducting magnet design, and relates to a superconducting magnet mechanical modeling analysis method, comprising the following steps: constructing a superconducting magnet material structure model, solving thermal stress and electromagnetic stress generated in the process of magnet cooling and operation, and analyzing the most dangerous area of stress in the magnet; constructing a material structure model of the coil in the dangerous area, solving the winding stress and thermal stress caused by cooling, taking the thermal stress as a prestress to solve the electromagnetic stress of the coil in operation, and analyzing the position of the strip with the largest stress; constructing a strip mechanical model, inputting the circumferential stress and radial stress of each layer of the strip with the largest stress in the superconducting coil as loads, taking the stress and strain of the inner and outer strips of the superconducting coil on the strip to be studied as constraints, solving the stress of the strip, and analyzing the delamination and tearing along the length direction of the strip. The application uses the superconducting coil mechanical model as a bridge to realize detection and evaluation of the mechanical failure of a single superconducting strip and the overall failure of the performance of the superconducting magnet.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of superconducting magnet design, and more particularly relates to a superconducting magnet mechanical modeling analysis method. BACKGROUND

[0002] With the development of technology and the increase of demand, the application of superconducting power technology is becoming more and more widespread, among which the application of superconducting magnets is the most extensive and the most effective. Superconducting magnets have the advantages of low energy consumption, high field strength, good uniformity and stability, etc., and play an important role in superconducting power engineering.

[0003] During the entire use of the superconducting magnet, it will bear thermal stress and electromagnetic stress caused by periodic processes such as cooling and excitation, and the intensity and frequency of which will affect the stable operation of the magnet. Once the stress intensity exceeds the allowable strength of the support material of the superconducting magnet, it will cause serious damage to the structure of the magnet. In addition, it is found in the development process of YBCO high-temperature superconducting magnets that the mechanical failure of the superconducting tape is closely related to the degradation of the performance of the magnet, especially the interlayer stress in the coil plays an important role in the safe and stable operation of the magnet.

[0004] Accurate mechanical modeling of the magnet and the tape, analysis of the force and electrical characteristics of a single high-temperature superconducting tape and the stress condition of the magnet structure, has important significance for the key preparation of the second-generation high-temperature superconducting magnet, such as strength optimization, reliability prediction, avoiding potential damage risk and improving the service life of the magnet, and is the technical basis for the development of the next generation of high-temperature superconducting motors, superconducting energy storage magnets and other equipment.

[0005] However, the current technology has the following defects: in terms of the correlation between the mechanical characteristics of a single tape and the mechanical properties of the magnet, especially the detection, analysis and evaluation of the mechanical failure of a single tape and the overall failure of the magnet performance caused by interlayer stress, there is still a lack of systematic and bottom-up overall research. SUMMARY

[0006] In view of the defects and improvement needs of the prior art, the present application provides a superconducting magnet mechanical modeling analysis method, which aims to realize the detection and evaluation of the mechanical failure of a single superconducting tape and the overall failure of the performance of a superconducting magnet.

[0007] To achieve the above purpose, according to one aspect of the present application, a superconducting magnet mechanical modeling analysis method is provided, comprising:

[0008] S1, based on the material and structural parameters of the superconducting magnet to be analyzed, a two-dimensional axisymmetric structure model of the superconducting magnet is constructed, mechanical material properties are added to the model to obtain a superconducting magnet structure model with added mechanical material properties; a solid mechanics module and a magnetic field module are added to the superconducting magnet structure model, the thermal stress and thermal strain of the superconducting magnet in the cooling process are solved, the thermal stress and thermal strain are correspondingly taken as prestress and prestrain, the stress of the superconducting magnet in the running process after cooling is solved, which is taken as an electromagnetic-thermal comprehensive stress, to determine the coil that bears the maximum stress and as a dangerous area coil;

