Stress Analysis and Optimal Design of Multi-layer Composite Flywheel
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摘要: 修正多层复合材料飞轮转子因过盈装配产生的应力的计算方法, 给出一种飞轮转子在纤维缠绕时产生的应力的计算方法; 研究基于改进海明距离的种群初始化方法和基于进化代数的反馈变异方法, 提出反馈自适应遗传算法(Feedback adaptive genetic algorithm, FAGA); 利用FAGA算法, 考虑应力约束、质量约束, 以储质量储能密度(EPM)、成本储能密度(EPC)为目标, 探讨多层复合材料飞轮优化问题。仿真分析验证了应力计算方法的合理性和FAGA算法的寻优能力, 揭示了应力约束、质量约束及设计目标对内外径比、转速、EPM、EPC的影响规律。Abstract: The stress calculation method of the flywheel rotor caused by interference assembly is improved. The calculation method of stress caused by filament winding is given. The feedback adaptive genetic algorithm (FAGA) is proposed which gives the population initialization method based on the improved Hamming distances and a feedback mutation method. Based on the FAGA algorithm, considering the stress constraints, mass constraints and different design objectives of the energy per unit mass (EPM) and the energy per unit cost (EPC), the optimization design is carried out. The simulation analysis verifies the rationality of the stress calculation method and the optimization ability of FAGA algorithm. At the same time, it also reveals the influence of the stress constraints, mass constraints and design objectives on the inside and outside diameter ratio, speed, EPM and EPC.
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Key words:
- flywheel rotor /
- composite /
- stress analysis /
- genetic algorithm /
- optimization design
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表 1 复合材料参数
材料参数 材料Ⅰ 材料Ⅱ 材料Ⅲ 纵向弹性模量Eθ/MPa 38 600 130 000 155 000 横向弹性模量Er/MPa 8 270 9 000 9 000 泊松比υθr 0.26 0.3 0.38 纵向拉伸强度XT/MPa 1 020 1 800 2 900 纵向压缩强度Xc/MPa 610 1 400 2 000 横向拉伸强度YT/MPa 40 80 80 横向压缩强度Yc/MPa 118 168 168 密度ρ/(kg·m-3) 2 300 1760 1570 表 2 三层飞轮装配应力对比
参数 本文方法-材料Ⅱ 文献[4]方法-材料Ⅱ 本文方法-材料Ⅰ/Ⅱ/Ⅲ 最小σθ/MPa -25.3 -24.6 -18.8 最小σr/MPa -6.1 -6.0 -3.6 最大σθ/MPa 24.6 24.5 26.1 表 3 文献[6]中材料参数
材料参数 金属芯轴 复合材料 纵向弹性模量Eθ/MPa 202 000 181 000 横向弹性模量Er/MPa 202 000 10 300 泊松比υθr 0.3 0.28 表 4 三层飞轮应力分析方案
参数 方案A 方案B 方案C δai(i=1, 2)/mm 0 0.2 0.2 T/(N·mm-2) 0 0 10 表 5 三层转子总应力对比
参数 第一层方案A/B/C 第二层方案A/B/C 第三层方案A/B/C 最大σθ/MPa 830/793/787 878/886/882 929/987/985 最大σr/MPa 7.9/5.3/5.0 8.4/4.2/4.0 1.7/0.4/0.3 表 6 算法优化对比
文献[13] IAGA FAGA 最优解(ω/α1/α2) 2014/0.844/0.8 2172/0.890/0.792 2190/0.9/0.75 1/EPM/(kg·MJ-1) 2.203 2.177 2.128 各层最大σθ/MPa 766/892/0 816/944/995 816/970/0 Mop/kg 91.0 96.5 87 收敛迭代次数 152 109 26 表 7 优化设计前后结果
名称 ω/α1/α2 各层最大σθ/MPa Mop/kg EPM/(kJ·kg-1) EPC/(kJ·CO-1) 优化前 2100/0.85/0.85 787/882/985 88.4 426 1479 目标EPC 1881/0.75/0.9 816/875/0 98.7 345 3180 目标EPM 2190/0.9/0.75 816/1058/0 87 470 1677 表 8 CN1、CN2下优化设计结果
应力约束 ω/α1/α2 各层最大总应力σθ/MPa EPM/(kJ·kg-1) CN1 2190/0.9/0.75 816/1058/0 470 CN2 2184/0.9/0.75 787/1027/0 467 表 9 优化设计对比
目标Gc/kg ω/α1/α2 各层最大σθ/MPa Mop/kg EPM/(kJ·kg-1) EPC/(kJ·CO-1) EPM/90 2190/0.9/0.75 816/1058/0 87 470 1677 EPC/90 2100/0.856/0.789 816/1007/0 90 430 1829 EPC或EPM/85 2190/0.9/0.808 816/882/985 85 466 1332 -
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