Modeling method for thermal deformation of steel-aluminum riveted part for automobile

Abstract

The invention discloses a modeling method for thermal deformation of a steel-aluminum riveted part for an automobile, which comprises the following steps of: S1, simulating modeling in a coating and baking process of the steel-aluminum riveted part under different working conditions, simplifying the establishment of a model, and representing the states of the steel-aluminum riveted part in different forming states; s2, setting key parameters of the steel plate and the aluminum plate at different temperatures; s3, actually measured parameters are obtained through experiments so as to verify key parameters; s4, stamping simulation modeling is carried out through stamping simulation software LS-DYNA; s5, comparing the simulation model with the actually measured temperature change of the steel and aluminum, and simplifying the baking temperature into a linear relation; and S6, performing error analysis on the thermal deformation value by taking the true value and the simulation value to obtain the actual model precision. The invention provides an effective calculation simulation modeling reference and method for further analyzing the thermal deformation of a steel-aluminum mixed specific actual part.

Description

Technical Field

[0001] The invention relates to forming technology, and more particularly to a modeling method for thermal deformation of a steel-aluminum riveted component for an automobile. Background Art

[0002] At present, with the further development of the automobile industry, energy conservation and safety have become the key directions of future development. Studies have shown that for every 10% decrease in automobile mass, its fuel economy will increase by 6-8% and emissions will decrease by 4%. Lightweighting is one of the most direct and effective means to achieve automobile energy conservation and emission reduction. Automobile aluminum plates have the advantages of low density, high specific strength, good pedestrian collision safety, and high recycling efficiency. In recent years, the use of aluminum instead of steel has achieved significant weight reduction effects, but the cost increase is also obvious. The steel-aluminum hybrid body structure can well combine the advantages of both to achieve lightweight and cost optimization.

[0003] When connecting steel and aluminum, it is necessary to consider the differences in thermal expansion coefficients and elastic moduli between steel and aluminum, as well as the large differences in heat dissipation rates. This is especially true for the use of aluminum in automobiles. The baking temperature of the steel-aluminum riveted parts in the painting process is high, and the strength and connection methods of the riveted parts are different during the baking and heating process. During the painting process, due to the different thermal expansion coefficients of steel and aluminum, the thermal expansion coefficient of aluminum is about twice that of steel under the same conditions. There is a risk of flexural deformation caused by the difference in thermal expansion of different parts under the condition of fixed constraints, which may cause quality defects and affect the delivery quality. In order to consider the impact of thermal deformation of riveted parts of painted steel-aluminum parts, it is necessary to establish an effective thermal deformation prediction model for steel-aluminum hybrid structures in combination with experiments, so as to provide an effective computational simulation modeling benchmark and method for further analysis of the thermal deformation of specific steel-aluminum hybrid parts.

[0004] Audi has also conducted extensive research on thermal deformation of steel-aluminum hybrid structures. Its engineer J.

[0005] Regensburger used Audi TT as a case study to study the effect of the creep aging behavior of aluminum alloy on the thermal deformation of the steel-aluminum body structure during baking. The focus was on the creep aging mechanism of aluminum alloy, and the overall modeling and simulation analysis of the thermal expansion properties of steel and aluminum materials was not performed.

[0006] Beihang University proposed a superplastic forming die design method based on finite element technology that considers thermal expansion (patent application number 201510778965.8; publication number CN105335568A). This technology uses different material thermal expansion properties in different simulation stages to solve the problem of part forming errors caused by the difference in thermal expansion properties between mold materials and part materials. This method focuses on thermal expansion forming compensation and mold repair of superplastic forming dies.

[0007] Zhuolang Textile Machinery Co., Ltd. has proposed an aluminum alloy movable cover plate with anti-thermal deformation function (patent publication number CN113802220A). This technology proposes to install a steel isothermal balance part with contact connection in the aluminum alloy cover plate frame to solve the problem of arc deformation of the structural bow bridge caused by the different thermal expansion characteristics of steel and aluminum.

