TOPOLOGY OPTIMIZATION-BASED METHOD FOR LIGHTWEIGHT AND THIN DESIGN OF ADDITIVE MANUFACTURING SILICON CARBIDE PRIMARY MIRROR
-
摘要: 拓扑优化方法和陶瓷增材制造技术的结合为开发轻质高性能的大口径碳化硅反射镜提供了一种有效的方法. 以反射镜背部支撑结构构型为设计对象, 以最大刚度为目标、反射镜质量为约束, 采用板筋布局与高度协同优化(heaviside-function based directional growth topology parameterization, H-DGTP)方法建立了具备陶瓷可制造性约束的轻薄化设计方法. 该方法针对典型大口径碳化硅空间反射镜的实际需求, 设计了具有陶瓷可制造性的反射镜镜体轻薄化构型; 进一步采用尺寸优化方法对拓扑优化的反射镜镜体结构进行了重构和精细化设计; 利用 DLP 陶瓷增材制造技术成功制备了反射镜陶瓷样件, 验证了所设计的反射镜镜体轻薄化构型满足陶瓷增材制造的可制造性要求. 对轻薄化设计方案进行了数值仿真, 反射镜法向轴沿x, y和z向自重载荷的均方根RMS值分别为3.27, 3.27和7.55 nm, 反射镜面密度为13.21 kg/m2. 分析结果表明, 优化后的大口径碳化硅空间反射镜在满足面形精度设计要求的同时大幅减轻了反射镜重量, 验证了该方法在增材制造碳化硅反射镜轻薄化设计方面的有效性.Abstract: To develop the lightweight and high-performance large-aperture silicon carbide (SiC) space primary mirrors, the combination of topology optimization methods and ceramic additive manufacturing techniques provides an effective strategy. The lightweight and thin design method was designed with the back support structure of the silicon carbide space primary mirror, with the maximum stiffness as the design objective and the total mass of the silicon carbide space primary mirror as the constraint. Additionally, this novel method was designed while considering the ceramic manufacturability constraints, based on the Heaviside-function based directional growth topology parameterization (H-DGTP) method. Firstly, the lightweight and thin design method designed a lightweight and thin configuration of the silicon carbide space primary mirror body with ceramic manufacturability, based on the actual requirements of a typical large-diameter silicon carbide space primary mirror. Then, the size optimization method was used to reconstruct and refine the topology-optimized silicon carbide space primary mirror structure. Furthermore, the ceramic sample of the silicon carbide space primary mirror was successfully prepared by the digital light processing (DLP) ceramic additive manufacturing technology, which verified that the designed lightweight and thin configuration of the mirror body meets the manufacturability requirements of ceramic additive manufacturing. Numerical simulation was carried out for the design scheme of the lightweight and thin method. The root mean square (RMS) values of the silicon carbide space primary mirror normal axis along the x, y, and z directions under self-weight load are 3.27 nm, 3.27 nm, and 7.55 nm, respectively. Moreover, the area density of the silicon carbide space primary mirror is 13.21 kg/m2. The analysis results show that the optimized large-aperture silicon carbide space primary mirror meets the design requirements of surface accuracy and greatly reduces the weight of the mirror. The results verify the effectiveness of the proposed method for the lightweight and thin design of additive manufacturing silicon carbide space primary mirror.
-
引 言
在空间应用中, 反射镜的结构形式是影响反射镜轻量化和面形精度的关键因素[1-2]. 随着长距离空间望远镜的不断发展, 大口径的反射镜面临着更严格的设计要求, 不仅要保证在足够的刚度和性能的前提下进一步减轻反射镜质量, 同时反射镜直径厚度比由传统的6 ~ 8逐渐向更大的比值发展, 以满足更轻薄的镜面设计[3-4]. 传统反射镜的设计受限于结构形式和加工的复杂性, 通常使用参数化设计方法对背部开放式的蜂窝板筋结构设计进行板筋厚度、高度和间距等参数的改进, 来保证反射镜的面形精度RMS满足小于波长的1/40 (波长λ = 632.8 nm)的性能需求, 但反射镜直径厚度比却难以进一步提高[4-7]. 因此, 为了满足大口径空间反射镜轻薄化、高精度的迫切需求. 需要引入更先进的设计方法来突破传统结构的局限性, 进一步扩展反射镜的设计空间, 设计出更轻更薄的反射镜.
