Non-linear analysis and quench control of chatter in plunge grinding

Yao Yan, Jian Xu*, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper aims at mitigating regenerative chatter in plunge grinding. To begin with, a dynamic model is proposed to investigate grinding dynamics, where eigenvalue and bifurcation analyses are adopted, respectively, for prediction of grinding stability and chatter. Generally, it is found that most grinding chatter is incurred by subcritical Hopf bifurcation. Compared with supercritical instability, the subcritical generates coexistence of stable and unstable grinding in the stable region and increases chatter amplitude in the chatter region. To avoid these adverse effects of the subcritical instability, bifurcation control is employed, where the cubic non-linearity of the relative velocity between grinding wheel and workpiece is used as feedback. With the increase of feedback gain, the subcritical instability is transformed to be supercritical not only locally but also globally. Finally, the conditionally stable region is completely removed and the chatter amplitude is decreased. After that, to further reduce the chatter amplitude, quench control is used as well. More specifically, an external sinusoid excitation is applied on the wheel to quench the existing grinding chatter, replacing the large-amplitude chatter by a small-amplitude forced vibration. Through the method of multiple scales, the condition for quenching the chatter is obtained. (C) 2014 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)134-144
Number of pages11
JournalInternational Journal of Non-Linear Mechanics
Volume70
Early online date2 Jul 2014
DOIs
Publication statusPublished - Apr 2015

Keywords

  • regenerative chatter
  • plunge grinding
  • method of multiple scales
  • bifurcation control
  • quench control
  • doubly regenerative stability
  • time-delay
  • bifurcation-analysis
  • HOPF-bifurcation
  • multiple scales
  • milling process
  • cutting process
  • model
  • vibrations
  • tool

Cite this

Non-linear analysis and quench control of chatter in plunge grinding. / Yan, Yao; Xu, Jian; Wiercigroch, Marian.

In: International Journal of Non-Linear Mechanics, Vol. 70, 04.2015, p. 134-144.

Research output: Contribution to journalArticle

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abstract = "This paper aims at mitigating regenerative chatter in plunge grinding. To begin with, a dynamic model is proposed to investigate grinding dynamics, where eigenvalue and bifurcation analyses are adopted, respectively, for prediction of grinding stability and chatter. Generally, it is found that most grinding chatter is incurred by subcritical Hopf bifurcation. Compared with supercritical instability, the subcritical generates coexistence of stable and unstable grinding in the stable region and increases chatter amplitude in the chatter region. To avoid these adverse effects of the subcritical instability, bifurcation control is employed, where the cubic non-linearity of the relative velocity between grinding wheel and workpiece is used as feedback. With the increase of feedback gain, the subcritical instability is transformed to be supercritical not only locally but also globally. Finally, the conditionally stable region is completely removed and the chatter amplitude is decreased. After that, to further reduce the chatter amplitude, quench control is used as well. More specifically, an external sinusoid excitation is applied on the wheel to quench the existing grinding chatter, replacing the large-amplitude chatter by a small-amplitude forced vibration. Through the method of multiple scales, the condition for quenching the chatter is obtained. (C) 2014 Elsevier Ltd. All rights reserved.",
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author = "Yao Yan and Jian Xu and Marian Wiercigroch",
note = "Date of Acceptance: 24/06/2014 Acknowledgements This research is supported by the State Key Program of National Natural Science Foundation of China under Grant no. 11032009, National Natural Science Foundation of China under Grant no. 11272236 and China Scholarship Council.",
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