Feedforward Compensation of Dynamics-Induced Form Errors in High-Speed Diamond Turning of Freeform Surfaces Using a Long-Stroke Fast Tool Servo

Abstract The fabrication of freeform optical components is increasingly demanded in emerging technologies such as augmented reality, imaging systems, and compact spectrometers. Fast-tool-servo (FTS) diamond turning has become a promising solution for high-speed, high-precision machining of such surfaces. However, achieving nanometric form accuracy remains challenging due to servo-induced dynamic errors, particularly overshoot and control delay. This study proposes a feedforward methodology to predict and compensate for dynamics-induced form errors in long-stroke FTS systems. By capturing FTS position signals and applying normalized cross-correlation (NCC) analysis, a repeatable motion error referred to as the time-shifted following error (TSFE) was identified through time delay compensation of the servo. The three-dimensional map of TSFE was constructed and integrated into the tool path to compensate for the error before machining. Experimental machining test of a dual-sinewave freeform shape achieved peak-to-valley (PV) form error of 0.26 µm, which was a 56% reduction compared to without measurement compensation. The repeatability of the three-dimensional map of TSFE showed a standard deviation of 0.007 µm on the PV, which confirmed that the TSFE map has enough repeatability to be used as a pre-compensation dataset. Additionally, the FTS system had latent TSFE error regardless the spindle rotation rates. In this study the TSFE map derivation of system indicated approximately 0.5 µm PV. These findings establish a fundamental and broadly applicable framework for improving form accuracy in high-speed freeform optics manufacturing using FTS, contributing to the advancement of ultra-precision machining technologies.