[0009] S2, based on the material and structural parameters of the dangerous area coil, a two-dimensional axisymmetric structure model of the dangerous area coil is constructed, mechanical material properties are added to the model to obtain a dangerous area coil structure model with added mechanical material properties; a solid mechanics module and a magnetic field module are added to the dangerous area coil structure model, the winding stress is solved, the winding stress is taken as the pre-stress, the thermal stress is solved; the thermal stress is taken as the pre-stress to solve the stress of the dangerous area coil, which is taken as a comprehensive stress including winding stress, thermal stress, electromagnetic stress and the radial and circumferential stress of each turn of the coil, to determine the position of the tape that bears the maximum comprehensive stress as the dangerous tape position;

[0010] S3, based on the material and structural parameters of one of the turns of tape at the dangerous tape position, a three-dimensional structure model of one superconducting tape is constructed, mechanical material parameters are added to the model to obtain a dangerous tape structure model; a solid mechanics module is added to the dangerous tape structure model, the radial and circumferential stress of the one of the turns of tape is set as the tape boundary condition, to verify whether the tape at the dangerous tape position will delaminate due to interlayer normal stress and tear along the length direction due to axial stress.

[0011] The beneficial effects of the present application are: the present application determines the coil that bears the maximum stress as the dangerous area coil from the superconducting magnet material structure modeling and mechanical modeling, further constructs the material structure model and mechanical model of the dangerous area coil, calculates the comprehensive stress including the radial and circumferential stress of each turn of the coil, determines the position of the tape that bears the maximum comprehensive stress as the dangerous tape position, and further establishes the material structure model and mechanical model of one of the turns of tape at the dangerous tape position, takes the radial and circumferential stress of the turn of tape calculated in the foregoing as the tape boundary constraint, to verify whether the tape will delaminate due to interlayer normal stress and tear along the length direction due to axial stress. The present application analyzes layer by layer from three levels, can accurately solve and calculate the winding stress, thermal stress, electromagnetic stress, tape interlayer stress and other stresses of the superconducting magnet in the running process, completes the mechanical dangerous area analysis of the superconducting magnet, superconducting coil and superconducting tape in all aspects and multiple dimensions, designs the magnet structure meeting the mechanical requirements, and is a perfect superconducting magnet mechanical analysis process.

[0012] Further, in the S1, when constructing the superconducting magnet structure model, the homogeneous modeling is adopted, and the equivalent multi-layer material composite material is a single-layer uniform material.

[0013] Further beneficial effects of the application are: constructing a homogeneous model, considering that the thickness of the superconducting layer, the buffer layer and the silver layer is extremely small, and the width-thickness ratio is extremely large, which will lead to poor grid quality and great calculation difficulty in subsequent grid division, so in the macro modeling of the superconducting magnet, the multi-layer composite material is equivalent to a single-layer uniform material, which improves the calculation efficiency of the model.

[0014] Further, in the S1, the implementation mode of the cooling process is:

[0015] The thermal expansion link is set, the volume reference temperature is set to the ambient temperature, and the temperature is simulated in the form of parameterized scanning to simulate the cooling process.

[0016] Further beneficial effects of the application are: using the thermal expansion link and the parameterized scanning method to replace the solid heat transfer module, the temperature change of the cooling process is discretized into multiple points in the form of parameterized scanning, and the steady state of each point in the cooling stage is studied, which can improve the calculation efficiency and simplify the complexity of the mechanical model.

[0017] Further, in the S2, when constructing the refined two-dimensional axisymmetric model, the longitudinal axis symmetry and the upper and lower axis symmetry of the coil are utilized to construct a quarter refined two-dimensional model.

[0018] Further beneficial effects of the application are: using the axis symmetry of the coil to simplify the superconducting coil model, reduce the difficulty of solving, and improve the solving efficiency.

[0019] Further, in the S2, when adding the mechanical material properties to the model, the materials of the Hastelloy base layer and the copper layer are empty materials, the Young's modulus and the initial yield stress data of each material at the existing temperature are obtained by interpolation fitting, and the corresponding coefficient interpolation function is obtained, the variable is temperature T, which is used to determine the Young's modulus and the initial yield stress of the Hastelloy base layer and the copper layer after the superconducting magnet undergoes the cooling process.

