Features of a real-time s-shaped acceleration/deceleration curve constructing with piecewise linear interpolation of complex-shaped surfaces

Alexander A. Zelensky
Federal State Educational Institution of Higher Education «Moscow State Technological University «STANKIN» (FGBOU VO «MST «STANKIN»), Department of High Performance Technologies and Processing, Assistant Professor, 1, Vadkovsky per., Moscow, GSP-4, 127055, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Tagir Kh. Abdullin
FGBOU VO «MST «STANKIN», laboratory of Electronic Modules Production Technologies, Leading Engineer, 1, Vadkovsky per., Moscow, GSP-4, 127055, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Andrei V. Alepko
FGBOU VO «MST «STANKIN», laboratory of Electronic Modules Production Technologies, Leading Engineer, 1, Vadkovsky per., Moscow, GSP-4, 127055, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Received 08 June 2021

Abstract
In this paper we considered the problem of an s-shaped acceleration/deceleration curve constructing in real time with linear-spline interpolation, taking into account given constraints on the contour acceleration, jerk, and feed rate. The input data for the s-curve were defined in the lookahead algorithm and the geometric smoothing module. The choice of a particular acceleration/deceleration strategy depends on the segment length, the allowable feed rates at the segment junction, and the given kinematic constraints. Each trajectory segment can have a maximum of seven time intervals and their rounding will produce inaccuracies when forming the velocity profile. Therefore, to compensate for rounding errors, the method of half division was applied, which made it possible to remove gaps in the velocity contour. The experimental data obtained indicate the correctness of the chosen approach for its implementation as part of the CNC for high-speed machining of surfaces with complex shapes.

Key words
Feed-rate planning algorithm, s-shaped acceleration/deceleration, trajectory smoothing, numerical control system, real-time, frame preview algorithm.

Acknowledgements
The research was carried out with financial support of Ministry of Science and Higher Education of Russian Federation in the frame of state assignment (project no.FSFS-2020-0031).

DOI
https://doi.org/10.31776/RTCJ.9304

Bibliographic description
Zelensky, A., Abdullin, T. and Alepko, A., 2021. Features of a real-time s-shaped acceleration/deceleration curve constructing with piecewise linear interpolation of complex-shaped surfaces. Robotics and Technical Cybernetics, 9(3), pp.186-195.

UDC identifier:
519.688

References

1. Xu Du, Jie Huang and Li-Min Zhu, 2015. A complete S-shape feed rate scheduling approach for NURBS interpolator. Journal of Computational Design and Engineering, 2(4), pp.206–217. DOI: 10.1016/j.jcde.2015.06.004.
2. Abdullin, T.H. and Har'kov, M.A., 2017. Algoritm operezhajushhego prosmotra dlja sistemy ChPU s primeneniem trapeceidal'nyh zakonov razgona/tormozhenija [Look-ahead algorithm for the CNC system using trapezoidal acceleration / deceleration laws]. In: XXIX Mezhdunarodnaja konferencija «Mashinovedenie i innovacii. Konferencija molodyh uchjonyh i studentov»: trudy [Proceedings of XXIX International Conference «Machine Science and Innovation. Conference of Young Scientists and Students»], pp.256–259. (in Russian).
3. Hu, J., Xiao, L., Wang, Y. and Wu, Z., 2006. An optimal feedrate model and solution algorithm for a high-speed machine of small line blocks with look-ahead. The International Journal of Advanced Manufacturing Technology, 28, рр.930–935. DOI: 10.1007/s00170-004-1884-2.
4. Wen-Bin Zhong et al., 2020. Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review. International Journal of Automation and Computing, 17, pp.1-16. DOI: 10.1007/s11633-019-1190-y.
5. Erkorkmaz, K., Layegh, S.E., Lazoglu, I. and Erdim, H., 2003. Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics. CIRP Annals - Manufacturing Technology, 62, pp.395–398. DOI: 10.1016/j.cirp.2013.03.084.
6. Dong, J.Y., Ferreira, P.M. and Stori, J.A., 2007. Feed-rate optimization with jerk constraints for generating minimum-time trajectories. International Journal of Machine Tools and Manufacture, 47(12-13), pp.1941–1955. DOI: 10.1016/j.ijmachtools.2007.03.006.
7. Sencer, B., Altintas, Y. and Croft, E., 2008. Feed optimization for five-axis CNC machine tools with drive constraints. International Journal of Machine Tools and Manufacture, 48(12–13), pp.733–745. DOI: 10.1016/j.ijmachtools.2008.01.002.
8. Beudaert, X., Lavernhe, S. and Tournier, C., 2012. Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path. International Journal of Machine Tools and Manufacture, 57, pp.73–82. DOI: 10.1016/j.ijmachtools.2012.02.005.
9. Sung-Ho Nam and Min-Yang Yang, 2004. A study on a generalized parametric interpolator with real-time jerk-limited acceleration. Computer-Aided Design, 36(1), pp.27–36. DOI: 10.1016/S0010-4485(03)00066-6.
10. Ming-Tzong Lin, Meng-Shiun Tsai and Hong-TzongYau, 2007. Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm. International Journal of Machine Tools and Manufacture, 47(15), pp.2246–2262. DOI: 10.1016/j.ijmachtools.2007.06.005.
11. Jingchuan Dong, Taiyong Wang, Bo Li and Yanyu Ding, 2014. Smooth feedrate planning for continuous short line tool path with contour error constraint. International Journal of Machine Tools and. Manufacture, 76, pp.1–12. DOI: 10.1016/j.ijmachtools.2013.09.009.
12. Zhao, H., Zhu, L.M. and Ding, H., 2013. A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments. International Journal of Machine Tools and Manufacture, 65, pp.88–98. DOI: 10.1016/j.ijmachtools.2012.10.005.
13. Zelenskij, A.A., Abdullin, T.H., Iljuhin, Ju.V. and Har'kov, M.A., 2019. Vysokoproizvoditel'naja cifrovaja sistema na osnove PLIS dlja upravlenija dvizheniem mnogokoordinatnyh stankov i promyshlennyh robotov [High-performance FPGA-based digital system for motion control of multi-axis machine tools and industrial robots]. Russian Engineering Research, 8, pp.5–8. (in Russian).
14. Hepeng Ni et al., 2018. An optimized feedrate scheduling method for CNC machining with round-off error compensation. The International Journal of Advanced Manufacturing Technology, 97, pp.2369–2381. DOI: 10.1007/s00170-018-1986-x.