Abstract
In practical machining areas, since parametric toolpath can ensure smaller approximation error in computer-aided design/computer-aided manufacturing (CAD/CAM) systems and provide stable feedrate in computer numerical control (CNC) systems, it can improve machining efficiency and machining quality simultaneously compared to linear and circular segments. Therefore, it is necessary to improve the performance of feedrate planning and interpolating for parametric toolpath. In this paper, the parametric toolpath is re-parameterized by the displacement to analyze the feedrate, acceleration, and jerk constraints in the Frenet-Serret frame, and a novel motion method including feedrate planning and interpolating is presented. Afterwards, a time-optimal method for the parametric trajectory is proposed based on linear programming algorithm to limit the multi-constraints and obtain Bang-Bang control. To improve machining accuracy further, a feedback interpolation method is introduced to eliminate the feedrate fluctuation. Finally, experiments are conducted to demonstrate the efficiency and contour performance of the proposed method compared to the conventional methods. The results show that the proposed method can ensure better contour performance and the cycling time is also reduced by 10.46% and 2.86% for 2D and 3D toolpath respectively.
Similar content being viewed by others
References
Wang G, Shu Q, Wang J, Li L (2017) Research on adaptive non-uniform rational B-spline real-time interpolation technology based on acceleration constraints. Int J Adv Manuf Technol 91(5–8):2089–2100
Annoni M, Bardine A (2012) A real-time configurable NURBS interpolator with bounded acceleration, jerk and chord error. CAD Comput Aided Des 44(6):509–521
Liu H, Liu Q, Yuan S (2017) Adaptive feedrate planning on parametric tool path with geometric and kinematic constraints for CNC machining. Int J Adv Manuf Technol 90(5–8):1889–1896
Liu X, Peng J, Lei S, Wang Z (2017) A novel approach for NURBS interpolation through the integration of acc-jerk-continuous-based control method and look-ahead algorithm. Int J Adv Manuf Technol 88(1–4):961–969
Jahanpour J, Alizadeh MR (2015) A novel acc-jerk-limited NURBS interpolation enhanced with an optimized S-shaped quintic feedrate scheduling scheme. Int J Adv Manuf Technol 77:1889–1905
Liang F, Zhao J, Ji S (2017) An iterative feed rate scheduling method with confined high-order constraints in parametric interpolation. Int J Adv Manuf Technol 92(5–8):2001–2015
Beudaert X, Lavernhe S, Tournier C (2012) Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path. Int J Mach Tools Manuf 57:73–82
Yuan M, Chen Z, Yao B, Zhu X (2017) Time optimal contouring control of industrial biaxial gantry: a highly efficient analytical solution of trajectory planning. IEEE-ASME T MECH 22(1):247–257
Ye P, Shi C, Yang K, Lv Q (2008) Interpolation of continuous micro line segment trajectories based on look-ahead algorithm in high-speed machining. Int J Adv Manuf Technol 37:881–897
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
Zhang Y, Ye P, Wu J, Zhang H (2017) An optimal curvature-smooth transition algorithm with axis jerk limitations along linear segments. Int J Adv Manuf Technol 95(1–4):875–888
Jia Z, Song D, Ma J, Hu G, Su W (2017) A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints. Int J Mach Tools Manuf 116:1–17
Zhao M, Chen G, Erkorkmaz K, Gao X-S (2016) Linear programming based feedrate optimization for contour machining of long spline toolpaths. Proc 31th ASPE Annual Mtg, San Diego
Zhang Q, Li S, Guo J, Gao X-S (2016) Time-optimal path tracking for robots under dynamics constraints based on convex optimization. Robotica 34(9):2116–2139
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
Chanda L, Cripps RJ (2018) Characterising the effects of shape on tool path motion. Int J Mach Tools Manuf 132:17–35
Lai J, Lin K, Tseng S, Ueng W (2008) On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk. Int J Adv Manuf Technol 37:104–121
Barre P, Bearee R, Borne P, Dumetz E (2005) Influence of a jerk controlled movement law on the vibratory behaviour of high-dynamics systems. J Intell Robot Syst Theory Appl 42:275–293
Heng M, Erkorkmaz K (2010) Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability. Int J Mach Tools Manuf 50:281–293
Zhao H, Zhu L, Ding H (2013) A parametric interpolator with minimal feed fluctuation for CNC machine tools using arc-length compensation and feedback correction. Int J Mach Tools Manuf 75:1–8
Yeh S, Hsu P (2002) Adaptive-feedrate interpolation for parametric curves with a confined chord error. CAD Comput Aided Des 34:229–237
Tsai M, Cheng C (2003) A real-time predictor-corrector interpolator for CNC machining. J Manuf Sci E-T ASME 125:449–460
Erkorkmaz K, Altintas Y (2005) Quintic spline interpolation with minimal feed fluctuation. J Manuf Sci E-T ASME 127:339–349
Wang Z, Hu C (2018) Dynamical model based contouring error position-loop feedforward control for multi-axis motion systems. IEEE T IND
Shi R, Lou Y (2017) A novel contouring error estimation for three-dimensional contouring control. IEEE Robot Autom Lett 2(1):128–134
Cheng M, Lee C (2007) Motion controller design for contour-following tasks based on real-time contour error estimation. IEEE T IND ELECTRON 54(3):1686–1695
Acknowledgements
The authors are grateful to Guangdong ELESY Electric Co. Ltd. for the technical assistance in Section 4.
Funding
This work was partially supported by the National Key Technology Support Program of China (No. 2015BAI0B16) and National Science and Technology Major Project of China (20181820249).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ye, P., Zhang, Y., Xiao, J. et al. A novel feedrate planning and interpolating method for parametric toolpath in Frenet-Serret frame. Int J Adv Manuf Technol 101, 1915–1925 (2019). https://doi.org/10.1007/s00170-018-3081-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-018-3081-8