Method for analyzing stress distribution in winding process of high-temperature superconducting coil

Abstract

The invention relates to the technical field of high-temperature superconducting coils, and provides a method for analyzing stress distribution in a high-temperature superconducting coil winding process, which comprises the following steps of: S1, establishing a skeleton model and setting material parameters; s2, applying a boundary load to the skeleton model and carrying out stress analysis to obtain a stress distribution result of the skeleton model for winding a first turn of coil; s3, a coil model is established, material parameters are set, the number of turns of the coil model is i, and i = 1; s4, applying a boundary load to the coil model and performing stress analysis to obtain a stress distribution result of the coil model when the (i + 1) th turn of coil is wound; s5, controlling the coil model to carry out iteration from i = 2 to i = N-1 through an external program; and S6, obtaining a final stress distribution result of the coil model. According to the method, the thought of the disassembly winding process and the finite element analysis method are combined, the coil model is controlled through an external program to carry out iteration, and the winding stress solution of the irregular coil with multiple turns is met.

Description

Technical Field

[0001] The present application relates to the technical field of high-temperature superconducting coils, and in particular to a method for analyzing stress distribution during the winding process of a high-temperature superconducting coil. Background Art

[0002] During the preparation and operation of high-temperature superconducting coils, such as REBCO (Rare-Earth-Barium-Copper-Oxide) coils, complex stresses and strains will be generated inside the coils. For REBCO high-temperature superconducting tapes, if the stress exceeds the threshold, damage will occur. Once damage occurs, its superconductivity will drop significantly. Therefore, detailed stress analysis of the coils is of great significance for protecting the coils.

[0003] The winding stress generated by the application of winding tension during coil winding is a difficult point in coil stress analysis. Existing analysis methods include analytical analysis method, life and death unit method, etc. Among them:

[0004] For the analytical method, it is necessary to obtain the stress distribution through mathematical derivation. For most non-circular coils, it is impossible to solve the stress distribution expression through the stress control equation. Therefore, the scope of application of this method is very small, and it is almost only applicable to circular coils. Currently, there are only cases for circular coils.

[0005] For the birth-death unit method (a type of finite element method), it is necessary to perform multi-layer modeling according to the number of coil turns and set the inter-layer contact during modeling, which is more troublesome for coils with multiple turns. In addition, the initial stress or initial strain of each layer needs to be calculated in advance or confirmed through iterative search. This process is very complicated for coils with irregular shapes. Currently, there are only cases for circular coils with few turns (10-20 turns).

[0006] Therefore, how to provide an analysis method for stress distribution during the winding process of a high-temperature superconducting coil that can solve the winding stress of multi-turn (thousands of turns) and irregular coils has become a technical problem that technical personnel in this field urgently need to solve. Summary of the invention

[0007] The purpose of this application is to provide an analysis method for stress distribution during the winding process of a high-temperature superconducting coil, which can satisfy the winding stress solution of a multi-turn (thousands of turns) and irregular coil.

[0008] In order to solve the above technical problems, the present application provides a method for analyzing stress distribution during the winding process of a high-temperature superconducting coil, comprising the following steps:

[0009] Step S1: establishing a skeleton model and setting material parameters of the skeleton model;

[0010] Step S2: applying a boundary load to the skeleton model, and performing a finite element stress analysis on the skeleton model to obtain a stress distribution result of the skeleton model when the first turn of the coil is wound;

[0011] Step S3: Establish a coil model and set material parameters of the coil model, wherein the coil model is fitted onto the skeleton model, and the number of turns of the coil model is i, i=1;

[0012] Step S4: applying a boundary load to the coil model, and performing finite element stress analysis on the coil model to obtain a stress distribution result of the coil model when the i+1th turn of the coil is wound;

[0013] Step S5: controlling the coil model to iterate from i=2 to i=N-1 through an external program, where N is the total number of turns of the coil model, and repeating step S4 in each iteration process;

[0014] Step S6: comprehensively obtaining the final stress distribution result of the coil model by comprehensively analyzing the stress distribution result of the coil model when each turn of the coil is wound.

