Prediction of the nonlinear hysteresis loop for fluid-film bearings by numerical continuation

Sghir, Radhouane; Chouchane, Mnaouar

doi:10.1177/0954406214538618

Cited by 12 publications

(8 citation statements)

References 20 publications

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“…However, the analysis based on direct solution of Reynolds (RNL) shows bifurcation leads to unstable limit cycle which then jumps to a larger stable limit cycle. This behavior for journal bearings is previously reported in Amamou 2011, Sghir andChouchane 2014).…”

Section: Stability Analysissupporting

confidence: 87%

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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Section: Stability Analysissupporting

confidence: 87%

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

El-Sayed

Sayed

2021

Preprint

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“…For the unbalance, the investigation uses the balanced rotor, a ¼ 0, as a reference. In this case, the bifurcation diagram is determined using numerical continuation as explained in details in reference [10]. The nondimensional unbalance is then increased progressively by a step of 0.05 form a ¼ 0 to a ¼ 0:2.…”

Section: Resultsmentioning

confidence: 99%

“…Numerical integration is used to predict the motion of the rotor for selected initial conditions. Later, numerical continuation was introduced and used to find the steady state motion of balanced rotors and their bifurcations [7][8][9][10]. Unbalance is inherently present in any rotor and should be considered in the modeling.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of an Unbalanced Journal Bearing with Nonlinear Hydrodynamic Forces

Sghir

Chouchane

2015

Proceedings of the 9th IFToMM International Conference on Rotor Dynamics

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The research reported in this paper is based on a nonlinear two degree of freedom model of an unbalanced rigid rotor bearing system. The nonlinearity is introduced into the model through closed form expressions of the short bearing hydrodynamic forces. The model in its nondimensional form depends on three nondimensional parameters: the bearing modulus, the rotor rotating speed and unbalance. For the balanced system, numerical continuation is applied to predict the branch of equilibrium positions of the journal and its bifurcation into stable or unstable limit cycles at the linear stability threshold speed. For the unbalanced system, however, numerical integration is used to find the bifurcation diagrams using the rotor speed as a bifurcation parameter. Poincaré sections are used to characterize the journal motion. The investigation is carried out for three bearing parameters covering a large domain of rotor bearing conditions. The effect of unbalance on the journal motion is investigated in each case. Compared to the balanced system, it has been found that unbalance may introduce, at different speed ranges, periodic oscillations at multiple periods of rotation, quasi-periodic oscillations and chaotic motion. The effect of unbalance on journal motion is highlighted and closely related to the bifurcation diagram of the balanced rotor.

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“…Several investigations have focussed on the nonlinear dynamic analysis of rotating machines supported by hydrodynamic bearings [1][2][3][4][5][6][7][8]. These studies have shown several phenomena that cannot be predicted and explained by linear analysis.…”

Section: Introductionmentioning

confidence: 99%

“…In subsequent research, the numerical continuation method, also known as the path following method was used to predict the solutions of nonlinear differential equation systems as a function of a control parameter [5][6][7][8]. Furthermore, continuation methods provide, in addition to the analytical methods used in [1][2][3][4], tools to accurately predict the size and shape of limit cycles and their bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Unbalance-induced whirl of a rotor supported by oil-film bearings

Sghir¹

2021

Comptes Rendus. Mécanique

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This paper presents a nonlinear stability analysis of an unbalanced rotor-bearing system using the numerical continuation method and the numerical integration method. In this study, the effect of unbalance on journal motion is highlighted and a relationship is established between the bifurcation diagram of a balanced rotor and that of an unbalanced rotor. The results show that the stable operating speed range, the shaft motion type, the whirl speed and the chaotic motion occurrence depend on the unbalance level, the bearing geometry, the oil viscosity, and the speed range of unstable limit cycles existence.

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Prediction of the nonlinear hysteresis loop for fluid-film bearings by numerical continuation

Cited by 12 publications

References 20 publications

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 Bearings Stiffness and Damping Coefficients

Stability Analysis of an Unbalanced Journal Bearing with Nonlinear Hydrodynamic Forces

Unbalance-induced whirl of a rotor supported by oil-film bearings

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