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Intermittent and chaotic vibrations in a regenerative cutting process

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  • Litak, Grzegorz
  • Sen, Asok K.
  • Syta, Arkadiusz

Abstract

We have examined a cutting process with dry friction and contact loss effects. To model the second pass of the tool through the workpiece, we used a harmonic function representing the surface corrugations. The mathematical model consists of a single differential equation of second order. By numerically solving the governing differential equation, we obtained the time series for the cutting depth for different excitation frequencies. The time series are analyzed using the methods of recurrence plots, recurrence quantification analysis and wavelet analysis. The results show an intermittent character of the system dynamics with transition to chaotic motion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:2115-2122
    DOI: 10.1016/j.chaos.2008.08.018
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    References listed on IDEAS

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    1. Gençay, Ramazan & Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon J., 2001. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics," Elsevier Monographs, Elsevier, edition 1, number 9780122796708.
    2. Sen, Asok K. & Litak, Grzegorz & Taccani, Rodolfo & Radu, Robert, 2008. "Wavelet analysis of cycle-to-cycle pressure variations in an internal combustion engine," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 886-893.
    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. 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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    Cited by:

    1. Krese, Blaž & Govekar, Edvard, 2011. "Recurrence quantification analysis of intermittent spontaneous to forced dripping transition in laser droplet generation," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 298-305.
    2. Yang Fu & Yun Zhang & Huang Gao & Ting Mao & Huamin Zhou & Ronglei Sun & Dequn Li, 2019. "Automatic feature constructing from vibration signals for machining state monitoring," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 995-1008, March.
    3. Litak, Grzegorz & Borowiec, Marek & Hunicz, Jacek & Koszałka, Grzegorz & Niewczas, Andrzej, 2009. "Vibrations of a delivery car excited by railway track crossing," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 270-276.

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