[0015] The stress distribution analysis method of the high-temperature superconducting coil winding process of the present embodiment combines the calculation idea of ​​disassembling the winding process with the advantage of the finite element method that can calculate the complex structure coil, and divides the winding process of the coil in the coil model into multiple parts according to the number of turns, each part corresponds to a finite element model, that is, the dynamic change of the model is realized by the step-by-step modeling method; at the same time, the effect of winding the first turn or winding the i+1th turn of the coil is simulated by applying a boundary load to the skeleton model or the coil model with i turns of the coil, and the application of the winding tension is simple and direct; the coil model is controlled by an external program to perform regular iterations, and after obtaining the stress distribution result of the coil model when winding each turn of the coil, the final stress distribution result of the coil model is obtained by synthesizing the obtained stress distribution results, which can simultaneously meet the winding stress solution of multiple turns (thousands of turns) and irregular coils, so that the stress distribution analysis method of the high-temperature superconducting coil winding process of the present embodiment has a wider range of application.

[0016] Optionally, the skeleton model and the coil model are two-dimensional models or three-dimensional models.

[0017] Optionally, the coil model has multiple turns, and the coil model is a plurality of coaxial rings which are radially arranged in sequence.

[0018] Optionally, the coil model has multiple turns, and the thickness of each turn of the coil is equal.

[0019] Optionally, the coil model after winding forms an integrated structure, and two adjacent turns of the coil will not slide relative to or separate from each other.

[0020] Optionally, in step S3, setting the material parameters of the coil model specifically includes the following steps:

[0021] Step S31, establishing a coordinate system for the coil model, wherein the basis vectors are respectively along the circumferential direction, radial direction and axial direction of the coil model;

[0022] The coil model sets corresponding material parameters along the circumferential direction, radial direction and axial direction respectively.

[0023] Optionally, in step S2, the boundary load is applied at a convex area of ​​an outer boundary of the skeleton model;

[0024] In the step S4, the boundary load is applied at a position which is a convex area of ​​an outer boundary of the coil model.

[0025] Optionally, the magnitude of the boundary load is calculated as:

[0026]

[0027] in:

[0028] P—boundary load;

[0029] T w — Winding tension;

[0030] ρ—radius of curvature where pressure is applied;

[0031] d—strip width.

[0032] Optionally, the final stress distribution result of the coil model includes a radial stress distribution result of the coil model, and the radial stress distribution result of the inner boundary of the i-th coil turn in the coil model is calculated as:

[0033] The algebraic sum of the radial stress distribution results generated by the i-th coil from the time of winding the i-th coil to the time of winding the N-th coil;

[0034] The radial stress distribution result of the middle or outer boundary of the i-th coil in the coil model is calculated as:

[0035] The algebraic sum of the radial stress distribution results generated by the i-th coil is obtained from winding the i+1-th coil to winding the N-th coil.

[0036] Optionally, the final stress distribution result of the coil model includes a hoop stress distribution result of the coil model, and the hoop stress distribution result of the inner boundary of the i-th coil turn in the coil model is calculated as:

[0037] From the time when the i-th coil is wound to the time when the N-th coil is wound, the algebraic sum of the hoop stress distribution results generated by the i-th coil is added with the initial prestress of the i-th coil;

[0038] The hoop stress distribution result of the middle or outer boundary of the i-th coil in the coil model is calculated as:

[0039] From the time when the i+1th coil is wound to the time when the Nth coil is wound, the algebraic sum of the circumferential stress distribution results generated by the i-th coil is added to the initial prestress of the i-th coil. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flowchart of a specific embodiment of the method for analyzing stress distribution in the high-temperature superconducting coil winding process provided in the present application;

[0041] Figure 2 It is a schematic diagram of the structure of a circular coil;

[0042] Figure 3 It is a schematic diagram of the structure of a racetrack coil;

[0043] Figure 4 It is a structural schematic diagram of a D-type coil;

[0044] Figure 5 Schematic diagram of the application position of the circular coil boundary load;

[0045] Figure 6 Schematic diagram of the application position of the boundary load of the racetrack coil;

[0046] Figure 7 Schematic diagram of the application position of the boundary load of the D-type coil;

[0047] Figure 8 It is a schematic diagram of establishing a rectangular coordinate system based on the D-type curve;

[0048] Fig. 9 The radial stress distribution result diagram of the circular coil calculated by the analysis method of the present application and the traditional analytical method;

[0049] Fig.10 This is a diagram showing the results of calculating the hoop stress distribution of a circular coil using the analysis method of this application and the traditional analytical method;

