Three-axis CNC milling is often used to machine sculptured parts. Due to the complex surface shape of these parts, well-planned tool paths can significantly increase the machining efficiency. In this work a new principle of CNC tool path planning for 3-axis sculptured surface machining is proposed. Generic formula to calculate the steepest tangent direction of a sculptured surface is derived, and the algorithm of the steepest-ascending tool path generation is introduced. A single steepest-ascending tool path has been verified to be more efficient than a single tool path of any other type. The relationship between machining efficiency and three key variables, tool feed direction, cutter shape, and surface shape, is revealed. The newly introduced principle is used in planning tool paths of a sculptured surface to demonstrate the advantages of the steepest-ascending tool paths. This new tool path scheme is further integrated into the more advanced steepest-directed and iso-cusped (SDIC) tool path generation technique. Applications of the new tool path principle and the SDIC tool paths to the machining of sculptured parts are demonstrated.

1.
Choi, B. K., and Jerard, R. B., 1998, Sculptured Surface Machining: Theory and Application, Kluwer Academic Publishers.
2.
Broomhead
,
P.
, and
Edkins
,
M.
,
1986
, “
Generation NC Data at the Machine Tool for the Manufacture of Free-Form Surfaces
,”
Int. J. Prod. Res.
,
24
(
1
), pp.
1
14
.
3.
Choi
,
B. K.
,
Lee
,
C.
,
Huang
,
J.
, and
Jun
,
C.
,
1988
, “
Compound Surface Modeling and Machining
,”
Comput.-Aided Des.
,
20
(
3
), pp.
127
136
.
4.
Huang
,
Y.
, and
Oliver
,
J. H.
,
1994
, “
Non-Constant Parameter NC Tool Path Generation on Sculptured Surfaces
,”
The International Journal of Advanced Manufacturing Technology
,
9
, pp.
281
290
.
5.
Yang
,
D. C. H.
, and
Han
,
Z.
,
1999
, “
Interference Detection and Optimal Tool Selection in 3-Axis NC Machining of Free-Form Surfaces
,”
Comput.-Aided Des.
,
31
, pp.
303
315
.
6.
Lin
,
R.
, and
Koren
,
Y.
,
1996
, “
Efficient Tool-Path Planning for Machining Free-Form Surfaces
,”
ASME J. Ind.
,
118
, pp.
20
28
.
7.
Sarma
,
R.
, and
Dutta
,
D.
,
1997
, “
The Geometry and Generation of NC Tool Paths
,”
ASME J. Mech. Des.
,
119
, pp.
253
258
.
8.
Suresh
,
K.
, and
Yang
,
D. C. H.
,
1994
, “
Constant Scallop Height Machining of Free-Form Surfaces
,”
ASME J. Ind.
,
116
, pp.
253
259
.
9.
Maeng
,
H.
,
Ly
,
M.
, and
Vickers
,
G. W.
,
1996
, “
Feature-Based Machining of Curved Surfaces Using the Steepest Directed Tree Approach
,”
Journal of Manufacturing Systems
,
15
(
6
), pp.
1
13
.
10.
Chen
,
Z.
,
Dong
,
Z.
, and
Vickers
,
G. W.
, 2003, “Most Efficient Tool Feed Direction in Three-Axis CNC Machining,” Journal of Integrated Manufacturing Systems,14(7).
11.
Chen, Z., Dong, Z., and Vickers, G. W., 2001, “Steepest-Directed Tool Path in 3-Axis CNC Machining—The Most Efficient Machining Scheme and its Mathematical Proof,” Proceedings of the ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2001/CIE-21301.
12.
Chen
,
Z.
,
Vickers
,
G. W.
, and
Dong
,
Z.
, 2003, “Integrated Steepest-Directed and Iso-Cusped Tool Path Generation for 3-Axis CNC Machining of Sculptured Parts,” Journal of Manufacturing Systems,22(3).
13.
Faux, I. D., and Pratt, M. J., 1979, Computational Geometry for Design and Manufacture, Ellis Horwood Limited, West Sussex, England.
14.
Riddle, D. F., 1970, Calculus and Analytic Geometry, Wadsworth Publishing Company, Inc., Belmont, California.
15.
Marsden, J., and Weinstein A., 1985, Calculus III, Springer-Verlag New York Inc., New York.
You do not currently have access to this content.