Analytical prediction of shear angle and frictional behaviour in vibration-assisted cutting

Vibration-assisted cutting (VAC), a promising technique, proved to enhance the machinability of difficult-to-cut materials. Its significant superiority with regard to conventional cutting (CC) is considered to be closely related to variation of a shear angle in the primary shear zone and specific frictional behaviour at tool-chip interface. This paper analyses kinematics of VAC, focusing on critical stages of tool-workpiece interaction. Based on the evolution of kinematic parameters, a transient shear angle and a tool-chip contact length are investigated in a cycle according to these stages. To predict the transient parameters, an analytical model of the cutting process is proposed based on non-equidistant shear-zone and tool-chip sliding-sticking zone theories. This model for VAC can not only predict the dominant parameters of the cutting process (e.g., cutting force, friction coefficient), but also the secondary ones (e.g., shear strain). Experimental validation of the developed model is performed with orthogonal VAC of titanium alloy, and the shear angles are measured with optical microscopy of chip samples. For various process parameters, the effective shear angle in VAC is larger than that in CC. However, the average shear angle in VAC is smaller than the shear angle in CC. The proposed model can not only effectively predict the shear angle and frictional behaviour in VAC, but also other process parameters in a vibration cycle, enriching the theory of the VAC process.