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Milling chatter detection of thin-walled parts based on GA-SE-SCK-VMD and RCMDE

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Abstract

In the milling process, it is easy to produce chatter due to the low rigidity of the thin-walled structure, which leads to the deterioration of workpiece surface quality and reduces the service life of cutting tools and machine tools. Therefore, a new chatter detection method for thin-walled parts based on optimal variational mode decomposition (OVMD) and refined composite multi-scale dispersion entropy (RCMDE) is proposed in this paper. Firstly, to solve the problem that the decomposition effect of the variational mode decomposition (VMD) algorithm is greatly affected by its parameter, a genetic algorithm (GA) is used to iteratively optimize the parameter of the VMD algorithm, and a new index, square envelope spectral correlated kurtosis (SE-SCK), is introduced as the fitness function of the genetic algorithm. Then, the energy ratio of the decomposed signal is calculated as the principle of selecting sub-components, and the sub-components with rich chatter information are selected for signal reconstruction. To solve the problem that the multi-scale dispersion entropy (MDE) will miss some information in the multi-scale process, RCMDE is introduced to detect milling chatter. Finally, the experiment of the variable cutting depth in side milling of titanium alloy thin-walled parts is carried out. The experimental results show that the OVMD algorithm proposed can solve the problem of difficult separation of chatter frequency bands caused by mode aliasing and lay a foundation for subsequent chatter feature extraction. RCMDE is more conducive to chatter detection than the single-scale DE when the scale factor is 4. The distinguishing effect of RCMDE on the machining state is more than 50% higher than that of MDE when the scale factor is 4.

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Availability of data and material

The datasets used or analyzed during the current study are available from the corresponding author upon reasonable request.

Code availability

Not applicable.

Abbreviations

K :

Decomposition levels in VMD algorithm

\(\alpha\) :

Penalty factor in VMD algorithm

\(\partial_{t}\) :

Shear deformation energy consumption

\(u_{k} \left( t \right)\) :

The kth modal component

\(\omega_{k}\) :

The center frequency of the kth modal component

u :

The original signal

\(\delta \left( t \right)\) :

The pulse function

\(*\) :

The convolution operator

\(\lambda\) :

Lagrange multiplier

\(u_{k}^{n + 1}\) :

The n + 1 iteration of the kth modal component

\(\omega_{k}^{n + 1}\) :

The n + 1 iteration of the central frequency of the kth modal component

\(\lambda^{n + 1}\) :

The n + 1 iteration of Lagrange multiplier

\(\tau\) :

Scale factor in RCMDE

\(\overline{p} \left( {r_{{v_{0} v_{1} \cdots v_{m - 1} }} } \right)\) :

The average value of the probability of the dispersion mode corresponding to the coarse-grained sequence

\(p_{k}^{\left( \tau \right)}\) :

The probability of the dispersion model corresponding to the kth coarsening sequence under scale

\(\widetilde{X}\) :

The zero mean filtered signal

N :

The length of signal

\(r_{{\widetilde{X}}} \left( 0 \right)\) :

The value of the autocorrelation function

\(SE\left( {\widetilde{X}} \right)\) :

The square envelope signal

\(r_{SE} \left( 0 \right)\) :

The value of the autocorrelation function of the square envelope signal

\(f_{s}\) :

The sampling frequency

\(f_{r}\) :

The spindle rotation frequency

\(SES\left( f \right)\) :

The square envelope spectrum

f :

The spindle rotation frequency

\(\iota\) :

Delay in RCMDE

m :

Embedding dimension in RCMDE

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Funding

This research was funded by Projects of International Cooperation and Exchanges NSFC (Grant Number 51720105009).

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin, 150080, China

    Xianli Liu, Hanbin Wang, Maoyue Li, Zhixue Wang & Boyang Meng

Authors
  1. Xianli Liu
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  2. Hanbin Wang
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  3. Maoyue Li
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  4. Zhixue Wang
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  5. Boyang Meng
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Contributions

Xianli Liu, Hanbin Wang, and Maoyue Li contributed to the conception of the study; Hanbin Wang studied the recognition of the machining state in the machining process of the thin-walled parts. Zhixue Wang contributed to the experimental verification. Boyang Meng helped perform the analysis with constructive discussions.

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Correspondence to Xianli Liu.

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Liu, X., Wang, H., Li, M. et al. Milling chatter detection of thin-walled parts based on GA-SE-SCK-VMD and RCMDE. Int J Adv Manuf Technol 124, 945–958 (2023). https://doi.org/10.1007/s00170-022-10235-x

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