Large-amplitude vibrations in drilling often occur at frequencies near multiples of the rotation frequency, even when these are much lower than the system’s first natural frequency. These vibrations are responsible for out-of-round, “lobed” holes. A simplified model of the mechanics of this phenomenon is presented in this paper. The model includes cutting and “rubbing” forces on the drill, but inertia and damping of the tool are neglected at low speeds. This quasi-static model remains dynamic because of the regenerative nature of cutting; the force on each cutting element depends on both the tool’s current position and its position at the time of the previous tooth passage. Characteristic solutions, including unstable retrograde “whirling” modes, are found in terms of eigenvalues and eigenvectors of a discrete state-transition matrix. These unstable modes correspond closely to behavior observed in drilling tests.
Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling
Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received December 2000; Revised July 2001. Associate Editor: Y. Altintas.
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Bayly, P. V., Lamar, M. T., and Calvert, S. G. (April 29, 2002). "Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling ." ASME. J. Manuf. Sci. Eng. May 2002; 124(2): 275–285. https://doi.org/10.1115/1.1459087
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