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.
Highlights
Machine tool chatter is the self-excited relative oscillation between the cutting tool and the workpiece developed under large metal removal rates
The research shows that Lyapunov exponent and Kolmogorov entropy are toned up when vibration acceleration time history goes from chatter free, transition to chatter
We find the curves of the Lyapunov exponent and Kolmogorov entropy against spindle speed have the same trend as shown in Figures 9 and 10, which, means we can use one of them to discuss the uncertainty of cutting vibration system
Summary
Machine tool chatter is the self-excited relative oscillation between the cutting tool and the workpiece developed under large metal removal rates. It deteriorates the workpiece surface, reduces tool and machine life, and may create dangerous accidents. Merritt [3] presented an elegant stability theory for orthogonal turning using system theory terminology His formulation was latter adopted by many investigators and led to major advances towards the understanding and prediction of the chatter phenomenon. Hanna [4], Shi and Tobias [5], Tlusty [6] and others carried out theoretical and experimental researches on cutting chatter, explained the mechanism of stabilization of chatter amplitudes and the phenomenon of finite amplitude instability, and presented a non-linear theory of machine tool chatter. The dynamic trait of the vibration acceleration time series evolution was studied in detail based on experiments during the transition from chatter free to chatter
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