Cutter runout is a common and inevitable phenomenon impacting the geometry accuracy in the milling process. However, most of the works on tool path planning neglect the cutter runout effect. In this paper, a new approach is presented to integrate the cutter runout effect into envelope surface modeling and tool path optimization for five-axis flank milling with a conical cutter. Based on the geometry model of cutter runout which consists of cutter axis and cutter tilt, an analytic expression of cutter edge combined with four runout parameters is derived. Then the envelope surface formed by each cutter edge is constructed using the envelope theory of sphere congruence. Due to the cutter runout effect, the envelope surfaces formed by the cutter edges are different from each other, and the valid envelope surface is the combination of these envelope surfaces which contribute to the final machined surface. To measure the machining errors, the geometry deviations between the valid envelope surface and the design surface are calculated with the distance function. On the basis of the differential property of the distance function, tool path optimization considering cutter runout is modeled as a mixed-integer linear programming (MILP) problem, which can be solved by the branch-and-bound method. Finally, numerical examples are given to confirm the validity and efficiency of the proposed approach. The results show that the geometry errors induced by runout can be reduced significantly using the proposed method.

References

References
1.
Ferry
,
W.
, and
Altintas
,
Y.
,
2008
, “
Virtual Five-Axis Flank Milling of Jet Engine Impellers-Part I: Mechanics of Five-Axis Flank Milling
,”
ASME J. Manuf. Sci. Eng.
,
130
(
1
), p.
011005
.10.1115/1.2815761
2.
Wu
,
C. Y.
,
2012
, “
Arbitrary Surface Flank Milling and Flank SAM in the Design and Manufacturing of Jet Engine Fan and Compressor Airfoils
,”
ASME
Turbo Expo 2012: Turbine Technical Conference and Exposition, Copenhagen, Denmark, June 11–15, Vol.
5
, pp.
21
30
.10.1115/GT2012-68051
3.
Harik
,
R. F.
,
Gong
,
H.
, and
Bernard
,
A.
,
2013
, “
5-Axis Flank Milling: A State-of-the-Art Review
,”
Comput.-Aided Des.
,
45
(
3
), pp.
796
808
.10.1016/j.cad.2012.08.004
4.
Chiou
,
J. C.
, and
Lee
,
Y. S.
,
2005
, “
Optimal Tool Orientation for Five-Axis Tool-End Machining by Swept Envelope Approach
,”
ASME J. Manuf. Sci. Eng.
,
127
(
4
), pp.
810
818
.10.1115/1.2035698
5.
Chiou
,
J. C.
, and
Lee
,
Y. S.
,
2002
, “
Swept Surface Determination for Five-Axis Numerical Control Machining
,”
Int. J. Mach. Tools Manuf.
,
42
(
14
), pp.
1497
1507
.10.1016/S0890-6955(02)00110-4
6.
Weinert
,
K.
,
Du
,
S. J.
,
Damm
,
P.
, and
Stautner
,
M.
,
2004
, “
Swept Volume Generation for the Simulation of Machining Processes
,”
Int. J. Mach. Tools Manuf.
,
44
(
6
), pp.
617
628
.10.1016/j.ijmachtools.2003.12.003
7.
Du
,
S. J.
,
Surmann
,
T.
,
Webber
,
O.
, and
Weinert
,
K.
,
2005
, “
Formulating Swept Profiles for Five-Axis Tool Motions
,”
Int. J. Mach. Tools Manuf.
,
45
(
7
), pp.
849
861
.10.1016/j.ijmachtools.2004.11.006
8.
Gong
,
H.
, and
Wang
,
N.
,
2009
, “
Analytical Calculation of the Envelope Surface for Generic Milling Tools Directly From CL-Data Based on the Moving Frame Method
,”
Comput.-Aided Des.
,
41
(
11
), pp.
848
855
.10.1016/j.cad.2009.05.004
9.
Zhu
,
L. M.
,
Zhang
,
X. M.
,
Zheng
,
G.
