# Research on Stagger Coupling Mode of Pulse Duration and Tool Vibration in Electrochemical Machining
## 4 Results and Discussion  
To get the highest feed rate, the feed rate was varied from 0.15 mm/min with a step of 0.05 mm/min, and the increase was continued in steps of 0.01 mm/min until a short circuit occurred in the next 0.05 mm/min. The experimental results showed that the highest feed rates for the pre-position coupling mode, symmetry coupling mode, and post-position coupling mode were 0.37, 0.32, and 0.30 mm/min, respectively. Figure 11 shows the instantaneous current for the three coupling modes at the end of machining and with the highest feed rate. The current for the three coupling modes had similar trends. In one vibration period, with the power on, the machining current rapidly reached a maximum and then had a trend from low to high. The peak current occurred shortly after the power was turned on because, its conductivity was high after filtering the electrolyte. Due to the sharp accumulation of electrolysis products, the conductivity decreased rapidly. Figure 11 shows that a higher peak current occurred in the pre-position coupling mode. In addition, just before the power was turned off, the current in the pre-position coupling mode was higher than that in the other modes. Figure 12 shows the average current for the three coupling modes with their highest feed rate at the end of machining. It can be seen that the average current of the pre-position coupling mode was higher than that of the other two modes. Associated with the instantaneous current of the three coupling modes, the pre-position coupling mode had a higher current density and dissolution velocity than the symmetry or post-position coupling modes, and maintained a small, stable inter-electrode gap, which could allow a better control of accuracy [23]. Thus, at the highest feed rate, the pre-position coupling mode could make machining more uniform and stable. The analysis of machining current therefore indicated that the pre-position coupling mode was more suitable than the symmetry or the post-position coupling modes for the PVECM process, even at the highest feed rate. Figure 11: Instantaneous current as a function of time for the three coupling modes at the end of machining and with the highest feed rate. Figure 13 shows the factor \(\psi\) for the three coupling modes and the corresponding workpieces. It also shows that, for all coupling modes, \(\psi\) gradually decreased with increasing feed rate. Compared with the symmetry coupling mode and the post-position coupling mode, the pre-position coupling mode had a higher feed rate and a smaller \(\psi\). The smallest \(\psi\) of the pre-position coupling mode was 0.076 at a feed rate of 0.37 mm/min, whereas the smallest \(\psi\) for the symmetry and the post-position coupling modes was 0.088 and 0.107 at feed rates of 0.32 and 0.30 mm/min, respectively. Thus, the pre-position coupling mode took machining efficiency and quality into account and offered a higher feed rate and a better machining localization. Figure 14 show the workpieces for the different coupling modes with different feed rates. A serious overcut occurred with the lower feed rate. The height difference of the workpiece surface was almost invisible (e.g., for the workpiece at 0.15 mm/min). The height difference was more obvious for the higher feed rate in one coupling mode. Thus, a better machining localization was obtained at higher feed rates. Figure 12: Average current for the three coupling modes with their highest feed rate at the end of machining. Figure 13: \(\psi\) vs. feed rate for the three coupling modes. The results also showed that at a given feed rate for the three coupling modes, \(\psi\) for the pre-position coupling mode was greater than for the symmetry coupling mode and the post-position coupling mode, and the smallest \(\psi\) occurred in the post-position coupling mode. For example, for a feed rate of 0.25 mm/min, \(\psi\) = 0.187, 0.184, and 0.148 in the pre-position, symmetry, and post-position coupling modes, respectively.