A novel feedrate planning and interpolating method for parametric toolpath in Frenet-Serret frame

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.

[1]  Yu Zhu,et al.  Dynamical Model Based Contouring Error Position-Loop Feedforward Control for Multiaxis Motion Systems , 2019, IEEE Transactions on Industrial Informatics.

[2]  Mi-Ching Tsai,et al.  A real-time predictor-corrector interpolator for CNC machining , 2003 .

[3]  Elizabeth A. Croft,et al.  Feed optimization for five-axis CNC machine tools with drive constraints , 2008 .

[4]  Qiang Liu,et al.  Adaptive feedrate planning on parametric tool path with geometric and kinematic constraints for CNC machining , 2017 .

[5]  Hui Zhang,et al.  An optimal curvature-smooth transition algorithm with axis jerk limitations along linear segments , 2018 .

[6]  Alessandro Bardine,et al.  A real-time configurable NURBS interpolator with bounded acceleration, jerk and chord error , 2012, Comput. Aided Des..

[7]  Pierre-Jean Barre,et al.  Influence of a Jerk Controlled Movement Law on the Vibratory Behaviour of High-Dynamics Systems , 2005, J. Intell. Robotic Syst..

[8]  Li Li,et al.  Research on adaptive non-uniform rational B-spline real-time interpolation technology based on acceleration constraints , 2017 .

[9]  Peiqing Ye,et al.  Interpolation of continuous micro line segment trajectories based on look-ahead algorithm in high-speed machining , 2008 .

[10]  Ming-Yang Cheng,et al.  Motion Controller Design for Contour-Following Tasks Based on Real-Time Contour Error Estimation , 2007, IEEE Transactions on Industrial Electronics.

[11]  Michele Heng,et al.  Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability , 2010 .

[12]  Javad Jahanpour,et al.  A novel acc-jerk-limited NURBS interpolation enhanced with an optimized S-shaped quintic feedrate scheduling scheme , 2014, The International Journal of Advanced Manufacturing Technology.

[13]  Bin Yao,et al.  Time Optimal Contouring Control of Industrial Biaxial Gantry: A Highly Efficient Analytical Solution of Trajectory Planning , 2017, IEEE/ASME Transactions on Mechatronics.

[14]  Han Ding,et al.  A parametric interpolator with minimal feed fluctuation for CNC machine tools using arc-length compensation and feedback correction , 2013 .

[15]  Xavier Beudaert,et al.  Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path , 2012 .

[16]  Ran Shi,et al.  A Novel Contouring Error Estimation for Three-Dimensional Contouring Control , 2017, IEEE Robotics and Automation Letters.

[17]  Ji Zhao,et al.  An iterative feed rate scheduling method with confined high-order constraints in parametric interpolation , 2017 .

[18]  Liu Xinhua,et al.  A novel approach for NURBS interpolation through the integration of acc-jerk-continuous-based control method and look-ahead algorithm , 2017 .

[19]  Yusuf Altintas,et al.  High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation , 2001 .

[20]  Syh-Shiuh Yeh,et al.  Adaptive-feedrate interpolation for parametric curves with a confined chord error , 2002, Comput. Aided Des..

[21]  Robert J. Cripps,et al.  Characterising the effects of shape on tool path motion , 2018 .

[22]  Zhenyuan Jia,et al.  A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints , 2017 .

[23]  Qiang Zhang,et al.  Time-optimal path tracking for robots under dynamics constraints based on convex optimization , 2015, Robotica.

[24]  Jiing-Yih Lai,et al.  On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk , 2008 .

[25]  Y. Altintas,et al.  Quintic Spline Interpolation With Minimal Feed Fluctuation , 2005 .