# Research on Micro-Vibration Analysis of Segmented Telescope Based on Opto-Mechanical Integration
## 4 Opto-Mechanical Integration Analysis
### Opto-Mechanical Integration Analysis Process  
Firstly, the optical system model is established through Zemax OpticStudio Standard Edition software, and the corresponding mechanical structure model is established through NX according to the design parameters of the optical model. SiC is used for the optics in the mechanism and lightweight aluminium alloys are used for the mounts and bases. The flexible joints and gaskets are made of indium steel, and the connecting rods between the primary mirror and the secondary mirror are made of carbon fibre, which has a very low coefficient of thermal expansion. The rest of the structure is made of titanium alloy, taking into account the need for strength, stiffness and lightness. In the modeling process, the thin-walled lightweight parts can be well simulated by using shell units to model the reflector assembly. Finite element modeling is widely used in engineering design and is a proven means of engineering analysis with high accuracy in dealing with linear models. In the selection of the reflector cell size, no less than three layers of mesh are designed based on experience, as shown in Figure 11.  
The truss is modeled by one-dimensional Beam cells as shown in Figure 12 below. To model the degrees of freedom of the truss rods well, each rod consists of more than 20 cells. The number of nodes in the finite element model of the whole machine is 251,765 and the number of cells is 278,139. Considering the special working conditions of the on-board satellite operation in orbit, the model adopts the free-freedom boundary conditions without any displacement constraints, and the first six-order modes of the model are shown in Table 2.  
Figure 11: Shell cell model of a sub-mirror assembly. Figure 12: Finite element modeling of segmented telescopes. In terms of the verification of finite element simulation accuracy, there are generally two ways to verify. On the one hand, one can judge whether the results converge by continuously reducing the cell size and increasing the degrees of freedom of the model. On the other hand, the accuracy of finite element simulation can be verified by physical objects. The present finite element model is verified to satisfy the accuracy requirements by the first method. The micro-vibration source is loaded on the support structure of the optical system, and the coordinate values of each node on the primary mirror surface before and after the change of 2000 moments are obtained by transient analysis. The error equation is constructed by the coordinate transformation relation, and the rigid body displacement of each sub-mirror is calculated by the least square method. Because the influence of the sub-mirror shape change on the WFE is negligible compared with that of the rigid body displacement, the surface shape change of the sub-mirror is not considered. The 2000 time points of the micro-vibration source signal correspond to 2000 states of the sub-mirrors, and the 18 sub-mirrors have 6 degrees of freedom change, the change of the data volume is large, so the real-time data transmission and read the simulation results of the data interface is written. Using the built-in DDE (Dynamic Data Exchange) server of the optical design software, a dynamic link is established with the numerical computation software, and the changes in the degrees of freedom of the sub-mirrors at each moment are transmitted to the optical design software for analysis, so that the evaluation parameters of the optical system at each moment can be obtained. The 18 sub-mirrors of the segmented primary mirror have 6 degrees of freedom of change at each moment, and the amount of change data is large. It is very inefficient to change the optical structure data of each moment manually and easy to input errors. Therefore, use MATLAB to write a real-time transmission of data and read the simulation results of the data interface. ZEMAX built-in Dynamic Data Exchange(DDE) server is used to establish a dynamic link with MATLAB.