Crater Geometry and Volume From Electro-Discharge Machined Surface Profiles by Data Dependent Systems

Abstract

This paper applies a recently developed methodology called Data Dependent Systems to model and analyse the process of Electro-Discharge Machined (EDM) surface generation. A first order stochastic differential equation is developed and physically interpreted from the EDM surface profile measurements under varying pulse duration and machining time. The impulse response function of this model is used to define a characteristic crater geometry. The depth and diameter to depth ratio of such a crater is determined and employed in deriving the radius of curvature and the volume. Experimental measurements are utilized to illustrate the development of regression equations and nomograms, useful in practice to obtain surfaces with desired geometry. It is shown that the depth diameter to depth ratio, and volume of the characteristic craters obtained from actual multiple discharge situation under operating conditions agree fairly well with the past single discharge physics investigations.