Real-time estimate and control contour errors for five-axis local smoothed toolpaths based on airthoid splines

Five-axis linear commands are blended as the local smoothed toolpaths by inserting clothoid and airthoid splines at corners in five-axis CNC machining. The contour error is the bottleneck to achieve the precise dimension of the machined parts, when following the local smoothed toolpaths. This paper presents a contour error estimation and control method for the five-axis smoothed toolpaths with airthoid splines, according to the geometric characteristics of the toolpaths. The tool-tip contour error is analytically calculated based on the expression of the smoothed toolpaths. Consequently, the tool-orientation contour error is obtained by synchronizing the tool-orientation contour point with the tool-tip item based on the motion time through the designed time scale coefficient, when the toolpaths are scheduled by the time-synchronization scheme. Furthermore, a contour error compensation strategy is constructed to adaptively determine the compensator gain. It can be qualified to maximally eliminate the contour errors and steadily hold the control stability of the feed drives, in spite of the modeling error between the nominal and actual control models. The simulation and experiment results show that the estimation algorithm has higher accuracy than traditional methods, and the compensation strategy effectively eliminates the five-axis contour error.