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摘要:
星载抛物面天线在轨运行时由于姿态调整或环境因素变化，可能产生振动，从而降低其工作性能。为了减弱振动的影响，需采取加装张紧绳索的方法来提升天线刚度。提出了一种新型张紧绳索多层设计方法，通过将抛物面天线划分为多层，调整各层绳索的张紧力，从而提高天线结构刚度，同时尽量降低张紧力引起的形面误差。为了验证所提方法的有效性，建立了天线的有限元模型。在此基础上进行了有限元分析，研究了不同张紧力参数配置下的结构刚度和形面误差，并以提升结构刚度的同时降低张紧力引起的形面误差为目标，对张紧力参数进行了优化设计。为了提高计算效率，采用响应面法建立代理模型参与优化迭代计算。采用非劣排序遗传算法（NSGA-Ⅱ）完成优化迭代计算，优化后的张紧力参数使天线的性能得到了进一步的提升，为构架式可展开抛物面天线的设计提供理论指导。
Abstract:Satellite-borne paraboloid antenna may vibrate during orbit operation due to attitude adjustment or environmental factors, thus reducing its performance. In order to reduce the influence of vibration, it is necessary to add tension rope to enhance the antenna stiffness. Therefore, a new multi-layer design method of tension rope is proposed. In this method, the paraboloid antenna is divided into multiple layers and the tension of each layer is adjusted to improve the structural stiffness of the antenna and reduce the shape error caused by the tension force as far as possible. In order to verify the effectiveness of the above method, the finite element model of the antenna is established. On this basis, the finite element analysis is carried out, and the structural stiffness and shape error under different tension parameters are studied. In order to improve the stiffness of the structure and reduce the shape error caused by the tension force, the tension parameters are optimized. In order to improve the efficiency of optimization calculation, the response surface method is used to establish a surrogate model to participate in the optimization iterative calculation. Non-inferior sorting genetic algorithm (NSGA-Ⅱ) is used to complete the iterative calculation. The optimized tension parameters further improve the performance of the antenna. This research can provide theoretical guidance for the design of truss deployable paraboloid antenna.
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Key words:
- paraboloid antenna /
- tension rope /
- shape error /
- finite element analysis /
- optimization design
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表 1 Bushing元位移刚度参数设置
Table 1. Parameter setting of displacement stiffness for Bushing coupling
位移刚度 数值/(N·mm-1) D11 108 D22 108 D33 108 
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表 2 Bushing元转动刚度参数设置
Table 2. Parameter setting of rotational stiffness for Bushing coupling
转动刚度 数值/(N·mm·rad-1) D44 108 D55 108 D66 10
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表 3 模型属性设置
Table 3. Model property setting
参数 杆 绳索 材料 铝合金 钢丝 弹性模量/MPa 7×104 1.5×105 密度/(t·mm-3) 2.84×10-9 7.9×10-9 泊松比 0.31 0.31 单元类型 Beam Truss 网格类型 Beam T3D2 截面尺寸/mm 直径: 15, 厚度: 1 直径：1
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表 4 无绳索天线固有频率及平均固有频率
Table 4. Natural frequency and average natural frequency of cordless antenna
阶层 固有频率(方案0)/Hz 1阶 0.490 2阶 0.800 3阶 1.841 4阶 4.350 5阶 6.732 6阶 8.203 C 0.962
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表 5 张紧力布置方案
Table 5. Tension arrangement scheme
阶层 张紧力/N 方案1 方案2 方案3 方案4 1层 200 140 220 290 2层 200 300 270 250 3层 200 170 190 110 4层 200 190 120 150
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表 6 不同方案各阶固有频率及平均固有频率
Table 6. Natural frequency and average natural frequency of each order for different schemes
阶层 固有频率/Hz 方案1 方案2 方案3 方案4 1阶 0.503 0.504 0.504 0.505 2阶 0.808 0.808 0.808 0.808 3阶 1.830 1.829 1.829 1.830 4阶 6.938 6.920 6.920 6.910 5阶 10.078 10.046 10.046 10.029 6阶 16.291 16.285 16.285 16.283 C 1.022 1.023 1.023 1.025
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表 7 不同方案形面误差
Table 7. Shape error of different schemes
方案 张紧力/N 形面误差/mm 1层 2层 3层 4层 方案1 200 200 200 200 0.177 方案2 140 300 170 190 0.066 方案3 220 270 190 120 0.109 方案4 290 250 110 150 0.056
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表 8 响应面精度系数
Table 8. Response surface accuracy coefficient
指标 RMSE R2 C 0.000 076 0.992 176 T 0.003 468 0.999 587
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表 9 优化算法参数配置
Table 9. Parameter configuration of optimization algorithm
参数 数值 种群数 12 进化代数 20 交叉指数 10 变异指数 20 交叉概率 0.9
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表 10 最优解验证
Table 10. Verification of optimal solution
名称 最优解 对照组 F1/N 271.95 200 F2/N 249.21 200 F3/N 103.38 200 F4/N 101.13 200 C/Hz 1.024 1.023 T/mm 0.020 0.177
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