## 3 Results and Discussion
### ECM Results of Revolution Surface  
To avoid stray corrosion in ECM, the cut-off current density (see Figure 3) using a mixed solution of NaNO\({}_{3}\) and NaOH should be higher than the maximum current density on the non-machined surface of the printed patterns. In order to choose the proper proportion of a mixed solution of NaNO\({}_{3}\) and NaOH to localize the anodic dissolution, the current density distribution on the anode surface was calculated using the finite element method. As shown in Figure 6, a potential difference of 20 V was applied between anode workpiece and cathode tool, and the electric potential distribution \(\varphi\) within the electrolyte domain satisfies Laplace's equation:  
\[\frac{\partial^{2}\varphi}{\partial x^{2}}+\frac{\partial^{2}\varphi}{ \partial y^{2}}=0 \tag{5}\]  
Figure 7 shows the current density distributions on the anode surface at different rotation angles. Each line represents a current density distribution at a certain rotation angle. A valley area of the current density can be found along the arc length, which corresponds with the surface of the printed pattern. Even though the current density in the valley area is much smaller than the other sections,  
Figure 5: SEM and EDX results for the corroded specimen in a mixed solution of 106 g/L NaNO\({}_{3}\) and 30 g/L NaOH. (**a**) SEM image of the specimen surface; (**b**) EDX of machining products. Figure 6: Numerical simulation model in cross-section. the value remains approximately 0.5 A/cm\({}^{2}\) in the center to more than 7 A/cm\({}^{2}\) in the margin area of the printed pattern. According to the current efficiency curve shown in Figure 3, the current efficiency was persistently high even at low current density in NaNO\({}_{3}\) solution, which will lead to serious stray corrosion on the surface of the printed pattern. Thus, a mixed solution of 106 g/L NaNO\({}_{3}\) and 30 g/L NaOH is suitable, with which the cut-off current density can reach a high value of 7.5 A/cm\({}^{2}\) (Figure 3). The surface of the printed pattern can be completely passivated. The material dissolution on the non-machined surface can be effectively eliminated, and thereby the anodic dissolution in ECM can be localized accordingly. Based on the studies above, the revolving Inconel 718 workpieces were tested during the ECM process shown in Figure 1. A neutral NaNO\({}_{3}\) solution and a mixed solution of 106 g/L NaNO\({}_{3}\) and 30 g/L NaOH were used, respectively. The machining parameters are listed in Table 1.  
Figure 8 shows images of the machined surfaces in different solutions. It can be seen that the rectangular shape was printed on the surface of the anode workpiece. However, the surface of the printed pattern was seriously corroded in 106 g/L NaNO\({}_{3}\) solution, leading to a rough machining surface, as shown in Figure 8a. In contrast, the initial bright rectangular shape can still be observed on the surface in the mixed solution of 106 g/L NaNO\({}_{3}\) and 30 g/L NaOH (Figure 8b), indicating a favorable localization effect. The surfaces of the printed patterns were measured using a profile meter three times in different areas, and the average roughness values were obtained. As shown in Figure 9, the average roughness Ra of the surface in NaNO\({}_{3}\) solution was as high as 2.34 um due to the serious stray corrosion. The surface roughness profile in the mixed solution of 106 g/L NaNO\({}_{3}\) and 30 g/L NaOH presents a period characteristic, and the average roughness Ra was determined to be only 1.48 um, which mainly depends on the initial roughness of turning. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Applied voltage & 20 V \\ Electrolyte & 106 g/L NaNO\({}_{3}\), 106 g/L NaNO\({}_{3}\) + 30 g/L NaOH \\ Diameter of cathode tool & 200 mm \\ Initial minimum inter-electrode gap & 0.5 mm \\ Rotational speed & 10 rpm \\ Machining time & 5 min \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental parameters used in electrochemical machining (ECM).