An analytical method for corner smoothing of five-axis linear paths using the conformal geometric algebra. (December 2022)

• Record Type: Journal Article
• Authors: Chen, Yongxue; Huang, Pengsheng; Ding, Ye
• Is Part Of: Computer aided design. Volume 153(2022)
• Publication Date: 2022-12
• Subjects: Five-axis machining -- Conformal geometric algebra -- Local smoothing -- G3 continuity; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2022.103408
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: The chain of linear path segments is widely used in five-axis machining, but the tangential discontinuity of the path reduces machining efficiency and accuracy. This paper proposes an analytical G 3 continuous corner smoothing method based on the conformal geometric algebra. Based on the locations of the tooltip point and a tool axis point, the toolpath is represented in the 6-dimensional Euclidean space. With the help of the representation of conformal transformations and circles in conformal geometric algebra, the path in the 6-dimensional space is smoothed by G 3 continuous circle-based splines under the constraints of the maximum deviation error tolerance. The proposed approach can generate a smooth toolpath that passes through the discrete cutter locations given in the original linear segments analytically. The cycle time of machining is improved thanks to the small curvature and G 3 continuity of the toolpath. The effectiveness and efficiency of the proposed method are validated by simulations and experiments. Highlights: A new analytical method for smoothing of 5-axis linear paths based on the conformal geometric algebra is proposed. The generated paths are G 3 continuous and pass through the initial discrete cutter locations. The proposed method performs high efficiency and significantly improves the feedrate of the tool.