Hyperchaotic qualities of the ball motion in a ball milling device

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Abstract
Ball collisions in milling devices are governed by complex dynamics ruled by impredictable impulsive forces. In this paper, nonlinear dynamics techniques are employed to analyze the time series describing the trajectory of a milling ball in an empty container obtained from a numerical model. The attractor underlying the system dynamics was reconstructed by the time delay method. In order to characterize the system dynamics the calculation of the spectrum of Lyapunov exponents was performed. Six Lyapunov exponents, divided into two terns with opposite sign, were obtained. The detection of the positive tern demonstrates the occurrence of the hyperchaotic qualities of the ball motion. A fractal Lyapunov dimension, equal to 5.62, was also obtained confirming the strange features of the attractor.