Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Composition to Test

[+] Author and Article Information
Philip V. Bayly, Sandra A. Metzler

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

Adam J. Schaut, Keith A. Young

Advanced Manufacturing Technology, The Boeing Company, St. Louis, MO 63130

J. Manuf. Sci. Eng 123(4), 552-561 (Nov 01, 2000) (10 pages) doi:10.1115/1.1381399 History: Received February 01, 2000; Revised November 01, 2000
Copyright © 2001 by ASME
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Results from a finite element model of a twisted beam (see Table 1) illustrating (a-b) torsional-axial coupling in the response to a static axial load, and (c-d) torsional-axial coupling in a dynamic mode shape. The left end of the beam is fixed; the right end is free.
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Schematic diagram of the drill fixture, showing the sensor locations (Si) and excitation forces (F *  * ) used in the modal analysis. Also shown is the “winged” collar used to provide a target for the non-contact displacement probes.
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Estimated FRFs between the response at the off-axis sensor, S1, and measured axial and transverse forces on the heel of the drill. (a,b) Imaginary and real components of the FRF between displacement, xs, at the sensor and axial forces (FZ1,FZ2) at the heel of the drill; (c,d) Imaginary and real components of the FRF between displacement xs at the sensor and transverse forces (Fθ1,Fθ2) at the heel of the drill. Bending mode change sign when drill is hit on the opposite sides; torsional modes do not.
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Measured thrust (a, Fz) and tangential force (b, Ft) on drill flutes as a function of cross-sectional area of chip (width of cut×feed per tooth). Example data is shown from drilling tests on tubular aluminum specimens with 0.8 mm wall thickness. Symbols: Tube inner radius 2.4 mm: ○. Tube inner radius 3.2 mm: ×. Solid lines represent linear fit with the minimum least squared error. Slopes are 1.0×108 and 1.6×108 N/m2(Fz);6.9×108 and 9.0×108 N/m2(Ft).
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Simulation results and comparison to analytical predictions of chatter stability and frequency. Feed was 0.203 mm/rev and radial depths of cut were 1.6, 3.2, and 4.8 mm. (a) Vibration amplitude as a function of spindle speed and chatter frequency; (b) Amplitude vs. spindle speed; (c) Chatter frequency vs. spindle speed; (d) Comparison of results of numerical integration (• unstable, × stable) with stability boundaries predicted from Eq. (17).
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Example time series and power spectra of data recorded from sensor S1 during (a-b) an unstable cut (1213 RPM, 4.8 mm DOC) and (c-d) a stable cut (1180 RPM, 4.8 mm DOC). The feed in both cases was 0.203 mm/rev.
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Example time series and power spectra of data recorded from sensors S1 (a-b, displacement due to torsion+x-bending), S2 (c-d, x-bending displacement) and S3 (e-f, y-bending displacement) during an unstable cut (1213 RPM, 4.8 mm DOC, 0.203 mm/rev).
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(a) Photograph of hole produced during an unstable cut (1242 RPM, 4.8 mm DOC, 0.203 mm/rev, 340 Hz chatter frequency). (b) Profile measured on the wall of the hole, 2 mm from the bottom. Roundness error: 0.024 mm; Magnification: 100×. (c) Profile of cross-section of the bottom of the hole, midway between the pilot hole and the outer wall. Roundness error: 0.154 mm; Magnification: 100×.
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Summary of cutting tests and comparison to analytical predictions of stability and frequency of chatter. Feed was 0.203 mm/rev and radial depths of cut were 1.6 mm, 3.2 mm, and 4.8 mm. (a) Chatter amplitude at sensor S1 as a function of chatter frequency and spindle speed; (b) Chatter amplitude vs. speed; (c) Chatter frequency vs. spindle speed; (d) Comparison of test results (• unstable, × stable) to stability boundaries predicted from Eq. (17). Compare to Fig. 5.



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