# Research on Stagger Coupling Mode of Pulse Duration and Tool Vibration in Electrochemical Machining
## 2 Analysis of the Simulation of a Dynamic PVECM Process
### Variation of Electrolyte Pressure and Gas Void Fraction  
The electrolyte pressure and gas void fraction in the inter-electrode gap were calculated during the PVECM process. As shown in Figure 3, the electrolyte pressure changed between the different machining stages. The electrolyte pressure gradually increased as the inter-electrode gap decreased. When the cathode attained the minimum inter-electrode gap, the electrolyte pressure in the inter-electrode gap was at maximum. Figure 4 shows the average electrolyte pressure in the inter-electrode gap during one half-period of tool vibration. As the gap narrowed (0 to 0.025 s), the electrolyte pressure was higher than it was as the gap expanded (0.025 to 0.05 s). The inter-electrode gap at 0 s was the same as at 0.05 s, but the electrolyte pressure differed clearly because the inter-electrode gap was narrowing after 0 s but expanding at 0.05 s.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Applied voltage (V) & 20 \\ Electrolyte conductivity & 16.1 S/m at 30 \({}^{\circ}\)C \\ Electrolyte inlet pressure (MPa) & 0.6 \\ Electrolyte outlet pressure (MPa) & 0.1 \\ Initial gap (mm) & 0.1 \\ Vibration frequency (Hz) & 10 \\ Vibration amplitude (mm) & 0.3 \\ Coefficient \(m\) & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter values used in calculations.  
Figure 3: Electrolyte pressure during the different machining stages with tool vibration.  
Figure 5 shows that the gas bubbles during the different machining stages mainly accumulated in the second half of the flow channel. The vibration of the tool cathode significantly influenced the accumulation of gas bubbles. As the cathode approached the workpiece, the gas void fraction started to rise, and the maximum gas void fraction occurred at the minimum inter-electrode gap. Figure 6 presents the average gas void fraction and tool displacement as a function of time over one half-period. The gas void fraction was not symmetrical at about \(t=0.025\) s, and the gas void fraction at 0 s was less than that at 0.05 s. This distinction had two main causes: first, the inter-electrode gap differed when the power was first turned on, and second, the inter-electrode gap narrowed from 0 to 0.025 s and expanded from 0.025 to 0.05 s.  
The analysis of electrolyte pressure and gas void fraction showed that the machining conditions as the gap narrowed differed from the electrolyte pressure and gas void fraction as the gap expanded. Therefore, two stagger coupling modes (i.e., the pre-position and the post-position coupling modes) of pulse duration and tool vibration in the PVECM process were investigated. Figure 7 shows a schematic  
Figure 4: Average pressure in the inter-electrode gap and tool displacement as a function of time during one half-period of tool vibration.  
Figure 5: Gas void fraction during the different machining stages with tool vibration.  
Figure 6: Average gas void fraction and tool displacement as a function of time during one half-period of tool vibration.  
diagram of the coupling of tool motion and pulse duration. The same pulse duration for the two stagger coupling modes was adopted. In the pre-position coupling mode, the machining is conducted during stages A-C and stops at point C. The decrease of the inter-electrode gap caused an increase in gap pressure. In the post-position coupling mode, the machining begins at point C and is conducted during stages C-E. Contrary to the pre-position coupling mode, the inter-electrode gap increased during the post-position coupling mode.  
Based on the above analysis, the symmetry coupling mode contained a gap-narrowing stage and a gap-expanding stage, which were quite distinct from each other. However, the pre-position coupling mode contained only a gap-narrowing stage and the post-position coupling mode contained only a gap-expanding stage. Thus, to evaluate the influence of the different coupling modes, three sets of comparative experiments were used to investigate the feed rate and machining localization.