Chatter formation during milling due to stochastic noise-induced resonance

Abstract

In this paper, the stochastic dynamical model of a single-degree-of-freedom milling operation is formulated, where a Gaussian white noise process models the high-frequency variation in the cutting force. With the help of this stochastic model, it is shown, that large-amplitude stable vibrations can occur near the critical machining parameters, due to stochastic noise-induced resonance. During the analysis, the second moment stability and stationary first and second moment behavior of the periodic stochastic delay differential equation (SDDE) describing the milling operation are investigated. The behavior of these quantities are then compared to the evolution of the so-called “chatter peak” in the Fourier-spectrum of the vibrations, that is used to experimentally determine the presence of chatter, in the stable machining parameter domain. Furthermore, it is discussed, how the statistical properties of the resonant vibrations can be used to predict the stability boundary and the formulation of chatter, while the machining parameters are kept in the safe region. The theoretical calculations are supported by experiments performed on a single-degree-of-freedom system.