Asymmetrical pythagorean-hodograph (PH) spline-based C3 continuous corner smoothing algorithm for five-axis tool paths with short segments

Abstract

• A real-time C 3 continuous corner smoothing algorithm is proposed for five-axis short linear segments. • The proposed method can achieve lower curvature based on asymmetrical PH splines. • Smoothing errors around the corners are bounded under given constraints. • The arc-length can be analytically calculated to achieve real-time interpolation. • Experiments verify that much lower curvature and higher machining efficiency can be realized. Local corner smoothing is widely used for the G01 motion commands to achieve the motion continuity of transition corners. Most splines constructed by the existing local corner smoothing methods oriented for five-axis machining mainly must be connected by linear segments. However, with respect to the five axis machining of the corners with short line segments, these kinds of methods need that both ends of the constructed splines usually must be shrunk with the same proportion to avoid the overlapping of adjacent splines. This will lead to relatively large curvatures of the obtained trajectories together with relatively low machining efficiency. This article proposes a new real-time corner smoothing algorithm for five-axis machine tools by constructing the C 3 continuous asymmetrical PH splines. The typical characteristic lies in that the control points related to the two ends of the PH spline can be independently adjusted through reasonably introducing two more adjustable variables, which are realized by analytically calculating and then adding two additional control points into the corresponding control polygon. As a result, the PH spline poses the property of the asymmetry about the angular bisector. Based on this, the short linear commands of tool tip and tool orientation can be smoothed only through inserting different lengths of asymmetrical PH splines that can be connected directly. The motion variance of the smoothed tool orientation related to the tool tip displacement is analytically proved to be C 3 continuous, and thus, the synchronization between tool tip and tool orientation is guaranteed. The outstanding advantage of the algorithm for short line segments is twofold. The first is that the performance of the drives can be more fully utilized to reduce cycle time since the curvature around corners are reduced by adopting the asymmetrical profile, and the second is that the synchronization procedure is greatly simplified since the algorithm eliminates the requirement to convert the intermediate line segments into a spline between the adjacent connected PH splines. Both simulation and the experimental results demonstrate that the proposed algorithm can realize a higher machining efficiency.