Chatter detection is crucial for both micro- and macro-milling, as chatter can cause detrimental damage on machining process and machined surface. Compared to macro-milling, micro-milling is more susceptible to external non-Gaussian noise interference, making it extremely difficult to extract chatter features and identify chatter modes at the micrometer scale due to the lower chatter component which is usually drowned out by noise. In this paper, an adaptive iterative reduction algorithm and a chatter quantification index: Rényi entanglement entropy, are proposed. With the physical significance of Rényi entanglement entropy elucidated, the application of Rényi entanglement entropy has been successfully expanded from the microscopic quantum entanglement field to the macroscopic nonlinear milling systems by redefining the state probability vector, probability and probability density matrix. Firstly, the adaptive iterative signal-to-noise separation algorithm is designed to increase the sensitivity of quantification indicator to chatter features. Then, to apply Rényi entanglement entropy to nonlinear micro- and macro-milling systems, the milling system is regarded as a mixed state without prior information, and the method considering causality for calculating state probability vectors and probability density matrices are presented. Finally, the relevance relation among subsystems is analyzed, and the physical significance of Rényi entanglement entropy in micro- and macro-milling systems is discussed. In addition, the relationships between parameter τ and chatter identification, feature space are analyzed. The research results demonstrate that the proposed Rényi entanglement entropy algorithm is effective in identification of multiple quasi-periodic chatter modes and can quantify the degree of cross-correlation among several subsystems in macroscopic nonlinear milling systems.

中文翻译：

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非线性微观/宏观铣削颤振识别中 Rényi 纠缠熵的研究


颤振检测对于微铣削和宏观铣削都至关重要，因为颤振会对加工过程和加工表面造成有害损害。与宏观铣削相比，微铣削更容易受到外部非高斯噪声干扰，由于较低的颤振分量通常被噪声淹没，因此在微米尺度上极难提取颤振特征和识别颤振模式。在本文中，提出了一种自适应迭代归约算法和一种喋喋不休量化指数：Rényi 纠缠熵。随着 Rényi 纠缠熵的物理意义的阐明，通过重新定义状态概率向量、概率和概率密度矩阵，Rényi 纠缠熵的应用成功地从微观量子纠缠场扩展到宏观非线性铣削系统。首先，设计自适应迭代信噪分离算法，提高量化指标对振颤特征的敏感性;然后，将 Rényi 纠缠熵应用于非线性微观和宏观铣削系统，将铣削系统视为无先验信息的混合状态，并提出了考虑因果关系计算状态概率向量和概率密度矩阵的方法。最后，分析了子系统之间的相关性，并讨论了 Rényi 纠缠熵在微观和宏观铣削系统中的物理意义。此外，分析了参数 τ 与颤振识别、特征空间之间的关系。 研究结果表明，所提出的 Rényi 纠缠熵算法可以有效地识别多个准周期颤振模式，并且可以量化宏观非线性铣削系统中多个子系统之间的互相关程度。