# Research on Design, Simulation, and Experiment of Separation Mechanism for Micro-Nano Satellites
## 4 Analysis
### Random Vibration Analysis  
Random vibrations from the spacecraft launch are one of the most severe loads on the structure's integrity. Random vibration analysis is used to verify the separation mechanism.  
Figure 10: First three-order natural frequencies of the separation mechanism.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No** & **Frequency (Hz)** & **Mode Shape** \\ \hline
1 & 243.6 & \(X\)-Direction \\
2 & 168.8 & \(Y\)-Direction \\
3 & 116.5 & \(Z\)-Direction \\ \hline \hline \end{tabular}
\end{table}
Table 5: Modal analysis results of separation mechanism.  
anism's strength and structural integrity by introducing random vibrations through the mechanical interface. The purpose of this analysis is to identify the structural response to acoustic noise generated by engine vibration and noise, as well as air friction, during the initial launch phase. The typical way to describe the severity of loading and potential damage caused by random vibration is in terms of the PSD (power spectral density) that the satellite will encounter during launch, which is a frequency domain measure of vibration amplitude power intensity. The average value of all the amplitudes within a given frequency range is used to evaluate the constantly changing acceleration amplitude [37].  
The random analysis is used to confirm the separation mechanism and MF satellite's dynamic mechanical performance. According to Section 4.2 of Table 4, the natural frequency meets design requirements, indicating that the combination's dynamic stiffness is sufficient to avoid resonance with a launch vehicle carrier when subjected to low-frequency sinusoidal excitation. The random vibration simulation conditions are specified by the launch vehicle design technicians, as shown in Table 6.  
The combination of the separation mechanism and the MF satellite was subjected to random vibration analysis using the simulation conditions listed in Table 6. As shown in Figure 11, six sample points were chosen from the MF satellite and two from the separation mechanism, and the results are shown in Table 7. As a result of the analysis, we can see that the response on the MF satellite is extremely low, while the maximum response value is observed on the Z-direction solar panel, which is capable of withstanding a response value of 30 g. Although the separation mechanism's cover door and side panel have a slightly larger response than the MF satellite's, the separation mechanism contains no electronic equipment and has a sufficient safety margin to withstand the response. It demonstrates that the system's dynamic performance meets the engineering application's requirements.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{3}{c}{**Acceptance Conditions**} \\ \cline{3-4}  & **Frequency (Hz)** & **Power Spectrum** & **Total RMS of** \\  & **Density (g\({}^{2}\)/Hz)** & **Acceleration (g)** \\ \hline  & 20–150 & +3 dB/oct \\  & 150–280 & 0.04 \\  & 280–320 & 0.15 \\ Value & 320–380 & 0.10 \\  & 380–850 & 0.05 \\  & 850–1000 & 0.02 \\  & 1000–2000 & 0.005 \\ \hline Direction & & 3 directions \\ \hline Time & & 1 min for each direction \\ \hline \hline \end{tabular}
\end{table}
Table 6: Random vibration test conditions.  
Figure 11: The arrangement of three-axis accelerometers.