An analytical force model for ultra-precision diamond sculpturing of micro-grooves with textured surfaces

The investigation on the cutting force for ultra-precision diamond sculpturing (UPDS) is important to understand its material removal mechanism and tool-workpiece reaction behaviors during cutting. However, few studies have focused on the cutting force model for UPDS of micro-grooves with textured surfaces. The prediction of the cutting force for UPDS is complicated due to its unique kinematics featuring oscillated servo motions, which inevitably leads to the dynamic material removal process featuring time varying plastic deformation directions. In the present study, an analytical cutting force model for UPDS of textured micro-grooves is proposed with the full consideration of the oscillations induced dynamic cutting conditions, round-edged effect as well as the shearing and ploughing mechanisms. Specifically, the nominal shearing force is derived by a dynamic slip-line model involving the time varying shear angle, stress, strain and strain rate in the deformation zone. A two-state model is adopted to describe sticking and sliding states of the chip on the tool rake face, based on which the frictional shearing force is calculated. When the depth of cut is lower than the critical chip thickness, the material is removed by the ploughing force that is of proportional relation to the tool-workpiece interference volume according to the indentation theory. Finally, the whole cutting force is obtained by discretization method, and the model is experimentally validated through sculpturing two types of textured micro-grooves with harmonic structures.