[0050] Fig.11 It is a schematic diagram of the positions of P1, P2 and P3 selected in the racetrack coil;

[0051] Fig.12 The radial stress distribution result diagram of the racetrack coil at positions P1, P2, and P3 calculated using the analysis method of this application;

[0052] Fig.13The hoop stress distribution result diagram of the racetrack coil at positions P1, P2, and P3 calculated using the analysis method of this application;

[0053] Fig.14 It is a schematic diagram of the positions of P1, P2, P3 and P4 selected in the D-type coil;

[0054] Fig.15 The radial stress distribution result diagram of the D-type coil at positions P1, P2, P3, and P4 is calculated using the analysis method of this application;

[0055] Fig.16 This is a diagram showing the hoop stress distribution results of the D-type coil at positions P1, P2, P3, and P4 calculated using the analysis method of this application;

[0056] in, Figure 2-Figure 8 The reference numerals in the figures are as follows:

[0057] 11- Skeleton model;

[0058] 12-coil model;

[0059] 01-D type curve. DETAILED DESCRIPTION

[0060] In order to enable those skilled in the art to better understand the technical solution of the present application, the present application is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0061] Please refer to Figure 1-Figure 4 , Figure 1 A flowchart of a specific embodiment of the method for analyzing stress distribution in the high-temperature superconducting coil winding process provided in the present application; Figure 2 It is a schematic diagram of the structure of a circular coil; Figure 3 It is a schematic diagram of the structure of a racetrack coil; Figure 4 It is a structural schematic diagram of a D-type coil.

[0062] This embodiment provides a method for analyzing stress distribution during the winding process of a high-temperature superconducting coil, comprising the following steps:

[0063] Step S1: establishing a skeleton model 11 and setting material parameters of the skeleton model 11;

[0064] Step S2: applying a boundary load to the skeleton model 11, and performing a finite element stress analysis on the skeleton model 11 to obtain a stress distribution result of the skeleton model 11 when the first turn of the coil is wound;

[0065] Step S3: Establish a coil model 12 and set material parameters of the coil model 12. The coil model 12 is fitted with the skeleton model 11. The number of turns of the coil model 12 is i, i=1;

[0066] Step S4: applying a boundary load to the coil model 12, and performing finite element stress analysis on the coil model 12 to obtain a stress distribution result of the coil model 12 when the i+1th turn of the coil is wound;

[0067] Step S5: Control the coil model 12 to iterate from i=2 to i=N-1 through an external program, where N is the total number of turns of the coil model 12, and repeat step S4 for each iteration process;

[0068] Step S6: The final stress distribution result of the coil model 12 is obtained by comprehensively analyzing the stress distribution result of the coil model 12 when each turn of the coil is wound.

[0069] The stress distribution analysis method of the high-temperature superconducting coil winding process of the present embodiment combines the calculation idea of ​​disassembling the winding process with the advantage of the finite element method that can calculate the complex structure coil, and divides the winding process of the coil in the coil model 12 into multiple parts according to the number of turns, each part corresponds to a finite element model, that is, the dynamic change of the model is realized by the step-by-step modeling method; at the same time, the effect of winding the first turn or winding the i+1th turn of the coil is simulated by applying a boundary load to the skeleton model 11 or the coil model 12 with i turns of the coil, and the application of the winding tension is simple and direct; the coil model 12 is controlled by an external program to perform regular iterations, and after obtaining the stress distribution result of the coil model 12 when winding each turn of the coil, the final stress distribution result of the coil model 12 is obtained by synthesizing the obtained stress distribution results, which can simultaneously meet the winding stress solution of multiple turns (thousands of turns) and irregular coils, so that the stress distribution analysis method of the high-temperature superconducting coil winding process of the present embodiment has a wider range of application.

[0070] Among them, in step S1, since the coil winding process assumes that the winding tension is uniformly applied to the coil, the coil is subjected to the same force in any plane in the winding axis direction. Therefore, the skeleton model 11 and the coil model 12 of this embodiment can be modeled using a three-dimensional model. At this time, the winding tension can be applied to the outer boundary of the three-dimensional model in any plane along the winding axis direction; or, a two-dimensional model can be used for modeling. At this time, the winding tension is applied to the outer boundary of the two-dimensional model, so as to achieve the purpose of simplifying the calculation without affecting the calculation results.

