Theoretical models of the electrical discharge machining process. I. A simple cathode erosion model

TLDR

Electrical discharge machining modeling has traditionally used conduction models, but this work adopts a point‑heat‑source approach that treats power as the boundary condition, reflecting the higher energy intensity and pressure of liquid dielectrics and their impact on cathode energy transfer mechanisms. The study presents a simple cathode erosion model and a universal, dimensionless formulation to identify key parameters for optimum pulse time and erodibility in EDM. The model assumes a constant fraction of supplied power reaches the cathode across currents and attributes cathode heating to photoelectric emission rather than ion bombardment during the brief EDM pulses. After calibration to one experimental point, the model predicts optimum pulse times within an average 16 % error across a two‑decade current range.

Abstract

A simple cathode erosion model for the electrical discharge machining (EDM) process is presented. This point heat-source model differs from previous conduction models in that it accepts power rather than temperature as the boundary condition at the plasma/cathode interface. Optimum pulse times are predicted to within an average of 16% over a two-decade range after the model is tuned to a single experimental point. A constant fraction of the total power supplied to the gap is transferred to the cathode over a wide range of currents. A universal, dimensionless model is then presented which identifies the key parameters of optimum pulse time factor (g) and erodibility (j) in terms of the thermophysical properties of the cathode material. Compton’s original energy balance for gas discharges is amended for EDM conditions. Here it is believed that the high density of the liquid dielectric causes plasmas of higher energy intensity and pressure than those for gas discharges. These differences of macroscopic dielectric properties affect the microscopic mechanisms for energy transfer at the cathode. In the very short time frames of EDM, our amended model uses the photoelectric effect rather than positive-ion bombardment as the dominant source of energy supplied to the cathode surface.