Characteristics of Dimension Functions Associated With Cutting Measurements

Abstract

The information dimension, D(0) , of attractors associated with orthogonal turning is determined from experimental tool-workpiece relative acceleration data. Let E≡dimension of a delay coordinate space, n≡number of generic data points and m≡ number of reference points on the attractor. It is shown that properties of D(0) as a function of E, denoted by D(0) :E, are unchanging, invariant, over large intervals of n and m. The qualitative properties of D(0) :E discriminate between various cutting cases. This discrimination can be based on relatively small data sets. The computation of D(0) is shown to be robust in the sense that estimated values of D(0) are invariant or slowly varying over intervals of n and m.