Nonlinear dynamic analysis of flexible workpiece and tool in turning operation with delay and internal resonance

In this work, the nonlinear dynamics of the tool and the thin cylindrical workpiece are studied simultaneously for turning operation. To capture the flexibility of thin workpiece, structural nonlinearity is taken into consideration. Regenerative chatter effect in turning operation is considered in terms of effective chip thickness which is driven by relative motion of the tool and the workpiece during the present cut and the earlier cut. Higher order method of multiple scales (MMS) is used to study the nonlinear responses and stability of tool and workpiece for both internal resonance and primary resonance conditions. The critical values of the cutting parameters like spindle speed, chip width (or depth of cut), cutting force coefficient, workpiece to tool stiffness ratio, and workpiece diameter to thickness ratio etc. are estimated using both time and frequency response curves to have stable chatter free turning operation. The effects of stiffness nonlinearities on the workpiece and the tool responses are also investigated.