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Abstract

A complex machining model describing the coupled tool—workpiece dynamics subject to nonlinear regenerative cutting forces, instantaneous depth-of-cut and workpiece whirling due to material imbalance is presented. The workpiece is modeled as a system of three rotors, namely, unmachined, being machined and machined, connected by a flexible shaft, thus enabling the motion of the workpiece relative to the tool and tool motion relative to the machining surface to be three-dimensionally established as functions of spindle speed, depth-of-cut, rate of material removal and whirling. A rich set of nonlinear behaviors of both the tool and workpiece including period-doubling bifurcation and chaos signifying the extent of machining instability at various depth-of-cuts is observed. Results presented herein agree favorably with physical experiments reported in the literature. It is found that, at and up to certain ranges of depth-of-cuts, whirling is non-negligible if the fundamental characteristics of machining dynamics are to be fully understood. Additionally, contrary to one's intuition, whirling is found to have insignificant impact on tool motions.

Keywords

Machining model coupled tool—workpiece dynamics nonlinear regenerative cutting forces instantaneous depth-of-cut workpiece whirling

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Machining Dynamics Involving Whirling Part I: Model Development and Validation

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