Cutting state identification

Cutting states associated with the orthogonal cutting of stiff cylinders are identified through an analysis of the singular values of a Toeplitz matrix of third order cumulants of acceleration measurements. The ratio of the two pairs of largest singular values is shown to differentiate between light cutting, medium cutting, pre-chatter and chatter states. Sequences of cutting experiments were performed in which either depth of cut or turning frequency was varied. Two sequences of experiments with variable turning frequency and five with variable depth of cut, 42 cutting experiments in all, provided a database for the calculation of third order cumulants. Ratios of singular values of cumulant matrices find application in the analysis and control of orthogonal cutting. (C) 1997 Academic Press Limited.