The present work proposes a new computational algorithm for analyzing Morton Effect using a Successive Iterative Synchronous Response Algorithm (SISRA). Previous studies on the Morton Effect were based on Eigen or Nyquist analysis for stability studies and predicted only an onset speed of instability. The outcome of SISRA is the convergence of response to a steady state orbit in a finite number of iterations. A progressive increase in the response with increasing running speed indicates the former instability. SISRA predicts both the synchronous response for the speed range of concern plus the speed where the response becomes divergent. SISRA is implemented in a Timochenko-beam-based finite-element rotordynamics software suite. SISRA analyzes the Morton Effect as a synchronous response problem with excitations from: (1) mechanical imbalance, (2) induced thermal bent shaft moments, and (3) mechanical imbalance that is induced by thermal bow. A general elliptical orbit can be decomposed into the sum of forward and backward circular orbits. As input, SISRA requires that, at a specified speed, equilibrium position, and orbit: (1) the predicted maximum differential temperature, and (2) the angle between hot spot (position of maximum temperature) and position of minimum film thickness. Two examples from the published literature are considered. SISRA predicted higher vibration levels, even before the motion diverges due to Morton Effect. In some cases, the synchronous response of the system due to Morton Effect is orders of magnitude greater than the response due only to mechanical imbalance. The combined effects of: (1) mechanical imbalance with induced thermal bent shaft moments, and (2) mechanical imbalance with thermally induced mechanical imbalance are also studied. The impact of induced thermal bent shaft moments is found to be greater than the mechanical imbalance induced by thermal bow. A parametric investigation on the impact of the changes of (1) bearing length to diameter ratio, (2) reduced viscosity of the lubricant, (3) bearing radial clearance to radius ratio and (4) overhung mass magnitude is performed to consider their respective impacts on synchronous response. Based on the available input data and the cases considered, reducing viscosity and reducing the overhung mass are found to be the best remedies to alleviate problems arising from the Morton Effect.

Rotors in fluid-film bearing supported turbomachinery are known to develop elliptical orbits as a result of rotor-bearing interactions, mass unbalance within the rotor, gravitational bending of the shaft and external excitation. In synchronous whirl, where the speed at which the shaft travels about the orbit is equal to the rotational speed of the rotor, temperature gradients may develop across the journal as a result of viscous shear in the bearing's lubricant film. This thermal gradient leads to bending of the shaft in a phenomenon known as The Morton Effect. Such thermally induced bending causes further growth of the elliptical orbit resulting in further bending leading to excessive vibration levels and premature bearing failure. This analysis examines the development of the Morton Effect in medium-speed turbochargers typical to shipboard propulsion engines and the effect that bearing clearance has on thermal stability. Floating ring and tilting pad journal bearings are considered with a single stage, overhung centrifugal compressor and an overhung axial turbine. Results indicate a correlation between bearing clearance and thermal stability in the rotor-bearing system. A model for the aerodynamic force generated as a result of interaction between air exiting a centrifugal compressor and the compressor's annulus in a turbocharger is then developed and applied to the rotor-bearing systems. Results suggest little correlation between this aerodynamic force and the development of the Morton Effect. / Master of Science

Unlike most instabilities, which are non-synchronous in nature, the Morton Effect is a synchronous phenomenon. This thermal instability occurs primarily in overhung rotors that are supported by fluid film bearings and is caused by differential viscous shearing within the bearing lubricant. The Morton Effect has also gained much attention within the last decade. Prior studies of the Morton Effect have used complex analysis in the frequency domain to model this instability. However, such an approach makes it difficult to develop a user-friendly design tool for engineers. The current research employs a steady-state analysis to predict the onset of the Morton Effect, and it uses an instability criterion which is based on a threshold unbalance caused by a force equal to 15% of the weight of the rotor. It is hoped that this method will provide a more easily adaptable platform for design and analytical purposes. The current model has demonstrated good agreement with other theoretical models and experimental data. This agreement applies to rotors that are supported by either plain or tilting pad journal bearings and it was found that a worse case scenario for the Morton Effect would involve centered, circular and large-amplitude bearing orbits. A test rotor was also designed and built. Initial experimental data revealed an unusual instability that might have been caused by the Morton Effect. / Ph. D.

The Morton Effect in the rotor - bearing systems may lead to an unstable operation. Up to the present, most of the established research efforts have been focused on the overhung rotor systems. In this dissertation, a systematic study on the Morton Effect induced instability in mid-span rotor systems is presented. First, the mechanism study is conducted. The simplified rotor models with isotropic linear bearing supports are adopted for the derivation of analytical expressions. The threshold speeds of instability in simple forms are obtained for the systems with the thermal imbalance acting concurrent with or perpendicular to the direction of the response displacement. For a perspective view of the system stability, a stability map for the damped rigid mid-span rotors with the thermal imbalance having arbitrary phase difference has been generated. It shows that the stable operating regions of the system are bounded by two curves of threshold of instability. The results show that the Morton Effect induced instability thresholds are actually affected by both the magnitude and relative phase of the thermal imbalance. The mechanism of the Morton Effect induced thermal instability of mid-span rotors supported by linear isotropic bearings can be explained through the fact that the Morton Effect introduces either negative stiffness or negative cross-coupled stiffness. Next, the steady-state response performance under the influence of the Morton Effect is discussed. The results show that the Morton Effect has a comprehensive impact on both the amplitude and phase lag of the steady-state unbalance response. It may shift both curves in a manner dependent on the relative magnitude and direction of the thermal imbalance. Then, the mid-span rotors supported by the hydrodynamic journal bearings are analyzed. The models to calculate the thermal bending of the shaft and the temperature distribution across the journal surface are established. The calculations of the temperature difference and its equivalent thermal imbalance are conducted and discussed with the comparison to the analytical results. It shows that the thermal imbalance may increase to the level of the mechanical imbalance and its influence on the system stability should be then included. The suggested thermal bending model also explains that the mid-span rotors are less liable to be influenced by the Morton Effect than are the overhung configurations, because of the restraining effect between the two supports. The simulation results of a symmetric mid-span rotor - hydrodynamic journal bearing system show that the inclusion of the Morton Effect may lead to an unstable operation of the system. Considering the existence of the oil film self-induced vibration due to the dynamic characteristics of fluid film bearings, the Morton Effect may make a further negative impact on the instabilities of the rotor system under some working conditions. Finally, the predictive solution method for the general mid-span rotors is discussed. The computer code, VT-MAP, is developed for the predictions of the Morton Effect induced instability of rotor systems in either mid-span and overhung configurations. / Ph. D.

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.