An advanced Fourier-based separation method for spindle error motion identification

Classical error separation methods (Donaldson reversal, multistep, and multiprobe methods) were developed by separating both the spindle synchronous radial error motions of precision measurement instruments and the roundness deviations of cylindrical or spherical material standards. The application of such methods improves the measurement uncertainty, even though some methods are time-consuming (multistep) or require a more complex set-up (e.g., the Donaldson reversal and multiprobe methods). In this study, an advanced Fourier-based method for error separation in roundness measurements is developed and implemented. It can be considered a fully stable method, achievable through a reduced number (two or three) of angular shifts, and uses at least one fixed probing system. The proposed Fourier-based method is optimised, tested, and validated on simulated datasets and scenarios combining synchronous and asynchronous spindle error motions and roundness deviations. The given results are accurate at the sub-nanometre level (<0.5 nm) and the effectiveness of the Fourier-based method for ultra-high accuracy applications is proven. Further, Monte Carlo simulations, performed to investigate the influence of artefact indexing errors on measurement uncertainties, confirmed the numerical investigation. Finally, an experiment was conducted on spherical material standards made of ceramic using a high-precision roundness measurement machine. The given results are more accurate (at nanometre level) than those of the 'classical' multistep methods.