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Vibration recognition for peripheral milling thin-walled workpieces using sample entropy and energy entropy

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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.

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Abbreviations

SE:

Sample entropy

EE:

Energy entropy

EMD:

Empirical mode decomposition

EEMD:

Ensemble empirical mode decomposition

IMF:

Intrinsic mode function

PCA:

Principal component analysis

GA:

Genetic algorithm

GE:

Grid explore

SVM:

Support vector machine

IM:

Intelligent manufacturing

AI:

Artificial intelligence

ANN:

Artificial neural network

SLD:

Stability lobe diagram

KF:

Kernel function

RBKF:

Radial basis KF

R i :

Energy of IMFs

E i :

EE of IMFs

λ1, λ2 :

The SE, EE, of n IMFs

γ :

The threshold for selecting the related IMFs

ρ i :

The eigenvalues of principal components

x(t):

The original signal

ni(t):

The ith white noise

xi(t):

The new signal with noise

xi, xj :

The samples or vectors

σ :

The width of KF

c :

Penalty factor

g :

Core parameter

ri(t):

The residual at the ith trial

x0, x1, x2 :

Sinusoidal signals, sinusoidal low frequency, discontinuity high frequency

x, y :

Two directions of machine tool

Kt, Kr :

Tangential cutting force coefficient, radial cutting force coefficient

x(1), x(2), ⋯, x(N) :

A N point time series

Xm(i):

A m dimension vector

d[Xm(i), Xm(j)]:

The distance between Xm(i) and Xm(j)

r :

Tolerance

A i :

The number of d[Xm(i), Xm(j)] ≤ r

\( {B}_i^m(r),{B}^m(r) \) :

The ratio of Ai to N − m + 1, the average of \( {B}_i^m(r) \)

SampEn(m, r):

The theoretical SE of the time series

SampEn(m, r, N):

The estimated value of the SE

u1(t), u2(t), ⋯un(t):

The frequency bands (IMFs)

T i :

The percentage that energy of IMF counts for the whole signal’s energy R

μ i :

Correlation coefficients

v i :

The contribution rate of the ith principal component

Q :

The contribution rate of the previous kth principal components

m :

The number of ensample

c ij :

The jth IMF at the ith trial (EMD)

c j :

The jth IMF by EEMD

I :

The number of IMFs of each trial

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Funding

This work was supported by the National Natural Science Foundation of China (51475087) and Fundamental Research Funds for Central Universities (N170306005 and N180305032).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Lida Zhu, Changfu Liu, Changyu Ju & Muxuan Guo

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  1. Lida Zhu
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  2. Changfu Liu
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  4. Muxuan Guo
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Correspondence to Lida Zhu.

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Zhu, L., Liu, C., Ju, C. et al. Vibration recognition for peripheral milling thin-walled workpieces using sample entropy and energy entropy. Int J Adv Manuf Technol 108, 3251–3266 (2020). https://doi.org/10.1007/s00170-020-05476-7

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