Non-circular parametric curve and curved surface interpolation and tool compensation for WEDM based on unit arc length increment method

Abstract

This paper proposes a novel non-circular parametric curve interpolation algorithm based on the unit arc length increment method (UALI). In this method, axial coordinates are taken as functions of arc length. The reference point moves by 1 basic length unit (BLU) along a curve in each interpolation period, and the corresponding projections on each coordinate are added into accumulators of each axis respectively. An axis will then move by 1 BLU when its accumulator exceeds 1 BLU. Theoretically, based on the UALI method, an interpolation algorithm is derived for parametric curves such as involutes, Archimedes spirals, cycloids, and parabolas. This interpolation algorithm is applicable for ruled surfaces of a workpiece with different parametric curves in the upper and lower planes. Tool compensation is considered for both non-tapered workpieces as well as tapered workpieces. Simulation results and experiment results demonstrate the advantages of this interpolation algorithm, and the accuracy of this interpolation algorithm is analyzed.