Flank wear is a critical phenomenon which has direct impact on quality of surface finish, dimensional precision and ultimately cost of the finished product. In any metal cutting operation, cutting tool wear estimation will help in identifying tool state, which is a critical factor in productivity. In this paper, the vibration signals are used for detecting flank wear in face milling .The vibration signals are analyzed using a novel non linear technique called recurrence quantification analysis (RQA). RQA includes time delay and dimensions embedding process so as to reconstruct the time series data of vibration signal, to obtain better information of the changes in nonlinear dynamics underlying the milling process. An investigation of this technique was carried out to see its capability in detecting flank wear in face milling. Experiments were conducted on universal milling machine using AISI H11 steel as work material. The investigation proved that RQA technique has a good potential in detecting flank wear in face milling. The RQA parameters such as percent recurrence (REC), trapping time (TT), percent laminarity (LAM) and entropy (ENT), and also the recurrence plots color patterns for different flank wear, can be used in detecting insert wear in face milling.

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We propose a methodology to obtain the amplitude of a nonlinear differential equation that may not satisfy Lyapunov’s global stability criterion. This theory is applied to the MEMS resonator which has a high-quality factor. The derivative of the Lyapunov function approximated for a finite time and an optimization problem was formulated. The local optima were obtained using the Karush–Kuhn–Tucker conditions, for which the amplitude was analytically formulated. The obtained amplitude, when compared with that by the numerical method, showed the validity of the analytical approximation for a useful range of the nonlinearity, but accurate only at an excitation frequency [Formula: see text]. This methodology will be useful to approximate the damping in a system if one obtains the amplitude from the experimental data near this excitation frequency.