A Legendre wavelet–based stability prediction method for high-speed milling processes

Abstract

Induced by the regeneration mechanism, chatter vibration that has adverse effects on surface finish and productivity could occur in most cutting processes. Therefore, accurately predicting chatter and taking timely suppression measures are desperately needed. This work develops a semi-analytical Legendre wavelet–based stability prediction method in high-speed milling, of which dynamics model is commonly modeled by time-periodic delay differential equations. To begin with, the milling dynamics model is transformed into state equation. Based on analysis of the vibration modes for milling dynamic system, the period for coefficient matrix could be divided into two subintervals. Thereafter, variable transformation is introduced to convert the forced vibration interval into the standard definition interval of Legendre wavelets, which can be discretized non-uniformly into the Chebyshev–Gauss–Lobatto sampling points. On this basis, finite series Legendre wavelets are utilized to accurately approximate the state term, while the derivative of state term can be obtained simultaneously via a new Legendre wavelet operational matrix. By employing the Kronecker product and Floquet theory, the transition matrix is eventually acquired for semi-analytically predicting stability. The superiority and versatility for the presented approach are validated through comparisons with existing algorithms. The results demonstrate that it obtains high accuracy, calculation speed, and applicability.

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Funding

This work was partially supported by the Natural Science Foundation of China (NSFC) (Grant No. 51935007) anfd the China Postdoctoral Science Foundation (Grant No. 2019M661496).

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Correspondence to Chengjin Qin or Jianfeng Tao.

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Qin, C., Tao, J., Shi, H. et al. A Legendre wavelet–based stability prediction method for high-speed milling processes. Int J Adv Manuf Technol 108, 2397–2408 (2020). https://doi.org/10.1007/s00170-020-05423-6

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Keywords

  • Milling operations
  • Dynamics model
  • Time-periodic delay differential equations
  • Legendre wavelet–based method
  • Stability prediction