| Summary: | Due to the high hardness and brittleness of sapphire, traditional machining methods are prone to surface scratches and microcracks. As an advanced processing technique, ultrasonic machining can reduce damage to hard–brittle materials and improve surface quality. In this study, an integrated ultrasonic longitudinal–torsional vibration system consisting of both a horn and a tool was designed. The resonant frequency and output amplitude of the horn were simulated and tested. The results indicated that the resonant frequency was 19.857 kHz, the longitudinal amplitude at the tool end was 4.2 µm, and the torsional amplitude was 1.8 µm. Experiments were then carried out to investigate the effects of various machining parameters on the reduction of sapphire surface roughness (Ra) and material removal rate (MRR). A comparative experiment was then conducted to evaluate the effects of ultrasonic longitudinal and longitudinal–torsional vibration on sapphire grinding. The ultrasonic longitudinal–torsional grinding experiments showed that the surface roughness of the sapphire workpiece was reduced from 960.6 nm to 82.6 nm, and the surface flatness was improved to 84.3 nm. Compared with longitudinal ultrasonic vibration, longitudinal torsional grinding reduced the surface roughness of sapphire workpieces by 48% and increased the surface flatness by 88.3%. The results of this study provide specific guidance for the longitudinal–torsional composite ultrasonic machining of hard–brittle materials.
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