[0008] The steel-aluminum modeling or design methods described in the above public documents have not been able to establish an effective method for characterizing the thermal deformation modeling of steel-aluminum hybrid structures. Summary of the invention

[0009] In view of the defects existing in the prior art, the purpose of the present invention is to provide a modeling method for the thermal deformation of steel-aluminum riveted parts for automobiles, so as to provide an effective calculation simulation modeling benchmark and method for further analyzing the thermal deformation of specific actual parts of steel-aluminum hybrid.

[0010] To achieve the above object, the present invention adopts the following technical solution:

[0011] A modeling method for thermal deformation of steel-aluminum riveted parts for automobiles, comprising the following steps:

[0012] S1. It is planned to model and simulate the coating and baking process of steel-aluminum riveted parts under different working conditions, simplify the model establishment, and characterize the states of steel-aluminum riveted parts in different forming states;

[0013] S2. Setting key parameters of steel plates and aluminum plates at different temperatures;

[0014] S3. Obtain measured parameters through experiments to verify key parameters;

[0015] S4. Perform stamping simulation modeling through stamping simulation software LS-DYNA;

[0016] S5, comparing the simulated model with the measured temperature changes of steel and aluminum, and simplifying the baking temperature into a linear relationship;

[0017] S6. Take the real value and the simulated value to perform error analysis on the thermal deformation value to obtain the actual model accuracy.

[0018] Preferably, the model is a flat plate model and a hemispherical model.

[0019] Preferably, the key parameters include elastic modulus, Poisson's ratio, yield strength, plastic hardening stiffness and thermal expansion coefficient.

[0020] Preferably, the measured parameters obtained experimentally in step S3 are specifically as follows:

[0021] The front and rear deformation morphology of the steel-aluminum riveted component is measured by three-dimensional scanning. Both the front and rear scanning require reference point positioning. The deformation of the steel-aluminum riveted component after heating is obtained by comparing the measurement results before and after heating.

[0022] The riveting position of the steel-aluminum riveted component is selected to have a preload force that represents the equivalent riveting strength of the component;

[0023] The temperature process of the coating and baking of the steel-aluminum riveted parts is controlled by a baking furnace with reference to the coating and baking of automobiles, and the temperature changes of different areas on the surfaces of the aluminum plate and the steel plate in the baking furnace are measured by thermocouples.

[0024] Preferably, the stamping simulation modeling by the stamping simulation software LS-DYNA in step S4 includes the following steps:

[0025] S41, selecting the flat plate model and the hemispherical model;

[0026] S42, meshing the flat plate model and the hemispherical model;

[0027] S43, constraining the boundary conditions of the flat plate model and the hemispherical model;

[0028] S44, using implicit calculation method of thin shell element;

[0029] S45, the flat plate model and the hemispherical model adopt a surface-to-surface automatic contact method.

[0030] Preferably, the step S41 is specifically as follows:

[0031] The flat plate model adopts a 1 / 4 symmetric model;

[0032] The hemispherical model adopts a full-size model.

[0033] Preferably, the step S42 is specifically as follows:

[0034] When processing the mesh of the plate model, it is directly divided based on the CAD model;

[0035] When processing the mesh of the hemispherical model, the geometry is directly generated by the punched mesh and then the mesh is divided.

[0036] Preferably, the step S43 is specifically as follows:

[0037] The boundary conditions of the flat plate model and the hemispherical model are to constrain one vertical degree of freedom at the bolt position, and to constrain all translational degrees of freedom at any of the bolt positions;

[0038] The plate model also needs to set symmetric boundary constraints on the symmetric boundaries.

[0039] Preferably, the actual model accuracy in step S6 is:

[0040] The relative errors of the warping displacements of the key centers and corner connection positions on the flat plate model and the hemispherical model are both 5%.

[0041] The present invention provides a modeling method for thermal deformation of a steel-aluminum riveted component for an automobile, which has the following beneficial effects:

[0042] 1) The established material model can reflect the different stamping forming characteristics of steel and aluminum materials through the flat plate model and the hemispherical model, and can truly reflect the deformation state of the material through mesh mapping and stress-strain mapping;

[0043] 2) Parameter acquisition and model establishment of thermal expansion, deformation morphology, and connection characteristic parameters of key steel and aluminum materials to ensure the accuracy and reliability of the simulation model;

