The effects on the onset of chatter by the dynamic interaction of the workpiece and its method of support, the turret, the lathe bed, the cutting forces and the cutting conditions are determined. A generalized modal analysis is used to solve the four governing equations in the frequency domain. It is found that there are four dimensionless quantities that couple the equations, the most important being N0, the ratio of the static stiffness of the workpiece to the translational stiffness of the turret. The dimensionless critical depth of cut Hc and corresponding chatter frequency coefficient Ωc2 are determined as a function of N0 for two feed rates, several surface speeds, and for two workpiece boundary conditions; cantilevered and clamped-hinged. It is shown that the magnitudes of Hc and Ωc2 are oscillatory as a function of N0, and the occurrence of their peak values is proportional to the surface speed of the workpiece to the fourth power. It is found that for the parameters selected the effect of the dynamic response of the lathe bed is to increase by 7 percent the values of N0 at which the peak values of Hc occur. It is also found that the value of the equivalent viscous damping of the system and the magnitude of the real part of the cutting force coefficient govern the magnitudes of Hc and Ωc2 as a function of N0.

1.
Al-Shareef
K. J. H.
, and
Brandon
J. A.
,
1990
, “
On the Effects of Variations in the Design Parameters on the Dynamic Performance of Machine Tool Spindle-Bearing Systems
,”
International J. of Machine Tools & Manufacture
, Vol.
30
, No.
3
, pp.
431
445
.
2.
Budynas, R. G., 1977, Advanced Strength and Applied Stress Analysis, McGraw-Hill Book Co., NY.
3.
Delio
T.
,
Tlusty
J.
, and
Smith
S.
,
1992
, “
Use of Audio Signals for Chatter Detection and Control
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
114
, No.
2
, pp.
146
157
.
4.
Jen, M. U., 1993, “The Dynamic Interaction of the Cutting Process and the Workpiece in Facing,” Ph.D. Dissertation, University of Maryland at College Park.
5.
Jen
M. U.
, and
Magrab
E. B.
,
1993
, “
Natural Frequencies and Mode Shapes of Beams Carrying a Two Degree-of-Freedom Spring-Mass System
,”
ASME Journal of Vibration and Acoustics
, Vol.
115
, No.
2
, pp.
202
209
.
6.
Katz
R.
,
Lee
C. W.
,
Ulsoy
A. G.
, and
Scott
A. G.
,
1987
, “
Dynamic Stability and Response of a Beam Subject to a Deflection Dependent Moving Load
,”
ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design
, Vol.
109
, pp.
361
365
.
7.
Katz
R.
,
Lee
C. W.
,
Ulsoy
A. G.
, and
Scott
R. A.
,
1988
, “
The Dynamic Response of a Rotating Shaft Subject to a Moving Load
,”
J. of Sound and Vibration
, Vol.
122
, No.
1
, pp.
131
148
.
8.
Lauderbaugh, L. K., and Larson, V., 1990, “Multi-input Time Force Model for Orthogonal Turning,” Modeling of Machine Tools: Accuracy, Dynamics, and Control, ASME WAM, PED-45, pp. 149–159.
9.
Lee
S. J.
, and
Kapoor
S. G.
,
1986
, “
Cutting Process Dynamics Simulation for Machine Tool Structure Design
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
108
, pp.
68
74
.
10.
Lin
Z. H.
, and
Hodgson
D. C.
,
1988
, “
In-Process Measurement and Assessment of Dynamic Characteristics of Machine Tool
,”
International J. of Machine Tools & Manufacture
, Vol.
28
, No.
2
, pp.
93
111
.
11.
Minis, I. E., 1988, “Prediction of Machine Tool Chatter in Turning,” Ph.D. Dissertation, University of Maryland at College Park.
12.
Minis
I. E.
,
Magrab
E. B.
, and
Pandelidis
I. O.
,
1990
, “
Improved Method for the Prediction of Chatter in Turning, Part 2: Determination of Cutting Process Parameters
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
112
, pp.
21
27
.
13.
Nair
R.
,
Danai
K.
, and
Malkin
S.
,
1992
, “
Turning Process Identification Through Force Transients
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
114
, No.
1
, pp.
1
7
.
14.
O¯ta
H.
, and
Ko¯no
K.
,
1974
, “
On Chatter Vibrations of Machine Tool or Work Due to Regenerative Effect and Time Lag
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
96
, pp.
1337
1756
.
15.
Srinivasan
K.
, and
Nachtigal
C. L.
,
1978
, “
Investigation of the Cutting Process Dynamics in Turning Operations
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
100
, pp.
323
331
.
16.
Taylor
S.
,
Khoo
B. K.
, and
Walton
D.
,
1990
, “
Microcomputer Optimization of Machine Tool Spindle Stiffnesses
,”
International J. of Machine Tools & Manufacture
, Vol.
30
, No.
1
, pp.
151
159
.
17.
Thomson, W. T., 1965, Vibration Theory and Applications, Prentice Hall, Englewood Cliffs, NJ.
18.
Trabelsi, H., and Kannatey-Asibu, E., 1990, “Tool Wear and Sound Radiation in Metal Cutting,” Modeling of Machine Tools: Accuracy, Dynamics, and Control, ASME WAM, PED-45, pp. 121–131.
19.
Wu
D. W.
, and
Liu
C. R.
,
1985
, “
An Analytical Model of Cutting Dynamics. Part 2: Verification
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
107
, pp.
112
118
.
20.
Yoshimura
M.
,
Hamada
T.
,
Yura
K.
, and
Hitomi
K.
,
1983
, “
Design Optimization of Machine-Tool Structues With Respect to Dynamic Characteristics
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
88
96
.
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