[0020] Further beneficial effects of the application are: for the Hastelloy base layer and the copper layer, part of the mechanical material properties changes with temperature, and this interpolation method can improve the accuracy of the model and make the calculation results more consistent with the actual situation.

[0021] Further, in the S2, when solving each stress, the network division mode of the coil structure model in the dangerous area is:

[0022] The superconducting layer, buffer layer, base layer and silver layer in the superconducting tape are divided by mapping, and the superconducting layer is further finely divided by using the required superconducting layer grid density; the copper layer, epoxy resin layer, polyimide layer and air domain are divided by using free triangular grid division.

[0023] Further beneficial effects of the present application are that this way of dividing the grid can improve the solving efficiency under the premise of ensuring the accuracy of the calculation results.

[0024] Further, in the S3, the stresses and strains of the inner and outer sides of the tape with the maximum comprehensive stress in the dangerous area coil structure model are extracted as constraint conditions added to the upper and lower sides of the refined three-dimensional structure model of the superconducting tape, and the interlayer normal stress and axial stress of the tape in the dangerous area coil structure model are calculated.

[0025] Further beneficial effects of the present application are that the method connects the superconducting coil model and the superconducting tape model, provides a basis for the mechanical constraint of the tape model, and improves the stress solving accuracy of the tape model.

[0026] The present application also provides a computer readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls the device where the storage medium is located to perform the above-mentioned superconducting magnet mechanical modeling and analysis method.

[0027] Overall, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0028] The present application determines the most dangerous area coil which bears the maximum stress from the superconducting magnet material structure modeling and mechanical modeling, further models the material structure and mechanical model of the dangerous area coil, calculates the comprehensive stress including the radial and circumferential stresses of each turn of the coil, and determines the position of the tape with the maximum comprehensive stress as the dangerous tape position, further establishes the material structure model and mechanical model of a single superconducting tape in the dangerous tape position, and uses the radial and circumferential stresses of the turn of the tape calculated in the foregoing as the boundary constraint of the tape to check whether the tape will delaminate due to the interlayer normal stress and tear along the length direction due to the axial stress. The present application constructs a systematic and multi-dimensional superconducting magnet mechanical analysis process, uses the mechanical model of the superconducting coil as a bridge to detect, analyze and evaluate the mechanical failure of a single superconducting tape and the overall failure of the superconducting magnet, which is of great significance to ensure the stable operation of the superconducting magnet, and can be used for designing a magnet structure meeting the mechanical requirements. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 A superconducting magnet mechanical modeling and analysis method flow chart is provided for the embodiments of the present application.

[0030] Figure 2 This is a schematic diagram of the YBCO layered ribbon structure in a superconducting magnet.

[0031] Figure 3 A schematic diagram of a disc-shaped coil wound from strip material and its stress state;

[0032] Figure 4 This is a framework diagram of a mechanical modeling and analysis method for superconducting magnets provided in an embodiment of the present invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0034] Example 1

[0035] A method for mechanical modeling and analysis of superconducting magnets, such as Figure 1 As shown, it includes:

[0036] S1. Material structure modeling and mechanical modeling of superconducting magnets

[0037] Material structure modeling of superconducting magnets: Obtain the material and structural parameters of the superconducting magnet to be analyzed, construct a two-dimensional axisymmetric structural model of the superconducting magnet, and add corresponding mechanical and material properties to each part of the model to obtain a superconducting magnet structural model with added mechanical and material properties; wherein, the two-dimensional axisymmetric structural model represents the geometric structure and support structure of the superconducting magnet.

[0038] Superconducting magnet mechanical modeling: Solid mechanics and magnetic field modules are added to the superconducting magnet structural model that already has mechanical material properties to solve for the thermal stress and thermal strain of the superconducting magnet during the cooling process. Thermal stress and thermal strain are used as prestress to solve for the stress experienced by the superconducting magnet during operation after the cooling process, which is considered as the electromagnetic-thermal combined stress, including the stress distribution, magnitude, and direction experienced by the superconducting magnet. Based on this combined stress, the coil bearing the highest stress is identified. Further analysis is then conducted on this coil bearing the highest stress.

