2.1 Principle of electrolytic grinding/milling of cemented carbide
Tool cathode is the key component to realize electrolytic grinding/milling . It is mainly composed of an emery coating adhered to a standard-size cylindrical metal rod. When the full-edge electrolytic grinding and milling process is performed, the whole tool cathode edge cuts into cemented carbide, as shown in Fig. 1. When the cemented carbide is connected with the tool cathode, the tool cathode uses the side edge to process it so as mill the plane. In the electrochemical machining process, the cemented carbide is the anode, and the bar with emery is the tool cathode. The electrolyte is sprayed to the tool cathode by external spraying and ejected from the surface of the cemented carbide. The gap between the tool cathode and the cemented carbide is the machining gap. Through the flow of electrolyte, a disturbed flow field is formed in the machining gap between the tool cathode and the cemented carbide. Under the action of electric field, a part of the tool cathode with emery forms an electric field with the cemented carbide. At this time, the cemented carbide loses electrons and dissolves in the electrolyte. Thus, the cemented carbide is removed. At the same time, the tool cathode gets electrons, and a reduction reaction, accompanied by black substances attached to the emery, is performed. This method can be used for processing of groove structures or large-cutting-depth processing. It has large one-time processing depth, removes the material efficiently, and has slow feed speed. It is mainly aimed at pre-processing of materials that are difficult to process.
According to the balance gap theory of electrochemical machining, the balance gap in the feed direction is △a0 (α = 0) basic equation:
![](data:image/png;base64,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)
where η is the current efficiency in processing, ω is the volume electrochemical equivalent (mm3/A·min), κ is the conductivity of electrolyte (Ω·mm), U is the processing voltage (V), δΕ is the sum of the cathodic and anodic polarization potential values, and Vx is the electrolysis speed (mm/min).
Assuming that the conductivity, electrolyte temperature, and bubble rate remain unchanged for a certain period of time, equation (1) can be optimized and differentiated into the numerical model of electrolytic grinding/milling :
![](data:image/png;base64,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)
where R is the cathode radius of the tool and α is the tool cathode arbitrarily fillet.
2.2 Numerical simulation of electrolytic grinding/milling of cemented carbide
2.2.1 Analysis model
According to the structural design requirements of cemented carbide electrolytic grinding/milling, the established analysis model is shown in Fig. 3. The total length of the tool cathode is 72.6 mm, radius is 4.1 mm, and length of the embedded emery part is 26.7 mm. The electric field distribution during full-edge electrolytic grinding/milling is mainly considered to judge whether the material removal is uniform in the process of electrolytic grinding/milling .
2.2.2 Electric field distribution of electrochemical milling
The current density distribution of milling electrochemical machining obtained under the condition of a machining voltage of 16 V and an initial gap of 0.5 mm is shown in Fig. 3. It can be seen from Fig. 3(a) that when the tool cathode is close to the cemented carbide, no large machining current is formed between them. Only a small machining current is generated in the area where the cemented carbide is closest to the tool cathode. As the tool cathode continues to cut into the cemented carbide, the relative processing area of the cemented carbide and tool cathode increases, and the amount of removed material increases. As shown in Fig. 3(b), the current density value in the processing gap remains uniform, and the current density decreases at the cutting in and out of the tool cathode processing edge. When the cutting amount reaches the cathode radius of the tool, the machining area reaches the maximum (semicircle), as shown in Fig. 3(c). At this time, the current density in the machining gap is 8 × 108 A/m2, when the tool cathode is completely cut in. As shown in Fig. 5(d), the processing current density remains unchanged. It can be seen from the whole process that, with the continuous cutting of the tool cathode, the area of cemented carbide milling electrochemical machining increases, and the current density in the machining gap increases. When the tool cathode cuts into a 1/2 diameter, the area of cemented carbide milling electrochemical machining remains unchanged, the amount of removed cemented carbide material per unit time remains unchanged, and the current density remains stable.