Abstract
An initial deterministic mathematical model for the dynamic motion of a simple pressurised liquid film bearing is derived and utilised to evaluate the possibility of bearing contact for thin film operation. For a very thin film bearing the flow incorporates a Navier slip boundary condition as parametrised by a slip length that in general is subject to significant variability and is difficult to determine with precision. This work considers the formulation of a modified Reynolds equation for the pressurised liquid flow in a highly rotating coned bearing. Coupling of the axial motion of the stator is induced by prescribed axial oscillations of the rotor through the liquid film. The bearing gap is obtained from solving a nonlinear second-order non-autonomous ordinary differential equation, via a mapping solver. Variability in the value of the slip length parameter is addressed by considering it as a random variable with prescribed mean and standard deviation. The method of derived distributions is used to exactly quantify the impact of variability in the slip length with a parametric study investigating the effect of both the deterministic and distribution parameters on the probability of contact. Additionally, as the axial rotor oscillations also have a random aspect due to possible varying excitations of the system, the probability of contact is investigated for both random amplitude of the periodic rotor oscillations and random slip length, resulting in a two parameter random input problem. The probability of contact is examined to obtain exact solutions and evaluate a range of bearing configurations.
Highlights
Pressurised liquid film bearings are considered in this work consisting of two structural components, a rotor and stator, separated by a thin liquid film which experiences relative rotational motion
Deterministic results obtained from the stroboscopic map solver are examined to investigate the value of the slip length parameter at decreasing values of a prescribed minimum value of the minimum face clearance (MFC) over the period
Truncation of the normal distribution is required to ensure the amplitude of rotor oscillations is non-negative and, as in realistic applications, the amplitude of rotor oscillations is restricted; in the results shown the upper limit is set at ε = 2 which is twice the equilibrium gap g = 1
Summary
Pressurised liquid film bearings are considered in this work consisting of two structural components, a rotor and stator, separated by a thin liquid film which experiences relative rotational motion. The thin liquid film is used to maintain a separation between the rotating and stationary elements under external axial loads on the bearing through the generation of a local film pressure These bearings operate as a combined hydrostatic and hydrodynamic bearing where the fluid gap is maintained by the pressurised fluid and the dynamics of the bearings rotational motion. In some practical applications such bearings operate at very high rotational speeds, requiring the inclusion of additional centrifugal inertia effects which are not considered in the classical lubrication formulation of this type of problems (Reynolds equation) Under these conditions, the bearing design requires precise detailed knowledge of variation in the bearing gap during operating condition in order to evaluate possible contact between the rotor and stator. Analysis of a pressurised fluid film bearing with parallel surfaces is given for a Newtonian flow with a no-slip condition by Garratt et al [1] where the bearing structure was coupled to the pressurised fluid flow and the dynamics investigated when the lower face undergoes prescribed periodic axial oscillations
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