## 4 Experimental Research on the Electrochemical Machining of an Inner Fillet
### Experimental Results and Discussion
#### 4.3.2 Filtet Radius as a Function of Processing Time  
Under a 10 V machining voltage, the experimental results of the fillet radius for different machining times are shown in Figure 8. At the beginning of the processing, the fillet radius changed rapidly. As the processing progressed, the corner radius further increased, but the growth rate slowed down. The experimental law is basically consistent with the change law of the chamfering radius obtained from the simulation. At the beginning of processing, the tip effect at the intersecting line was significant, and the workpiece dissolved quickly. As the processing progressed, the intersecting lines formed fillets, the tip effect was weakened, the electrolytic product reduced the conductivity of the electrolyte, and the dissolution rate of the workpiece slowed down. When the processing time increased to 420 s, the fillet radius was greater than 1 mm, the chamfering processing efficiency became very low, and the fillet radius basically did not increase.  
Figure 6: Schematic diagram of workpiece and cathode dimensions. (**a**) Workpiece size; (**b**) cathode size.  
Figure 7: Physical section of the cathode and workpiece.  
According to the variation law of the fillet radius with the processing time in Figure 8, it is speculated that the fillet radius may be approximately a quadratic function of the processing time. A 95% confidence was used, the experimental results were analyzed by quadratic regression, and the results are shown in Table 5. For univariate quadratic regression, this can be treated as a polynomial regression and the significance can be validated using an F-test. According to Table 5, the calculated F-statistic value is 1017.89. By querying the F-distribution function, when the significance level was 0.05, the first degree of freedom was 2, and the second degree of freedom was 13 and the standard F-statistic value was 3.81. The calculated F-statistic value of 1017.89 was much higher than the standard F-statistic value of 3.81, and the results of the regression analysis passed the F-test. The significance of the regression results was validated, and it can be seen that the fillet radius and the processing time satisfy the quadratic regression equation. The quadratic fitting relationship between the fillet radius \(R\) (mm) and the processing time \(t\) (s) is shown in Formula (2). According to the Formula (2), the processing time of the expected radius can be calculated, and a controllable chamfering processing of the small intersecting hole can be realized.  
\[R=-0.0000046t^{2}+0.0044t+0.0122 \tag{2}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Machining** & **Processing Phenomenon** \\
**Voltage (V)** & Few bubbles appear; electrolysis products can be discharged in time; fillets are regular in shape. \\ \hline
6 & Small amounts of bubbles appear; electrolysis products can be discharged in time; fillets are regular in shape. \\ \hline
8 & Small amounts of bubbles appear; electrolysis products can be discharged in time; fillets are regular in shape. \\ \hline
10 & Many bubbles appear; small amounts of electrolysis products remain between the insulating sleeves and the workpiece, which does not affect normal processing; fillets are regular in shape. \\ \hline
12 & Many bubbles appear; small amounts of electrolysis products remain between the insulating sleeves and the workpiece; the shape of the fillet is deformed, and the hole walls on both sides of the fillet are unevenly corroded. \\ \hline
14 & A large number of bubbles appear; a large number of electrolysis products remain between the insulating sleeves and the workpiece; the shape of the fillet is deformed, and the hole walls on both sides of the fillet are severely corroded. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Influence of machining voltage on the machining effect.  
Figure 8: Variation of fillet radius with processing time.