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.
On the cross terms of the damping coefficients of finite width journal bearings.