[0044] 3) The selection of analysis models, meshing, boundary condition constraints, algorithm selection, optimization and setting of contact conditions in the model fully consider the actual working conditions and calculation accuracy and efficiency to form a set of effective thermal deformation modeling methods for characterizing steel-aluminum hybrid riveted parts;

[0045] 4) It can further analyze the thermal deformation of specific steel-aluminum hybrid components and provide effective computational simulation modeling benchmarks and methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic flow chart of the modeling method of the present invention;

[0047] Figure 2 Schematic diagrams of a flat plate model and a hemispherical model in step S1 of an embodiment of a modeling method of the present invention, (a) is a flat plate model, and (b) is a hemispherical model;

[0048] Figure 3 is a schematic diagram of the true stress-strain curve of the aluminum material under different temperature gradients in step S2 of the modeling method embodiment of the present invention;

[0049] Figure 4 is a schematic diagram of step S44 of an embodiment of the modeling method of the present invention;

[0050] Figure 5 Schematic diagram of a baking temperature curve in an embodiment of the modeling method of the present invention, (a) is an actual baking temperature curve, and (b) is a simplified baking temperature curve;

[0051] Figure 6 Schematic diagram of step S6 of the modeling method embodiment of the present invention. DETAILED DESCRIPTION

[0052] In order to better understand the above technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0053] Combination Figure 1 As shown, a modeling method for thermal deformation of a steel-aluminum riveted component for an automobile provided by the present invention comprises the following steps:

[0054] S1. For typical automobile steel-aluminum riveted body parts; it is planned to model and simulate the coating and baking process of steel-aluminum connection parts under different working conditions, simplify the establishment of flat plate models and hemispherical models, and characterize the states of steel-aluminum riveted parts in different forming states; through experimental tests and manual reference, ensure that the different elastic moduli, tensile properties and thermal expansion coefficients of steel and aluminum plates that change with temperature are truly and accurately imported into the simulation modeling model;

[0055] S2. Since the yield strength of steel is relatively high, in order to improve the calculation efficiency, it is necessary to set the elastic modulus, Poisson's ratio, yield strength, plastic hardening stiffness and thermal expansion coefficient of steel at different temperatures; the yield strength of aluminum plate is relatively low, so it is necessary to set the elastic modulus, Poisson's ratio, plastic stress-strain curve and thermal expansion coefficient of aluminum plate at different temperatures;

[0056] S3, 3) The measured parameters of deformation morphology, riveting fastening method and preload force, and baking temperature system are the key imported parameters for simulation modeling accuracy. The main steps of experimental verification are to anchor the aluminum plate on the steel plate with preload force control, perform three-dimensional scanning measurement before heating, and then send it into the baking furnace for heating. After heating to the specified temperature, keep it warm for a period of time, then take it out of the baking furnace and air cool it to room temperature, and then perform a second three-dimensional scanning measurement. The key parameter acquisition method of experimental verification is as follows: the front and rear deformation morphology of the riveted parts is measured by three-dimensional scanning. Both the front and rear scans need to set reference points for positioning. The deformation of the steel and aluminum parts after heating is obtained by comparing the measurement results before and after heating; the preload force at the riveted part characterizes the equivalent riveting strength of the parts; the temperature process of paint baking refers to the paint baking of the car to control the baking furnace, and the temperature changes of different areas on the surface of the aluminum plate and the steel plate in the baking furnace are measured by thermocouples. Temperature monitoring measures the temperature changes of different areas on the surface of the aluminum plate and the steel plate in the heating furnace by thermocouples;

[0057] S4. Use stamping simulation software LS-DYNA to perform stamping simulation modeling, as follows:

[0058] S41, Selection of flat plate model and hemispherical model: Considering the symmetry of the flat plate model and saving calculation time, the flat plate model adopts a 1 / 4 symmetric model. Considering the mapping of stamping results, the hemispherical model adopts a full-size model. The simulation methods of the flat plate model and the hemispherical model are very similar, but the hemispherical model needs to map the stress and strain caused by stamping to the analysis model before simulation;

[0059] S42. Meshing of flat plate model and hemispherical model: When processing the mesh of flat plate model, it is directly divided on the basis of CAD model; when processing the mesh of hemispherical model, the geometry is directly generated by stamping mesh, and then the mesh is divided. When dividing the mesh, the accuracy of the model and the calculation time should be taken into account. The method is to subdivide the mesh at the key position and increase the mesh size at other unimportant positions;

