Stability of Interrupted Cutting by Temporal Finite Element Analysis

P. V. Bayly; J. E. Halley; B. P. Mann; M. A. Davies

doi:10.1115/1.1556860

Journal of Manufacturing Science and Engineering | Volume 125 | Issue 2 | TECHNICAL PAPERS

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TECHNICAL PAPERS

Stability of Interrupted Cutting by Temporal Finite Element Analysis

P. V. Bayly, J. E. Halley, B. P. Mann and M. A. Davies

[+] 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

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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 a_j1 and a_j2 specify the initial position and velocity of the tool as it enters the j^th element; the coefficients a_j3 and a_j4 specify the position and velocity of the tool at the end of the j^th element.

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Stability boundaries showing the effect of increasing the fraction of time in the cut (ρ). Parameters: k=2.2×10⁶ N/m,f_n=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).

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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.

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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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Bayly PV, Halley JE, Mann BP, Davies MA. Stability of Interrupted Cutting by Temporal Finite Element Analysis. ASME. J. Manuf. Sci. Eng. 2003;125(2):220-225. doi:10.1115/1.1556860.

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