[0039] S2. Refined material structure modeling and mechanical modeling of superconducting coils

[0040] Refined material structure modeling of superconducting coils: The coil bearing the greatest stress is taken as the dangerous region coil. The material and structural parameters of the dangerous region coil are obtained. A refined two-dimensional axisymmetric model of the characterizing geometry and support structure of the dangerous region coil is constructed. Corresponding mechanical and material properties are added to each part of the model to obtain the dangerous region coil structure model with added mechanical and material properties.

[0041] Refined mechanical modeling of superconducting coils: Add solid mechanics and magnetic field modules to the coil structure model in the dangerous area that has already been added with mechanical material properties, solve for winding stress, treat the winding stress as prestress, solve for thermal stress, treat the solved thermal stress as prestress, solve for the stress on the coil in the dangerous area, and use it as a comprehensive stress including winding stress, thermal stress, electromagnetic stress, and radial and circumferential stress of each turn of the coil strip to determine the location of the strip with the greatest comprehensive stress;

[0042] S3. Layered material structure modeling and layered mechanical modeling of superconducting tapes.

[0043] Superconducting tape layered material structure modeling: Obtain the structural and mechanical material parameters of one turn of the tape at the location of the tape with the greatest comprehensive stress on the coil in the dangerous area, construct a refined three-dimensional structural model of a superconducting tape, and add corresponding mechanical material parameters to the material of each layer of the model tape;

[0044] Delamination mechanical modeling of superconducting tape: A solid mechanics module is added to the refined three-dimensional structural model of the superconducting tape mentioned above. The radial and circumferential stresses of one turn of the superconducting tape at the location of the tape with the greatest comprehensive stress on the dangerous area coil are set as the boundary conditions of the tape. The method is to verify whether the tape at the dangerous location will delaminate due to interlayer normal stress and tear along the length direction due to axial stress.

[0045] The following is a description of this implementation method:

[0046] (1) In each of the above steps, when adding material properties, add them according to mechanical needs, such as Young's modulus, Poisson's ratio, coefficient of thermal expansion, initial yield stress, isotropic tangent modulus and other parameters, reduce unused material property definitions and simplify the model.

[0047] The resistivity of the superconducting magnet can be established according to the EJ pow law, and the relationship is as follows:

[0048]

[0049] In this context, Ec is the critical quench criterion, and J... c (B,T,ε) represents the critical current density of the strip. Factors affecting the critical current density include magnetic induction intensity, temperature, and stress, and n represents the superconductivity index.

[0050] (2) When calculating the comprehensive stress in each of the above steps, a step-by-step calculation is adopted. For example, in S1 above, the first step is to solve for the thermal residual strain and thermal stress caused by the cooling process, and the second step is to solve for the electromagnetic stress. The pre-strain and pre-stress solved in the first step are used as constraints to obtain the electromagnetic-thermal comprehensive stress generated by the superconducting magnet flowing through the background magnetic field after cooling. This partial decoupling of the solution process for thermal stress and electromagnetic stress is consistent with the actual operation of the superconducting magnet and improves the accuracy of the calculation.

[0051] Additionally, for S1, after adding a solid mechanics module and a magnetic field module to the already added mechanical material properties of the dangerous area coil structure model, the magnet is set as a linear elastic material; a plasticity condition is added to prevent the stress-strain relationship from remaining linear after the material exceeds its yield strength, thus distorting the model. The principle of solving the superconducting magnet's mechanics in two-dimensional cylindrical coordinates is as follows:

[0052] The mechanical equilibrium equations of a superconducting magnet are:

[0053]

[0054] In the formula, σ is the normal stress, τ is the shear stress, and f is the load.

[0055] The formulas for calculating strain in each direction are:

[0056]

[0057] In the formula, ε is normal strain, γ is shear strain, u is radial displacement, and w is axial displacement.

