Simulation and Experimental Study on Improving Electrochemical Machining Stability of Highly Convex Structures on Casing Surfaces Using Backwater Pressure

Casing parts are regarded as key components of aero-engines. Most casing parts are attached to convex structures of different shapes, whose heights range from hundreds of microns to tens of millimeters. Using profiling blocky electrodes for electrochemical machining (ECM) of casing parts is a commonly adopted method, especially when highly convex structures. However, with an increase in the convex structure height, the flow fields of the machining areas become more complex, and short circuits may occur at any time. In this study, a method to improve the flow field characteristics within a machining area by adjusting the backwater pressure is proposed and validated through simulation and experiment analyses. The simulation results demonstrated that the back-pressure method can significantly improve the uniformity of the flow field around the convex structure compared with the extraction and open outlet modes. Subsequently, the back-pressure value was optimized at 0.5 MPa according to the simulation results. The experimental results showed that using the optimized back-pressure parameters, the cathode feed-rate increased from 0.6 to 0.7 mm/min, and a 16.1 mm tall convex structure was successfully machined. This indicates that the back-pressure method is suitable and effective for electrochemical machining of highly convex structures with blocky electrodes. In this study, we propose a method to improve the electrochemical machining stability of a convex structure on a casing surface using backwater pressure, which has achieved remarkable results.


Introduction
Casing parts are regarded as key aero-engine components and play an important role in connection, loadbearing, and support [1][2][3]. To function properly during the extreme working conditions of aero-engines, casing parts are typically made of hard-to-cut materials with excellent high-temperature performance, such as nickelbased alloys. Moreover, most casing parts are thin-walled revolving parts with complex convex structures on their outer surfaces, and their heights vary from several to tens of millimeters [4,5]. Therefore, manufacturing these parts is a significant challenge for traditional machining methods owing to significant tool wear, high machining cost, and long machining periods [6][7][8][9].
Electrochemical machining (ECM) is a non-contact machining method based on the electrochemical dissolution of anode materials without limitations on the mechanical properties of alloys [10,11]. Owing to the advantages of a high material removal rate, no tool wear, etc., ECM has recently become an important processing method for casing parts [12][13][14]. Zhu et al. proposed the so-called counter-rotating electrochemical machining (CRECM) technology [15][16][17]. Through the counter-rotating movement of the rotary tool electrode and workpiece, the one-time formation of a convex structure on the casing surface can be realized, which effectively improves the machining efficiency and machining quality of the casing parts. Zhang et al. carried out a research on mask electrochemical machining (M-ECM) of casing parts, achieving a few key breakthroughs such as the preparation of the protective film of the rotary surface and uniformity control of the flow field, and realized engineering applications for a certain type of casing part [18,19]. However, to date, the above methods are mainly used for machining casing parts with relatively low convexity.
Using profiling blocky electrodes for ECM of convex structures on casing parts is a widely used method, especially for processing highly convex structures on largersized casing parts, owing to its high machining efficiency. Li et al. designed a series of working stations and blocky cathode tools. By matching the positions of the working stations and cathode tools, a complex concave-convex structure was gradually formed on the casing part surface [20]. Sheng et al. conducted experimental research on the ECM of a convex structure on the casing surface using a blocky electrode. Based on the experimental results, they optimized the flow field and process parameters and improved the machining quality of the casing parts [21,22].
However, the flow field is an important factor affecting the machining performance of ECM [23,24]. Compared with other ECM methods, such as CRECM and M-ECM, the machining area of the blocky electrode method is larger, and the uniformity of the flow field within the machining gap is more difficult to control. With an increase in the feed depth of the blocky electrode, the machining gap flow field becomes more complex; subsequently, short circuits may occur at any time. Therefore, ensuring the uniformity and stability of the flow field in the machining gap and avoiding the "dead water area" phenomenon have become the most important factors in the ECM process of a highly convex structure using a blocky electrode.
In this study, the flow field characteristics during the ECM process of highly convex structures with blocky electrodes are emphasized, and a back-pressure method is proposed to improve the flow field of the machining area. Three operation modes, namely, extraction, open, and back-pressure on the backwater outlet, were studied in detail using a computational fluid dynamics (CFD) software, and an optimized flow field state was obtained. The subsequent experimental results indicated that the back-pressure method is suitable and effective for ECM of highly convex structures with a blocky electrode. Figure 1 shows a schematic for the electrochemical machining of a highly convex structure on the surface of a casing part with a blocky electrode. The blank of the casing part is fixed on the working table of the machine tool with a clamp. It is aligned to the proper relative position with the cathode tool via a rotating disk before machining. The electrolyte is pumped into the electrode inlet and directly delivered to the machining gap through an internal flow channel. When a stable voltage difference is applied between the cathode tool and anode workpiece, electrochemical dissolution occurs on the anode surface. The blocky cathode tool is continuously fed along the normal direction of the casing surface at a constant feed rate until the set machining depth is reached.

