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.
An incompressible air-flow model for a fluid film bearing is derived using a modified Reynolds equation for the thin-film dynamics of a rapidly rotating rotor and stator. Mathematical and numerical modelling is applied to the coupled processes of the fluid-flow through the bearing and the axial motion of the rotor and stator. This work focuses on extending previous studies to incorporate the dynamics of a coned rotor operating at high speeds and an incompressible lubrication approximation. The dynamics of fully coupled unsteady bearing motion and associated forcing of the rotor with axial periodic oscillations is studied. The axial motion of the stator is modelled as a spring-mass-damper system that responds to the rotor displacement through the film dynamics. In order to solve the modified Reynolds equation and stator equation simultaneously a new variable is introduced, namely the time dependent face clearance. This leads to explicit analytical expressions for the pressure and force in terms of the face clearance and the stator equation is transformed to a nonlinear second-order non-autonomous ordinary differential equation for the face clearance. Applying a transient solver gives solutions settling down to a stable periodic behaviour which motivates seeking a solver for periodic solutions. A Fourier spectral collocation scheme is derived to compute the periodic time dependent face clearance. Both solvers have matching periodic solutions of O(1) with an absolute error of order of magnitude 10 −5. The dynamics of the unsteady bearing are examined for a range of pressure gradients and configurations including an asymptotic investigation of small face clearance associated with a start-up transient. Results are provided relating to changes in the width of bearing, strength of spring holding stator to its housing, damping of the stator and strength of the force coupling and rotor mass. The dynamics of the bearing are also investigated relative to values of key system parameters including the coning of the rotor, rotation speed and value of the bearing squeeze number. A parameter investigation is undertaken to highlight ideal bearing configurations to maximise load carrying capacity, fluid stiffness and damping.
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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