A Comparative Study of Numerical Simulations and Stability Analysis for a Classical Case of Regenerative Chatter in Milling

Regenerative chatter remains one of the major challenges encountered in machining, motivating continuous efforts to predict its onset through mathematical modeling. A common approach to studying this phenomenon is the stability analysis of the system’s vibration equations. This method relies on linearizing the system dynamics around a nominal cutting regime — defined by a particular combination of cutting parameters — and analyzing the behavior of small perturbations in its vicinity. In its classical formulation, however, this approach focuses solely on stability and does not account for system vibrations outside this scope. As a result, it cannot predict forced vibrations that may reach significant amplitudes near resonance, even when the nominal regime checks as stable. In this paper, we revisit a classical academic case of milling of a single degree of freedom system (discussed by Budak in 1998) and trace the historical development of its analysis. We also consider the influence of several parameters including feed rate, which often falls outside the scope of traditional stability analysis. The results of stability analysis are compared with predictions of a numerical design-of-experiment obtained via the time-domain simulations based on the finite-elements and dexels. Stability boundaries predicted by Zero Order Approach and Updated Zeroth-Order Semi-Discretization Method match the simulated transition to high vibrations, while time-domain simulations reveal resonance-driven forced-vibration hotspots in nominally stable regions (resonances and sub-resonances). Doubling feed per tooth yields near-linear scaling of forced response without a notable shift of the stability boundary positions. A near-linear scaling of post-critical vibrations amplitude was observed as well and discussed.