Nonlinear dynamics of a regenerative cutting process

Litak, Grzegorz; Schubert, Sven; Radons, Günter

doi:10.1007/s11071-012-0344-z

Cited by 44 publications

(30 citation statements)

References 36 publications

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“…On the other hand, in the chaotic ( fig. 9(c)) case we observe a monotonic substantial increase of the CMSE values with decreasing r which is typical for a chaotic response [17,30]. The slightly decreasing trend of CMSE against the scale factor r indicates long range correlated noise [33] which could be interpreted as an effect of chaotic behaviour.…”

Section: Composite Multiscale Entropy Analysismentioning

confidence: 58%

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Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

et al. 2016

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Abstract. The use of bistable laminates is a potential approach to realize broadband piezoelectric-based energy harvesting by introducing elastic non-linearities to the system. In this paper the dynamic response of a piezoelectric material attached to a bistable laminate beam is examined based on the experimental measurement of the generated voltage-time series. The system was subjected to harmonic excitations and exhibited single-well and snap-through vibrations of both periodic and chaotic character. The ability to identify the vibration modes of the energy harvester is important since different levels of power are expected in each dynamic mode. We identify the dynamics of the selected system response using return maps, multiscale entropy, and "0-1" test. The potential of the approaches to identify periodic and chaotic modes and snap-through events in the non-linear bistable harvester is described.

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Section: Composite Multiscale Entropy Analysismentioning

confidence: 58%

“…To improve our understanding of the behaviour of complex systems that manifest themselves in non-linear behaviour, sample entropy analysis is becoming increasingly popular [17,29,30]. This method provides, for measured signals, a relative level of complexity for finite length time series.…”

Section: Composite Multiscale Entropy Analysismentioning

confidence: 99%

Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

et al. 2016

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“…However, the Lyapunov exponent can be difficult to estimate in any non-smooth simulated system or measured data [32]. Therefore the 0-1 test can provide a suitable algorithm to identify the chaotic solution [33,[36][37][38].…”

Section: The 0-1 Testmentioning

confidence: 99%

“…The disadvantage of the test, its strong dependence on the chosen parameter c, can be overcome by a proposed modification. Gottwald and Melbourne [34,36,37] suggested randomly chosen values of c are taken and the median of the corresponding K c -values are computed.…”

Section: The 0-1 Testmentioning

confidence: 99%

Regular and chaotic vibration in a piezoelectric energy harvester

2015

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We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0-1 test. The appearance of chaotic vibrations reduces the level of harvested energy.

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“…Moradi et al [22] investigated the occurrence of various types of bifurcation in milling process with tool-wear and process damping effects. Litak et al [23] examined the regenerative cutting process by using a single-degree-offreedom nonsmooth model with a friction component and a time delay term. Elias and Namboothiri [24] put forward a cross-recurrence plot methodology to recognize the transition from regular cutting to the chatter cutting.…”

Section: Introductionmentioning

confidence: 99%

Suppression of Hopf bifurcation in metal cutting by extrusion machining

et al. 2016

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Hopf bifurcation is a common phenomenon during the metal cutting process, which results in poor surface finish of the workpiece and inhomogeneous grain structure in materials. Therefore, understanding and controlling Hopf bifurcation in metal cutting are necessary. In this work, the systematic low-speed extrusion machining experiments were conducted to suppress Hopf bifurcation phenomenon. It is found that the suppression of Hopf bifurcation is achieved with the increasing constraint extrusion degree. In order to reveal the mechanism of the suppression of Hopf bifurcation, a new nonlinear dynamic model for extrusion machining is developed where the convection, the diffusion, the extrusion of constraint, the thermal-softening deformation and the fracture-type damage are included. the present theoretical model is effective to characterize the suppression of Hopf bifurcation in metal cutting. Based on the numerical calculation of the theoretical model, the mechanisms underlying in extrusion machining are further revealed: Fracture-type deformation is more important than the thermal-softeningtype deformation in low-speed extrusion machining; however, the thermal-softening-type deformation is the primary deformation mode for high-speed extrusion machining.

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Nonlinear dynamics of a regenerative cutting process

Cited by 44 publications

References 36 publications

Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

Dynamics of a vibrational energy harvester with a bistable beam: voltage response identification by multiscale entropy and “0-1” test

Regular and chaotic vibration in a piezoelectric energy harvester

Suppression of Hopf bifurcation in metal cutting by extrusion machining

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