Nonlinear techniques to characterize precharter and chatter vibrations in the machining of metals

In this paper we report on the use of Poincare sections, phase plane portraits and false nearest neighbor techniques to understand bifurcations in the lathe cutting of aluminum. The experiments presented here offer further evidence of deterministic tool vibrations below the classical onset of chatter. While classical chatter exhibits strong periodic content, these prechatter dynamics exhibit both quasiperiodic and chaotic vibrations. The method of false nearest neighbors predicts an embedding dimenion between 4 and G for prechatter cutting conditions while showing a random characteristic for no-cutting running of the machine. A one-dimensional delay-differential equation model is presented which exhibits some of the characteristics of the Poincare sections of the experimental time series.