In this study, in order to investigate the effective friction coefficient in elliptical ultrasonic assisted grinding (EUAG) of sapphire, the single abrasive grain scratching experiments are performed to simulate the grinding process by setting up the elliptical ultrasonic vibrator attached with the sapphire substrate on a multi-axis CNC grinder. The single grain diamond tool slides on the elliptically vibrated surface at a serial of pressures, and the grinding forces are measured. The friction coefficients under different pressure and vibration amplitude are obtained by calculating the ratio of tangential grinding force to normal grinding force, i.e., Ft/ Fn. Comparing friction coefficients in both scratching with and without vibration, there is a critical pressure Fpc at a range of pressure. As the pressure is less than Fpc, the friction coefficient in EUAG is smaller than that in conventional grinding (CG), and once the increasing pressure is more than Fpc, that is much higher than that in CG. When the pressure is slight, ploughing occurs and no chips are generated, and actually at low pressure, the ratio Ft/ Fn can be close to the effective friction coefficient in EUAG. Thus, the experimental results at low pressure indicate that the effective friction coefficient in EUAG is less than that in CG, and is decreasing with the increasing vibration amplitude.
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