Dynamics of Metal Cutting with Frictional and Regenerative Effects

Chatter in machining is characterised by undesirable high-amplitude mechanical vibrations in a system, yielding a multitude of adverse consequences. Some implications include suboptimal finishing, imprecision, energy wastage, material depletion, recycling costs, reprocessing expenses, waste disposal, and augmented production time expenditures. These vibrations emanate from various sources of instability during cutting operations, including frictional, regenerative, mode-coupling, and thermo-mechanical effects, which are strongly nonlinear in nature. Of particular significance in the domains of precision manufacturing are frictional and regenerative chatters. Frictional chatter, also known as primary chatter, emerges due to velocity-dependent cutting forces and friction between the chip and the tool’s rake face. In contrast, regenerative chatter, the secondary form, arises from workpiece geometry influences stemming from preceding passes, subsequently impacting the dynamics during subsequent passes and giving rise to fluctuating forces and vibrations. This work delves into the modelling of metal cutting in this context, analysing nonlinear behaviour through bifurcation diagrams, with rake angle, flank angle, and static friction coefficients serving as pivotal parameters. A down-up approach is taken where initially the simpler case of orthogonal macro-machining is dealt with, followed by a more complex micro-machining example of handheld drillbits where torsional and bending vibration modes dominate the dynamical behaviour.