## 2 Simulation Analysis  
### Flow-Field Simulation Model  
The layout form of the liquid outlet on the end face of the tool cathode has an important influence on the distribution of the electrolyte flow rate in the processing area. Two layout forms of the liquid outlet are designed, and as shown in Figure 1 six liquid outlets are set on the end face of tool A with a diameter of 1 mm, and one outlet is located in the center of the circle. The centers of the remaining liquid outlets are all located at the intersection of the bisector and concentric circle. There are two concentric circles on the end face with diameters of 5 mm and 8 mm, respectively. Because here, only the influence of the layout form on the flow field distribution is studied, it is necessary to avoid the influence of inconsistent discharge areas. Therefore, the measure of the area of the liquid outlets on tools A and B should be consistent. Tool B also has six outlets with a diameter of 1 mm, and the center of each outlet is located at the intersection of the bisector and concentric circles. There are three concentric circles on the end face, with diameters of 4, 6, and 8 mm. In addition, the tool cathode has an outer diameter of 10 mm, inner diameter of 9 mm, side wall thickness of 0.5 mm, and end wall thickness of 1 mm. During ECM, the electrolyte enters the machining gap from the liquid outlet at the bottom of the tool cathode and finally flows out from the upper surface and back of the groove. Figure 2 shows the distribution of the electrolyte inside the tool cathode and the machining gap. The tool cathode moves in the three-dimensional space according to the set path and rotates with the spindle at a constant speed. Therefore, here, the sliding grid model is used to simulate the periodic rotation at a certain instant, which divides the calculation zone into two parts: the rotation zone and the stationary zone. The interface between the rotating and stationary domains is the grid interface. In the calculation process, the rotating domain rotates around the rotation axis with a change in the calculation steps, whereas the stationary domain remains stationary. The two regions realize the coupling of the flow field through kinetic transfer at the grid interface. According to the above analysis, a three-dimensional model of the machining flow field was established, as shown in Figure 3. The model consisted of two parts: a stationary  
Figure 1: Design of the liquid outlet form of different cathode tools. (**A**) Tool A electrolyte outlet layout; (**B**) Tool B electrolyte outlet layout. Figure 2: Schematic of electrolyte distribution. zone and a rotation zone. The electrolyte inside the tool cathode was the rotation zone, and the electrolyte outside the tool cathode was the stationary zone. An observation surface was set up in the flow field model, which coincided with the machined surface. The geometric parameters of the flow field model were as follows: the outer diameter of the tool cathode was 10 mm, the width of the groove was 10.4 mm, the gap between the tool cathode and the surface to be machined was 0.2 mm, and the gap between the tool cathode and the machined surface was 0.7 mm. In addition, to reduce the amount of grid calculation, the length of the groove was set to 7 mm and the height of the fluid inside the tool cathode was set to 2 mm. The FLUENT 18.0 module of the WORKBENCH software was adopted for the simulation calculation of the flow field in the machining gap. The boundary conditions and the calculation parameters are listed in Table 1. After the calculation, the machined surface was selected as the observation surface to examine the flow rate distribution of the electrolyte in the machining area. To simplify the calculation process of the flow field simulation, the following assumptions were made for the physical model [23]:  
1. The fluid is a viscous continuous incompressible fluid. That is, the influence of changes in pressure and temperature on the density and volume of the fluid is ignored. 2.