1.8 m长条形轻质SiC反射镜支撑位置设计

Support Position Design of 1.8 m Rectangular Light-Weight SiC Mirror

反射镜在自重作用下的形变是影响光学表面质量的重要误差源之一。对于圆形的反射镜来说,其内部有一个中性面,当柔性支撑的回转中心与中性面重合时,反射镜表面受到重力影响后的形变最小。但由于长条形反射镜不再具有回转对称性,其原有的中性面位置公式将不再适用。本文提出了一种长条形反射镜中性面位置即最佳安装位置的计算方法。通过计算柔性支撑的柔度矩阵,得到反射镜组件的整体力学模型,并以此推导出了长条形反射镜中性面位置计算公式。最终将其与有限元分析和光学检测试验得到的结果进行对比,验证了中性面位置计算公式的准确性。在光学检测试验中,反射镜组件在不同方向重力作用下表面面形的均方根(RMS)值均小于0.03λ;反射镜扫频振动试验得到的三个方向上的最小共振频率分别为106.30、151.55、104.00 Hz。该结果满足反射镜组件对于面形精度、结构刚性和稳定性的要求。

Objective The large-scale off-axis three-mirror anastigmatic(TMA) space-borne telescope enables the space optical remote sensing camera to meet the requirements of light weight, long focal length, large field of view, and high resolution.Meanwhile, it has a compact structure and many optimizable variables without dispersion and center blocking, which has become a research hotspot. The rectangular space mirror with a large size and high aspect ratio is an important part of the TMA, and the size of its structural rigidity, stability, the advantages and disadvantages of surface figure error, and thermal stability will directly affect the imaging quality of the whole camera. However, due to its structure asymmetry, the flexible mount design for the mirror of the TMA space camera, and the mounting and positioning of the mirror assembly are current technical difficulties. A reasonable support scheme design can eliminate the deformation of the mirror and its support assembly in processing and assembly to ensure the smaller surface figure error of the mirror. For a mirror where the gravity direction is perpendicular to the direction of the optical axis, there exists in the mirror body such a plane of action: If the actual support point of the flexible mount is on or near this surface, the gravitational moments of the various parts of the mirror body are balanced and the bending deformation of the mirror body is minimal due to its weight. This plane of action is known as the neutral plane of the mirror. For a circular mirror, the neutral surface is a plane at some distance from the center of gravity and perpendicular to the optical axis. However, as the rectangular space mirrors employed in TMA lose rotational symmetry compared to traditional circular mirrors, the supporting theories and empirical formulas in circular mirrors are difficult to extend to rectangular space mirrors.Methods We introduce a method to calculate the neutral plane position and optimal mounting position for a rectangular space mirror. First, we conduct structural design for the main reflective mirror assembly with the dimension of 1820 mm×520 mm. Meanwhile, we adopt reaction-bonded silicon carbide(RB-SiC) as the material for the mirror and implement a partially closed-back support structure and a triangular lightweight form at the back. Then, by evaluating the flexibility matrix of the flexible mount, we build the mechanical model of the mirror component. Subsequently, a new formula for determining the neutral surface position of a rectangular mirror is derived from this theoretical model. The validity of this theoretical derivation is confirmed by comparisons with results obtained from finite element analysis(FEA) and optical inspection experiments.Results and Discussions By calculation, we derive the mathematical formula [Eq.(4)] for determining the neutral surface position in the rectangular mirror. It is worth noting that, unlike circular mirrors, rectangular space mirrors lack symmetry,leading to an optimal support position consisting of curved surfaces rather than a single vertical plane. Therefore, the design for different locations should be differentiated during determining the installation depth of the flexible mounts. Based on these calculations, we determine the optimal support positions along the mirror axis and apply them to the XX-1 camera design.Conclusions We investigate the optimal mounting position of the flexible mount for rectangular space mirror assemblies with large dimensions and aspect ratios. Additionally, we build a mechanical model and according to this model, the surface figure error can be minimized under the axial force Fz = 2.24 N. By considering a support depth of 2ε2+ ε1=20.59 mm, we calculate the neutral surface position and the optimal support position. Afterwards, we fabricate and assemble the mirror assembly based on the optimized design, and perform optical inspection and dynamic tests on the mirror assembly. In the optical inspection test, the root mean square(RMS) value of the surface figure of the mirror assembly under various gravity directions is less than 0.03λ. The minimum resonance frequencies in three directions obtained from the swept-frequency vibration test are 106.30, 151.55, and 104.00 Hz, meeting the requirements of surface figure accuracy, structural rigidity, and stability of the mirror assembly.