This dissertation deals with three research topics; i) the catcher bearings life prediction method, ii) the Morton effect, and iii) the two dimensional modified Reynolds equation. Firstly, catcher bearings (CB) are an essential component for rotating machine with active magnetic bearings (AMBs) suspensions. The CB's role is to protect the magnetic bearing and other close clearance component in the event of an AMB failure. The contact load, the Hertzian stress, and the sub/surface shear stress between rotor, races, and balls are calculated, using a nonlinear ball bearing model with thermal growth, during the rotor drop event. Fatigue life of the CB in terms of the number of drop occurrences prior to failure is calculated by applying the Rainflow Counting Algorithm to the sub/surface shear stress-time history. Numerical simulations including high fidelity bearing models and a Timoshenko beam finite element rotor model show that CB life is dramatically reduced when high-speed backward whirl occurs. Secondly, the theoretical models and simulation results about the synchronous thermal instability phenomenon known as Morton Effect is presented in this dissertation. A transient analysis of the rotor supported by tilting pad journal bearing is performed to obtain asymmetric temperature distribution of the journal by solving variable viscosity Reynolds equation, energy equation, heat conduction equation, and equations of motion for rotor. The tilting pad bearing is fully nonlinear model. In addition, thermal mode approach and staggered integration scheme are utilized in order to reduce computation time. The simulation results indicate that the temperature of the journal varies sinusoidally along the circumferential direction and linearly across the diameter, and the vibration envelope increased and decreased, which considers as a limit cycle that is stable oscillation of the envelope of the amplitude of synchronous vibration. Thirdly, the Reynolds equation plays an important role to predict pressure distribution in the fluid film for the fluid film bearing analysis. One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. In elastohydrodynamic lubrication (EHL) which the lubricant is subjected to extremely high pressure, however, the pressure independent viscosity assumption should be reconsidered. With considering pressure-dependent viscosity, the 2D modified Reynolds equation is derived in this study. The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the plain journal bearing and ball bearing cases. The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations. / PDF file replaced 10-21-2012 at the request of the Thesis Office.