Delayed dynamical sytem strongly coupled to a nonlinear energy sink : application to machining chatter

Gourc, Etienne; Seguy, Sébastien; Michon, Guilhem; Berlioz, Alain

doi:10.1051/matecconf/20120105002

Cited by 6 publications

(7 citation statements)

References 12 publications

(14 reference statements)

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“…Here, v and w are the physical quantities for the center of mass (with a factor of 1 þ e) and the relative displacement, respectively. Then, the equations of motion (22) become…”

Section: Analytical Study: Basins Of Attraction For Suppression Mechamentioning

confidence: 99%

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Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

Nankali

Lee

Kalmár‐Nagy

2016

Journal of Computational and Nonlinear Dynamics

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We study the dynamics of targeted energy transfers in suppressing chatter instability in a single-degree-of-freedom (SDOF) machine tool system. The nonlinear regenerative (time-delayed) cutting force is a main source of machine tool vibrations (chatter). We introduce an ungrounded nonlinear energy sink (NES) coupled to the tool, by which energy transfers from the tool to the NES and efficient dissipation can be realized during chatter. Studying variations of a transition curve with respect to the NES parameters, we analytically show that the location of the Hopf bifurcation point is influenced only by the NES mass and damping coefficient. We demonstrate that application of a well-designed NES renders the subcritical limit cycle oscillations (LCOs) into supercritical ones, followed by Neimark-Sacker and saddle-node bifurcations, which help to increase the stability margin in machining. Numerical and asymptotic bifurcation analyses are performed and three suppression mechanisms are identified. The asymptotic stability analysis is performed to study the domains of attraction for these suppression mechanisms which exhibit good agreement with the bifurcations sets obtained from the numerical continuation methods. The results will help to design nonlinear energy sinks for passive control of regenerative instabilities in machining.

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“…Here, v and w are the physical quantities for the center of mass (with a factor of 1 þ e) and the relative displacement, respectively. Then, the equations of motion (22) become…”

Section: Analytical Study: Basins Of Attraction For Suppression Mechamentioning

confidence: 99%

“…They derived the equation of the slow invariant manifold (SIM) and explained the behavior of the system by studying the location of the fixed points of the slow flow on this manifold. Moreover, Gourc et al [22] have studied the passive control of chatter instability in turning processes using a vibro-impact nonlinear energy sink.…”

Section: Introductionmentioning

confidence: 99%

Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

Nankali

Lee

Kalmár‐Nagy

2016

Journal of Computational and Nonlinear Dynamics

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“…The behavior of an embedded NES on a lathe cutting tool has been previously studied in [12], it was shown that passive control of chatter by using a NES is possible and good correspondence between analytical prediction and numerical integration was observed. However, only a linear cutting law was considered.…”

Section: Analysis Of Some Response Regimesmentioning

confidence: 96%

“…The idea of attaching a nonlinear oscillator to a lathe is relatively new [11,12]. In recent studies, it has been demonstrated that addition of a small mass attachment with a strong nonlinear coupling (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Chatter Control in Turning Process with a Nonlinear Energy Sink

Gourc

Seguy

Michon

et al. 2013

AMR

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This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.

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Quenching chatter instability in turning process with a vibro-impact nonlinear energy sink

Gourc

Seguy

Michon

et al. 2015

Journal of Sound and Vibration

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a b s t r a c tThis paper investigates the passive control of chatter instability in turning processes using a vibro-impact nonlinear energy sink (NES). The workpiece is assumed to be rigid and the tool is flexible. A dynamical model including a nonlinear cutting law is presented and the stability lobes diagram is obtained. The behavior of the system with the vibro-impact NES is investigated using an asymptotic analysis. A control mechanism by successive beating is revealed, similarly to the strongly modulated response in the case of NES with cubic stiffness. It is shown that such a response regime may be beneficial for chatter mitigation. An original experimental procedure is proposed to verify the sizing of the vibro-impact NES. An experimental setup is developed with a vibro-impact NES embedded on the lathe tool and the results are analyzed and validated.

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Delayed dynamical sytem strongly coupled to a nonlinear energy sink : application to machining chatter

Cited by 6 publications

References 12 publications

Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

Chatter Control in Turning Process with a Nonlinear Energy Sink

Quenching chatter instability in turning process with a vibro-impact nonlinear energy sink

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