Machining Principle and Flow Field Characteristics
To realize the back-pressure machining method proposed in this study, a special block electrode was carefully designed, as shown in Figure 2. The red area signifies the main machining area and rhombic window corresponds to the non-machining area, which ensures that the anode workpiece surface forms a convex structure. The upper end of the blocky electrode has an inlet and back-water outlet. The inlet is responsible for delivering the high-speed electrolyte to the entire machining area. The backwater outlet is connected to the window area to adjust the flowfield state of the window area. The rhombic window is crucial for ensuring the proper formation of the convex structure. The flow field state is also complicated. Therefore, the pressure mode of the backwater outlet has a significant influence on the flow-field state of the machining gap and formation of the convex structure.

Theoretical Model of the Flow Field
A complex CFD model of the flow field was established, as shown in Figure 3, where the light blue area is the inlet, orange red area is the backwater outlet, and dark gray area is the outlet. To simplify the simulation process, the following assumptions are made [25]: (1) The electrolyte is assumed to be continuously flowing and incompressible. (2) The shear stress between adjacent layers of infinitesimally small fluid sections was assumed to be proportional to the rate of shear in the direction perpendicular to the motion. The fluid flow follows conservation of momentum and mass equations, which can be described as follows: where, u i is the ith component of the mean electrolyte, x i is the ith cartesian coordinate, x j is the jth cartesian coordinate, τ ij is the ijth component of the stress tensor, and p and v are the mean pressure and kinematic viscosity of the electrolyte, respectively. In the simulation model, the electrolyte flow path was complex, and its size changes significantly. Moreover, the flow field was in a complex turbulent state. In this study, the renormalization group (RNG) k-ε turbulence model was used, which is suitable for flows with high streamline curvatures and strain rates.

Simulation Analysis and Results
The CFD model adopted in this study is shown in Figure 3. The light-blue area is the inlet of the electrolyte, which provides the necessary pressure for the machining process. To reduce the electrolyte velocity in the convex structure area, which does not require machining, the backwater outlet is set to release the electrolyte pressure.
The parameters used in the simulation were set as follows: the inter-electrode gap was 0.5 mm, pressures of inlet and outlet were 1 and 0 MPa, respectively, extraction outlet pressure was 0.4 MPa, open outlet pressure was 0 MPa, and backwater pressure was set between 0 and 1 MPa.

Influence of Flow Mode on the Flow Field
In this study, three modes, namely, extraction outlet, open outlet, and back-pressure outlet, are designed to obtain a better flow field state. Figure 4 shows the flow field in the machining gap with an outlet pressure of 0 MPa, extraction pressure of 0.4 MPa, and back-pressure In contrast, the flow field of the convex edge region is significantly improved when the back-pressure mode is applied. Therefore, we can conclude that the back-pressure outlet mode is beneficial for improving the flow field state of the machining gap and enhancing the uniformity and stability of the machining process compared with the extraction and open outlet modes.

