A variable mass, cylindrical plasma model (VMCPM) is developed for sparks created by electrical discharge in a liquid media. The model consist of three differential equations—one each from fluid dynamics, an energy balance, and the radiation equation—combined with a plasma equation of state. A thermophysical property subroutine allows realistic estimation of plasma enthalpy, mass density, and particle fractions by inclusion of the heats of dissociation and ionization for a plasma created from deionized water. Problems with the zero-time boundary conditions are overcome by an electron balance procedure. Numerical solution of the model provides plasma radius, temperature, pressure, and mass as a function of pulse time for fixed current, electrode gap, and power fraction remaining in the plasma. Moderately high temperatures (≳5000 K) and pressures (≳4 bar) persist in the sparks even after long pulse times (to ∼500 μs). Quantitative proof that superheating is the dominant mechanism for electrical discharge machining (EDM) erosion is thus provided for the first time. Some quantitative inconsistencies developed between our (1) cathode, (2) anode, and (3) plasma models (this series) are discussed with indication as to how they will be rectified in a fourth article to follow shortly in this journal. While containing oversimplifications, these three models are believed to contain the respective dominant physics of the EDM process but need be brought into numerical consistency for each time increment of the numerical solution.

No abstract

A model is presented to explain the recently reported mechanism of thermal spalling for shaping high melting point ceramics by electrical discharge machining. Since previous models fail to explain the experimental observations completely, an expanding circular heat source created by growth of plasma is assumed to act on the surface. Erosion of materials by spalling is caused by thermally induced compressive stresses during heating-up periods and tensile stresses during cooling-down periods. This model explains material removal for anodic erosion in general (wire-cutting machines) and for cathodic erosion (die-sinking machines) whenever long pulse duration is used. Simulation of the model for TiB2 provides a local melt front that penetrates to a depth of submicrometer, then recedes as pulse duration increases. Spalling develops flakes with thickness correlated to pulse duration. The results were verified by the experimental observations which showed that large flakes having the predicted maximum thickness as well as few quenched spherical droplets containing titanium were obtained.

Erosion in electrical discharge machining has been described as occurring by melting and flushing the liquid formed. Recently, however, thermal spalling was reported as the mechanism for machining refractory materials with low thermal conductivity and high thermal expansion. The process is described, here, by a model based on a ceramic surface exposed to a constant circular heating source which supplies a constant flux over the pulse duration. The calculations were based on TiBz mechanical properties along a and c directions. Theoretical predictions were verified by machining hexagonal TiBz. Large flakes of TiBz with sizes close to grain size and maximum thickness close to the predicted values were collected, together with spherical particles of Cu and Zn eroded from cutting wire. The cutting surfaces consist of cleavage planes sometimes contaminated with Cu, Zn, and impurities from the dielectric fluid. [

This article provides an analysis of the wire electrical discharge machining (EDM) process. The causes of wire vibration, bowing, and breakage are identified. The cross sectional configuration of an eroded wire is derived from basic physics under the assumption that the erosion rate is constant. This configuration is verified experimentally with further explanation as to why numerous experimental studies have yielded different configurations. A computational model has been developed that can evaluate the systematic effects that lead to wire breakage by determining the stress induced by wire erosion and the stress induced by the sparks during the operation of a wire-cutting EDM machine. This model is also capable of determining the extent of wire bowing and vibrations in these machines but only in the frontal direction. The model is supported by data from experiments performed on an AGIECUT 612 wire machine cutting a 10 mm high copper bar with a 0.15 mm brass wire to acquire wire breakage data. The nearly parabolic shape of the bowed wire agrees with the results of other authors making more restrictive assumptions.