Stability-guided low-power longitudinal-torsional ultrasonic-assisted polishing of sapphire

Sapphire polishing is limited by unstable pad–abrasive–workpiece contact, which weakens removal uniformity and elevates damage risk. Here we show that longitudinal-torsional ultrasonic-assisted polishing (LTUAP) can stabilize this interface while retaining low-power operation. A unified kinematic model for conventional polishing (CP), longitudinal ultrasonic-assisted polishing (LUAP), and LTUAP identifies a tangential micro-displacement term, (Formula presented), that enriches abrasive trajectories beyond those produced by longitudinal-only assistance under the stated model assumptions. We then separate mechanism screening from deployment-point selection through a two-stage protocol: uniaxial cyclic compression to identify a conservative effective stabilization window, followed by triaxial dynamic polishing to select a preferred deployment point using time- and frequency-domain metrics. In uniaxial tests, the conservative effective window is 45%–75% on the normalized power-setting scale, and the holding-stage fluctuation metric decreases from 0.061 to 0.038 at 45%, a 37.7% reduction. Under realistic polishing conditions, the preferred deployment point shifts to 5%, where the composite spectral-stability score reaches 0.8073 with harmonic purity of 99.62%. Combining this low-power deployment point with a three-step Archimedean spiral improves final polishing performance, increasing areal removal rate by 28.1% for LTUAP and 139.7% for LTUAP with pre-excitation (LTUAP-PE) relative to CP, while reducing Ra from 34.879 nm to 12.858 and 9.027 nm and total power spectral density (PSD)-integrated texture RMS from 129.7 nm to 76.9 and 26.5 nm, respectively. These results establish a stability-guided decision protocol linking interface signatures, deployment-point selection, and trajectory design in sapphire polishing.