An Analytical Model for Determining the Shear Angle in 1D Vibration-Assisted Micro Machining

In the metal cutting process, an increased shear angle generally leads to lower cutting forces and improved machining performance. It has been reported earlier that 2D vibration-assisted machining (VAM) increases the equivalent shear angle and decreases the chip thickness via an elliptical pulling motion of the tool rake face moving away from the deformed chip. Researchers have conducted several experimental and finite element studies and revealed that an increase of shear angle in 1D VAM as well and this process which started much earlier than 2D VAM is widely used in the machining industries. However, no systematic analysis of chip deformation in 1D VAM has so far been carried out regarding the equivalent shear angle. In this research study, several cutting tests have been conducted initially at a very low frequency (0.5 Hz) and the deformation of chip was found smaller compared to conventional machining. Based on the force analysis, an energy-based analytical model has been derived to evaluate the equivalent shear angle. The model was then verified at ultrasonic 1D VAM against cutting speed ratios. Four different metals have been tested including stainless steel, brass, annealed tool steel, and titanium. The results show that a lower speed ratio in ultrasonic 1D VAM will lead to a decreased chip thickness and as such decreased chip compression ratio. The developed model has been found to be able to well predict the equivalent shear angle for ultrasonic 1D VAM of several types of metal.