## 3 Simulation Study of Cathode Shape  
### Cathode Shape Design  
According to the requirements of fillet processing of inner intersecting hole, the ideal cathode shape is a concave shape that is opposite to the fillet shape. However, during the formation process of the fillet, the shape and size are constantly changing, and the state of the machining gap changes accordingly; thus, the final shape of the fillet is only approximate to the ideal shape. To achieve precise control of the radius of the fillet, the key is that the distribution of the electric field is conducive to the formation and control of the fillet during processing. At the same time, the electrode shape should also be considered for ease of processing. Therefore, four cathode shapes: cylindrical, conical, hemispherical, and concave, are designed in this paper, as shown in Figure 2 (only the chamfered parts of the workpiece are drawn in the figure). A reasonable cathode shape was determined by finite element simulation, as follows:  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Comparison Items** & \begin{tabular}{c} **Conventional Electrochemical** \\ **Machining Solution for** \\ **Intersecting-Hole Chamfering** \\ \end{tabular} & \begin{tabular}{c} **Built-In Fixed Cathode** \\ **Electrochemical Machining Solution for** \\ **Solution for Intersecting-Hole** \\ **Chamfering** \\ \end{tabular} \\ \hline Small hole diameter & \begin{tabular}{c} Limited by the diameter of the \\ cathode, the rigidity of the \\ cathode is insufficient, and it is \\ suitable for processing \\ intersecting holes with larger \\ diameters. \\ \end{tabular} & \begin{tabular}{c} The cathode is outside the small \\ hole, the rigidity of the \\ not limited by the diameter size, \\ and the processing stability is \\ good. \\ \end{tabular} \\ \hline Flow field state & \begin{tabular}{c} The cathode occupies small holes, \\ and the uniformity of the \\ electrolyte flow field is affected. \\ \end{tabular} & \begin{tabular}{c} The electrolyte flow field is \\ uniform, which is beneficial for \\ improving the processing quality. \\ \end{tabular} \\ \hline Electric field state & \begin{tabular}{c} The manufacturing process of the \\ cathode is poor, the processing \\ part is difficult to form into a \\ specific shape, and the electric \\ field distribution state is not \\ conducive to the formation of \\ fillets. \\ \end{tabular} & \begin{tabular}{c} The manufacturing process of the \\ cathode is good, the processing \\ part is easy to form into a \\ shape, and the electric field \\ distribution state is conducive to \\ the formation of fillets. \\ \end{tabular} \\ \hline Rounded shape & \
\begin{tabular}{c} The gap of the electrolyte outlet \\ changes, and the shape of the \\ filler is not easy to control. \\ \end{tabular} &
\begin{tabular}{c} The machining gap is \\ symmetrical on both sides of the \\ intersecting line, and the shape of \\ the fillet is easily controllable. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the two processing schemes.  
Figure 1: Electrochemical chamfering schemes for small-sized inner intersecting holes. (**a**) Conventional electrochemical intersecting hole chamfering scheme; (**b**) built-in fixed cathode electrochemical intersecting hole chamfering scheme.