Abstract
In traditional processing, a large number of G01 blocks are adopted to discretize free surface or curve for NC machining. But, the continuity of G01 line segments is only C0, which may lead to discontinuity of axis acceleration, resulting in the frequent fluctuation of tool motion at the junctions in high-speed machining, deteriorating the quality of work piece, and reducing processing efficiency. To solve this problem, a local smoothing interpolation method is proposed in this paper. At first, the analytic relationship between the continuity of the trajectory and the continuity of the axes motion is first systematically described by formula. Based on this relationship, a local smoothing algorithm and a feed-rate scheduling method are proposed to generate a C2 continuous tool path motion with axis-acceleration continuity. The local smoothing algorithm smoothes the corners of G01 blocks by the cubic B-spline according to the cornering error tolerance specified by the user. After the feed rate at critical points of smoothed tool path was determined by a modified bidirectional scanning algorithm by considering constrains of chord error and kinematic property, an iterative S-shape feed rate scheduling is employed to minimize residual distance caused by round of time while ensuring the continuity of feed rate and acceleration. Then, a look-ahead interpolation strategy combined with smoothing algorithm and feed-rate scheduling as mentioned is proposed for real-time interpolation of short line segments. At last, simulations are conducted to verify the effectiveness of the proposed methods. Compared with the traditional G01 interpolation, it can significantly improve the processing efficiency and shorten the processing time within error tolerance.
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Yang J, Altintas Y (2013) Generalized kinematics of five-axis serial machines with non-singular tool path generation. Int J Mach Tools Manuf 75:119–132. https://doi.org/10.1016/j.ijmachtools.2013.09.002
Tsai M, Nien H, Yau H (2010) Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining. Int J Adv Manuf Technol 47(5–8):621–638. https://doi.org/10.1007/s00170-009-2220-7
Yang J, Chen Y, Chen Y, Zhang D (2015) A tool path generation and contour error estimation method for four-axis serial machines. Mechatronics 31:78–88. https://doi.org/10.1016/j.mechatronics.2015.03.001
Wang J, Yau H (2009) Real-time NURBS interpolator: application to short linear segments. Int J Adv Manuf Technol 41(11–12):1169–1185. https://doi.org/10.1007/s00170-008-1564-8
Li W, Liu Y, Yamazaki K, Fujisima M, Mori M (2008) The design of a NURBS pre-interpolator for five-axis machining. Int J Adv Manuf Technol 36(9–10):927–935. https://doi.org/10.1007/s00170-006-0905-8
Zhang M, Yan W, Yuan C, Wang D, Gao X (2011) Curve fitting and optimal interpolation on CNC machines based on quadratic B-splines. Sci China Inf Sci 54(7):1407–1418. https://doi.org/10.1007/s11432-011-4237-4
S Yeh HS (2009) Implementation of online NURBS curve fitting process on CNC machines. Int J Adv Manuf Technol 40(5–6):531–540. https://doi.org/10.1007/s00170-007-1361-9
Pateloup V, Duc E, Ray P (2010) Bspline approximation of circle arc and straight line for pocket machining. Comput Aided Des 42(9):817–827. https://doi.org/10.1016/j.cad.2010.05.003
Zhao H, Zhu L, Ding H (2013) A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments. Int J Mach Tools Manuf 65:88–98. https://doi.org/10.1016/j.ijmachtools.2012.10.005
Beudaert X, Lavernhe S, Tournier C (2013) 5-axis local corner rounding of linear tool path discontinuities. Int J Mach Tools Manuf 73:9–16. https://doi.org/10.1016/j.ijmachtools.2013.05.008
Tulsyan S, Altintas Y (2015) Local toolpath smoothing for five-axis machine tools. Int J Mach Tools Manuf 96:15–26. https://doi.org/10.1016/j.ijmachtools.2015.04.014
SJ Yutkowitz. (2005). Apparatus and method for smooth cornering in a motion control system
