Cutting states associated with the orthogonal cutting of stiff cylinde
rs are identified through an analysis of the singular values of a Toep
litz matrix of third order cumulants of acceleration measurements. The
ratio of the two pairs of largest singular values is shown to differe
ntiate between light cutting, medium cutting, pre-chatter and chatter
states. Sequences of cutting experiments were performed in which eithe
r depth of cut or turning frequency was varied. Two sequences of exper
iments with variable turning frequency and five with variable depth of
cut, 42 cutting experiments in all, provided a database for the calcu
lation of third order cumulants. Ratios of singular values of cumulant
matrices find application in the analysis and control of orthogonal c
utting. (C) 1997 Academic Press Limited.