[0060] S43, the boundary conditions of the flat plate model and the hemispherical model are constrained: the boundary conditions of the two models are to constrain a vertical degree of freedom at the bolt position and constrain all translational degrees of freedom on one of the bolts; the flat plate model also needs to set symmetric boundary constraints on the symmetric boundaries;

[0061] S44. Implicit calculation using thin shell elements: The deformation analysis for thermal-solid coupling is easy to converge, which can ensure the calculation accuracy and have an advantage in calculation time.

[0062] The surface-to-surface automatic contact method is used in S45, flat plate model, and hemispherical model: no excessive constraints are made, which is consistent with the actual situation. The measured preload force is set in the simulation to represent the actual riveting strength;

[0063] S5. According to the real baking thermal deformation characteristics, after comparing the simulation model with the measured temperature changes of steel and aluminum, it is analyzed that the influence of heat convection and heat conduction is very small and can be ignored. Only thermal expansion needs to be considered as the main influencing factor, and the baking temperature can be simplified into a linear relationship to improve the calculation efficiency;

[0064] S6. The modeling parameters are optimized according to the above points, and the error analysis of thermal deformation values ​​is carried out using real values ​​and simulated values. The actual model accuracy is relatively consistent with the actual one. The relative errors of the warping displacements at the key center and corner connection positions of the flat plate and hemispherical models are both within 5%, with high calculation efficiency and easy convergence.

[0065] Example

[0066] The present embodiment provides a modeling method for thermal deformation of a steel-aluminum riveted component for an automobile, comprising the following steps:

[0067] S1. Select typical automobile steel DC56D+Z (2.0mm) and aluminum 6016 (0.9mm); for typical automobile steel-aluminum riveted body parts; plan to model and simulate the coating and baking process of steel-aluminum connection parts under different working conditions, simplify the establishment of flat plate model and hemispherical model, characterize the state of steel-aluminum riveted parts in different forming states, and the coating and baking process is 185℃+20min; obtain the elastic modulus, Poisson's ratio, thermal expansion coefficient and plastic stress-strain curve at different temperatures through experiments and manuals, and accurately import the simulation modeling model, such as Figure 2 shown.

[0068] As shown in Table 1, the elastic modulus and thermal expansion coefficient range from room temperature to coating baking, and the temperature difference in each temperature range is 50°C. The plastic stress-strain curves at different temperatures range from room temperature T = 20°C to coating baking, and the temperature range of each curve is △T = 60°C.

[0069] Table 1 Comparison of thermal expansion coefficients of steel and aluminum

[0070]

[0071] S2. Metal materials have different mechanical properties under different temperature conditions. In order to accurately predict the thermal deformation of steel-aluminum hybrid structures, it is necessary to select a suitable material model for simulation. It is necessary to set the elastic modulus, Poisson's ratio, yield strength, plastic hardening stiffness and thermal expansion coefficient of steel at different temperatures; the yield strength of aluminum plates is relatively low, so it is necessary to set the elastic modulus, Poisson's ratio, plastic stress-strain curve and thermal expansion coefficient of aluminum plates at different temperatures, such as Figure 3 shown.

[0072] S3, deformation morphology, riveting fastening method and preload, baking temperature system measured parameters are the key input parameters of simulation modeling accuracy. The main steps of experimental verification are to anchor the aluminum plate preload control on the steel plate, perform three-dimensional scanning measurement before heating, and then send it into the heating furnace for baking. After heating to 185℃, keep it warm for 20 minutes, then take it out of the baking furnace and air cool it to room temperature, and then perform a second three-dimensional scanning measurement. The key parameter acquisition method of experimental verification is as follows: the front and rear deformation morphology of the riveted parts is measured by three-dimensional scanning. Both the front and rear scans need to set reference points for positioning. The reference points are located at the three corners of the steel plate and the initial coordinates are calibrated. The deformation of the steel and aluminum parts after heating is obtained by comparing the measurement results before and after heating; the preload is selected at the riveting part to characterize the equivalent riveting strength of the parts; the temperature process of coating baking is controlled by referring to the automobile coating baking, and the temperature changes of different areas on the surface of the aluminum plate and steel plate in the baking furnace are measured by thermocouples. Temperature monitoring uses thermocouples to measure the temperature changes in different areas of the surface of the aluminum plate and steel plate in the heating furnace.

