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RESEARCH PAPERS

Influence of Torsional Motion on the Axial Vibrations of a Drilling Tool

[+] Author and Article Information
Sergey A. Voronov

 Bauman Moscow State Technical University, 5, 2-nd Baumanskaya, Moscow, Russia 105005voronov@rk5.bmstu.ru

Alexander M. Gouskov

 Bauman Moscow State Technical University, 5, 2-nd Baumanskaya, Moscow, Russia 105005gouskov@rk5.bmstu.ru

Alexey S. Kvashnin

 Bauman Moscow State Technical University, 5, 2-nd Baumanskaya, Moscow, Russia 105005a-kvashnin@yandex.ru

Eric A. Butcher

 University of Alaska, P.O. Box 757500, Fairbanks, AK 99775ffeab@uaf.edu

S. C. Sinha

 Auburn University, 202 Ross Hall, Auburn, AL 36849ssinha@eng.auburn.edu

J. Comput. Nonlinear Dynam 2(1), 58-64 (Sep 01, 2006) (7 pages) doi:10.1115/1.2389212 History: Received February 17, 2006; Revised September 01, 2006

The nonlinear dynamics of a tool commonly employed in deep hole drilling is analyzed. The tool is modeled as a two-degree of freedom system that vibrates in the axial and torsional directions as a result of the cutting process. The mechanical model of cutting forces is a nonlinear function of cutting tool displacement including state variables with time delay. The equations of new surface formation are constructed as a specific set. These equations naturally include the regeneration effect of oscillations while cutting, and it is possible to analyze continuous and intermittent cutting as stationary and nonstationary processes, respectively. The influence of the axial and torsional dynamics of the tool on chip formation is considered. The Poincaré maps of state variables for various sets of operating conditions are presented. The obtained results allow the prediction of conditions for stable continuous cutting and unstable regions. The time domain simulation allows determination of the chip shape most suitable for certain workpiece material and tool geometry. It is also shown that disregarding tool torsional vibrations may significantly change the chip formation process.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 4

Poincaré map of the amplitude of (a) axial vibrations; (b) chip thickness versus excitation amplitude

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Figure 5

Poincaré maps of (a) axial vibration; (b) torsional vibration versus tool axial stiffness in case of self-exited vibration

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Figure 6

Poincaré maps of uncut chip thickness η versus tool axial stiffness: 1—single-DOF system; 2—two-DOF system

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Figure 7

Variation of (a) axial displacement and (b) twisting angle versus angle of rotation β

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Figure 8

Poincaré map of (a) amplitude of axial displacement; (b) amplitude of torsional vibration; versus dimensionless cutting stiffness κ

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Figure 9

Poincaré map of chip thickness amplitude versus dimensionless cutting stiffness, κ: 1—single-DOF system; 2—two-DOF system

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Figure 10

Influence of torsional stiffness on (a) amplitude of axial displacement; (b) amplitude of torsional vibration; fax=2.7, ζ=0.02, n=6000rpm

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Figure 11

Influence of torsional stiffness on chip thickness amplitude fax=2.7, ζ=0.02, n=6000rpm

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Figure 3

Stability diagram in parameters κ versus fax

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Figure 2

Schematic model of a drill

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Figure 1

Photograph of the vibratory drilling setup: 1—vibrator; 2—tool; 3—workpiece

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