## 5 Mechanical Simulation Analysis of Turntable System  
### Modeling of Spaceborne Optoelectronic Tracking and Sighting Turntable  
In practical engineering applications, finite element analysis (FEA) is frequently used to determine the mechanical performance parameters of gimbal systems. Ensuring close alignment of simulation results with actual conditions necessitates the development of a finite element model that precisely mirrors the static and dynamic characteristics of the gimbal. The gimbal's stiffness properties are determined by material attributes, cross-sectional properties of the components, and connection methods among different components. In gimbal systems, modeling non-linear connection parts (e.g., axial connections and locking mechanism connections) through finite element analysis is susceptible to distortion phenomena [3] (pp. 203-217).  
[PERSON] [14] eliminated pins, bolts, and additional structures during the finite element model simplification of the turntable, utilizing an MPC element to model the locking mechanism's connection and a combination of MPC and spring elements to equivalently represent the bearing part's stiffness. This approach results in exaggerated stiffness at the joint surfaces, deviating significantly from real-world conditions. [PERSON] [22] employed a spring element to model the turntable's bearing connection, deriving axial and radial stiffness coefficients from mechanical test data. While this technique accurately represents the bearing's displacement stiffness, it overlooks the bearing's angular stiffness impact. Despite these modeling approaches achieving an equivalent representation of bearings and locking mechanisms, they fall short in accurately capturing the turntable system's true dynamic characteristics.  
This paper employs a generalized spring element to model the shafting and locking mechanism within the rotary table system. The stiffness matrix for the Bushing element at each connection point is derived through theoretical calculations and experimental parameter identification. The motor, harmonic reducer, and other components are removed to simplify the shafting, while firework bolts are eliminated, retaining only the locking supports to finalize the locking mechanism's simplification. Five Bushing elements are established within the azimuth shafting system, the left and right pitch shifting systems, and the locking mechanism, with their stiffness coefficients detailed in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Eigenfrequency** & **Empirical Design Model** & **Optimal Design Model** & **Increase Percentage** \\ \hline mode1 & 318.37 & 354.93 & 11.48\% \\ \hline mode2 & 364.94 & 359.12 & \(-1.59\%\) \\ \hline mode3 & 430.42 & 525.85 & 22.17\% \\ \hline mode4 & 484.98 & 538.92 & 11.12\% \\ \hline mode5 & 519.98 & 749.83 & 44.20\% \\ \hline \hline \end{tabular} Note: The dynamic stiffness of a structure is usually measured in terms of first-order natural frequencies.  
\end{table}
Table 2: Comparison of the first five natural frequencies of the U-shaped frame.  
To simplify mesh division and decrease finite element analysis computations, parts of the turntable excluding the shaft system and locking mechanism are streamlined, with features like fillets and holes eliminated. Connecting surfaces between components are rigidly connected. Mass lost through model simplification is compensated by adding 0-dimensional Point Mass. A reinforcement support constraint is applied to the azimuth shaft seat's bottom surface and the locking support, finalizing the turntable's finite element model with 2,029,280 nodes and 1,181,231 grids. Figure 12 displays the meshing model of the turntable.