Real-time global smoothing and interpolation for five-axis short line segment toolpaths through G0-G1-C2 two layered fairing

Abstract

Short line segment toolpaths widely used in five-axis CNC machine tools has the defects of low-order continuity, the tangential and curvature discontinuities at the corners, which result in frequent fluctuation of feedrate, thus degrading the machining quality and efficiency. Therefore, smoothing interpolation of the path becomes significant. Although the local corner smoothing methods are relative mature, the global smoothing methods can hardly be fulfilled in real time, because either the replacing of line segments by global smooth curves or the scheduling of five-axis feedrate requires time-consuming iterative or pre-processed computing. To deal with above problem, this paper proposes a real-time global smoothing and interpolation method for five-axis short line segment toolpaths. This is realized by a G0-G1-C2 two layered fairing method, containing a G0-G1 outer-layer smoothing step and a G1-C2 inner-layer smoothing step. In the outer layer, a piecewise dual B-spline with globally G1 continuity is constructed for replacing the G0 continuous line-segment toolpath. Further, in the inner layer, a FIR (Finite Impulse Response) convolving algorithm is presented for generating C2-continuous axial trajectories with bounded acceleration and jerk, according to the G1 dual-spline path. Both of the two layers are lightweight in computation, which makes the proposed global smoothing method have strong real-time capability. Verification and comparison tests demonstrate that the proposed method performs similarly with existing off-line methods in smoothing results, but performs overwhelmingly in real-time capability, and its single-step computation calls for merely about 12 % of the total interpolation period.