Real-time local smoothing for five-axis linear toolpath considering smoothing error constraints

Five-axis linear toolpaths (or G01 blocks) are widely used in CNC machine tools. The tangential and curvature discontinuities at the corners of linear toolpath result in feed fluctuation and deteriorate the machining efficiency and quality. Several methods have been proposed to locally smooth the corners for three-axis toolpath, but local smoothing for five-axis toolpath is still challenging due to two main difficulties: control of the tool orientation smoothing error and parameter synchronization between tool position and tool orientation. This paper proposes a real-time G(2) continuous local smoothing method by replacing the corners of tool position and tool orientation paths with cubic B-splines. The two difficulties in five-axis local smoothing are both resolved in simple and analytical ways. With a two-step method, the tool orientation smoothing error is directly and analytically constrained. By converting the remaining linear segments into B-splines, the C-1 continuity of the smooth tool position and smooth tool orientation paths is achieved. The parameter synchronization is realized by sharing the parameter of the tool orientation with that of the tool position. Compared with the existing analytical methods, the proposed method has a higher computation efficiency and a tighter tolerance in control of the orientation smoothing error. We have developed an open-source benchmark which validates the computation efficiency and error control ability of the proposed method. After smoothing and synchronization, the inserted B-spline of tool position is traversed with constant feedrate and the feedrate of the remaining linear segment is planned with jerk-bounded trajectory profile. The proposed smoothing method can be implemented on-line and has been integrated into a self-developed open-architecture CNC system. Its effectiveness for on-line generating smooth motion has been validated via simulations and experiments.