, and
Ding
,
H.
,
2009
, “
Analytical Expression of the Swept Surface of a Rotary Cutter Using the Envelope Theory of Sphere Congruence
,”
ASME J. Manuf. Sci. Eng.
,
131
(
4
), p.
041017
.10.1115/1.3168443
10.
Lartigue
,
C.
,
Duc
,
E.
, and
Affouard
,
A.
,
2003
, “
Tool Path Deformation in 5-Axis Flank Milling Using Envelope Surface
,”
Comput.-Aided Des.
,
35
(
4
), pp.
375
382
.10.1016/S0010-4485(02)00058-1
11.
Gong
,
H.
,
Cao
,
L. X.
, and
Liu
,
J.
,
2005
, “
Improved Positioning of Cylindrical Cutter for Flank Milling Ruled Surfaces
,”
Comput.-Aided Des.
,
37
(
12
), pp.
1205
1213
.10.1016/j.cad.2004.11.006
12.
Gong
,
H.
, and
Wang
,
N.
,
2009
, “
Optimize Tool Paths of Flank Milling With Generic Cutters Based on Approximation Using the Tool Envelope Surface
,”
Comput.-Aided Des.
,
41
(
12
), pp.
981
989
.10.1016/j.cad.2009.06.013
13.
Zhu
,
L. M.
,
Zhang
,
X. M.
,
Ding
,
H.
, and
Xiong
,
Y. L.
,
2010
, “
Geometry of Signed Point-to-Surface Distance Function and Its Application to Surface Approximation
,”
ASME J. Comput. Inf. Sci. Eng.
,
10
(
4
), p.
041003
.10.1115/1.3510588
14.
Zhu
,
L. M.
,
Zheng
,
G.
,
Ding
,
H.
, and
Xiong
,
Y. L.
,
2010
, “
Global Optimization of Tool Path for Five-Axis Flank Milling With a Conical Cutter
,”
Comput.-Aided Des.
,
42
(
10
), pp.
903
910
.10.1016/j.cad.2010.06.005
15.
Zhu
,
L. M.
,
Ding
,
H.
, and
Xiong
,
Y. L.
,
2012
, “
Simultaneous Optimization of Tool Path and Shape for Five-Axis Flank Milling
,”
Comput.-Aided Des.
,
44
(
12
), pp.
1229
1234
.10.1016/j.cad.2012.06.003
16.
Sun
,
Y. W.
, and
Guo
,
Q.
,
2012
, “
Analytical Modeling and Simulation of the Envelope Surface in Five-Axis Flank Milling With Cutter Runout
,”
ASME J. Manuf. Sci. Eng.
,
134
(
2
), p.
021010
.10.1115/1.4005802
17.
Kline
,
W. A.
, and
DeVor
,
R.
,
1983
, “
The Effect of Runout on Cutting Geometry and Forces in End Milling
,”
Int. J. Mach. Tool Des. Res.
,
23
(
2
), pp.
123
140
.10.1016/0020-7357(83)90012-4
18.
Zheng
,
L.
, and
Liang
,
S. Y.
,
1997
, “
Identification of Cutter Axis Tilt in End Milling
,”
ASME J. Manuf. Sci. Eng.
,
119
(
2
), pp.
178
185
.10.1115/1.2831093
19.
Wan
,
M.
,
Zhang
,
W. H.
,
Dang
,
J. W.
, and
Yang
,
Y.
,
2009
, “
New Procedures for Calibration of Instantaneous Cutting Force Coefficients and Cutter Runout Parameters in Peripheral Milling
,”
Int. J. Mach. Tools Manuf.
,
49
(
14
), pp.
1144
1151
.10.1016/j.ijmachtools.2009.08.005
20.
Li
,
H. Z.
, and
Li
,
X. P.
,
2005
, “
A Numerical Study of the Effects of Cutter Runout on Milling Process Geometry Based on True Tooth Trajectory
,”
Int. J. Adv. Manuf. Technol.
