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C. S. Hsu, “Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept,” Journal of Applied Mechanics, Transactions ASME, Vol. 4, No. 49, 1982, pp. 895-902. doi:10.1115/1.3162633

has been cited by the following article:

• TITLE: Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter

  AUTHORS: Fansen Kong, Peng Liu, Xiaoming Wang

  KEYWORDS: Chatter, Uncertainty, Reconstructed Attractor, Lyapunov Exponent and Kolmogorov Entropy

  JOURNAL NAME: Journal of Modern Physics, Vol.2 No.9, September 19, 2011

  ABSTRACT: The vibration acceleration time history of the cutter holder was separated into three parts; namely, chatter free, transition and chatter processes. The reconstructed attractor and probability distribution of vibration acceleration time series were studied in order to observe the system’s behavior. The Lyapunov exponent andKolmogorov entropy were used to help judge the cutting state. Meanwhile, the relation curves of the Lyapunov exponent and entropy versus machining parameters were plotted and discussed. The research shows that Lyapunov exponent and Kolmogorov entropy are toned up when vibration acceleration time his- tory goes from chatter free, transition to chatter. When cutting state transited from chatter free to chatter, the Lyapunov exponent and Kolmogorov entropy increase with increasing amplitude. In addition, the relation curves looks like stability lobes. The experimental study allow us to select optimal machining parameters for decreasing the uncertainty of cutting vibration.