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TECHNICAL PAPERS

A Real-Time Predictor-Corrector Interpolator for CNC Machining

[+] Author and Article Information
Mi-Ching Tsai, Chung-Wei Cheng

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, TAIWAN Republic of China

J. Manuf. Sci. Eng 125(3), 449-460 (Jul 23, 2003) (12 pages) doi:10.1115/1.1578670 History: Received November 01, 2001; Online July 23, 2003
Copyright © 2003 by ASME
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References

Koren,  Y., Lo,  C. C., and Shpitalni,  M., 1993, “CNC Interpolators: Algorithms and Analysis,” ASME Manuf. Sci. and Eng., PED-64, pp. 83–92.
Shpitalni,  M., Koren,  Y., and Lo,  C. C., 1994, “Realtime Curve Interpolators,” Comput.-Aided Des., 26, pp. 832–838.
Wang,  F. C., and Wright,  P. K., 1998, “Open Architecture Controllers for Machine Tools, Part 2: A Real Time Quintic Spline Interpolator,” ASME J. Manuf. Sci. Eng., 120, pp. 425–432.
Kuo, J. C., Tsai, M. C., and Cheng, M. Y., 2000, “Real-Time NURBS Interpolator for Precision Command Generation,” The Sixth International Conference on Automation Technology, Taiwan, Vol. 1, pp. 503–508.
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Yang,  D. C. H., and T.,  Kong, 1994, “Parametric Interpolator Versus Linear Interpolator for Precision CNC Machining,” Comput.-Aided Des., 26, pp. 225–234.
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Yeh,  S. S., and Hsu,  P. L., 1999, “The Speed-Controlled Interpolator for Machining Parametric Curves,” Comput.-Aided Des., 31, pp. 349–357.
Farouki,  R. T., and Tsai,  Y. F., 2001, “Exact Taylor Series Coefficients for Variable-Feedrate CNC Curve Interpolators,” Comput.-Aided Des., 33, pp. 155–165.
Lo,  C. C., 1997, “Feedback Interpolators for CNC Machine Tools,” ASME Manuf. Sci. Eng., 119, pp. 587–592.
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Figures

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Machining method for parametric curves or surface segments
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The flowchart of proposed PCI
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A parametric curve represented in NURBS form
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Sufficient condition for the proposed PCI
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Iteration numbers of the corrector for the case of ε=0.1%
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The feedrate command errors caused by (a) first-order Taylor’s expansion (b) second-order Taylor’s expansion (c) PCI at ε=1.0% (d) PCI at ε=0.5% (e) PCI at ε=0.1%
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Trapezoidal velocity profile for variable feedrate control  
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The feedrate command generated by (a) first-order Taylor’s expansion (b) second-order Taylor’s expansion (c) PCI at ε=1.0% (d) PCI at ε=0.5% (e) PCI at ε=0.1%
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The block diagram of an experimental system
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Block diagram of the servo controller
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Feedrate and feedrate error along the curve path by different Taylor’s expansion interpolators (feedrate command=200 mm/s)
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Position tracking for the case of ε=0.1% using PCI (feedrate command=200 mm/s)
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Velocity tracking for the case of ε=0.1% using PCI (feedrate command=200 mm/s)

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