ANALYSIS OF SURFACE FINISHED BY ULTRA-PRECISION DIAMOND CUTTING BASED ON THEORY OF COMPLEX SYSTES

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The surface profiles obtained by an ultra-precision cutting were analyzed based on theory of the complex systems. The mirror surface profiles consists of the theoretical profile defined by feed and nose radius of the tool and the irregular profile generated by random factors such as the step of grain boundary, the dislocation and so on. In order to separate the profiles by the individual factors from the surface profile and understand the characteristics, we applied the technique of the wavelet transform and the theory of the chaos. Through the investigation of the validity, the following remarks were obtained.1. The average of the wavelet coefficients was suggested as a new parameter for the characterization of the ultra-precision cut surface. The validity of the method to evaluated the surface profile by applying the wavelet transform.2. The wavelet-transformed profiles were analyzed based on the theory of the complex systems. It was found that several profiles had the chaotic characteristics by analyzing the pattern of attractor reconstructed in three-dimensional phase space and Lyapunov exponents. The wavelet components from level -1 to level -8 have the chaotic characteristics. Particularly, the profiles of level -4 and -5 presented the strong chaotic characteristics from point of view of Lyapunov spectrum.3. It was identified that the profiles of the ultra-precision cut surface consisted of three fluctuating components of periodic, random and chaotic ones. It is expected that an unknown characteristics of cut surface can be understood by analyzed the individual wavelet profiles.