Intra-wave modulations in milling processes

Intra-wave modulation effects with oscillating time-varying frequencies have been observed in physical systems including mechanical, ocean, power, and even biological ones. Such phenomena correspond to actual physical processes with which the underlying dynamics of these systems can be understood. In this work, we study intrawave modulation effects in milling processes with the aid of iterative nonlinear chirp mode decomposition (INCMD), a recently proposed technique for analyzing complex dynamic responses. A nonlinear non-stationary template signal is provided to model milling vibration responses, and an INCMD-based strategy is developed to extract embedded modulation features. Through dynamic simulations and experimental verification, it has been demonstrated that distinct intra-wave modulation frequencies that are exactly equal to theoretical chatter frequencies calculated based on the Floquet theory exist to indicate different cutting states, and milling instability is accompanied by the variation of such a characteristic quantity. Bessel functions can mathematically relate explicit modulation patterns with intricate spectral distributions of milling responses. Moreover, the switch of the modulation pattern, which remains noticeable in the presence of noise, emerges far earlier than visible chatter marks do, indicating the superiority of the chatter detection and even prediction utilizing intra-wave modulation features.