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Nonlinear dynamics of regenerative cutting processes—Comparison of two models

Author

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  • Wang, X.S.
  • Hu, J.
  • Gao, J.B.

Abstract

Understanding the nonlinear dynamics of cutting processes is essential for the improvement of machining technology. We study machine cutting processes by two different models, one has been recently introduced by Litak [Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons & Fractals 2002;13:1531–5] and the other is the classic delay differential equation model. Although chaotic solutions have been found in both models, well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Careful analysis shows that the chaotic motion from the Litak’s model has sharper spectral peaks, a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed.

Suggested Citation

  • Wang, X.S. & Hu, J. & Gao, J.B., 2006. "Nonlinear dynamics of regenerative cutting processes—Comparison of two models," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1219-1228.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:5:p:1219-1228
    DOI: 10.1016/j.chaos.2005.08.131
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    Cited by:

    1. Litak, Grzegorz & Kasperek, Rafał & Zaleski, Kazimierz, 2009. "Effect of high-frequency excitation in regenerative turning of metals and brittle materials," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2077-2082.
    2. Litak, Grzegorz & Sen, Asok K. & Syta, Arkadiusz, 2009. "Intermittent and chaotic vibrations in a regenerative cutting process," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2115-2122.
    3. Litak, Grzegorz & Syta, Arkadiusz & Wiercigroch, Marian, 2009. "Identification of chaos in a cutting process by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2095-2101.
    4. Litak, Grzegorz & Polyakov, Yuriy S. & Timashev, Serge F. & Rusinek, Rafał, 2013. "Dynamics of stainless steel turning: Analysis by flicker-noise spectroscopy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6052-6063.

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