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TECHNICAL PAPERS

Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling

[+] Author and Article Information
Philip V. Bayly, Michael T. Lamar, Sean G. Calvert

Mechanical Engineering, Box 1185, Washington University, 1 Brookings Drive, St. Louis, MO 63130

J. Manuf. Sci. Eng 124(2), 275-285 (Apr 29, 2002) (11 pages) doi:10.1115/1.1459087 History: Received December 01, 2000; Revised July 01, 2001; Online April 29, 2002
Copyright © 2002 by ASME
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References

Figures

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Photograph and measured profile of a three-lobed hole
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Schematic iagram of the drill (side and end views) showing the effect of lateral displacement on the area of the uncut chip. The nominal feed per tooth is h; the variation in chip thickness δh is due to axis deflection x=[δx,δy]T.
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(a) Force vector at one location on the primary edge of the drill. The distance r and angle θ define the nominal location of the cutting element. The force may be measured by cutting a round tube with a single-fluted drill. (b) Vectors representing the change in cutting force per unit area (dFci/dAi) at twelve points on the cutting edges.
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Schematic diagrams of rubbing or “process damping.” (a) Effect of penetration rate (slope) on potential interference between the tool’s clearance face and the workpiece in orthogonal cutting. (b) Locus of points on the surface of the workpiece produced as the tool undergoes radial oscillations while rotating. Slopes due to vibration vary as 1/radius.
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Schematic diagram of the measurement system
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Measurements of force on the work piece as a function of uncut chip area. Each row corresponds to an element on the primary cutting edge: (a-b) Element 1 (innermost), r0=1.2; (c-d) Element 2, r0=2.0 mm; (e-f ) Element 3, r0=2.7 mm; (g-h) Element 4, r0=3.5 mm; (i-j) Element 5 (outermost), r0=4.3 mm. The slope in each plot represents an estimate of the derivative dFcx/dA or dFcy/dA for that element.
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Solutions to quasi-static model with bending and cutting only. (a-b) Locus of characteristic exponents γii+jωi as the cutting stiffness matrix Kc is increased from 1 to 10 times its nominal value. The results at the nominal value of Kc are circled. (c) Tool axis trajectory in the rotating frame (backward whirl). (d) Time series of tool motion in the rotating frame. (e-f ) Trajectories of tool axis and outermost cutting teeth in the fixed (u-v) frame for the 3 cyc/rev mode.
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Solutions to quasi-static model with bending, cutting and rubbing. Chisel point cutting and rubbing terms were removed from the model to simulate drilling with a pilot hole. (a-b) Locus of characteristic exponents γii+jωi as rubbing stiffness parameter κr is increased from 1 (circled) to 6. (c) Tool axis trajectory in the rotating frame (backward whirl). (d) Time series of tool motion in the rotating frame. (e-f ) Trajectories of tool axis and outermost cutting teeth in the fixed (u-v) frame for the least stable (∼7 cyc/rev) mode.
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Experimental measurements of tool vibration during drilling with no pilot hole (1000 rpm, 0.1 mm/rev). (a) Trajectory of tool axis in the rotating frame. (b) Time series of tool axis motion. (c) Power spectrum of tool axis motion in the rotating frame. (d-e) Tool axis trajectory and trajectories of outermost cutting teeth, in the fixed (u-v) frame.
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Solutions to quasi-static model with bending, cutting and rubbing. (a-b) Locus of characteristic exponents γii+jωi as rubbing stiffness parameter κr is increased from 1 (circled) to 6. (c) Tool axis trajectory in the rotating frame (backward whirl). (d) Time series of tool motion in the rotating frame. (e-f ) Trajectories of tool axis and outermost cutting teeth in the fixed (u-v) frame for the least stable (∼3 cyc/rev) mode. This mode is de-stabilized and its frequency shifted slightly by rubbing.
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Experimental measurements of tool vibration during drilling with 1.6 mm pilot hole (1000 rpm, 0.2 mm/rev feed). (a) Trajectory of tool axis in the rotating frame. (b) Time series of tool axis motion. (c) Power spectrum of tool axis motion in the rotating frame. (d-e) Tool axis trajectory and trajectories of outermost cutting teeth in the fixed (u-v) frame.
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(a) Profile of hole produced by drill motion in Fig. 10 (no pilot hole, 1000 rpm, 0.1 mm/rev). (b) Power spectrum of the hole profile. (c) Three-dimensional profile of hole.

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