This paper presents an analytical model of the tool path for staircase traversal of convex polygonal surfaces, and an algorithm—referred to as OPTPATH—developed based on the model to find the sweep angle that gives a near optimal tool path length. The OPTPATH algorithm can be used for staircase traversal with or without (i) overlaps between successive sweep passes, and (ii) rapid traversal along edge passes. This flexibility of OPTPATH renders it applicable not only to conventional operations such as face and pocket milling, but also to other processes such as robotic deburring, rapid prototyping, and robotic spray painting. The effective tool path lengths provided by OPTPATH are compared with those given by the following two algorithms: (i) a common industrial heuristic—referred to as the IH algorithm—and (ii) an algorithm proposed by Prabhu et al. (Prabhu, P. V., Gramopadhye, A. K., and Wang, H. P., 1990, Int. J. Prod. Res., 28, No. 1, pp. 101–130) referred to as PGW algorithm. This comparison is conducted using 100 randomly generated convex polygons of different shapes and a set of seven different tool diameters. It is found that OPTPATH performs better than both the IH as well as PGW algorithms. The superiority of OPTPATH over the two algorithms becomes more pronounced for large tool diameters. [S1087-1357(00)71501-2]

Issue Section:
Technical Papers
Keywords:
machining, numerical control, CAD/CAM, tools, robot kinematics, manufacturing processes
Topics:
Algorithms, Milling, Theorems (Mathematics), Robotics
1.
Prabhu
,
P. V.
,
Gramopadhye
,
A. K.
, and
Wang
,
H. P.
,
1990
, “
A General Mathematical Model for Optimizing NC Tool Path for Face Milling of Convex Polygonal Surfaces
,”
Int. J. Prod. Res.
,
28
, No.
1
, pp.
101
–
130
.
2.
DeGarmo, E. Paul, Temple Black, J., and Kohser, Ronals A., 1988, Materials and Processes in Manufacturing, New York: Macmillan Publishing Company.
3.
Pekelharing
,
A. J.
,
1978
, “
The Exit Failure in Interrupted Cutting
,”
Ann. CIRP
,
27
, No.
1
, pp.
5
–
10
.
4.
Wang
,
W. P.
,
1988
, “
Solid Modeling for Optimization Metal Removal of Three-Dimensional NC End Milling
,”
J. Manuf. Syst.
,
7
, No.
1
, pp.
57
–
65
.
5.
Bala
,
M.
, and
Chang
,
T. C.
,
1991
, “
Automatic Cutter Selection and Optimal Cutter Path Generation for Prismatic Parts
,”
Int. J. Prod. Res.
,
29
, No.
11
, pp.
2163
–
2176
.
6.
McFalls, R. D., and Munson, V. R., 1966, “How to Figure Milling Times,” American Machinist, Special Report No. 581, p. 69.
7.
Yellowly
,
I.
,
Wong
,
A.
, and
DeSmit
,
B.
,
1978
, “
The Economics of Peripheral Milling
,”
Manuf. Eng. Trans.
,
9
, pp.
388
–
394
.
8.
Chang
,
T. C.
,
Wysk
,
R. A.
,
Davis
,
R. P.
, and
Choi
,
B.
,
1982
, “
Milling Parameter Optimization Through a Discrete Variable Transformation
,”
Int. J. Prod. Res.
,
20
, No.
4
, pp.
506
–
522
.
9.
Lakkaraju
,
R.
,
Raman
,
S.
, and
Irani
,
S. A.
,
1992
, “
An Analytical Model for Optimization of NC Tool Cutting Path
,”
Int. J. Prod. Res.
,
30
, No.
1
, pp.
109
–
127
.
10.
Raman
,
S.
, and
Lakkaraju
,
R.
,
1992
, “
The Incorporation of Tool Life Variables in NC Path Planning
,”
Int. J. Prod. Res.
,
30
, No.
11
, pp.
2545
–
2558
.
11.
Raman
,
S.
, and
Lakkaraju
,
R.
,
1993
, “
The Effect of Tool Life and Other Process Variables in NC Path Planning
,”
Computers and Industrial Engineering
,
24
, No.
2
, pp.
315
–
328
.
12.
Groover, M. P., 1996, Fundamentals of Modern Manufacturing: Materials, Processes, and Systems, Upper Saddle River, NJ, Prentice Hall.
13.
Doyle, L. E., Keyser, C. A., Leach, J. L., Schrader, G. F., and Singer, M. B., 1985, Manufacturing Processes and Materials for Engineers, Englewood Cliffs, NJ, Prentice-Hall.
14.
Metal Cutting Institute, 1979, “Milling Cutters and End Mills—Applications and Sharpening,” Milling Cutter Division, Metal Cutting Tool Institute, New York.
15.
Chandawarkar, A., and Wysk, R. A., 1986, “A Linear Programming Approach to Numerically Controlled Face Milling,” Proceedings of the NBS Symposium on Optimization of Manufacturing, Gaithersberg, MD.
16.
Wang
,
H.-P.
,
Chang
,
T. C.
,
Wysk
,
R. A.
, and
Chandawarkar
,
A.
,
1987
, “
On The Efficiency of NC Tool Path Planning For Face Milling Operations
,”
ASME J. Eng. Ind.
,
109
, No.
4
, pp.
370
–
376
.
17.
Rose, M. E., 1988, Generation of Efficient Numerical Control Tool Paths Using an Interactive Computer-Aided Design System, unpublished Master’s Thesis, Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, University Park.
18.
Ananad
,
S.
,
Raman
,
S.
, and
Wysk
,
R. A.
,
1988
, “
Vision Assisted NC Milling Path Generation
,”
J. Manuf. Syst.
,
7
, No.
3
, pp.
233
–
240
.
19.
Somasundaram
,
S.
, and
Raman
,
S.
,
1992
, “
NC Path Planning for Face Milling of Convex Polygonal Surfaces: Further Analysis
,”
J. Design Manuf.
,
2
, No.
1
, pp.
19
–
28
.
20.
Deshmukh
,
A.
, and
Wang
,
H.-P.
,
1993
, “
Tool Path Planning for NC Milling of Convex Polygonal Faces: Minimization of Non-Cutting Area
,”
Int. J. Advanced Manuf. Technol.
,
8
, pp.
17
–
24
.
21.
Kamarthi
,
S. V.
,
Pittner
,
S.
,
Bukkapatnam
,
T. S.
,
1997
, “
Foundations for Analytical Models of Staircase Traversal of Convex Polygonal Surfaces
,”
Int. J. Prod. Res.
,
35
, No.
7
, pp.
2009
–
2024
.
22.
Gillespie, L. K., 1987, Robotic Deburring Handbook, Dearborn, MI, SME Press.
Copyright © 2000
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