近年来, 拓扑优化方法与增材制造技术的快速发展为解决大口径反射镜的设计问题提供了新的思路[8]. 拓扑优化方法通过在反射镜的设计域内寻找最优的结构形式以获得性能更优、重量更轻的反射镜结构. 研究表明, 与传统的设计方法相比, Qu 等[9-10]采用拓扑优化设计的反射镜在轻量化率和结构刚度等方面均优于传统的三角形和六边形孔构型. Liu等[11]的对比分析也表明了拓扑优化设计的反射镜在面形精度和结构轻量化率上优于传统三角形和四边形孔轻量化构型. 拓扑优化方法突破了传统规则几何的限制, 进一步提升了反射镜的轻量化率, 在设计上拥有更大的自由度和灵活性. 一方面, 拓扑优化设计方法可以在反射镜的传统构型设计的基础上进一步地优化设计[12-13], 另一方面也可以直接修改初始结构得到非常规设计的反射镜结构构型[14-15], 但这对制造工艺提出了更高的要求. 随着增材制造技术的进步, 拓扑优化设计的具有复杂几何构型的金属材料反射镜可以直接制备[16-19]. 这打破了传统减材工艺的几何限制, 为制造高精度及高轻量化的反射镜提供了更多的可能[20-21]. 但对碳化硅陶瓷反射镜的增材制造仍集中在传统的蜂窝板筋布局的制备[22-24]. 同时在实际应用中, 拓扑优化的高自由度设计和不同增材制造工艺的可制造性之间还存在一些限制, 例如拓扑优化结构内部封闭的孔洞空隙[25-26]和结构的悬垂[27-28]等. 显然, 针对大口径碳化硅空间反射镜, 必须在考虑满足性能约束的轻量化要求的同时, 考虑可制造性问题. 因此迫切需要建立考虑可制造性的增材制造碳化硅反射镜轻薄化设计方法, 实现大口径碳化硅空间反射镜的性能优化和成功制备.
本文研究考虑可制造性的增材制造碳化硅反射镜轻薄化设计问题, 建立基于拓扑优化的增材制造碳化硅反射镜轻薄化设计方法. 该方法能够考虑大口径碳化硅反射镜的轻薄化与高面形精度的性能要求、可制造需求等, 实现设计、制造和性能之间的协同优化. 以典型大口径碳化硅空间反射镜为例, 基于所建立的方法对反射镜背部支撑结构的构型进行了设计, 并对设计方案进行了制备和性能表征. 分析结果表明, 获得的设计具有良好的性能和可制造性.
1. 轻薄化反射镜设计方法
为了保证结构的可制造和易制造, 结构需要具有一定的几何特征. 本文选用板筋增强式结构作为可制造和易制造的结构特征. 通过设计板筋的布局和高度分布, 以提升结构的性能. 本文基于Liu等[29]提出的H-DGTP方法建立保持板筋形式的可制造性约束, 以结构刚度最大化为目标建立拓扑优化模型, 来获得板筋的合理分布. 通过拓扑优化结果的可编辑重构和基于参数优化的精细化设计, 以获得反射镜轻薄化设计构型.
1.1 板筋布局设计的拓扑优化模型
H-DGTP (heaviside-function based directional growth topology parameterization)方法是一种板筋布局与高度协同优化模型, 该方法能够实现基于三维模型板筋式结构的板筋布局与高度协同优化设计. 根据H-DGTP方法[29]的思想, 板筋布局通过设计反射镜背面(基面)的法线方向一定厚度的区域(设计域)的材料分布实现, 如图1所示. 通过引进基面各处的相对密度变量$ {\rho _j} $描述板筋的有无, 并引进参数$ {\eta _j} $描述板筋高度. 各单元的材料相对密度$ {\rho _e} $可由基面对应位置的相对密度$ {\rho _j} $和高度描述参数$ {\eta _j} $确定
![]()
图 1 H-DGTP 方法单元密度参数化示意图Figure 1. Schematic diagram of the elemental density parameterization of the H-DGTP method$$ \left.\begin{split} & {\rho _e}{\text{ = }}{\rho _j} \times H({s_e},{\eta _j}),\quad j = 1,2,\cdots,N_{{\mathrm{eg}}} \\ & H({s_e},{\eta _j}) = \left\{\begin{aligned} & {1,\qquad {s_e} < {\eta _j}} \\ & {0,\qquad {s_e} \geqslant {\eta _j}} \end{aligned} \right. \end{split}\right\} $$ (1) 式中, $ {\rho _j} \in \left[ {0,1} \right] $为板筋结构基面的单元相对密度, $ {s_e} = {x \mathord{\left/ {\vphantom {x {{L_x}}}} \right. } {{L_x}}} \in \left[ {0,1} \right] $为单元组内任意单元归一化后的中心点坐标, $x$为单元中心点沿打印方向到基面的距离, ${L_x}$为打印方向上单元组的高度, $ {\eta _j} $为板筋的高度设计变量, $ N_\text{eg} $为设计域内基面单元的数目. $ H $为Heaviside函数, 其光滑近似函数可定义为
$$ H(s,\eta ) = \frac{{{e^{\beta \times (\eta - s)}}}}{{1 + {e^{\beta \times (\eta - s)}}}} $$ (2) 式中, $\beta > 0$决定了近似函数的光滑程度.
