Reverse Engineering Algorithm for Cutting of Ruled Geometries by Wire

Abrasive wire cutting (AWC) and wire electric discharge machining (WEDM) are efficient and econom-ical processes for the fabrication of precision parts from bulk material. Operating costs and manufacturing lead times are low compared to more general methods such as 5-axis CNC milling, turning, or electro-discharge machining. In this paper, an algorithm based on differential geometry in Euclidean space is proposed for reverse engineering of ruled geometries. The algorithm can determine whether a given geometry is producible by wire cutting, and can also de-rive the associated wire trajectories. Implementation is demonstrated by producing complex turbine blade geometries on 4-axis wire cutting machines with an overall shape accuracy of 20–40 μm peak-to-valley.