Large-amplitude vibrations in drilling often occur near multiples of the rotation frequency, even when these frequencies 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.

Original languageEnglish
Number of pages12
StatePublished - 2001
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: Sep 9 2001Sep 12 2001


Conference18th Biennial Conference on Mechanical Vibration and Noise
Country/TerritoryUnited States
CityPittsburgh, PA


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