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Real time FFT identification based time-varying chatter frequency mitigation in thin-wall workpiece milling

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Abstract

Due to the detrimental effect on tool life, material removal efficiency, and workpiece surface equality, chatter has become a major obstacle to high-performance milling. According to the previous research, the active noise equalizer (ANE) can decrease chatter frequencies with having a little influence on normal frequencies, which satisfies the initial control requirement for optimization of actuator performance. Recent researches show that chatter frequencies are time-varying with broadband characteristic in thin-walled component milling. However, tradition studies focused on invariant line spectrum chatter frequency suppression, which cannot meet the time-varied need. To this end, in this research, the real-time fast Fourier transform (FFT) identification is introduced into ANE, which can update the reference chatter frequencies for time-varying chatter frequencies’ suppression in thin-walled workpiece milling. However, during the period between two FFT, the identified frequencies remain unchanged, which will deviate from the real chatter frequencies and disable the controller. In order to deal with this problem, the modified narrowband filtered-x least mean square (NFXLMS) is combined with the real-time FFT identification for time-varying chatter frequencies suppression. The modified NFXLMS is a narrowband active control algorithm, which can handle the small change of chatter frequencies during the period between two FFT. Simulation results show that the proposed two control algorithms can both suppress the time-varying chatter frequencies effectively. The modified NFXLMS has better control effect than ANE, but it has larger impacts every time the chatter frequencies are identified by FFT. Finally, the thin-wall workpiece milling tests are implemented. The off-line simulation based on practical experimental data is carried out that indicates that the developed algorithms work well in practice.

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Data availability

The data that support the findings of this study are available on request.

Code availability

Code can be partially shared upon request.

Abbreviations

\(D\) :

The diameter of milling tool

\({c}_{x}\), \({c}_{y}\) :

The modal damping in the x and y directions

\({f}_{t}\) :

The feed per tooth

\({F}_{x},{F}_{y}\) :

The milling force in the x and y directions

\({h}_{j}\left(z,t\right)\) :

The instantaneous uncut chip thickness

\({k}_{x},{k}_{y}\) :

The modal stiffness in the x and y directions

\({K}_{t},{K}_{n}\) :

The tangential and radial shearing force coefficients

\({K}_{te},{K}_{ne}\) :

The tangential and radial ploughing force coefficients

\({m}_{x},{m}_{y}\) :

The modal mass in the x and y directions

\(N\) :

The tooth number

\(\Omega\) :

The spindle speed

\(\phi_j\left(z,t\right)\) :

The angular position of the jth tooth at the zth axial disk

\(\phi_{st}\), \(\phi_{ex}\) :

The start and exit angles of the cutter tooth

\(\gamma\) :

The helix angle

\({x}_{a}\left(n\right), {x}_{b}\left(n\right)\) :

The reference signals defined by reference chatter frequencies

\({{\varvec{w}}}_{a}\left(n\right), {{\varvec{w}}}_{b}\left(n\right)\) :

The coefficient vector of controller

\(\beta\) :

The gain factor

\(e\left(n\right),{e}_{s}\left(n\right)\) :

The error signal

\(d\left(n\right)\) :

The primary vibration signal through primary path

\(s\left(n\right)\) :

The impulse response function between actuators and tooltip

\({\mu }_{l},{\mu }_{\omega }\) :

The convergence factor of adaptive algorithm

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Funding

This work was supported in part by the National Science Foundation of China under Grant 52105480 and 52175114, and the China Postdoctoral Science Foundation under Grant 2021M692589.

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China

    Chenxi Wang, Xingwu Zhang & Xuefeng Chen

Authors
  1. Chenxi Wang
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  2. Xingwu Zhang
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  3. Xuefeng Chen
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Correspondence to Xingwu Zhang.

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Wang, C., Zhang, X. & Chen, X. Real time FFT identification based time-varying chatter frequency mitigation in thin-wall workpiece milling. Int J Adv Manuf Technol 119, 7403–7413 (2022). https://doi.org/10.1007/s00170-022-08755-7

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  • DOI: https://doi.org/10.1007/s00170-022-08755-7

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