Fundamental geometry analysis of wire electrical discharge machining in corner cutting

Abstract

Fundamental geometry properties of wire electrical discharge machining (WEDM) process in corner cutting is studied. The concept of discharge-angle is introduced, and its mathematical expression is derived by analytical geometry. A model to estimate the metal removal rate (MRR) in geometrical cutting is developed by considering wire deflection with transformed exponential trajectory of wire centre. The computed MRR is compared with measured sparking frequency of the process since they are equivalent to each other for an iso-energy type machine. A very good agreement is obtained. Both of the discharge-angle and MRR drop drastically to a minimum value depending on the corner angle being cut as the guides arrive at the corner apex, and then recover to the same level of straight-path cutting sluggishly. Hence the observed phenomenon of increased gap-voltage and decreased sparking frequency in corner cutting can be physically interpreted. In addition, the variation of the machining load caused by the change of MRR, which was taken as unknown disturbance in the past, can be predicted and used for control purpose.