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

Abstract

The mechanism of torsional chatter in drilling differs qualitatively and quantitatively from other types of chatter. In this paper we show that torsional chatter can be explained by the torsional-axial coupling inherent in a twisted beam; the beam “untwists” and extends in response to an increase in cutting torque. Based on a model of this mechanism, predictions of stability boundaries and chatter frequencies are derived by frequency domain analysis, and confirmed by numerical simulation and experimental tests. The effect of the torsional-axial coupling is opposite that of traditional cutting in that an increase in cutting forces leads to axial extension and greater chip load. Because of this sign difference, the limiting depth of cut is governed by the positive real part of the frequency response function, which explains the unexpected fact that torsional chatter occurs below the natural frequency of the tool.

Investigations of Nonlinear Forces in Metal Cutting

“…The forces drop before the tool tip encounters the next minimum of the chip thickness, in reaction to the shearplane snapping down to meet the minimum, which causes the chip to narrow down and offer less resistance. This phase lead of the force over the chip thickness has been observed in experiments carried out in Dr. Philip Bayly's lab at Washington University (for representative publications from Dr. Bayly's group see [2,3,4]). A tube cutting experiment with a vibrating tool was set up on a lathe, creating an essentially single degree of freedom system with one dominant mode.…”