Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics

Xie, Lihan; Baguet, Sébastien; Prabel, Benoit; Dufour, Régis

doi:10.1115/1.4032182

Cited by 12 publications

(7 citation statements)

References 25 publications

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“…The gravity does not lead to stable motion and the rotor is more able to develop 15 a forward whirl motion, as explained by Wilkes et al [8]. The forward whirl motion is frequency-limited and this is consistent with many of the previous studies concerning the rotor-stator interaction, see references [9, 10,11,12,13].…”

Section: Introductionsupporting

confidence: 79%

Touchdown bearing models for rotor-AMB systems

Jarroux

Dufour

Mahfoud

et al. 2019

Journal of Sound and Vibration

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This paper investigates numerically and experimentally the rotor drop dynamics when unexpected Active Magnetic Bearings (AMBs) shut down occurs.In such an event, the rotor behaviour drops on two touchdown bearings (TDBs) composed of a ball bearing and a ribbon damper providing stiffness and damping to the overall system. The aim of this paper is to establish and to validate the rotor-drop system model. A first experimental set up is used to identify the dynamic characteristics of the corrugated ribbon damper and to test the Kelvin-Voigt model and the generalized Dahl model. Then, three TDB models are proposed including either the first or the second ribbon damper models. The second experimental set-up is devoted to the rotor drop response of an industrial scale rotor-AMB system equipped with two TDBs. Rotor drop simulations in the time domain are carried out by using the Finite Element method and the three TDB models. Predicted and measured rotor drop responses are compared regarding the displacements as well as transmitted loads and permits evaluating the model efficiency.

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Section: Introductionsupporting

confidence: 79%

Touchdown bearing models for rotor-AMB systems

Jarroux

Dufour

Mahfoud

et al. 2019

Journal of Sound and Vibration

Self Cite

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“…With an augmented system supporting the degeneracy, the robustness of the continuation of extremum points is improved. Moreover, this system has the same structure as the standard extended system used to characterize LP bifurcations [32].…”

Section: Extremum Pointmentioning

confidence: 99%

“…By applying the HBM to the differential Eq. (14) as detailled in [32], the following nonlinear algebraic system of size L = n(2H + 1) in the frequency domain is obtained:…”

Section: Nltva Modelmentioning

confidence: 99%

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A multi-parametric recursive continuation method for nonlinear dynamical systems

Grenat

Baguet

Lamarque

et al. 2019

Mechanical Systems and Signal Processing

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The aim of this paper is to provide an efficient multi-parametric recursive continuation method of specific solution points of a nonlinear dynamical system such as bifurcation points. The proposed method explores the topology of specific points found on the frequency response curves by tracking extremum points in the successive codimensions of the problem with respect to multiple system parameters. To do so, the characterization of extremum points by a constraint equation and its associated extended system are presented. As a result, a recursive algorithm is generated by successively appending new constraint equations to the extended system at each new level of continuation. Then, the methodology is applied to a nonlinear tuned vibration absorber (NLTVA). The limit of existence of isolated solutions and extremum points optimizing the region without isolated solution are found and used to improve the NLTVA.

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“…In this paper, we combine HBM and standard extended systems. We already used this approach in [48] in the case of limit points. Here, this work is extended to all types of codimension-1 bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems

Xie

Baguet

Prabel

et al. 2017

Mechanical Systems and Signal Processing

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The aim of this paper is to provide an efficient frequency-domain method for bifurcation analysis of nonlinear dynamical systems. The proposed method consists in directly tracking the bifurcation points when a system parameter such as the excitation or nonlinearity level is varied. To this end, a so-called extended system comprising the equation of motion and an additional equation characterizing the bifurcation of interest is solved by means of the Harmonic Balance Method coupled with an arc-length continuation technique. In particular, an original extended system for the detection and tracking of Neimark-Sacker (secondary Hopf) bifurcations is introduced. By applying the methodology to a nonlinear energy sink and to a rotor-stator rubbing system, it is shown that the bifurcation tracking can be used to efficiently compute the boundaries of stability and/or dynamical regimes, i.e., safe operating zones.

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Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics

Cited by 12 publications

References 25 publications

Touchdown bearing models for rotor-AMB systems

Touchdown bearing models for rotor-AMB systems

A multi-parametric recursive continuation method for nonlinear dynamical systems

Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems

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