[0058] The components of each strain are:

[0059]

[0060] All three formulas above are applicable to both elastic and plastic deformation. The superscript e indicates the elastic deformation component, the superscript p indicates the plastic deformation component, and the superscript th indicates the thermal strain component.

[0061] For S2, when performing mechanical modeling, add a solid mechanics module and a magnetic field module. The magnetic field module can add an axial background magnetic field, set an ideal magnetic conductor constraint for the axis of symmetry, set the coil type to a single-conductor coil group, and allow current flow through the superconducting layer. The solid mechanics module can set the coil to a linear elastic material, add thermal expansion elements, plastic conditions, prestress and prestrain constraints, select the superconducting layer in the superconducting coil as the volume load, set the load type to force per unit volume, and select Lorentz force contribution. The specified displacement is set to 0 in the inner r direction.

[0062] Two studies were set up to simulate the magnet cooling process and the flow under the back field, respectively. Study 1 was set as steady state, with the magnet cooling temperature set as the parameter, using parametric scanning, solid mechanics as the physical field, and physical field control as the dependent variable. Study 2 was set as steady state, with solid mechanics and magnetic field as the physical fields, and user control as the dependent variable value. The solution of Study 1 was used as the known conditions and constraints of Study 2.

[0063] Simplified diagram of strip structure as follows Figure 2 As shown, the coil structure is simplified as follows: Figure 3 As shown, the main directions of force on the coil are radial and circumferential, and the main sources of force are thermal stress, electromagnetic stress, and winding stress.

[0064] Thermal stress: During the coil cooling process, the different materials in each layer have different coefficients of thermal expansion and different degrees of shrinkage. The tightly bonded layers interact to generate thermal stress and strain in the circumferential and radial directions. The expression for thermal strain is:

[0065] ε th =[α r ΔT α θ ΔT α z ΔT 0] T ;

[0066] In the formula, α r α θ α z ΔT represents the coefficients of thermal expansion in the radial, circumferential, and axial directions, and ΔT represents the cooling temperature.

[0067] Electromagnetic stress: When current flows through a superconducting coil, the superimposed magnetic field of the background magnetic field and the self-field generates an electromagnetic force, which mainly acts in the radial direction of the coil. The expression is as follows:

[0068]

[0069] In the formula, J θ B is the circumferential current density introduced into the superconducting layer. r and B z This is to superimpose the radial and axial components of the magnetic field.

[0070] Winding stress: During the winding process of the superconducting coil, a certain preload is applied to the inner and outer strips to reduce the influence of the epoxy resin layer's instability at low temperatures. Neglecting shear stress and axial preload, the radial stress differential equation and its general solution are obtained as follows:

[0071]

[0072]

[0073] In the formula, E is Young's modulus.

[0074] Based on the radial stress equation, the stress boundary conditions on the inner and outer sides of the coil can be obtained.

[0075]

[0076]

[0077] In the formula, d is the strip thickness, ν is Poisson's ratio, and σ is... p It is the winding preload along the length of the strip, which is assumed to be uniformly distributed across the coil cross-section.

[0078] The radial stress solution can be obtained from the boundary conditions. Solving for the winding stress is an additive process. The winding stress borne by a certain layer of strip is the superposition of the stress of all the outer strips, as shown below.

[0079]

[0080] In the formula, σ rw,i and σ θw,i These represent the radial winding stress and circumferential winding stress on the i-th turn of the coil after winding, respectively. The circumferential winding stress also needs to be increased by the winding preload of the strip itself.

[0081] In the above S2, when solving for the comprehensive stress, the comprehensive stress includes the radial and circumferential stresses of each turn of the coil strip. The solved radial and circumferential stresses can be used as constraints and loads for the next step of mechanical analysis of a single strip, which can prepare for further analysis of strip delamination and tearing along the length direction.

