Correcting distortion and rotation direction of an elliptical trajectory in elliptical vibration cutting by modulating phase and relative magnitude of the sinusoidal excitation voltages

Abstract

In elliptical vibration cutting, cutting performance is largely affected by the shape and the rotational direction of a micro-scale elliptical trajectory generated at the cutting edge. In this study, change in the shape of the ellipse, which was created by two parallel piezoelectric actuators attached at the tool, was experimentally observed as the excitation frequency to the piezoelectric actuators was increased from 10 Hz to 25 kHz to investigate the effect of the excitation frequency on the elliptical trajectory. For the whole range of experimental frequencies, the major axis of the ellipse becomes tilted, and the aspect ratio of the ellipse is significantly distorted as the excitation frequency approaches the resonant frequency of the elliptical vibration cutting device. To correct the distortion and rotational direction of the elliptical trajectory, an analytical model describing the elliptical path of the tool was developed and verified with experimental results. Based on the analytical model, the distortions in the elliptical trajectories created at various frequencies were corrected for tilt and aspect ratio by changing the phase and relative magnitude of the sinusoidal excitation voltages.