[0071] As mentioned above, the stress distribution analysis method during the winding process of the high-temperature superconducting coil in this embodiment can meet the winding stress solution of irregular coils. Therefore, the skeleton model 11 and coil model 12 established in this embodiment can be circular, racetrack-shaped or D-shaped.

[0072] It can be understood that, in practice, the coil is spiral and its mechanical structure is very complex. To simplify calculation and modeling, this embodiment makes the following assumptions:

[0073] (1) When the number of turns of the coil model 12 is multiple, the coil model 12 is simplified into a plurality of coaxial rings sequentially arranged along the radial direction, that is, the coil winding process is regarded as a process of increasing the number of coaxial rings, thereby improving the analysis efficiency without substantially affecting the results.

[0074] (2) When the coil model 12 has multiple turns, the thickness of each coil turn is equal, which facilitates the external program to control the coil model 12 to perform regular iterations.

[0075] (3) The wound coil model 12 forms an integrated structure, and two adjacent turns of the coil will not slide or separate relative to each other, which is convenient for modeling.

[0076] (4) When solving the analytical solution of coil winding stress, since the coil is not sealed during winding, the coil and the frame can still slide relative to each other. The generalized plane stress condition is generally used, that is, the coil axial stress σ z =0.

[0077] (5) The influence of geometric parameters caused by strain is not considered.

[0078] (6) The manufacturing process does not take into account the residual stress generated by the conductor.

[0079] (7) Ignore the effect of shear stress.

[0080] Furthermore, since the REBCO high temperature superconducting tape used to wind the coil is a layered structure, its material parameters in the circumferential direction and radial direction are different, showing anisotropy, and therefore need to be set separately. Based on this, in step S3, setting the material parameters of the coil model 12 specifically includes the following steps:

[0081] Step S31, establishing a coordinate system for the coil model 12, wherein the basis vectors are respectively along the circumferential direction, radial direction and axial direction of the coil model 12;

[0082] The coil model 12 sets corresponding material parameters along the circumferential direction, radial direction and axial direction respectively.

[0083] The material of the skeleton model 11 is an isotropic material, and the material parameters can be directly set.

[0084] Meanwhile, the analysis method of stress distribution during the winding process of the high-temperature superconducting coil in this embodiment is applicable to the case where the strip material for winding the coil has a rectangular cross section.

[0085] Please refer to Figure 5-Figure 7 , Figure 5 Schematic diagram of the application position of the circular coil boundary load; Figure 6 Schematic diagram of the application position of the boundary load of the racetrack coil; Figure 7 Schematic diagram of the application position of the boundary load of the D-type coil.

[0086] As mentioned above, in this embodiment, the coil winding process is regarded as a process in which multiple coaxial rings are sleeved on the outer periphery of the skeleton one by one. Winding the i+1th turn of the coil is equivalent to sleeved the i+1th ring on the outer periphery of the skeleton. The effect on the internal coil is manifested as pressure, and only the convex area will be subject to the pressure, and the concave area or the straight area will not be subject to the pressure. Therefore, in step S2 of this embodiment, the application position of the boundary load is the convex area of ​​the outer boundary of the skeleton model 11;

[0087] In step S4 , the boundary load is applied to the convex region of the outer boundary of the coil model 12 .

[0088] like Figure 5 As shown, when the skeleton model 11 and the coil model 12 are circular, the boundary load is uniformly applied to the outer periphery of the skeleton model 11 or the coil model 12 along the circumferential direction; Figure 6 As shown, when the skeleton model 11 and the coil model 12 are in the shape of a racetrack, the boundary load is applied to the convex areas at both ends of the skeleton model 11 or the coil model 12; Figure 7 As shown, when the skeleton model 11 and the coil model 12 are in a D-shape, the boundary load is applied to the convex area of ​​the skeleton model 11 or the coil model 12 .

[0089] Furthermore, the magnitude of the boundary load is calculated as:

[0090]

[0091] in:

[0092] P—boundary load;

[0093] T w — Winding tension;

[0094] ρ—radius of curvature where pressure is applied;

[0095] d—strip width.

[0096] It can be understood that when the skeleton model 11 and the coil model 12 are circular or runway-shaped, the curvature radii of the boundary load application positions are equal, so the magnitudes of the applied boundary loads are also equal; when the skeleton model 11 and the coil model 12 are D-shaped, the curvature radii of the boundary load application positions are different, so the magnitudes of the applied boundary loads are also different, and it is necessary to first calculate the curvature radius of the corresponding position and then calculate the corresponding boundary load.

