# Lightweight Design and Evaluation of Square Reflector
## 3 Analysis and Evaluation of Simulation Results
### Vibration Test and System Evaluation  
The space camera will experience a short-term mechanical environment during the launch phase [21]. In order to ensure the stability of the mirror assembly during the orbital operation phase, it is necessary to conduct mechanical tests on the components during the ground phase. The mechanical tests include a characteristic-level frequency sweep test, sinusoidal vibration test, and random vibration test to investigate whether the frequency drift of the mirror assembly occurs during the vibration process.  
The test process is to first conduct a 0.2 g characteristic sine sweep test at 10-500 Hz, then an 8 g sine vibration test at 0-100 Hz, followed by a 0.2 g characteristic sine sweep test at 10-500 Hz, a 5.66 grms Random vibration test at 20-2000 Hz (time 2 min), and finally a 0.2 g characteristic level sine sweep test at 10-500 Hz.  
In the mechanical test, two test points are pasted; one is located at the center of the reflector, and the other is in the center of the support base. The measurement point can reflect the changes in the test product in the mechanical test.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**working condition** & **Gravity load** & **Forced displacement** \\ \hline Surface error & & & \\ RMS/\(\lambda\) (\(\lambda\) = 632.8 nm) & & & \\ \hline Y: RMS = 6.71 nm & & & \\ (\(\lambda\)/94.3) & & X: RMS = 5.44 nm (\(\lambda\)/116.3) & & RMS = 0.91 nm \\ \hline
**working condition** & **Temperature load** & **Axial temperature** & **Radial temperature** \\  & **(15 \({}^{\circ}\)C–25 \({}^{\circ}\)C)** & **gradient load** & **gradient load** \\  & **(5 \({}^{\circ}\)C)** & **(5 \({}^{\circ}\)C)** & **(5 \({}^{\circ}\)C)** \\ \hline  & & & \\ Surface error & & & \\ RMS/\(\lambda\) (\(\lambda\) = 632.8 nm) & & & \\ \hline RMS = 1.14 nm (\(\lambda\)/555.1) & & RMS = 0.78 nm & RMS = 0.68 nm (\(\lambda\)/930.6) \\  & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: RMS of mirror shape error under different environments.  
Two control points are pasted at the edge position of the vibration tooling to control the excitation of the mechanical test. After the vibration test, the test point values of the components before and after the test are compared to determine whether the designed components are qualified or not. As shown in Figure 7, the mechanical test diagram of the mirror assembly is shown. After the vibration tooling required for the mechanical test is connected to the test platform, the product under test is connected to the vibration tooling. Shown in Figure 8.  
After testing, the first-order intrinsic frequency of the reflex mirror component is 167.8 Hz. The peak of the pink curve represents the value of the first-order frequency. The simulation calculation result is 173.3 Hz, and the real test result error is 5.5 Hz, which fully meets the analysis accuracy requirements and verifies the effectiveness of the finite element model. In the sine vibration test of 0-100 Hz, both measuring points are not large, as shown in Figure 9. In the random vibration test, the largest position of the response is the center of the reflector. The peak of the pink curve represents the maximum square acceleration of 16.91 g. As shown in Figure 10, the response was amplified by 2.97 times. The test results of this paper meet the environmental tests, indicating that the reflex is still highly stable after the mechanical test.  
Figure 8: Schematic diagram of the characteristic sweep frequency test curve of the mirror assembly.  
Figure 7: Mechanical test diagram of mirror assembly.