,
25
(
5–6
), pp.
435
443
.10.1007/s00170-003-1874-9
21.
Zhang
,
W. H.
,
Tan
,
G.
,
Wan
,
M.
,
Gao
,
T.
, and
Bassir
,
D. H.
,
2008
, “
A New Algorithm for the Numerical Simulation of Machined Surface Topography in Multiaxis Ball-End Milling
,”
ASME J. Manuf. Sci. Eng.
,
130
(
1
), p.
011003
.10.1115/1.2815337
22.
Desai
,
K.
,
Agarwal
,
P. K.
, and
Rao
,
P.
,
2009
, “
Process Geometry Modeling With Cutter Runout for Milling of Curved Surfaces
,”
Int. J. Mach. Tools Manuf.
,
49
(
12
), pp.
1015
1028
.10.1016/j.ijmachtools.2009.05.007
23.
Yang
,
Y.
,
Zhang
,
W. H.
, and
Wan
,
M.
,
2011
, “
Effect of Cutter Runout on Process Geometry and Forces in Peripheral Milling of Curved Surfaces With Variable Curvature
,”
Int. J. Mach. Tools Manuf.
,
51
(
5
), pp.
420
427
.10.1016/j.ijmachtools.2011.01.005
24.
Guo
,
Q.
,
Sun
,
Y. W.
, and
Guo
,
D. M.
,
2011
, “
Analytical Modeling of Geometric Errors Induced by Cutter Runout and Tool Path Optimization for Five-Axis Flank Machining
,”
Sci. China Technol. Sci.
,
54
(
12
), pp.
3180
3190
.10.1007/s11431-011-4606-7
25.
Yu
,
L.
,
Wang
,
Y. H.
, and
Jin
,
Y. Q.
,
2013
, “
Envelope Surface Formed by Cutting Edge Under Runout Error in Five-Axis Flank Milling
,”
Int. J. Adv. Manuf. Technol.
,
69
(
1–4
), pp.
543
553
.10.1007/s00170-013-5040-8
26.
Zhu
,
L. M.
,
Zheng
,
G.
, and
Ding
,
H.
,
2009
, “
Formulating the Swept Envelope of Rotary Cutter Undergoing General Spatial Motion for Multi-Axis NC Machining
,”
Int. J. Mach. Tools Manuf.
,
49
(
2
), pp.
199
202
.10.1016/j.ijmachtools.2008.10.004
27.
Liang
,
S. Y.
, and
Wang
,
J.
,
1994
, “
Milling Force Convolution Modeling for Identification of Cutter Axis Offset
,”
Int. J. Mach. Tools Manuf.
,
34
(
8
), pp.
1177
1190
.10.1016/0890-6955(94)90021-3
28.
Arizmendi
,
M.
,
Fernndez
,
J.
,
Gill
,
A.
, and
Veiga
,
F.
,
2010
, “
Identification of Tool Parallel Axis Offset Through the Analysis of the Topography of Surfaces Machined by Peripheral Milling
,”
Int. J. Mach. Tools Manuf.
,
50
(
12
), pp.
1097
1114
.10.1016/j.ijmachtools.2010.07.006
29.
Engin
,
S.
, and
Altintas
,
Y.
,
2001
, “
Mechanics and Dynamics of General Milling Cutters: Part I: Helical End Mills
,”
Int. J. Mach. Tools Manuf.
,
41
(
15
), pp.
2195
2212
.10.1016/S0890-6955(01)00045-1
30.
Schrijver
,
A.
,
1998
,
Theory of Linear and Integer Programming
,
Wiley
,
New York
.
31.
Pauly
,
M.
,
Kobbelt
,
L.
, and
Gross
,
M. H.
,
2002
,
Multiresolution Modeling of Point-Sampled Geometry
, Swiss Federal Institute of Technology, Computer Science Department, Institute of Visual Computing,
Computer Graphics Lab, CGL
, Zurich, Switzerland.
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