Multi-objective Optimization of Asymmetric Null-Flux Coils for Superconducting Electrodynamic Suspension System
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摘要:
为提高超导电动悬浮系统性能,基于全局灵敏度分析和多目标优化算法,提出一种非对称悬浮线圈优化设计方法. 首先,基于空间谐波法建立超导电动悬浮系统的数学模型,计算超导磁体的磁感应强度以及悬浮线圈的电磁力;其次,对此模型进行非对称优化设计,采用Sobol’敏感性分析方法,以悬浮力和每公里悬浮线圈质量为目标,计算各设计参数的灵敏度,并基于灵敏度分析结果进行非支配排序遗传算法Ⅱ(NSGA-Ⅱ)优化设计;最后,通过有限元进行仿真分析,验证空间谐波法解析模型,并对优化前后的模型进行比较. 研究结果表明:空间谐波法建立的悬浮系统模型与有限元模型具有一致性;相比优化前,优化后的非对称悬浮系统悬浮力提高8.3%,每公里铺设线圈质量降低12.9%;垂直位移0.02~0.04 m时,悬浮力由262.2 kN增加到270.2 kN,磁阻力由4.5 kN增加到5.4 kN;水平位移0.17~0.20 m时,悬浮力由306.5 kN减小到228.8 kN,磁阻力由6.2 kN减小为4.6k N;悬浮力、磁阻力的波动分别约为6%、65%. 研究揭示了悬浮力和磁阻力随着位移方向的变化规律,验证了非对称设计在提升悬浮力和轻量化方面的优势,为超导电动悬浮系统的优化设计提供理论参考.
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关键词:
- 电动悬浮 /
- 灵敏度分析 /
- 非支配排序遗传算法II /
- 有限元仿真 /
- 超导磁体
Abstract:In order to improve the performance of superconducting electrodynamic suspension system, an optimal design method of asymmetric null-flux coils was proposed based on global sensitivity analysis and multi-objective optimization algorithm. Firstly, the mathematical model of superconducting electrodynamic suspension system was established based on space harmonic method. Then the magnetic flux intensity of the superconducting magnets and electromagnetic forces of the null-flux coils were calculated. Secondly, the model was designed asymmetrically. Sobol' sensitivity analysis method was used to calculate the sensitivity of each design parameter with the levitation force and the mass of the null-flux coils per kilometer as the objectives. Based on the optimization parameters obtained from the sensitivity analysis, NSGA-II optimization design was carried out and the optimization results were obtained. Finally, finite element method was carried out to verify the analytic model of space harmonic method. The model before and after optimization was compared. The results indicated that the suspension system model established by space harmonic method was consistent with the finite element model. Compared with the initial system, the levitation force of the optimized asymmetric suspension system was increased by 8.3%, the mass of null-flux coils per kilometer was reduced by 12.9%, the levitation force increased from 262.2 kN to 270.2 kN and the drag force increased from 4.5 kN to 5.4 kN when the vertical deviation was 0.02~0.04 m. The levitation force decreased from 306.5 kN to 228.8 kN and the drag force decreased from 6.2 kN to 4.6 kN when the horizontal deviation was 0.17~0.2 m. The levitation force fluctuation was about 6% and the drag force fluctuation was about 65%. It revealed the variation patterns of levitation and drag forces with respect to offset directions, demonstrating the advantages of asymmetric design in enhancing levitation force and achieving lightweight performance. This provided a theoretical reference for the optimal design of superconducting electrodynamic suspension systems.
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表 1 EDS系统关键参数
Table 1. Main parameters of EDS
线圈 符号 描述 幅值 8字线圈 a1 长度与极距比例 0.778 b1u 上线圈高度占比 0.500 b1b 下线圈高度占比 0.500 b1 上下线圈总高度/m 0.680 zu 上线圈中心高度/m 0.380 zb 下线圈中心高度/m 0.380 c1 线圈截面长度/m 0.060 c2 线圈截面宽度/m 0.040 Ng 线圈匝数 24 Sg 截面线圈每匝面积/mm2 100 τ1 极距/m 0.450 g 上下线圈间隙/m 0.080 r1 线圈圆角半径/m 0.115 超导线圈 a0 长度与极距比例 0.793 b0 高度/m 0.500 d1 线圈截面长度/m 0.040 超导线圈 d2 线圈截面宽度/m 0.070 Ns 线圈匝数 1400 Is 额定电流/A 500 τ0 极距/m 1.350 y1 8字线圈与超导线圈水平距离/m 0.185 Δz 8字线圈与超导线圈中心垂直位移/m 0 表 2 设计参数及其变量范围
Table 2. Value range of design parameters
参数 变量范围 参数 变量范围 a1 [0.700,0.900] g/m [0.060,0.100] b1u [0.200,0.300] τ1/m [0.400,0.600] b1/m [0.200,0.800] a0 [0.700,0.800] r1/m [0.100,0.200] b0/m [0.200,0.600] n1/匝数 [2,12] 表 3 优化方案参数
Table 3. Indicator comparison of initial and optimization scheme
参数 目标值 参数 目标值 a1 0.580 τ1/m 0.600 b1u 0.350 a0 0.800 n1/匝 12 b0/m 0.500 -
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