The Self-Excitation Damping Ratio: A Chatter Criterion for Time-Domain Milling Simulations

[+] Author and Article Information
Neil D. Sims

Advanced Manufacturing Research Centre with Boeing, Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3DJ, UKn.sims@Sheffield.ac.uk

J. Manuf. Sci. Eng 127(3), 433-445 (Dec 14, 2004) (13 pages) doi:10.1115/1.1948393 History: Received September 22, 2004; Revised December 14, 2004

Regenerative chatter is known to be a key factor that limits the productivity of high speed machining. Consequently, a great deal of research has focused on developing predictive models of milling dynamics, to aid engineers involved in both research and manufacturing practice. Time-domain models suffer from being computationally intensive, particularly when they are used to predict the boundary of chatter stability, when a large number of simulation runs are required under different milling conditions. Furthermore, to identify the boundary of stability each simulation must run for sufficient time for the chatter effect to manifest itself in the numerical data, and this is a major contributor to the inefficiency of the chatter prediction process. In the present article, a new chatter criterion is proposed for time-domain milling simulations, that aims to overcome this drawback by considering the transient response of the modeled behavior, rather than the steady-state response. Using a series of numerical investigations, it is shown that in many cases the new criterion can enable the numerical prediction to be computed more than five times faster than was previously possible. In addition, the analysis yields greater detail concerning the nature of the chatter vibrations, and the degree of stability that is observed.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 7

Effect of the depth of cut on (a) the stability criterion ζ and self-excited vibration magnitude and (b) chip thickness in the last tool revolution

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Figure 9

Convergence at 14,000rpm. (a) Self-excitation vibrations for 200 tooth revolutions; (b) chip thickness for first 100 revolutions at 6 mm depth of cut.

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Figure 10

Damping and sensitivity analysis. (a) Stability lobes with predictions of system damping. (b) Damping ratio at 4500rpm and 5600rpm. (c) Maximum chip thickness (5600 rpm). (d) PTP forces (5600 rpm). (e) Variance of once-per revolution samples (5600 rpm).

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Figure 5

Flow chart to illustrate evaluation of the chatter criterion, ζ

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Figure 6

Example of chatter detection for a stable cut. (A) Chip thickness against time, divided into ten frames; (B) y-direction vibration against time, divided into ten frames; (C) discrete Fourier transform (DFT) of (B); (D) DFT with tooth-passing frequency harmonics removed; (E) data in (D) plotted against frame number, (F) logarithm of the useful data in (E).

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Figure 8

Convergence of stability lobes as the simulated number of tool revolutions increases. (a) Self-excitation damping ratio (ξ=0) stability criterion; (b) “nondimensional chip thickness” stability criterion (6); (c) “peak-to-peak forces” stability criterion (5).

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Figure 1

Free vibrations of a linear, viscously damped system with positive (ζ=0.1), zero (ζ=0), and negative (ζ=−0.1) damping, corresponding to stable, marginally stable, and unstable self-excited vibration systems

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Figure 2

Chip thickness calculation; (a) six-tooth, with an array of discrete surface points for each tooth, (b) close up of one tooth, showing updating of the surface points, (c) calculation of the chip thickness h

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Figure 3

Updating the surface points when the tooth is not engaged in the cut

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Figure 4

Simulink block diagram of the milling simulation

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Figure 11

Low radial immersion cutting. (a) Stability lobes using “nondimensional chip thickness” method (η) and damping ratio method (ζ). (b) Self-excited vibrations at 18,500 rpm. (c) Self-excited vibrations at 21,400 rpm.




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