Enhancing cathode design by considering complex motion and variations of electric field distribution in counter-rotating electrochemical machining

• The motion trajectories of the window at different angles can be rotated to coincide with each other during counter-rotating electrochemical machining. • The difference of stray current density between windows with different angles is the main reason for the difference of sidewall dissolution. • The cathode design is corrected by predicting sidewall dissolution, resulting in a design accuracy of 0.065mm. The counter-rotating electrochemical machining (CRECM) shows unique potential in the machining of thin-walled rotating parts with complex convex structures. CREM realizes the shaping of complex convex structures through the relative rotation of the cathode and anode. The complex motion pattern and electric field distribution make it difficult to apply the existing cathode design methods to CRECM. To solve this problem, the matrix equations of cathode motion based on the kinematics and the electric field simulation model are established. The motion trajectories and edge contours at different angles are analyzed. The rotational overlap theory of motion trajectories under the windows at different angles is proved. Besides, the relationship between electric field distribution and the convex structure forming under different angle windows is studied, and the fundamental reason for deviations occurs when the convex profile is rotated to coincide is revealed. Therefore, a prediction model of the sidewall dissolution is established to correct this deviation, thereby deriving a high-precision design formula for the cathode windows of the high convex structures. By designing a cathode with oval-like windows to curry out CRECM experiments, the array-arranged (30×5) circular high convex structure with a maximum roundness error of 0.065 mm is successfully fabricated.