Development of Real-Time Look-Ahead Methodology Based on Quintic PH Curve with G2 Continuity for High-Speed Machining

Jing Shi; Qing Zhen Bi; Yu Han Wang; Gang Liu

doi:10.4028/www.scientific.net/AMM.464.258

Paper Titles

The Scalability Studies of CAN Bus Based on SONEC
p.235

Stochastic Error Modeling of MEMS Inertial Sensor with Implementation to GPS-Aided INU System for UAV Motion Sensing
p.240

A Research and Development of Composite Boring and Milling CNC System Based on PMAC
p.247

Application of PID in Controllable Pitch Propeller of a Multipurpose Ocean Tug
p.253

Development of Real-Time Look-Ahead Methodology Based on Quintic PH Curve with G² Continuity for High-Speed Machining
p.258

Research of Self-Adjust Compromise Control Strategy about Comfort and Stability of Quarter Vehicle
p.265

The Analysis and Research of Hedge Trimmer Robotics about Manipulator Kinematics
p.273

Nonlinear Control of an Inverted Pendulum on a Cart by a Single Control Law
p.279

Smooth Trajectory Planning for 3-UPU Parallel Manipulator
p.285

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 464Development of Real-Time Look-Ahead Methodology...

Development of Real-Time Look-Ahead Methodology Based on Quintic PH Curve with G² Continuity for High-Speed Machining

Abstract:

Curving tool paths composed of straight lines, which are often represented as G01 blocks, are still the most widespread format form in the machining process chain of CAD/CAM/CNC. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. In this paper, a real-time look-ahead interpolation methodology is proposed, which adopts a curvature-continuous PH curve as a transition to blend corner at the junction of adjacent lines in the tool path. The blending algorithm can guarantee the approximation error exactly, and the control points of the curve can be calculated analytically. On the other hand, the arc length and the curvature of the transition curve, which are important items in speed planning, also have analytical expressions. All the advantages are the guarantee of calculation efficiency during the interpolation. Except for a curvature-continuous tool path, our look-ahead algorithm adopts a speed planning window strategy to achieve a balance between the calculation capabilities and the real-time interpolation requirements. In this window, the corner transition algorithm and speed planning are implemented simultaneously and dynamically during the interpolation. By defining the width of this window, which is actually the number of linear segments contained in this window, can adjust the time consuming of speed planning. Simulation and experiments on our own developed CNC platform are conducted. The results demonstrate the feasibility and efficiency of the proposed algorithms.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 464)

Pages:

258-264

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.464.258

Citation:

Cite this paper

Online since:

November 2013

Authors:

Jing Shi, Qing Zhen Bi, Yu Han Wang*, Gang Liu

Keywords:

G² Continuity, Interpolation, Path-Smoothing, pH Curve, Speed Planning, Transition Scheme

Export:

RIS, BibTeX

Price:

Permissions:

Request Permissions

* - Corresponding Author

References

[1] Tsai, M. -S., H. -W. Nien, et al. (2009). Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining., The International Journal of Advanced Manufacturing Technology 47(5-8): 621-638.

DOI: 10.1007/s00170-009-2220-7

Google Scholar

[2] Ernesto, C. and R. Farouki (2012). High-speed cornering by CNC machines under prescribed bounds on axis accelerations and toolpath contour error., The International Journal of Advanced Manufacturing Technology 58(1): 327-338.

DOI: 10.1007/s00170-011-3394-3

Google Scholar

[3] Erkorkmaz, K., C. -H. Yeung, et al. (2006). Virtual CNC system. Part II. High speed contouring application., International Journal of Machine Tools and Manufacture 46(10): 1124-1138.

DOI: 10.1016/j.ijmachtools.2005.08.001

Google Scholar

[4] Bi Qingzhen, Yuhan Wang, Limin Zhu, et al. (2011).

Google Scholar

[5] Zhang, L. B., Y. P. You, et al. (2010). The transition algorithm based on parametric spline curve for high-speed machining of continuous short line segments., The International Journal of Advanced Manufacturing Technology 52(1-4): 245-254.

DOI: 10.1007/s00170-010-2718-z

Google Scholar

[6] Jahanpour, J. (2012). High speed contouring enhanced with C2 PH quintic spline curves., Scientia Iranica 19(2): 311-319.

DOI: 10.1016/j.scient.2012.02.017

Google Scholar

[7] Farouki, R. T. (2008). Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Springer Berlin Heidelberg. 1: 381-391.

DOI: 10.1007/978-3-540-73398-0_17

Google Scholar

[8] Farouki, R. T. and S. Shah (1996). Real-time CNC interpolators for Pythagorean-hodograph curves., Computer Aided Geometric Design 13(7): 583-600.

DOI: 10.1016/0167-8396(95)00047-x

Google Scholar

[9] Walton, D. J. and D. S. Meek (2009). G2 blends of linear segments with cubics and Pythagorean-hodograph quintics., International Journal of Computer Mathematics 86(9): 1498-1511.

DOI: 10.1080/00207160701828157

Google Scholar

[10] D. Walton and D. Meek, Curvature extrema of planar parametric polynomial cubic curves, Journal of computational and applied mathematics, vol. 134, no. 1-2, pp.69-83, (2001).

DOI: 10.1016/s0377-0427(00)00529-x

Google Scholar

[11] G. Farin, Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code, Academic Press, Inc. Orlando, FL, USA, (1996).

Google Scholar

[12] Leng, H., Y. Wu, Pan, X. (2006). Research on flexible acceleration and deceleration method of NC system. Technology and Innovation Conference, 2006. ITIC 2006. International.

DOI: 10.1049/cp:20061088

Google Scholar