Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

Larsen, Jon Steffen; Santos, Ilmar

doi:10.1007/s40430-014-0220-5

Cited by 16 publications

(30 citation statements)

References 36 publications

(47 reference statements)

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“…Using a simple and widely studied GFB configuration [21] supporting a point mass as starting point, OSI predictions from the extended perturbation method are compared to results from both a classical perturbation method and a simultaneous nonlinear time integration. These two reference models are identical to those previously presented by the authors [11,12,14] and have been experimentally validated. It should be emphasized that the vibrations occurring at the investigated OSI stems from a self-excited instability and thus are related exclusively to the homogeneous part of the equation system.…”

Section: Introductionmentioning

confidence: 76%

The Classical Linearization Technique’s Validity for Compliant Bearings

Osmanski

Larsen²,

Santos

2018

Mechanisms and Machine Science

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The Gas Foil Bearing (GFB) is a promising and environmentally friendly technology allowing support of high-speed rotating machinery with low power loss and without oil or electronics. Unfortunately, GFBs provide limited damping, making an accurate prediction of the Onset Speed of Instability (OSI) critical. This has traditionally been assessed using linearised coefficients derived from the perturbed Reynolds Equation with compliance included implicitly. Recent work has, however, revealed significant discrepancies between OSIs predicted using these techniques and those observed from nonlinear analysis. In the present work, the perturbation method's underlying assumption on the pressure field is investigated by including the hitherto neglected pressurecompliance dependency directly. This leads to an extended perturbation akin to that commonly applied to tilting pad bearings and is shown to predict OSIs with much better agreement to time integration results. The extended perturbation method is cumbersome, but serves to highlight the error introduced when applying the classical perturbation method -as developed for rigid bearings by J. W. Lund -to GFBs.

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Section: Introductionmentioning

confidence: 76%

The Classical Linearization Technique’s Validity for Compliant Bearings

Osmanski

Larsen²,

Santos

2018

Mechanisms and Machine Science

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“…The theoretical predictions are based on the simple elastic foundation model as well as an improved model implementing a detailed foil structure finite element formulation [39] coupled with the zeroth order steady state equation. The finite element formulation takes into account large deflections and friction in the sliding contact points.…”

Section: Resultsmentioning

confidence: 99%

“…The Equations (7)- (9) constitute the SEFM. Solutions of these equations are obtained numerically by use of an FE approach [39].…”

Section: Theoretical Modelmentioning

confidence: 99%

“…[39] and a mechanical loss factor η can be included by making K complex [5,[37][38][39]. Here, (11) is used in complex form to include a loss factor.…”

Section: Simple Elastic Foundation Modelmentioning

confidence: 99%

“…In this work, the structural non-linear FE model is coupled with the fluid film FE model and solved iteratively in order to obtain a more accurate estimate of the steady state foil deflection h c0 . The coupling of the structure and fluid film is straight forward as the solution of the zeroth order steady state Equation (7) follows an iterative Newton-Raphson scheme [39]. Between each iteration one may simply solve the structural model for the deflected height h c .…”

Section: Coupled Fluid Structure Modelmentioning

confidence: 99%

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Experimental and theoretical analysis of a rigid rotor supported by air foil bearings

Larsen

Hansen

Santos

2014

Mechanics & Industry

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-The popularity of compressors utilizing foil bearings is increasing. Their mechanical design is challenging, and an accurate prediction of the bearing coefficients is important. A mathematical model taking into account the foil structure, and the detailed geometry of a three pad foil bearing are presented. The steady state solution and dynamic coefficients are obtained through zeroth and first order perturbed equations respectively. Analysis of the foil structure reveals the importance of distinguishing between a static foil stiffness for the zeroth order equation and a dynamic stiffness for the first order equation. Calculated bearing coefficients are compared to experimental results obtained from a dedicated test rig. Generally, good agreement is observed and minor discrepancies for the damping coefficients are discussed.

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