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TECHNICAL PAPERS

Analysis of Tool Oscillation and Hole Roundness Error in a Quasi-Static Model of Reaming

[+] Author and Article Information
Philip V. Bayly

Mechanical Engineering, Box 1185, Washington University, 1 Brookings Drive, St. Louis, MO 63130e-mail: pvb@me.wustl.edu

Keith A. Young, Jeremiah E. Halley

The Boeing Company St. Louis, MO 63130

Sean G. Calvert

Washington University, St. Louis, MO 63130

J. Manuf. Sci. Eng 123(3), 387-396 (Nov 01, 2000) (10 pages) doi:10.1115/1.1383551 History: Received July 01, 1998; Revised November 01, 2000
Copyright © 2001 by ASME
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References

Figures

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Examples of lobed holes made with a 6-flute reamer
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Reamer geometry and terminology
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(a) Schematic diagram of the reaming process showing the nominal chip load (b) the effect of tool displacement on chip load
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(a) Cutting forces on a reamer in a rotating coordinate system (b) tool axis displacement and radial displacement of each tooth
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Schematic diagram of the system used to measure displacement of the reamer axis. Capacitance probes were used to sense a collar mounted on the blades of the reamer, 25 mm from the tip.
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(a) Positions of the eigenvalues of a reaming system in the complex plane as the rubbing coefficient kr is increased logarithmically from 0.211 to 211 N/mm. The tool has six evenly spaced teeth. Circles indicate the initial eigenvalue locations. Key parameters: kc=663 N/mm (corresponding to ks=2.4×103 N/mm2,Rnominal=0.254 mm and Hnominal=0.025 mm); tool stiffness kxx=16.9 N/mm; margin width: 4 degrees; (b) Eigenvalue locations as the margin width is increased from 0.5 to 6 degrees. Parameters are as in Fig. 6(a), except the rubbing coefficient is fixed at kr=21.1 N/mm. Units of eigenvalues are cycles/rev.  
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Examples of hole profiles and tool axis motion corresponding to single-mode behavior in each of the following modes: (a–c) Mode 1: λ1=−0.003+0.991i,u1=[−i,1] (backward, ∼1/rev); (d–f) Mode 2: λ2=−0.011+5.000i,u2=[i,1] (forward, ∼5/rev); (g–i) Mode 3: λ3=0.001+6.979i,u3=[−i,1] (backward, ∼7/rev); (j−1) Mode 5: λ5=0.000+12.967i,u5=[−i,1] (backward, ∼13/rev). Units of eigenvalues are cyc/rev; eigenvectors (and corresponding profiles) are dimensionless.
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(a) Positions of the eigenvalues of a reaming system in the complex plane as the rubbing coefficient kr is increased from 0.211 to 211 N/mm. The tool has six irregularly spaced teeth at 0, 55, 120, 180, 255, and 315 degrees. Circles indicate the initial eigenvalue locations. Parameters are as in Fig. 6; (b) Eigenvalue locations as the margin width is increased from 0.5 to 6 degrees. Parameters are as in Fig. 6. Units of eigenvalues are cycles/rev.
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Axis motion and 5-lobed hole profiles from a simulation of reaming with a 6-flute tool with a small rubbing coefficient: kr=1.05 N/mm. Other parameters are as in Fig. 6. (a) Tooth paths in 3-D; (b) Tool axis trajectory; (c) Hole profile after ten revolutions; (d) Power spectra of hole profiles plotted vs. revolution number (depth into hole). All units are in mm.
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Axis motion and 7-lobed hole profiles from a simulation of reaming with a 6-flute tool with rubbing coefficient kr=21.1 N/mm. Other parameters are as in Fig. 6. (a) Tooth paths in 3-D; (b) Tool axis motion; (c) Hole profile after ten revolutions; (d) Power spectra of hole profiles plotted vs. revolution number (depth into hole). All units are in mm.
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Example raw data from cutting tests. (a) displacement in the (fixed) u direction vs time (b) power spectral density (PSD) of displacement in the (fixed) u direction (c) displacement in the (fixed) ν direction vs time (d) PSD of displacement in the (rotating) x direction. Components at N/rev in the fixed frame appear as (N−1)/rev or (N+1)/rev in the rotating frame. Key parameters: speed 250 RPM; reamer diameter 12.70 mm (0.5000 in.) and set length 159 mm; initial hole diameter 6.15 mm (0.242 in.); feed of 0.15 mm/rev (0.012 in/rev).
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Tool axis motion during reaming of a 5-lobed hole (feed of 0.152 mm/rev, panels (a)–(d)) and a 7-lobed hole (feed of 0.152 mm/rev, panels (e)–(h)). (a,e) PSDs of displacement in the (rotating) x direction. (b,f ) Trajectories in the rotating x−y frame, including only frequency components between 3 and 9 cyc/rev. (c,g) Trajectories in the x−y frame, including only frequency components between 9 and 15 cyc/rev. (d,h) Trajectories in the x−y frame, including all frequency components up to 75 cyc/rev. Other parameters: speed 250 RPM; reamer diameter 12.70 mm (0.5000 in.); reamer set length 159 mm; initial hole diameter 11.9 mm (0.470 in.).
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Profiles of a 5-lobed hole (feed of 0.152 mm/rev, panels (a)–(e)) and a 7-lobed hole (feed of 0.152 mm/rev, panels (f )–(j )). Holes correspond to tool axis motion shown in Fig. 12. (a,f ) PSDs of hole profile. (b,g) Hole profiles including only frequency components between 3 and 9 cyc/rev. (c,h) Hole profiles including only frequency components between 9 and 15 cyc/rev. (d,i ) Hole profiles including all frequency components up to 180 cyc/rev. Units are μm.
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Summary plots of frequency components as a function of radial depth of cut (RDOC) and feed. (a,c,e) Amplitudes of 5/rev, 7/rev, and 13/rev components plotted vs. RDOC for a constant feed of 0.152 mm/rev or 0.025 mm/tooth. (b,d,f ) Amplitudes of 5/rev, 7/rev, and 13/rev components plotted vs. feed for a constant RDOC of 0.41 mm. The mean amplitude for each cutting condition (N=4 holes each) is indicated by the (•) symbol. The standard deviation is shown by a vertical line.

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