An analytical force model for ball-end milling based on a predictive machining theory considering cutter runout

Abstract

The work is motivated by the fact that cutting forces are commonly calculated by the mechanistic or numer- ical models which are considered time-consuming and im- practical for various cutting conditions and workpiece-tool pair, and the irregular distribution of cutting forces is generat- ed due to the uneven redistribution of the instantaneous uncut chip thickness (IUCT) caused by the cutter runout in ball-end milling process. Therefore, this paper presents an analytical force model considering the cutter runout for ball-end milling based on a predictive machining theory, which regards the workpiece material properties, tool geometry, cutting condi- tions, and types of milling as the input data. In this model, the shear flow stress is estimated by introducing a modified Johnson-Cook constitutive law which considers the phenom- enon of the work hardening, temperature softening, and ma- terial size-effect. Each cutting edge of the ball-end cutter is discretized into a series of infinitesimal elements along the cutter axis and the cutting action of which is equivalent to the classical oblique cutting process. Thus, the cutting force componentsappliedoneachelement can becalculatedusinga predictive oblique cutting model and the total instantaneous cutting forces are obtained by summing up the forces contrib- uted by all cutting edges. What is more, this model takes into account the effect of the edge radius, varying sliding friction coefficient and cutter runout on the cutting forces. Finally, the proposed analytical model of cutting forces is verified by the published results and experimental data. Good agreement shows the effectiveness of the proposed analytical model and highlights the importance of the cutter runout on the forces.