Multiscale Thermomechanical Coupling Analysis of Racetrack-Type NbTi Suspension Coils Under Random Pressure Loads
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摘要:
为研究随机压力载荷下跑道型NbTi超导线圈的力热耦合行为，本文建立了线圈的多尺度有限元模型，分析其在随机载荷下的应力、接触压力与温度场演化规律，并量化摩擦系数对局部温升的影响. 首先，基于多尺度计算均匀化方法，获取NbTi股线的正交各向异性等效参数，其与精细化模拟结果的相对误差小于1.05%；随后，利用该等效参数建立宏观NbTi线圈模型，结合力热耦合单元与摩擦生热属性，模拟随机压力载荷下的线圈响应. 研究结果表明：不锈钢层承担了主要载荷，其最大米塞斯（Mises）应力为245.7 MPa，而内部股线最大Mises应力仅为59.8 MPa；接触压力集中于股线与不锈钢层及股线匝间的界面，且随外载波动显著；局部温升呈现累积效应，加载初期升温缓慢，超过能量阈值后迅速上升，且摩擦系数显著影响温度峰值，当摩擦系数从0.20降低到0.01时，对应峰值温度下降了75.7%，且摩擦系数越高，高温区域占比越大；降温过程中不锈钢与NbTi股线热膨胀系数差异引发的热失配应力和应变使线圈峰值温度升至原工况的2.7倍，显著加剧股线局部温升与失超风险. 本研究揭示了摩擦系数和降温热失配效应与局部温升的定量关系，为降低NbTi股线失超风险和优化线圈结构与运行安全提供了理论依据.
Abstract:To investigate the coupled thermomechanical behavior of racetrack-shaped NbTi superconducting coils under random pressure loads, a multiscale finite element model of the coil was established to analyze the evolution of stress, contact pressure, and temperature fields under random loading and to quantify the influence of the friction coefficient on local temperature rise. First, the orthotropic equivalent parameters of the NbTi strand were obtained using the multiscale computational homogenization method, with relative errors of less than 1.05% compared with the detailed simulation results. Subsequently, a macroscopic NbTi coil model was established using these equivalent parameters, and the coil response under random pressure loading was simulated by incorporating coupled thermomechanical elements and frictional heat generation. The results show that the stainless steel layer carries most of the load, with a maximum von Mises stress of 245.7 MPa, whereas the maximum von Mises stress in the internal strands is only 59.8 MPa. The contact pressure is concentrated at the interfaces between the strands and the stainless steel layer and between adjacent strand turns, fluctuating significantly with the external loads. The local temperature rise exhibits a cumulative effect, increasing slowly during the initial loading stage but rising rapidly once the energy threshold is exceeded. Moreover, the friction coefficient significantly affects the peak temperature. When the friction coefficient decreases from 0.20 to 0.01, the corresponding peak temperature decreases by 75.7%, and a higher friction coefficient results in a larger proportion of the high-temperature region. During cooling, thermal mismatch stresses and strains caused by the difference in the coefficients of thermal expansion of stainless steel and NbTi strands raise the coil’s peak temperature to 2.7 times its value under the original operating conditions, significantly increasing local strand heating and the risk of a quench. The quantitative relationships among the friction coefficient, thermal mismatch during cooling, and local temperature rise are revealed, providing a theoretical basis for reducing the quench risk of NbTi strands, optimizing coil structure, and improving operational safety.
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图 1 细观NbTi股线RVE模型和均匀化过程以及精细化和均匀化得到的细观RVE应力应变曲线
Figure 1. Mesoscale RVE model of NbTi strand, homogenization process, and stress-strain curves obtained from detailed simulation and homogenization
图 2 实验股线横截面和数值模拟与实验测量的应力-应变曲线
Figure 2. Cross-section of NbTi strand specimen and stress-strain curves from numerical simulation and experimental measurements
图 11 考虑与不考虑降温过程时内部股线的接触压力
Figure 11. Statistical distributions of contact pressure and temperature in internal strands with and without cooling
图 3 宏观跑道型NbTi线圈模型和接触设置
Figure 3. Macroscopic racetrack-type NbTi coil model and contact settings
图 6 不同加载时间下内部股线的接触压力和温度分布
Figure 6. Contact pressure and temperature distributions in internal strands at different loading times
图 7 不同加载时间下线段A和B的接触压力和温度
Figure 7. Contact pressure and temperature along line segments A and B at different loading times
图 8 不同摩擦系数时内部股线的接触压力和温度分布
Figure 8. Contact pressure and temperature distributions in internal strands at different friction coefficients
图 9 不同摩擦系数时内部股线的接触压力和温度统计分布情况
Figure 9. Statistical distributions of contact pressure and temperature in internal strands at different friction coefficients
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