[0073] Baking furnace control, and use thermocouples to measure the temperature changes of different areas on the surface of aluminum and steel plates in the baking furnace. Temperature monitoring uses thermocouples to measure the temperature changes of different areas on the surface of aluminum and steel plates in the heating furnace.

[0074] S4. Use stamping simulation software LS-DYNA to perform stamping simulation modeling:

[0075] S41. Selection of analysis model: Considering the symmetry of the flat plate model and saving calculation time, the flat plate model adopts a 1 / 4 symmetric model. Considering the mapping of stamping results, the hemispherical model adopts a full-size model. The simulation methods of the flat plate model and the hemispherical model are very similar, but the hemispherical model needs to map the stress and strain caused by stamping to the analysis model before simulation. The dynain file of the aluminum plate stamping springback analysis is imported into the hemispherical model through Hypermesh. The dynain file contains the mesh information and stress and strain information after the stamping springback analysis.

[0076] S42. Mesh division: When processing the mesh of the flat plate model, it is directly divided on the basis of the CAD model. When processing the mesh of the hemispherical model, the geometry is directly generated through the stamping mesh, and then the mesh is divided. The linear static simulation mesh size has a great influence on the results, and for the sake of computational efficiency, the mesh size of the model needs to be optimized. When dividing the mesh, the accuracy of the model and the calculation time must be taken into account. The method is to subdivide the mesh at key locations and increase the mesh size at other unimportant locations. In this example, the flat plate model uses a 2mm mesh, and the bolt hole location is about 1mm; the hemispherical model uses 1.5mm at locations with large stamping deformation because of large stress and strain. Other locations use 4mm, or a simple 2mm mesh can be used.

[0077] S43, Boundary condition constraints: The boundary conditions of both models are to constrain one vertical degree of freedom at the bolt position and constrain all translational degrees of freedom on one of the bolts. The plate model also needs to set symmetric boundary constraints on the symmetric boundaries.

[0078] S44. The calculation adopts the implicit algorithm of thin shell element, such as Figure 4 As shown in the figure, the steel plate and the aluminum plate are shell elements, the gasket is a shell element, and the riveted bolt is a beam element; the implicit algorithm is easy to converge for the deformation analysis of thermal-solid coupling, which can ensure the calculation accuracy and have an advantage in calculation time.

[0079] The surface-to-surface automatic contact method is used in the S45, plate and hemisphere models, without any excessive constraints, which is consistent with the actual situation. The principle of the preload in the model is to apply a relative axial force on the bolt beam unit. The simulation setting uses a preload of 10000N to characterize the actual riveting strength.

[0080] S5. According to the actual thermal deformation characteristics of baking, the temperature change during baking is carried out in a long time without drastic energy changes. Considering heat conduction and heat convection, it is necessary to input an accurate temperature curve, and the analysis time is longer. After comparing the simulation model with the measured temperature changes of steel and aluminum, the influence of heat convection and heat conduction is very small and can be ignored. Only thermal expansion needs to be considered as the main influencing factor. The baking temperature can be simplified to the second linear loading mode. The second loading mode only requires three loading steps, which can greatly reduce the calculation time. Figure 5 shown.

[0081] S6. Model accuracy verification

[0082] The modeling parameters were optimized according to the above points, and the error analysis of thermal deformation values ​​was performed using the real values ​​and simulated values. The actual model accuracy was found to be consistent with the actual one. The relative errors of the warping displacements at the key central connection positions of the flat plate and hemispherical models were within 5%. Figure 6 As shown, the absolute error of the warping displacement at the center of the plate is 0.03mm, and the overall relative error is 2.14%. Therefore, the CAE model of thermal deformation of steel-aluminum riveted parts established by this patent has high reliability, efficiency and practicality, and can be used as a modeling benchmark for thermal simulation modeling analysis of specific automotive steel-aluminum hybrid covered parts.

