The Development of the Stress-Free Polishing System Based on the Positioning Error Analysis for the Deterministic Polishing of Jet Electrochemical Machining

Deterministic polishing based on jet electrochemical machining (Jet-ECM) is a stress-free machining method for low-rigidity and ultra-precision workpieces. The nozzle is equivalent to a special tool in deterministic polishing, and the workpiece material is removed using the mechanism of electrochemical dissolution at the position where the nozzle passes. By precisely regulating the nozzle’s movement speed and dwell time, the quantity of material removed from the workpiece at a designated position can be finely adjusted. With this mechanism, the improvement of the workpiece shape accuracy can be achieved by planning the nozzle trajectory and nozzle movement speed. However, due to the positioning errors of the polishing device, the actual position of the nozzle may deviate from the theoretical position, resulting in errors in material removal amount, which affects the accuracy and stability of the polishing process. This study established a mathematical model to analyze the influence of nozzle positioning errors in deterministic polishing based on Jet-ECM. This model has been used to design a specific deterministic polishing device based on Jet-ECM. With the proposed deterministic polishing device, the surface shape of the workpiece is converged. The surface peak-to-valley (PV) value of the φ 50 mm workpiece (valid dimensions = 90% of the central region) indicated that the shape error of the surface was reduced from 2.67 μm to 1.24 μm in 34 min. The power spectral density (PSD) method was used to evaluate the height distribution and height characteristics of the workpiece surface. The results show that the low frequency spatial error is reduced significantly after processing. This study improves the accuracy of the stress-free deterministic polishing methods and further expands the use of deterministic polishing in industry.