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TECHNICAL PAPERS

Stability of Interrupted Cutting by Temporal Finite Element Analysis

[+] Author and Article Information
P. V. Bayly, B. P. Mann

Washington University, St. Louis, Missouri 63130

J. E. Halley

The Boeing Co., St. Louis, Missouri 63166

M. A. Davies

NIST, Gaithersburg, Maryland 20899

J. Manuf. Sci. Eng 125(2), 220-225 (Apr 15, 2003) (6 pages) doi:10.1115/1.1556860 History: Received March 01, 2001; Revised July 01, 2002; Online April 15, 2003
Copyright © 2003 by ASME
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References

Koenigsberger, F., and Tlusty, J., 1970, Structures of Machine Tools, Pergamon Press, Oxford.
Tobias, S. A, 1965, Machine Tool Vibration, Wiley, New York.
Smith,  S., and Tlusty,  J., 1991, “An Overview of the Modeling and Simulation of the Milling Process,” ASME J. Eng. Ind., 113, pp. 169–175.
Altintas,  Y., and Budak,  E., 1995, “Analytical Prediction of Stability Lobes in Milling,” CIRP Ann., 44, pp. 357–362.
Davies,  M. A., Pratt,  J. R., Dutterer,  B., and Burns,  T. J., 2001, “Interrupted Machining: A Doubling in the Number of Stability Lobes,” ASME J. Manuf. Sci. Eng., 124, pp. 217–225.
Davies,  M. A., Pratt,  J. R., Dutterer,  B., and Burns,  T. J., 2000, “The Stability of Low Radial Immersion Machining,” CIRP Ann., 49, pp. 37–40.
Corpus, W. T., and Endres, W. J., 2000, “A High-Order Solution for the Added Stability Lobes in Intermittent Machining,” ASME Publication MED-Vol. 11, Proceedings of the ASME Manufacturing Engineering Division, pp. 871–878.
Insperger,  T., and Stepan,  G., 2000, “Stability of the Milling Process,” Periodica Polytechnica Ser. Mech. Eng., 44, pp. 47–57.
Bayly, P. V., Halley, J. E., Davies, M. A., and Pratt, J. R., 2000, “Stability Analysis of Interrupted Cutting with Finite Time in the Cut,” ASME Publication MED-Vol. 11, Proceedings of the ASME Manufacturing Engineering Division, pp. 989–996.
Peters,  D. A., and Idzapanah,  A. P., 1988, “hp-Version Finite Elements for the Space-Time Domain,” Computational Mechanics, 3, pp. 73–88.
Meirovitch, L., 1997, Principles and Techniques of Vibrations, pp. 544–548, Prentice Hall, New Jersey.
Tlusty, J., 1985, “Machine Dynamics,” Handbook of High-Speed Machining Technology, R. I. King, ed., Chapman and Hall, New York.
Schmitz,  T. L., Davies,  M. A., Medicus,  K., and Snyder,  J., 2001, “Improving High-Speed Machining Material Removal Rates by Rapid Dynamic Analysis,” CIRP Ann., 50, pp. 263–268.

Figures

Grahic Jump Location
Schematic diagram of the interrupted cutting process. When the tool is in contact with the work piece, the cutting force is proportional to the cross-sectional area of the uncut chip. The tool vibrates freely when not in contact with the work piece. The coefficients aj1 and aj2 specify the initial position and velocity of the tool as it enters the jth element; the coefficients aj3 and aj4 specify the position and velocity of the tool at the end of the jth element.
Grahic Jump Location
Stability boundaries showing the effect of increasing the fraction of time in the cut (ρ). Parameters: k=2.2×106 N/m,fn=146.8 Hz,ς=0.0038,C=2.0×108 N/m2. Number of elements: E=20ρ. Panel (e) shows a comparison of TFEA lobes with the stability lobes derived by the impulse approximation of Davies et al., 2000 (dotted lines). Panel (f) shows a comparison with stability lobes for continuous cutting derived by the method of Tlusty (1985) (dotted lines).
Grahic Jump Location
Experimental data from continuous sampling (a,c,e,g,i,k) and 1/rev sampling (b,d,f,h,j,l) during milling of 1-DOF flexure. Parameters are as in Fig. 2; fraction of time in the cut ρ=0.1. Row 1 (a,b): 2900 rpm, 2 mm DOC, stable; Row 2 (c,d): 3200 rpm, 2 mm DOC, unstable; Row 3 (e,f ): 3500 rpm, 2 mm DOC, stable; Row 4 (g,h): 3550 rpm, 2 mm DOC, unstable; Row 5 (i,j): 3540 rpm, 2 mm DOC, unstable; Row 6 (k,l): 3540 rpm, 4 mm DOC, stable.
Grahic Jump Location
Comparison of (a) predicted stability boundaries (lines) with results from simulation (⋅ stable, x unstable); (b) experimental data (⋅ stable, x unstable). Parameters are as in Fig. 2; fraction of time in the cut ρ=0.1. Note that in experimental cutting tests at 3540 rpm a DOC of 5 mm is stable and a DOC of 1 mm, for example, is unstable. Analogous behavior is predicted by analysis and observed in simulation.

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