Chaotic Characteristics of Mirror-Finished Surface Produced by Ultra-Precision Turning

Abstract

Mirror-like surfaces obtained by the ultra-precision turning using diamond cutting tools are smooth to the eye, but rough under a microscope. Although a lot of work has been done on the roughness of the mirror-finished surface, its inhomogeneous static structure is not yet well analyzed. This has led to attempt to discuss quantitatively whether the surface texture was indeed chaotic or not. In the paper, the trajectory on the attractor reconstructed in phase space from a measured surface profile was characterized by the Lyapunov exponent and the correlation dimension. The characterization shows that the mirror-finished surface has the strange attractor, the positive Lyapunov exponent and the finite correlation dimension and hence it has the chaotic characteristics. Further, the mirror-finished surface produced by the ultra-precision turning becomes more chaotic as the feed rate and the cutting speed decrease.