Application of the Wigner distribution to monitoring cutting tool condition
This thesis is about the application of the Wigner distribution to cutting tool monitoring and control. After reviewing traditional methods, a new method is proposed. This is to regard the surface texture and geometric error of form of a machined workpiece as the fingerprint of a cutting process, to analyse it, and to extract cutting tool vibration information from it, which can then be used for cutting tool monitoring. In order to analyse the surface texture effectively, three analysing tools, i.e. the Fourier transform, the ambiguity function, the Wigner distribution (WD), are examined and compared with each other, and it is concluded that the WD is best able to analyse both stationary and nonstationary signals. Furthermore, computer simulation of both chirp signals and frequency modulated signals is then carried out, and it is shown that the WD can be used to extract useful parameters successively. In order to demonstrate the suitability of the WD for machine tool condi- tion monitoring, first cutting tool vibration are measured directly by two linear variable differential transformers mounted on the cutting tool, and then these measured data about vibration are used to verify those parameters extracted from the surface of the machined workpiece by the WD. It is found that • the extracted frequencies in both horizontal and vertical direction are within 10% of those measured, • the extracted amplitudes in both horizontal and vertical direction are highly correlated with those measured. This result confirms the feasibility of this technique. In spite of being an off-line process, this technique is simple, reliable, and can reveal the direct effect of cutting processes.