Semi-analytic modelling of cutting forces in micro ball-end milling of NAK80 steel with wear-varying cutting edge and associated nonlinear process characteristics

Cutting edge of miniature ball-end mill is one of decisive importance for the machining performance by affecting the thermal and mechanical load in cutting process. In this paper, a semi-analytic model is proposed to estimate the cutting forces in micro ball-end milling of NAK80 steel considering wear-varying cutting edge and the associated nonlinear process characteristics. The wear-varying cutting edge geometry under the different wear stage is obtained by 3D optical profilometer. The measured results indicate that cutting edge of miniature ball-end mill under the different wear stage includes not only the enlarged cutting edge radius but also the extended flank wear land, which can be described by a combination of edge radius and flank wear land width. The influence laws of the edge radius and flank wear land width on tangential and feed force coefficients are investigated, and the enlarged edge radius and extended flank wear land under different wear stage could be separated from each other by utilizing the cutting force coefficients data based on their different sensitivity on cutting forces. A semi-analytic method is developed to predict the shearing/plowing/friction forces in primary and tertiary shear zones based on classical oblique cutting and slip-line field model. The nonlinear tool-chip friction behavior with the phenomenon that the ratio of tool-chip contact length to uncut chip thickness and friction factor nonlinearly change with the ratio of uncut chip thickness to edge radius are investigated and employed to estimate rake/shear/friction angles, and the nonlinear strain gradient plasticity effect with the fact that effective strain gradient is affected by not only rake angle and shear angle, but also primary shear zone thickness that obviously increases with reduce of the ratio of uncut chip thickness to edge radius are considered to estimate the shear flow stress. The nonlinear behavior derived from the tool-chip/workpiece friction and material constitutive affects the contribution level of size effect on cutting forces in micro ball-end milling. Finally, to calibrate and validate the effectiveness of the proposed cutting forces model, a set of micro ball-end milling of NAK80 steel experiments are performed on a three axis ultra-precision machine by using same solid carbide tool with wear-varying cutting edge under different wear stage. The comparisons between the predicted and measured results show that the proposed model can provide higher accuracy and better understanding for micro ball-end milling of NAK80 steel.