In spline toolpath interpolation, a crucial point is solving the mapping between the spline parameter (u) and actual arc length (s) accurately, so that the toolpath is traveled without undesirable fluctuations or discontinuities in the feedrate profile. To achieve this, various techniques have been proposed in literature, including Taylor series interpolation, iterative numerical methods, and approximating the mapping between u and s with a feed correction polynomial. This paper presents a new way to parameterize the seventh order feed correction polynomial, which was introduced by Erkorkmaz and Altintas (2005, “Quintic Spline Interpolation With Minimal Feed Fluctuation,” ASME J. Manuf. Sci. Eng., 127(2), pp. 339–349). The proposed technique has a closed-form solution that can be efficiently implemented in real-time, rather than having to construct and solve a linear equation system with 14 unknowns for each spline segment. In this paper, the new solution is derived step by step, and simulation case studies are presented which demonstrate that the new method accurately parameterizes the feed correction polynomial in approximately 43% less computational time, compared to applying the former solution of Erkorkmaz and Altintas (2005, “Quintic Spline Interpolation With Minimal Feed Fluctuation,” ASME J. Manuf. Sci. Eng., 127(2), pp. 339–349). This is because matrix multiplication operations and a dedicated linear equation solver, which are cumbersome to implement inside a real-time computer numerical controller (CNC), are avoided in the new solution.
Efficient Fitting of the Feed Correction Polynomial for Real-Time Spline Interpolation
Precision Controls Laboratory,
Department of Mechanical and Mechatronics Engineering,
Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received March 16, 2014; final manuscript received March 29, 2015; published online July 8, 2015. Assoc. Editor: Xiaoping Qian.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Erkorkmaz, K. (August 1, 2015). "Efficient Fitting of the Feed Correction Polynomial for Real-Time Spline Interpolation." ASME. J. Manuf. Sci. Eng. August 2015; 137(4): 044501. https://doi.org/10.1115/1.4030300
Download citation file:
- Ris (Zotero)
- Reference Manager