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摘要:
抛物面天线作为卫星上重要的功能组件，是实现遥感测量和无线通信等功能的基础。为了解决模块化抛物面天线折展机构构型设计与刚度匹配困难的问题，提出一种基于剪刀机构的肋单元折展机构的构型方法，并设计了肋单元折展机构。通过运动学分析，验证了该机构通过参数的修改，可以实现同一折展机构展开状态包络不同抛物面拟合球面。给出一种包络锥法实现多模块折展机构展开过程的求解思路，为可转动肋单元的运动副配置提供依据。构建多模块折展机构的有限元模型，以提高固有频率和降低整体质量为优化目标，对肋单元折展机构的构型参数进行优化。采用非劣排序遗传算法完成优化迭代计算,得到具有高刚度、轻量化的折展机构设计参数，在相同条件下优化后调和平均固有频率提高了67.4%，天线整体质量下降了35.2%。
Abstract:As an important functional component of a satellite, a parabolic antenna is a basis for realizing remote sensing measurement and wireless communication. In order to solve the difficulty of configuration design and stiffness matching of modular parabolic antenna deployable mechanism, a configuration method of rib element deployable mechanism based on scissors mechanism is proposed, and the rib element deployable mechanism is designed. Through kinematic analysis, it is verified that the same deployable mechanism can envelope different paraboloid-fitted spheres through the modification of parameters. The configuration of kinematic pairs of rotatable rib parts is based on a concept for solving the unfolding process of the multi-module deployable mechanism by the envelope cone approach.The configuration parameters of the rib element deployable mechanism are improved to increase natural frequency and decrease overall quality, and the finite element model of the multi-module deployable mechanism is built. The non-inferior sorting genetic algorithm is used to complete the optimization iterative calculation, and the design parameters of deployable mechanisms with high structural stiffness and lightweight are obtained. Under the same conditions, the harmonic average natural frequency is increased by 67.4%, and the overall quality of the antenna is reduced by 35.2% after optimization.
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图 1 模块化抛物面折展机构组成示意图
Figure 1. Composition diagram of modular parabolic deployable mechanism
图 2 肋单元折展机构实物图
①折杆；②顶端滑块；③多级套筒；④剪刀杆；⑤底端固定块；⑥公共端轴线；⑦自由端轴线
Figure 2. Physical picture of rib unit deployable mechanis
图 3 肋单元折展机构展开收拢状态简图
Figure 3. Schematic diagram of unfolding and folding state of rib unit deployable mechanism
图 5 过程拟合球面半径和过程两侧滑块所在直线夹角随滑块行程变化曲线
Figure 5. Curves of fitting spherical radius and included angle of line changed with slider stroke
图 6 多模块机构包络锥示意图
Figure 6. Schematic diagram of envelope cone of multi- module mechanism
图 7 中心基本模块和第2层模块1包络锥示意图
Figure 7. Schematic diagram of envelope cone of central module and layer 2 module 1
图 8 中心基本模块和第2层模块i及模块i+1包络锥示意图
Figure 8. Schematic diagram of envelope cone of central module,layer 2 module i and module i + 1
图 9 七模块抛物面折展机构有限元模型
Figure 9. Finite element model of seven module parabolic deployable mechanism
表 1 杆件与绳索材料参数
Table 1. Material parameters of rods and rope
类型 弹性模量/MPa 密度/(103 kg·m−3) 泊松比 杆件 7×104 2.84 0.3 绳索 1.5×105 7.9 0.3 
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表 2 杆件与绳索截面参数
Table 2. Section parameters of rods and rope
杆件截
面编号杆件外
圆半径杆件厚
度/mm应用杆件
(见图3)绳索截面
半径/mm绳索截面
张紧压强/MPa1 $ {r_1} $ 1 CD、DE、KI、JM 0.75 113.32 2 $ {r_2} $ 1 OJ、AK、BC、EF、
MG、IH0.75 113.32 3 $ {r_3} $ 12 AB、FG 0.75 113.32 4 $ {r_3} $ 4 OA、GH 0.75 113.32
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表 3 固定构型参数
Table 3. Fixed configuration parameters
$ {\theta _1} $/(°) $ R $/mm $ {l}_{C'E'} $/mm $ {r_2} $/mm $ {r_3} $/mm 7.318 9402 20 11 13
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表 4 优化数学模型自变量取值范围
Table 4. Range of independent variables of optimization mathematical model
类型 $ {l_{OJ}} $/mm $ {l_{BC}} $/mm $ {l_{AB}} $/mm $ {r_1} $/mm 下界 24 24 20 5 上界 40 40 30 20
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表 5 优化数学模型更新后自变量取值范围
Table 5. Range of independent variables after updating the optimization mathematical model
类型 x/mm y/mm lAB/mm r1/mm 下界 0 0 20 5 上界 23.6 1.03 30 20
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表 6 优化算法参数
Table 6. Optimization algorithm parameters
种群数 进化代数 交叉概率 交叉指数 变异指数 24 40 0.9 10 20
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表 7 优化前后对比
Table 7. Comparison before and after optimization
类型 $ {l_{OJ}} $/mm $ {l_{BC}} $/mm $ {l_{BC}} $/mm $ {l_{BC}} $/mm $ {l_{BC}} $/mm $ {l_{BC}} $/mm 初始值 39 40 25 12.5 1.216 77.565 最优解 39.513 39.782 21.295 7.944 2.036 50.293
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