[0097] like Figure 8 As shown, the D-type coil is obtained by extending the D-type curve 01 to both sides at equal distances. In order to facilitate the subsequent description, a rectangular coordinate system is established based on the D-type curve 01. The x-axis of the coordinate system is tangent to the D-type curve 01, and the coordinates of the tangent point are ( , 0), then any point (x 0 ,y 0 ) is calculated as:

[0098]

[0099] in:

[0100] —D-type coil upper point (x 0 ,y 0 ) at the radius of curvature;

[0101] x—point (x 0 ,y 0 ) on the D-type curve 01 is the function variable of the above integral variable limit function, which is reflected as the upper limit of the integral interval in the function;

[0102] y—point (x 0 ,y 0 ) on the D-type curve 01;

[0103] k, —Structural parameters determined by the shape of the D-curve 01;

[0104] t—integral variable of the integrand;

[0105] d 0 —Point(x 0 ,y 0 ) to the D-curve 01, which is positive on the outside of the D-curve 01 and negative on the inside.

[0106] Furthermore, the final stress distribution result of the coil model 12 includes the radial stress distribution result of the coil model 12. The radial stress distribution result of the inner boundary of the i-th coil turn in the coil model 12 is calculated as:

[0107] The algebraic sum of the radial stress distribution results generated by the i-th coil from the time of winding the i-th coil to the time of winding the N-th coil;

[0108] The radial stress distribution result of the middle or outer boundary of the i-th coil turn in the coil model 12 is calculated as:

[0109] The algebraic sum of the radial stress distribution results generated by the i-th coil is obtained from winding the i+1-th coil to winding the N-th coil.

[0110] The boundary of the ith coil turn close to the skeleton model 11 is the inner boundary, the boundary away from the skeleton model 11 is the outer boundary, and the middle of the ith coil turn is the area between the inner boundary and the outer boundary of the ith coil turn.

[0111] It can be understood that the inner boundary of the i-th turn of the coil is also equivalent to the outer boundary of the i-1-th turn of the coil, and the inner boundary of the first turn of the coil is equivalent to the outer boundary of the skeleton model 11. Therefore, if the radial stress of the inner boundary of the i-th turn of the coil is calculated, the i-th turn of the coil will generate radial stress from the time when the i-th turn of the coil is wound to the time when the N-th turn of the coil is wound. Therefore, the radial stress generated by the i-th turn of the coil when the i-th turn of the coil is wound to the radial stress generated by the i-th turn of the coil when the N-th turn of the coil is wound can be summarized to obtain the final radial stress distribution result of the inner boundary of the i-th turn of the coil.

[0112] For the first turn of the coil, the radial stress distribution result of the inner boundary of the first turn of the coil is calculated as: the algebraic sum of the radial stress distribution results generated by the first turn of the coil from winding the first turn of the coil to winding the Nth turn of the coil. The radial stress distribution result generated by the first turn of the coil when winding the first turn of the coil is the radial stress distribution result of the skeleton model 11 when winding the first turn of the coil obtained in step S2.

[0113] If the radial stress in the middle or outer boundary of the i-th turn of the coil is calculated, the i-th turn of the coil will generate radial stress from the time when the i+1-th turn of the coil is wound to the time when the N-th turn of the coil is wound. Therefore, the radial stress generated by the i-th turn of the coil when the i+1-th turn of the coil is wound to the radial stress generated by the i-th turn of the coil when the N-th turn of the coil is wound can be summarized to obtain the final radial stress distribution result in the middle or outer boundary of the i-th turn of the coil.

[0114] Furthermore, the final stress distribution result of the coil model 12 includes the hoop stress distribution result of the coil model 12. The hoop stress distribution result of the inner boundary of the i-th coil turn in the coil model 12 is calculated as:

[0115] From the time when the i-th coil is wound to the time when the N-th coil is wound, the algebraic sum of the hoop stress distribution results generated by the i-th coil is added with the initial prestress of the i-th coil;

[0116] The circumferential stress distribution result of the middle or outer boundary of the i-th coil turn in the coil model 12 is calculated as:

[0117] From the time when the i+1th coil is wound to the time when the Nth coil is wound, the algebraic sum of the circumferential stress distribution results generated by the i-th coil is added with the initial prestress of the i-th coil.

