Time-series analysis of behavior of a two-link nozzle in a dishwasher

Abstract

The two-link nozzle in the dishwasher-dryer is composed of two links which rotate by the water flow. Although the behavior of the two-link nozzle is related closely to the washing performance of the dishwasher, its behavior is complex. In this sense, in order to improve the washing performance of the dishwasher, it is necessary to analyze the behavior of the two-link nozzle and to clarify the washing mechanism. This study aims at providing the basis for the analysis of the behavior of the two-link nozzle. The motion of the nozzle is detected by image processing, and the behavior of the nozzle is analyzed based on the derived time-series from the viewpoint of the deterministic chaos. The result is reported. The following calculations are made as the data analysis: (1) analysis of the Poincaré section and the circle map, based on the attractor reconstructed from the time-series; (2) calculation of the maximum Lyapunov exponent; and (3) calculation of the fractal dimension. As the result of analysis, the fractal dimension of approximately 2.4 as well as the positive maximum Lyapunov exponent are obtained from the time-series data detected by the image processing. The noninvertible structure is observed in the circle map. Those results suggest that the behavior of the two-link nozzle is related closely to the deterministic chaos.