Hyperchaotic qualities of the ball motion in a ball milling device

Ball collisions in milling devices are governed by complex dynamics ruled b y impredictable impulsive forces. In this paper, nonlinear dynamics techniq ues are employed to analyze the time series describing the trajectory of a milling ball in an empty container obtained from a numerical model. The att ractor underlying the system dynamics was reconstructed by the time delay m ethod. In order to characterize the system dynamics the calculation of the spectrum of Lyapunov exponents was performed. Six Lyapunov exponents, divid ed into two terns with opposite sign, were obtained. The detection of the p ositive tern demonstrates the occurrence of the hyperchaotic qualities of t he ball motion. A fractal Lyapunov dimension, equal to 5.62, was also obtai ned confirming the strange features of the attractor. (C) 1999 American Ins titute of Physics. [S1054-1500(99)00101-9].