# A Study of Precision Current Efficiency Curve Measurement with a Casing-Type Anode
## 2 Principles of Casing-Type Anode Measurement  
The schematic diagram of the conventional constant voltage method is shown in Figure 1. The key components of the measuring system include a cathode tool, anode workpiece, constant voltage source, and current measuring equipment. The measurement process is consistent with most of the ECM processes because of the feed action and application of the constant voltage source. In this method, the relationship between the current density and the material removal rate can be obtained by analyzing the recordeddata of feed rate \(v\) and the processing current. Obtaining the accurate value of current density distribution on the anode workpiece in an equilibrium state is the key to achieving the accurate current efficiency of the target material. During the measurement, the high-velocity electrolyte is pumped into the inter-electrode gap, so that bubble and Joule heat can be quickly removed to ensure the purity of the electrolyte. The tool and workpiece are connected to the cathode and anode of the power supply, respectively. The power supply outputs a constant voltage. The current distribution on the anode workpiece can be assumed as uniform based on the use of an electrode with flat end. The cathode tool is fixed in the fixture and static, while the anode workpiece is moved relative to the cathode tool at a constant speed. Under the electrochemical reaction, the anode material dissolves into the electrolyte. The dissolution rate \(v_{a}\) is given by [PERSON]'s law:  
\[v_{a}=\eta\omega i, \tag{1}\]  
where \(\eta\) is the current efficiency, \(\omega\) is the volume electrochemical equivalent, and \(i\) is the current density. As the process continues, the ECM process enters an equilibrium state. In this state, the shape of the inter-electrode gap and the processing current do not continue to change, and the anode material dissolution rate is equal to the cathode feed rate \(v\). \[v_{a}=v \tag{2}\]  
The current density \(i\) can be calculated using Equation (3):  
\[i=\frac{I}{S_{end}}, \tag{3}\]  
where \(I\) is the processing current and \(S_{end}\) is the end face area of the workpiece. Using Equations (1)-(3), the current efficiency \(\eta\) can be obtained. However, it is difficult to accurately measure and calculate the volume electrochemical equivalent, \(\omega\), of metal alloys. Thus, \(\eta\omega\) is used to characterize the current efficiency, and it can be obtained from Equation (4). By adjusting the feed rate, \(v\), the current efficiency at different current densities, \(i\), can be obtained. \[\eta\omega=\frac{vS_{\text{end}}}{I} \tag{4}\]  
Figure 1: Schematic diagram of the conventional constant voltage method. In the above description, the measurement is based on the assumption of uniform current density distribution. However, the edge of the workpiece is processed into fillets as a result of the tip effect of the electric field, as shown in Figure 2. The current density distribution in the edge area is different from that in the central region. Besides, the sidwall of the workpiece is exposed to the processing zone during the measurement, and the stray current distribution on the sidewall can lead to a higher measurement value than the actual value. According to Equation (4), the current efficiency measured by the conventional constant voltage method is smaller than the actual value. To reduce the influence of both edge effects and stray current, this study proposes a current efficiency curve measurement with a casing-type anode. Figure 3 shows the schematic diagram of the measurement setup with a casing-type anode. In this method, the target material is divided into two parts: the mandril and the casing. There is a small gap between the mandril and the casing to ensure that the mandril and the casing do not conduct directly.