Abstract

Toolpath represented by linear segments leads to tangency discontinuity between blocks, which results in fluctuation of feedrate and reduction of machining efficiency and quality. To eliminate these unwanted external factors, optimal corner smoothing operation is essential for computerized numerical control systems to achieve a smooth toolpath. This work proposes a corner smoothing approach by generating a B-spline transition curve with seven control points. By adjusting the position of the control points, the resulting transition curve is not limited to smooth the corner in the convex side of the corner, but shuttles back and forth between the convex and concave sides to decrease the maximum curvature, while respecting the given error tolerance. The approximation errors in convex and concave sides can be analytically calculated. Experimental results demonstrate the effectiveness of the proposed method on machining efficiency improvement.

References

1.
Tulsyan
,
S.
, and
Altintas
,
Y.
,
2015
, “
Local Toolpath Smoothing for Five-Axis Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
96
, pp.
15
26
.
2.
Zhang
,
D.
,
Wang
,
Z.
, and
Tomizuka
,
M.
,
2020
, “
A Variable-Parameter-Model-Based Feedforward Compensation Method for Tracking Control
,”
IEEE/CAA J. Autom. Sin.
,
7
(
3
), pp.
693
701
.
3.
Huang
,
N.
,
Lynn
,
R.
, and
Kurfess
,
T.
,
2017
, “
Aggressive Spiral Toolpaths for Pocket Machining Based on Medial Axis Transformation
,”
ASME J. Manuf. Sci. Eng.
,
139
(
5
), p.
051011
.
4.
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
.
5.
Lee
,
A.-C.
,
Lin
,
M.-T.
,
Pan
,
Y.-R.
, and
Lin
,
W.-Y.
,
2011
, “
The Feedrate Scheduling of NURBS Interpolator for CNC Machine Tools
,”
Comput. Aided Des.
,
43
(
6
), pp.
612
628
.
6.
Zhang
,
K.
,
Yuan
,
C. M.
,
Gao
,
X. S.
, and
Li
,
H.
,
2012
, “
A Greedy Algorithm for Feedrate Planning of CNC Machines Along Curved Tool Paths With Confined Jerk
,”
Robot. Comput. Integr. Manuf.
,
28
(
4
), pp.
472
483
.
7.
Erkorkmaz
,
K.
,
Chen
,
Q.-G. C.
,
Zhao
,
M.-Y.
,
Beudaert
,
X.
, and
Gao
,
X.-S.
,
2017
, “
Linear Programming and Windowing Based Feedrate Optimization for Spline Toolpaths
,”
CIRP Ann.
,
66
(
1
), pp.
393
396
.
8.
Tajima
,
S.
, and
Sencer
,
B.
,
2016
, “
Kinematic Corner Smoothing for High Speed Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
108
, pp.
27
43
.
9.
Yang
,
Z.
,
Shen
,
L. Y.
,
Yuan
,
C. M.
, and
Gao
,
X. S.
,
2015
, “
Curve Fitting and Optimal Interpolation for CNC Machining Under Confined Error Using Quadratic B-Splines
,”
Comput. Aided Des.
,
66
, pp.
62
72
.
10.
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
.
11.
Sencer
,
B.
,
Ishizaki
,
K.
, and
Shamoto
,
E.
,
2015
, “
High Speed Cornering Strategy With Confined Contour Error and Vibration Suppression for CNC Machine Tools
,”
CIRP Ann.
,
64
(
1
), pp.
369
372
.
12.
Lin
,
M. T.
,
Lee
,
J. C.
,
Shen
,
C. C.
,
Lee
,
C. Y.
, and
Wang
,
J. T.
,
2018
, “
Local Corner Smoothing With Kinematic and Real-Time Constraints for Five-Axis Linear Tool Path
,”
2018 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)
,
Auckland, New Zealand
,
July 9–12
, IEEE, pp.
816
821
.
13.
Zhao
,
X.
,
Zhao