[0082] Regarding S3, when modeling the layered material structure of superconducting tapes, each layer of the tape is constructed separately. The method for adding temperature-related mechanical parameters is the same as that for modeling the material structure of superconducting coils. Constructing a three-dimensional model is beneficial for analyzing the tape delamination phenomenon that may be caused by interlayer stress.

[0083] When modeling the layered mechanics of superconducting tape, a solid mechanics module is added to set tape constraints. The stress and strain on the inner and outer sides of the tape in the coil mechanics model are extracted and added as constraints on both sides of the tape model. The radial and circumferential combined stresses of each layer of the tape in the coil mechanics model are extracted and applied as loads to each layer of the tape.

[0084] Contact pairs are created between the layers with the highest stress. The focus is on analyzing whether delamination will occur. The delamination strength of the strip is about an order of magnitude lower than the longitudinal tensile strength because the tensile stress along the strip direction can be borne by the stronger base layer. However, the superconducting layer and buffer layer next to the alloy base layer are brittle ceramic materials. Under the action of interlayer stresses such as tension and peeling, the superconducting layer and buffer layer will fail before the alloy base layer, making the strip prone to delamination. Contact links are set up in the solid mechanics module, adhesion and peeling conditions are added, adhesion activation criteria and adhesion stiffness are defined, and the peeling cohesion model is defined as displacement-based damage.

[0085] This allows us to verify whether the combined radial and circumferential stresses acting on the coils in a superconducting magnet, when applied to each turn of the superconducting tape, will cause delamination or tearing along its length.

[0086] (3) In S3, a three-dimensional refined strip model can be constructed to visualize the tearing and delamination of the strip, which is beneficial for more intuitive analysis of the mechanical situation.

[0087] In summary, this embodiment's method begins with modeling the superconducting magnet's material structure and mechanics. It identifies the coil experiencing the highest stress as the most dangerous region, then models the material structure and mechanics of this dangerous region coil, calculating the combined stress, including radial and circumferential stresses on each turn of the coil strip. The location of the strip experiencing the highest combined stress is then identified as the dangerous strip location. Furthermore, a material structure and mechanics model of a single turn of the superconducting strip within this dangerous location is established. The calculated radial and circumferential stresses of this turn are used as boundary constraints to verify whether the strip will delaminate due to interlayer normal stress or tear along its length due to axial stress. This invention provides a refined analysis at three levels, accurately calculating the winding stress, thermal stress, electromagnetic stress, and interlayer stress experienced by the superconducting magnet during operation. It comprehensively and multidimensionally analyzes the mechanically dangerous regions of the superconducting magnet, superconducting coil, and superconducting strip, designing a magnet structure that meets mechanical requirements. This constitutes a complete superconducting magnet mechanics analysis process.

[0088] As a preferred implementation, when constructing a superconducting magnet structure model with added mechanical material properties, homogenization modeling is adopted, and the equivalent multilayer composite material is a single-layer homogeneous material.

[0089] To construct a homogenized model, considering the extremely small thickness and high aspect ratio of the superconducting layer, buffer layer, and silver layer, subsequent mesh generation would result in poor mesh quality and high computational difficulty. Therefore, in the macroscopic modeling of the superconducting magnet, the multilayer composite material is equated to a single-layer homogeneous material to improve the model's computational efficiency. In other words, this approach, performing calculations at the macroscopic level of the magnet, reduces the requirements for mesh size generation, decreases the solution difficulty, and improves solution efficiency.

[0090] As a preferred embodiment, in the above S1, the cooling process is implemented by setting a thermal expansion stage and setting the volume reference temperature to the ambient temperature, and simulating the cooling process by using a parametric scanning method for the temperature.

[0091] By using the thermal expansion element and parametric scanning method to replace the solid heat transfer module, the temperature change during the cooling process is discretized into multiple points. By studying the steady-state situation of each point corresponding to the cooling stage, the computational efficiency can be improved and the complexity of the mechanical model can be simplified.

[0092] As a preferred implementation, in the above S2, when constructing a refined two-dimensional axisymmetric model, the longitudinal axisymmetric and vertical axisymmetric of the coil are used to construct a quarter-refined two-dimensional model.

