A Stochastic Approach to Thermal Modeling Applied to Electro-Discharge Machining

The usual method of making some simplifying assumptions and formulating thermal models that yield results confirmed by experiments does not work in many cases where the problem is complex and random. Electro-Discharge Machining (EDM) is such a process that is not only complicated and random but also physically little understood. The paper illustrates thermal modeling of this process with the help of a recently developed stochastic methodology called Data Dependent Systems (DDS). An equation to the melting iosthermal curve is defined from the DDS (stochastic empirical) model obtained from readily measurable surface profiles of actual machined surfaces created by the random superposition of electrical discharges. This equation of the melting isothermal curve is then combined with the heat conduction equation, under rather realistic and intuitively obvious assumptions, to develop a transient temperature distribution. The form of this (hybrid) thermal model is mathematically much simpler and yet its predictions are much closer to the experimental results, compared to the complicated models proposed in the literature.