,
H.
,
Wan
,
S.
,
Li
,
X.
, and
Ding
,
H.
,
2019
, “
An Analytical Decoupled Corner Smoothing Method for Five-Axis Linear Tool Paths
,”
IEEE Access
,
7
, pp.
22763
22772
.
14.
Yan
,
Y. C.
,
Zhang
,
L. Q.
, and
Zhang
,
K.
,
2016
, “
Corner Smoothing Transition Algorithm for Five-Axis Linear Tool Path
,”
Procedia CIRP
,
56
, pp.
604
609
.
15.
Farouki
,
R. T.
,
2014
, “
Construction of G2 Rounded Corners With Pythagorean-Hodograph Curves
,”
Comput. Aided Geom. Des.
,
31
(
2
), pp.
127
139
.
16.
Bi
,
Q. Z.
,
Shi
,
J.
,
Wang
,
Y. H.
,
Zhu
,
L.
, and
Ding
,
H.
,
2015
, “
Analytical Curvature-Continuous Dual-Bézier Corner Transition for Five-Axis Linear Tool Path
,”
Int. J. Mach. Tools Manuf.
,
91
, pp.
96
108
.
17.
Fan
,
W.
,
Lee
,
C. H.
, and
Chen
,
J. H.
,
2015
, “
A Realtime Curvature-Smooth Interpolation Scheme and Motion Planning for CNC Machining of Short Line Segments
,”
Int. J. Mach. Tools Manuf.
,
96
, pp.
27
46
.
18.
Jia
,
Z.
,
Song
,
D.
,
Ma
,
J.
,
Hu
,
G.
, and
Su
,
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
.
19.
Wang
,
W.
,
Hu
,
C.
,
Zhou
,
K.
, and
He
,
S.
,
2019
, “
Corner Trajectory Smoothing With Asymmetrical Transition Profile for CNC Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
144
, p.
103423
.
20.
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
.
21.
Zhang
,
Y.
,
Wang
,
T.
,
Peng
,
P.
,
Dong
,
J.
,
Cao
,
L.
, and
Tian
,
C.
,
2021
, “
Feedrate Blending Method for Five-Axis Linear Tool Path Under Geometric and Kinematic Constraints
,”
Int. J. Mech. Sci.
,
195
, p.
106262
.
22.
Zhao
,
H.
,
Zhu
,
L. M.
, and
Ding
,
H.
,
2013
, “
A Real-Time Look-Ahead Interpolation Methodology With Curvature-Continuous B-Spline Transition Scheme for CNC Machining of Short Line Segments
,”
Int. J. Mach. Tools Manuf.
,
65
, pp.
88
98
.
23.
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
.
24.
Huang
,
J.
,
Du
,
X.
, and
Zhu
,
L. M.
,
2018
, “
Real-Time Local Smoothing for Five-Axis Linear Toolpath Considering Smoothing Error Constraints
,”
Int. J. Mach. Tools Manuf.
,
124
, pp.
67
79
.
25.
Yang
,
J.
, and
Yuen
,
A.
,
2017
, “
An Analytical Local Corner Smoothing Algorithm for Five-Axis CNC Machining
,”
Int. J. Mach. Tools Manuf.
,
123
, pp.
22
35
.
26.
Bi
,
Q. Z.
,
Huang
,
J.
,
Lu
,
Y. A.
,
Zhu
,
L. M.
, and
Ding
,
H.
,
2019
, “
A General, Fast and Robust B-Spline Fitting Scheme for Micro-Line Tool Path Under Chord Error Constraint
,”
Sci. China Technol. Sci.
,
62
(
2
), pp.
321
332
.
27.
Duan
,
M.
, and
Okwudire
,
C.
,
2016
, “
Minimum-Time Cornering for CNC Machines Using an Optimal Control Method With NURBS Parameterization
,”
Int. J. Adv. Manuf. Technol.
,
85
(
5–8
), pp.
1405
1418
.
28.
Mercy
,
T.
,
Jacquod
,
N.
,
Herzog
,
R.
, and
Pipeleers
,
G.
,
2018
, “
Spline-Based Trajectory Generation for CNC Machines
,”
IEEE Trans. Ind. Electron.
,
66
(
8
), pp.
6098
6107
.
29.
Piegl
,
L.
, and
Tiller
,
W.
,
2012
,
The NURBS Book
,
Springer Science & Business Media
.
30.
Yang
,
M.
,
Yang
,
J.
, and
Ding
,
H.
,
2018
, “
A Two-Stage Friction Model and Its Application in Tracking Error Pre-Compensation of CNC Machine Tools
,”
Precis. Eng.
,
51
, pp.
426
436
.
You do not currently have access to this content.