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Identification of chaos in a cutting process by the 0–1 test |
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| Authors: | Grzegorz Litak Arkadiusz Syta Marian Wiercigroch |
| Institution: | aDepartment of Applied Mechanics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, Poland;bInstitute of Physics, Technical University of Chemnitz, Reichenhainer Street 70, 09126 Chemnitz, Germany;cCentre for Applied Dynamics Research, Department of Engineering, Fraser Noble Building, King’s College, University of Aberdeen, Aberdeen, AB24 3UE Scotland, UK |
| 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. |
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