## 5 Mechanical Simulation Analysis of Turntable System
### Static Overload Analysis and Modal Analysis of the Turntable  
#### 5.2.1 Static Overload Analysis of Turntable  
During the launch, the spaceborne turntable will encounter acceleration loads significantly exceeding gravitational forces, necessitating high structural stiffness to withstand deformation from external loads and prevent structural failure or damage from excessive deformation. Prior to the ground static overload test, the finite element method (FEM) can simulate and assess the structure's maximum stress and displacement, including their locations, serving as a reference for the test and guiding structural strength design. Although the primary acceleration load originates from the vertical direction, additional loads are present in both the X and Y directions. Considering safety margins, engineering experience dictates applying acceleration loads of 4 g in both the X and Y directions and 20 g in the  
Figure 12: Meshing model of the turntable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Stiffness Coefficients**} \\ \hline \(K_{x}\) & \(K_{y}\) & \(K_{z}\) & \(K_{\theta_{x}}\) & \(K_{\theta_{y}}\) & \(K_{\theta_{x}}\) \\  & **N/mm** & **N/mm** & **N\(\cdot\)mm/\({}^{c}\)** & **N\(\cdot\)mm/\({}^{c}\)** & **N\(\cdot\)mm/\({}^{c}\)** \\ \hline Azimuth shafting & \(2.5\times 10^{5}\) & \(2.5\times 10^{5}\) & \(1.1\times 10^{5}\) & \(2.5\times 10^{7}\) & \(4.5\times 10^{7}\) & \(5.5\times 10^{5}\) \\ Left-pitching shafting & \(1.6\times 10^{5}\) & \(1.6\times 10^{5}\) & 70,000 & \(5.1\times 10^{7}\) & \(5.1\times 10^{7}\) & \(4.0\times 10^{5}\) \\ Right-pitching shafting & 30,000 & 30,000 & 300 & 0 & 0 & 0 \\ Pitching locking devices & 50,000 & 50,000 & 30,000 & 0 & \(3.0\times 10^{7}\) & \(3.0\times 10^{7}\) \\ Azimuth locking devices & 15,000 & 15,000 & 25,000 & 0 & 0 & 0 \\ \hline \hline \end{tabular} Note: The stiffness matrix of the Bushing element at each connection part is obtained by theoretical calculation and experimental parameter identification.  
\end{table}
Table 3: Five Bushing element stiffness coefficients.  
Z direction to the turntable, allowing for analysis of deformation and stress distributions under various loading conditions. Table 4 displays the stress and displacement cloud maps for the spaceborne turntable under various acceleration loads.  
\begin{table}
\begin{tabular}{c c c} \hline
**Loading Method** & **Stress Cloud Diagram** & **Displacement Cloud Diagram** \\ \hline \hline \multirow{4}{*}{X\_4g} & \multirow{4}{*}{X\_4g} & \multirow{4}{*}{X\_3719 2023} \\  & & & \\  &  
The reliability margin for aerospace products is established to offset uncertainties in product design and usage, thereby enhancing product reliability. Spacecraft structural failures do not occur under designed loads, and it is recommended that the safety margin be greater than 0 [23]. The safety margin value (MS) for structural strength design is calculated using the safety factor method, as defined by the following formula:  
\[MS=\frac{[\sigma]}{\sigma_{max}\times f}-1 \tag{6}\]  
For the metal material structure, when [\(\sigma\)] is the yield strength of the material, the safety factor f is taken from 1.25 to 1.5 [23]. The yield strength 455 MPa, the maximum stress value 91.297 MPa, and the safety factor 1.5 are replaced into Formula (6), and the safety margin MS value is calculated to be about 2.32, which meets the reliability requirements of spacecraft structure design.