The stability characteristics of a milling system are investigated in this paper. A model is developed that includes the gyroscopic effects of the rotating spindle and on the basis of this model new insight into the physics of chatter instability is obtained. In the analysis the basic Fourier series method for solving a harmonically time-varying system without time lag is extended to obtain a finite-order characteristic equation for the milling system in terms of the system matrices. The complex eigenvalues of the resulting characteristic equation can be efficiently predicted by using Mu¨ller’s optimization algorithm with deflation, and the stability lobes can be predicted by using a nonlinear optimization procedure at different rotating speeds based on the Nyquist stability criterion. In this study it was found that including the gyroscopic effects of the rotating spindle increases the real parts of the eigenvalues of the system. This reduces the critical axial depth of cut. It is also found that the milling forces primarily excite the backward-wave modes but stabilize the forward-wave modes of the rotating spindle.

Issue Section:
Technical Papers
Keywords:
machining, stability, Nyquist criterion, eigenvalues and eigenfunctions, Fourier series, optimisation
Topics:
Milling, Stability, Chatter, Eigenvalues, Fourier series
1.
Tobias, S. A., and Fishwick, W., 1958, A Theory of Regenerative Chatter, The Engineer, London.
2.
Tlusty, J., and Polacek, M., 1963, “The Stability of Machine Tools Against Self-Excited Vibrations in Machining,” ASME International Research in Production Engineering, pp. 465–474.
3.
Merritt
,
H. E.
,
1965
, “
Theory of Self-Excited Machine Tool Chatter
,”
ASME J. Eng. Indus.
,
87
, pp.
447
–
454
.
4.
Sridhar
,
R.
,
Hohn
,
R. E.
, and
Long
,
G. W.
,
1968
, “
A General Formulation of the Milling Processing Equation. Contribution to Machine Tool Chatter Research—5
,”
ASME J. Eng. Indus.
,
90
, pp.
317
–
324
.
5.
Sridhar
,
R.
,
Hohn
,
R. E.
, and
Long
,
G. W.
,
1968
, “
A Stability Algorithm for a General Milling Processing. Contribution to Machine Tool Chatter Research—7
,”
ASME J. Eng. Indus.
,
90
, pp.
330
–
334
.
6.
Tlusty
,
J.
, and
Ismail
,
F.
,
1981
, “
Basic Nonlinear Linearity in Machine Chatter
,”
Ann. CIRP
,
30
, pp.
21
–
25
.
7.
Smith
,
S.
, and
Tlusty
,
J.
,
1993
, “
Efficient Simulation Programs for Chatter in Milling
,”
Ann. CIRP
,
42/1
, pp.
463
–
466
.
8.
Minis
,
I.
, and
Yanushevsky
,
T.
,
1993
, “
A New Theoretical Approach for the Prediction of Machine Tool Chatter
,”
ASME J. Eng. Indus.
,
115
, pp.
1
–
8
.
9.
Minis
,
I.
,
Yanushevsky
,
T.
,
Tembo
,
R.
, and
Hocken
,
R.
,
1990
, “
Analysis of Linear and Nonlinear Chatter in Milling
,”
Ann. CIRP
,
39
, pp.
459
–
462
.
10.
Budak, E., 1994, “Mechanics and Dynamics of Milling Thin Walled Structure,” Ph.D. Dissertation, Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada.
11.
Altintas
,
Y.
, and
Budak
,
E.
,
1995
, “
Analytical Prediction of Stability Lobes in Milling
,”
Ann. CIRP
,
44
, No.
1
, pp.
357
–
362
.
12.
Muller
,
D. E.
,
1956
, “
A Method of Solving Algebraic Equations Using an Automatic Computer
,”
Math Tables Other Aids Comput.
,
10
, pp.
208
–
215
.
13.
Gerald, C. F., and Wheatley, P. O., 1994, Applied Numerical Analysis, 5th ed., Addison-Wesley, Reading, MA.
14.
Nelson
,
H. D.
,
1980
, “
A Finite Rotating Shaft Element Using Timoshenko Beam Theory
,”
ASME J. Mech. Des.
,
102
, pp.
793
–
803
.
15.
Botltin, V. V., 1964, The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco.
16.
Lengoc
,
L.
,
1995
, “
Wide Bandsaw Blade Under Cutting Condition, Part II: Stability of a Plate Moving in Its Plane While Subjected to Parametric Excitation
,”
J. Sound Vib.
,
186
, pp.
143
–
162
.
17.
Tian, J., 1998, Ph.D. Dissertation, Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada.
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