Chatter, the vibration between the workpiece and cutting tool, is a common phenomenon during the milling process. Traditionally, the Fourier transform analysis is mainly used to extract the features and determine whether chatter occurs. In this paper, an innovative and practical chatter identification method combining fractional order chaotic system and extension theory is proposed. A lathe spindle with embedded sensors is used in this study. The boundary of chattering state of the lathe spindle is decided by the center of gravity of phase plane of dynamic errors. The boundaries are then fed into extension model and relational function calculation is performed. In this way, chatter identification can be easily achieved based on the position of the chaotic center of gravity. The three chaotic systems, i.e. Lorenz, Chen-Lee, and Sprott, of different fractional orders are used and their results are compared. Compared with the traditional methods, the Fourier transform is time-consuming in terms of mathematical operations and adverse to the establishment of a real-time system. This paper uses the characteristics of the chaotic systems sensitive to input signals in order to more capably detect the boundary state from normal cutting to chattering cutting and more efficiently identify the chatter. The experiment results indicate that the Chen-Lee system (93.5%) exhibits have better chatter diagnosis rate than Lorenz (92.75%) and Sprott (69%) systems. The Chen-Lee system even reaches a diagnosis rate of 100% for orders 0.5 ∼ 0.7. Therefore, the method presented in this paper has a very high diagnosis rate and is thus very effective for chatter identification of machine tools. INDEX TERMS Fraction-order chaotic system, chatter, spindle, machine tool.

Machining refers to a variety of processes, in which a cutting tool is used to remove the unwanted material from a workpiece. Tool wear, advertently or inadvertently, occurs after long-time use. It is crucial to monitor the tool wear so that the cutting tool can deliver the best performance and meet the technological challenges nowadays. In this paper, through different fractional-order chaotic systems, i.e., Chen-Lee, Lorenz, and Sprott, extension theory is proposed to predict the tool life. The results of the three chaotic systems are compared. The centroid of the 2-D plane of dynamic errors is used as the characteristics. Four wear states are defined in accordance with different levels of surface roughness, i.e., normal, slight, moderate, and severe. The boundaries of the four states are identified according to the locations of the centroid generated with the systems of different fraction orders. The boundaries are then fed into the extension model, and the relational function calculation is performed. In this way, the identification of tool state can be easily achieved. The experiment results indicate that Chen-Lee system and the Lorenz systems exhibit the same diagnosis rate (97.375%), higher than that of the Sprott system (35.75%). It is demonstrated that the two chaotic systems are fit for use with the method proposed in this paper. It is also proven that Chen-Lee and Lorenz fractional-order master-slave chaotic systems are very effective for tool life monitoring. The robustness of diagnosis is also greatly improved. INDEX TERMS Fractional order chaotic system, cutting, wear, machine tool.