# Research on Multi-Physical Field Coupling Simulation of Local Electrochemical Machining
## 1 Introduction  
Casing is one of the most important parts of an aeroengine. It is a large thin-walled rotary part, on which there are many isolated convex structures distributed [1, 2, 3]. Moreover, this kind of component is usually made of difficult-to-cut materials, such as nickel-based superalloy and titanium alloy [4, 5]. Therefore, a series of problems, such as large tool loss, long processing cycle, and workpiece deformation will occur in traditional machining, which was always a difficult manufacturing problem in the aerospace field [6, 7, 8]. In recent years, electrochemical machining (ECM) was more and more applied in the field of aerospace, because it can ignore the physical characteristics of processed materials, remove materials with chemical energy, with no tool wear, no cutting force, and high processing efficiency [9, 10, 11]. As a special ECM method, counter-rotating electrochemical machining (CRECM) is mainly used for machining thin-wall rotary parts with a complex concave and convex surface, so it is very suitable for machining casing [12, 13]. The principle of CRECM is shown in Figure 1. A cylindrical cathode tool with an inner insulated window rotates inversely with the anode workpiece at the same speed. At the same time, the cathodetool is normally fed along the surface of the anode at a constant feed rate, and the high-speed electrolyte flows between the two electrodes. During the counter-rotation of the electrodes, the material on the surface of the anode workpiece begins to dissolve under the action of electrolysis, while the material on the corresponding part of the cathode window is retained. Compared with ordinary electrochemical machining, because the material is removed layer by layer in electrochemical machining, there is no joint mark on the machining surface, and the uniformity of wall thickness can be effectively controlled [14; 15]. However, with the development of CRECM technology, some problems were also found. For the high convex structure of the casing surface, CRECM is sometimes difficult to obtain the desired design accuracy in one machining. The sidewall taper of the convex will decrease with the increase in convex width. Thus, to achieve a uniform straight sidewall and obtain desired machining accuracy, a subsequent local machining process is necessary. Local electrochemical machining is proposed under this background, it is a method to process the local area around the pre-shaped convex structure by CRECM, which can effectively improve the pre-shaped convex side wall. In order to predict the ECM result accurately, improve the machining precision, the ECM process simulation was the focus of research at home and abroad. [PERSON] et al. developed a mathematical model to predict the geometry evolution of workpieces in electrochemical cavity sinking [16]. However, that mathematical model is based on a simplified electric field model, which often had significant errors with the actual machining results. In the actual process of ECM, there are often a variety of physical and chemical phenomena, including electric field, multiphase flow field, electrochemical dissolution, etc. With the development of research, multi-physical field coupling simulation began to appear. [PERSON] and [PERSON] presented the potential models and moving boundary models to simulate the current density distribution and anodic dissolution in ECM considering the temperature field [17]. [PERSON] and [PERSON] developed a two-dimensional two-phase numerical model to predict the thermal fluid field [18]. [PERSON] et al. developed a 3D coupled multi-physics field finite element model to simulate the ECM craftsmanship [19]. [PERSON] et al. researched the influence of the coupling influence of the magnetic field, electric field, and electrolyte flow in ECM on the accuracy of ECM [20].