A new method for on-line chatter detection is presented. The proposed method characterizes the significant transition from high dimensional to low dimensional dynamics in the cutting process at the onset of chatter. Based on the observation that cutting signals contain fractal patterns, a wavelet-based maximum likelihood (ML) estimation algorithm is applied to on-line chatter detection. The presented chatter detection index γ is independent of the cutting conditions and gives excellent detection accuracy and permissible computational efficiency, which makes it suitable for on-line implementation. The validity of the proposed method is demonstrated through the tests with extensive actual data obtained from turning and milling processes.

1.
Tlusty
,
J.
, and
Andrews
,
G.
,
1983
, “
A Critical Review of Sensors for Unmanned Machining
,”
CIRP Ann.
,
32
(
2
), pp.
563
571
.
2.
Delio
,
T.
,
Tlusty
,
J.
, and
Smith
,
S.
,
1992
, “
Use of Audio Signals for Chatter Detection and Control
,”
ASME J. Ind.
,
114
, pp.
146
157
.
3.
Braun
,
S.
,
1975
, “
Signal Processing for the Determination of Chatter Threshold
,”
CIRP Ann.
,
24
(
1
), pp.
315
320
.
4.
Rahman
,
M.
,
1988
, “
In-Process Detection of Chatter Threshold
,”
ASME J. Ind.
,
110
, pp.
44
50
.
5.
Li
,
X. Q.
,
Wong
,
Y. S.
, and
Nee
,
A. Y. C.
,
1998
, “
A Comprehensive Identification of Tool Failure and Chatter using a Parallel Multi-ART2 Neural Network
,”
ASME J. Manuf. Sci. Eng.
,
120
, pp.
433
442
.
6.
Li
,
X. Q.
,
Wong
,
Y. S.
, and
Nee
,
A. Y. C.
,
1997
, “
Tool Wear and Chatter Detection Using the Coherence Function of Two Crossed Accelerations
,”
Int. J. Mach. Tools Manuf.
,
37
(
4
), pp.
425
435
.
7.
Grabec
,
I.
,
1988
, “
Chaotic Dynamics of the Cutting Process
,”
Int. J. Mach. Tools Manuf.
,
28
(
1
), pp.
19
32
.
8.
Gradisek
,
J.
,
Govekar
,
E.
, and
Grabec
,
I.
,
1998
, “
Using Coarse-grained Entropy Rate to Detect Chatter in Cutting
,”
J. Sound Vib.
,
214
(
5
), pp.
941
952
.
9.
Bukkapatnam, S. T. S., Lakhtakia, A., Kumara, S. R. T., and Satapathy, G., 1995, “Characterization of Nonlinearity of Cutting Tool Vibrations and Chatter,” Proceedings of the ASME Materials Division, 69(2), pp. 1207–1223.
10.
Berger
,
B. S.
,
Minis
,
I.
,
Harley
,
J.
,
Rokni
,
M.
, and
Papadopoulos
,
M.
,
1998
, “
Wavelet-based Cutting State Identification
,”
J. Sound Vib.
,
213
(
5
), pp.
813
827
.
11.
Khraisheh
,
M. K.
,
Pezeshki
,
C.
, and
Bayoumi
,
A. E.
,
1995
, “
Time Series-Based Analysis for Primary Chatter In Metal Cutting
,”
J. Sound Vib.
,
180
, pp.
67
87
.
12.
Wornell
,
G. W.
,
1990
, “
A Karhunen-Loeve-like Expansion for 1/f Processes via Wavelets
,”
IEEE Trans. Inf. Theory
36
(
4
), pp.
859
861
.
13.
Wornell
,
G. W.
, and
Oppenheim
,
A. V.
,
1992
, “
Estimation of Fractal Signals from Noisy Measurements using Wavelets
,”
IEEE Trans. Signal Process.
,
40
(
3
), pp.
611
623
.
14.
Wornell, G. W., 1996, Signal Processing with Fractals; A Wavelet-based Approach, Prentice Hall, Upper Saddle River, NJ.
15.
Jiang
,
J. D.
,
Chen
,
J.
, and
Qu
,
L. S.
,
1999
, “
The Application of Correlation Dimension in Gear Box Condition Monitoring
,”
J. Sound Vib.
,
223
(
4
), pp.
529
541
.
16.
Laird
,
N. M.
,
1982
, “
Computation of Variance Components using the EM Algorithm
,”
J. Stat. Comput. Simul.
,
14
(
3–4
), pp.
295
303
.
17.
Papoulis, A., 1991, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York.
18.
Rao
,
B. C.
, and
Shin
,
Y. C.
,
1999
, “
A Comprehensive Dynamic Cutting Force Model for Chatter Prediction in Turning
,”
Int. J. Mach. Tools Manuf.
,
39
, pp.
1631
1654
.
19.
Daubechies, I., 1992, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA.
20.
Jensen
,
S. A.
, and
Shin
,
Y. C.
,
1999
, “
Stability Analysis in Face Milling Operation: Part 1-Theory for Stability Lobe Prediction
,”
ASME J. Manuf. Sci. Eng.
,
21
(
4
), pp.
600
605
.
21.
Jensen
,
S. A.
, and
Shin
,
Y. C.
,
1999
, “
Stability Analysis in Face Milling Operation: Part 2-Experimental Validation and Influencing Factors
,”
ASME J. Manuf. Sci. Eng.
,
21
(
4
), pp.
606
614
.
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