结构柔顺度与均方根(root mean square, RMS)值都是与结构整体位移相关的响应函数, 均可用于衡量结构整体刚度[30-31]. 本文选择结构柔顺度最小作为设计目标函数, 通过设计在质量约束条件下结构的柔顺度最小来实现最大化结构的整体刚度. 结构柔顺度的计算公式为
$$ c({\boldsymbol{X}}) = {{{\boldsymbol{u}}}^{\text{T}}}{{\boldsymbol{f}}} $$ (3) 式中, ${\boldsymbol{u}}$为结构的位移向量, ${\boldsymbol{f}}$为结构的载荷向量.
质量约束表示为
$$ g({{\boldsymbol{X}}}) = {\rho ^0}\sum\limits_{e = 1}^{N_{\mathrm{ele}}} {{\rho _e}} {v_e} - M $$ (4) 式中, ${\rho ^0}$为碳化硅材料的密度, ${v_e}$为单元体积, $M$为给定的反射镜质量, $ N_{\mathrm{ele}} $为单元总数.
因此, 轻薄化设计的拓扑优化模型表示为
$$ \begin{split} & \text{find } {\boldsymbol{X}} = (\rho_1, \eta_1, \rho_2, \eta_2, \ldots, \rho_{N_{\text{eg}}}, \eta_{N_{\text{eg}}})^\top \\ &\text{minimize } \quad c({\boldsymbol{X}}) \\ & \text{subject to } \quad {\boldsymbol{Ku}} = {\boldsymbol{f}} \\ & \quad g({\boldsymbol{X}}) \leqslant 0 \\ & \quad 0 \leqslant \rho_j \leqslant 1, \quad 0 \leqslant \eta_j \leqslant 1, \quad \text{for } j = 1, 2, \ldots, N_{\text{eg}} \end{split}$$ (5) 式中, $ {\boldsymbol{K}} $为结构整体刚度矩阵.
1.2 重构模型
基于拓扑优化获得的概念设计, 可进行反射镜模型的可编辑重构. 拓扑优化的概念设计简化并转化为实际工程应用的标准几何形状时, 往往难以保持其最优性[32]. 因此采用特征设计和参数化建模方法, 对几何模型中不规则区域进行规则化处理, 使其转化为标准几何形状. 如图2(a)所示, 在重构过程中, 首先根据拓扑优化结果初步确定板筋位置和高度, 将每个板筋分成不同组件, 并设定其为等厚度分布并取整, 如图2(b)所示. 该厚度将作为反射镜精细化设计的优化参数.
![]()
图 2 反射镜模型重构设计示意图Figure 2. Schematic diagram of the primary mirror reconstruction design1.3 尺寸优化模型
在轻薄化设计方法中, 通过拓扑优化设计确定反射镜的板筋形状、位置(包括布局和高度). 在此基础上, 尺寸优化对板筋的厚度进行精细化设计, 在满足性能要求的同时, 进一步减轻反射镜重量. 因此, 基于反射镜重构模型的精细化设计模型描述为: 通过优化设计板筋的厚度${t_i}$, 在满足反射镜在不同姿态下的面形精度要求的情况下实现质量最小化设计. 面形精度通过光轴方向与重力方向重合(z轴方向)和垂直方向(x轴方向和y轴方向)下的均方根(RMS)值来表征. 轻薄化设计的尺寸优化模型表示为
$$ \begin{split} & {\text{find }}{\boldsymbol{t}} = \left\{ {{t_i}} \right\},\quad i = 1,2,\cdots,n \\ & \min m \quad \\ & {\text{s}}{\text{.t}}{\text{. }}{\boldsymbol{Ku}} = {\boldsymbol{f}} \\ &\qquad \underline{{{t}_{i}}} \leqslant {t_i} \leqslant {{\bar t}_i} \\ &\qquad {x_\text{RMS}} \leqslant {{\bar x}_\text{RMS}} \\ &\qquad {y_\text{RMS}} \leqslant {{\bar y}_\text{RMS}} \\ &\qquad {z_\text{RMS}} \leqslant {{\bar z}_\text{RMS}} \end{split} $$ (6) 式中, $ m $为反射镜质量, $ {x_\text{RMS}},{y_\text{RMS}} $和$ {z_\text{RMS}} $为反射镜法向轴沿x, y和z向自重载荷下的均方根RMS值, $ \underline{{{t}_{i}}} $和$ {\bar t_i} $分别表示为板筋厚度的优化下限值和上限值, $ {\overline{x}}_\text{RMS}, {\overline{y}}_\text{RMS} $和$ {\bar z_\text{RMS}} $分别表示为x, y和z向自重载荷下的均方根RMS的优化上限值. 其中, 镜面的均方根RMS值计算式为[31, 33]
$$ RMS({\boldsymbol{X}}) = \sqrt {\sum\limits_{i = 1}^{Ns} {{w_i}E_i^2} } $$ (7) 式中, $Ns$为镜面上的节点总数, ${w_i}$为整个镜面表面的i个节点的权重系数, $ {E_i} = u_i^n - {Z_{i1}} - {Z_{i2}} - {Z_{i3}} $, 其中, $u_i^n$为镜面上第i个节点的法向位移, $ {Z_{i1}} $,$ {Z_{i2}} $和$ {Z_{i3}} $为Zernike多项式的低阶项, 分别代表镜面的偏移、倾斜和散焦.
