On the chaotic nature of electro-discharge machining

The long-accepted thermoelectric model for electro-discharge machining is being brought into question. Several experimental facts prompt the proposal of a new theory based on the effect of gap pollution on the ignition of discharges. The first experimental proof comes from the recently reported observation of debris chains and clusters. In this view, each step of the process depends on the previous ones through a deterministic relation, even if the overall evolution is unpredictable. The paper establishes mathematical grounds for the abovementioned intuitions by setting up and solving a recursive equation for the machining energy employed at each discharge event. By means of numerical and algebraic tools, the above equation is studied and shows a chaotic evolution similar to that of the logistic map. Results reconcile the apparent paradox between deterministic nature and stochastic localization of the discharges and introduce a description of the chaotic dynamics of electro-discharge processes.