Farouki RT (2014) Construction of rounded corners with Pythagorean-hodograph curves. Comput Aided Geom D 31(2):127–139. https://doi.org/10.1016/j.cagd.2014.02.002
Q Bi, Y Wang, L Zhu, H Ding. (2011). A practical continuous-curvature Bézier transition algorithm for high-speed machining of linear tool path (7102, pp. 465–476). Berlin, Heidelberg: Springer Berlin Heidelberg. (Reprinted. doi: https://doi.org/10.1007/978-3-642-25489-5_45
Annoni M, Bardine A, Campanelli S, Foglia P, Prete CA (2012) A real-time configurable NURBS interpolator with bounded acceleration, jerk and chord error. Comput Aided Des 44(6):509–521. https://doi.org/10.1016/j.cad.2012.01.009
Lu L, Zhang L, Ji S, Han Y, Zhao J (2016) An offline predictive feedrate scheduling method for parametric interpolation considering the constraints in trajectory and drive systems. Int J Adv Manuf Technol 83(9–12):2143–2157. https://doi.org/10.1007/s00170-015-8112-0
Sencer B, Altintas Y, Croft E (2008) Feed optimization for five-axis CNC machine tools with drive constraints. Int J Mach Tools Manuf 48(7–8):733–745. https://doi.org/10.1016/j.ijmachtools.2008.01.002
Dong J, Ferreira PM, Stori JA (2007) Feed-rate optimization with jerk constraints for generating minimum-time trajectories. Int J Mach Tools Manuf 47(12–13):1941–1955. https://doi.org/10.1016/j.ijmachtools.2007.03.006
Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int J Mach Tools Manuf 41(9):1323–1345. https://doi.org/10.1016/S0890-6955(01)00002-5
Lin M, Tsai M, Yau H (2007) Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm. Int J Mach Tools Manuf 47(15):2246–2262. https://doi.org/10.1016/j.ijmachtools.2007.06.005
Piegl L, Tiller W (1997) NURBS book. Springer, Berlin/Heidelberg
Noble B (1964) Numerical methods. Oliver and Boyd, New York
Liu M, Huang Y, Yin L, Guo J, Shao X, Zhang G (2014) Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools. Int J Mach Tools Manuf 87:1–15. https://doi.org/10.1016/j.ijmachtools.2014.07.002
Lee A, Lin M, Pan Y, Lin W (2011) The feedrate scheduling of NURBS interpolator for CNC machine tools. Comput Aided Des 43(6):612–628. https://doi.org/10.1016/j.cad.2011.02.014
Du X, Huang J, Zhu L (2015) A complete S-shape feed rate scheduling approach for NURBS interpolator. J Comput Des Eng 2(4):206–217. https://doi.org/10.1016/j.jcde.2015.06.004
Beudaert X, Pechard P, Tournier C (2011) 5-axis tool path smoothing based on drive constraints. Int J Mach Tools Manuf 51(12):958–965. https://doi.org/10.1016/j.ijmachtools.2011.08.014
Lei WT, Wang SB (2009) Robust real-time NURBS path interpolators. Int J Mach Tools Manuf 49(7–8):625–633. https://doi.org/10.1016/j.ijmachtools.2009.01.007
Zhang X, Song Z (2012) An iterative feedrate optimization method for real-time NURBS interpolator. Int J Adv Manuf Technol 62(9–12):1273–1280. https://doi.org/10.1007/s00170-011-3847-8
Baek DK, Yang S, Ko TJ (2013) Precision NURBS interpolator based on recursive characteristics of NURBS. Int J Adv Manuf Technol 65(1–4):403–410. https://doi.org/10.1007/s00170-012-4179-z
Chen M, Zhao W, Xi X (2015) Augmented Taylor’s expansion method for B-spline curve interpolation for CNC machine tools. Int J Mach Tools Manuf 94:109–119. https://doi.org/10.1016/j.ijmachtools.2015.04.013
Yang J, Altintas Y (2015) A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools. Int J Mach Tools Manuf 88:9–23. https://doi.org/10.1016/j.ijmachtools.2014.08.004
Funding
The authors would like to thank the Important Science and Technology Specific Projects of Anhui Province, Nos. JZ2016AKKZ1067 and JZ2016AKKZ1069, and the National Natural Science Foundation of China under Grant Nos. 51575154 and 51505118.
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Han, J., Jiang, Y., Tian, X. et al. A local smoothing interpolation method for short line segments to realize continuous motion of tool axis acceleration. Int J Adv Manuf Technol 95, 1729–1742 (2018). https://doi.org/10.1007/s00170-017-1264-3
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DOI: https://doi.org/10.1007/s00170-017-1264-3