2. 典型反射镜的轻薄化设计
2.1 拓扑优化设计
2.1.1 反射镜几何特征
为验证轻薄化设计方法, 本文选取典型碳化硅反射镜进行设计. 反射镜采用极坐标系进行建模(原点位于镜面圆心处, z负方向指向镜面正法向, 如图3所示), 镜体为圆柱形, 光学表面呈球形凹形. 初始模型质量为29.91 kg, 外径D = 510 mm, 内径d = 116 mm, 总厚度T = 53 mm, 背部三点轴向支撑孔直径Ds = 50 mm, 支撑环半径R = 160 mm. 主镜采用碳化硅陶瓷材料, 弹性模量为350 GPa, 泊松比为0.17, 密度为3.0 g/cm3. 设计需求为镜面厚度为2.5 mm, 支撑孔的厚度为2.5 mm. 通常情况下[34], 反射镜的设计要求在自重载荷下反射镜在x, y和z向的光学面形RMS值 ≤ λ/60 (λ = 632.8 nm). 薄镜的面密度≤15 kg/m2, 即反射镜重量$M$不超过3 kg.
2.1.2 反射镜拓扑优化设计
由于反射镜结构具有高度的对称性, 拓扑优化计算仅需要1/6的反射镜模型, 有效降低了拓扑优化的计算负担. 优化后的模型质量约束为0.5 kg. 采用三维八节点线性实体单元进行模型离散化, 并沿厚度方向均匀布置网格, 共计
211444 个单元,223168 个节点. 图4展示了反射镜的不可设计域与可设计域的位置分布. 其中, 镜面背部的支撑孔和反射镜镜面均作为不可设计域, 如图4中灰色的区域所示. 而可设计域为图4中的红色区域, 即除镜面及支撑孔之外的区域.在反射镜优化过程中, 考虑了反射镜法向轴沿x, y和z向的自重影响(G = 9800 N/kg). 通过拓扑优化求解, 获得反射镜背部结构的材料最优分布形式. 如图5所示, 反射镜背部材料集中分布在各个支撑孔周围, 呈树枝状延伸布局, 高度随距离支撑孔的远近而变化, 远离支撑孔处, 板筋高度越低. 同时, 在第一阶段的拓扑优化设计保持了板筋结构形式, 避免了悬挑镂空的结构存在, 保证了制造可行性. 在轻薄化最终的拓扑优化设计结果中, 反射镜质量为2.97 kg, 较初始质量减少约90%.
通过对反射镜最终拓扑优化模型进行分析, 图6展示了反射镜法向轴沿x, y和z向自重载荷下的镜面法向位移云图, 并用GX-max表示在x向自重载荷下的镜面法向位移最大值. 根据公式(7)计算, 反射镜法向轴沿x, y和z向自重载荷下的均方根RMS值分别为2.04, 3.18和7.63 nm, 均优于λ/60 (λ = 632.8 nm). 结果如表1所示, 第一阶段拓扑优化设计的反射镜完全满足设计需求.
![]()
图 6 反射镜拓扑优化模型在x, y和z方向的镜面法向位移云图Figure 6. Normal displacement contour for the topology optimization model of the primary mirror in x, y and z-direction表 1 拓扑优化设计的反射镜性能Table 1. Performance of the topology optimization design of the primary mirrorGX-max/nm GY-max/nm GZ-max/nm xRMS/nm yRMS/nm zRMS/nm 1.44 16.20 36.62 2.04 3.18 7.63 2.2 尺寸优化设计结果
2.2.1 反射镜重构设计
对反射镜拓扑优化概念模型进行可编辑重构和合理设计, 并转化为更规则的简单几何形式. 图7展示了反射镜的重构模型, 质量为2.96 kg. 通过对重构后的反射镜模型进行分析, 图8展示其法向轴沿x, y和z向自重载荷下的镜面法向位移云图, 并计算了相应方向的均方根RMS值.
