## 5 Self-Insulation Performance Simulation Analysis
Similarly, position 2 exhibits potential values ranging from 79.74 kV to 80.12 kV, maintaining a variation below 0.38 kV. Position 3 demonstrates potentials between 42.50 kV and 43.70 kV, with the overall differential limited to 1.2 kV. Further measurements indicate potential variations below 4 kV at position 4 and 1.3 kV at position 5, respectively. These observations collectively demonstrate well-controlled potential distributions throughout the system. The \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**Item**} & \multicolumn{2}{c}{**Technical Detail**} \\ \hline \multirow{3}{*}{Computer workstation parameters} & CPU & Intel Core i5-9400 \\  & RAM & 24 GB \\  & ROM & 1 TB solid state drive \\  & Operating system & Windows 11 64-bit \\ \hline \multirow{2}{*}{FEM calculation platform} & FEM software & COMSOL 6.0 \\  & Used physical field toolbox & Static electricity field toolbox \\ \hline \multirow{6}{*}{Simulation boundary conditions} & Approximation for the & Using a calculation area \\  & infinite boundary & significantly larger than the \\  & Geometric shape of the & mechanical arm \\  & calculation area & Cube (4 \(\times\) 4 \(\times\) 4 m) \\  & High-voltage & 220 kV at the surface of \\  & boundary condition & the cable \\  & Theoretical infinite & 0 V at infinity \\  & boundary condition & Using a grounding boundary \\  & Approximate infinite & condition (0 V) at the \\  & boundary condition & boundary of the \\  & calculation area \\  & Relative permittivity of the & 3.2 \\  & mechanical arm & \\ \hline \multirow{6}{*}{Meshing method} & Mesh density & Ultra fine \\  & Element type & Tetrahedral \\  & Element number & 1,113,950 \\ \cline{1-1}  & Maximum mesh size & 0.13 m \\ \cline{1-1}  & Minimum mesh size & 0.005 m \\ \hline \multirow{6}{*}{FEM equation solving} & Solver & Nonlinear Newton iteration \\  & & solver (COMSOL built-in) \\ \cline{1-1}  & Residual tolerance & 0.01 \\ \cline{1-1}  & Maximum number & 10,000 \\ \cline{1-1}  & of iterations & \\ \hline \end{tabular}
\end{table} 
Table 3: Finite element model material settings. For the simulation data of each cross-section, the calculation results of various mathematical characteristics are shown in Table 4.  
In order to prove the validity of the fitting between the simulation results and the low-voltage experimental results, we also conducted an electric field simulation of a robotic arm model with a size reduced by 0.5 times at 220 kV level, and an electric field simulation of a robotic arm model with the same size reduction at 220 V level. The results are shown in Figure 17. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Position Number** & **1** & **2** & **3** & **4** & **5** \\ \hline Section height (m) & 1.43 & 1.20 & 0.75 & 0.30 & 0.06 \\ Average field value (V/m) & 518,838 & 132,756 & 53,853 & 33,074 & 25,811 \\ Maximum field (V/m) & 554,350 & 143,015 & 54,389 & 45,195 & 27,292 \\ Minimum field (V/m) & 217,724 & 51,955 & 45,201 & 31,803 & 11,339 \\ Standard deviation (V/m) & 75,416 & 20,394 & 1501 & 1735 & 3310 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mathematical characteristics of simulation results. Figure 16: Electric field distribution results: (**a**) position 1; (**b**) position 2; (**c**) position 3; (**d**) position 4; (**e**) position 5. From the electric field distribution curves from the bottom to the top of the original-size manipulator and the 1:2-scaled manipulator at 220 kV, it can be seen that when the size of the manipulator is reduced, the electric field distribution curves almost overlap. This is due to the self-insulating design of the mechanical arm, which has a negligible effect on the electric field. Therefore, using a 1:2-scaled manipulator does not affect the analysis of the electric field strength at the top of the manipulator. The maximum electric field strength is \(1.8\times 10^{6}\) V/m, which is less than the air breakdown field strength.