In the five-axis machining, the dual nonuniform rational B-spline (NURBS) interpolator performs better than the conventional linear interpolator in improving machining efficiency and quality. However, a successful dual NURBS interpolator faces with two aspects of issues. First, the feedrate should be reasonably scheduled according to axial drive constraints. Furthermore, the axial trajectories should be precisely and rapidly calculated according to the scheduled feedrate. To schedule the feedrate, existing methods use either overall constant speed or frequent time-varying speed. However, the former one is adverse to the motion efficiency, while the latter one is adverse to the motion stability. To deal with these issues, this study schedules feedrate-sensitive and nonsensitive regions and plans constant speed at the sensitive regions and smooth transition speed within the nonsensitive regions, thus balancing the motion stability and the efficiency. In addition, to calculate the axial trajectories, existing methods, using inverse kinematics, result in multiple solutions due to the existence of antitrigonometric functions, and this requires complicated selection of the solutions, otherwise the axial positions will be discontinuity. To deal with this issue, this study proposes a Jacobi matrix-based Adams prediction–correction numerical algorithm, which uses the incremental value of the tool pose to calculate the consecutive unique solution of the five-axis positions directly. By integrating above techniques, a systematic five-axis dual NURBS interpolator with the constant speed at feedrate-sensitive regions under axial drive constraints is presented. Experimental tests are conducted to evaluate the effectiveness of the proposed method.

References

1.
Yang
,
J.
,
Ding
,
H.
,
Zhao
,
H.
, and
Yan
,
S.
,
2016
, “
A Generalized Online Estimation Algorithm of Multi-Axis Contouring Errors for CNC Machine Tools With Rotary Axes
,”
Int. J. Adv. Manuf. Technol.
84
(
5–8
), pp.
1239
1251
.
2.
Jia
,
Z.-y.
,
Ma
,
J.-w.
,
Song
,
D.-n.
,
Wang
,
F.-j.
, and
Liu
,
W.
,
2018
, “
A Review of Contouring-Error Reduction Method in Multi-Axis CNC Machining
,”
Int. J. Mach. Tools Manuf.
,
125
, pp.
34
54
.
3.
Huang
,
T.
,
Zhang
,
X.-M.
,
Leopold
,
J.
, and
Ding
,
H.
,
2018
, “
Tool Orientation Planning in Milling With Process Dynamic Constraints: A Minimax Optimization Approach
,”
ASME J. Manuf. Sci. Eng.
140
(
11
), p.
111002
.
4.
Tulsyan
,
S.
, and
Altintas
,
Y.
,
2015
, “
Local Toolpath Smoothing for Five-Axis Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
96
, pp.
15
26
.
5.
Hu
,
Q.
,
Chen
,
Y.
,
Jin
,
X.
, and
Yang
,
J.
,
2019
, “
A Real-Time C3 Continuous Local Corner Smoothing and Interpolation Algorithm for CNC Machine Tools
,”
ASME J. Manuf. Sci. Eng.
141
(
4
), p.
041004
.
6.
Li
,
Y.
,
Feng
,
J.
,
Wang
,
Y.
, and
Yang
,
J.
,
2009
, “
Variable-Period Feed Interpolation Algorithm for High-Speed Five-Axis Machining
,”
Int. J. Adv. Manuf. Technol.
40
(
7–8
), pp.
769
775
.
7.
Fan
,
W.
,
Gao
,
X.-S.
,
Lee
,
C.-H.
,
Zhang
,
K.
, and
Zhang
,
Q.
,
2013
, “
Time-optimal Interpolation for Five-Axis CNC Machining Along Parametric Tool Path Based on Linear Programming
,”
Int. J. Adv. Manuf. Technol.
69
(
5–8
), pp.
1373
1388
.
8.
Beudaert
,
X.
,
Pechard
,
P.-Y.
, and
Tournier
,
C.
,
2011
, “
5-Axis Tool Path Smoothing Based on Drive Constraints
,”
Int. J. Mach. Tools Manuf.
51
(
12
), pp.
958
965
.
9.
Beudaert
,
X.
,
Lavernhe
,
S.
, and
Tournier
,
C.
,
2012
, “
Feedrate Interpolation With Axis Jerk Constraints on 5-Axis NURBS and G1 Tool Path
,”
Int. J. Mach. Tools Manuf.
,
57
, pp.
73
82
.
10.
Dong
,
J.
, and
Stori
,
J. A.
,
2006
, “
A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization
,”
J. Dyn. Sys. Meas. Control
,
128
(
2
), pp.
379
390
.
11.
Dong
,
J.
,
Ferreira
,
P.
, and
Stori
,
J.
,
2007
, “
Feed-Rate Optimization With Jerk Constraints for Generating Minimum-Time Trajectories
,”
Int. J. Mach. Tools Manuf.