![]()
图 8 反射镜重构模型在x, y和z方向的镜面法向位移云图Figure 8. Normal displacement contour for the reconstructed model of the primary mirror in x, y and z-direction如表2所示, 与拓扑优化模型的结果相比, 反射镜重构模型的性能有所降低, 这是由于重构过程中对拓扑优化模型进行了部分规则化处理导致了结构改变, 影响了反射镜结构效率, 但重构模型的性能仍均满足设计需求.
表 2 重构设计的反射镜性能Table 2. Performance of the reconstructed design of the primary mirrorGX-max/nm GY-max/nm GZ-max/nm xRMS/nm yRMS/nm zRMS/nm 17.37 16.28 36.77 3.39 3.93 6.83 2.2.2 反射镜尺寸优化设计
在尺寸优化计算时仍使用了1/6的反射镜模型, 如图9所示. 本文选定反射镜主要的8个板筋的厚度作为设计变量, 表3给出了设计变量的初始值和优化上下限值. 其中, 板筋厚度的初始值与优化上限值一致, 这是由于在拓扑优化阶段, 对反射镜板筋形状和位置布局均已经进行了优化设计, 因此为了实现进一步的减重, 将板筋厚度的优化上限值作为初始变量. 另外, 所有设计变量增量均为0.5 mm.
![]()
图 9 尺寸优化设计变量示意图Figure 9. Schematic diagram of the design variables in size optimization表 3 尺寸优化的设计变量Table 3. Design variables in size optimizationZone 1 2 3 4 5 6 7 8 lower bound/mm 0 0 0 0 0 0 0 0 upper bound/mm 3 3 5 5 5 3 3 3 initial value/mm 3 3 5 5 5 3 3 3 optimized value/mm 0.5 0.5 4.5 4.5 4.5 0.5 0.5 0.5 根据尺寸优化的结果, 图10展示了轻薄化设计的反射镜背部结构示意图. 表4对比了最终尺寸优化后的轻薄化设计模型与拓扑优化模型、初始重构模型的性能. 结果表明, 轻薄化设计在保证反射镜均方根RMS值符合设计要求的同时, 实现了结构的进一步减重. 尽管部分性能有所降低, 但面密度从拓扑优化模型的14.56 kg/m2降至13.21 kg/m2, 总质量减少了约9%. 另外, 镜面的面密度为7.13 kg/m2, 表明非设计域中的镜面厚度仍是影响镜面面密度的关键因素.
表 4 反射镜性能比较Table 4. Comparison of primary mirror performancePrimary mirror
designMass/kg Area density/
(kg·m−2)xRMS/
nmyRMS/
nmzRMS/
nmtopology optimization
design2.97 14.56 2.04 3.18 7.63 reconstructed
design2.96 14.47 3.39 3.93 6.83 lightweight and
thin design2.70 13.21 3.27 3.27 7.55 3. 反射镜可制造性验证
为验证轻薄化设计的可制备性, 使用嘉善饶稷科技有限公司生产的CeramPlus工业级陶瓷3D打印机(DLP-FLEX HD)进行反射镜制备. 受材料限制和成本考虑, 采用氧化铝陶瓷材料进行测试, 并将反射镜等比例缩放至直径为130 mm. 为避免反射镜板筋局部尺寸过小, 制备模型采用反射镜重构模型(图7). 由于优化过程中未考虑外部制造约束, 制备前需要增加支撑结构以确保打印稳定性. 为简化后续制备工艺, 打印方向设置为镜面向上. 图11展示了陶瓷DLP打印机主要的打印流程. 首先, 将CAD反射镜模型以STL文件格式导入计算机, 随后通过特定软件进行逐层切片, 切片厚度为50 μm. 之后打印机逐层制备陶瓷反射镜生坯, 最后清理表面未固化的陶瓷浆料. 制备的反射镜生坯如图12所示. 表5给出了反射镜生坯的测量尺寸结果, 选取了反射镜外径D、中心孔径d和尺寸优化中的设计变量1和3的板筋厚度进行尺寸测量, 根据5次有效测量结果得到实测均值和标准差. 实验数据证明, 轻薄化设计的反射镜具有良好的可制造性, 所制备的陶瓷反射镜还原度较高, 整体成型质量较好.