[0118] If the hoop stress of the inner boundary of the i-th coil turn is calculated, the i-th coil turn will generate hoop stress from the time when the i-th coil turn is wound to the time when the N-th coil turn is wound, and the i-th coil turn itself has an initial prestress when the i-th coil turn is wound. Therefore, the hoop stress generated by the i-th coil turn when the i-th coil turn is wound to the hoop stress generated by the i-th coil turn when the N-th coil turn is wound is summarized, and the initial prestress of the i-th coil turn is added to obtain the final hoop stress distribution result of the inner boundary of the i-th coil turn.

[0119] For the first turn of the coil, the circumferential stress distribution result of the inner boundary of the first turn of the coil is calculated as: the algebraic sum of the circumferential stress distribution results generated by the first turn of the coil from winding the first turn of the coil to winding the Nth turn of the coil, plus the initial prestress of the first turn of the coil, the circumferential stress distribution result generated by the first turn of the coil when winding the first turn of the coil is, that is, the circumferential stress distribution result of the skeleton model 11 when winding the first turn of the coil obtained in step S2.

[0120] If the hoop stress in the middle or outer boundary of the i-th coil turn is calculated, the i-th coil turn will generate hoop stress from the time when the i+1-th coil turn is wound to the time when the N-th coil turn is wound, and the i-th coil turn itself has an initial prestress when the i-th coil turn is wound. Therefore, the hoop stress generated by the i-th coil turn from the time when the i+1-th coil turn is wound to the hoop stress generated by the i-th coil turn when the N-th coil turn is wound is summarized, and the initial prestress of the i-th coil turn is added to obtain the final hoop stress distribution result in the middle or outer boundary of the i-th coil turn.

[0121] Please refer to Figure 9-10 , Fig. 9 The radial stress distribution result diagram of the circular coil calculated by the analysis method of the present application and the traditional analytical method; Fig.10 This is a diagram showing the annular stress distribution results of a circular coil calculated using the analysis method of this application and the traditional analytical method.

[0122] In order to verify the accuracy of the analysis method of this application, this paper will use the analysis method of this application and the traditional analytical method to calculate the radial stress distribution results and the annular stress distribution results of the circular coil for comparison. It can be seen that the results are almost completely consistent and have high accuracy.

[0123] Please refer to Figure 11-13 , Fig.11 It is a schematic diagram of the positions of P1, P2 and P3 selected in the racetrack coil; Fig.12 The radial stress distribution result diagram of the racetrack coil at positions P1, P2, and P3 calculated using the analysis method of this application; Fig.13 This is a diagram showing the results of calculating the circumferential stress distribution of the racetrack coil at positions P1, P2, and P3 using the analysis method of this application.

[0124] Among them, the positions of P1, P2, and P3 refer to the line segment along the straight line where the arrow is located, from the inner boundary of the first turn of the coil to the outer boundary of the last turn.

[0125] from Fig.12It can be seen that the radial stress in the convex areas (P1) at both ends of the racetrack-shaped coil is relatively large, and the radial stress in the straight edge (P3) is almost zero. This is because the equivalent pressure to which the coil is subjected when it is wound is inversely proportional to the radius of curvature. The radius of curvature of the convex area is larger, and the pressure it is subjected to during winding is greater, while the curvature of the straight edge is 0, and the pressure it is subjected to is almost zero.

[0126] from Fig.13 It can be seen that the circumferential stresses at different positions are similar because the shear stress is ignored. There is no shear stress between different rings. According to the principle of force balance, the circumferential forces of the same circular ring are equal.

[0127] Please refer to Figure 14-16 , Fig.14 It is a schematic diagram of the positions of P1, P2, P3 and P4 selected in the D-type coil; Fig.15 The radial stress distribution result diagram of the D-type coil at positions P1, P2, P3, and P4 is calculated using the analysis method of this application; Fig.16 This is a diagram showing the circumferential stress distribution results of a D-type coil at positions P1, P2, P3, and P4 calculated using the analysis method of this application.

[0128] Among them, the positions of P1, P2, P3, and P4 refer to the line segment along the straight line where the arrow is located, from the inner boundary of the first turn of the coil to the outer boundary of the last turn.

