No abstract

Fluid film bearings are commonly analyzed with the conventional Reynolds equation, without any temporal inertia effects, developed for oil or other high viscosity lubricants. In applications with rapidly time varying external loads, e.g. ships on wavy oceans, temporal inertia effect should be taken into account. As rotating speeds increase in industrial machines and the reduced Reynolds number increases above the turbulent threshold, a form of linearized turbulence model is often used to increase the effective viscosity to take the turbulence into account. Other than the turbulence effect, with high reduced Reynolds number, convective inertia effect gains importance. Water or other low viscosity fluid film bearings used in subsea machines and compressors are potential applications with a highly reduced Reynolds number.” This paper extends the theory originally developed by Tichy [1] for impulsive loads to high reduced Reynolds number lubrication in different bearing configurations. Both fluid shear and pressure gradient terms are included in the velocity profiles across the lubricant film. The incompressible continuity equation and Navier Stokes equations, including the temporal inertia term, are simplified using an averaged velocity approach to obtain an extended form of Reynolds equation which applies to both laminar and turbulent flow. All terms in the Navier Stokes equation, including both the convective and temporal inertia terms are included in the analysis. The inclusion of the temporal inertia term creates a fluid acceleration term in the extended Reynolds equation. A primary advantage of this formulation is that fluid film bearings lubricated with low viscosity lubricants which are subject to high force slew rates can be analyzed with this extended Reynolds equation. A short bearing form of the extended Reynolds equation is developed with appropriate boundary conditions. A full kinematic analysis of the short journal bearing is developed including time derivatives up to and including shaft accelerations. Linearized stiffness, damping and mass coefficients are developed for a plain short journal bearing. A time transient solution is developed for the pressure and bearing loads in plain journal bearings supporting a symmetric rigid rotor when the rotor is subjected to rapidly applied large forces. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects will be presented and discussed.

This paper extends the theory originally developed by Tichy (Tichy and Bou-Said, 1991, Hydrodynamic Lubrication and Bearing Behavior With Impulsive Loads,” STLE Tribol. Trans. 34, pp. 505–512) for impulsive loads to high reduced Reynolds number lubrication. The incompressible continuity equation and Navier-Stokes equations, including inertia terms, are simplified using an averaged velocity approach to obtain an extended form of short bearing Reynolds equation which applies to both laminar and turbulent flows. A full kinematic analysis of the short journal bearing is developed. Pressure profiles and linearized stiffness, damping and mass coefficients are calculated for different operating conditions. A time transient solution is developed. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects are presented and discussed. In the specific cases considered in this paper, the primary conclusion is that the turbulence effects are significantly more important than inertia effects.

Water lubricated bearings used in nuclear coolant pumps and sub-sea applications exhibit large lubricant inertia forces in the magnitude order of viscous forces. To model these bearings the traditional Reynolds equation is not adequate. An extended Reynolds equation is developed in this study which takes into account the turbulence and inertia effects: both convective and temporal. The most complete form of temporal inertia which applies to the turbulent regime as well, is developed that consists of primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu’s approach [1,2]. The turbulence model is also Constantinescu’s which is tuned with a CFD work. The dynamic coefficients including the lubricant added mass coefficients of a full cylindrical fixed geometry water bearing are obtained. It is observed that the convective inertia increases the load capacity and stability of the bearing. Significant lubricant added mass coefficients comparable to the shaft mass are calculated, which exhibit destabilizing effects in general.

This study addresses the nonlinear dynamic behavior of O-ring seals as the centering spring in squeeze film dampers. An analytical model is developed to predict the restoring and hysteresis characteristics of elastomer O-rings and extends the existing models to non-axisymmetric load conditions. Also, the inclusion of axial seals increases the damping capacity of squeeze film dampers. O-rings forces are investigated for different sizes, installation preloads, and operating conditions and contrasted with squeeze film damper’s hydrodynamic forces. This model is incorporated in linear and time transient rotordynamic analyses of a vertical turbocharger. It is shown that the O-rings contribution in rotor response for low rotational speeds and low amplitude vibrations is dominant and can not be ignored.