![]()
图 12 DLP制备的反射镜生坯Figure 12. DLP-stereolithography manufactured green body of the primary mirror表 5 反射镜生坯的尺寸测量结果Table 5. The dimensional measurement results of the green body of the primary mirrorMeasurement location Total diameter (D) Center hole diameter (d) Stiffener
thickness (T1)Stiffener thickness (T3) nominal value/mm 130.00 29.57 0.76 1.27 measured mean/mm 130.03 29.53 0.81 1.33 standard deviation/mm 0.03 0.03 0.01 0.01 4. 结 论
本文以大口径碳化硅空间反射镜为例, 提出了一种基于拓扑优化的增材制造结构轻薄化设计方法. 结果表明, 轻薄化设计的反射镜法向轴沿x, y和z向自重载荷下的均方根RMS值分别为3.27, 3.27和7.55 nm, 面密度为13.21 kg/m2. 与拓扑优化的概念构型相比, 轻薄化设计在可编辑重构和精细化设计后, 能够满足性能需求并实现结构减重设计, 反射镜总质量下降了约9%, 实现了碳化硅空间反射镜更高程度的轻量化. 并通过DLP陶瓷增材制造技术验证了轻薄化设计反射镜的可制造性. 该方法在保持结构的可制造性和满足面形精度的前提下, 进一步挖掘了轻量化的潜力, 为反射镜优化设计和制造提供了一套完整可行的设计方案.
-
![]()
图 1 H-DGTP 方法单元密度参数化示意图
Figure 1. Schematic diagram of the elemental density parameterization of the H-DGTP method
![]()
图 2 反射镜模型重构设计示意图
Figure 2. Schematic diagram of the primary mirror reconstruction design
![]()
图 6 反射镜拓扑优化模型在x, y和z方向的镜面法向位移云图
Figure 6. Normal displacement contour for the topology optimization model of the primary mirror in x, y and z-direction
![]()
图 8 反射镜重构模型在x, y和z方向的镜面法向位移云图
Figure 8. Normal displacement contour for the reconstructed model of the primary mirror in x, y and z-direction
![]()
图 9 尺寸优化设计变量示意图
Figure 9. Schematic diagram of the design variables in size optimization
![]()
图 12 DLP制备的反射镜生坯
Figure 12. DLP-stereolithography manufactured green body of the primary mirror
表 1 拓扑优化设计的反射镜性能
Table 1 Performance of the topology optimization design of the primary mirror
GX-max/nm GY-max/nm GZ-max/nm xRMS/nm yRMS/nm zRMS/nm 1.44 16.20 36.62 2.04 3.18 7.63 
下载: 导出CSV
表 2 重构设计的反射镜性能
Table 2 Performance of the reconstructed design of the primary mirror
GX-max/nm GY-max/nm GZ-max/nm xRMS/nm yRMS/nm zRMS/nm 17.37 16.28 36.77 3.39 3.93 6.83
下载: 导出CSV
表 3 尺寸优化的设计变量
Table 3 Design variables in size optimization
Zone 1 2 3 4 5 6 7 8 lower bound/mm 0 0 0 0 0 0 0 0 upper bound/mm 3 3 5 5 5 3 3 3 initial value/mm 3 3 5 5 5 3 3 3 optimized value/mm 0.5 0.5 4.5 4.5 4.5 0.5 0.5 0.5
下载: 导出CSV
表 4 反射镜性能比较
Table 4 Comparison of primary mirror performance
Primary mirror
designMass/kg Area density/
(kg·m−2)xRMS/
nmyRMS/
nmzRMS/
nmtopology optimization
design2.97 14.56 2.04 3.18 7.63 reconstructed
design2.96 14.47 3.39 3.93 6.83 lightweight and
thin design2.70 13.21 3.27 3.27 7.55
下载: 导出CSV
表 5 反射镜生坯的尺寸测量结果
Table 5 The dimensional measurement results of the green body of the primary mirror
Measurement location Total diameter (D) Center hole diameter (d) Stiffener
thickness (T1)Stiffener thickness (T3) nominal value/mm 130.00 29.57 0.76 1.27 measured mean/mm 130.03 29.53 0.81 1.33 standard deviation/mm 0.03 0.03 0.01 0.01
下载: 导出CSV
-
[1] Malamed ER, Petrov YuN, Sokolov IM. Designs of the primary mirrors of space telescopes. Journal of Optical Technology, 2002, 69(9): 622-626 doi: 10.1364/JOT.69.000622
[2] Savitskiĭ AM, Sokolov IM. Questions of constructing lightened primary mirrors of space telescopes. Journal of Optical Technology, 2009, 76(10): 666-669 doi: 10.1364/JOT.76.000666
[3] Jr Yoder PR. Opto-Mechanical Systems Design. Third Edition. Boca Raton: CRC Press, 2006: 449-479
[4] Cheng JQ. The Principles of Astronomical Telescope Design. New York: Springer New York NY, 2009: 87-139
[5] Liu XH, Gu KH, Li MX, et al. Optimization design of large-aperture primary mirror for a space remote camera. Sensors, 2023, 23: 5441 doi: 10.3390/s23125441
[6] Wang ZC, Chen T, Cao YY, et al. Lightweight 2m SiC mirror ground-based telescopes. Photonics, 2024, 11: 581 doi: 10.3390/photonics11060581
