Characterization of machining chattering dynamics: An R/S scaling analysis approach

Self-excited vibrations in machining, well known as chatter, are a kind of dynamical instability that represents a serious productivity issue because of a poor surface finishing, early damage, and breakage of cutting tools they tend to. Chatter presents a highly nonlinear nature characterized by subcritical Hopf and period-doubling bifurcations, as well as limit cycles, quasiperiodic, and even chaotic behavior. Several efforts on modeling, monitoring, and control of chatter have been developed, such as linear and nonlinear predictive analyses based on the regenerative theory, analysis of signals in frequency domain or time domain, and control strategies based on pairs of sensors and actuators. Monitoring signals is particularly important since the real behavior of the process can be measured, by displacement, acceleration or audio transducers. In this work, an analysis of the predictability of a long-term signal, based on the rescaled range (R/S) analysis and the dynamical behavior of the Hurst exponent, is presented as an effective method to identify and monitor correlations and nonlinear behavior of machining. This method was validated experimentally with acceleration signals from a milling process. Fractal nature of vibrations was confirmed. Results were in agreement with a theoretical stability analysis of different conditions of machining, e.g., unstable conditions presented a Hurst exponent value of about 0.5 and even lower (anti-correlated dynamics), whereas stable conditions were characterized by a Hurst exponent larger than 0.5 (correlated dynamics). The results lead to the conclusion that R/S scaling analysis is an effective method to monitor and predict the emergence of chatter behavior in machining.