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Non-linear oscillations of milling

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  • B. Balachandran
  • D. Gilsinn

Abstract

The principal features of two mathematical models that can be used to study non-linear oscillations of a workpiece - tool system during a milling operation are presented and explained in this article. These models are non-linear, non-homogeneous, delay-differential systems with time-periodic coefficients. In the treatment presented here, the sources of non-linearities are the multiple regenerative effect and the loss-of-contact effect. The time-delay effect is taken into account, and the dependence of this delay effect on the feed rate is modelled. A variable time delay is introduced to capture the influence of the feed-rate in one of the models. Two formulations that can be used to carry out stability analysis of periodic solutions are presented. The models presented and the stability-analysis formulations are relevant for predicting and understanding chatter in milling.

Suggested Citation

  • B. Balachandran & D. Gilsinn, 2005. "Non-linear oscillations of milling," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 11(3), pages 273-290, September.
    • Handle: RePEc:taf:nmcmxx:v:11:y:2005:i:3:p:273-290
    DOI: 10.1080/13873950500076479
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    Cited by:

    1. Chinh Ngo & Jeehyun Jung & Chuong Nguyen & Jongwon Seok, 2017. "An accurate regenerative chatter model in the ball-end milling process that considers high feed rate and shallow axial immersion conditions," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 23(5), pages 453-475, September.

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