Theoretical and experimental analysis of machining errors on small arced corners during WEDM finishing stages

Accurate machining in small-radius paths is a challenge associated with Wire Electrical Discharge Machining (WEDM). This article experimentally and theoretically analyzes the machining errors of the arced paths through successive machining stages. The machining errors of a three-stage WEDM on both straight and arced paths are first experimentally analyzed. Mathematical expressions are derived to relate new theoretical concepts, including spark angle and spark density, for each finishing stage on both straight and arced paths. Then, the effects of these concepts on machining errors of the finishing stages are determined. The causes of the machining errors of the first and second finishing stages on male and female arced paths are theoretically analyzed, and a novel mathematical methodology for the prediction of these errors is developed. The experimental machining errors of the first and second finishing stages on the different arced paths are compared and evaluated with related theoretical ones. Results reveal that the mathematical methodology predicts and compensates the machining errors of the first finishing stage with the accuracy of 78% and of the second finishing stage with the accuracy of 83%. There is a good improvement which can be employed in WEDM applications and to increase the wire electrical discharge (WED) machine capability.