[0093] By utilizing the axisymmetry of the coil, the superconducting coil model is simplified, reducing the difficulty of the solution and improving the solution efficiency.

[0094] As a preferred embodiment, in S2 above, when adding corresponding mechanical material properties to each part of the model, the materials for adding the Hastelloy base layer and copper layer are empty materials. The Young's modulus and initial yield stress data of each material at the existing temperature are used to obtain the interpolation function with corresponding coefficients through interpolation fitting. The variable is temperature T, which is used to determine the Young's modulus and initial yield stress of the Hastelloy base layer and copper layer at the temperature after the superconducting magnet has undergone the cooling process.

[0095] For the Hastelloy base layer and copper layer, some mechanical material properties change with temperature. Sampling this interpolation method can improve the accuracy of the model and make the calculation results more consistent with the actual situation.

[0096] As a preferred embodiment, in S2 above, the method for dividing the coil structure model in the critical area into a network when solving for each stress is as follows:

[0097] The superconducting layer, buffer layer, substrate layer and silver layer in the superconducting tape are partitioned by mapping. The superconducting layer is further refined by using the required superconducting layer mesh density. The copper layer, epoxy resin layer, polyimide layer and air domain are partitioned by free triangular mesh.

[0098] This method of meshing can improve solution efficiency while ensuring the accuracy of calculation results.

[0099] As a preferred implementation, in S3 above, the stress and strain on the inner and outer sides of the strip with the highest comprehensive stress in the coil structure model of the hazardous region are extracted and added as constraints to the upper and lower sides of the refined three-dimensional structural model of the superconducting strip. The interlayer normal stress and axial stress of the strip in the coil structure model of the hazardous region are then calculated. This method connects the superconducting coil model and the superconducting strip model, providing a basis for the mechanical constraints of the strip model and improving the accuracy of stress calculation in the strip model.

[0100] In general, such as Figure 4 As shown, this invention discloses a method for mechanical modeling and analysis of superconducting magnets, including: constructing a material structure model of the superconducting magnet, adding material mechanical properties, solving for the thermal stress and electromagnetic stress generated during the cooling and operation of the magnet, and analyzing the dangerous area with the greatest stress in the magnet; constructing a material structure model of the superconducting coil in the dangerous area of ​​the magnet, adding material mechanical properties layer by layer, solving for the coil winding stress and the thermal stress caused by cooling, using these as prestresses to solve for the electromagnetic stress during coil operation, and analyzing the location of the strip with the greatest stress; constructing a mechanical model of the superconducting strip, using the circumferential and radial stresses of each layer of the strip with the greatest stress in the superconducting coil as load inputs, using the stresses of the inner and outer strips of the superconducting coil as constraints, solving for the stress on the strip, and analyzing the strip delamination and tearing along the length direction. This invention constructs a systematic, multi-dimensional mechanical analysis process for superconducting magnets. Using the mechanical model of superconducting coils as a bridge, it detects, analyzes, and evaluates the mechanical failure of a single superconducting tape and the overall performance failure of the superconducting magnet. This is of great significance for ensuring the stable operation of superconducting magnets and can also be used to design magnet structures that meet mechanical requirements.

[0101] Example 2

[0102] The present invention also provides a computer-readable storage medium comprising a stored computer program, wherein, when the computer program is executed by a processor, it controls the device where the storage medium is located to perform a superconducting magnet mechanical modeling and analysis method as described above.

[0103] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.

