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Technical Brief

A New Metric for Automated Stability Identification in Time Domain Milling Simulation

[+] Author and Article Information
Andrew Honeycutt

Department of Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
9201 University City Boulevard,
Charlotte, NC 28223
e-mail: ahoney15@uncc.edu

Tony L. Schmitz

Department of Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
9201 University City Boulevard,
Charlotte, NC 28223
e-mail: tony.schmitz@uncc.edu

1Corresponding author.

Manuscript received August 24, 2015; final manuscript received January 4, 2016; published online March 8, 2016. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 138(7), 074501 (Mar 08, 2016) (7 pages) Paper No: MANU-15-1444; doi: 10.1115/1.4032586 History: Received August 24, 2015; Revised January 04, 2016

A new metric is presented to automatically establish the stability limit for time domain milling simulation signals. It is based on periodically sampled data. Because stable cuts exhibit forced vibration, the sampled points repeat over time. Periodically sampled points for unstable cuts, on the other hand, do not repeat with each tooth passage. The metric leverages this difference to define a numerical value of nominally zero for a stable cut and a value greater than zero for an unstable cut. The metric is described and is applied to numerical and experimental results.

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Figures

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Fig. 1

Flow diagram for the time domain simulation

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Fig. 3

Stable cut, b  = 0.5 mm (left) time response for x (feed) direction displacement; (right) Poincaré map which plots x displacement versus velocity. The once-per-tooth sampled points are displayed as circles.

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Fig. 4

Period-2, b  = 2.5 mm (left) time response for x (feed) direction displacement; (right) Poincaré map

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Fig. 5

Secondary Hopf, b  = 5.0 mm (left) time response; (right) Poincaré map

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Fig. 6

Bifurcation diagram for selected spindle speed (30,000 rpm) and system dynamics

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Fig. 7

Simulated stability map (M=1μm contour)

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Fig. 8

Milling experimental setup with laser vibrometer (LV), piezo-accelerometer (PA), laser tachometer (LT), and capacitance probe (CP)

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Fig. 9

Bifurcation diagram for 3800 rpm, 26% radial immersion (left) simulated; (right) experiment

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Fig. 10

Poincaré maps for 3800 rpm, 4.5 mm axial depth (left) simulated; (right) experiment

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Fig. 11

Simulated stability map for experimental setup (M=1μm contour)

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Fig. 12

M values for experiments (3800 rpm)

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