,
47
(
12–13
), pp.
1941
1955
.
12.
Sencer
,
B.
,
Altintas
,
Y.
, and
Croft
,
E.
,
2008
, “
Feed Optimization for Five-Axis CNC Machine Tools With Drive Constraints
,”
Int. J. Mach. Tools Manuf.
48
(
7–8
), pp.
733
745
.
13.
Sun
,
Y.
,
Zhao
,
Y.
,
Bao
,
Y.
, and
Guo
,
D.
,
2014
, “
A Novel Adaptive-Feedrate Interpolation Method for NURBS Tool Path With Drive Constraints
,”
Int. J. Mach. Tools Manuf.
,
77
, pp.
74
81
.
14.
Sun
,
Y.
,
Zhao
,
Y.
,
Xu
,
J.
, and
Guo
,
D.
,
2014
, “
The Feedrate Scheduling of Parametric Interpolator With Geometry, Process and Drive Constraints for Multi-Axis CNC Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
85
, pp.
49
57
.
15.
Huang
,
J.-T.
, and
Yang
,
D. C. H.
,
1992
, “
Precision Command Generation for Computer Controlled Machines
,”
ASME Prod. Eng. Div. Publ. Ped.
,
58
, pp.
89
104
.
16.
Koren
,
Y.
,
Lo
,
C. C.
, and
Shpitalni
,
M.
,
1993
, “
CNC Interpolators: Algorithms and Analysis
,”
ASME Prod. Eng. Div. Publ. Ped.
,
64
, pp.
83
92
.
17.
Tikhon
,
M.
,
Ko
,
T. J.
,
Lee
,
S. H.
, and
Kim
,
H. S.
,
2004
, “
NURBS Interpolator for Constant Material Removal Rate in Open NC Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
44
(
11
), pp.
237
245
.
18.
Tsai
,
M. C.
, and
Cheng
,
C. W.
,
2003
, “
A Real-Time Predictor-Corrector Interpolator for CNC Machining
,”
ASME J. Manuf. Sci. Eng.
,
125
(
3
), pp.
449
460
.
19.
Cheng
,
C. W.
,
Tsai
,
M. C.
, and
Maciejowski
,
J.
,
2006
, “
Feedrate Control for Non-Uniform Rational B-Spline Motion Command Generation
,”
Proc. Inst. Mech. Eng. B: J. Eng. Manuf.
,
220
(
11
), pp.
1855
1861
.
20.
Erkorkmaz
,
K.
,
2015
, “
Efficient Fitting of the Feed Correction Polynomial for Real-Time Spline Interpolation
,”
ASME J. Manuf. Sci. Eng.
137
(
4
), p.
044501
.
21.
Lin
,
M.-T.
, and
Wu
,
S.-K.
,
2013
, “
Modeling and Improvement of Dynamic Contour Errors for Five-Axis Machine Tools Under Synchronous Measuring Paths
,”
Int. J. Mach. Tools Manuf.
,
72
, pp.
58
72
.
22.
Jung
,
Y. H.
,
Lee
,
D. W.
,
Kim
,
J. S.
, and
Mok
,
H. S.
,
2002
, “
NC Post-Processor for 5-Axis Milling Machine of Table-Rotating/Tilting Type
,”
J. Mater. Process. Technol.
130
(
SI
), pp.
641
646
.
23.
Langeron
,
J. M.
,
Duc
,
E.
,
Lartigue
,
C.
, and
Bourdet
,
P.
,
2004
, “
A new Format for 5-Axis Tool Path Computation, Using Bspline Curves
,”
Comput. Aided Des.
36
(
12
), pp.
1219
1229
.
24.
Jia
,
Z.-y.
,
Song
,
D.-n.
,
Ma
,
J.-w.
,
Hu
,
G.-q.
, and
Su
,
W.-w.
,
2017
, “
A NURBS Interpolator With Constant Speed at Feedrate-Sensitive Regions Under Drive and Contour-Error Constraints
,”
Int. J. Mach. Tools Manuf.
,
116
, pp.
1
17
.
25.
Beudaert
,
X.
,
Lavernhe
,
S.
, and
Tournier
,
C.
,
2013
, “
5-Axis Local Corner Rounding of Linear Tool Path Discontinuities
,”
Int. J. Mach. Tools Manuf.
,
73
, pp.
9
16
.
26.
Hu
,
Q.
,
Chen
,
Y.
,
Yang
,
J.
, and
Zhang
,
D.
,
2018
, “
An Analytical C3 Continuous Local Corner Smoothing Algorithm for Four-Axis Computer Numerical Control Machine Tools
,”
ASME J. Manuf. Sci. Eng.
140
(
5
), p.
051004
.
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