CHARACTERISTICS OF DIMENSION FUNCTIONS ASSOCIATED WITH CUTTING MEASUREMENTS

The information dimension, D(0), of attractors associated with orthogo nal turning is determined from experimental tool-workpiece relative ac celeration data. Let E = dimension of a delay coordinate space, n = nu mber of generic data points and m = number of reference points on the attractor. If is shown that properties of D(0) as a function off, deno ted by D(0):E, are unchanging, invariant, over targe intervals of n an d m. The qualitative properties of D(0):E discriminate between various cutting cases. This discrimination can be based on relatively small d ata sets. The computation of D(0) is shown to be robust in the sense t hat estimated values of D(0) are in variant or slowly varying over int ervals of n and m.