Quantitative Analysis of Geometrical Irregularity for Several Bowls

Abstract

In order to evaluate the relaxation and surface irregularity of the famous artist's bowl and other analytical objects, an analytical procedure was developed by applying the concept of fractals, a hyperbola model of the Richardson effect, and FFT analysis. The main results of this study are summarized as follows: (1) To evaluate the irregular surface of relaxation quantitatively, an analytical system using a high-resolution laser sensor was developed, and an analytical-procedure-developed mesh method was established. (2) It was found that the famous artist's bowl has a fractal nature and a relative self-similarity in wide resolution ranges. (3) The geometrical irregularity of the surface can be effectively evaluated by combining the fractal dimension D and the FFT parameters. (4) In order to apply the design of a mechanical structure in a later study, the target value of the fractal dimension was estimated as D＝2.33.