大型Nb₃Sn复合超导线圈的热应力分析及其优化设计

Thermal Stress Analysis and Optimal Design of Large-Scale Nb₃Sn Composite Superconducting Coils

由于Nb3Sn超导线中各材料具有不同的热膨胀系数,因此Nb3Sn超导线圈从高温制备成型到低温运行过程中,会产生一定的热应变。当其通入电流后,还会受到自场作用下的洛伦兹力,从而产生很大的力学变形。由于Nb3Sn超导材料具有很高的应变敏感性,而超导线中产生的应变会影响超导磁体结构的稳定性,因此计算超导磁体在热应力与电磁体力下的力学行为具有重要的科学意义。本文基于双向均质化方法,首先采用有限元软件分析了Nb3Sn线圈在热应力作用下各材料应力–应变随着匝数和层数的变化规律。接着,通过改变超导线中Nb3Sn芯丝数量、Nb3Sn芯丝大小和铜基直径大小等因素,分析各材料应力应变随铜超比的变化规律。当芯丝数量越多、芯丝尺寸越大或者铜基直径越小时,超导线圈的强度越大,从而从力学性能方面对超导线结构进行优化设计。最后,我们考虑了超导线圈在热应力和电磁体力共同作用下,超导线圈内各材料应力和应变的变化规律。

Since each material in the Nb3Sn superconducting wire has a different coefficient of thermal expan-sion, the Nb3Sn superconducting coil will generate a certain amount of thermal strain during the process from high-temperature treatments and molding to low-temperature operation. When it is exposed to a transport current, it will also be subjected to Lorentz force under the action of the self-field, thus generating a large mechanical deformation. Since Nb3Sn superconducting materials have high strain sensitivity and the strain generated in the superconducting wire affects the stability of the superconducting magnets, it is of scientific importance to calculate the mechanical behavior of superconducting magnets under thermal stress and electromagnetic body force. In this paper, based on the bidirectional homogenization method, finite element software is used to first analyze the variations of stress-strain of each material with the number of turns and layers under thermal stress in Nb3Sn coils. Secondly, by changing the number of Nb3Sn core wires, the size of Nb3Sn core wires and the diameter of the copper base in the superconducting wires, the stress and strain of each material with the copper excess ratio were analyzed. When the number of core wires is larger, the size of the core wires is larger or the diameter of the copper base is smaller. Thus, it provides a tool to optimize the design of superconducting coils structure in terms of mechanical properties. Finally, we consider the developments of stress and strain of each material in the superconducting coil under the combined effect of thermal stress and electromagnetic force.