Threshold stability curves for a nonlinear rotor-bearing system

Smolík, Luboš; Rendl, Jan; Dyk, Štěpán; Polach, Pavel; Hajžman, Michal

doi:10.1016/j.jsv.2018.10.042

Cited by 21 publications

(14 citation statements)

References 23 publications

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“…The whirl frequencies are calculated analytically in accordance with the theory from Ref. [33] and the onset of instability is evaluated according to the Routh-Hourwitz stability criterion. Time series that represent a response during the run-up is divided into overlapping segments and each segment is analyzed using the fast Fourier transform (FFT).…”

Section: Instability Thresholds Comparison Of the Campbell Diagrams mentioning

confidence: 99%

Predictive capability of various linearization approaches for floating-ring bearings in nonlinear dynamics of turbochargers

Dyk

Smolík

Rendl

2020

Mechanism and Machine Theory

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A floating-ring bearing (FRB) is composed of a journal, a floating ring and a housing which are separated by two thin oil films. This system is inherently nonlinear and if it is lightly loaded or operated at high speeds, it is prone to the fluid-induced instability. The threshold speed for the instability of a journal bearing with one oil film can be estimated using linearized forces acting in the film. However, the linear analysis of FRB might be problematic because results of such an analysis are usually difficult to interpret. Nevertheless, the linear analysis can provide some fundamental insights into system behaviour. This work aims to evaluate in detail the use of linear theory in the stability analysis of rotating systems supported on FRBs. Several approaches for the linearization of the forces acting in FRB are proposed and analysed. The results are visualized in the form of a holistic Campbell diagram which together depicts natural frequencies, whirl frequencies, modal damping and precession of mode shapes. Moreover, it is demonstrated that the holistic Campbell diagram can be used to interpret-and to some extent, also to predict-results of nonlinear analysis.

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Section: Instability Thresholds Comparison Of the Campbell Diagrams mentioning

confidence: 99%

Predictive capability of various linearization approaches for floating-ring bearings in nonlinear dynamics of turbochargers

Dyk

Smolík

Rendl

2020

Mechanism and Machine Theory

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“…They investigated the stability based on both linear bearing coefficients and on bearing force from the analytical solution. Smolík et al (2019) investigated the stability of rotor bearing system based on the threshold stability curves. They used different approaches to calculate the bearing forces, infinitely short, infinitely short approximation with correction factor for finite length bearing, finite difference, and finite element.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

El-Sayed

Sayed

2021

Preprint

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Journal bearings have many applications in industry due to its high load carrying capacity. In addition proper design of journal bearings enables safe operation at very high speeds. However, they are susceptible to oil whirl instability which may cause bearing failure. The fluid film pressure distribution inside the journal bearing is described by Reynolds equation. Many studies had been done to approximate the bearing performance using first order bearing coefficients. Although this analysis is stable for evaluating the threshold speed but it is insensitive to limit cycles above the threshold speed. Mush literature show that above the threshold speed, subcritical or supercritical bifurcations may be observed. Therefore, the aim of the present paper is to evaluate the third order bearing coefficients for a finite length journal bearing using finite perturbation method. The values of these coefficients are evaluated using infinitesimal perturbation analysis. These values are used to investigate the bifurcation stability of flexible Jeffcott rotor supported by two symmetric journal bearings. The effect of rotor stiffness ratio on the bifurcation stability of the system is investigated. The results of this work show that the third order parameters can be used to evaluate the type of bifurcation above the threshold speed.

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“…They investigated the stability based on both linear bearing coefficients and on bearing forces from the analytical solution. Smolik et al [39] investigated the stability of rotor bearing system based on the threshold stability curves. They used different approaches to calculate the bearing forces, infinitely short, infinitely short approximation with correction factor for finite length bearing, finite difference, and finite element.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

El-Sayed

Sayed

2021

Nonlinear Dyn

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Hydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

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Threshold stability curves for a nonlinear rotor-bearing system

Cited by 21 publications

References 23 publications

Predictive capability of various linearization approaches for floating-ring bearings in nonlinear dynamics of turbochargers

Predictive capability of various linearization approaches for floating-ring bearings in nonlinear dynamics of turbochargers

Bifurcation Analysis of Rotor/Bearing System using Third Order Journal Bearings Stiffness and Damping Coefficients

Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

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