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The present paper proposes an analytical stability model of regenerative chatter in orthogonal turning operations. Tool geometry is initially developed as a solid model and analysed at different tool overhang conditions. In each case, stiffness, fundamental bending mode, and corresponding damping ratios of the tool are evaluated. With these data, the cutting tool can be represented with a lumped-parameter, single-degree-of-freedom vibration oscillator. Workpiece dynamics, on the other hand, is considered independently using a discrete finite element beam model. At some contact node of the workpiece, tool mass imposes a regenerative cutting force and second-order dynamic delay differential equations are formulated in terms of tool and modal parameters. The stability criterion is formulated from a characteristic equation. The effects of tool overhang and workpiece cross-section on stability using the proposed model are reported. Experimental analysis is carried out to show the effect of tool overhang on cutting dynamics.

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