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Research Papers

Milling Stability Interrogation by Subharmonic Sampling

[+] 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

Mem. ASME
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 May 24, 2016; final manuscript received September 16, 2016; published online October 19, 2016. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 139(4), 041009 (Oct 19, 2016) (9 pages) Paper No: MANU-16-1296; doi: 10.1115/1.4034894 History: Received May 24, 2016; Revised September 16, 2016

This paper describes the use of subharmonic sampling to distinguish between different instability types in milling. It is demonstrated that sampling time-domain milling signals at integer multiples of the tooth period enables secondary Hopf and period-n bifurcations to be automatically differentiated. A numerical metric is applied, where the normalized sum of the absolute values of the differences between successively sampled points is used to distinguish between the potential bifurcation types. A new stability map that individually identifies stable and individual bifurcation zones is presented. The map is constructed using time-domain simulation and the new subharmonic sampling metric.

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References

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Figures

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Fig. 1

Cutting force geometry. The normal and tangential direction cutting forces, Fn and Ft, are identified. The fixed x and y directions, as well as the rotating normal direction, n, are also shown. The angle ϕ defines the tooth angle. The tool feed is to the right for the clockwise tool rotation, and the axial depth is in the z direction.

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Fig. 2

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

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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Fig. 6

Simulation results for a spindle speed of 4070 rpm at an axial depth of 3.6 mm. The workpiece x and y displacements are shown. (Top row) Time history (left) and Poincaré map (right) for once per tooth sampling (τsampling period). (Bottom row) Time history (left) and Poincaré map (right) for subharmonic sampling at 2τ.

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Fig. 7

(a) Once per tooth sampling (τ sampling period), (b) 2τ sampling period, (c) 3τ sampling period, and (d) 4τ sampling period. The zones that appear to be stable and unstable, depending on the sampling period, are marked.

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Fig. 8

Simulation results for a spindle speed of 4070 rpm at an axial depth of 3.6 mm. The workpiece x and y displacements are shown. (Top row) Time history (left) and Poincaré map (right) for once per tooth sampling (τsampling period). (Bottom row) Time history (left) and Poincaré map (right) for subharmonic sampling at 4τ.

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Fig. 9

Bifurcation diagram for an axial depth of 6.4 mm. Hopf (Hopf), period-2 (2), stable (stable), and combination Hopf and period-2 (Hopf-2) behaviors are specified.

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Fig. 10

Simulation results for a spindle speed of 4150 rpm at an axial depth of 6.4 mm. The workpiece x and y displacements are shown. (Top row) Time history (left) and Poincaré map (right) for once per tooth sampling. (Bottom row) Higher magnification views of the two elliptical distributions of once per tooth sampled points.

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Fig. 11

New stability map. Period-2 (circle), period-3 (triangle), period-4 (square), period-5 (+), period-6 (diamond), period-7 (×), and secondary Hopf (dot) bifurcations are individually identified. The box indicates the spindle speed range and axial depth (6.4 mm) for the bifurcation diagram in Fig. 9.

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