【摘要】 离轴三反光学系统多采用长条形反射镜，为尽可能提高反射镜面形精度，其支撑结构形式多为柔性支撑；为了在保证结构力学性能的基础上满足轻量化的需求，支撑亦多采用壳体点阵结构。本文基于尺寸优化技术，建立了长条形反射镜的参数化有限元模型以及双轴圆弧切口柔性铰链支撑的多参数优化模型，分别应用可行方向法及自适应响应面优化算法得到了质量约束下刚度最优的反射镜面板、筋板厚度参数以及刚度约束下镜面面形最优的柔铰支撑几何尺寸参数，并应用参数试验方法对该柔性支撑安装角度及安装轴向位置进行了独立变量的影响分析。对于背板的设计，本文提出了一种基于点云三维重建的点阵结构设计仿真优化方法，采用贪婪三角化投影算法对点阵结构包络生成的点云进行网格重构，保证了点阵结构模型的连续性与真实性。经过仿真验证，优化参数下重力、温度、强迫位移各工况下反射镜综合面形误差（0.018λ）和装调方向重力下刚体位移（0.007 mm）均达到最优。表明基于点云三维重建的点阵结构设计仿真优化方法合理可行，可推广应用于类似结构形式的反射镜支撑。更多还原

【Abstract】 Objective The design of the mirror body and its supporting structure exert an important influence on the system imaging quality. It is necessary to reduce the structural mass as much as possible, improve the surface shape accuracy of the mirror as much as possible, and ensure the dynamic and static stiffness and thermal dimensional stability of the system to reduce the transmission cost. Meanwhile, this has always been a difficult point in designing spatial optical machine structures.Reasonable flexible support design can solve the contradiction of mirror surface shape decline caused by temperature load and assembly stress on the premise of satisfying the mirror support stiffness. Computer-aided design/computer-aided engineering(CAD/CAE) technology is employed to predict and optimize the parameters of the flexible structure, and the direction and amount of parameter correction are determined according to the simulation results before design iteration. It is an efficient design solution for mirror support systems. In recent years, compared with traditional materials, the additive manufacturing lattice structure has been widely applied in space remote sensing cameras due to its excellent characteristics such as higher lightweight efficiency, specific stiffness/strength, and mechanical properties that can be designed. The complex lattice structures result in huge analysis and calculation amounts. At present, scholars at home and abroad mostly adopt the equivalent homogenization analysis method for lattice structures, and an urgent problem is to predict the mechanical properties of lattice filled structures quickly and effectively. To this end, a mechanical simulation technique based on accurate finite element modeling is proposed.Methods Based on the size optimization technique, we build a parametric finite element model of a rectangular reflective mirror and a multi-parameter optimization model of biaxial circular cut-out flexure hinge support. First, the feasible direction method and adaptive response surface optimization algorithm are applied respectively to obtain the thickness parameters of the mirror plate and the rib plate(Table 3) and the geometric size parameters of the flexible hinge support(Table 4). The influence of independent variables on the installation angle(Fig. 6) and the installation axial position(Fig.7) of the flexible support is analyzed by the parametric test method. Second, a simulation optimization method of lattice structure design based on three-dimensional point cloud reconstruction is studied. Lattice filling and point cloud generation(Fig. 10) are utilized to reconstruct the grid of point clouds generated by the lattice structure envelope(Fig. 11), which can ensure the continuity and authenticity of the lattice structure model and obtain the backplane support parameters(Table 5).Finally, finite element modeling(Fig. 13) and simulation verification(Table 6) are carried out for the mirror assembly.Results and Discussions The optimization results show that when the installation angle β is 20°, the installation position is 13 mm±0. 5 mm, and the geometric parameter r/t/b is 1/2/3 mm(Table 4), the composite surface shape of the mirror reaches the optimal value(0. 018λ)(Table 6). When the skin and lattice structure parameter R/a/T of the backplane support is 0. 8/6/4. 5 mm(Table 5), the rigid body displacement of the mirror reaches the optimal value(0. 007 mm). At the same time, the first order fundamental frequency and component mass meet the design requirements.Conclusions We propose a simulation optimization method for lattice structure design based on three-dimensional point cloud reconstruction. The results show that the simulation optimization method is reasonable and feasible, and can meet the design requirements of mirror support structures with similar structural forms.更多还原