Miniature components with complex shape can be created by micromilling with excellent form and finish. However, for difficult-to-machine materials, such as Ti-alloys, failure of low-flexural stiffness microtools is a big limitation. High spindle speeds (20,000–100,000 rpm) can be used to reduce the undeformed chip thickness and the cutting forces to reduce the catastrophic failure of the tool. This reduced uncut chip thicknesses, in some cases lower than the cutting edge radius, can result in intermittent chip formation which can lead to dynamic variation in cutting forces. In addition, the run-out and the misalignment effects are amplified at higher rotational speeds which can induce dynamic force variation. These dynamic force variations coupled with low-flexural rigidity of micro end mill can render the process unstable. Consequently, accurate prediction of forces and stability is essential in high-speed micromilling. Most of the previous studies reported in the literature use constant cutting coefficients in the mechanistic cutting force model which does not yield accurate results. Recent work has shown significant improvement in the prediction of cutting forces with velocity–chip load dependent coefficients but a single-function velocity–chip model fails to predict the forces accurately at very high speeds (>80,000 rpm). This inaccurate force prediction affects the predicted stability boundary at those speeds. Hence, this paper presents a segmented approach, wherein a function is fit for a given range of speeds to determine the chip load dependent cutting coefficients. The segmented velocity–chip load dependent cutting coefficient improves the cutting force prediction at high speeds, which yields much accurate stability boundary. This paper employs two degrees-of-freedom (2DOF) model with forcing functions based on segmented velocity–chip load dependent cutting coefficients. Stability lobe diagram based on 2DOF model has been created for different speed ranges using Nyquist stability criterion. Chatter onset has been identified experimentally via accelerometer data and the power spectral density (PSD) analysis of the machined surface topography. Critical spatial chatter frequencies and magnitudes of PSD corresponding to onset of instability have also been determined for different conditions.

References

References
1.
Jin
,
X.
, and
Altintas
,
Y.
,
2013
, “
Chatter Stability Model of Micro-Milling With Process Damping
,”
ASME J. Manuf. Sci. Eng.
,
135
(
3
), p.
031011
.
2.
Weule
,
H.
,
Hüntrup
,
V.
, and
Tritschler
,
H.
,
2001
, “
Micro-Cutting of Steel to Meet New Requirements in Miniaturization
,”
CIRP Ann. Manuf. Technol.
,
50
(
1
), pp.
61
64
.
3.
Kim
,
C. J.
,
Mayor
,
J. R.
, and
Ni
,
J.
,
2004
, “
A Static Model of Chip Formation in Microscale Milling
,”
ASME J. Manuf. Sci. Eng.
,
126
(
4
), pp.
710
718
.
4.
Vogler
,
M. P.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
,
2004
, “
On the Modeling and Analysis of Machining Performance in Micro-Endmilling—Part I: Surface Generation
,”
ASME J. Manuf. Sci. Eng.
,
126
(
4
), pp.
685
694
.
5.
Tlusty
,
J.
,
1993
, “
High-Speed Machining
,”
CIRP Ann. Manuf. Technol.
,
42
(
2
), pp.
733
738
.
6.
Quintana
,
G.
, and
Ciurana
,
J.
,
2011
, “
Chatter in Machining Processes: A Review
,”
Int. J. Mach. Tools Manuf.
,
51
(
5
), pp.
363
376
.
7.
Altintas
,
Y.
,
2000
,
Manufacturing Automation: Principles of Metal Cutting and Machine Tool Vibrations
,
Cambridge University Press
,
New York
.
8.
Ducobu
,
F.
,
Filippi
,
E.
, and
Rivière-Lorphèvre
,
E.
,
2009
, “
Chip Formation and Minimum Chip Thickness in Micro-Milling
,” 12th
CIRP
Conference on Modeling of Machining Operations
, pp.
339
346
.http://www.geniemeca.fpms.ac.be/recherche/Articles/ducob2009a.pdf
9.
Yuan
,
Z. J.
,
Zhou
,
M.
, and
Dong
,
S.
,
1996
, “
Effect of Diamond Tool Sharpness on Minimum Cutting Thickness and Cutting Surface Integrity in Ultraprecision Machining
,”
J. Mater. Process. Technol.
,
62
(
4
), pp.
327
330
.
10.
Filiz
,
S.
,
Conley
,
C. M.
,
Wasserman
,
M. B.
, and
Ozdoganlar
,
O. B.
,
2007
, “
An Experimental Investigation of Micro-Machinability of Copper 101 Using Tungsten Carbide Micro-Endmills
,”
Int. J. Mach. Tools Manuf.
,
47
(
7
), pp.
1088
1100
.
11.
Singh
,
K. K.
,
Kartik
,
V.
, and
Singh
,
R.
,
2015
, “
Modeling Dynamic Stability in High-Speed Micromilling of Ti–6Al–4V Via Velocity and Chip Load Dependent Cutting Coefficients
,”
Int. J. Mach. Tools Manuf.
,
96
, pp.
56
66
.
12.
Landers
,
R. G.
, and
Ulsoy
,
A. G.
,
2008
, “
Nonlinear Feed Effect in Machining Chatter Analysis
,”
ASME J. Manuf. Sci. Eng.
,
130
(
1
), p.
011017
.
13.
Malekian
,
M.
,
Park
,
S. S.
, and
Jun
,
M. B.
,
2009
, “
Modeling of Dynamic Micro-Milling Cutting Forces
,”
Int. J. Mach. Tools Manuf.
