Fluid Film Lubrication

Szeri, A. Z.

doi:10.1017/cbo9780511782022

Cited by 111 publications

(78 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(3) and ( 4 ), and considering ˙ θ = −˙ ϕ [23] , turbulent Reynolds equation may be written as: By short bearing approximation ( L / D ) ≤ 0.5, it may be assumed axial pressure flow dominates circumferential pressure flow [24] . Since the first term in Reynolds' equation disappears, updated turbulence Reynolds' equation for turbulent short bearing theory can be written as:…”

Section: Turbulent Short Bearing Theory Formulationmentioning

confidence: 99%

“…The system of coupled nonlinear ODEs of Eqs. (24) and ( 25 ) Fig. 12 , the journal center trajectory is started at the position near by the center of the bearing, that are x 1 = 0 .…”

Section: Equations Of Motions and Linear Stability Analysis Of Short mentioning

confidence: 99%

“…The equations of motion as given in Eqs. (24) and ( 25 ) have the suitable form of ˙ x = f ( x , ¯ ) and possess a steady state equilibrium position x s for the application of the Hopf bifurcation theory. Here, the non-dimensional running speed ¯ is considered as the system parameter when all other parameters of the rotor-bearing system are fixed.…”

Section: Application Of Hopf Bifurcation Theory In Flexible Rotor Beamentioning

confidence: 99%

“…Here, the non-dimensional running speed ¯ is considered as the system parameter when all other parameters of the rotor-bearing system are fixed. According to HBT, if the parameter ¯ in the equations of motion ( 24 ) and ( 25 ) becomes greater than some critical value ¯ cr , an isolated stationary point x s ( ¯ ) will lose its linear stability by having a complex conjugate pair of eigenvalues of the linearized system crossing the imaginary axis of the complex plane [27] . Hence, this critical value ¯ cr is the non-dimensional form of the threshold speed of instability of a rotor-bearing system.…”

Section: Application Of Hopf Bifurcation Theory In Flexible Rotor Beamentioning

confidence: 99%

See 3 more Smart Citations

Dynamic analysis of short and long journal bearings in laminar and turbulent regimes, application in critical shaft stiffness determination

Hemmati

Miraskari

Gadala

2017

Applied Mathematical Modelling

View full text Add to dashboard Cite

Linear and nonlinear stability analysis Hopf bifurcation theory Short and long journal bearings Constantinescu's and Ng −Pan −Elrod turbulent models Critical shaft stiffness a b s t r a c t Linear and non-linear stability of a flexible rotor-bearing system supported on short and long journal bearings is studied for both laminar and turbulent operating conditions. The turbulent pressure distribution and forces are calculated analytically from the modified Reynolds equation based on two turbulent models; Constantinescu's and Ng-Pan-Elrod. Hopf bifurcation theory was utilized to estimate the local stability of periodic solutions near bifurcating operating points. The shaft stiffness was found to play an important role in bifurcating regions on the stable boundaries. It was found that for shafts supported on short journal bearings with shaft stiffness above a critical value, the dangerous subcritical region can be eliminated from a range of operating conditions with high static load. The results presented have been verified by published results in the open literature.

show abstract

Section: Turbulent Short Bearing Theory Formulationmentioning

confidence: 99%

“…The system of coupled nonlinear ODEs of Eqs. (24) and ( 25 ) Fig. 12 , the journal center trajectory is started at the position near by the center of the bearing, that are x 1 = 0 .…”

Section: Equations Of Motions and Linear Stability Analysis Of Short mentioning

confidence: 99%

Section: Application Of Hopf Bifurcation Theory In Flexible Rotor Beamentioning

confidence: 99%

Section: Application Of Hopf Bifurcation Theory In Flexible Rotor Beamentioning

confidence: 99%

See 2 more Smart Citations

Dynamic analysis of short and long journal bearings in laminar and turbulent regimes, application in critical shaft stiffness determination

Hemmati

Miraskari

Gadala

2017

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…Surprisingly, our simulations reveal that its time-dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.Introduction.-Transport of particles in nanoconfinement is of great scientific and industrial importance with applications in heterogeneous catalysis [1], oil recovery [2], or lubrication [3][4][5][6]. In recent years artificial nanoporous materials such as metal organic frameworks [7,8], zeolites [9,10], and biocompatible scaffolds [11] have also triggered many novel applications, including gas storage [12], repairing or regenerating tissues [11], size-selective molecular sieving [13], lab-on-a chip technology and nanofluidics [14,15].…”

mentioning

confidence: 99%

Diverging Time Scale in the Dimensional Crossover for Liquids in Strong Confinement

Mandal

Franosch

2017

Phys. Rev. Lett.

View full text Add to dashboard Cite

We study a strongly interacting dense hard-sphere system confined between two parallel plates by event-driven molecular dynamics simulations to address the fundamental question of the nature of the 3D to 2D crossover. As the fluid becomes more and more confined the dynamics of the transverse and lateral degrees of freedom decouple, which is accompanied by a diverging time scale separating 2D from 3D behavior. Relying on the time-correlation function of the transversal kinetic energy the scaling behavior and its density-dependence is explored. Surprisingly, our simulations reveal that its time-dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.Introduction.-Transport of particles in nanoconfinement is of great scientific and industrial importance with applications in heterogeneous catalysis [1], oil recovery [2], or lubrication [3][4][5][6]. In recent years artificial nanoporous materials such as metal organic frameworks [7,8], zeolites [9,10], and biocompatible scaffolds [11] have also triggered many novel applications, including gas storage [12], repairing or regenerating tissues [11], size-selective molecular sieving [13], lab-on-a chip technology and nanofluidics [14,15]. The efficiency of such nanodevices often crucially depends on higher surface to volume ratio, such that the distance between the confining walls may even reach atomic scale [16], or the system effectively becomes quasi-2D. Nevertheless, despite its long history, a deep understanding of the transport mechanisms in nanoconfinement and how the dimensional crossover occurs dynamically is still far from satisfactory.Early theoretical studies on transport in nanoconfinement starting from Knudsen and Smoluchowski [17,18] focused on dilute hard-sphere gases where exact results could be obtained analytically in the low-density limit [17][18][19][20][21][22] by assuming particle-wall collisions as diffusive. In contrast, confinement effects on dense strongly interacting systems have only recently come into focus [23]. There, the simplest geometry to investigate the effects of strong confinement is a slit where fluid particles are restricted to a narrow space between two smooth parallel plates, but also tubes or spherical confinements have been realized experimentally [24][25][26]. Computer simulations and experiments for the planar confinement have revealed an exotic equilibrium phase behavior due to commensurable stacking [27][28][29][30][31][32][33][34] as well as the hexatic phases in the limit of quasi-2D confinement [35,36]. Confinement induced order-disorder phase transitions for certain nonpolar liquids have also been reported in several experiments [37], but the interpretation has been challenged in favor of a glass transition [38][39][40]. The structural properties of strongly confined liquids have been measured directly only recently by x-ray scattering [41,42].The structural changes by ...

show abstract