Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling
Author:
Bayly Philip V.1, Lamar Michael T.1, Calvert Sean G.1
Affiliation:
1. Mechanical Engineering, Box 1185, Washington University, 1 Brookings Drive, St. Louis, MO 63130
Abstract
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.
Publisher
ASME International
Subject
Industrial and Manufacturing Engineering,Computer Science Applications,Mechanical Engineering,Control and Systems Engineering
Reference33 articles.
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