Distribution of Discharge Location in EDM Using Chaos Theory

Abstract

In this paper we describe the analysis of the distribution of discharge location using chaos theory in Electrical Discharge Machining (EDM). Chaos is a nonlinear phenomenon which is determined by a relatively simple rule, although it appears complicated and random. It was found that the discharge location is simply determined by the gap distribution and the debris particle distribution in spite of the complicacy and randomness of these distributions. Namely, the discharge occurs at the location where the gap is narrow and the debris density is high. Consequently, we analyzed the discharge location distribution using chaos theory and found the following: 1) the distribution of discharge location is irregular, 2) a bifurcation is observed, 3) the attractor dimension is relatively small, and 4) at least one of the Lyapunov exponents is larger than zero. By calculating the attractor dimension, we also found that there is a correlation between the attractor dimension and machining stability, that is, the higher the attractor dimension is, the greater the stability of machining is. This means the machining stability, which has not been detectable so far, can be distinguished by calculating the attractor dimension.