[7] 袁健, 任建岳. 碳化硅反射镜轻量化结构的改进与优化. 光子学报, 2015, 44(8): 812004 (Yuan Jian, Ren Jianyue. Improvement and optimization of lightweight structure for SiC reflective mirror. Acta Photonica Sinica, 2015, 44(8): 812004 (in Chinese) doi: 10.3788/gzxb20154408.0812004 Yuan Jian, Ren Jianyue. Improvement and optimization of lightweight structure for SiC reflective mirror. Acta Photonica Sinica, 2015, 44(8): 812004 (in Chinese) doi: 10.3788/gzxb20154408.0812004
[8] Hurtado-Pérez AB, Pablo-Sotelo ADJ, Ramírez-López F, et al. On topology optimisation methods and additive manufacture for satellite structures: A review. Aerospace, 2023, 10: 1025 doi: 10.3390/aerospace10121025
[9] Qu YJ, Wang W, Liu B, et al. Topology optimization design of space rectangular mirror//Xu M, Yang J. Advanced Optical Design and Manufacturing Technology and Astronomical Telescopes and Instrumentation, International Symposium on Optoelectronic Technology and Application, Beijing, 2016-05-09-11. China: SPIE, 2016. 1015421
[10] Qu YJ, Jiang YR, Feng LJ, et al. Lightweight design of multi-objective topology for a large-aperture space mirror. Applied Sciences, 2018, 8: 2259 doi: 10.3390/app8112259
[11] Liu JZ, Jiang B. Topology optimization design of a space mirror//Liu SG, Zhuang SL, Petelin MI, eds. Selected Papers of the Photoelectronic Technology Committee Conferences, The Photoelectronic Technology Committee Conferences, Hefei, Suzhou, and Harbin, 2015-06-14-19. China: SPIE, 2015. 97952Y
[12] Liu FC, Li W, Zhao WG, et al. Topology optimization based parametric design of balloon borne telescope’s primary mirror. Applied Sciences, 2021, 11: 5077 doi: 10.3390/app11115077
[13] Jiang P, Wang XY, Wang KJ, et al. Lightweight structure and unequal length flexible support design of a 1.3 × 1.2 m rectangular, horizontally supported mirror. Applied Optics, 2024, 63(27): 7244-7251 doi: 10.1364/AO.531478
[14] Park KS, Lee JH, Youn SK. Lightweight mirror design method using topology optimization. Optical Engineering, 2005, 44(5): 053002 doi: 10.1117/1.1901685
[15] Liu ST, Hu R, Li QH, et al. Topology optimization-based lightweight primary mirror design of a large-aperture space telescope. Applied Optics, 2014, 53: 8318-8325 doi: 10.1364/AO.53.008318
[16] Blakey-Milner B, Gradl P, Snedden G, et al. Metal additive manufacturing in aerospace: A review. Materials & Design, 2021, 209: 110008
[17] Taghizadeh M, Zhu ZH. A comprehensive review on metal laser additive manufacturing in space: Modeling and perspectives. Acta Astronautica, 2024, 222: 403-421 doi: 10.1016/j.actaastro.2024.06.027
[18] Fu Q, Yan L, Tan SL, et al. Lightweight and high-stiffness metal optical systems based on additive manufacturing. Micromachines, 2024, 15: 128 doi: 10.3390/mi15010128
[19] Tenegi Sanginés F, Vega Moreno A, Gracia F, et al. Lightweight metal mirrors manufactured by AM, applied to astronomical instrumentation: first steps towards all-in-one opto-mechanical components//Navarro R, Jedamzik R, eds. Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation VI, SPIE Astronomical Telescopes + Instrumentation, Yokohama, 2024-6-16-21. Japan: SPIE, 2024. 13100
[20] 孙宇欣, 樊延超, 董得义等. 增材制造空间反射镜结构拓扑优化技术发展综述. 激光杂志, 2022, 43(7): 1-14 (Sun Yuxin, Fan Yanchao, Dong Deyi, et al. A review of space mirror topology optimization technology based on additive manufacturing. Laser Journal, 2022, 43(7): 1-14 (in Chinese) Sun Yuxin, Fan Yanchao, Dong Deyi, et al. A review of space mirror topology optimization technology based on additive manufacturing. Laser Journal, 2022, 43(7): 1-14 (in Chinese)
