Analytical modelling of cutting forces in ultra-precision fly grooving considering effects of trans-scale chip thickness variation and material microstructure

Although ultra-precision fly grooving (UPFG) is widely applied to fabricate micro-structured surfaces, few studies have focused on the cutting force model of UPFG. The unique kinematics of UPFG leads to the trans-scale variation of undeformed chip thickness from nanoscale to microscale, in which case the influence of material microstructure and size effect is prominent. This study proposes an analytical cutting force model for UPFG with full consideration of the kinematics, chip formation mechanism, material microstructure, material elastic recovery, size effect, and tool geometry. Specifically, by correlating micro-forming theory to crystal plastic theory, a hybrid slip-line model (HSLM) is developed to determine the flow stress in primary deformation zone, which can quantify the influence of size effect and microstructure, such as grain size, grain boundary, dislocation density, and crystal anisotropy, on flow stress. Then, the normal cutting force and frictional cutting force are estimated by analyzing the stress distribution and frictional states at tool-chip interface. The rubbing force induced by material elastic recovery is determined based on indentation theory. Finally, the models are experimentally validated by fly cutting of polycrystalline copper with different machining parameters, and it is also demonstrated that the proposed HSLM can capture the periodic transformation of cutting mechanism in UPFG from ploughing (compressive stress) to shearing (tensile stress) with tool rotation.