This paper presents a predictor-corrector interpolator (PCI) for the CNC machining of parts with parametric curves or surfaces. In contrast to existing parametric interpolators, the proposed method uses a simple algorithm as a predictor and the current feedrate command feedback compensation scheme as the corrector. The predictor adjusts itself according to the current feedrate command feedback, it also has the capability of predicting the next reference point of the parametric curves from the current reference point. As a result, the deviations between the current and desired feedrate commands will always fall within the specified feedrate command tolerances. This study aims at developing the mathematical analysis of the PCI, where the convergence condition is derived for the corrector. In this present approach, the user can specify either constant or variable federate and also its feedrate command accuracy. Both the simulation and experiment results are presented to demonstrate the feasibility of the proposed PCI for machining the parametric curves represented in the Non-Uniform Rational B-Spline (NURBS) form.

Issue Section:
Technical Papers
Keywords:
machining, computerised numerical control, real-time systems, feedback, parameter estimation, splines (mathematics), interpolation
Topics:
Algorithms, Computer numerical control machine tools, Feedback, Machining, Servomechanisms, Simulation, Errors
1.
Koren
,
Y.
,
Lo
,
C. C.
, and
Shpitalni
,
M.
,
1993
, “
CNC Interpolators: Algorithms and Analysis
,”
ASME Manuf. Sci. and Eng.
,
PED-64
, pp.
83
–
92
.
2.
Shpitalni
,
M.
,
Koren
,
Y.
, and
Lo
,
C. C.
,
1994
, “
Realtime Curve Interpolators
,”
Comput.-Aided Des.
,
26
, pp.
832
–
838
.
3.
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
.
4.
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.
5.
Huang, J. T., and Yang, D. C. H., 1992, “Precision Command Generation for Computer Controlled Machines,” ASME Precision Machining: Technology and Machine Development and Improvement, PED-58, pp. 89–104.
6.
Yang
,
D. C. H.
, and
Kong
,
T.
,
1994
, “
Parametric Interpolator Versus Linear Interpolator for Precision CNC Machining
,”
Comput.-Aided Des.
,
26
, pp.
225
–
234
.
7.
Zhang
,
Q. G.
, and
Greenway
,
R. B.
,
1998
, “
Development and Implementation of a NURBS Curve Motion Interpolator
,”
Rob. Comput.-Integr. Manufact.
,
14
, pp.
27
–
36
.
8.
Yeh
,
S. S.
, and
Hsu
,
P. L.
,
1999
, “
The Speed-Controlled Interpolator for Machining Parametric Curves
,”
Comput.-Aided Des.
,
31
, pp.
349
–
357
.
9.
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
.
10.
Lo
,
C. C.
,
1997
, “
Feedback Interpolators for CNC Machine Tools
,”
ASME Manuf. Sci. Eng.
,
119
, pp.
587
–
592
.
11.
Nakamura, S., 1993, Applied Numerical Methods in C, Prentice-Hall International, Inc., USA.
12.
Piegl
,
L.
,
1991
, “
On NURBS: A Survey
,”
IEEE Comput. Graphics. Appl.
,
11
, pp.
55
–
71
.
13.
Mortenson, M. E., 1997, Geometric Modeling, John Wiley & Sons, Inc., USA.
14.
Guenter
,
B.
, and
Parent
,
R.
,
1990
, “
Computing the Arc Length of Parametric Curves
,”
IEEE Comput. Graphics Appl.
,
10
, pp.
72
–
78
.
Copyright © 2003
 by ASME
You do not currently have access to this content.