THE E.D.M. PROCESS STUDIED USING THE CUBIC SPLINE OF REGRESSION TYPE STEFAN’S PROBLEM

Glad CONTIU, Marcel Sabin POPA, Florina-Liliana URECHE

Abstract


The abbreviation E.D.M. means “ELECTRICAL DISCHARGE MACHINING” and refers to the materials processing (micro-smelting) by electrical discharge of spark or flame type. The numerous applications of this process are in domain of the polishing, micro-penetration, micro-cutting operations. The de-crystallization in this case is made quickly and at very high temperature. This means that we deal with a STEFAN problem of jump type. The boundary condition of Neumann type refers to the thermal flux, traversing the processed surface. Therefore, at the crater’s free boundary, produced by EDM, it requires that jump of the thermal flux to not transcend a given value. In most of cases is used as a distribution of the thermal field, the GAUSS distribution. Because of the high grade instability of the solution, representing the thermal field, the boundary condition must not contain rough approximations. The Gauss function becomes null only if the crater radius tends to infinity. But is well-known that the crater radius is very small, therefore the flux approximation by the Gauss function can’t be null. We eliminate this drawback replacing  the Gauss function with  a cardinal cubic Spline of regression, having the Gauss function’s carriage and which becomes null with its derivative at the crater’s boundary. Although the obtained mathematical model is a laborious one, its use not contains difficulties, considering the possibility to use some performance numerical software.

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References


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