Influence of Backwater Pressure on the Flow Field
In this section, the flow field of the machining gap under different back pressure values is discussed in detail. Figure 5 shows the electrolyte velocity distribution of the machining gap at back pressure values of 0.2, 0.6 and 1 MPa. It could be noticed that with an increase in the back pressure, the flow field around the convex structure also improves. To better explain the abovementioned phenomena, we plot spline curves of the top area and surrounding area of the convex structure (as shown in Figure 3) and extract the electrolyte velocity parameters accordingly. Figure 6a shows the electrolyte velocity distribution of spline curve 1 around the convex structure with respect to different back pressure values. It could be observed that the average electrolyte velocity along curve 1 is approximately 10 m/s, which meets the demand of electrochemical machining for electrolyte velocity. However, Figure 6a also shows that the electrolyte velocity along curve 1 fluctuates significantly, especially when the back pressure is less than 0.4 MPa, and the minimum electrolyte velocity is less than 4 m/s. This is significantly lower than the electrolyte velocity requirements of ECM processes, which is approximately 10-30 m/s [26,27]. Accordingly, this area may become dangerous owing to the possibility of short circuits under such circumstances. Furthermore, Figure 6a shows that with the increase in back pressure, the electrolyte velocity along curve 1 gradually increases and that of the dangerous area also improves accordingly. Therefore, increasing the back pressure is beneficial for maintaining the stability of an ECM process. Figure 6b shows the electrolyte velocity distribution of spline curve 2 in the top area of the convex structure with different back pressure values. It should be noted that the top area of the convex structure is a non-machining area; therefore, a lower electrolyte velocity should be employed to avoid stray corrosion and enhance the forming height of the convex structure. As shown in Consequently, we can assume that there will be more stray corrosion to the top area of the convex structure.
In summary, the back-pressure method can improve the flow field state of the machining gap; however, using a too high back pressure value will cause excessive stray corrosion in the top area of the convex structure, which is undesirable during the process. Therefore, a back pressure value of 0.5 MPa will be applied preferentially in the following experiments.

Experimental Verification
To further verify the effectiveness of the method proposed in this study, ECM processes of highly convex structures on a certain casing part surface were conducted in controlled experiments. The experimental setup consisted of a tool motion control system, electrolyte circulation system, power supply system, and current direction system, shown in Figure 7a. The cathode fixture was made of fiber-reinforced plastic material, whereas the workpiece fixture was made of stainless-steel material. The assembly site for the machining process is shown in Figure 7b. During the machining process, the open outlet pressure was kept constant at 0 MPa, and the backwater pressure outlet was adjustable. The experimental conditions and parameters are presented in Table 1.  Figure 8a. The blocky electrode tool was also damaged as shown in Figure 9. Figure 10 shows the current signal collected during machining. It can be observed that the machining time was approximately 14 min, and the corresponding convex structure height was approximately 8.4 mm, which is significantly higher than that obtained by other electrochemical machining methods such as CRECM and M-ECM [10,11]. This illustrates that the blocky electrode method has a significant advantage in machining highly convex structures on the surface of casing parts Figure 8b shows the sample machined under the backpressure mode with a back pressure value of 0.5 MPa. The feed rate was increased to 0.7 mm/min and machining time was extended to 23 min. The forming height of the convex structure was approximately 16.1 mm, which was more than twice the forming height of the open outlet mode. Moreover, the forming contour was very sharp.
The results indicate that the back-pressure method can significantly improve the stability during the electrochemical machining of a highly convex structure with a blockly electrode and greatly increase the forming height of the convex structure. This conclusion agrees well with the simulation results obtained in Section 4, which further proves that the back-pressure method is feasible and reliable for ECM of a highly convex structure using a blocky electrode.

Conclusions
(1) Simulation experiments regarding three modes were performed. The results demonstrated that the back-pressure mode can significantly improve the uniformity of the flow field around the convex structure and eliminate potentially dangerous areas compared with the extraction and open outlet modes. (2) The back-pressure mode was studied in detail. The results indicated that with an increase in the back pressure, the flow field around the convex could be significantly improved. However, the velocity at the top of the convex was significantly increased as well, which may aggravate unnecessary stray corrosion. Then, an optimized back pressure value of Electrolyte temperature (℃) 30 0.5 MPa was obtained according to the simulation results, which realized a uniform and stable distribution of the flow field in the machining area. (3) Experiments were conducted to verify the effectiveness of the simulation results. The experimental results demonstrated that under the optimized back pressure conditions, the cathode feed-rate increased from 0.6 to 0.7 mm/min, and an approximately 16.1 mm tall convex structure could be successfully machined. The results indicated that the back-pressure method was suitable and effective for electrochemical machining of highly convex structures with blocky electrodes.