Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter

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 history 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.

A hybrid decision making approach to prevent chatter vibrations

“…There are a lot of studies about chatter vibrations in the recent literature. Kong and Liu [3] used the Lyapunov exponent and Kolmogrov entropy values to find the proper cutting states. An experimental study was conducted to select optimum machining parameters using these values.…”

Simulation of robust chaotic signal with given properties

“…Currently, chaotic signals are used in various fields of science and technology is in engineering and process automation [4], finance [9], geology [6], medicine, in agriculture and for the simulation of traffic in computer networks [3], and many others [11]. This shows the great importance of interdisciplinary research results in the theory of chaotic dynamics.…”