[0083] This patent proposes a thermal deformation modeling method for steel-aluminum riveted parts for automobiles. It combines experiments to fully obtain parameter models of thermal expansion, deformation morphology, and connection characteristics of key materials, and uses the mainstream thermal-mechanical coupling simulation platform LS-DYNA for stamping simulation modeling and optimization. It establishes a set of reliable and efficient modeling benchmarks and methods for characterizing the thermal deformation of steel-aluminum riveted parts for automobiles, providing effective computational simulation modeling benchmarks and methods for further analyzing the thermal deformation of specific actual steel-aluminum hybrid parts.

[0084] The modeling method for thermal deformation of steel-aluminum riveted components for automobiles proposed in the present invention can be further applied to thermal deformation modeling simulation analysis of specific actual steel-aluminum hybrid components, and is universal and practical.

[0085] Those skilled in the art should recognize that the above embodiments are only used to illustrate the present invention, and are not intended to limit the present invention. As long as they are within the spirit of the present invention, any changes or modifications to the above embodiments will fall within the scope of the claims of the present invention.

Claims

1. A modeling method for thermal deformation of steel-aluminum riveted parts for automobiles, characterized in that: The following steps are involved: S1. It is planned to model and simulate the coating and baking process of steel-aluminum riveted parts under different working conditions, simplify the model establishment, and characterize the states of steel-aluminum riveted parts in different forming states; S2. Setting key parameters of steel plates and aluminum plates at different temperatures; S3. Obtain measured parameters through experiments to verify key parameters; S4. Perform stamping simulation modeling through stamping simulation software LS-DYNA; S5, comparing the simulated model with the measured temperature changes of steel and aluminum, and simplifying the baking temperature into a linear relationship; S6. Take the real value and the simulated value to perform error analysis on the thermal deformation value to obtain the actual model accuracy.

2. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 1 is characterized in that: The models are a flat plate model and a hemispherical model.

3. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 1 is characterized in that: The key parameters include elastic modulus, Poisson's ratio, yield strength, plastic hardening stiffness and thermal expansion coefficient.

4. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 2 is characterized in that: The measured parameters obtained in the experiment in step S3 are specifically as follows: The front and rear deformation morphology of the steel-aluminum riveted component is measured by three-dimensional scanning. Both the front and rear scanning require reference point positioning. The deformation of the steel-aluminum riveted component after heating is obtained by comparing the measurement results before and after heating. The riveting position of the steel-aluminum riveted component is selected to have a preload force that represents the equivalent riveting strength of the component; The temperature process of the coating and baking of the steel-aluminum riveted parts is controlled by a baking furnace with reference to the coating and baking of automobiles, and the temperature changes of different areas on the surfaces of the aluminum plate and the steel plate in the baking furnace are measured by thermocouples.

5. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 2 is characterized in that: The stamping simulation modeling by the stamping simulation software LS-DYNA in step S4 includes the following steps: S41, selecting the flat plate model and the hemispherical model; S42, meshing the flat plate model and the hemispherical model; S43, constraining the boundary conditions of the flat plate model and the hemispherical model; S44, using implicit calculation method of thin shell element; S45, the flat plate model and the hemispherical model adopt a surface-to-surface automatic contact method.

6. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 5 is characterized in that: The step S41 is specifically as follows: The flat plate model adopts a 1 / 4 symmetric model; The hemispherical model adopts a full-size model.

7. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 5 is characterized in that: The step S42 is specifically as follows: When processing the mesh of the plate model, it is directly divided based on the CAD model; When processing the mesh of the hemispherical model, the geometry is directly generated by the punched mesh and then the mesh is divided.

8. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 5 is characterized in that: The step S43 is specifically as follows: The boundary conditions of the flat plate model and the hemispherical model are to constrain one vertical degree of freedom at the bolt position, and to constrain all translational degrees of freedom at any of the bolt positions; The plate model also needs to set symmetric boundary constraints on the symmetric boundaries.

9. The modeling method for thermal deformation of steel-aluminum riveted parts for automobiles according to claim 1, characterized in that: The actual model accuracy in step S6 is: The relative errors of the warping displacements of the key centers and corner connection positions on the flat plate model and the hemispherical model are both 5%.

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