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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

Rudd,  J. L., and Gray,  T. D., 1978, “Quantification of Fastener-Hole Quality,” J. Aircr., 15, No. 3, pp. 143–147.
Renshaw,  T., Wongwiwat,  K., and Sarrantonio,  A., 1983, “Comparison of Properties of Joints Prepared by Ultrasonic Welding and Other Means,” J. Aircr., 20, No. 6, pp. 552–556.
Kiyota, H., and Sakuma, K., 1982, “Behavior of Tool and Its Effect on Sectional Profile of Hole in Reaming,” Memoirs of the Faculty of Engineering, Kyushu University, Vol. 42, pp. 335–354.
Sakuma,  K., and Kiyota,  H., 1986a, “Hole Accuracy with Carbide-Tipped Reamers: 1st Report,” Bull. Jpn. Soc. Precis. Eng., , 19, pp. 89–95.
Sakuma,  K., and Kiyota,  H., 1986b, “Hole Accuracy with Carbide-Tipped Reamers:2nd report,” Bull. Jpn. Soc. Precis. Eng., 20, pp. 103–108.
Varterasian, J. H., 1974, Society of Manufacturing Engineers Technical Paper MR74-144, pp. 1–15.
Bayly, P. V., 1997, “Optimal ‘White-Noise’ Spacing of Reamer Blades,” Proceedings of the 1997 ASM International Non-Ferrous Processing and Technology Conference, T. Bains and D. S. MacKenzie, eds., pp. 419–423, ASM International, Materials Park.
Tobias, S. A., 1965, Machine Tool Vibration, Wiley, New York.
Koenigsberger, F., and Tlusty, J., 1970, Structures of Machine Tools, Pergamon Press, Oxford.
Tlusty, J., 1985, “Machine Dynamics,” in Handbook of High-Speed Machining Technology, R. I. King, ed., Chapman and Hall, New York.
Minis,  I., and Yanushevsky,  R., 1993, “A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling,” ASME J. Eng. Ind., 115, pp. 1–8.
Altintas,  Y., and Budak,  E., 1995, “Analytical Prediction of Stability Lobes in Milling,” CIRP Ann., 44, No. 1, pp. 357–362.
Zhang,  G. M., and Kapoor,  S. G., 1987, “Dynamic Modeling and Analysis of the Boring Machining System,” ASME J. Eng. Ind., 109, pp. 219–226.
Nayfeh,  A. H., Chin,  C.-M., and Pratt,  J., 1997, “Perturbation Methods in Nonlinear Dynamics-Applications to Machining Dynamics,” ASME J. Manuf. Sci. Eng., 119, No. 4(A), pp. 485–493.
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Friedman,  M. Y., Kitamura,  I., and Wu,  S. M., 1974, “Rounding Mechanism of Reaming,” CIRP Ann., 23, No. 1, pp. 27–28.
Lee,  S. J., Eman,  K. F., and Wu,  S. M., 1987, “An Analysis of the Drill Wandering Motion,” ASME J. Eng. Ind., 109, pp. 297–305.
Zelentsov,  V. V., 1981, “The Lobing of Drilled Holes,” Soviet Engineering Research, 1, No. 10, pp. 46–48.
Reinhall,  P. G., and Storti,  D. W., 1986, “Modeling and Analysis of the Dynamics of a Drill Penetrating a Thin Plate,” ASME J. Appl. Mech., 53, pp. 690–694.
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Fujii,  H., Marui,  E., and Ema,  S., 1986b, “Whirling Vibration in Drilling, Part II: Influence of Drill Geometries, Particularly of the Drill Flank, on the Initiation of Vibration,” ASME J. Eng. Ind., 108, pp. 163–168.
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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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