A real-time interpolation algorithm for five-axis linear toolpaths with convolution-based local smoothing considering consecutive short segments

Local smoothing stands as the most prevalent technique for optimizing linear toolpaths in CNC machining. Nevertheless, its performance deteriorates markedly when applied to consecutive short segments, severely impacting machining efficiency. This paper proposes a real-time local smoothing and interpolation algorithm, in which a post-processing toolpath smoothing based on a second-order sliding convolution window is implemented to achieve $C^2$ continuity of the interpolated path while simultaneously satisfying constraints of tool tip and rotation smoothing errors. For consecutive short linear segments, convolution-based smoothing enables cross-segment optimization with enhanced geometric consistency, whereas linear regions in long segments are preserved which do not require an additional establishment of synchronization with the smooth region. Preceding the smoothing process, the jerk-limited feedrate scheduling operates at the level of primitive linear segments as the sole minimal unit, thereby circumventing challenges inherent in blended-path (linear and spline segments) interpolation. With adhering to the geometric constraints of the trajectory profile and the machine tool’s kinematic capabilities, this algorithm effectively enhances the scheduled feedrate by identifying the motion-limited axis of each segment. The effectiveness of the proposed algorithm is verified through simulations and experiments.