[0129] from Fig.15 It can be seen that the difference in radial stress at different positions is caused by the different curvature radii at different positions of the D-type coil.

[0130] from Fig.16 It can be seen that the circumferential stresses at different positions are similar because the shear stress is ignored. There is no shear stress between different rings. According to the principle of force balance, the circumferential forces of the same circular ring are equal.

[0131] The above are only preferred implementations of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for analyzing stress distribution during the winding process of a high-temperature superconducting coil, characterized in that: The steps include: Step S1: establishing a skeleton model (11) and setting material parameters of the skeleton model (11); Step S2: applying a boundary load to the skeleton model (11), and performing a finite element stress analysis on the skeleton model (11), to obtain a stress distribution result of the skeleton model (11) when the first turn of the coil is wound; Step S3: establishing a coil model (12) and setting material parameters of the coil model (12), wherein the coil model (12) is fitted onto the skeleton model (11), and the number of turns of the coil model (12) is i, where i=1; Step S4: applying a boundary load to the coil model (12), and performing a finite element stress analysis on the coil model (12), to obtain a stress distribution result of the coil model (12) when the i+1th turn of the coil is wound; Step S5: controlling the coil model (12) to iterate from i=2 to i=N-1 through an external program, where N is the total number of turns of the coil model (12), and repeating step S4 in each iteration process; Step S6: comprehensively analyzing the stress distribution results of the coil model (12) when each turn of the coil is wound to obtain the final stress distribution results of the coil model (12).

2. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to claim 1, characterized in that: The skeleton model (11) and the coil model (12) are two-dimensional models or three-dimensional models.

3. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to claim 1, characterized in that: The number of turns of the coil model (12) is multiple, and the coil model (12) is a plurality of coaxial rings which are sequentially mounted in the radial direction.

4. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to claim 1, characterized in that: The coil model (12) has a plurality of turns, and the thickness of each turn of the coil is equal.

5. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to claim 1, characterized in that: The coil model (12) that has been wound forms an integrated structure, and two adjacent turns of the coil will not slide relative to each other or separate.

6. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to any one of claims 1 to 5, characterized in that: In the step S3, setting the material parameters of the coil model (12) specifically includes the following steps: Step S31, establishing a coordinate system for the coil model (12), wherein the basis vectors are respectively along the circumferential direction, radial direction and axial direction of the coil model (12); The coil model (12) sets corresponding material parameters along the circumferential direction, radial direction and axial direction respectively.

7. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to any one of claims 1 to 5, characterized in that: In step S2, the boundary load is applied at a position which is a convex area of ​​an outer boundary of the skeleton model (11); In step S4, the boundary load is applied at a position which is a convex area of ​​an outer boundary of the coil model (12).

8. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to any one of claims 1 to 5, characterized in that: The magnitude of the boundary load is calculated as: ； in: P—boundary load; T w — Winding tension; ρ—radius of curvature where pressure is applied; d—strip width.

9. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to any one of claims 1 to 5, characterized in that: The final stress distribution result of the coil model (12) includes a radial stress distribution result of the coil model (12), and the radial stress distribution result of the inner boundary of the i-th coil turn in the coil model (12) is calculated as: The algebraic sum of the radial stress distribution results generated by the i-th coil from the time of winding the i-th coil to the time of winding the N-th coil; The radial stress distribution result of the middle or outer boundary of the i-th coil turn in the coil model (12) is calculated as: The algebraic sum of the radial stress distribution results generated by the i-th coil is obtained from winding the i+1-th coil to winding the N-th coil.

10. The method for analyzing stress distribution during the winding process of a high-temperature superconducting coil according to any one of claims 1 to 5, characterized in that: The final stress distribution result of the coil model (12) includes the hoop stress distribution result of the coil model (12), and the hoop stress distribution result of the inner boundary of the i-th coil turn in the coil model (12) is calculated as: From the time when the i-th coil is wound to the time when the N-th coil is wound, the algebraic sum of the hoop stress distribution results generated by the i-th coil is added with the initial prestress of the i-th coil; The circumferential stress distribution result of the middle or outer boundary of the i-th coil turn in the coil model (12) is calculated as: From the time when the i+1th coil is wound to the time when the Nth coil is wound, the algebraic sum of the circumferential stress distribution results generated by the i-th coil is added to the initial prestress of the i-th coil.

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