,
49
(
7
), pp.
586
598
.
14.
Afazov
,
S. M.
,
Ratchev
,
S. M.
,
Segal
,
J.
, and
Popov
,
A. A.
,
2012
, “
Chatter Modelling in Micro-Milling by Considering Process Nonlinearities
,”
Int. J. Mach. Tools Manuf.
,
56
, pp.
28
38
.
15.
Mascardelli
,
B. A.
,
Park
,
S. S.
, and
Freiheit
,
T.
,
2008
, “
Substructure Coupling of Microend Mills to Aid in the Suppression of Chatter
,”
ASME J. Manuf. Sci. Eng.
,
130
(
1
), p.
011010
.
16.
Park
,
S. S.
, and
Rahnama
,
R.
,
2010
, “
Robust Chatter Stability in Micro-Milling Operations
,”
CIRP Ann. Manuf. Technol.
,
59
(
1
), pp.
391
394
.
17.
Jun
,
M. B.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
,
2006
, “
Investigation of the Dynamics of Microend Milling—Part I: Model Development
,”
ASME J. Manuf. Sci. Eng.
,
128
(
4
), pp.
893
900
.
18.
Jun
,
M. B.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
,
2006
, “
Investigation of the Dynamics of Microend Milling—Part II: Model Validation and Interpretation
,”
ASME J. Manuf. Sci. Eng.
,
128
(
4
), pp.
901
912
.
19.
Altintaş
,
Y.
, and
Budak
,
E.
,
1995
, “
Analytical Prediction of Stability Lobes in Milling
,”
CIRP Ann. Manuf. Technol.
,
44
(
1
), pp.
357
362
.
20.
Ogata
,
K.
,
1998
,
System Dynamics
, Vol.
3
,
Prentice Hall
,
Upper Saddle River, NJ
.
21.
Wang
,
Q. G.
,
Zhang
,
Z.
,
Astrom
,
K. J.
, and
Chek
,
L. S.
,
2009
, “
Guaranteed Dominant Pole Placement With PID Controllers
,”
J. Process Control
,
19
(
2
), pp.
349
352
.
22.
Faassen
,
R. P. H.
,
Van de Wouw
,
N.
,
Oosterling
,
J. A. J.
, and
Nijmeijer
,
H.
,
2003
, “
Prediction of Regenerative Chatter by Modelling and Analysis of High-Speed Milling
,”
Int. J. Mach. Tools Manuf.
,
43
(
14
), pp.
1437
1446
.
23.
Jayaram
,
S.
,
Kapoor
,
S. G.
, and
DeVor
,
R. E.
,
2000
, “
Analytical Stability Analysis of Variable Spindle Speed Machining
,”
ASME J. Manuf. Sci. Eng.
,
122
(
3
), pp.
391
397
.
24.
Sastry
,
S.
,
Kapoor
,
S. G.
, and
DeVor
,
R. E.
,
2002
, “
Floquet Theory Based Approach for Stability Analysis of the Variable Speed Face-Milling Process
,”
ASME J. Manuf. Sci. Eng.
,
124
(
1
), pp.
10
17
.
25.
Hall
,
S. R.
, and
Wereley
,
N. M.
,
1990
, “
Generalized Nyquist Stability Criterion for Linear Time Periodic Systems
,”
American Control Conference
, (
ACC
), San Diego, CA, May 23–25, pp.
1518
1525
.http://ieeexplore.ieee.org/document/4790991/
26.
Eynian
,
M.
,
2010
, “
Chatter Stability of Turning and Milling With Process Damping
,”
Doctoral dissertation
, University of British Columbia, Vancouver, BC.https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0069056
27.
Araujo
,
A. C.
,
Silveira
,
J. L.
,
Jun
,
M. B.
,
Kapoor
,
S. G.
, and
DeVor
,
R.
,
2006
, “
A Model for Thread Milling Cutting Forces
,”
Int. J. Mach. Tools Manuf.
,
46
(
15
), pp.
2057
2065
.
28.
Yang
,
L.
,
DeVor
,
R. E.
, and
Kapoor
,
S. G.
,
2005
, “
Analysis of Force Shape Characteristics and Detection of Depth-of-Cut Variations in End Milling
,”
ASME J. Manuf. Sci. Eng.
,
127
(
3
), pp.
454
462
.
29.
Schmitz
,
T. L.
, and
Smith
,
K. S.
,
2008
,
Machining Dynamics: Frequency Response to Improved Productivity
,
Springer Science & Business Media
,
New York
.
30.
Elson
,
J. M.
, and
Bennett
,
J. M.
,
1995
, “
Calculation of the Power Spectral Density From Surface Profile Data
,”
Appl. Opt.
,
34
(
1
), pp.
201
208
.
31.
Takasu
,
S.
,
Masuda
,
M.
,
Nishiguchi
,
T.
, and
Kobayashi
,
A.
,
1985
, “
Influence of Study Vibration With Small Amplitude Upon Surface Roughness in Diamond Machining
,”
CIRP Ann. Manuf. Technol.
,
34
(
1
), pp.
463
467
.
32.
Sata
,
T.
,
Li
,
M.
,
Takata
,
S.
,
Hiraoka
,
H.
,
Li
,
C. Q.
,
Xing
,
X. Z.
, and
Xiao
,
X. G.
,
1985
, “
Analysis of Surface Roughness Generation in Turning Operation and Its Applications
,”
CIRP Ann. Manuf. Technol.
,
34
(
1
), pp.
473
476
.
You do not currently have access to this content.