Dual-Bézier path smoothing and interpolation for five-axis linear tool path in workpiece coordinate system

Abstract

The tool path composed of consecutive short linear segments (G01 blocks) is still the widespread tool path representation form in five-axis machining. The inherent shortcoming of linear tool path is first-order discontinuity at the corner, which is the bottleneck to achieve high-speed and high-accuracy machining. In this article, a dual-Bézier path smoothing algorithm for five-axis linear tool path in workpiece coordinate system is proposed. There are three steps involved in our method. First, the corner error distribution model is introduced to assign the given tolerance to the smoothing approximation error constraint and the chord error constraint to ensure the interpolation trajectory error within the given tolerance. Second, segment junctions of the linear tool path in workpiece coordinate system are smoothed by double G2 continuous cubic Bézier curves. One cubic Bézier curve is used to round the corner of the tool tip point path, and the other Bézier curve is used to round the corner of the tool axis point path. This algorithm takes the conditions of approximation error constraint, the parameterized synchronization constraint, and continuous curvature constraint into consideration. Hence, the tangency and curvature continuities are both guaranteed in the new path. Third, an adaptive feedrate scheduling method is introduced to interpolate the new path. Simulation and experiment are performed to verify the effectiveness of the proposed method in five-axis tool path smoothing, speed smoothing, and trajectory accuracy controlling.