Compensation method for complex optics considering the arc grinding wheel profile error

The profile accuracy of arc grinding wheels directly affects the precision of complex optics during grinding. However, existing studies have yet to systematically elucidate the distinct effects of wheel profile errors across different frequency bands on workpiece form errors. In this study, the generation mechanism of workpiece form error during the arc-envelope grinding process is revealed, considering the influence of wheel profile error across different frequency bands through kinematic simulation. The mapping relationship between profile errors and form errors is further analyzed, showing that the mapping coefficient is governed by both amplitude and frequency. The effects of neglecting wheel profile errors on the compensation effectiveness are analyzed for the conventional form error reverse compensation methods, revealing that conventional approaches cannot achieve complete convergence of error profiles and magnitudes. To address this issue, what we believe to be a novel compensation method considering profile errors of arc grinding wheels is proposed. Experimental results demonstrate that the cylindrical workpiece form error was significantly reduced from 8.8 µm PV to 2.1 µm PV after only a single compensation iteration, achieving a 38.2% improvement in compensation accuracy compared to the conventional shape-correction compensation method after two iterations. This method effectively enhances the grinding precision of complex optics while reducing iteration cycles of grinding-measurement-compensation processes.