# Thermal Stability Design of Asymmetric Support Structure for an Off-Axis Space Camera
## 2 Low Thermal Deformation Optical Mechanical Structure
### Design of Zero-Expansion Laminated Plates  
The support structure consists of frames and a bearing cylinder, and its basic structure is a CFRP laminated plane. Therefore, the thermal stability of the support structure is closely related to the CTE of the CFRP laminates. The CFRP laminates are made of car-bon fiber and adhesive resin in a certain proportion. The CTE of CFRP laminates is deter-mined by the properties and proportions of the carbon fiber and adhesive resin [13]. Cy-anate esters are widely used in CFRP design due to their low coefficient of thermal expan-sion [26]. In this paper, M40/cyanate ester unidirectional prepreg is used as the basic ma-terial of the support structure, and the basic properties of the material are shown in Table 1.  
Considering the formability of the material and the design principle of composite laminates, three layering methods are chosen for this kind of material in order to achieve zero expansion:  
1. \(\pm\theta/0^{\circ}/90^{\circ}\);
2. \(\pm\theta/0^{\circ}/\mp\theta\);
3. \(\pm\theta/90^{\circ}/\mp\theta\).  
The definition of the fold angle for the laminated plate is shown in Figure 3.  
For the three different types of laying angles presented above, the relationship between the thermal expansion coefficient and the laying angle can be calculated. When us-ing \(\pm\theta/0^{\circ}/90^{\circ}\) in the laying scheme, the relationship between the thermal expansion coef-ficient and the folding angle of multi-layer composites was calculated. The calculation results are shown in Figure 4a. Similarly, the thermal expansion coefficients of the com-posite laminates at the other two folding angles were calculated, and are shown in Figure 4b,c.  
It can be easily observed in Figure 4 and Table 2 that the theoretical CTE in the \(0^{\circ}\) direction is \(0.383\times 10^{-6}/^{\circ}\)C when the laying angle is \(\pm 20^{\circ}/0^{\circ}/90^{\circ}\). When the laying angle is \(\pm 50^{\circ}/0^{\circ}/\mp 50^{\circ}\), the theoretical CTE in the \(0^{\circ}\) direction is \(0.168\times 10^{-6}/^{\circ}\)C. Both of the two plies can meet the requirements of low thermal expansion coefficients.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Basic Properties of M40/Cyanate** & **Parameter Values** \\ \hline Coefficient of thermal expansion in \(0^{\circ}\) direction & \(-0.17\times 10^{-6}/^{\circ}\)C \\ Coefficient of thermal expansion in \(90^{\circ}\) direction & \(28.5\times 10^{-6}/^{\circ}\)C \\ Elastic Module in \(0^{\circ}\) direction & \(200\) GPa \\ Elastic Module in \(90^{\circ}\) direction & \(7\) GPa \\ Poisson ratio & \(0.3\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of M40/cyanate.  
Figure 3: Plying angle definition of the plane.  
Figure 4: The relationship between the CTE and ply angel of M40 composite material with respect to the plying style: (**a**) \(\pm\)0/0\({}^{\circ}\)/90\({}^{\circ}\), (**b**) \(\pm\)0/0\({}^{\circ}\)/\(\mp\)0, (**c**) \(\pm\)0/90\({}^{\circ}\)/\(\mp\)0.  
In the practical application of the off-axis remote sensor considered in this paper, the elastic modulus is also an important parameter, which must be carefully considered in the practical application of composite materials. The elastic moduli corresponding to the above two plies are shown in Table 3. Considering the elastic modulus requirements, we chose \(\pm 20^{\circ}/0^{\circ}/90^{\circ}\) as the best practical winding angle for the CFRP plane structure. In this case, the maximum stiffness of the laminate can be obtained while meeting the CTE re-quirements.