Dynamics of a parallel, high-speed, lubricated thrust bearing with Navier slip boundary conditions

Bailey, Nicola; Cliffe, K. A.; Hibberd, S.; Power, H.

doi:10.1093/imamat/hxu053

Cited by 11 publications

(19 citation statements)

References 29 publications

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“…A first-order Navier slip model, as considered by Bailey et al (2014Bailey et al ( , 2015, is implemented, where the velocity boundary conditions comprise of tangential components where continuity of the velocity across the fluid-solid boundary is modified by a slip condition induced by the wall shear, together with a normal component of a no flux condition. The dimensionless velocity boundary conditions to leading order are…”

Section: Air Flow Modelmentioning

confidence: 99%

“…Although, in both cases (parallel and coned bearing) the fluid gap can become very small, even of the order of nano scale, leading to the possible invalidation of the classical no-slip velocity condition. A slip boundary condition of the Navier type is incorporated in the analysis by Bailey et al (2014Bailey et al ( , 2015 in cases of parallel and coned liquid lubricated bearings, respectively. The obtained results indicate that face contact does not occur in parallel bearings however the bearing gap can become very small.…”

Section: Introductionmentioning

confidence: 99%

“…Of significant importance is the analysis of the fluid structure coupling dynamics of such bearings working under extreme conditions, where possible disturbances can displace the rotor to magnitudes larger than the initial equilibrium film thickness. In this work, air bearings with a small face clearance are analysed to examine their dynamical behaviour, extending the study of incompressible flow bearings with a slip condition by Bailey et al (2014Bailey et al ( , 2015 to compressible flow. In the case of incompressible flow, it is possible to obtain an analytical solution of the corresponding linear Reynolds equation for the pressure field, enabling the coupled bearing problem to be formulated as a single second order non-autonomous ordinary differential equation for the bearing gap.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of incompressible flow, it is possible to obtain an analytical solution of the corresponding linear Reynolds equation for the pressure field, enabling the coupled bearing problem to be formulated as a single second order non-autonomous ordinary differential equation for the bearing gap. Also the asymptotic solution at a small gap condition can be found and used to verify the numerical results of the complete dynamic behaviour of the bearing when near contact conditions are predicted (for more details see Bailey et al (2013Bailey et al ( , 2014Bailey et al ( , 2015). Unfortunately in the present case of compressible flow, due to the nonlinear form of the resulting Reynolds equation, this approach is not easy to implement.…”

Section: Introductionmentioning

confidence: 99%

“…Although their model agreed reasonably with experimental results for some cases, examination over a range of cases revealed limitations due to neglecting compressibility effects. Conditions for compressibility effects to be neglected for bearing flow have previously been derived by Bailey et al (2014); the conservation of mass reduces to the statement of solenoidal velocity field and the compressible flow in the bearing behaves as if it were incompressible flow for sufficiently small radial and azimuthal speeds.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

2017

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A gas lubricated bearing model is derived which is appropriate for a very small bearing face separation by including velocity slip boundary conditions and centrifugal inertia effects. The bearing dynamics are examined when an external harmonic force is imposed on the bearing due to bearing begin situated within a larger complex dynamical system. A compressible Reynolds equation is formulated for the gas film which is coupled to the bearing structure through an axial force balance where the rotor and stator correspond to spring-mass-damper systems. Surface slip boundary conditions are derived on the bearing faces, characterised by the slip length parameter. The coupled bearing system is analysed using a stroboscopic map solver with the modified Reynolds equation and structural equations solved simultaneously. For a sufficiently large forcing amplitude a flapping motion of the bearing faces is induced when the rotor and stator are in close proximity. The minimum bearing gap over the time period of the external forcing is examined for a range of bearing parameters.

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Section: Air Flow Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

2017

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Effect of Uncertainty in External Forcing on a Fluid Lubricated Bearing

Bailey

Hibberd

Power

et al. 2018

Mechanisms and Machine Science

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Developments in industrial applications motivate improvements in fluid lubricated bearing technology, enabling smaller face clearances and increased rotation rates. Associated film lubrication technology aims to improve efficiency and reliability. A bearing model is developed to evaluate the effect of external, potentially destabilising, random forcing applied to a pair of highly rotating axisymmetric bearing faces, separated by a thin fluid film. Two cases of random external force are examined. A first study considers an imposed random force disturbance constrained to a fixed period, where the average minimum face clearance together with the probability it reaches a specified gap tolerance. More general uncertainties are associated with more complex external forcing and takes the form of a white or coloured noise. In this case the average time for the face clearance to reach a prescribed tolerance is examined. Results can inform bearing design, providing an indication of the effect of disturbances on the average lifetime and identify constraints on operating conditions for safe and reliable behaviour.

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Dynamics of a high speed coned thrust bearing with a Navier slip boundary condition

et al. 2015

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A modified Reynolds equation for flow dynamically represented as incompressible is used to model the dynamics of a thin film bearing with slip flow and a rapidly rotating coned rotor. Previous studies including a Navier slip length shear condition on the bearing faces are extended to investigate applications with a coned bearing gap. A modified Reynolds equation for the film flow is coupled, through the pressure exerted by the fluid film, to the dynamic motion of the stator. Introducing a new variable leads to explicit analytical expressions for the pressure field and force on the stator with the equation for the time-dependent face clearance transformed to a nonlinear second-order non-autonomous ordinary differential equation. The face clearance for periodic axial motion of the coned rotor is obtained using a stroboscopic map solver; a focus is investigating bearing behaviour under extreme conditions. The coupled fluid flow and unsteady bearing dynamics are examined for a range of configurations to evaluate potential face contact over a range of bearing surface conditions.

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Dynamics of a parallel, high-speed, lubricated thrust bearing with Navier slip boundary conditions

Cited by 11 publications

References 29 publications

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

Effect of Uncertainty in External Forcing on a Fluid Lubricated Bearing

Dynamics of a high speed coned thrust bearing with a Navier slip boundary condition

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