[21] Wu YZ, Fang JG, Wu C, et al. Additively manufactured materials and structures: A state-of-the-art review on their mechanical characteristics and energy absorption. International Journal of Mechanical Sciences, 2023, 246: 108102 doi: 10.1016/j.ijmecsci.2023.108102
[22] Ding GJ, He RJ, Zhang KQ, et al. Stereolithography 3D printing of SiC ceramic with potential for lightweight optical mirror. Ceramics International, 2020, 46: 18785-18790 doi: 10.1016/j.ceramint.2020.04.196
[23] Shen XT, Sun XJ, Wang CB, et al. Topology optimization of a double-sided space mirror based on additive manufacturing of SiC. Structural and Multidisciplinary Optimization, 2024, 67: 130 doi: 10.1007/s00158-024-03842-7
[24] Zhang H, Yang Y, Hu KH, et al. Stereolithography-based additive manufacturing of lightweight and high-strength Cf/SiC ceramics. Additive Manufacturing, 2020, 34: 101199 doi: 10.1016/j.addma.2020.101199
[25] Liu ST, Li QH, Chen WJ, et al. An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures. Frontiers of Mechanical Engineering, 2015, 10(2): 126-137 doi: 10.1007/s11465-015-0340-3
[26] Luo YF, Sigmund O, Li QH, et al. Topology optimization of structures with infill-supported enclosed voids for additive manufacturing. Additive Manufacturing, 2022, 55: 102795 doi: 10.1016/j.addma.2022.102795
[27] Yang D, Pan C, Zhou Y, et al. Optimized design and additive manufacture of double-sided metal mirror with self-supporting lattice structure. Materials & Design, 2022, 219: 110759
[28] 魏伟, 吴海鑫, 吴晓萱等. 增材制造自支撑设计综述. 中国激光, 2024, 51(10): 1002307 (Wei Wei, Wu Haixin, Wu Xiaoxuan, et al. Review of self-supporting design for additive manufacturing. Chinese Journal of Lasers, 2024, 51(10): 1002307 (in Chinese) doi: 10.3788/CJL240434 Wei Wei, Wu Haixin, Wu Xiaoxuan, et al. Review of self-supporting design for additive manufacturing. Chinese Journal of Lasers, 2024, 51(10): 1002307 (in Chinese) doi: 10.3788/CJL240434
[29] Liu ST, Li QH, Chen WJ, et al. H-DGTP—a Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures. Structural and Multidisciplinary Optimization, 2015, 52: 903-913 doi: 10.1007/s00158-015-1281-5
[30] 李超, 董得义, 樊延超等. 基于增材制造技术空间反射镜结构拓扑优化设计方法研究与试验验证. 机电工程技术, 2022, 51(7): 25-30 (Li Chao, Dong Deyi, Fan Yanchao, et al. Research and experimental verification on topology optimization design method of space mirror structure based on additive manufacturing technology. Mechanical and Electrical Engineering Technology, 2022, 51(7): 25-30 (in Chinese) Li Chao, Dong Deyi, Fan Yanchao, et al. Research and experimental verification on topology optimization design method of space mirror structure based on additive manufacturing technology. Mechanical and Electrical Engineering Technology, 2022, 51(7): 25-30 (in Chinese)
[31] Fan YC, Dong DY, Li C, et al. Research and experimental verification on topology-optimization design method of space mirror based on additive-manufacturing technology. Machines, 2021, 9: 354 doi: 10.3390/machines9120354
[32] Wang YJ, Xiao M, Xia ZH, et al. From computer-aided design (CAD) toward human-aided design (HAD): An isogeometric topology optimization approach. Engineering, 2023, 22: 94-105 doi: 10.1016/j.eng.2022.07.013
[33] Hu R, Chen WJ, Li QH, et al. Design optimization method for additive manufacturing of the primary mirror of a large-aperture space telescope. Journal of Aerospace Engineering, 2017, 30(3): 04016093 doi: 10.1061/(ASCE)AS.1943-5525.0000690
[34] Zhang K, Xie XL, Wang C, et al. Optomechanical performances of advanced lightweight mirrors based on additive manufacturing. Micromachines, 2022, 13: 1334 doi: 10.3390/mi13081334
计量
- 文章访问数: 26
- HTML全文浏览量: 4
- PDF下载量: 18
