Thermodynamic Equivalent Parameters Characterization Of Superconducting Composite Coil Structure In Extremely Low/Variable Temperature Environment

With the continuous development of superconducting magnet theory and application research,superconducting magnets play an increasingly important role in medical,energy,transportation,power systems,international science and engineering,and national defense.Superconducting magnets are usually composite structures,and they operate in extreme multi-field environments such as extremely low temperature,strong magnetic field and large current.The structural deformation generated in such extreme environments can easily lead to the failure of their superconducting electromagnetic properties to meet the design requirements or even lead to quench.Due to the inherent complexity and nonlinearity of superconducting physics,its mechanical theoretical framework and analysis approach have not been effectively solved.Among them,the equivalent parameter characterization methods of superconducting composite structures in extreme environments are still limited,and the relevant design parameters are scarce,which seriously restrict the structural optimization design and engineering application of superconducting magnets.At present,the characterization of thermal-mechanical equivalent parameters of superconducting composite structures is involved in their winding,optimization design and operation at extremely low temperatures.In the aspect of numerical simulation,the current isotropic finite element model is idealized,and it is difficult to accurately characterize the parameters of superconducting composite structures under extreme changes and other operating environments.However,in the aspect of experimental research,the conventional and normal temperature experimental methods are not suitable for extreme environments,and the experimental characterization and technical means of the equivalent parameters of superconducting composite structures in extremely low/variable temperature environments are scarce.In order to solve the above problems,on the one hand,from the point of view of micromechanics,combined with the characteristics of superconducting composite structure,considering the effect of temperature on material properties,the thermal-mechanical equivalent parameters of superconducting coils are studied by numerical simulation.On the other hand,based on the self-developed measurement system of thermal expansion coefficient of extremely low/variable temperature materials,the experimental characterization of thermal-mechanical equivalent parameters of superconducting composite structures is carried out,and the experimental results are analyzed and compared with the numerical simulation results in detail.The main tasks are as follows:（1）Based on the representative volume element theory and the structural characteristics of NbTi/Cu superconducting composite coil,an orthotropic finite element model is established.The influence of temperature on the material parameters is considered and the mesh independence of the model is analyzed.The numerical simulation of NbTi/Cu superconducting coil was carried out.The results show that the predicted results of the orthotropic representative volume element model are in good agreement with the experimental values,which verifies the reliability of the finite element model.（2）A parametric finite element model of Nb₃Sn superconducting composite coil is established according to the structural characteristics of the superconducting composite coil after high temperature treatment.The equivalent parameters of Nb₃Sn superconducting composite coil are numerically simulated and analyzed,and the numerical results are compared with the experimental results.The results show that the parameterized finite element model is consistent with the corresponding experimental results.The parametric finite element model can conveniently and accurately characterize the equivalent parameters of Nb₃Sn superconducting coils after high temperature treatment,which is of great significance for their structural optimization design,improvement of electromagnetic performance and reliability.（3）A system for measuring the thermal expansion coefficient of superconducting composite structure in extremely low/variable temperature environment is developed.The functions of each subsystem are introduced.Based on this system,the experimental characterization of thermal expansion coefficients of conventional cryogenic materials and Nb₃Sn superconducting composite coil specimens at very low/variable temperature（room temperature～4.2 K）was carried out.The parameterized finite element model and thermal expansion coefficient measurement system proposed in this paper enrich the characterization methods of thermo-mechanical equivalent parameters of superconducting composite structures in extreme multi-field environment on the one hand,and on the other hand,provide important parameters and thermo-mechanical basic test platform for structural design,fabrication and experiment of various large-scale superconducting magnets in China.