This paper presents process optimization for the five-axis flank milling of jet engine impellers based on the mechanics model explained in Part I. The process is optimized by varying the feed automatically as the tool-workpiece engagements, i.e., the process, vary along the tool path. The feed is adjusted by limiting feed-dependent peak outputs to a set of user-defined constraints. The constraints are the tool shank bending stress, tool deflection, maximum chip load (to avoid edge chipping), and the torque limit of the machine. The linear and angular feeds of the tool are optimized by two different methods—a multiconstraint based virtual adaptive control of the process and a nonlinear root-finding algorithm. The five-axis milling process is simulated in a virtual environment, and the resulting process outputs are stored at each position along the tool path. The process is recursively fitted to a first-order process with a time-varying gain and a fixed time constant, and a simple proportional-integral controller is adaptively tuned to operate the machine at threshold levels by manipulating the feed rate. As an alternative to the virtual adaptive process control, the feed rate is optimized by a nonlinear root-finding algorithm. The virtual cutting process is modeled as a black box function of feed and the optimum feed is solved for iteratively, respecting tool stress, tool deflection, torque, and chip load constraints. Both methods are shown to produce almost identical optimized feed rate profiles for the roughing tool path discussed in Paper I. The new feed rate profiles are shown to considerably reduce the cycle time of the impeller while avoiding process faults that may damage the part or the machine.

1.
Budak
,
E.
, 2003, “
An Analytical Design Method for Milling Cutters With Nonconstant Pitch to Increase Stability—Part I: Theory
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
125
, pp.
29
34
.
2.
Budak
,
E.
, 2003, “
An Analytical Design Method for Milling Cutters With Nonconstant Pitch to Increase Stability—Part II: Application
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
125
, pp.
35
38
.
3.
Feng
,
H. Y.
, and
Su
,
N.
, 2000, “
Integrated Tool Path and Feed Rate Optimization for the Finishing Machining of 3D Plane Surfaces
,”
Int. J. Mach. Tools Manuf.
0890-6955,
40
, pp.
1557
1572
.
4.
Tounsi
,
N.
, and
Elbestawi
,
M. A.
, 2001, “
Enhancement of Productivity by Intelligent Programming of Feed Rate in 3-Axis Milling
,”
Mach. Sci. Technol.
1091-0344,
5
(
3
), pp.
393
414
.
5.
Zhu
,
R.
,
Kapoor
,
S. G.
, and
DeVor
,
R. E.
, 2001, “
Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
123
, pp.
369
379
.
6.
Fussell
,
B. K.
,
Hemmett
,
J. G.
, and
Jerard
,
R. B.
, 1999, “
Modeling of Five-Axis End Mill Cutting Using Axially Discretized Tool Moves
,”
C. R. Hebd. Seances Acad. Sci., Ser. A B, Sci. Math. Sci. Phys
0997-4482,
27
, pp.
81
86
.
7.
Fussell
,
B. K.
,
Jerard
,
R. B.
, and
Hemmett
,
J. G.
, 2001, “
Robust Feedrate Selection for 3-Axis NC Machining Using Discrete Models
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
123
, pp.
214
224
.
8.
Jerard
,
R. B.
,
Fussell
,
B. K.
,
Hemmett
,
J. G.
, and
Ercan
,
M. T.
, 2000, “
Toolpath Feedrate Optimization: A Case Study
,”
Proceedings of the 2000 NSF Design and Manufacturing Research Conference
,
Vancouver, Canada
, Jan. 3–6, pp.
1
6
.
9.
Chu
,
C. N.
,
Kim
,
S. Y.
, and
Lee
,
J. M.
, 1997, “
Feed-Rate Optimization of Ball End Milling Considering Local Shape Features
,”
CIRP Ann.
0007-8506,
46
(
1
), pp.
433
436
.
10.
Yazar
,
Z.
,
Koch
,
K.
,
Merrick
,
T.
, and
Altan
,
T.
, 1994, “
Feed Rate Optimization Based on Cutting Force Calculations in 3-Axis Milling of Dies and Molds With Sculptured Surfaces
,”
Int. J. Mach. Tools Manuf.
0890-6955,
34
(
3
), pp.
365
377
.
11.
Erdim
,
H.
,
Lazoglu
,
I.
, and
Ozturk
,
B.
, 2005, “
Feedrate Scheduling Strategies for Free-Form Surfaces
,”
Int. J. Mach. Tools Manuf.
0890-6955,
46
(
7–8
), pp.
747
757
.
12.
Guzel
,
B. U.
, and
Lazoglu
,
I.
, 2003, “
Increasing Productivity in Sculptured Surface Machining Via Off-Line Piecewise Variable Feedrate Scheduling Based on the Force System Model
,”
Int. J. Mach. Tools Manuf.
0890-6955,
44
, pp.
21
28
.
13.
Budak
,
E.
, 2000, “
Improving Productivity and Part Quality in Milling of Titanium Based Impellers by Chatter Suppression and Force Control
,”
CIRP Ann.
0007-8506,
49/1
, pp.
31
36
.
14.
Press
,
W. H.
,
Vetterling
,
W. T.
,
Teukolsky
,
S. A.
, and
Flannery
,
B. P.
, 2002,
Numerical Recipes in C++: The Art of Scientific Computing
,
2nd ed.
,
Cambridge University Press
,
Cambridge, England
.
15.
Popov
,
E.
, 1990,
Engineering Mechanics of Solids
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
16.
Nemes
,
J. A.
,
Asamoah-Attiah
,
S.
, and
Budak
,
E.
, 2001, “
Cutting Load Capacity of End Mills With Complex Geometry
,”
CIRP Ann.
0007-8506,
50
(
1
), pp.
65
68
.
17.
Goodwin
,
C. G.
, and
Sin
,
K. S.
, 1984,
Adaptive Filtering Prediction and Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
18.
Cao
,
Y.
, 2006, “
Modeling of High-Speed Machine-Tool Spindle Systems
,” Ph.D. thesis, The University of British Columbia.
19.
Hutchinson
,
J. R.
, 2001, “
Shear Coefficients for Timoshenko Beam Theory
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
68
, pp.
87
92
.
20.
Engin
,
S.
, and
Altintas
,
Y.
, 2001, “
Mechanics and Dynamics of General Milling Cutters. Part I: Helical End Mills
,”
Int. J. Mach. Tools Manuf.
0890-6955,
41
, pp.
2195
2212
.
21.
Merdol
,
S. D.
, 2004, “
Mechanics and Dynamics of Serrated Cylindrical and Tapered End Mills
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
126
, pp.
317
326
.
You do not currently have access to this content.