[0104] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for mechanical modeling and analysis of superconducting magnets, characterized in that, include: S1. Based on the material and structural parameters of the superconducting magnet to be analyzed, a two-dimensional axisymmetric structural model of the superconducting magnet is constructed. Mechanical material properties are added to this model to obtain a superconducting magnet structural model with added mechanical material properties. Solid mechanics and magnetic field modules are added to the superconducting magnet structural model to solve the thermal stress and thermal strain of the superconducting magnet during the cooling process. The thermal stress and thermal strain are used as prestress and prestrain respectively to solve the stress on the superconducting magnet during operation after cooling. This stress is used as the electromagnetic-thermal combined stress to determine the coil with the greatest stress and as the coil in the danger zone. S2. Based on the material and structural parameters of the coil in the hazardous area, construct a two-dimensional axisymmetric structural model of the coil in the hazardous area. Add mechanical material properties to this model to obtain a structural model of the coil in the hazardous area with added mechanical material properties. Add a solid mechanics module and a magnetic field module to the structural model of the coil in the hazardous area to solve for the winding stress. Use the winding stress as prestress to solve for the thermal stress. Use the thermal stress as prestress to solve for the stress on the coil in the hazardous area. The combined stress includes the winding stress, thermal stress, electromagnetic stress, and the radial and circumferential stresses of each turn of the coil strip. Use this combined stress to determine the location of the strip with the greatest combined stress, which is the location of the hazardous strip. S3. Based on the material and structural parameters of one turn of the strip at the location of the dangerous strip, construct the material of each layer of the strip, and construct a three-dimensional structural model of a superconducting strip. Add corresponding mechanical material parameters to the material of each layer of the model strip to obtain the structural model of the dangerous strip. Add a solid mechanics module to the structural model of the dangerous strip, set the radial and circumferential stresses of one turn of the strip as the boundary conditions of the strip, extract the radial and circumferential combined stresses of each layer of the strip in the coil mechanics model, and apply them as loads to each layer of the strip. Create contact pairs between the layers with the greatest stress, and focus on analyzing whether delamination will occur. Verify whether the strip at the location of the dangerous strip will delaminate due to interlayer normal stress and tear along the length direction due to axial stress. In step S3, the stress and strain on the inner and outer sides of the strip with the greatest comprehensive stress in the coil structure model of the dangerous area are extracted and added as constraints to the upper and lower sides of the refined three-dimensional structure model of the superconducting strip, and the interlayer normal stress and axial stress of the strip in the coil structure model of the dangerous area are calculated.

2. The method for mechanical modeling and analysis of superconducting magnets according to claim 1, characterized in that, In S1, when constructing the superconducting magnet structure model, homogenization modeling is adopted, and the equivalent multilayer material composite material is a single-layer homogeneous material.

3. The method for mechanical modeling and analysis of superconducting magnets according to claim 1, characterized in that, In step S1, the cooling process is implemented as follows: A thermal expansion stage is set up, and the volume reference temperature is set to the ambient temperature. The temperature is simulated using a parametric scanning method to simulate the cooling process.

4. The method for mechanical modeling and analysis of superconducting magnets according to claim 1, characterized in that, In S2, when constructing a refined two-dimensional axisymmetric model, the longitudinal axisymmetric and vertical axisymmetric properties of the coil are used to construct a quarter-refined two-dimensional model.

5. The method for mechanical modeling and analysis of superconducting magnets according to claim 1, characterized in that, In S2, when adding mechanical material properties to the model, the materials for the Hastelloy base layer and copper layer are empty materials. The Young's modulus and initial yield stress data of each material at the existing temperature are used. Interpolation fitting is performed to obtain the interpolation function with corresponding coefficients. The variable is temperature T, which is used to determine the Young's modulus and initial yield stress of the Hastelloy base layer and copper layer at the temperature after the superconducting magnet has undergone the cooling process.

6. The method for mechanical modeling and analysis of superconducting magnets according to claim 1, characterized in that, In S2, when solving for each stress, the method for dividing the coil structure model in the critical area into a network is as follows: The superconducting layer, buffer layer, substrate layer and silver layer in the superconducting tape are partitioned by mapping. The superconducting layer is further refined by using the required superconducting layer mesh density. The copper layer, epoxy resin layer, polyimide layer and air domain are partitioned by free triangular mesh.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed by a processor, it controls the device where the storage medium is located to perform a superconducting magnet mechanical modeling and analysis method as described in any one of claims 1 to 6.

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