THEORETICAL-MODELS OF THE ELECTRICAL-DISCHARGE MACHINING PROCESS .3. THE VARIABLE MASS, CYLINDRICAL PLASMA MODEL

A variable mass, cylindrical plasma model (VMCPM) is developed for spa rks created by electrical discharge in a liquid media. The model consi st of three differential equations-one each from fluid dynamics, an en ergy balance, and the radiation equation-combined with a plasma equati on of state. A thermophysical property subroutine allows realistic est imation of plasma enthalpy, mass density, and particle fractions by in clusion of the heats of dissociation and ionization for a plasma creat ed from deionized water. Problems with the zero-time boundary conditio ns are overcome by an electron balance procedure. Numerical solution o f 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 puls e times (to approximately 500 mus). Quantitative proof that superheati ng is the dominant mechanism for electrical discharge machining (EDM) erosion is thus provided for the first time. Some quantitative inconsi stencies 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. W hile containing oversimplifications, these three models are believed t o contain the respective dominant physics of the EDM process but need be brought into numerical consistency for each time increment of the n umerical solution.