Vibration recognition for peripheral milling thin-walled workpieces using sample entropy and energy entropy
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ORIGINAL ARTICLE
Vibration recognition for peripheral milling thin-walled workpieces using sample entropy and energy entropy Lida Zhu 1 & Changfu Liu 1 & Changyu Ju 1 & Muxuan Guo 1 Received: 12 January 2020 / Accepted: 12 May 2020 / Published online: 18 June 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Due to the poor rigidity of thin-walled parts, vibration (chatter) is extremely easy to occur during the cutting process, affecting the precision, surface quality, and efficiency of part processing. The chatter in milling thin-walled workpieces becomes a more complex, nonlinear, and unstable signal as the dynamics of thin-walled workpieces change with time and position. To realize chatter detection, a method using ensemble empirical mode decomposition (EEMD) and nonlinear dimensionless indicators is proposed in this paper. Firstly, the EEMD is adopted to decompose the raw signal because it is suited for nonlinear and nonstationary signal. Subsequently, the correlation analysis is used to obtain chatter-related intrinsic mode function (IMF) components. When chatter occurs in the milling, time series complexity is changed and energy is transferred to the chatter bands. Therefore, the nonlinear sample entropy (SE) and energy entropy (EE) of IMFs can be extracted as two indicators. Then, principal component analysis (PCA) is adopted to further reduce the feature vector dimension. After that, an improved support vector machine (SVM) is developed to identify the chatter. Among them, genetic algorithm (GA) and grid explore (GE) are used to explore the best parameters of the SVM. In addition, off-line chatter prediction is employed to determine the cutting status under different machining parameters used in the experiments. At last, the cutting force signals are performed to verify the proposed method. The results show the proposed method using SE and EE can effectively detect the chatter, which provides an option for chatter detection. Keywords Chatter detection . Thin-walled workpieces . Sample entropy . Energy entropy . Improved support vector machine . Off-line chatter prediction
Nomenclature SE EE EMD EEMD IMF PCA GA GE SVM IM AI ANN
Sample entropy Energy entropy Empirical mode decomposition Ensemble empirical mode decomposition Intrinsic mode function Principal component analysis Genetic algorithm Grid explore Support vector machine Intelligent manufacturing Artificial intelligence Artificial neural network
* Lida Zhu [email protected] 1
School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China
SLD KF RBKF Ri Ei λ1, λ2 γ ρi x(t) ni(t) xi(t) xi, xj σ c g ri(t) x0, x1, x2 x, y
Stability lobe diagram Kernel function Radial basis KF Energy of IMFs EE of IMFs The SE, EE, of n IMFs The threshold for selecting the related IMFs The eigenvalues of principal components The original signal The ith white noise The new signal with noise The samples or vectors The width of KF Penalty factor Core parameter The residual at the ith trial Sinusoidal signals, sinu
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