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Identification of chaos in a cutting process by the 0–1 test

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  • Litak, Grzegorz
  • Syta, Arkadiusz
  • Wiercigroch, Marian

Abstract

We have examined the cutting process by using a two degrees of freedom non-smooth model with a friction component. Instead of the standard Lyapunov exponent treatment a statistical ‘0–1’ test based on the asymptotic properties of a non-harmonic Brownian motion chain has been successively applied to reveal the nature of the cutting process. In this test we calculated the control parameter K which is approaching asymptotically to 0 or 1 for regular and chaotic motions, respectively. The presented approach is independent on the integration procedure as we defined a characteristic distance between the points forming the time series used in the test separately.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2095-2101
    DOI: 10.1016/j.chaos.2007.09.093
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    References listed on IDEAS

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    1. Syta, Arkadiusz & Litak, Grzegorz, 2008. "Stochastic description of the deterministic Ricker’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 262-268.
    2. P. Gaspard & M. E. Briggs & M. K. Francis & J. V. Sengers & R. W. Gammon & J. R. Dorfman & R. V. Calabrese, 1998. "Experimental evidence for microscopic chaos," Nature, Nature, vol. 394(6696), pages 865-868, August.
    3. 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.
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    1. Litak, G. & Syta, A. & Budhraja, M. & Saha, L.M., 2009. "Detection of the chaotic behaviour of a bouncing ball by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1511-1517.
    2. Ding, Shun-Liang & Song, En-Zhe & Yang, Li-Ping & Litak, Grzegorz & Yao, Chong & Ma, Xiu-Zhen, 2016. "Investigation on nonlinear dynamic characteristics of combustion instability in the lean-burn premixed natural gas engine," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 99-110.
    3. Belaire-Franch, Jorge, 2020. "The finite sample behavior of the 0–1 test for chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    4. 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.

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