Cross-recurrence plot quantification analysis of input and output signals for the detection of chatter in turning

Metal cutting is a complex nonlinear dynamical process. Analysis of signals from turning operation shows that the machining exhibits a low-dimensional chaos. The self-excited vibration caused by the regenerative effect, usually called chatter, can be created during machining by increasing one cutting parameter, while keeping all other cutting parameters constant. A cross-recurrence plot (CRP) enables the study of synchronisation or time differences in two time series. CRP-based methodology is used to find the point of transition from normal cutting to chatter cutting. In this method, two signals, one input signal (power to the lathe motor) and one output signal (cutting tool vibration), are recorded simultaneously at a constant sampling rate during cutting. A time series is generated from the recorded values, and cross-recurrence plot is prepared. This CRP can be quantified using Cross-Recurrence Quantification Analysis (CRQA). Abrupt variation in the CRQA parameters indicates the onset of chatter vibration. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP-based methodology is capable of recognising the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material.